LMFDB - Embedded newform 4033.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67615 q^{2} +2.74461 q^{3} +0.809463 q^{4} +2.71622 q^{5} -4.60037 q^{6} +4.10502 q^{7} +1.99551 q^{8} +4.53291 q^{9} +O(q^{10})$	\(q-1.67615 q^{2} +2.74461 q^{3} +0.809463 q^{4} +2.71622 q^{5} -4.60037 q^{6} +4.10502 q^{7} +1.99551 q^{8} +4.53291 q^{9} -4.55277 q^{10} +1.91424 q^{11} +2.22166 q^{12} -4.23793 q^{13} -6.88061 q^{14} +7.45497 q^{15} -4.96370 q^{16} +2.89021 q^{17} -7.59782 q^{18} +3.69859 q^{19} +2.19868 q^{20} +11.2667 q^{21} -3.20854 q^{22} -0.144566 q^{23} +5.47691 q^{24} +2.37783 q^{25} +7.10339 q^{26} +4.20725 q^{27} +3.32286 q^{28} +1.44579 q^{29} -12.4956 q^{30} -0.547502 q^{31} +4.32885 q^{32} +5.25385 q^{33} -4.84442 q^{34} +11.1501 q^{35} +3.66922 q^{36} -1.00000 q^{37} -6.19938 q^{38} -11.6315 q^{39} +5.42024 q^{40} -8.63328 q^{41} -18.8846 q^{42} +1.99094 q^{43} +1.54951 q^{44} +12.3124 q^{45} +0.242314 q^{46} -4.35038 q^{47} -13.6234 q^{48} +9.85120 q^{49} -3.98559 q^{50} +7.93252 q^{51} -3.43045 q^{52} -3.44384 q^{53} -7.05196 q^{54} +5.19949 q^{55} +8.19162 q^{56} +10.1512 q^{57} -2.42335 q^{58} -9.18600 q^{59} +6.03452 q^{60} -0.400515 q^{61} +0.917693 q^{62} +18.6077 q^{63} +2.67161 q^{64} -11.5111 q^{65} -8.80622 q^{66} +7.87908 q^{67} +2.33952 q^{68} -0.396779 q^{69} -18.6892 q^{70} +5.67148 q^{71} +9.04548 q^{72} +9.83375 q^{73} +1.67615 q^{74} +6.52622 q^{75} +2.99388 q^{76} +7.85799 q^{77} +19.4961 q^{78} +15.0385 q^{79} -13.4825 q^{80} -2.05145 q^{81} +14.4706 q^{82} -5.27272 q^{83} +9.11998 q^{84} +7.85044 q^{85} -3.33710 q^{86} +3.96814 q^{87} +3.81989 q^{88} +6.86704 q^{89} -20.6373 q^{90} -17.3968 q^{91} -0.117021 q^{92} -1.50268 q^{93} +7.29187 q^{94} +10.0462 q^{95} +11.8810 q^{96} +1.54287 q^{97} -16.5120 q^{98} +8.67708 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * 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 $

$2$	−1.67615	−1.18521	−0.592607	−	0.805492i	$-0.701901\pi$
$2$	−1.67615	−1.18521	−0.592607	+	0.805492i	$0.701901\pi$
$3$	2.74461	1.58460	0.792302	−	0.610129i	$-0.208882\pi$
$3$	2.74461	1.58460	0.792302	+	0.610129i	$0.208882\pi$
$4$	0.809463	0.404732
$5$	2.71622	1.21473	0.607364	−	0.794423i	$-0.292227\pi$
$5$	2.71622	1.21473	0.607364	+	0.794423i	$0.292227\pi$
$6$	−4.60037	−1.87809
$7$	4.10502	1.55155	0.775776	−	0.631008i	$-0.217359\pi$
$7$	4.10502	1.55155	0.775776	+	0.631008i	$0.217359\pi$
$8$	1.99551	0.705520
$9$	4.53291	1.51097
$10$	−4.55277	−1.43971
$11$	1.91424	0.577165	0.288582	−	0.957455i	$-0.406816\pi$
$11$	1.91424	0.577165	0.288582	+	0.957455i	$0.406816\pi$
$12$	2.22166	0.641339
$13$	−4.23793	−1.17539	−0.587696	−	0.809082i	$-0.699965\pi$
$13$	−4.23793	−1.17539	−0.587696	+	0.809082i	$0.699965\pi$
$14$	−6.88061	−1.83892
$15$	7.45497	1.92486
$16$	−4.96370	−1.24092
$17$	2.89021	0.700979	0.350490	−	0.936567i	$-0.386015\pi$
$17$	2.89021	0.700979	0.350490	+	0.936567i	$0.386015\pi$
$18$	−7.59782	−1.79082
$19$	3.69859	0.848516	0.424258	−	0.905541i	$-0.360535\pi$
$19$	3.69859	0.848516	0.424258	+	0.905541i	$0.360535\pi$
$20$	2.19868	0.491639
$21$	11.2667	2.45860
$22$	−3.20854	−0.684064
$23$	−0.144566	−0.0301442	−0.0150721	−	0.999886i	$-0.504798\pi$
$23$	−0.144566	−0.0301442	−0.0150721	+	0.999886i	$0.504798\pi$
$24$	5.47691	1.11797
$25$	2.37783	0.475566
$26$	7.10339	1.39309
$27$	4.20725	0.809685
$28$	3.32286	0.627962
$29$	1.44579	0.268476	0.134238	−	0.990949i	$-0.457141\pi$
$29$	1.44579	0.268476	0.134238	+	0.990949i	$0.457141\pi$
$30$	−12.4956	−2.28138
$31$	−0.547502	−0.0983343	−0.0491672	−	0.998791i	$-0.515657\pi$
$31$	−0.547502	−0.0983343	−0.0491672	+	0.998791i	$0.515657\pi$
$32$	4.32885	0.765240
$33$	5.25385	0.914578
$34$	−4.84442	−0.830810
$35$	11.1501	1.88471
$36$	3.66922	0.611537
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−6.19938	−1.00567
$39$	−11.6315	−1.86253
$40$	5.42024	0.857016
$41$	−8.63328	−1.34829	−0.674146	−	0.738598i	$-0.735488\pi$
$41$	−8.63328	−1.34829	−0.674146	+	0.738598i	$0.735488\pi$
$42$	−18.8846	−2.91396
$43$	1.99094	0.303616	0.151808	−	0.988410i	$-0.451491\pi$
$43$	1.99094	0.303616	0.151808	+	0.988410i	$0.451491\pi$
$44$	1.54951	0.233597
$45$	12.3124	1.83542
$46$	0.242314	0.0357273
$47$	−4.35038	−0.634568	−0.317284	−	0.948331i	$-0.602771\pi$
$47$	−4.35038	−0.634568	−0.317284	+	0.948331i	$0.602771\pi$
$48$	−13.6234	−1.96637
$49$	9.85120	1.40731
$50$	−3.98559	−0.563647
$51$	7.93252	1.11077
$52$	−3.43045	−0.475718
$53$	−3.44384	−0.473048	−0.236524	−	0.971626i	$-0.576008\pi$
$53$	−3.44384	−0.473048	−0.236524	+	0.971626i	$0.576008\pi$
$54$	−7.05196	−0.959650
$55$	5.19949	0.701099
$56$	8.19162	1.09465
$57$	10.1512	1.34456
$58$	−2.42335	−0.318202
$59$	−9.18600	−1.19592	−0.597958	−	0.801527i	$-0.704021\pi$
$59$	−9.18600	−1.19592	−0.597958	+	0.801527i	$0.704021\pi$
$60$	6.03452	0.779053
$61$	−0.400515	−0.0512807	−0.0256404	−	0.999671i	$-0.508162\pi$
$61$	−0.400515	−0.0512807	−0.0256404	+	0.999671i	$0.508162\pi$
$62$	0.917693	0.116547
$63$	18.6077	2.34435
$64$	2.67161	0.333951
$65$	−11.5111	−1.42778
$66$	−8.80622	−1.08397
$67$	7.87908	0.962583	0.481292	−	0.876561i	$-0.340168\pi$
$67$	7.87908	0.962583	0.481292	+	0.876561i	$0.340168\pi$
$68$	2.33952	0.283709
$69$	−0.396779	−0.0477666
$70$	−18.6892	−2.23379
$71$	5.67148	0.673081	0.336541	−	0.941669i	$-0.390743\pi$
$71$	5.67148	0.673081	0.336541	+	0.941669i	$0.390743\pi$
$72$	9.04548	1.06602
$73$	9.83375	1.15095	0.575476	−	0.817818i	$-0.304817\pi$
$73$	9.83375	1.15095	0.575476	+	0.817818i	$0.304817\pi$
$74$	1.67615	0.194848
$75$	6.52622	0.753583
$76$	2.99388	0.343421
$77$	7.85799	0.895502
$78$	19.4961	2.20750
$79$	15.0385	1.69197	0.845983	−	0.533210i	$-0.179014\pi$
$79$	15.0385	1.69197	0.845983	+	0.533210i	$0.179014\pi$
$80$	−13.4825	−1.50739
$81$	−2.05145	−0.227939
$82$	14.4706	1.59801
$83$	−5.27272	−0.578756	−0.289378	−	0.957215i	$-0.593449\pi$
$83$	−5.27272	−0.578756	−0.289378	+	0.957215i	$0.593449\pi$
$84$	9.11998	0.995072
$85$	7.85044	0.851500
$86$	−3.33710	−0.359849
$87$	3.96814	0.425429
$88$	3.81989	0.407202
$89$	6.86704	0.727905	0.363953	−	0.931417i	$-0.381427\pi$
$89$	6.86704	0.727905	0.363953	+	0.931417i	$0.381427\pi$
$90$	−20.6373	−2.17536
$91$	−17.3968	−1.82368
$92$	−0.117021	−0.0122003
$93$	−1.50268	−0.155821
$94$	7.29187	0.752099
$95$	10.0462	1.03072
$96$	11.8810	1.21260
$97$	1.54287	0.156655	0.0783273	−	0.996928i	$-0.475042\pi$
$97$	1.54287	0.156655	0.0783273	+	0.996928i	$0.475042\pi$
$98$	−16.5120	−1.66797
$99$	8.67708	0.872079
$100$	1.92476	0.192476
$101$	0.546193	0.0543482	0.0271741	−	0.999631i	$-0.491349\pi$
$101$	0.546193	0.0543482	0.0271741	+	0.999631i	$0.491349\pi$
$102$	−13.2961	−1.31651
$103$	−7.36203	−0.725403	−0.362701	−	0.931905i	$-0.618145\pi$
$103$	−7.36203	−0.725403	−0.362701	+	0.931905i	$0.618145\pi$
$104$	−8.45685	−0.829262
$105$	30.6028	2.98653
$106$	5.77238	0.560663
$107$	−2.93351	−0.283593	−0.141797	−	0.989896i	$-0.545288\pi$
$107$	−2.93351	−0.283593	−0.141797	+	0.989896i	$0.545288\pi$
$108$	3.40561	0.327705
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−8.71510	−0.830952
$111$	−2.74461	−0.260507
$112$	−20.3761	−1.92536
$113$	8.74176	0.822356	0.411178	−	0.911555i	$-0.365117\pi$
$113$	8.74176	0.822356	0.411178	+	0.911555i	$0.365117\pi$
$114$	−17.0149	−1.59359
$115$	−0.392673	−0.0366170
$116$	1.17031	0.108661
$117$	−19.2102	−1.77598
$118$	15.3971	1.41742
$119$	11.8644	1.08761
$120$	14.8765	1.35803
$121$	−7.33569	−0.666881
$122$	0.671322	0.0607786
$123$	−23.6950	−2.13651
$124$	−0.443183	−0.0397990
$125$	−7.12238	−0.637045
$126$	−31.1892	−2.77855
$127$	−3.38076	−0.299994	−0.149997	−	0.988686i	$-0.547926\pi$
$127$	−3.38076	−0.299994	−0.149997	+	0.988686i	$0.547926\pi$
$128$	−13.1357	−1.16104
$129$	5.46436	0.481110
$130$	19.2943	1.69223
$131$	−4.91916	−0.429789	−0.214895	−	0.976637i	$-0.568941\pi$
$131$	−4.91916	−0.429789	−0.214895	+	0.976637i	$0.568941\pi$
$132$	4.25280	0.370159
$133$	15.1828	1.31652
$134$	−13.2065	−1.14087
$135$	11.4278	0.983548
$136$	5.76745	0.494555
$137$	8.92434	0.762457	0.381229	−	0.924481i	$-0.375501\pi$
$137$	8.92434	0.762457	0.381229	+	0.924481i	$0.375501\pi$
$138$	0.665059	0.0566136
$139$	−12.9429	−1.09780	−0.548902	−	0.835887i	$-0.684954\pi$
$139$	−12.9429	−1.09780	−0.548902	+	0.835887i	$0.684954\pi$
$140$	9.02562	0.762804
$141$	−11.9401	−1.00554
$142$	−9.50623	−0.797745
$143$	−8.11242	−0.678395
$144$	−22.5000	−1.87500
$145$	3.92708	0.326126
$146$	−16.4828	−1.36413
$147$	27.0377	2.23004
$148$	−0.809463	−0.0665375
$149$	−13.1704	−1.07896	−0.539481	−	0.841998i	$-0.681379\pi$
$149$	−13.1704	−1.07896	−0.539481	+	0.841998i	$0.681379\pi$
$150$	−10.9389	−0.893157
$151$	−7.83269	−0.637415	−0.318708	−	0.947853i	$-0.603249\pi$
$151$	−7.83269	−0.637415	−0.318708	+	0.947853i	$0.603249\pi$
$152$	7.38059	0.598645
$153$	13.1011	1.05916
$154$	−13.1711	−1.06136
$155$	−1.48713	−0.119450
$156$	−9.41527	−0.753825
$157$	−14.2794	−1.13962	−0.569808	−	0.821778i	$-0.692983\pi$
$157$	−14.2794	−1.13962	−0.569808	+	0.821778i	$0.692983\pi$
$158$	−25.2067	−2.00534
$159$	−9.45202	−0.749594
$160$	11.7581	0.929559
$161$	−0.593448	−0.0467702
$162$	3.43854	0.270157
$163$	−23.2689	−1.82256	−0.911279	−	0.411790i	$-0.864904\pi$
$163$	−23.2689	−1.82256	−0.911279	+	0.411790i	$0.864904\pi$
$164$	−6.98832	−0.545696
$165$	14.2706	1.11096
$166$	8.83785	0.685950
$167$	13.5887	1.05152	0.525761	−	0.850632i	$-0.323781\pi$
$167$	13.5887	1.05152	0.525761	+	0.850632i	$0.323781\pi$
$168$	22.4828	1.73459
$169$	4.96008	0.381545
$170$	−13.1585	−1.00921
$171$	16.7654	1.28208
$172$	1.61159	0.122883
$173$	7.40168	0.562739	0.281369	−	0.959600i	$-0.409211\pi$
$173$	7.40168	0.562739	0.281369	+	0.959600i	$0.409211\pi$
$174$	−6.65117	−0.504224
$175$	9.76104	0.737865
$176$	−9.50170	−0.716218
$177$	−25.2120	−1.89505
$178$	−11.5102	−0.862723
$179$	11.7235	0.876259	0.438130	−	0.898912i	$-0.355641\pi$
$179$	11.7235	0.876259	0.438130	+	0.898912i	$0.355641\pi$
$180$	9.96641	0.742852
$181$	−5.76337	−0.428388	−0.214194	−	0.976791i	$-0.568713\pi$
$181$	−5.76337	−0.428388	−0.214194	+	0.976791i	$0.568713\pi$
$182$	29.1596	2.16145
$183$	−1.09926	−0.0812597
$184$	−0.288484	−0.0212673
$185$	−2.71622	−0.199700
$186$	2.51872	0.184681
$187$	5.53256	0.404581
$188$	−3.52147	−0.256830
$189$	17.2708	1.25627
$190$	−16.8389	−1.22162
$191$	8.62588	0.624146	0.312073	−	0.950058i	$-0.398977\pi$
$191$	8.62588	0.624146	0.312073	+	0.950058i	$0.398977\pi$
$192$	7.33254	0.529180
$193$	−22.0940	−1.59036	−0.795182	−	0.606371i	$-0.792624\pi$
$193$	−22.0940	−1.59036	−0.795182	+	0.606371i	$0.792624\pi$
$194$	−2.58607	−0.185669
$195$	−31.5937	−2.26247
$196$	7.97418	0.569585
$197$	−0.134331	−0.00957066	−0.00478533	−	0.999989i	$-0.501523\pi$
$197$	−0.134331	−0.00957066	−0.00478533	+	0.999989i	$0.501523\pi$
$198$	−14.5440	−1.03360
$199$	−10.6189	−0.752753	−0.376377	−	0.926467i	$-0.622830\pi$
$199$	−10.6189	−0.752753	−0.376377	+	0.926467i	$0.622830\pi$
$200$	4.74499	0.335521
$201$	21.6251	1.52531
$202$	−0.915499	−0.0644143
$203$	5.93500	0.416555
$204$	6.42108	0.449566
$205$	−23.4499	−1.63781
$206$	12.3398	0.859757
$207$	−0.655306	−0.0455469
$208$	21.0358	1.45857
$209$	7.07999	0.489733
$210$	−51.2947	−3.53967
$211$	−10.6826	−0.735421	−0.367711	−	0.929940i	$-0.619858\pi$
$211$	−10.6826	−0.735421	−0.367711	+	0.929940i	$0.619858\pi$
$212$	−2.78766	−0.191458
$213$	15.5660	1.06657
$214$	4.91699	0.336119
$215$	5.40782	0.368810
$216$	8.39562	0.571249
$217$	−2.24751	−0.152571
$218$	−1.67615	−0.113523
$219$	26.9898	1.82380
$220$	4.20879	0.283757
$221$	−12.2485	−0.823925
$222$	4.60037	0.308757
$223$	26.5832	1.78014	0.890071	−	0.455822i	$-0.150655\pi$
$223$	26.5832	1.78014	0.890071	+	0.455822i	$0.150655\pi$
$224$	17.7700	1.18731
$225$	10.7785	0.718566
$226$	−14.6525	−0.974667
$227$	−2.84451	−0.188797	−0.0943983	−	0.995535i	$-0.530093\pi$
$227$	−2.84451	−0.188797	−0.0943983	+	0.995535i	$0.530093\pi$
$228$	8.21704	0.544186
$229$	7.63710	0.504674	0.252337	−	0.967639i	$-0.418801\pi$
$229$	7.63710	0.504674	0.252337	+	0.967639i	$0.418801\pi$
$230$	0.658178	0.0433989
$231$	21.5672	1.41902
$232$	2.88509	0.189416
$233$	−6.67243	−0.437126	−0.218563	−	0.975823i	$-0.570137\pi$
$233$	−6.67243	−0.437126	−0.218563	+	0.975823i	$0.570137\pi$
$234$	32.1990	2.10492
$235$	−11.8166	−0.770828
$236$	−7.43573	−0.484025
$237$	41.2749	2.68110
$238$	−19.8864	−1.28905
$239$	1.19486	0.0772889	0.0386444	−	0.999253i	$-0.487696\pi$
$239$	1.19486	0.0772889	0.0386444	+	0.999253i	$0.487696\pi$
$240$	−37.0042	−2.38861
$241$	14.7898	0.952694	0.476347	−	0.879257i	$-0.341961\pi$
$241$	14.7898	0.952694	0.476347	+	0.879257i	$0.341961\pi$
$242$	12.2957	0.790396
$243$	−18.2522	−1.17088
$244$	−0.324202	−0.0207549
$245$	26.7580	1.70951
$246$	39.7163	2.53222
$247$	−15.6744	−0.997338
$248$	−1.09255	−0.0693769
$249$	−14.4716	−0.917100
$250$	11.9382	0.755035
$251$	−9.71904	−0.613460	−0.306730	−	0.951797i	$-0.599235\pi$
$251$	−9.71904	−0.613460	−0.306730	+	0.951797i	$0.599235\pi$
$252$	15.0622	0.948832
$253$	−0.276735	−0.0173982
$254$	5.66665	0.355557
$255$	21.5464	1.34929
$256$	16.6741	1.04213
$257$	−0.456236	−0.0284592	−0.0142296	−	0.999899i	$-0.504530\pi$
$257$	−0.456236	−0.0284592	−0.0142296	+	0.999899i	$0.504530\pi$
$258$	−9.15907	−0.570219
$259$	−4.10502	−0.255074
$260$	−9.31785	−0.577868
$261$	6.55364	0.405660
$262$	8.24523	0.509392
$263$	11.8189	0.728785	0.364393	−	0.931245i	$-0.381277\pi$
$263$	11.8189	0.728785	0.364393	+	0.931245i	$0.381277\pi$
$264$	10.4841	0.645253
$265$	−9.35422	−0.574625
$266$	−25.4486	−1.56035
$267$	18.8474	1.15344
$268$	6.37783	0.389588
$269$	−4.97259	−0.303184	−0.151592	−	0.988443i	$-0.548440\pi$
$269$	−4.97259	−0.303184	−0.151592	+	0.988443i	$0.548440\pi$
$270$	−19.1546	−1.16571
$271$	−26.6427	−1.61843	−0.809214	−	0.587514i	$-0.800107\pi$
$271$	−26.6427	−1.61843	−0.809214	+	0.587514i	$0.800107\pi$
$272$	−14.3461	−0.869862
$273$	−47.7475	−2.88981
$274$	−14.9585	−0.903675
$275$	4.55173	0.274480
$276$	−0.321178	−0.0193326
$277$	6.44545	0.387270	0.193635	−	0.981074i	$-0.437972\pi$
$277$	6.44545	0.387270	0.193635	+	0.981074i	$0.437972\pi$
$278$	21.6942	1.30113
$279$	−2.48178	−0.148580
$280$	22.2502	1.32970
$281$	6.11863	0.365007	0.182503	−	0.983205i	$-0.441580\pi$
$281$	6.11863	0.365007	0.182503	+	0.983205i	$0.441580\pi$
$282$	20.0134	1.19178
$283$	0.00633344	0.000376484 0	0.000188242	−	1.00000i	$-0.499940\pi$
$283$	0.00633344	0.000376484 0	0.000188242		1.00000i	$0.499940\pi$
$284$	4.59086	0.272417
$285$	27.5729	1.63328
$286$	13.5976	0.804043
$287$	−35.4398	−2.09195
$288$	19.6223	1.15625
$289$	−8.64667	−0.508628
$290$	−6.58235	−0.386529
$291$	4.23458	0.248236
$292$	7.96006	0.465827
$293$	0.279937	0.0163541	0.00817704	−	0.999967i	$-0.497397\pi$
$293$	0.279937	0.0163541	0.00817704	+	0.999967i	$0.497397\pi$
$294$	−45.3192	−2.64307
$295$	−24.9512	−1.45271
$296$	−1.99551	−0.115987
$297$	8.05368	0.467322
$298$	22.0755	1.27880
$299$	0.612662	0.0354312
$300$	5.28274	0.304999
$301$	8.17285	0.471075
$302$	13.1287	0.755473
$303$	1.49909	0.0861204
$304$	−18.3587	−1.05294
$305$	−1.08789	−0.0622922
$306$	−21.9593	−1.25533
$307$	−19.5433	−1.11539	−0.557697	−	0.830044i	$-0.688315\pi$
$307$	−19.5433	−1.11539	−0.557697	+	0.830044i	$0.688315\pi$
$308$	6.36076	0.362438
$309$	−20.2059	−1.14948
$310$	2.49265	0.141573
$311$	−0.716849	−0.0406488	−0.0203244	−	0.999793i	$-0.506470\pi$
$311$	−0.716849	−0.0406488	−0.0203244	+	0.999793i	$0.506470\pi$
$312$	−23.2108	−1.31405
$313$	9.59530	0.542359	0.271179	−	0.962529i	$-0.412586\pi$
$313$	9.59530	0.542359	0.271179	+	0.962529i	$0.412586\pi$
$314$	23.9343	1.35069
$315$	50.5425	2.84775
$316$	12.1731	0.684792
$317$	11.7454	0.659685	0.329843	−	0.944036i	$-0.393004\pi$
$317$	11.7454	0.659685	0.329843	+	0.944036i	$0.393004\pi$
$318$	15.8430	0.888430
$319$	2.76759	0.154955
$320$	7.25667	0.405660
$321$	−8.05136	−0.449383
$322$	0.994705	0.0554327
$323$	10.6897	0.594792
$324$	−1.66058	−0.0922543
$325$	−10.0771	−0.558976
$326$	39.0020	2.16012
$327$	2.74461	0.151778
$328$	−17.2278	−0.951247
$329$	−17.8584	−0.984565
$330$	−23.9196	−1.31673
$331$	−16.0018	−0.879539	−0.439769	−	0.898111i	$-0.644940\pi$
$331$	−16.0018	−0.879539	−0.439769	+	0.898111i	$0.644940\pi$
$332$	−4.26807	−0.234241
$333$	−4.53291	−0.248402
$334$	−22.7766	−1.24628
$335$	21.4013	1.16928
$336$	−55.9245	−3.05093
$337$	13.7178	0.747257	0.373629	−	0.927578i	$-0.378113\pi$
$337$	13.7178	0.747257	0.373629	+	0.927578i	$0.378113\pi$
$338$	−8.31382	−0.452212
$339$	23.9928	1.30311
$340$	6.35464	0.344629
$341$	−1.04805	−0.0567551
$342$	−28.1012	−1.51954
$343$	11.7042	0.631969
$344$	3.97295	0.214207
$345$	−1.07774	−0.0580234
$346$	−12.4063	−0.666966
$347$	−12.1338	−0.651376	−0.325688	−	0.945477i	$-0.605596\pi$
$347$	−12.1338	−0.651376	−0.325688	+	0.945477i	$0.605596\pi$
$348$	3.21206	0.172185
$349$	−0.855030	−0.0457687	−0.0228844	−	0.999738i	$-0.507285\pi$
$349$	−0.855030	−0.0457687	−0.0228844	+	0.999738i	$0.507285\pi$
$350$	−16.3609	−0.874528
$351$	−17.8300	−0.951697
$352$	8.28646	0.441670
$353$	1.43968	0.0766265	0.0383132	−	0.999266i	$-0.487802\pi$
$353$	1.43968	0.0766265	0.0383132	+	0.999266i	$0.487802\pi$
$354$	42.2591	2.24604
$355$	15.4050	0.817611
$356$	5.55862	0.294606
$357$	32.5632	1.72343
$358$	−19.6504	−1.03855
$359$	2.83340	0.149541	0.0747707	−	0.997201i	$-0.476178\pi$
$359$	2.83340	0.149541	0.0747707	+	0.997201i	$0.476178\pi$
$360$	24.5695	1.29493
$361$	−5.32040	−0.280021
$362$	9.66025	0.507732
$363$	−20.1336	−1.05674
$364$	−14.0821	−0.738101
$365$	26.7106	1.39810
$366$	1.84252	0.0963101
$367$	4.62632	0.241492	0.120746	−	0.992683i	$-0.461471\pi$
$367$	4.62632	0.241492	0.120746	+	0.992683i	$0.461471\pi$
$368$	0.717583	0.0374066
$369$	−39.1339	−2.03723
$370$	4.55277	0.236687
$371$	−14.1371	−0.733959
$372$	−1.21637	−0.0630657
$373$	−0.0118352	−0.000612804 0	−0.000306402	−	1.00000i	$-0.500098\pi$
$373$	−0.0118352	−0.000612804 0	−0.000306402		1.00000i	$0.500098\pi$
$374$	−9.27337	−0.479515
$375$	−19.5482	−1.00946
$376$	−8.68124	−0.447701
$377$	−6.12716	−0.315565
$378$	−28.9484	−1.48895
$379$	−9.17946	−0.471517	−0.235759	−	0.971812i	$-0.575757\pi$
$379$	−9.17946	−0.471517	−0.235759	+	0.971812i	$0.575757\pi$
$380$	8.13201	0.417163
$381$	−9.27889	−0.475372
$382$	−14.4582	−0.739747
$383$	−18.0530	−0.922466	−0.461233	−	0.887279i	$-0.652593\pi$
$383$	−18.0530	−0.922466	−0.461233	+	0.887279i	$0.652593\pi$
$384$	−36.0525	−1.83979
$385$	21.3440	1.08779
$386$	37.0328	1.88492
$387$	9.02475	0.458754
$388$	1.24890	0.0634031
$389$	31.0241	1.57298	0.786492	−	0.617601i	$-0.211895\pi$
$389$	31.0241	1.57298	0.786492	+	0.617601i	$0.211895\pi$
$390$	52.9556	2.68151
$391$	−0.417827	−0.0211304
$392$	19.6582	0.992889
$393$	−13.5012	−0.681045
$394$	0.225158	0.0113433
$395$	40.8479	2.05528
$396$	7.02377	0.352958
$397$	−27.7419	−1.39233	−0.696163	−	0.717884i	$-0.745111\pi$
$397$	−27.7419	−1.39233	−0.696163	+	0.717884i	$0.745111\pi$
$398$	17.7988	0.892173
$399$	41.6710	2.08616
$400$	−11.8028	−0.590141
$401$	30.8770	1.54192	0.770962	−	0.636881i	$-0.219776\pi$
$401$	30.8770	1.54192	0.770962	+	0.636881i	$0.219776\pi$
$402$	−36.2467	−1.80782
$403$	2.32028	0.115581
$404$	0.442123	0.0219964
$405$	−5.57219	−0.276884
$406$	−9.94792	−0.493707
$407$	−1.91424	−0.0948853
$408$	15.8294	0.783674
$409$	4.07288	0.201391	0.100695	−	0.994917i	$-0.467893\pi$
$409$	4.07288	0.201391	0.100695	+	0.994917i	$0.467893\pi$
$410$	39.3054	1.94115
$411$	24.4939	1.20819
$412$	−5.95929	−0.293593
$413$	−37.7087	−1.85553
$414$	1.09839	0.0539828
$415$	−14.3219	−0.703032
$416$	−18.3454	−0.899456
$417$	−35.5233	−1.73958
$418$	−11.8671	−0.580439
$419$	−19.3719	−0.946378	−0.473189	−	0.880961i	$-0.656897\pi$
$419$	−19.3719	−0.946378	−0.473189	+	0.880961i	$0.656897\pi$
$420$	24.7718	1.20874
$421$	34.3575	1.67448	0.837242	−	0.546832i	$-0.184166\pi$
$421$	34.3575	1.67448	0.837242	+	0.546832i	$0.184166\pi$
$422$	17.9056	0.871632
$423$	−19.7199	−0.958813
$424$	−6.87223	−0.333745
$425$	6.87243	0.333362
$426$	−26.0909	−1.26411
$427$	−1.64412	−0.0795647
$428$	−2.37457	−0.114779
$429$	−22.2655	−1.07499
$430$	−9.06430	−0.437119
$431$	35.6813	1.71871	0.859354	−	0.511382i	$-0.170866\pi$
$431$	35.6813	1.71871	0.859354	+	0.511382i	$0.170866\pi$
$432$	−20.8835	−1.00476
$433$	−11.4012	−0.547908	−0.273954	−	0.961743i	$-0.588332\pi$
$433$	−11.4012	−0.547908	−0.273954	+	0.961743i	$0.588332\pi$
$434$	3.76715	0.180829
$435$	10.7783	0.516781
$436$	0.809463	0.0387663
$437$	−0.534692	−0.0255778
$438$	−45.2389	−2.16160
$439$	−23.8314	−1.13741	−0.568705	−	0.822541i	$-0.692555\pi$
$439$	−23.8314	−1.13741	−0.568705	+	0.822541i	$0.692555\pi$
$440$	10.3756	0.494639
$441$	44.6546	2.12641
$442$	20.5303	0.976527
$443$	−0.767021	−0.0364423	−0.0182211	−	0.999834i	$-0.505800\pi$
$443$	−0.767021	−0.0364423	−0.0182211	+	0.999834i	$0.505800\pi$
$444$	−2.22166	−0.105436
$445$	18.6524	0.884207
$446$	−44.5573	−2.10985
$447$	−36.1477	−1.70973
$448$	10.9670	0.518143
$449$	16.8339	0.794439	0.397219	−	0.917724i	$-0.369975\pi$
$449$	16.8339	0.794439	0.397219	+	0.917724i	$0.369975\pi$
$450$	−18.0663	−0.851654
$451$	−16.5262	−0.778187
$452$	7.07614	0.332833
$453$	−21.4977	−1.01005
$454$	4.76781	0.223764
$455$	−47.2535	−2.21528
$456$	20.2569	0.948615
$457$	−2.65452	−0.124173	−0.0620867	−	0.998071i	$-0.519776\pi$
$457$	−2.65452	−0.124173	−0.0620867	+	0.998071i	$0.519776\pi$
$458$	−12.8009	−0.598146
$459$	12.1598	0.567573
$460$	−0.317855	−0.0148200
$461$	36.7419	1.71124	0.855621	−	0.517603i	$-0.173176\pi$
$461$	36.7419	1.71124	0.855621	+	0.517603i	$0.173176\pi$
$462$	−36.1497	−1.68184
$463$	33.7709	1.56947	0.784733	−	0.619834i	$-0.212800\pi$
$463$	33.7709	1.56947	0.784733	+	0.619834i	$0.212800\pi$
$464$	−7.17646	−0.333159
$465$	−4.08161	−0.189280
$466$	11.1840	0.518087
$467$	−0.527229	−0.0243972	−0.0121986	−	0.999926i	$-0.503883\pi$
$467$	−0.527229	−0.0243972	−0.0121986	+	0.999926i	$0.503883\pi$
$468$	−15.5499	−0.718796
$469$	32.3438	1.49350
$470$	19.8063	0.913596
$471$	−39.1913	−1.80584
$472$	−18.3308	−0.843743
$473$	3.81114	0.175236
$474$	−69.1828	−3.17767
$475$	8.79462	0.403525
$476$	9.60378	0.440189
$477$	−15.6106	−0.714762
$478$	−2.00275	−0.0916038
$479$	−20.5403	−0.938508	−0.469254	−	0.883063i	$-0.655477\pi$
$479$	−20.5403	−0.938508	−0.469254	+	0.883063i	$0.655477\pi$
$480$	32.2714	1.47298
$481$	4.23793	0.193233
$482$	−24.7898	−1.12915
$483$	−1.62879	−0.0741123
$484$	−5.93797	−0.269908
$485$	4.19077	0.190293
$486$	30.5933	1.38774
$487$	−19.5726	−0.886917	−0.443459	−	0.896295i	$-0.646249\pi$
$487$	−19.5726	−0.886917	−0.443459	+	0.896295i	$0.646249\pi$
$488$	−0.799233	−0.0361796
$489$	−63.8641	−2.88803
$490$	−44.8503	−2.02613
$491$	−26.3573	−1.18949	−0.594745	−	0.803914i	$-0.702747\pi$
$491$	−26.3573	−1.18949	−0.594745	+	0.803914i	$0.702747\pi$
$492$	−19.1803	−0.864713
$493$	4.17864	0.188196
$494$	26.2726	1.18206
$495$	23.5688	1.05934
$496$	2.71763	0.122025
$497$	23.2816	1.04432
$498$	24.2565	1.08696
$499$	39.7722	1.78045	0.890225	−	0.455521i	$-0.150547\pi$
$499$	39.7722	1.78045	0.890225	+	0.455521i	$0.150547\pi$
$500$	−5.76531	−0.257832
$501$	37.2956	1.66625
$502$	16.2905	0.727082
$503$	32.4473	1.44675	0.723377	−	0.690454i	$-0.242589\pi$
$503$	32.4473	1.44675	0.723377	+	0.690454i	$0.242589\pi$
$504$	37.1319	1.65399
$505$	1.48358	0.0660184
$506$	0.463847	0.0206205
$507$	13.6135	0.604597
$508$	−2.73660	−0.121417
$509$	42.5121	1.88432	0.942158	−	0.335170i	$-0.108794\pi$
$509$	42.5121	1.88432	0.942158	+	0.335170i	$0.108794\pi$
$510$	−36.1150	−1.59920
$511$	40.3677	1.78576
$512$	−1.67686	−0.0741074
$513$	15.5609	0.687031
$514$	0.764718	0.0337303
$515$	−19.9969	−0.881167
$516$	4.42320	0.194721
$517$	−8.32767	−0.366250
$518$	6.88061	0.302317
$519$	20.3147	0.891718
$520$	−22.9706	−1.00733
$521$	22.9064	1.00355	0.501774	−	0.864999i	$-0.332681\pi$
$521$	22.9064	1.00355	0.501774	+	0.864999i	$0.332681\pi$
$522$	−10.9848	−0.480794
$523$	28.5492	1.24837	0.624184	−	0.781277i	$-0.285431\pi$
$523$	28.5492	1.24837	0.624184	+	0.781277i	$0.285431\pi$
$524$	−3.98188	−0.173949
$525$	26.7903	1.16922
$526$	−19.8102	−0.863766
$527$	−1.58240	−0.0689303
$528$	−26.0785	−1.13492
$529$	−22.9791	−0.999091
$530$	15.6790	0.681054
$531$	−41.6393	−1.80699
$532$	12.2899	0.532836
$533$	36.5873	1.58477
$534$	−31.5910	−1.36707
$535$	−7.96805	−0.344489
$536$	15.7228	0.679122
$537$	32.1766	1.38852
$538$	8.33479	0.359338
$539$	18.8576	0.812253
$540$	9.25038	0.398073
$541$	33.4447	1.43790	0.718951	−	0.695061i	$-0.244623\pi$
$541$	33.4447	1.43790	0.718951	+	0.695061i	$0.244623\pi$
$542$	44.6570	1.91818
$543$	−15.8182	−0.678826
$544$	12.5113	0.536417
$545$	2.71622	0.116350
$546$	80.0318	3.42505
$547$	−19.8658	−0.849402	−0.424701	−	0.905334i	$-0.639621\pi$
$547$	−19.8658	−0.849402	−0.424701	+	0.905334i	$0.639621\pi$
$548$	7.22392	0.308591
$549$	−1.81550	−0.0774837
$550$	−7.62937	−0.325317
$551$	5.34739	0.227806
$552$	−0.791777	−0.0337003
$553$	61.7335	2.62517
$554$	−10.8035	−0.458997
$555$	−7.45497	−0.316446
$556$	−10.4768	−0.444316
$557$	−37.9225	−1.60683	−0.803414	−	0.595420i	$-0.796986\pi$
$557$	−37.9225	−1.60683	−0.803414	+	0.595420i	$0.796986\pi$
$558$	4.15982	0.176099
$559$	−8.43747	−0.356867
$560$	−55.3458	−2.33879
$561$	15.1847	0.641100
$562$	−10.2557	−0.432611
$563$	7.04880	0.297072	0.148536	−	0.988907i	$-0.452544\pi$
$563$	7.04880	0.297072	0.148536	+	0.988907i	$0.452544\pi$
$564$	−9.66508	−0.406973
$565$	23.7445	0.998939
$566$	−0.0106158	−0.000446214 0
$567$	−8.42126	−0.353660
$568$	11.3175	0.474872
$569$	7.66255	0.321231	0.160615	−	0.987017i	$-0.448652\pi$
$569$	7.66255	0.321231	0.160615	+	0.987017i	$0.448652\pi$
$570$	−46.2162	−1.93578
$571$	20.7765	0.869471	0.434735	−	0.900558i	$-0.356842\pi$
$571$	20.7765	0.869471	0.434735	+	0.900558i	$0.356842\pi$
$572$	−6.56671	−0.274568
$573$	23.6747	0.989025
$574$	59.4023	2.47940
$575$	−0.343754	−0.0143355
$576$	12.1102	0.504590
$577$	−17.2031	−0.716175	−0.358088	−	0.933688i	$-0.616571\pi$
$577$	−17.2031	−0.716175	−0.358088	+	0.933688i	$0.616571\pi$
$578$	14.4931	0.602833
$579$	−60.6396	−2.52010
$580$	3.17882	0.131994
$581$	−21.6446	−0.897971
$582$	−7.09778	−0.294212
$583$	−6.59234	−0.273027
$584$	19.6234	0.812021
$585$	−52.1790	−2.15734
$586$	−0.469215	−0.0193831
$587$	9.78309	0.403792	0.201896	−	0.979407i	$-0.435290\pi$
$587$	9.78309	0.403792	0.201896	+	0.979407i	$0.435290\pi$
$588$	21.8861	0.902566
$589$	−2.02499	−0.0834382
$590$	41.8218	1.72178
$591$	−0.368686	−0.0151657
$592$	4.96370	0.204007
$593$	−8.73984	−0.358902	−0.179451	−	0.983767i	$-0.557432\pi$
$593$	−8.73984	−0.358902	−0.179451	+	0.983767i	$0.557432\pi$
$594$	−13.4991	−0.553877
$595$	32.2262	1.32115
$596$	−10.6610	−0.436690
$597$	−29.1448	−1.19282
$598$	−1.02691	−0.0419935
$599$	−18.1333	−0.740909	−0.370454	−	0.928851i	$-0.620798\pi$
$599$	−18.1333	−0.740909	−0.370454	+	0.928851i	$0.620798\pi$
$600$	13.0232	0.531668
$601$	7.79576	0.317996	0.158998	−	0.987279i	$-0.449174\pi$
$601$	7.79576	0.317996	0.158998	+	0.987279i	$0.449174\pi$
$602$	−13.6989	−0.558325
$603$	35.7152	1.45443
$604$	−6.34027	−0.257982
$605$	−19.9253	−0.810079
$606$	−2.51269	−0.102071
$607$	−33.8499	−1.37392	−0.686962	−	0.726693i	$-0.741056\pi$
$607$	−33.8499	−1.37392	−0.686962	+	0.726693i	$0.741056\pi$
$608$	16.0107	0.649318
$609$	16.2893	0.660075
$610$	1.82346	0.0738295
$611$	18.4366	0.745866
$612$	10.6048	0.428675
$613$	−11.5736	−0.467452	−0.233726	−	0.972302i	$-0.575092\pi$
$613$	−11.5736	−0.467452	−0.233726	+	0.972302i	$0.575092\pi$
$614$	32.7574	1.32198
$615$	−64.3608	−2.59528
$616$	15.6807	0.631795
$617$	34.2395	1.37843	0.689215	−	0.724557i	$-0.257956\pi$
$617$	34.2395	1.37843	0.689215	+	0.724557i	$0.257956\pi$
$618$	33.8681	1.36237
$619$	32.3929	1.30198	0.650991	−	0.759086i	$-0.274354\pi$
$619$	32.3929	1.30198	0.650991	+	0.759086i	$0.274354\pi$
$620$	−1.20378	−0.0483450
$621$	−0.608226	−0.0244073
$622$	1.20154	0.0481775
$623$	28.1894	1.12938
$624$	57.7352	2.31126
$625$	−31.2351	−1.24940
$626$	−16.0831	−0.642811
$627$	19.4319	0.776034
$628$	−11.5586	−0.461239
$629$	−2.89021	−0.115240
$630$	−84.7166	−3.37519
$631$	19.0851	0.759766	0.379883	−	0.925035i	$-0.375964\pi$
$631$	19.0851	0.759766	0.379883	+	0.925035i	$0.375964\pi$
$632$	30.0096	1.19372
$633$	−29.3197	−1.16535
$634$	−19.6869	−0.781868
$635$	−9.18288	−0.364411
$636$	−7.65107	−0.303385
$637$	−41.7487	−1.65414
$638$	−4.63888	−0.183655
$639$	25.7083	1.01701
$640$	−35.6794	−1.41035
$641$	−35.5900	−1.40572	−0.702861	−	0.711327i	$-0.748094\pi$
$641$	−35.5900	−1.40572	−0.702861	+	0.711327i	$0.748094\pi$
$642$	13.4952	0.532615
$643$	16.3029	0.642925	0.321463	−	0.946922i	$-0.395826\pi$
$643$	16.3029	0.642925	0.321463	+	0.946922i	$0.395826\pi$
$644$	−0.480374	−0.0189294
$645$	14.8424	0.584419
$646$	−17.9175	−0.704956
$647$	−3.35778	−0.132008	−0.0660040	−	0.997819i	$-0.521025\pi$
$647$	−3.35778	−0.132008	−0.0660040	+	0.997819i	$0.521025\pi$
$648$	−4.09370	−0.160816
$649$	−17.5842	−0.690241
$650$	16.8906	0.662506
$651$	−6.16855	−0.241764
$652$	−18.8353	−0.737647
$653$	−46.4825	−1.81900	−0.909500	−	0.415705i	$-0.863535\pi$
$653$	−46.4825	−1.81900	−0.909500	+	0.415705i	$0.863535\pi$
$654$	−4.60037	−0.179889
$655$	−13.3615	−0.522077
$656$	42.8530	1.67313
$657$	44.5755	1.73906
$658$	29.9333	1.16692
$659$	−46.0392	−1.79343	−0.896716	−	0.442606i	$-0.854054\pi$
$659$	−46.0392	−1.79343	−0.896716	+	0.442606i	$0.854054\pi$
$660$	11.5515	0.449642
$661$	23.8115	0.926160	0.463080	−	0.886316i	$-0.346744\pi$
$661$	23.8115	0.926160	0.463080	+	0.886316i	$0.346744\pi$
$662$	26.8214	1.04244
$663$	−33.6175	−1.30560
$664$	−10.5218	−0.408324
$665$	41.2398	1.59921
$666$	7.59782	0.294409
$667$	−0.209013	−0.00809300
$668$	10.9995	0.425584
$669$	72.9606	2.82082
$670$	−35.8717	−1.38584
$671$	−0.766682	−0.0295974
$672$	48.7719	1.88142
$673$	0.905504	0.0349046	0.0174523	−	0.999848i	$-0.494444\pi$
$673$	0.905504	0.0349046	0.0174523	+	0.999848i	$0.494444\pi$
$674$	−22.9931	−0.885660
$675$	10.0041	0.385059
$676$	4.01500	0.154423
$677$	−14.6122	−0.561594	−0.280797	−	0.959767i	$-0.590599\pi$
$677$	−14.6122	−0.561594	−0.280797	+	0.959767i	$0.590599\pi$
$678$	−40.2154	−1.54446
$679$	6.33351	0.243058
$680$	15.6657	0.600750
$681$	−7.80707	−0.299168
$682$	1.75669	0.0672670
$683$	27.9084	1.06789	0.533943	−	0.845521i	$-0.320710\pi$
$683$	27.9084	1.06789	0.533943	+	0.845521i	$0.320710\pi$
$684$	13.5710	0.518899
$685$	24.2404	0.926179
$686$	−19.6180	−0.749019
$687$	20.9609	0.799708
$688$	−9.88242	−0.376764
$689$	14.5948	0.556017
$690$	1.80644	0.0687701
$691$	0.984695	0.0374595	0.0187298	−	0.999825i	$-0.494038\pi$
$691$	0.984695	0.0374595	0.0187298	+	0.999825i	$0.494038\pi$
$692$	5.99138	0.227758
$693$	35.6196	1.35308
$694$	20.3380	0.772020
$695$	−35.1557	−1.33353
$696$	7.91847	0.300149
$697$	−24.9520	−0.945125
$698$	1.43315	0.0542457
$699$	−18.3133	−0.692671
$700$	7.90120	0.298637
$701$	13.5251	0.510836	0.255418	−	0.966831i	$-0.417787\pi$
$701$	13.5251	0.510836	0.255418	+	0.966831i	$0.417787\pi$
$702$	29.8857	1.12796
$703$	−3.69859	−0.139495
$704$	5.11410	0.192745
$705$	−32.4319	−1.22146
$706$	−2.41311	−0.0908187
$707$	2.24213	0.0843241
$708$	−20.4082	−0.766988
$709$	−38.3376	−1.43980	−0.719900	−	0.694078i	$-0.755812\pi$
$709$	−38.3376	−1.43980	−0.719900	+	0.694078i	$0.755812\pi$
$710$	−25.8210	−0.969044
$711$	68.1683	2.55651
$712$	13.7033	0.513552
$713$	0.0791504	0.00296421
$714$	−54.5806	−2.04263
$715$	−22.0351	−0.824065
$716$	9.48978	0.354650
$717$	3.27942	0.122472
$718$	−4.74920	−0.177238
$719$	3.79808	0.141644	0.0708222	−	0.997489i	$-0.477438\pi$
$719$	3.79808	0.141644	0.0708222	+	0.997489i	$0.477438\pi$
$720$	−61.1148	−2.27762
$721$	−30.2213	−1.12550
$722$	8.91777	0.331885
$723$	40.5923	1.50964
$724$	−4.66524	−0.173382
$725$	3.43784	0.127678
$726$	33.7469	1.25246
$727$	−39.5746	−1.46774	−0.733871	−	0.679289i	$-0.762288\pi$
$727$	−39.5746	−1.46774	−0.733871	+	0.679289i	$0.762288\pi$
$728$	−34.7156	−1.28664
$729$	−43.9409	−1.62744
$730$	−44.7708	−1.65704
$731$	5.75424	0.212828
$732$	−0.889811	−0.0328884
$733$	30.5232	1.12740	0.563699	−	0.825980i	$-0.309378\pi$
$733$	30.5232	1.12740	0.563699	+	0.825980i	$0.309378\pi$
$734$	−7.75439	−0.286220
$735$	73.4404	2.70889
$736$	−0.625806	−0.0230675
$737$	15.0825	0.555569
$738$	65.5941	2.41455
$739$	−31.4706	−1.15767	−0.578833	−	0.815446i	$-0.696491\pi$
$739$	−31.4706	−1.15767	−0.578833	+	0.815446i	$0.696491\pi$
$740$	−2.19868	−0.0808250
$741$	−43.0202	−1.58039
$742$	23.6958	0.869899
$743$	−19.8997	−0.730048	−0.365024	−	0.930998i	$-0.618939\pi$
$743$	−19.8997	−0.730048	−0.365024	+	0.930998i	$0.618939\pi$
$744$	−2.99862	−0.109935
$745$	−35.7737	−1.31065
$746$	0.0198375	0.000726304 0
$747$	−23.9008	−0.874484
$748$	4.47840	0.163747
$749$	−12.0421	−0.440010
$750$	32.7656	1.19643
$751$	45.4302	1.65777	0.828885	−	0.559419i	$-0.188976\pi$
$751$	45.4302	1.65777	0.828885	+	0.559419i	$0.188976\pi$
$752$	21.5940	0.787451
$753$	−26.6750	−0.972092
$754$	10.2700	0.374012
$755$	−21.2753	−0.774287
$756$	13.9801	0.508452
$757$	−11.9068	−0.432762	−0.216381	−	0.976309i	$-0.569425\pi$
$757$	−11.9068	−0.432762	−0.216381	+	0.976309i	$0.569425\pi$
$758$	15.3861	0.558849
$759$	−0.759530	−0.0275692
$760$	20.0473	0.727191
$761$	−29.0959	−1.05472	−0.527362	−	0.849641i	$-0.676819\pi$
$761$	−29.0959	−1.05472	−0.527362	+	0.849641i	$0.676819\pi$
$762$	15.5528	0.563417
$763$	4.10502	0.148612
$764$	6.98233	0.252612
$765$	35.5853	1.28659
$766$	30.2595	1.09332
$767$	38.9297	1.40567
$768$	45.7641	1.65137
$769$	20.8464	0.751739	0.375869	−	0.926673i	$-0.377344\pi$
$769$	20.8464	0.751739	0.375869	+	0.926673i	$0.377344\pi$
$770$	−35.7757	−1.28927
$771$	−1.25219	−0.0450966
$772$	−17.8843	−0.643670
$773$	−12.3920	−0.445709	−0.222854	−	0.974852i	$-0.571537\pi$
$773$	−12.3920	−0.445709	−0.222854	+	0.974852i	$0.571537\pi$
$774$	−15.1268	−0.543722
$775$	−1.30187	−0.0467644
$776$	3.07882	0.110523
$777$	−11.2667	−0.404191
$778$	−52.0009	−1.86432
$779$	−31.9310	−1.14405
$780$	−25.5739	−0.915692
$781$	10.8566	0.388479
$782$	0.700339	0.0250441
$783$	6.08280	0.217381
$784$	−48.8984	−1.74637
$785$	−38.7858	−1.38432
$786$	22.6300	0.807184
$787$	15.5911	0.555763	0.277881	−	0.960615i	$-0.410368\pi$
$787$	15.5911	0.555763	0.277881	+	0.960615i	$0.410368\pi$
$788$	−0.108736	−0.00387355
$789$	32.4384	1.15484
$790$	−68.4670	−2.43595
$791$	35.8851	1.27593
$792$	17.3152	0.615269
$793$	1.69736	0.0602749
$794$	46.4994	1.65020
$795$	−25.6737	−0.910554
$796$	−8.59560	−0.304663
$797$	−3.62411	−0.128373	−0.0641863	−	0.997938i	$-0.520445\pi$
$797$	−3.62411	−0.128373	−0.0641863	+	0.997938i	$0.520445\pi$
$798$	−69.8466	−2.47254
$799$	−12.5735	−0.444819
$800$	10.2933	0.363922
$801$	31.1277	1.09984
$802$	−51.7544	−1.82751
$803$	18.8241	0.664290
$804$	17.5047	0.617343
$805$	−1.61193	−0.0568131
$806$	−3.88912	−0.136989
$807$	−13.6478	−0.480427
$808$	1.08993	0.0383438
$809$	10.6178	0.373302	0.186651	−	0.982426i	$-0.440237\pi$
$809$	10.6178	0.373302	0.186651	+	0.982426i	$0.440237\pi$
$810$	9.33980	0.328167
$811$	43.8035	1.53815	0.769074	−	0.639160i	$-0.220718\pi$
$811$	43.8035	1.53815	0.769074	+	0.639160i	$0.220718\pi$
$812$	4.80416	0.168593
$813$	−73.1239	−2.56457
$814$	3.20854	0.112459
$815$	−63.2032	−2.21391
$816$	−39.3746	−1.37839
$817$	7.36368	0.257622
$818$	−6.82674	−0.238691
$819$	−78.8582	−2.75553
$820$	−18.9818	−0.662873
$821$	−29.3933	−1.02583	−0.512916	−	0.858439i	$-0.671435\pi$
$821$	−29.3933	−1.02583	−0.512916	+	0.858439i	$0.671435\pi$
$822$	−41.0553	−1.43197
$823$	−6.72084	−0.234274	−0.117137	−	0.993116i	$-0.537372\pi$
$823$	−6.72084	−0.234274	−0.117137	+	0.993116i	$0.537372\pi$
$824$	−14.6910	−0.511786
$825$	12.4928	0.434942
$826$	63.2053	2.19920
$827$	−11.6934	−0.406618	−0.203309	−	0.979115i	$-0.565170\pi$
$827$	−11.6934	−0.406618	−0.203309	+	0.979115i	$0.565170\pi$
$828$	−0.530446	−0.0184343
$829$	15.9615	0.554367	0.277183	−	0.960817i	$-0.410599\pi$
$829$	15.9615	0.554367	0.277183	+	0.960817i	$0.410599\pi$
$830$	24.0055	0.833243
$831$	17.6903	0.613669
$832$	−11.3221	−0.392523
$833$	28.4721	0.986498
$834$	59.5422	2.06178
$835$	36.9097	1.27731
$836$	5.73100	0.198211
$837$	−2.30348	−0.0796199
$838$	32.4701	1.12166
$839$	51.2410	1.76903	0.884517	−	0.466507i	$-0.154488\pi$
$839$	51.2410	1.76903	0.884517	+	0.466507i	$0.154488\pi$
$840$	61.0683	2.10706
$841$	−26.9097	−0.927920
$842$	−57.5882	−1.98462
$843$	16.7933	0.578391
$844$	−8.64718	−0.297648
$845$	13.4727	0.463473
$846$	33.0534	1.13640
$847$	−30.1131	−1.03470
$848$	17.0942	0.587017
$849$	0.0173829	0.000596578 0
$850$	−11.5192	−0.395105
$851$	0.144566	0.00495567
$852$	12.6001	0.431673
$853$	−21.2613	−0.727974	−0.363987	−	0.931404i	$-0.618585\pi$
$853$	−21.2613	−0.727974	−0.363987	+	0.931404i	$0.618585\pi$
$854$	2.75579	0.0943012
$855$	45.5384	1.55738
$856$	−5.85386	−0.200081
$857$	38.0481	1.29970	0.649850	−	0.760063i	$-0.274832\pi$
$857$	38.0481	1.29970	0.649850	+	0.760063i	$0.274832\pi$
$858$	37.3202	1.27409
$859$	−25.6229	−0.874243	−0.437121	−	0.899402i	$-0.644002\pi$
$859$	−25.6229	−0.874243	−0.437121	+	0.899402i	$0.644002\pi$
$860$	4.37743	0.149269
$861$	−97.2686	−3.31491
$862$	−59.8070	−2.03704
$863$	32.0646	1.09149	0.545745	−	0.837951i	$-0.316247\pi$
$863$	32.0646	1.09149	0.545745	+	0.837951i	$0.316247\pi$
$864$	18.2125	0.619604
$865$	20.1045	0.683575
$866$	19.1101	0.649388
$867$	−23.7318	−0.805974
$868$	−1.81928	−0.0617502
$869$	28.7873	0.976543
$870$	−18.0660	−0.612496
$871$	−33.3910	−1.13141
$872$	1.99551	0.0675766
$873$	6.99369	0.236701
$874$	0.896222	0.0303151
$875$	−29.2375	−0.988409
$876$	21.8473	0.738151
$877$	−11.7937	−0.398246	−0.199123	−	0.979974i	$-0.563809\pi$
$877$	−11.7937	−0.398246	−0.199123	+	0.979974i	$0.563809\pi$
$878$	39.9449	1.34807
$879$	0.768318	0.0259147
$880$	−25.8087	−0.870010
$881$	19.3540	0.652052	0.326026	−	0.945361i	$-0.394290\pi$
$881$	19.3540	0.652052	0.326026	+	0.945361i	$0.394290\pi$
$882$	−74.8476	−2.52025
$883$	8.63206	0.290492	0.145246	−	0.989396i	$-0.453603\pi$
$883$	8.63206	0.290492	0.145246	+	0.989396i	$0.453603\pi$
$884$	−9.91473	−0.333469
$885$	−68.4814	−2.30198
$886$	1.28564	0.0431919
$887$	−16.9953	−0.570645	−0.285323	−	0.958432i	$-0.592101\pi$
$887$	−16.9953	−0.570645	−0.285323	+	0.958432i	$0.592101\pi$
$888$	−5.47691	−0.183793
$889$	−13.8781	−0.465456
$890$	−31.2641	−1.04797
$891$	−3.92697	−0.131559
$892$	21.5181	0.720480
$893$	−16.0903	−0.538441
$894$	60.5888	2.02639
$895$	31.8437	1.06442
$896$	−53.9224	−1.80142
$897$	1.68152	0.0561444
$898$	−28.2160	−0.941579
$899$	−0.791573	−0.0264004
$900$	8.72479	0.290826
$901$	−9.95344	−0.331597
$902$	27.7003	0.922318
$903$	22.4313	0.746468
$904$	17.4443	0.580189
$905$	−15.6546	−0.520375
$906$	36.0333	1.19713
$907$	−32.5132	−1.07958	−0.539791	−	0.841799i	$-0.681497\pi$
$907$	−32.5132	−1.07958	−0.539791	+	0.841799i	$0.681497\pi$
$908$	−2.30252	−0.0764119
$909$	2.47584	0.0821186
$910$	79.2037	2.62558
$911$	55.8703	1.85107	0.925533	−	0.378668i	$-0.123618\pi$
$911$	55.8703	1.85107	0.925533	+	0.378668i	$0.123618\pi$
$912$	−50.3875	−1.66850
$913$	−10.0933	−0.334038
$914$	4.44937	0.147172
$915$	−2.98583	−0.0987084
$916$	6.18195	0.204257
$917$	−20.1933	−0.666840
$918$	−20.3817	−0.672695
$919$	7.39955	0.244089	0.122044	−	0.992525i	$-0.461055\pi$
$919$	7.39955	0.244089	0.122044	+	0.992525i	$0.461055\pi$
$920$	−0.783585	−0.0258340
$921$	−53.6388	−1.76746
$922$	−61.5848	−2.02819
$923$	−24.0354	−0.791134
$924$	17.4578	0.574320
$925$	−2.37783	−0.0781825
$926$	−56.6049	−1.86015
$927$	−33.3714	−1.09606
$928$	6.25861	0.205449
$929$	8.61691	0.282712	0.141356	−	0.989959i	$-0.454854\pi$
$929$	8.61691	0.282712	0.141356	+	0.989959i	$0.454854\pi$
$930$	6.84137	0.224337
$931$	36.4356	1.19413
$932$	−5.40109	−0.176919
$933$	−1.96748	−0.0644122
$934$	0.883712	0.0289159
$935$	15.0276	0.491456
$936$	−38.3341	−1.25299
$937$	36.5312	1.19342	0.596712	−	0.802456i	$-0.296474\pi$
$937$	36.5312	1.19342	0.596712	+	0.802456i	$0.296474\pi$
$938$	−54.2129	−1.77011
$939$	26.3354	0.859424
$940$	−9.56508	−0.311978
$941$	3.30775	0.107830	0.0539148	−	0.998546i	$-0.482830\pi$
$941$	3.30775	0.107830	0.0539148	+	0.998546i	$0.482830\pi$
$942$	65.6904	2.14031
$943$	1.24808	0.0406431
$944$	45.5965	1.48404
$945$	46.9113	1.52603
$946$	−6.38802	−0.207692
$947$	−49.3942	−1.60509	−0.802547	−	0.596588i	$-0.796523\pi$
$947$	−49.3942	−1.60509	−0.802547	+	0.596588i	$0.796523\pi$
$948$	33.4106	1.08512
$949$	−41.6748	−1.35282
$950$	−14.7411	−0.478263
$951$	32.2365	1.04534
$952$	23.6755	0.767328
$953$	−53.1869	−1.72289	−0.861446	−	0.507849i	$-0.830441\pi$
$953$	−53.1869	−1.72289	−0.861446	+	0.507849i	$0.830441\pi$
$954$	26.1657	0.847146
$955$	23.4297	0.758169
$956$	0.967193	0.0312813
$957$	7.59596	0.245543
$958$	34.4285	1.11233
$959$	36.6346	1.18299
$960$	19.9168	0.642811
$961$	−30.7002	−0.990330
$962$	−7.10339	−0.229023
$963$	−13.2973	−0.428501
$964$	11.9718	0.385585
$965$	−60.0122	−1.93186
$966$	2.73008	0.0878389
$967$	−51.7676	−1.66473	−0.832367	−	0.554225i	$-0.813015\pi$
$967$	−51.7676	−1.66473	−0.832367	+	0.554225i	$0.813015\pi$
$968$	−14.6385	−0.470498
$969$	29.3392	0.942510
$970$	−7.02433	−0.225538
$971$	23.7770	0.763041	0.381521	−	0.924360i	$-0.375400\pi$
$971$	23.7770	0.763041	0.381521	+	0.924360i	$0.375400\pi$
$972$	−14.7745	−0.473892
$973$	−53.1309	−1.70330
$974$	32.8064	1.05119
$975$	−27.6577	−0.885755
$976$	1.98804	0.0636355
$977$	−16.6066	−0.531292	−0.265646	−	0.964071i	$-0.585585\pi$
$977$	−16.6066	−0.531292	−0.265646	+	0.964071i	$0.585585\pi$
$978$	107.045	3.42294
$979$	13.1452	0.420121
$980$	21.6596	0.691891
$981$	4.53291	0.144725
$982$	44.1787	1.40980
$983$	−20.6426	−0.658397	−0.329198	−	0.944261i	$-0.606779\pi$
$983$	−20.6426	−0.658397	−0.329198	+	0.944261i	$0.606779\pi$
$984$	−47.2837	−1.50735
$985$	−0.364871	−0.0116258
$986$	−7.00401	−0.223053
$987$	−49.0144	−1.56015
$988$	−12.6878	−0.403654
$989$	−0.287823	−0.00915223
$990$	−39.5048	−1.25554
$991$	42.3525	1.34537	0.672685	−	0.739929i	$-0.265141\pi$
$991$	42.3525	1.34537	0.672685	+	0.739929i	$0.265141\pi$
$992$	−2.37006	−0.0752493
$993$	−43.9188	−1.39372
$994$	−39.0233	−1.23774
$995$	−28.8432	−0.914391
$996$	−11.7142	−0.371179
$997$	−21.6258	−0.684896	−0.342448	−	0.939537i	$-0.611256\pi$
$997$	−21.6258	−0.684896	−0.342448	+	0.939537i	$0.611256\pi$
$998$	−66.6641	−2.11021
$999$	−4.20725	−0.133111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.16	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.16	✓	82	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67615 q^{2} +2.74461 q^{3} +0.809463 q^{4} +2.71622 q^{5} -4.60037 q^{6} +4.10502 q^{7} +1.99551 q^{8} +4.53291 q^{9} +O(q^{10})\)	\(q-1.67615 q^{2} +2.74461 q^{3} +0.809463 q^{4} +2.71622 q^{5} -4.60037 q^{6} +4.10502 q^{7} +1.99551 q^{8} +4.53291 q^{9} -4.55277 q^{10} +1.91424 q^{11} +2.22166 q^{12} -4.23793 q^{13} -6.88061 q^{14} +7.45497 q^{15} -4.96370 q^{16} +2.89021 q^{17} -7.59782 q^{18} +3.69859 q^{19} +2.19868 q^{20} +11.2667 q^{21} -3.20854 q^{22} -0.144566 q^{23} +5.47691 q^{24} +2.37783 q^{25} +7.10339 q^{26} +4.20725 q^{27} +3.32286 q^{28} +1.44579 q^{29} -12.4956 q^{30} -0.547502 q^{31} +4.32885 q^{32} +5.25385 q^{33} -4.84442 q^{34} +11.1501 q^{35} +3.66922 q^{36} -1.00000 q^{37} -6.19938 q^{38} -11.6315 q^{39} +5.42024 q^{40} -8.63328 q^{41} -18.8846 q^{42} +1.99094 q^{43} +1.54951 q^{44} +12.3124 q^{45} +0.242314 q^{46} -4.35038 q^{47} -13.6234 q^{48} +9.85120 q^{49} -3.98559 q^{50} +7.93252 q^{51} -3.43045 q^{52} -3.44384 q^{53} -7.05196 q^{54} +5.19949 q^{55} +8.19162 q^{56} +10.1512 q^{57} -2.42335 q^{58} -9.18600 q^{59} +6.03452 q^{60} -0.400515 q^{61} +0.917693 q^{62} +18.6077 q^{63} +2.67161 q^{64} -11.5111 q^{65} -8.80622 q^{66} +7.87908 q^{67} +2.33952 q^{68} -0.396779 q^{69} -18.6892 q^{70} +5.67148 q^{71} +9.04548 q^{72} +9.83375 q^{73} +1.67615 q^{74} +6.52622 q^{75} +2.99388 q^{76} +7.85799 q^{77} +19.4961 q^{78} +15.0385 q^{79} -13.4825 q^{80} -2.05145 q^{81} +14.4706 q^{82} -5.27272 q^{83} +9.11998 q^{84} +7.85044 q^{85} -3.33710 q^{86} +3.96814 q^{87} +3.81989 q^{88} +6.86704 q^{89} -20.6373 q^{90} -17.3968 q^{91} -0.117021 q^{92} -1.50268 q^{93} +7.29187 q^{94} +10.0462 q^{95} +11.8810 q^{96} +1.54287 q^{97} -16.5120 q^{98} +8.67708 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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