LMFDB - Embedded newform 315.4.g.a.314.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,4,Mod(314,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("315.314");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	315.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$18.5856016518$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			314.28
Character	$\chi$	$=$	315.314
Dual form			315.4.g.a.314.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.826832 q^{2} -7.31635 q^{4} +(10.4220 + 4.04737i) q^{5} +(17.7925 - 5.14054i) q^{7} -12.6640 q^{8} +(8.61727 + 3.34649i) q^{10} +28.3906i q^{11} -29.3975 q^{13} +(14.7114 - 4.25037i) q^{14} +48.0598 q^{16} +45.3024i q^{17} -49.0172i q^{19} +(-76.2513 - 29.6119i) q^{20} +23.4742i q^{22} +136.385 q^{23} +(92.2377 + 84.3636i) q^{25} -24.3068 q^{26} +(-130.177 + 37.6100i) q^{28} -132.662i q^{29} +237.775i q^{31} +141.050 q^{32} +37.4575i q^{34} +(206.240 + 18.4380i) q^{35} +431.261i q^{37} -40.5290i q^{38} +(-131.985 - 51.2560i) q^{40} +219.448 q^{41} +426.407i q^{43} -207.715i q^{44} +112.768 q^{46} +446.515i q^{47} +(290.150 - 182.927i) q^{49} +(76.2650 + 69.7545i) q^{50} +215.082 q^{52} +330.253 q^{53} +(-114.907 + 295.887i) q^{55} +(-225.326 + 65.1001i) q^{56} -109.689i q^{58} +236.477 q^{59} -574.170i q^{61} +196.600i q^{62} -267.854 q^{64} +(-306.382 - 118.982i) q^{65} +104.847i q^{67} -331.448i q^{68} +(170.526 + 15.2451i) q^{70} -814.084i q^{71} -292.012 q^{73} +356.580i q^{74} +358.627i q^{76} +(145.943 + 505.140i) q^{77} +37.4033 q^{79} +(500.881 + 194.515i) q^{80} +181.446 q^{82} -1252.61i q^{83} +(-183.355 + 472.143i) q^{85} +352.567i q^{86} -359.539i q^{88} -1408.41 q^{89} +(-523.056 + 151.119i) q^{91} -997.844 q^{92} +369.193i q^{94} +(198.391 - 510.859i) q^{95} +107.815 q^{97} +(239.905 - 151.250i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 192 q^{4} + 768 q^{16} - 432 q^{25} + 816 q^{46} + 456 q^{49} + 7968 q^{64} + 1464 q^{70} + 4368 q^{79} - 1440 q^{85} - 4392 q^{91}+O(q^{100}) $ 48 * q + 192 * q^4 + 768 * q^16 - 432 * q^25 + 816 * q^46 + 456 * q^49 + 7968 * q^64 + 1464 * q^70 + 4368 * q^79 - 1440 * q^85 - 4392 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.826832			0.292329			0.146165	−	0.989260i	$-0.453307\pi$
$2$	0.826832			0.292329			0.146165	+	0.989260i	$0.453307\pi$
$3$		0			0
$3$		0			0
$4$	−7.31635			−0.914544
$5$	10.4220	+	4.04737i	0.932175	+	0.362007i
$5$	10.4220	+	4.04737i	0.932175	+	0.362007i
$6$		0			0
$7$	17.7925	−	5.14054i	0.960707	−	0.277563i
$7$	17.7925	−	5.14054i	0.960707	−	0.277563i
$8$	−12.6640			−0.559677
$9$		0			0
$10$	8.61727	+	3.34649i	0.272502	+	0.105825i
$11$			28.3906i			0.778188i	0.921198	+	0.389094i	$0.127212\pi$
$11$			28.3906i			0.778188i	−0.921198	+	0.389094i	$0.872788\pi$
$12$		0			0
$13$	−29.3975			−0.627184			−0.313592	−	0.949558i	$-0.601532\pi$
$13$	−29.3975			−0.627184			−0.313592	+	0.949558i	$0.601532\pi$
$14$	14.7114	−	4.25037i	0.280843	−	0.0811399i
$15$		0			0
$16$	48.0598			0.750934
$17$			45.3024i			0.646320i	0.946344	+	0.323160i	$0.104745\pi$
$17$			45.3024i			0.646320i	−0.946344	+	0.323160i	$0.895255\pi$
$18$		0			0
$19$		−	49.0172i		−	0.591859i	−0.955210	−	0.295929i	$-0.904371\pi$
$19$		−	49.0172i		−	0.591859i	0.955210	−	0.295929i	$-0.0956293\pi$
$20$	−76.2513	−	29.6119i	−0.852515	−	0.331072i
$21$		0			0
$22$			23.4742i			0.227487i
$23$	136.385			1.23645			0.618225	−	0.786001i	$-0.287852\pi$
$23$	136.385			1.23645			0.618225	+	0.786001i	$0.287852\pi$
$24$		0			0
$25$	92.2377	+	84.3636i	0.737901	+	0.674909i
$26$	−24.3068			−0.183344
$27$		0			0
$28$	−130.177	+	37.6100i	−0.878609	+	0.253844i
$29$		−	132.662i		−	0.849472i	−0.905317	−	0.424736i	$-0.860367\pi$
$29$		−	132.662i		−	0.849472i	0.905317	−	0.424736i	$-0.139633\pi$
$30$		0			0
$31$			237.775i			1.37760i	0.724951	+	0.688801i	$0.241862\pi$
$31$			237.775i			1.37760i	−0.724951	+	0.688801i	$0.758138\pi$
$32$	141.050			0.779197
$33$		0			0
$34$			37.4575i			0.188938i
$35$	206.240	+	18.4380i	0.996028	+	0.0890455i
$36$		0			0
$37$			431.261i			1.91618i	0.286459	+	0.958092i	$0.407522\pi$
$37$			431.261i			1.91618i	−0.286459	+	0.958092i	$0.592478\pi$
$38$		−	40.5290i		−	0.173018i
$39$		0			0
$40$	−131.985	−	51.2560i	−0.521717	−	0.202607i
$41$	219.448			0.835901			0.417951	−	0.908470i	$-0.362748\pi$
$41$	219.448			0.835901			0.417951	+	0.908470i	$0.362748\pi$
$42$		0			0
$43$			426.407i			1.51224i	0.654432	+	0.756121i	$0.272908\pi$
$43$			426.407i			1.51224i	−0.654432	+	0.756121i	$0.727092\pi$
$44$		−	207.715i		−	0.711687i
$45$		0			0
$46$	112.768			0.361450
$47$			446.515i			1.38576i	0.721052	+	0.692881i	$0.243659\pi$
$47$			446.515i			1.38576i	−0.721052	+	0.692881i	$0.756341\pi$
$48$		0			0
$49$	290.150	−	182.927i	0.845917	−	0.533314i
$50$	76.2650	+	69.7545i	0.215710	+	0.197295i
$51$		0			0
$52$	215.082			0.573587
$53$	330.253			0.855920			0.427960	−	0.903798i	$-0.359232\pi$
$53$	330.253			0.855920			0.427960	+	0.903798i	$0.359232\pi$
$54$		0			0
$55$	−114.907	+	295.887i	−0.281710	+	0.725408i
$56$	−225.326	+	65.1001i	−0.537686	+	0.155346i
$57$		0			0
$58$		−	109.689i		−	0.248326i
$59$	236.477			0.521807			0.260904	−	0.965365i	$-0.415980\pi$
$59$	236.477			0.521807			0.260904	+	0.965365i	$0.415980\pi$
$60$		0			0
$61$		−	574.170i		−	1.20516i	−0.798057	−	0.602581i	$-0.794139\pi$
$61$		−	574.170i		−	1.20516i	0.798057	−	0.602581i	$-0.205861\pi$
$62$			196.600i			0.402713i
$63$		0			0
$64$	−267.854			−0.523152
$65$	−306.382	−	118.982i	−0.584646	−	0.227045i
$66$		0			0
$67$			104.847i			0.191181i	0.995421	+	0.0955905i	$0.0304739\pi$
$67$			104.847i			0.191181i	−0.995421	+	0.0955905i	$0.969526\pi$
$68$		−	331.448i		−	0.591088i
$69$		0			0
$70$	170.526	+	15.2451i	0.291168	+	0.0260306i
$71$		−	814.084i		−	1.36076i	−0.732859	−	0.680380i	$-0.761815\pi$
$71$		−	814.084i		−	1.36076i	0.732859	−	0.680380i	$-0.238185\pi$
$72$		0			0
$73$	−292.012			−0.468184			−0.234092	−	0.972214i	$-0.575212\pi$
$73$	−292.012			−0.468184			−0.234092	+	0.972214i	$0.575212\pi$
$74$			356.580i			0.560157i
$75$		0			0
$76$			358.627i			0.541281i
$77$	145.943	+	505.140i	0.215997	+	0.747611i
$78$		0			0
$79$	37.4033			0.0532683			0.0266342	−	0.999645i	$-0.491521\pi$
$79$	37.4033			0.0532683			0.0266342	+	0.999645i	$0.491521\pi$
$80$	500.881	+	194.515i	0.700002	+	0.271844i
$81$		0			0
$82$	181.446			0.244358
$83$		−	1252.61i		−	1.65653i	−0.560337	−	0.828265i	$-0.689328\pi$
$83$		−	1252.61i		−	1.65653i	0.560337	−	0.828265i	$-0.310672\pi$
$84$		0			0
$85$	−183.355	+	472.143i	−0.233973	+	0.602484i
$86$			352.567i			0.442072i
$87$		0			0
$88$		−	359.539i		−	0.435534i
$89$	−1408.41			−1.67743			−0.838713	−	0.544573i	$-0.816692\pi$
$89$	−1408.41			−1.67743			−0.838713	+	0.544573i	$0.816692\pi$
$90$		0			0
$91$	−523.056	+	151.119i	−0.602540	+	0.174083i
$92$	−997.844			−1.13079
$93$		0			0
$94$			369.193i			0.405099i
$95$	198.391	−	510.859i	0.214257	−	0.551716i
$96$		0			0
$97$	107.815			0.112856			0.0564278	−	0.998407i	$-0.482029\pi$
$97$	107.815			0.112856			0.0564278	+	0.998407i	$0.482029\pi$
$98$	239.905	−	151.250i	0.247286	−	0.155903i
$99$		0			0
$100$	−674.843	−	617.233i	−0.674843	−	0.617233i
$101$	539.488			0.531496			0.265748	−	0.964043i	$-0.414381\pi$
$101$	539.488			0.531496			0.265748	+	0.964043i	$0.414381\pi$
$102$		0			0
$103$	−1514.36			−1.44868			−0.724341	−	0.689442i	$-0.757856\pi$
$103$	−1514.36			−1.44868			−0.724341	+	0.689442i	$0.757856\pi$
$104$	372.291			0.351021
$105$		0			0
$106$	273.064			0.250210
$107$	744.581			0.672723			0.336361	−	0.941733i	$-0.390804\pi$
$107$	744.581			0.672723			0.336361	+	0.941733i	$0.390804\pi$
$108$		0			0
$109$	732.203			0.643416			0.321708	−	0.946839i	$-0.395743\pi$
$109$	732.203			0.643416			0.321708	+	0.946839i	$0.395743\pi$
$110$	−95.0087	+	244.649i	−0.0823520	+	0.212058i
$111$		0			0
$112$	855.106	−	247.053i	0.721428	−	0.208432i
$113$	389.394			0.324169			0.162085	−	0.986777i	$-0.448178\pi$
$113$	389.394			0.324169			0.162085	+	0.986777i	$0.448178\pi$
$114$		0			0
$115$	1421.41	+	552.002i	1.15259	+	0.447604i
$116$			970.601i			0.776880i
$117$		0			0
$118$	195.526			0.152540
$119$	232.879	+	806.045i	0.179395	+	0.620924i
$120$		0			0
$121$	524.977			0.394423
$122$		−	474.742i		−	0.352304i
$123$		0			0
$124$		−	1739.64i		−	1.25988i
$125$	619.854	+	1252.56i	0.443531	+	0.896259i
$126$		0			0
$127$		−	577.565i		−	0.403548i	−0.979432	−	0.201774i	$-0.935329\pi$
$127$		−	577.565i		−	0.403548i	0.979432	−	0.201774i	$-0.0646706\pi$
$128$	−1349.87			−0.932129
$129$		0			0
$130$	−253.326	−	98.3784i	−0.170909	−	0.0663720i
$131$	−1292.47			−0.862013			−0.431006	−	0.902349i	$-0.641841\pi$
$131$	−1292.47			−0.862013			−0.431006	+	0.902349i	$0.641841\pi$
$132$		0			0
$133$	−251.975	−	872.141i	−0.164278	−	0.568603i
$134$			86.6910i			0.0558878i
$135$		0			0
$136$		−	573.711i		−	0.361730i
$137$	−1930.34			−1.20379			−0.601897	−	0.798574i	$-0.705588\pi$
$137$	−1930.34			−1.20379			−0.601897	+	0.798574i	$0.705588\pi$
$138$		0			0
$139$			553.182i			0.337556i	0.985654	+	0.168778i	$0.0539821\pi$
$139$			553.182i			0.337556i	−0.985654	+	0.168778i	$0.946018\pi$
$140$	−1508.93	−	134.899i	−0.910911	−	0.0814360i
$141$		0			0
$142$		−	673.110i		−	0.397790i
$143$		−	834.611i		−	0.488067i
$144$		0			0
$145$	536.931	−	1382.61i	0.307515	−	0.791857i
$146$	−241.445			−0.136864
$147$		0			0
$148$		−	3155.25i		−	1.75243i
$149$			152.312i			0.0837443i	0.999123	+	0.0418722i	$0.0133322\pi$
$149$			152.312i			0.0837443i	−0.999123	+	0.0418722i	$0.986668\pi$
$150$		0			0
$151$	−2044.30			−1.10174			−0.550871	−	0.834590i	$-0.685704\pi$
$151$	−2044.30			−1.10174			−0.550871	+	0.834590i	$0.685704\pi$
$152$			620.756i			0.331250i
$153$		0			0
$154$	120.670	+	417.666i	0.0631421	+	0.218549i
$155$	−962.362	+	2478.10i	−0.498702	+	1.28417i
$156$		0			0
$157$	−197.116			−0.100201			−0.0501005	−	0.998744i	$-0.515954\pi$
$157$	−197.116			−0.100201			−0.0501005	+	0.998744i	$0.515954\pi$
$158$	30.9262			0.0155719
$159$		0			0
$160$	1470.02	+	570.880i	0.726348	+	0.282075i
$161$	2426.64	−	701.095i	1.18787	−	0.343193i
$162$		0			0
$163$		−	517.479i		−	0.248663i	−0.992241	−	0.124332i	$-0.960321\pi$
$163$		−	517.479i		−	0.248663i	0.992241	−	0.124332i	$-0.0396786\pi$
$164$	−1605.56			−0.764468
$165$		0			0
$166$		−	1035.70i		−	0.484252i
$167$		−	1875.67i		−	0.869126i	−0.900641	−	0.434563i	$-0.856903\pi$
$167$		−	1875.67i		−	0.869126i	0.900641	−	0.434563i	$-0.143097\pi$
$168$		0			0
$169$	−1332.79			−0.606640
$170$	−151.604	+	390.383i	−0.0683970	+	0.176124i
$171$		0			0
$172$		−	3119.74i		−	1.38301i
$173$		−	2958.61i		−	1.30022i	−0.759839	−	0.650112i	$-0.774722\pi$
$173$		−	2958.61i		−	1.30022i	0.759839	−	0.650112i	$-0.225278\pi$
$174$		0			0
$175$	2074.82	+	1026.89i	0.896237	+	0.443575i
$176$			1364.44i			0.584368i
$177$		0			0
$178$	−1164.52			−0.490361
$179$		−	1260.22i		−	0.526221i	−0.964766	−	0.263110i	$-0.915252\pi$
$179$		−	1260.22i		−	0.526221i	0.964766	−	0.263110i	$-0.0847483\pi$
$180$		0			0
$181$			3345.13i			1.37371i	0.726795	+	0.686855i	$0.241009\pi$
$181$			3345.13i			1.37371i	−0.726795	+	0.686855i	$0.758991\pi$
$182$	−432.479	+	124.950i	−0.176140	+	0.0508896i
$183$		0			0
$184$	−1727.19			−0.692012
$185$	−1745.47	+	4494.62i	−0.693673	+	1.78622i
$186$		0			0
$187$	−1286.16			−0.502959
$188$		−	3266.86i		−	1.26734i
$189$		0			0
$190$	164.036	−	422.395i	0.0626337	−	0.161283i
$191$			131.631i			0.0498665i	0.999689	+	0.0249333i	$0.00793733\pi$
$191$			131.631i			0.0498665i	−0.999689	+	0.0249333i	$0.992063\pi$
$192$		0			0
$193$			1592.33i			0.593877i	0.954897	+	0.296938i	$0.0959656\pi$
$193$			1592.33i			0.593877i	−0.954897	+	0.296938i	$0.904034\pi$
$194$	89.1452			0.0329910
$195$		0			0
$196$	−2122.84	+	1338.36i	−0.773628	+	0.487739i
$197$	3202.73			1.15830			0.579150	−	0.815221i	$-0.303385\pi$
$197$	3202.73			1.15830			0.579150	+	0.815221i	$0.303385\pi$
$198$		0			0
$199$		−	3334.37i		−	1.18777i	−0.804549	−	0.593887i	$-0.797593\pi$
$199$		−	3334.37i		−	1.18777i	0.804549	−	0.593887i	$-0.202407\pi$
$200$	−1168.10	−	1068.38i	−0.412986	−	0.377731i
$201$		0			0
$202$	446.066			0.155372
$203$	−681.954	−	2360.39i	−0.235782	−	0.816094i
$204$		0			0
$205$	2287.09	+	888.185i	0.779207	+	0.302602i
$206$	−1252.12			−0.423492
$207$		0			0
$208$	−1412.84			−0.470974
$209$	1391.63			0.460578
$210$		0			0
$211$	4252.21			1.38737			0.693684	−	0.720280i	$-0.255987\pi$
$211$	4252.21			1.38737			0.693684	+	0.720280i	$0.255987\pi$
$212$	−2416.25			−0.782776
$213$		0			0
$214$	615.643			0.196656
$215$	−1725.82	+	4444.03i	−0.547443	+	1.40967i
$216$		0			0
$217$	1222.29	+	4230.62i	0.382372	+	1.32347i
$218$	605.409			0.188089
$219$		0			0
$220$	840.699	−	2164.82i	0.257636	−	0.663417i
$221$		−	1331.78i		−	0.405362i
$222$		0			0
$223$	−4306.52			−1.29321			−0.646605	−	0.762825i	$-0.723812\pi$
$223$	−4306.52			−1.29321			−0.646605	+	0.762825i	$0.723812\pi$
$224$	2509.63	−	725.072i	0.748580	−	0.216276i
$225$		0			0
$226$	321.964			0.0947642
$227$			2383.72i			0.696973i	0.937314	+	0.348486i	$0.113304\pi$
$227$			2383.72i			0.696973i	−0.937314	+	0.348486i	$0.886696\pi$
$228$		0			0
$229$		−	3858.50i		−	1.11344i	−0.830701	−	0.556718i	$-0.812060\pi$
$229$		−	3858.50i		−	1.11344i	0.830701	−	0.556718i	$-0.187940\pi$
$230$	1175.27	+	456.413i	0.336935	+	0.130848i
$231$		0			0
$232$			1680.04i			0.475430i
$233$	7086.74			1.99257			0.996283	−	0.0861410i	$-0.0274536\pi$
$233$	7086.74			1.99257			0.996283	+	0.0861410i	$0.0274536\pi$
$234$		0			0
$235$	−1807.21	+	4653.59i	−0.501656	+	1.29177i
$236$	−1730.15			−0.477216
$237$		0			0
$238$	192.552	+	666.464i	0.0524423	+	0.181514i
$239$		−	4485.49i		−	1.21398i	−0.794708	−	0.606992i	$-0.792376\pi$
$239$		−	4485.49i		−	1.21398i	0.794708	−	0.606992i	$-0.207624\pi$
$240$		0			0
$241$		−	2843.89i		−	0.760130i	−0.924960	−	0.380065i	$-0.875902\pi$
$241$		−	2843.89i		−	0.760130i	0.924960	−	0.380065i	$-0.124098\pi$
$242$	434.067			0.115301
$243$		0			0
$244$			4200.83i			1.10217i
$245$	3764.32	−	732.128i	0.981607	−	0.190914i
$246$		0			0
$247$			1440.98i			0.371205i
$248$		−	3011.19i		−	0.771012i
$249$		0			0
$250$	512.515	+	1035.66i	0.129657	+	0.262003i
$251$	2437.40			0.612937			0.306469	−	0.951881i	$-0.400853\pi$
$251$	2437.40			0.612937			0.306469	+	0.951881i	$0.400853\pi$
$252$		0			0
$253$			3872.06i			0.962191i
$254$		−	477.549i		−	0.117969i
$255$		0			0
$256$	1026.72			0.250663
$257$			3443.72i			0.835849i	0.908482	+	0.417925i	$0.137242\pi$
$257$			3443.72i			0.835849i	−0.908482	+	0.417925i	$0.862758\pi$
$258$		0			0
$259$	2216.92	+	7673.23i	0.531863	+	1.84089i
$260$	2241.59	+	870.516i	0.534684	+	0.207643i
$261$		0			0
$262$	−1068.66			−0.251991
$263$	1705.38			0.399841			0.199920	−	0.979812i	$-0.435932\pi$
$263$	1705.38			0.399841			0.199920	+	0.979812i	$0.435932\pi$
$264$		0			0
$265$	3441.91	+	1336.66i	0.797868	+	0.309849i
$266$	−208.341	−	721.114i	−0.0480233	−	0.166219i
$267$		0			0
$268$		−	767.099i		−	0.174843i
$269$	506.954			0.114905			0.0574527	−	0.998348i	$-0.481702\pi$
$269$	506.954			0.114905			0.0574527	+	0.998348i	$0.481702\pi$
$270$		0			0
$271$		−	5993.32i		−	1.34343i	−0.740812	−	0.671713i	$-0.765559\pi$
$271$		−	5993.32i		−	1.34343i	0.740812	−	0.671713i	$-0.234441\pi$
$272$			2177.22i			0.485344i
$273$		0			0
$274$	−1596.06			−0.351904
$275$	−2395.13	+	2618.68i	−0.525206	+	0.574226i
$276$		0			0
$277$			3208.46i			0.695948i	0.937504	+	0.347974i	$0.113130\pi$
$277$			3208.46i			0.695948i	−0.937504	+	0.347974i	$0.886870\pi$
$278$			457.389i			0.0986775i
$279$		0			0
$280$	−2611.84	−	233.500i	−0.557454	−	0.0498367i
$281$			3342.44i			0.709585i	0.934945	+	0.354793i	$0.115449\pi$
$281$			3342.44i			0.709585i	−0.934945	+	0.354793i	$0.884551\pi$
$282$		0			0
$283$	−5164.91			−1.08488			−0.542442	−	0.840093i	$-0.682500\pi$
$283$	−5164.91			−1.08488			−0.542442	+	0.840093i	$0.682500\pi$
$284$			5956.12i			1.24447i
$285$		0			0
$286$		−	690.083i		−	0.142676i
$287$	3904.53	−	1128.08i	0.803057	−	0.232016i
$288$		0			0
$289$	2860.69			0.582270
$290$	443.952	−	1143.18i	0.0898957	−	0.231483i
$291$		0			0
$292$	2136.46			0.428175
$293$		−	4460.79i		−	0.889427i	−0.895673	−	0.444714i	$-0.853305\pi$
$293$		−	4460.79i		−	0.889427i	0.895673	−	0.444714i	$-0.146695\pi$
$294$		0			0
$295$	2464.57	+	957.107i	0.486416	+	0.188898i
$296$		−	5461.51i		−	1.07244i
$297$		0			0
$298$			125.937i			0.0244809i
$299$	−4009.39			−0.775481
$300$		0			0
$301$	2191.96	+	7586.86i	0.419743	+	1.45282i
$302$	−1690.30			−0.322071
$303$		0			0
$304$		−	2355.76i		−	0.444447i
$305$	2323.88	−	5984.02i	0.436278	−	1.12342i
$306$		0			0
$307$	3908.97			0.726699			0.363349	−	0.931653i	$-0.381633\pi$
$307$	3908.97			0.726699			0.363349	+	0.931653i	$0.381633\pi$
$308$	−1067.77	−	3695.78i	−0.197538	−	0.683723i
$309$		0			0
$310$	−795.712	+	2048.97i	−0.145785	+	0.375399i
$311$	−3769.10			−0.687221			−0.343611	−	0.939112i	$-0.611650\pi$
$311$	−3769.10			−0.687221			−0.343611	+	0.939112i	$0.611650\pi$
$312$		0			0
$313$	−10274.7			−1.85546			−0.927732	−	0.373248i	$-0.878244\pi$
$313$	−10274.7			−1.85546			−0.927732	+	0.373248i	$0.878244\pi$
$314$	−162.982			−0.0292917
$315$		0			0
$316$	−273.656			−0.0487162
$317$	2065.38			0.365941			0.182970	−	0.983118i	$-0.441429\pi$
$317$	2065.38			0.365941			0.182970	+	0.983118i	$0.441429\pi$
$318$		0			0
$319$	3766.34			0.661050
$320$	−2791.58	−	1084.10i	−0.487669	−	0.189385i
$321$		0			0
$322$	2006.43	−	579.688i	0.347248	−	0.100325i
$323$	2220.60			0.382530
$324$		0			0
$325$	−2711.55	−	2480.08i	−0.462800	−	0.423292i
$326$		−	427.868i		−	0.0726915i
$327$		0			0
$328$	−2779.09			−0.467835
$329$	2295.33	+	7944.63i	0.384637	+	1.33131i
$330$		0			0
$331$	−4704.88			−0.781280			−0.390640	−	0.920544i	$-0.627746\pi$
$331$	−4704.88			−0.781280			−0.390640	+	0.920544i	$0.627746\pi$
$332$			9164.54i			1.51497i
$333$		0			0
$334$		−	1550.87i		−	0.254071i
$335$	−424.355	+	1092.72i	−0.0692089	+	0.178214i
$336$		0			0
$337$			192.322i			0.0310874i	0.999879	+	0.0155437i	$0.00494792\pi$
$337$			192.322i			0.0310874i	−0.999879	+	0.0155437i	$0.995052\pi$
$338$	−1101.99			−0.177339
$339$		0			0
$340$	1341.49	−	3454.36i	0.213978	−	0.550998i
$341$	−6750.56			−1.07203
$342$		0			0
$343$	4222.16	−	4746.26i	0.664650	−	0.747154i
$344$		−	5400.03i		−	0.846367i
$345$		0			0
$346$		−	2446.27i		−	0.380093i
$347$	−1373.84			−0.212541			−0.106270	−	0.994337i	$-0.533891\pi$
$347$	−1373.84			−0.212541			−0.106270	+	0.994337i	$0.533891\pi$
$348$		0			0
$349$			7854.76i			1.20474i	0.798216	+	0.602372i	$0.205778\pi$
$349$			7854.76i			1.20474i	−0.798216	+	0.602372i	$0.794222\pi$
$350$	1715.53	+	849.066i	0.261996	+	0.129670i
$351$		0			0
$352$			4004.48i			0.606362i
$353$		−	5594.76i		−	0.843567i	−0.906697	−	0.421784i	$-0.861404\pi$
$353$		−	5594.76i		−	0.843567i	0.906697	−	0.421784i	$-0.138596\pi$
$354$		0			0
$355$	3294.90	−	8484.41i	0.492605	−	1.26847i
$356$	10304.4			1.53408
$357$		0			0
$358$		−	1041.99i		−	0.153830i
$359$			309.402i			0.0454864i	0.999741	+	0.0227432i	$0.00724001\pi$
$359$			309.402i			0.0454864i	−0.999741	+	0.0227432i	$0.992760\pi$
$360$		0			0
$361$	4456.31			0.649703
$362$			2765.86i			0.401575i
$363$		0			0
$364$	3826.86	−	1105.64i	0.551050	−	0.159207i
$365$	−3043.36	−	1181.88i	−0.436430	−	0.169486i
$366$		0			0
$367$	6696.16			0.952417			0.476208	−	0.879332i	$-0.342011\pi$
$367$	6696.16			0.952417			0.476208	+	0.879332i	$0.342011\pi$
$368$	6554.65			0.928491
$369$		0			0
$370$	−1443.21	+	3716.29i	−0.202781	+	0.522164i
$371$	5876.05	−	1697.68i	0.822289	−	0.237572i
$372$		0			0
$373$			5431.49i			0.753973i	0.926219	+	0.376986i	$0.123040\pi$
$373$			5431.49i			0.753973i	−0.926219	+	0.376986i	$0.876960\pi$
$374$	−1063.44			−0.147030
$375$		0			0
$376$		−	5654.68i		−	0.775580i
$377$			3899.93i			0.532776i
$378$		0			0
$379$	−11019.2			−1.49345			−0.746726	−	0.665132i	$-0.768375\pi$
$379$	−11019.2			−1.49345			−0.746726	+	0.665132i	$0.768375\pi$
$380$	−1451.49	+	3737.62i	−0.195948	+	0.504569i
$381$		0			0
$382$			108.837i			0.0145774i
$383$		−	2258.58i		−	0.301327i	−0.988585	−	0.150663i	$-0.951859\pi$
$383$		−	2258.58i		−	0.301327i	0.988585	−	0.150663i	$-0.0481409\pi$
$384$		0			0
$385$	−523.465	+	5855.27i	−0.0692942	+	0.775097i
$386$			1316.59i			0.173607i
$387$		0			0
$388$	−788.815			−0.103211
$389$			6828.55i			0.890029i	0.895523	+	0.445014i	$0.146801\pi$
$389$			6828.55i			0.890029i	−0.895523	+	0.445014i	$0.853199\pi$
$390$		0			0
$391$			6178.59i			0.799142i
$392$	−3674.47	+	2316.59i	−0.473440	+	0.298484i
$393$		0			0
$394$	2648.12			0.338605
$395$	389.818	+	151.385i	0.0496554	+	0.0192835i
$396$		0			0
$397$	−9018.17			−1.14007			−0.570037	−	0.821619i	$-0.693071\pi$
$397$	−9018.17			−1.14007			−0.570037	+	0.821619i	$0.693071\pi$
$398$		−	2756.96i		−	0.347221i
$399$		0			0
$400$	4432.92	+	4054.49i	0.554115	+	0.506812i
$401$			36.8320i			0.00458679i	0.999997	+	0.00229339i	$0.000730010\pi$
$401$			36.8320i			0.00458679i	−0.999997	+	0.00229339i	$0.999270\pi$
$402$		0			0
$403$		−	6989.98i		−	0.864010i
$404$	−3947.09			−0.486076
$405$		0			0
$406$	−563.862	−	1951.65i	−0.0689261	−	0.238568i
$407$	−12243.7			−1.49115
$408$		0			0
$409$			6187.75i			0.748079i	0.927413	+	0.374040i	$0.122028\pi$
$409$			6187.75i			0.748079i	−0.927413	+	0.374040i	$0.877972\pi$
$410$	1891.04	+	734.379i	0.227785	+	0.0884595i
$411$		0			0
$412$	11079.6			1.32488
$413$	4207.52	−	1215.62i	0.501304	−	0.144835i
$414$		0			0
$415$	5069.78	−	13054.8i	0.599676	−	1.54418i
$416$	−4146.51			−0.488700
$417$		0			0
$418$	1150.64			0.134640
$419$	10841.5			1.26406			0.632030	−	0.774944i	$-0.282222\pi$
$419$	10841.5			1.26406			0.632030	+	0.774944i	$0.282222\pi$
$420$		0			0
$421$	−5747.40			−0.665347			−0.332673	−	0.943042i	$-0.607951\pi$
$421$	−5747.40			−0.665347			−0.332673	+	0.943042i	$0.607951\pi$
$422$	3515.87			0.405568
$423$		0			0
$424$	−4182.34			−0.479039
$425$	−3821.87	+	4178.59i	−0.436207	+	0.476920i
$426$		0			0
$427$	−2951.55	−	10215.9i	−0.334509	−	1.15781i
$428$	−5447.61			−0.615234
$429$		0			0
$430$	−1426.97	+	3674.46i	−0.160033	+	0.412089i
$431$			6064.98i			0.677819i	0.940819	+	0.338909i	$0.110058\pi$
$431$			6064.98i			0.677819i	−0.940819	+	0.338909i	$0.889942\pi$
$432$		0			0
$433$	12816.5			1.42245			0.711224	−	0.702966i	$-0.248141\pi$
$433$	12816.5			1.42245			0.711224	+	0.702966i	$0.248141\pi$
$434$	1010.63	+	3498.01i	0.111778	+	0.386889i
$435$		0			0
$436$	−5357.06			−0.588432
$437$		−	6685.23i		−	0.731803i
$438$		0			0
$439$		−	17636.4i		−	1.91740i	−0.284412	−	0.958702i	$-0.591798\pi$
$439$		−	17636.4i		−	1.91740i	0.284412	−	0.958702i	$-0.408202\pi$
$440$	1455.19	−	3747.13i	0.157667	−	0.405994i
$441$		0			0
$442$		−	1101.15i		−	0.118499i
$443$	−13711.7			−1.47057			−0.735285	−	0.677758i	$-0.762952\pi$
$443$	−13711.7			−1.47057			−0.735285	+	0.677758i	$0.762952\pi$
$444$		0			0
$445$	−14678.5	−	5700.34i	−1.56366	−	0.607241i
$446$	−3560.77			−0.378043
$447$		0			0
$448$	−4765.80	+	1376.91i	−0.502596	+	0.145208i
$449$		−	18974.4i		−	1.99434i	−0.0752125	−	0.997168i	$-0.523963\pi$
$449$		−	18974.4i		−	1.99434i	0.0752125	−	0.997168i	$-0.476037\pi$
$450$		0			0
$451$			6230.24i			0.650489i
$452$	−2848.95			−0.296467
$453$		0			0
$454$			1970.93i			0.203745i
$455$	−6062.94	−	542.031i	−0.624693	−	0.0558479i
$456$		0			0
$457$		−	9232.85i		−	0.945064i	−0.881313	−	0.472532i	$-0.843340\pi$
$457$		−	9232.85i		−	0.945064i	0.881313	−	0.472532i	$-0.156660\pi$
$458$		−	3190.33i		−	0.325490i
$459$		0			0
$460$	−10399.6	−	4038.64i	−1.05409	−	0.409353i
$461$	−7896.43			−0.797773			−0.398887	−	0.917000i	$-0.630603\pi$
$461$	−7896.43			−0.797773			−0.398887	+	0.917000i	$0.630603\pi$
$462$		0			0
$463$		−	14282.0i		−	1.43356i	−0.697298	−	0.716781i	$-0.745615\pi$
$463$		−	14282.0i		−	1.43356i	0.697298	−	0.716781i	$-0.254385\pi$
$464$		−	6375.70i		−	0.637897i
$465$		0			0
$466$	5859.54			0.582485
$467$		−	6302.33i		−	0.624490i	−0.950002	−	0.312245i	$-0.898919\pi$
$467$		−	6302.33i		−	0.624490i	0.950002	−	0.312245i	$-0.101081\pi$
$468$		0			0
$469$	538.972	+	1865.50i	0.0530648	+	0.183669i
$470$	−1494.26	+	3847.74i	−0.146649	+	0.377623i
$471$		0			0
$472$	−2994.75			−0.292044
$473$	−12105.9			−1.17681
$474$		0			0
$475$	4135.27	−	4521.23i	0.399451	−	0.436733i
$476$	−1703.82	−	5897.31i	−0.164064	−	0.567863i
$477$		0			0
$478$		−	3708.75i		−	0.354883i
$479$	−285.694			−0.0272520			−0.0136260	−	0.999907i	$-0.504337\pi$
$479$	−285.694			−0.0272520			−0.0136260	+	0.999907i	$0.504337\pi$
$480$		0			0
$481$		−	12678.0i		−	1.20180i
$482$		−	2351.42i		−	0.222208i
$483$		0			0
$484$	−3840.91			−0.360717
$485$	1123.66	+	436.369i	0.105201	+	0.0408546i
$486$		0			0
$487$		−	10713.2i		−	0.996837i	−0.866937	−	0.498418i	$-0.833914\pi$
$487$		−	10713.2i		−	0.996837i	0.866937	−	0.498418i	$-0.166086\pi$
$488$			7271.31i			0.674502i
$489$		0			0
$490$	3112.46	−	605.347i	0.286952	−	0.0558097i
$491$			15460.4i			1.42102i	0.703688	+	0.710509i	$0.251535\pi$
$491$			15460.4i			1.42102i	−0.703688	+	0.710509i	$0.748465\pi$
$492$		0			0
$493$	6009.90			0.549031
$494$			1191.45i			0.108514i
$495$		0			0
$496$			11427.4i			1.03449i
$497$	−4184.83	−	14484.6i	−0.377697	−	1.30729i
$498$		0			0
$499$	−17987.7			−1.61371			−0.806853	−	0.590752i	$-0.798831\pi$
$499$	−17987.7			−1.61371			−0.806853	+	0.590752i	$0.798831\pi$
$500$	−4535.07	−	9164.16i	−0.405629	−	0.819668i
$501$		0			0
$502$	2015.32			0.179179
$503$			15205.5i			1.34788i	0.738788	+	0.673938i	$0.235398\pi$
$503$			15205.5i			1.34788i	−0.738788	+	0.673938i	$0.764602\pi$
$504$		0			0
$505$	5622.57	+	2183.51i	0.495447	+	0.192405i
$506$			3201.54i			0.281276i
$507$		0			0
$508$			4225.66i			0.369062i
$509$	−11925.6			−1.03849			−0.519245	−	0.854625i	$-0.673787\pi$
$509$	−11925.6			−1.03849			−0.519245	+	0.854625i	$0.673787\pi$
$510$		0			0
$511$	−5195.64	+	1501.10i	−0.449788	+	0.129951i
$512$	11647.9			1.00541
$513$		0			0
$514$			2847.38i			0.244343i
$515$	−15782.7	−	6129.16i	−1.35043	−	0.524434i
$516$		0			0
$517$	−12676.8			−1.07838
$518$	1833.02	+	6344.47i	0.155479	+	0.538147i
$519$		0			0
$520$	3880.03	+	1506.80i	0.327213	+	0.127072i
$521$	20909.0			1.75823			0.879116	−	0.476608i	$-0.158134\pi$
$521$	20909.0			1.75823			0.879116	+	0.476608i	$0.158134\pi$
$522$		0			0
$523$	12045.2			1.00708			0.503539	−	0.863973i	$-0.332031\pi$
$523$	12045.2			1.00708			0.503539	+	0.863973i	$0.332031\pi$
$524$	9456.16			0.788348
$525$		0			0
$526$	1410.06			0.116885
$527$	−10771.8			−0.890371
$528$		0			0
$529$	6433.99			0.528807
$530$	2845.88	+	1105.19i	0.233240	+	0.0905780i
$531$		0			0
$532$	1843.54	+	6380.89i	0.150240	+	0.520012i
$533$	−6451.21			−0.524264
$534$		0			0
$535$	7760.05	+	3013.59i	0.627095	+	0.243531i
$536$		−	1327.79i		−	0.107000i
$537$		0			0
$538$	419.166			0.0335902
$539$	5193.39	+	8237.51i	0.415019	+	0.658283i
$540$		0			0
$541$	5762.89			0.457978			0.228989	−	0.973429i	$-0.426458\pi$
$541$	5762.89			0.457978			0.228989	+	0.973429i	$0.426458\pi$
$542$		−	4955.47i		−	0.392723i
$543$		0			0
$544$			6389.89i			0.503611i
$545$	7631.05	+	2963.49i	0.599777	+	0.232921i
$546$		0			0
$547$		−	1926.27i		−	0.150569i	−0.997162	−	0.0752847i	$-0.976013\pi$
$547$		−	1926.27i		−	0.150569i	0.997162	−	0.0752847i	$-0.0239866\pi$
$548$	14123.0			1.10092
$549$		0			0
$550$	−1980.37	+	2165.21i	−0.153533	+	0.167863i
$551$	−6502.72			−0.502768
$552$		0			0
$553$	665.500	−	192.273i	0.0511753	−	0.0147853i
$554$			2652.86i			0.203446i
$555$		0			0
$556$		−	4047.28i		−	0.308710i
$557$	17984.6			1.36810			0.684050	−	0.729435i	$-0.260217\pi$
$557$	17984.6			1.36810			0.684050	+	0.729435i	$0.260217\pi$
$558$		0			0
$559$		−	12535.3i		−	0.948454i
$560$	9911.86	+	886.126i	0.747951	+	0.0668673i
$561$		0			0
$562$			2763.64i			0.207433i
$563$			20203.7i			1.51240i	0.654339	+	0.756201i	$0.272947\pi$
$563$			20203.7i			1.51240i	−0.654339	+	0.756201i	$0.727053\pi$
$564$		0			0
$565$	4058.28	+	1576.02i	0.302183	+	0.117352i
$566$	−4270.51			−0.317143
$567$		0			0
$568$			10309.6i			0.761586i
$569$			10780.5i			0.794271i	0.917760	+	0.397135i	$0.129996\pi$
$569$			10780.5i			0.794271i	−0.917760	+	0.397135i	$0.870004\pi$
$570$		0			0
$571$	1504.63			0.110275			0.0551374	−	0.998479i	$-0.482440\pi$
$571$	1504.63			0.110275			0.0551374	+	0.998479i	$0.482440\pi$
$572$			6106.30i			0.446359i
$573$		0			0
$574$	3228.39	−	932.732i	0.234757	−	0.0678249i
$575$	12579.9	+	11506.0i	0.912377	+	0.834490i
$576$		0			0
$577$	−6884.35			−0.496706			−0.248353	−	0.968670i	$-0.579889\pi$
$577$	−6884.35			−0.496706			−0.248353	+	0.968670i	$0.579889\pi$
$578$	2365.31			0.170215
$579$		0			0
$580$	−3928.38	+	10115.6i	−0.281236	+	0.724188i
$581$	−6439.10	−	22287.1i	−0.459792	−	1.59144i
$582$		0			0
$583$			9376.07i			0.666067i
$584$	3698.05			0.262032
$585$		0			0
$586$		−	3688.32i		−	0.260005i
$587$		−	17688.1i		−	1.24373i	−0.783126	−	0.621863i	$-0.786376\pi$
$587$		−	17688.1i		−	1.24373i	0.783126	−	0.621863i	$-0.213624\pi$
$588$		0			0
$589$	11655.1			0.815346
$590$	2037.78	+	791.367i	0.142194	+	0.0552204i
$591$		0			0
$592$			20726.3i			1.43893i
$593$			19118.0i			1.32391i	0.749542	+	0.661956i	$0.230274\pi$
$593$			19118.0i			1.32391i	−0.749542	+	0.661956i	$0.769726\pi$
$594$		0			0
$595$	−835.286	+	9343.17i	−0.0575519	+	0.643753i
$596$		−	1114.37i		−	0.0765878i
$597$		0			0
$598$	−3315.09			−0.226696
$599$		−	9875.37i		−	0.673617i	−0.941573	−	0.336809i	$-0.890652\pi$
$599$		−	9875.37i		−	0.673617i	0.941573	−	0.336809i	$-0.109348\pi$
$600$		0			0
$601$		−	7712.80i		−	0.523480i	−0.965138	−	0.261740i	$-0.915704\pi$
$601$		−	7712.80i		−	0.523480i	0.965138	−	0.261740i	$-0.0842964\pi$
$602$	1812.38	+	6273.06i	0.122703	+	0.424702i
$603$		0			0
$604$	14956.8			1.00759
$605$	5471.32	+	2124.77i	0.367671	+	0.142784i
$606$		0			0
$607$	−15291.3			−1.02249			−0.511246	−	0.859434i	$-0.670816\pi$
$607$	−15291.3			−1.02249			−0.511246	+	0.859434i	$0.670816\pi$
$608$		−	6913.86i		−	0.461175i
$609$		0			0
$610$	1921.45	−	4947.78i	0.127537	−	0.328409i
$611$		−	13126.4i		−	0.869129i
$612$		0			0
$613$			11961.5i			0.788124i	0.919084	+	0.394062i	$0.128931\pi$
$613$			11961.5i			0.788124i	−0.919084	+	0.394062i	$0.871069\pi$
$614$	3232.06			0.212435
$615$		0			0
$616$	−1848.23	−	6397.12i	−0.120888	−	0.418421i
$617$	19087.8			1.24546			0.622729	−	0.782438i	$-0.286024\pi$
$617$	19087.8			1.24546			0.622729	+	0.782438i	$0.286024\pi$
$618$		0			0
$619$			573.960i			0.0372688i	0.999826	+	0.0186344i	$0.00593186\pi$
$619$			573.960i			0.0372688i	−0.999826	+	0.0186344i	$0.994068\pi$
$620$	7040.98	−	18130.6i	0.456085	−	1.17443i
$621$		0			0
$622$	−3116.41			−0.200895
$623$	−25059.2	+	7239.98i	−1.61152	+	0.465592i
$624$		0			0
$625$	1390.57	+	15563.0i	0.0889966	+	0.996032i
$626$	−8495.44			−0.542406
$627$		0			0
$628$	1442.17			0.0916382
$629$	−19537.1			−1.23847
$630$		0			0
$631$	3155.96			0.199107			0.0995537	−	0.995032i	$-0.468258\pi$
$631$	3155.96			0.199107			0.0995537	+	0.995032i	$0.468258\pi$
$632$	−473.677			−0.0298131
$633$		0			0
$634$	1707.72			0.106975
$635$	2337.61	−	6019.40i	0.146087	−	0.376177i
$636$		0			0
$637$	−8529.67	+	5377.59i	−0.530546	+	0.334486i
$638$	3114.13			0.193244
$639$		0			0
$640$	−14068.4	−	5463.41i	−0.868908	−	0.337438i
$641$			18216.0i			1.12244i	0.827665	+	0.561222i	$0.189669\pi$
$641$			18216.0i			1.12244i	−0.827665	+	0.561222i	$0.810331\pi$
$642$		0			0
$643$	20836.6			1.27794			0.638969	−	0.769233i	$-0.279361\pi$
$643$	20836.6			1.27794			0.638969	+	0.769233i	$0.279361\pi$
$644$	−17754.2	+	5129.46i	−1.08636	+	0.313865i
$645$		0			0
$646$	1836.06			0.111825
$647$		−	27732.5i		−	1.68513i	−0.538595	−	0.842564i	$-0.681045\pi$
$647$		−	27732.5i		−	1.68513i	0.538595	−	0.842564i	$-0.318955\pi$
$648$		0			0
$649$			6713.70i			0.406064i
$650$	−2242.00	−	2050.61i	−0.135290	−	0.123741i
$651$		0			0
$652$			3786.06i			0.227413i
$653$	26601.0			1.59415			0.797074	−	0.603881i	$-0.206380\pi$
$653$	26601.0			1.59415			0.797074	+	0.603881i	$0.206380\pi$
$654$		0			0
$655$	−13470.2	−	5231.10i	−0.803547	−	0.312055i
$656$	10546.6			0.627707
$657$		0			0
$658$	1897.85	+	6568.88i	0.112441	+	0.389182i
$659$			5108.02i			0.301943i	0.988538	+	0.150971i	$0.0482401\pi$
$659$			5108.02i			0.301943i	−0.988538	+	0.150971i	$0.951760\pi$
$660$		0			0
$661$			6545.68i			0.385170i	0.981280	+	0.192585i	$0.0616871\pi$
$661$			6545.68i			0.385170i	−0.981280	+	0.192585i	$0.938313\pi$
$662$	−3890.15			−0.228391
$663$		0			0
$664$			15863.1i			0.927121i
$665$	903.780	−	10109.3i	0.0527024	−	0.589508i
$666$		0			0
$667$		−	18093.2i		−	1.05033i
$668$			13723.1i			0.794854i
$669$		0			0
$670$	−350.870	+	903.497i	−0.0202318	+	0.0520972i
$671$	16301.0			0.937844
$672$		0			0
$673$		−	695.255i		−	0.0398219i	−0.999802	−	0.0199109i	$-0.993662\pi$
$673$		−	695.255i		−	0.0398219i	0.999802	−	0.0199109i	$-0.00633826\pi$
$674$			159.018i			0.00908776i
$675$		0			0
$676$	9751.14			0.554799
$677$		−	12444.0i		−	0.706445i	−0.935539	−	0.353222i	$-0.885086\pi$
$677$		−	12444.0i		−	0.706445i	0.935539	−	0.353222i	$-0.114914\pi$
$678$		0			0
$679$	1918.31	−	554.230i	0.108421	−	0.0313246i
$680$	2322.02	−	5979.24i	0.130949	−	0.337196i
$681$		0			0
$682$	−5581.58			−0.313387
$683$	1997.14			0.111887			0.0559434	−	0.998434i	$-0.482183\pi$
$683$	1997.14			0.111887			0.0559434	+	0.998434i	$0.482183\pi$
$684$		0			0
$685$	−20118.0	−	7812.77i	−1.12215	−	0.435782i
$686$	3491.01	−	3924.36i	0.194297	−	0.218415i
$687$		0			0
$688$			20493.0i			1.13559i
$689$	−9708.61			−0.536820
$690$		0			0
$691$			29424.1i			1.61989i	0.586506	+	0.809945i	$0.300503\pi$
$691$			29424.1i			1.61989i	−0.586506	+	0.809945i	$0.699497\pi$
$692$			21646.2i			1.18911i
$693$		0			0
$694$	−1135.94			−0.0621319
$695$	−2238.93	+	5765.29i	−0.122198	+	0.314662i
$696$		0			0
$697$			9941.50i			0.540260i
$698$			6494.56i			0.352182i
$699$		0			0
$700$	−15180.1	−	7513.10i	−0.819648	−	0.405669i
$701$		−	573.289i		−	0.0308885i	−0.999881	−	0.0154442i	$-0.995084\pi$
$701$		−	573.289i		−	0.0308885i	0.999881	−	0.0154442i	$-0.00491625\pi$
$702$		0			0
$703$	21139.2			1.13411
$704$		−	7604.51i		−	0.407111i
$705$		0			0
$706$		−	4625.93i		−	0.246599i
$707$	9598.87	−	2773.26i	0.510612	−	0.147524i
$708$		0			0
$709$	16111.0			0.853402			0.426701	−	0.904393i	$-0.359676\pi$
$709$	16111.0			0.853402			0.426701	+	0.904393i	$0.359676\pi$
$710$	2724.32	−	7015.18i	0.144003	−	0.370810i
$711$		0			0
$712$	17836.1			0.938817
$713$			32429.0i			1.70333i
$714$		0			0
$715$	3377.97	−	8698.34i	0.176684	−	0.454964i
$716$			9220.23i			0.481252i
$717$		0			0
$718$			255.824i			0.0132970i
$719$	12693.6			0.658404			0.329202	−	0.944259i	$-0.393220\pi$
$719$	12693.6			0.658404			0.329202	+	0.944259i	$0.393220\pi$
$720$		0			0
$721$	−26944.3	+	7784.63i	−1.39176	+	0.402101i
$722$	3684.62			0.189927
$723$		0			0
$724$		−	24474.1i		−	1.25632i
$725$	11191.8	−	12236.4i	0.573316	−	0.626827i
$726$		0			0
$727$	−13990.8			−0.713742			−0.356871	−	0.934154i	$-0.616156\pi$
$727$	−13990.8			−0.713742			−0.356871	+	0.934154i	$0.616156\pi$
$728$	6624.01	−	1913.78i	0.337228	−	0.0974304i
$729$		0			0
$730$	−2516.35	−	977.216i	−0.127581	−	0.0495457i
$731$	−19317.2			−0.977392
$732$		0			0
$733$	11159.4			0.562324			0.281162	−	0.959660i	$-0.409280\pi$
$733$	11159.4			0.562324			0.281162	+	0.959660i	$0.409280\pi$
$734$	5536.60			0.278419
$735$		0			0
$736$	19237.1			0.963437
$737$	−2976.67			−0.148775
$738$		0			0
$739$	−5715.80			−0.284518			−0.142259	−	0.989829i	$-0.545437\pi$
$739$	−5715.80			−0.284518			−0.142259	+	0.989829i	$0.545437\pi$
$740$	12770.5	−	32884.2i	0.634394	−	1.63358i
$741$		0			0
$742$	4858.50	−	1403.70i	0.240379	−	0.0694492i
$743$	−12643.2			−0.624271			−0.312136	−	0.950038i	$-0.601044\pi$
$743$	−12643.2			−0.624271			−0.312136	+	0.950038i	$0.601044\pi$
$744$		0			0
$745$	−616.463	+	1587.40i	−0.0303161	+	0.0780644i
$746$			4490.93i			0.220408i
$747$		0			0
$748$	9409.99			0.459978
$749$	13248.0	−	3827.55i	0.646290	−	0.186723i
$750$		0			0
$751$	−22154.8			−1.07649			−0.538243	−	0.842790i	$-0.680912\pi$
$751$	−22154.8			−1.07649			−0.538243	+	0.842790i	$0.680912\pi$
$752$			21459.4i			1.04062i
$753$		0			0
$754$			3224.58i			0.155746i
$755$	−21305.8	−	8274.04i	−1.02702	−	0.398839i
$756$		0			0
$757$			19624.0i			0.942203i	0.882079	+	0.471102i	$0.156144\pi$
$757$			19624.0i			0.942203i	−0.882079	+	0.471102i	$0.843856\pi$
$758$	−9111.03			−0.436580
$759$		0			0
$760$	−2512.43	+	6469.54i	−0.119915	+	0.308783i
$761$	25556.5			1.21738			0.608689	−	0.793409i	$-0.291696\pi$
$761$	25556.5			1.21738			0.608689	+	0.793409i	$0.291696\pi$
$762$		0			0
$763$	13027.8	−	3763.92i	0.618135	−	0.178589i
$764$		−	963.061i		−	0.0456051i
$765$		0			0
$766$		−	1867.47i		−	0.0880865i
$767$	−6951.82			−0.327269
$768$		0			0
$769$		−	28712.6i		−	1.34643i	−0.739448	−	0.673214i	$-0.764913\pi$
$769$		−	28712.6i		−	1.34643i	0.739448	−	0.673214i	$-0.235087\pi$
$770$	−432.818	+	4841.33i	−0.0202567	+	0.226584i
$771$		0			0
$772$		−	11650.0i		−	0.543126i
$773$			20110.6i			0.935743i	0.883796	+	0.467872i	$0.154979\pi$
$773$			20110.6i			0.935743i	−0.883796	+	0.467872i	$0.845021\pi$
$774$		0			0
$775$	−20059.5	+	21931.8i	−0.929755	+	1.01653i
$776$	−1365.38			−0.0631627
$777$		0			0
$778$			5646.06i			0.260181i
$779$		−	10756.7i		−	0.494736i
$780$		0			0
$781$	23112.3			1.05893
$782$			5108.65i			0.233613i
$783$		0			0
$784$	13944.5	−	8791.42i	0.635228	−	0.400484i
$785$	−2054.35	−	797.800i	−0.0934049	−	0.0362735i
$786$		0			0
$787$	−20449.5			−0.926233			−0.463117	−	0.886297i	$-0.653269\pi$
$787$	−20449.5			−0.926233			−0.463117	+	0.886297i	$0.653269\pi$
$788$	−23432.3			−1.05932
$789$		0			0
$790$	322.314	+	125.170i	0.0145157	+	0.00563714i
$791$	6928.32	−	2001.70i	0.311432	−	0.0899776i
$792$		0			0
$793$			16879.2i			0.755859i
$794$	−7456.51			−0.333277
$795$		0			0
$796$			24395.4i			1.08627i
$797$		−	16119.3i		−	0.716405i	−0.933644	−	0.358202i	$-0.883390\pi$
$797$		−	16119.3i		−	0.716405i	0.933644	−	0.358202i	$-0.116610\pi$
$798$		0			0
$799$	−20228.2			−0.895646
$800$	13010.1	+	11899.5i	0.574970	+	0.525887i
$801$		0			0
$802$			30.4538i			0.00134085i
$803$		−	8290.38i		−	0.364335i
$804$		0			0
$805$	28128.2	+	2514.68i	1.23154	+	0.110100i
$806$		−	5779.54i		−	0.252575i
$807$		0			0
$808$	−6832.10			−0.297466
$809$		−	3994.80i		−	0.173609i	−0.996225	−	0.0868045i	$-0.972334\pi$
$809$		−	3994.80i		−	0.173609i	0.996225	−	0.0868045i	$-0.0276655\pi$
$810$		0			0
$811$		−	44132.3i		−	1.91084i	−0.295244	−	0.955422i	$-0.595401\pi$
$811$		−	44132.3i		−	1.91084i	0.295244	−	0.955422i	$-0.404599\pi$
$812$	4989.42	+	17269.5i	0.215633	+	0.746354i
$813$		0			0
$814$	−10123.5			−0.435908
$815$	2094.43	−	5393.19i	0.0900179	−	0.231798i
$816$		0			0
$817$	20901.3			0.895034
$818$			5116.23i			0.218685i
$819$		0			0
$820$	−16733.2	−	6498.27i	−0.712618	−	0.276743i
$821$		−	44691.2i		−	1.89980i	−0.312558	−	0.949899i	$-0.601186\pi$
$821$		−	44691.2i		−	1.89980i	0.312558	−	0.949899i	$-0.398814\pi$
$822$		0			0
$823$		−	2206.71i		−	0.0934641i	−0.998907	−	0.0467321i	$-0.985119\pi$
$823$		−	2206.71i		−	0.0934641i	0.998907	−	0.0467321i	$-0.0148807\pi$
$824$	19177.9			0.810794
$825$		0			0
$826$	3478.91	−	1005.11i	0.146546	−	0.0423394i
$827$	−3960.83			−0.166544			−0.0832718	−	0.996527i	$-0.526537\pi$
$827$	−3960.83			−0.166544			−0.0832718	+	0.996527i	$0.526537\pi$
$828$		0			0
$829$			10967.1i			0.459473i	0.973253	+	0.229737i	$0.0737865\pi$
$829$			10967.1i			0.459473i	−0.973253	+	0.229737i	$0.926214\pi$
$830$	4191.85	−	10794.1i	0.175303	−	0.451408i
$831$		0			0
$832$	7874.22			0.328113
$833$	8287.02	+	13144.5i	0.344692	+	0.546733i
$834$		0			0
$835$	7591.54	−	19548.3i	0.314630	−	0.810178i
$836$	−10181.6			−0.421218
$837$		0			0
$838$	8964.09			0.369522
$839$	−45551.1			−1.87437			−0.937186	−	0.348829i	$-0.886579\pi$
$839$	−45551.1			−1.87437			−0.937186	+	0.348829i	$0.886579\pi$
$840$		0			0
$841$	6789.82			0.278397
$842$	−4752.13			−0.194500
$843$		0			0
$844$	−31110.7			−1.26881
$845$	−13890.4	−	5394.28i	−0.565495	−	0.219608i
$846$		0			0
$847$	9340.67	−	2698.67i	0.378925	−	0.109477i
$848$	15871.9			0.642739
$849$		0			0
$850$	−3160.04	+	3454.99i	−0.127516	+	0.139418i
$851$			58817.7i			2.36927i
$852$		0			0
$853$	−40724.0			−1.63466			−0.817330	−	0.576170i	$-0.804547\pi$
$853$	−40724.0			−1.63466			−0.817330	+	0.576170i	$0.804547\pi$
$854$	−2440.43	−	8446.87i	−0.0977867	−	0.338461i
$855$		0			0
$856$	−9429.40			−0.376507
$857$		−	440.205i		−	0.0175462i	−0.999962	−	0.00877312i	$-0.997207\pi$
$857$		−	440.205i		−	0.0175462i	0.999962	−	0.00877312i	$-0.00279261\pi$
$858$		0			0
$859$			32558.4i			1.29322i	0.762820	+	0.646610i	$0.223814\pi$
$859$			32558.4i			1.29322i	−0.762820	+	0.646610i	$0.776186\pi$
$860$	12626.7	−	32514.0i	0.500660	−	1.28921i
$861$		0			0
$862$			5014.72i			0.198146i
$863$	−36423.2			−1.43669			−0.718343	−	0.695689i	$-0.755099\pi$
$863$	−36423.2			−1.43669			−0.718343	+	0.695689i	$0.755099\pi$
$864$		0			0
$865$	11974.6	−	30834.7i	0.470690	−	1.21204i
$866$	10597.1			0.415823
$867$		0			0
$868$	−8942.72	−	30952.7i	−0.349696	−	1.21037i
$869$			1061.90i			0.0414528i
$870$		0			0
$871$		−	3082.24i		−	0.119906i
$872$	−9272.66			−0.360105
$873$		0			0
$874$		−	5527.56i		−	0.213928i
$875$	17467.6	+	19099.8i	0.674872	+	0.737934i
$876$		0			0
$877$		−	1594.15i		−	0.0613805i	−0.999529	−	0.0306902i	$-0.990229\pi$
$877$		−	1594.15i		−	0.0613805i	0.999529	−	0.0306902i	$-0.00977054\pi$
$878$		−	14582.4i		−	0.560513i
$879$		0			0
$880$	−5522.40	+	14220.3i	−0.211546	+	0.544733i
$881$	−39169.0			−1.49788			−0.748942	−	0.662636i	$-0.769438\pi$
$881$	−39169.0			−1.49788			−0.748942	+	0.662636i	$0.769438\pi$
$882$		0			0
$883$		−	31712.0i		−	1.20860i	−0.796757	−	0.604300i	$-0.793453\pi$
$883$		−	31712.0i		−	1.20860i	0.796757	−	0.604300i	$-0.206547\pi$
$884$			9743.74i			0.370721i
$885$		0			0
$886$	−11337.3			−0.429891
$887$		−	26948.5i		−	1.02012i	−0.860140	−	0.510058i	$-0.829624\pi$
$887$		−	26948.5i		−	1.02012i	0.860140	−	0.510058i	$-0.170376\pi$
$888$		0			0
$889$	−2969.00	−	10276.3i	−0.112010	−	0.387691i
$890$	−12136.6	−	4713.22i	−0.457102	−	0.177514i
$891$		0			0
$892$	31508.0			1.18270
$893$	21886.9			0.820176
$894$		0			0
$895$	5100.58	−	13134.1i	0.190496	−	0.490530i
$896$	−24017.6	+	6939.05i	−0.895504	+	0.258725i
$897$		0			0
$898$		−	15688.6i		−	0.583002i
$899$	31543.7			1.17023
$900$		0			0
$901$			14961.3i			0.553198i
$902$			5151.36i			0.190157i
$903$		0			0
$904$	−4931.31			−0.181430
$905$	−13539.0	+	34863.1i	−0.497293	+	1.28054i
$906$		0			0
$907$		−	37901.0i		−	1.38752i	−0.720205	−	0.693762i	$-0.755952\pi$
$907$		−	37901.0i		−	1.38752i	0.720205	−	0.693762i	$-0.244048\pi$
$908$		−	17440.1i		−	0.637412i
$909$		0			0
$910$	−5013.03	−	448.169i	−0.182616	−	0.0163260i
$911$		−	911.051i		−	0.0331333i	−0.999863	−	0.0165667i	$-0.994726\pi$
$911$		−	911.051i		−	0.0331333i	0.999863	−	0.0165667i	$-0.00527357\pi$
$912$		0			0
$913$	35562.3			1.28909
$914$		−	7634.01i		−	0.276270i
$915$		0			0
$916$			28230.1i			1.01829i
$917$	−22996.3	+	6644.00i	−0.828142	+	0.239263i
$918$		0			0
$919$	5135.53			0.184337			0.0921684	−	0.995743i	$-0.470620\pi$
$919$	5135.53			0.184337			0.0921684	+	0.995743i	$0.470620\pi$
$920$	−18000.9	−	6990.58i	−0.645077	−	0.250514i
$921$		0			0
$922$	−6529.02			−0.233212
$923$			23932.0i			0.853447i
$924$		0			0
$925$	−36382.7	+	39778.5i	−1.29325	+	1.41396i
$926$		−	11808.8i		−	0.419072i
$927$		0			0
$928$		−	18711.9i		−	0.661906i
$929$	40564.4			1.43259			0.716295	−	0.697798i	$-0.245837\pi$
$929$	40564.4			1.43259			0.716295	+	0.697798i	$0.245837\pi$
$930$		0			0
$931$	−8966.56	−	14222.3i	−0.315647	−	0.500664i
$932$	−51849.1			−1.82229
$933$		0			0
$934$		−	5210.96i		−	0.182557i
$935$	−13404.4	−	5205.56i	−0.468846	−	0.182075i
$936$		0			0
$937$	−6899.40			−0.240548			−0.120274	−	0.992741i	$-0.538377\pi$
$937$	−6899.40			−0.240548			−0.120274	+	0.992741i	$0.538377\pi$
$938$	445.639	+	1542.45i	0.0155124	+	0.0536918i
$939$		0			0
$940$	13222.2	−	34047.3i	0.458787	−	1.18138i
$941$	38885.2			1.34710			0.673550	−	0.739142i	$-0.264769\pi$
$941$	38885.2			1.34710			0.673550	+	0.739142i	$0.264769\pi$
$942$		0			0
$943$	29929.5			1.03355
$944$	11365.0			0.391843
$945$		0			0
$946$	−10009.6			−0.344016
$947$	8149.29			0.279637			0.139818	−	0.990177i	$-0.455348\pi$
$947$	8149.29			0.279637			0.139818	+	0.990177i	$0.455348\pi$
$948$		0			0
$949$	8584.42			0.293638
$950$	3419.17	−	3738.30i	0.116771	−	0.127670i
$951$		0			0
$952$	−2949.19	−	10207.8i	−0.100403	−	0.347517i
$953$	−51647.7			−1.75554			−0.877772	−	0.479078i	$-0.840971\pi$
$953$	−51647.7			−1.75554			−0.877772	+	0.479078i	$0.840971\pi$
$954$		0			0
$955$	−532.760	+	1371.87i	−0.0180521	+	0.0464844i
$956$			32817.4i			1.11024i
$957$		0			0
$958$	−236.221			−0.00796654
$959$	−34345.6	+	9922.98i	−1.15649	+	0.334129i
$960$		0			0
$961$	−26745.9			−0.897785
$962$		−	10482.6i		−	0.351321i
$963$		0			0
$964$			20806.9i			0.695172i
$965$	−6444.73	+	16595.3i	−0.214988	+	0.553597i
$966$		0			0
$967$		−	45387.6i		−	1.50937i	−0.656085	−	0.754687i	$-0.727789\pi$
$967$		−	45387.6i		−	1.50937i	0.656085	−	0.754687i	$-0.272211\pi$
$968$	−6648.33			−0.220749
$969$		0			0
$970$	929.075	+	360.803i	0.0307534	+	0.0119430i
$971$	−4741.74			−0.156714			−0.0783572	−	0.996925i	$-0.524967\pi$
$971$	−4741.74			−0.156714			−0.0783572	+	0.996925i	$0.524967\pi$
$972$		0			0
$973$	2843.66	+	9842.53i	0.0936932	+	0.324293i
$974$		−	8857.98i		−	0.291405i
$975$		0			0
$976$		−	27594.5i		−	0.904997i
$977$	34962.8			1.14489			0.572447	−	0.819942i	$-0.305994\pi$
$977$	34962.8			1.14489			0.572447	+	0.819942i	$0.305994\pi$
$978$		0			0
$979$		−	39985.5i		−	1.30535i
$980$	−27541.1	+	5356.50i	−0.897722	+	0.174599i
$981$		0			0
$982$			12783.2i			0.415405i
$983$			6636.49i			0.215332i	0.994187	+	0.107666i	$0.0343377\pi$
$983$			6636.49i			0.215332i	−0.994187	+	0.107666i	$0.965662\pi$
$984$		0			0
$985$	33379.0	+	12962.6i	1.07974	+	0.419313i
$986$	4969.18			0.160498
$987$		0			0
$988$		−	10542.7i		−	0.339483i
$989$			58155.7i			1.86981i
$990$		0			0
$991$	37122.5			1.18994			0.594972	−	0.803747i	$-0.297163\pi$
$991$	37122.5			1.18994			0.594972	+	0.803747i	$0.297163\pi$
$992$			33538.1i			1.07342i
$993$		0			0
$994$	−3460.15	−	11976.3i	−0.110412	−	0.382160i
$995$	13495.4	−	34750.9i	0.429983	−	1.10721i
$996$		0			0
$997$	−3367.88			−0.106983			−0.0534913	−	0.998568i	$-0.517035\pi$
$997$	−3367.88			−0.106983			−0.0534913	+	0.998568i	$0.517035\pi$
$998$	−14872.8			−0.471733
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.4.g.a.314.28	yes	48
3.2	odd	2	inner	315.4.g.a.314.23	yes	48
5.4	even	2	inner	315.4.g.a.314.24	yes	48
7.6	odd	2	inner	315.4.g.a.314.26	yes	48
15.14	odd	2	inner	315.4.g.a.314.27	yes	48
21.20	even	2	inner	315.4.g.a.314.21	✓	48
35.34	odd	2	inner	315.4.g.a.314.22	yes	48
105.104	even	2	inner	315.4.g.a.314.25	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.4.g.a.314.21	✓	48	21.20	even	2	inner
315.4.g.a.314.22	yes	48	35.34	odd	2	inner
315.4.g.a.314.23	yes	48	3.2	odd	2	inner
315.4.g.a.314.24	yes	48	5.4	even	2	inner
315.4.g.a.314.25	yes	48	105.104	even	2	inner
315.4.g.a.314.26	yes	48	7.6	odd	2	inner
315.4.g.a.314.27	yes	48	15.14	odd	2	inner
315.4.g.a.314.28	yes	48	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.826832 q^{2} -7.31635 q^{4} +(10.4220 + 4.04737i) q^{5} +(17.7925 - 5.14054i) q^{7} -12.6640 q^{8} +(8.61727 + 3.34649i) q^{10} +28.3906i q^{11} -29.3975 q^{13} +(14.7114 - 4.25037i) q^{14} +48.0598 q^{16} +45.3024i q^{17} -49.0172i q^{19} +(-76.2513 - 29.6119i) q^{20} +23.4742i q^{22} +136.385 q^{23} +(92.2377 + 84.3636i) q^{25} -24.3068 q^{26} +(-130.177 + 37.6100i) q^{28} -132.662i q^{29} +237.775i q^{31} +141.050 q^{32} +37.4575i q^{34} +(206.240 + 18.4380i) q^{35} +431.261i q^{37} -40.5290i q^{38} +(-131.985 - 51.2560i) q^{40} +219.448 q^{41} +426.407i q^{43} -207.715i q^{44} +112.768 q^{46} +446.515i q^{47} +(290.150 - 182.927i) q^{49} +(76.2650 + 69.7545i) q^{50} +215.082 q^{52} +330.253 q^{53} +(-114.907 + 295.887i) q^{55} +(-225.326 + 65.1001i) q^{56} -109.689i q^{58} +236.477 q^{59} -574.170i q^{61} +196.600i q^{62} -267.854 q^{64} +(-306.382 - 118.982i) q^{65} +104.847i q^{67} -331.448i q^{68} +(170.526 + 15.2451i) q^{70} -814.084i q^{71} -292.012 q^{73} +356.580i q^{74} +358.627i q^{76} +(145.943 + 505.140i) q^{77} +37.4033 q^{79} +(500.881 + 194.515i) q^{80} +181.446 q^{82} -1252.61i q^{83} +(-183.355 + 472.143i) q^{85} +352.567i q^{86} -359.539i q^{88} -1408.41 q^{89} +(-523.056 + 151.119i) q^{91} -997.844 q^{92} +369.193i q^{94} +(198.391 - 510.859i) q^{95} +107.815 q^{97} +(239.905 - 151.250i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 192 q^{4} + 768 q^{16} - 432 q^{25} + 816 q^{46} + 456 q^{49} + 7968 q^{64} + 1464 q^{70} + 4368 q^{79} - 1440 q^{85} - 4392 q^{91}+O(q^{100}) \) 48 * q + 192 * q^4 + 768 * q^16 - 432 * q^25 + 816 * q^46 + 456 * q^49 + 7968 * q^64 + 1464 * q^70 + 4368 * q^79 - 1440 * q^85 - 4392 * q^91

Introduction

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