LMFDB - Embedded newform 3330.2.d.q.1999.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3330,2,Mod(1999,3330)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3330.1999"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3330, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3330.d (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-14,-4,0,0,0,0,-6,12,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.5901838731$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 20x^{12} + 154x^{10} + 580x^{8} + 1105x^{6} + 960x^{4} + 256x^{2} + 16 $ x^14 + 20x^12 + 154x^10 + 580x^8 + 1105x^6 + 960x^4 + 256x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1999.1
Root			$1.58005i$ of defining polynomial
Character	$\chi$	$=$	3330.1999
Dual form			3330.2.d.q.1999.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.20427 - 0.375782i) q^{5} -0.496550i q^{7} +1.00000i q^{8} +(-0.375782 + 2.20427i) q^{10} -3.54201 q^{11} -3.71758i q^{13} -0.496550 q^{14} +1.00000 q^{16} +6.87767i q^{17} -3.45902 q^{19} +(2.20427 + 0.375782i) q^{20} +3.54201i q^{22} -5.34439i q^{23} +(4.71758 + 1.65665i) q^{25} -3.71758 q^{26} +0.496550i q^{28} -5.00638 q^{29} -4.05558 q^{31} -1.00000i q^{32} +6.87767 q^{34} +(-0.186594 + 1.09453i) q^{35} -1.00000i q^{37} +3.45902i q^{38} +(0.375782 - 2.20427i) q^{40} +7.78001 q^{41} -5.91114i q^{43} +3.54201 q^{44} -5.34439 q^{46} +9.61254i q^{47} +6.75344 q^{49} +(1.65665 - 4.71758i) q^{50} +3.71758i q^{52} +12.0867i q^{53} +(7.80754 + 1.33102i) q^{55} +0.496550 q^{56} +5.00638i q^{58} -11.4710 q^{59} +1.18246 q^{61} +4.05558i q^{62} -1.00000 q^{64} +(-1.39700 + 8.19453i) q^{65} -6.56561i q^{67} -6.87767i q^{68} +(1.09453 + 0.186594i) q^{70} +15.7252 q^{71} +0.584892i q^{73} -1.00000 q^{74} +3.45902 q^{76} +1.75879i q^{77} +1.89142 q^{79} +(-2.20427 - 0.375782i) q^{80} -7.78001i q^{82} +3.12508i q^{83} +(2.58450 - 15.1602i) q^{85} -5.91114 q^{86} -3.54201i q^{88} -2.39557 q^{89} -1.84596 q^{91} +5.34439i q^{92} +9.61254 q^{94} +(7.62460 + 1.29984i) q^{95} +9.01936i q^{97} -6.75344i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{4} - 4 q^{5} - 6 q^{10} + 12 q^{11} - 12 q^{14} + 14 q^{16} + 4 q^{19} + 4 q^{20} + 10 q^{25} + 4 q^{26} - 16 q^{29} + 12 q^{31} - 12 q^{34} - 8 q^{35} + 6 q^{40} + 56 q^{41} - 12 q^{44} - 8 q^{46}+ \cdots + 12 q^{95}+O(q^{100}) $ 14 * q - 14 * q^4 - 4 * q^5 - 6 * q^10 + 12 * q^11 - 12 * q^14 + 14 * q^16 + 4 * q^19 + 4 * q^20 + 10 * q^25 + 4 * q^26 - 16 * q^29 + 12 * q^31 - 12 * q^34 - 8 * q^35 + 6 * q^40 + 56 * q^41 - 12 * q^44 - 8 * q^46 + 18 * q^49 - 24 * q^50 + 12 * q^56 - 28 * q^59 + 12 * q^61 - 14 * q^64 + 12 * q^65 - 16 * q^70 + 48 * q^71 - 14 * q^74 - 4 * q^76 - 20 * q^79 - 4 * q^80 + 12 * q^85 + 12 * q^86 - 36 * q^89 - 32 * q^91 + 32 * q^94 + 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3330\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$1$	$-1$

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
$5$	−2.20427	−	0.375782i	−0.985778	−	0.168055i
$5$	−2.20427	−	0.375782i	−0.985778	−	0.168055i
$6$		0			0
$7$		−	0.496550i		−	0.187678i	−0.995587	−	0.0938391i	$-0.970086\pi$
$7$		−	0.496550i		−	0.187678i	0.995587	−	0.0938391i	$-0.0299139\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.375782	+	2.20427i	−0.118833	+	0.697050i
$11$	−3.54201			−1.06796			−0.533979	−	0.845498i	$-0.679304\pi$
$11$	−3.54201			−1.06796			−0.533979	+	0.845498i	$0.679304\pi$
$12$		0			0
$13$		−	3.71758i		−	1.03107i	−0.856868	−	0.515535i	$-0.827593\pi$
$13$		−	3.71758i		−	1.03107i	0.856868	−	0.515535i	$-0.172407\pi$
$14$	−0.496550			−0.132709
$15$		0			0
$16$	1.00000			0.250000
$17$			6.87767i			1.66808i	0.551704	+	0.834040i	$0.313978\pi$
$17$			6.87767i			1.66808i	−0.551704	+	0.834040i	$0.686022\pi$
$18$		0			0
$19$	−3.45902			−0.793554			−0.396777	−	0.917915i	$-0.629871\pi$
$19$	−3.45902			−0.793554			−0.396777	+	0.917915i	$0.629871\pi$
$20$	2.20427	+	0.375782i	0.492889	+	0.0840273i
$21$		0			0
$22$			3.54201i			0.755160i
$23$		−	5.34439i		−	1.11438i	−0.830384	−	0.557191i	$-0.811879\pi$
$23$		−	5.34439i		−	1.11438i	0.830384	−	0.557191i	$-0.188121\pi$
$24$		0			0
$25$	4.71758	+	1.65665i	0.943515	+	0.331329i
$26$	−3.71758			−0.729077
$27$		0			0
$28$			0.496550i			0.0938391i
$29$	−5.00638			−0.929662			−0.464831	−	0.885400i	$-0.653885\pi$
$29$	−5.00638			−0.929662			−0.464831	+	0.885400i	$0.653885\pi$
$30$		0			0
$31$	−4.05558			−0.728404			−0.364202	−	0.931320i	$-0.618658\pi$
$31$	−4.05558			−0.728404			−0.364202	+	0.931320i	$0.618658\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	6.87767			1.17951
$35$	−0.186594	+	1.09453i	−0.0315402	+	0.185009i
$36$		0			0
$37$		−	1.00000i		−	0.164399i
$37$		−	1.00000i		−	0.164399i
$38$			3.45902i			0.561127i
$39$		0			0
$40$	0.375782	−	2.20427i	0.0594163	−	0.348525i
$41$	7.78001			1.21503			0.607516	−	0.794307i	$-0.292166\pi$
$41$	7.78001			1.21503			0.607516	+	0.794307i	$0.292166\pi$
$42$		0			0
$43$		−	5.91114i		−	0.901440i	−0.892665	−	0.450720i	$-0.851167\pi$
$43$		−	5.91114i		−	0.901440i	0.892665	−	0.450720i	$-0.148833\pi$
$44$	3.54201			0.533979
$45$		0			0
$46$	−5.34439			−0.787987
$47$			9.61254i			1.40213i	0.713096	+	0.701066i	$0.247292\pi$
$47$			9.61254i			1.40213i	−0.713096	+	0.701066i	$0.752708\pi$
$48$		0			0
$49$	6.75344			0.964777
$50$	1.65665	−	4.71758i	0.234285	−	0.667166i
$51$		0			0
$52$			3.71758i			0.515535i
$53$			12.0867i			1.66024i	0.557586	+	0.830119i	$0.311728\pi$
$53$			12.0867i			1.66024i	−0.557586	+	0.830119i	$0.688272\pi$
$54$		0			0
$55$	7.80754	+	1.33102i	1.05277	+	0.179475i
$56$	0.496550			0.0663543
$57$		0			0
$58$			5.00638i			0.657370i
$59$	−11.4710			−1.49340			−0.746699	−	0.665162i	$-0.768363\pi$
$59$	−11.4710			−1.49340			−0.746699	+	0.665162i	$0.768363\pi$
$60$		0			0
$61$	1.18246			0.151399			0.0756995	−	0.997131i	$-0.475881\pi$
$61$	1.18246			0.151399			0.0756995	+	0.997131i	$0.475881\pi$
$62$			4.05558i			0.515060i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.39700	+	8.19453i	−0.173276	+	1.01641i
$66$		0			0
$67$		−	6.56561i		−	0.802117i	−0.916052	−	0.401058i	$-0.868642\pi$
$67$		−	6.56561i		−	0.802117i	0.916052	−	0.401058i	$-0.131358\pi$
$68$		−	6.87767i		−	0.834040i
$69$		0			0
$70$	1.09453	+	0.186594i	0.130821	+	0.0223023i
$71$	15.7252			1.86624			0.933118	−	0.359570i	$-0.117077\pi$
$71$	15.7252			1.86624			0.933118	+	0.359570i	$0.117077\pi$
$72$		0			0
$73$			0.584892i			0.0684564i	0.999414	+	0.0342282i	$0.0108973\pi$
$73$			0.584892i			0.0684564i	−0.999414	+	0.0342282i	$0.989103\pi$
$74$	−1.00000			−0.116248
$75$		0			0
$76$	3.45902			0.396777
$77$			1.75879i			0.200432i
$78$		0			0
$79$	1.89142			0.212801			0.106401	−	0.994323i	$-0.466067\pi$
$79$	1.89142			0.212801			0.106401	+	0.994323i	$0.466067\pi$
$80$	−2.20427	−	0.375782i	−0.246444	−	0.0420137i
$81$		0			0
$82$		−	7.78001i		−	0.859158i
$83$			3.12508i			0.343022i	0.985182	+	0.171511i	$0.0548648\pi$
$83$			3.12508i			0.343022i	−0.985182	+	0.171511i	$0.945135\pi$
$84$		0			0
$85$	2.58450	−	15.1602i	0.280329	−	1.64436i
$86$	−5.91114			−0.637415
$87$		0			0
$88$		−	3.54201i		−	0.377580i
$89$	−2.39557			−0.253930			−0.126965	−	0.991907i	$-0.540524\pi$
$89$	−2.39557			−0.253930			−0.126965	+	0.991907i	$0.540524\pi$
$90$		0			0
$91$	−1.84596			−0.193509
$92$			5.34439i			0.557191i
$93$		0			0
$94$	9.61254			0.991458
$95$	7.62460	+	1.29984i	0.782267	+	0.133360i
$96$		0			0
$97$			9.01936i			0.915777i	0.889010	+	0.457888i	$0.151394\pi$
$97$			9.01936i			0.915777i	−0.889010	+	0.457888i	$0.848606\pi$
$98$		−	6.75344i		−	0.682200i
$99$		0			0
$100$	−4.71758	−	1.65665i	−0.471758	−	0.165665i
$101$	14.7627			1.46895			0.734473	−	0.678638i	$-0.237430\pi$
$101$	14.7627			1.46895			0.734473	+	0.678638i	$0.237430\pi$
$102$		0			0
$103$			5.94242i			0.585524i	0.956185	+	0.292762i	$0.0945743\pi$
$103$			5.94242i			0.585524i	−0.956185	+	0.292762i	$0.905426\pi$
$104$	3.71758			0.364538
$105$		0			0
$106$	12.0867			1.17397
$107$		−	18.4010i		−	1.77889i	−0.457040	−	0.889446i	$-0.651090\pi$
$107$		−	18.4010i		−	1.77889i	0.457040	−	0.889446i	$-0.348910\pi$
$108$		0			0
$109$	7.95537			0.761987			0.380993	−	0.924578i	$-0.375582\pi$
$109$	7.95537			0.761987			0.380993	+	0.924578i	$0.375582\pi$
$110$	1.33102	−	7.80754i	0.126908	−	0.744420i
$111$		0			0
$112$		−	0.496550i		−	0.0469196i
$113$			5.17289i			0.486624i	0.969948	+	0.243312i	$0.0782339\pi$
$113$			5.17289i			0.486624i	−0.969948	+	0.243312i	$0.921766\pi$
$114$		0			0
$115$	−2.00832	+	11.7805i	−0.187277	+	1.09853i
$116$	5.00638			0.464831
$117$		0			0
$118$			11.4710i			1.05599i
$119$	3.41511			0.313062
$120$		0			0
$121$	1.54586			0.140532
$122$		−	1.18246i		−	0.107055i
$123$		0			0
$124$	4.05558			0.364202
$125$	−9.77626	−	5.42446i	−0.874415	−	0.485179i
$126$		0			0
$127$			7.96574i			0.706845i	0.935464	+	0.353423i	$0.114982\pi$
$127$			7.96574i			0.706845i	−0.935464	+	0.353423i	$0.885018\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	8.19453	+	1.39700i	0.718708	+	0.122525i
$131$	13.8424			1.20941			0.604707	−	0.796448i	$-0.293290\pi$
$131$	13.8424			1.20941			0.604707	+	0.796448i	$0.293290\pi$
$132$		0			0
$133$			1.71758i			0.148933i
$134$	−6.56561			−0.567182
$135$		0			0
$136$	−6.87767			−0.589755
$137$			6.51716i			0.556798i	0.960465	+	0.278399i	$0.0898038\pi$
$137$			6.51716i			0.556798i	−0.960465	+	0.278399i	$0.910196\pi$
$138$		0			0
$139$	0.871885			0.0739523			0.0369761	−	0.999316i	$-0.488227\pi$
$139$	0.871885			0.0739523			0.0369761	+	0.999316i	$0.488227\pi$
$140$	0.186594	−	1.09453i	0.0157701	−	0.0925045i
$141$		0			0
$142$		−	15.7252i		−	1.31963i
$143$			13.1677i			1.10114i
$144$		0			0
$145$	11.0354	+	1.88131i	0.916440	+	0.156234i
$146$	0.584892			0.0484060
$147$		0			0
$148$			1.00000i			0.0821995i
$149$	−5.91226			−0.484351			−0.242176	−	0.970232i	$-0.577861\pi$
$149$	−5.91226			−0.484351			−0.242176	+	0.970232i	$0.577861\pi$
$150$		0			0
$151$	20.7775			1.69085			0.845423	−	0.534098i	$-0.179349\pi$
$151$	20.7775			1.69085			0.845423	+	0.534098i	$0.179349\pi$
$152$		−	3.45902i		−	0.280564i
$153$		0			0
$154$	1.75879			0.141727
$155$	8.93958	+	1.52401i	0.718045	+	0.122412i
$156$		0			0
$157$		−	21.5052i		−	1.71630i	−0.513398	−	0.858151i	$-0.671614\pi$
$157$		−	21.5052i		−	1.71630i	0.513398	−	0.858151i	$-0.328386\pi$
$158$		−	1.89142i		−	0.150473i
$159$		0			0
$160$	−0.375782	+	2.20427i	−0.0297081	+	0.174263i
$161$	−2.65376			−0.209145
$162$		0			0
$163$		−	0.613583i		−	0.0480595i	−0.999711	−	0.0240298i	$-0.992350\pi$
$163$		−	0.613583i		−	0.0480595i	0.999711	−	0.0240298i	$-0.00764964\pi$
$164$	−7.78001			−0.607516
$165$		0			0
$166$	3.12508			0.242553
$167$			6.80339i			0.526462i	0.964733	+	0.263231i	$0.0847882\pi$
$167$			6.80339i			0.526462i	−0.964733	+	0.263231i	$0.915212\pi$
$168$		0			0
$169$	−0.820374			−0.0631057
$170$	−15.1602	−	2.58450i	−1.16274	−	0.198222i
$171$		0			0
$172$			5.91114i			0.450720i
$173$			12.2021i			0.927712i	0.885911	+	0.463856i	$0.153534\pi$
$173$			12.2021i			0.927712i	−0.885911	+	0.463856i	$0.846466\pi$
$174$		0			0
$175$	0.822607	−	2.34251i	0.0621833	−	0.177077i
$176$	−3.54201			−0.266989
$177$		0			0
$178$			2.39557i			0.179556i
$179$	−6.14040			−0.458955			−0.229478	−	0.973314i	$-0.573702\pi$
$179$	−6.14040			−0.458955			−0.229478	+	0.973314i	$0.573702\pi$
$180$		0			0
$181$	22.7890			1.69389			0.846945	−	0.531680i	$-0.178439\pi$
$181$	22.7890			1.69389			0.846945	+	0.531680i	$0.178439\pi$
$182$			1.84596i			0.136832i
$183$		0			0
$184$	5.34439			0.393993
$185$	−0.375782	+	2.20427i	−0.0276280	+	0.162061i
$186$		0			0
$187$		−	24.3608i		−	1.78144i
$188$		−	9.61254i		−	0.701066i
$189$		0			0
$190$	1.29984	−	7.62460i	0.0943000	−	0.553147i
$191$	−25.8808			−1.87267			−0.936333	−	0.351112i	$-0.885804\pi$
$191$	−25.8808			−1.87267			−0.936333	+	0.351112i	$0.885804\pi$
$192$		0			0
$193$			13.0441i			0.938937i	0.882949	+	0.469468i	$0.155554\pi$
$193$			13.0441i			0.938937i	−0.882949	+	0.469468i	$0.844446\pi$
$194$	9.01936			0.647552
$195$		0			0
$196$	−6.75344			−0.482388
$197$		−	5.19264i		−	0.369960i	−0.982742	−	0.184980i	$-0.940778\pi$
$197$		−	5.19264i		−	0.369960i	0.982742	−	0.184980i	$-0.0592220\pi$
$198$		0			0
$199$	17.0131			1.20602			0.603012	−	0.797732i	$-0.293967\pi$
$199$	17.0131			1.20602			0.603012	+	0.797732i	$0.293967\pi$
$200$	−1.65665	+	4.71758i	−0.117142	+	0.333583i
$201$		0			0
$202$		−	14.7627i		−	1.03870i
$203$			2.48592i			0.174477i
$204$		0			0
$205$	−17.1492	−	2.92358i	−1.19775	−	0.204192i
$206$	5.94242			0.414028
$207$		0			0
$208$		−	3.71758i		−	0.257768i
$209$	12.2519			0.847481
$210$		0			0
$211$	21.0189			1.44700			0.723500	−	0.690325i	$-0.242532\pi$
$211$	21.0189			1.44700			0.723500	+	0.690325i	$0.242532\pi$
$212$		−	12.0867i		−	0.830119i
$213$		0			0
$214$	−18.4010			−1.25787
$215$	−2.22130	+	13.0297i	−0.151491	+	0.888620i
$216$		0			0
$217$			2.01380i			0.136706i
$218$		−	7.95537i		−	0.538806i
$219$		0			0
$220$	−7.80754	−	1.33102i	−0.526384	−	0.0897376i
$221$	25.5683			1.71991
$222$		0			0
$223$			20.6518i			1.38295i	0.722401	+	0.691475i	$0.243039\pi$
$223$			20.6518i			1.38295i	−0.722401	+	0.691475i	$0.756961\pi$
$224$	−0.496550			−0.0331771
$225$		0			0
$226$	5.17289			0.344095
$227$			12.1125i			0.803933i	0.915654	+	0.401966i	$0.131673\pi$
$227$			12.1125i			0.803933i	−0.915654	+	0.401966i	$0.868327\pi$
$228$		0			0
$229$	28.1773			1.86201			0.931005	−	0.365007i	$-0.118933\pi$
$229$	28.1773			1.86201			0.931005	+	0.365007i	$0.118933\pi$
$230$	11.7805	+	2.00832i	0.776780	+	0.132425i
$231$		0			0
$232$		−	5.00638i		−	0.328685i
$233$			2.68018i			0.175584i	0.996139	+	0.0877922i	$0.0279812\pi$
$233$			2.68018i			0.175584i	−0.996139	+	0.0877922i	$0.972019\pi$
$234$		0			0
$235$	3.61221	−	21.1886i	0.235635	−	1.38219i
$236$	11.4710			0.746699
$237$		0			0
$238$		−	3.41511i		−	0.221369i
$239$	29.2248			1.89040			0.945198	−	0.326499i	$-0.105869\pi$
$239$	29.2248			1.89040			0.945198	+	0.326499i	$0.105869\pi$
$240$		0			0
$241$	−18.0343			−1.16169			−0.580845	−	0.814014i	$-0.697278\pi$
$241$	−18.0343			−1.16169			−0.580845	+	0.814014i	$0.697278\pi$
$242$		−	1.54586i		−	0.0993714i
$243$		0			0
$244$	−1.18246			−0.0756995
$245$	−14.8864	−	2.53782i	−0.951056	−	0.162135i
$246$		0			0
$247$			12.8592i			0.818209i
$248$		−	4.05558i		−	0.257530i
$249$		0			0
$250$	−5.42446	+	9.77626i	−0.343073	+	0.618305i
$251$	0.340971			0.0215219			0.0107610	−	0.999942i	$-0.496575\pi$
$251$	0.340971			0.0215219			0.0107610	+	0.999942i	$0.496575\pi$
$252$		0			0
$253$			18.9299i			1.19011i
$254$	7.96574			0.499815
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	30.0718i		−	1.87583i	−0.346867	−	0.937914i	$-0.612754\pi$
$257$		−	30.0718i		−	1.87583i	0.346867	−	0.937914i	$-0.387246\pi$
$258$		0			0
$259$	−0.496550			−0.0308541
$260$	1.39700	−	8.19453i	0.0866381	−	0.508203i
$261$		0			0
$262$		−	13.8424i		−	0.855185i
$263$		−	24.3337i		−	1.50048i	−0.661167	−	0.750239i	$-0.729938\pi$
$263$		−	24.3337i		−	1.50048i	0.661167	−	0.750239i	$-0.270062\pi$
$264$		0			0
$265$	4.54197	−	26.6423i	0.279011	−	1.63663i
$266$	1.71758			0.105311
$267$		0			0
$268$			6.56561i			0.401058i
$269$	−15.3738			−0.937360			−0.468680	−	0.883368i	$-0.655270\pi$
$269$	−15.3738			−0.937360			−0.468680	+	0.883368i	$0.655270\pi$
$270$		0			0
$271$	−4.72205			−0.286844			−0.143422	−	0.989662i	$-0.545811\pi$
$271$	−4.72205			−0.286844			−0.143422	+	0.989662i	$0.545811\pi$
$272$			6.87767i			0.417020i
$273$		0			0
$274$	6.51716			0.393716
$275$	−16.7097	−	5.86786i	−1.00763	−	0.353845i
$276$		0			0
$277$			11.8424i			0.711543i	0.934573	+	0.355772i	$0.115782\pi$
$277$			11.8424i			0.711543i	−0.934573	+	0.355772i	$0.884218\pi$
$278$		−	0.871885i		−	0.0522922i
$279$		0			0
$280$	−1.09453	−	0.186594i	−0.0654106	−	0.0111511i
$281$	−1.19006			−0.0709929			−0.0354964	−	0.999370i	$-0.511301\pi$
$281$	−1.19006			−0.0709929			−0.0354964	+	0.999370i	$0.511301\pi$
$282$		0			0
$283$			1.23874i			0.0736357i	0.999322	+	0.0368179i	$0.0117221\pi$
$283$			1.23874i			0.0736357i	−0.999322	+	0.0368179i	$0.988278\pi$
$284$	−15.7252			−0.933118
$285$		0			0
$286$	13.1677			0.778623
$287$		−	3.86316i		−	0.228035i
$288$		0			0
$289$	−30.3024			−1.78249
$290$	1.88131	−	11.0354i	0.110474	−	0.648021i
$291$		0			0
$292$		−	0.584892i		−	0.0342282i
$293$			16.7526i			0.978700i	0.872087	+	0.489350i	$0.162766\pi$
$293$			16.7526i			0.978700i	−0.872087	+	0.489350i	$0.837234\pi$
$294$		0			0
$295$	25.2852	+	4.31060i	1.47216	+	0.250973i
$296$	1.00000			0.0581238
$297$		0			0
$298$			5.91226i			0.342488i
$299$	−19.8682			−1.14901
$300$		0			0
$301$	−2.93518			−0.169181
$302$		−	20.7775i		−	1.19561i
$303$		0			0
$304$	−3.45902			−0.198388
$305$	−2.60646	−	0.444348i	−0.149246	−	0.0254433i
$306$		0			0
$307$			24.0420i			1.37215i	0.727530	+	0.686075i	$0.240668\pi$
$307$			24.0420i			1.37215i	−0.727530	+	0.686075i	$0.759332\pi$
$308$		−	1.75879i		−	0.100216i
$309$		0			0
$310$	1.52401	−	8.93958i	0.0865581	−	0.507734i
$311$	1.92653			0.109244			0.0546218	−	0.998507i	$-0.482605\pi$
$311$	1.92653			0.109244			0.0546218	+	0.998507i	$0.482605\pi$
$312$		0			0
$313$		−	5.09813i		−	0.288163i	−0.989566	−	0.144082i	$-0.953977\pi$
$313$		−	5.09813i		−	0.288163i	0.989566	−	0.144082i	$-0.0460228\pi$
$314$	−21.5052			−1.21361
$315$		0			0
$316$	−1.89142			−0.106401
$317$		−	4.16726i		−	0.234056i	−0.993129	−	0.117028i	$-0.962663\pi$
$317$		−	4.16726i		−	0.234056i	0.993129	−	0.117028i	$-0.0373368\pi$
$318$		0			0
$319$	17.7327			0.992839
$320$	2.20427	+	0.375782i	0.123222	+	0.0210068i
$321$		0			0
$322$			2.65376i			0.147888i
$323$		−	23.7900i		−	1.32371i
$324$		0			0
$325$	6.15870	−	17.5380i	0.341623	−	0.972830i
$326$	−0.613583			−0.0339832
$327$		0			0
$328$			7.78001i			0.429579i
$329$	4.77311			0.263150
$330$		0			0
$331$	5.98808			0.329135			0.164567	−	0.986366i	$-0.447377\pi$
$331$	5.98808			0.329135			0.164567	+	0.986366i	$0.447377\pi$
$332$		−	3.12508i		−	0.171511i
$333$		0			0
$334$	6.80339			0.372265
$335$	−2.46723	+	14.4723i	−0.134799	+	0.790709i
$336$		0			0
$337$			9.11787i			0.496682i	0.968673	+	0.248341i	$0.0798854\pi$
$337$			9.11787i			0.496682i	−0.968673	+	0.248341i	$0.920115\pi$
$338$			0.820374i			0.0446225i
$339$		0			0
$340$	−2.58450	+	15.1602i	−0.140164	+	0.822178i
$341$	14.3649			0.777904
$342$		0			0
$343$		−	6.82927i		−	0.368746i
$344$	5.91114			0.318707
$345$		0			0
$346$	12.2021			0.655991
$347$			2.91755i			0.156622i	0.996929	+	0.0783111i	$0.0249528\pi$
$347$			2.91755i			0.156622i	−0.996929	+	0.0783111i	$0.975047\pi$
$348$		0			0
$349$	−32.7480			−1.75296			−0.876479	−	0.481440i	$-0.840114\pi$
$349$	−32.7480			−1.75296			−0.876479	+	0.481440i	$0.840114\pi$
$350$	−2.34251	−	0.822607i	−0.125213	−	0.0439702i
$351$		0			0
$352$			3.54201i			0.188790i
$353$			25.7163i			1.36874i	0.729135	+	0.684370i	$0.239923\pi$
$353$			25.7163i			1.36874i	−0.729135	+	0.684370i	$0.760077\pi$
$354$		0			0
$355$	−34.6625	−	5.90923i	−1.83969	−	0.313630i
$356$	2.39557			0.126965
$357$		0			0
$358$			6.14040i			0.324530i
$359$	−22.2120			−1.17230			−0.586152	−	0.810201i	$-0.699358\pi$
$359$	−22.2120			−1.17230			−0.586152	+	0.810201i	$0.699358\pi$
$360$		0			0
$361$	−7.03518			−0.370273
$362$		−	22.7890i		−	1.19776i
$363$		0			0
$364$	1.84596			0.0967547
$365$	0.219792	−	1.28926i	0.0115044	−	0.0674828i
$366$		0			0
$367$		−	7.76575i		−	0.405369i	−0.979244	−	0.202684i	$-0.935033\pi$
$367$		−	7.76575i		−	0.405369i	0.979244	−	0.202684i	$-0.0649666\pi$
$368$		−	5.34439i		−	0.278595i
$369$		0			0
$370$	2.20427	+	0.375782i	0.114594	+	0.0195360i
$371$	6.00166			0.311591
$372$		0			0
$373$			15.0340i			0.778430i	0.921147	+	0.389215i	$0.127254\pi$
$373$			15.0340i			0.778430i	−0.921147	+	0.389215i	$0.872746\pi$
$374$	−24.3608			−1.25967
$375$		0			0
$376$	−9.61254			−0.495729
$377$			18.6116i			0.958546i
$378$		0			0
$379$	−8.08640			−0.415370			−0.207685	−	0.978196i	$-0.566593\pi$
$379$	−8.08640			−0.415370			−0.207685	+	0.978196i	$0.566593\pi$
$380$	−7.62460	−	1.29984i	−0.391134	−	0.0666802i
$381$		0			0
$382$			25.8808i			1.32418i
$383$			13.8770i			0.709084i	0.935040	+	0.354542i	$0.115363\pi$
$383$			13.8770i			0.709084i	−0.935040	+	0.354542i	$0.884637\pi$
$384$		0			0
$385$	0.660920	−	3.87683i	0.0336836	−	0.197582i
$386$	13.0441			0.663928
$387$		0			0
$388$		−	9.01936i		−	0.457888i
$389$	5.36823			0.272180			0.136090	−	0.990696i	$-0.456546\pi$
$389$	5.36823			0.272180			0.136090	+	0.990696i	$0.456546\pi$
$390$		0			0
$391$	36.7569			1.85888
$392$			6.75344i			0.341100i
$393$		0			0
$394$	−5.19264			−0.261601
$395$	−4.16919	−	0.710760i	−0.209775	−	0.0357622i
$396$		0			0
$397$			26.3508i			1.32251i	0.750161	+	0.661255i	$0.229976\pi$
$397$			26.3508i			1.32251i	−0.750161	+	0.661255i	$0.770024\pi$
$398$		−	17.0131i		−	0.852787i
$399$		0			0
$400$	4.71758	+	1.65665i	0.235879	+	0.0828323i
$401$	−18.6718			−0.932425			−0.466212	−	0.884673i	$-0.654382\pi$
$401$	−18.6718			−0.932425			−0.466212	+	0.884673i	$0.654382\pi$
$402$		0			0
$403$			15.0769i			0.751036i
$404$	−14.7627			−0.734473
$405$		0			0
$406$	2.48592			0.123374
$407$			3.54201i			0.175571i
$408$		0			0
$409$	4.43008			0.219053			0.109527	−	0.993984i	$-0.465067\pi$
$409$	4.43008			0.219053			0.109527	+	0.993984i	$0.465067\pi$
$410$	−2.92358	+	17.1492i	−0.144385	+	0.846939i
$411$		0			0
$412$		−	5.94242i		−	0.292762i
$413$			5.69593i			0.280279i
$414$		0			0
$415$	1.17435	−	6.88850i	0.0576464	−	0.338143i
$416$	−3.71758			−0.182269
$417$		0			0
$418$		−	12.2519i		−	0.599260i
$419$	−39.1429			−1.91225			−0.956127	−	0.292952i	$-0.905362\pi$
$419$	−39.1429			−1.91225			−0.956127	+	0.292952i	$0.905362\pi$
$420$		0			0
$421$	−28.0272			−1.36596			−0.682982	−	0.730436i	$-0.739317\pi$
$421$	−28.0272			−1.36596			−0.682982	+	0.730436i	$0.739317\pi$
$422$		−	21.0189i		−	1.02318i
$423$		0			0
$424$	−12.0867			−0.586983
$425$	−11.3939	+	32.4459i	−0.552683	+	1.57386i
$426$		0			0
$427$		−	0.587152i		−	0.0284143i
$428$			18.4010i			0.889446i
$429$		0			0
$430$	13.0297	+	2.22130i	0.628349	+	0.107120i
$431$	24.2322			1.16722			0.583611	−	0.812033i	$-0.301639\pi$
$431$	24.2322			1.16722			0.583611	+	0.812033i	$0.301639\pi$
$432$		0			0
$433$		−	10.8428i		−	0.521071i	−0.965464	−	0.260535i	$-0.916101\pi$
$433$		−	10.8428i		−	0.521071i	0.965464	−	0.260535i	$-0.0838991\pi$
$434$	2.01380			0.0966655
$435$		0			0
$436$	−7.95537			−0.380993
$437$			18.4863i			0.884322i
$438$		0			0
$439$	−12.4210			−0.592822			−0.296411	−	0.955060i	$-0.595790\pi$
$439$	−12.4210			−0.592822			−0.296411	+	0.955060i	$0.595790\pi$
$440$	−1.33102	+	7.80754i	−0.0634540	+	0.372210i
$441$		0			0
$442$		−	25.5683i		−	1.21616i
$443$		−	22.9845i		−	1.09203i	−0.837777	−	0.546013i	$-0.816145\pi$
$443$		−	22.9845i		−	1.09203i	0.837777	−	0.546013i	$-0.183855\pi$
$444$		0			0
$445$	5.28048	+	0.900213i	0.250319	+	0.0426742i
$446$	20.6518			0.977893
$447$		0			0
$448$			0.496550i			0.0234598i
$449$	8.60738			0.406208			0.203104	−	0.979157i	$-0.434897\pi$
$449$	8.60738			0.406208			0.203104	+	0.979157i	$0.434897\pi$
$450$		0			0
$451$	−27.5569			−1.29760
$452$		−	5.17289i		−	0.243312i
$453$		0			0
$454$	12.1125			0.568466
$455$	4.06899	+	0.693679i	0.190757	+	0.0325202i
$456$		0			0
$457$		−	18.0982i		−	0.846597i	−0.905990	−	0.423299i	$-0.860872\pi$
$457$		−	18.0982i		−	0.846597i	0.905990	−	0.423299i	$-0.139128\pi$
$458$		−	28.1773i		−	1.31664i
$459$		0			0
$460$	2.00832	−	11.7805i	0.0936385	−	0.549266i
$461$	34.8960			1.62527			0.812634	−	0.582774i	$-0.198033\pi$
$461$	34.8960			1.62527			0.812634	+	0.582774i	$0.198033\pi$
$462$		0			0
$463$			11.7593i			0.546501i	0.961943	+	0.273251i	$0.0880989\pi$
$463$			11.7593i			0.546501i	−0.961943	+	0.273251i	$0.911901\pi$
$464$	−5.00638			−0.232415
$465$		0			0
$466$	2.68018			0.124157
$467$			15.0384i			0.695893i	0.937514	+	0.347947i	$0.113121\pi$
$467$			15.0384i			0.695893i	−0.937514	+	0.347947i	$0.886879\pi$
$468$		0			0
$469$	−3.26015			−0.150540
$470$	−21.1886	−	3.61221i	−0.977357	−	0.166619i
$471$		0			0
$472$		−	11.4710i		−	0.527996i
$473$			20.9373i			0.962700i
$474$		0			0
$475$	−16.3182	−	5.73037i	−0.748730	−	0.262927i
$476$	−3.41511			−0.156531
$477$		0			0
$478$		−	29.2248i		−	1.33671i
$479$	−5.76027			−0.263193			−0.131597	−	0.991303i	$-0.542010\pi$
$479$	−5.76027			−0.263193			−0.131597	+	0.991303i	$0.542010\pi$
$480$		0			0
$481$	−3.71758			−0.169507
$482$			18.0343i			0.821439i
$483$		0			0
$484$	−1.54586			−0.0702662
$485$	3.38931	−	19.8811i	0.153901	−	0.902752i
$486$		0			0
$487$			35.6982i			1.61764i	0.588056	+	0.808820i	$0.299893\pi$
$487$			35.6982i			1.61764i	−0.588056	+	0.808820i	$0.700107\pi$
$488$			1.18246i			0.0535276i
$489$		0			0
$490$	−2.53782	+	14.8864i	−0.114647	+	0.672498i
$491$	8.81455			0.397795			0.198898	−	0.980020i	$-0.436264\pi$
$491$	8.81455			0.397795			0.198898	+	0.980020i	$0.436264\pi$
$492$		0			0
$493$		−	34.4322i		−	1.55075i
$494$	12.8592			0.578561
$495$		0			0
$496$	−4.05558			−0.182101
$497$		−	7.80834i		−	0.350252i
$498$		0			0
$499$	6.15485			0.275529			0.137764	−	0.990465i	$-0.456008\pi$
$499$	6.15485			0.275529			0.137764	+	0.990465i	$0.456008\pi$
$500$	9.77626	+	5.42446i	0.437207	+	0.242589i
$501$		0			0
$502$		−	0.340971i		−	0.0152183i
$503$		−	28.2064i		−	1.25766i	−0.777542	−	0.628832i	$-0.783534\pi$
$503$		−	28.2064i		−	1.25766i	0.777542	−	0.628832i	$-0.216466\pi$
$504$		0			0
$505$	−32.5410	−	5.54756i	−1.44805	−	0.246863i
$506$	18.9299			0.841536
$507$		0			0
$508$		−	7.96574i		−	0.353423i
$509$	25.3036			1.12156			0.560782	−	0.827964i	$-0.310501\pi$
$509$	25.3036			1.12156			0.560782	+	0.827964i	$0.310501\pi$
$510$		0			0
$511$	0.290428			0.0128478
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−30.0718			−1.32641
$515$	2.23305	−	13.0987i	0.0984000	−	0.577196i
$516$		0			0
$517$		−	34.0477i		−	1.49742i
$518$			0.496550i			0.0218172i
$519$		0			0
$520$	−8.19453	−	1.39700i	−0.359354	−	0.0612624i
$521$	−20.4093			−0.894148			−0.447074	−	0.894497i	$-0.647534\pi$
$521$	−20.4093			−0.894148			−0.447074	+	0.894497i	$0.647534\pi$
$522$		0			0
$523$			14.6912i			0.642403i	0.947011	+	0.321201i	$0.104087\pi$
$523$			14.6912i			0.642403i	−0.947011	+	0.321201i	$0.895913\pi$
$524$	−13.8424			−0.604707
$525$		0			0
$526$	−24.3337			−1.06100
$527$		−	27.8930i		−	1.21504i
$528$		0			0
$529$	−5.56248			−0.241847
$530$	−26.6423	−	4.54197i	−1.15727	−	0.197290i
$531$		0			0
$532$		−	1.71758i		−	0.0744664i
$533$		−	28.9228i		−	1.25278i
$534$		0			0
$535$	−6.91476	+	40.5607i	−0.298951	+	1.75359i
$536$	6.56561			0.283591
$537$		0			0
$538$			15.3738i			0.662813i
$539$	−23.9208			−1.03034
$540$		0			0
$541$	−35.0439			−1.50665			−0.753327	−	0.657647i	$-0.771552\pi$
$541$	−35.0439			−1.50665			−0.753327	+	0.657647i	$0.771552\pi$
$542$			4.72205i			0.202830i
$543$		0			0
$544$	6.87767			0.294878
$545$	−17.5358	−	2.98948i	−0.751150	−	0.128055i
$546$		0			0
$547$			31.7165i			1.35610i	0.735017	+	0.678049i	$0.237174\pi$
$547$			31.7165i			1.35610i	−0.735017	+	0.678049i	$0.762826\pi$
$548$		−	6.51716i		−	0.278399i
$549$		0			0
$550$	−5.86786	+	16.7097i	−0.250206	+	0.712505i
$551$	17.3172			0.737736
$552$		0			0
$553$		−	0.939184i		−	0.0399382i
$554$	11.8424			0.503137
$555$		0			0
$556$	−0.871885			−0.0369761
$557$			46.5635i			1.97296i	0.163883	+	0.986480i	$0.447598\pi$
$557$			46.5635i			1.97296i	−0.163883	+	0.986480i	$0.552402\pi$
$558$		0			0
$559$	−21.9751			−0.929448
$560$	−0.186594	+	1.09453i	−0.00788505	+	0.0462523i
$561$		0			0
$562$			1.19006i			0.0501995i
$563$		−	29.5886i		−	1.24701i	−0.781819	−	0.623505i	$-0.785708\pi$
$563$		−	29.5886i		−	1.24701i	0.781819	−	0.623505i	$-0.214292\pi$
$564$		0			0
$565$	1.94388	−	11.4024i	0.0817795	−	0.479703i
$566$	1.23874			0.0520683
$567$		0			0
$568$			15.7252i			0.659814i
$569$	15.6452			0.655879			0.327940	−	0.944699i	$-0.393646\pi$
$569$	15.6452			0.655879			0.327940	+	0.944699i	$0.393646\pi$
$570$		0			0
$571$	−5.53574			−0.231663			−0.115832	−	0.993269i	$-0.536953\pi$
$571$	−5.53574			−0.231663			−0.115832	+	0.993269i	$0.536953\pi$
$572$		−	13.1677i		−	0.550569i
$573$		0			0
$574$	−3.86316			−0.161245
$575$	8.85375	−	25.2126i	0.369227	−	1.05144i
$576$		0			0
$577$			3.19899i			0.133176i	0.997781	+	0.0665878i	$0.0212112\pi$
$577$			3.19899i			0.133176i	−0.997781	+	0.0665878i	$0.978789\pi$
$578$			30.3024i			1.26041i
$579$		0			0
$580$	−11.0354	−	1.88131i	−0.458220	−	0.0781170i
$581$	1.55176			0.0643777
$582$		0			0
$583$		−	42.8113i		−	1.77306i
$584$	−0.584892			−0.0242030
$585$		0			0
$586$	16.7526			0.692046
$587$			12.4110i			0.512258i	0.966643	+	0.256129i	$0.0824472\pi$
$587$			12.4110i			0.512258i	−0.966643	+	0.256129i	$0.917553\pi$
$588$		0			0
$589$	14.0283			0.578028
$590$	4.31060	−	25.2852i	0.177464	−	1.04097i
$591$		0			0
$592$		−	1.00000i		−	0.0410997i
$593$		−	6.15234i		−	0.252646i	−0.991989	−	0.126323i	$-0.959682\pi$
$593$		−	6.15234i		−	0.252646i	0.991989	−	0.126323i	$-0.0403176\pi$
$594$		0			0
$595$	−7.52781	−	1.28333i	−0.308610	−	0.0526116i
$596$	5.91226			0.242176
$597$		0			0
$598$			19.8682i			0.812470i
$599$	−23.1885			−0.947456			−0.473728	−	0.880671i	$-0.657092\pi$
$599$	−23.1885			−0.947456			−0.473728	+	0.880671i	$0.657092\pi$
$600$		0			0
$601$	−4.72864			−0.192885			−0.0964426	−	0.995339i	$-0.530746\pi$
$601$	−4.72864			−0.192885			−0.0964426	+	0.995339i	$0.530746\pi$
$602$			2.93518i			0.119629i
$603$		0			0
$604$	−20.7775			−0.845423
$605$	−3.40748	−	0.580904i	−0.138534	−	0.0236171i
$606$		0			0
$607$		−	22.8973i		−	0.929374i	−0.885475	−	0.464687i	$-0.846167\pi$
$607$		−	22.8973i		−	0.929374i	0.885475	−	0.464687i	$-0.153833\pi$
$608$			3.45902i			0.140282i
$609$		0			0
$610$	−0.444348	+	2.60646i	−0.0179911	+	0.105533i
$611$	35.7353			1.44570
$612$		0			0
$613$		−	37.1669i		−	1.50116i	−0.660781	−	0.750579i	$-0.729775\pi$
$613$		−	37.1669i		−	1.50116i	0.660781	−	0.750579i	$-0.270225\pi$
$614$	24.0420			0.970257
$615$		0			0
$616$	−1.75879			−0.0708635
$617$		−	20.4816i		−	0.824558i	−0.911058	−	0.412279i	$-0.864733\pi$
$617$		−	20.4816i		−	0.824558i	0.911058	−	0.412279i	$-0.135267\pi$
$618$		0			0
$619$	6.10796			0.245500			0.122750	−	0.992438i	$-0.460829\pi$
$619$	6.10796			0.245500			0.122750	+	0.992438i	$0.460829\pi$
$620$	−8.93958	−	1.52401i	−0.359022	−	0.0612058i
$621$		0			0
$622$		−	1.92653i		−	0.0772469i
$623$			1.18952i			0.0476572i
$624$		0			0
$625$	19.5111	+	15.6307i	0.780442	+	0.625228i
$626$	−5.09813			−0.203762
$627$		0			0
$628$			21.5052i			0.858151i
$629$	6.87767			0.274231
$630$		0			0
$631$	−6.11608			−0.243477			−0.121739	−	0.992562i	$-0.538847\pi$
$631$	−6.11608			−0.243477			−0.121739	+	0.992562i	$0.538847\pi$
$632$			1.89142i			0.0752366i
$633$		0			0
$634$	−4.16726			−0.165503
$635$	2.99338	−	17.5586i	0.118789	−	0.696792i
$636$		0			0
$637$		−	25.1064i		−	0.994753i
$638$		−	17.7327i		−	0.702043i
$639$		0			0
$640$	0.375782	−	2.20427i	0.0148541	−	0.0871313i
$641$	32.5928			1.28734			0.643670	−	0.765303i	$-0.277411\pi$
$641$	32.5928			1.28734			0.643670	+	0.765303i	$0.277411\pi$
$642$		0			0
$643$			5.81189i			0.229199i	0.993412	+	0.114599i	$0.0365584\pi$
$643$			5.81189i			0.229199i	−0.993412	+	0.114599i	$0.963442\pi$
$644$	2.65376			0.104573
$645$		0			0
$646$	−23.7900			−0.936005
$647$		−	2.02466i		−	0.0795975i	−0.999208	−	0.0397988i	$-0.987328\pi$
$647$		−	2.02466i		−	0.0795975i	0.999208	−	0.0397988i	$-0.0126717\pi$
$648$		0			0
$649$	40.6305			1.59489
$650$	−17.5380	−	6.15870i	−0.687895	−	0.241564i
$651$		0			0
$652$			0.613583i			0.0240298i
$653$			11.7965i			0.461632i	0.972997	+	0.230816i	$0.0741395\pi$
$653$			11.7965i			0.461632i	−0.972997	+	0.230816i	$0.925861\pi$
$654$		0			0
$655$	−30.5123	−	5.20171i	−1.19221	−	0.203248i
$656$	7.78001			0.303758
$657$		0			0
$658$		−	4.77311i		−	0.186075i
$659$	2.97175			0.115763			0.0578816	−	0.998323i	$-0.481565\pi$
$659$	2.97175			0.115763			0.0578816	+	0.998323i	$0.481565\pi$
$660$		0			0
$661$	46.6484			1.81441			0.907207	−	0.420684i	$-0.138210\pi$
$661$	46.6484			1.81441			0.907207	+	0.420684i	$0.138210\pi$
$662$		−	5.98808i		−	0.232733i
$663$		0			0
$664$	−3.12508			−0.121276
$665$	0.645434	−	3.78600i	0.0250288	−	0.146815i
$666$		0			0
$667$			26.7560i			1.03600i
$668$		−	6.80339i		−	0.263231i
$669$		0			0
$670$	14.4723	+	2.46723i	0.559116	+	0.0953176i
$671$	−4.18830			−0.161688
$672$		0			0
$673$			40.5210i			1.56197i	0.624549	+	0.780986i	$0.285283\pi$
$673$			40.5210i			1.56197i	−0.624549	+	0.780986i	$0.714717\pi$
$674$	9.11787			0.351207
$675$		0			0
$676$	0.820374			0.0315529
$677$			37.5485i			1.44311i	0.692358	+	0.721554i	$0.256572\pi$
$677$			37.5485i			1.44311i	−0.692358	+	0.721554i	$0.743428\pi$
$678$		0			0
$679$	4.47856			0.171871
$680$	15.1602	+	2.58450i	0.581368	+	0.0991111i
$681$		0			0
$682$		−	14.3649i		−	0.550061i
$683$			41.4027i			1.58423i	0.610372	+	0.792115i	$0.291020\pi$
$683$			41.4027i			1.58423i	−0.610372	+	0.792115i	$0.708980\pi$
$684$		0			0
$685$	2.44903	−	14.3656i	0.0935726	−	0.548879i
$686$	−6.82927			−0.260743
$687$		0			0
$688$		−	5.91114i		−	0.225360i
$689$	44.9333			1.71182
$690$		0			0
$691$	−31.8562			−1.21187			−0.605934	−	0.795515i	$-0.707200\pi$
$691$	−31.8562			−1.21187			−0.605934	+	0.795515i	$0.707200\pi$
$692$		−	12.2021i		−	0.463856i
$693$		0			0
$694$	2.91755			0.110749
$695$	−1.92187	−	0.327638i	−0.0729005	−	0.0124280i
$696$		0			0
$697$			53.5083i			2.02677i
$698$			32.7480i			1.23953i
$699$		0			0
$700$	−0.822607	+	2.34251i	−0.0310916	+	0.0885387i
$701$	−15.2993			−0.577847			−0.288923	−	0.957352i	$-0.593297\pi$
$701$	−15.2993			−0.577847			−0.288923	+	0.957352i	$0.593297\pi$
$702$		0			0
$703$			3.45902i			0.130459i
$704$	3.54201			0.133495
$705$		0			0
$706$	25.7163			0.967845
$707$		−	7.33043i		−	0.275689i
$708$		0			0
$709$	32.3797			1.21604			0.608022	−	0.793920i	$-0.291963\pi$
$709$	32.3797			1.21604			0.608022	+	0.793920i	$0.291963\pi$
$710$	−5.90923	+	34.6625i	−0.221770	+	1.30086i
$711$		0			0
$712$		−	2.39557i		−	0.0897779i
$713$			21.6746i			0.811720i
$714$		0			0
$715$	4.94818	−	29.0251i	0.185051	−	1.08548i
$716$	6.14040			0.229478
$717$		0			0
$718$			22.2120i			0.828944i
$719$	0.735423			0.0274266			0.0137133	−	0.999906i	$-0.495635\pi$
$719$	0.735423			0.0274266			0.0137133	+	0.999906i	$0.495635\pi$
$720$		0			0
$721$	2.95071			0.109890
$722$			7.03518i			0.261822i
$723$		0			0
$724$	−22.7890			−0.846945
$725$	−23.6180	−	8.29380i	−0.877150	−	0.308024i
$726$		0			0
$727$			0.888125i			0.0329387i	0.999864	+	0.0164694i	$0.00524260\pi$
$727$			0.888125i			0.0329387i	−0.999864	+	0.0164694i	$0.994757\pi$
$728$		−	1.84596i		−	0.0684159i
$729$		0			0
$730$	−1.28926	−	0.219792i	−0.0477176	−	0.00813485i
$731$	40.6549			1.50367
$732$		0			0
$733$			42.3706i			1.56499i	0.622655	+	0.782496i	$0.286054\pi$
$733$			42.3706i			1.56499i	−0.622655	+	0.782496i	$0.713946\pi$
$734$	−7.76575			−0.286639
$735$		0			0
$736$	−5.34439			−0.196997
$737$			23.2555i			0.856626i
$738$		0			0
$739$	−50.2906			−1.84997			−0.924985	−	0.380004i	$-0.875923\pi$
$739$	−50.2906			−1.84997			−0.924985	+	0.380004i	$0.875923\pi$
$740$	0.375782	−	2.20427i	0.0138140	−	0.0810304i
$741$		0			0
$742$		−	6.00166i		−	0.220328i
$743$		−	47.8441i		−	1.75523i	−0.479367	−	0.877615i	$-0.659134\pi$
$743$		−	47.8441i		−	1.75523i	0.479367	−	0.877615i	$-0.340866\pi$
$744$		0			0
$745$	13.0322	+	2.22172i	0.477463	+	0.0813975i
$746$	15.0340			0.550433
$747$		0			0
$748$			24.3608i			0.890719i
$749$	−9.13702			−0.333859
$750$		0			0
$751$	1.39619			0.0509475			0.0254738	−	0.999675i	$-0.491891\pi$
$751$	1.39619			0.0509475			0.0254738	+	0.999675i	$0.491891\pi$
$752$			9.61254i			0.350533i
$753$		0			0
$754$	18.6116			0.677795
$755$	−45.7990	−	7.80779i	−1.66680	−	0.284154i
$756$		0			0
$757$		−	27.0437i		−	0.982919i	−0.870900	−	0.491460i	$-0.836464\pi$
$757$		−	27.0437i		−	0.982919i	0.870900	−	0.491460i	$-0.163536\pi$
$758$			8.08640i			0.293711i
$759$		0			0
$760$	−1.29984	+	7.62460i	−0.0471500	+	0.276573i
$761$	33.9022			1.22895			0.614477	−	0.788935i	$-0.289367\pi$
$761$	33.9022			1.22895			0.614477	+	0.788935i	$0.289367\pi$
$762$		0			0
$763$		−	3.95024i		−	0.143008i
$764$	25.8808			0.936333
$765$		0			0
$766$	13.8770			0.501398
$767$			42.6444i			1.53980i
$768$		0			0
$769$	−28.9215			−1.04294			−0.521468	−	0.853271i	$-0.674615\pi$
$769$	−28.9215			−1.04294			−0.521468	+	0.853271i	$0.674615\pi$
$770$	−3.87683	−	0.660920i	−0.139711	−	0.0238179i
$771$		0			0
$772$		−	13.0441i		−	0.469468i
$773$			37.1725i			1.33700i	0.743711	+	0.668502i	$0.233064\pi$
$773$			37.1725i			1.33700i	−0.743711	+	0.668502i	$0.766936\pi$
$774$		0			0
$775$	−19.1325	−	6.71866i	−0.687260	−	0.241341i
$776$	−9.01936			−0.323776
$777$		0			0
$778$		−	5.36823i		−	0.192460i
$779$	−26.9112			−0.964194
$780$		0			0
$781$	−55.6988			−1.99306
$782$		−	36.7569i		−	1.31443i
$783$		0			0
$784$	6.75344			0.241194
$785$	−8.08125	+	47.4032i	−0.288432	+	1.69189i
$786$		0			0
$787$		−	23.5117i		−	0.838100i	−0.907963	−	0.419050i	$-0.862363\pi$
$787$		−	23.5117i		−	0.838100i	0.907963	−	0.419050i	$-0.137637\pi$
$788$			5.19264i			0.184980i
$789$		0			0
$790$	−0.710760	+	4.16919i	−0.0252877	+	0.148333i
$791$	2.56860			0.0913288
$792$		0			0
$793$		−	4.39590i		−	0.156103i
$794$	26.3508			0.935156
$795$		0			0
$796$	−17.0131			−0.603012
$797$			19.7198i			0.698512i	0.937027	+	0.349256i	$0.113566\pi$
$797$			19.7198i			0.698512i	−0.937027	+	0.349256i	$0.886434\pi$
$798$		0			0
$799$	−66.1119			−2.33887
$800$	1.65665	−	4.71758i	0.0585712	−	0.166792i
$801$		0			0
$802$			18.6718i			0.659324i
$803$		−	2.07169i		−	0.0731085i
$804$		0			0
$805$	5.84958	+	0.997233i	0.206171	+	0.0351478i
$806$	15.0769			0.531063
$807$		0			0
$808$			14.7627i			0.519351i
$809$	−36.7627			−1.29251			−0.646254	−	0.763122i	$-0.723665\pi$
$809$	−36.7627			−1.29251			−0.646254	+	0.763122i	$0.723665\pi$
$810$		0			0
$811$	−8.28861			−0.291052			−0.145526	−	0.989354i	$-0.546487\pi$
$811$	−8.28861			−0.291052			−0.145526	+	0.989354i	$0.546487\pi$
$812$		−	2.48592i		−	0.0872387i
$813$		0			0
$814$	3.54201			0.124147
$815$	−0.230573	+	1.35250i	−0.00807662	+	0.0473760i
$816$		0			0
$817$			20.4467i			0.715341i
$818$		−	4.43008i		−	0.154894i
$819$		0			0
$820$	17.1492	+	2.92358i	0.598876	+	0.102096i
$821$	22.5596			0.787335			0.393668	−	0.919253i	$-0.371206\pi$
$821$	22.5596			0.787335			0.393668	+	0.919253i	$0.371206\pi$
$822$		0			0
$823$			6.98917i			0.243627i	0.992553	+	0.121814i	$0.0388710\pi$
$823$			6.98917i			0.243627i	−0.992553	+	0.121814i	$0.961129\pi$
$824$	−5.94242			−0.207014
$825$		0			0
$826$	5.69593			0.198187
$827$		−	21.6447i		−	0.752660i	−0.926486	−	0.376330i	$-0.877186\pi$
$827$		−	21.6447i		−	0.752660i	0.926486	−	0.376330i	$-0.122814\pi$
$828$		0			0
$829$	−21.7009			−0.753705			−0.376853	−	0.926273i	$-0.622994\pi$
$829$	−21.7009			−0.753705			−0.376853	+	0.926273i	$0.622994\pi$
$830$	−6.88850	−	1.17435i	−0.239103	−	0.0407621i
$831$		0			0
$832$			3.71758i			0.128884i
$833$			46.4479i			1.60933i
$834$		0			0
$835$	2.55659	−	14.9965i	0.0884744	−	0.518975i
$836$	−12.2519			−0.423741
$837$		0			0
$838$			39.1429i			1.35217i
$839$	49.4436			1.70698			0.853492	−	0.521107i	$-0.174481\pi$
$839$	49.4436			1.70698			0.853492	+	0.521107i	$0.174481\pi$
$840$		0			0
$841$	−3.93615			−0.135729
$842$			28.0272i			0.965882i
$843$		0			0
$844$	−21.0189			−0.723500
$845$	1.80832	+	0.308282i	0.0622082	+	0.0106052i
$846$		0			0
$847$		−	0.767595i		−	0.0263749i
$848$			12.0867i			0.415060i
$849$		0			0
$850$	32.4459	+	11.3939i	1.11289	+	0.390806i
$851$	−5.34439			−0.183203
$852$		0			0
$853$			36.1003i			1.23605i	0.786158	+	0.618026i	$0.212067\pi$
$853$			36.1003i			1.23605i	−0.786158	+	0.618026i	$0.787933\pi$
$854$	−0.587152			−0.0200919
$855$		0			0
$856$	18.4010			0.628933
$857$		−	13.1584i		−	0.449484i	−0.974418	−	0.224742i	$-0.927846\pi$
$857$		−	13.1584i		−	0.449484i	0.974418	−	0.224742i	$-0.0721539\pi$
$858$		0			0
$859$	12.3713			0.422104			0.211052	−	0.977475i	$-0.432311\pi$
$859$	12.3713			0.422104			0.211052	+	0.977475i	$0.432311\pi$
$860$	2.22130	−	13.0297i	0.0757456	−	0.444310i
$861$		0			0
$862$		−	24.2322i		−	0.825351i
$863$			43.8288i			1.49195i	0.665974	+	0.745975i	$0.268016\pi$
$863$			43.8288i			1.49195i	−0.665974	+	0.745975i	$0.731984\pi$
$864$		0			0
$865$	4.58534	−	26.8968i	0.155906	−	0.914518i
$866$	−10.8428			−0.368453
$867$		0			0
$868$		−	2.01380i		−	0.0683528i
$869$	−6.69943			−0.227263
$870$		0			0
$871$	−24.4082			−0.827039
$872$			7.95537i			0.269403i
$873$		0			0
$874$	18.4863			0.625310
$875$	−2.69352	+	4.85440i	−0.0910575	+	0.164109i
$876$		0			0
$877$			45.7434i			1.54465i	0.635230	+	0.772323i	$0.280905\pi$
$877$			45.7434i			1.54465i	−0.635230	+	0.772323i	$0.719095\pi$
$878$			12.4210i			0.419189i
$879$		0			0
$880$	7.80754	+	1.33102i	0.263192	+	0.0448688i
$881$	−35.0483			−1.18081			−0.590404	−	0.807108i	$-0.701032\pi$
$881$	−35.0483			−1.18081			−0.590404	+	0.807108i	$0.701032\pi$
$882$		0			0
$883$		−	2.61087i		−	0.0878628i	−0.999035	−	0.0439314i	$-0.986012\pi$
$883$		−	2.61087i		−	0.0878628i	0.999035	−	0.0439314i	$-0.0139883\pi$
$884$	−25.5683			−0.859954
$885$		0			0
$886$	−22.9845			−0.772178
$887$		−	39.4227i		−	1.32368i	−0.749643	−	0.661842i	$-0.769775\pi$
$887$		−	39.4227i		−	1.32368i	0.749643	−	0.661842i	$-0.230225\pi$
$888$		0			0
$889$	3.95539			0.132660
$890$	0.900213	−	5.28048i	0.0301752	−	0.177002i
$891$		0			0
$892$		−	20.6518i		−	0.691475i
$893$		−	33.2500i		−	1.11267i
$894$		0			0
$895$	13.5351	+	2.30745i	0.452428	+	0.0771296i
$896$	0.496550			0.0165886
$897$		0			0
$898$		−	8.60738i		−	0.287232i
$899$	20.3038			0.677169
$900$		0			0
$901$	−83.1285			−2.76941
$902$			27.5569i			0.917544i
$903$		0			0
$904$	−5.17289			−0.172048
$905$	−50.2330	−	8.56368i	−1.66980	−	0.284666i
$906$		0			0
$907$		−	14.8779i		−	0.494014i	−0.969014	−	0.247007i	$-0.920553\pi$
$907$		−	14.8779i		−	0.494014i	0.969014	−	0.247007i	$-0.0794471\pi$
$908$		−	12.1125i		−	0.401966i
$909$		0			0
$910$	0.693679	−	4.06899i	0.0229952	−	0.134886i
$911$	−15.5279			−0.514462			−0.257231	−	0.966350i	$-0.582810\pi$
$911$	−15.5279			−0.514462			−0.257231	+	0.966350i	$0.582810\pi$
$912$		0			0
$913$		−	11.0691i		−	0.366332i
$914$	−18.0982			−0.598635
$915$		0			0
$916$	−28.1773			−0.931005
$917$		−	6.87343i		−	0.226981i
$918$		0			0
$919$	−9.50166			−0.313431			−0.156715	−	0.987644i	$-0.550091\pi$
$919$	−9.50166			−0.313431			−0.156715	+	0.987644i	$0.550091\pi$
$920$	−11.7805	−	2.00832i	−0.388390	−	0.0662124i
$921$		0			0
$922$		−	34.8960i		−	1.14924i
$923$		−	58.4596i		−	1.92422i
$924$		0			0
$925$	1.65665	−	4.71758i	0.0544702	−	0.155113i
$926$	11.7593			0.386435
$927$		0			0
$928$			5.00638i			0.164343i
$929$	3.26639			0.107167			0.0535835	−	0.998563i	$-0.482936\pi$
$929$	3.26639			0.107167			0.0535835	+	0.998563i	$0.482936\pi$
$930$		0			0
$931$	−23.3603			−0.765602
$932$		−	2.68018i		−	0.0877922i
$933$		0			0
$934$	15.0384			0.492071
$935$	−9.15434	+	53.6977i	−0.299379	+	1.75610i
$936$		0			0
$937$			21.1558i			0.691129i	0.938395	+	0.345564i	$0.112312\pi$
$937$			21.1558i			0.691129i	−0.938395	+	0.345564i	$0.887688\pi$
$938$			3.26015i			0.106448i
$939$		0			0
$940$	−3.61221	+	21.1886i	−0.117817	+	0.691096i
$941$	−44.2693			−1.44314			−0.721569	−	0.692343i	$-0.756579\pi$
$941$	−44.2693			−1.44314			−0.721569	+	0.692343i	$0.756579\pi$
$942$		0			0
$943$		−	41.5794i		−	1.35401i
$944$	−11.4710			−0.373350
$945$		0			0
$946$	20.9373			0.680731
$947$			2.22824i			0.0724081i	0.999344	+	0.0362041i	$0.0115266\pi$
$947$			2.22824i			0.0724081i	−0.999344	+	0.0362041i	$0.988473\pi$
$948$		0			0
$949$	2.17438			0.0705834
$950$	−5.73037	+	16.3182i	−0.185918	+	0.529432i
$951$		0			0
$952$			3.41511i			0.110684i
$953$		−	49.2029i		−	1.59384i	−0.604085	−	0.796920i	$-0.706461\pi$
$953$		−	49.2029i		−	1.59384i	0.604085	−	0.796920i	$-0.293539\pi$
$954$		0			0
$955$	57.0481	+	9.72552i	1.84603	+	0.314710i
$956$	−29.2248			−0.945198
$957$		0			0
$958$			5.76027i			0.186106i
$959$	3.23610			0.104499
$960$		0			0
$961$	−14.5522			−0.469427
$962$			3.71758i			0.119859i
$963$		0			0
$964$	18.0343			0.580845
$965$	4.90174	−	28.7527i	0.157793	−	0.925583i
$966$		0			0
$967$		−	25.7871i		−	0.829258i	−0.909991	−	0.414629i	$-0.863911\pi$
$967$		−	25.7871i		−	0.829258i	0.909991	−	0.414629i	$-0.136089\pi$
$968$			1.54586i			0.0496857i
$969$		0			0
$970$	−19.8811	−	3.38931i	−0.638342	−	0.108824i
$971$	21.8335			0.700672			0.350336	−	0.936624i	$-0.386067\pi$
$971$	21.8335			0.700672			0.350336	+	0.936624i	$0.386067\pi$
$972$		0			0
$973$		−	0.432934i		−	0.0138792i
$974$	35.6982			1.14384
$975$		0			0
$976$	1.18246			0.0378497
$977$			32.7998i			1.04936i	0.851300	+	0.524679i	$0.175814\pi$
$977$			32.7998i			1.04936i	−0.851300	+	0.524679i	$0.824186\pi$
$978$		0			0
$979$	8.48515			0.271187
$980$	14.8864	+	2.53782i	0.475528	+	0.0810676i
$981$		0			0
$982$		−	8.81455i		−	0.281284i
$983$			11.2017i			0.357277i	0.983915	+	0.178639i	$0.0571693\pi$
$983$			11.2017i			0.357277i	−0.983915	+	0.178639i	$0.942831\pi$
$984$		0			0
$985$	−1.95130	+	11.4460i	−0.0621735	+	0.364698i
$986$	−34.4322			−1.09655
$987$		0			0
$988$		−	12.8592i		−	0.409105i
$989$	−31.5914			−1.00455
$990$		0			0
$991$	47.3642			1.50457			0.752287	−	0.658835i	$-0.228951\pi$
$991$	47.3642			1.50457			0.752287	+	0.658835i	$0.228951\pi$
$992$			4.05558i			0.128765i
$993$		0			0
$994$	−7.80834			−0.247666
$995$	−37.5013	−	6.39319i	−1.18887	−	0.202678i
$996$		0			0
$997$		−	29.7496i		−	0.942178i	−0.882086	−	0.471089i	$-0.843861\pi$
$997$		−	29.7496i		−	0.942178i	0.882086	−	0.471089i	$-0.156139\pi$
$998$		−	6.15485i		−	0.194828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3330.2.d.q.1999.1	✓	14
3.2	odd	2		3330.2.d.r.1999.14	yes	14
5.4	even	2	inner	3330.2.d.q.1999.8	yes	14
15.14	odd	2		3330.2.d.r.1999.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3330.2.d.q.1999.1	✓	14	1.1	even	1	trivial
3330.2.d.q.1999.8	yes	14	5.4	even	2	inner
3330.2.d.r.1999.7	yes	14	15.14	odd	2
3330.2.d.r.1999.14	yes	14	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3330.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-2.20427 - 0.375782i) q^{5} -0.496550i q^{7} +1.00000i q^{8} +(-0.375782 + 2.20427i) q^{10} -3.54201 q^{11} -3.71758i q^{13} -0.496550 q^{14} +1.00000 q^{16} +6.87767i q^{17} -3.45902 q^{19} +(2.20427 + 0.375782i) q^{20} +3.54201i q^{22} -5.34439i q^{23} +(4.71758 + 1.65665i) q^{25} -3.71758 q^{26} +0.496550i q^{28} -5.00638 q^{29} -4.05558 q^{31} -1.00000i q^{32} +6.87767 q^{34} +(-0.186594 + 1.09453i) q^{35} -1.00000i q^{37} +3.45902i q^{38} +(0.375782 - 2.20427i) q^{40} +7.78001 q^{41} -5.91114i q^{43} +3.54201 q^{44} -5.34439 q^{46} +9.61254i q^{47} +6.75344 q^{49} +(1.65665 - 4.71758i) q^{50} +3.71758i q^{52} +12.0867i q^{53} +(7.80754 + 1.33102i) q^{55} +0.496550 q^{56} +5.00638i q^{58} -11.4710 q^{59} +1.18246 q^{61} +4.05558i q^{62} -1.00000 q^{64} +(-1.39700 + 8.19453i) q^{65} -6.56561i q^{67} -6.87767i q^{68} +(1.09453 + 0.186594i) q^{70} +15.7252 q^{71} +0.584892i q^{73} -1.00000 q^{74} +3.45902 q^{76} +1.75879i q^{77} +1.89142 q^{79} +(-2.20427 - 0.375782i) q^{80} -7.78001i q^{82} +3.12508i q^{83} +(2.58450 - 15.1602i) q^{85} -5.91114 q^{86} -3.54201i q^{88} -2.39557 q^{89} -1.84596 q^{91} +5.34439i q^{92} +9.61254 q^{94} +(7.62460 + 1.29984i) q^{95} +9.01936i q^{97} -6.75344i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{4} - 4 q^{5} - 6 q^{10} + 12 q^{11} - 12 q^{14} + 14 q^{16} + 4 q^{19} + 4 q^{20} + 10 q^{25} + 4 q^{26} - 16 q^{29} + 12 q^{31} - 12 q^{34} - 8 q^{35} + 6 q^{40} + 56 q^{41} - 12 q^{44} - 8 q^{46}+ \cdots + 12 q^{95}+O(q^{100}) \) 14 * q - 14 * q^4 - 4 * q^5 - 6 * q^10 + 12 * q^11 - 12 * q^14 + 14 * q^16 + 4 * q^19 + 4 * q^20 + 10 * q^25 + 4 * q^26 - 16 * q^29 + 12 * q^31 - 12 * q^34 - 8 * q^35 + 6 * q^40 + 56 * q^41 - 12 * q^44 - 8 * q^46 + 18 * q^49 - 24 * q^50 + 12 * q^56 - 28 * q^59 + 12 * q^61 - 14 * q^64 + 12 * q^65 - 16 * q^70 + 48 * q^71 - 14 * q^74 - 4 * q^76 - 20 * q^79 - 4 * q^80 + 12 * q^85 + 12 * q^86 - 36 * q^89 - 32 * q^91 + 32 * q^94 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more