LMFDB - Embedded newform 6026.2.a.j.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.82338 q^{3} +1.00000 q^{4} -3.52183 q^{5} +2.82338 q^{6} +3.82891 q^{7} -1.00000 q^{8} +4.97150 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.82338 q^{3} +1.00000 q^{4} -3.52183 q^{5} +2.82338 q^{6} +3.82891 q^{7} -1.00000 q^{8} +4.97150 q^{9} +3.52183 q^{10} +0.327645 q^{11} -2.82338 q^{12} -0.108441 q^{13} -3.82891 q^{14} +9.94347 q^{15} +1.00000 q^{16} -7.83336 q^{17} -4.97150 q^{18} +2.78922 q^{19} -3.52183 q^{20} -10.8105 q^{21} -0.327645 q^{22} +1.00000 q^{23} +2.82338 q^{24} +7.40326 q^{25} +0.108441 q^{26} -5.56629 q^{27} +3.82891 q^{28} +7.73834 q^{29} -9.94347 q^{30} -3.33898 q^{31} -1.00000 q^{32} -0.925067 q^{33} +7.83336 q^{34} -13.4848 q^{35} +4.97150 q^{36} +5.79036 q^{37} -2.78922 q^{38} +0.306172 q^{39} +3.52183 q^{40} +8.97054 q^{41} +10.8105 q^{42} +6.14168 q^{43} +0.327645 q^{44} -17.5088 q^{45} -1.00000 q^{46} -7.13394 q^{47} -2.82338 q^{48} +7.66057 q^{49} -7.40326 q^{50} +22.1166 q^{51} -0.108441 q^{52} -1.61791 q^{53} +5.56629 q^{54} -1.15391 q^{55} -3.82891 q^{56} -7.87505 q^{57} -7.73834 q^{58} -6.37283 q^{59} +9.94347 q^{60} +14.3096 q^{61} +3.33898 q^{62} +19.0354 q^{63} +1.00000 q^{64} +0.381912 q^{65} +0.925067 q^{66} -2.59437 q^{67} -7.83336 q^{68} -2.82338 q^{69} +13.4848 q^{70} +6.48082 q^{71} -4.97150 q^{72} -12.2329 q^{73} -5.79036 q^{74} -20.9023 q^{75} +2.78922 q^{76} +1.25452 q^{77} -0.306172 q^{78} +15.3404 q^{79} -3.52183 q^{80} +0.801293 q^{81} -8.97054 q^{82} -4.17194 q^{83} -10.8105 q^{84} +27.5877 q^{85} -6.14168 q^{86} -21.8483 q^{87} -0.327645 q^{88} -15.5053 q^{89} +17.5088 q^{90} -0.415212 q^{91} +1.00000 q^{92} +9.42721 q^{93} +7.13394 q^{94} -9.82317 q^{95} +2.82338 q^{96} -14.4465 q^{97} -7.66057 q^{98} +1.62888 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) $ 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * 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
$3$	−2.82338	−1.63008	−0.815041	−	0.579404i	$-0.803286\pi$
$3$	−2.82338	−1.63008	−0.815041	+	0.579404i	$0.803286\pi$
$4$	1.00000	0.500000
$5$	−3.52183	−1.57501	−0.787504	−	0.616309i	$-0.788627\pi$
$5$	−3.52183	−1.57501	−0.787504	+	0.616309i	$0.788627\pi$
$6$	2.82338	1.15264
$7$	3.82891	1.44719	0.723597	−	0.690223i	$-0.242488\pi$
$7$	3.82891	1.44719	0.723597	+	0.690223i	$0.242488\pi$
$8$	−1.00000	−0.353553
$9$	4.97150	1.65717
$10$	3.52183	1.11370
$11$	0.327645	0.0987886	0.0493943	−	0.998779i	$-0.484271\pi$
$11$	0.327645	0.0987886	0.0493943	+	0.998779i	$0.484271\pi$
$12$	−2.82338	−0.815041
$13$	−0.108441	−0.0300762	−0.0150381	−	0.999887i	$-0.504787\pi$
$13$	−0.108441	−0.0300762	−0.0150381	+	0.999887i	$0.504787\pi$
$14$	−3.82891	−1.02332
$15$	9.94347	2.56739
$16$	1.00000	0.250000
$17$	−7.83336	−1.89987	−0.949934	−	0.312450i	$-0.898850\pi$
$17$	−7.83336	−1.89987	−0.949934	+	0.312450i	$0.898850\pi$
$18$	−4.97150	−1.17179
$19$	2.78922	0.639892	0.319946	−	0.947436i	$-0.396335\pi$
$19$	2.78922	0.639892	0.319946	+	0.947436i	$0.396335\pi$
$20$	−3.52183	−0.787504
$21$	−10.8105	−2.35904
$22$	−0.327645	−0.0698541
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.82338	0.576321
$25$	7.40326	1.48065
$26$	0.108441	0.0212671
$27$	−5.56629	−1.07123
$28$	3.82891	0.723597
$29$	7.73834	1.43697	0.718487	−	0.695541i	$-0.244835\pi$
$29$	7.73834	1.43697	0.718487	+	0.695541i	$0.244835\pi$
$30$	−9.94347	−1.81542
$31$	−3.33898	−0.599698	−0.299849	−	0.953987i	$-0.596936\pi$
$31$	−3.33898	−0.599698	−0.299849	+	0.953987i	$0.596936\pi$
$32$	−1.00000	−0.176777
$33$	−0.925067	−0.161033
$34$	7.83336	1.34341
$35$	−13.4848	−2.27934
$36$	4.97150	0.828583
$37$	5.79036	0.951929	0.475964	−	0.879464i	$-0.342099\pi$
$37$	5.79036	0.951929	0.475964	+	0.879464i	$0.342099\pi$
$38$	−2.78922	−0.452472
$39$	0.306172	0.0490267
$40$	3.52183	0.556850
$41$	8.97054	1.40096	0.700481	−	0.713671i	$-0.252969\pi$
$41$	8.97054	1.40096	0.700481	+	0.713671i	$0.252969\pi$
$42$	10.8105	1.66810
$43$	6.14168	0.936597	0.468298	−	0.883570i	$-0.344867\pi$
$43$	6.14168	0.936597	0.468298	+	0.883570i	$0.344867\pi$
$44$	0.327645	0.0493943
$45$	−17.5088	−2.61005
$46$	−1.00000	−0.147442
$47$	−7.13394	−1.04059	−0.520296	−	0.853986i	$-0.674178\pi$
$47$	−7.13394	−1.04059	−0.520296	+	0.853986i	$0.674178\pi$
$48$	−2.82338	−0.407520
$49$	7.66057	1.09437
$50$	−7.40326	−1.04698
$51$	22.1166	3.09694
$52$	−0.108441	−0.0150381
$53$	−1.61791	−0.222237	−0.111119	−	0.993807i	$-0.535443\pi$
$53$	−1.61791	−0.222237	−0.111119	+	0.993807i	$0.535443\pi$
$54$	5.56629	0.757477
$55$	−1.15391	−0.155593
$56$	−3.82891	−0.511660
$57$	−7.87505	−1.04308
$58$	−7.73834	−1.01609
$59$	−6.37283	−0.829671	−0.414836	−	0.909896i	$-0.636161\pi$
$59$	−6.37283	−0.829671	−0.414836	+	0.909896i	$0.636161\pi$
$60$	9.94347	1.28370
$61$	14.3096	1.83216	0.916080	−	0.400995i	$-0.131336\pi$
$61$	14.3096	1.83216	0.916080	+	0.400995i	$0.131336\pi$
$62$	3.33898	0.424050
$63$	19.0354	2.39824
$64$	1.00000	0.125000
$65$	0.381912	0.0473703
$66$	0.925067	0.113868
$67$	−2.59437	−0.316953	−0.158476	−	0.987363i	$-0.550658\pi$
$67$	−2.59437	−0.316953	−0.158476	+	0.987363i	$0.550658\pi$
$68$	−7.83336	−0.949934
$69$	−2.82338	−0.339895
$70$	13.4848	1.61174
$71$	6.48082	0.769131	0.384566	−	0.923098i	$-0.374351\pi$
$71$	6.48082	0.769131	0.384566	+	0.923098i	$0.374351\pi$
$72$	−4.97150	−0.585897
$73$	−12.2329	−1.43175	−0.715877	−	0.698226i	$-0.753973\pi$
$73$	−12.2329	−1.43175	−0.715877	+	0.698226i	$0.753973\pi$
$74$	−5.79036	−0.673115
$75$	−20.9023	−2.41358
$76$	2.78922	0.319946
$77$	1.25452	0.142966
$78$	−0.306172	−0.0346671
$79$	15.3404	1.72593	0.862967	−	0.505261i	$-0.168604\pi$
$79$	15.3404	1.72593	0.862967	+	0.505261i	$0.168604\pi$
$80$	−3.52183	−0.393752
$81$	0.801293	0.0890326
$82$	−8.97054	−0.990630
$83$	−4.17194	−0.457930	−0.228965	−	0.973435i	$-0.573534\pi$
$83$	−4.17194	−0.457930	−0.228965	+	0.973435i	$0.573534\pi$
$84$	−10.8105	−1.17952
$85$	27.5877	2.99231
$86$	−6.14168	−0.662274
$87$	−21.8483	−2.34238
$88$	−0.327645	−0.0349270
$89$	−15.5053	−1.64356	−0.821780	−	0.569805i	$-0.807019\pi$
$89$	−15.5053	−1.64356	−0.821780	+	0.569805i	$0.807019\pi$
$90$	17.5088	1.84558
$91$	−0.415212	−0.0435261
$92$	1.00000	0.104257
$93$	9.42721	0.977556
$94$	7.13394	0.735810
$95$	−9.82317	−1.00784
$96$	2.82338	0.288160
$97$	−14.4465	−1.46682	−0.733409	−	0.679788i	$-0.762072\pi$
$97$	−14.4465	−1.46682	−0.733409	+	0.679788i	$0.762072\pi$
$98$	−7.66057	−0.773835
$99$	1.62888	0.163709
$100$	7.40326	0.740326
$101$	0.345923	0.0344206	0.0172103	−	0.999852i	$-0.494522\pi$
$101$	0.345923	0.0344206	0.0172103	+	0.999852i	$0.494522\pi$
$102$	−22.1166	−2.18987
$103$	−15.8530	−1.56204	−0.781020	−	0.624506i	$-0.785301\pi$
$103$	−15.8530	−1.56204	−0.781020	+	0.624506i	$0.785301\pi$
$104$	0.108441	0.0106335
$105$	38.0727	3.71551
$106$	1.61791	0.157146
$107$	7.18900	0.694987	0.347494	−	0.937682i	$-0.387033\pi$
$107$	7.18900	0.694987	0.347494	+	0.937682i	$0.387033\pi$
$108$	−5.56629	−0.535617
$109$	19.8013	1.89662	0.948308	−	0.317350i	$-0.102793\pi$
$109$	19.8013	1.89662	0.948308	+	0.317350i	$0.102793\pi$
$110$	1.15391	0.110021
$111$	−16.3484	−1.55172
$112$	3.82891	0.361798
$113$	7.18913	0.676297	0.338148	−	0.941093i	$-0.390199\pi$
$113$	7.18913	0.676297	0.338148	+	0.941093i	$0.390199\pi$
$114$	7.87505	0.737566
$115$	−3.52183	−0.328412
$116$	7.73834	0.718487
$117$	−0.539116	−0.0498413
$118$	6.37283	0.586666
$119$	−29.9932	−2.74948
$120$	−9.94347	−0.907710
$121$	−10.8926	−0.990241
$122$	−14.3096	−1.29553
$123$	−25.3273	−2.28368
$124$	−3.33898	−0.299849
$125$	−8.46387	−0.757032
$126$	−19.0354	−1.69581
$127$	−2.27012	−0.201440	−0.100720	−	0.994915i	$-0.532115\pi$
$127$	−2.27012	−0.201440	−0.100720	+	0.994915i	$0.532115\pi$
$128$	−1.00000	−0.0883883
$129$	−17.3403	−1.52673
$130$	−0.381912	−0.0334959
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−0.925067	−0.0805167
$133$	10.6797	0.926047
$134$	2.59437	0.224120
$135$	19.6035	1.68720
$136$	7.83336	0.671705
$137$	1.74105	0.148748	0.0743739	−	0.997230i	$-0.476304\pi$
$137$	1.74105	0.148748	0.0743739	+	0.997230i	$0.476304\pi$
$138$	2.82338	0.240342
$139$	−18.8368	−1.59772	−0.798858	−	0.601519i	$-0.794562\pi$
$139$	−18.8368	−1.59772	−0.798858	+	0.601519i	$0.794562\pi$
$140$	−13.4848	−1.13967
$141$	20.1419	1.69625
$142$	−6.48082	−0.543858
$143$	−0.0355302	−0.00297119
$144$	4.97150	0.414291
$145$	−27.2531	−2.26325
$146$	12.2329	1.01240
$147$	−21.6287	−1.78391
$148$	5.79036	0.475964
$149$	−9.45510	−0.774592	−0.387296	−	0.921956i	$-0.626591\pi$
$149$	−9.45510	−0.774592	−0.387296	+	0.921956i	$0.626591\pi$
$150$	20.9023	1.70666
$151$	−9.42429	−0.766938	−0.383469	−	0.923554i	$-0.625271\pi$
$151$	−9.42429	−0.766938	−0.383469	+	0.923554i	$0.625271\pi$
$152$	−2.78922	−0.226236
$153$	−38.9435	−3.14840
$154$	−1.25452	−0.101092
$155$	11.7593	0.944529
$156$	0.306172	0.0245133
$157$	18.5085	1.47714	0.738570	−	0.674176i	$-0.235501\pi$
$157$	18.5085	1.47714	0.738570	+	0.674176i	$0.235501\pi$
$158$	−15.3404	−1.22042
$159$	4.56799	0.362265
$160$	3.52183	0.278425
$161$	3.82891	0.301761
$162$	−0.801293	−0.0629556
$163$	−21.3899	−1.67538	−0.837691	−	0.546144i	$-0.816095\pi$
$163$	−21.3899	−1.67538	−0.837691	+	0.546144i	$0.816095\pi$
$164$	8.97054	0.700481
$165$	3.25792	0.253629
$166$	4.17194	0.323806
$167$	23.2285	1.79748	0.898739	−	0.438484i	$-0.144484\pi$
$167$	23.2285	1.79748	0.898739	+	0.438484i	$0.144484\pi$
$168$	10.8105	0.834048
$169$	−12.9882	−0.999095
$170$	−27.5877	−2.11588
$171$	13.8666	1.06041
$172$	6.14168	0.468298
$173$	−0.832202	−0.0632711	−0.0316356	−	0.999499i	$-0.510072\pi$
$173$	−0.832202	−0.0632711	−0.0316356	+	0.999499i	$0.510072\pi$
$174$	21.8483	1.65632
$175$	28.3464	2.14279
$176$	0.327645	0.0246971
$177$	17.9929	1.35243
$178$	15.5053	1.16217
$179$	−6.75994	−0.505262	−0.252631	−	0.967563i	$-0.581296\pi$
$179$	−6.75994	−0.505262	−0.252631	+	0.967563i	$0.581296\pi$
$180$	−17.5088	−1.30503
$181$	−0.129846	−0.00965138	−0.00482569	−	0.999988i	$-0.501536\pi$
$181$	−0.129846	−0.00965138	−0.00482569	+	0.999988i	$0.501536\pi$
$182$	0.415212	0.0307776
$183$	−40.4016	−2.98657
$184$	−1.00000	−0.0737210
$185$	−20.3926	−1.49930
$186$	−9.42721	−0.691237
$187$	−2.56656	−0.187685
$188$	−7.13394	−0.520296
$189$	−21.3129	−1.55028
$190$	9.82317	0.712647
$191$	−11.7767	−0.852135	−0.426068	−	0.904691i	$-0.640101\pi$
$191$	−11.7767	−0.852135	−0.426068	+	0.904691i	$0.640101\pi$
$192$	−2.82338	−0.203760
$193$	4.89866	0.352614	0.176307	−	0.984335i	$-0.443585\pi$
$193$	4.89866	0.352614	0.176307	+	0.984335i	$0.443585\pi$
$194$	14.4465	1.03720
$195$	−1.07828	−0.0772175
$196$	7.66057	0.547184
$197$	15.7886	1.12489	0.562447	−	0.826833i	$-0.309860\pi$
$197$	15.7886	1.12489	0.562447	+	0.826833i	$0.309860\pi$
$198$	−1.62888	−0.115760
$199$	5.39743	0.382614	0.191307	−	0.981530i	$-0.438727\pi$
$199$	5.39743	0.382614	0.191307	+	0.981530i	$0.438727\pi$
$200$	−7.40326	−0.523490
$201$	7.32491	0.516659
$202$	−0.345923	−0.0243390
$203$	29.6294	2.07958
$204$	22.1166	1.54847
$205$	−31.5927	−2.20653
$206$	15.8530	1.10453
$207$	4.97150	0.345543
$208$	−0.108441	−0.00751906
$209$	0.913875	0.0632140
$210$	−38.0727	−2.62726
$211$	−15.2139	−1.04737	−0.523685	−	0.851912i	$-0.675443\pi$
$211$	−15.2139	−1.04737	−0.523685	+	0.851912i	$0.675443\pi$
$212$	−1.61791	−0.111119
$213$	−18.2978	−1.25375
$214$	−7.18900	−0.491430
$215$	−21.6299	−1.47515
$216$	5.56629	0.378738
$217$	−12.7846	−0.867878
$218$	−19.8013	−1.34111
$219$	34.5382	2.33388
$220$	−1.15391	−0.0777964
$221$	0.849460	0.0571409
$222$	16.3484	1.09723
$223$	16.6498	1.11495	0.557477	−	0.830193i	$-0.311770\pi$
$223$	16.6498	1.11495	0.557477	+	0.830193i	$0.311770\pi$
$224$	−3.82891	−0.255830
$225$	36.8053	2.45369
$226$	−7.18913	−0.478214
$227$	−1.51893	−0.100815	−0.0504076	−	0.998729i	$-0.516052\pi$
$227$	−1.51893	−0.100815	−0.0504076	+	0.998729i	$0.516052\pi$
$228$	−7.87505	−0.521538
$229$	12.8755	0.850836	0.425418	−	0.904997i	$-0.360127\pi$
$229$	12.8755	0.850836	0.425418	+	0.904997i	$0.360127\pi$
$230$	3.52183	0.232222
$231$	−3.54200	−0.233046
$232$	−7.73834	−0.508047
$233$	−23.4391	−1.53555	−0.767773	−	0.640722i	$-0.778635\pi$
$233$	−23.4391	−1.53555	−0.767773	+	0.640722i	$0.778635\pi$
$234$	0.539116	0.0352431
$235$	25.1245	1.63894
$236$	−6.37283	−0.414836
$237$	−43.3119	−2.81341
$238$	29.9932	1.94417
$239$	−14.8386	−0.959828	−0.479914	−	0.877316i	$-0.659332\pi$
$239$	−14.8386	−0.959828	−0.479914	+	0.877316i	$0.659332\pi$
$240$	9.94347	0.641848
$241$	−20.0939	−1.29436	−0.647181	−	0.762336i	$-0.724052\pi$
$241$	−20.0939	−1.29436	−0.647181	+	0.762336i	$0.724052\pi$
$242$	10.8926	0.700206
$243$	14.4365	0.926103
$244$	14.3096	0.916080
$245$	−26.9792	−1.72364
$246$	25.3273	1.61481
$247$	−0.302467	−0.0192455
$248$	3.33898	0.212025
$249$	11.7790	0.746464
$250$	8.46387	0.535302
$251$	4.94950	0.312410	0.156205	−	0.987725i	$-0.450074\pi$
$251$	4.94950	0.312410	0.156205	+	0.987725i	$0.450074\pi$
$252$	19.0354	1.19912
$253$	0.327645	0.0205988
$254$	2.27012	0.142440
$255$	−77.8908	−4.87771
$256$	1.00000	0.0625000
$257$	2.49348	0.155539	0.0777696	−	0.996971i	$-0.475220\pi$
$257$	2.49348	0.155539	0.0777696	+	0.996971i	$0.475220\pi$
$258$	17.3403	1.07956
$259$	22.1708	1.37763
$260$	0.381912	0.0236852
$261$	38.4711	2.38130
$262$	1.00000	0.0617802
$263$	−0.792876	−0.0488908	−0.0244454	−	0.999701i	$-0.507782\pi$
$263$	−0.792876	−0.0488908	−0.0244454	+	0.999701i	$0.507782\pi$
$264$	0.925067	0.0569339
$265$	5.69801	0.350026
$266$	−10.6797	−0.654814
$267$	43.7775	2.67914
$268$	−2.59437	−0.158476
$269$	−16.4054	−1.00026	−0.500128	−	0.865952i	$-0.666714\pi$
$269$	−16.4054	−1.00026	−0.500128	+	0.865952i	$0.666714\pi$
$270$	−19.6035	−1.19303
$271$	4.83470	0.293687	0.146843	−	0.989160i	$-0.453089\pi$
$271$	4.83470	0.293687	0.146843	+	0.989160i	$0.453089\pi$
$272$	−7.83336	−0.474967
$273$	1.17230	0.0709511
$274$	−1.74105	−0.105181
$275$	2.42564	0.146272
$276$	−2.82338	−0.169948
$277$	−25.4805	−1.53097	−0.765487	−	0.643451i	$-0.777502\pi$
$277$	−25.4805	−1.53097	−0.765487	+	0.643451i	$0.777502\pi$
$278$	18.8368	1.12976
$279$	−16.5997	−0.993799
$280$	13.4848	0.805869
$281$	29.3759	1.75242	0.876208	−	0.481932i	$-0.160065\pi$
$281$	29.3759	1.75242	0.876208	+	0.481932i	$0.160065\pi$
$282$	−20.1419	−1.19943
$283$	12.4878	0.742322	0.371161	−	0.928569i	$-0.378960\pi$
$283$	12.4878	0.742322	0.371161	+	0.928569i	$0.378960\pi$
$284$	6.48082	0.384566
$285$	27.7346	1.64285
$286$	0.0355302	0.00210095
$287$	34.3474	2.02746
$288$	−4.97150	−0.292948
$289$	44.3615	2.60950
$290$	27.2531	1.60036
$291$	40.7880	2.39103
$292$	−12.2329	−0.715877
$293$	25.8775	1.51178	0.755889	−	0.654700i	$-0.227205\pi$
$293$	25.8775	1.51178	0.755889	+	0.654700i	$0.227205\pi$
$294$	21.6287	1.26141
$295$	22.4440	1.30674
$296$	−5.79036	−0.336558
$297$	−1.82377	−0.105826
$298$	9.45510	0.547719
$299$	−0.108441	−0.00627133
$300$	−20.9023	−1.20679
$301$	23.5159	1.35544
$302$	9.42429	0.542307
$303$	−0.976673	−0.0561084
$304$	2.78922	0.159973
$305$	−50.3960	−2.88567
$306$	38.9435	2.22625
$307$	19.7923	1.12960	0.564802	−	0.825226i	$-0.308953\pi$
$307$	19.7923	1.12960	0.564802	+	0.825226i	$0.308953\pi$
$308$	1.25452	0.0714831
$309$	44.7591	2.54625
$310$	−11.7593	−0.667883
$311$	25.2663	1.43272	0.716359	−	0.697732i	$-0.245807\pi$
$311$	25.2663	1.43272	0.716359	+	0.697732i	$0.245807\pi$
$312$	−0.306172	−0.0173336
$313$	20.0872	1.13539	0.567697	−	0.823237i	$-0.307834\pi$
$313$	20.0872	1.13539	0.567697	+	0.823237i	$0.307834\pi$
$314$	−18.5085	−1.04450
$315$	−67.0395	−3.77725
$316$	15.3404	0.862967
$317$	18.2957	1.02759	0.513795	−	0.857913i	$-0.328239\pi$
$317$	18.2957	1.02759	0.513795	+	0.857913i	$0.328239\pi$
$318$	−4.56799	−0.256160
$319$	2.53542	0.141957
$320$	−3.52183	−0.196876
$321$	−20.2973	−1.13289
$322$	−3.82891	−0.213377
$323$	−21.8490	−1.21571
$324$	0.801293	0.0445163
$325$	−0.802820	−0.0445324
$326$	21.3899	1.18467
$327$	−55.9066	−3.09164
$328$	−8.97054	−0.495315
$329$	−27.3152	−1.50594
$330$	−3.25792	−0.179343
$331$	19.4867	1.07109	0.535543	−	0.844508i	$-0.320107\pi$
$331$	19.4867	1.07109	0.535543	+	0.844508i	$0.320107\pi$
$332$	−4.17194	−0.228965
$333$	28.7867	1.57750
$334$	−23.2285	−1.27101
$335$	9.13693	0.499204
$336$	−10.8105	−0.589761
$337$	26.9904	1.47026	0.735131	−	0.677925i	$-0.237121\pi$
$337$	26.9904	1.47026	0.735131	+	0.677925i	$0.237121\pi$
$338$	12.9882	0.706467
$339$	−20.2977	−1.10242
$340$	27.5877	1.49615
$341$	−1.09400	−0.0592433
$342$	−13.8666	−0.749821
$343$	2.52928	0.136568
$344$	−6.14168	−0.331137
$345$	9.94347	0.535338
$346$	0.832202	0.0447395
$347$	12.4498	0.668342	0.334171	−	0.942512i	$-0.391544\pi$
$347$	12.4498	0.668342	0.334171	+	0.942512i	$0.391544\pi$
$348$	−21.8483	−1.17119
$349$	24.1424	1.29232	0.646158	−	0.763204i	$-0.276375\pi$
$349$	24.1424	1.29232	0.646158	+	0.763204i	$0.276375\pi$
$350$	−28.3464	−1.51518
$351$	0.603616	0.0322187
$352$	−0.327645	−0.0174635
$353$	−32.0487	−1.70578	−0.852889	−	0.522092i	$-0.825152\pi$
$353$	−32.0487	−1.70578	−0.852889	+	0.522092i	$0.825152\pi$
$354$	−17.9929	−0.956314
$355$	−22.8243	−1.21139
$356$	−15.5053	−0.821780
$357$	84.6825	4.48187
$358$	6.75994	0.357274
$359$	−0.472858	−0.0249565	−0.0124783	−	0.999922i	$-0.503972\pi$
$359$	−0.472858	−0.0249565	−0.0124783	+	0.999922i	$0.503972\pi$
$360$	17.5088	0.922792
$361$	−11.2202	−0.590538
$362$	0.129846	0.00682456
$363$	30.7541	1.61417
$364$	−0.415212	−0.0217630
$365$	43.0822	2.25503
$366$	40.4016	2.11182
$367$	−12.9466	−0.675808	−0.337904	−	0.941181i	$-0.609718\pi$
$367$	−12.9466	−0.675808	−0.337904	+	0.941181i	$0.609718\pi$
$368$	1.00000	0.0521286
$369$	44.5970	2.32163
$370$	20.3926	1.06016
$371$	−6.19485	−0.321621
$372$	9.42721	0.488778
$373$	−27.7659	−1.43766	−0.718831	−	0.695185i	$-0.755322\pi$
$373$	−27.7659	−1.43766	−0.718831	+	0.695185i	$0.755322\pi$
$374$	2.56656	0.132714
$375$	23.8968	1.23402
$376$	7.13394	0.367905
$377$	−0.839156	−0.0432187
$378$	21.3129	1.09621
$379$	13.8990	0.713945	0.356972	−	0.934115i	$-0.383809\pi$
$379$	13.8990	0.713945	0.356972	+	0.934115i	$0.383809\pi$
$380$	−9.82317	−0.503918
$381$	6.40942	0.328364
$382$	11.7767	0.602551
$383$	10.0633	0.514210	0.257105	−	0.966384i	$-0.417231\pi$
$383$	10.0633	0.514210	0.257105	+	0.966384i	$0.417231\pi$
$384$	2.82338	0.144080
$385$	−4.41821	−0.225173
$386$	−4.89866	−0.249335
$387$	30.5333	1.55210
$388$	−14.4465	−0.733409
$389$	3.29888	0.167260	0.0836299	−	0.996497i	$-0.473349\pi$
$389$	3.29888	0.167260	0.0836299	+	0.996497i	$0.473349\pi$
$390$	1.07828	0.0546010
$391$	−7.83336	−0.396150
$392$	−7.66057	−0.386917
$393$	2.82338	0.142421
$394$	−15.7886	−0.795420
$395$	−54.0264	−2.71836
$396$	1.62888	0.0818545
$397$	−14.7227	−0.738911	−0.369456	−	0.929248i	$-0.620456\pi$
$397$	−14.7227	−0.738911	−0.369456	+	0.929248i	$0.620456\pi$
$398$	−5.39743	−0.270549
$399$	−30.1529	−1.50953
$400$	7.40326	0.370163
$401$	−2.54871	−0.127277	−0.0636383	−	0.997973i	$-0.520270\pi$
$401$	−2.54871	−0.127277	−0.0636383	+	0.997973i	$0.520270\pi$
$402$	−7.32491	−0.365333
$403$	0.362083	0.0180366
$404$	0.345923	0.0172103
$405$	−2.82202	−0.140227
$406$	−29.6294	−1.47048
$407$	1.89718	0.0940397
$408$	−22.1166	−1.09493
$409$	14.6744	0.725602	0.362801	−	0.931867i	$-0.381821\pi$
$409$	14.6744	0.725602	0.362801	+	0.931867i	$0.381821\pi$
$410$	31.5927	1.56025
$411$	−4.91565	−0.242471
$412$	−15.8530	−0.781020
$413$	−24.4010	−1.20069
$414$	−4.97150	−0.244336
$415$	14.6929	0.721244
$416$	0.108441	0.00531677
$417$	53.1835	2.60441
$418$	−0.913875	−0.0446991
$419$	3.69626	0.180574	0.0902870	−	0.995916i	$-0.471222\pi$
$419$	3.69626	0.180574	0.0902870	+	0.995916i	$0.471222\pi$
$420$	38.0727	1.85776
$421$	−30.4350	−1.48331	−0.741655	−	0.670781i	$-0.765959\pi$
$421$	−30.4350	−1.48331	−0.741655	+	0.670781i	$0.765959\pi$
$422$	15.2139	0.740603
$423$	−35.4664	−1.72443
$424$	1.61791	0.0785728
$425$	−57.9924	−2.81305
$426$	18.2978	0.886533
$427$	54.7903	2.65149
$428$	7.18900	0.347494
$429$	0.100315	0.00484328
$430$	21.6299	1.04309
$431$	9.93154	0.478385	0.239193	−	0.970972i	$-0.423117\pi$
$431$	9.93154	0.478385	0.239193	+	0.970972i	$0.423117\pi$
$432$	−5.56629	−0.267808
$433$	−10.0104	−0.481068	−0.240534	−	0.970641i	$-0.577323\pi$
$433$	−10.0104	−0.481068	−0.240534	+	0.970641i	$0.577323\pi$
$434$	12.7846	0.613683
$435$	76.9459	3.68927
$436$	19.8013	0.948308
$437$	2.78922	0.133427
$438$	−34.5382	−1.65030
$439$	29.5333	1.40955	0.704774	−	0.709432i	$-0.251048\pi$
$439$	29.5333	1.40955	0.704774	+	0.709432i	$0.251048\pi$
$440$	1.15391	0.0550104
$441$	38.0845	1.81355
$442$	−0.849460	−0.0404047
$443$	27.7968	1.32066	0.660332	−	0.750973i	$-0.270415\pi$
$443$	27.7968	1.32066	0.660332	+	0.750973i	$0.270415\pi$
$444$	−16.3484	−0.775861
$445$	54.6070	2.58862
$446$	−16.6498	−0.788391
$447$	26.6954	1.26265
$448$	3.82891	0.180899
$449$	−15.9364	−0.752085	−0.376043	−	0.926602i	$-0.622715\pi$
$449$	−15.9364	−0.752085	−0.376043	+	0.926602i	$0.622715\pi$
$450$	−36.8053	−1.73502
$451$	2.93915	0.138399
$452$	7.18913	0.338148
$453$	26.6084	1.25017
$454$	1.51893	0.0712871
$455$	1.46231	0.0685540
$456$	7.87505	0.368783
$457$	9.70684	0.454067	0.227033	−	0.973887i	$-0.427097\pi$
$457$	9.70684	0.454067	0.227033	+	0.973887i	$0.427097\pi$
$458$	−12.8755	−0.601632
$459$	43.6028	2.03520
$460$	−3.52183	−0.164206
$461$	6.98256	0.325210	0.162605	−	0.986691i	$-0.448010\pi$
$461$	6.98256	0.325210	0.162605	+	0.986691i	$0.448010\pi$
$462$	3.54200	0.164789
$463$	−15.3548	−0.713596	−0.356798	−	0.934181i	$-0.616132\pi$
$463$	−15.3548	−0.713596	−0.356798	+	0.934181i	$0.616132\pi$
$464$	7.73834	0.359243
$465$	−33.2010	−1.53966
$466$	23.4391	1.08579
$467$	−20.6667	−0.956340	−0.478170	−	0.878267i	$-0.658700\pi$
$467$	−20.6667	−0.956340	−0.478170	+	0.878267i	$0.658700\pi$
$468$	−0.539116	−0.0249206
$469$	−9.93362	−0.458692
$470$	−25.1245	−1.15891
$471$	−52.2567	−2.40786
$472$	6.37283	0.293333
$473$	2.01229	0.0925250
$474$	43.3119	1.98938
$475$	20.6494	0.947458
$476$	−29.9932	−1.37474
$477$	−8.04345	−0.368284
$478$	14.8386	0.678701
$479$	1.71457	0.0783405	0.0391703	−	0.999233i	$-0.487529\pi$
$479$	1.71457	0.0783405	0.0391703	+	0.999233i	$0.487529\pi$
$480$	−9.94347	−0.453855
$481$	−0.627914	−0.0286304
$482$	20.0939	0.915252
$483$	−10.8105	−0.491894
$484$	−10.8926	−0.495120
$485$	50.8780	2.31025
$486$	−14.4365	−0.654854
$487$	−7.59439	−0.344134	−0.172067	−	0.985085i	$-0.555045\pi$
$487$	−7.59439	−0.344134	−0.172067	+	0.985085i	$0.555045\pi$
$488$	−14.3096	−0.647766
$489$	60.3918	2.73101
$490$	26.9792	1.21880
$491$	5.32369	0.240255	0.120127	−	0.992758i	$-0.461670\pi$
$491$	5.32369	0.240255	0.120127	+	0.992758i	$0.461670\pi$
$492$	−25.3273	−1.14184
$493$	−60.6172	−2.73006
$494$	0.302467	0.0136086
$495$	−5.73665	−0.257843
$496$	−3.33898	−0.149924
$497$	24.8145	1.11308
$498$	−11.7790	−0.527830
$499$	−8.98971	−0.402435	−0.201217	−	0.979547i	$-0.564490\pi$
$499$	−8.98971	−0.402435	−0.201217	+	0.979547i	$0.564490\pi$
$500$	−8.46387	−0.378516
$501$	−65.5831	−2.93004
$502$	−4.94950	−0.220907
$503$	−34.6139	−1.54336	−0.771679	−	0.636012i	$-0.780583\pi$
$503$	−34.6139	−1.54336	−0.771679	+	0.636012i	$0.780583\pi$
$504$	−19.0354	−0.847905
$505$	−1.21828	−0.0542128
$506$	−0.327645	−0.0145656
$507$	36.6708	1.62861
$508$	−2.27012	−0.100720
$509$	27.9661	1.23958	0.619788	−	0.784769i	$-0.287219\pi$
$509$	27.9661	1.23958	0.619788	+	0.784769i	$0.287219\pi$
$510$	77.8908	3.44906
$511$	−46.8388	−2.07203
$512$	−1.00000	−0.0441942
$513$	−15.5256	−0.685474
$514$	−2.49348	−0.109983
$515$	55.8315	2.46023
$516$	−17.3403	−0.763364
$517$	−2.33740	−0.102799
$518$	−22.1708	−0.974128
$519$	2.34963	0.103137
$520$	−0.381912	−0.0167479
$521$	36.6324	1.60489	0.802447	−	0.596723i	$-0.203531\pi$
$521$	36.6324	1.60489	0.802447	+	0.596723i	$0.203531\pi$
$522$	−38.4711	−1.68384
$523$	−25.0534	−1.09551	−0.547754	−	0.836640i	$-0.684517\pi$
$523$	−25.0534	−1.09551	−0.547754	+	0.836640i	$0.684517\pi$
$524$	−1.00000	−0.0436852
$525$	−80.0329	−3.49292
$526$	0.792876	0.0345710
$527$	26.1554	1.13935
$528$	−0.925067	−0.0402584
$529$	1.00000	0.0434783
$530$	−5.69801	−0.247506
$531$	−31.6825	−1.37490
$532$	10.6797	0.463024
$533$	−0.972777	−0.0421357
$534$	−43.7775	−1.89444
$535$	−25.3184	−1.09461
$536$	2.59437	0.112060
$537$	19.0859	0.823618
$538$	16.4054	0.707288
$539$	2.50995	0.108111
$540$	19.6035	0.843601
$541$	17.4747	0.751298	0.375649	−	0.926762i	$-0.377420\pi$
$541$	17.4747	0.751298	0.375649	+	0.926762i	$0.377420\pi$
$542$	−4.83470	−0.207668
$543$	0.366605	0.0157325
$544$	7.83336	0.335852
$545$	−69.7366	−2.98719
$546$	−1.17230	−0.0501700
$547$	21.6053	0.923777	0.461888	−	0.886938i	$-0.347172\pi$
$547$	21.6053	0.923777	0.461888	+	0.886938i	$0.347172\pi$
$548$	1.74105	0.0743739
$549$	71.1403	3.03619
$550$	−2.42564	−0.103430
$551$	21.5840	0.919508
$552$	2.82338	0.120171
$553$	58.7372	2.49776
$554$	25.4805	1.08256
$555$	57.5762	2.44398
$556$	−18.8368	−0.798858
$557$	16.5219	0.700054	0.350027	−	0.936740i	$-0.386172\pi$
$557$	16.5219	0.700054	0.350027	+	0.936740i	$0.386172\pi$
$558$	16.5997	0.702722
$559$	−0.666012	−0.0281693
$560$	−13.4848	−0.569835
$561$	7.24638	0.305942
$562$	−29.3759	−1.23915
$563$	5.44588	0.229516	0.114758	−	0.993393i	$-0.463391\pi$
$563$	5.44588	0.229516	0.114758	+	0.993393i	$0.463391\pi$
$564$	20.1419	0.848125
$565$	−25.3189	−1.06517
$566$	−12.4878	−0.524901
$567$	3.06808	0.128847
$568$	−6.48082	−0.271929
$569$	−29.6198	−1.24173	−0.620864	−	0.783919i	$-0.713218\pi$
$569$	−29.6198	−1.24173	−0.620864	+	0.783919i	$0.713218\pi$
$570$	−27.7346	−1.16167
$571$	18.0429	0.755071	0.377536	−	0.925995i	$-0.376772\pi$
$571$	18.0429	0.755071	0.377536	+	0.925995i	$0.376772\pi$
$572$	−0.0355302	−0.00148559
$573$	33.2503	1.38905
$574$	−34.3474	−1.43363
$575$	7.40326	0.308737
$576$	4.97150	0.207146
$577$	−30.4237	−1.26656	−0.633278	−	0.773924i	$-0.718291\pi$
$577$	−30.4237	−1.26656	−0.633278	+	0.773924i	$0.718291\pi$
$578$	−44.3615	−1.84520
$579$	−13.8308	−0.574789
$580$	−27.2531	−1.13162
$581$	−15.9740	−0.662714
$582$	−40.7880	−1.69071
$583$	−0.530101	−0.0219545
$584$	12.2329	0.506202
$585$	1.89867	0.0785005
$586$	−25.8775	−1.06899
$587$	38.6433	1.59498	0.797490	−	0.603332i	$-0.206161\pi$
$587$	38.6433	1.59498	0.797490	+	0.603332i	$0.206161\pi$
$588$	−21.6287	−0.891954
$589$	−9.31315	−0.383742
$590$	−22.4440	−0.924004
$591$	−44.5774	−1.83367
$592$	5.79036	0.237982
$593$	27.2959	1.12091	0.560454	−	0.828185i	$-0.310627\pi$
$593$	27.2959	1.12091	0.560454	+	0.828185i	$0.310627\pi$
$594$	1.82377	0.0748300
$595$	105.631	4.33045
$596$	−9.45510	−0.387296
$597$	−15.2390	−0.623692
$598$	0.108441	0.00443450
$599$	−0.705019	−0.0288063	−0.0144032	−	0.999896i	$-0.504585\pi$
$599$	−0.705019	−0.0288063	−0.0144032	+	0.999896i	$0.504585\pi$
$600$	20.9023	0.853331
$601$	−7.42718	−0.302961	−0.151480	−	0.988460i	$-0.548404\pi$
$601$	−7.42718	−0.302961	−0.151480	+	0.988460i	$0.548404\pi$
$602$	−23.5159	−0.958438
$603$	−12.8979	−0.525244
$604$	−9.42429	−0.383469
$605$	38.3620	1.55964
$606$	0.976673	0.0396746
$607$	−8.25242	−0.334955	−0.167478	−	0.985876i	$-0.553562\pi$
$607$	−8.25242	−0.334955	−0.167478	+	0.985876i	$0.553562\pi$
$608$	−2.78922	−0.113118
$609$	−83.6552	−3.38988
$610$	50.3960	2.04048
$611$	0.773614	0.0312971
$612$	−38.9435	−1.57420
$613$	−20.0532	−0.809943	−0.404971	−	0.914329i	$-0.632719\pi$
$613$	−20.0532	−0.809943	−0.404971	+	0.914329i	$0.632719\pi$
$614$	−19.7923	−0.798751
$615$	89.1982	3.59682
$616$	−1.25452	−0.0505462
$617$	9.15028	0.368376	0.184188	−	0.982891i	$-0.441034\pi$
$617$	9.15028	0.368376	0.184188	+	0.982891i	$0.441034\pi$
$618$	−44.7591	−1.80047
$619$	43.3156	1.74100	0.870501	−	0.492166i	$-0.163795\pi$
$619$	43.3156	1.74100	0.870501	+	0.492166i	$0.163795\pi$
$620$	11.7593	0.472265
$621$	−5.56629	−0.223368
$622$	−25.2663	−1.01308
$623$	−59.3685	−2.37855
$624$	0.306172	0.0122567
$625$	−7.20802	−0.288321
$626$	−20.0872	−0.802845
$627$	−2.58022	−0.103044
$628$	18.5085	0.738570
$629$	−45.3580	−1.80854
$630$	67.0395	2.67092
$631$	47.4169	1.88764	0.943819	−	0.330463i	$-0.107205\pi$
$631$	47.4169	1.88764	0.943819	+	0.330463i	$0.107205\pi$
$632$	−15.3404	−0.610210
$633$	42.9548	1.70730
$634$	−18.2957	−0.726616
$635$	7.99496	0.317270
$636$	4.56799	0.181133
$637$	−0.830723	−0.0329144
$638$	−2.53542	−0.100378
$639$	32.2194	1.27458
$640$	3.52183	0.139212
$641$	−30.2139	−1.19338	−0.596688	−	0.802473i	$-0.703517\pi$
$641$	−30.2139	−1.19338	−0.596688	+	0.802473i	$0.703517\pi$
$642$	20.2973	0.801071
$643$	−1.92861	−0.0760569	−0.0380285	−	0.999277i	$-0.512108\pi$
$643$	−1.92861	−0.0760569	−0.0380285	+	0.999277i	$0.512108\pi$
$644$	3.82891	0.150880
$645$	61.0696	2.40461
$646$	21.8490	0.859637
$647$	26.5071	1.04210	0.521051	−	0.853525i	$-0.325540\pi$
$647$	26.5071	1.04210	0.521051	+	0.853525i	$0.325540\pi$
$648$	−0.801293	−0.0314778
$649$	−2.08802	−0.0819620
$650$	0.802820	0.0314892
$651$	36.0960	1.41471
$652$	−21.3899	−0.837691
$653$	31.9712	1.25113	0.625565	−	0.780172i	$-0.284869\pi$
$653$	31.9712	1.25113	0.625565	+	0.780172i	$0.284869\pi$
$654$	55.9066	2.18612
$655$	3.52183	0.137609
$656$	8.97054	0.350241
$657$	−60.8159	−2.37265
$658$	27.3152	1.06486
$659$	−19.7926	−0.771011	−0.385506	−	0.922705i	$-0.625973\pi$
$659$	−19.7926	−0.771011	−0.385506	+	0.922705i	$0.625973\pi$
$660$	3.25792	0.126815
$661$	29.1618	1.13426	0.567132	−	0.823627i	$-0.308053\pi$
$661$	29.1618	1.13426	0.567132	+	0.823627i	$0.308053\pi$
$662$	−19.4867	−0.757372
$663$	−2.39835	−0.0931443
$664$	4.17194	0.161903
$665$	−37.6120	−1.45853
$666$	−28.7867	−1.11546
$667$	7.73834	0.299630
$668$	23.2285	0.898739
$669$	−47.0088	−1.81746
$670$	−9.13693	−0.352990
$671$	4.68847	0.180996
$672$	10.8105	0.417024
$673$	−19.4785	−0.750843	−0.375421	−	0.926854i	$-0.622502\pi$
$673$	−19.4785	−0.750843	−0.375421	+	0.926854i	$0.622502\pi$
$674$	−26.9904	−1.03963
$675$	−41.2087	−1.58612
$676$	−12.9882	−0.499548
$677$	−39.9425	−1.53512	−0.767558	−	0.640979i	$-0.778528\pi$
$677$	−39.9425	−1.53512	−0.767558	+	0.640979i	$0.778528\pi$
$678$	20.2977	0.779528
$679$	−55.3143	−2.12277
$680$	−27.5877	−1.05794
$681$	4.28853	0.164337
$682$	1.09400	0.0418913
$683$	−12.3971	−0.474362	−0.237181	−	0.971465i	$-0.576223\pi$
$683$	−12.3971	−0.474362	−0.237181	+	0.971465i	$0.576223\pi$
$684$	13.8666	0.530204
$685$	−6.13167	−0.234279
$686$	−2.52928	−0.0965683
$687$	−36.3525	−1.38693
$688$	6.14168	0.234149
$689$	0.175449	0.00668406
$690$	−9.94347	−0.378541
$691$	43.3552	1.64931	0.824654	−	0.565637i	$-0.191370\pi$
$691$	43.3552	1.64931	0.824654	+	0.565637i	$0.191370\pi$
$692$	−0.832202	−0.0316356
$693$	6.23686	0.236919
$694$	−12.4498	−0.472589
$695$	66.3399	2.51642
$696$	21.8483	0.828158
$697$	−70.2694	−2.66164
$698$	−24.1424	−0.913805
$699$	66.1775	2.50306
$700$	28.3464	1.07139
$701$	−24.6969	−0.932790	−0.466395	−	0.884577i	$-0.654447\pi$
$701$	−24.6969	−0.932790	−0.466395	+	0.884577i	$0.654447\pi$
$702$	−0.603616	−0.0227820
$703$	16.1506	0.609132
$704$	0.327645	0.0123486
$705$	−70.9361	−2.67161
$706$	32.0487	1.20617
$707$	1.32451	0.0498133
$708$	17.9929	0.676216
$709$	−15.4884	−0.581678	−0.290839	−	0.956772i	$-0.593934\pi$
$709$	−15.4884	−0.581678	−0.290839	+	0.956772i	$0.593934\pi$
$710$	22.8243	0.856581
$711$	76.2649	2.86016
$712$	15.5053	0.581086
$713$	−3.33898	−0.125046
$714$	−84.6825	−3.16916
$715$	0.125131	0.00467965
$716$	−6.75994	−0.252631
$717$	41.8950	1.56460
$718$	0.472858	0.0176469
$719$	45.1462	1.68367	0.841834	−	0.539737i	$-0.181476\pi$
$719$	45.1462	1.68367	0.841834	+	0.539737i	$0.181476\pi$
$720$	−17.5088	−0.652513
$721$	−60.6997	−2.26057
$722$	11.2202	0.417574
$723$	56.7328	2.10992
$724$	−0.129846	−0.00482569
$725$	57.2889	2.12766
$726$	−30.7541	−1.14139
$727$	27.4508	1.01809	0.509047	−	0.860738i	$-0.329998\pi$
$727$	27.4508	1.01809	0.509047	+	0.860738i	$0.329998\pi$
$728$	0.415212	0.0153888
$729$	−43.1637	−1.59866
$730$	−43.0822	−1.59454
$731$	−48.1099	−1.77941
$732$	−40.4016	−1.49329
$733$	7.55553	0.279070	0.139535	−	0.990217i	$-0.455439\pi$
$733$	7.55553	0.279070	0.139535	+	0.990217i	$0.455439\pi$
$734$	12.9466	0.477868
$735$	76.1727	2.80967
$736$	−1.00000	−0.0368605
$737$	−0.850032	−0.0313113
$738$	−44.5970	−1.64164
$739$	−3.32158	−0.122186	−0.0610932	−	0.998132i	$-0.519459\pi$
$739$	−3.32158	−0.122186	−0.0610932	+	0.998132i	$0.519459\pi$
$740$	−20.3926	−0.749648
$741$	0.853981	0.0313718
$742$	6.19485	0.227420
$743$	50.6700	1.85890	0.929451	−	0.368945i	$-0.120281\pi$
$743$	50.6700	1.85890	0.929451	+	0.368945i	$0.120281\pi$
$744$	−9.42721	−0.345618
$745$	33.2992	1.21999
$746$	27.7659	1.01658
$747$	−20.7408	−0.758866
$748$	−2.56656	−0.0938427
$749$	27.5261	1.00578
$750$	−23.8968	−0.872587
$751$	0.0216308	0.000789319 0	0.000394659	−	1.00000i	$-0.499874\pi$
$751$	0.0216308	0.000789319 0	0.000394659		1.00000i	$0.499874\pi$
$752$	−7.13394	−0.260148
$753$	−13.9743	−0.509253
$754$	0.839156	0.0305603
$755$	33.1907	1.20793
$756$	−21.3129	−0.775141
$757$	−26.0869	−0.948146	−0.474073	−	0.880486i	$-0.657217\pi$
$757$	−26.0869	−0.948146	−0.474073	+	0.880486i	$0.657217\pi$
$758$	−13.8990	−0.504835
$759$	−0.925067	−0.0335778
$760$	9.82317	0.356324
$761$	41.0035	1.48638	0.743189	−	0.669082i	$-0.233313\pi$
$761$	41.0035	1.48638	0.743189	+	0.669082i	$0.233313\pi$
$762$	−6.40942	−0.232189
$763$	75.8173	2.74477
$764$	−11.7767	−0.426068
$765$	137.152	4.95875
$766$	−10.0633	−0.363601
$767$	0.691078	0.0249534
$768$	−2.82338	−0.101880
$769$	28.2086	1.01723	0.508614	−	0.860994i	$-0.330158\pi$
$769$	28.2086	1.01723	0.508614	+	0.860994i	$0.330158\pi$
$770$	4.41821	0.159221
$771$	−7.04006	−0.253541
$772$	4.89866	0.176307
$773$	−28.7898	−1.03550	−0.517748	−	0.855533i	$-0.673230\pi$
$773$	−28.7898	−1.03550	−0.517748	+	0.855533i	$0.673230\pi$
$774$	−30.5333	−1.09750
$775$	−24.7193	−0.887944
$776$	14.4465	0.518598
$777$	−62.5966	−2.24564
$778$	−3.29888	−0.118271
$779$	25.0208	0.896465
$780$	−1.07828	−0.0386087
$781$	2.12340	0.0759814
$782$	7.83336	0.280120
$783$	−43.0739	−1.53933
$784$	7.66057	0.273592
$785$	−65.1838	−2.32651
$786$	−2.82338	−0.100707
$787$	−38.0401	−1.35598	−0.677992	−	0.735070i	$-0.737149\pi$
$787$	−38.0401	−1.35598	−0.677992	+	0.735070i	$0.737149\pi$
$788$	15.7886	0.562447
$789$	2.23859	0.0796961
$790$	54.0264	1.92217
$791$	27.5266	0.978732
$792$	−1.62888	−0.0578799
$793$	−1.55176	−0.0551045
$794$	14.7227	0.522489
$795$	−16.0877	−0.570571
$796$	5.39743	0.191307
$797$	−36.7408	−1.30143	−0.650714	−	0.759323i	$-0.725530\pi$
$797$	−36.7408	−1.30143	−0.650714	+	0.759323i	$0.725530\pi$
$798$	30.1529	1.06740
$799$	55.8827	1.97699
$800$	−7.40326	−0.261745
$801$	−77.0846	−2.72365
$802$	2.54871	0.0899982
$803$	−4.00805	−0.141441
$804$	7.32491	0.258330
$805$	−13.4848	−0.475276
$806$	−0.362083	−0.0127538
$807$	46.3188	1.63050
$808$	−0.345923	−0.0121695
$809$	−11.9200	−0.419085	−0.209543	−	0.977800i	$-0.567197\pi$
$809$	−11.9200	−0.419085	−0.209543	+	0.977800i	$0.567197\pi$
$810$	2.82202	0.0991555
$811$	−27.2609	−0.957261	−0.478631	−	0.878016i	$-0.658867\pi$
$811$	−27.2609	−0.957261	−0.478631	+	0.878016i	$0.658867\pi$
$812$	29.6294	1.03979
$813$	−13.6502	−0.478734
$814$	−1.89718	−0.0664961
$815$	75.3314	2.63874
$816$	22.1166	0.774235
$817$	17.1305	0.599321
$818$	−14.6744	−0.513078
$819$	−2.06423	−0.0721300
$820$	−31.5927	−1.10326
$821$	−47.3023	−1.65086	−0.825430	−	0.564504i	$-0.809067\pi$
$821$	−47.3023	−1.65086	−0.825430	+	0.564504i	$0.809067\pi$
$822$	4.91565	0.171453
$823$	9.96670	0.347417	0.173709	−	0.984797i	$-0.444425\pi$
$823$	9.96670	0.347417	0.173709	+	0.984797i	$0.444425\pi$
$824$	15.8530	0.552265
$825$	−6.84851	−0.238435
$826$	24.4010	0.849019
$827$	−49.4420	−1.71927	−0.859634	−	0.510910i	$-0.829308\pi$
$827$	−49.4420	−1.71927	−0.859634	+	0.510910i	$0.829308\pi$
$828$	4.97150	0.172771
$829$	48.5467	1.68610	0.843049	−	0.537837i	$-0.180758\pi$
$829$	48.5467	1.68610	0.843049	+	0.537837i	$0.180758\pi$
$830$	−14.6929	−0.509997
$831$	71.9412	2.49561
$832$	−0.108441	−0.00375953
$833$	−60.0080	−2.07915
$834$	−53.1835	−1.84159
$835$	−81.8069	−2.83104
$836$	0.913875	0.0316070
$837$	18.5857	0.642416
$838$	−3.69626	−0.127685
$839$	40.5652	1.40047	0.700233	−	0.713915i	$-0.253080\pi$
$839$	40.5652	1.40047	0.700233	+	0.713915i	$0.253080\pi$
$840$	−38.0727	−1.31363
$841$	30.8819	1.06489
$842$	30.4350	1.04886
$843$	−82.9393	−2.85658
$844$	−15.2139	−0.523685
$845$	45.7423	1.57358
$846$	35.4664	1.21936
$847$	−41.7070	−1.43307
$848$	−1.61791	−0.0555594
$849$	−35.2578	−1.21004
$850$	57.9924	1.98912
$851$	5.79036	0.198491
$852$	−18.2978	−0.626873
$853$	17.7306	0.607086	0.303543	−	0.952818i	$-0.401830\pi$
$853$	17.7306	0.607086	0.303543	+	0.952818i	$0.401830\pi$
$854$	−54.7903	−1.87489
$855$	−48.8358	−1.67015
$856$	−7.18900	−0.245715
$857$	12.7586	0.435826	0.217913	−	0.975968i	$-0.430075\pi$
$857$	12.7586	0.435826	0.217913	+	0.975968i	$0.430075\pi$
$858$	−0.100315	−0.00342471
$859$	−7.61460	−0.259807	−0.129903	−	0.991527i	$-0.541467\pi$
$859$	−7.61460	−0.259807	−0.129903	+	0.991527i	$0.541467\pi$
$860$	−21.6299	−0.737574
$861$	−96.9759	−3.30493
$862$	−9.93154	−0.338269
$863$	−6.24674	−0.212641	−0.106321	−	0.994332i	$-0.533907\pi$
$863$	−6.24674	−0.212641	−0.106321	+	0.994332i	$0.533907\pi$
$864$	5.56629	0.189369
$865$	2.93087	0.0996526
$866$	10.0104	0.340166
$867$	−125.250	−4.25370
$868$	−12.7846	−0.433939
$869$	5.02621	0.170503
$870$	−76.9459	−2.60871
$871$	0.281337	0.00953275
$872$	−19.8013	−0.670555
$873$	−71.8206	−2.43076
$874$	−2.78922	−0.0943469
$875$	−32.4074	−1.09557
$876$	34.5382	1.16694
$877$	8.88950	0.300177	0.150089	−	0.988673i	$-0.452044\pi$
$877$	8.88950	0.300177	0.150089	+	0.988673i	$0.452044\pi$
$878$	−29.5333	−0.996701
$879$	−73.0620	−2.46432
$880$	−1.15391	−0.0388982
$881$	−17.3945	−0.586036	−0.293018	−	0.956107i	$-0.594660\pi$
$881$	−17.3945	−0.586036	−0.293018	+	0.956107i	$0.594660\pi$
$882$	−38.0845	−1.28237
$883$	19.6201	0.660268	0.330134	−	0.943934i	$-0.392906\pi$
$883$	19.6201	0.660268	0.330134	+	0.943934i	$0.392906\pi$
$884$	0.849460	0.0285704
$885$	−63.3680	−2.13009
$886$	−27.7968	−0.933851
$887$	20.7249	0.695875	0.347938	−	0.937518i	$-0.386882\pi$
$887$	20.7249	0.695875	0.347938	+	0.937518i	$0.386882\pi$
$888$	16.3484	0.548617
$889$	−8.69209	−0.291523
$890$	−54.6070	−1.83043
$891$	0.262539	0.00879540
$892$	16.6498	0.557477
$893$	−19.8982	−0.665867
$894$	−26.6954	−0.892827
$895$	23.8074	0.795792
$896$	−3.82891	−0.127915
$897$	0.306172	0.0102228
$898$	15.9364	0.531805
$899$	−25.8381	−0.861750
$900$	36.8053	1.22684
$901$	12.6737	0.422222
$902$	−2.93915	−0.0978629
$903$	−66.3945	−2.20947
$904$	−7.18913	−0.239107
$905$	0.457295	0.0152010
$906$	−26.6084	−0.884005
$907$	5.21482	0.173155	0.0865776	−	0.996245i	$-0.472407\pi$
$907$	5.21482	0.173155	0.0865776	+	0.996245i	$0.472407\pi$
$908$	−1.51893	−0.0504076
$909$	1.71975	0.0570407
$910$	−1.46231	−0.0484750
$911$	−6.92099	−0.229303	−0.114651	−	0.993406i	$-0.536575\pi$
$911$	−6.92099	−0.229303	−0.114651	+	0.993406i	$0.536575\pi$
$912$	−7.87505	−0.260769
$913$	−1.36691	−0.0452383
$914$	−9.70684	−0.321074
$915$	142.287	4.70387
$916$	12.8755	0.425418
$917$	−3.82891	−0.126442
$918$	−43.6028	−1.43911
$919$	47.1816	1.55638	0.778189	−	0.628031i	$-0.216139\pi$
$919$	47.1816	1.55638	0.778189	+	0.628031i	$0.216139\pi$
$920$	3.52183	0.116111
$921$	−55.8812	−1.84135
$922$	−6.98256	−0.229958
$923$	−0.702788	−0.0231326
$924$	−3.54200	−0.116523
$925$	42.8675	1.40948
$926$	15.3548	0.504589
$927$	−78.8131	−2.58856
$928$	−7.73834	−0.254023
$929$	51.2847	1.68260	0.841298	−	0.540572i	$-0.181792\pi$
$929$	51.2847	1.68260	0.841298	+	0.540572i	$0.181792\pi$
$930$	33.2010	1.08870
$931$	21.3671	0.700277
$932$	−23.4391	−0.767773
$933$	−71.3363	−2.33545
$934$	20.6667	0.676234
$935$	9.03897	0.295606
$936$	0.539116	0.0176216
$937$	−28.7544	−0.939366	−0.469683	−	0.882835i	$-0.655632\pi$
$937$	−28.7544	−0.939366	−0.469683	+	0.882835i	$0.655632\pi$
$938$	9.93362	0.324344
$939$	−56.7138	−1.85079
$940$	25.1245	0.819471
$941$	13.0345	0.424912	0.212456	−	0.977171i	$-0.431854\pi$
$941$	13.0345	0.424912	0.212456	+	0.977171i	$0.431854\pi$
$942$	52.2567	1.70261
$943$	8.97054	0.292121
$944$	−6.37283	−0.207418
$945$	75.0602	2.44171
$946$	−2.01229	−0.0654251
$947$	−32.4346	−1.05398	−0.526991	−	0.849871i	$-0.676680\pi$
$947$	−32.4346	−1.05398	−0.526991	+	0.849871i	$0.676680\pi$
$948$	−43.3119	−1.40671
$949$	1.32655	0.0430618
$950$	−20.6494	−0.669954
$951$	−51.6559	−1.67506
$952$	29.9932	0.972087
$953$	36.7106	1.18917	0.594586	−	0.804032i	$-0.297316\pi$
$953$	36.7106	1.18917	0.594586	+	0.804032i	$0.297316\pi$
$954$	8.04345	0.260416
$955$	41.4757	1.34212
$956$	−14.8386	−0.479914
$957$	−7.15848	−0.231401
$958$	−1.71457	−0.0553951
$959$	6.66632	0.215267
$960$	9.94347	0.320924
$961$	−19.8512	−0.640363
$962$	0.627914	0.0202448
$963$	35.7401	1.15171
$964$	−20.0939	−0.647181
$965$	−17.2522	−0.555369
$966$	10.8105	0.347822
$967$	50.7460	1.63188	0.815941	−	0.578135i	$-0.196219\pi$
$967$	50.7460	1.63188	0.815941	+	0.578135i	$0.196219\pi$
$968$	10.8926	0.350103
$969$	61.6881	1.98171
$970$	−50.8780	−1.63359
$971$	43.0700	1.38218	0.691091	−	0.722768i	$-0.257130\pi$
$971$	43.0700	1.38218	0.691091	+	0.722768i	$0.257130\pi$
$972$	14.4365	0.463052
$973$	−72.1245	−2.31220
$974$	7.59439	0.243340
$975$	2.26667	0.0725915
$976$	14.3096	0.458040
$977$	2.34487	0.0750192	0.0375096	−	0.999296i	$-0.488058\pi$
$977$	2.34487	0.0750192	0.0375096	+	0.999296i	$0.488058\pi$
$978$	−60.3918	−1.93112
$979$	−5.08023	−0.162365
$980$	−26.9792	−0.861819
$981$	98.4419	3.14301
$982$	−5.32369	−0.169886
$983$	44.9852	1.43480	0.717402	−	0.696659i	$-0.245331\pi$
$983$	44.9852	1.43480	0.717402	+	0.696659i	$0.245331\pi$
$984$	25.3273	0.807404
$985$	−55.6048	−1.77172
$986$	60.6172	1.93044
$987$	77.1214	2.45480
$988$	−0.302467	−0.00962277
$989$	6.14168	0.195294
$990$	5.73665	0.182323
$991$	43.6669	1.38712	0.693562	−	0.720397i	$-0.256040\pi$
$991$	43.6669	1.38712	0.693562	+	0.720397i	$0.256040\pi$
$992$	3.33898	0.106013
$993$	−55.0185	−1.74596
$994$	−24.8145	−0.787067
$995$	−19.0088	−0.602620
$996$	11.7790	0.373232
$997$	47.9278	1.51789	0.758945	−	0.651155i	$-0.225715\pi$
$997$	47.9278	1.51789	0.758945	+	0.651155i	$0.225715\pi$
$998$	8.98971	0.284564
$999$	−32.2308	−1.01974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.4	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.4	✓	33	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.82338 q^{3} +1.00000 q^{4} -3.52183 q^{5} +2.82338 q^{6} +3.82891 q^{7} -1.00000 q^{8} +4.97150 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.82338 q^{3} +1.00000 q^{4} -3.52183 q^{5} +2.82338 q^{6} +3.82891 q^{7} -1.00000 q^{8} +4.97150 q^{9} +3.52183 q^{10} +0.327645 q^{11} -2.82338 q^{12} -0.108441 q^{13} -3.82891 q^{14} +9.94347 q^{15} +1.00000 q^{16} -7.83336 q^{17} -4.97150 q^{18} +2.78922 q^{19} -3.52183 q^{20} -10.8105 q^{21} -0.327645 q^{22} +1.00000 q^{23} +2.82338 q^{24} +7.40326 q^{25} +0.108441 q^{26} -5.56629 q^{27} +3.82891 q^{28} +7.73834 q^{29} -9.94347 q^{30} -3.33898 q^{31} -1.00000 q^{32} -0.925067 q^{33} +7.83336 q^{34} -13.4848 q^{35} +4.97150 q^{36} +5.79036 q^{37} -2.78922 q^{38} +0.306172 q^{39} +3.52183 q^{40} +8.97054 q^{41} +10.8105 q^{42} +6.14168 q^{43} +0.327645 q^{44} -17.5088 q^{45} -1.00000 q^{46} -7.13394 q^{47} -2.82338 q^{48} +7.66057 q^{49} -7.40326 q^{50} +22.1166 q^{51} -0.108441 q^{52} -1.61791 q^{53} +5.56629 q^{54} -1.15391 q^{55} -3.82891 q^{56} -7.87505 q^{57} -7.73834 q^{58} -6.37283 q^{59} +9.94347 q^{60} +14.3096 q^{61} +3.33898 q^{62} +19.0354 q^{63} +1.00000 q^{64} +0.381912 q^{65} +0.925067 q^{66} -2.59437 q^{67} -7.83336 q^{68} -2.82338 q^{69} +13.4848 q^{70} +6.48082 q^{71} -4.97150 q^{72} -12.2329 q^{73} -5.79036 q^{74} -20.9023 q^{75} +2.78922 q^{76} +1.25452 q^{77} -0.306172 q^{78} +15.3404 q^{79} -3.52183 q^{80} +0.801293 q^{81} -8.97054 q^{82} -4.17194 q^{83} -10.8105 q^{84} +27.5877 q^{85} -6.14168 q^{86} -21.8483 q^{87} -0.327645 q^{88} -15.5053 q^{89} +17.5088 q^{90} -0.415212 q^{91} +1.00000 q^{92} +9.42721 q^{93} +7.13394 q^{94} -9.82317 q^{95} +2.82338 q^{96} -14.4465 q^{97} -7.66057 q^{98} +1.62888 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

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