LMFDB - Embedded newform 3024.2.q.k.2881.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.q (of order $3$, degree $2$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2881.1
Character	$\chi$	$=$	3024.2881
Dual form			3024.2.q.k.2305.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76479 + 3.05671i) q^{5} +(2.63986 - 0.176417i) q^{7} +O(q^{10})$	$q+(-1.76479 + 3.05671i) q^{5} +(2.63986 - 0.176417i) q^{7} +(1.16036 + 2.00981i) q^{11} +(-2.35884 - 4.08563i) q^{13} +(0.636946 - 1.10322i) q^{17} +(-2.78386 - 4.82178i) q^{19} +(1.64855 - 2.85537i) q^{23} +(-3.72899 - 6.45880i) q^{25} +(4.32116 - 7.48447i) q^{29} -8.51642 q^{31} +(-4.11956 + 8.38064i) q^{35} +(-2.84024 - 4.91943i) q^{37} +(-1.66553 - 2.88478i) q^{41} +(-0.0444165 + 0.0769317i) q^{43} +7.05213 q^{47} +(6.93775 - 0.931432i) q^{49} +(-3.41816 + 5.92042i) q^{53} -8.19121 q^{55} -7.99490 q^{59} +13.3553 q^{61} +16.6514 q^{65} -6.12804 q^{67} +1.30202 q^{71} +(6.64529 - 11.5100i) q^{73} +(3.41777 + 5.10092i) q^{77} +10.0281 q^{79} +(-5.90243 + 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(-0.561496 - 0.972540i) q^{89} +(-6.94778 - 10.3694i) q^{91} +19.6517 q^{95} +(-3.50818 + 6.07635i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 3 q^{5} + 5 q^{7}+O(q^{10}) $ 22 * q - 3 * q^5 + 5 * q^7	$ 22 q - 3 q^{5} + 5 q^{7} - 3 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} + 2 q^{23} - 10 q^{25} - 9 q^{29} - 8 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{47} + 15 q^{49} - 11 q^{53} - 22 q^{55} + 38 q^{59} + 26 q^{61} + 26 q^{65} + 52 q^{67} - 48 q^{71} - 35 q^{73} - 17 q^{77} + 20 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} - 24 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q - 3 * q^5 + 5 * q^7 - 3 * q^11 - 3 * q^13 - 7 * q^17 + q^19 + 2 * q^23 - 10 * q^25 - 9 * q^29 - 8 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 - 10 * q^47 + 15 * q^49 - 11 * q^53 - 22 * q^55 + 38 * q^59 + 26 * q^61 + 26 * q^65 + 52 * q^67 - 48 * q^71 - 35 * q^73 - 17 * q^77 + 20 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 - 24 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.76479	+	3.05671i	−0.789239	+	1.36700i	0.137194	+	0.990544i	$0.456192\pi$
$5$	−1.76479	+	3.05671i	−0.789239	+	1.36700i	−0.926433	+	0.376459i	$0.877142\pi$
$6$		0			0
$7$	2.63986	−	0.176417i	0.997774	−	0.0666792i
$7$	2.63986	−	0.176417i	0.997774	−	0.0666792i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.16036	+	2.00981i	0.349863	+	0.605981i	0.986225	−	0.165410i	$-0.0528948\pi$
$11$	1.16036	+	2.00981i	0.349863	+	0.605981i	−0.636362	+	0.771391i	$0.719561\pi$
$12$		0			0
$13$	−2.35884	−	4.08563i	−0.654224	−	1.13315i	−0.982088	−	0.188424i	$-0.939662\pi$
$13$	−2.35884	−	4.08563i	−0.654224	−	1.13315i	0.327864	−	0.944725i	$-0.393671\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.636946	−	1.10322i	0.154482	−	0.267571i	−0.778388	−	0.627783i	$-0.783962\pi$
$17$	0.636946	−	1.10322i	0.154482	−	0.267571i	0.932870	+	0.360212i	$0.117296\pi$
$18$		0			0
$19$	−2.78386	−	4.82178i	−0.638661	−	1.10619i	−0.985727	−	0.168352i	$-0.946155\pi$
$19$	−2.78386	−	4.82178i	−0.638661	−	1.10619i	0.347066	−	0.937841i	$-0.387178\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.64855	−	2.85537i	0.343746	−	0.595386i	−0.641379	−	0.767224i	$-0.721637\pi$
$23$	1.64855	−	2.85537i	0.343746	−	0.595386i	0.985125	+	0.171838i	$0.0549707\pi$
$24$		0			0
$25$	−3.72899	−	6.45880i	−0.745798	−	1.29176i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.32116	−	7.48447i	0.802419	−	1.38983i	−0.115601	−	0.993296i	$-0.536879\pi$
$29$	4.32116	−	7.48447i	0.802419	−	1.38983i	0.918020	−	0.396535i	$-0.129787\pi$
$30$		0			0
$31$	−8.51642			−1.52959			−0.764797	−	0.644272i	$-0.777161\pi$
$31$	−8.51642			−1.52959			−0.764797	+	0.644272i	$0.777161\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−4.11956	+	8.38064i	−0.696332	+	1.41659i
$36$		0			0
$37$	−2.84024	−	4.91943i	−0.466932	−	0.808750i	0.532354	−	0.846522i	$-0.321307\pi$
$37$	−2.84024	−	4.91943i	−0.466932	−	0.808750i	−0.999286	+	0.0377716i	$0.987974\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.66553	−	2.88478i	−0.260112	−	0.450528i	0.706159	−	0.708053i	$-0.250426\pi$
$41$	−1.66553	−	2.88478i	−0.260112	−	0.450528i	−0.966272	+	0.257525i	$0.917093\pi$
$42$		0			0
$43$	−0.0444165	+	0.0769317i	−0.00677346	+	0.0117320i	−0.869392	−	0.494123i	$-0.835489\pi$
$43$	−0.0444165	+	0.0769317i	−0.00677346	+	0.0117320i	0.862619	+	0.505855i	$0.168823\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.05213			1.02866			0.514330	−	0.857593i	$-0.328041\pi$
$47$	7.05213			1.02866			0.514330	+	0.857593i	$0.328041\pi$
$48$		0			0
$49$	6.93775	−	0.931432i	0.991108	−	0.133062i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.41816	+	5.92042i	−0.469520	+	0.813233i	−0.999393	−	0.0348444i	$-0.988906\pi$
$53$	−3.41816	+	5.92042i	−0.469520	+	0.813233i	0.529873	+	0.848077i	$0.322240\pi$
$54$		0			0
$55$	−8.19121			−1.10450
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.99490			−1.04085			−0.520423	−	0.853908i	$-0.674226\pi$
$59$	−7.99490			−1.04085			−0.520423	+	0.853908i	$0.674226\pi$
$60$		0			0
$61$	13.3553			1.70997			0.854985	−	0.518653i	$-0.173566\pi$
$61$	13.3553			1.70997			0.854985	+	0.518653i	$0.173566\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	16.6514			2.06536
$66$		0			0
$67$	−6.12804			−0.748660			−0.374330	−	0.927296i	$-0.622127\pi$
$67$	−6.12804			−0.748660			−0.374330	+	0.927296i	$0.622127\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.30202			0.154522			0.0772609	−	0.997011i	$-0.475383\pi$
$71$	1.30202			0.154522			0.0772609	+	0.997011i	$0.475383\pi$
$72$		0			0
$73$	6.64529	−	11.5100i	0.777772	−	1.34714i	−0.155451	−	0.987844i	$-0.549683\pi$
$73$	6.64529	−	11.5100i	0.777772	−	1.34714i	0.933223	−	0.359297i	$-0.116984\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.41777	+	5.10092i	0.389491	+	0.581303i
$78$		0			0
$79$	10.0281			1.12824			0.564122	−	0.825691i	$-0.309215\pi$
$79$	10.0281			1.12824			0.564122	+	0.825691i	$0.309215\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.90243	+	10.2233i	−0.647876	+	1.12215i	0.335753	+	0.941950i	$0.391009\pi$
$83$	−5.90243	+	10.2233i	−0.647876	+	1.12215i	−0.983629	+	0.180204i	$0.942324\pi$
$84$		0			0
$85$	2.24815	+	3.89392i	0.243847	+	0.422355i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.561496	−	0.972540i	−0.0595185	−	0.103089i	0.834731	−	0.550658i	$-0.185623\pi$
$89$	−0.561496	−	0.972540i	−0.0595185	−	0.103089i	−0.894249	+	0.447569i	$0.852290\pi$
$90$		0			0
$91$	−6.94778	−	10.3694i	−0.728325	−	1.08700i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	19.6517			2.01622
$96$		0			0
$97$	−3.50818	+	6.07635i	−0.356202	+	0.616960i	−0.987323	−	0.158724i	$-0.949262\pi$
$97$	−3.50818	+	6.07635i	−0.356202	+	0.616960i	0.631121	+	0.775685i	$0.282595\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.87055	−	8.43605i	−0.484638	−	0.839418i	0.515206	−	0.857066i	$-0.327715\pi$
$101$	−4.87055	−	8.43605i	−0.484638	−	0.839418i	−0.999844	+	0.0176482i	$0.994382\pi$
$102$		0			0
$103$	5.14279	−	8.90757i	0.506734	−	0.877689i	−0.493236	−	0.869896i	$-0.664186\pi$
$103$	5.14279	−	8.90757i	0.506734	−	0.877689i	0.999970	−	0.00779301i	$-0.00248062\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.72201	+	4.71465i	0.263146	+	0.455783i	0.967076	−	0.254487i	$-0.0819065\pi$
$107$	2.72201	+	4.71465i	0.263146	+	0.455783i	−0.703930	+	0.710269i	$0.748573\pi$
$108$		0			0
$109$	0.417404	−	0.722965i	0.0399800	−	0.0692475i	−0.845343	−	0.534224i	$-0.820604\pi$
$109$	0.417404	−	0.722965i	0.0399800	−	0.0692475i	0.885323	+	0.464977i	$0.153937\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.44881	−	9.43761i	−0.512581	−	0.887815i	−0.999894	−	0.0145882i	$-0.995356\pi$
$113$	−5.44881	−	9.43761i	−0.512581	−	0.887815i	0.487313	−	0.873227i	$-0.337977\pi$
$114$		0			0
$115$	5.81870	+	10.0783i	0.542596	+	0.939804i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.48682	−	3.02472i	0.136297	−	0.277276i
$120$		0			0
$121$	2.80711	−	4.86205i	0.255192	−	0.442005i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	8.67565			0.775974
$126$		0			0
$127$	9.90354			0.878797			0.439399	−	0.898292i	$-0.355192\pi$
$127$	9.90354			0.878797			0.439399	+	0.898292i	$0.355192\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.59220	+	14.8821i	−0.750704	+	1.30026i	0.196778	+	0.980448i	$0.436952\pi$
$131$	−8.59220	+	14.8821i	−0.750704	+	1.30026i	−0.947482	+	0.319809i	$0.896381\pi$
$132$		0			0
$133$	−8.19964	−	12.2377i	−0.710999	−	1.06115i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.04696	−	13.9377i	−0.687498	−	1.19078i	−0.972645	−	0.232298i	$-0.925376\pi$
$137$	−8.04696	−	13.9377i	−0.687498	−	1.19078i	0.285147	−	0.958484i	$-0.407958\pi$
$138$		0			0
$139$	−1.11151	−	1.92519i	−0.0942768	−	0.163292i	0.815030	−	0.579419i	$-0.196721\pi$
$139$	−1.11151	−	1.92519i	−0.0942768	−	0.163292i	−0.909307	+	0.416127i	$0.863387\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.47422	−	9.48163i	0.457778	−	0.792894i
$144$		0			0
$145$	15.2519	+	26.4171i	1.26660	+	2.19382i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.46846	−	6.00755i	0.284147	−	0.492158i	−0.688255	−	0.725469i	$-0.741623\pi$
$149$	3.46846	−	6.00755i	0.284147	−	0.492158i	0.972402	+	0.233312i	$0.0749562\pi$
$150$		0			0
$151$	7.75834	+	13.4378i	0.631365	+	1.09356i	0.987273	+	0.159035i	$0.0508383\pi$
$151$	7.75834	+	13.4378i	0.631365	+	1.09356i	−0.355908	+	0.934521i	$0.615828\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	15.0297	−	26.0322i	1.20722	−	2.09096i
$156$		0			0
$157$	0.802110			0.0640154			0.0320077	−	0.999488i	$-0.489810\pi$
$157$	0.802110			0.0640154			0.0320077	+	0.999488i	$0.489810\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.84821	−	7.82862i	0.303281	−	0.616982i
$162$		0			0
$163$	−1.77500	−	3.07438i	−0.139028	−	0.240804i	0.788101	−	0.615546i	$-0.211065\pi$
$163$	−1.77500	−	3.07438i	−0.139028	−	0.240804i	−0.927129	+	0.374742i	$0.877731\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.865131	+	1.49845i	0.0669459	+	0.115954i	0.897556	−	0.440901i	$-0.145341\pi$
$167$	0.865131	+	1.49845i	0.0669459	+	0.115954i	−0.830610	+	0.556855i	$0.812008\pi$
$168$		0			0
$169$	−4.62823	+	8.01633i	−0.356018	+	0.616641i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.23458			−0.169892			−0.0849462	−	0.996386i	$-0.527072\pi$
$173$	−2.23458			−0.169892			−0.0849462	+	0.996386i	$0.527072\pi$
$174$		0			0
$175$	−10.9835	−	16.3925i	−0.830272	−	1.23916i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.350412	+	0.606931i	−0.0261910	+	0.0453641i	−0.878824	−	0.477146i	$-0.841671\pi$
$179$	−0.350412	+	0.606931i	−0.0261910	+	0.0453641i	0.852633	+	0.522511i	$0.175004\pi$
$180$		0			0
$181$	−19.6339			−1.45938			−0.729688	−	0.683780i	$-0.760335\pi$
$181$	−19.6339			−1.45938			−0.729688	+	0.683780i	$0.760335\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	20.0497			1.47408
$186$		0			0
$187$	2.95636			0.216190
$188$		0			0
$189$		0			0
$190$		0			0
$191$	16.0858			1.16393			0.581963	−	0.813215i	$-0.302285\pi$
$191$	16.0858			1.16393			0.581963	+	0.813215i	$0.302285\pi$
$192$		0			0
$193$	−0.585463			−0.0421426			−0.0210713	−	0.999778i	$-0.506708\pi$
$193$	−0.585463			−0.0421426			−0.0210713	+	0.999778i	$0.506708\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.2923			1.23203			0.616014	−	0.787735i	$-0.288746\pi$
$197$	17.2923			1.23203			0.616014	+	0.787735i	$0.288746\pi$
$198$		0			0
$199$	12.2119	−	21.1517i	0.865681	−	1.49940i	−0.000687656	−	1.00000i	$-0.500219\pi$
$199$	12.2119	−	21.1517i	0.865681	−	1.49940i	0.866369	−	0.499404i	$-0.166448\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.0869	−	20.5203i	0.707960	−	1.44024i
$204$		0			0
$205$	11.7573			0.821164
$206$		0			0
$207$		0			0
$208$		0			0
$209$	6.46058	−	11.1900i	0.446888	−	0.774032i
$210$		0			0
$211$	5.58733	+	9.67754i	0.384648	+	0.666230i	0.991720	−	0.128417i	$-0.0409895\pi$
$211$	5.58733	+	9.67754i	0.384648	+	0.666230i	−0.607072	+	0.794647i	$0.707656\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.156772	−	0.271537i	−0.0106918	−	0.0185187i
$216$		0			0
$217$	−22.4822	+	1.50244i	−1.52619	+	0.101992i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.00981			−0.404263
$222$		0			0
$223$	1.32951	−	2.30277i	0.0890303	−	0.154205i	−0.818071	−	0.575117i	$-0.804957\pi$
$223$	1.32951	−	2.30277i	0.0890303	−	0.154205i	0.907101	+	0.420912i	$0.138290\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.95786	−	10.3193i	−0.395437	−	0.684917i	0.597720	−	0.801705i	$-0.296073\pi$
$227$	−5.95786	−	10.3193i	−0.395437	−	0.684917i	−0.993157	+	0.116788i	$0.962740\pi$
$228$		0			0
$229$	14.8064	−	25.6454i	0.978434	−	1.69470i	0.310330	−	0.950629i	$-0.399561\pi$
$229$	14.8064	−	25.6454i	0.978434	−	1.69470i	0.668104	−	0.744068i	$-0.267106\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.84417	−	3.19420i	−0.120816	−	0.209259i	0.799274	−	0.600967i	$-0.205218\pi$
$233$	−1.84417	−	3.19420i	−0.120816	−	0.209259i	−0.920090	+	0.391708i	$0.871884\pi$
$234$		0			0
$235$	−12.4456	+	21.5563i	−0.811859	+	1.40618i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.03590	+	13.9186i	0.519799	+	0.900319i	0.999735	+	0.0230153i	$0.00732663\pi$
$239$	8.03590	+	13.9186i	0.519799	+	0.900319i	−0.479936	+	0.877304i	$0.659340\pi$
$240$		0			0
$241$	−2.24933	−	3.89596i	−0.144892	−	0.250961i	0.784440	−	0.620204i	$-0.212950\pi$
$241$	−2.24933	−	3.89596i	−0.144892	−	0.250961i	−0.929333	+	0.369243i	$0.879617\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9.39658	+	22.8505i	−0.600326	+	1.45986i
$246$		0			0
$247$	−13.1333	+	22.7476i	−0.835654	+	1.44740i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−17.2696			−1.09005			−0.545023	−	0.838421i	$-0.683479\pi$
$251$	−17.2696			−1.09005			−0.545023	+	0.838421i	$0.683479\pi$
$252$		0			0
$253$	7.65167			0.481057
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.41087	−	4.17574i	0.150386	−	0.260476i	−0.780984	−	0.624552i	$-0.785282\pi$
$257$	2.41087	−	4.17574i	0.150386	−	0.260476i	0.931369	+	0.364076i	$0.118615\pi$
$258$		0			0
$259$	−8.36571	−	12.4856i	−0.519820	−	0.775815i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−14.0452	−	24.3270i	−0.866062	−	1.50006i	−0.865988	−	0.500064i	$-0.833310\pi$
$263$	−14.0452	−	24.3270i	−0.866062	−	1.50006i	−7.41948e−5	−	1.00000i	$-0.500024\pi$
$264$		0			0
$265$	−12.0647	−	20.8966i	−0.741128	−	1.28367i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.4126	+	21.4993i	−0.756810	+	1.31083i	0.187659	+	0.982234i	$0.439910\pi$
$269$	−12.4126	+	21.4993i	−0.756810	+	1.31083i	−0.944469	+	0.328599i	$0.893423\pi$
$270$		0			0
$271$	4.79671	+	8.30815i	0.291379	+	0.504684i	0.974136	−	0.225962i	$-0.0725524\pi$
$271$	4.79671	+	8.30815i	0.291379	+	0.504684i	−0.682757	+	0.730646i	$0.739219\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.65398	−	14.9891i	0.521854	−	0.903878i
$276$		0			0
$277$	−8.46914	−	14.6690i	−0.508862	−	0.881374i	−0.999947	−	0.0102629i	$-0.996733\pi$
$277$	−8.46914	−	14.6690i	−0.508862	−	0.881374i	0.491086	−	0.871111i	$-0.336600\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.4291	+	19.7958i	−0.681805	+	1.18092i	0.292625	+	0.956227i	$0.405471\pi$
$281$	−11.4291	+	19.7958i	−0.681805	+	1.18092i	−0.974430	+	0.224693i	$0.927862\pi$
$282$		0			0
$283$	−8.35621			−0.496725			−0.248363	−	0.968667i	$-0.579892\pi$
$283$	−8.35621			−0.496725			−0.248363	+	0.968667i	$0.579892\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.90570	−	7.32161i	−0.289574	−	0.432181i
$288$		0			0
$289$	7.68860	+	13.3170i	0.452271	+	0.783356i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.16141	+	3.74368i	0.126271	+	0.218708i	0.922229	−	0.386644i	$-0.126366\pi$
$293$	2.16141	+	3.74368i	0.126271	+	0.218708i	−0.795958	+	0.605352i	$0.793032\pi$
$294$		0			0
$295$	14.1093	−	24.4381i	0.821477	−	1.42284i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−15.5546			−0.899548
$300$		0			0
$301$	−0.103682	+	0.210925i	−0.00597610	+	0.0121575i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−23.5693	+	40.8233i	−1.34958	+	2.33753i
$306$		0			0
$307$	9.22888			0.526720			0.263360	−	0.964698i	$-0.415169\pi$
$307$	9.22888			0.526720			0.263360	+	0.964698i	$0.415169\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−19.1073			−1.08348			−0.541738	−	0.840548i	$-0.682233\pi$
$311$	−19.1073			−1.08348			−0.541738	+	0.840548i	$0.682233\pi$
$312$		0			0
$313$	5.67903			0.320997			0.160499	−	0.987036i	$-0.448690\pi$
$313$	5.67903			0.320997			0.160499	+	0.987036i	$0.448690\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	28.2681			1.58770			0.793848	−	0.608116i	$-0.208075\pi$
$317$	28.2681			1.58770			0.793848	+	0.608116i	$0.208075\pi$
$318$		0			0
$319$	20.0565			1.12295
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7.09266			−0.394646
$324$		0			0
$325$	−17.5922	+	30.4705i	−0.975838	+	1.69020i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	18.6167	−	1.24411i	1.02637	−	0.0685902i
$330$		0			0
$331$	6.68091			0.367216			0.183608	−	0.983000i	$-0.441222\pi$
$331$	6.68091			0.367216			0.183608	+	0.983000i	$0.441222\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.8147	−	18.7317i	0.590872	−	1.02342i
$336$		0			0
$337$	−3.49421	−	6.05215i	−0.190342	−	0.329681i	0.755022	−	0.655700i	$-0.227626\pi$
$337$	−3.49421	−	6.05215i	−0.190342	−	0.329681i	−0.945363	+	0.326018i	$0.894293\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−9.88215	−	17.1164i	−0.535148	−	0.926904i
$342$		0			0
$343$	18.1504	−	3.68279i	0.980030	−	0.198852i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.28821			0.444934			0.222467	−	0.974940i	$-0.428589\pi$
$347$	8.28821			0.444934			0.222467	+	0.974940i	$0.428589\pi$
$348$		0			0
$349$	3.05373	−	5.28921i	0.163462	−	0.283125i	−0.772646	−	0.634837i	$-0.781067\pi$
$349$	3.05373	−	5.28921i	0.163462	−	0.283125i	0.936108	+	0.351712i	$0.114400\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.3604	−	23.1409i	−0.711104	−	1.23167i	−0.964443	−	0.264290i	$-0.914862\pi$
$353$	−13.3604	−	23.1409i	−0.711104	−	1.23167i	0.253340	−	0.967377i	$-0.418471\pi$
$354$		0			0
$355$	−2.29780	+	3.97991i	−0.121955	+	0.211232i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	2.45603	+	4.25397i	0.129624	+	0.224516i	0.923531	−	0.383523i	$-0.125289\pi$
$359$	2.45603	+	4.25397i	0.129624	+	0.224516i	−0.793907	+	0.608040i	$0.791956\pi$
$360$		0			0
$361$	−5.99972	+	10.3918i	−0.315775	+	0.546938i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	23.4551	+	40.6255i	1.22770	+	2.12643i
$366$		0			0
$367$	−15.3532	−	26.5925i	−0.801430	−	1.38812i	−0.918675	−	0.395015i	$-0.870740\pi$
$367$	−15.3532	−	26.5925i	−0.801430	−	1.38812i	0.117245	−	0.993103i	$-0.462594\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.97901	+	16.2321i	−0.414250	+	0.842730i
$372$		0			0
$373$	−8.29190	+	14.3620i	−0.429338	+	0.743635i	−0.996815	−	0.0797543i	$-0.974586\pi$
$373$	−8.29190	+	14.3620i	−0.429338	+	0.743635i	0.567477	+	0.823390i	$0.307920\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−40.7716			−2.09985
$378$		0			0
$379$	−4.08857			−0.210016			−0.105008	−	0.994471i	$-0.533487\pi$
$379$	−4.08857			−0.210016			−0.105008	+	0.994471i	$0.533487\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.1769	+	26.2871i	−0.775503	+	1.34321i	0.159009	+	0.987277i	$0.449170\pi$
$383$	−15.1769	+	26.2871i	−0.775503	+	1.34321i	−0.934511	+	0.355933i	$0.884163\pi$
$384$		0			0
$385$	−21.6237	+	1.44507i	−1.10205	+	0.0736474i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.73382	−	3.00307i	−0.0879082	−	0.152261i	0.818719	−	0.574195i	$-0.194685\pi$
$389$	−1.73382	−	3.00307i	−0.0879082	−	0.152261i	−0.906627	+	0.421934i	$0.861352\pi$
$390$		0			0
$391$	−2.10007	−	3.63743i	−0.106205	−	0.183953i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−17.6974	+	30.6529i	−0.890455	+	1.54231i
$396$		0			0
$397$	−7.04243	−	12.1979i	−0.353450	−	0.612193i	0.633402	−	0.773823i	$-0.281658\pi$
$397$	−7.04243	−	12.1979i	−0.353450	−	0.612193i	−0.986851	+	0.161630i	$0.948325\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.46593	+	9.46726i	−0.272955	+	0.472772i	−0.969617	−	0.244627i	$-0.921334\pi$
$401$	−5.46593	+	9.46726i	−0.272955	+	0.472772i	0.696662	+	0.717400i	$0.254668\pi$
$402$		0			0
$403$	20.0888	+	34.7949i	1.00070	+	1.73326i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.59142	−	11.4167i	0.326725	−	0.565904i
$408$		0			0
$409$	15.9879			0.790553			0.395276	−	0.918562i	$-0.370649\pi$
$409$	15.9879			0.790553			0.395276	+	0.918562i	$0.370649\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−21.1054	+	1.41043i	−1.03853	+	0.0694029i
$414$		0			0
$415$	−20.8331	−	36.0841i	−1.02266	−	1.77130i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.56197	−	6.16951i	−0.174014	−	0.301400i	0.765806	−	0.643072i	$-0.222340\pi$
$419$	−3.56197	−	6.16951i	−0.174014	−	0.301400i	−0.939819	+	0.341671i	$0.889007\pi$
$420$		0			0
$421$	−16.6326	+	28.8086i	−0.810625	+	1.40404i	0.101802	+	0.994805i	$0.467539\pi$
$421$	−16.6326	+	28.8086i	−0.810625	+	1.40404i	−0.912427	+	0.409239i	$0.865794\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−9.50066			−0.460849
$426$		0			0
$427$	35.2561	−	2.35610i	1.70616	−	0.114019i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.62382	+	4.54459i	−0.126385	+	0.218905i	−0.922273	−	0.386538i	$-0.873671\pi$
$431$	−2.62382	+	4.54459i	−0.126385	+	0.218905i	0.795889	+	0.605443i	$0.207004\pi$
$432$		0			0
$433$	22.1053			1.06231			0.531156	−	0.847274i	$-0.321758\pi$
$433$	22.1053			1.06231			0.531156	+	0.847274i	$0.321758\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−18.3573			−0.878149
$438$		0			0
$439$	−34.6165			−1.65216			−0.826079	−	0.563555i	$-0.809433\pi$
$439$	−34.6165			−1.65216			−0.826079	+	0.563555i	$0.809433\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.40923			−0.209489			−0.104744	−	0.994499i	$-0.533402\pi$
$443$	−4.40923			−0.209489			−0.104744	+	0.994499i	$0.533402\pi$
$444$		0			0
$445$	3.96370			0.187897
$446$		0			0
$447$		0			0
$448$		0			0
$449$	19.6336			0.926568			0.463284	−	0.886210i	$-0.346671\pi$
$449$	19.6336			0.926568			0.463284	+	0.886210i	$0.346671\pi$
$450$		0			0
$451$	3.86525	−	6.69481i	0.182007	−	0.315246i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	43.9575	−	2.93759i	2.06076	−	0.137716i
$456$		0			0
$457$	−30.8392			−1.44259			−0.721297	−	0.692626i	$-0.756454\pi$
$457$	−30.8392			−1.44259			−0.721297	+	0.692626i	$0.756454\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.6297	−	23.6074i	0.634800	−	1.09951i	−0.351757	−	0.936091i	$-0.614416\pi$
$461$	13.6297	−	23.6074i	0.634800	−	1.09951i	0.986557	−	0.163415i	$-0.0522510\pi$
$462$		0			0
$463$	0.959750	+	1.66234i	0.0446034	+	0.0772553i	0.887465	−	0.460875i	$-0.152464\pi$
$463$	0.959750	+	1.66234i	0.0446034	+	0.0772553i	−0.842862	+	0.538130i	$0.819131\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.88655	+	8.46376i	0.226123	+	0.391656i	0.956656	−	0.291221i	$-0.0940616\pi$
$467$	4.88655	+	8.46376i	0.226123	+	0.391656i	−0.730533	+	0.682877i	$0.760728\pi$
$468$		0			0
$469$	−16.1772	+	1.08109i	−0.746994	+	0.0499201i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.206158			−0.00947913
$474$		0			0
$475$	−20.7619	+	35.9607i	−0.952623	+	1.64999i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.68809	−	13.3162i	−0.351278	−	0.608431i	0.635196	−	0.772351i	$-0.280919\pi$
$479$	−7.68809	−	13.3162i	−0.351278	−	0.608431i	−0.986474	+	0.163920i	$0.947586\pi$
$480$		0			0
$481$	−13.3993	+	23.2083i	−0.610956	+	1.05821i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−12.3824	−	21.4470i	−0.562258	−	0.973859i
$486$		0			0
$487$	−5.18342	+	8.97794i	−0.234883	+	0.406829i	−0.959239	−	0.282597i	$-0.908804\pi$
$487$	−5.18342	+	8.97794i	−0.234883	+	0.406829i	0.724356	+	0.689427i	$0.242137\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.94718	−	12.0329i	−0.313522	−	0.543035i	0.665600	−	0.746308i	$-0.268175\pi$
$491$	−6.94718	−	12.0329i	−0.313522	−	0.543035i	−0.979122	+	0.203273i	$0.934842\pi$
$492$		0			0
$493$	−5.50469	−	9.53440i	−0.247919	−	0.429408i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.43717	−	0.229699i	0.154178	−	0.0103034i
$498$		0			0
$499$	−1.70488	+	2.95294i	−0.0763210	+	0.132192i	−0.901660	−	0.432446i	$-0.857651\pi$
$499$	−1.70488	+	2.95294i	−0.0763210	+	0.132192i	0.825339	+	0.564638i	$0.190984\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	43.8911			1.95701			0.978504	−	0.206227i	$-0.0661185\pi$
$503$	43.8911			1.95701			0.978504	+	0.206227i	$0.0661185\pi$
$504$		0			0
$505$	34.3821			1.52998
$506$		0			0
$507$		0			0
$508$		0			0
$509$	19.6674	−	34.0649i	0.871742	−	1.50990i	0.0115483	−	0.999933i	$-0.496324\pi$
$509$	19.6674	−	34.0649i	0.871742	−	1.50990i	0.860193	−	0.509968i	$-0.170343\pi$
$510$		0			0
$511$	15.5121	−	31.5571i	0.686215	−	1.39600i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	18.1519	+	31.4400i	0.799869	+	1.38541i
$516$		0			0
$517$	8.18305	+	14.1735i	0.359890	+	0.623348i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−12.4779	+	21.6124i	−0.546669	+	0.946858i	0.451831	+	0.892104i	$0.350771\pi$
$521$	−12.4779	+	21.6124i	−0.546669	+	0.946858i	−0.998500	+	0.0547547i	$0.982562\pi$
$522$		0			0
$523$	15.1575	+	26.2536i	0.662792	+	1.14799i	0.979879	+	0.199594i	$0.0639622\pi$
$523$	15.1575	+	26.2536i	0.662792	+	1.14799i	−0.317086	+	0.948397i	$0.602704\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.42449	+	9.39550i	−0.236295	+	0.409274i
$528$		0			0
$529$	6.06457	+	10.5041i	0.263677	+	0.456702i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.85744	+	13.6095i	−0.340343	+	0.589492i
$534$		0			0
$535$	−19.2151			−0.830742
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.92233	+	12.8628i	0.427385	+	0.554039i
$540$		0			0
$541$	−14.2812	−	24.7357i	−0.613996	−	1.06347i	−0.990560	−	0.137082i	$-0.956228\pi$
$541$	−14.2812	−	24.7357i	−0.613996	−	1.06347i	0.376563	−	0.926391i	$-0.377106\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.47326	+	2.55177i	0.0631077	+	0.109306i
$546$		0			0
$547$	−3.89233	+	6.74171i	−0.166424	+	0.288255i	−0.937160	−	0.348900i	$-0.886555\pi$
$547$	−3.89233	+	6.74171i	−0.166424	+	0.288255i	0.770736	+	0.637154i	$0.219889\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−48.1179			−2.04989
$552$		0			0
$553$	26.4727	−	1.76912i	1.12573	−	0.0752305i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	23.2470	−	40.2650i	0.985008	−	1.70608i	0.343108	−	0.939296i	$-0.388520\pi$
$557$	23.2470	−	40.2650i	0.985008	−	1.70608i	0.641900	−	0.766788i	$-0.278146\pi$
$558$		0			0
$559$	0.419086			0.0177254
$560$		0			0
$561$		0			0
$562$		0			0
$563$	27.9826			1.17933			0.589663	−	0.807650i	$-0.299261\pi$
$563$	27.9826			1.17933			0.589663	+	0.807650i	$0.299261\pi$
$564$		0			0
$565$	38.4641			1.61820
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.89957			−0.373090			−0.186545	−	0.982446i	$-0.559729\pi$
$569$	−8.89957			−0.373090			−0.186545	+	0.982446i	$0.559729\pi$
$570$		0			0
$571$	32.3304			1.35298			0.676492	−	0.736450i	$-0.263500\pi$
$571$	32.3304			1.35298			0.676492	+	0.736450i	$0.263500\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−24.5897			−1.02546
$576$		0			0
$577$	−16.8414	+	29.1701i	−0.701115	+	1.21437i	0.266960	+	0.963707i	$0.413981\pi$
$577$	−16.8414	+	29.1701i	−0.701115	+	1.21437i	−0.968075	+	0.250659i	$0.919353\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−13.7780	+	28.0294i	−0.571610	+	1.16286i
$582$		0			0
$583$	−15.8652			−0.657071
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.24076	+	2.14907i	−0.0512118	+	0.0887015i	−0.890495	−	0.454993i	$-0.849642\pi$
$587$	−1.24076	+	2.14907i	−0.0512118	+	0.0887015i	0.839283	+	0.543695i	$0.182975\pi$
$588$		0			0
$589$	23.7085	+	41.0643i	0.976891	+	1.69202i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	15.0903	+	26.1371i	0.619684	+	1.07332i	0.989543	+	0.144236i	$0.0460725\pi$
$593$	15.0903	+	26.1371i	0.619684	+	1.07332i	−0.369859	+	0.929088i	$0.620594\pi$
$594$		0			0
$595$	6.62177	+	9.88280i	0.271466	+	0.405155i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.4083			−0.670424			−0.335212	−	0.942143i	$-0.608808\pi$
$599$	−16.4083			−0.670424			−0.335212	+	0.942143i	$0.608808\pi$
$600$		0			0
$601$	−2.96998	+	5.14416i	−0.121148	+	0.209835i	−0.920221	−	0.391400i	$-0.871991\pi$
$601$	−2.96998	+	5.14416i	−0.121148	+	0.209835i	0.799073	+	0.601235i	$0.205324\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.90793	+	17.1610i	0.402815	+	0.697695i
$606$		0			0
$607$	−2.97573	+	5.15412i	−0.120781	+	0.209199i	−0.920076	−	0.391740i	$-0.871873\pi$
$607$	−2.97573	+	5.15412i	−0.120781	+	0.209199i	0.799295	+	0.600939i	$0.205207\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.6348	−	28.8124i	−0.672974	−	1.16562i
$612$		0			0
$613$	15.5920	−	27.0062i	0.629756	−	1.09077i	−0.357845	−	0.933781i	$-0.616488\pi$
$613$	15.5920	−	27.0062i	0.629756	−	1.09077i	0.987601	−	0.156988i	$-0.0501783\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.1437	+	19.3014i	0.448627	+	0.777045i	0.998297	−	0.0583367i	$-0.0185797\pi$
$617$	11.1437	+	19.3014i	0.448627	+	0.777045i	−0.549670	+	0.835382i	$0.685246\pi$
$618$		0			0
$619$	17.2943	+	29.9547i	0.695118	+	1.20398i	0.970141	+	0.242543i	$0.0779814\pi$
$619$	17.2943	+	29.9547i	0.695118	+	1.20398i	−0.275022	+	0.961438i	$0.588685\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.65384	−	2.46831i	−0.0662599	−	0.0988909i
$624$		0			0
$625$	3.33422	−	5.77504i	0.133369	−	0.231002i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.23631			−0.288530
$630$		0			0
$631$	26.2933			1.04672			0.523360	−	0.852112i	$-0.324678\pi$
$631$	26.2933			1.04672			0.523360	+	0.852112i	$0.324678\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−17.4777	+	30.2723i	−0.693582	+	1.20132i
$636$		0			0
$637$	−20.1705	−	26.1480i	−0.799185	−	1.03602i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−16.2673	−	28.1758i	−0.642519	−	1.11288i	−0.984869	−	0.173303i	$-0.944556\pi$
$641$	−16.2673	−	28.1758i	−0.642519	−	1.11288i	0.342349	−	0.939573i	$-0.388777\pi$
$642$		0			0
$643$	−5.21987	−	9.04107i	−0.205851	−	0.356545i	0.744552	−	0.667564i	$-0.232663\pi$
$643$	−5.21987	−	9.04107i	−0.205851	−	0.356545i	−0.950404	+	0.311019i	$0.899330\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.685824	−	1.18788i	0.0269625	−	0.0467005i	−0.852229	−	0.523168i	$-0.824750\pi$
$647$	0.685824	−	1.18788i	0.0269625	−	0.0467005i	0.879192	+	0.476468i	$0.158083\pi$
$648$		0			0
$649$	−9.27699	−	16.0682i	−0.364154	−	0.630733i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.62567	+	6.27985i	−0.141883	+	0.245749i	−0.928206	−	0.372067i	$-0.878649\pi$
$653$	−3.62567	+	6.27985i	−0.141883	+	0.245749i	0.786322	+	0.617816i	$0.211982\pi$
$654$		0			0
$655$	−30.3269	−	52.5277i	−1.18497	−	2.05243i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.3187	+	23.0686i	−0.518822	+	0.898626i	0.480939	+	0.876754i	$0.340296\pi$
$659$	−13.3187	+	23.0686i	−0.518822	+	0.898626i	−0.999761	+	0.0218722i	$0.993037\pi$
$660$		0			0
$661$	−34.8199			−1.35434			−0.677168	−	0.735828i	$-0.736793\pi$
$661$	−34.8199			−1.35434			−0.677168	+	0.735828i	$0.736793\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	51.8779	−	3.46689i	2.01174	−	0.134440i
$666$		0			0
$667$	−14.2473	−	24.6770i	−0.551657	−	0.955498i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	15.4970	+	26.8416i	0.598255	+	1.03621i
$672$		0			0
$673$	8.23841	−	14.2693i	0.317567	−	0.550043i	−0.662412	−	0.749139i	$-0.730467\pi$
$673$	8.23841	−	14.2693i	0.317567	−	0.550043i	0.979980	+	0.199096i	$0.0638007\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.1654			0.813450			0.406725	−	0.913551i	$-0.366671\pi$
$677$	21.1654			0.813450			0.406725	+	0.913551i	$0.366671\pi$
$678$		0			0
$679$	−8.18916	+	16.6596i	−0.314271	+	0.639339i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.0756	−	24.3796i	0.538587	−	0.932859i	−0.460394	−	0.887715i	$-0.652292\pi$
$683$	14.0756	−	24.3796i	0.538587	−	0.932859i	0.998980	−	0.0451447i	$-0.0143749\pi$
$684$		0			0
$685$	56.8049			2.17040
$686$		0			0
$687$		0			0
$688$		0			0
$689$	32.2515			1.22869
$690$		0			0
$691$	−19.0796			−0.725822			−0.362911	−	0.931824i	$-0.618217\pi$
$691$	−19.0796			−0.725822			−0.362911	+	0.931824i	$0.618217\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.84632			0.297628
$696$		0			0
$697$	−4.24341			−0.160731
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−23.8508			−0.900834			−0.450417	−	0.892818i	$-0.648725\pi$
$701$	−23.8508			−0.900834			−0.450417	+	0.892818i	$0.648725\pi$
$702$		0			0
$703$	−15.8136	+	27.3900i	−0.596422	+	1.03303i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14.3459	−	21.4108i	−0.539532	−	0.805235i
$708$		0			0
$709$	20.0986			0.754817			0.377409	−	0.926047i	$-0.376815\pi$
$709$	20.0986			0.754817			0.377409	+	0.926047i	$0.376815\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−14.0397	+	24.3175i	−0.525792	+	0.910698i
$714$		0			0
$715$	19.3217	+	33.4662i	0.722592	+	1.25157i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.29246	−	5.70270i	−0.122788	−	0.212675i	0.798078	−	0.602554i	$-0.205850\pi$
$719$	−3.29246	−	5.70270i	−0.122788	−	0.212675i	−0.920866	+	0.389879i	$0.872517\pi$
$720$		0			0
$721$	12.0048	−	24.4220i	0.447082	−	0.909524i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−64.4542			−2.39377
$726$		0			0
$727$	−18.2342	+	31.5826i	−0.676269	+	1.17133i	0.299827	+	0.953994i	$0.403071\pi$
$727$	−18.2342	+	31.5826i	−0.676269	+	1.17133i	−0.976096	+	0.217339i	$0.930262\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.0565818	+	0.0980026i	0.00209276	+	0.00362476i
$732$		0			0
$733$	−11.6824	+	20.2345i	−0.431498	+	0.747377i	−0.997003	−	0.0773684i	$-0.975348\pi$
$733$	−11.6824	+	20.2345i	−0.431498	+	0.747377i	0.565504	+	0.824745i	$0.308682\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.11077	−	12.3162i	−0.261928	−	0.453673i
$738$		0			0
$739$	−14.4596	+	25.0448i	−0.531906	+	0.921288i	0.467400	+	0.884046i	$0.345191\pi$
$739$	−14.4596	+	25.0448i	−0.531906	+	0.921288i	−0.999306	+	0.0372422i	$0.988143\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	11.6794	+	20.2292i	0.428474	+	0.742139i	0.996738	−	0.0807074i	$-0.0257179\pi$
$743$	11.6794	+	20.2292i	0.428474	+	0.742139i	−0.568264	+	0.822847i	$0.692385\pi$
$744$		0			0
$745$	12.2422	+	21.2042i	0.448521	+	0.776860i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	8.01747	+	11.9658i	0.292952	+	0.437222i
$750$		0			0
$751$	−0.856616	+	1.48370i	−0.0312584	+	0.0541411i	−0.881231	−	0.472685i	$-0.843285\pi$
$751$	−0.856616	+	1.48370i	−0.0312584	+	0.0541411i	0.849973	+	0.526826i	$0.176618\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−54.7675			−1.99319
$756$		0			0
$757$	28.4587			1.03435			0.517175	−	0.855880i	$-0.326984\pi$
$757$	28.4587			1.03435			0.517175	+	0.855880i	$0.326984\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−17.0525	+	29.5358i	−0.618154	+	1.07067i	0.371669	+	0.928365i	$0.378786\pi$
$761$	−17.0525	+	29.5358i	−0.618154	+	1.07067i	−0.989822	+	0.142308i	$0.954548\pi$
$762$		0			0
$763$	0.974346	−	1.98216i	0.0352737	−	0.0717592i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18.8587	+	32.6642i	0.680947	+	1.17943i
$768$		0			0
$769$	2.48467	+	4.30357i	0.0895995	+	0.155191i	0.907342	−	0.420394i	$-0.138108\pi$
$769$	2.48467	+	4.30357i	0.0895995	+	0.155191i	−0.817742	+	0.575584i	$0.804775\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.74814	−	9.95607i	0.206746	−	0.358095i	−0.743941	−	0.668245i	$-0.767046\pi$
$773$	5.74814	−	9.95607i	0.206746	−	0.358095i	0.950688	+	0.310150i	$0.100379\pi$
$774$		0			0
$775$	31.7576	+	55.0058i	1.14077	+	1.97587i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.27320	+	16.0617i	−0.332247	+	0.575469i
$780$		0			0
$781$	1.51082	+	2.61682i	0.0540615	+	0.0936373i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.41556	+	2.45182i	−0.0505235	+	0.0875092i
$786$		0			0
$787$	−48.6011			−1.73244			−0.866221	−	0.499661i	$-0.833458\pi$
$787$	−48.6011			−1.73244			−0.866221	+	0.499661i	$0.833458\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−16.0491	−	23.9527i	−0.570639	−	0.851661i
$792$		0			0
$793$	−31.5030	−	54.5647i	−1.11870	−	1.93765i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.8556	−	29.1947i	−0.597056	−	1.03413i	−0.993253	−	0.115965i	$-0.963004\pi$
$797$	−16.8556	−	29.1947i	−0.597056	−	1.03413i	0.396198	−	0.918165i	$-0.370330\pi$
$798$		0			0
$799$	4.49183	−	7.78007i	0.158909	−	0.275239i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	30.8438			1.08846
$804$		0			0
$805$	17.1385	+	25.5788i	0.604054	+	0.901533i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.93617	−	13.7459i	0.279021	−	0.483278i	−0.692121	−	0.721782i	$-0.743323\pi$
$809$	7.93617	−	13.7459i	0.279021	−	0.483278i	0.971142	+	0.238503i	$0.0766568\pi$
$810$		0			0
$811$	−27.2524			−0.956963			−0.478481	−	0.878098i	$-0.658813\pi$
$811$	−27.2524			−0.956963			−0.478481	+	0.878098i	$0.658813\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.5300			0.438907
$816$		0			0
$817$	0.494597			0.0173038
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.3389			−0.849433			−0.424717	−	0.905326i	$-0.639626\pi$
$821$	−24.3389			−0.849433			−0.424717	+	0.905326i	$0.639626\pi$
$822$		0			0
$823$	11.5380			0.402188			0.201094	−	0.979572i	$-0.435550\pi$
$823$	11.5380			0.402188			0.201094	+	0.979572i	$0.435550\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−34.8582			−1.21214			−0.606069	−	0.795412i	$-0.707255\pi$
$827$	−34.8582			−1.21214			−0.606069	+	0.795412i	$0.707255\pi$
$828$		0			0
$829$	−7.64018	+	13.2332i	−0.265354	+	0.459607i	−0.967656	−	0.252272i	$-0.918822\pi$
$829$	−7.64018	+	13.2332i	−0.265354	+	0.459607i	0.702302	+	0.711879i	$0.252156\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.39140	−	8.24716i	0.117505	−	0.285747i
$834$		0			0
$835$	−6.10711			−0.211345
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.39990	+	14.5490i	−0.289997	+	0.502289i	−0.973809	−	0.227369i	$-0.926988\pi$
$839$	−8.39990	+	14.5490i	−0.289997	+	0.502289i	0.683812	+	0.729658i	$0.260321\pi$
$840$		0			0
$841$	−22.8448	−	39.5684i	−0.787753	−	1.36443i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−16.3357	−	28.2943i	−0.561967	−	0.973355i
$846$		0			0
$847$	6.55263	−	13.3304i	0.225151	−	0.458037i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−18.7291			−0.642024
$852$		0			0
$853$	−11.4270	+	19.7921i	−0.391253	+	0.677670i	−0.992615	−	0.121306i	$-0.961292\pi$
$853$	−11.4270	+	19.7921i	−0.391253	+	0.677670i	0.601362	+	0.798977i	$0.294625\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.5871	−	30.4618i	−0.600765	−	1.04056i	−0.992705	−	0.120565i	$-0.961529\pi$
$857$	−17.5871	−	30.4618i	−0.600765	−	1.04056i	0.391940	−	0.919991i	$-0.371804\pi$
$858$		0			0
$859$	5.28520	−	9.15424i	0.180329	−	0.312339i	−0.761664	−	0.647973i	$-0.775617\pi$
$859$	5.28520	−	9.15424i	0.180329	−	0.312339i	0.941993	+	0.335634i	$0.108950\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.29326	−	12.6323i	−0.248265	−	0.430008i	0.714779	−	0.699350i	$-0.246527\pi$
$863$	−7.29326	−	12.6323i	−0.248265	−	0.430008i	−0.963045	+	0.269342i	$0.913194\pi$
$864$		0			0
$865$	3.94358	−	6.83048i	0.134086	−	0.232243i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	11.6362	+	20.1545i	0.394731	+	0.683694i
$870$		0			0
$871$	14.4551	+	25.0369i	0.489791	+	0.848343i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	22.9025	−	1.53053i	0.774247	−	0.0517413i
$876$		0			0
$877$	−5.65914	+	9.80192i	−0.191096	+	0.330987i	−0.945614	−	0.325292i	$-0.894537\pi$
$877$	−5.65914	+	9.80192i	−0.191096	+	0.330987i	0.754518	+	0.656279i	$0.227871\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.733220			0.0247028			0.0123514	−	0.999924i	$-0.496068\pi$
$881$	0.733220			0.0247028			0.0123514	+	0.999924i	$0.496068\pi$
$882$		0			0
$883$	14.1726			0.476944			0.238472	−	0.971149i	$-0.423353\pi$
$883$	14.1726			0.476944			0.238472	+	0.971149i	$0.423353\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.8162	−	29.1266i	0.564634	−	0.977975i	−0.432449	−	0.901658i	$-0.642351\pi$
$887$	16.8162	−	29.1266i	0.564634	−	0.977975i	0.997084	−	0.0763170i	$-0.0243161\pi$
$888$		0			0
$889$	26.1440	−	1.74715i	0.876842	−	0.0585975i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−19.6321	−	34.0038i	−0.656964	−	1.13790i
$894$		0			0
$895$	−1.23681	−	2.14221i	−0.0413419	−	0.0716063i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−36.8008	+	63.7408i	−1.22737	+	2.12588i
$900$		0			0
$901$	4.35436	+	7.54198i	0.145065	+	0.251260i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	34.6498	−	60.0152i	1.15180	−	1.99497i
$906$		0			0
$907$	4.79255	+	8.30094i	0.159134	+	0.275628i	0.934557	−	0.355814i	$-0.115796\pi$
$907$	4.79255	+	8.30094i	0.159134	+	0.275628i	−0.775423	+	0.631443i	$0.782463\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.37499	+	16.2380i	−0.310607	+	0.537988i	−0.978494	−	0.206275i	$-0.933866\pi$
$911$	−9.37499	+	16.2380i	−0.310607	+	0.537988i	0.667887	+	0.744263i	$0.267199\pi$
$912$		0			0
$913$	−27.3959			−0.906672
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−20.0568	+	40.8026i	−0.662333	+	1.34742i
$918$		0			0
$919$	−21.2895	−	36.8745i	−0.702276	−	1.21638i	−0.967666	−	0.252236i	$-0.918834\pi$
$919$	−21.2895	−	36.8745i	−0.702276	−	1.21638i	0.265390	−	0.964141i	$-0.414499\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.07126	−	5.31958i	−0.101092	−	0.175096i
$924$		0			0
$925$	−21.1824	+	36.6890i	−0.696474	+	1.20633i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−38.1524			−1.25174			−0.625869	−	0.779928i	$-0.715256\pi$
$929$	−38.1524			−1.25174			−0.625869	+	0.779928i	$0.715256\pi$
$930$		0			0
$931$	−23.8049	−	30.8594i	−0.780173	−	1.01137i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.21736	+	9.03673i	−0.170626	+	0.295533i
$936$		0			0
$937$	6.48960			0.212006			0.106003	−	0.994366i	$-0.466195\pi$
$937$	6.48960			0.212006			0.106003	+	0.994366i	$0.466195\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.466471			0.0152065			0.00760326	−	0.999971i	$-0.497580\pi$
$941$	0.466471			0.0152065			0.00760326	+	0.999971i	$0.497580\pi$
$942$		0			0
$943$	−10.9828			−0.357650
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.1115			−0.491058			−0.245529	−	0.969389i	$-0.578962\pi$
$947$	−15.1115			−0.491058			−0.245529	+	0.969389i	$0.578962\pi$
$948$		0			0
$949$	−62.7006			−2.03535
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−19.6802			−0.637503			−0.318751	−	0.947838i	$-0.603264\pi$
$953$	−19.6802			−0.637503			−0.318751	+	0.947838i	$0.603264\pi$
$954$		0			0
$955$	−28.3881	+	49.1696i	−0.918616	+	1.59109i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−23.7017	−	35.3741i	−0.765368	−	1.14229i
$960$		0			0
$961$	41.5293			1.33966
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.03322	−	1.78959i	0.0332606	−	0.0576090i
$966$		0			0
$967$	−8.83228	−	15.2980i	−0.284027	−	0.491949i	0.688346	−	0.725383i	$-0.258337\pi$
$967$	−8.83228	−	15.2980i	−0.284027	−	0.491949i	−0.972373	+	0.233433i	$0.925004\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−11.7523	−	20.3555i	−0.377148	−	0.653240i	0.613498	−	0.789697i	$-0.289762\pi$
$971$	−11.7523	−	20.3555i	−0.377148	−	0.653240i	−0.990646	+	0.136456i	$0.956429\pi$
$972$		0			0
$973$	−3.27386	−	4.88614i	−0.104955	−	0.156642i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.43379			0.173842			0.0869211	−	0.996215i	$-0.472297\pi$
$977$	5.43379			0.173842			0.0869211	+	0.996215i	$0.472297\pi$
$978$		0			0
$979$	1.30308	−	2.25700i	0.0416466	−	0.0721341i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.05345	+	1.82463i	0.0335998	+	0.0581966i	0.882336	−	0.470619i	$-0.155969\pi$
$983$	1.05345	+	1.82463i	0.0335998	+	0.0581966i	−0.848736	+	0.528816i	$0.822636\pi$
$984$		0			0
$985$	−30.5174	+	52.8577i	−0.972366	+	1.68419i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.146446	+	0.253651i	0.00465670	+	0.00806564i
$990$		0			0
$991$	−8.91172	+	15.4356i	−0.283090	+	0.490327i	−0.972144	−	0.234383i	$-0.924693\pi$
$991$	−8.91172	+	15.4356i	−0.283090	+	0.490327i	0.689054	+	0.724710i	$0.258026\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	43.1031	+	74.6567i	1.36646	+	2.36678i
$996$		0			0
$997$	18.2477	+	31.6060i	0.577911	+	1.00097i	0.995719	+	0.0924360i	$0.0294653\pi$
$997$	18.2477	+	31.6060i	0.577911	+	1.00097i	−0.417807	+	0.908536i	$0.637201\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.q.k.2881.1		22
3.2	odd	2		1008.2.q.k.529.4		22
4.3	odd	2		1512.2.q.c.1369.1		22
7.2	even	3		3024.2.t.l.289.11		22
9.4	even	3		3024.2.t.l.1873.11		22
9.5	odd	6		1008.2.t.k.193.5		22
12.11	even	2		504.2.q.d.25.8	✓	22
21.2	odd	6		1008.2.t.k.961.5		22
28.23	odd	6		1512.2.t.d.289.11		22
36.23	even	6		504.2.t.d.193.7	yes	22
36.31	odd	6		1512.2.t.d.361.11		22
63.23	odd	6		1008.2.q.k.625.4		22
63.58	even	3	inner	3024.2.q.k.2305.1		22
84.23	even	6		504.2.t.d.457.7	yes	22
252.23	even	6		504.2.q.d.121.8	yes	22
252.247	odd	6		1512.2.q.c.793.1		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.8	✓	22	12.11	even	2
504.2.q.d.121.8	yes	22	252.23	even	6
504.2.t.d.193.7	yes	22	36.23	even	6
504.2.t.d.457.7	yes	22	84.23	even	6
1008.2.q.k.529.4		22	3.2	odd	2
1008.2.q.k.625.4		22	63.23	odd	6
1008.2.t.k.193.5		22	9.5	odd	6
1008.2.t.k.961.5		22	21.2	odd	6
1512.2.q.c.793.1		22	252.247	odd	6
1512.2.q.c.1369.1		22	4.3	odd	2
1512.2.t.d.289.11		22	28.23	odd	6
1512.2.t.d.361.11		22	36.31	odd	6
3024.2.q.k.2305.1		22	63.58	even	3	inner
3024.2.q.k.2881.1		22	1.1	even	1	trivial
3024.2.t.l.289.11		22	7.2	even	3
3024.2.t.l.1873.11		22	9.4	even	3

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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.76479 + 3.05671i) q^{5} +(2.63986 - 0.176417i) q^{7} +O(q^{10})\)	\(q+(-1.76479 + 3.05671i) q^{5} +(2.63986 - 0.176417i) q^{7} +(1.16036 + 2.00981i) q^{11} +(-2.35884 - 4.08563i) q^{13} +(0.636946 - 1.10322i) q^{17} +(-2.78386 - 4.82178i) q^{19} +(1.64855 - 2.85537i) q^{23} +(-3.72899 - 6.45880i) q^{25} +(4.32116 - 7.48447i) q^{29} -8.51642 q^{31} +(-4.11956 + 8.38064i) q^{35} +(-2.84024 - 4.91943i) q^{37} +(-1.66553 - 2.88478i) q^{41} +(-0.0444165 + 0.0769317i) q^{43} +7.05213 q^{47} +(6.93775 - 0.931432i) q^{49} +(-3.41816 + 5.92042i) q^{53} -8.19121 q^{55} -7.99490 q^{59} +13.3553 q^{61} +16.6514 q^{65} -6.12804 q^{67} +1.30202 q^{71} +(6.64529 - 11.5100i) q^{73} +(3.41777 + 5.10092i) q^{77} +10.0281 q^{79} +(-5.90243 + 10.2233i) q^{83} +(2.24815 + 3.89392i) q^{85} +(-0.561496 - 0.972540i) q^{89} +(-6.94778 - 10.3694i) q^{91} +19.6517 q^{95} +(-3.50818 + 6.07635i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{5} + 5 q^{7}+O(q^{10}) \) 22 * q - 3 * q^5 + 5 * q^7	\( 22 q - 3 q^{5} + 5 q^{7} - 3 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} + 2 q^{23} - 10 q^{25} - 9 q^{29} - 8 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} - 10 q^{47} + 15 q^{49} - 11 q^{53} - 22 q^{55} + 38 q^{59} + 26 q^{61} + 26 q^{65} + 52 q^{67} - 48 q^{71} - 35 q^{73} - 17 q^{77} + 20 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} - 24 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q - 3 * q^5 + 5 * q^7 - 3 * q^11 - 3 * q^13 - 7 * q^17 + q^19 + 2 * q^23 - 10 * q^25 - 9 * q^29 - 8 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 - 10 * q^47 + 15 * q^49 - 11 * q^53 - 22 * q^55 + 38 * q^59 + 26 * q^61 + 26 * q^65 + 52 * q^67 - 48 * q^71 - 35 * q^73 - 17 * q^77 + 20 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 - 24 * q^95 - 29 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more