LMFDB - Embedded newform 48.11.e.d.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,11,Mod(17,48)]

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([0, 0, 1]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("48.17");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	48.e (of order $2$, degree $1$, not 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:	$30.4971481283$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{85})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 37x^{2} + 38x + 531 $ x^4 - 2x^3 - 37x^2 + 38*x + 531
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			17.1
Root			$5.10977 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	48.17
Dual form			48.11.e.d.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-242.269 - 18.8335i) q^{3} +4818.41i q^{5} -670.530 q^{7} +(58339.6 + 9125.53i) q^{9} +O(q^{10})$	\(q+(-242.269 - 18.8335i) q^{3} +4818.41i q^{5} -670.530 q^{7} +(58339.6 + 9125.53i) q^{9} +233268. i q^{11} +307781. q^{13} +(90747.4 - 1.16735e6i) q^{15} -672324. i q^{17} +1.55119e6 q^{19} +(162449. + 12628.4i) q^{21} +5.57551e6i q^{23} -1.34515e7 q^{25} +(-1.39620e7 - 3.30957e6i) q^{27} +2.97313e7i q^{29} -3.09368e7 q^{31} +(4.39325e6 - 5.65137e7i) q^{33} -3.23089e6i q^{35} -8.56690e7 q^{37} +(-7.45657e7 - 5.79657e6i) q^{39} -3.59054e7i q^{41} +3.66253e7 q^{43} +(-4.39706e7 + 2.81104e8i) q^{45} +3.28877e7i q^{47} -2.82026e8 q^{49} +(-1.26622e7 + 1.62883e8i) q^{51} -4.59194e8i q^{53} -1.12398e9 q^{55} +(-3.75805e8 - 2.92143e7i) q^{57} -4.88657e8i q^{59} -6.12928e7 q^{61} +(-3.91184e7 - 6.11894e6i) q^{63} +1.48301e9i q^{65} +6.70776e8 q^{67} +(1.05006e8 - 1.35077e9i) q^{69} +1.23330e9i q^{71} +1.08126e9 q^{73} +(3.25888e9 + 2.53338e8i) q^{75} -1.56413e8i q^{77} +1.86628e9 q^{79} +(3.32023e9 + 1.06476e9i) q^{81} -1.09562e9i q^{83} +3.23953e9 q^{85} +(5.59944e8 - 7.20298e9i) q^{87} -5.19876e9i q^{89} -2.06376e8 q^{91} +(7.49503e9 + 5.82647e8i) q^{93} +7.47427e9i q^{95} -1.07471e10 q^{97} +(-2.12870e9 + 1.36088e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 84 q^{3} + 45112 q^{7} + 159012 q^{9}+O(q^{10}) $ 4 * q - 84 * q^3 + 45112 * q^7 + 159012 * q^9	$ 4 q - 84 q^{3} + 45112 q^{7} + 159012 q^{9} + 275240 q^{13} + 1180800 q^{15} + 1568728 q^{19} + 9628008 q^{21} - 33732380 q^{25} - 34619508 q^{27} + 21785848 q^{31} + 25974144 q^{33} - 71014168 q^{37} - 217287240 q^{39} + 470688664 q^{43} + 312318720 q^{45} - 50058420 q^{49} + 708576768 q^{51} - 2701359360 q^{55} - 1058753208 q^{57} - 1184038744 q^{61} + 905007096 q^{63} + 297365848 q^{67} + 596268288 q^{69} + 6534269000 q^{73} + 5150031180 q^{75} - 199282568 q^{79} + 1458964548 q^{81} - 12880512000 q^{85} - 210268800 q^{87} - 8317232080 q^{91} + 31744468392 q^{93} - 39176355064 q^{97} + 2626912512 q^{99}+O(q^{100}) $ 4 * q - 84 * q^3 + 45112 * q^7 + 159012 * q^9 + 275240 * q^13 + 1180800 * q^15 + 1568728 * q^19 + 9628008 * q^21 - 33732380 * q^25 - 34619508 * q^27 + 21785848 * q^31 + 25974144 * q^33 - 71014168 * q^37 - 217287240 * q^39 + 470688664 * q^43 + 312318720 * q^45 - 50058420 * q^49 + 708576768 * q^51 - 2701359360 * q^55 - 1058753208 * q^57 - 1184038744 * q^61 + 905007096 * q^63 + 297365848 * q^67 + 596268288 * q^69 + 6534269000 * q^73 + 5150031180 * q^75 - 199282568 * q^79 + 1458964548 * q^81 - 12880512000 * q^85 - 210268800 * q^87 - 8317232080 * q^91 + 31744468392 * q^93 - 39176355064 * q^97 + 2626912512 * q^99

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
$3$	−242.269	−	18.8335i	−0.996992	−	0.0775039i
$3$	−242.269	−	18.8335i	−0.996992	−	0.0775039i
$4$		0			0
$5$			4818.41i			1.54189i	0.636900	+	0.770946i	$0.280216\pi$
$5$			4818.41i			1.54189i	−0.636900	+	0.770946i	$0.719784\pi$
$6$		0			0
$7$	−670.530			−0.0398959			−0.0199479	−	0.999801i	$-0.506350\pi$
$7$	−670.530			−0.0398959			−0.0199479	+	0.999801i	$0.506350\pi$
$8$		0			0
$9$	58339.6	+	9125.53i	0.987986	+	0.154542i
$10$		0			0
$11$			233268.i			1.44841i	0.689583	+	0.724206i	$0.257794\pi$
$11$			233268.i			1.44841i	−0.689583	+	0.724206i	$0.742206\pi$
$12$		0			0
$13$	307781.			0.828943			0.414471	−	0.910062i	$-0.363967\pi$
$13$	307781.			0.828943			0.414471	+	0.910062i	$0.363967\pi$
$14$		0			0
$15$	90747.4	−	1.16735e6i	0.119503	−	1.53725i
$16$		0			0
$17$		−	672324.i		−	0.473515i	−0.971569	−	0.236758i	$-0.923915\pi$
$17$		−	672324.i		−	0.473515i	0.971569	−	0.236758i	$-0.0760847\pi$
$18$		0			0
$19$	1.55119e6			0.626465			0.313233	−	0.949676i	$-0.398588\pi$
$19$	1.55119e6			0.626465			0.313233	+	0.949676i	$0.398588\pi$
$20$		0			0
$21$	162449.	+	12628.4i	0.0397758	+	0.00309209i
$22$		0			0
$23$			5.57551e6i			0.866255i	0.901333	+	0.433127i	$0.142590\pi$
$23$			5.57551e6i			0.866255i	−0.901333	+	0.433127i	$0.857410\pi$
$24$		0			0
$25$	−1.34515e7			−1.37743
$26$		0			0
$27$	−1.39620e7	−	3.30957e6i	−0.973037	−	0.230650i
$28$		0			0
$29$			2.97313e7i			1.44952i	0.689001	+	0.724760i	$0.258049\pi$
$29$			2.97313e7i			1.44952i	−0.689001	+	0.724760i	$0.741951\pi$
$30$		0			0
$31$	−3.09368e7			−1.08061			−0.540303	−	0.841471i	$-0.681690\pi$
$31$	−3.09368e7			−1.08061			−0.540303	+	0.841471i	$0.681690\pi$
$32$		0			0
$33$	4.39325e6	−	5.65137e7i	0.112258	−	1.44406i
$34$		0			0
$35$		−	3.23089e6i		−	0.0615151i
$36$		0			0
$37$	−8.56690e7			−1.23542			−0.617711	−	0.786406i	$-0.711940\pi$
$37$	−8.56690e7			−1.23542			−0.617711	+	0.786406i	$0.711940\pi$
$38$		0			0
$39$	−7.45657e7	−	5.79657e6i	−0.826449	−	0.0642463i
$40$		0			0
$41$		−	3.59054e7i		−	0.309913i	−0.987921	−	0.154957i	$-0.950476\pi$
$41$		−	3.59054e7i		−	0.309913i	0.987921	−	0.154957i	$-0.0495238\pi$
$42$		0			0
$43$	3.66253e7			0.249137			0.124569	−	0.992211i	$-0.460245\pi$
$43$	3.66253e7			0.249137			0.124569	+	0.992211i	$0.460245\pi$
$44$		0			0
$45$	−4.39706e7	+	2.81104e8i	−0.238287	+	1.52337i
$46$		0			0
$47$			3.28877e7i			0.143398i	0.997426	+	0.0716992i	$0.0228421\pi$
$47$			3.28877e7i			0.143398i	−0.997426	+	0.0716992i	$0.977158\pi$
$48$		0			0
$49$	−2.82026e8			−0.998408
$50$		0			0
$51$	−1.26622e7	+	1.62883e8i	−0.0366993	+	0.472091i
$52$		0			0
$53$		−	4.59194e8i		−	1.09804i	−0.835810	−	0.549019i	$-0.815002\pi$
$53$		−	4.59194e8i		−	1.09804i	0.835810	−	0.549019i	$-0.184998\pi$
$54$		0			0
$55$	−1.12398e9			−2.23330
$56$		0			0
$57$	−3.75805e8	−	2.92143e7i	−0.624581	−	0.0485535i
$58$		0			0
$59$		−	4.88657e8i		−	0.683508i	−0.939789	−	0.341754i	$-0.888979\pi$
$59$		−	4.88657e8i		−	0.683508i	0.939789	−	0.341754i	$-0.111021\pi$
$60$		0			0
$61$	−6.12928e7			−0.0725705			−0.0362852	−	0.999341i	$-0.511552\pi$
$61$	−6.12928e7			−0.0725705			−0.0362852	+	0.999341i	$0.511552\pi$
$62$		0			0
$63$	−3.91184e7	−	6.11894e6i	−0.0394166	−	0.00616557i
$64$		0			0
$65$			1.48301e9i			1.27814i
$66$		0			0
$67$	6.70776e8			0.496825			0.248413	−	0.968654i	$-0.420091\pi$
$67$	6.70776e8			0.496825			0.248413	+	0.968654i	$0.420091\pi$
$68$		0			0
$69$	1.05006e8	−	1.35077e9i	0.0671382	−	0.863649i
$70$		0			0
$71$			1.23330e9i			0.683561i	0.939780	+	0.341781i	$0.111030\pi$
$71$			1.23330e9i			0.683561i	−0.939780	+	0.341781i	$0.888970\pi$
$72$		0			0
$73$	1.08126e9			0.521573			0.260787	−	0.965396i	$-0.416018\pi$
$73$	1.08126e9			0.521573			0.260787	+	0.965396i	$0.416018\pi$
$74$		0			0
$75$	3.25888e9	+	2.53338e8i	1.37329	+	0.106756i
$76$		0			0
$77$		−	1.56413e8i		−	0.0577857i
$78$		0			0
$79$	1.86628e9			0.606515			0.303258	−	0.952909i	$-0.401926\pi$
$79$	1.86628e9			0.606515			0.303258	+	0.952909i	$0.401926\pi$
$80$		0			0
$81$	3.32023e9	+	1.06476e9i	0.952234	+	0.305370i
$82$		0			0
$83$		−	1.09562e9i		−	0.278145i	−0.990282	−	0.139072i	$-0.955588\pi$
$83$		−	1.09562e9i		−	0.278145i	0.990282	−	0.139072i	$-0.0444121\pi$
$84$		0			0
$85$	3.23953e9			0.730109
$86$		0			0
$87$	5.59944e8	−	7.20298e9i	0.112344	−	1.44516i
$88$		0			0
$89$		−	5.19876e9i		−	0.931000i	−0.885048	−	0.465500i	$-0.845874\pi$
$89$		−	5.19876e9i		−	0.931000i	0.885048	−	0.465500i	$-0.154126\pi$
$90$		0			0
$91$	−2.06376e8			−0.0330714
$92$		0			0
$93$	7.49503e9	+	5.82647e8i	1.07735	+	0.0837512i
$94$		0			0
$95$			7.47427e9i			0.965941i
$96$		0			0
$97$	−1.07471e10			−1.25150			−0.625750	−	0.780024i	$-0.715207\pi$
$97$	−1.07471e10			−1.25150			−0.625750	+	0.780024i	$0.715207\pi$
$98$		0			0
$99$	−2.12870e9	+	1.36088e10i	−0.223840	+	1.43101i
$100$		0			0
$101$			1.08154e10i			1.02905i	0.857475	+	0.514525i	$0.172032\pi$
$101$			1.08154e10i			1.02905i	−0.857475	+	0.514525i	$0.827968\pi$
$102$		0			0
$103$	2.83446e9			0.244503			0.122251	−	0.992499i	$-0.460989\pi$
$103$	2.83446e9			0.244503			0.122251	+	0.992499i	$0.460989\pi$
$104$		0			0
$105$	−6.08488e7	+	7.82744e8i	−0.00476766	+	0.0613301i
$106$		0			0
$107$		−	2.41202e10i		−	1.71974i	−0.510515	−	0.859869i	$-0.670545\pi$
$107$		−	2.41202e10i		−	1.71974i	0.510515	−	0.859869i	$-0.329455\pi$
$108$		0			0
$109$	−5.43424e9			−0.353188			−0.176594	−	0.984284i	$-0.556508\pi$
$109$	−5.43424e9			−0.353188			−0.176594	+	0.984284i	$0.556508\pi$
$110$		0			0
$111$	2.07549e10	+	1.61344e9i	1.23170	+	0.0957500i
$112$		0			0
$113$		−	1.39305e10i		−	0.756092i	−0.925787	−	0.378046i	$-0.876596\pi$
$113$		−	1.39305e10i		−	0.756092i	0.925787	−	0.378046i	$-0.123404\pi$
$114$		0			0
$115$	−2.68651e10			−1.33567
$116$		0			0
$117$	1.79558e10	+	2.80866e9i	0.818984	+	0.128106i
$118$		0			0
$119$			4.50813e8i			0.0188913i
$120$		0			0
$121$	−2.84767e10			−1.09790
$122$		0			0
$123$	−6.76223e8	+	8.69877e9i	−0.0240195	+	0.308981i
$124$		0			0
$125$		−	1.77600e10i		−	0.581958i
$126$		0			0
$127$	−4.08412e10			−1.23617			−0.618087	−	0.786110i	$-0.712092\pi$
$127$	−4.08412e10			−1.23617			−0.618087	+	0.786110i	$0.712092\pi$
$128$		0			0
$129$	−8.87317e9	−	6.89781e8i	−0.248388	−	0.0193091i
$130$		0			0
$131$			4.15498e10i			1.07699i	0.842628	+	0.538495i	$0.181007\pi$
$131$			4.15498e10i			1.07699i	−0.842628	+	0.538495i	$0.818993\pi$
$132$		0			0
$133$	−1.04012e9			−0.0249934
$134$		0			0
$135$	1.59469e10	−	6.72748e10i	0.355637	−	1.50032i
$136$		0			0
$137$			9.25532e10i			1.91773i	0.283854	+	0.958867i	$0.408387\pi$
$137$			9.25532e10i			1.91773i	−0.283854	+	0.958867i	$0.591613\pi$
$138$		0			0
$139$	−7.95575e10			−1.53323			−0.766615	−	0.642107i	$-0.778061\pi$
$139$	−7.95575e10			−1.53323			−0.766615	+	0.642107i	$0.778061\pi$
$140$		0			0
$141$	6.19389e8	−	7.96767e9i	0.0111139	−	0.142967i
$142$		0			0
$143$			7.17955e10i			1.20065i
$144$		0			0
$145$	−1.43258e11			−2.23500
$146$		0			0
$147$	6.83261e10	+	5.31152e9i	0.995405	+	0.0773806i
$148$		0			0
$149$		−	8.07804e10i		−	1.09995i	−0.835180	−	0.549977i	$-0.814636\pi$
$149$		−	8.07804e10i		−	1.09995i	0.835180	−	0.549977i	$-0.185364\pi$
$150$		0			0
$151$	−3.08654e10			−0.393176			−0.196588	−	0.980486i	$-0.562986\pi$
$151$	−3.08654e10			−0.393176			−0.196588	+	0.980486i	$0.562986\pi$
$152$		0			0
$153$	6.13531e9	−	3.92231e10i	0.0731778	−	0.467827i
$154$		0			0
$155$		−	1.49066e11i		−	1.66618i
$156$		0			0
$157$	9.71322e10			1.01828			0.509138	−	0.860685i	$-0.329964\pi$
$157$	9.71322e10			1.01828			0.509138	+	0.860685i	$0.329964\pi$
$158$		0			0
$159$	−8.64822e9	+	1.11249e11i	−0.0851023	+	1.09473i
$160$		0			0
$161$		−	3.73855e9i		−	0.0345600i
$162$		0			0
$163$	1.39440e11			1.21185			0.605927	−	0.795520i	$-0.292802\pi$
$163$	1.39440e11			1.21185			0.605927	+	0.795520i	$0.292802\pi$
$164$		0			0
$165$	2.72306e11	+	2.11685e10i	2.22658	+	0.173089i
$166$		0			0
$167$		−	1.25840e11i		−	0.968804i	−0.874845	−	0.484402i	$-0.839037\pi$
$167$		−	1.25840e11i		−	0.968804i	0.874845	−	0.484402i	$-0.160963\pi$
$168$		0			0
$169$	−4.31296e10			−0.312854
$170$		0			0
$171$	9.04958e10	+	1.41554e10i	0.618939	+	0.0968149i
$172$		0			0
$173$			1.26257e11i			0.814750i	0.913261	+	0.407375i	$0.133556\pi$
$173$			1.26257e11i			0.814750i	−0.913261	+	0.407375i	$0.866444\pi$
$174$		0			0
$175$	9.01961e9			0.0549538
$176$		0			0
$177$	−9.20310e9	+	1.18386e11i	−0.0529746	+	0.681452i
$178$		0			0
$179$			2.96543e11i			1.61370i	0.590758	+	0.806848i	$0.298829\pi$
$179$			2.96543e11i			1.61370i	−0.590758	+	0.806848i	$0.701171\pi$
$180$		0			0
$181$	2.48451e11			1.27893			0.639466	−	0.768819i	$-0.279155\pi$
$181$	2.48451e11			1.27893			0.639466	+	0.768819i	$0.279155\pi$
$182$		0			0
$183$	1.48493e10	+	1.15435e9i	0.0723522	+	0.00562450i
$184$		0			0
$185$		−	4.12789e11i		−	1.90489i
$186$		0			0
$187$	1.56832e11			0.685846
$188$		0			0
$189$	9.36194e9	+	2.21916e9i	0.0388201	+	0.00920196i
$190$		0			0
$191$		−	1.58050e11i		−	0.621769i	−0.950448	−	0.310884i	$-0.899375\pi$
$191$		−	1.58050e11i		−	0.621769i	0.950448	−	0.310884i	$-0.100625\pi$
$192$		0			0
$193$	−3.78369e11			−1.41296			−0.706479	−	0.707734i	$-0.749717\pi$
$193$	−3.78369e11			−1.41296			−0.706479	+	0.707734i	$0.749717\pi$
$194$		0			0
$195$	2.79303e10	−	3.59288e11i	0.0990609	−	1.27430i
$196$		0			0
$197$			1.89406e11i			0.638356i	0.947695	+	0.319178i	$0.103407\pi$
$197$			1.89406e11i			0.638356i	−0.947695	+	0.319178i	$0.896593\pi$
$198$		0			0
$199$	−5.02942e10			−0.161158			−0.0805791	−	0.996748i	$-0.525677\pi$
$199$	−5.02942e10			−0.161158			−0.0805791	+	0.996748i	$0.525677\pi$
$200$		0			0
$201$	−1.62508e11	−	1.26330e10i	−0.495331	−	0.0385059i
$202$		0			0
$203$		−	1.99357e10i		−	0.0578298i
$204$		0			0
$205$	1.73007e11			0.477853
$206$		0			0
$207$	−5.08795e10	+	3.25273e11i	−0.133872	+	0.855848i
$208$		0			0
$209$			3.61843e11i			0.907380i
$210$		0			0
$211$	−4.74970e11			−1.13567			−0.567837	−	0.823141i	$-0.692220\pi$
$211$	−4.74970e11			−1.13567			−0.567837	+	0.823141i	$0.692220\pi$
$212$		0			0
$213$	2.32273e10	−	2.98791e11i	0.0529787	−	0.681505i
$214$		0			0
$215$			1.76476e11i			0.384143i
$216$		0			0
$217$	2.07440e10			0.0431117
$218$		0			0
$219$	−2.61955e11	−	2.03638e10i	−0.520004	−	0.0404240i
$220$		0			0
$221$		−	2.06928e11i		−	0.392517i
$222$		0			0
$223$	2.35580e11			0.427183			0.213592	−	0.976923i	$-0.431484\pi$
$223$	2.35580e11			0.427183			0.213592	+	0.976923i	$0.431484\pi$
$224$		0			0
$225$	−7.84754e11	−	1.22752e11i	−1.36088	−	0.212870i
$226$		0			0
$227$			4.27026e11i			0.708475i	0.935155	+	0.354238i	$0.115260\pi$
$227$			4.27026e11i			0.708475i	−0.935155	+	0.354238i	$0.884740\pi$
$228$		0			0
$229$	1.03671e12			1.64619			0.823096	−	0.567902i	$-0.192245\pi$
$229$	1.03671e12			1.64619			0.823096	+	0.567902i	$0.192245\pi$
$230$		0			0
$231$	−2.94580e9	+	3.78941e10i	−0.00447862	+	0.0576119i
$232$		0			0
$233$			1.03766e12i			1.51103i	0.655130	+	0.755516i	$0.272614\pi$
$233$			1.03766e12i			1.51103i	−0.655130	+	0.755516i	$0.727386\pi$
$234$		0			0
$235$	−1.58466e11			−0.221105
$236$		0			0
$237$	−4.52142e11	−	3.51485e10i	−0.604691	−	0.0470073i
$238$		0			0
$239$		−	1.23687e12i		−	1.58612i	−0.609144	−	0.793060i	$-0.708487\pi$
$239$		−	1.23687e12i		−	1.58612i	0.609144	−	0.793060i	$-0.291513\pi$
$240$		0			0
$241$	−1.03912e12			−1.27814			−0.639072	−	0.769147i	$-0.720682\pi$
$241$	−1.03912e12			−1.27814			−0.639072	+	0.769147i	$0.720682\pi$
$242$		0			0
$243$	−7.84337e11	−	3.20490e11i	−0.925702	−	0.378253i
$244$		0			0
$245$		−	1.35892e12i		−	1.53944i
$246$		0			0
$247$	4.77426e11			0.519304
$248$		0			0
$249$	−2.06344e10	+	2.65436e11i	−0.0215573	+	0.277308i
$250$		0			0
$251$			5.66781e11i			0.568914i	0.958689	+	0.284457i	$0.0918133\pi$
$251$			5.66781e11i			0.568914i	−0.958689	+	0.284457i	$0.908187\pi$
$252$		0			0
$253$	−1.30059e12			−1.25469
$254$		0			0
$255$	−7.84839e11	−	6.10116e10i	−0.727913	−	0.0565864i
$256$		0			0
$257$		−	1.27943e12i		−	1.14117i	−0.821239	−	0.570584i	$-0.806717\pi$
$257$		−	1.27943e12i		−	1.14117i	0.821239	−	0.570584i	$-0.193283\pi$
$258$		0			0
$259$	5.74436e10			0.0492882
$260$		0			0
$261$	−2.71314e11	+	1.73451e12i	−0.224011	+	1.43211i
$262$		0			0
$263$			1.68583e12i			1.33978i	0.742459	+	0.669892i	$0.233660\pi$
$263$			1.68583e12i			1.33978i	−0.742459	+	0.669892i	$0.766340\pi$
$264$		0			0
$265$	2.21259e12			1.69306
$266$		0			0
$267$	−9.79107e10	+	1.25950e12i	−0.0721562	+	0.928200i
$268$		0			0
$269$			1.34023e12i			0.951523i	0.879574	+	0.475761i	$0.157827\pi$
$269$			1.34023e12i			0.951523i	−0.879574	+	0.475761i	$0.842173\pi$
$270$		0			0
$271$	1.75349e12			1.19966			0.599829	−	0.800129i	$-0.295235\pi$
$271$	1.75349e12			1.19966			0.599829	+	0.800129i	$0.295235\pi$
$272$		0			0
$273$	4.99985e10	+	3.88677e9i	0.0329719	+	0.00256316i
$274$		0			0
$275$		−	3.13780e12i		−	1.99509i
$276$		0			0
$277$	1.69580e12			1.03986			0.519930	−	0.854209i	$-0.325958\pi$
$277$	1.69580e12			1.03986			0.519930	+	0.854209i	$0.325958\pi$
$278$		0			0
$279$	−1.80484e12	−	2.82315e11i	−1.06762	−	0.166999i
$280$		0			0
$281$		−	2.44175e11i		−	0.139370i	−0.997569	−	0.0696851i	$-0.977801\pi$
$281$		−	2.44175e11i		−	0.139370i	0.997569	−	0.0696851i	$-0.0221995\pi$
$282$		0			0
$283$	9.96409e11			0.548916			0.274458	−	0.961599i	$-0.411502\pi$
$283$	9.96409e11			0.548916			0.274458	+	0.961599i	$0.411502\pi$
$284$		0			0
$285$	1.40766e11	−	1.81078e12i	0.0748643	−	0.963036i
$286$		0			0
$287$			2.40756e10i			0.0123643i
$288$		0			0
$289$	1.56397e12			0.775783
$290$		0			0
$291$	2.60368e12	+	2.02404e11i	1.24774	+	0.0969962i
$292$		0			0
$293$			1.57571e12i			0.729690i	0.931068	+	0.364845i	$0.118878\pi$
$293$			1.57571e12i			0.729690i	−0.931068	+	0.364845i	$0.881122\pi$
$294$		0			0
$295$	2.35455e12			1.05390
$296$		0			0
$297$	7.72018e11	−	3.25690e12i	0.334076	−	1.40936i
$298$		0			0
$299$			1.71603e12i			0.718076i
$300$		0			0
$301$	−2.45583e10			−0.00993955
$302$		0			0
$303$	2.03692e11	−	2.62024e12i	0.0797554	−	1.02595i
$304$		0			0
$305$		−	2.95334e11i		−	0.111896i
$306$		0			0
$307$	3.29823e12			1.20945			0.604726	−	0.796434i	$-0.293283\pi$
$307$	3.29823e12			1.20945			0.604726	+	0.796434i	$0.293283\pi$
$308$		0			0
$309$	−6.86702e11	−	5.33827e10i	−0.243768	−	0.0189499i
$310$		0			0
$311$			1.67301e12i			0.575038i	0.957775	+	0.287519i	$0.0928304\pi$
$311$			1.67301e12i			0.575038i	−0.957775	+	0.287519i	$0.907170\pi$
$312$		0			0
$313$	1.73318e12			0.576930			0.288465	−	0.957490i	$-0.406855\pi$
$313$	1.73318e12			0.576930			0.288465	+	0.957490i	$0.406855\pi$
$314$		0			0
$315$	2.94836e10	−	1.88489e11i	0.00950664	−	0.0607761i
$316$		0			0
$317$			1.33100e12i			0.415798i	0.978150	+	0.207899i	$0.0666625\pi$
$317$			1.33100e12i			0.415798i	−0.978150	+	0.207899i	$0.933337\pi$
$318$		0			0
$319$	−6.93538e12			−2.09950
$320$		0			0
$321$	−4.54267e11	+	5.84358e12i	−0.133286	+	1.71456i
$322$		0			0
$323$		−	1.04290e12i		−	0.296641i
$324$		0			0
$325$	−4.14010e12			−1.14181
$326$		0			0
$327$	1.31655e12	+	1.02345e11i	0.352126	+	0.0273735i
$328$		0			0
$329$		−	2.20522e10i		−	0.00572100i
$330$		0			0
$331$	−4.71961e12			−1.18786			−0.593931	−	0.804516i	$-0.702425\pi$
$331$	−4.71961e12			−1.18786			−0.593931	+	0.804516i	$0.702425\pi$
$332$		0			0
$333$	−4.99789e12	−	7.81775e11i	−1.22058	−	0.190924i
$334$		0			0
$335$			3.23208e12i			0.766051i
$336$		0			0
$337$	4.15283e12			0.955422			0.477711	−	0.878517i	$-0.341467\pi$
$337$	4.15283e12			0.955422			0.477711	+	0.878517i	$0.341467\pi$
$338$		0			0
$339$	−2.62360e11	+	3.37493e12i	−0.0586001	+	0.753818i
$340$		0			0
$341$		−	7.21658e12i		−	1.56516i
$342$		0			0
$343$	3.78515e11			0.0797282
$344$		0			0
$345$	6.50859e12	+	5.05963e11i	1.33165	+	0.103520i
$346$		0			0
$347$		−	4.39939e12i		−	0.874470i	−0.899347	−	0.437235i	$-0.855958\pi$
$347$		−	4.39939e12i		−	0.874470i	0.899347	−	0.437235i	$-0.144042\pi$
$348$		0			0
$349$	−9.24002e12			−1.78462			−0.892310	−	0.451423i	$-0.850917\pi$
$349$	−9.24002e12			−1.78462			−0.892310	+	0.451423i	$0.850917\pi$
$350$		0			0
$351$	−4.29724e12	−	1.01862e12i	−0.806592	−	0.191195i
$352$		0			0
$353$		−	9.20733e11i		−	0.167981i	−0.996467	−	0.0839905i	$-0.973233\pi$
$353$		−	9.20733e11i		−	0.167981i	0.996467	−	0.0839905i	$-0.0267665\pi$
$354$		0			0
$355$	−5.94255e12			−1.05398
$356$		0			0
$357$	8.49037e9	−	1.09218e11i	0.00146415	−	0.0188345i
$358$		0			0
$359$		−	6.17595e12i		−	1.03569i	−0.855473	−	0.517847i	$-0.826733\pi$
$359$		−	6.17595e12i		−	1.03569i	0.855473	−	0.517847i	$-0.173267\pi$
$360$		0			0
$361$	−3.72488e12			−0.607542
$362$		0			0
$363$	6.89902e12	+	5.36315e11i	1.09460	+	0.0850916i
$364$		0			0
$365$			5.20995e12i			0.804209i
$366$		0			0
$367$	8.19379e12			1.23071			0.615353	−	0.788252i	$-0.289013\pi$
$367$	8.19379e12			1.23071			0.615353	+	0.788252i	$0.289013\pi$
$368$		0			0
$369$	3.27656e11	−	2.09471e12i	0.0478945	−	0.306190i
$370$		0			0
$371$			3.07903e11i			0.0438072i
$372$		0			0
$373$	−9.07322e12			−1.25666			−0.628329	−	0.777947i	$-0.716261\pi$
$373$	−9.07322e12			−1.25666			−0.628329	+	0.777947i	$0.716261\pi$
$374$		0			0
$375$	−3.34481e11	+	4.30269e12i	−0.0451041	+	0.580208i
$376$		0			0
$377$			9.15072e12i			1.20157i
$378$		0			0
$379$	−1.17817e13			−1.50665			−0.753324	−	0.657650i	$-0.771551\pi$
$379$	−1.17817e13			−1.50665			−0.753324	+	0.657650i	$0.771551\pi$
$380$		0			0
$381$	9.89455e12	+	7.69180e11i	1.23246	+	0.0958083i
$382$		0			0
$383$			6.82336e12i			0.827950i	0.910288	+	0.413975i	$0.135860\pi$
$383$			6.82336e12i			0.827950i	−0.910288	+	0.413975i	$0.864140\pi$
$384$		0			0
$385$	7.53664e11			0.0890993
$386$		0			0
$387$	2.13670e12	+	3.34225e11i	0.246144	+	0.0385021i
$388$		0			0
$389$		−	7.07814e11i		−	0.0794642i	−0.999210	−	0.0397321i	$-0.987350\pi$
$389$		−	7.07814e11i		−	0.0794642i	0.999210	−	0.0397321i	$-0.0126504\pi$
$390$		0			0
$391$	3.74855e12			0.410185
$392$		0			0
$393$	7.82526e11	−	1.00662e13i	0.0834710	−	1.07375i
$394$		0			0
$395$			8.99251e12i			0.935181i
$396$		0			0
$397$	1.26553e12			0.128328			0.0641639	−	0.997939i	$-0.479562\pi$
$397$	1.26553e12			0.128328			0.0641639	+	0.997939i	$0.479562\pi$
$398$		0			0
$399$	2.51989e11	+	1.95890e10i	0.0249182	+	0.00193708i
$400$		0			0
$401$		−	1.50259e13i		−	1.44917i	−0.689187	−	0.724583i	$-0.742032\pi$
$401$		−	1.50259e13i		−	1.44917i	0.689187	−	0.724583i	$-0.257968\pi$
$402$		0			0
$403$	−9.52175e12			−0.895760
$404$		0			0
$405$	−5.13045e12	+	1.59983e13i	−0.470848	+	1.46824i
$406$		0			0
$407$		−	1.99839e13i		−	1.78940i
$408$		0			0
$409$	−1.70362e12			−0.148852			−0.0744261	−	0.997227i	$-0.523712\pi$
$409$	−1.70362e12			−0.148852			−0.0744261	+	0.997227i	$0.523712\pi$
$410$		0			0
$411$	1.74310e12	−	2.24228e13i	0.148632	−	1.91197i
$412$		0			0
$413$			3.27659e11i			0.0272692i
$414$		0			0
$415$	5.27917e12			0.428869
$416$		0			0
$417$	1.92743e13	+	1.49834e12i	1.52862	+	0.118831i
$418$		0			0
$419$			2.22448e13i			1.72250i	0.508185	+	0.861248i	$0.330317\pi$
$419$			2.22448e13i			1.72250i	−0.508185	+	0.861248i	$0.669683\pi$
$420$		0			0
$421$	1.82948e11			0.0138330			0.00691650	−	0.999976i	$-0.497798\pi$
$421$	1.82948e11			0.0138330			0.00691650	+	0.999976i	$0.497798\pi$
$422$		0			0
$423$	−3.00118e11	+	1.91865e12i	−0.0221610	+	0.141676i
$424$		0			0
$425$			9.04375e12i			0.652235i
$426$		0			0
$427$	4.10986e10			0.00289526
$428$		0			0
$429$	1.35216e12	−	1.73938e13i	0.0930552	−	1.19704i
$430$		0			0
$431$			6.64491e12i			0.446789i	0.974728	+	0.223395i	$0.0717139\pi$
$431$			6.64491e12i			0.446789i	−0.974728	+	0.223395i	$0.928286\pi$
$432$		0			0
$433$	7.28337e12			0.478512			0.239256	−	0.970956i	$-0.423096\pi$
$433$	7.28337e12			0.478512			0.239256	+	0.970956i	$0.423096\pi$
$434$		0			0
$435$	3.47069e13	+	2.69804e12i	2.22828	+	0.173222i
$436$		0			0
$437$			8.64868e12i			0.542678i
$438$		0			0
$439$	1.52600e13			0.935907			0.467954	−	0.883753i	$-0.344991\pi$
$439$	1.52600e13			0.935907			0.467954	+	0.883753i	$0.344991\pi$
$440$		0			0
$441$	−1.64533e13	−	2.57363e12i	−0.986414	−	0.154296i
$442$		0			0
$443$		−	1.83304e13i		−	1.07437i	−0.843465	−	0.537184i	$-0.819488\pi$
$443$		−	1.83304e13i		−	1.07437i	0.843465	−	0.537184i	$-0.180512\pi$
$444$		0			0
$445$	2.50498e13			1.43550
$446$		0			0
$447$	−1.52138e12	+	1.95706e13i	−0.0852508	+	1.09665i
$448$		0			0
$449$		−	8.33876e12i		−	0.456951i	−0.973550	−	0.228475i	$-0.926626\pi$
$449$		−	8.33876e12i		−	0.456951i	0.973550	−	0.228475i	$-0.0733741\pi$
$450$		0			0
$451$	8.37559e12			0.448883
$452$		0			0
$453$	7.47774e12	+	5.81303e11i	0.391994	+	0.0304727i
$454$		0			0
$455$		−	9.94405e11i		−	0.0509925i
$456$		0			0
$457$	4.12288e11			0.0206833			0.0103416	−	0.999947i	$-0.496708\pi$
$457$	4.12288e11			0.0206833			0.0103416	+	0.999947i	$0.496708\pi$
$458$		0			0
$459$	−2.22510e12	+	9.38700e12i	−0.109216	+	0.460748i
$460$		0			0
$461$		−	1.66247e11i		−	0.00798453i	−0.999992	−	0.00399226i	$-0.998729\pi$
$461$		−	1.66247e11i		−	0.00798453i	0.999992	−	0.00399226i	$-0.00127078\pi$
$462$		0			0
$463$	−1.27323e13			−0.598416			−0.299208	−	0.954188i	$-0.596722\pi$
$463$	−1.27323e13			−0.598416			−0.299208	+	0.954188i	$0.596722\pi$
$464$		0			0
$465$	−2.80743e12	+	3.61142e13i	−0.129135	+	1.66116i
$466$		0			0
$467$		−	2.26689e13i		−	1.02058i	−0.860004	−	0.510288i	$-0.829539\pi$
$467$		−	2.26689e13i		−	1.02058i	0.860004	−	0.510288i	$-0.170461\pi$
$468$		0			0
$469$	−4.49775e11			−0.0198213
$470$		0			0
$471$	−2.35321e13	−	1.82934e12i	−1.01521	−	0.0789203i
$472$		0			0
$473$			8.54352e12i			0.360854i
$474$		0			0
$475$	−2.08658e13			−0.862913
$476$		0			0
$477$	4.19039e12	−	2.67892e13i	0.169693	−	1.08485i
$478$		0			0
$479$		−	2.39654e13i		−	0.950402i	−0.879877	−	0.475201i	$-0.842375\pi$
$479$		−	2.39654e13i		−	0.950402i	0.879877	−	0.475201i	$-0.157625\pi$
$480$		0			0
$481$	−2.63673e13			−1.02409
$482$		0			0
$483$	−7.04098e10	+	9.05734e11i	−0.00267853	+	0.0344560i
$484$		0			0
$485$		−	5.17838e13i		−	1.92968i
$486$		0			0
$487$	1.13824e13			0.415516			0.207758	−	0.978180i	$-0.433383\pi$
$487$	1.13824e13			0.415516			0.207758	+	0.978180i	$0.433383\pi$
$488$		0			0
$489$	−3.37821e13	−	2.62615e12i	−1.20821	−	0.0939235i
$490$		0			0
$491$			3.59512e13i			1.25981i	0.776672	+	0.629906i	$0.216906\pi$
$491$			3.59512e13i			1.25981i	−0.776672	+	0.629906i	$0.783094\pi$
$492$		0			0
$493$	1.99891e13			0.686370
$494$		0			0
$495$	−6.55727e13	−	1.02569e13i	−2.20647	−	0.345137i
$496$		0			0
$497$		−	8.26965e11i		−	0.0272713i
$498$		0			0
$499$	1.33630e13			0.431917			0.215958	−	0.976403i	$-0.430712\pi$
$499$	1.33630e13			0.431917			0.215958	+	0.976403i	$0.430712\pi$
$500$		0			0
$501$	−2.37000e12	+	3.04871e13i	−0.0750862	+	0.965890i
$502$		0			0
$503$			3.54934e13i			1.10232i	0.834399	+	0.551160i	$0.185815\pi$
$503$			3.54934e13i			1.10232i	−0.834399	+	0.551160i	$0.814185\pi$
$504$		0			0
$505$	−5.21132e13			−1.58668
$506$		0			0
$507$	1.04490e13	+	8.12280e11i	0.311913	+	0.0242474i
$508$		0			0
$509$			6.07337e13i			1.77763i	0.458269	+	0.888813i	$0.348470\pi$
$509$			6.07337e13i			1.77763i	−0.458269	+	0.888813i	$0.651530\pi$
$510$		0			0
$511$	−7.25016e11			−0.0208086
$512$		0			0
$513$	−2.16577e13	−	5.13377e12i	−0.609574	−	0.144494i
$514$		0			0
$515$			1.36576e13i			0.376997i
$516$		0			0
$517$	−7.67166e12			−0.207700
$518$		0			0
$519$	2.37785e12	−	3.05881e13i	0.0631464	−	0.812299i
$520$		0			0
$521$			2.06244e13i			0.537270i	0.963242	+	0.268635i	$0.0865726\pi$
$521$			2.06244e13i			0.537270i	−0.963242	+	0.268635i	$0.913427\pi$
$522$		0			0
$523$	−5.24376e13			−1.34009			−0.670045	−	0.742320i	$-0.733725\pi$
$523$	−5.24376e13			−1.34009			−0.670045	+	0.742320i	$0.733725\pi$
$524$		0			0
$525$	−2.18517e12	−	1.69871e11i	−0.0547885	−	0.00425914i
$526$		0			0
$527$			2.07996e13i			0.511683i
$528$		0			0
$529$	1.03402e13			0.249603
$530$		0			0
$531$	4.45925e12	−	2.85080e13i	0.105631	−	0.675297i
$532$		0			0
$533$		−	1.10510e13i		−	0.256900i
$534$		0			0
$535$	1.16221e14			2.65165
$536$		0			0
$537$	5.58492e12	−	7.18431e13i	0.125068	−	1.60884i
$538$		0			0
$539$		−	6.57877e13i		−	1.44611i
$540$		0			0
$541$	8.20249e13			1.76994			0.884972	−	0.465645i	$-0.154178\pi$
$541$	8.20249e13			1.76994			0.884972	+	0.465645i	$0.154178\pi$
$542$		0			0
$543$	−6.01919e13	−	4.67919e12i	−1.27509	−	0.0991223i
$544$		0			0
$545$		−	2.61844e13i		−	0.544578i
$546$		0			0
$547$	1.62332e13			0.331488			0.165744	−	0.986169i	$-0.446997\pi$
$547$	1.62332e13			0.331488			0.165744	+	0.986169i	$0.446997\pi$
$548$		0			0
$549$	−3.57580e12	−	5.59329e11i	−0.0716987	−	0.0112152i
$550$		0			0
$551$			4.61189e13i			0.908074i
$552$		0			0
$553$	−1.25140e12			−0.0241974
$554$		0			0
$555$	−7.77424e12	+	1.00006e14i	−0.147636	+	1.89916i
$556$		0			0
$557$			1.12168e13i			0.209215i	0.994514	+	0.104608i	$0.0333587\pi$
$557$			1.12168e13i			0.209215i	−0.994514	+	0.104608i	$0.966641\pi$
$558$		0			0
$559$	1.12726e13			0.206521
$560$		0			0
$561$	−3.79955e13	−	2.95369e12i	−0.683783	−	0.0531557i
$562$		0			0
$563$		−	7.98522e13i		−	1.41171i	−0.708357	−	0.705854i	$-0.750563\pi$
$563$		−	7.98522e13i		−	1.41171i	0.708357	−	0.705854i	$-0.249437\pi$
$564$		0			0
$565$	6.71230e13			1.16581
$566$		0			0
$567$	−2.22632e12	−	7.13953e11i	−0.0379902	−	0.0121830i
$568$		0			0
$569$			9.95594e11i			0.0166925i	0.999965	+	0.00834624i	$0.00265672\pi$
$569$			9.95594e11i			0.0166925i	−0.999965	+	0.00834624i	$0.997343\pi$
$570$		0			0
$571$	−1.07836e14			−1.77657			−0.888283	−	0.459297i	$-0.848101\pi$
$571$	−1.07836e14			−1.77657			−0.888283	+	0.459297i	$0.848101\pi$
$572$		0			0
$573$	−2.97664e12	+	3.82907e13i	−0.0481895	+	0.619899i
$574$		0			0
$575$		−	7.49989e13i		−	1.19321i
$576$		0			0
$577$	3.31000e13			0.517546			0.258773	−	0.965938i	$-0.416682\pi$
$577$	3.31000e13			0.517546			0.258773	+	0.965938i	$0.416682\pi$
$578$		0			0
$579$	9.16671e13	+	7.12600e12i	1.40871	+	0.109510i
$580$		0			0
$581$			7.34648e11i			0.0110968i
$582$		0			0
$583$	1.07116e14			1.59041
$584$		0			0
$585$	−1.35333e13	+	8.65184e13i	−0.197526	+	1.26278i
$586$		0			0
$587$			1.21022e14i			1.73650i	0.496131	+	0.868248i	$0.334754\pi$
$587$			1.21022e14i			1.73650i	−0.496131	+	0.868248i	$0.665246\pi$
$588$		0			0
$589$	−4.79889e13			−0.676961
$590$		0			0
$591$	3.56717e12	−	4.58873e13i	0.0494751	−	0.636436i
$592$		0			0
$593$			8.43944e12i			0.115091i	0.998343	+	0.0575453i	$0.0183274\pi$
$593$			8.43944e12i			0.115091i	−0.998343	+	0.0575453i	$0.981673\pi$
$594$		0			0
$595$	−2.17220e12			−0.0291283
$596$		0			0
$597$	1.21847e13	+	9.47213e11i	0.160673	+	0.0124904i
$598$		0			0
$599$			3.11882e13i			0.404443i	0.979340	+	0.202221i	$0.0648160\pi$
$599$			3.11882e13i			0.404443i	−0.979340	+	0.202221i	$0.935184\pi$
$600$		0			0
$601$	2.87401e13			0.366535			0.183267	−	0.983063i	$-0.441333\pi$
$601$	2.87401e13			0.366535			0.183267	+	0.983063i	$0.441333\pi$
$602$		0			0
$603$	3.91328e13	+	6.12119e12i	0.490857	+	0.0767802i
$604$		0			0
$605$		−	1.37212e14i		−	1.69284i
$606$		0			0
$607$	4.47536e13			0.543106			0.271553	−	0.962423i	$-0.412463\pi$
$607$	4.47536e13			0.543106			0.271553	+	0.962423i	$0.412463\pi$
$608$		0			0
$609$	−3.75459e11	+	4.82981e12i	−0.00448204	+	0.0576559i
$610$		0			0
$611$			1.01222e13i			0.118869i
$612$		0			0
$613$	6.78051e13			0.783358			0.391679	−	0.920102i	$-0.371894\pi$
$613$	6.78051e13			0.783358			0.391679	+	0.920102i	$0.371894\pi$
$614$		0			0
$615$	−4.19143e13	−	3.25832e12i	−0.476416	−	0.0370355i
$616$		0			0
$617$			2.48261e12i			0.0277641i	0.999904	+	0.0138820i	$0.00441893\pi$
$617$			2.48261e12i			0.0277641i	−0.999904	+	0.0138820i	$0.995581\pi$
$618$		0			0
$619$	−1.64000e13			−0.180464			−0.0902320	−	0.995921i	$-0.528761\pi$
$619$	−1.64000e13			−0.180464			−0.0902320	+	0.995921i	$0.528761\pi$
$620$		0			0
$621$	1.84526e13	−	7.78454e13i	0.199801	−	0.842898i
$622$		0			0
$623$			3.48592e12i			0.0371431i
$624$		0			0
$625$	−4.57873e13			−0.480114
$626$		0			0
$627$	6.81476e12	−	8.76635e13i	0.0703255	−	0.904651i
$628$		0			0
$629$			5.75973e13i			0.584991i
$630$		0			0
$631$	1.37258e13			0.137211			0.0686056	−	0.997644i	$-0.478145\pi$
$631$	1.37258e13			0.137211			0.0686056	+	0.997644i	$0.478145\pi$
$632$		0			0
$633$	1.15070e14	+	8.94532e12i	1.13226	+	0.0880192i
$634$		0			0
$635$		−	1.96790e14i		−	1.90605i
$636$		0			0
$637$	−8.68020e13			−0.827623
$638$		0			0
$639$	−1.12545e13	+	7.19503e13i	−0.105639	+	0.675349i
$640$		0			0
$641$			5.42348e13i			0.501173i	0.968094	+	0.250587i	$0.0806235\pi$
$641$			5.42348e13i			0.501173i	−0.968094	+	0.250587i	$0.919377\pi$
$642$		0			0
$643$	5.54693e13			0.504659			0.252329	−	0.967641i	$-0.418803\pi$
$643$	5.54693e13			0.504659			0.252329	+	0.967641i	$0.418803\pi$
$644$		0			0
$645$	3.32365e12	−	4.27546e13i	0.0297726	−	0.382987i
$646$		0			0
$647$			5.56652e13i			0.490979i	0.969399	+	0.245489i	$0.0789486\pi$
$647$			5.56652e13i			0.490979i	−0.969399	+	0.245489i	$0.921051\pi$
$648$		0			0
$649$	1.13988e14			0.990002
$650$		0			0
$651$	−5.02564e12	−	3.90682e11i	−0.0429820	−	0.00334132i
$652$		0			0
$653$			5.56792e13i			0.468951i	0.972122	+	0.234475i	$0.0753372\pi$
$653$			5.56792e13i			0.468951i	−0.972122	+	0.234475i	$0.924663\pi$
$654$		0			0
$655$	−2.00204e14			−1.66060
$656$		0			0
$657$	6.30802e13	+	9.86706e12i	0.515307	+	0.0806048i
$658$		0			0
$659$			1.52699e14i			1.22860i	0.789074	+	0.614298i	$0.210561\pi$
$659$			1.52699e14i			1.22860i	−0.789074	+	0.614298i	$0.789439\pi$
$660$		0			0
$661$	−2.08036e14			−1.64866			−0.824329	−	0.566111i	$-0.808447\pi$
$661$	−2.08036e14			−1.64866			−0.824329	+	0.566111i	$0.808447\pi$
$662$		0			0
$663$	−3.89717e12	+	5.01323e13i	−0.0304216	+	0.391336i
$664$		0			0
$665$		−	5.01172e12i		−	0.0385371i
$666$		0			0
$667$	−1.65767e14			−1.25565
$668$		0			0
$669$	−5.70737e13	−	4.43679e12i	−0.425898	−	0.0331084i
$670$		0			0
$671$		−	1.42977e13i		−	0.105112i
$672$		0			0
$673$	−9.45260e13			−0.684662			−0.342331	−	0.939579i	$-0.611216\pi$
$673$	−9.45260e13			−0.684662			−0.342331	+	0.939579i	$0.611216\pi$
$674$		0			0
$675$	1.87810e14	+	4.45186e13i	1.34029	+	0.317704i
$676$		0			0
$677$			1.70106e14i			1.19612i	0.801451	+	0.598060i	$0.204062\pi$
$677$			1.70106e14i			1.19612i	−0.801451	+	0.598060i	$0.795938\pi$
$678$		0			0
$679$	7.20622e12			0.0499297
$680$		0			0
$681$	8.04237e12	−	1.03455e14i	0.0549096	−	0.706344i
$682$		0			0
$683$			2.23578e14i			1.50427i	0.659009	+	0.752135i	$0.270976\pi$
$683$			2.23578e14i			1.50427i	−0.659009	+	0.752135i	$0.729024\pi$
$684$		0			0
$685$	−4.45960e14			−2.95694
$686$		0			0
$687$	−2.51163e14	−	1.95249e13i	−1.64124	−	0.127586i
$688$		0			0
$689$		−	1.41331e14i		−	0.910210i
$690$		0			0
$691$	1.10134e13			0.0699090			0.0349545	−	0.999389i	$-0.488871\pi$
$691$	1.10134e13			0.0699090			0.0349545	+	0.999389i	$0.488871\pi$
$692$		0			0
$693$	1.42735e12	−	9.12509e12i	0.00893029	−	0.0570915i
$694$		0			0
$695$		−	3.83341e14i		−	2.36408i
$696$		0			0
$697$	−2.41401e13			−0.146749
$698$		0			0
$699$	1.95426e13	−	2.51392e14i	0.117111	−	1.50649i
$700$		0			0
$701$			1.10962e14i			0.655516i	0.944762	+	0.327758i	$0.106293\pi$
$701$			1.10962e14i			0.655516i	−0.944762	+	0.327758i	$0.893707\pi$
$702$		0			0
$703$	−1.32889e14			−0.773948
$704$		0			0
$705$	3.83915e13	+	2.98447e12i	0.220440	+	0.0171365i
$706$		0			0
$707$		−	7.25206e12i		−	0.0410548i
$708$		0			0
$709$	2.08219e14			1.16222			0.581112	−	0.813824i	$-0.302618\pi$
$709$	2.08219e14			1.16222			0.581112	+	0.813824i	$0.302618\pi$
$710$		0			0
$711$	1.08878e14	+	1.70308e13i	0.599229	+	0.0937318i
$712$		0			0
$713$		−	1.72489e14i		−	0.936080i
$714$		0			0
$715$	−3.45940e14			−1.85127
$716$		0			0
$717$	−2.32946e13	+	2.99656e14i	−0.122931	+	1.58135i
$718$		0			0
$719$			2.74910e14i			1.43069i	0.698771	+	0.715346i	$0.253731\pi$
$719$			2.74910e14i			1.43069i	−0.698771	+	0.715346i	$0.746269\pi$
$720$		0			0
$721$	−1.90059e12			−0.00975465
$722$		0			0
$723$	2.51746e14	+	1.95702e13i	1.27430	+	0.0990613i
$724$		0			0
$725$		−	3.99930e14i		−	1.99661i
$726$		0			0
$727$	2.99071e14			1.47266			0.736330	−	0.676622i	$-0.236557\pi$
$727$	2.99071e14			1.47266			0.736330	+	0.676622i	$0.236557\pi$
$728$		0			0
$729$	1.83985e14	+	9.24165e13i	0.893602	+	0.448861i
$730$		0			0
$731$		−	2.46241e13i		−	0.117970i
$732$		0			0
$733$	1.19922e14			0.566734			0.283367	−	0.959012i	$-0.408549\pi$
$733$	1.19922e14			0.566734			0.283367	+	0.959012i	$0.408549\pi$
$734$		0			0
$735$	−2.55931e13	+	3.29223e14i	−0.119313	+	1.53481i
$736$		0			0
$737$			1.56471e14i			0.719608i
$738$		0			0
$739$	7.29345e13			0.330911			0.165455	−	0.986217i	$-0.447091\pi$
$739$	7.29345e13			0.330911			0.165455	+	0.986217i	$0.447091\pi$
$740$		0			0
$741$	−1.15666e14	−	8.99158e12i	−0.517742	−	0.0402481i
$742$		0			0
$743$		−	1.07061e14i		−	0.472809i	−0.971655	−	0.236405i	$-0.924031\pi$
$743$		−	1.07061e14i		−	0.472809i	0.971655	−	0.236405i	$-0.0759691\pi$
$744$		0			0
$745$	3.89234e14			1.69601
$746$		0			0
$747$	9.99815e12	−	6.39183e13i	0.0429850	−	0.274803i
$748$		0			0
$749$			1.61733e13i			0.0686104i
$750$		0			0
$751$	−1.83777e14			−0.769292			−0.384646	−	0.923064i	$-0.625677\pi$
$751$	−1.83777e14			−0.769292			−0.384646	+	0.923064i	$0.625677\pi$
$752$		0			0
$753$	1.06744e13	−	1.37313e14i	0.0440931	−	0.567203i
$754$		0			0
$755$		−	1.48722e14i		−	0.606236i
$756$		0			0
$757$	−1.73049e14			−0.696130			−0.348065	−	0.937470i	$-0.613161\pi$
$757$	−1.73049e14			−0.696130			−0.348065	+	0.937470i	$0.613161\pi$
$758$		0			0
$759$	3.15093e14	+	2.44946e13i	1.25092	+	0.0972438i
$760$		0			0
$761$			1.10156e14i			0.431604i	0.976437	+	0.215802i	$0.0692365\pi$
$761$			1.10156e14i			0.431604i	−0.976437	+	0.215802i	$0.930764\pi$
$762$		0			0
$763$	3.64382e12			0.0140907
$764$		0			0
$765$	1.88993e14	+	2.95625e13i	0.721338	+	0.112832i
$766$		0			0
$767$		−	1.50399e14i		−	0.566589i
$768$		0			0
$769$	2.30458e14			0.856959			0.428480	−	0.903551i	$-0.359049\pi$
$769$	2.30458e14			0.856959			0.428480	+	0.903551i	$0.359049\pi$
$770$		0			0
$771$	−2.40960e13	+	3.09965e14i	−0.0884451	+	1.13774i
$772$		0			0
$773$			1.50965e14i			0.546991i	0.961873	+	0.273495i	$0.0881798\pi$
$773$			1.50965e14i			0.546991i	−0.961873	+	0.273495i	$0.911820\pi$
$774$		0			0
$775$	4.16146e14			1.48846
$776$		0			0
$777$	−1.39168e13	−	1.08186e12i	−0.0491399	−	0.00382003i
$778$		0			0
$779$		−	5.56961e13i		−	0.194150i
$780$		0			0
$781$	−2.87690e14			−0.990079
$782$		0			0
$783$	9.83979e13	−	4.15109e14i	0.334331	−	1.41044i
$784$		0			0
$785$			4.68023e14i			1.57007i
$786$		0			0
$787$	3.42081e14			1.13306			0.566532	−	0.824039i	$-0.308285\pi$
$787$	3.42081e14			1.13306			0.566532	+	0.824039i	$0.308285\pi$
$788$		0			0
$789$	3.17500e13	−	4.08424e14i	0.103839	−	1.33575i
$790$		0			0
$791$			9.34082e12i			0.0301649i
$792$		0			0
$793$	−1.88647e13			−0.0601568
$794$		0			0
$795$	−5.36042e14	−	4.16707e13i	−1.68796	−	0.131218i
$796$		0			0
$797$		−	5.22986e14i		−	1.62629i	−0.582059	−	0.813146i	$-0.697753\pi$
$797$		−	5.22986e14i		−	1.62629i	0.582059	−	0.813146i	$-0.302247\pi$
$798$		0			0
$799$	2.21112e13			0.0679013
$800$		0			0
$801$	4.74415e13	−	3.03294e14i	0.143878	−	0.919816i
$802$		0			0
$803$			2.52223e14i			0.755453i
$804$		0			0
$805$	1.80139e13			0.0532878
$806$		0			0
$807$	2.52412e13	−	3.24697e14i	0.0737468	−	0.948660i
$808$		0			0
$809$		−	3.45374e14i		−	0.996661i	−0.866987	−	0.498331i	$-0.833947\pi$
$809$		−	3.45374e14i		−	0.996661i	0.866987	−	0.498331i	$-0.166053\pi$
$810$		0			0
$811$	−3.60870e14			−1.02860			−0.514301	−	0.857610i	$-0.671948\pi$
$811$	−3.60870e14			−1.02860			−0.514301	+	0.857610i	$0.671948\pi$
$812$		0			0
$813$	−4.24817e14	−	3.30243e13i	−1.19605	−	0.0929782i
$814$		0			0
$815$			6.71881e14i			1.86855i
$816$		0			0
$817$	5.68128e13			0.156076
$818$		0			0
$819$	−1.20399e13	−	1.88329e12i	−0.0326741	−	0.00511090i
$820$		0			0
$821$			6.68322e14i			1.79172i	0.444336	+	0.895860i	$0.353440\pi$
$821$			6.68322e14i			1.79172i	−0.444336	+	0.895860i	$0.646560\pi$
$822$		0			0
$823$	−4.35331e13			−0.115298			−0.0576488	−	0.998337i	$-0.518360\pi$
$823$	−4.35331e13			−0.115298			−0.0576488	+	0.998337i	$0.518360\pi$
$824$		0			0
$825$	−5.90957e13	+	7.60193e14i	−0.154627	+	1.98909i
$826$		0			0
$827$		−	2.21008e13i		−	0.0571321i	−0.999592	−	0.0285661i	$-0.990906\pi$
$827$		−	2.21008e13i		−	0.0571321i	0.999592	−	0.0285661i	$-0.00909409\pi$
$828$		0			0
$829$	7.62973e14			1.94866			0.974331	−	0.225119i	$-0.0722770\pi$
$829$	7.62973e14			1.94866			0.974331	+	0.225119i	$0.0722770\pi$
$830$		0			0
$831$	−4.10839e14	−	3.19377e13i	−1.03673	−	0.0805933i
$832$		0			0
$833$			1.89613e14i			0.472761i
$834$		0			0
$835$	6.06349e14			1.49379
$836$		0			0
$837$	4.31940e14	+	1.02388e14i	1.05147	+	0.249241i
$838$		0			0
$839$		−	8.55289e13i		−	0.205732i	−0.994695	−	0.102866i	$-0.967199\pi$
$839$		−	8.55289e13i		−	0.205732i	0.994695	−	0.102866i	$-0.0328014\pi$
$840$		0			0
$841$	−4.63244e14			−1.10111
$842$		0			0
$843$	−4.59867e12	+	5.91561e13i	−0.0108017	+	0.138951i
$844$		0			0
$845$		−	2.07816e14i		−	0.482387i
$846$		0			0
$847$	1.90945e13			0.0438017
$848$		0			0
$849$	−2.41399e14	−	1.87658e13i	−0.547265	−	0.0425431i
$850$		0			0
$851$		−	4.77649e14i		−	1.07019i
$852$		0			0
$853$	1.82179e14			0.403415			0.201708	−	0.979446i	$-0.435351\pi$
$853$	1.82179e14			0.403415			0.201708	+	0.979446i	$0.435351\pi$
$854$		0			0
$855$	−6.82067e13	+	4.36046e14i	−0.149278	+	0.954337i
$856$		0			0
$857$		−	8.52398e14i		−	1.84390i	−0.387305	−	0.921952i	$-0.626594\pi$
$857$		−	8.52398e14i		−	1.84390i	0.387305	−	0.921952i	$-0.373406\pi$
$858$		0			0
$859$	−2.60062e14			−0.556046			−0.278023	−	0.960574i	$-0.589679\pi$
$859$	−2.60062e14			−0.556046			−0.278023	+	0.960574i	$0.589679\pi$
$860$		0			0
$861$	4.53427e11	−	5.83278e12i	0.000958279	−	0.0123271i
$862$		0			0
$863$		−	2.71494e14i		−	0.567161i	−0.958948	−	0.283580i	$-0.908478\pi$
$863$		−	2.71494e14i		−	0.567161i	0.958948	−	0.283580i	$-0.0915223\pi$
$864$		0			0
$865$	−6.08358e14			−1.25626
$866$		0			0
$867$	−3.78903e14	−	2.94551e13i	−0.773450	−	0.0601263i
$868$		0			0
$869$			4.35344e14i			0.878484i
$870$		0			0
$871$	2.06452e14			0.411840
$872$		0			0
$873$	−6.26979e14	−	9.80726e13i	−1.23646	−	0.193409i
$874$		0			0
$875$			1.19086e13i			0.0232177i
$876$		0			0
$877$	1.90122e14			0.366466			0.183233	−	0.983069i	$-0.441344\pi$
$877$	1.90122e14			0.366466			0.183233	+	0.983069i	$0.441344\pi$
$878$		0			0
$879$	2.96761e13	−	3.81746e14i	0.0565539	−	0.727495i
$880$		0			0
$881$		−	6.12829e14i		−	1.15468i	−0.816506	−	0.577338i	$-0.804092\pi$
$881$		−	6.12829e14i		−	1.15468i	0.816506	−	0.577338i	$-0.195908\pi$
$882$		0			0
$883$	4.57367e14			0.852042			0.426021	−	0.904713i	$-0.359915\pi$
$883$	4.57367e14			0.852042			0.426021	+	0.904713i	$0.359915\pi$
$884$		0			0
$885$	−5.70435e14	−	4.43443e13i	−1.05073	−	0.0816811i
$886$		0			0
$887$			5.97146e14i			1.08758i	0.839221	+	0.543791i	$0.183012\pi$
$887$			5.97146e14i			1.08758i	−0.839221	+	0.543791i	$0.816988\pi$
$888$		0			0
$889$	2.73852e13			0.0493182
$890$		0			0
$891$	−2.48375e14	+	7.74505e14i	−0.442302	+	1.37923i
$892$		0			0
$893$			5.10150e13i			0.0898340i
$894$		0			0
$895$	−1.42886e15			−2.48815
$896$		0			0
$897$	3.23189e13	−	4.15742e14i	0.0556537	−	0.715916i
$898$		0			0
$899$		−	9.19792e14i		−	1.56636i
$900$		0			0
$901$	−3.08727e14			−0.519938
$902$		0			0
$903$	5.94973e12	+	4.62519e11i	0.00990965	+	0.000770354i
$904$		0			0
$905$			1.19714e15i			1.97198i
$906$		0			0
$907$	7.96198e14			1.29713			0.648567	−	0.761158i	$-0.275369\pi$
$907$	7.96198e14			1.29713			0.648567	+	0.761158i	$0.275369\pi$
$908$		0			0
$909$	−9.86964e13	+	6.30967e14i	−0.159031	+	1.01669i
$910$		0			0
$911$		−	5.95524e14i		−	0.949089i	−0.880231	−	0.474545i	$-0.842613\pi$
$911$		−	5.95524e14i		−	0.949089i	0.880231	−	0.474545i	$-0.157387\pi$
$912$		0			0
$913$	2.55574e14			0.402869
$914$		0			0
$915$	−5.56216e12	+	7.15503e13i	−0.00867237	+	0.111559i
$916$		0			0
$917$		−	2.78603e13i		−	0.0429675i
$918$		0			0
$919$	−5.55318e14			−0.847157			−0.423579	−	0.905859i	$-0.639226\pi$
$919$	−5.55318e14			−0.847157			−0.423579	+	0.905859i	$0.639226\pi$
$920$		0			0
$921$	−7.99058e14	−	6.21170e13i	−1.20581	−	0.0937373i
$922$		0			0
$923$			3.79586e14i			0.566633i
$924$		0			0
$925$	1.15237e15			1.70171
$926$		0			0
$927$	1.65361e14	+	2.58659e13i	0.241566	+	0.0377859i
$928$		0			0
$929$			1.49292e14i			0.215754i	0.994164	+	0.107877i	$0.0344053\pi$
$929$			1.49292e14i			0.215754i	−0.994164	+	0.107877i	$0.965595\pi$
$930$		0			0
$931$	−4.37475e14			−0.625468
$932$		0			0
$933$	3.15085e13	−	4.05318e14i	0.0445677	−	0.573308i
$934$		0			0
$935$			7.55681e14i			1.05750i
$936$		0			0
$937$	−3.07315e14			−0.425487			−0.212743	−	0.977108i	$-0.568240\pi$
$937$	−3.07315e14			−0.425487			−0.212743	+	0.977108i	$0.568240\pi$
$938$		0			0
$939$	−4.19897e14	−	3.26419e13i	−0.575195	−	0.0447143i
$940$		0			0
$941$		−	2.63150e14i		−	0.356661i	−0.983971	−	0.178330i	$-0.942930\pi$
$941$		−	2.63150e14i		−	0.356661i	0.983971	−	0.178330i	$-0.0570696\pi$
$942$		0			0
$943$	2.00191e14			0.268464
$944$		0			0
$945$	−1.06929e13	+	4.51097e13i	−0.0141884	+	0.0598565i
$946$		0			0
$947$			1.20121e15i			1.57713i	0.614950	+	0.788566i	$0.289176\pi$
$947$			1.20121e15i			1.57713i	−0.614950	+	0.788566i	$0.710824\pi$
$948$		0			0
$949$	3.32790e14			0.432354
$950$		0			0
$951$	2.50674e13	−	3.22461e14i	0.0322260	−	0.414547i
$952$		0			0
$953$		−	3.27942e13i		−	0.0417189i	−0.999782	−	0.0208594i	$-0.993360\pi$
$953$		−	3.27942e13i		−	0.0417189i	0.999782	−	0.0208594i	$-0.00664025\pi$
$954$		0			0
$955$	7.61552e14			0.958700
$956$		0			0
$957$	1.68023e15	+	1.30617e14i	2.09319	+	0.162720i
$958$		0			0
$959$		−	6.20597e13i		−	0.0765097i
$960$		0			0
$961$	1.37458e14			0.167708
$962$		0			0
$963$	2.20110e14	−	1.40716e15i	0.265771	−	1.69908i
$964$		0			0
$965$		−	1.82314e15i		−	2.17863i
$966$		0			0
$967$	9.87053e14			1.16737			0.583684	−	0.811981i	$-0.301611\pi$
$967$	9.87053e14			1.16737			0.583684	+	0.811981i	$0.301611\pi$
$968$		0			0
$969$	−1.96414e13	+	2.52663e14i	−0.0229908	+	0.295748i
$970$		0			0
$971$		−	5.42431e14i		−	0.628418i	−0.949354	−	0.314209i	$-0.898261\pi$
$971$		−	5.42431e14i		−	0.628418i	0.949354	−	0.314209i	$-0.101739\pi$
$972$		0			0
$973$	5.33457e13			0.0611695
$974$		0			0
$975$	1.00302e15	+	7.79725e13i	1.13838	+	0.0884949i
$976$		0			0
$977$			9.53859e14i			1.07155i	0.844361	+	0.535774i	$0.179980\pi$
$977$			9.53859e14i			1.07155i	−0.844361	+	0.535774i	$0.820020\pi$
$978$		0			0
$979$	1.21271e15			1.34847
$980$		0			0
$981$	−3.17031e14	−	4.95903e13i	−0.348945	−	0.0545823i
$982$		0			0
$983$		−	6.30884e14i		−	0.687356i	−0.939088	−	0.343678i	$-0.888327\pi$
$983$		−	6.30884e14i		−	0.687356i	0.939088	−	0.343678i	$-0.111673\pi$
$984$		0			0
$985$	−9.12638e14			−0.984277
$986$		0			0
$987$	−4.15319e11	+	5.34256e12i	−0.000443400	+	0.00570379i
$988$		0			0
$989$			2.04205e14i			0.215816i
$990$		0			0
$991$	−4.94498e14			−0.517364			−0.258682	−	0.965963i	$-0.583288\pi$
$991$	−4.94498e14			−0.517364			−0.258682	+	0.965963i	$0.583288\pi$
$992$		0			0
$993$	1.14342e15	+	8.88866e13i	1.18429	+	0.0920640i
$994$		0			0
$995$		−	2.42338e14i		−	0.248488i
$996$		0			0
$997$	1.62993e15			1.65460			0.827301	−	0.561759i	$-0.189875\pi$
$997$	1.62993e15			1.65460			0.827301	+	0.561759i	$0.189875\pi$
$998$		0			0
$999$	1.19611e15	+	2.83527e14i	1.20211	+	0.284949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.11.e.d.17.1		4
3.2	odd	2	inner	48.11.e.d.17.2		4
4.3	odd	2		6.11.b.a.5.4	yes	4
8.3	odd	2		192.11.e.g.65.1		4
8.5	even	2		192.11.e.h.65.4		4
12.11	even	2		6.11.b.a.5.2	✓	4
20.3	even	4		150.11.b.a.149.6		8
20.7	even	4		150.11.b.a.149.3		8
20.19	odd	2		150.11.d.a.101.1		4
24.5	odd	2		192.11.e.h.65.3		4
24.11	even	2		192.11.e.g.65.2		4
36.7	odd	6		162.11.d.d.53.3		8
36.11	even	6		162.11.d.d.53.2		8
36.23	even	6		162.11.d.d.107.3		8
36.31	odd	6		162.11.d.d.107.2		8
60.23	odd	4		150.11.b.a.149.4		8
60.47	odd	4		150.11.b.a.149.5		8
60.59	even	2		150.11.d.a.101.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.11.b.a.5.2	✓	4	12.11	even	2
6.11.b.a.5.4	yes	4	4.3	odd	2
48.11.e.d.17.1		4	1.1	even	1	trivial
48.11.e.d.17.2		4	3.2	odd	2	inner
150.11.b.a.149.3		8	20.7	even	4
150.11.b.a.149.4		8	60.23	odd	4
150.11.b.a.149.5		8	60.47	odd	4
150.11.b.a.149.6		8	20.3	even	4
150.11.d.a.101.1		4	20.19	odd	2
150.11.d.a.101.3		4	60.59	even	2
162.11.d.d.53.2		8	36.11	even	6
162.11.d.d.53.3		8	36.7	odd	6
162.11.d.d.107.2		8	36.31	odd	6
162.11.d.d.107.3		8	36.23	even	6
192.11.e.g.65.1		4	8.3	odd	2
192.11.e.g.65.2		4	24.11	even	2
192.11.e.h.65.3		4	24.5	odd	2
192.11.e.h.65.4		4	8.5	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	48.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-242.269 - 18.8335i) q^{3} +4818.41i q^{5} -670.530 q^{7} +(58339.6 + 9125.53i) q^{9} +O(q^{10})\)	\(q+(-242.269 - 18.8335i) q^{3} +4818.41i q^{5} -670.530 q^{7} +(58339.6 + 9125.53i) q^{9} +233268. i q^{11} +307781. q^{13} +(90747.4 - 1.16735e6i) q^{15} -672324. i q^{17} +1.55119e6 q^{19} +(162449. + 12628.4i) q^{21} +5.57551e6i q^{23} -1.34515e7 q^{25} +(-1.39620e7 - 3.30957e6i) q^{27} +2.97313e7i q^{29} -3.09368e7 q^{31} +(4.39325e6 - 5.65137e7i) q^{33} -3.23089e6i q^{35} -8.56690e7 q^{37} +(-7.45657e7 - 5.79657e6i) q^{39} -3.59054e7i q^{41} +3.66253e7 q^{43} +(-4.39706e7 + 2.81104e8i) q^{45} +3.28877e7i q^{47} -2.82026e8 q^{49} +(-1.26622e7 + 1.62883e8i) q^{51} -4.59194e8i q^{53} -1.12398e9 q^{55} +(-3.75805e8 - 2.92143e7i) q^{57} -4.88657e8i q^{59} -6.12928e7 q^{61} +(-3.91184e7 - 6.11894e6i) q^{63} +1.48301e9i q^{65} +6.70776e8 q^{67} +(1.05006e8 - 1.35077e9i) q^{69} +1.23330e9i q^{71} +1.08126e9 q^{73} +(3.25888e9 + 2.53338e8i) q^{75} -1.56413e8i q^{77} +1.86628e9 q^{79} +(3.32023e9 + 1.06476e9i) q^{81} -1.09562e9i q^{83} +3.23953e9 q^{85} +(5.59944e8 - 7.20298e9i) q^{87} -5.19876e9i q^{89} -2.06376e8 q^{91} +(7.49503e9 + 5.82647e8i) q^{93} +7.47427e9i q^{95} -1.07471e10 q^{97} +(-2.12870e9 + 1.36088e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 84 q^{3} + 45112 q^{7} + 159012 q^{9}+O(q^{10}) \) 4 * q - 84 * q^3 + 45112 * q^7 + 159012 * q^9	\( 4 q - 84 q^{3} + 45112 q^{7} + 159012 q^{9} + 275240 q^{13} + 1180800 q^{15} + 1568728 q^{19} + 9628008 q^{21} - 33732380 q^{25} - 34619508 q^{27} + 21785848 q^{31} + 25974144 q^{33} - 71014168 q^{37} - 217287240 q^{39} + 470688664 q^{43} + 312318720 q^{45} - 50058420 q^{49} + 708576768 q^{51} - 2701359360 q^{55} - 1058753208 q^{57} - 1184038744 q^{61} + 905007096 q^{63} + 297365848 q^{67} + 596268288 q^{69} + 6534269000 q^{73} + 5150031180 q^{75} - 199282568 q^{79} + 1458964548 q^{81} - 12880512000 q^{85} - 210268800 q^{87} - 8317232080 q^{91} + 31744468392 q^{93} - 39176355064 q^{97} + 2626912512 q^{99}+O(q^{100}) \) 4 * q - 84 * q^3 + 45112 * q^7 + 159012 * q^9 + 275240 * q^13 + 1180800 * q^15 + 1568728 * q^19 + 9628008 * q^21 - 33732380 * q^25 - 34619508 * q^27 + 21785848 * q^31 + 25974144 * q^33 - 71014168 * q^37 - 217287240 * q^39 + 470688664 * q^43 + 312318720 * q^45 - 50058420 * q^49 + 708576768 * q^51 - 2701359360 * q^55 - 1058753208 * q^57 - 1184038744 * q^61 + 905007096 * q^63 + 297365848 * q^67 + 596268288 * q^69 + 6534269000 * q^73 + 5150031180 * q^75 - 199282568 * q^79 + 1458964548 * q^81 - 12880512000 * q^85 - 210268800 * q^87 - 8317232080 * q^91 + 31744468392 * q^93 - 39176355064 * q^97 + 2626912512 * q^99

Introduction

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