LMFDB - Embedded newform 1530.2.d.g.919.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(919,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1530.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1530.d (of order $2$ , degree $1$ , 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:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.5161984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{6} - 4x^{3} + 25x^{2} - 20x + 8$ x^6 - 4x^3 + 25x^2 - 20*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 170)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			919.4
Root			$1.32001 - 1.32001i$ of defining polynomial
Character	$\chi$	$=$	1530.919
Dual form			1530.2.d.g.919.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(-1.80487 - 1.32001i) q^{5} -2.64002i q^{7} -1.00000i q^{8} +(1.32001 - 1.80487i) q^{10} -2.00000 q^{11} +0.484862i q^{13} +2.64002 q^{14} +1.00000 q^{16} +1.00000i q^{17} -5.76491 q^{19} +(1.80487 + 1.32001i) q^{20} -2.00000i q^{22} +1.35998i q^{23} +(1.51514 + 4.76491i) q^{25} -0.484862 q^{26} +2.64002i q^{28} +8.15516 q^{29} -2.09461 q^{31} +1.00000i q^{32} -1.00000 q^{34} +(-3.48486 + 4.76491i) q^{35} +11.1396i q^{37} -5.76491i q^{38} +(-1.32001 + 1.80487i) q^{40} +0.249771 q^{41} +1.03028i q^{43} +2.00000 q^{44} -1.35998 q^{46} +6.01468i q^{47} +0.0302761 q^{49} +(-4.76491 + 1.51514i) q^{50} -0.484862i q^{52} +7.70436i q^{53} +(3.60975 + 2.64002i) q^{55} -2.64002 q^{56} +8.15516i q^{58} +8.73463 q^{59} -11.3747 q^{61} -2.09461i q^{62} -1.00000 q^{64} +(0.640023 - 0.875115i) q^{65} +4.96972i q^{67} -1.00000i q^{68} +(-4.76491 - 3.48486i) q^{70} -8.34438 q^{71} +0.484862i q^{73} -11.1396 q^{74} +5.76491 q^{76} +5.28005i q^{77} -9.85952 q^{79} +(-1.80487 - 1.32001i) q^{80} +0.249771i q^{82} +17.5298i q^{83} +(1.32001 - 1.80487i) q^{85} -1.03028 q^{86} +2.00000i q^{88} -8.73463 q^{89} +1.28005 q^{91} -1.35998i q^{92} -6.01468 q^{94} +(10.4049 + 7.60975i) q^{95} -6.73463i q^{97} +0.0302761i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$6 q - 6 q^{4} - 2 q^{5} - 12 q^{11} + 6 q^{16} - 2 q^{19} + 2 q^{20} + 10 q^{25} - 2 q^{26} + 34 q^{29} + 6 q^{31} - 6 q^{34} - 20 q^{35} - 32 q^{41} + 12 q^{44} - 24 q^{46} + 2 q^{49} + 4 q^{50} + 4 q^{55}+ \cdots + 14 q^{95}+O(q^{100})$ 6 * q - 6 * q^4 - 2 * q^5 - 12 * q^11 + 6 * q^16 - 2 * q^19 + 2 * q^20 + 10 * q^25 - 2 * q^26 + 34 * q^29 + 6 * q^31 - 6 * q^34 - 20 * q^35 - 32 * q^41 + 12 * q^44 - 24 * q^46 + 2 * q^49 + 4 * q^50 + 4 * q^55 + 18 * q^59 - 18 * q^61 - 6 * q^64 - 12 * q^65 + 4 * q^70 + 2 * q^71 + 16 * q^74 + 2 * q^76 - 8 * q^79 - 2 * q^80 - 8 * q^86 - 18 * q^89 - 24 * q^91 + 30 * q^94 + 14 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$ .

$n$	$307$	$1261$	$1361$
$\chi(n)$	$-1$	$1$	$1$

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

)

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.80487	−	1.32001i	−0.807164	−	0.590327i
$5$	−1.80487	−	1.32001i	−0.807164	−	0.590327i
$6$		0			0
$7$		−	2.64002i		−	0.997835i	−0.866649	−	0.498918i	$-0.833731\pi$
$7$		−	2.64002i		−	0.997835i	0.866649	−	0.498918i	$-0.166269\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.32001	−	1.80487i	0.417424	−	0.570751i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$			0.484862i			0.134477i	0.997737	+	0.0672383i	$0.0214188\pi$
$13$			0.484862i			0.134477i	−0.997737	+	0.0672383i	$0.978581\pi$
$14$	2.64002			0.705576
$15$		0			0
$16$	1.00000			0.250000
$17$			1.00000i			0.242536i
$17$			1.00000i			0.242536i
$18$		0			0
$19$	−5.76491			−1.32256			−0.661280	−	0.750139i	$-0.729987\pi$
$19$	−5.76491			−1.32256			−0.661280	+	0.750139i	$0.729987\pi$
$20$	1.80487	+	1.32001i	0.403582	+	0.295164i
$21$		0			0
$22$		−	2.00000i		−	0.426401i
$23$			1.35998i			0.283575i	0.989897	+	0.141787i	$0.0452849\pi$
$23$			1.35998i			0.283575i	−0.989897	+	0.141787i	$0.954715\pi$
$24$		0			0
$25$	1.51514	+	4.76491i	0.303028	+	0.952982i
$26$	−0.484862			−0.0950893
$27$		0			0
$28$			2.64002i			0.498918i
$29$	8.15516			1.51438			0.757188	−	0.653197i	$-0.226573\pi$
$29$	8.15516			1.51438			0.757188	+	0.653197i	$0.226573\pi$
$30$		0			0
$31$	−2.09461			−0.376203			−0.188101	−	0.982150i	$-0.560233\pi$
$31$	−2.09461			−0.376203			−0.188101	+	0.982150i	$0.560233\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−1.00000			−0.171499
$35$	−3.48486	+	4.76491i	−0.589049	+	0.805417i
$36$		0			0
$37$			11.1396i			1.83133i	0.401939	+	0.915667i	$0.368337\pi$
$37$			11.1396i			1.83133i	−0.401939	+	0.915667i	$0.631663\pi$
$38$		−	5.76491i		−	0.935192i
$39$		0			0
$40$	−1.32001	+	1.80487i	−0.208712	+	0.285376i
$41$	0.249771			0.0390077			0.0195038	−	0.999810i	$-0.493791\pi$
$41$	0.249771			0.0390077			0.0195038	+	0.999810i	$0.493791\pi$
$42$		0			0
$43$			1.03028i			0.157116i	0.996910	+	0.0785578i	$0.0250315\pi$
$43$			1.03028i			0.157116i	−0.996910	+	0.0785578i	$0.974968\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	−1.35998			−0.200518
$47$			6.01468i			0.877331i	0.898650	+	0.438666i	$0.144549\pi$
$47$			6.01468i			0.877331i	−0.898650	+	0.438666i	$0.855451\pi$
$48$		0			0
$49$	0.0302761			0.00432516
$50$	−4.76491	+	1.51514i	−0.673860	+	0.214273i
$51$		0			0
$52$		−	0.484862i		−	0.0672383i
$53$			7.70436i			1.05827i	0.848536	+	0.529137i	$0.177484\pi$
$53$			7.70436i			1.05827i	−0.848536	+	0.529137i	$0.822516\pi$
$54$		0			0
$55$	3.60975	+	2.64002i	0.486738	+	0.355981i
$56$	−2.64002			−0.352788
$57$		0			0
$58$			8.15516i			1.07083i
$59$	8.73463			1.13715			0.568576	−	0.822631i	$-0.307494\pi$
$59$	8.73463			1.13715			0.568576	+	0.822631i	$0.307494\pi$
$60$		0			0
$61$	−11.3747			−1.45638			−0.728188	−	0.685378i	$-0.759637\pi$
$61$	−11.3747			−1.45638			−0.728188	+	0.685378i	$0.759637\pi$
$62$		−	2.09461i		−	0.266016i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.640023	−	0.875115i	0.0793851	−	0.108545i
$66$		0			0
$67$			4.96972i			0.607148i	0.952808	+	0.303574i	$0.0981800\pi$
$67$			4.96972i			0.607148i	−0.952808	+	0.303574i	$0.901820\pi$
$68$		−	1.00000i		−	0.121268i
$69$		0			0
$70$	−4.76491	−	3.48486i	−0.569516	−	0.416521i
$71$	−8.34438			−0.990296			−0.495148	−	0.868809i	$-0.664886\pi$
$71$	−8.34438			−0.990296			−0.495148	+	0.868809i	$0.664886\pi$
$72$		0			0
$73$			0.484862i			0.0567488i	0.999597	+	0.0283744i	$0.00903306\pi$
$73$			0.484862i			0.0567488i	−0.999597	+	0.0283744i	$0.990967\pi$
$74$	−11.1396			−1.29495
$75$		0			0
$76$	5.76491			0.661280
$77$			5.28005i			0.601717i
$78$		0			0
$79$	−9.85952			−1.10928			−0.554641	−	0.832090i	$-0.687144\pi$
$79$	−9.85952			−1.10928			−0.554641	+	0.832090i	$0.687144\pi$
$80$	−1.80487	−	1.32001i	−0.201791	−	0.147582i
$81$		0			0
$82$			0.249771i			0.0275826i
$83$			17.5298i			1.92415i	0.272790	+	0.962074i	$0.412054\pi$
$83$			17.5298i			1.92415i	−0.272790	+	0.962074i	$0.587946\pi$
$84$		0			0
$85$	1.32001	−	1.80487i	0.143175	−	0.195766i
$86$	−1.03028			−0.111098
$87$		0			0
$88$			2.00000i			0.213201i
$89$	−8.73463			−0.925869			−0.462935	−	0.886392i	$-0.653204\pi$
$89$	−8.73463			−0.925869			−0.462935	+	0.886392i	$0.653204\pi$
$90$		0			0
$91$	1.28005			0.134185
$92$		−	1.35998i		−	0.141787i
$93$		0			0
$94$	−6.01468			−0.620367
$95$	10.4049	+	7.60975i	1.06752	+	0.780744i
$96$		0			0
$97$		−	6.73463i		−	0.683798i	−0.939737	−	0.341899i	$-0.888930\pi$
$97$		−	6.73463i		−	0.683798i	0.939737	−	0.341899i	$-0.111070\pi$
$98$			0.0302761i			0.00305835i
$99$		0			0
$100$	−1.51514	−	4.76491i	−0.151514	−	0.476491i
$101$	−13.5298			−1.34627			−0.673134	−	0.739521i	$-0.735052\pi$
$101$	−13.5298			−1.34627			−0.673134	+	0.739521i	$0.735052\pi$
$102$		0			0
$103$		−	11.2195i		−	1.10549i	−0.833351	−	0.552745i	$-0.813580\pi$
$103$		−	11.2195i		−	1.10549i	0.833351	−	0.552745i	$-0.186420\pi$
$104$	0.484862			0.0475446
$105$		0			0
$106$	−7.70436			−0.748313
$107$		−	19.4693i		−	1.88216i	−0.338177	−	0.941082i	$-0.609810\pi$
$107$		−	19.4693i		−	1.88216i	0.338177	−	0.941082i	$-0.390190\pi$
$108$		0			0
$109$	12.6547			1.21210			0.606050	−	0.795426i	$-0.292753\pi$
$109$	12.6547			1.21210			0.606050	+	0.795426i	$0.292753\pi$
$110$	−2.64002	+	3.60975i	−0.251716	+	0.344176i
$111$		0			0
$112$		−	2.64002i		−	0.249459i
$113$		−	7.51514i		−	0.706965i	−0.935441	−	0.353482i	$-0.884997\pi$
$113$		−	7.51514i		−	0.706965i	0.935441	−	0.353482i	$-0.115003\pi$
$114$		0			0
$115$	1.79518	−	2.45459i	0.167402	−	0.228891i
$116$	−8.15516			−0.757188
$117$		0			0
$118$			8.73463i			0.804088i
$119$	2.64002			0.242011
$120$		0			0
$121$	−7.00000			−0.636364
$122$		−	11.3747i		−	1.02981i
$123$		0			0
$124$	2.09461			0.188101
$125$	3.55510	−	10.6001i	0.317978	−	0.948098i
$126$		0			0
$127$			14.7952i			1.31286i	0.754387	+	0.656430i	$0.227934\pi$
$127$			14.7952i			1.31286i	−0.754387	+	0.656430i	$0.772066\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	0.875115	+	0.640023i	0.0767526	+	0.0561338i
$131$	2.49954			0.218386			0.109193	−	0.994021i	$-0.465173\pi$
$131$	2.49954			0.218386			0.109193	+	0.994021i	$0.465173\pi$
$132$		0			0
$133$			15.2195i			1.31970i
$134$	−4.96972			−0.429319
$135$		0			0
$136$	1.00000			0.0857493
$137$			2.06055i			0.176045i	0.996118	+	0.0880224i	$0.0280547\pi$
$137$			2.06055i			0.176045i	−0.996118	+	0.0880224i	$0.971945\pi$
$138$		0			0
$139$	15.5904			1.32236			0.661179	−	0.750228i	$-0.270056\pi$
$139$	15.5904			1.32236			0.661179	+	0.750228i	$0.270056\pi$
$140$	3.48486	−	4.76491i	0.294525	−	0.402708i
$141$		0			0
$142$		−	8.34438i		−	0.700245i
$143$		−	0.969724i		−	0.0810924i
$144$		0			0
$145$	−14.7190	−	10.7649i	−1.22235	−	0.893977i
$146$	−0.484862			−0.0401275
$147$		0			0
$148$		−	11.1396i		−	0.915667i
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$	−15.8401			−1.28905			−0.644526	−	0.764582i	$-0.722945\pi$
$151$	−15.8401			−1.28905			−0.644526	+	0.764582i	$0.722945\pi$
$152$			5.76491i			0.467596i
$153$		0			0
$154$	−5.28005			−0.425478
$155$	3.78051	+	2.76491i	0.303657	+	0.222083i
$156$		0			0
$157$		−	1.34060i		−	0.106991i	−0.998568	−	0.0534957i	$-0.982964\pi$
$157$		−	1.34060i		−	0.106991i	0.998568	−	0.0534957i	$-0.0170364\pi$
$158$		−	9.85952i		−	0.784381i
$159$		0			0
$160$	1.32001	−	1.80487i	0.104356	−	0.142688i
$161$	3.59037			0.282961
$162$		0			0
$163$			16.2498i			1.27278i	0.771367	+	0.636390i	$0.219573\pi$
$163$			16.2498i			1.27278i	−0.771367	+	0.636390i	$0.780427\pi$
$164$	−0.249771			−0.0195038
$165$		0			0
$166$	−17.5298			−1.36058
$167$		−	2.95035i		−	0.228305i	−0.993463	−	0.114152i	$-0.963585\pi$
$167$		−	2.95035i		−	0.228305i	0.993463	−	0.114152i	$-0.0364152\pi$
$168$		0			0
$169$	12.7649			0.981916
$170$	1.80487	+	1.32001i	0.138427	+	0.101240i
$171$		0			0
$172$		−	1.03028i		−	0.0785578i
$173$			6.14048i			0.466852i	0.972375	+	0.233426i	$0.0749937\pi$
$173$			6.14048i			0.466852i	−0.972375	+	0.233426i	$0.925006\pi$
$174$		0			0
$175$	12.5795	−	4.00000i	0.950919	−	0.302372i
$176$	−2.00000			−0.150756
$177$		0			0
$178$		−	8.73463i		−	0.654688i
$179$	−15.5904			−1.16528			−0.582639	−	0.812731i	$-0.697980\pi$
$179$	−15.5904			−1.16528			−0.582639	+	0.812731i	$0.697980\pi$
$180$		0			0
$181$	4.10929			0.305441			0.152721	−	0.988269i	$-0.451197\pi$
$181$	4.10929			0.305441			0.152721	+	0.988269i	$0.451197\pi$
$182$			1.28005i			0.0948834i
$183$		0			0
$184$	1.35998			0.100259
$185$	14.7044	−	20.1055i	1.08109	−	1.47819i
$186$		0			0
$187$		−	2.00000i		−	0.146254i
$188$		−	6.01468i		−	0.438666i
$189$		0			0
$190$	−7.60975	+	10.4049i	−0.552069	+	0.754853i
$191$	−6.06055			−0.438526			−0.219263	−	0.975666i	$-0.570365\pi$
$191$	−6.06055			−0.438526			−0.219263	+	0.975666i	$0.570365\pi$
$192$		0			0
$193$			12.5601i			0.904095i	0.891994	+	0.452048i	$0.149306\pi$
$193$			12.5601i			0.904095i	−0.891994	+	0.452048i	$0.850694\pi$
$194$	6.73463			0.483518
$195$		0			0
$196$	−0.0302761			−0.00216258
$197$			26.0487i			1.85590i	0.372710	+	0.927948i	$0.378429\pi$
$197$			26.0487i			1.85590i	−0.372710	+	0.927948i	$0.621571\pi$
$198$		0			0
$199$	−3.37466			−0.239223			−0.119612	−	0.992821i	$-0.538165\pi$
$199$	−3.37466			−0.239223			−0.119612	+	0.992821i	$0.538165\pi$
$200$	4.76491	−	1.51514i	0.336930	−	0.107136i
$201$		0			0
$202$		−	13.5298i		−	0.951955i
$203$		−	21.5298i		−	1.51110i
$204$		0			0
$205$	−0.450805	−	0.329700i	−0.0314856	−	0.0230273i
$206$	11.2195			0.781699
$207$		0			0
$208$			0.484862i			0.0336191i
$209$	11.5298			0.797534
$210$		0			0
$211$	18.0294			1.24119			0.620596	−	0.784130i	$-0.286891\pi$
$211$	18.0294			1.24119			0.620596	+	0.784130i	$0.286891\pi$
$212$		−	7.70436i		−	0.529137i
$213$		0			0
$214$	19.4693			1.33089
$215$	1.35998	−	1.85952i	0.0927496	−	0.126818i
$216$		0			0
$217$			5.52982i			0.375388i
$218$			12.6547i			0.857085i
$219$		0			0
$220$	−3.60975	−	2.64002i	−0.243369	−	0.177990i
$221$	−0.484862			−0.0326153
$222$		0			0
$223$		−	23.2947i		−	1.55993i	−0.625823	−	0.779965i	$-0.715237\pi$
$223$		−	23.2947i		−	1.55993i	0.625823	−	0.779965i	$-0.284763\pi$
$224$	2.64002			0.176394
$225$		0			0
$226$	7.51514			0.499900
$227$		−	17.4839i		−	1.16045i	−0.814456	−	0.580225i	$-0.802965\pi$
$227$		−	17.4839i		−	1.16045i	0.814456	−	0.580225i	$-0.197035\pi$
$228$		0			0
$229$	−0.719953			−0.0475758			−0.0237879	−	0.999717i	$-0.507573\pi$
$229$	−0.719953			−0.0475758			−0.0237879	+	0.999717i	$0.507573\pi$
$230$	2.45459	+	1.79518i	0.161851	+	0.118371i
$231$		0			0
$232$		−	8.15516i		−	0.535413i
$233$			11.0450i			0.723579i	0.932260	+	0.361790i	$0.117834\pi$
$233$			11.0450i			0.723579i	−0.932260	+	0.361790i	$0.882166\pi$
$234$		0			0
$235$	7.93945	−	10.8557i	0.517912	−	0.708150i
$236$	−8.73463			−0.568576
$237$		0			0
$238$			2.64002i			0.171127i
$239$	−5.59037			−0.361611			−0.180805	−	0.983519i	$-0.557870\pi$
$239$	−5.59037			−0.361611			−0.180805	+	0.983519i	$0.557870\pi$
$240$		0			0
$241$	−8.37088			−0.539215			−0.269608	−	0.962970i	$-0.586894\pi$
$241$	−8.37088			−0.539215			−0.269608	+	0.962970i	$0.586894\pi$
$242$		−	7.00000i		−	0.449977i
$243$		0			0
$244$	11.3747			0.728188
$245$	−0.0546445	−	0.0399648i	−0.00349111	−	0.00255326i
$246$		0			0
$247$		−	2.79518i		−	0.177853i
$248$			2.09461i			0.133008i
$249$		0			0
$250$	10.6001	+	3.55510i	0.670407	+	0.224844i
$251$	−19.4693			−1.22889			−0.614445	−	0.788960i	$-0.710620\pi$
$251$	−19.4693			−1.22889			−0.614445	+	0.788960i	$0.710620\pi$
$252$		0			0
$253$		−	2.71995i		−	0.171002i
$254$	−14.7952			−0.928332
$255$		0			0
$256$	1.00000			0.0625000
$257$			13.9394i			0.869519i	0.900547	+	0.434759i	$0.143167\pi$
$257$			13.9394i			0.869519i	−0.900547	+	0.434759i	$0.856833\pi$
$258$		0			0
$259$	29.4087			1.82737
$260$	−0.640023	+	0.875115i	−0.0396926	+	0.0542723i
$261$		0			0
$262$			2.49954i			0.154422i
$263$			16.2645i			1.00291i	0.865184	+	0.501454i	$0.167202\pi$
$263$			16.2645i			1.00291i	−0.865184	+	0.501454i	$0.832798\pi$
$264$		0			0
$265$	10.1698	−	13.9054i	0.624728	−	0.854201i
$266$	−15.2195			−0.933167
$267$		0			0
$268$		−	4.96972i		−	0.303574i
$269$	10.4049			0.634400			0.317200	−	0.948359i	$-0.397257\pi$
$269$	10.4049			0.634400			0.317200	+	0.948359i	$0.397257\pi$
$270$		0			0
$271$	−24.0294			−1.45968			−0.729840	−	0.683618i	$-0.760405\pi$
$271$	−24.0294			−1.45968			−0.729840	+	0.683618i	$0.760405\pi$
$272$			1.00000i			0.0606339i
$273$		0			0
$274$	−2.06055			−0.124483
$275$	−3.03028	−	9.52982i	−0.182733	−	0.574670i
$276$		0			0
$277$		−	18.9503i		−	1.13862i	−0.822124	−	0.569308i	$-0.807211\pi$
$277$		−	18.9503i		−	1.13862i	0.822124	−	0.569308i	$-0.192789\pi$
$278$			15.5904i			0.935048i
$279$		0			0
$280$	4.76491	+	3.48486i	0.284758	+	0.208260i
$281$	−19.6438			−1.17185			−0.585926	−	0.810365i	$-0.699269\pi$
$281$	−19.6438			−1.17185			−0.585926	+	0.810365i	$0.699269\pi$
$282$		0			0
$283$			25.7943i			1.53331i	0.642059	+	0.766655i	$0.278080\pi$
$283$			25.7943i			1.53331i	−0.642059	+	0.766655i	$0.721920\pi$
$284$	8.34438			0.495148
$285$		0			0
$286$	0.969724			0.0573410
$287$		−	0.659401i		−	0.0389232i
$288$		0			0
$289$	−1.00000			−0.0588235
$290$	10.7649	−	14.7190i	0.632137	−	0.864332i
$291$		0			0
$292$		−	0.484862i		−	0.0283744i
$293$			22.9239i			1.33923i	0.742710	+	0.669613i	$0.233540\pi$
$293$			22.9239i			1.33923i	−0.742710	+	0.669613i	$0.766460\pi$
$294$		0			0
$295$	−15.7649	−	11.5298i	−0.917868	−	0.671292i
$296$	11.1396			0.647474
$297$		0			0
$298$			10.0000i			0.579284i
$299$	−0.659401			−0.0381341
$300$		0			0
$301$	2.71995			0.156775
$302$		−	15.8401i		−	0.911498i
$303$		0			0
$304$	−5.76491			−0.330640
$305$	20.5298	+	15.0147i	1.17553	+	0.859738i
$306$		0			0
$307$			10.4702i			0.597565i	0.954321	+	0.298782i	$0.0965805\pi$
$307$			10.4702i			0.597565i	−0.954321	+	0.298782i	$0.903420\pi$
$308$		−	5.28005i		−	0.300859i
$309$		0			0
$310$	−2.76491	+	3.78051i	−0.157036	+	0.214718i
$311$	9.73841			0.552215			0.276107	−	0.961127i	$-0.410955\pi$
$311$	9.73841			0.552215			0.276107	+	0.961127i	$0.410955\pi$
$312$		0			0
$313$			9.50046i			0.536998i	0.963280	+	0.268499i	$0.0865275\pi$
$313$			9.50046i			0.536998i	−0.963280	+	0.268499i	$0.913472\pi$
$314$	1.34060			0.0756544
$315$		0			0
$316$	9.85952			0.554641
$317$			13.0790i			0.734591i	0.930104	+	0.367295i	$0.119716\pi$
$317$			13.0790i			0.734591i	−0.930104	+	0.367295i	$0.880284\pi$
$318$		0			0
$319$	−16.3103			−0.913203
$320$	1.80487	+	1.32001i	0.100896	+	0.0737909i
$321$		0			0
$322$			3.59037i			0.200083i
$323$		−	5.76491i		−	0.320768i
$324$		0			0
$325$	−2.31032	+	0.734633i	−0.128154	+	0.0407501i
$326$	−16.2498			−0.899992
$327$		0			0
$328$		−	0.249771i		−	0.0137913i
$329$	15.8789			0.875432
$330$		0			0
$331$	24.8851			1.36781			0.683904	−	0.729572i	$-0.260281\pi$
$331$	24.8851			1.36781			0.683904	+	0.729572i	$0.260281\pi$
$332$		−	17.5298i		−	0.962074i
$333$		0			0
$334$	2.95035			0.161436
$335$	6.56009	−	8.96972i	0.358416	−	0.490068i
$336$		0			0
$337$		−	27.5445i		−	1.50044i	−0.661186	−	0.750222i	$-0.729947\pi$
$337$		−	27.5445i		−	1.50044i	0.661186	−	0.750222i	$-0.270053\pi$
$338$			12.7649i			0.694320i
$339$		0			0
$340$	−1.32001	+	1.80487i	−0.0715877	+	0.0978830i
$341$	4.18922			0.226859
$342$		0			0
$343$		−	18.5601i		−	1.00215i
$344$	1.03028			0.0555488
$345$		0			0
$346$	−6.14048			−0.330114
$347$			4.48486i			0.240760i	0.992728	+	0.120380i	$0.0384113\pi$
$347$			4.48486i			0.240760i	−0.992728	+	0.120380i	$0.961589\pi$
$348$		0			0
$349$	−34.2186			−1.83168			−0.915839	−	0.401545i	$-0.868473\pi$
$349$	−34.2186			−1.83168			−0.915839	+	0.401545i	$0.868473\pi$
$350$	4.00000	+	12.5795i	0.213809	+	0.672401i
$351$		0			0
$352$		−	2.00000i		−	0.106600i
$353$			4.90917i			0.261289i	0.991429	+	0.130644i	$0.0417046\pi$
$353$			4.90917i			0.261289i	−0.991429	+	0.130644i	$0.958295\pi$
$354$		0			0
$355$	15.0606	+	11.0147i	0.799331	+	0.584599i
$356$	8.73463			0.462935
$357$		0			0
$358$		−	15.5904i		−	0.823977i
$359$	−13.7796			−0.727259			−0.363629	−	0.931544i	$-0.618463\pi$
$359$	−13.7796			−0.727259			−0.363629	+	0.931544i	$0.618463\pi$
$360$		0			0
$361$	14.2342			0.749167
$362$			4.10929i			0.215979i
$363$		0			0
$364$	−1.28005			−0.0670927
$365$	0.640023	−	0.875115i	0.0335004	−	0.0458056i
$366$		0			0
$367$			4.39025i			0.229169i	0.993413	+	0.114585i	$0.0365537\pi$
$367$			4.39025i			0.229169i	−0.993413	+	0.114585i	$0.963446\pi$
$368$			1.35998i			0.0708937i
$369$		0			0
$370$	20.1055	+	14.7044i	1.04524	+	0.764443i
$371$	20.3397			1.05598
$372$		0			0
$373$			0.220411i			0.0114125i	0.999984	+	0.00570623i	$0.00181636\pi$
$373$			0.220411i			0.0114125i	−0.999984	+	0.00570623i	$0.998184\pi$
$374$	2.00000			0.103418
$375$		0			0
$376$	6.01468			0.310183
$377$			3.95413i			0.203648i
$378$		0			0
$379$	−26.3103			−1.35147			−0.675735	−	0.737144i	$-0.736174\pi$
$379$	−26.3103			−1.35147			−0.675735	+	0.737144i	$0.736174\pi$
$380$	−10.4049	−	7.60975i	−0.533762	−	0.390372i
$381$		0			0
$382$		−	6.06055i		−	0.310085i
$383$		−	36.1433i		−	1.84684i	−0.383793	−	0.923419i	$-0.625382\pi$
$383$		−	36.1433i		−	1.84684i	0.383793	−	0.923419i	$-0.374618\pi$
$384$		0			0
$385$	6.96972	−	9.52982i	0.355210	−	0.485684i
$386$	−12.5601			−0.639292
$387$		0			0
$388$			6.73463i			0.341899i
$389$	3.77959			0.191633			0.0958164	−	0.995399i	$-0.469454\pi$
$389$	3.77959			0.191633			0.0958164	+	0.995399i	$0.469454\pi$
$390$		0			0
$391$	−1.35998			−0.0687770
$392$		−	0.0302761i		−	0.00152917i
$393$		0			0
$394$	−26.0487			−1.31232
$395$	17.7952	+	13.0147i	0.895373	+	0.654840i
$396$		0			0
$397$			12.2304i			0.613826i	0.951738	+	0.306913i	$0.0992960\pi$
$397$			12.2304i			0.613826i	−0.951738	+	0.306913i	$0.900704\pi$
$398$		−	3.37466i		−	0.169156i
$399$		0			0
$400$	1.51514	+	4.76491i	0.0757569	+	0.238245i
$401$	11.7796			0.588245			0.294122	−	0.955768i	$-0.404973\pi$
$401$	11.7796			0.588245			0.294122	+	0.955768i	$0.404973\pi$
$402$		0			0
$403$		−	1.01560i		−	0.0505905i
$404$	13.5298			0.673134
$405$		0			0
$406$	21.5298			1.06851
$407$		−	22.2791i		−	1.10434i
$408$		0			0
$409$	15.7649			0.779525			0.389762	−	0.920916i	$-0.372557\pi$
$409$	15.7649			0.779525			0.389762	+	0.920916i	$0.372557\pi$
$410$	0.329700	−	0.450805i	0.0162827	−	0.0222637i
$411$		0			0
$412$			11.2195i			0.552745i
$413$		−	23.0596i		−	1.13469i
$414$		0			0
$415$	23.1396	−	31.6391i	1.13588	−	1.55310i
$416$	−0.484862			−0.0237723
$417$		0			0
$418$			11.5298i			0.563942i
$419$	18.1892			0.888601			0.444301	−	0.895878i	$-0.353452\pi$
$419$	18.1892			0.888601			0.444301	+	0.895878i	$0.353452\pi$
$420$		0			0
$421$	9.03028			0.440109			0.220054	−	0.975488i	$-0.429377\pi$
$421$	9.03028			0.440109			0.220054	+	0.975488i	$0.429377\pi$
$422$			18.0294i			0.877655i
$423$		0			0
$424$	7.70436			0.374157
$425$	−4.76491	+	1.51514i	−0.231132	+	0.0734950i
$426$		0			0
$427$			30.0294i			1.45322i
$428$			19.4693i			0.941082i
$429$		0			0
$430$	1.85952	+	1.35998i	0.0896739	+	0.0655839i
$431$	−20.4196			−0.983578			−0.491789	−	0.870714i	$-0.663657\pi$
$431$	−20.4196			−0.983578			−0.491789	+	0.870714i	$0.663657\pi$
$432$		0			0
$433$		−	11.5904i		−	0.556998i	−0.960437	−	0.278499i	$-0.910163\pi$
$433$		−	11.5904i		−	0.556998i	0.960437	−	0.278499i	$-0.0898368\pi$
$434$	−5.52982			−0.265440
$435$		0			0
$436$	−12.6547			−0.606050
$437$		−	7.84014i		−	0.375045i
$438$		0			0
$439$	2.01938			0.0963796			0.0481898	−	0.998838i	$-0.484655\pi$
$439$	2.01938			0.0963796			0.0481898	+	0.998838i	$0.484655\pi$
$440$	2.64002	−	3.60975i	0.125858	−	0.172088i
$441$		0			0
$442$		−	0.484862i		−	0.0230625i
$443$		−	27.4087i		−	1.30223i	−0.758980	−	0.651114i	$-0.774302\pi$
$443$		−	27.4087i		−	1.30223i	0.758980	−	0.651114i	$-0.225698\pi$
$444$		0			0
$445$	15.7649	+	11.5298i	0.747328	+	0.546566i
$446$	23.2947			1.10304
$447$		0			0
$448$			2.64002i			0.124729i
$449$	29.7190			1.40253			0.701264	−	0.712902i	$-0.252619\pi$
$449$	29.7190			1.40253			0.701264	+	0.712902i	$0.252619\pi$
$450$		0			0
$451$	−0.499542			−0.0235225
$452$			7.51514i			0.353482i
$453$		0			0
$454$	17.4839			0.820562
$455$	−2.31032	−	1.68968i	−0.108310	−	0.0792133i
$456$		0			0
$457$			39.4693i			1.84629i	0.384447	+	0.923147i	$0.374392\pi$
$457$			39.4693i			1.84629i	−0.384447	+	0.923147i	$0.625608\pi$
$458$		−	0.719953i		−	0.0336412i
$459$		0			0
$460$	−1.79518	+	2.45459i	−0.0837009	+	0.114446i
$461$	−14.6888			−0.684124			−0.342062	−	0.939677i	$-0.611125\pi$
$461$	−14.6888			−0.684124			−0.342062	+	0.939677i	$0.611125\pi$
$462$		0			0
$463$		−	35.1055i		−	1.63149i	−0.578411	−	0.815746i	$-0.696327\pi$
$463$		−	35.1055i		−	1.63149i	0.578411	−	0.815746i	$-0.303673\pi$
$464$	8.15516			0.378594
$465$		0			0
$466$	−11.0450			−0.511648
$467$			9.96881i			0.461301i	0.973037	+	0.230651i	$0.0740855\pi$
$467$			9.96881i			0.461301i	−0.973037	+	0.230651i	$0.925915\pi$
$468$		0			0
$469$	13.1202			0.605834
$470$	10.8557	+	7.93945i	0.500738	+	0.366219i
$471$		0			0
$472$		−	8.73463i		−	0.402044i
$473$		−	2.06055i		−	0.0947443i
$474$		0			0
$475$	−8.73463	−	27.4693i	−0.400772	−	1.26038i
$476$	−2.64002			−0.121005
$477$		0			0
$478$		−	5.59037i		−	0.255698i
$479$	−2.28383			−0.104351			−0.0521754	−	0.998638i	$-0.516615\pi$
$479$	−2.28383			−0.104351			−0.0521754	+	0.998638i	$0.516615\pi$
$480$		0			0
$481$	−5.40115			−0.246271
$482$		−	8.37088i		−	0.381283i
$483$		0			0
$484$	7.00000			0.318182
$485$	−8.88979	+	12.1552i	−0.403665	+	0.551937i
$486$		0			0
$487$		−	10.8292i		−	0.490720i	−0.969432	−	0.245360i	$-0.921094\pi$
$487$		−	10.8292i		−	0.490720i	0.969432	−	0.245360i	$-0.0789061\pi$
$488$			11.3747i			0.514906i
$489$		0			0
$490$	0.0399648	−	0.0546445i	0.00180543	−	0.00246859i
$491$	−24.7952			−1.11899			−0.559496	−	0.828833i	$-0.689005\pi$
$491$	−24.7952			−1.11899			−0.559496	+	0.828833i	$0.689005\pi$
$492$		0			0
$493$			8.15516i			0.367290i
$494$	2.79518			0.125761
$495$		0			0
$496$	−2.09461			−0.0940507
$497$			22.0294i			0.988152i
$498$		0			0
$499$	−5.15138			−0.230607			−0.115304	−	0.993330i	$-0.536784\pi$
$499$	−5.15138			−0.230607			−0.115304	+	0.993330i	$0.536784\pi$
$500$	−3.55510	+	10.6001i	−0.158989	+	0.474049i
$501$		0			0
$502$		−	19.4693i		−	0.868956i
$503$		−	29.0109i		−	1.29353i	−0.762688	−	0.646766i	$-0.776121\pi$
$503$		−	29.0109i		−	1.29353i	0.762688	−	0.646766i	$-0.223879\pi$
$504$		0			0
$505$	24.4196	+	17.8595i	1.08666	+	0.794738i
$506$	2.71995			0.120917
$507$		0			0
$508$		−	14.7952i		−	0.656430i
$509$	−27.4693			−1.21755			−0.608777	−	0.793341i	$-0.708340\pi$
$509$	−27.4693			−1.21755			−0.608777	+	0.793341i	$0.708340\pi$
$510$		0			0
$511$	1.28005			0.0566259
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−13.9394			−0.614843
$515$	−14.8099	+	20.2498i	−0.652601	+	0.892312i
$516$		0			0
$517$		−	12.0294i		−	0.529051i
$518$			29.4087i			1.29214i
$519$		0			0
$520$	−0.875115	−	0.640023i	−0.0383763	−	0.0280669i
$521$	−5.68968			−0.249269			−0.124635	−	0.992203i	$-0.539776\pi$
$521$	−5.68968			−0.249269			−0.124635	+	0.992203i	$0.539776\pi$
$522$		0			0
$523$		−	7.52982i		−	0.329256i	−0.986356	−	0.164628i	$-0.947358\pi$
$523$		−	7.52982i		−	0.329256i	0.986356	−	0.164628i	$-0.0526424\pi$
$524$	−2.49954			−0.109193
$525$		0			0
$526$	−16.2645			−0.709164
$527$		−	2.09461i		−	0.0912426i
$528$		0			0
$529$	21.1505			0.919585
$530$	13.9054	+	10.1698i	0.604012	+	0.441750i
$531$		0			0
$532$		−	15.2195i		−	0.659849i
$533$			0.121104i			0.00524561i
$534$		0			0
$535$	−25.6997	+	35.1396i	−1.11109	+	1.51922i
$536$	4.96972			0.214659
$537$		0			0
$538$			10.4049i			0.448588i
$539$	−0.0605522			−0.00260817
$540$		0			0
$541$	26.0100			1.11826			0.559128	−	0.829081i	$-0.311136\pi$
$541$	26.0100			1.11826			0.559128	+	0.829081i	$0.311136\pi$
$542$		−	24.0294i		−	1.03215i
$543$		0			0
$544$	−1.00000			−0.0428746
$545$	−22.8401	−	16.7044i	−0.978364	−	0.715536i
$546$		0			0
$547$		−	11.5833i		−	0.495264i	−0.968854	−	0.247632i	$-0.920348\pi$
$547$		−	11.5833i		−	0.495264i	0.968854	−	0.247632i	$-0.0796524\pi$
$548$		−	2.06055i		−	0.0880224i
$549$		0			0
$550$	9.52982	−	3.03028i	0.406353	−	0.129211i
$551$	−47.0138			−2.00285
$552$		0			0
$553$			26.0294i			1.10688i
$554$	18.9503			0.805123
$555$		0			0
$556$	−15.5904			−0.661179
$557$		−	5.95413i		−	0.252284i	−0.992012	−	0.126142i	$-0.959740\pi$
$557$		−	5.95413i		−	0.252284i	0.992012	−	0.126142i	$-0.0402596\pi$
$558$		0			0
$559$	−0.499542			−0.0211284
$560$	−3.48486	+	4.76491i	−0.147262	+	0.201354i
$561$		0			0
$562$		−	19.6438i		−	0.828624i
$563$		−	34.5289i		−	1.45522i	−0.685991	−	0.727610i	$-0.740631\pi$
$563$		−	34.5289i		−	1.45522i	0.685991	−	0.727610i	$-0.259369\pi$
$564$		0			0
$565$	−9.92007	+	13.5639i	−0.417340	+	0.570637i
$566$	−25.7943			−1.08421
$567$		0			0
$568$			8.34438i			0.350122i
$569$	12.7952			0.536402			0.268201	−	0.963363i	$-0.413571\pi$
$569$	12.7952			0.536402			0.268201	+	0.963363i	$0.413571\pi$
$570$		0			0
$571$	−4.22041			−0.176619			−0.0883094	−	0.996093i	$-0.528146\pi$
$571$	−4.22041			−0.176619			−0.0883094	+	0.996093i	$0.528146\pi$
$572$			0.969724i			0.0405462i
$573$		0			0
$574$	0.659401			0.0275229
$575$	−6.48016	+	2.06055i	−0.270242	+	0.0859310i
$576$		0			0
$577$		−	35.5592i		−	1.48035i	−0.672415	−	0.740174i	$-0.734743\pi$
$577$		−	35.5592i		−	1.48035i	0.672415	−	0.740174i	$-0.265257\pi$
$578$		−	1.00000i		−	0.0415945i
$579$		0			0
$580$	14.7190	+	10.7649i	0.611175	+	0.446989i
$581$	46.2791			1.91998
$582$		0			0
$583$		−	15.4087i		−	0.638164i
$584$	0.484862			0.0200637
$585$		0			0
$586$	−22.9239			−0.946976
$587$			43.6803i			1.80288i	0.432906	+	0.901439i	$0.357488\pi$
$587$			43.6803i			1.80288i	−0.432906	+	0.901439i	$0.642512\pi$
$588$		0			0
$589$	12.0752			0.497551
$590$	11.5298	−	15.7649i	0.474675	−	0.649031i
$591$		0			0
$592$			11.1396i			0.457833i
$593$			20.1505i			0.827480i	0.910395	+	0.413740i	$0.135778\pi$
$593$			20.1505i			0.827480i	−0.910395	+	0.413740i	$0.864222\pi$
$594$		0			0
$595$	−4.76491	−	3.48486i	−0.195342	−	0.142865i
$596$	−10.0000			−0.409616
$597$		0			0
$598$		−	0.659401i		−	0.0269649i
$599$	33.4986			1.36872			0.684358	−	0.729146i	$-0.260082\pi$
$599$	33.4986			1.36872			0.684358	+	0.729146i	$0.260082\pi$
$600$		0			0
$601$	7.93945			0.323857			0.161928	−	0.986803i	$-0.448229\pi$
$601$	7.93945			0.323857			0.161928	+	0.986803i	$0.448229\pi$
$602$			2.71995i			0.110857i
$603$		0			0
$604$	15.8401			0.644526
$605$	12.6341	+	9.24008i	0.513650	+	0.375663i
$606$		0			0
$607$			38.9797i			1.58214i	0.611727	+	0.791069i	$0.290475\pi$
$607$			38.9797i			1.58214i	−0.611727	+	0.791069i	$0.709525\pi$
$608$		−	5.76491i		−	0.233798i
$609$		0			0
$610$	−15.0147	+	20.5298i	−0.607927	+	0.831228i
$611$	−2.91629			−0.117980
$612$		0			0
$613$		−	28.5142i		−	1.15168i	−0.817563	−	0.575839i	$-0.804675\pi$
$613$		−	28.5142i		−	1.15168i	0.817563	−	0.575839i	$-0.195325\pi$
$614$	−10.4702			−0.422542
$615$		0			0
$616$	5.28005			0.212739
$617$			1.07615i			0.0433241i	0.999765	+	0.0216621i	$0.00689579\pi$
$617$			1.07615i			0.0433241i	−0.999765	+	0.0216621i	$0.993104\pi$
$618$		0			0
$619$	0.719953			0.0289374			0.0144687	−	0.999895i	$-0.495394\pi$
$619$	0.719953			0.0289374			0.0144687	+	0.999895i	$0.495394\pi$
$620$	−3.78051	−	2.76491i	−0.151829	−	0.111041i
$621$		0			0
$622$			9.73841i			0.390475i
$623$			23.0596i			0.923865i
$624$		0			0
$625$	−20.4087	+	14.4390i	−0.816349	+	0.577560i
$626$	−9.50046			−0.379715
$627$		0			0
$628$			1.34060i			0.0534957i
$629$	−11.1396			−0.444164
$630$		0			0
$631$	3.81078			0.151705			0.0758524	−	0.997119i	$-0.475832\pi$
$631$	3.81078			0.151705			0.0758524	+	0.997119i	$0.475832\pi$
$632$			9.85952i			0.392191i
$633$		0			0
$634$	−13.0790			−0.519434
$635$	19.5298	−	26.7034i	0.775017	−	1.05969i
$636$		0			0
$637$			0.0146797i			0.000581632i
$638$		−	16.3103i		−	0.645732i
$639$		0			0
$640$	−1.32001	+	1.80487i	−0.0521780	+	0.0713439i
$641$	−35.7796			−1.41321			−0.706604	−	0.707609i	$-0.749774\pi$
$641$	−35.7796			−1.41321			−0.706604	+	0.707609i	$0.749774\pi$
$642$		0			0
$643$		−	11.3094i		−	0.445999i	−0.974819	−	0.223000i	$-0.928415\pi$
$643$		−	11.3094i		−	0.445999i	0.974819	−	0.223000i	$-0.0715849\pi$
$644$	−3.59037			−0.141480
$645$		0			0
$646$	5.76491			0.226817
$647$		−	49.4528i		−	1.94419i	−0.234591	−	0.972094i	$-0.575375\pi$
$647$		−	49.4528i		−	1.94419i	0.234591	−	0.972094i	$-0.424625\pi$
$648$		0			0
$649$	−17.4693			−0.685729
$650$	−0.734633	−	2.31032i	−0.0288147	−	0.0906183i
$651$		0			0
$652$		−	16.2498i		−	0.636390i
$653$		−	46.1311i		−	1.80525i	−0.430429	−	0.902624i	$-0.641638\pi$
$653$		−	46.1311i		−	1.80525i	0.430429	−	0.902624i	$-0.358362\pi$
$654$		0			0
$655$	−4.51136	−	3.29942i	−0.176273	−	0.128919i
$656$	0.249771			0.00975191
$657$		0			0
$658$			15.8789i			0.619024i
$659$	−23.6732			−0.922176			−0.461088	−	0.887355i	$-0.652541\pi$
$659$	−23.6732			−0.922176			−0.461088	+	0.887355i	$0.652541\pi$
$660$		0			0
$661$	−32.1287			−1.24966			−0.624830	−	0.780761i	$-0.714832\pi$
$661$	−32.1287			−1.24966			−0.624830	+	0.780761i	$0.714832\pi$
$662$			24.8851i			0.967187i
$663$		0			0
$664$	17.5298			0.680289
$665$	20.0899	−	27.4693i	0.779053	−	1.06521i
$666$		0			0
$667$			11.0908i			0.429439i
$668$			2.95035i			0.114152i
$669$		0			0
$670$	8.96972	+	6.56009i	0.346531	+	0.253439i
$671$	22.7493			0.878227
$672$		0			0
$673$			47.7631i			1.84113i	0.390588	+	0.920566i	$0.372272\pi$
$673$			47.7631i			1.84113i	−0.390588	+	0.920566i	$0.627728\pi$
$674$	27.5445			1.06097
$675$		0			0
$676$	−12.7649			−0.490958
$677$		−	8.82168i		−	0.339045i	−0.985526	−	0.169522i	$-0.945778\pi$
$677$		−	8.82168i		−	0.339045i	0.985526	−	0.169522i	$-0.0542225\pi$
$678$		0			0
$679$	−17.7796			−0.682318
$680$	−1.80487	−	1.32001i	−0.0692137	−	0.0506201i
$681$		0			0
$682$			4.18922i			0.160413i
$683$			28.5142i			1.09107i	0.838089	+	0.545533i	$0.183673\pi$
$683$			28.5142i			1.09107i	−0.838089	+	0.545533i	$0.816327\pi$
$684$		0			0
$685$	2.71995	−	3.71904i	0.103924	−	0.142097i
$686$	18.5601			0.708628
$687$		0			0
$688$			1.03028i			0.0392789i
$689$	−3.73555			−0.142313
$690$		0			0
$691$	−50.4078			−1.91760			−0.958801	−	0.284077i	$-0.908313\pi$
$691$	−50.4078			−1.91760			−0.958801	+	0.284077i	$0.908313\pi$
$692$		−	6.14048i		−	0.233426i
$693$		0			0
$694$	−4.48486			−0.170243
$695$	−28.1386	−	20.5795i	−1.06736	−	0.780624i
$696$		0			0
$697$			0.249771i			0.00946075i
$698$		−	34.2186i		−	1.29519i
$699$		0			0
$700$	−12.5795	+	4.00000i	−0.475459	+	0.151186i
$701$	−10.4702			−0.395453			−0.197727	−	0.980257i	$-0.563356\pi$
$701$	−10.4702			−0.395453			−0.197727	+	0.980257i	$0.563356\pi$
$702$		0			0
$703$		−	64.2186i		−	2.42205i
$704$	2.00000			0.0753778
$705$		0			0
$706$	−4.90917			−0.184759
$707$			35.7190i			1.34335i
$708$		0			0
$709$	5.90539			0.221782			0.110891	−	0.993833i	$-0.464630\pi$
$709$	5.90539			0.221782			0.110891	+	0.993833i	$0.464630\pi$
$710$	−11.0147	+	15.0606i	−0.413374	+	0.565212i
$711$		0			0
$712$			8.73463i			0.327344i
$713$		−	2.84862i		−	0.106682i
$714$		0			0
$715$	−1.28005	+	1.75023i	−0.0478710	+	0.0654549i
$716$	15.5904			0.582639
$717$		0			0
$718$		−	13.7796i		−	0.514250i
$719$	−43.8354			−1.63479			−0.817393	−	0.576080i	$-0.804582\pi$
$719$	−43.8354			−1.63479			−0.817393	+	0.576080i	$0.804582\pi$
$720$		0			0
$721$	−29.6197			−1.10310
$722$			14.2342i			0.529741i
$723$		0			0
$724$	−4.10929			−0.152721
$725$	12.3562	+	38.8586i	0.458898	+	1.44317i
$726$		0			0
$727$			6.60597i			0.245002i	0.992468	+	0.122501i	$0.0390914\pi$
$727$			6.60597i			0.245002i	−0.992468	+	0.122501i	$0.960909\pi$
$728$		−	1.28005i		−	0.0474417i
$729$		0			0
$730$	0.875115	+	0.640023i	0.0323894	+	0.0236883i
$731$	−1.03028			−0.0381061
$732$		0			0
$733$			44.6188i			1.64803i	0.566565	+	0.824017i	$0.308272\pi$
$733$			44.6188i			1.64803i	−0.566565	+	0.824017i	$0.691728\pi$
$734$	−4.39025			−0.162047
$735$		0			0
$736$	−1.35998			−0.0501294
$737$		−	9.93945i		−	0.366124i
$738$		0			0
$739$	−34.4149			−1.26597			−0.632987	−	0.774163i	$-0.718171\pi$
$739$	−34.4149			−1.26597			−0.632987	+	0.774163i	$0.718171\pi$
$740$	−14.7044	+	20.1055i	−0.540543	+	0.739093i
$741$		0			0
$742$			20.3397i			0.746693i
$743$			28.0412i			1.02873i	0.857571	+	0.514365i	$0.171973\pi$
$743$			28.0412i			1.02873i	−0.857571	+	0.514365i	$0.828027\pi$
$744$		0			0
$745$	−18.0487	−	13.2001i	−0.661255	−	0.483615i
$746$	−0.220411			−0.00806983
$747$		0			0
$748$			2.00000i			0.0731272i
$749$	−51.3993			−1.87809
$750$		0			0
$751$	−47.4040			−1.72980			−0.864899	−	0.501947i	$-0.832617\pi$
$751$	−47.4040			−1.72980			−0.864899	+	0.501947i	$0.832617\pi$
$752$			6.01468i			0.219333i
$753$		0			0
$754$	−3.95413			−0.144001
$755$	28.5895	+	20.9092i	1.04048	+	0.760963i
$756$		0			0
$757$			35.9759i			1.30757i	0.756682	+	0.653784i	$0.226819\pi$
$757$			35.9759i			1.30757i	−0.756682	+	0.653784i	$0.773181\pi$
$758$		−	26.3103i		−	0.955634i
$759$		0			0
$760$	7.60975	−	10.4049i	0.276035	−	0.377427i
$761$	−13.1807			−0.477801			−0.238901	−	0.971044i	$-0.576787\pi$
$761$	−13.1807			−0.477801			−0.238901	+	0.971044i	$0.576787\pi$
$762$		0			0
$763$		−	33.4087i		−	1.20948i
$764$	6.06055			0.219263
$765$		0			0
$766$	36.1433			1.30591
$767$			4.23509i			0.152920i
$768$		0			0
$769$	6.11399			0.220476			0.110238	−	0.993905i	$-0.464839\pi$
$769$	6.11399			0.220476			0.110238	+	0.993905i	$0.464839\pi$
$770$	9.52982	+	6.96972i	0.343431	+	0.251171i
$771$		0			0
$772$		−	12.5601i		−	0.452048i
$773$			44.5601i			1.60272i	0.598186	+	0.801358i	$0.295889\pi$
$773$			44.5601i			1.60272i	−0.598186	+	0.801358i	$0.704111\pi$
$774$		0			0
$775$	−3.17362	−	9.98062i	−0.114000	−	0.358515i
$776$	−6.73463			−0.241759
$777$		0			0
$778$			3.77959i			0.135505i
$779$	−1.43991			−0.0515900
$780$		0			0
$781$	16.6888			0.597171
$782$		−	1.35998i		−	0.0486327i
$783$		0			0
$784$	0.0302761			0.00108129
$785$	−1.76961	+	2.41961i	−0.0631600	+	0.0863597i
$786$		0			0
$787$		−	26.3856i		−	0.940543i	−0.882522	−	0.470272i	$-0.844156\pi$
$787$		−	26.3856i		−	0.940543i	0.882522	−	0.470272i	$-0.155844\pi$
$788$		−	26.0487i		−	0.927948i
$789$		0			0
$790$	−13.0147	+	17.7952i	−0.463042	+	0.633124i
$791$	−19.8401			−0.705434
$792$		0			0
$793$		−	5.51514i		−	0.195848i
$794$	−12.2304			−0.434040
$795$		0			0
$796$	3.37466			0.119612
$797$		−	12.4390i		−	0.440612i	−0.975431	−	0.220306i	$-0.929294\pi$
$797$		−	12.4390i		−	0.440612i	0.975431	−	0.220306i	$-0.0707055\pi$
$798$		0			0
$799$	−6.01468			−0.212784
$800$	−4.76491	+	1.51514i	−0.168465	+	0.0535682i
$801$		0			0
$802$			11.7796i			0.415952i
$803$		−	0.969724i		−	0.0342208i
$804$		0			0
$805$	−6.48016	−	4.73933i	−0.228396	−	0.167039i
$806$	1.01560			0.0357729
$807$		0			0
$808$			13.5298i			0.475977i
$809$	5.96125			0.209586			0.104793	−	0.994494i	$-0.466582\pi$
$809$	5.96125			0.209586			0.104793	+	0.994494i	$0.466582\pi$
$810$		0			0
$811$	−27.8089			−0.976504			−0.488252	−	0.872703i	$-0.662365\pi$
$811$	−27.8089			−0.976504			−0.488252	+	0.872703i	$0.662365\pi$
$812$			21.5298i			0.755548i
$813$		0			0
$814$	22.2791			0.780883
$815$	21.4499	−	29.3288i	0.751357	−	1.02734i
$816$		0			0
$817$		−	5.93945i		−	0.207795i
$818$			15.7649i			0.551207i
$819$		0			0
$820$	0.450805	+	0.329700i	0.0157428	+	0.0115136i
$821$	9.05677			0.316083			0.158042	−	0.987432i	$-0.449482\pi$
$821$	9.05677			0.316083			0.158042	+	0.987432i	$0.449482\pi$
$822$		0			0
$823$			6.54828i			0.228259i	0.993466	+	0.114129i	$0.0364078\pi$
$823$			6.54828i			0.228259i	−0.993466	+	0.114129i	$0.963592\pi$
$824$	−11.2195			−0.390850
$825$		0			0
$826$	23.0596			0.802347
$827$		−	15.7115i		−	0.546341i	−0.961966	−	0.273171i	$-0.911928\pi$
$827$		−	15.7115i		−	0.546341i	0.961966	−	0.273171i	$-0.0880724\pi$
$828$		0			0
$829$	1.87890			0.0652567			0.0326284	−	0.999468i	$-0.489612\pi$
$829$	1.87890			0.0652567			0.0326284	+	0.999468i	$0.489612\pi$
$830$	31.6391	+	23.1396i	1.09821	+	0.803186i
$831$		0			0
$832$		−	0.484862i		−	0.0168096i
$833$			0.0302761i			0.00104900i
$834$		0			0
$835$	−3.89449	+	5.32500i	−0.134774	+	0.184279i
$836$	−11.5298			−0.398767
$837$		0			0
$838$			18.1892i			0.628336i
$839$	−48.6841			−1.68076			−0.840380	−	0.541997i	$-0.817668\pi$
$839$	−48.6841			−1.68076			−0.840380	+	0.541997i	$0.817668\pi$
$840$		0			0
$841$	37.5067			1.29333
$842$			9.03028i			0.311204i
$843$		0			0
$844$	−18.0294			−0.620596
$845$	−23.0390	−	16.8498i	−0.792567	−	0.579652i
$846$		0			0
$847$			18.4802i			0.634986i
$848$			7.70436i			0.264569i
$849$		0			0
$850$	−1.51514	−	4.76491i	−0.0519688	−	0.163435i
$851$	−15.1495			−0.519320
$852$		0			0
$853$		−	35.9494i		−	1.23089i	−0.788182	−	0.615443i	$-0.788977\pi$
$853$		−	35.9494i		−	1.23089i	0.788182	−	0.615443i	$-0.211023\pi$
$854$	−30.0294			−1.02758
$855$		0			0
$856$	−19.4693			−0.665446
$857$			13.4158i			0.458276i	0.973394	+	0.229138i	$0.0735907\pi$
$857$			13.4158i			0.458276i	−0.973394	+	0.229138i	$0.926409\pi$
$858$		0			0
$859$	23.8860			0.814980			0.407490	−	0.913210i	$-0.366404\pi$
$859$	23.8860			0.814980			0.407490	+	0.913210i	$0.366404\pi$
$860$	−1.35998	+	1.85952i	−0.0463748	+	0.0634090i
$861$		0			0
$862$		−	20.4196i		−	0.695495i
$863$		−	15.5979i		−	0.530960i	−0.964116	−	0.265480i	$-0.914470\pi$
$863$		−	15.5979i		−	0.530960i	0.964116	−	0.265480i	$-0.0855304\pi$
$864$		0			0
$865$	8.10551	−	11.0828i	0.275596	−	0.376826i
$866$	11.5904			0.393857
$867$		0			0
$868$		−	5.52982i		−	0.187694i
$869$	19.7190			0.668922
$870$		0			0
$871$	−2.40963			−0.0816472
$872$		−	12.6547i		−	0.428542i
$873$		0			0
$874$	7.84014			0.265197
$875$	−27.9844	−	9.38555i	−0.946046	−	0.317290i
$876$		0			0
$877$			33.3893i			1.12748i	0.825953	+	0.563739i	$0.190638\pi$
$877$			33.3893i			1.12748i	−0.825953	+	0.563739i	$0.809362\pi$
$878$			2.01938i			0.0681507i
$879$		0			0
$880$	3.60975	+	2.64002i	0.121685	+	0.0889952i
$881$	35.1202			1.18323			0.591615	−	0.806221i	$-0.298491\pi$
$881$	35.1202			1.18323			0.591615	+	0.806221i	$0.298491\pi$
$882$		0			0
$883$			22.2110i			0.747460i	0.927537	+	0.373730i	$0.121921\pi$
$883$			22.2110i			0.747460i	−0.927537	+	0.373730i	$0.878079\pi$
$884$	0.484862			0.0163077
$885$		0			0
$886$	27.4087			0.920814
$887$			5.17076i			0.173617i	0.996225	+	0.0868085i	$0.0276668\pi$
$887$			5.17076i			0.173617i	−0.996225	+	0.0868085i	$0.972333\pi$
$888$		0			0
$889$	39.0596			1.31002
$890$	−11.5298	+	15.7649i	−0.386480	+	0.528441i
$891$		0			0
$892$			23.2947i			0.779965i
$893$		−	34.6741i		−	1.16032i
$894$		0			0
$895$	28.1386	+	20.5795i	0.940571	+	0.687896i
$896$	−2.64002			−0.0881970
$897$		0			0
$898$			29.7190i			0.991737i
$899$	−17.0819			−0.569713
$900$		0			0
$901$	−7.70436			−0.256669
$902$		−	0.499542i		−	0.0166329i
$903$		0			0
$904$	−7.51514			−0.249950
$905$	−7.41675	−	5.42431i	−0.246541	−	0.180310i
$906$		0			0
$907$		−	3.85482i		−	0.127997i	−0.997950	−	0.0639986i	$-0.979615\pi$
$907$		−	3.85482i		−	0.127997i	0.997950	−	0.0639986i	$-0.0203853\pi$
$908$			17.4839i			0.580225i
$909$		0			0
$910$	1.68968	−	2.31032i	0.0560122	−	0.0765865i
$911$	22.6400			0.750097			0.375049	−	0.927005i	$-0.377626\pi$
$911$	22.6400			0.750097			0.375049	+	0.927005i	$0.377626\pi$
$912$		0			0
$913$		−	35.0596i		−	1.16030i
$914$	−39.4693			−1.30553
$915$		0			0
$916$	0.719953			0.0237879
$917$		−	6.59885i		−	0.217913i
$918$		0			0
$919$	−31.5298			−1.04007			−0.520036	−	0.854144i	$-0.674082\pi$
$919$	−31.5298			−1.04007			−0.520036	+	0.854144i	$0.674082\pi$
$920$	−2.45459	−	1.79518i	−0.0809253	−	0.0591855i
$921$		0			0
$922$		−	14.6888i		−	0.483749i
$923$		−	4.04587i		−	0.133172i
$924$		0			0
$925$	−53.0790	+	16.8780i	−1.74523	+	0.554945i
$926$	35.1055			1.15364
$927$		0			0
$928$			8.15516i			0.267706i
$929$	−11.1589			−0.366113			−0.183057	−	0.983102i	$-0.558599\pi$
$929$	−11.1589			−0.366113			−0.183057	+	0.983102i	$0.558599\pi$
$930$		0			0
$931$	−0.174539			−0.00572028
$932$		−	11.0450i		−	0.361790i
$933$		0			0
$934$	−9.96881			−0.326189
$935$	−2.64002	+	3.60975i	−0.0863380	+	0.118051i
$936$		0			0
$937$			24.5307i			0.801384i	0.916213	+	0.400692i	$0.131230\pi$
$937$			24.5307i			0.801384i	−0.916213	+	0.400692i	$0.868770\pi$
$938$			13.1202i			0.428389i
$939$		0			0
$940$	−7.93945	+	10.8557i	−0.258956	+	0.354075i
$941$	−35.3747			−1.15318			−0.576590	−	0.817033i	$-0.695617\pi$
$941$	−35.3747			−1.15318			−0.576590	+	0.817033i	$0.695617\pi$
$942$		0			0
$943$			0.339682i			0.0110616i
$944$	8.73463			0.284288
$945$		0			0
$946$	2.06055			0.0669943
$947$			2.23509i			0.0726307i	0.999340	+	0.0363154i	$0.0115621\pi$
$947$			2.23509i			0.0726307i	−0.999340	+	0.0363154i	$0.988438\pi$
$948$		0			0
$949$	−0.235091			−0.00763138
$950$	27.4693	−	8.73463i	0.891221	−	0.283389i
$951$		0			0
$952$		−	2.64002i		−	0.0855637i
$953$			5.65092i			0.183051i	0.995803	+	0.0915257i	$0.0291744\pi$
$953$			5.65092i			0.183051i	−0.995803	+	0.0915257i	$0.970826\pi$
$954$		0			0
$955$	10.9385	+	8.00000i	0.353963	+	0.258874i
$956$	5.59037			0.180805
$957$		0			0
$958$		−	2.28383i		−	0.0737871i
$959$	5.43991			0.175664
$960$		0			0
$961$	−26.6126			−0.858471
$962$		−	5.40115i		−	0.174140i
$963$		0			0
$964$	8.37088			0.269608
$965$	16.5795	−	22.6694i	0.533712	−	0.729753i
$966$		0			0
$967$			40.9991i			1.31844i	0.751949	+	0.659221i	$0.229114\pi$
$967$			40.9991i			1.31844i	−0.751949	+	0.659221i	$0.770886\pi$
$968$			7.00000i			0.224989i
$969$		0			0
$970$	−12.1552	−	8.88979i	−0.390279	−	0.285434i
$971$	45.3846			1.45646			0.728231	−	0.685332i	$-0.240343\pi$
$971$	45.3846			1.45646			0.728231	+	0.685332i	$0.240343\pi$
$972$		0			0
$973$		−	41.1589i		−	1.31950i
$974$	10.8292			0.346991
$975$		0			0
$976$	−11.3747			−0.364094
$977$			4.72752i			0.151247i	0.997136	+	0.0756233i	$0.0240946\pi$
$977$			4.72752i			0.151247i	−0.997136	+	0.0756233i	$0.975905\pi$
$978$		0			0
$979$	17.4693			0.558320
$980$	0.0546445	+	0.0399648i	0.00174556	+	0.00127663i
$981$		0			0
$982$		−	24.7952i		−	0.791246i
$983$			14.3297i			0.457046i	0.973538	+	0.228523i	$0.0733897\pi$
$983$			14.3297i			0.457046i	−0.973538	+	0.228523i	$0.926610\pi$
$984$		0			0
$985$	34.3846	−	47.0147i	1.09559	−	1.49801i
$986$	−8.15516			−0.259713
$987$		0			0
$988$			2.79518i			0.0889267i
$989$	−1.40115			−0.0445540
$990$		0			0
$991$	16.8827			0.536296			0.268148	−	0.963378i	$-0.413588\pi$
$991$	16.8827			0.536296			0.268148	+	0.963378i	$0.413588\pi$
$992$		−	2.09461i		−	0.0665039i
$993$		0			0
$994$	−22.0294			−0.698729
$995$	6.09083	+	4.45459i	0.193092	+	0.141220i
$996$		0			0
$997$			18.5189i			0.586500i	0.956036	+	0.293250i	$0.0947368\pi$
$997$			18.5189i			0.586500i	−0.956036	+	0.293250i	$0.905263\pi$
$998$		−	5.15138i		−	0.163064i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.d.g.919.4		6
3.2	odd	2		170.2.c.b.69.2	✓	6
5.2	odd	4		7650.2.a.dj.1.3		3
5.3	odd	4		7650.2.a.do.1.1		3
5.4	even	2	inner	1530.2.d.g.919.1		6
12.11	even	2		1360.2.e.c.1089.3		6
15.2	even	4		850.2.a.q.1.2		3
15.8	even	4		850.2.a.p.1.2		3
15.14	odd	2		170.2.c.b.69.5	yes	6
60.23	odd	4		6800.2.a.bp.1.2		3
60.47	odd	4		6800.2.a.bk.1.2		3
60.59	even	2		1360.2.e.c.1089.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.c.b.69.2	✓	6	3.2	odd	2
170.2.c.b.69.5	yes	6	15.14	odd	2
850.2.a.p.1.2		3	15.8	even	4
850.2.a.q.1.2		3	15.2	even	4
1360.2.e.c.1089.3		6	12.11	even	2
1360.2.e.c.1089.4		6	60.59	even	2
1530.2.d.g.919.1		6	5.4	even	2	inner
1530.2.d.g.919.4		6	1.1	even	1	trivial
6800.2.a.bk.1.2		3	60.47	odd	4
6800.2.a.bp.1.2		3	60.23	odd	4
7650.2.a.dj.1.3		3	5.2	odd	4
7650.2.a.do.1.1		3	5.3	odd	4

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1530.2.d.g.919.4

Level	$1530$
Weight	$2$
Character	1530.919
Analytic conductor	$12.217$
Analytic rank	$0$
Dimension	$6$
Inner twists	$2$