LMFDB - Embedded newform 3024.2.t.l.1873.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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, 4, 2]))

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (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			1873.11
Character	$\chi$	$=$	3024.1873
Dual form			3024.2.t.l.289.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.52959 q^{5} +(-1.16715 + 2.37440i) q^{7} +O(q^{10})$	$q+3.52959 q^{5} +(-1.16715 + 2.37440i) q^{7} -2.32073 q^{11} +(-2.35884 + 4.08563i) q^{13} +(0.636946 - 1.10322i) q^{17} +(-2.78386 - 4.82178i) q^{19} -3.29710 q^{23} +7.45798 q^{25} +(4.32116 + 7.48447i) q^{29} +(4.25821 + 7.37543i) q^{31} +(-4.11956 + 8.38064i) q^{35} +(-2.84024 - 4.91943i) q^{37} +(-1.66553 + 2.88478i) q^{41} +(-0.0444165 - 0.0769317i) q^{43} +(-3.52607 + 6.10733i) q^{47} +(-4.27552 - 5.54256i) q^{49} +(-3.41816 + 5.92042i) q^{53} -8.19121 q^{55} +(3.99745 + 6.92378i) q^{59} +(-6.67764 + 11.5660i) q^{61} +(-8.32572 + 14.4206i) q^{65} +(3.06402 + 5.30704i) q^{67} +1.30202 q^{71} +(6.64529 - 11.5100i) q^{73} +(2.70864 - 5.51033i) q^{77} +(-5.01403 + 8.68455i) q^{79} +(-5.90243 - 10.2233i) q^{83} +(2.24815 - 3.89392i) q^{85} +(-0.561496 - 0.972540i) q^{89} +(-6.94778 - 10.3694i) q^{91} +(-9.82586 - 17.0189i) q^{95} +(-3.50818 - 6.07635i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) $ 22 * q + 6 * q^5 - 7 * q^7	$ 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) $ 22 * q + 6 * q^5 - 7 * q^7 + 6 * q^11 - 3 * q^13 - 7 * q^17 + q^19 - 4 * q^23 + 20 * q^25 - 9 * q^29 + 4 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 + 5 * q^47 - 15 * q^49 - 11 * q^53 - 22 * q^55 - 19 * q^59 - 13 * q^61 - 13 * q^65 - 26 * q^67 - 48 * q^71 - 35 * q^73 + 4 * q^77 - 10 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 + 12 * q^95 - 29 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	3.52959			1.57848			0.789239	−	0.614086i	$-0.210475\pi$
$5$	3.52959			1.57848			0.789239	+	0.614086i	$0.210475\pi$
$6$		0			0
$7$	−1.16715	+	2.37440i	−0.441141	+	0.897438i
$7$	−1.16715	+	2.37440i	−0.441141	+	0.897438i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.32073			−0.699726			−0.349863	−	0.936801i	$-0.613772\pi$
$11$	−2.32073			−0.699726			−0.349863	+	0.936801i	$0.613772\pi$
$12$		0			0
$13$	−2.35884	+	4.08563i	−0.654224	+	1.13315i	0.327864	+	0.944725i	$0.393671\pi$
$13$	−2.35884	+	4.08563i	−0.654224	+	1.13315i	−0.982088	+	0.188424i	$0.939662\pi$
$14$		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
$23$	−3.29710			−0.687492			−0.343746	−	0.939063i	$-0.611696\pi$
$23$	−3.29710			−0.687492			−0.343746	+	0.939063i	$0.611696\pi$
$24$		0			0
$25$	7.45798			1.49160
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.32116	+	7.48447i	0.802419	+	1.38983i	0.918020	+	0.396535i	$0.129787\pi$
$29$	4.32116	+	7.48447i	0.802419	+	1.38983i	−0.115601	+	0.993296i	$0.536879\pi$
$30$		0			0
$31$	4.25821	+	7.37543i	0.764797	+	1.32467i	0.940354	+	0.340197i	$0.110494\pi$
$31$	4.25821	+	7.37543i	0.764797	+	1.32467i	−0.175557	+	0.984469i	$0.556173\pi$
$32$		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	−0.966272	−	0.257525i	$-0.917093\pi$
$41$	−1.66553	+	2.88478i	−0.260112	+	0.450528i	0.706159	+	0.708053i	$0.250426\pi$
$42$		0			0
$43$	−0.0444165	−	0.0769317i	−0.00677346	−	0.0117320i	0.862619	−	0.505855i	$-0.168823\pi$
$43$	−0.0444165	−	0.0769317i	−0.00677346	−	0.0117320i	−0.869392	+	0.494123i	$0.835489\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.52607	+	6.10733i	−0.514330	+	0.890845i	0.485532	+	0.874219i	$0.338626\pi$
$47$	−3.52607	+	6.10733i	−0.514330	+	0.890845i	−0.999862	+	0.0166264i	$0.994707\pi$
$48$		0			0
$49$	−4.27552	−	5.54256i	−0.610789	−	0.791794i
$50$		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
$59$	3.99745	+	6.92378i	0.520423	+	0.901400i	0.999718	+	0.0237457i	$0.00755920\pi$
$59$	3.99745	+	6.92378i	0.520423	+	0.901400i	−0.479295	+	0.877654i	$0.659107\pi$
$60$		0			0
$61$	−6.67764	+	11.5660i	−0.854985	+	1.48088i	0.0216747	+	0.999765i	$0.493100\pi$
$61$	−6.67764	+	11.5660i	−0.854985	+	1.48088i	−0.876659	+	0.481112i	$0.840233\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.32572	+	14.4206i	−1.03268	+	1.78865i
$66$		0			0
$67$	3.06402	+	5.30704i	0.374330	+	0.648358i	0.990226	−	0.139469i	$-0.0445394\pi$
$67$	3.06402	+	5.30704i	0.374330	+	0.648358i	−0.615897	+	0.787827i	$0.711206\pi$
$68$		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
$77$	2.70864	−	5.51033i	0.308678	−	0.627961i
$78$		0			0
$79$	−5.01403	+	8.68455i	−0.564122	+	0.977088i	0.433009	+	0.901390i	$0.357452\pi$
$79$	−5.01403	+	8.68455i	−0.564122	+	0.977088i	−0.997131	+	0.0756985i	$0.975881\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.90243	−	10.2233i	−0.647876	−	1.12215i	−0.983629	−	0.180204i	$-0.942324\pi$
$83$	−5.90243	−	10.2233i	−0.647876	−	1.12215i	0.335753	−	0.941950i	$-0.391009\pi$
$84$		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
$95$	−9.82586	−	17.0189i	−1.00811	−	1.74610i
$96$		0			0
$97$	−3.50818	−	6.07635i	−0.356202	−	0.616960i	0.631121	−	0.775685i	$-0.282595\pi$
$97$	−3.50818	−	6.07635i	−0.356202	−	0.616960i	−0.987323	+	0.158724i	$0.949262\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.74111			0.969277			0.484638	−	0.874715i	$-0.338951\pi$
$101$	9.74111			0.969277			0.484638	+	0.874715i	$0.338951\pi$
$102$		0			0
$103$	−10.2856			−1.01347			−0.506734	−	0.862103i	$-0.669147\pi$
$103$	−10.2856			−1.01347			−0.506734	+	0.862103i	$0.669147\pi$
$104$		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	0.487313	+	0.873227i	$0.337977\pi$
$113$	−5.44881	+	9.43761i	−0.512581	+	0.887815i	−0.999894	+	0.0145882i	$0.995356\pi$
$114$		0			0
$115$	−11.6374			−1.08519
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.87608	+	2.79999i	0.171980	+	0.256674i
$120$		0			0
$121$	−5.61421			−0.510383
$122$		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
$131$	17.1844			1.50141			0.750704	−	0.660639i	$-0.229715\pi$
$131$	17.1844			1.50141			0.750704	+	0.660639i	$0.229715\pi$
$132$		0			0
$133$	14.6980	−	0.982238i	1.27448	−	0.0851708i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	16.0939			1.37500			0.687498	−	0.726186i	$-0.258709\pi$
$137$	16.0939			1.37500			0.687498	+	0.726186i	$0.258709\pi$
$138$		0			0
$139$	−1.11151	+	1.92519i	−0.0942768	+	0.163292i	−0.909307	−	0.416127i	$-0.863387\pi$
$139$	−1.11151	+	1.92519i	−0.0942768	+	0.163292i	0.815030	+	0.579419i	$0.196721\pi$
$140$		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
$149$	−6.93692			−0.568295			−0.284147	−	0.958781i	$-0.591710\pi$
$149$	−6.93692			−0.568295			−0.284147	+	0.958781i	$0.591710\pi$
$150$		0			0
$151$	−15.5167			−1.26273			−0.631365	−	0.775486i	$-0.717505\pi$
$151$	−15.5167			−1.26273			−0.631365	+	0.775486i	$0.717505\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	15.0297	+	26.0322i	1.20722	+	2.09096i
$156$		0			0
$157$	−0.401055	−	0.694648i	−0.0320077	−	0.0554389i	0.849578	−	0.527463i	$-0.176857\pi$
$157$	−0.401055	−	0.694648i	−0.0320077	−	0.0554389i	−0.881586	+	0.472024i	$0.843523\pi$
$158$		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	−0.830610	−	0.556855i	$-0.812008\pi$
$167$	0.865131	−	1.49845i	0.0669459	−	0.115954i	0.897556	+	0.440901i	$0.145341\pi$
$168$		0			0
$169$	−4.62823	−	8.01633i	−0.356018	−	0.616641i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.11729	−	1.93521i	0.0849462	−	0.147131i	−0.820422	−	0.571758i	$-0.806262\pi$
$173$	1.11729	−	1.93521i	0.0849462	−	0.147131i	0.905368	+	0.424627i	$0.139595\pi$
$174$		0			0
$175$	−8.70458	+	17.7082i	−0.658005	+	1.33861i
$176$		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
$185$	−10.0249	−	17.3636i	−0.737042	−	1.27659i
$186$		0			0
$187$	−1.47818	+	2.56028i	−0.108095	+	0.187226i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.04289	+	13.9307i	−0.581963	+	1.00799i	0.413284	+	0.910602i	$0.364382\pi$
$191$	−8.04289	+	13.9307i	−0.581963	+	1.00799i	−0.995247	+	0.0973872i	$0.968951\pi$
$192$		0			0
$193$	0.292732	+	0.507026i	0.0210713	+	0.0364965i	0.876369	−	0.481641i	$-0.159959\pi$
$193$	0.292732	+	0.507026i	0.0210713	+	0.0364965i	−0.855297	+	0.518137i	$0.826626\pi$
$194$		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
$203$	−22.8145	+	1.52465i	−1.60127	+	0.107009i
$204$		0			0
$205$	−5.87864	+	10.1821i	−0.410582	+	0.711149i
$206$		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	−0.607072	−	0.794647i	$-0.707656\pi$
$211$	5.58733	−	9.67754i	0.384648	−	0.666230i	0.991720	+	0.128417i	$0.0409895\pi$
$212$		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
$221$	3.00490	+	5.20464i	0.202132	+	0.350102i
$222$		0			0
$223$	1.32951	+	2.30277i	0.0890303	+	0.154205i	0.907101	−	0.420912i	$-0.138290\pi$
$223$	1.32951	+	2.30277i	0.0890303	+	0.154205i	−0.818071	+	0.575117i	$0.804957\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	11.9157			0.790874			0.395437	−	0.918493i	$-0.370593\pi$
$227$	11.9157			0.790874			0.395437	+	0.918493i	$0.370593\pi$
$228$		0			0
$229$	−29.6128			−1.95687			−0.978434	−	0.206561i	$-0.933773\pi$
$229$	−29.6128			−1.95687			−0.978434	+	0.206561i	$0.933773\pi$
$230$		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	−0.479936	−	0.877304i	$-0.659340\pi$
$239$	8.03590	−	13.9186i	0.519799	−	0.900319i	0.999735	−	0.0230153i	$-0.00732663\pi$
$240$		0			0
$241$	4.49867			0.289785			0.144892	−	0.989447i	$-0.453716\pi$
$241$	4.49867			0.289785			0.144892	+	0.989447i	$0.453716\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−15.0908	−	19.5629i	−0.964117	−	1.24983i
$246$		0			0
$247$	26.2667			1.67131
$248$		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
$257$	−4.82173			−0.300771			−0.150386	−	0.988627i	$-0.548052\pi$
$257$	−4.82173			−0.300771			−0.150386	+	0.988627i	$0.548052\pi$
$258$		0			0
$259$	14.9957	−	1.00213i	0.931786	−	0.0622693i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	28.0903			1.73212			0.866062	−	0.499936i	$-0.166643\pi$
$263$	28.0903			1.73212			0.866062	+	0.499936i	$0.166643\pi$
$264$		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
$275$	−17.3080			−1.04371
$276$		0			0
$277$	16.9383			1.01772			0.508862	−	0.860848i	$-0.330067\pi$
$277$	16.9383			1.01772			0.508862	+	0.860848i	$0.330067\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.4291	−	19.7958i	−0.681805	−	1.18092i	−0.974430	−	0.224693i	$-0.927862\pi$
$281$	−11.4291	−	19.7958i	−0.681805	−	1.18092i	0.292625	−	0.956227i	$-0.405471\pi$
$282$		0			0
$283$	4.17811	+	7.23669i	0.248363	+	0.430177i	0.963072	−	0.269245i	$-0.0867742\pi$
$283$	4.17811	+	7.23669i	0.248363	+	0.430177i	−0.714709	+	0.699422i	$0.753441\pi$
$284$		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	−0.795958	−	0.605352i	$-0.793032\pi$
$293$	2.16141	−	3.74368i	0.126271	−	0.218708i	0.922229	+	0.386644i	$0.126366\pi$
$294$		0			0
$295$	14.1093	+	24.4381i	0.821477	+	1.42284i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	7.77732	−	13.4707i	0.449774	−	0.779031i
$300$		0			0
$301$	0.234507	−	0.0156716i	0.0135168	−	0.000903298i
$302$		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
$311$	9.55365	+	16.5474i	0.541738	+	0.938317i	0.998804	+	0.0488847i	$0.0155667\pi$
$311$	9.55365	+	16.5474i	0.541738	+	0.938317i	−0.457067	+	0.889432i	$0.651100\pi$
$312$		0			0
$313$	−2.83951	+	4.91818i	−0.160499	+	0.277992i	−0.935048	−	0.354522i	$-0.884644\pi$
$313$	−2.83951	+	4.91818i	−0.160499	+	0.277992i	0.774549	+	0.632514i	$0.217977\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−14.1341	+	24.4809i	−0.793848	+	1.37499i	0.129720	+	0.991551i	$0.458592\pi$
$317$	−14.1341	+	24.4809i	−0.793848	+	1.37499i	−0.923568	+	0.383434i	$0.874741\pi$
$318$		0			0
$319$	−10.0282	−	17.3694i	−0.561474	−	0.972501i
$320$		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
$329$	−10.3858	−	15.5005i	−0.572586	−	0.854568i
$330$		0			0
$331$	−3.34045	+	5.78584i	−0.183608	+	0.318018i	−0.943107	−	0.332491i	$-0.892111\pi$
$331$	−3.34045	+	5.78584i	−0.183608	+	0.318018i	0.759499	+	0.650509i	$0.225444\pi$
$332$		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	−0.945363	−	0.326018i	$-0.894293\pi$
$337$	−3.49421	+	6.05215i	−0.190342	+	0.329681i	0.755022	+	0.655700i	$0.227626\pi$
$338$		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
$347$	−4.14410	−	7.17780i	−0.222467	−	0.385324i	0.733089	−	0.680132i	$-0.238078\pi$
$347$	−4.14410	−	7.17780i	−0.222467	−	0.385324i	−0.955557	+	0.294808i	$0.904744\pi$
$348$		0			0
$349$	3.05373	+	5.28921i	0.163462	+	0.283125i	0.936108	−	0.351712i	$-0.114400\pi$
$349$	3.05373	+	5.28921i	0.163462	+	0.283125i	−0.772646	+	0.634837i	$0.781067\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	26.7208			1.42221			0.711104	−	0.703087i	$-0.248196\pi$
$353$	26.7208			1.42221			0.711104	+	0.703087i	$0.248196\pi$
$354$		0			0
$355$	4.59561			0.243909
$356$		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
$367$	30.7064			1.60286			0.801430	−	0.598089i	$-0.204073\pi$
$367$	30.7064			1.60286			0.801430	+	0.598089i	$0.204073\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−10.0679	−	15.0261i	−0.522701	−	0.780116i
$372$		0			0
$373$	16.5838			0.858676			0.429338	−	0.903144i	$-0.358747\pi$
$373$	16.5838			0.858676			0.429338	+	0.903144i	$0.358747\pi$
$374$		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
$383$	30.3538			1.55101			0.775503	−	0.631344i	$-0.217496\pi$
$383$	30.3538			1.55101			0.775503	+	0.631344i	$0.217496\pi$
$384$		0			0
$385$	9.56038	−	19.4492i	0.487242	−	0.991223i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.46764			0.175816			0.0879082	−	0.996129i	$-0.471982\pi$
$389$	3.46764			0.175816			0.0879082	+	0.996129i	$0.471982\pi$
$390$		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
$401$	10.9319			0.545911			0.272955	−	0.962027i	$-0.411999\pi$
$401$	10.9319			0.545911			0.272955	+	0.962027i	$0.411999\pi$
$402$		0			0
$403$	−40.1777			−2.00139
$404$		0			0
$405$		0			0
$406$		0			0
$407$	6.59142	+	11.4167i	0.326725	+	0.565904i
$408$		0			0
$409$	−7.99397	−	13.8460i	−0.395276	−	0.684639i	0.597860	−	0.801600i	$-0.296018\pi$
$409$	−7.99397	−	13.8460i	−0.395276	−	0.684639i	−0.993136	+	0.116962i	$0.962685\pi$
$410$		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	−0.939819	−	0.341671i	$-0.889007\pi$
$419$	−3.56197	+	6.16951i	−0.174014	+	0.301400i	0.765806	+	0.643072i	$0.222340\pi$
$420$		0			0
$421$	−16.6326	−	28.8086i	−0.810625	−	1.40404i	−0.912427	−	0.409239i	$-0.865794\pi$
$421$	−16.6326	−	28.8086i	−0.810625	−	1.40404i	0.101802	−	0.994805i	$-0.467539\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.75033	−	8.22781i	0.230425	−	0.399107i
$426$		0			0
$427$	−19.6685	−	29.3547i	−0.951826	−	1.42057i
$428$		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
$437$	9.17865	+	15.8979i	0.439074	+	0.760499i
$438$		0			0
$439$	17.3083	−	29.9788i	0.826079	−	1.43081i	−0.0750132	−	0.997183i	$-0.523900\pi$
$439$	17.3083	−	29.9788i	0.826079	−	1.43081i	0.901092	−	0.433628i	$-0.142767\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.20461	−	3.81850i	0.104744	−	0.181423i	−0.808889	−	0.587961i	$-0.799931\pi$
$443$	2.20461	−	3.81850i	0.104744	−	0.181423i	0.913634	+	0.406538i	$0.133264\pi$
$444$		0			0
$445$	−1.98185	−	3.43266i	−0.0939486	−	0.162724i
$446$		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
$455$	−24.5228	−	36.5995i	−1.14965	−	1.71581i
$456$		0			0
$457$	15.4196	−	26.7075i	0.721297	−	1.24932i	−0.239183	−	0.970975i	$-0.576879\pi$
$457$	15.4196	−	26.7075i	0.721297	−	1.24932i	0.960480	−	0.278349i	$-0.0897872\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.6297	+	23.6074i	0.634800	+	1.09951i	0.986557	+	0.163415i	$0.0522510\pi$
$461$	13.6297	+	23.6074i	0.634800	+	1.09951i	−0.351757	+	0.936091i	$0.614416\pi$
$462$		0			0
$463$	0.959750	−	1.66234i	0.0446034	−	0.0772553i	−0.842862	−	0.538130i	$-0.819131\pi$
$463$	0.959750	−	1.66234i	0.0446034	−	0.0772553i	0.887465	+	0.460875i	$0.152464\pi$
$464$		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
$473$	0.103079	+	0.178538i	0.00473957	+	0.00820917i
$474$		0			0
$475$	−20.7619	−	35.9607i	−0.952623	−	1.64999i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.3762			0.702556			0.351278	−	0.936271i	$-0.385747\pi$
$479$	15.3762			0.702556			0.351278	+	0.936271i	$0.385747\pi$
$480$		0			0
$481$	26.7986			1.22191
$482$		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	−0.979122	−	0.203273i	$-0.934842\pi$
$491$	−6.94718	+	12.0329i	−0.313522	+	0.543035i	0.665600	+	0.746308i	$0.268175\pi$
$492$		0			0
$493$	11.0094			0.495837
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.51966	+	3.09152i	−0.0681660	+	0.138674i
$498$		0			0
$499$	3.40977			0.152642			0.0763210	−	0.997083i	$-0.475683\pi$
$499$	3.40977			0.152642			0.0763210	+	0.997083i	$0.475683\pi$
$500$		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
$509$	−39.3348			−1.74348			−0.871742	−	0.489966i	$-0.837009\pi$
$509$	−39.3348			−1.74348			−0.871742	+	0.489966i	$0.837009\pi$
$510$		0			0
$511$	19.5732	+	29.2124i	0.865868	+	1.29228i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−36.3038			−1.59974
$516$		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
$527$	10.8490			0.472589
$528$		0			0
$529$	−12.1291			−0.527354
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−7.85744	−	13.6095i	−0.340343	−	0.589492i
$534$		0			0
$535$	9.60755	+	16.6408i	0.415371	+	0.719443i
$536$		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	0.770736	−	0.637154i	$-0.219889\pi$
$547$	−3.89233	−	6.74171i	−0.166424	−	0.288255i	−0.937160	+	0.348900i	$0.886555\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	24.0590	−	41.6714i	1.02495	−	1.77526i
$552$		0			0
$553$	−14.7684	−	22.0415i	−0.628018	−	0.937299i
$554$		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
$563$	−13.9913	−	24.2336i	−0.589663	−	1.02133i	−0.994276	−	0.106838i	$-0.965927\pi$
$563$	−13.9913	−	24.2336i	−0.589663	−	1.02133i	0.404614	−	0.914488i	$-0.367406\pi$
$564$		0			0
$565$	−19.2320	+	33.3109i	−0.809098	+	1.40140i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.44979	−	7.70726i	0.186545	−	0.323105i	−0.757551	−	0.652776i	$-0.773604\pi$
$569$	4.44979	−	7.70726i	0.186545	−	0.323105i	0.944096	+	0.329671i	$0.106938\pi$
$570$		0			0
$571$	−16.1652	−	27.9989i	−0.676492	−	1.17172i	−0.976031	−	0.217634i	$-0.930166\pi$
$571$	−16.1652	−	27.9989i	−0.676492	−	1.17172i	0.299539	−	0.954084i	$-0.403167\pi$
$572$		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
$581$	31.1632	−	2.08257i	1.29287	−	0.0863997i
$582$		0			0
$583$	7.93262	−	13.7397i	0.328536	−	0.569040i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.24076	−	2.14907i	−0.0512118	−	0.0887015i	0.839283	−	0.543695i	$-0.182975\pi$
$587$	−1.24076	−	2.14907i	−0.0512118	−	0.0887015i	−0.890495	+	0.454993i	$0.849642\pi$
$588$		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
$599$	8.20414	+	14.2100i	0.335212	+	0.580604i	0.983526	−	0.180769i	$-0.0578588\pi$
$599$	8.20414	+	14.2100i	0.335212	+	0.580604i	−0.648314	+	0.761373i	$0.724525\pi$
$600$		0			0
$601$	−2.96998	−	5.14416i	−0.121148	−	0.209835i	0.799073	−	0.601235i	$-0.205324\pi$
$601$	−2.96998	−	5.14416i	−0.121148	−	0.209835i	−0.920221	+	0.391400i	$0.871991\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−19.8159			−0.805629
$606$		0			0
$607$	5.95146			0.241563			0.120781	−	0.992679i	$-0.461460\pi$
$607$	5.95146			0.241563			0.120781	+	0.992679i	$0.461460\pi$
$608$		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	−0.549670	−	0.835382i	$-0.685246\pi$
$617$	11.1437	−	19.3014i	0.448627	−	0.777045i	0.998297	+	0.0583367i	$0.0185797\pi$
$618$		0			0
$619$	−34.5887			−1.39024			−0.695118	−	0.718895i	$-0.744648\pi$
$619$	−34.5887			−1.39024			−0.695118	+	0.718895i	$0.744648\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.96454	−	0.198115i	0.118772	−	0.00793729i
$624$		0			0
$625$	−6.66844			−0.266738
$626$		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
$635$	34.9554			1.38716
$636$		0			0
$637$	32.7301	−	4.39419i	1.29681	−	0.174104i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	32.5346			1.28504			0.642519	−	0.766269i	$-0.277889\pi$
$641$	32.5346			1.28504			0.642519	+	0.766269i	$0.277889\pi$
$642$		0			0
$643$	−5.21987	+	9.04107i	−0.205851	+	0.356545i	−0.950404	−	0.311019i	$-0.899330\pi$
$643$	−5.21987	+	9.04107i	−0.205851	+	0.356545i	0.744552	+	0.667564i	$0.232663\pi$
$644$		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
$653$	7.25134			0.283767			0.141883	−	0.989883i	$-0.454684\pi$
$653$	7.25134			0.283767			0.141883	+	0.989883i	$0.454684\pi$
$654$		0			0
$655$	60.6538			2.36994
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−13.3187	−	23.0686i	−0.518822	−	0.898626i	−0.999761	−	0.0218722i	$-0.993037\pi$
$659$	−13.3187	−	23.0686i	−0.518822	−	0.898626i	0.480939	−	0.876754i	$-0.340296\pi$
$660$		0			0
$661$	17.4099	+	30.1549i	0.677168	+	1.17289i	0.975830	+	0.218531i	$0.0701265\pi$
$661$	17.4099	+	30.1549i	0.677168	+	1.17289i	−0.298662	+	0.954359i	$0.596540\pi$
$662$		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	0.979980	−	0.199096i	$-0.0638007\pi$
$673$	8.23841	+	14.2693i	0.317567	+	0.550043i	−0.662412	+	0.749139i	$0.730467\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.5827	+	18.3297i	−0.406725	+	0.704469i	−0.994521	−	0.104541i	$-0.966663\pi$
$677$	−10.5827	+	18.3297i	−0.406725	+	0.704469i	0.587795	+	0.809010i	$0.299996\pi$
$678$		0			0
$679$	18.5223	−	1.23780i	0.710819	−	0.0475026i
$680$		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
$689$	−16.1258	−	27.9306i	−0.614343	−	1.06407i
$690$		0			0
$691$	9.53980	−	16.5234i	0.362911	−	0.628580i	−0.625528	−	0.780202i	$-0.715116\pi$
$691$	9.53980	−	16.5234i	0.362911	−	0.628580i	0.988439	+	0.151622i	$0.0484496\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−3.92316	+	6.79511i	−0.148814	+	0.257753i
$696$		0			0
$697$	2.12171	+	3.67490i	0.0803653	+	0.139197i
$698$		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
$707$	−11.3693	+	23.1293i	−0.427588	+	0.869865i
$708$		0			0
$709$	−10.0493	+	17.4059i	−0.377409	+	0.653691i	−0.990684	−	0.136178i	$-0.956518\pi$
$709$	−10.0493	+	17.4059i	−0.377409	+	0.653691i	0.613276	+	0.789869i	$0.289851\pi$
$710$		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
$725$	32.2271	+	55.8190i	1.19688	+	2.07307i
$726$		0			0
$727$	−18.2342	−	31.5826i	−0.676269	−	1.17133i	−0.976096	−	0.217339i	$-0.930262\pi$
$727$	−18.2342	−	31.5826i	−0.676269	−	1.17133i	0.299827	−	0.953994i	$-0.403071\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.113164			−0.00418551
$732$		0			0
$733$	23.3647			0.862997			0.431498	−	0.902114i	$-0.357985\pi$
$733$	23.3647			0.862997			0.431498	+	0.902114i	$0.357985\pi$
$734$		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	−0.568264	−	0.822847i	$-0.692385\pi$
$743$	11.6794	−	20.2292i	0.428474	−	0.742139i	0.996738	+	0.0807074i	$0.0257179\pi$
$744$		0			0
$745$	−24.4845			−0.897041
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−14.3714	+	0.960415i	−0.525121	+	0.0350928i
$750$		0			0
$751$	1.71323			0.0625167			0.0312584	−	0.999511i	$-0.490049\pi$
$751$	1.71323			0.0625167			0.0312584	+	0.999511i	$0.490049\pi$
$752$		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
$761$	34.1051			1.23631			0.618154	−	0.786057i	$-0.287881\pi$
$761$	34.1051			1.23631			0.618154	+	0.786057i	$0.287881\pi$
$762$		0			0
$763$	1.22943	+	1.83489i	0.0445084	+	0.0664275i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−37.7173			−1.36189
$768$		0			0
$769$	2.48467	−	4.30357i	0.0895995	−	0.155191i	−0.817742	−	0.575584i	$-0.804775\pi$
$769$	2.48467	−	4.30357i	0.0895995	−	0.155191i	0.907342	+	0.420394i	$0.138108\pi$
$770$		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
$779$	18.5464			0.664494
$780$		0			0
$781$	−3.02165			−0.108123
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.41556	−	2.45182i	−0.0505235	−	0.0875092i
$786$		0			0
$787$	24.3005	+	42.0898i	0.866221	+	1.50034i	0.865830	+	0.500339i	$0.166791\pi$
$787$	24.3005	+	42.0898i	0.866221	+	1.50034i	0.000391003		1.00000i	$0.499876\pi$
$788$		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	0.396198	+	0.918165i	$0.370330\pi$
$797$	−16.8556	+	29.1947i	−0.597056	+	1.03413i	−0.993253	+	0.115965i	$0.963004\pi$
$798$		0			0
$799$	4.49183	+	7.78007i	0.158909	+	0.275239i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15.4219	+	26.7115i	−0.544228	+	0.942630i
$804$		0			0
$805$	13.5826	−	27.6318i	0.478723	−	0.973892i
$806$		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
$815$	−6.26500	−	10.8513i	−0.219454	−	0.380105i
$816$		0			0
$817$	−0.247299	+	0.428334i	−0.00865188	+	0.0149855i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.1694	−	21.0781i	0.424717	−	0.735631i	−0.571677	−	0.820479i	$-0.693707\pi$
$821$	12.1694	−	21.0781i	0.424717	−	0.735631i	0.996394	+	0.0848477i	$0.0270404\pi$
$822$		0			0
$823$	−5.76898	−	9.99217i	−0.201094	−	0.348305i	0.747787	−	0.663939i	$-0.231116\pi$
$823$	−5.76898	−	9.99217i	−0.201094	−	0.348305i	−0.948881	+	0.315633i	$0.897783\pi$
$824$		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
$833$	−8.83795	+	1.18654i	−0.306217	+	0.0411113i
$834$		0			0
$835$	3.05356	−	5.28891i	0.105673	−	0.183030i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.39990	−	14.5490i	−0.289997	−	0.502289i	0.683812	−	0.729658i	$-0.260321\pi$
$839$	−8.39990	−	14.5490i	−0.289997	−	0.502289i	−0.973809	+	0.227369i	$0.926988\pi$
$840$		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
$851$	9.36454	+	16.2199i	0.321012	+	0.556009i
$852$		0			0
$853$	−11.4270	−	19.7921i	−0.391253	−	0.677670i	0.601362	−	0.798977i	$-0.294625\pi$
$853$	−11.4270	−	19.7921i	−0.391253	−	0.677670i	−0.992615	+	0.121306i	$0.961292\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	35.1743			1.20153			0.600765	−	0.799426i	$-0.294863\pi$
$857$	35.1743			1.20153			0.600765	+	0.799426i	$0.294863\pi$
$858$		0			0
$859$	−10.5704			−0.360658			−0.180329	−	0.983606i	$-0.557716\pi$
$859$	−10.5704			−0.360658			−0.180329	+	0.983606i	$0.557716\pi$
$860$		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
$871$	−28.9101			−0.979582
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−10.1258	+	20.5994i	−0.342314	+	0.696388i
$876$		0			0
$877$	11.3183			0.382191			0.191096	−	0.981571i	$-0.438796\pi$
$877$	11.3183			0.382191			0.191096	+	0.981571i	$0.438796\pi$
$878$		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
$887$	−33.6325			−1.12927			−0.564634	−	0.825341i	$-0.690983\pi$
$887$	−33.6325			−1.12927			−0.564634	+	0.825341i	$0.690983\pi$
$888$		0			0
$889$	−11.5589	+	23.5149i	−0.387674	+	0.788666i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	39.2643			1.31393
$894$		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
$905$	−69.2996			−2.30360
$906$		0			0
$907$	−9.58510			−0.318268			−0.159134	−	0.987257i	$-0.550870\pi$
$907$	−9.58510			−0.318268			−0.159134	+	0.987257i	$0.550870\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.37499	−	16.2380i	−0.310607	−	0.537988i	0.667887	−	0.744263i	$-0.267199\pi$
$911$	−9.37499	−	16.2380i	−0.310607	−	0.537988i	−0.978494	+	0.206275i	$0.933866\pi$
$912$		0			0
$913$	13.6979	+	23.7255i	0.453336	+	0.785201i
$914$		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
$929$	19.0762	−	33.0409i	0.625869	−	1.08404i	−0.362503	−	0.931983i	$-0.618078\pi$
$929$	19.0762	−	33.0409i	0.625869	−	1.08404i	0.988372	−	0.152054i	$-0.0485889\pi$
$930$		0			0
$931$	−14.8226	+	36.0453i	−0.485790	+	1.18134i
$932$		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
$941$	−0.233235	−	0.403976i	−0.00760326	−	0.0131692i	0.862199	−	0.506570i	$-0.169087\pi$
$941$	−0.233235	−	0.403976i	−0.00760326	−	0.0131692i	−0.869802	+	0.493401i	$0.835754\pi$
$942$		0			0
$943$	5.49142	−	9.51142i	0.178825	−	0.309734i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.55575	−	13.0869i	0.245529	−	0.425268i	−0.716751	−	0.697329i	$-0.754372\pi$
$947$	7.55575	−	13.0869i	0.245529	−	0.425268i	0.962280	+	0.272060i	$0.0877051\pi$
$948$		0			0
$949$	31.3503	+	54.3003i	1.01767	+	1.76266i
$950$		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
$959$	−18.7840	+	38.2133i	−0.606568	+	1.23397i
$960$		0			0
$961$	−20.7647	+	35.9655i	−0.669828	+	1.16018i
$962$		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	−0.972373	−	0.233433i	$-0.925004\pi$
$967$	−8.83228	+	15.2980i	−0.284027	+	0.491949i	0.688346	+	0.725383i	$0.258337\pi$
$968$		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
$977$	−2.71689	−	4.70580i	−0.0869211	−	0.150552i	0.819287	−	0.573384i	$-0.194369\pi$
$977$	−2.71689	−	4.70580i	−0.0869211	−	0.150552i	−0.906208	+	0.422832i	$0.861036\pi$
$978$		0			0
$979$	1.30308	+	2.25700i	0.0416466	+	0.0721341i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−2.10690			−0.0671997			−0.0335998	−	0.999435i	$-0.510697\pi$
$983$	−2.10690			−0.0671997			−0.0335998	+	0.999435i	$0.510697\pi$
$984$		0			0
$985$	61.0348			1.94473
$986$		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
$997$	−36.4954			−1.15582			−0.577911	−	0.816100i	$-0.696132\pi$
$997$	−36.4954			−1.15582			−0.577911	+	0.816100i	$0.696132\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.l.1873.11		22
3.2	odd	2		1008.2.t.k.193.5		22
4.3	odd	2		1512.2.t.d.361.11		22
7.2	even	3		3024.2.q.k.2305.1		22
9.2	odd	6		1008.2.q.k.529.4		22
9.7	even	3		3024.2.q.k.2881.1		22
12.11	even	2		504.2.t.d.193.7	yes	22
21.2	odd	6		1008.2.q.k.625.4		22
28.23	odd	6		1512.2.q.c.793.1		22
36.7	odd	6		1512.2.q.c.1369.1		22
36.11	even	6		504.2.q.d.25.8	✓	22
63.2	odd	6		1008.2.t.k.961.5		22
63.16	even	3	inner	3024.2.t.l.289.11		22
84.23	even	6		504.2.q.d.121.8	yes	22
252.79	odd	6		1512.2.t.d.289.11		22
252.191	even	6		504.2.t.d.457.7	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.8	✓	22	36.11	even	6
504.2.q.d.121.8	yes	22	84.23	even	6
504.2.t.d.193.7	yes	22	12.11	even	2
504.2.t.d.457.7	yes	22	252.191	even	6
1008.2.q.k.529.4		22	9.2	odd	6
1008.2.q.k.625.4		22	21.2	odd	6
1008.2.t.k.193.5		22	3.2	odd	2
1008.2.t.k.961.5		22	63.2	odd	6
1512.2.q.c.793.1		22	28.23	odd	6
1512.2.q.c.1369.1		22	36.7	odd	6
1512.2.t.d.289.11		22	252.79	odd	6
1512.2.t.d.361.11		22	4.3	odd	2
3024.2.q.k.2305.1		22	7.2	even	3
3024.2.q.k.2881.1		22	9.7	even	3
3024.2.t.l.289.11		22	63.16	even	3	inner
3024.2.t.l.1873.11		22	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+3.52959 q^{5} +(-1.16715 + 2.37440i) q^{7} +O(q^{10})\)	\(q+3.52959 q^{5} +(-1.16715 + 2.37440i) q^{7} -2.32073 q^{11} +(-2.35884 + 4.08563i) q^{13} +(0.636946 - 1.10322i) q^{17} +(-2.78386 - 4.82178i) q^{19} -3.29710 q^{23} +7.45798 q^{25} +(4.32116 + 7.48447i) q^{29} +(4.25821 + 7.37543i) q^{31} +(-4.11956 + 8.38064i) q^{35} +(-2.84024 - 4.91943i) q^{37} +(-1.66553 + 2.88478i) q^{41} +(-0.0444165 - 0.0769317i) q^{43} +(-3.52607 + 6.10733i) q^{47} +(-4.27552 - 5.54256i) q^{49} +(-3.41816 + 5.92042i) q^{53} -8.19121 q^{55} +(3.99745 + 6.92378i) q^{59} +(-6.67764 + 11.5660i) q^{61} +(-8.32572 + 14.4206i) q^{65} +(3.06402 + 5.30704i) q^{67} +1.30202 q^{71} +(6.64529 - 11.5100i) q^{73} +(2.70864 - 5.51033i) q^{77} +(-5.01403 + 8.68455i) q^{79} +(-5.90243 - 10.2233i) q^{83} +(2.24815 - 3.89392i) q^{85} +(-0.561496 - 0.972540i) q^{89} +(-6.94778 - 10.3694i) q^{91} +(-9.82586 - 17.0189i) q^{95} +(-3.50818 - 6.07635i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 6 q^{5} - 7 q^{7}+O(q^{10}) \) 22 * q + 6 * q^5 - 7 * q^7	\( 22 q + 6 q^{5} - 7 q^{7} + 6 q^{11} - 3 q^{13} - 7 q^{17} + q^{19} - 4 q^{23} + 20 q^{25} - 9 q^{29} + 4 q^{31} + 14 q^{35} + 2 q^{37} - 16 q^{41} + 5 q^{47} - 15 q^{49} - 11 q^{53} - 22 q^{55} - 19 q^{59} - 13 q^{61} - 13 q^{65} - 26 q^{67} - 48 q^{71} - 35 q^{73} + 4 q^{77} - 10 q^{79} - 28 q^{83} - 20 q^{85} - 6 q^{89} + 37 q^{91} + 12 q^{95} - 29 q^{97}+O(q^{100}) \) 22 * q + 6 * q^5 - 7 * q^7 + 6 * q^11 - 3 * q^13 - 7 * q^17 + q^19 - 4 * q^23 + 20 * q^25 - 9 * q^29 + 4 * q^31 + 14 * q^35 + 2 * q^37 - 16 * q^41 + 5 * q^47 - 15 * q^49 - 11 * q^53 - 22 * q^55 - 19 * q^59 - 13 * q^61 - 13 * q^65 - 26 * q^67 - 48 * q^71 - 35 * q^73 + 4 * q^77 - 10 * q^79 - 28 * q^83 - 20 * q^85 - 6 * q^89 + 37 * q^91 + 12 * q^95 - 29 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more