LMFDB - Embedded newform 5054.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.a (trivial)

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:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.151572.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} + 8x + 4 $ x^4 - x^3 - 10x^2 + 8x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.352271$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.352271 q^{3} +1.00000 q^{4} +4.32518 q^{5} -0.352271 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.87591 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.352271 q^{3} +1.00000 q^{4} +4.32518 q^{5} -0.352271 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.87591 q^{9} -4.32518 q^{10} +2.35227 q^{11} +0.352271 q^{12} -0.801544 q^{13} -1.00000 q^{14} +1.52363 q^{15} +1.00000 q^{16} +6.22818 q^{17} +2.87591 q^{18} +4.32518 q^{20} +0.352271 q^{21} -2.35227 q^{22} -1.77445 q^{23} -0.352271 q^{24} +13.7072 q^{25} +0.801544 q^{26} -2.06991 q^{27} +1.00000 q^{28} +5.83126 q^{29} -1.52363 q^{30} -5.12672 q^{31} -1.00000 q^{32} +0.828636 q^{33} -6.22818 q^{34} +4.32518 q^{35} -2.87591 q^{36} +10.6504 q^{37} -0.282361 q^{39} -4.32518 q^{40} -3.64773 q^{41} -0.352271 q^{42} +0.873277 q^{43} +2.35227 q^{44} -12.4388 q^{45} +1.77445 q^{46} -5.83126 q^{47} +0.352271 q^{48} +1.00000 q^{49} -13.7072 q^{50} +2.19400 q^{51} -0.801544 q^{52} +1.12672 q^{53} +2.06991 q^{54} +10.1740 q^{55} -1.00000 q^{56} -5.83126 q^{58} -14.2011 q^{59} +1.52363 q^{60} -2.72209 q^{61} +5.12672 q^{62} -2.87591 q^{63} +1.00000 q^{64} -3.46682 q^{65} -0.828636 q^{66} +4.58045 q^{67} +6.22818 q^{68} -0.625088 q^{69} -4.32518 q^{70} +14.0026 q^{71} +2.87591 q^{72} -9.23080 q^{73} -10.6504 q^{74} +4.82864 q^{75} +2.35227 q^{77} +0.282361 q^{78} -7.04727 q^{79} +4.32518 q^{80} +7.89855 q^{81} +3.64773 q^{82} +15.5560 q^{83} +0.352271 q^{84} +26.9380 q^{85} -0.873277 q^{86} +2.05418 q^{87} -2.35227 q^{88} +7.29546 q^{89} +12.4388 q^{90} -0.801544 q^{91} -1.77445 q^{92} -1.80600 q^{93} +5.83126 q^{94} -0.352271 q^{96} +3.05681 q^{97} -1.00000 q^{98} -6.76491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} - 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 - 4 * q^8 + 9 * q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} - 4 q^{8} + 9 q^{9} - q^{10} + 7 q^{11} - q^{12} - 5 q^{13} - 4 q^{14} - 12 q^{15} + 4 q^{16} + 2 q^{17} - 9 q^{18} + q^{20} - q^{21} - 7 q^{22} + 5 q^{23} + q^{24} + 15 q^{25} + 5 q^{26} - q^{27} + 4 q^{28} + 4 q^{29} + 12 q^{30} - 6 q^{31} - 4 q^{32} + 19 q^{33} - 2 q^{34} + q^{35} + 9 q^{36} + 10 q^{37} - 6 q^{39} - q^{40} - 17 q^{41} + q^{42} + 18 q^{43} + 7 q^{44} - 19 q^{45} - 5 q^{46} - 4 q^{47} - q^{48} + 4 q^{49} - 15 q^{50} + 22 q^{51} - 5 q^{52} - 10 q^{53} + q^{54} - 10 q^{55} - 4 q^{56} - 4 q^{58} - 20 q^{59} - 12 q^{60} + 9 q^{61} + 6 q^{62} + 9 q^{63} + 4 q^{64} - 3 q^{65} - 19 q^{66} - 7 q^{67} + 2 q^{68} + 24 q^{69} - q^{70} + 21 q^{71} - 9 q^{72} + 21 q^{73} - 10 q^{74} + 35 q^{75} + 7 q^{77} + 6 q^{78} + 8 q^{79} + q^{80} + 40 q^{81} + 17 q^{82} - 12 q^{83} - q^{84} + 10 q^{85} - 18 q^{86} + 36 q^{87} - 7 q^{88} + 34 q^{89} + 19 q^{90} - 5 q^{91} + 5 q^{92} + 6 q^{93} + 4 q^{94} + q^{96} + 5 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 - 4 * q^8 + 9 * q^9 - q^10 + 7 * q^11 - q^12 - 5 * q^13 - 4 * q^14 - 12 * q^15 + 4 * q^16 + 2 * q^17 - 9 * q^18 + q^20 - q^21 - 7 * q^22 + 5 * q^23 + q^24 + 15 * q^25 + 5 * q^26 - q^27 + 4 * q^28 + 4 * q^29 + 12 * q^30 - 6 * q^31 - 4 * q^32 + 19 * q^33 - 2 * q^34 + q^35 + 9 * q^36 + 10 * q^37 - 6 * q^39 - q^40 - 17 * q^41 + q^42 + 18 * q^43 + 7 * q^44 - 19 * q^45 - 5 * q^46 - 4 * q^47 - q^48 + 4 * q^49 - 15 * q^50 + 22 * q^51 - 5 * q^52 - 10 * q^53 + q^54 - 10 * q^55 - 4 * q^56 - 4 * q^58 - 20 * q^59 - 12 * q^60 + 9 * q^61 + 6 * q^62 + 9 * q^63 + 4 * q^64 - 3 * q^65 - 19 * q^66 - 7 * q^67 + 2 * q^68 + 24 * q^69 - q^70 + 21 * q^71 - 9 * q^72 + 21 * q^73 - 10 * q^74 + 35 * q^75 + 7 * q^77 + 6 * q^78 + 8 * q^79 + q^80 + 40 * q^81 + 17 * q^82 - 12 * q^83 - q^84 + 10 * q^85 - 18 * q^86 + 36 * q^87 - 7 * q^88 + 34 * q^89 + 19 * q^90 - 5 * q^91 + 5 * q^92 + 6 * q^93 + 4 * q^94 + q^96 + 5 * q^97 - 4 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.352271	0.203384	0.101692	−	0.994816i	$-0.467574\pi$
$3$	0.352271	0.203384	0.101692	+	0.994816i	$0.467574\pi$
$4$	1.00000	0.500000
$5$	4.32518	1.93428	0.967139	−	0.254247i	$-0.0818276\pi$
$5$	4.32518	1.93428	0.967139	+	0.254247i	$0.0818276\pi$
$6$	−0.352271	−0.143814
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.87591	−0.958635
$10$	−4.32518	−1.36774
$11$	2.35227	0.709236	0.354618	−	0.935011i	$-0.384611\pi$
$11$	2.35227	0.709236	0.354618	+	0.935011i	$0.384611\pi$
$12$	0.352271	0.101692
$13$	−0.801544	−0.222308	−0.111154	−	0.993803i	$-0.535455\pi$
$13$	−0.801544	−0.222308	−0.111154	+	0.993803i	$0.535455\pi$
$14$	−1.00000	−0.267261
$15$	1.52363	0.393401
$16$	1.00000	0.250000
$17$	6.22818	1.51055	0.755277	−	0.655405i	$-0.227502\pi$
$17$	6.22818	1.51055	0.755277	+	0.655405i	$0.227502\pi$
$18$	2.87591	0.677857
$19$	0	0
$19$	0	0
$20$	4.32518	0.967139
$21$	0.352271	0.0768718
$22$	−2.35227	−0.501506
$23$	−1.77445	−0.369999	−0.184999	−	0.982739i	$-0.559228\pi$
$23$	−1.77445	−0.369999	−0.184999	+	0.982739i	$0.559228\pi$
$24$	−0.352271	−0.0719070
$25$	13.7072	2.74143
$26$	0.801544	0.157196
$27$	−2.06991	−0.398354
$28$	1.00000	0.188982
$29$	5.83126	1.08284	0.541419	−	0.840753i	$-0.317887\pi$
$29$	5.83126	1.08284	0.541419	+	0.840753i	$0.317887\pi$
$30$	−1.52363	−0.278176
$31$	−5.12672	−0.920787	−0.460393	−	0.887715i	$-0.652292\pi$
$31$	−5.12672	−0.920787	−0.460393	+	0.887715i	$0.652292\pi$
$32$	−1.00000	−0.176777
$33$	0.828636	0.144247
$34$	−6.22818	−1.06812
$35$	4.32518	0.731089
$36$	−2.87591	−0.479318
$37$	10.6504	1.75091	0.875454	−	0.483302i	$-0.160563\pi$
$37$	10.6504	1.75091	0.875454	+	0.483302i	$0.160563\pi$
$38$	0	0
$39$	−0.282361	−0.0452139
$40$	−4.32518	−0.683871
$41$	−3.64773	−0.569680	−0.284840	−	0.958575i	$-0.591940\pi$
$41$	−3.64773	−0.569680	−0.284840	+	0.958575i	$0.591940\pi$
$42$	−0.352271	−0.0543566
$43$	0.873277	0.133174	0.0665868	−	0.997781i	$-0.478789\pi$
$43$	0.873277	0.133174	0.0665868	+	0.997781i	$0.478789\pi$
$44$	2.35227	0.354618
$45$	−12.4388	−1.85427
$46$	1.77445	0.261629
$47$	−5.83126	−0.850577	−0.425289	−	0.905058i	$-0.639827\pi$
$47$	−5.83126	−0.850577	−0.425289	+	0.905058i	$0.639827\pi$
$48$	0.352271	0.0508459
$49$	1.00000	0.142857
$50$	−13.7072	−1.93849
$51$	2.19400	0.307222
$52$	−0.801544	−0.111154
$53$	1.12672	0.154767	0.0773836	−	0.997001i	$-0.475343\pi$
$53$	1.12672	0.154767	0.0773836	+	0.997001i	$0.475343\pi$
$54$	2.06991	0.281679
$55$	10.1740	1.37186
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−5.83126	−0.765683
$59$	−14.2011	−1.84882	−0.924412	−	0.381396i	$-0.875443\pi$
$59$	−14.2011	−1.84882	−0.924412	+	0.381396i	$0.875443\pi$
$60$	1.52363	0.196700
$61$	−2.72209	−0.348528	−0.174264	−	0.984699i	$-0.555755\pi$
$61$	−2.72209	−0.348528	−0.174264	+	0.984699i	$0.555755\pi$
$62$	5.12672	0.651094
$63$	−2.87591	−0.362330
$64$	1.00000	0.125000
$65$	−3.46682	−0.430006
$66$	−0.828636	−0.101998
$67$	4.58045	0.559591	0.279795	−	0.960060i	$-0.409733\pi$
$67$	4.58045	0.559591	0.279795	+	0.960060i	$0.409733\pi$
$68$	6.22818	0.755277
$69$	−0.625088	−0.0752517
$70$	−4.32518	−0.516958
$71$	14.0026	1.66181	0.830903	−	0.556417i	$-0.187824\pi$
$71$	14.0026	1.66181	0.830903	+	0.556417i	$0.187824\pi$
$72$	2.87591	0.338929
$73$	−9.23080	−1.08038	−0.540192	−	0.841542i	$-0.681648\pi$
$73$	−9.23080	−1.08038	−0.540192	+	0.841542i	$0.681648\pi$
$74$	−10.6504	−1.23808
$75$	4.82864	0.557563
$76$	0	0
$77$	2.35227	0.268066
$78$	0.282361	0.0319710
$79$	−7.04727	−0.792880	−0.396440	−	0.918061i	$-0.629754\pi$
$79$	−7.04727	−0.792880	−0.396440	+	0.918061i	$0.629754\pi$
$80$	4.32518	0.483570
$81$	7.89855	0.877616
$82$	3.64773	0.402824
$83$	15.5560	1.70749	0.853745	−	0.520691i	$-0.174325\pi$
$83$	15.5560	1.70749	0.853745	+	0.520691i	$0.174325\pi$
$84$	0.352271	0.0384359
$85$	26.9380	2.92183
$86$	−0.873277	−0.0941679
$87$	2.05418	0.220232
$88$	−2.35227	−0.250753
$89$	7.29546	0.773317	0.386659	−	0.922223i	$-0.373629\pi$
$89$	7.29546	0.773317	0.386659	+	0.922223i	$0.373629\pi$
$90$	12.4388	1.31117
$91$	−0.801544	−0.0840247
$92$	−1.77445	−0.184999
$93$	−1.80600	−0.187273
$94$	5.83126	0.601449
$95$	0	0
$96$	−0.352271	−0.0359535
$97$	3.05681	0.310372	0.155186	−	0.987885i	$-0.450402\pi$
$97$	3.05681	0.310372	0.155186	+	0.987885i	$0.450402\pi$
$98$	−1.00000	−0.101015
$99$	−6.76491	−0.679899
$100$	13.7072	1.37072
$101$	1.52363	0.151607	0.0758036	−	0.997123i	$-0.475848\pi$
$101$	1.52363	0.151607	0.0758036	+	0.997123i	$0.475848\pi$
$102$	−2.19400	−0.217239
$103$	−11.5236	−1.13546	−0.567729	−	0.823216i	$-0.692178\pi$
$103$	−11.5236	−1.13546	−0.567729	+	0.823216i	$0.692178\pi$
$104$	0.801544	0.0785979
$105$	1.52363	0.148691
$106$	−1.12672	−0.109437
$107$	16.0053	1.54729	0.773643	−	0.633621i	$-0.218432\pi$
$107$	16.0053	1.54729	0.773643	+	0.633621i	$0.218432\pi$
$108$	−2.06991	−0.199177
$109$	−7.24035	−0.693500	−0.346750	−	0.937958i	$-0.612715\pi$
$109$	−7.24035	−0.693500	−0.346750	+	0.937958i	$0.612715\pi$
$110$	−10.1740	−0.970052
$111$	3.75181	0.356106
$112$	1.00000	0.0944911
$113$	1.47637	0.138885	0.0694424	−	0.997586i	$-0.477878\pi$
$113$	1.47637	0.138885	0.0694424	+	0.997586i	$0.477878\pi$
$114$	0	0
$115$	−7.67482	−0.715681
$116$	5.83126	0.541419
$117$	2.30517	0.213113
$118$	14.2011	1.30732
$119$	6.22818	0.570936
$120$	−1.52363	−0.139088
$121$	−5.46682	−0.496984
$122$	2.72209	0.246446
$123$	−1.28499	−0.115864
$124$	−5.12672	−0.460393
$125$	37.6601	3.36842
$126$	2.87591	0.256206
$127$	−6.23080	−0.552894	−0.276447	−	0.961029i	$-0.589157\pi$
$127$	−6.23080	−0.552894	−0.276447	+	0.961029i	$0.589157\pi$
$128$	−1.00000	−0.0883883
$129$	0.307630	0.0270853
$130$	3.46682	0.304060
$131$	−3.66528	−0.320237	−0.160118	−	0.987098i	$-0.551188\pi$
$131$	−3.66528	−0.320237	−0.160118	+	0.987098i	$0.551188\pi$
$132$	0.828636	0.0721235
$133$	0	0
$134$	−4.58045	−0.395690
$135$	−8.95273	−0.770528
$136$	−6.22818	−0.534062
$137$	3.39691	0.290218	0.145109	−	0.989416i	$-0.453647\pi$
$137$	3.39691	0.290218	0.145109	+	0.989416i	$0.453647\pi$
$138$	0.625088	0.0532110
$139$	−5.19663	−0.440773	−0.220386	−	0.975413i	$-0.570732\pi$
$139$	−5.19663	−0.440773	−0.220386	+	0.975413i	$0.570732\pi$
$140$	4.32518	0.365544
$141$	−2.05418	−0.172994
$142$	−14.0026	−1.17507
$143$	−1.88545	−0.157669
$144$	−2.87591	−0.239659
$145$	25.2213	2.09451
$146$	9.23080	0.763947
$147$	0.352271	0.0290548
$148$	10.6504	0.875454
$149$	14.6504	1.20020	0.600102	−	0.799923i	$-0.295127\pi$
$149$	14.6504	1.20020	0.600102	+	0.799923i	$0.295127\pi$
$150$	−4.82864	−0.394257
$151$	5.46682	0.444884	0.222442	−	0.974946i	$-0.428597\pi$
$151$	5.46682	0.444884	0.222442	+	0.974946i	$0.428597\pi$
$152$	0	0
$153$	−17.9116	−1.44807
$154$	−2.35227	−0.189551
$155$	−22.1740	−1.78106
$156$	−0.282361	−0.0226069
$157$	−3.45190	−0.275492	−0.137746	−	0.990468i	$-0.543986\pi$
$157$	−3.45190	−0.275492	−0.137746	+	0.990468i	$0.543986\pi$
$158$	7.04727	0.560651
$159$	0.396912	0.0314771
$160$	−4.32518	−0.341935
$161$	−1.77445	−0.139846
$162$	−7.89855	−0.620568
$163$	8.65990	0.678296	0.339148	−	0.940733i	$-0.389861\pi$
$163$	8.65990	0.678296	0.339148	+	0.940733i	$0.389861\pi$
$164$	−3.64773	−0.284840
$165$	3.58400	0.279014
$166$	−15.5560	−1.20738
$167$	−6.05944	−0.468894	−0.234447	−	0.972129i	$-0.575328\pi$
$167$	−6.05944	−0.468894	−0.234447	+	0.972129i	$0.575328\pi$
$168$	−0.352271	−0.0271783
$169$	−12.3575	−0.950579
$170$	−26.9380	−2.06605
$171$	0	0
$172$	0.873277	0.0665868
$173$	15.6259	1.18801	0.594007	−	0.804460i	$-0.297545\pi$
$173$	15.6259	1.18801	0.594007	+	0.804460i	$0.297545\pi$
$174$	−2.05418	−0.155727
$175$	13.7072	1.03616
$176$	2.35227	0.177309
$177$	−5.00263	−0.376021
$178$	−7.29546	−0.546818
$179$	11.3995	0.852042	0.426021	−	0.904713i	$-0.359915\pi$
$179$	11.3995	0.852042	0.426021	+	0.904713i	$0.359915\pi$
$180$	−12.4388	−0.927134
$181$	3.27791	0.243645	0.121823	−	0.992552i	$-0.461126\pi$
$181$	3.27791	0.243645	0.121823	+	0.992552i	$0.461126\pi$
$182$	0.801544	0.0594144
$183$	−0.958913	−0.0708849
$184$	1.77445	0.130814
$185$	46.0647	3.38674
$186$	1.80600	0.132422
$187$	14.6504	1.07134
$188$	−5.83126	−0.425289
$189$	−2.06991	−0.150564
$190$	0	0
$191$	−3.23865	−0.234340	−0.117170	−	0.993112i	$-0.537382\pi$
$191$	−3.23865	−0.234340	−0.117170	+	0.993112i	$0.537382\pi$
$192$	0.352271	0.0254230
$193$	12.0568	0.867868	0.433934	−	0.900945i	$-0.357125\pi$
$193$	12.0568	0.867868	0.433934	+	0.900945i	$0.357125\pi$
$194$	−3.05681	−0.219466
$195$	−1.22126	−0.0874563
$196$	1.00000	0.0714286
$197$	−20.9380	−1.49177	−0.745884	−	0.666075i	$-0.767973\pi$
$197$	−20.9380	−1.49177	−0.745884	+	0.666075i	$0.767973\pi$
$198$	6.76491	0.480761
$199$	9.12672	0.646976	0.323488	−	0.946232i	$-0.395144\pi$
$199$	9.12672	0.646976	0.323488	+	0.946232i	$0.395144\pi$
$200$	−13.7072	−0.969243
$201$	1.61356	0.113812
$202$	−1.52363	−0.107203
$203$	5.83126	0.409275
$204$	2.19400	0.153611
$205$	−15.7771	−1.10192
$206$	11.5236	0.802890
$207$	5.10316	0.354694
$208$	−0.801544	−0.0555771
$209$	0	0
$210$	−1.52363	−0.105141
$211$	−4.00000	−0.275371	−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000	−0.275371	−0.137686	+	0.990476i	$0.543966\pi$
$212$	1.12672	0.0773836
$213$	4.93272	0.337984
$214$	−16.0053	−1.09410
$215$	3.77708	0.257595
$216$	2.06991	0.140840
$217$	−5.12672	−0.348025
$218$	7.24035	0.490378
$219$	−3.25174	−0.219732
$220$	10.1740	0.685930
$221$	−4.99216	−0.335809
$222$	−3.75181	−0.251805
$223$	−12.2534	−0.820551	−0.410276	−	0.911962i	$-0.634568\pi$
$223$	−12.2534	−0.820551	−0.410276	+	0.911962i	$0.634568\pi$
$224$	−1.00000	−0.0668153
$225$	−39.4205	−2.62803
$226$	−1.47637	−0.0982064
$227$	−23.3531	−1.55000	−0.774999	−	0.631962i	$-0.782250\pi$
$227$	−23.3531	−1.55000	−0.774999	+	0.631962i	$0.782250\pi$
$228$	0	0
$229$	−25.8830	−1.71040	−0.855198	−	0.518302i	$-0.826564\pi$
$229$	−25.8830	−1.71040	−0.855198	+	0.518302i	$0.826564\pi$
$230$	7.67482	0.506063
$231$	0.828636	0.0545203
$232$	−5.83126	−0.382841
$233$	−2.60309	−0.170534	−0.0852670	−	0.996358i	$-0.527174\pi$
$233$	−2.60309	−0.170534	−0.0852670	+	0.996358i	$0.527174\pi$
$234$	−2.30517	−0.150693
$235$	−25.2213	−1.64525
$236$	−14.2011	−0.924412
$237$	−2.48255	−0.161259
$238$	−6.22818	−0.403713
$239$	−23.2781	−1.50573	−0.752867	−	0.658173i	$-0.771330\pi$
$239$	−23.2781	−1.50573	−0.752867	+	0.658173i	$0.771330\pi$
$240$	1.52363	0.0983502
$241$	−8.94319	−0.576081	−0.288041	−	0.957618i	$-0.593004\pi$
$241$	−8.94319	−0.576081	−0.288041	+	0.957618i	$0.593004\pi$
$242$	5.46682	0.351421
$243$	8.99216	0.576847
$244$	−2.72209	−0.174264
$245$	4.32518	0.276326
$246$	1.28499	0.0819279
$247$	0	0
$248$	5.12672	0.325547
$249$	5.47992	0.347276
$250$	−37.6601	−2.38183
$251$	27.3872	1.72867	0.864334	−	0.502918i	$-0.167740\pi$
$251$	27.3872	1.72867	0.864334	+	0.502918i	$0.167740\pi$
$252$	−2.87591	−0.181165
$253$	−4.17399	−0.262417
$254$	6.23080	0.390955
$255$	9.48946	0.594253
$256$	1.00000	0.0625000
$257$	8.49209	0.529722	0.264861	−	0.964287i	$-0.414674\pi$
$257$	8.49209	0.529722	0.264861	+	0.964287i	$0.414674\pi$
$258$	−0.307630	−0.0191522
$259$	10.6504	0.661781
$260$	−3.46682	−0.215003
$261$	−16.7702	−1.03805
$262$	3.66528	0.226442
$263$	−5.74918	−0.354510	−0.177255	−	0.984165i	$-0.556722\pi$
$263$	−5.74918	−0.354510	−0.177255	+	0.984165i	$0.556722\pi$
$264$	−0.828636	−0.0509990
$265$	4.87328	0.299363
$266$	0	0
$267$	2.56998	0.157280
$268$	4.58045	0.279795
$269$	−8.42218	−0.513509	−0.256755	−	0.966477i	$-0.582653\pi$
$269$	−8.42218	−0.513509	−0.256755	+	0.966477i	$0.582653\pi$
$270$	8.95273	0.544846
$271$	20.7298	1.25925	0.629623	−	0.776901i	$-0.283209\pi$
$271$	20.7298	1.25925	0.629623	+	0.776901i	$0.283209\pi$
$272$	6.22818	0.377639
$273$	−0.282361	−0.0170892
$274$	−3.39691	−0.205215
$275$	32.2430	1.94432
$276$	−0.625088	−0.0376259
$277$	17.4442	1.04812	0.524060	−	0.851682i	$-0.324417\pi$
$277$	17.4442	1.04812	0.524060	+	0.851682i	$0.324417\pi$
$278$	5.19663	0.311673
$279$	14.7440	0.882698
$280$	−4.32518	−0.258479
$281$	2.12409	0.126713	0.0633564	−	0.997991i	$-0.479820\pi$
$281$	2.12409	0.126713	0.0633564	+	0.997991i	$0.479820\pi$
$282$	2.05418	0.122325
$283$	−27.6696	−1.64479	−0.822394	−	0.568919i	$-0.807362\pi$
$283$	−27.6696	−1.64479	−0.822394	+	0.568919i	$0.807362\pi$
$284$	14.0026	0.830903
$285$	0	0
$286$	1.88545	0.111489
$287$	−3.64773	−0.215319
$288$	2.87591	0.169464
$289$	21.7902	1.28178
$290$	−25.2213	−1.48104
$291$	1.07683	0.0631247
$292$	−9.23080	−0.540192
$293$	−13.2326	−0.773058	−0.386529	−	0.922277i	$-0.626326\pi$
$293$	−13.2326	−0.773058	−0.386529	+	0.922277i	$0.626326\pi$
$294$	−0.352271	−0.0205449
$295$	−61.4222	−3.57614
$296$	−10.6504	−0.619039
$297$	−4.86899	−0.282527
$298$	−14.6504	−0.848672
$299$	1.42230	0.0822538
$300$	4.82864	0.278781
$301$	0.873277	0.0503349
$302$	−5.46682	−0.314580
$303$	0.536732	0.0308344
$304$	0	0
$305$	−11.7735	−0.674150
$306$	17.9116	1.02394
$307$	24.9398	1.42339	0.711695	−	0.702489i	$-0.247928\pi$
$307$	24.9398	1.42339	0.711695	+	0.702489i	$0.247928\pi$
$308$	2.35227	0.134033
$309$	−4.05944	−0.230934
$310$	22.1740	1.25940
$311$	15.9458	0.904204	0.452102	−	0.891966i	$-0.350674\pi$
$311$	15.9458	0.904204	0.452102	+	0.891966i	$0.350674\pi$
$312$	0.282361	0.0159855
$313$	−12.7203	−0.718992	−0.359496	−	0.933147i	$-0.617051\pi$
$313$	−12.7203	−0.718992	−0.359496	+	0.933147i	$0.617051\pi$
$314$	3.45190	0.194802
$315$	−12.4388	−0.700847
$316$	−7.04727	−0.396440
$317$	−32.9091	−1.84836	−0.924178	−	0.381961i	$-0.875249\pi$
$317$	−32.9091	−1.84836	−0.924178	+	0.381961i	$0.875249\pi$
$318$	−0.396912	−0.0222577
$319$	13.7167	0.767989
$320$	4.32518	0.241785
$321$	5.63819	0.314693
$322$	1.77445	0.0988863
$323$	0	0
$324$	7.89855	0.438808
$325$	−10.9869	−0.609444
$326$	−8.65990	−0.479628
$327$	−2.55056	−0.141046
$328$	3.64773	0.201412
$329$	−5.83126	−0.321488
$330$	−3.58400	−0.197293
$331$	−19.0079	−1.04477	−0.522384	−	0.852710i	$-0.674957\pi$
$331$	−19.0079	−1.04477	−0.522384	+	0.852710i	$0.674957\pi$
$332$	15.5560	0.853745
$333$	−30.6294	−1.67848
$334$	6.05944	0.331558
$335$	19.8113	1.08240
$336$	0.352271	0.0192180
$337$	28.1914	1.53568	0.767842	−	0.640639i	$-0.221330\pi$
$337$	28.1914	1.53568	0.767842	+	0.640639i	$0.221330\pi$
$338$	12.3575	0.672161
$339$	0.520081	0.0282469
$340$	26.9380	1.46092
$341$	−12.0594	−0.653055
$342$	0	0
$343$	1.00000	0.0539949
$344$	−0.873277	−0.0470840
$345$	−2.70362	−0.145558
$346$	−15.6259	−0.840053
$347$	22.7292	1.22017	0.610083	−	0.792338i	$-0.291136\pi$
$347$	22.7292	1.22017	0.610083	+	0.792338i	$0.291136\pi$
$348$	2.05418	0.110116
$349$	−4.72981	−0.253181	−0.126590	−	0.991955i	$-0.540403\pi$
$349$	−4.72981	−0.253181	−0.126590	+	0.991955i	$0.540403\pi$
$350$	−13.7072	−0.732679
$351$	1.65912	0.0885575
$352$	−2.35227	−0.125376
$353$	−5.76135	−0.306646	−0.153323	−	0.988176i	$-0.548997\pi$
$353$	−5.76135	−0.306646	−0.153323	+	0.988176i	$0.548997\pi$
$354$	5.00263	0.265887
$355$	60.5639	3.21440
$356$	7.29546	0.386659
$357$	2.19400	0.116119
$358$	−11.3995	−0.602484
$359$	−19.9511	−1.05298	−0.526489	−	0.850182i	$-0.676492\pi$
$359$	−19.9511	−1.05298	−0.526489	+	0.850182i	$0.676492\pi$
$360$	12.4388	0.655583
$361$	0	0
$362$	−3.27791	−0.172283
$363$	−1.92580	−0.101078
$364$	−0.801544	−0.0420123
$365$	−39.9249	−2.08976
$366$	0.958913	0.0501232
$367$	−1.24035	−0.0647456	−0.0323728	−	0.999476i	$-0.510306\pi$
$367$	−1.24035	−0.0647456	−0.0323728	+	0.999476i	$0.510306\pi$
$368$	−1.77445	−0.0924997
$369$	10.4905	0.546115
$370$	−46.0647	−2.39479
$371$	1.12672	0.0584965
$372$	−1.80600	−0.0936365
$373$	24.8733	1.28789	0.643945	−	0.765072i	$-0.277297\pi$
$373$	24.8733	1.28789	0.643945	+	0.765072i	$0.277297\pi$
$374$	−14.6504	−0.757552
$375$	13.2665	0.685081
$376$	5.83126	0.300725
$377$	−4.67402	−0.240724
$378$	2.06991	0.106465
$379$	32.4274	1.66569	0.832843	−	0.553510i	$-0.186712\pi$
$379$	32.4274	1.66569	0.832843	+	0.553510i	$0.186712\pi$
$380$	0	0
$381$	−2.19493	−0.112450
$382$	3.23865	0.165704
$383$	−14.5105	−0.741454	−0.370727	−	0.928742i	$-0.620891\pi$
$383$	−14.5105	−0.741454	−0.370727	+	0.928742i	$0.620891\pi$
$384$	−0.352271	−0.0179767
$385$	10.1740	0.518515
$386$	−12.0568	−0.613676
$387$	−2.51146	−0.127665
$388$	3.05681	0.155186
$389$	25.5236	1.29410	0.647050	−	0.762448i	$-0.276003\pi$
$389$	25.5236	1.29410	0.647050	+	0.762448i	$0.276003\pi$
$390$	1.22126	0.0618409
$391$	−11.0516	−0.558903
$392$	−1.00000	−0.0505076
$393$	−1.29117	−0.0651309
$394$	20.9380	1.05484
$395$	−30.4807	−1.53365
$396$	−6.76491	−0.339949
$397$	11.6373	0.584057	0.292029	−	0.956410i	$-0.405670\pi$
$397$	11.6373	0.584057	0.292029	+	0.956410i	$0.405670\pi$
$398$	−9.12672	−0.457481
$399$	0	0
$400$	13.7072	0.685358
$401$	−25.1740	−1.25713	−0.628565	−	0.777757i	$-0.716357\pi$
$401$	−25.1740	−1.25713	−0.628565	+	0.777757i	$0.716357\pi$
$402$	−1.61356	−0.0804770
$403$	4.10929	0.204699
$404$	1.52363	0.0758036
$405$	34.1626	1.69755
$406$	−5.83126	−0.289401
$407$	25.0525	1.24181
$408$	−2.19400	−0.108619
$409$	31.6277	1.56389	0.781945	−	0.623347i	$-0.214228\pi$
$409$	31.6277	1.56389	0.781945	+	0.623347i	$0.214228\pi$
$410$	15.7771	0.779174
$411$	1.19663	0.0590256
$412$	−11.5236	−0.567729
$413$	−14.2011	−0.698790
$414$	−5.10316	−0.250806
$415$	67.2824	3.30276
$416$	0.801544	0.0392989
$417$	−1.83062	−0.0896460
$418$	0	0
$419$	−19.9205	−0.973182	−0.486591	−	0.873630i	$-0.661760\pi$
$419$	−19.9205	−0.973182	−0.486591	+	0.873630i	$0.661760\pi$
$420$	1.52363	0.0743457
$421$	14.4274	0.703150	0.351575	−	0.936160i	$-0.385646\pi$
$421$	14.4274	0.703150	0.351575	+	0.936160i	$0.385646\pi$
$422$	4.00000	0.194717
$423$	16.7702	0.815393
$424$	−1.12672	−0.0547185
$425$	85.3707	4.14109
$426$	−4.93272	−0.238991
$427$	−2.72209	−0.131731
$428$	16.0053	0.773643
$429$	−0.664189	−0.0320673
$430$	−3.77708	−0.182147
$431$	−14.6504	−0.705683	−0.352841	−	0.935683i	$-0.614784\pi$
$431$	−14.6504	−0.705683	−0.352841	+	0.935683i	$0.614784\pi$
$432$	−2.06991	−0.0995886
$433$	−18.0043	−0.865233	−0.432616	−	0.901578i	$-0.642410\pi$
$433$	−18.0043	−0.865233	−0.432616	+	0.901578i	$0.642410\pi$
$434$	5.12672	0.246091
$435$	8.88472	0.425989
$436$	−7.24035	−0.346750
$437$	0	0
$438$	3.25174	0.155374
$439$	−21.6336	−1.03252	−0.516258	−	0.856433i	$-0.672675\pi$
$439$	−21.6336	−1.03252	−0.516258	+	0.856433i	$0.672675\pi$
$440$	−10.1740	−0.485026
$441$	−2.87591	−0.136948
$442$	4.99216	0.237453
$443$	−3.45465	−0.164135	−0.0820677	−	0.996627i	$-0.526152\pi$
$443$	−3.45465	−0.164135	−0.0820677	+	0.996627i	$0.526152\pi$
$444$	3.75181	0.178053
$445$	31.5542	1.49581
$446$	12.2534	0.580217
$447$	5.16089	0.244102
$448$	1.00000	0.0472456
$449$	−19.5069	−0.920587	−0.460294	−	0.887767i	$-0.652256\pi$
$449$	−19.5069	−0.920587	−0.460294	+	0.887767i	$0.652256\pi$
$450$	39.4205	1.85830
$451$	−8.58045	−0.404037
$452$	1.47637	0.0694424
$453$	1.92580	0.0904821
$454$	23.3531	1.09601
$455$	−3.46682	−0.162527
$456$	0	0
$457$	−13.2876	−0.621568	−0.310784	−	0.950480i	$-0.600592\pi$
$457$	−13.2876	−0.621568	−0.310784	+	0.950480i	$0.600592\pi$
$458$	25.8830	1.20943
$459$	−12.8918	−0.601736
$460$	−7.67482	−0.357840
$461$	16.1915	0.754115	0.377058	−	0.926190i	$-0.376936\pi$
$461$	16.1915	0.754115	0.377058	+	0.926190i	$0.376936\pi$
$462$	−0.828636	−0.0385517
$463$	21.5010	0.999236	0.499618	−	0.866246i	$-0.333474\pi$
$463$	21.5010	0.999236	0.499618	+	0.866246i	$0.333474\pi$
$464$	5.83126	0.270710
$465$	−7.81125	−0.362238
$466$	2.60309	0.120586
$467$	−7.95536	−0.368130	−0.184065	−	0.982914i	$-0.558926\pi$
$467$	−7.95536	−0.368130	−0.184065	+	0.982914i	$0.558926\pi$
$468$	2.30517	0.106556
$469$	4.58045	0.211505
$470$	25.2213	1.16337
$471$	−1.21600	−0.0560305
$472$	14.2011	0.653658
$473$	2.05418	0.0944515
$474$	2.48255	0.114027
$475$	0	0
$476$	6.22818	0.285468
$477$	−3.24035	−0.148365
$478$	23.2781	1.06471
$479$	−26.6356	−1.21701	−0.608506	−	0.793549i	$-0.708231\pi$
$479$	−26.6356	−1.21701	−0.608506	+	0.793549i	$0.708231\pi$
$480$	−1.52363	−0.0695441
$481$	−8.53673	−0.389241
$482$	8.94319	0.407351
$483$	−0.625088	−0.0284425
$484$	−5.46682	−0.248492
$485$	13.2213	0.600347
$486$	−8.99216	−0.407893
$487$	5.34964	0.242415	0.121208	−	0.992627i	$-0.461323\pi$
$487$	5.34964	0.242415	0.121208	+	0.992627i	$0.461323\pi$
$488$	2.72209	0.123223
$489$	3.05063	0.137954
$490$	−4.32518	−0.195392
$491$	0.456352	0.0205949	0.0102974	−	0.999947i	$-0.496722\pi$
$491$	0.456352	0.0205949	0.0102974	+	0.999947i	$0.496722\pi$
$492$	−1.28499	−0.0579318
$493$	36.3181	1.63569
$494$	0	0
$495$	−29.2594	−1.31511
$496$	−5.12672	−0.230197
$497$	14.0026	0.628104
$498$	−5.47992	−0.245561
$499$	−5.99046	−0.268170	−0.134085	−	0.990970i	$-0.542809\pi$
$499$	−5.99046	−0.268170	−0.134085	+	0.990970i	$0.542809\pi$
$500$	37.6601	1.68421
$501$	−2.13456	−0.0953653
$502$	−27.3872	−1.22235
$503$	28.2929	1.26152	0.630758	−	0.775979i	$-0.282744\pi$
$503$	28.2929	1.26152	0.630758	+	0.775979i	$0.282744\pi$
$504$	2.87591	0.128103
$505$	6.58999	0.293251
$506$	4.17399	0.185557
$507$	−4.35320	−0.193332
$508$	−6.23080	−0.276447
$509$	19.0990	0.846548	0.423274	−	0.906002i	$-0.360881\pi$
$509$	19.0990	0.846548	0.423274	+	0.906002i	$0.360881\pi$
$510$	−9.48946	−0.420200
$511$	−9.23080	−0.408347
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−8.49209	−0.374570
$515$	−49.8418	−2.19629
$516$	0.307630	0.0135427
$517$	−13.7167	−0.603260
$518$	−10.6504	−0.467950
$519$	5.50455	0.241623
$520$	3.46682	0.152030
$521$	24.1294	1.05713	0.528563	−	0.848894i	$-0.322731\pi$
$521$	24.1294	1.05713	0.528563	+	0.848894i	$0.322731\pi$
$522$	16.7702	0.734010
$523$	−11.9205	−0.521249	−0.260625	−	0.965440i	$-0.583928\pi$
$523$	−11.9205	−0.521249	−0.260625	+	0.965440i	$0.583928\pi$
$524$	−3.66528	−0.160118
$525$	4.82864	0.210739
$526$	5.74918	0.250676
$527$	−31.9301	−1.39090
$528$	0.828636	0.0360618
$529$	−19.8513	−0.863101
$530$	−4.87328	−0.211682
$531$	40.8410	1.77235
$532$	0	0
$533$	2.92382	0.126645
$534$	−2.56998	−0.111214
$535$	69.2256	2.99288
$536$	−4.58045	−0.197845
$537$	4.01573	0.173291
$538$	8.42218	0.363106
$539$	2.35227	0.101319
$540$	−8.95273	−0.385264
$541$	11.8411	0.509088	0.254544	−	0.967061i	$-0.418075\pi$
$541$	11.8411	0.509088	0.254544	+	0.967061i	$0.418075\pi$
$542$	−20.7298	−0.890422
$543$	1.15471	0.0495534
$544$	−6.22818	−0.267031
$545$	−31.3158	−1.34142
$546$	0.282361	0.0120839
$547$	35.4747	1.51679	0.758394	−	0.651796i	$-0.225984\pi$
$547$	35.4747	1.51679	0.758394	+	0.651796i	$0.225984\pi$
$548$	3.39691	0.145109
$549$	7.82847	0.334111
$550$	−32.2430	−1.37485
$551$	0	0
$552$	0.625088	0.0266055
$553$	−7.04727	−0.299680
$554$	−17.4442	−0.741132
$555$	16.2273	0.688808
$556$	−5.19663	−0.220386
$557$	11.6976	0.495644	0.247822	−	0.968806i	$-0.420285\pi$
$557$	11.6976	0.495644	0.247822	+	0.968806i	$0.420285\pi$
$558$	−14.7440	−0.624162
$559$	−0.699970	−0.0296056
$560$	4.32518	0.182772
$561$	5.16089	0.217893
$562$	−2.12409	−0.0895995
$563$	−12.2562	−0.516537	−0.258268	−	0.966073i	$-0.583152\pi$
$563$	−12.2562	−0.516537	−0.258268	+	0.966073i	$0.583152\pi$
$564$	−2.05418	−0.0864968
$565$	6.38554	0.268642
$566$	27.6696	1.16304
$567$	7.89855	0.331708
$568$	−14.0026	−0.587537
$569$	5.80862	0.243510	0.121755	−	0.992560i	$-0.461148\pi$
$569$	5.80862	0.243510	0.121755	+	0.992560i	$0.461148\pi$
$570$	0	0
$571$	37.2308	1.55806	0.779030	−	0.626986i	$-0.215712\pi$
$571$	37.2308	1.55806	0.779030	+	0.626986i	$0.215712\pi$
$572$	−1.88545	−0.0788346
$573$	−1.14088	−0.0476610
$574$	3.64773	0.152253
$575$	−24.3227	−1.01433
$576$	−2.87591	−0.119829
$577$	−17.3444	−0.722058	−0.361029	−	0.932555i	$-0.617574\pi$
$577$	−17.3444	−0.722058	−0.361029	+	0.932555i	$0.617574\pi$
$578$	−21.7902	−0.906352
$579$	4.24726	0.176510
$580$	25.2213	1.04726
$581$	15.5560	0.645371
$582$	−1.07683	−0.0446359
$583$	2.65036	0.109767
$584$	9.23080	0.381973
$585$	9.97025	0.412219
$586$	13.2326	0.546635
$587$	−33.7561	−1.39327	−0.696633	−	0.717428i	$-0.745319\pi$
$587$	−33.7561	−1.39327	−0.696633	+	0.717428i	$0.745319\pi$
$588$	0.352271	0.0145274
$589$	0	0
$590$	61.4222	2.52871
$591$	−7.37584	−0.303401
$592$	10.6504	0.437727
$593$	−15.5079	−0.636833	−0.318417	−	0.947951i	$-0.603151\pi$
$593$	−15.5079	−0.636833	−0.318417	+	0.947951i	$0.603151\pi$
$594$	4.86899	0.199777
$595$	26.9380	1.10435
$596$	14.6504	0.600102
$597$	3.21508	0.131584
$598$	−1.42230	−0.0581622
$599$	38.1215	1.55760	0.778801	−	0.627271i	$-0.215828\pi$
$599$	38.1215	1.55760	0.778801	+	0.627271i	$0.215828\pi$
$600$	−4.82864	−0.197128
$601$	13.4799	0.549857	0.274929	−	0.961465i	$-0.411346\pi$
$601$	13.4799	0.549857	0.274929	+	0.961465i	$0.411346\pi$
$602$	−0.873277	−0.0355921
$603$	−13.1729	−0.536443
$604$	5.46682	0.222442
$605$	−23.6450	−0.961305
$606$	−0.536732	−0.0218032
$607$	−6.25345	−0.253820	−0.126910	−	0.991914i	$-0.540506\pi$
$607$	−6.25345	−0.253820	−0.126910	+	0.991914i	$0.540506\pi$
$608$	0	0
$609$	2.05418	0.0832398
$610$	11.7735	0.476696
$611$	4.67402	0.189090
$612$	−17.9116	−0.724035
$613$	5.51999	0.222950	0.111475	−	0.993767i	$-0.464442\pi$
$613$	5.51999	0.222950	0.111475	+	0.993767i	$0.464442\pi$
$614$	−24.9398	−1.00649
$615$	−5.55781	−0.224112
$616$	−2.35227	−0.0947757
$617$	22.7823	0.917182	0.458591	−	0.888647i	$-0.348354\pi$
$617$	22.7823	0.917182	0.458591	+	0.888647i	$0.348354\pi$
$618$	4.05944	0.163295
$619$	−10.6879	−0.429584	−0.214792	−	0.976660i	$-0.568907\pi$
$619$	−10.6879	−0.429584	−0.214792	+	0.976660i	$0.568907\pi$
$620$	−22.1740	−0.890529
$621$	3.67296	0.147391
$622$	−15.9458	−0.639369
$623$	7.29546	0.292286
$624$	−0.282361	−0.0113035
$625$	94.3507	3.77403
$626$	12.7203	0.508404
$627$	0	0
$628$	−3.45190	−0.137746
$629$	66.3323	2.64484
$630$	12.4388	0.495574
$631$	−20.5069	−0.816366	−0.408183	−	0.912900i	$-0.633838\pi$
$631$	−20.5069	−0.816366	−0.408183	+	0.912900i	$0.633838\pi$
$632$	7.04727	0.280325
$633$	−1.40908	−0.0560060
$634$	32.9091	1.30699
$635$	−26.9493	−1.06945
$636$	0.396912	0.0157386
$637$	−0.801544	−0.0317583
$638$	−13.7167	−0.543050
$639$	−40.2702	−1.59307
$640$	−4.32518	−0.170968
$641$	22.3016	0.880862	0.440431	−	0.897787i	$-0.354826\pi$
$641$	22.3016	0.880862	0.440431	+	0.897787i	$0.354826\pi$
$642$	−5.63819	−0.222521
$643$	−2.79200	−0.110106	−0.0550529	−	0.998483i	$-0.517533\pi$
$643$	−2.79200	−0.110106	−0.0550529	+	0.998483i	$0.517533\pi$
$644$	−1.77445	−0.0699232
$645$	1.33056	0.0523906
$646$	0	0
$647$	−5.69144	−0.223754	−0.111877	−	0.993722i	$-0.535686\pi$
$647$	−5.69144	−0.223754	−0.111877	+	0.993722i	$0.535686\pi$
$648$	−7.89855	−0.310284
$649$	−33.4048	−1.31125
$650$	10.9869	0.430942
$651$	−1.80600	−0.0707825
$652$	8.65990	0.339148
$653$	0.485267	0.0189900	0.00949499	−	0.999955i	$-0.496978\pi$
$653$	0.485267	0.0189900	0.00949499	+	0.999955i	$0.496978\pi$
$654$	2.55056	0.0997349
$655$	−15.8530	−0.619427
$656$	−3.64773	−0.142420
$657$	26.5469	1.03569
$658$	5.83126	0.227326
$659$	−17.8023	−0.693481	−0.346741	−	0.937961i	$-0.612712\pi$
$659$	−17.8023	−0.693481	−0.346741	+	0.937961i	$0.612712\pi$
$660$	3.58400	0.139507
$661$	19.8793	0.773217	0.386608	−	0.922244i	$-0.373647\pi$
$661$	19.8793	0.773217	0.386608	+	0.922244i	$0.373647\pi$
$662$	19.0079	0.738762
$663$	−1.75859	−0.0682981
$664$	−15.5560	−0.603689
$665$	0	0
$666$	30.6294	1.18687
$667$	−10.3473	−0.400649
$668$	−6.05944	−0.234447
$669$	−4.31653	−0.166887
$670$	−19.8113	−0.765375
$671$	−6.40309	−0.247189
$672$	−0.352271	−0.0135891
$673$	−23.8339	−0.918729	−0.459365	−	0.888248i	$-0.651923\pi$
$673$	−23.8339	−0.918729	−0.459365	+	0.888248i	$0.651923\pi$
$674$	−28.1914	−1.08589
$675$	−28.3726	−1.09206
$676$	−12.3575	−0.475289
$677$	−24.7893	−0.952728	−0.476364	−	0.879248i	$-0.658046\pi$
$677$	−24.7893	−0.952728	−0.476364	+	0.879248i	$0.658046\pi$
$678$	−0.520081	−0.0199736
$679$	3.05681	0.117310
$680$	−26.9380	−1.03302
$681$	−8.22661	−0.315244
$682$	12.0594	0.461780
$683$	−39.3592	−1.50604	−0.753020	−	0.657998i	$-0.771403\pi$
$683$	−39.3592	−1.50604	−0.753020	+	0.657998i	$0.771403\pi$
$684$	0	0
$685$	14.6922	0.561362
$686$	−1.00000	−0.0381802
$687$	−9.11782	−0.347867
$688$	0.873277	0.0332934
$689$	−0.903118	−0.0344061
$690$	2.70362	0.102925
$691$	27.8226	1.05842	0.529211	−	0.848490i	$-0.322488\pi$
$691$	27.8226	1.05842	0.529211	+	0.848490i	$0.322488\pi$
$692$	15.6259	0.594007
$693$	−6.76491	−0.256978
$694$	−22.7292	−0.862787
$695$	−22.4764	−0.852577
$696$	−2.05418	−0.0778637
$697$	−22.7187	−0.860532
$698$	4.72981	0.179026
$699$	−0.916992	−0.0346838
$700$	13.7072	0.518082
$701$	−37.5332	−1.41761	−0.708805	−	0.705404i	$-0.750765\pi$
$701$	−37.5332	−1.41761	−0.708805	+	0.705404i	$0.750765\pi$
$702$	−1.65912	−0.0626196
$703$	0	0
$704$	2.35227	0.0886545
$705$	−8.88472	−0.334618
$706$	5.76135	0.216831
$707$	1.52363	0.0573022
$708$	−5.00263	−0.188010
$709$	11.3802	0.427391	0.213696	−	0.976900i	$-0.431450\pi$
$709$	11.3802	0.427391	0.213696	+	0.976900i	$0.431450\pi$
$710$	−60.5639	−2.27292
$711$	20.2673	0.760082
$712$	−7.29546	−0.273409
$713$	9.09712	0.340690
$714$	−2.19400	−0.0821086
$715$	−8.15490	−0.304976
$716$	11.3995	0.426021
$717$	−8.20019	−0.306242
$718$	19.9511	0.744567
$719$	−40.3218	−1.50375	−0.751874	−	0.659306i	$-0.770850\pi$
$719$	−40.3218	−1.50375	−0.751874	+	0.659306i	$0.770850\pi$
$720$	−12.4388	−0.463567
$721$	−11.5236	−0.429163
$722$	0	0
$723$	−3.15042	−0.117166
$724$	3.27791	0.121823
$725$	79.9301	2.96853
$726$	1.92580	0.0714732
$727$	1.55781	0.0577758	0.0288879	−	0.999583i	$-0.490803\pi$
$727$	1.55781	0.0577758	0.0288879	+	0.999583i	$0.490803\pi$
$728$	0.801544	0.0297072
$729$	−20.5280	−0.760295
$730$	39.9249	1.47769
$731$	5.43892	0.201166
$732$	−0.958913	−0.0354424
$733$	−22.7825	−0.841489	−0.420745	−	0.907179i	$-0.638231\pi$
$733$	−22.7825	−0.841489	−0.420745	+	0.907179i	$0.638231\pi$
$734$	1.24035	0.0457821
$735$	1.52363	0.0562001
$736$	1.77445	0.0654072
$737$	10.7745	0.396882
$738$	−10.4905	−0.386162
$739$	−2.64081	−0.0971439	−0.0485719	−	0.998820i	$-0.515467\pi$
$739$	−2.64081	−0.0971439	−0.0485719	+	0.998820i	$0.515467\pi$
$740$	46.0647	1.69337
$741$	0	0
$742$	−1.12672	−0.0413633
$743$	−18.7955	−0.689541	−0.344770	−	0.938687i	$-0.612043\pi$
$743$	−18.7955	−0.689541	−0.344770	+	0.938687i	$0.612043\pi$
$744$	1.80600	0.0662110
$745$	63.3654	2.32153
$746$	−24.8733	−0.910675
$747$	−44.7375	−1.63686
$748$	14.6504	0.535670
$749$	16.0053	0.584819
$750$	−13.2665	−0.484426
$751$	−42.6889	−1.55774	−0.778869	−	0.627186i	$-0.784206\pi$
$751$	−42.6889	−1.55774	−0.778869	+	0.627186i	$0.784206\pi$
$752$	−5.83126	−0.212644
$753$	9.64773	0.351583
$754$	4.67402	0.170218
$755$	23.6450	0.860529
$756$	−2.06991	−0.0752819
$757$	43.8374	1.59330	0.796650	−	0.604441i	$-0.206604\pi$
$757$	43.8374	1.59330	0.796650	+	0.604441i	$0.206604\pi$
$758$	−32.4274	−1.17782
$759$	−1.47038	−0.0533713
$760$	0	0
$761$	5.22462	0.189392	0.0946962	−	0.995506i	$-0.469812\pi$
$761$	5.22462	0.189392	0.0946962	+	0.995506i	$0.469812\pi$
$762$	2.19493	0.0795140
$763$	−7.24035	−0.262118
$764$	−3.23865	−0.117170
$765$	−77.4711	−2.80097
$766$	14.5105	0.524287
$767$	11.3828	0.411009
$768$	0.352271	0.0127115
$769$	−32.9678	−1.18885	−0.594425	−	0.804151i	$-0.702620\pi$
$769$	−32.9678	−1.18885	−0.594425	+	0.804151i	$0.702620\pi$
$770$	−10.1740	−0.366645
$771$	2.99152	0.107737
$772$	12.0568	0.433934
$773$	43.6906	1.57144	0.785721	−	0.618582i	$-0.212292\pi$
$773$	43.6906	1.57144	0.785721	+	0.618582i	$0.212292\pi$
$774$	2.51146	0.0902727
$775$	−70.2729	−2.52428
$776$	−3.05681	−0.109733
$777$	3.75181	0.134595
$778$	−25.5236	−0.915067
$779$	0	0
$780$	−1.22126	−0.0437281
$781$	32.9380	1.17861
$782$	11.0516	0.395204
$783$	−12.0702	−0.431354
$784$	1.00000	0.0357143
$785$	−14.9301	−0.532878
$786$	1.29117	0.0460545
$787$	26.7431	0.953288	0.476644	−	0.879097i	$-0.341853\pi$
$787$	26.7431	0.953288	0.476644	+	0.879097i	$0.341853\pi$
$788$	−20.9380	−0.745884
$789$	−2.02527	−0.0721015
$790$	30.4807	1.08445
$791$	1.47637	0.0524935
$792$	6.76491	0.240381
$793$	2.18188	0.0774807
$794$	−11.6373	−0.412991
$795$	1.71671	0.0608856
$796$	9.12672	0.323488
$797$	7.16861	0.253925	0.126963	−	0.991907i	$-0.459477\pi$
$797$	7.16861	0.253925	0.126963	+	0.991907i	$0.459477\pi$
$798$	0	0
$799$	−36.3181	−1.28484
$800$	−13.7072	−0.484622
$801$	−20.9810	−0.741329
$802$	25.1740	0.888925
$803$	−21.7134	−0.766248
$804$	1.61356	0.0569058
$805$	−7.67482	−0.270502
$806$	−4.10929	−0.144744
$807$	−2.96689	−0.104439
$808$	−1.52363	−0.0536013
$809$	1.58109	0.0555881	0.0277941	−	0.999614i	$-0.491152\pi$
$809$	1.58109	0.0555881	0.0277941	+	0.999614i	$0.491152\pi$
$810$	−34.1626	−1.20035
$811$	1.41001	0.0495121	0.0247561	−	0.999694i	$-0.492119\pi$
$811$	1.41001	0.0495121	0.0247561	+	0.999694i	$0.492119\pi$
$812$	5.83126	0.204637
$813$	7.30251	0.256110
$814$	−25.0525	−0.878091
$815$	37.4556	1.31201
$816$	2.19400	0.0768055
$817$	0	0
$818$	−31.6277	−1.10584
$819$	2.30517	0.0805490
$820$	−15.7771	−0.550960
$821$	−33.2114	−1.15909	−0.579543	−	0.814941i	$-0.696769\pi$
$821$	−33.2114	−1.15909	−0.579543	+	0.814941i	$0.696769\pi$
$822$	−1.19663	−0.0417374
$823$	−47.1198	−1.64249	−0.821247	−	0.570572i	$-0.806721\pi$
$823$	−47.1198	−1.64249	−0.821247	+	0.570572i	$0.806721\pi$
$824$	11.5236	0.401445
$825$	11.3583	0.395444
$826$	14.2011	0.494119
$827$	16.1284	0.560840	0.280420	−	0.959877i	$-0.409526\pi$
$827$	16.1284	0.560840	0.280420	+	0.959877i	$0.409526\pi$
$828$	5.10316	0.177347
$829$	46.9266	1.62983	0.814914	−	0.579582i	$-0.196784\pi$
$829$	46.9266	1.62983	0.814914	+	0.579582i	$0.196784\pi$
$830$	−67.2824	−2.33541
$831$	6.14508	0.213170
$832$	−0.801544	−0.0277885
$833$	6.22818	0.215794
$834$	1.83062	0.0633893
$835$	−26.2082	−0.906971
$836$	0	0
$837$	10.6119	0.366799
$838$	19.9205	0.688144
$839$	−8.19400	−0.282888	−0.141444	−	0.989946i	$-0.545175\pi$
$839$	−8.19400	−0.282888	−0.141444	+	0.989946i	$0.545175\pi$
$840$	−1.52363	−0.0525704
$841$	5.00365	0.172540
$842$	−14.4274	−0.497202
$843$	0.748257	0.0257713
$844$	−4.00000	−0.137686
$845$	−53.4485	−1.83868
$846$	−16.7702	−0.576570
$847$	−5.46682	−0.187842
$848$	1.12672	0.0386918
$849$	−9.74720	−0.334523
$850$	−85.3707	−2.92819
$851$	−18.8985	−0.647834
$852$	4.93272	0.168992
$853$	−16.7791	−0.574504	−0.287252	−	0.957855i	$-0.592742\pi$
$853$	−16.7791	−0.574504	−0.287252	+	0.957855i	$0.592742\pi$
$854$	2.72209	0.0931480
$855$	0	0
$856$	−16.0053	−0.547048
$857$	−9.47899	−0.323796	−0.161898	−	0.986807i	$-0.551762\pi$
$857$	−9.47899	−0.323796	−0.161898	+	0.986807i	$0.551762\pi$
$858$	0.664189	0.0226750
$859$	−5.59354	−0.190849	−0.0954246	−	0.995437i	$-0.530421\pi$
$859$	−5.59354	−0.190849	−0.0954246	+	0.995437i	$0.530421\pi$
$860$	3.77708	0.128797
$861$	−1.28499	−0.0437923
$862$	14.6504	0.498993
$863$	−46.1241	−1.57008	−0.785042	−	0.619443i	$-0.787359\pi$
$863$	−46.1241	−1.57008	−0.785042	+	0.619443i	$0.787359\pi$
$864$	2.06991	0.0704198
$865$	67.5848	2.29795
$866$	18.0043	0.611812
$867$	7.67604	0.260692
$868$	−5.12672	−0.174012
$869$	−16.5771	−0.562339
$870$	−8.88472	−0.301220
$871$	−3.67143	−0.124402
$872$	7.24035	0.245189
$873$	−8.79110	−0.297534
$874$	0	0
$875$	37.6601	1.27314
$876$	−3.25174	−0.109866
$877$	16.7982	0.567233	0.283617	−	0.958938i	$-0.408466\pi$
$877$	16.7982	0.567233	0.283617	+	0.958938i	$0.408466\pi$
$878$	21.6336	0.730099
$879$	−4.66147	−0.157227
$880$	10.1740	0.342965
$881$	−29.9153	−1.00787	−0.503937	−	0.863741i	$-0.668115\pi$
$881$	−29.9153	−1.00787	−0.503937	+	0.863741i	$0.668115\pi$
$882$	2.87591	0.0968368
$883$	−26.9284	−0.906214	−0.453107	−	0.891456i	$-0.649684\pi$
$883$	−26.9284	−0.906214	−0.453107	+	0.891456i	$0.649684\pi$
$884$	−4.99216	−0.167904
$885$	−21.6373	−0.727329
$886$	3.45465	0.116061
$887$	24.6907	0.829033	0.414516	−	0.910042i	$-0.363951\pi$
$887$	24.6907	0.829033	0.414516	+	0.910042i	$0.363951\pi$
$888$	−3.75181	−0.125903
$889$	−6.23080	−0.208974
$890$	−31.5542	−1.05770
$891$	18.5795	0.622437
$892$	−12.2534	−0.410276
$893$	0	0
$894$	−5.16089	−0.172606
$895$	49.3050	1.64809
$896$	−1.00000	−0.0334077
$897$	0.501035	0.0167291
$898$	19.5069	0.650953
$899$	−29.8953	−0.997063
$900$	−39.4205	−1.31402
$901$	7.01743	0.233784
$902$	8.58045	0.285698
$903$	0.307630	0.0102373
$904$	−1.47637	−0.0491032
$905$	14.1775	0.471278
$906$	−1.92580	−0.0639805
$907$	−36.1383	−1.19995	−0.599975	−	0.800018i	$-0.704823\pi$
$907$	−36.1383	−1.19995	−0.599975	+	0.800018i	$0.704823\pi$
$908$	−23.3531	−0.774999
$909$	−4.38183	−0.145336
$910$	3.46682	0.114924
$911$	−41.0210	−1.35909	−0.679543	−	0.733636i	$-0.737822\pi$
$911$	−41.0210	−1.35909	−0.679543	+	0.733636i	$0.737822\pi$
$912$	0	0
$913$	36.5919	1.21101
$914$	13.2876	0.439515
$915$	−4.14747	−0.137111
$916$	−25.8830	−0.855198
$917$	−3.66528	−0.121038
$918$	12.8918	0.425492
$919$	−19.4521	−0.641664	−0.320832	−	0.947136i	$-0.603963\pi$
$919$	−19.4521	−0.641664	−0.320832	+	0.947136i	$0.603963\pi$
$920$	7.67482	0.253031
$921$	8.78556	0.289494
$922$	−16.1915	−0.533240
$923$	−11.2237	−0.369433
$924$	0.828636	0.0272601
$925$	145.986	4.80000
$926$	−21.5010	−0.706566
$927$	33.1409	1.08849
$928$	−5.83126	−0.191421
$929$	8.86009	0.290690	0.145345	−	0.989381i	$-0.453571\pi$
$929$	8.86009	0.290690	0.145345	+	0.989381i	$0.453571\pi$
$930$	7.81125	0.256141
$931$	0	0
$932$	−2.60309	−0.0852670
$933$	5.61725	0.183900
$934$	7.95536	0.260307
$935$	63.3654	2.07227
$936$	−2.30517	−0.0753467
$937$	−35.7413	−1.16762	−0.583809	−	0.811891i	$-0.698438\pi$
$937$	−35.7413	−1.16762	−0.583809	+	0.811891i	$0.698438\pi$
$938$	−4.58045	−0.149557
$939$	−4.48098	−0.146231
$940$	−25.2213	−0.822627
$941$	40.6128	1.32394	0.661970	−	0.749531i	$-0.269721\pi$
$941$	40.6128	1.32394	0.661970	+	0.749531i	$0.269721\pi$
$942$	1.21600	0.0396196
$943$	6.47272	0.210781
$944$	−14.2011	−0.462206
$945$	−8.95273	−0.291232
$946$	−2.05418	−0.0667873
$947$	−41.3845	−1.34482	−0.672408	−	0.740181i	$-0.734740\pi$
$947$	−41.3845	−1.34482	−0.672408	+	0.740181i	$0.734740\pi$
$948$	−2.48255	−0.0806294
$949$	7.39890	0.240178
$950$	0	0
$951$	−11.5929	−0.375926
$952$	−6.22818	−0.201856
$953$	−5.45100	−0.176575	−0.0882877	−	0.996095i	$-0.528139\pi$
$953$	−5.45100	−0.176575	−0.0882877	+	0.996095i	$0.528139\pi$
$954$	3.24035	0.104910
$955$	−14.0077	−0.453279
$956$	−23.2781	−0.752867
$957$	4.83200	0.156196
$958$	26.6356	0.860557
$959$	3.39691	0.109692
$960$	1.52363	0.0491751
$961$	−4.71671	−0.152152
$962$	8.53673	0.275235
$963$	−46.0296	−1.48328
$964$	−8.94319	−0.288041
$965$	52.1479	1.67870
$966$	0.625088	0.0201119
$967$	1.62573	0.0522799	0.0261400	−	0.999658i	$-0.491678\pi$
$967$	1.62573	0.0522799	0.0261400	+	0.999658i	$0.491678\pi$
$968$	5.46682	0.175710
$969$	0	0
$970$	−13.2213	−0.424509
$971$	35.1634	1.12845	0.564224	−	0.825622i	$-0.309176\pi$
$971$	35.1634	1.12845	0.564224	+	0.825622i	$0.309176\pi$
$972$	8.99216	0.288424
$973$	−5.19663	−0.166596
$974$	−5.34964	−0.171414
$975$	−3.87037	−0.123951
$976$	−2.72209	−0.0871320
$977$	−37.2289	−1.19106	−0.595528	−	0.803334i	$-0.703057\pi$
$977$	−37.2289	−1.19106	−0.595528	+	0.803334i	$0.703057\pi$
$978$	−3.05063	−0.0975484
$979$	17.1609	0.548465
$980$	4.32518	0.138163
$981$	20.8226	0.664813
$982$	−0.456352	−0.0145628
$983$	−1.29546	−0.0413187	−0.0206594	−	0.999787i	$-0.506577\pi$
$983$	−1.29546	−0.0413187	−0.0206594	+	0.999787i	$0.506577\pi$
$984$	1.28499	0.0409639
$985$	−90.5605	−2.88550
$986$	−36.3181	−1.15661
$987$	−2.05418	−0.0653854
$988$	0	0
$989$	−1.54959	−0.0492740
$990$	29.2594	0.929926
$991$	13.7843	0.437872	0.218936	−	0.975739i	$-0.429741\pi$
$991$	13.7843	0.437872	0.218936	+	0.975739i	$0.429741\pi$
$992$	5.12672	0.162774
$993$	−6.69592	−0.212489
$994$	−14.0026	−0.444136
$995$	39.4747	1.25143
$996$	5.47992	0.173638
$997$	−0.857580	−0.0271598	−0.0135799	−	0.999908i	$-0.504323\pi$
$997$	−0.857580	−0.0271598	−0.0135799	+	0.999908i	$0.504323\pi$
$998$	5.99046	0.189625
$999$	−22.0453	−0.697482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.w.1.3		4
19.7	even	3		266.2.f.d.239.2	yes	8
19.11	even	3		266.2.f.d.197.2	✓	8
19.18	odd	2		5054.2.a.x.1.2		4
57.11	odd	6		2394.2.o.v.1261.4		8
57.26	odd	6		2394.2.o.v.505.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.f.d.197.2	✓	8	19.11	even	3
266.2.f.d.239.2	yes	8	19.7	even	3
2394.2.o.v.505.4		8	57.26	odd	6
2394.2.o.v.1261.4		8	57.11	odd	6
5054.2.a.w.1.3		4	1.1	even	1	trivial
5054.2.a.x.1.2		4	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.352271 q^{3} +1.00000 q^{4} +4.32518 q^{5} -0.352271 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.87591 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.352271 q^{3} +1.00000 q^{4} +4.32518 q^{5} -0.352271 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.87591 q^{9} -4.32518 q^{10} +2.35227 q^{11} +0.352271 q^{12} -0.801544 q^{13} -1.00000 q^{14} +1.52363 q^{15} +1.00000 q^{16} +6.22818 q^{17} +2.87591 q^{18} +4.32518 q^{20} +0.352271 q^{21} -2.35227 q^{22} -1.77445 q^{23} -0.352271 q^{24} +13.7072 q^{25} +0.801544 q^{26} -2.06991 q^{27} +1.00000 q^{28} +5.83126 q^{29} -1.52363 q^{30} -5.12672 q^{31} -1.00000 q^{32} +0.828636 q^{33} -6.22818 q^{34} +4.32518 q^{35} -2.87591 q^{36} +10.6504 q^{37} -0.282361 q^{39} -4.32518 q^{40} -3.64773 q^{41} -0.352271 q^{42} +0.873277 q^{43} +2.35227 q^{44} -12.4388 q^{45} +1.77445 q^{46} -5.83126 q^{47} +0.352271 q^{48} +1.00000 q^{49} -13.7072 q^{50} +2.19400 q^{51} -0.801544 q^{52} +1.12672 q^{53} +2.06991 q^{54} +10.1740 q^{55} -1.00000 q^{56} -5.83126 q^{58} -14.2011 q^{59} +1.52363 q^{60} -2.72209 q^{61} +5.12672 q^{62} -2.87591 q^{63} +1.00000 q^{64} -3.46682 q^{65} -0.828636 q^{66} +4.58045 q^{67} +6.22818 q^{68} -0.625088 q^{69} -4.32518 q^{70} +14.0026 q^{71} +2.87591 q^{72} -9.23080 q^{73} -10.6504 q^{74} +4.82864 q^{75} +2.35227 q^{77} +0.282361 q^{78} -7.04727 q^{79} +4.32518 q^{80} +7.89855 q^{81} +3.64773 q^{82} +15.5560 q^{83} +0.352271 q^{84} +26.9380 q^{85} -0.873277 q^{86} +2.05418 q^{87} -2.35227 q^{88} +7.29546 q^{89} +12.4388 q^{90} -0.801544 q^{91} -1.77445 q^{92} -1.80600 q^{93} +5.83126 q^{94} -0.352271 q^{96} +3.05681 q^{97} -1.00000 q^{98} -6.76491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} - 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 - 4 * q^8 + 9 * q^9	\( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + q^{5} + q^{6} + 4 q^{7} - 4 q^{8} + 9 q^{9} - q^{10} + 7 q^{11} - q^{12} - 5 q^{13} - 4 q^{14} - 12 q^{15} + 4 q^{16} + 2 q^{17} - 9 q^{18} + q^{20} - q^{21} - 7 q^{22} + 5 q^{23} + q^{24} + 15 q^{25} + 5 q^{26} - q^{27} + 4 q^{28} + 4 q^{29} + 12 q^{30} - 6 q^{31} - 4 q^{32} + 19 q^{33} - 2 q^{34} + q^{35} + 9 q^{36} + 10 q^{37} - 6 q^{39} - q^{40} - 17 q^{41} + q^{42} + 18 q^{43} + 7 q^{44} - 19 q^{45} - 5 q^{46} - 4 q^{47} - q^{48} + 4 q^{49} - 15 q^{50} + 22 q^{51} - 5 q^{52} - 10 q^{53} + q^{54} - 10 q^{55} - 4 q^{56} - 4 q^{58} - 20 q^{59} - 12 q^{60} + 9 q^{61} + 6 q^{62} + 9 q^{63} + 4 q^{64} - 3 q^{65} - 19 q^{66} - 7 q^{67} + 2 q^{68} + 24 q^{69} - q^{70} + 21 q^{71} - 9 q^{72} + 21 q^{73} - 10 q^{74} + 35 q^{75} + 7 q^{77} + 6 q^{78} + 8 q^{79} + q^{80} + 40 q^{81} + 17 q^{82} - 12 q^{83} - q^{84} + 10 q^{85} - 18 q^{86} + 36 q^{87} - 7 q^{88} + 34 q^{89} + 19 q^{90} - 5 q^{91} + 5 q^{92} + 6 q^{93} + 4 q^{94} + q^{96} + 5 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - q^3 + 4 * q^4 + q^5 + q^6 + 4 * q^7 - 4 * q^8 + 9 * q^9 - q^10 + 7 * q^11 - q^12 - 5 * q^13 - 4 * q^14 - 12 * q^15 + 4 * q^16 + 2 * q^17 - 9 * q^18 + q^20 - q^21 - 7 * q^22 + 5 * q^23 + q^24 + 15 * q^25 + 5 * q^26 - q^27 + 4 * q^28 + 4 * q^29 + 12 * q^30 - 6 * q^31 - 4 * q^32 + 19 * q^33 - 2 * q^34 + q^35 + 9 * q^36 + 10 * q^37 - 6 * q^39 - q^40 - 17 * q^41 + q^42 + 18 * q^43 + 7 * q^44 - 19 * q^45 - 5 * q^46 - 4 * q^47 - q^48 + 4 * q^49 - 15 * q^50 + 22 * q^51 - 5 * q^52 - 10 * q^53 + q^54 - 10 * q^55 - 4 * q^56 - 4 * q^58 - 20 * q^59 - 12 * q^60 + 9 * q^61 + 6 * q^62 + 9 * q^63 + 4 * q^64 - 3 * q^65 - 19 * q^66 - 7 * q^67 + 2 * q^68 + 24 * q^69 - q^70 + 21 * q^71 - 9 * q^72 + 21 * q^73 - 10 * q^74 + 35 * q^75 + 7 * q^77 + 6 * q^78 + 8 * q^79 + q^80 + 40 * q^81 + 17 * q^82 - 12 * q^83 - q^84 + 10 * q^85 - 18 * q^86 + 36 * q^87 - 7 * q^88 + 34 * q^89 + 19 * q^90 - 5 * q^91 + 5 * q^92 + 6 * q^93 + 4 * q^94 + q^96 + 5 * q^97 - 4 * q^98 + 14 * q^99

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