LMFDB - Embedded newform 2070.2.d.h.829.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2070,2,Mod(829,2070)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2070, 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("2070.829");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2070.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:	$16.5290332184$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} + 10x^{12} + 55x^{10} + 58x^{8} + 495x^{6} + 810x^{4} + 729x^{2} + 6561 $ x^16 + x^14 + 10x^12 + 55x^10 + 58x^8 + 495x^6 + 810x^4 + 729x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			829.15
Root			$0.0988560 + 1.72923i$ of defining polynomial
Character	$\chi$	$=$	2070.829
Dual form			2070.2.d.h.829.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(1.85322 - 1.25123i) q^{5} +5.08270i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.85322 - 1.25123i) q^{5} +5.08270i q^{7} -1.00000i q^{8} +(1.25123 + 1.85322i) q^{10} +5.96419 q^{11} -5.47812i q^{13} -5.08270 q^{14} +1.00000 q^{16} -6.91691i q^{17} +0.502455 q^{19} +(-1.85322 + 1.25123i) q^{20} +5.96419i q^{22} -1.00000i q^{23} +(1.86886 - 4.63760i) q^{25} +5.47812 q^{26} -5.08270i q^{28} +2.82495 q^{29} +5.73772 q^{31} +1.00000i q^{32} +6.91691 q^{34} +(6.35961 + 9.41936i) q^{35} +1.37626i q^{37} +0.502455i q^{38} +(-1.25123 - 1.85322i) q^{40} -2.65317 q^{41} -6.53140i q^{43} -5.96419 q^{44} +1.00000 q^{46} +3.26719i q^{47} -18.8338 q^{49} +(4.63760 + 1.86886i) q^{50} +5.47812i q^{52} +2.50246i q^{53} +(11.0530 - 7.46256i) q^{55} +5.08270 q^{56} +2.82495i q^{58} -2.65317 q^{59} -9.88989 q^{61} +5.73772i q^{62} -1.00000 q^{64} +(-6.85438 - 10.1522i) q^{65} -8.29438i q^{67} +6.91691i q^{68} +(-9.41936 + 6.35961i) q^{70} +1.93476 q^{71} -10.0661i q^{73} -1.37626 q^{74} -0.502455 q^{76} +30.3142i q^{77} +9.92182 q^{79} +(1.85322 - 1.25123i) q^{80} -2.65317i q^{82} +14.4243i q^{83} +(-8.65463 - 12.8186i) q^{85} +6.53140 q^{86} -5.96419i q^{88} +10.4615 q^{89} +27.8436 q^{91} +1.00000i q^{92} -3.26719 q^{94} +(0.931161 - 0.628686i) q^{95} +2.82495i q^{97} -18.8338i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} + 16 q^{16} - 32 q^{19} + 32 q^{31} + 8 q^{34} + 16 q^{46} - 96 q^{49} + 24 q^{55} + 24 q^{61} - 16 q^{64} - 8 q^{70} + 32 q^{76} - 24 q^{79} + 24 q^{85} + 80 q^{91} - 32 q^{94}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^16 - 32 * q^19 + 32 * q^31 + 8 * q^34 + 16 * q^46 - 96 * q^49 + 24 * q^55 + 24 * q^61 - 16 * q^64 - 8 * q^70 + 32 * q^76 - 24 * q^79 + 24 * q^85 + 80 * q^91 - 32 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times$.

$n$	$461$	$1657$	$1891$
$\chi(n)$	$1$	$-1$	$1$

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
$5$	1.85322	−	1.25123i	0.828786	−	0.559566i
$5$	1.85322	−	1.25123i	0.828786	−	0.559566i
$6$		0			0
$7$			5.08270i			1.92108i	0.278143	+	0.960540i	$0.410281\pi$
$7$			5.08270i			1.92108i	−0.278143	+	0.960540i	$0.589719\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.25123	+	1.85322i	0.395673	+	0.586040i
$11$	5.96419			1.79827			0.899135	−	0.437671i	$-0.144197\pi$
$11$	5.96419			1.79827			0.899135	+	0.437671i	$0.144197\pi$
$12$		0			0
$13$		−	5.47812i		−	1.51936i	−0.650298	−	0.759679i	$-0.725356\pi$
$13$		−	5.47812i		−	1.51936i	0.650298	−	0.759679i	$-0.274644\pi$
$14$	−5.08270			−1.35841
$15$		0			0
$16$	1.00000			0.250000
$17$		−	6.91691i		−	1.67760i	−0.544442	−	0.838799i	$-0.683259\pi$
$17$		−	6.91691i		−	1.67760i	0.544442	−	0.838799i	$-0.316741\pi$
$18$		0			0
$19$	0.502455			0.115271			0.0576356	−	0.998338i	$-0.481644\pi$
$19$	0.502455			0.115271			0.0576356	+	0.998338i	$0.481644\pi$
$20$	−1.85322	+	1.25123i	−0.414393	+	0.279783i
$21$		0			0
$22$			5.96419i			1.27157i
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$		0			0
$25$	1.86886	−	4.63760i	0.373772	−	0.927521i
$26$	5.47812			1.07435
$27$		0			0
$28$		−	5.08270i		−	0.960540i
$29$	2.82495			0.524581			0.262290	−	0.964989i	$-0.415522\pi$
$29$	2.82495			0.524581			0.262290	+	0.964989i	$0.415522\pi$
$30$		0			0
$31$	5.73772			1.03052			0.515262	−	0.857033i	$-0.327694\pi$
$31$	5.73772			1.03052			0.515262	+	0.857033i	$0.327694\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	6.91691			1.18624
$35$	6.35961	+	9.41936i	1.07497	+	1.59216i
$36$		0			0
$37$			1.37626i			0.226255i	0.993580	+	0.113127i	$0.0360868\pi$
$37$			1.37626i			0.226255i	−0.993580	+	0.113127i	$0.963913\pi$
$38$			0.502455i			0.0815090i
$39$		0			0
$40$	−1.25123	−	1.85322i	−0.197836	−	0.293020i
$41$	−2.65317			−0.414355			−0.207178	−	0.978303i	$-0.566428\pi$
$41$	−2.65317			−0.414355			−0.207178	+	0.978303i	$0.566428\pi$
$42$		0			0
$43$		−	6.53140i		−	0.996029i	−0.867169	−	0.498014i	$-0.834063\pi$
$43$		−	6.53140i		−	0.996029i	0.867169	−	0.498014i	$-0.165937\pi$
$44$	−5.96419			−0.899135
$45$		0			0
$46$	1.00000			0.147442
$47$			3.26719i			0.476569i	0.971195	+	0.238284i	$0.0765851\pi$
$47$			3.26719i			0.476569i	−0.971195	+	0.238284i	$0.923415\pi$
$48$		0			0
$49$	−18.8338			−2.69055
$50$	4.63760	+	1.86886i	0.655856	+	0.264297i
$51$		0			0
$52$			5.47812i			0.759679i
$53$			2.50246i			0.343739i	0.985120	+	0.171869i	$0.0549807\pi$
$53$			2.50246i			0.343739i	−0.985120	+	0.171869i	$0.945019\pi$
$54$		0			0
$55$	11.0530	−	7.46256i	1.49038	−	1.00625i
$56$	5.08270			0.679204
$57$		0			0
$58$			2.82495i			0.370934i
$59$	−2.65317			−0.345413			−0.172707	−	0.984973i	$-0.555251\pi$
$59$	−2.65317			−0.345413			−0.172707	+	0.984973i	$0.555251\pi$
$60$		0			0
$61$	−9.88989			−1.26627			−0.633135	−	0.774041i	$-0.718232\pi$
$61$	−9.88989			−1.26627			−0.633135	+	0.774041i	$0.718232\pi$
$62$			5.73772i			0.728691i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−6.85438	−	10.1522i	−0.850181	−	1.25922i
$66$		0			0
$67$		−	8.29438i		−	1.01332i	−0.862146	−	0.506660i	$-0.830880\pi$
$67$		−	8.29438i		−	1.01332i	0.862146	−	0.506660i	$-0.169120\pi$
$68$			6.91691i			0.838799i
$69$		0			0
$70$	−9.41936	+	6.35961i	−1.12583	+	0.760119i
$71$	1.93476			0.229614			0.114807	−	0.993388i	$-0.463375\pi$
$71$	1.93476			0.229614			0.114807	+	0.993388i	$0.463375\pi$
$72$		0			0
$73$		−	10.0661i		−	1.17814i	−0.808081	−	0.589071i	$-0.799494\pi$
$73$		−	10.0661i		−	1.17814i	0.808081	−	0.589071i	$-0.200506\pi$
$74$	−1.37626			−0.159986
$75$		0			0
$76$	−0.502455			−0.0576356
$77$			30.3142i			3.45462i
$78$		0			0
$79$	9.92182			1.11629			0.558146	−	0.829743i	$-0.311513\pi$
$79$	9.92182			1.11629			0.558146	+	0.829743i	$0.311513\pi$
$80$	1.85322	−	1.25123i	0.207196	−	0.139891i
$81$		0			0
$82$		−	2.65317i		−	0.292994i
$83$			14.4243i			1.58327i	0.610994	+	0.791635i	$0.290770\pi$
$83$			14.4243i			1.58327i	−0.610994	+	0.791635i	$0.709230\pi$
$84$		0			0
$85$	−8.65463	−	12.8186i	−0.938726	−	1.39037i
$86$	6.53140			0.704299
$87$		0			0
$88$		−	5.96419i		−	0.635785i
$89$	10.4615			1.10891			0.554457	−	0.832212i	$-0.312926\pi$
$89$	10.4615			1.10891			0.554457	+	0.832212i	$0.312926\pi$
$90$		0			0
$91$	27.8436			2.91881
$92$			1.00000i			0.104257i
$93$		0			0
$94$	−3.26719			−0.336985
$95$	0.931161	−	0.628686i	0.0955351	−	0.0645018i
$96$		0			0
$97$			2.82495i			0.286831i	0.989663	+	0.143415i	$0.0458084\pi$
$97$			2.82495i			0.286831i	−0.989663	+	0.143415i	$0.954192\pi$
$98$		−	18.8338i		−	1.90250i
$99$		0			0
$100$	−1.86886	+	4.63760i	−0.186886	+	0.463760i
$101$	12.0008			1.19413			0.597063	−	0.802194i	$-0.296334\pi$
$101$	12.0008			1.19413			0.597063	+	0.802194i	$0.296334\pi$
$102$		0			0
$103$			17.8019i			1.75408i	0.480421	+	0.877038i	$0.340484\pi$
$103$			17.8019i			1.75408i	−0.480421	+	0.877038i	$0.659516\pi$
$104$	−5.47812			−0.537174
$105$		0			0
$106$	−2.50246			−0.243060
$107$			10.9488i			1.05846i	0.848477	+	0.529232i	$0.177520\pi$
$107$			10.9488i			1.05846i	−0.848477	+	0.529232i	$0.822480\pi$
$108$		0			0
$109$	3.41936			0.327516			0.163758	−	0.986501i	$-0.447638\pi$
$109$	3.41936			0.327516			0.163758	+	0.986501i	$0.447638\pi$
$110$	7.46256	+	11.0530i	0.711527	+	1.05386i
$111$		0			0
$112$			5.08270i			0.480270i
$113$			11.9218i			1.12151i	0.827982	+	0.560755i	$0.189489\pi$
$113$			11.9218i			1.12151i	−0.827982	+	0.560755i	$0.810511\pi$
$114$		0			0
$115$	−1.25123	−	1.85322i	−0.116678	−	0.172814i
$116$	−2.82495			−0.262290
$117$		0			0
$118$		−	2.65317i		−	0.244244i
$119$	35.1566			3.22280
$120$		0			0
$121$	24.5715			2.23378
$122$		−	9.88989i		−	0.895389i
$123$		0			0
$124$	−5.73772			−0.515262
$125$	−2.33929	−	10.9329i	−0.209232	−	0.977866i
$126$		0			0
$127$		−	1.14392i		−	0.101506i	−0.998711	−	0.0507531i	$-0.983838\pi$
$127$		−	1.14392i		−	0.101506i	0.998711	−	0.0507531i	$-0.0161621\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	10.1522	−	6.85438i	0.890404	−	0.601169i
$131$	−19.4406			−1.69853			−0.849267	−	0.527964i	$-0.822956\pi$
$131$	−19.4406			−1.69853			−0.849267	+	0.527964i	$0.822956\pi$
$132$		0			0
$133$			2.55383i			0.221445i
$134$	8.29438			0.716525
$135$		0			0
$136$	−6.91691			−0.593120
$137$		−	2.91691i		−	0.249208i	−0.992207	−	0.124604i	$-0.960234\pi$
$137$		−	2.91691i		−	0.249208i	0.992207	−	0.124604i	$-0.0397661\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$	−6.35961	−	9.41936i	−0.537485	−	0.796082i
$141$		0			0
$142$			1.93476i			0.162362i
$143$		−	32.6725i		−	2.73222i
$144$		0			0
$145$	5.23526	−	3.53466i	0.434765	−	0.293537i
$146$	10.0661			0.833073
$147$		0			0
$148$		−	1.37626i		−	0.113127i
$149$	11.7653			0.963850			0.481925	−	0.876212i	$-0.339938\pi$
$149$	11.7653			0.963850			0.481925	+	0.876212i	$0.339938\pi$
$150$		0			0
$151$	−15.5715			−1.26719			−0.633597	−	0.773663i	$-0.718422\pi$
$151$	−15.5715			−1.26719			−0.633597	+	0.773663i	$0.718422\pi$
$152$		−	0.502455i		−	0.0407545i
$153$		0			0
$154$	−30.3142			−2.44279
$155$	10.6333	−	7.17919i	0.854084	−	0.576647i
$156$		0			0
$157$			9.76127i			0.779034i	0.921019	+	0.389517i	$0.127358\pi$
$157$			9.76127i			0.779034i	−0.921019	+	0.389517i	$0.872642\pi$
$158$			9.92182i			0.789338i
$159$		0			0
$160$	1.25123	+	1.85322i	0.0989182	+	0.146510i
$161$	5.08270			0.400573
$162$		0			0
$163$			13.7088i			1.07375i	0.843661	+	0.536876i	$0.180396\pi$
$163$			13.7088i			1.07375i	−0.843661	+	0.536876i	$0.819604\pi$
$164$	2.65317			0.207178
$165$		0			0
$166$	−14.4243			−1.11954
$167$			4.73281i			0.366236i	0.983091	+	0.183118i	$0.0586190\pi$
$167$			4.73281i			0.366236i	−0.983091	+	0.183118i	$0.941381\pi$
$168$		0			0
$169$	−17.0098			−1.30845
$170$	12.8186	−	8.65463i	0.983139	−	0.663780i
$171$		0			0
$172$			6.53140i			0.498014i
$173$		−	14.8289i		−	1.12742i	−0.825972	−	0.563711i	$-0.809373\pi$
$173$		−	14.8289i		−	1.12742i	0.825972	−	0.563711i	$-0.190627\pi$
$174$		0			0
$175$	23.5715	+	9.49885i	1.78184	+	0.718045i
$176$	5.96419			0.449568
$177$		0			0
$178$			10.4615i			0.784121i
$179$	3.62530			0.270968			0.135484	−	0.990780i	$-0.456741\pi$
$179$	3.62530			0.270968			0.135484	+	0.990780i	$0.456741\pi$
$180$		0			0
$181$	5.06098			0.376180			0.188090	−	0.982152i	$-0.439770\pi$
$181$	5.06098			0.376180			0.188090	+	0.982152i	$0.439770\pi$
$182$			27.8436i			2.06391i
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	1.72201	+	2.55051i	0.126605	+	0.187517i
$186$		0			0
$187$		−	41.2537i		−	3.01677i
$188$		−	3.26719i		−	0.238284i
$189$		0			0
$190$	0.628686	+	0.931161i	0.0456097	+	0.0675535i
$191$	−2.75251			−0.199165			−0.0995823	−	0.995029i	$-0.531751\pi$
$191$	−2.75251			−0.199165			−0.0995823	+	0.995029i	$0.531751\pi$
$192$		0			0
$193$			10.1654i			0.731721i	0.930670	+	0.365861i	$0.119225\pi$
$193$			10.1654i			0.731721i	−0.930670	+	0.365861i	$0.880775\pi$
$194$	−2.82495			−0.202820
$195$		0			0
$196$	18.8338			1.34527
$197$		−	0.534384i		−	0.0380733i	−0.999819	−	0.0190366i	$-0.993940\pi$
$197$		−	0.534384i		−	0.0380733i	0.999819	−	0.0190366i	$-0.00605991\pi$
$198$		0			0
$199$	5.92182			0.419787			0.209893	−	0.977724i	$-0.432688\pi$
$199$	5.92182			0.419787			0.209893	+	0.977724i	$0.432688\pi$
$200$	−4.63760	−	1.86886i	−0.327928	−	0.132148i
$201$		0			0
$202$			12.0008i			0.844375i
$203$			14.3584i			1.00776i
$204$		0			0
$205$	−4.91691	+	3.31972i	−0.343412	+	0.231859i
$206$	−17.8019			−1.24032
$207$		0			0
$208$		−	5.47812i		−	0.379839i
$209$	2.99674			0.207289
$210$		0			0
$211$	−28.6725			−1.97390			−0.986950	−	0.161028i	$-0.948519\pi$
$211$	−28.6725			−1.97390			−0.986950	+	0.161028i	$0.948519\pi$
$212$		−	2.50246i		−	0.171869i
$213$		0			0
$214$	−10.9488			−0.748447
$215$	−8.17226	−	12.1041i	−0.557344	−	0.825494i
$216$		0			0
$217$			29.1631i			1.97972i
$218$			3.41936i			0.231589i
$219$		0			0
$220$	−11.0530	+	7.46256i	−0.745190	+	0.503125i
$221$	−37.8917			−2.54887
$222$		0			0
$223$		−	12.6468i		−	0.846891i	−0.905922	−	0.423446i	$-0.860820\pi$
$223$		−	12.6468i		−	0.846891i	0.905922	−	0.423446i	$-0.139180\pi$
$224$	−5.08270			−0.339602
$225$		0			0
$226$	−11.9218			−0.793028
$227$			7.06098i			0.468654i	0.972158	+	0.234327i	$0.0752886\pi$
$227$			7.06098i			0.468654i	−0.972158	+	0.234327i	$0.924711\pi$
$228$		0			0
$229$	0.424275			0.0280369			0.0140184	−	0.999902i	$-0.495538\pi$
$229$	0.424275			0.0280369			0.0140184	+	0.999902i	$0.495538\pi$
$230$	1.85322	−	1.25123i	0.122198	−	0.0825035i
$231$		0			0
$232$		−	2.82495i		−	0.185467i
$233$			20.5666i			1.34736i	0.739021	+	0.673682i	$0.235288\pi$
$233$			20.5666i			1.34736i	−0.739021	+	0.673682i	$0.764712\pi$
$234$		0			0
$235$	4.08800	+	6.05483i	0.266672	+	0.394974i
$236$	2.65317			0.172707
$237$		0			0
$238$			35.1566i			2.27886i
$239$	−7.15916			−0.463088			−0.231544	−	0.972824i	$-0.574378\pi$
$239$	−7.15916			−0.463088			−0.231544	+	0.972824i	$0.574378\pi$
$240$		0			0
$241$	12.2945			0.791960			0.395980	−	0.918259i	$-0.370405\pi$
$241$	12.2945			0.791960			0.395980	+	0.918259i	$0.370405\pi$
$242$			24.5715i			1.57952i
$243$		0			0
$244$	9.88989			0.633135
$245$	−34.9032	+	23.5654i	−2.22989	+	1.50554i
$246$		0			0
$247$		−	2.75251i		−	0.175138i
$248$		−	5.73772i		−	0.364345i
$249$		0			0
$250$	10.9329	−	2.33929i	0.691456	−	0.147950i
$251$	−17.2640			−1.08969			−0.544847	−	0.838535i	$-0.683412\pi$
$251$	−17.2640			−1.08969			−0.544847	+	0.838535i	$0.683412\pi$
$252$		0			0
$253$		−	5.96419i		−	0.374965i
$254$	1.14392			0.0717757
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	23.3093i		−	1.45399i	−0.686642	−	0.726996i	$-0.740916\pi$
$257$		−	23.3093i		−	1.45399i	0.686642	−	0.726996i	$-0.259084\pi$
$258$		0			0
$259$	−6.99509			−0.434654
$260$	6.85438	+	10.1522i	0.425090	+	0.629611i
$261$		0			0
$262$		−	19.4406i		−	1.20104i
$263$			15.2994i			0.943404i	0.881758	+	0.471702i	$0.156360\pi$
$263$			15.2994i			0.943404i	−0.881758	+	0.471702i	$0.843640\pi$
$264$		0			0
$265$	3.13114	+	4.63760i	0.192344	+	0.284886i
$266$	−2.55383			−0.156585
$267$		0			0
$268$			8.29438i			0.506660i
$269$	−8.45746			−0.515660			−0.257830	−	0.966190i	$-0.583008\pi$
$269$	−8.45746			−0.515660			−0.257830	+	0.966190i	$0.583008\pi$
$270$		0			0
$271$	24.3682			1.48026			0.740131	−	0.672462i	$-0.234763\pi$
$271$	24.3682			1.48026			0.740131	+	0.672462i	$0.234763\pi$
$272$		−	6.91691i		−	0.419399i
$273$		0			0
$274$	2.91691			0.176217
$275$	11.1462	−	27.6595i	0.672143	−	1.66793i
$276$		0			0
$277$		−	25.4653i		−	1.53006i	−0.643992	−	0.765032i	$-0.722723\pi$
$277$		−	25.4653i		−	1.53006i	0.643992	−	0.765032i	$-0.277277\pi$
$278$		−	8.00000i		−	0.479808i
$279$		0			0
$280$	9.41936	−	6.35961i	0.562915	−	0.380060i
$281$	19.8360			1.18332			0.591659	−	0.806188i	$-0.298473\pi$
$281$	19.8360			1.18332			0.591659	+	0.806188i	$0.298473\pi$
$282$		0			0
$283$			4.94970i			0.294229i	0.989119	+	0.147115i	$0.0469986\pi$
$283$			4.94970i			0.294229i	−0.989119	+	0.147115i	$0.953001\pi$
$284$	−1.93476			−0.114807
$285$		0			0
$286$	32.6725			1.93197
$287$		−	13.4853i		−	0.796010i
$288$		0			0
$289$	−30.8436			−1.81433
$290$	3.53466	+	5.23526i	0.207562	+	0.307425i
$291$		0			0
$292$			10.0661i			0.589071i
$293$			8.97298i			0.524207i	0.965040	+	0.262104i	$0.0844162\pi$
$293$			8.97298i			0.524207i	−0.965040	+	0.262104i	$0.915584\pi$
$294$		0			0
$295$	−4.91691	+	3.31972i	−0.286274	+	0.193281i
$296$	1.37626			0.0799932
$297$		0			0
$298$			11.7653i			0.681545i
$299$	−5.47812			−0.316808
$300$		0			0
$301$	33.1971			1.91345
$302$		−	15.5715i		−	0.896041i
$303$		0			0
$304$	0.502455			0.0288178
$305$	−18.3282	+	12.3745i	−1.04947	+	0.708562i
$306$		0			0
$307$		−	2.75251i		−	0.157094i	−0.996910	−	0.0785470i	$-0.974972\pi$
$307$		−	2.75251i		−	0.157094i	0.996910	−	0.0785470i	$-0.0250281\pi$
$308$		−	30.3142i		−	1.72731i
$309$		0			0
$310$	7.17919	+	10.6333i	0.407751	+	0.603929i
$311$	22.1836			1.25792			0.628959	−	0.777439i	$-0.283481\pi$
$311$	22.1836			1.25792			0.628959	+	0.777439i	$0.283481\pi$
$312$		0			0
$313$			19.4311i			1.09831i	0.835720	+	0.549155i	$0.185051\pi$
$313$			19.4311i			1.09831i	−0.835720	+	0.549155i	$0.814949\pi$
$314$	−9.76127			−0.550860
$315$		0			0
$316$	−9.92182			−0.558146
$317$			17.3633i			0.975220i	0.873062	+	0.487610i	$0.162131\pi$
$317$			17.3633i			0.975220i	−0.873062	+	0.487610i	$0.837869\pi$
$318$		0			0
$319$	16.8486			0.943338
$320$	−1.85322	+	1.25123i	−0.103598	+	0.0699457i
$321$		0			0
$322$			5.08270i			0.283248i
$323$		−	3.47544i		−	0.193378i
$324$		0			0
$325$	−25.4054	−	10.2378i	−1.40924	−	0.567893i
$326$	−13.7088			−0.759258
$327$		0			0
$328$			2.65317i			0.146497i
$329$	−16.6061			−0.915527
$330$		0			0
$331$	−18.6627			−1.02580			−0.512898	−	0.858449i	$-0.671428\pi$
$331$	−18.6627			−1.02580			−0.512898	+	0.858449i	$0.671428\pi$
$332$		−	14.4243i		−	0.791635i
$333$		0			0
$334$	−4.73281			−0.258968
$335$	−10.3782	−	15.3713i	−0.567019	−	0.839825i
$336$		0			0
$337$			6.16963i			0.336081i	0.985780	+	0.168041i	$0.0537440\pi$
$337$			6.16963i			0.336081i	−0.985780	+	0.168041i	$0.946256\pi$
$338$		−	17.0098i		−	0.925212i
$339$		0			0
$340$	8.65463	+	12.8186i	0.469363	+	0.695184i
$341$	34.2208			1.85316
$342$		0			0
$343$		−	60.1477i		−	3.24767i
$344$	−6.53140			−0.352149
$345$		0			0
$346$	14.8289			0.797207
$347$		−	14.8387i		−	0.796585i	−0.917259	−	0.398292i	$-0.869603\pi$
$347$		−	14.8387i		−	0.796585i	0.917259	−	0.398292i	$-0.130397\pi$
$348$		0			0
$349$	−29.8436			−1.59749			−0.798747	−	0.601667i	$-0.794503\pi$
$349$	−29.8436			−1.59749			−0.798747	+	0.601667i	$0.794503\pi$
$350$	−9.49885	+	23.5715i	−0.507735	+	1.25995i
$351$		0			0
$352$			5.96419i			0.317892i
$353$			15.2770i			0.813113i	0.913626	+	0.406557i	$0.133271\pi$
$353$			15.2770i			0.813113i	−0.913626	+	0.406557i	$0.866729\pi$
$354$		0			0
$355$	3.58555	−	2.42083i	0.190301	−	0.128484i
$356$	−10.4615			−0.554457
$357$		0			0
$358$			3.62530i			0.191603i
$359$	−22.2387			−1.17371			−0.586856	−	0.809692i	$-0.699634\pi$
$359$	−22.2387			−1.17371			−0.586856	+	0.809692i	$0.699634\pi$
$360$		0			0
$361$	−18.7475			−0.986713
$362$			5.06098i			0.265999i
$363$		0			0
$364$	−27.8436			−1.45940
$365$	−12.5949	−	18.6546i	−0.659249	−	0.976428i
$366$		0			0
$367$		−	24.7675i		−	1.29285i	−0.762976	−	0.646427i	$-0.776262\pi$
$367$		−	24.7675i		−	1.29285i	0.762976	−	0.646427i	$-0.223738\pi$
$368$		−	1.00000i		−	0.0521286i
$369$		0			0
$370$	−2.55051	+	1.72201i	−0.132594	+	0.0895230i
$371$	−12.7192			−0.660349
$372$		0			0
$373$			12.5138i			0.647939i	0.946068	+	0.323970i	$0.105018\pi$
$373$			12.5138i			0.647939i	−0.946068	+	0.323970i	$0.894982\pi$
$374$	41.2537			2.13318
$375$		0			0
$376$	3.26719			0.168493
$377$		−	15.4754i		−	0.797026i
$378$		0			0
$379$	−36.3461			−1.86697			−0.933487	−	0.358612i	$-0.883250\pi$
$379$	−36.3461			−1.86697			−0.933487	+	0.358612i	$0.883250\pi$
$380$	−0.931161	+	0.628686i	−0.0477675	+	0.0322509i
$381$		0			0
$382$		−	2.75251i		−	0.140831i
$383$			5.46562i			0.279280i	0.990202	+	0.139640i	$0.0445945\pi$
$383$			5.46562i			0.279280i	−0.990202	+	0.139640i	$0.955405\pi$
$384$		0			0
$385$	37.9299	+	56.1789i	1.93309	+	2.86314i
$386$	−10.1654			−0.517405
$387$		0			0
$388$		−	2.82495i		−	0.143415i
$389$	8.83150			0.447775			0.223887	−	0.974615i	$-0.428125\pi$
$389$	8.83150			0.447775			0.223887	+	0.974615i	$0.428125\pi$
$390$		0			0
$391$	−6.91691			−0.349803
$392$			18.8338i			0.951252i
$393$		0			0
$394$	0.534384			0.0269219
$395$	18.3873	−	12.4145i	0.925167	−	0.624639i
$396$		0			0
$397$		−	10.3198i		−	0.517935i	−0.965886	−	0.258967i	$-0.916618\pi$
$397$		−	10.3198i		−	0.517935i	0.965886	−	0.258967i	$-0.0833823\pi$
$398$			5.92182i			0.296834i
$399$		0			0
$400$	1.86886	−	4.63760i	0.0934430	−	0.231880i
$401$	3.69456			0.184497			0.0922487	−	0.995736i	$-0.470595\pi$
$401$	3.69456			0.184497			0.0922487	+	0.995736i	$0.470595\pi$
$402$		0			0
$403$		−	31.4319i		−	1.56574i
$404$	−12.0008			−0.597063
$405$		0			0
$406$	−14.3584			−0.712595
$407$			8.20824i			0.406868i
$408$		0			0
$409$	−0.166181			−0.00821710			−0.00410855	−	0.999992i	$-0.501308\pi$
$409$	−0.166181			−0.00821710			−0.00410855	+	0.999992i	$0.501308\pi$
$410$	−3.31972	−	4.91691i	−0.163949	−	0.242829i
$411$		0			0
$412$		−	17.8019i		−	0.877038i
$413$		−	13.4853i		−	0.663566i
$414$		0			0
$415$	18.0481	+	26.7314i	0.885944	+	1.31219i
$416$	5.47812			0.268587
$417$		0			0
$418$			2.99674i			0.146575i
$419$	−9.04287			−0.441773			−0.220886	−	0.975300i	$-0.570895\pi$
$419$	−9.04287			−0.441773			−0.220886	+	0.975300i	$0.570895\pi$
$420$		0			0
$421$	−28.7925			−1.40326			−0.701630	−	0.712542i	$-0.747544\pi$
$421$	−28.7925			−1.40326			−0.701630	+	0.712542i	$0.747544\pi$
$422$		−	28.6725i		−	1.39576i
$423$		0			0
$424$	2.50246			0.121530
$425$	−32.0779	−	12.9267i	−1.55601	−	0.627039i
$426$		0			0
$427$		−	50.2673i		−	2.43261i
$428$		−	10.9488i		−	0.529232i
$429$		0			0
$430$	12.1041	−	8.17226i	0.583713	−	0.394101i
$431$	−11.1375			−0.536476			−0.268238	−	0.963353i	$-0.586441\pi$
$431$	−11.1375			−0.536476			−0.268238	+	0.963353i	$0.586441\pi$
$432$		0			0
$433$		−	27.3277i		−	1.31328i	−0.754202	−	0.656642i	$-0.771976\pi$
$433$		−	27.3277i		−	1.31328i	0.754202	−	0.656642i	$-0.228024\pi$
$434$	−29.1631			−1.39987
$435$		0			0
$436$	−3.41936			−0.163758
$437$		−	0.502455i		−	0.0240357i
$438$		0			0
$439$	−1.46562			−0.0699500			−0.0349750	−	0.999388i	$-0.511135\pi$
$439$	−1.46562			−0.0699500			−0.0349750	+	0.999388i	$0.511135\pi$
$440$	−7.46256	−	11.0530i	−0.355763	−	0.526929i
$441$		0			0
$442$		−	37.8917i		−	1.80232i
$443$		−	4.00000i		−	0.190046i	−0.995475	−	0.0950229i	$-0.969708\pi$
$443$		−	4.00000i		−	0.190046i	0.995475	−	0.0950229i	$-0.0302924\pi$
$444$		0			0
$445$	19.3874	−	13.0897i	0.919053	−	0.620511i
$446$	12.6468			0.598842
$447$		0			0
$448$		−	5.08270i		−	0.240135i
$449$	−24.7643			−1.16870			−0.584351	−	0.811501i	$-0.698651\pi$
$449$	−24.7643			−1.16870			−0.584351	+	0.811501i	$0.698651\pi$
$450$		0			0
$451$	−15.8240			−0.745123
$452$		−	11.9218i		−	0.560755i
$453$		0			0
$454$	−7.06098			−0.331388
$455$	51.6004	−	34.8387i	2.41907	−	1.63326i
$456$		0			0
$457$			20.2410i			0.946832i	0.880839	+	0.473416i	$0.156979\pi$
$457$			20.2410i			0.946832i	−0.880839	+	0.473416i	$0.843021\pi$
$458$			0.424275i			0.0198251i
$459$		0			0
$460$	1.25123	+	1.85322i	0.0583388	+	0.0864069i
$461$	28.4447			1.32480			0.662401	−	0.749150i	$-0.269538\pi$
$461$	28.4447			1.32480			0.662401	+	0.749150i	$0.269538\pi$
$462$		0			0
$463$			9.22016i			0.428497i	0.976779	+	0.214249i	$0.0687303\pi$
$463$			9.22016i			0.428497i	−0.976779	+	0.214249i	$0.931270\pi$
$464$	2.82495			0.131145
$465$		0			0
$466$	−20.5666			−0.952731
$467$			16.7188i			0.773654i	0.922152	+	0.386827i	$0.126429\pi$
$467$			16.7188i			0.773654i	−0.922152	+	0.386827i	$0.873571\pi$
$468$		0			0
$469$	42.1578			1.94667
$470$	−6.05483	+	4.08800i	−0.279288	+	0.188565i
$471$		0			0
$472$			2.65317i			0.122122i
$473$		−	38.9545i		−	1.79113i
$474$		0			0
$475$	0.939018	−	2.33019i	0.0430851	−	0.106916i
$476$	−35.1566			−1.61140
$477$		0			0
$478$		−	7.15916i		−	0.327452i
$479$	10.1654			0.464469			0.232234	−	0.972660i	$-0.425396\pi$
$479$	10.1654			0.464469			0.232234	+	0.972660i	$0.425396\pi$
$480$		0			0
$481$	7.53929			0.343762
$482$			12.2945i			0.560000i
$483$		0			0
$484$	−24.5715			−1.11689
$485$	3.53466	+	5.23526i	0.160501	+	0.237721i
$486$		0			0
$487$			1.78988i			0.0811071i	0.999177	+	0.0405536i	$0.0129121\pi$
$487$			1.78988i			0.0811071i	−0.999177	+	0.0405536i	$0.987088\pi$
$488$			9.88989i			0.447694i
$489$		0			0
$490$	−23.5654	−	34.9032i	−1.06458	−	1.57677i
$491$	3.77019			0.170146			0.0850731	−	0.996375i	$-0.472888\pi$
$491$	3.77019			0.170146			0.0850731	+	0.996375i	$0.472888\pi$
$492$		0			0
$493$		−	19.5399i		−	0.880035i
$494$	2.75251			0.123841
$495$		0			0
$496$	5.73772			0.257631
$497$			9.83382i			0.441107i
$498$		0			0
$499$	−12.0639			−0.540052			−0.270026	−	0.962853i	$-0.587032\pi$
$499$	−12.0639			−0.540052			−0.270026	+	0.962853i	$0.587032\pi$
$500$	2.33929	+	10.9329i	0.104616	+	0.488933i
$501$		0			0
$502$		−	17.2640i		−	0.770530i
$503$			6.99509i			0.311896i	0.987765	+	0.155948i	$0.0498432\pi$
$503$			6.99509i			0.311896i	−0.987765	+	0.155948i	$0.950157\pi$
$504$		0			0
$505$	22.2402	−	15.0158i	0.989675	−	0.668192i
$506$	5.96419			0.265140
$507$		0			0
$508$			1.14392i			0.0507531i
$509$	−41.3626			−1.83336			−0.916682	−	0.399617i	$-0.869143\pi$
$509$	−41.3626			−1.83336			−0.916682	+	0.399617i	$0.869143\pi$
$510$		0			0
$511$	51.1627			2.26331
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	23.3093			1.02813
$515$	22.2743	+	32.9909i	0.981521	+	1.45375i
$516$		0			0
$517$			19.4861i			0.857000i
$518$		−	6.99509i		−	0.307347i
$519$		0			0
$520$	−10.1522	+	6.85438i	−0.445202	+	0.300584i
$521$	27.4476			1.20250			0.601250	−	0.799061i	$-0.294669\pi$
$521$	27.4476			1.20250			0.601250	+	0.799061i	$0.294669\pi$
$522$		0			0
$523$		−	0.108041i		−	0.00472429i	−0.999997	−	0.00236215i	$-0.999248\pi$
$523$		−	0.108041i		−	0.00472429i	0.999997	−	0.00236215i	$-0.000751895\pi$
$524$	19.4406			0.849267
$525$		0			0
$526$	−15.2994			−0.667087
$527$		−	39.6873i		−	1.72881i
$528$		0			0
$529$	−1.00000			−0.0434783
$530$	−4.63760	+	3.13114i	−0.201445	+	0.136008i
$531$		0			0
$532$		−	2.55383i		−	0.110722i
$533$			14.5344i			0.629554i
$534$		0			0
$535$	13.6995	+	20.2906i	0.592281	+	0.877240i
$536$	−8.29438			−0.358262
$537$		0			0
$538$		−	8.45746i		−	0.364627i
$539$	−112.328			−4.83833
$540$		0			0
$541$	13.8436			0.595185			0.297592	−	0.954693i	$-0.403816\pi$
$541$	13.8436			0.595185			0.297592	+	0.954693i	$0.403816\pi$
$542$			24.3682i			1.04670i
$543$		0			0
$544$	6.91691			0.296560
$545$	6.33684	−	4.27840i	0.271440	−	0.183267i
$546$		0			0
$547$			34.8304i			1.48924i	0.667489	+	0.744620i	$0.267369\pi$
$547$			34.8304i			1.48924i	−0.667489	+	0.744620i	$0.732631\pi$
$548$			2.91691i			0.124604i
$549$		0			0
$550$	27.6595	+	11.1462i	1.17941	+	0.475277i
$551$	1.41941			0.0604690
$552$		0			0
$553$			50.4296i			2.14449i
$554$	25.4653			1.08192
$555$		0			0
$556$	8.00000			0.339276
$557$		−	12.6686i		−	0.536787i	−0.963309	−	0.268394i	$-0.913507\pi$
$557$		−	12.6686i		−	0.536787i	0.963309	−	0.268394i	$-0.0864928\pi$
$558$		0			0
$559$	−35.7798			−1.51332
$560$	6.35961	+	9.41936i	0.268743	+	0.398041i
$561$		0			0
$562$			19.8360i			0.836732i
$563$		−	35.7335i		−	1.50599i	−0.658027	−	0.752994i	$-0.728609\pi$
$563$		−	35.7335i		−	1.50599i	0.658027	−	0.752994i	$-0.271391\pi$
$564$		0			0
$565$	14.9169	+	22.0938i	0.627559	+	0.929492i
$566$	−4.94970			−0.208051
$567$		0			0
$568$		−	1.93476i		−	0.0811809i
$569$	17.0835			0.716178			0.358089	−	0.933687i	$-0.383428\pi$
$569$	17.0835			0.716178			0.358089	+	0.933687i	$0.383428\pi$
$570$		0			0
$571$	34.3363			1.43693			0.718464	−	0.695564i	$-0.244845\pi$
$571$	34.3363			1.43693			0.718464	+	0.695564i	$0.244845\pi$
$572$			32.6725i			1.36611i
$573$		0			0
$574$	13.4853			0.562864
$575$	−4.63760	−	1.86886i	−0.193401	−	0.0779368i
$576$		0			0
$577$			13.1447i			0.547222i	0.961840	+	0.273611i	$0.0882182\pi$
$577$			13.1447i			0.547222i	−0.961840	+	0.273611i	$0.911782\pi$
$578$		−	30.8436i		−	1.28293i
$579$		0			0
$580$	−5.23526	+	3.53466i	−0.217382	+	0.146769i
$581$	−73.3142			−3.04159
$582$		0			0
$583$			14.9251i			0.618135i
$584$	−10.0661			−0.416536
$585$		0			0
$586$	−8.97298			−0.370670
$587$			1.70547i			0.0703925i	0.999380	+	0.0351962i	$0.0112056\pi$
$587$			1.70547i			0.0703925i	−0.999380	+	0.0351962i	$0.988794\pi$
$588$		0			0
$589$	2.88295			0.118790
$590$	−3.31972	−	4.91691i	−0.136671	−	0.202426i
$591$		0			0
$592$			1.37626i			0.0565637i
$593$		−	21.3191i		−	0.875470i	−0.899104	−	0.437735i	$-0.855781\pi$
$593$		−	21.3191i		−	0.875470i	0.899104	−	0.437735i	$-0.144219\pi$
$594$		0			0
$595$	65.1529	−	43.9889i	2.67101	−	1.80337i
$596$	−11.7653			−0.481925
$597$		0			0
$598$		−	5.47812i		−	0.224017i
$599$	2.21539			0.0905183			0.0452592	−	0.998975i	$-0.485589\pi$
$599$	2.21539			0.0905183			0.0452592	+	0.998975i	$0.485589\pi$
$600$		0			0
$601$	35.4054			1.44421			0.722107	−	0.691781i	$-0.243174\pi$
$601$	35.4054			1.44421			0.722107	+	0.691781i	$0.243174\pi$
$602$			33.1971i			1.35301i
$603$		0			0
$604$	15.5715			0.633597
$605$	45.5365	−	30.7446i	1.85132	−	1.24995i
$606$		0			0
$607$		−	22.3111i		−	0.905580i	−0.891617	−	0.452790i	$-0.850429\pi$
$607$		−	22.3111i		−	0.905580i	0.891617	−	0.452790i	$-0.149571\pi$
$608$			0.502455i			0.0203772i
$609$		0			0
$610$	−12.3745	−	18.3282i	−0.501029	−	0.742085i
$611$	17.8981			0.724079
$612$		0			0
$613$			9.77867i			0.394957i	0.980307	+	0.197478i	$0.0632752\pi$
$613$			9.77867i			0.394957i	−0.980307	+	0.197478i	$0.936725\pi$
$614$	2.75251			0.111082
$615$		0			0
$616$	30.3142			1.22139
$617$		−	15.5536i		−	0.626165i	−0.949726	−	0.313083i	$-0.898638\pi$
$617$		−	15.5536i		−	0.626165i	0.949726	−	0.313083i	$-0.101362\pi$
$618$		0			0
$619$	−35.9941			−1.44672			−0.723362	−	0.690469i	$-0.757404\pi$
$619$	−35.9941			−1.44672			−0.723362	+	0.690469i	$0.757404\pi$
$620$	−10.6333	+	7.17919i	−0.427042	+	0.288323i
$621$		0			0
$622$			22.1836i			0.889482i
$623$			53.1725i			2.13031i
$624$		0			0
$625$	−18.0147	−	17.3341i	−0.720589	−	0.693362i
$626$	−19.4311			−0.776623
$627$		0			0
$628$		−	9.76127i		−	0.389517i
$629$	9.51943			0.379565
$630$		0			0
$631$	32.0600			1.27629			0.638144	−	0.769917i	$-0.279702\pi$
$631$	32.0600			1.27629			0.638144	+	0.769917i	$0.279702\pi$
$632$		−	9.92182i		−	0.394669i
$633$		0			0
$634$	−17.3633			−0.689584
$635$	−1.43130	−	2.11993i	−0.0567994	−	0.0841268i
$636$		0			0
$637$			103.174i			4.08790i
$638$			16.8486i			0.667040i
$639$		0			0
$640$	−1.25123	−	1.85322i	−0.0494591	−	0.0732550i
$641$	33.8883			1.33851			0.669255	−	0.743033i	$-0.266614\pi$
$641$	33.8883			1.33851			0.669255	+	0.743033i	$0.266614\pi$
$642$		0			0
$643$		−	2.78935i		−	0.110001i	−0.998486	−	0.0550007i	$-0.982484\pi$
$643$		−	2.78935i		−	0.110001i	0.998486	−	0.0550007i	$-0.0175161\pi$
$644$	−5.08270			−0.200286
$645$		0			0
$646$	3.47544			0.136739
$647$			41.1529i			1.61789i	0.587886	+	0.808944i	$0.299960\pi$
$647$			41.1529i			1.61789i	−0.587886	+	0.808944i	$0.700040\pi$
$648$		0			0
$649$	−15.8240			−0.621146
$650$	10.2378	−	25.4054i	0.401561	−	0.996480i
$651$		0			0
$652$		−	13.7088i		−	0.536876i
$653$			42.6725i			1.66991i	0.550321	+	0.834953i	$0.314505\pi$
$653$			42.6725i			1.66991i	−0.550321	+	0.834953i	$0.685495\pi$
$654$		0			0
$655$	−36.0277	+	24.3246i	−1.40772	+	0.950441i
$656$	−2.65317			−0.103589
$657$		0			0
$658$		−	16.6061i		−	0.647375i
$659$	31.2214			1.21621			0.608106	−	0.793856i	$-0.291930\pi$
$659$	31.2214			1.21621			0.608106	+	0.793856i	$0.291930\pi$
$660$		0			0
$661$	−49.0968			−1.90965			−0.954823	−	0.297176i	$-0.903955\pi$
$661$	−49.0968			−1.90965			−0.954823	+	0.297176i	$0.903955\pi$
$662$		−	18.6627i		−	0.725348i
$663$		0			0
$664$	14.4243			0.559770
$665$	3.19542	+	4.73281i	0.123913	+	0.183530i
$666$		0			0
$667$		−	2.82495i		−	0.109383i
$668$		−	4.73281i		−	0.183118i
$669$		0			0
$670$	15.3713	−	10.3782i	0.593846	−	0.400943i
$671$	−58.9852			−2.27710
$672$		0			0
$673$		−	27.5169i		−	1.06070i	−0.847780	−	0.530348i	$-0.822061\pi$
$673$		−	27.5169i		−	1.06070i	0.847780	−	0.530348i	$-0.177939\pi$
$674$	−6.16963			−0.237645
$675$		0			0
$676$	17.0098			0.654224
$677$		−	36.8166i		−	1.41498i	−0.706725	−	0.707489i	$-0.749828\pi$
$677$		−	36.8166i		−	1.41498i	0.706725	−	0.707489i	$-0.250172\pi$
$678$		0			0
$679$	−14.3584			−0.551024
$680$	−12.8186	+	8.65463i	−0.491570	+	0.331890i
$681$		0			0
$682$			34.2208i			1.31038i
$683$			4.28470i			0.163950i	0.996634	+	0.0819748i	$0.0261227\pi$
$683$			4.28470i			0.163950i	−0.996634	+	0.0819748i	$0.973877\pi$
$684$		0			0
$685$	−3.64972	−	5.40568i	−0.139449	−	0.206540i
$686$	60.1477			2.29645
$687$		0			0
$688$		−	6.53140i		−	0.249007i
$689$	13.7088			0.522262
$690$		0			0
$691$	−7.01473			−0.266853			−0.133426	−	0.991059i	$-0.542598\pi$
$691$	−7.01473			−0.266853			−0.133426	+	0.991059i	$0.542598\pi$
$692$			14.8289i			0.563711i
$693$		0			0
$694$	14.8387			0.563270
$695$	−14.8258	+	10.0098i	−0.562374	+	0.379694i
$696$		0			0
$697$			18.3517i			0.695121i
$698$		−	29.8436i		−	1.12960i
$699$		0			0
$700$	−23.5715	−	9.49885i	−0.890920	−	0.359023i
$701$	−6.07899			−0.229600			−0.114800	−	0.993389i	$-0.536623\pi$
$701$	−6.07899			−0.229600			−0.114800	+	0.993389i	$0.536623\pi$
$702$		0			0
$703$			0.691506i			0.0260807i
$704$	−5.96419			−0.224784
$705$		0			0
$706$	−15.2770			−0.574958
$707$			60.9965i			2.29401i
$708$		0			0
$709$	−20.6003			−0.773660			−0.386830	−	0.922151i	$-0.626430\pi$
$709$	−20.6003			−0.773660			−0.386830	+	0.922151i	$0.626430\pi$
$710$	2.42083	+	3.58555i	0.0908521	+	0.134563i
$711$		0			0
$712$		−	10.4615i		−	0.392060i
$713$		−	5.73772i		−	0.214879i
$714$		0			0
$715$	−40.8808	−	60.5495i	−1.52886	−	2.26442i
$716$	−3.62530			−0.135484
$717$		0			0
$718$		−	22.2387i		−	0.829939i
$719$	12.6642			0.472294			0.236147	−	0.971717i	$-0.424115\pi$
$719$	12.6642			0.472294			0.236147	+	0.971717i	$0.424115\pi$
$720$		0			0
$721$	−90.4818			−3.36972
$722$		−	18.7475i		−	0.697711i
$723$		0			0
$724$	−5.06098			−0.188090
$725$	5.27944	−	13.1010i	0.196073	−	0.486559i
$726$		0			0
$727$		−	31.5107i		−	1.16867i	−0.811514	−	0.584333i	$-0.801356\pi$
$727$		−	31.5107i		−	1.16867i	0.811514	−	0.584333i	$-0.198644\pi$
$728$		−	27.8436i		−	1.03195i
$729$		0			0
$730$	18.6546	−	12.5949i	0.690439	−	0.466159i
$731$	−45.1771			−1.67093
$732$		0			0
$733$		−	16.5282i		−	0.610483i	−0.952275	−	0.305241i	$-0.901263\pi$
$733$		−	16.5282i		−	0.610483i	0.952275	−	0.305241i	$-0.0987372\pi$
$734$	24.7675			0.914186
$735$		0			0
$736$	1.00000			0.0368605
$737$		−	49.4692i		−	1.82222i
$738$		0			0
$739$	28.9607			1.06534			0.532668	−	0.846324i	$-0.321189\pi$
$739$	28.9607			1.06534			0.532668	+	0.846324i	$0.321189\pi$
$740$	−1.72201	−	2.55051i	−0.0633023	−	0.0937585i
$741$		0			0
$742$		−	12.7192i		−	0.466937i
$743$			30.0098i			1.10095i	0.834850	+	0.550477i	$0.185554\pi$
$743$			30.0098i			1.10095i	−0.834850	+	0.550477i	$0.814446\pi$
$744$		0			0
$745$	21.8037	−	14.7211i	0.798825	−	0.539338i
$746$	−12.5138			−0.458162
$747$		0			0
$748$			41.2537i			1.50839i
$749$	−55.6496			−2.03339
$750$		0			0
$751$	17.8580			0.651646			0.325823	−	0.945431i	$-0.394359\pi$
$751$	17.8580			0.651646			0.325823	+	0.945431i	$0.394359\pi$
$752$			3.26719i			0.119142i
$753$		0			0
$754$	15.4754			0.563582
$755$	−28.8575	+	19.4835i	−1.05023	+	0.709079i
$756$		0			0
$757$		−	4.07497i		−	0.148107i	−0.997254	−	0.0740536i	$-0.976406\pi$
$757$		−	4.07497i		−	0.148107i	0.997254	−	0.0740536i	$-0.0235936\pi$
$758$		−	36.3461i		−	1.32015i
$759$		0			0
$760$	−0.628686	−	0.931161i	−0.0228048	−	0.0337767i
$761$	54.1543			1.96309			0.981545	−	0.191231i	$-0.0612478\pi$
$761$	54.1543			1.96309			0.981545	+	0.191231i	$0.0612478\pi$
$762$		0			0
$763$			17.3796i			0.629184i
$764$	2.75251			0.0995823
$765$		0			0
$766$	−5.46562			−0.197481
$767$			14.5344i			0.524806i
$768$		0			0
$769$	−44.6824			−1.61129			−0.805644	−	0.592400i	$-0.798180\pi$
$769$	−44.6824			−1.61129			−0.805644	+	0.592400i	$0.798180\pi$
$770$	−56.1789	+	37.9299i	−2.02455	+	1.36690i
$771$		0			0
$772$		−	10.1654i		−	0.365861i
$773$		−	11.3952i		−	0.409858i	−0.978777	−	0.204929i	$-0.934304\pi$
$773$		−	11.3952i		−	0.409858i	0.978777	−	0.204929i	$-0.0656963\pi$
$774$		0			0
$775$	10.7230	−	26.6093i	0.385181	−	0.955833i
$776$	2.82495			0.101410
$777$		0			0
$778$			8.83150i			0.316625i
$779$	−1.33310			−0.0477632
$780$		0			0
$781$	11.5393			0.412908
$782$		−	6.91691i		−	0.247348i
$783$		0			0
$784$	−18.8338			−0.672636
$785$	12.2136	+	18.0898i	0.435921	+	0.645653i
$786$		0			0
$787$		−	23.7487i		−	0.846550i	−0.906001	−	0.423275i	$-0.860880\pi$
$787$		−	23.7487i		−	0.846550i	0.906001	−	0.423275i	$-0.139120\pi$
$788$			0.534384i			0.0190366i
$789$		0			0
$790$	12.4145	+	18.3873i	0.441686	+	0.654192i
$791$	−60.5950			−2.15451
$792$		0			0
$793$			54.1780i			1.92392i
$794$	10.3198			0.366235
$795$		0			0
$796$	−5.92182			−0.209893
$797$		−	14.3903i		−	0.509731i	−0.966977	−	0.254865i	$-0.917969\pi$
$797$		−	14.3903i		−	0.509731i	0.966977	−	0.254865i	$-0.0820312\pi$
$798$		0			0
$799$	22.5989			0.799491
$800$	4.63760	+	1.86886i	0.163964	+	0.0660741i
$801$		0			0
$802$			3.69456i			0.130459i
$803$		−	60.0358i		−	2.11862i
$804$		0			0
$805$	9.41936	−	6.35961i	0.331989	−	0.224147i
$806$	31.4319			1.10714
$807$		0			0
$808$		−	12.0008i		−	0.422187i
$809$	19.1964			0.674909			0.337454	−	0.941342i	$-0.390434\pi$
$809$	19.1964			0.674909			0.337454	+	0.941342i	$0.390434\pi$
$810$		0			0
$811$	−8.48035			−0.297785			−0.148893	−	0.988853i	$-0.547571\pi$
$811$	−8.48035			−0.297785			−0.148893	+	0.988853i	$0.547571\pi$
$812$		−	14.3584i		−	0.503880i
$813$		0			0
$814$	−8.20824			−0.287699
$815$	17.1528	+	25.4054i	0.600835	+	0.889911i
$816$		0			0
$817$		−	3.28173i		−	0.114813i
$818$		−	0.166181i		−	0.00581037i
$819$		0			0
$820$	4.91691	−	3.31972i	0.171706	−	0.115930i
$821$	−41.3626			−1.44356			−0.721782	−	0.692120i	$-0.756677\pi$
$821$	−41.3626			−1.44356			−0.721782	+	0.692120i	$0.756677\pi$
$822$		0			0
$823$		−	39.9258i		−	1.39173i	−0.718175	−	0.695863i	$-0.755022\pi$
$823$		−	39.9258i		−	1.39173i	0.718175	−	0.695863i	$-0.244978\pi$
$824$	17.8019			0.620159
$825$		0			0
$826$	13.4853			0.469212
$827$		−	5.41936i		−	0.188450i	−0.995551	−	0.0942249i	$-0.969963\pi$
$827$		−	5.41936i		−	0.188450i	0.995551	−	0.0942249i	$-0.0300373\pi$
$828$		0			0
$829$	−8.71038			−0.302524			−0.151262	−	0.988494i	$-0.548334\pi$
$829$	−8.71038			−0.302524			−0.151262	+	0.988494i	$0.548334\pi$
$830$	−26.7314	+	18.0481i	−0.927860	+	0.626457i
$831$		0			0
$832$			5.47812i			0.189920i
$833$			130.272i			4.51365i
$834$		0			0
$835$	5.92182	+	8.77094i	0.204933	+	0.303531i
$836$	−2.99674			−0.103644
$837$		0			0
$838$		−	9.04287i		−	0.312381i
$839$	29.1441			1.00617			0.503083	−	0.864238i	$-0.332199\pi$
$839$	29.1441			1.00617			0.503083	+	0.864238i	$0.332199\pi$
$840$		0			0
$841$	−21.0196			−0.724815
$842$		−	28.7925i		−	0.992254i
$843$		0			0
$844$	28.6725			0.986950
$845$	−31.5230	+	21.2832i	−1.08442	+	0.732163i
$846$		0			0
$847$			124.890i			4.29126i
$848$			2.50246i			0.0859347i
$849$		0			0
$850$	12.9267	−	32.0779i	0.443383	−	1.10026i
$851$	1.37626			0.0471774
$852$		0			0
$853$			24.9817i			0.855356i	0.903931	+	0.427678i	$0.140668\pi$
$853$			24.9817i			0.855356i	−0.903931	+	0.427678i	$0.859332\pi$
$854$	50.2673			1.72011
$855$		0			0
$856$	10.9488			0.374224
$857$			6.57645i			0.224647i	0.993672	+	0.112324i	$0.0358293\pi$
$857$			6.57645i			0.224647i	−0.993672	+	0.112324i	$0.964171\pi$
$858$		0			0
$859$	−34.9509			−1.19251			−0.596254	−	0.802796i	$-0.703345\pi$
$859$	−34.9509			−1.19251			−0.596254	+	0.802796i	$0.703345\pi$
$860$	8.17226	+	12.1041i	0.278672	+	0.412747i
$861$		0			0
$862$		−	11.1375i		−	0.379346i
$863$			47.6873i			1.62329i	0.584148	+	0.811647i	$0.301429\pi$
$863$			47.6873i			1.62329i	−0.584148	+	0.811647i	$0.698571\pi$
$864$		0			0
$865$	−18.5543	−	27.4813i	−0.630866	−	0.934391i
$866$	27.3277			0.928632
$867$		0			0
$868$		−	29.1631i		−	0.989860i
$869$	59.1756			2.00739
$870$		0			0
$871$	−45.4376			−1.53959
$872$		−	3.41936i		−	0.115794i
$873$		0			0
$874$	0.502455			0.0169958
$875$	55.5685	−	11.8899i	1.87856	−	0.401952i
$876$		0			0
$877$		−	42.9225i		−	1.44939i	−0.689070	−	0.724695i	$-0.741981\pi$
$877$		−	42.9225i		−	1.44939i	0.689070	−	0.724695i	$-0.258019\pi$
$878$		−	1.46562i		−	0.0494622i
$879$		0			0
$880$	11.0530	−	7.46256i	0.372595	−	0.251563i
$881$	23.1981			0.781564			0.390782	−	0.920483i	$-0.372205\pi$
$881$	23.1981			0.781564			0.390782	+	0.920483i	$0.372205\pi$
$882$		0			0
$883$			46.1492i			1.55304i	0.630090	+	0.776522i	$0.283018\pi$
$883$			46.1492i			1.55304i	−0.630090	+	0.776522i	$0.716982\pi$
$884$	37.8917			1.27443
$885$		0			0
$886$	4.00000			0.134383
$887$		−	47.8955i		−	1.60817i	−0.594511	−	0.804087i	$-0.702655\pi$
$887$		−	47.8955i		−	1.60817i	0.594511	−	0.804087i	$-0.297345\pi$
$888$		0			0
$889$	5.81418			0.195001
$890$	13.0897	+	19.3874i	0.438767	+	0.649868i
$891$		0			0
$892$			12.6468i			0.423446i
$893$			1.64162i			0.0549346i
$894$		0			0
$895$	6.71849	−	4.53608i	0.224574	−	0.151624i
$896$	5.08270			0.169801
$897$		0			0
$898$		−	24.7643i		−	0.826397i
$899$	16.2088			0.540593
$900$		0			0
$901$	17.3093			0.576655
$902$		−	15.8240i		−	0.526882i
$903$		0			0
$904$	11.9218			0.396514
$905$	9.37912	−	6.33244i	0.311773	−	0.210497i
$906$		0			0
$907$			43.6322i			1.44878i	0.689388	+	0.724392i	$0.257879\pi$
$907$			43.6322i			1.44878i	−0.689388	+	0.724392i	$0.742121\pi$
$908$		−	7.06098i		−	0.234327i
$909$		0			0
$910$	34.8387	+	51.6004i	1.15489	+	1.71054i
$911$	−28.9818			−0.960210			−0.480105	−	0.877211i	$-0.659401\pi$
$911$	−28.9818			−0.960210			−0.480105	+	0.877211i	$0.659401\pi$
$912$		0			0
$913$			86.0291i			2.84715i
$914$	−20.2410			−0.669511
$915$		0			0
$916$	−0.424275			−0.0140184
$917$		−	98.8107i		−	3.26302i
$918$		0			0
$919$	−6.84323			−0.225737			−0.112869	−	0.993610i	$-0.536004\pi$
$919$	−6.84323			−0.225737			−0.112869	+	0.993610i	$0.536004\pi$
$920$	−1.85322	+	1.25123i	−0.0610989	+	0.0412518i
$921$		0			0
$922$			28.4447i			0.936776i
$923$		−	10.5989i		−	0.348866i
$924$		0			0
$925$	6.38253	+	2.57203i	0.209856	+	0.0845677i
$926$	−9.22016			−0.302993
$927$		0			0
$928$			2.82495i			0.0927336i
$929$	17.8415			0.585361			0.292680	−	0.956210i	$-0.405453\pi$
$929$	17.8415			0.585361			0.292680	+	0.956210i	$0.405453\pi$
$930$		0			0
$931$	−9.46315			−0.310142
$932$		−	20.5666i		−	0.673682i
$933$		0			0
$934$	−16.7188			−0.547056
$935$	−51.6178	−	76.4523i	−1.68808	−	2.50026i
$936$		0			0
$937$			8.01018i			0.261681i	0.991403	+	0.130841i	$0.0417676\pi$
$937$			8.01018i			0.261681i	−0.991403	+	0.130841i	$0.958232\pi$
$938$			42.1578i			1.37650i
$939$		0			0
$940$	−4.08800	−	6.05483i	−0.133336	−	0.197487i
$941$	−24.8819			−0.811126			−0.405563	−	0.914067i	$-0.632925\pi$
$941$	−24.8819			−0.811126			−0.405563	+	0.914067i	$0.632925\pi$
$942$		0			0
$943$			2.65317i			0.0863991i
$944$	−2.65317			−0.0863533
$945$		0			0
$946$	38.9545			1.26652
$947$			4.65635i			0.151311i	0.997134	+	0.0756555i	$0.0241049\pi$
$947$			4.65635i			0.151311i	−0.997134	+	0.0756555i	$0.975895\pi$
$948$		0			0
$949$	−55.1431			−1.79002
$950$	2.33019	+	0.939018i	0.0756013	+	0.0304658i
$951$		0			0
$952$		−	35.1566i		−	1.13943i
$953$		−	14.2360i		−	0.461149i	−0.973055	−	0.230574i	$-0.925939\pi$
$953$		−	14.2360i		−	0.461149i	0.973055	−	0.230574i	$-0.0740605\pi$
$954$		0			0
$955$	−5.10101	+	3.44402i	−0.165065	+	0.111446i
$956$	7.15916			0.231544
$957$		0			0
$958$			10.1654i			0.328429i
$959$	14.8258			0.478749
$960$		0			0
$961$	1.92141			0.0619810
$962$			7.53929i			0.243077i
$963$		0			0
$964$	−12.2945			−0.395980
$965$	12.7192	+	18.8387i	0.409446	+	0.606440i
$966$		0			0
$967$		−	10.2742i		−	0.330397i	−0.986260	−	0.165199i	$-0.947173\pi$
$967$		−	10.2742i		−	0.330397i	0.986260	−	0.165199i	$-0.0528265\pi$
$968$		−	24.5715i		−	0.789759i
$969$		0			0
$970$	−5.23526	+	3.53466i	−0.168094	+	0.113491i
$971$	24.3333			0.780893			0.390447	−	0.920626i	$-0.372321\pi$
$971$	24.3333			0.780893			0.390447	+	0.920626i	$0.372321\pi$
$972$		0			0
$973$		−	40.6616i		−	1.30355i
$974$	−1.78988			−0.0573514
$975$		0			0
$976$	−9.88989			−0.316568
$977$			6.58455i			0.210658i	0.994437	+	0.105329i	$0.0335896\pi$
$977$			6.58455i			0.210658i	−0.994437	+	0.105329i	$0.966410\pi$
$978$		0			0
$979$	62.3942			1.99413
$980$	34.9032	−	23.5654i	1.11494	−	0.752769i
$981$		0			0
$982$			3.77019i			0.120311i
$983$		−	25.5940i		−	0.816321i	−0.912910	−	0.408160i	$-0.866170\pi$
$983$		−	25.5940i		−	0.816321i	0.912910	−	0.408160i	$-0.133830\pi$
$984$		0			0
$985$	−0.668636	−	0.990331i	−0.0213045	−	0.0315546i
$986$	19.5399			0.622279
$987$		0			0
$988$			2.75251i			0.0875690i
$989$	−6.53140			−0.207686
$990$		0			0
$991$	−18.8065			−0.597408			−0.298704	−	0.954346i	$-0.596554\pi$
$991$	−18.8065			−0.597408			−0.298704	+	0.954346i	$0.596554\pi$
$992$			5.73772i			0.182173i
$993$		0			0
$994$	−9.83382			−0.311910
$995$	10.9744	−	7.40954i	0.347913	−	0.234898i
$996$		0			0
$997$			17.5862i			0.556960i	0.960442	+	0.278480i	$0.0898306\pi$
$997$			17.5862i			0.556960i	−0.960442	+	0.278480i	$0.910169\pi$
$998$		−	12.0639i		−	0.381875i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2070.2.d.h.829.15	yes	16
3.2	odd	2	inner	2070.2.d.h.829.2	✓	16
5.4	even	2	inner	2070.2.d.h.829.7	yes	16
15.14	odd	2	inner	2070.2.d.h.829.10	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2070.2.d.h.829.2	✓	16	3.2	odd	2	inner
2070.2.d.h.829.7	yes	16	5.4	even	2	inner
2070.2.d.h.829.10	yes	16	15.14	odd	2	inner
2070.2.d.h.829.15	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2070.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.85322 - 1.25123i) q^{5} +5.08270i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(1.85322 - 1.25123i) q^{5} +5.08270i q^{7} -1.00000i q^{8} +(1.25123 + 1.85322i) q^{10} +5.96419 q^{11} -5.47812i q^{13} -5.08270 q^{14} +1.00000 q^{16} -6.91691i q^{17} +0.502455 q^{19} +(-1.85322 + 1.25123i) q^{20} +5.96419i q^{22} -1.00000i q^{23} +(1.86886 - 4.63760i) q^{25} +5.47812 q^{26} -5.08270i q^{28} +2.82495 q^{29} +5.73772 q^{31} +1.00000i q^{32} +6.91691 q^{34} +(6.35961 + 9.41936i) q^{35} +1.37626i q^{37} +0.502455i q^{38} +(-1.25123 - 1.85322i) q^{40} -2.65317 q^{41} -6.53140i q^{43} -5.96419 q^{44} +1.00000 q^{46} +3.26719i q^{47} -18.8338 q^{49} +(4.63760 + 1.86886i) q^{50} +5.47812i q^{52} +2.50246i q^{53} +(11.0530 - 7.46256i) q^{55} +5.08270 q^{56} +2.82495i q^{58} -2.65317 q^{59} -9.88989 q^{61} +5.73772i q^{62} -1.00000 q^{64} +(-6.85438 - 10.1522i) q^{65} -8.29438i q^{67} +6.91691i q^{68} +(-9.41936 + 6.35961i) q^{70} +1.93476 q^{71} -10.0661i q^{73} -1.37626 q^{74} -0.502455 q^{76} +30.3142i q^{77} +9.92182 q^{79} +(1.85322 - 1.25123i) q^{80} -2.65317i q^{82} +14.4243i q^{83} +(-8.65463 - 12.8186i) q^{85} +6.53140 q^{86} -5.96419i q^{88} +10.4615 q^{89} +27.8436 q^{91} +1.00000i q^{92} -3.26719 q^{94} +(0.931161 - 0.628686i) q^{95} +2.82495i q^{97} -18.8338i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} + 16 q^{16} - 32 q^{19} + 32 q^{31} + 8 q^{34} + 16 q^{46} - 96 q^{49} + 24 q^{55} + 24 q^{61} - 16 q^{64} - 8 q^{70} + 32 q^{76} - 24 q^{79} + 24 q^{85} + 80 q^{91} - 32 q^{94}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^16 - 32 * q^19 + 32 * q^31 + 8 * q^34 + 16 * q^46 - 96 * q^49 + 24 * q^55 + 24 * q^61 - 16 * q^64 - 8 * q^70 + 32 * q^76 - 24 * q^79 + 24 * q^85 + 80 * q^91 - 32 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more