LMFDB - Embedded newform 650.4.c.e.649.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,4,Mod(649,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.649"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	650.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-8,0,16,0,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$38.3512415037$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{217})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 109x^{2} + 2916 $ x^4 + 109*x^2 + 2916
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			649.3
Root			$6.86546i$ of defining polynomial
Character	$\chi$	$=$	650.649
Dual form			650.4.c.e.649.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +5.86546i q^{3} +4.00000 q^{4} -11.7309i q^{6} -3.86546 q^{7} -8.00000 q^{8} -7.40362 q^{9} +53.1928i q^{11} +23.4618i q^{12} +(-31.3273 - 34.8655i) q^{13} +7.73092 q^{14} +16.0000 q^{16} -43.3273i q^{17} +14.8072 q^{18} +148.386i q^{19} -22.6727i q^{21} -106.386i q^{22} -122.655i q^{23} -46.9237i q^{24} +(62.6546 + 69.7309i) q^{26} +114.942i q^{27} -15.4618 q^{28} -83.8836 q^{29} -190.269i q^{31} -32.0000 q^{32} -312.000 q^{33} +86.6546i q^{34} -29.6145 q^{36} -131.713 q^{37} -296.771i q^{38} +(204.502 - 183.749i) q^{39} +387.695i q^{41} +45.3454i q^{42} +74.6365i q^{43} +212.771i q^{44} +245.309i q^{46} -298.789 q^{47} +93.8474i q^{48} -328.058 q^{49} +254.135 q^{51} +(-125.309 - 139.462i) q^{52} +100.386i q^{53} -229.884i q^{54} +30.9237 q^{56} -870.349 q^{57} +167.767 q^{58} -479.309i q^{59} -479.811 q^{61} +380.538i q^{62} +28.6184 q^{63} +64.0000 q^{64} +624.000 q^{66} +415.273 q^{67} -173.309i q^{68} +719.426 q^{69} -293.946i q^{71} +59.2290 q^{72} -106.727 q^{73} +263.426 q^{74} +593.542i q^{76} -205.614i q^{77} +(-409.004 + 367.498i) q^{78} +906.044 q^{79} -874.084 q^{81} -775.389i q^{82} -22.1605 q^{83} -90.6908i q^{84} -149.273i q^{86} -492.016i q^{87} -425.542i q^{88} -665.433i q^{89} +(121.094 + 134.771i) q^{91} -490.618i q^{92} +1116.02 q^{93} +597.578 q^{94} -187.695i q^{96} -1254.24 q^{97} +656.116 q^{98} -393.819i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 16 q^{4} + 14 q^{7} - 32 q^{8} - 118 q^{9} + 22 q^{13} - 28 q^{14} + 64 q^{16} + 236 q^{18} - 44 q^{26} + 56 q^{28} - 748 q^{29} - 128 q^{32} - 1248 q^{33} - 472 q^{36} - 26 q^{37} + 52 q^{39}+ \cdots + 2212 q^{98}+O(q^{100}) $ 4 * q - 8 * q^2 + 16 * q^4 + 14 * q^7 - 32 * q^8 - 118 * q^9 + 22 * q^13 - 28 * q^14 + 64 * q^16 + 236 * q^18 - 44 * q^26 + 56 * q^28 - 748 * q^29 - 128 * q^32 - 1248 * q^33 - 472 * q^36 - 26 * q^37 + 52 * q^39 - 930 * q^47 - 1106 * q^49 + 1046 * q^51 + 88 * q^52 - 112 * q^56 - 2244 * q^57 + 1496 * q^58 - 564 * q^61 - 1064 * q^63 + 256 * q^64 + 2496 * q^66 + 188 * q^67 + 1876 * q^69 + 944 * q^72 - 1900 * q^73 + 52 * q^74 - 104 * q^78 + 1444 * q^79 - 668 * q^81 + 2504 * q^83 + 1162 * q^91 - 1664 * q^93 + 1860 * q^94 - 1128 * q^97 + 2212 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.00000			−0.707107
$2$	−2.00000			−0.707107
$3$			5.86546i			1.12881i	0.825499	+	0.564404i	$0.190894\pi$
$3$			5.86546i			1.12881i	−0.825499	+	0.564404i	$0.809106\pi$
$4$	4.00000			0.500000
$5$		0			0
$5$		0			0
$6$		−	11.7309i		−	0.798188i
$7$	−3.86546			−0.208715			−0.104358	−	0.994540i	$-0.533279\pi$
$7$	−3.86546			−0.208715			−0.104358	+	0.994540i	$0.533279\pi$
$8$	−8.00000			−0.353553
$9$	−7.40362			−0.274208
$10$		0			0
$11$			53.1928i			1.45802i	0.684503	+	0.729010i	$0.260019\pi$
$11$			53.1928i			1.45802i	−0.684503	+	0.729010i	$0.739981\pi$
$12$			23.4618i			0.564404i
$13$	−31.3273	−	34.8655i	−0.668356	−	0.743841i
$13$	−31.3273	−	34.8655i	−0.668356	−	0.743841i
$14$	7.73092			0.147584
$15$		0			0
$16$	16.0000			0.250000
$17$		−	43.3273i		−	0.618142i	−0.951039	−	0.309071i	$-0.899982\pi$
$17$		−	43.3273i		−	0.618142i	0.951039	−	0.309071i	$-0.100018\pi$
$18$	14.8072			0.193894
$19$			148.386i			1.79168i	0.444374	+	0.895841i	$0.353426\pi$
$19$			148.386i			1.79168i	−0.444374	+	0.895841i	$0.646574\pi$
$20$		0			0
$21$		−	22.6727i		−	0.235599i
$22$		−	106.386i		−	1.03098i
$23$		−	122.655i		−	1.11197i	−0.831193	−	0.555984i	$-0.812342\pi$
$23$		−	122.655i		−	1.11197i	0.831193	−	0.555984i	$-0.187658\pi$
$24$		−	46.9237i		−	0.399094i
$25$		0			0
$26$	62.6546	+	69.7309i	0.472599	+	0.525975i
$27$			114.942i			0.819280i
$28$	−15.4618			−0.104358
$29$	−83.8836			−0.537131			−0.268565	−	0.963261i	$-0.586550\pi$
$29$	−83.8836			−0.537131			−0.268565	+	0.963261i	$0.586550\pi$
$30$		0			0
$31$		−	190.269i		−	1.10237i	−0.834384	−	0.551183i	$-0.814177\pi$
$31$		−	190.269i		−	1.10237i	0.834384	−	0.551183i	$-0.185823\pi$
$32$	−32.0000			−0.176777
$33$	−312.000			−1.64583
$34$			86.6546i			0.437092i
$35$		0			0
$36$	−29.6145			−0.137104
$37$	−131.713			−0.585228			−0.292614	−	0.956231i	$-0.594525\pi$
$37$	−131.713			−0.585228			−0.292614	+	0.956231i	$0.594525\pi$
$38$		−	296.771i		−	1.26691i
$39$	204.502	−	183.749i	0.839654	−	0.754446i
$40$		0			0
$41$			387.695i			1.47677i	0.674377	+	0.738387i	$0.264412\pi$
$41$			387.695i			1.47677i	−0.674377	+	0.738387i	$0.735588\pi$
$42$			45.3454i			0.166594i
$43$			74.6365i			0.264697i	0.991203	+	0.132348i	$0.0422518\pi$
$43$			74.6365i			0.264697i	−0.991203	+	0.132348i	$0.957748\pi$
$44$			212.771i			0.729010i
$45$		0			0
$46$			245.309i			0.786280i
$47$	−298.789			−0.927295			−0.463648	−	0.886020i	$-0.653460\pi$
$47$	−298.789			−0.927295			−0.463648	+	0.886020i	$0.653460\pi$
$48$			93.8474i			0.282202i
$49$	−328.058			−0.956438
$50$		0			0
$51$	254.135			0.697764
$52$	−125.309	−	139.462i	−0.334178	−	0.371921i
$53$			100.386i			0.260170i	0.991503	+	0.130085i	$0.0415250\pi$
$53$			100.386i			0.260170i	−0.991503	+	0.130085i	$0.958475\pi$
$54$		−	229.884i		−	0.579318i
$55$		0			0
$56$	30.9237			0.0737920
$57$	−870.349			−2.02247
$58$	167.767			0.379809
$59$		−	479.309i		−	1.05764i	−0.848734	−	0.528820i	$-0.822635\pi$
$59$		−	479.309i		−	1.05764i	0.848734	−	0.528820i	$-0.177365\pi$
$60$		0			0
$61$	−479.811			−1.00711			−0.503553	−	0.863964i	$-0.667974\pi$
$61$	−479.811			−1.00711			−0.503553	+	0.863964i	$0.667974\pi$
$62$			380.538i			0.779490i
$63$	28.6184			0.0572314
$64$	64.0000			0.125000
$65$		0			0
$66$	624.000			1.16377
$67$	415.273			0.757219			0.378609	−	0.925557i	$-0.376402\pi$
$67$	415.273			0.757219			0.378609	+	0.925557i	$0.376402\pi$
$68$		−	173.309i		−	0.309071i
$69$	719.426			1.25520
$70$		0			0
$71$		−	293.946i		−	0.491337i	−0.969354	−	0.245669i	$-0.920993\pi$
$71$		−	293.946i		−	0.491337i	0.969354	−	0.245669i	$-0.0790075\pi$
$72$	59.2290			0.0969472
$73$	−106.727			−0.171116			−0.0855579	−	0.996333i	$-0.527267\pi$
$73$	−106.727			−0.171116			−0.0855579	+	0.996333i	$0.527267\pi$
$74$	263.426			0.413819
$75$		0			0
$76$			593.542i			0.895841i
$77$		−	205.614i		−	0.304311i
$78$	−409.004	+	367.498i	−0.593725	+	0.533474i
$79$	906.044			1.29035			0.645177	−	0.764033i	$-0.276784\pi$
$79$	906.044			1.29035			0.645177	+	0.764033i	$0.276784\pi$
$80$		0			0
$81$	−874.084			−1.19902
$82$		−	775.389i		−	1.04424i
$83$	−22.1605			−0.0293064			−0.0146532	−	0.999893i	$-0.504664\pi$
$83$	−22.1605			−0.0293064			−0.0146532	+	0.999893i	$0.504664\pi$
$84$		−	90.6908i		−	0.117800i
$85$		0			0
$86$		−	149.273i		−	0.187169i
$87$		−	492.016i		−	0.606317i
$88$		−	425.542i		−	0.515488i
$89$		−	665.433i		−	0.792537i	−0.918135	−	0.396269i	$-0.870305\pi$
$89$		−	665.433i		−	0.792537i	0.918135	−	0.396269i	$-0.129695\pi$
$90$		0			0
$91$	121.094	+	134.771i	0.139496	+	0.155251i
$92$		−	490.618i		−	0.555984i
$93$	1116.02			1.24436
$94$	597.578			0.655697
$95$		0			0
$96$		−	187.695i		−	0.199547i
$97$	−1254.24			−1.31287			−0.656437	−	0.754381i	$-0.727937\pi$
$97$	−1254.24			−1.31287			−0.656437	+	0.754381i	$0.727937\pi$
$98$	656.116			0.676304
$99$		−	393.819i		−	0.399801i
$100$		0			0
$101$	1757.21			1.73118			0.865588	−	0.500757i	$-0.166945\pi$
$101$	1757.21			1.73118			0.865588	+	0.500757i	$0.166945\pi$
$102$	−508.269			−0.493394
$103$		−	86.2769i		−	0.0825351i	−0.999148	−	0.0412676i	$-0.986860\pi$
$103$		−	86.2769i		−	0.0825351i	0.999148	−	0.0412676i	$-0.0131396\pi$
$104$	250.618	+	278.924i	0.236300	+	0.262988i
$105$		0			0
$106$		−	200.771i		−	0.183968i
$107$		−	2100.93i		−	1.89817i	−0.315013	−	0.949087i	$-0.602009\pi$
$107$		−	2100.93i		−	1.89817i	0.315013	−	0.949087i	$-0.397991\pi$
$108$			459.767i			0.409640i
$109$		−	2166.87i		−	1.90411i	−0.305920	−	0.952057i	$-0.598964\pi$
$109$		−	2166.87i		−	1.90411i	0.305920	−	0.952057i	$-0.401036\pi$
$110$		0			0
$111$		−	772.556i		−	0.660611i
$112$	−61.8474			−0.0521788
$113$		−	356.779i		−	0.297017i	−0.988911	−	0.148509i	$-0.952553\pi$
$113$		−	356.779i		−	0.297017i	0.988911	−	0.148509i	$-0.0474472\pi$
$114$	1740.70			1.43010
$115$		0			0
$116$	−335.534			−0.268565
$117$	231.935	+	258.131i	0.183269	+	0.203967i
$118$			958.618i			0.747864i
$119$			167.480i			0.129016i
$120$		0			0
$121$	−1498.47			−1.12582
$122$	959.622			0.712132
$123$	−2274.01			−1.66699
$124$		−	761.076i		−	0.551183i
$125$		0			0
$126$	−57.2368			−0.0404687
$127$			997.666i			0.697075i	0.937295	+	0.348538i	$0.113322\pi$
$127$			997.666i			0.697075i	−0.937295	+	0.348538i	$0.886678\pi$
$128$	−128.000			−0.0883883
$129$	−437.777			−0.298792
$130$		0			0
$131$	−1680.88			−1.12106			−0.560530	−	0.828134i	$-0.689403\pi$
$131$	−1680.88			−1.12106			−0.560530	+	0.828134i	$0.689403\pi$
$132$	−1248.00			−0.822913
$133$		−	573.578i		−	0.373951i
$134$	−830.546			−0.535435
$135$		0			0
$136$			346.618i			0.218546i
$137$	−1578.58			−0.984433			−0.492217	−	0.870473i	$-0.663813\pi$
$137$	−1578.58			−0.984433			−0.492217	+	0.870473i	$0.663813\pi$
$138$	−1438.85			−0.887559
$139$	−1724.07			−1.05204			−0.526021	−	0.850472i	$-0.676316\pi$
$139$	−1724.07			−1.05204			−0.526021	+	0.850472i	$0.676316\pi$
$140$		0			0
$141$		−	1752.54i		−	1.04674i
$142$			587.891i			0.347428i
$143$	1854.59	−	1666.39i	1.08454	−	0.974477i
$144$	−118.458			−0.0685520
$145$		0			0
$146$	213.454			0.120997
$147$		−	1924.21i		−	1.07964i
$148$	−526.851			−0.292614
$149$		−	2729.67i		−	1.50083i	−0.660970	−	0.750413i	$-0.729855\pi$
$149$		−	2729.67i		−	1.50083i	0.660970	−	0.750413i	$-0.270145\pi$
$150$		0			0
$151$			484.316i			0.261014i	0.991447	+	0.130507i	$0.0416604\pi$
$151$			484.316i			0.261014i	−0.991447	+	0.130507i	$0.958340\pi$
$152$		−	1187.08i		−	0.633456i
$153$			320.779i			0.169500i
$154$			411.229i			0.215180i
$155$		0			0
$156$	818.008	−	734.996i	0.419827	−	0.377223i
$157$		−	235.775i		−	0.119853i	−0.998203	−	0.0599264i	$-0.980913\pi$
$157$		−	235.775i		−	0.119853i	0.998203	−	0.0599264i	$-0.0190866\pi$
$158$	−1812.09			−0.912418
$159$	−588.807			−0.293682
$160$		0			0
$161$			474.116i			0.232085i
$162$	1748.17			0.847834
$163$	1455.22			0.699274			0.349637	−	0.936885i	$-0.386305\pi$
$163$	1455.22			0.699274			0.349637	+	0.936885i	$0.386305\pi$
$164$			1550.78i			0.738387i
$165$		0			0
$166$	44.3209			0.0207227
$167$	−1630.52			−0.755528			−0.377764	−	0.925902i	$-0.623307\pi$
$167$	−1630.52			−0.755528			−0.377764	+	0.925902i	$0.623307\pi$
$168$			181.382i			0.0832970i
$169$	−234.201	+	2184.48i	−0.106600	+	0.994302i
$170$		0			0
$171$		−	1098.59i		−	0.491294i
$172$			298.546i			0.132348i
$173$		−	960.241i		−	0.421999i	−0.977486	−	0.210999i	$-0.932328\pi$
$173$		−	960.241i		−	0.421999i	0.977486	−	0.210999i	$-0.0676718\pi$
$174$			984.031i			0.428731i
$175$		0			0
$176$			851.084i			0.364505i
$177$	2811.37			1.19387
$178$			1330.87i			0.560408i
$179$	2100.32			0.877012			0.438506	−	0.898728i	$-0.355508\pi$
$179$	2100.32			0.877012			0.438506	+	0.898728i	$0.355508\pi$
$180$		0			0
$181$	3385.80			1.39041			0.695206	−	0.718811i	$-0.255313\pi$
$181$	3385.80			1.39041			0.695206	+	0.718811i	$0.255313\pi$
$182$	−242.189	−	269.542i	−0.0986386	−	0.109779i
$183$		−	2814.31i		−	1.13683i
$184$			981.237i			0.393140i
$185$		0			0
$186$	−2232.03			−0.879895
$187$	2304.70			0.901263
$188$	−1195.16			−0.463648
$189$		−	444.303i		−	0.170996i
$190$		0			0
$191$	−3728.07			−1.41232			−0.706162	−	0.708050i	$-0.749575\pi$
$191$	−3728.07			−1.41232			−0.706162	+	0.708050i	$0.749575\pi$
$192$			375.389i			0.141101i
$193$	−2573.20			−0.959705			−0.479852	−	0.877349i	$-0.659310\pi$
$193$	−2573.20			−0.959705			−0.479852	+	0.877349i	$0.659310\pi$
$194$	2508.48			0.928343
$195$		0			0
$196$	−1312.23			−0.478219
$197$	1941.54			0.702178			0.351089	−	0.936342i	$-0.385812\pi$
$197$	1941.54			0.702178			0.351089	+	0.936342i	$0.385812\pi$
$198$			787.638i			0.282702i
$199$	−2290.69			−0.815994			−0.407997	−	0.912983i	$-0.633773\pi$
$199$	−2290.69			−0.815994			−0.407997	+	0.912983i	$0.633773\pi$
$200$		0			0
$201$			2435.77i			0.854755i
$202$	−3514.42			−1.22413
$203$	324.249			0.112107
$204$	1016.54			0.348882
$205$		0			0
$206$			172.554i			0.0583611i
$207$			908.088i			0.304911i
$208$	−501.237	−	557.847i	−0.167089	−	0.185960i
$209$	−7893.04			−2.61231
$210$		0			0
$211$	1175.23			0.383440			0.191720	−	0.981450i	$-0.438593\pi$
$211$	1175.23			0.383440			0.191720	+	0.981450i	$0.438593\pi$
$212$			401.542i			0.130085i
$213$	1724.13			0.554625
$214$			4201.86i			1.34221i
$215$		0			0
$216$		−	919.534i		−	0.289659i
$217$			735.478i			0.230080i
$218$			4333.74i			1.34641i
$219$		−	626.003i		−	0.193157i
$220$		0			0
$221$	−1510.63	+	1357.33i	−0.459800	+	0.413139i
$222$			1545.11i			0.467122i
$223$	4350.88			1.30653			0.653265	−	0.757129i	$-0.273399\pi$
$223$	4350.88			1.30653			0.653265	+	0.757129i	$0.273399\pi$
$224$	123.695			0.0368960
$225$		0			0
$226$			713.558i			0.210023i
$227$	−3645.85			−1.06601			−0.533003	−	0.846113i	$-0.678937\pi$
$227$	−3645.85			−1.06601			−0.533003	+	0.846113i	$0.678937\pi$
$228$	−3481.40			−1.01123
$229$			3239.15i			0.934713i	0.884069	+	0.467357i	$0.154794\pi$
$229$			3239.15i			0.934713i	−0.884069	+	0.467357i	$0.845206\pi$
$230$		0			0
$231$	1206.02			0.343509
$232$	671.068			0.189904
$233$		−	2182.68i		−	0.613700i	−0.951758	−	0.306850i	$-0.900725\pi$
$233$		−	2182.68i		−	0.613700i	0.951758	−	0.306850i	$-0.0992750\pi$
$234$	−463.871	−	516.261i	−0.129591	−	0.144227i
$235$		0			0
$236$		−	1917.24i		−	0.528820i
$237$			5314.36i			1.45656i
$238$		−	334.960i		−	0.0912278i
$239$		−	58.8048i		−	0.0159153i	−0.999968	−	0.00795767i	$-0.997467\pi$
$239$		−	58.8048i		−	0.0159153i	0.999968	−	0.00795767i	$-0.00253303\pi$
$240$		0			0
$241$		−	202.261i		−	0.0540614i	−0.999635	−	0.0270307i	$-0.991395\pi$
$241$		−	202.261i		−	0.0540614i	0.999635	−	0.0270307i	$-0.00860518\pi$
$242$	2996.94			0.796077
$243$		−	2023.48i		−	0.534182i
$244$	−1919.24			−0.503553
$245$		0			0
$246$	4548.02			1.17874
$247$	5173.53	−	4648.52i	1.33273	−	1.19748i
$248$			1522.15i			0.389745i
$249$		−	129.981i		−	0.0330813i
$250$		0			0
$251$	113.992			0.0286658			0.0143329	−	0.999897i	$-0.495438\pi$
$251$	113.992			0.0286658			0.0143329	+	0.999897i	$0.495438\pi$
$252$	114.474			0.0286157
$253$	6524.34			1.62127
$254$		−	1995.33i		−	0.492907i
$255$		0			0
$256$	256.000			0.0625000
$257$			4234.73i			1.02784i	0.857838	+	0.513920i	$0.171807\pi$
$257$			4234.73i			1.02784i	−0.857838	+	0.513920i	$0.828193\pi$
$258$	875.555			0.211278
$259$	509.131			0.122146
$260$		0			0
$261$	621.042			0.147286
$262$	3361.75			0.792709
$263$			228.481i			0.0535695i	0.999641	+	0.0267847i	$0.00852686\pi$
$263$			228.481i			0.0535695i	−0.999641	+	0.0267847i	$0.991473\pi$
$264$	2496.00			0.581887
$265$		0			0
$266$			1147.16i			0.264424i
$267$	3903.07			0.894623
$268$	1661.09			0.378609
$269$	−1219.30			−0.276365			−0.138183	−	0.990407i	$-0.544126\pi$
$269$	−1219.30			−0.276365			−0.138183	+	0.990407i	$0.544126\pi$
$270$		0			0
$271$			5891.13i			1.32052i	0.751037	+	0.660260i	$0.229554\pi$
$271$			5891.13i			1.32052i	−0.751037	+	0.660260i	$0.770446\pi$
$272$		−	693.237i		−	0.154535i
$273$	−790.494	+	710.274i	−0.175249	+	0.157464i
$274$	3157.16			0.696100
$275$		0			0
$276$	2877.70			0.627599
$277$			6139.39i			1.33170i	0.746087	+	0.665849i	$0.231931\pi$
$277$			6139.39i			1.33170i	−0.746087	+	0.665849i	$0.768069\pi$
$278$	3448.14			0.743905
$279$			1408.68i			0.302278i
$280$		0			0
$281$		−	1852.24i		−	0.393221i	−0.980482	−	0.196611i	$-0.937006\pi$
$281$		−	1852.24i		−	0.393221i	0.980482	−	0.196611i	$-0.0629935\pi$
$282$			3505.07i			0.740156i
$283$		−	172.290i		−	0.0361892i	−0.999836	−	0.0180946i	$-0.994240\pi$
$283$		−	172.290i		−	0.0361892i	0.999836	−	0.0180946i	$-0.00576001\pi$
$284$		−	1175.78i		−	0.245669i
$285$		0			0
$286$	−3709.18	+	3332.77i	−0.766883	+	0.689059i
$287$		−	1498.62i		−	0.308225i
$288$	236.916			0.0484736
$289$	3035.75			0.617900
$290$		0			0
$291$		−	7356.70i		−	1.48198i
$292$	−426.908			−0.0855579
$293$	−5725.00			−1.14150			−0.570748	−	0.821125i	$-0.693347\pi$
$293$	−5725.00			−1.14150			−0.570748	+	0.821125i	$0.693347\pi$
$294$			3848.42i			0.763417i
$295$		0			0
$296$	1053.70			0.206910
$297$	−6114.07			−1.19453
$298$			5459.33i			1.06124i
$299$	−4276.41	+	3842.44i	−0.827127	+	0.743190i
$300$		0			0
$301$		−	288.504i		−	0.0552462i
$302$		−	968.631i		−	0.184564i
$303$			10306.8i			1.95417i
$304$			2374.17i			0.447921i
$305$		0			0
$306$		−	641.558i		−	0.119854i
$307$	2115.94			0.393364			0.196682	−	0.980467i	$-0.436983\pi$
$307$	2115.94			0.393364			0.196682	+	0.980467i	$0.436983\pi$
$308$		−	822.458i		−	0.152155i
$309$	506.054			0.0931663
$310$		0			0
$311$	−3912.14			−0.713303			−0.356651	−	0.934238i	$-0.616082\pi$
$311$	−3912.14			−0.713303			−0.356651	+	0.934238i	$0.616082\pi$
$312$	−1636.02	+	1469.99i	−0.296863	+	0.266737i
$313$			3751.20i			0.677413i	0.940892	+	0.338706i	$0.109989\pi$
$313$			3751.20i			0.677413i	−0.940892	+	0.338706i	$0.890011\pi$
$314$			471.550i			0.0847487i
$315$		0			0
$316$	3624.18			0.645177
$317$	−8277.14			−1.46653			−0.733266	−	0.679942i	$-0.762005\pi$
$317$	−8277.14			−1.46653			−0.733266	+	0.679942i	$0.762005\pi$
$318$	1177.61			0.207665
$319$		−	4462.00i		−	0.783147i
$320$		0			0
$321$	12322.9			2.14268
$322$		−	948.233i		−	0.164109i
$323$	6429.14			1.10751
$324$	−3496.34			−0.599509
$325$		0			0
$326$	−2910.44			−0.494462
$327$	12709.7			2.14938
$328$		−	3101.56i		−	0.522119i
$329$	1154.96			0.193541
$330$		0			0
$331$			887.123i			0.147313i	0.997284	+	0.0736567i	$0.0234669\pi$
$331$			887.123i			0.147313i	−0.997284	+	0.0736567i	$0.976533\pi$
$332$	−88.6419			−0.0146532
$333$	975.152			0.160474
$334$	3261.04			0.534239
$335$		0			0
$336$		−	362.763i		−	0.0588999i
$337$			6563.94i			1.06101i	0.847681	+	0.530506i	$0.177998\pi$
$337$			6563.94i			1.06101i	−0.847681	+	0.530506i	$0.822002\pi$
$338$	468.401	−	4368.96i	0.0753777	−	0.703078i
$339$	2092.67			0.335275
$340$		0			0
$341$	10120.9			1.60727
$342$			2197.18i			0.347397i
$343$	2593.95			0.408338
$344$		−	597.092i		−	0.0935844i
$345$		0			0
$346$			1920.48i			0.298398i
$347$			8654.04i			1.33883i	0.742890	+	0.669414i	$0.233455\pi$
$347$			8654.04i			1.33883i	−0.742890	+	0.669414i	$0.766545\pi$
$348$		−	1968.06i		−	0.303159i
$349$		−	10173.5i		−	1.56039i	−0.625535	−	0.780196i	$-0.715119\pi$
$349$		−	10173.5i		−	1.56039i	0.625535	−	0.780196i	$-0.284881\pi$
$350$		0			0
$351$	4007.50	−	3600.82i	0.609414	−	0.547571i
$352$		−	1702.17i		−	0.257744i
$353$	921.610			0.138958			0.0694792	−	0.997583i	$-0.477866\pi$
$353$	921.610			0.138958			0.0694792	+	0.997583i	$0.477866\pi$
$354$	−5622.74			−0.844195
$355$		0			0
$356$		−	2661.73i		−	0.396269i
$357$	−982.347			−0.145634
$358$	−4200.64			−0.620141
$359$			2056.77i			0.302374i	0.988505	+	0.151187i	$0.0483096\pi$
$359$			2056.77i			0.302374i	−0.988505	+	0.151187i	$0.951690\pi$
$360$		0			0
$361$	−15159.3			−2.21013
$362$	−6771.60			−0.983169
$363$		−	8789.21i		−	1.27084i
$364$	484.378	+	539.084i	0.0697480	+	0.0776255i
$365$		0			0
$366$			5628.63i			0.803861i
$367$		−	2211.81i		−	0.314593i	−0.987551	−	0.157296i	$-0.949722\pi$
$367$		−	2211.81i		−	0.314593i	0.987551	−	0.157296i	$-0.0502778\pi$
$368$		−	1962.47i		−	0.277992i
$369$		−	2870.34i		−	0.404944i
$370$		0			0
$371$		−	388.036i		−	0.0543014i
$372$	4464.06			0.622180
$373$			10546.1i			1.46396i	0.681325	+	0.731981i	$0.261404\pi$
$373$			10546.1i			1.46396i	−0.681325	+	0.731981i	$0.738596\pi$
$374$	−4609.40			−0.637289
$375$		0			0
$376$	2390.31			0.327848
$377$	2627.85	+	2924.64i	0.358994	+	0.399540i
$378$			888.606i			0.120913i
$379$			12239.0i			1.65877i	0.558680	+	0.829384i	$0.311308\pi$
$379$			12239.0i			1.65877i	−0.558680	+	0.829384i	$0.688692\pi$
$380$		0			0
$381$	−5851.77			−0.786864
$382$	7456.14			0.998664
$383$	−7234.70			−0.965211			−0.482605	−	0.875838i	$-0.660309\pi$
$383$	−7234.70			−0.965211			−0.482605	+	0.875838i	$0.660309\pi$
$384$		−	750.779i		−	0.0997735i
$385$		0			0
$386$	5146.40			0.678614
$387$		−	552.580i		−	0.0725820i
$388$	−5016.96			−0.656437
$389$	−11781.1			−1.53554			−0.767768	−	0.640728i	$-0.778633\pi$
$389$	−11781.1			−1.53554			−0.767768	+	0.640728i	$0.778633\pi$
$390$		0			0
$391$	−5314.29			−0.687354
$392$	2624.47			0.338152
$393$		−	9859.12i		−	1.26546i
$394$	−3883.08			−0.496514
$395$		0			0
$396$		−	1575.28i		−	0.199900i
$397$	−11724.0			−1.48214			−0.741072	−	0.671425i	$-0.765683\pi$
$397$	−11724.0			−1.48214			−0.741072	+	0.671425i	$0.765683\pi$
$398$	4581.38			0.576995
$399$	3364.30			0.422120
$400$		0			0
$401$		−	1707.99i		−	0.212701i	−0.994329	−	0.106350i	$-0.966084\pi$
$401$		−	1707.99i		−	0.212701i	0.994329	−	0.106350i	$-0.0339165\pi$
$402$		−	4871.53i		−	0.604403i
$403$	−6633.82	+	5960.62i	−0.819985	+	0.736773i
$404$	7028.83			0.865588
$405$		0			0
$406$	−648.497			−0.0792718
$407$		−	7006.17i		−	0.853275i
$408$	−2033.08			−0.246697
$409$			9607.06i			1.16146i	0.814095	+	0.580732i	$0.197234\pi$
$409$			9607.06i			1.16146i	−0.814095	+	0.580732i	$0.802766\pi$
$410$		0			0
$411$		−	9259.11i		−	1.11124i
$412$		−	345.108i		−	0.0412676i
$413$			1852.75i			0.220746i
$414$		−	1816.18i		−	0.215604i
$415$		0			0
$416$	1002.47	+	1115.69i	0.118150	+	0.131494i
$417$		−	10112.5i		−	1.18755i
$418$	15786.1			1.84718
$419$	2708.67			0.315817			0.157908	−	0.987454i	$-0.449525\pi$
$419$	2708.67			0.315817			0.157908	+	0.987454i	$0.449525\pi$
$420$		0			0
$421$			10957.4i			1.26848i	0.773137	+	0.634239i	$0.218686\pi$
$421$			10957.4i			1.26848i	−0.773137	+	0.634239i	$0.781314\pi$
$422$	−2350.45			−0.271133
$423$	2212.12			0.254272
$424$		−	803.084i		−	0.0919840i
$425$		0			0
$426$	−3448.25			−0.392179
$427$	1854.69			0.210199
$428$		−	8403.73i		−	0.949087i
$429$	9774.12	+	10878.0i	1.10000	+	1.22423i
$430$		0			0
$431$		−	9513.13i		−	1.06318i	−0.847001	−	0.531591i	$-0.821594\pi$
$431$		−	9513.13i		−	1.06318i	0.847001	−	0.531591i	$-0.178406\pi$
$432$			1839.07i			0.204820i
$433$			7271.33i			0.807016i	0.914976	+	0.403508i	$0.132209\pi$
$433$			7271.33i			0.807016i	−0.914976	+	0.403508i	$0.867791\pi$
$434$		−	1470.96i		−	0.162691i
$435$		0			0
$436$		−	8667.48i		−	0.952057i
$437$	18200.2			1.99229
$438$			1252.01i			0.136583i
$439$	−9615.25			−1.04535			−0.522677	−	0.852531i	$-0.675067\pi$
$439$	−9615.25			−1.04535			−0.522677	+	0.852531i	$0.675067\pi$
$440$		0			0
$441$	2428.82			0.262263
$442$	3021.25	−	2714.65i	0.325127	−	0.292133i
$443$		−	4782.54i		−	0.512924i	−0.966554	−	0.256462i	$-0.917443\pi$
$443$		−	4782.54i		−	0.512924i	0.966554	−	0.256462i	$-0.0825569\pi$
$444$		−	3090.23i		−	0.330305i
$445$		0			0
$446$	−8701.75			−0.923857
$447$	16010.7			1.69414
$448$	−247.389			−0.0260894
$449$		−	6868.72i		−	0.721949i	−0.932576	−	0.360974i	$-0.882444\pi$
$449$		−	6868.72i		−	0.721949i	0.932576	−	0.360974i	$-0.117556\pi$
$450$		0			0
$451$	−20622.6			−2.15317
$452$		−	1427.12i		−	0.148509i
$453$	−2840.73			−0.294634
$454$	7291.70			0.753781
$455$		0			0
$456$	6962.79			0.715050
$457$	−8401.47			−0.859966			−0.429983	−	0.902837i	$-0.641480\pi$
$457$	−8401.47			−0.859966			−0.429983	+	0.902837i	$0.641480\pi$
$458$		−	6478.31i		−	0.660942i
$459$	4980.12			0.506431
$460$		0			0
$461$			15930.5i			1.60945i	0.593650	+	0.804723i	$0.297686\pi$
$461$			15930.5i			1.60945i	−0.593650	+	0.804723i	$0.702314\pi$
$462$	−2412.05			−0.242897
$463$	−11572.2			−1.16156			−0.580781	−	0.814060i	$-0.697253\pi$
$463$	−11572.2			−1.16156			−0.580781	+	0.814060i	$0.697253\pi$
$464$	−1342.14			−0.134283
$465$		0			0
$466$			4365.36i			0.433952i
$467$		−	10862.4i		−	1.07634i	−0.842837	−	0.538169i	$-0.819116\pi$
$467$		−	10862.4i		−	1.07634i	0.842837	−	0.538169i	$-0.180884\pi$
$468$	927.742	+	1032.52i	0.0916344	+	0.101984i
$469$	−1605.22			−0.158043
$470$		0			0
$471$	1382.93			0.135291
$472$			3834.47i			0.373932i
$473$	−3970.12			−0.385933
$474$		−	10628.7i		−	1.02994i
$475$		0			0
$476$			669.920i			0.0645078i
$477$		−	743.216i		−	0.0713407i
$478$			117.610i			0.0112538i
$479$		−	2085.72i		−	0.198954i	−0.995040	−	0.0994769i	$-0.968283\pi$
$479$		−	2085.72i		−	0.198954i	0.995040	−	0.0994769i	$-0.0317169\pi$
$480$		0			0
$481$	4126.21	+	4592.23i	0.391141	+	0.435317i
$482$			404.522i			0.0382272i
$483$	−2780.91			−0.261979
$484$	−5993.88			−0.562911
$485$		0			0
$486$			4046.96i			0.377723i
$487$	−11829.6			−1.10072			−0.550358	−	0.834929i	$-0.685509\pi$
$487$	−11829.6			−1.10072			−0.550358	+	0.834929i	$0.685509\pi$
$488$	3838.49			0.356066
$489$			8535.54i			0.789347i
$490$		0			0
$491$	−2700.04			−0.248169			−0.124085	−	0.992272i	$-0.539599\pi$
$491$	−2700.04			−0.248169			−0.124085	+	0.992272i	$0.539599\pi$
$492$	−9096.03			−0.833497
$493$			3634.45i			0.332023i
$494$	−10347.1	+	9297.04i	−0.942381	+	0.846748i
$495$		0			0
$496$		−	3044.31i		−	0.275591i
$497$			1136.24i			0.102550i
$498$			259.963i			0.0233920i
$499$		−	3013.67i		−	0.270361i	−0.990821	−	0.135181i	$-0.956839\pi$
$499$		−	3013.67i		−	0.270361i	0.990821	−	0.135181i	$-0.0431615\pi$
$500$		0			0
$501$		−	9563.74i		−	0.852847i
$502$	−227.984			−0.0202698
$503$		−	13902.0i		−	1.23233i	−0.787619	−	0.616163i	$-0.788686\pi$
$503$		−	13902.0i		−	1.23233i	0.787619	−	0.616163i	$-0.211314\pi$
$504$	−228.947			−0.0202344
$505$		0			0
$506$	−13048.7			−1.14641
$507$	−12813.0	−	1373.69i	−1.12238	−	0.120331i
$508$			3990.67i			0.348538i
$509$		−	1630.66i		−	0.142000i	−0.997476	−	0.0709999i	$-0.977381\pi$
$509$		−	1630.66i		−	0.142000i	0.997476	−	0.0709999i	$-0.0226190\pi$
$510$		0			0
$511$	412.549			0.0357145
$512$	−512.000			−0.0441942
$513$	−17055.7			−1.46789
$514$		−	8469.46i		−	0.726793i
$515$		0			0
$516$	−1751.11			−0.149396
$517$		−	15893.4i		−	1.35202i
$518$	−1018.26			−0.0863703
$519$	5632.25			0.476355
$520$		0			0
$521$	8654.86			0.727785			0.363893	−	0.931441i	$-0.381447\pi$
$521$	8654.86			0.727785			0.363893	+	0.931441i	$0.381447\pi$
$522$	−1242.08			−0.104147
$523$			5093.00i			0.425816i	0.977072	+	0.212908i	$0.0682934\pi$
$523$			5093.00i			0.425816i	−0.977072	+	0.212908i	$0.931707\pi$
$524$	−6723.51			−0.560530
$525$		0			0
$526$		−	456.963i		−	0.0378793i
$527$	−8243.85			−0.681418
$528$	−4992.00			−0.411456
$529$	−2877.15			−0.236472
$530$		0			0
$531$			3548.62i			0.290013i
$532$		−	2294.31i		−	0.186976i
$533$	13517.2	−	12145.4i	1.09849	−	0.987011i
$534$	−7806.15			−0.632594
$535$		0			0
$536$	−3322.18			−0.267717
$537$			12319.3i			0.989979i
$538$	2438.61			0.195420
$539$		−	17450.3i		−	1.39451i
$540$		0			0
$541$		−	5004.07i		−	0.397674i	−0.980033	−	0.198837i	$-0.936284\pi$
$541$		−	5004.07i		−	0.397674i	0.980033	−	0.198837i	$-0.0637165\pi$
$542$		−	11782.3i		−	0.933748i
$543$			19859.3i			1.56951i
$544$			1386.47i			0.109273i
$545$		0			0
$546$	1580.99	−	1420.55i	0.123920	−	0.111344i
$547$			10856.3i			0.848598i	0.905522	+	0.424299i	$0.139479\pi$
$547$			10856.3i			0.848598i	−0.905522	+	0.424299i	$0.860521\pi$
$548$	−6314.33			−0.492217
$549$	3552.34			0.276157
$550$		0			0
$551$		−	12447.1i		−	0.962368i
$552$	−5755.41			−0.443780
$553$	−3502.28			−0.269316
$554$		−	12278.8i		−	0.941653i
$555$		0			0
$556$	−6896.28			−0.526021
$557$	−23083.8			−1.75600			−0.878001	−	0.478658i	$-0.841123\pi$
$557$	−23083.8			−1.75600			−0.878001	+	0.478658i	$0.841123\pi$
$558$		−	2817.36i		−	0.213743i
$559$	2602.24	−	2338.16i	0.196892	−	0.176912i
$560$		0			0
$561$			13518.1i			1.01735i
$562$			3704.48i			0.278050i
$563$			15495.9i			1.15999i	0.814619	+	0.579996i	$0.196946\pi$
$563$			15495.9i			1.15999i	−0.814619	+	0.579996i	$0.803054\pi$
$564$		−	7010.14i		−	0.523369i
$565$		0			0
$566$			344.579i			0.0255897i
$567$	3378.74			0.250253
$568$			2351.57i			0.173714i
$569$	18165.5			1.33838			0.669188	−	0.743094i	$-0.266642\pi$
$569$	18165.5			1.33838			0.669188	+	0.743094i	$0.266642\pi$
$570$		0			0
$571$	8289.75			0.607557			0.303779	−	0.952743i	$-0.401752\pi$
$571$	8289.75			0.607557			0.303779	+	0.952743i	$0.401752\pi$
$572$	7418.36	−	6665.54i	0.542268	−	0.487238i
$573$		−	21866.9i		−	1.59424i
$574$			2997.24i			0.217948i
$575$		0			0
$576$	−473.832			−0.0342760
$577$	5336.46			0.385026			0.192513	−	0.981294i	$-0.438336\pi$
$577$	5336.46			0.385026			0.192513	+	0.981294i	$0.438336\pi$
$578$	−6071.49			−0.436922
$579$		−	15093.0i		−	1.08332i
$580$		0			0
$581$	85.6604			0.00611668
$582$			14713.4i			1.04792i
$583$	−5339.78			−0.379333
$584$	853.816			0.0604986
$585$		0			0
$586$	11450.0			0.807159
$587$	6877.72			0.483601			0.241800	−	0.970326i	$-0.422262\pi$
$587$	6877.72			0.483601			0.241800	+	0.970326i	$0.422262\pi$
$588$		−	7696.85i		−	0.539818i
$589$	28233.2			1.97509
$590$		0			0
$591$			11388.0i			0.792624i
$592$	−2107.41			−0.146307
$593$	8358.37			0.578814			0.289407	−	0.957206i	$-0.406542\pi$
$593$	8358.37			0.578814			0.289407	+	0.957206i	$0.406542\pi$
$594$	12228.1			0.844658
$595$		0			0
$596$		−	10918.7i		−	0.750413i
$597$		−	13436.0i		−	0.921101i
$598$	8552.82	−	7684.87i	0.584867	−	0.525515i
$599$	14896.0			1.01609			0.508043	−	0.861332i	$-0.330369\pi$
$599$	14896.0			1.01609			0.508043	+	0.861332i	$0.330369\pi$
$600$		0			0
$601$	7661.60			0.520005			0.260003	−	0.965608i	$-0.416277\pi$
$601$	7661.60			0.520005			0.260003	+	0.965608i	$0.416277\pi$
$602$			577.009i			0.0390650i
$603$	−3074.52			−0.207636
$604$			1937.26i			0.130507i
$605$		0			0
$606$		−	20613.7i		−	1.38180i
$607$		−	22718.2i		−	1.51912i	−0.650440	−	0.759558i	$-0.725415\pi$
$607$		−	22718.2i		−	1.51912i	0.650440	−	0.759558i	$-0.274585\pi$
$608$		−	4748.34i		−	0.316728i
$609$			1901.87i			0.126548i
$610$		0			0
$611$	9360.26	+	10417.4i	0.619763	+	0.689761i
$612$			1283.12i			0.0847498i
$613$	12080.9			0.795995			0.397997	−	0.917387i	$-0.369705\pi$
$613$	12080.9			0.795995			0.397997	+	0.917387i	$0.369705\pi$
$614$	−4231.87			−0.278151
$615$		0			0
$616$			1644.92i			0.107590i
$617$	−21104.3			−1.37703			−0.688514	−	0.725223i	$-0.741737\pi$
$617$	−21104.3			−1.37703			−0.688514	+	0.725223i	$0.741737\pi$
$618$	−1012.11			−0.0658785
$619$		−	12516.1i		−	0.812706i	−0.913716	−	0.406353i	$-0.866800\pi$
$619$		−	12516.1i		−	0.812706i	0.913716	−	0.406353i	$-0.133200\pi$
$620$		0			0
$621$	14098.1			0.911013
$622$	7824.28			0.504381
$623$			2572.21i			0.165415i
$624$	3272.03	−	2939.98i	0.209914	−	0.188611i
$625$		0			0
$626$		−	7502.40i		−	0.479003i
$627$		−	46296.3i		−	2.94880i
$628$		−	943.100i		−	0.0599264i
$629$			5706.76i			0.361754i
$630$		0			0
$631$			10069.7i			0.635288i	0.948210	+	0.317644i	$0.102892\pi$
$631$			10069.7i			0.635288i	−0.948210	+	0.317644i	$0.897108\pi$
$632$	−7248.35			−0.456209
$633$			6893.24i			0.432831i
$634$	16554.3			1.03699
$635$		0			0
$636$	−2355.23			−0.146841
$637$	10277.2	+	11437.9i	0.639241	+	0.711438i
$638$			8924.00i			0.553769i
$639$			2176.26i			0.134729i
$640$		0			0
$641$	3388.87			0.208818			0.104409	−	0.994534i	$-0.466705\pi$
$641$	3388.87			0.208818			0.104409	+	0.994534i	$0.466705\pi$
$642$	−24645.9			−1.51510
$643$	24633.3			1.51080			0.755400	−	0.655264i	$-0.227443\pi$
$643$	24633.3			1.51080			0.755400	+	0.655264i	$0.227443\pi$
$644$			1896.47i			0.116042i
$645$		0			0
$646$	−12858.3			−0.783131
$647$			1908.12i			0.115945i	0.998318	+	0.0579723i	$0.0184635\pi$
$647$			1908.12i			0.115945i	−0.998318	+	0.0579723i	$0.981537\pi$
$648$	6992.67			0.423917
$649$	25495.8			1.54206
$650$		0			0
$651$	−4313.91			−0.259717
$652$	5820.88			0.349637
$653$		−	10331.4i		−	0.619141i	−0.950877	−	0.309570i	$-0.899815\pi$
$653$		−	10331.4i		−	0.619141i	0.950877	−	0.309570i	$-0.100185\pi$
$654$	−25419.4			−1.51984
$655$		0			0
$656$			6203.12i			0.369194i
$657$	790.166			0.0469213
$658$	−2309.91			−0.136854
$659$	−19039.8			−1.12547			−0.562737	−	0.826636i	$-0.690251\pi$
$659$	−19039.8			−1.12547			−0.562737	+	0.826636i	$0.690251\pi$
$660$		0			0
$661$			28643.0i			1.68545i	0.538343	+	0.842726i	$0.319050\pi$
$661$			28643.0i			1.68545i	−0.538343	+	0.842726i	$0.680950\pi$
$662$		−	1774.25i		−	0.104166i
$663$	−7961.35	−	8860.52i	−0.466355	−	0.519026i
$664$	177.284			0.0103614
$665$		0			0
$666$	−1950.30			−0.113473
$667$			10288.7i			0.597272i
$668$	−6522.07			−0.377764
$669$			25519.9i			1.47482i
$670$		0			0
$671$		−	25522.5i		−	1.46838i
$672$			725.526i			0.0416485i
$673$			18372.8i			1.05233i	0.850382	+	0.526166i	$0.176371\pi$
$673$			18372.8i			1.05233i	−0.850382	+	0.526166i	$0.823629\pi$
$674$		−	13127.9i		−	0.750248i
$675$		0			0
$676$	−936.802	+	8737.93i	−0.0533001	+	0.497151i
$677$			12837.4i			0.728779i	0.931247	+	0.364389i	$0.118722\pi$
$677$			12837.4i			0.728779i	−0.931247	+	0.364389i	$0.881278\pi$
$678$	−4185.34			−0.237075
$679$	4848.22			0.274017
$680$		0			0
$681$		−	21384.6i		−	1.20332i
$682$	−20241.9			−1.13651
$683$	−12224.7			−0.684871			−0.342436	−	0.939541i	$-0.611252\pi$
$683$	−12224.7			−0.684871			−0.342436	+	0.939541i	$0.611252\pi$
$684$		−	4394.36i		−	0.245647i
$685$		0			0
$686$	−5187.90			−0.288739
$687$	−18999.1			−1.05511
$688$			1194.18i			0.0661742i
$689$	3499.99	−	3144.81i	0.193525	−	0.173886i
$690$		0			0
$691$			7662.99i			0.421873i	0.977500	+	0.210936i	$0.0676513\pi$
$691$			7662.99i			0.421873i	−0.977500	+	0.210936i	$0.932349\pi$
$692$		−	3840.96i		−	0.210999i
$693$			1522.29i			0.0834446i
$694$		−	17308.1i		−	0.946694i
$695$		0			0
$696$			3936.13i			0.214366i
$697$	16797.8			0.912856
$698$			20347.1i			1.10336i
$699$	12802.4			0.692750
$700$		0			0
$701$	15215.8			0.819818			0.409909	−	0.912126i	$-0.365560\pi$
$701$	15215.8			0.819818			0.409909	+	0.912126i	$0.365560\pi$
$702$	−8015.00	+	7201.63i	−0.430921	+	0.387191i
$703$		−	19544.3i		−	1.04854i
$704$			3404.34i			0.182253i
$705$		0			0
$706$	−1843.22			−0.0982585
$707$	−6792.42			−0.361323
$708$	11245.5			0.596936
$709$		−	15410.9i		−	0.816314i	−0.912912	−	0.408157i	$-0.866172\pi$
$709$		−	15410.9i		−	0.816314i	0.912912	−	0.408157i	$-0.133828\pi$
$710$		0			0
$711$	−6708.01			−0.353825
$712$			5323.47i			0.280204i
$713$	−23337.4			−1.22579
$714$	1964.69			0.102979
$715$		0			0
$716$	8401.27			0.438506
$717$	344.917			0.0179654
$718$		−	4113.55i		−	0.213811i
$719$	1155.79			0.0599494			0.0299747	−	0.999551i	$-0.490457\pi$
$719$	1155.79			0.0599494			0.0299747	+	0.999551i	$0.490457\pi$
$720$		0			0
$721$			333.500i			0.0172263i
$722$	30318.5			1.56280
$723$	1186.36			0.0610249
$724$	13543.2			0.695206
$725$		0			0
$726$			17578.4i			0.898618i
$727$			18048.8i			0.920759i	0.887722	+	0.460379i	$0.152287\pi$
$727$			18048.8i			0.920759i	−0.887722	+	0.460379i	$0.847713\pi$
$728$	−968.755	−	1078.17i	−0.0493193	−	0.0548895i
$729$	−11731.6			−0.596029
$730$		0			0
$731$	3233.80			0.163620
$732$		−	11257.3i		−	0.568415i
$733$	7855.68			0.395847			0.197924	−	0.980217i	$-0.436580\pi$
$733$	7855.68			0.395847			0.197924	+	0.980217i	$0.436580\pi$
$734$			4423.62i			0.222450i
$735$		0			0
$736$			3924.95i			0.196570i
$737$			22089.5i			1.10404i
$738$			5740.69i			0.286338i
$739$			302.801i			0.0150727i	0.999972	+	0.00753635i	$0.00239892\pi$
$739$			302.801i			0.0150727i	−0.999972	+	0.00753635i	$0.997601\pi$
$740$		0			0
$741$	27265.7	+	30345.1i	1.35173	+	1.50439i
$742$			776.072i			0.0383969i
$743$	−17199.9			−0.849265			−0.424633	−	0.905366i	$-0.639597\pi$
$743$	−17199.9			−0.849265			−0.424633	+	0.905366i	$0.639597\pi$
$744$	−8928.13			−0.439948
$745$		0			0
$746$		−	21092.2i		−	1.03518i
$747$	164.068			0.00803604
$748$	9218.79			0.450632
$749$			8121.07i			0.396178i
$750$		0			0
$751$	−12999.7			−0.631644			−0.315822	−	0.948819i	$-0.602280\pi$
$751$	−12999.7			−0.631644			−0.315822	+	0.948819i	$0.602280\pi$
$752$	−4780.63			−0.231824
$753$			668.616i			0.0323582i
$754$	−5255.69	−	5849.28i	−0.253847	−	0.282517i
$755$		0			0
$756$		−	1777.21i		−	0.0854981i
$757$		−	6046.81i		−	0.290324i	−0.989408	−	0.145162i	$-0.953630\pi$
$757$		−	6046.81i		−	0.290324i	0.989408	−	0.145162i	$-0.0463703\pi$
$758$		−	24477.9i		−	1.17293i
$759$			38268.2i			1.83010i
$760$		0			0
$761$		−	26902.3i		−	1.28148i	−0.767758	−	0.640740i	$-0.778628\pi$
$761$		−	26902.3i		−	1.28148i	0.767758	−	0.640740i	$-0.221372\pi$
$762$	11703.5			0.556397
$763$			8375.95i			0.397418i
$764$	−14912.3			−0.706162
$765$		0			0
$766$	14469.4			0.682507
$767$	−16711.3	+	15015.5i	−0.786716	+	0.706880i
$768$			1501.56i			0.0705505i
$769$		−	2068.29i		−	0.0969887i	−0.998823	−	0.0484943i	$-0.984558\pi$
$769$		−	2068.29i		−	0.0969887i	0.998823	−	0.0484943i	$-0.0154423\pi$
$770$		0			0
$771$	−24838.6			−1.16024
$772$	−10292.8			−0.479852
$773$	8389.72			0.390371			0.195186	−	0.980766i	$-0.437469\pi$
$773$	8389.72			0.390371			0.195186	+	0.980766i	$0.437469\pi$
$774$			1105.16i			0.0513232i
$775$		0			0
$776$	10033.9			0.464171
$777$			2986.29i			0.137880i
$778$	23562.1			1.08579
$779$	−57528.3			−2.64591
$780$		0			0
$781$	15635.8			0.716379
$782$	10628.6			0.486033
$783$		−	9641.73i		−	0.440060i
$784$	−5248.93			−0.239109
$785$		0			0
$786$			19718.2i			0.894817i
$787$	21458.3			0.971928			0.485964	−	0.873979i	$-0.338469\pi$
$787$	21458.3			0.971928			0.485964	+	0.873979i	$0.338469\pi$
$788$	7766.16			0.351089
$789$	−1340.15			−0.0604697
$790$		0			0
$791$			1379.11i			0.0619920i
$792$			3150.55i			0.141351i
$793$	15031.2	+	16728.8i	0.673106	+	0.749128i
$794$	23448.0			1.04803
$795$		0			0
$796$	−9162.76			−0.407997
$797$		−	6049.72i		−	0.268873i	−0.990922	−	0.134437i	$-0.957078\pi$
$797$		−	6049.72i		−	0.268873i	0.990922	−	0.134437i	$-0.0429225\pi$
$798$	−6728.60			−0.298484
$799$			12945.7i			0.573200i
$800$		0			0
$801$			4926.62i			0.217320i
$802$			3415.98i			0.150402i
$803$		−	5677.10i		−	0.249490i
$804$			9743.07i			0.427378i
$805$		0			0
$806$	13267.6	−	11921.2i	0.579817	−	0.520977i
$807$		−	7151.78i		−	0.311964i
$808$	−14057.7			−0.612063
$809$	33364.1			1.44996			0.724981	−	0.688769i	$-0.241848\pi$
$809$	33364.1			1.44996			0.724981	+	0.688769i	$0.241848\pi$
$810$		0			0
$811$			2210.77i			0.0957221i	0.998854	+	0.0478611i	$0.0152405\pi$
$811$			2210.77i			0.0957221i	−0.998854	+	0.0478611i	$0.984760\pi$
$812$	1296.99			0.0560537
$813$	−34554.2			−1.49061
$814$			14012.3i			0.603356i
$815$		0			0
$816$	4066.15			0.174441
$817$	−11075.0			−0.474253
$818$		−	19214.1i		−	0.821279i
$819$	−896.537	−	997.794i	−0.0382510	−	0.0425711i
$820$		0			0
$821$			25402.9i			1.07986i	0.841709	+	0.539932i	$0.181550\pi$
$821$			25402.9i			1.07986i	−0.841709	+	0.539932i	$0.818450\pi$
$822$			18518.2i			0.785763i
$823$			42030.9i			1.78020i	0.455765	+	0.890100i	$0.349366\pi$
$823$			42030.9i			1.78020i	−0.455765	+	0.890100i	$0.650634\pi$
$824$			690.215i			0.0291806i
$825$		0			0
$826$		−	3705.50i		−	0.156091i
$827$	27713.0			1.16527			0.582633	−	0.812735i	$-0.302022\pi$
$827$	27713.0			1.16527			0.582633	+	0.812735i	$0.302022\pi$
$828$			3632.35i			0.152455i
$829$	−23579.7			−0.987886			−0.493943	−	0.869494i	$-0.664445\pi$
$829$	−23579.7			−0.987886			−0.493943	+	0.869494i	$0.664445\pi$
$830$		0			0
$831$	−36010.4			−1.50323
$832$	−2004.95	−	2231.39i	−0.0835445	−	0.0929802i
$833$			14213.9i			0.591214i
$834$			20224.9i			0.839727i
$835$		0			0
$836$	−31572.1			−1.30615
$837$	21869.9			0.903146
$838$	−5417.34			−0.223316
$839$		−	8648.03i		−	0.355856i	−0.984044	−	0.177928i	$-0.943061\pi$
$839$		−	8648.03i		−	0.355856i	0.984044	−	0.177928i	$-0.0569394\pi$
$840$		0			0
$841$	−17352.5			−0.711491
$842$		−	21914.7i		−	0.896949i
$843$	10864.2			0.443872
$844$	4700.91			0.191720
$845$		0			0
$846$	−4424.24			−0.179797
$847$	5792.27			0.234976
$848$			1606.17i			0.0650425i
$849$	1010.56			0.0408507
$850$		0			0
$851$			16155.2i			0.650755i
$852$	6896.51			0.277313
$853$	23117.7			0.927942			0.463971	−	0.885851i	$-0.346424\pi$
$853$	23117.7			0.927942			0.463971	+	0.885851i	$0.346424\pi$
$854$	−3709.38			−0.148633
$855$		0			0
$856$			16807.5i			0.671106i
$857$			3246.65i			0.129409i	0.997904	+	0.0647045i	$0.0206105\pi$
$857$			3246.65i			0.129409i	−0.997904	+	0.0647045i	$0.979390\pi$
$858$	−19548.2	−	21756.0i	−0.777816	−	0.865663i
$859$	−29452.5			−1.16986			−0.584928	−	0.811085i	$-0.698877\pi$
$859$	−29452.5			−1.16986			−0.584928	+	0.811085i	$0.698877\pi$
$860$		0			0
$861$	8790.09			0.347927
$862$			19026.3i			0.751783i
$863$	−15485.4			−0.610809			−0.305405	−	0.952223i	$-0.598792\pi$
$863$	−15485.4			−0.610809			−0.305405	+	0.952223i	$0.598792\pi$
$864$		−	3678.14i		−	0.144830i
$865$		0			0
$866$		−	14542.7i		−	0.570646i
$867$			17806.0i			0.697491i
$868$			2941.91i			0.115040i
$869$			48195.0i			1.88136i
$870$		0			0
$871$	−13009.4	−	14478.7i	−0.506092	−	0.563251i
$872$			17335.0i			0.673206i
$873$	9285.92			0.360001
$874$	−36400.3			−1.40876
$875$		0			0
$876$		−	2504.01i		−	0.0965784i
$877$	13702.1			0.527578			0.263789	−	0.964580i	$-0.415028\pi$
$877$	13702.1			0.527578			0.263789	+	0.964580i	$0.415028\pi$
$878$	19230.5			0.739178
$879$		−	33579.8i		−	1.28853i
$880$		0			0
$881$	−16868.6			−0.645084			−0.322542	−	0.946555i	$-0.604537\pi$
$881$	−16868.6			−0.645084			−0.322542	+	0.946555i	$0.604537\pi$
$882$	−4857.64			−0.185448
$883$		−	15162.4i		−	0.577867i	−0.957349	−	0.288934i	$-0.906699\pi$
$883$		−	15162.4i		−	0.577867i	0.957349	−	0.288934i	$-0.0933007\pi$
$884$	−6042.50	+	5429.31i	−0.229900	+	0.206569i
$885$		0			0
$886$			9565.09i			0.362692i
$887$			13173.9i			0.498686i	0.968415	+	0.249343i	$0.0802147\pi$
$887$			13173.9i			0.498686i	−0.968415	+	0.249343i	$0.919785\pi$
$888$			6180.45i			0.233561i
$889$		−	3856.44i		−	0.145490i
$890$		0			0
$891$		−	46494.9i		−	1.74819i
$892$	17403.5			0.653265
$893$		−	44336.0i		−	1.66142i
$894$	−32021.5			−1.19794
$895$		0			0
$896$	494.779			0.0184480
$897$	−22537.7	−	25083.1i	−0.838919	−	0.933668i
$898$			13737.4i			0.510495i
$899$			15960.4i			0.592114i
$900$		0			0
$901$	4349.43			0.160822
$902$	41245.1			1.52252
$903$	1692.21			0.0623624
$904$			2854.23i			0.105011i
$905$		0			0
$906$	5681.47			0.208338
$907$			32190.1i			1.17845i	0.807969	+	0.589225i	$0.200567\pi$
$907$			32190.1i			1.17845i	−0.807969	+	0.589225i	$0.799433\pi$
$908$	−14583.4			−0.533003
$909$	−13009.7			−0.474703
$910$		0			0
$911$	13646.0			0.496281			0.248141	−	0.968724i	$-0.420180\pi$
$911$	13646.0			0.496281			0.248141	+	0.968724i	$0.420180\pi$
$912$	−13925.6			−0.505617
$913$		−	1178.78i		−	0.0427293i
$914$	16802.9			0.608088
$915$		0			0
$916$			12956.6i			0.467357i
$917$	6497.36			0.233982
$918$	−9960.23			−0.358101
$919$	−34923.6			−1.25356			−0.626780	−	0.779196i	$-0.715628\pi$
$919$	−34923.6			−1.25356			−0.626780	+	0.779196i	$0.715628\pi$
$920$		0			0
$921$			12410.9i			0.444033i
$922$		−	31860.9i		−	1.13805i
$923$	−10248.6	+	9208.52i	−0.365477	+	0.328388i
$924$	4824.09			0.171754
$925$		0			0
$926$	23144.3			0.821349
$927$			638.761i			0.0226318i
$928$	2684.27			0.0949522
$929$			4287.49i			0.151419i	0.997130	+	0.0757094i	$0.0241221\pi$
$929$			4287.49i			0.151419i	−0.997130	+	0.0757094i	$0.975878\pi$
$930$		0			0
$931$		−	48679.1i		−	1.71363i
$932$		−	8730.72i		−	0.306850i
$933$		−	22946.5i		−	0.805182i
$934$			21724.7i			0.761086i
$935$		0			0
$936$	−1855.48	−	2065.04i	−0.0647953	−	0.0721134i
$937$			14174.1i			0.494182i	0.968992	+	0.247091i	$0.0794746\pi$
$937$			14174.1i			0.494182i	−0.968992	+	0.247091i	$0.920525\pi$
$938$	3210.44			0.111753
$939$	−22002.5			−0.764669
$940$		0			0
$941$			11317.1i			0.392058i	0.980598	+	0.196029i	$0.0628047\pi$
$941$			11317.1i			0.392058i	−0.980598	+	0.196029i	$0.937195\pi$
$942$	−2765.86			−0.0956651
$943$	47552.5			1.64212
$944$		−	7668.95i		−	0.264410i
$945$		0			0
$946$	7940.24			0.272896
$947$	40514.3			1.39022			0.695110	−	0.718904i	$-0.255356\pi$
$947$	40514.3			1.39022			0.695110	+	0.718904i	$0.255356\pi$
$948$			21257.5i			0.728281i
$949$	3343.47	+	3721.09i	0.114366	+	0.127283i
$950$		0			0
$951$		−	48549.3i		−	1.65543i
$952$		−	1339.84i		−	0.0456139i
$953$			49479.9i			1.68186i	0.541144	+	0.840930i	$0.317991\pi$
$953$			49479.9i			1.68186i	−0.541144	+	0.840930i	$0.682009\pi$
$954$			1486.43i			0.0504455i
$955$		0			0
$956$		−	235.219i		−	0.00795767i
$957$	26171.7			0.884023
$958$			4171.44i			0.140682i
$959$	6101.95			0.205466
$960$		0			0
$961$	−6411.32			−0.215210
$962$	−8252.41	−	9184.46i	−0.276578	−	0.307816i
$963$			15554.5i			0.520495i
$964$		−	809.045i		−	0.0270307i
$965$		0			0
$966$	5561.82			0.185247
$967$	46779.9			1.55568			0.777838	−	0.628465i	$-0.216316\pi$
$967$	46779.9			1.55568			0.777838	+	0.628465i	$0.216316\pi$
$968$	11987.8			0.398038
$969$			37709.9i			1.25017i
$970$		0			0
$971$	24378.5			0.805710			0.402855	−	0.915264i	$-0.368018\pi$
$971$	24378.5			0.805710			0.402855	+	0.915264i	$0.368018\pi$
$972$		−	8093.91i		−	0.267091i
$973$	6664.32			0.219577
$974$	23659.1			0.778323
$975$		0			0
$976$	−7676.98			−0.251777
$977$	−24237.6			−0.793685			−0.396842	−	0.917887i	$-0.629894\pi$
$977$	−24237.6			−0.793685			−0.396842	+	0.917887i	$0.629894\pi$
$978$		−	17071.1i		−	0.558152i
$979$	35396.2			1.15554
$980$		0			0
$981$			16042.7i			0.522124i
$982$	5400.08			0.175482
$983$	−32953.2			−1.06922			−0.534611	−	0.845098i	$-0.679542\pi$
$983$	−32953.2			−1.06922			−0.534611	+	0.845098i	$0.679542\pi$
$984$	18192.1			0.589372
$985$		0			0
$986$		−	7268.90i		−	0.234776i
$987$			6774.36i			0.218470i
$988$	20694.1	−	18594.1i	0.666364	−	0.598741i
$989$	9154.51			0.294334
$990$		0			0
$991$	−30254.8			−0.969804			−0.484902	−	0.874569i	$-0.661145\pi$
$991$	−30254.8			−0.969804			−0.484902	+	0.874569i	$0.661145\pi$
$992$			6088.61i			0.194873i
$993$	−5203.39			−0.166288
$994$		−	2272.47i		−	0.0725135i
$995$		0			0
$996$		−	519.925i		−	0.0165406i
$997$			4794.46i			0.152299i	0.997096	+	0.0761495i	$0.0242626\pi$
$997$			4794.46i			0.152299i	−0.997096	+	0.0761495i	$0.975737\pi$
$998$			6027.34i			0.191174i
$999$		−	15139.3i		−	0.479466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.4.c.e.649.3		4
5.2	odd	4		26.4.b.a.25.2	✓	4
5.3	odd	4		650.4.d.d.51.3		4
5.4	even	2		650.4.c.f.649.2		4
13.12	even	2		650.4.c.f.649.3		4
15.2	even	4		234.4.b.b.181.3		4
20.7	even	4		208.4.f.d.129.1		4
40.27	even	4		832.4.f.h.129.4		4
40.37	odd	4		832.4.f.j.129.2		4
65.2	even	12		338.4.c.i.191.1		4
65.7	even	12		338.4.c.h.315.1		4
65.12	odd	4		26.4.b.a.25.4	yes	4
65.17	odd	12		338.4.e.g.23.3		8
65.22	odd	12		338.4.e.g.23.1		8
65.32	even	12		338.4.c.i.315.1		4
65.37	even	12		338.4.c.h.191.1		4
65.38	odd	4		650.4.d.d.51.1		4
65.42	odd	12		338.4.e.g.147.3		8
65.47	even	4		338.4.a.i.1.2		2
65.57	even	4		338.4.a.f.1.2		2
65.62	odd	12		338.4.e.g.147.1		8
65.64	even	2	inner	650.4.c.e.649.2		4
195.77	even	4		234.4.b.b.181.2		4
260.207	even	4		208.4.f.d.129.2		4
520.77	odd	4		832.4.f.j.129.1		4
520.467	even	4		832.4.f.h.129.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.b.a.25.2	✓	4	5.2	odd	4
26.4.b.a.25.4	yes	4	65.12	odd	4
208.4.f.d.129.1		4	20.7	even	4
208.4.f.d.129.2		4	260.207	even	4
234.4.b.b.181.2		4	195.77	even	4
234.4.b.b.181.3		4	15.2	even	4
338.4.a.f.1.2		2	65.57	even	4
338.4.a.i.1.2		2	65.47	even	4
338.4.c.h.191.1		4	65.37	even	12
338.4.c.h.315.1		4	65.7	even	12
338.4.c.i.191.1		4	65.2	even	12
338.4.c.i.315.1		4	65.32	even	12
338.4.e.g.23.1		8	65.22	odd	12
338.4.e.g.23.3		8	65.17	odd	12
338.4.e.g.147.1		8	65.62	odd	12
338.4.e.g.147.3		8	65.42	odd	12
650.4.c.e.649.2		4	65.64	even	2	inner
650.4.c.e.649.3		4	1.1	even	1	trivial
650.4.c.f.649.2		4	5.4	even	2
650.4.c.f.649.3		4	13.12	even	2
650.4.d.d.51.1		4	65.38	odd	4
650.4.d.d.51.3		4	5.3	odd	4
832.4.f.h.129.3		4	520.467	even	4
832.4.f.h.129.4		4	40.27	even	4
832.4.f.j.129.1		4	520.77	odd	4
832.4.f.j.129.2		4	40.37	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	650.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +5.86546i q^{3} +4.00000 q^{4} -11.7309i q^{6} -3.86546 q^{7} -8.00000 q^{8} -7.40362 q^{9} +53.1928i q^{11} +23.4618i q^{12} +(-31.3273 - 34.8655i) q^{13} +7.73092 q^{14} +16.0000 q^{16} -43.3273i q^{17} +14.8072 q^{18} +148.386i q^{19} -22.6727i q^{21} -106.386i q^{22} -122.655i q^{23} -46.9237i q^{24} +(62.6546 + 69.7309i) q^{26} +114.942i q^{27} -15.4618 q^{28} -83.8836 q^{29} -190.269i q^{31} -32.0000 q^{32} -312.000 q^{33} +86.6546i q^{34} -29.6145 q^{36} -131.713 q^{37} -296.771i q^{38} +(204.502 - 183.749i) q^{39} +387.695i q^{41} +45.3454i q^{42} +74.6365i q^{43} +212.771i q^{44} +245.309i q^{46} -298.789 q^{47} +93.8474i q^{48} -328.058 q^{49} +254.135 q^{51} +(-125.309 - 139.462i) q^{52} +100.386i q^{53} -229.884i q^{54} +30.9237 q^{56} -870.349 q^{57} +167.767 q^{58} -479.309i q^{59} -479.811 q^{61} +380.538i q^{62} +28.6184 q^{63} +64.0000 q^{64} +624.000 q^{66} +415.273 q^{67} -173.309i q^{68} +719.426 q^{69} -293.946i q^{71} +59.2290 q^{72} -106.727 q^{73} +263.426 q^{74} +593.542i q^{76} -205.614i q^{77} +(-409.004 + 367.498i) q^{78} +906.044 q^{79} -874.084 q^{81} -775.389i q^{82} -22.1605 q^{83} -90.6908i q^{84} -149.273i q^{86} -492.016i q^{87} -425.542i q^{88} -665.433i q^{89} +(121.094 + 134.771i) q^{91} -490.618i q^{92} +1116.02 q^{93} +597.578 q^{94} -187.695i q^{96} -1254.24 q^{97} +656.116 q^{98} -393.819i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 16 q^{4} + 14 q^{7} - 32 q^{8} - 118 q^{9} + 22 q^{13} - 28 q^{14} + 64 q^{16} + 236 q^{18} - 44 q^{26} + 56 q^{28} - 748 q^{29} - 128 q^{32} - 1248 q^{33} - 472 q^{36} - 26 q^{37} + 52 q^{39}+ \cdots + 2212 q^{98}+O(q^{100}) \) 4 * q - 8 * q^2 + 16 * q^4 + 14 * q^7 - 32 * q^8 - 118 * q^9 + 22 * q^13 - 28 * q^14 + 64 * q^16 + 236 * q^18 - 44 * q^26 + 56 * q^28 - 748 * q^29 - 128 * q^32 - 1248 * q^33 - 472 * q^36 - 26 * q^37 + 52 * q^39 - 930 * q^47 - 1106 * q^49 + 1046 * q^51 + 88 * q^52 - 112 * q^56 - 2244 * q^57 + 1496 * q^58 - 564 * q^61 - 1064 * q^63 + 256 * q^64 + 2496 * q^66 + 188 * q^67 + 1876 * q^69 + 944 * q^72 - 1900 * q^73 + 52 * q^74 - 104 * q^78 + 1444 * q^79 - 668 * q^81 + 2504 * q^83 + 1162 * q^91 - 1664 * q^93 + 1860 * q^94 - 1128 * q^97 + 2212 * q^98

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