LMFDB - Embedded newform 48.22.c.b.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,22,Mod(47,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("48.47");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	48.c (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:	$134.149125258$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + \cdots + 19\!\cdots\!25 $ x^12 - 6x^11 + 3182127878233901x^10 - 15910639391169450x^9 + 2949791405179242195959757687774x^8 - 11799165620716873320002683734462x^7 + 682000631839372425124278806828415083272235741x^6 - 2046001895518075978293163911495449925866548230x^5 + 59260078440248319369713813298073838065457842543215913467250x^4 - 118520156880493228736268429816616214081899513055279731372122x^3 + 1920946563324157816614046813331801092034051013576929032751993118806159193x^2 - 1920946563324098556535606567058433273738820068657811948770593657954959590*x + 19712403329393476880677174731487464005719014685725602860466895919544911300998405793425
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{68}\cdot 3^{56}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.7
Root			$0.500000 - 3.70354e7i$ of defining polynomial
Character	$\chi$	$=$	48.47
Dual form			48.22.c.b.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(30363.0 - 97665.0i) q^{3} -3.55520e7i q^{5} -1.36883e9i q^{7} +(-8.61653e9 - 5.93080e9i) q^{9} +O(q^{10})$	\(q+(30363.0 - 97665.0i) q^{3} -3.55520e7i q^{5} -1.36883e9i q^{7} +(-8.61653e9 - 5.93080e9i) q^{9} +8.13058e10 q^{11} -1.01527e11 q^{13} +(-3.47219e12 - 1.07947e12i) q^{15} +1.39503e13i q^{17} -9.45210e12i q^{19} +(-1.33686e14 - 4.15616e13i) q^{21} -1.97092e14 q^{23} -7.87110e14 q^{25} +(-8.40855e14 + 6.61456e14i) q^{27} +3.11066e15i q^{29} +3.21136e15i q^{31} +(2.46869e15 - 7.94072e15i) q^{33} -4.86645e16 q^{35} +2.51240e16 q^{37} +(-3.08267e15 + 9.91566e15i) q^{39} -1.94790e16i q^{41} -2.27069e16i q^{43} +(-2.10852e17 + 3.06335e17i) q^{45} +2.64317e17 q^{47} -1.31514e18 q^{49} +(1.36245e18 + 4.23573e17i) q^{51} +1.40537e18i q^{53} -2.89059e18i q^{55} +(-9.23139e17 - 2.86994e17i) q^{57} -1.50456e17 q^{59} -1.64227e17 q^{61} +(-8.11823e18 + 1.17945e19i) q^{63} +3.60950e18i q^{65} -1.03110e19i q^{67} +(-5.98430e18 + 1.92490e19i) q^{69} -1.34577e19 q^{71} -4.29171e19 q^{73} +(-2.38990e19 + 7.68731e19i) q^{75} -1.11293e20i q^{77} -1.61084e20i q^{79} +(3.90703e19 + 1.02206e20i) q^{81} +1.59123e20 q^{83} +4.95961e20 q^{85} +(3.03802e20 + 9.44489e19i) q^{87} -4.43760e20i q^{89} +1.38973e20i q^{91} +(3.13637e20 + 9.75065e19i) q^{93} -3.36042e20 q^{95} -1.06077e21 q^{97} +(-7.00574e20 - 4.82208e20i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6223178268 q^{9}+O(q^{10}) $ 12 * q + 6223178268 * q^9	$ 12 q + 6223178268 q^{9} - 1558099630680 q^{13} - 467668605656952 q^{21} - 23\!\cdots\!04 q^{25}+ \cdots - 47\!\cdots\!00 q^{97}+O(q^{100}) $ 12 * q + 6223178268 * q^9 - 1558099630680 * q^13 - 467668605656952 * q^21 - 2333948474211204 * q^25 - 2878569233493120 * q^33 + 198571664231829960 * q^37 - 520853659458386688 * q^45 - 1537469097010171836 * q^49 + 8983812160349471160 * q^57 + 18823450709508882792 * q^61 - 13723185548090697984 * q^69 - 141762419773124388360 * q^73 - 221765489935045328916 * q^81 + 938387558833131211776 * q^85 + 1143752665751371267560 * q^93 - 4719945853939671321000 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	30363.0	−	97665.0i	0.296873	−	0.954917i
$3$	30363.0	−	97665.0i	0.296873	−	0.954917i
$4$		0			0
$5$		−	3.55520e7i		−	1.62809i	−0.580799	−	0.814047i	$-0.697260\pi$
$5$		−	3.55520e7i		−	1.62809i	0.580799	−	0.814047i	$-0.302740\pi$
$6$		0			0
$7$		−	1.36883e9i		−	1.83155i	−0.401692	−	0.915775i	$-0.631578\pi$
$7$		−	1.36883e9i		−	1.83155i	0.401692	−	0.915775i	$-0.368422\pi$
$8$		0			0
$9$	−8.61653e9	−	5.93080e9i	−0.823732	−	0.566979i
$10$		0			0
$11$	8.13058e10			0.945144			0.472572	−	0.881292i	$-0.343326\pi$
$11$	8.13058e10			0.945144			0.472572	+	0.881292i	$0.343326\pi$
$12$		0			0
$13$	−1.01527e11			−0.204257			−0.102129	−	0.994771i	$-0.532565\pi$
$13$	−1.01527e11			−0.204257			−0.102129	+	0.994771i	$0.532565\pi$
$14$		0			0
$15$	−3.47219e12	−	1.07947e12i	−1.55469	−	0.483338i
$16$		0			0
$17$			1.39503e13i			1.67830i	0.543900	+	0.839150i	$0.316947\pi$
$17$			1.39503e13i			1.67830i	−0.543900	+	0.839150i	$0.683053\pi$
$18$		0			0
$19$		−	9.45210e12i		−	0.353684i	−0.984239	−	0.176842i	$-0.943412\pi$
$19$		−	9.45210e12i		−	0.353684i	0.984239	−	0.176842i	$-0.0565882\pi$
$20$		0			0
$21$	−1.33686e14	−	4.15616e13i	−1.74898	−	0.543738i
$22$		0			0
$23$	−1.97092e14			−0.992035			−0.496018	−	0.868313i	$-0.665205\pi$
$23$	−1.97092e14			−0.992035			−0.496018	+	0.868313i	$0.665205\pi$
$24$		0			0
$25$	−7.87110e14			−1.65069
$26$		0			0
$27$	−8.40855e14	+	6.61456e14i	−0.785962	+	0.618275i
$28$		0			0
$29$			3.11066e15i			1.37301i	0.727126	+	0.686504i	$0.240856\pi$
$29$			3.11066e15i			1.37301i	−0.727126	+	0.686504i	$0.759144\pi$
$30$		0			0
$31$			3.21136e15i			0.703706i	0.936055	+	0.351853i	$0.114448\pi$
$31$			3.21136e15i			0.703706i	−0.936055	+	0.351853i	$0.885552\pi$
$32$		0			0
$33$	2.46869e15	−	7.94072e15i	0.280588	−	0.902534i
$34$		0			0
$35$	−4.86645e16			−2.98193
$36$		0			0
$37$	2.51240e16			0.858954			0.429477	−	0.903078i	$-0.358698\pi$
$37$	2.51240e16			0.858954			0.429477	+	0.903078i	$0.358698\pi$
$38$		0			0
$39$	−3.08267e15	+	9.91566e15i	−0.0606386	+	0.195049i
$40$		0			0
$41$		−	1.94790e16i		−	0.226639i	−0.993559	−	0.113320i	$-0.963852\pi$
$41$		−	1.94790e16i		−	0.226639i	0.993559	−	0.113320i	$-0.0361484\pi$
$42$		0			0
$43$		−	2.27069e16i		−	0.160228i	−0.996786	−	0.0801141i	$-0.974472\pi$
$43$		−	2.27069e16i		−	0.160228i	0.996786	−	0.0801141i	$-0.0255285\pi$
$44$		0			0
$45$	−2.10852e17	+	3.06335e17i	−0.923095	+	1.34111i
$46$		0			0
$47$	2.64317e17			0.732990			0.366495	−	0.930420i	$-0.380558\pi$
$47$	2.64317e17			0.732990			0.366495	+	0.930420i	$0.380558\pi$
$48$		0			0
$49$	−1.31514e18			−2.35457
$50$		0			0
$51$	1.36245e18	+	4.23573e17i	1.60264	+	0.498243i
$52$		0			0
$53$			1.40537e18i			1.10381i	0.833908	+	0.551903i	$0.186098\pi$
$53$			1.40537e18i			1.10381i	−0.833908	+	0.551903i	$0.813902\pi$
$54$		0			0
$55$		−	2.89059e18i		−	1.53878i
$56$		0			0
$57$	−9.23139e17	−	2.86994e17i	−0.337739	−	0.104999i
$58$		0			0
$59$	−1.50456e17			−0.0383234			−0.0191617	−	0.999816i	$-0.506100\pi$
$59$	−1.50456e17			−0.0383234			−0.0191617	+	0.999816i	$0.506100\pi$
$60$		0			0
$61$	−1.64227e17			−0.0294769			−0.0147384	−	0.999891i	$-0.504692\pi$
$61$	−1.64227e17			−0.0294769			−0.0147384	+	0.999891i	$0.504692\pi$
$62$		0			0
$63$	−8.11823e18	+	1.17945e19i	−1.03845	+	1.50871i
$64$		0			0
$65$			3.60950e18i			0.332550i
$66$		0			0
$67$		−	1.03110e19i		−	0.691059i	−0.938408	−	0.345529i	$-0.887699\pi$
$67$		−	1.03110e19i		−	0.691059i	0.938408	−	0.345529i	$-0.112301\pi$
$68$		0			0
$69$	−5.98430e18	+	1.92490e19i	−0.294509	+	0.947311i
$70$		0			0
$71$	−1.34577e19			−0.490636			−0.245318	−	0.969443i	$-0.578892\pi$
$71$	−1.34577e19			−0.490636			−0.245318	+	0.969443i	$0.578892\pi$
$72$		0			0
$73$	−4.29171e19			−1.16880			−0.584401	−	0.811465i	$-0.698670\pi$
$73$	−4.29171e19			−1.16880			−0.584401	+	0.811465i	$0.698670\pi$
$74$		0			0
$75$	−2.38990e19	+	7.68731e19i	−0.490046	+	1.57627i
$76$		0			0
$77$		−	1.11293e20i		−	1.73108i
$78$		0			0
$79$		−	1.61084e20i		−	1.91411i	−0.289905	−	0.957055i	$-0.593624\pi$
$79$		−	1.61084e20i		−	1.91411i	0.289905	−	0.957055i	$-0.406376\pi$
$80$		0			0
$81$	3.90703e19	+	1.02206e20i	0.357070	+	0.934078i
$82$		0			0
$83$	1.59123e20			1.12568			0.562838	−	0.826567i	$-0.309709\pi$
$83$	1.59123e20			1.12568			0.562838	+	0.826567i	$0.309709\pi$
$84$		0			0
$85$	4.95961e20			2.73243
$86$		0			0
$87$	3.03802e20	+	9.44489e19i	1.31111	+	0.407610i
$88$		0			0
$89$		−	4.43760e20i		−	1.50853i	−0.656571	−	0.754264i	$-0.727994\pi$
$89$		−	4.43760e20i		−	1.50853i	0.656571	−	0.754264i	$-0.272006\pi$
$90$		0			0
$91$			1.38973e20i			0.374107i
$92$		0			0
$93$	3.13637e20	+	9.75065e19i	0.671981	+	0.208912i
$94$		0			0
$95$	−3.36042e20			−0.575831
$96$		0			0
$97$	−1.06077e21			−1.46056			−0.730278	−	0.683150i	$-0.760610\pi$
$97$	−1.06077e21			−1.46056			−0.730278	+	0.683150i	$0.760610\pi$
$98$		0			0
$99$	−7.00574e20	−	4.82208e20i	−0.778546	−	0.535877i
$100$		0			0
$101$		−	1.15660e21i		−	1.04185i	−0.853601	−	0.520927i	$-0.825586\pi$
$101$		−	1.15660e21i		−	1.04185i	0.853601	−	0.520927i	$-0.174414\pi$
$102$		0			0
$103$			1.98586e21i			1.45598i	0.685585	+	0.727992i	$0.259546\pi$
$103$			1.98586e21i			1.45598i	−0.685585	+	0.727992i	$0.740454\pi$
$104$		0			0
$105$	−1.47760e21	+	4.75282e21i	−0.885257	+	2.84750i
$106$		0			0
$107$	−2.46370e21			−1.21076			−0.605380	−	0.795937i	$-0.706979\pi$
$107$	−2.46370e21			−1.21076			−0.605380	+	0.795937i	$0.706979\pi$
$108$		0			0
$109$	−1.35594e20			−0.0548609			−0.0274304	−	0.999624i	$-0.508732\pi$
$109$	−1.35594e20			−0.0548609			−0.0274304	+	0.999624i	$0.508732\pi$
$110$		0			0
$111$	7.62838e20	−	2.45373e21i	0.255001	−	0.820230i
$112$		0			0
$113$		−	4.56440e21i		−	1.26491i	−0.774596	−	0.632456i	$-0.782047\pi$
$113$		−	4.56440e21i		−	1.26491i	0.774596	−	0.632456i	$-0.217953\pi$
$114$		0			0
$115$			7.00703e21i			1.61513i
$116$		0			0
$117$	8.74813e20	+	6.02138e20i	0.168253	+	0.115810i
$118$		0			0
$119$	1.90955e22			3.07389
$120$		0			0
$121$	−7.89623e20			−0.106702
$122$		0			0
$123$	−1.90241e21	−	5.91440e20i	−0.216422	−	0.0672832i
$124$		0			0
$125$			1.10308e22i			1.05938i
$126$		0			0
$127$			3.26959e21i			0.265800i	0.991129	+	0.132900i	$0.0424289\pi$
$127$			3.26959e21i			0.265800i	−0.991129	+	0.132900i	$0.957571\pi$
$128$		0			0
$129$	−2.21767e21	−	6.89449e20i	−0.153005	−	0.0475675i
$130$		0			0
$131$	−2.36405e22			−1.38774			−0.693870	−	0.720100i	$-0.744096\pi$
$131$	−2.36405e22			−1.38774			−0.693870	+	0.720100i	$0.744096\pi$
$132$		0			0
$133$	−1.29383e22			−0.647790
$134$		0			0
$135$	2.35161e22	+	2.98941e22i	1.00661	+	1.27962i
$136$		0			0
$137$		−	2.16152e22i		−	0.792854i	−0.918066	−	0.396427i	$-0.870250\pi$
$137$		−	2.16152e22i		−	0.792854i	0.918066	−	0.396427i	$-0.129750\pi$
$138$		0			0
$139$			3.40010e22i			1.07111i	0.844499	+	0.535557i	$0.179898\pi$
$139$			3.40010e22i			1.07111i	−0.844499	+	0.535557i	$0.820102\pi$
$140$		0			0
$141$	8.02546e21	−	2.58145e22i	0.217605	−	0.699944i
$142$		0			0
$143$	−8.25476e21			−0.193053
$144$		0			0
$145$	1.10590e23			2.23539
$146$		0			0
$147$	−3.99315e22	+	1.28443e23i	−0.699010	+	2.24842i
$148$		0			0
$149$			4.03375e22i			0.612708i	0.951918	+	0.306354i	$0.0991091\pi$
$149$			4.03375e22i			0.612708i	−0.951918	+	0.306354i	$0.900891\pi$
$150$		0			0
$151$			2.84800e22i			0.376082i	0.982161	+	0.188041i	$0.0602138\pi$
$151$			2.84800e22i			0.376082i	−0.982161	+	0.188041i	$0.939786\pi$
$152$		0			0
$153$	8.27364e22	−	1.20203e23i	0.951561	−	1.38247i
$154$		0			0
$155$	1.14170e23			1.14570
$156$		0			0
$157$	−1.30679e23			−1.14619			−0.573097	−	0.819488i	$-0.694258\pi$
$157$	−1.30679e23			−1.14619			−0.573097	+	0.819488i	$0.694258\pi$
$158$		0			0
$159$	1.37255e23	+	4.26711e22i	1.05404	+	0.327691i
$160$		0			0
$161$			2.69785e23i			1.81696i
$162$		0			0
$163$			2.56766e23i			1.51903i	0.650487	+	0.759517i	$0.274565\pi$
$163$			2.56766e23i			1.51903i	−0.650487	+	0.759517i	$0.725435\pi$
$164$		0			0
$165$	−2.82309e23	−	8.77668e22i	−1.46941	−	0.456824i
$166$		0			0
$167$	3.27675e23			1.50286			0.751432	−	0.659810i	$-0.229363\pi$
$167$	3.27675e23			1.50286			0.751432	+	0.659810i	$0.229363\pi$
$168$		0			0
$169$	−2.36757e23			−0.958279
$170$		0			0
$171$	−5.60585e22	+	8.14444e22i	−0.200531	+	0.291341i
$172$		0			0
$173$			2.54074e23i			0.804408i	0.915550	+	0.402204i	$0.131756\pi$
$173$			2.54074e23i			0.804408i	−0.915550	+	0.402204i	$0.868244\pi$
$174$		0			0
$175$			1.07742e24i			3.02332i
$176$		0			0
$177$	−4.56829e21	+	1.46943e22i	−0.0113772	+	0.0365956i
$178$		0			0
$179$	4.15928e22			0.0920579			0.0460290	−	0.998940i	$-0.485343\pi$
$179$	4.15928e22			0.0920579			0.0460290	+	0.998940i	$0.485343\pi$
$180$		0			0
$181$	1.99467e23			0.392867			0.196433	−	0.980517i	$-0.437064\pi$
$181$	1.99467e23			0.392867			0.196433	+	0.980517i	$0.437064\pi$
$182$		0			0
$183$	−4.98642e21	+	1.60392e22i	−0.00875090	+	0.0281480i
$184$		0			0
$185$		−	8.93208e23i		−	1.39846i
$186$		0			0
$187$			1.13424e24i			1.58624i
$188$		0			0
$189$	9.05418e23	+	1.15098e24i	1.13240	+	1.43953i
$190$		0			0
$191$	−1.63158e24			−1.82708			−0.913542	−	0.406745i	$-0.866664\pi$
$191$	−1.63158e24			−1.82708			−0.913542	+	0.406745i	$0.866664\pi$
$192$		0			0
$193$	5.17016e23			0.518982			0.259491	−	0.965746i	$-0.416445\pi$
$193$	5.17016e23			0.518982			0.259491	+	0.965746i	$0.416445\pi$
$194$		0			0
$195$	3.52522e23	+	1.09595e23i	0.317558	+	0.0987253i
$196$		0			0
$197$		−	1.35824e24i		−	1.09921i	−0.835424	−	0.549606i	$-0.814778\pi$
$197$		−	1.35824e24i		−	1.09921i	0.835424	−	0.549606i	$-0.185222\pi$
$198$		0			0
$199$			1.58981e24i			1.15715i	0.815631	+	0.578573i	$0.196390\pi$
$199$			1.58981e24i			1.15715i	−0.815631	+	0.578573i	$0.803610\pi$
$200$		0			0
$201$	−1.00702e24	−	3.13072e23i	−0.659903	−	0.205157i
$202$		0			0
$203$	4.25795e24			2.51473
$204$		0			0
$205$	−6.92517e23			−0.368990
$206$		0			0
$207$	1.69825e24	+	1.16891e24i	0.817171	+	0.562463i
$208$		0			0
$209$		−	7.68511e23i		−	0.334283i
$210$		0			0
$211$		−	3.51376e24i		−	1.38295i	−0.722400	−	0.691476i	$-0.756961\pi$
$211$		−	3.51376e24i		−	1.38295i	0.722400	−	0.691476i	$-0.243039\pi$
$212$		0			0
$213$	−4.08617e23	+	1.31435e24i	−0.145657	+	0.468516i
$214$		0			0
$215$	−8.07277e23			−0.260867
$216$		0			0
$217$	4.39579e24			1.28887
$218$		0			0
$219$	−1.30309e24	+	4.19150e24i	−0.346986	+	1.11611i
$220$		0			0
$221$		−	1.41634e24i		−	0.342805i
$222$		0			0
$223$		−	3.91484e24i		−	0.862012i	−0.902349	−	0.431006i	$-0.858159\pi$
$223$		−	3.91484e24i		−	0.862012i	0.902349	−	0.431006i	$-0.141841\pi$
$224$		0			0
$225$	6.78216e24	+	4.66819e24i	1.35973	+	0.935906i
$226$		0			0
$227$	−2.66708e24			−0.487264			−0.243632	−	0.969868i	$-0.578339\pi$
$227$	−2.66708e24			−0.487264			−0.243632	+	0.969868i	$0.578339\pi$
$228$		0			0
$229$	−8.18167e24			−1.36323			−0.681616	−	0.731711i	$-0.738722\pi$
$229$	−8.18167e24			−1.36323			−0.681616	+	0.731711i	$0.738722\pi$
$230$		0			0
$231$	−1.08695e25	−	3.37920e24i	−1.65304	−	0.513911i
$232$		0			0
$233$		−	6.36272e24i		−	0.883904i	−0.897039	−	0.441952i	$-0.854286\pi$
$233$		−	6.36272e24i		−	0.883904i	0.897039	−	0.441952i	$-0.145714\pi$
$234$		0			0
$235$		−	9.39701e24i		−	1.19338i
$236$		0			0
$237$	−1.57322e25	−	4.89098e24i	−1.82782	−	0.568249i
$238$		0			0
$239$	−7.64315e24			−0.813007			−0.406504	−	0.913649i	$-0.633252\pi$
$239$	−7.64315e24			−0.813007			−0.406504	+	0.913649i	$0.633252\pi$
$240$		0			0
$241$	−2.50959e24			−0.244581			−0.122291	−	0.992494i	$-0.539024\pi$
$241$	−2.50959e24			−0.244581			−0.122291	+	0.992494i	$0.539024\pi$
$242$		0			0
$243$	1.11682e25	−	7.12520e23i	0.997971	−	0.0636695i
$244$		0			0
$245$			4.67558e25i			3.83347i
$246$		0			0
$247$			9.59647e23i			0.0722426i
$248$		0			0
$249$	4.83145e24	−	1.55408e25i	0.334183	−	1.07493i
$250$		0			0
$251$	−1.37900e25			−0.876984			−0.438492	−	0.898735i	$-0.644487\pi$
$251$	−1.37900e25			−0.876984			−0.438492	+	0.898735i	$0.644487\pi$
$252$		0			0
$253$	−1.60247e25			−0.937616
$254$		0			0
$255$	1.50589e25	−	4.84380e25i	0.811186	−	2.60924i
$256$		0			0
$257$		−	1.53289e25i		−	0.760701i	−0.924842	−	0.380350i	$-0.875803\pi$
$257$		−	1.53289e25i		−	0.760701i	0.924842	−	0.380350i	$-0.124197\pi$
$258$		0			0
$259$		−	3.43903e25i		−	1.57322i
$260$		0			0
$261$	1.84487e25	−	2.68031e25i	0.778467	−	1.13099i
$262$		0			0
$263$	4.28430e25			1.66857			0.834286	−	0.551332i	$-0.185880\pi$
$263$	4.28430e25			1.66857			0.834286	+	0.551332i	$0.185880\pi$
$264$		0			0
$265$	4.99636e25			1.79710
$266$		0			0
$267$	−4.33398e25	−	1.34739e25i	−1.44052	−	0.447842i
$268$		0			0
$269$		−	2.46839e25i		−	0.758602i	−0.925273	−	0.379301i	$-0.876164\pi$
$269$		−	2.46839e25i		−	0.758602i	0.925273	−	0.379301i	$-0.123836\pi$
$270$		0			0
$271$			4.10139e24i			0.116615i	0.998299	+	0.0583073i	$0.0185703\pi$
$271$			4.10139e24i			0.116615i	−0.998299	+	0.0583073i	$0.981430\pi$
$272$		0			0
$273$	1.35728e25	+	4.21964e24i	0.357241	+	0.111063i
$274$		0			0
$275$	−6.39966e25			−1.56014
$276$		0			0
$277$	3.49763e25			0.790199			0.395100	−	0.918638i	$-0.370710\pi$
$277$	3.49763e25			0.790199			0.395100	+	0.918638i	$0.370710\pi$
$278$		0			0
$279$	1.90459e25	−	2.76708e25i	0.398986	−	0.579666i
$280$		0			0
$281$			2.73843e25i			0.532212i	0.963944	+	0.266106i	$0.0857371\pi$
$281$			2.73843e25i			0.532212i	−0.963944	+	0.266106i	$0.914263\pi$
$282$		0			0
$283$		−	4.89255e25i		−	0.882629i	−0.897353	−	0.441314i	$-0.854512\pi$
$283$		−	4.89255e25i		−	0.882629i	0.897353	−	0.441314i	$-0.145488\pi$
$284$		0			0
$285$	−1.02032e25	+	3.28195e25i	−0.170949	+	0.549871i
$286$		0			0
$287$	−2.66633e25			−0.415101
$288$		0			0
$289$	−1.25519e26			−1.81669
$290$		0			0
$291$	−3.22082e25	+	1.03600e26i	−0.433600	+	1.39471i
$292$		0			0
$293$		−	7.20642e25i		−	0.902838i	−0.892312	−	0.451419i	$-0.850918\pi$
$293$		−	7.20642e25i		−	0.902838i	0.892312	−	0.451419i	$-0.149082\pi$
$294$		0			0
$295$			5.34902e24i			0.0623940i
$296$		0			0
$297$	−6.83663e25	+	5.37802e25i	−0.742847	+	0.584359i
$298$		0			0
$299$	2.00102e25			0.202630
$300$		0			0
$301$	−3.10818e25			−0.293466
$302$		0			0
$303$	−1.12959e26	−	3.51177e25i	−0.994884	−	0.309299i
$304$		0			0
$305$			5.83860e24i			0.0479911i
$306$		0			0
$307$		−	1.74780e26i		−	1.34134i	−0.741755	−	0.670671i	$-0.766006\pi$
$307$		−	1.74780e26i		−	1.34134i	0.741755	−	0.670671i	$-0.233994\pi$
$308$		0			0
$309$	1.93948e26	+	6.02965e25i	1.39034	+	0.432243i
$310$		0			0
$311$	1.44780e26			0.969894			0.484947	−	0.874544i	$-0.338839\pi$
$311$	1.44780e26			0.969894			0.484947	+	0.874544i	$0.338839\pi$
$312$		0			0
$313$	−3.52618e25			−0.220846			−0.110423	−	0.993885i	$-0.535221\pi$
$313$	−3.52618e25			−0.220846			−0.110423	+	0.993885i	$0.535221\pi$
$314$		0			0
$315$	4.19319e26	+	2.88620e26i	2.45632	+	1.69069i
$316$		0			0
$317$		−	1.26009e25i		−	0.0690686i	−0.999404	−	0.0345343i	$-0.989005\pi$
$317$		−	1.26009e25i		−	0.0690686i	0.999404	−	0.0345343i	$-0.0109948\pi$
$318$		0			0
$319$			2.52914e26i			1.29769i
$320$		0			0
$321$	−7.48052e25	+	2.40617e26i	−0.359442	+	1.15617i
$322$		0			0
$323$	1.31860e26			0.593588
$324$		0			0
$325$	7.99132e25			0.337165
$326$		0			0
$327$	−4.11704e24	+	1.32428e25i	−0.0162867	+	0.0523876i
$328$		0			0
$329$		−	3.61804e26i		−	1.34251i
$330$		0			0
$331$			3.75401e26i			1.30708i	0.756892	+	0.653540i	$0.226717\pi$
$331$			3.75401e26i			1.30708i	−0.756892	+	0.653540i	$0.773283\pi$
$332$		0			0
$333$	−2.16481e26	−	1.49005e26i	−0.707548	−	0.487009i
$334$		0			0
$335$	−3.66577e26			−1.12511
$336$		0			0
$337$	−2.88457e26			−0.831702			−0.415851	−	0.909433i	$-0.636516\pi$
$337$	−2.88457e26			−0.831702			−0.415851	+	0.909433i	$0.636516\pi$
$338$		0			0
$339$	−4.45782e26	−	1.38589e26i	−1.20789	−	0.375519i
$340$		0			0
$341$			2.61102e26i			0.665104i
$342$		0			0
$343$			1.03564e27i			2.48097i
$344$		0			0
$345$	6.84341e26	+	2.12754e26i	1.54231	+	0.479488i
$346$		0			0
$347$	3.55460e26			0.753931			0.376965	−	0.926227i	$-0.376968\pi$
$347$	3.55460e26			0.753931			0.376965	+	0.926227i	$0.376968\pi$
$348$		0			0
$349$	−6.03239e25			−0.120454			−0.0602272	−	0.998185i	$-0.519183\pi$
$349$	−6.03239e25			−0.120454			−0.0602272	+	0.998185i	$0.519183\pi$
$350$		0			0
$351$	8.53697e25	−	6.71559e25i	0.160538	−	0.126287i
$352$		0			0
$353$			1.42270e25i			0.0252046i	0.999921	+	0.0126023i	$0.00401155\pi$
$353$			1.42270e25i			0.0252046i	−0.999921	+	0.0126023i	$0.995988\pi$
$354$		0			0
$355$			4.78450e26i			0.798801i
$356$		0			0
$357$	5.79797e26	−	1.86496e27i	0.912556	−	2.93531i
$358$		0			0
$359$	−1.85469e26			−0.275283			−0.137641	−	0.990482i	$-0.543952\pi$
$359$	−1.85469e26			−0.275283			−0.137641	+	0.990482i	$0.543952\pi$
$360$		0			0
$361$	6.24867e26			0.874907
$362$		0			0
$363$	−2.39753e25	+	7.71185e25i	−0.0316770	+	0.101892i
$364$		0			0
$365$			1.52579e27i			1.90292i
$366$		0			0
$367$			5.69151e26i			0.670246i	0.942174	+	0.335123i	$0.108778\pi$
$367$			5.69151e26i			0.670246i	−0.942174	+	0.335123i	$0.891222\pi$
$368$		0			0
$369$	−1.15526e26	+	1.67841e26i	−0.128500	+	0.186690i
$370$		0			0
$371$	1.92370e27			2.02167
$372$		0			0
$373$	−1.39733e26			−0.138789			−0.0693945	−	0.997589i	$-0.522107\pi$
$373$	−1.39733e26			−0.138789			−0.0693945	+	0.997589i	$0.522107\pi$
$374$		0			0
$375$	1.07733e27	+	3.34929e26i	1.01162	+	0.314503i
$376$		0			0
$377$		−	3.15817e26i		−	0.280447i
$378$		0			0
$379$		−	1.28970e27i		−	1.08337i	−0.840581	−	0.541686i	$-0.817786\pi$
$379$		−	1.28970e27i		−	1.08337i	0.840581	−	0.541686i	$-0.182214\pi$
$380$		0			0
$381$	3.19325e26	+	9.92746e25i	0.253817	+	0.0789089i
$382$		0			0
$383$	1.08252e25			0.00814420			0.00407210	−	0.999992i	$-0.498704\pi$
$383$	1.08252e25			0.00814420			0.00407210	+	0.999992i	$0.498704\pi$
$384$		0			0
$385$	−3.95671e27			−2.81836
$386$		0			0
$387$	−1.34670e26	+	1.95655e26i	−0.0908460	+	0.131985i
$388$		0			0
$389$			7.32643e25i			0.0468190i	0.999726	+	0.0234095i	$0.00745215\pi$
$389$			7.32643e25i			0.0468190i	−0.999726	+	0.0234095i	$0.992548\pi$
$390$		0			0
$391$		−	2.74949e27i		−	1.66493i
$392$		0			0
$393$	−7.17796e26	+	2.30885e27i	−0.411983	+	1.32518i
$394$		0			0
$395$	−5.72685e27			−3.11635
$396$		0			0
$397$	−2.26195e27			−1.16730			−0.583650	−	0.812006i	$-0.698376\pi$
$397$	−2.26195e27			−1.16730			−0.583650	+	0.812006i	$0.698376\pi$
$398$		0			0
$399$	−3.92845e26	+	1.26362e27i	−0.192312	+	0.618586i
$400$		0			0
$401$			5.07907e26i			0.235922i	0.993018	+	0.117961i	$0.0376358\pi$
$401$			5.07907e26i			0.235922i	−0.993018	+	0.117961i	$0.962364\pi$
$402$		0			0
$403$		−	3.26041e26i		−	0.143737i
$404$		0			0
$405$	3.63363e27	−	1.38903e27i	1.52077	−	0.581344i
$406$		0			0
$407$	2.04272e27			0.811835
$408$		0			0
$409$	1.42237e27			0.536928			0.268464	−	0.963290i	$-0.413484\pi$
$409$	1.42237e27			0.536928			0.268464	+	0.963290i	$0.413484\pi$
$410$		0			0
$411$	−2.11105e27	−	6.56302e26i	−0.757109	−	0.235377i
$412$		0			0
$413$			2.05948e26i			0.0701911i
$414$		0			0
$415$		−	5.65715e27i		−	1.83271i
$416$		0			0
$417$	3.32070e27	+	1.03237e27i	1.02283	+	0.317986i
$418$		0			0
$419$	5.74722e26			0.168349			0.0841745	−	0.996451i	$-0.473175\pi$
$419$	5.74722e26			0.168349			0.0841745	+	0.996451i	$0.473175\pi$
$420$		0			0
$421$	3.15296e27			0.878531			0.439265	−	0.898357i	$-0.355239\pi$
$421$	3.15296e27			0.878531			0.439265	+	0.898357i	$0.355239\pi$
$422$		0			0
$423$	−2.27750e27	−	1.56761e27i	−0.603787	−	0.415590i
$424$		0			0
$425$		−	1.09804e28i		−	2.77035i
$426$		0			0
$427$			2.24798e26i			0.0539883i
$428$		0			0
$429$	−2.50639e26	+	8.06200e26i	−0.0573122	+	0.184349i
$430$		0			0
$431$	−5.60602e26			−0.122080			−0.0610398	−	0.998135i	$-0.519442\pi$
$431$	−5.60602e26			−0.122080			−0.0610398	+	0.998135i	$0.519442\pi$
$432$		0			0
$433$	−4.72416e27			−0.979945			−0.489973	−	0.871738i	$-0.662993\pi$
$433$	−4.72416e27			−0.979945			−0.489973	+	0.871738i	$0.662993\pi$
$434$		0			0
$435$	3.35785e27	−	1.08008e28i	0.663627	−	2.13461i
$436$		0			0
$437$			1.86294e27i			0.350867i
$438$		0			0
$439$		−	4.42156e27i		−	0.793776i	−0.917867	−	0.396888i	$-0.870090\pi$
$439$		−	4.42156e27i		−	0.793776i	0.917867	−	0.396888i	$-0.129910\pi$
$440$		0			0
$441$	1.13319e28	+	7.79981e27i	1.93954	+	1.33499i
$442$		0			0
$443$	5.39591e26			0.0880695			0.0440347	−	0.999030i	$-0.485979\pi$
$443$	5.39591e26			0.0880695			0.0440347	+	0.999030i	$0.485979\pi$
$444$		0			0
$445$	−1.57766e28			−2.45603
$446$		0			0
$447$	3.93956e27	+	1.22477e27i	0.585085	+	0.181897i
$448$		0			0
$449$		−	2.75637e27i		−	0.390617i	−0.980742	−	0.195309i	$-0.937429\pi$
$449$		−	2.75637e27i		−	0.390617i	0.980742	−	0.195309i	$-0.0625709\pi$
$450$		0			0
$451$		−	1.58375e27i		−	0.214207i
$452$		0			0
$453$	2.78150e27	+	8.64739e26i	0.359127	+	0.111649i
$454$		0			0
$455$	4.94078e27			0.609082
$456$		0			0
$457$	3.15103e27			0.370964			0.185482	−	0.982648i	$-0.440615\pi$
$457$	3.15103e27			0.370964			0.185482	+	0.982648i	$0.440615\pi$
$458$		0			0
$459$	−9.22751e27	−	1.17302e28i	−1.03765	−	1.31908i
$460$		0			0
$461$			7.89127e27i			0.847788i	0.905712	+	0.423894i	$0.139337\pi$
$461$			7.89127e27i			0.847788i	−0.905712	+	0.423894i	$0.860663\pi$
$462$		0			0
$463$			1.39692e28i			1.43407i	0.697035	+	0.717037i	$0.254502\pi$
$463$			1.39692e28i			1.43407i	−0.697035	+	0.717037i	$0.745498\pi$
$464$		0			0
$465$	3.46655e27	−	1.11504e28i	0.340128	−	1.09405i
$466$		0			0
$467$	−9.34461e27			−0.876463			−0.438232	−	0.898862i	$-0.644395\pi$
$467$	−9.34461e27			−0.876463			−0.438232	+	0.898862i	$0.644395\pi$
$468$		0			0
$469$	−1.41139e28			−1.26571
$470$		0			0
$471$	−3.96779e27	+	1.27627e28i	−0.340274	+	1.09452i
$472$		0			0
$473$		−	1.84620e27i		−	0.151439i
$474$		0			0
$475$			7.43985e27i			0.583823i
$476$		0			0
$477$	8.33494e27	−	1.21094e28i	0.625834	−	0.909241i
$478$		0			0
$479$	−2.21401e28			−1.59095			−0.795477	−	0.605984i	$-0.792780\pi$
$479$	−2.21401e28			−1.59095			−0.795477	+	0.605984i	$0.792780\pi$
$480$		0			0
$481$	−2.55077e27			−0.175448
$482$		0			0
$483$	2.63485e28	+	8.19147e27i	1.73505	+	0.539407i
$484$		0			0
$485$			3.77126e28i			2.37792i
$486$		0			0
$487$		−	1.55360e28i		−	0.938180i	−0.883150	−	0.469090i	$-0.844582\pi$
$487$		−	1.55360e28i		−	0.938180i	0.883150	−	0.469090i	$-0.155418\pi$
$488$		0			0
$489$	2.50770e28	+	7.79618e27i	1.45055	+	0.450961i
$490$		0			0
$491$	8.88611e27			0.492443			0.246222	−	0.969214i	$-0.420811\pi$
$491$	8.88611e27			0.492443			0.246222	+	0.969214i	$0.420811\pi$
$492$		0			0
$493$	−4.33946e28			−2.30432
$494$		0			0
$495$	−1.71435e28	+	2.49068e28i	−0.872458	+	1.26755i
$496$		0			0
$497$			1.84213e28i			0.898624i
$498$		0			0
$499$		−	8.00716e27i		−	0.374475i	−0.982315	−	0.187237i	$-0.940047\pi$
$499$		−	8.00716e27i		−	0.374475i	0.982315	−	0.187237i	$-0.0599534\pi$
$500$		0			0
$501$	9.94918e27	−	3.20023e28i	0.446160	−	1.43511i
$502$		0			0
$503$	4.50080e28			1.93565			0.967824	−	0.251629i	$-0.0809662\pi$
$503$	4.50080e28			1.93565			0.967824	+	0.251629i	$0.0809662\pi$
$504$		0			0
$505$	−4.11193e28			−1.69624
$506$		0			0
$507$	−7.18864e27	+	2.31228e28i	−0.284488	+	0.915077i
$508$		0			0
$509$		−	3.13277e28i		−	1.18957i	−0.803883	−	0.594787i	$-0.797236\pi$
$509$		−	3.13277e28i		−	1.18957i	0.803883	−	0.594787i	$-0.202764\pi$
$510$		0			0
$511$			5.87461e28i			2.14072i
$512$		0			0
$513$	6.25216e27	+	7.94785e27i	0.218674	+	0.277982i
$514$		0			0
$515$	7.06012e28			2.37048
$516$		0			0
$517$	2.14905e28			0.692781
$518$		0			0
$519$	2.48142e28	+	7.71445e27i	0.768143	+	0.238807i
$520$		0			0
$521$		−	4.52720e28i		−	1.34597i	−0.739658	−	0.672983i	$-0.765013\pi$
$521$		−	4.52720e28i		−	1.34597i	0.739658	−	0.672983i	$-0.234987\pi$
$522$		0			0
$523$		−	2.14432e28i		−	0.612382i	−0.951970	−	0.306191i	$-0.900945\pi$
$523$		−	2.14432e28i		−	0.612382i	0.951970	−	0.306191i	$-0.0990547\pi$
$524$		0			0
$525$	1.05226e29	+	3.27136e28i	2.88702	+	0.897543i
$526$		0			0
$527$	−4.47994e28			−1.18103
$528$		0			0
$529$	−6.26278e26			−0.0158665
$530$		0			0
$531$	1.29641e27	+	8.92324e26i	0.0315682	+	0.0217285i
$532$		0			0
$533$			1.97765e27i			0.0462928i
$534$		0			0
$535$			8.75895e28i			1.97123i
$536$		0			0
$537$	1.26288e27	−	4.06216e27i	0.0273295	−	0.0879076i
$538$		0			0
$539$	−1.06928e29			−2.22541
$540$		0			0
$541$	6.03725e28			1.20856			0.604279	−	0.796773i	$-0.293461\pi$
$541$	6.03725e28			1.20856			0.604279	+	0.796773i	$0.293461\pi$
$542$		0			0
$543$	6.05640e27	−	1.94809e28i	0.116632	−	0.375155i
$544$		0			0
$545$			4.82065e27i			0.0893186i
$546$		0			0
$547$			4.25089e28i			0.757901i	0.925417	+	0.378951i	$0.123715\pi$
$547$			4.25089e28i			0.757901i	−0.925417	+	0.378951i	$0.876285\pi$
$548$		0			0
$549$	1.41507e27	+	9.73997e26i	0.0242810	+	0.0167128i
$550$		0			0
$551$	2.94023e28			0.485612
$552$		0			0
$553$	−2.20495e29			−3.50579
$554$		0			0
$555$	−8.72351e28	−	2.71204e28i	−1.33541	−	0.415165i
$556$		0			0
$557$		−	8.71218e28i		−	1.28424i	−0.766603	−	0.642122i	$-0.778054\pi$
$557$		−	8.71218e28i		−	1.28424i	0.766603	−	0.642122i	$-0.221946\pi$
$558$		0			0
$559$			2.30537e27i			0.0327278i
$560$		0			0
$561$	1.10775e29	+	3.44389e28i	1.51472	+	0.470911i
$562$		0			0
$563$	−1.63734e28			−0.215676			−0.107838	−	0.994168i	$-0.534393\pi$
$563$	−1.63734e28			−0.215676			−0.107838	+	0.994168i	$0.534393\pi$
$564$		0			0
$565$	−1.62274e29			−2.05940
$566$		0			0
$567$	1.39902e29	−	5.34804e28i	1.71081	−	0.653992i
$568$		0			0
$569$			1.60930e29i			1.89653i	0.317487	+	0.948263i	$0.397161\pi$
$569$			1.60930e29i			1.89653i	−0.317487	+	0.948263i	$0.602839\pi$
$570$		0			0
$571$		−	5.06590e28i		−	0.575411i	−0.957719	−	0.287705i	$-0.907108\pi$
$571$		−	5.06590e28i		−	0.575411i	0.957719	−	0.287705i	$-0.0928924\pi$
$572$		0			0
$573$	−4.95397e28	+	1.59348e29i	−0.542413	+	1.74471i
$574$		0			0
$575$	1.55133e29			1.63754
$576$		0			0
$577$	2.67417e27			0.0272171			0.0136086	−	0.999907i	$-0.495668\pi$
$577$	2.67417e27			0.0272171			0.0136086	+	0.999907i	$0.495668\pi$
$578$		0			0
$579$	1.56981e28	−	5.04943e28i	0.154072	−	0.495585i
$580$		0			0
$581$		−	2.17812e29i		−	2.06173i
$582$		0			0
$583$			1.14264e29i			1.04326i
$584$		0			0
$585$	2.14072e28	−	3.11014e28i	0.188549	−	0.273932i
$586$		0			0
$587$	−1.08450e29			−0.921575			−0.460787	−	0.887511i	$-0.652433\pi$
$587$	−1.08450e29			−0.921575			−0.460787	+	0.887511i	$0.652433\pi$
$588$		0			0
$589$	3.03541e28			0.248890
$590$		0			0
$591$	−1.32653e29	−	4.12403e28i	−1.04966	−	0.326327i
$592$		0			0
$593$			7.92155e28i			0.604973i	0.953154	+	0.302486i	$0.0978166\pi$
$593$			7.92155e28i			0.604973i	−0.953154	+	0.302486i	$0.902183\pi$
$594$		0			0
$595$		−	6.78885e29i		−	5.00458i
$596$		0			0
$597$	1.55269e29	+	4.82714e28i	1.10498	+	0.343526i
$598$		0			0
$599$	8.02774e28			0.551584			0.275792	−	0.961217i	$-0.411060\pi$
$599$	8.02774e28			0.551584			0.275792	+	0.961217i	$0.411060\pi$
$600$		0			0
$601$	1.12347e29			0.745383			0.372692	−	0.927955i	$-0.378435\pi$
$601$	1.12347e29			0.745383			0.372692	+	0.927955i	$0.378435\pi$
$602$		0			0
$603$	−6.11524e28	+	8.88450e28i	−0.391816	+	0.569247i
$604$		0			0
$605$			2.80727e28i			0.173721i
$606$		0			0
$607$			7.77330e28i			0.464648i	0.972638	+	0.232324i	$0.0746330\pi$
$607$			7.77330e28i			0.464648i	−0.972638	+	0.232324i	$0.925367\pi$
$608$		0			0
$609$	1.29284e29	−	4.15852e29i	0.746558	−	2.40136i
$610$		0			0
$611$	−2.68354e28			−0.149719
$612$		0			0
$613$	−2.58302e29			−1.39249			−0.696247	−	0.717802i	$-0.745148\pi$
$613$	−2.58302e29			−1.39249			−0.696247	+	0.717802i	$0.745148\pi$
$614$		0			0
$615$	−2.10269e28	+	6.76346e28i	−0.109543	+	0.352355i
$616$		0			0
$617$			1.88675e29i			0.949995i	0.879987	+	0.474997i	$0.157551\pi$
$617$			1.88675e29i			0.949995i	−0.879987	+	0.474997i	$0.842449\pi$
$618$		0			0
$619$		−	7.62056e28i		−	0.370881i	−0.982655	−	0.185441i	$-0.940629\pi$
$619$		−	7.62056e28i		−	0.370881i	0.982655	−	0.185441i	$-0.0593713\pi$
$620$		0			0
$621$	1.65726e29	−	1.30368e29i	0.779702	−	0.613350i
$622$		0			0
$623$	−6.07431e29			−2.76294
$624$		0			0
$625$	1.68452e28			0.0740860
$626$		0			0
$627$	−7.50565e28	−	2.33343e28i	−0.319212	−	0.0992396i
$628$		0			0
$629$			3.50487e29i			1.44158i
$630$		0			0
$631$		−	3.16492e29i		−	1.25909i	−0.776966	−	0.629543i	$-0.783242\pi$
$631$		−	3.16492e29i		−	1.25909i	0.776966	−	0.629543i	$-0.216758\pi$
$632$		0			0
$633$	−3.43172e29	−	1.06688e29i	−1.32060	−	0.410561i
$634$		0			0
$635$	1.16241e29			0.432747
$636$		0			0
$637$	1.33522e29			0.480939
$638$		0			0
$639$	1.15959e29	+	7.98151e28i	0.404153	+	0.278180i
$640$		0			0
$641$		−	3.12846e29i		−	1.05517i	−0.849504	−	0.527583i	$-0.823098\pi$
$641$		−	3.12846e29i		−	1.05517i	0.849504	−	0.527583i	$-0.176902\pi$
$642$		0			0
$643$		−	2.05138e29i		−	0.669624i	−0.942285	−	0.334812i	$-0.891327\pi$
$643$		−	2.05138e29i		−	0.669624i	0.942285	−	0.334812i	$-0.108673\pi$
$644$		0			0
$645$	−2.45113e28	+	7.88426e28i	−0.0774444	+	0.249106i
$646$		0			0
$647$	3.82322e29			1.16932			0.584661	−	0.811278i	$-0.301228\pi$
$647$	3.82322e29			1.16932			0.584661	+	0.811278i	$0.301228\pi$
$648$		0			0
$649$	−1.22329e28			−0.0362211
$650$		0			0
$651$	1.33469e29	−	4.29315e29i	0.382632	−	1.23077i
$652$		0			0
$653$		−	1.78353e29i		−	0.495099i	−0.968875	−	0.247549i	$-0.920375\pi$
$653$		−	1.78353e29i		−	0.495099i	0.968875	−	0.247549i	$-0.0796252\pi$
$654$		0			0
$655$			8.40468e29i			2.25937i
$656$		0			0
$657$	3.69797e29	+	2.54533e29i	0.962779	+	0.662685i
$658$		0			0
$659$	6.40298e28			0.161467			0.0807337	−	0.996736i	$-0.474274\pi$
$659$	6.40298e28			0.161467			0.0807337	+	0.996736i	$0.474274\pi$
$660$		0			0
$661$	4.51347e29			1.10254			0.551271	−	0.834327i	$-0.314143\pi$
$661$	4.51347e29			1.10254			0.551271	+	0.834327i	$0.314143\pi$
$662$		0			0
$663$	−1.38326e29	−	4.30042e28i	−0.327350	−	0.101770i
$664$		0			0
$665$			4.59982e29i			1.05466i
$666$		0			0
$667$		−	6.13086e29i		−	1.36207i
$668$		0			0
$669$	−3.82343e29	−	1.18866e29i	−0.823150	−	0.255909i
$670$		0			0
$671$	−1.33526e28			−0.0278599
$672$		0			0
$673$	−3.16425e29			−0.639901			−0.319951	−	0.947434i	$-0.603666\pi$
$673$	−3.16425e29			−0.639901			−0.319951	+	0.947434i	$0.603666\pi$
$674$		0			0
$675$	6.61845e29	−	5.20639e29i	1.29738	−	1.02058i
$676$		0			0
$677$		−	5.55817e29i		−	1.05621i	−0.849178	−	0.528106i	$-0.822902\pi$
$677$		−	5.55817e29i		−	1.05621i	0.849178	−	0.528106i	$-0.177098\pi$
$678$		0			0
$679$			1.45201e30i			2.67508i
$680$		0			0
$681$	−8.09805e28	+	2.60480e29i	−0.144656	+	0.465297i
$682$		0			0
$683$	6.76496e26			0.00117179			0.000585893	−	1.00000i	$-0.499814\pi$
$683$	6.76496e26			0.00117179			0.000585893		1.00000i	$0.499814\pi$
$684$		0			0
$685$	−7.68464e29			−1.29084
$686$		0			0
$687$	−2.48420e29	+	7.99063e29i	−0.404707	+	1.30177i
$688$		0			0
$689$		−	1.42683e29i		−	0.225460i
$690$		0			0
$691$			1.14106e30i			1.74900i	0.485023	+	0.874501i	$0.338811\pi$
$691$			1.14106e30i			1.74900i	−0.485023	+	0.874501i	$0.661189\pi$
$692$		0			0
$693$	−6.60059e29	+	9.58963e29i	−0.981485	+	1.42595i
$694$		0			0
$695$	1.20880e30			1.74388
$696$		0			0
$697$	2.71737e29			0.380369
$698$		0			0
$699$	−6.21414e29	−	1.93191e29i	−0.844055	−	0.262408i
$700$		0			0
$701$			6.98936e29i			0.921294i	0.887584	+	0.460647i	$0.152383\pi$
$701$			6.98936e29i			0.921294i	−0.887584	+	0.460647i	$0.847617\pi$
$702$		0			0
$703$		−	2.37474e29i		−	0.303798i
$704$		0			0
$705$	−9.17759e29	−	2.85321e29i	−1.13957	−	0.354282i
$706$		0			0
$707$	−1.58318e30			−1.90821
$708$		0			0
$709$	8.53396e29			0.998539			0.499270	−	0.866447i	$-0.333602\pi$
$709$	8.53396e29			0.998539			0.499270	+	0.866447i	$0.333602\pi$
$710$		0			0
$711$	−9.55355e29	+	1.38798e30i	−1.08526	+	1.57672i
$712$		0			0
$713$		−	6.32934e29i		−	0.698101i
$714$		0			0
$715$			2.93473e29i			0.314308i
$716$		0			0
$717$	−2.32069e29	+	7.46468e29i	−0.241360	+	0.776354i
$718$		0			0
$719$	4.51890e29			0.456435			0.228218	−	0.973610i	$-0.426710\pi$
$719$	4.51890e29			0.456435			0.228218	+	0.973610i	$0.426710\pi$
$720$		0			0
$721$	2.71829e30			2.66671
$722$		0			0
$723$	−7.61986e28	+	2.45099e29i	−0.0726097	+	0.233555i
$724$		0			0
$725$		−	2.44843e30i		−	2.26641i
$726$		0			0
$727$			5.79335e29i			0.520977i	0.965477	+	0.260488i	$0.0838835\pi$
$727$			5.79335e29i			0.520977i	−0.965477	+	0.260488i	$0.916116\pi$
$728$		0			0
$729$	2.69512e29	−	1.11238e30i	0.235472	−	0.971881i
$730$		0			0
$731$	3.16768e29			0.268911
$732$		0			0
$733$	1.47112e29			0.121354			0.0606772	−	0.998157i	$-0.480674\pi$
$733$	1.47112e29			0.121354			0.0606772	+	0.998157i	$0.480674\pi$
$734$		0			0
$735$	4.56640e30	+	1.41965e30i	3.66064	+	1.13805i
$736$		0			0
$737$		−	8.38343e29i		−	0.653150i
$738$		0			0
$739$		−	1.59263e30i		−	1.20600i	−0.797741	−	0.603000i	$-0.793972\pi$
$739$		−	1.59263e30i		−	1.20600i	0.797741	−	0.603000i	$-0.206028\pi$
$740$		0			0
$741$	9.37238e28	+	2.91377e28i	0.0689857	+	0.0214469i
$742$		0			0
$743$	5.91119e29			0.422953			0.211477	−	0.977383i	$-0.432173\pi$
$743$	5.91119e29			0.422953			0.211477	+	0.977383i	$0.432173\pi$
$744$		0			0
$745$	1.43408e30			0.997546
$746$		0			0
$747$	−1.37109e30	−	9.43727e29i	−0.927256	−	0.638234i
$748$		0			0
$749$			3.37237e30i			2.21757i
$750$		0			0
$751$			3.06438e29i			0.195940i	0.995189	+	0.0979701i	$0.0312349\pi$
$751$			3.06438e29i			0.195940i	−0.995189	+	0.0979701i	$0.968765\pi$
$752$		0			0
$753$	−4.18707e29	+	1.34680e30i	−0.260353	+	0.837447i
$754$		0			0
$755$	1.01252e30			0.612297
$756$		0			0
$757$	1.30557e30			0.767881			0.383940	−	0.923358i	$-0.374567\pi$
$757$	1.30557e30			0.767881			0.383940	+	0.923358i	$0.374567\pi$
$758$		0			0
$759$	−4.86558e29	+	1.56505e30i	−0.278353	+	0.895346i
$760$		0			0
$761$		−	5.41042e29i		−	0.301087i	−0.988603	−	0.150544i	$-0.951898\pi$
$761$		−	5.41042e29i		−	0.301087i	0.988603	−	0.150544i	$-0.0481024\pi$
$762$		0			0
$763$			1.85605e29i			0.100480i
$764$		0			0
$765$	−4.27347e30	−	2.94145e30i	−2.25079	−	1.54923i
$766$		0			0
$767$	1.52754e28			0.00782783
$768$		0			0
$769$	−9.95470e29			−0.496366			−0.248183	−	0.968713i	$-0.579833\pi$
$769$	−9.95470e29			−0.496366			−0.248183	+	0.968713i	$0.579833\pi$
$770$		0			0
$771$	−1.49710e30	−	4.65432e29i	−0.726406	−	0.225832i
$772$		0			0
$773$			2.95905e30i			1.39723i	0.715498	+	0.698615i	$0.246200\pi$
$773$			2.95905e30i			1.39723i	−0.715498	+	0.698615i	$0.753800\pi$
$774$		0			0
$775$		−	2.52769e30i		−	1.16160i
$776$		0			0
$777$	−3.35873e30	−	1.04419e30i	−1.50229	−	0.467046i
$778$		0			0
$779$	−1.84117e29			−0.0801588
$780$		0			0
$781$	−1.09419e30			−0.463722
$782$		0			0
$783$	−2.05757e30	−	2.61561e30i	−0.848897	−	1.07913i
$784$		0			0
$785$			4.64589e30i			1.86611i
$786$		0			0
$787$		−	1.17587e29i		−	0.0459859i	−0.999736	−	0.0229930i	$-0.992680\pi$
$787$		−	1.17587e29i		−	0.0459859i	0.999736	−	0.0229930i	$-0.00731953\pi$
$788$		0			0
$789$	1.30084e30	−	4.18426e30i	0.495354	−	1.59335i
$790$		0			0
$791$	−6.24787e30			−2.31675
$792$		0			0
$793$	1.66735e28			0.00602087
$794$		0			0
$795$	1.51704e30	−	4.87969e30i	0.533511	−	1.71608i
$796$		0			0
$797$		−	2.73219e30i		−	0.935835i	−0.883772	−	0.467917i	$-0.845004\pi$
$797$		−	2.73219e30i		−	0.935835i	0.883772	−	0.467917i	$-0.154996\pi$
$798$		0			0
$799$			3.68730e30i			1.23018i
$800$		0			0
$801$	−2.63185e30	+	3.82368e30i	−0.855304	+	1.24262i
$802$		0			0
$803$	−3.48941e30			−1.10469
$804$		0			0
$805$	9.59140e30			2.95818
$806$		0			0
$807$	−2.41075e30	−	7.49476e29i	−0.724402	−	0.225209i
$808$		0			0
$809$			1.64561e30i			0.481801i	0.970550	+	0.240901i	$0.0774428\pi$
$809$			1.64561e30i			0.481801i	−0.970550	+	0.240901i	$0.922557\pi$
$810$		0			0
$811$		−	3.93458e30i		−	1.12248i	−0.827652	−	0.561241i	$-0.810324\pi$
$811$		−	3.93458e30i		−	1.12248i	0.827652	−	0.561241i	$-0.189676\pi$
$812$		0			0
$813$	4.00562e29	+	1.24530e29i	0.111357	+	0.0346198i
$814$		0			0
$815$	9.12855e30			2.47313
$816$		0			0
$817$	−2.14628e29			−0.0566702
$818$		0			0
$819$	8.24222e29	−	1.19747e30i	0.212111	−	0.308164i
$820$		0			0
$821$		−	1.85981e28i		−	0.00466515i	−0.999997	−	0.00233257i	$-0.999258\pi$
$821$		−	1.85981e28i		−	0.00466515i	0.999997	−	0.00233257i	$-0.000742482\pi$
$822$		0			0
$823$			2.35040e29i			0.0574702i	0.999587	+	0.0287351i	$0.00914792\pi$
$823$			2.35040e29i			0.0574702i	−0.999587	+	0.0287351i	$0.990852\pi$
$824$		0			0
$825$	−1.94313e30	+	6.25022e30i	−0.463164	+	1.48980i
$826$		0			0
$827$	2.97803e30			0.692025			0.346012	−	0.938230i	$-0.387536\pi$
$827$	2.97803e30			0.692025			0.346012	+	0.938230i	$0.387536\pi$
$828$		0			0
$829$	1.27916e30			0.289803			0.144902	−	0.989446i	$-0.453713\pi$
$829$	1.27916e30			0.289803			0.144902	+	0.989446i	$0.453713\pi$
$830$		0			0
$831$	1.06199e30	−	3.41596e30i	0.234589	−	0.754574i
$832$		0			0
$833$		−	1.83466e31i		−	3.95168i
$834$		0			0
$835$		−	1.16495e31i		−	2.44680i
$836$		0			0
$837$	−2.12418e30	−	2.70029e30i	−0.435084	−	0.553086i
$838$		0			0
$839$	−3.30738e30			−0.660668			−0.330334	−	0.943864i	$-0.607161\pi$
$839$	−3.30738e30			−0.660668			−0.330334	+	0.943864i	$0.607161\pi$
$840$		0			0
$841$	−4.54335e30			−0.885154
$842$		0			0
$843$	2.67448e30	+	8.31468e29i	0.508218	+	0.158000i
$844$		0			0
$845$			8.41718e30i			1.56017i
$846$		0			0
$847$			1.08086e30i			0.195430i
$848$		0			0
$849$	−4.77831e30	−	1.48553e30i	−0.842837	−	0.262029i
$850$		0			0
$851$	−4.95173e30			−0.852112
$852$		0			0
$853$	9.54603e30			1.60272			0.801361	−	0.598182i	$-0.204110\pi$
$853$	9.54603e30			1.60272			0.801361	+	0.598182i	$0.204110\pi$
$854$		0			0
$855$	2.89551e30	+	1.99299e30i	0.474331	+	0.326484i
$856$		0			0
$857$			6.28873e30i			1.00523i	0.864511	+	0.502614i	$0.167628\pi$
$857$			6.28873e30i			1.00523i	−0.864511	+	0.502614i	$0.832372\pi$
$858$		0			0
$859$		−	6.97554e30i		−	1.08805i	−0.839069	−	0.544026i	$-0.816899\pi$
$859$		−	6.97554e30i		−	1.08805i	0.839069	−	0.544026i	$-0.183101\pi$
$860$		0			0
$861$	−8.09578e29	+	2.60407e30i	−0.123233	+	0.396387i
$862$		0			0
$863$	−1.06325e31			−1.57951			−0.789755	−	0.613422i	$-0.789793\pi$
$863$	−1.06325e31			−1.57951			−0.789755	+	0.613422i	$0.789793\pi$
$864$		0			0
$865$	9.03286e30			1.30965
$866$		0			0
$867$	−3.81113e30	+	1.22588e31i	−0.539328	+	1.73479i
$868$		0			0
$869$		−	1.30970e31i		−	1.80911i
$870$		0			0
$871$			1.04685e30i			0.141154i
$872$		0			0
$873$	9.14016e30	+	6.29122e30i	1.20311	+	0.828104i
$874$		0			0
$875$	1.50993e31			1.94031
$876$		0			0
$877$	−9.26733e30			−1.16268			−0.581338	−	0.813662i	$-0.697471\pi$
$877$	−9.26733e30			−1.16268			−0.581338	+	0.813662i	$0.697471\pi$
$878$		0			0
$879$	−7.03815e30	−	2.18809e30i	−0.862135	−	0.268029i
$880$		0			0
$881$		−	5.29699e29i		−	0.0633552i	−0.999498	−	0.0316776i	$-0.989915\pi$
$881$		−	5.29699e29i		−	0.0633552i	0.999498	−	0.0316776i	$-0.0100850\pi$
$882$		0			0
$883$			1.17325e31i			1.37026i	0.728421	+	0.685130i	$0.240254\pi$
$883$			1.17325e31i			1.37026i	−0.728421	+	0.685130i	$0.759746\pi$
$884$		0			0
$885$	5.22412e29	+	1.62412e29i	0.0595811	+	0.0185231i
$886$		0			0
$887$	−3.21463e30			−0.358041			−0.179020	−	0.983845i	$-0.557293\pi$
$887$	−3.21463e30			−0.358041			−0.179020	+	0.983845i	$0.557293\pi$
$888$		0			0
$889$	4.47550e30			0.486826
$890$		0			0
$891$	3.17664e30	+	8.30992e30i	0.337483	+	0.882838i
$892$		0			0
$893$		−	2.49835e30i		−	0.259247i
$894$		0			0
$895$		−	1.47871e30i		−	0.149879i
$896$		0			0
$897$	6.07570e29	−	1.95430e30i	0.0601556	−	0.193495i
$898$		0			0
$899$	−9.98945e30			−0.966195
$900$		0			0
$901$	−1.96053e31			−1.85252
$902$		0			0
$903$	−9.43736e29	+	3.03560e30i	−0.0871222	+	0.280236i
$904$		0			0
$905$		−	7.09144e30i		−	0.639624i
$906$		0			0
$907$			1.03172e31i			0.909251i	0.890683	+	0.454626i	$0.150227\pi$
$907$			1.03172e31i			0.909251i	−0.890683	+	0.454626i	$0.849773\pi$
$908$		0			0
$909$	−6.85953e30	+	9.96584e30i	−0.590709	+	0.858209i
$910$		0			0
$911$	1.92471e31			1.61966			0.809829	−	0.586666i	$-0.199560\pi$
$911$	1.92471e31			1.61966			0.809829	+	0.586666i	$0.199560\pi$
$912$		0			0
$913$	1.29376e31			1.06393
$914$		0			0
$915$	5.70227e29	+	1.77277e29i	0.0458275	+	0.0142473i
$916$		0			0
$917$			3.23597e31i			2.54172i
$918$		0			0
$919$			1.58189e31i			1.21441i	0.794546	+	0.607204i	$0.207709\pi$
$919$			1.58189e31i			1.21441i	−0.794546	+	0.607204i	$0.792291\pi$
$920$		0			0
$921$	−1.70699e31	−	5.30685e30i	−1.28087	−	0.398208i
$922$		0			0
$923$	1.36633e30			0.100216
$924$		0			0
$925$	−1.97753e31			−1.41787
$926$		0			0
$927$	1.17777e31	−	1.71112e31i	0.825512	−	1.19934i
$928$		0			0
$929$			1.61527e31i			1.10683i	0.832906	+	0.553414i	$0.186675\pi$
$929$			1.61527e31i			1.10683i	−0.832906	+	0.553414i	$0.813325\pi$
$930$		0			0
$931$			1.24308e31i			0.832776i
$932$		0			0
$933$	4.39595e30	−	1.41399e31i	0.287936	−	0.926168i
$934$		0			0
$935$	4.03245e31			2.58254
$936$		0			0
$937$	−2.33084e31			−1.45964			−0.729822	−	0.683637i	$-0.760397\pi$
$937$	−2.33084e31			−1.45964			−0.729822	+	0.683637i	$0.760397\pi$
$938$		0			0
$939$	−1.07065e30	+	3.44384e30i	−0.0655632	+	0.210889i
$940$		0			0
$941$		−	9.65228e30i		−	0.578015i	−0.957327	−	0.289007i	$-0.906675\pi$
$941$		−	9.65228e30i		−	0.578015i	0.957327	−	0.289007i	$-0.0933252\pi$
$942$		0			0
$943$			3.83915e30i			0.224834i
$944$		0			0
$945$	4.09198e31	−	3.21895e31i	2.34369	−	1.84366i
$946$		0			0
$947$	−1.47142e31			−0.824258			−0.412129	−	0.911125i	$-0.635215\pi$
$947$	−1.47142e31			−0.824258			−0.412129	+	0.911125i	$0.635215\pi$
$948$		0			0
$949$	4.35726e30			0.238736
$950$		0			0
$951$	−1.23067e30	−	3.82602e29i	−0.0659548	−	0.0205046i
$952$		0			0
$953$			2.06433e31i			1.08219i	0.840961	+	0.541096i	$0.181990\pi$
$953$			2.06433e31i			1.08219i	−0.840961	+	0.541096i	$0.818010\pi$
$954$		0			0
$955$			5.80061e31i			2.97466i
$956$		0			0
$957$	2.47009e31	+	7.67924e30i	1.23919	+	0.385250i
$958$		0			0
$959$	−2.95874e31			−1.45215
$960$		0			0
$961$	1.05127e31			0.504798
$962$		0			0
$963$	2.12285e31	+	1.46117e31i	0.997342	+	0.686475i
$964$		0			0
$965$		−	1.83810e31i		−	0.844951i
$966$		0			0
$967$		−	1.75379e31i		−	0.788860i	−0.918926	−	0.394430i	$-0.870942\pi$
$967$		−	1.75379e31i		−	0.788860i	0.918926	−	0.394430i	$-0.129058\pi$
$968$		0			0
$969$	4.00365e30	−	1.28781e31i	0.176221	−	0.566828i
$970$		0			0
$971$	−1.39045e31			−0.598899			−0.299449	−	0.954112i	$-0.596803\pi$
$971$	−1.39045e31			−0.598899			−0.299449	+	0.954112i	$0.596803\pi$
$972$		0			0
$973$	4.65414e31			1.96180
$974$		0			0
$975$	2.42640e30	−	7.80471e30i	0.100095	−	0.321965i
$976$		0			0
$977$		−	2.26862e31i		−	0.915942i	−0.888967	−	0.457971i	$-0.848576\pi$
$977$		−	2.26862e31i		−	0.915942i	0.888967	−	0.457971i	$-0.151424\pi$
$978$		0			0
$979$		−	3.60803e31i		−	1.42578i
$980$		0			0
$981$	1.16835e30	+	8.04181e29i	0.0451907	+	0.0311049i
$982$		0			0
$983$	−4.70993e31			−1.78321			−0.891606	−	0.452813i	$-0.850421\pi$
$983$	−4.70993e31			−1.78321			−0.891606	+	0.452813i	$0.850421\pi$
$984$		0			0
$985$	−4.82883e31			−1.78962
$986$		0			0
$987$	−3.53356e31	−	1.09855e31i	−1.28198	−	0.398555i
$988$		0			0
$989$			4.47535e30i			0.158952i
$990$		0			0
$991$			1.02957e31i			0.357999i	0.983849	+	0.179000i	$0.0572861\pi$
$991$			1.02957e31i			0.357999i	−0.983849	+	0.179000i	$0.942714\pi$
$992$		0			0
$993$	3.66636e31	+	1.13983e31i	1.24815	+	0.388037i
$994$		0			0
$995$	5.65210e31			1.88394
$996$		0			0
$997$	−4.94089e31			−1.61252			−0.806262	−	0.591558i	$-0.798513\pi$
$997$	−4.94089e31			−1.61252			−0.806262	+	0.591558i	$0.798513\pi$
$998$		0			0
$999$	−2.11256e31	+	1.66184e31i	−0.675105	+	0.531070i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.22.c.b.47.7	yes	12
3.2	odd	2	inner	48.22.c.b.47.5	✓	12
4.3	odd	2	inner	48.22.c.b.47.6	yes	12
12.11	even	2	inner	48.22.c.b.47.8	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.22.c.b.47.5	✓	12	3.2	odd	2	inner
48.22.c.b.47.6	yes	12	4.3	odd	2	inner
48.22.c.b.47.7	yes	12	1.1	even	1	trivial
48.22.c.b.47.8	yes	12	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	48.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(30363.0 - 97665.0i) q^{3} -3.55520e7i q^{5} -1.36883e9i q^{7} +(-8.61653e9 - 5.93080e9i) q^{9} +O(q^{10})\)	\(q+(30363.0 - 97665.0i) q^{3} -3.55520e7i q^{5} -1.36883e9i q^{7} +(-8.61653e9 - 5.93080e9i) q^{9} +8.13058e10 q^{11} -1.01527e11 q^{13} +(-3.47219e12 - 1.07947e12i) q^{15} +1.39503e13i q^{17} -9.45210e12i q^{19} +(-1.33686e14 - 4.15616e13i) q^{21} -1.97092e14 q^{23} -7.87110e14 q^{25} +(-8.40855e14 + 6.61456e14i) q^{27} +3.11066e15i q^{29} +3.21136e15i q^{31} +(2.46869e15 - 7.94072e15i) q^{33} -4.86645e16 q^{35} +2.51240e16 q^{37} +(-3.08267e15 + 9.91566e15i) q^{39} -1.94790e16i q^{41} -2.27069e16i q^{43} +(-2.10852e17 + 3.06335e17i) q^{45} +2.64317e17 q^{47} -1.31514e18 q^{49} +(1.36245e18 + 4.23573e17i) q^{51} +1.40537e18i q^{53} -2.89059e18i q^{55} +(-9.23139e17 - 2.86994e17i) q^{57} -1.50456e17 q^{59} -1.64227e17 q^{61} +(-8.11823e18 + 1.17945e19i) q^{63} +3.60950e18i q^{65} -1.03110e19i q^{67} +(-5.98430e18 + 1.92490e19i) q^{69} -1.34577e19 q^{71} -4.29171e19 q^{73} +(-2.38990e19 + 7.68731e19i) q^{75} -1.11293e20i q^{77} -1.61084e20i q^{79} +(3.90703e19 + 1.02206e20i) q^{81} +1.59123e20 q^{83} +4.95961e20 q^{85} +(3.03802e20 + 9.44489e19i) q^{87} -4.43760e20i q^{89} +1.38973e20i q^{91} +(3.13637e20 + 9.75065e19i) q^{93} -3.36042e20 q^{95} -1.06077e21 q^{97} +(-7.00574e20 - 4.82208e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6223178268 q^{9}+O(q^{10}) \) 12 * q + 6223178268 * q^9	\( 12 q + 6223178268 q^{9} - 1558099630680 q^{13} - 467668605656952 q^{21} - 23\!\cdots\!04 q^{25}+ \cdots - 47\!\cdots\!00 q^{97}+O(q^{100}) \) 12 * q + 6223178268 * q^9 - 1558099630680 * q^13 - 467668605656952 * q^21 - 2333948474211204 * q^25 - 2878569233493120 * q^33 + 198571664231829960 * q^37 - 520853659458386688 * q^45 - 1537469097010171836 * q^49 + 8983812160349471160 * q^57 + 18823450709508882792 * q^61 - 13723185548090697984 * q^69 - 141762419773124388360 * q^73 - 221765489935045328916 * q^81 + 938387558833131211776 * q^85 + 1143752665751371267560 * q^93 - 4719945853939671321000 * q^97

Introduction

L-functions

Modular forms

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Database

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