LMFDB - Embedded newform 6019.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61467 q^{2} +0.516414 q^{3} +4.83649 q^{4} -3.96792 q^{5} -1.35025 q^{6} +3.66433 q^{7} -7.41648 q^{8} -2.73332 q^{9} +O(q^{10})$	\(q-2.61467 q^{2} +0.516414 q^{3} +4.83649 q^{4} -3.96792 q^{5} -1.35025 q^{6} +3.66433 q^{7} -7.41648 q^{8} -2.73332 q^{9} +10.3748 q^{10} -4.05913 q^{11} +2.49763 q^{12} -1.00000 q^{13} -9.58102 q^{14} -2.04909 q^{15} +9.71866 q^{16} +6.83477 q^{17} +7.14672 q^{18} +5.65862 q^{19} -19.1908 q^{20} +1.89231 q^{21} +10.6133 q^{22} -4.75842 q^{23} -3.82998 q^{24} +10.7444 q^{25} +2.61467 q^{26} -2.96077 q^{27} +17.7225 q^{28} +2.57174 q^{29} +5.35769 q^{30} -3.95962 q^{31} -10.5781 q^{32} -2.09619 q^{33} -17.8707 q^{34} -14.5398 q^{35} -13.2197 q^{36} -7.21708 q^{37} -14.7954 q^{38} -0.516414 q^{39} +29.4280 q^{40} -9.50552 q^{41} -4.94777 q^{42} -5.45391 q^{43} -19.6319 q^{44} +10.8456 q^{45} +12.4417 q^{46} +9.77351 q^{47} +5.01885 q^{48} +6.42734 q^{49} -28.0929 q^{50} +3.52957 q^{51} -4.83649 q^{52} +2.55531 q^{53} +7.74142 q^{54} +16.1063 q^{55} -27.1765 q^{56} +2.92219 q^{57} -6.72423 q^{58} +1.66855 q^{59} -9.91039 q^{60} +6.44218 q^{61} +10.3531 q^{62} -10.0158 q^{63} +8.22091 q^{64} +3.96792 q^{65} +5.48085 q^{66} -12.3003 q^{67} +33.0563 q^{68} -2.45732 q^{69} +38.0167 q^{70} +11.6516 q^{71} +20.2716 q^{72} +9.66772 q^{73} +18.8703 q^{74} +5.54854 q^{75} +27.3678 q^{76} -14.8740 q^{77} +1.35025 q^{78} +17.0304 q^{79} -38.5628 q^{80} +6.67097 q^{81} +24.8538 q^{82} -5.34508 q^{83} +9.15216 q^{84} -27.1198 q^{85} +14.2602 q^{86} +1.32808 q^{87} +30.1044 q^{88} +1.55773 q^{89} -28.3576 q^{90} -3.66433 q^{91} -23.0140 q^{92} -2.04480 q^{93} -25.5545 q^{94} -22.4529 q^{95} -5.46268 q^{96} -8.63999 q^{97} -16.8054 q^{98} +11.0949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.61467	−1.84885	−0.924425	−	0.381364i	$-0.875454\pi$
$2$	−2.61467	−1.84885	−0.924425	+	0.381364i	$0.875454\pi$
$3$	0.516414	0.298152	0.149076	−	0.988826i	$-0.452370\pi$
$3$	0.516414	0.298152	0.149076	+	0.988826i	$0.452370\pi$
$4$	4.83649	2.41825
$5$	−3.96792	−1.77451	−0.887253	−	0.461283i	$-0.847389\pi$
$5$	−3.96792	−1.77451	−0.887253	+	0.461283i	$0.847389\pi$
$6$	−1.35025	−0.551238
$7$	3.66433	1.38499	0.692494	−	0.721424i	$-0.256512\pi$
$7$	3.66433	1.38499	0.692494	+	0.721424i	$0.256512\pi$
$8$	−7.41648	−2.62212
$9$	−2.73332	−0.911105
$10$	10.3748	3.28079
$11$	−4.05913	−1.22387	−0.611937	−	0.790907i	$-0.709609\pi$
$11$	−4.05913	−1.22387	−0.611937	+	0.790907i	$0.709609\pi$
$12$	2.49763	0.721004
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−9.58102	−2.56063
$15$	−2.04909	−0.529072
$16$	9.71866	2.42966
$17$	6.83477	1.65768	0.828838	−	0.559489i	$-0.189002\pi$
$17$	6.83477	1.65768	0.828838	+	0.559489i	$0.189002\pi$
$18$	7.14672	1.68450
$19$	5.65862	1.29818	0.649088	−	0.760713i	$-0.275151\pi$
$19$	5.65862	1.29818	0.649088	+	0.760713i	$0.275151\pi$
$20$	−19.1908	−4.29119
$21$	1.89231	0.412937
$22$	10.6133	2.26276
$23$	−4.75842	−0.992199	−0.496099	−	0.868266i	$-0.665235\pi$
$23$	−4.75842	−0.992199	−0.496099	+	0.868266i	$0.665235\pi$
$24$	−3.82998	−0.781791
$25$	10.7444	2.14887
$26$	2.61467	0.512779
$27$	−2.96077	−0.569800
$28$	17.7225	3.34924
$29$	2.57174	0.477559	0.238780	−	0.971074i	$-0.423253\pi$
$29$	2.57174	0.477559	0.238780	+	0.971074i	$0.423253\pi$
$30$	5.35769	0.978175
$31$	−3.95962	−0.711169	−0.355584	−	0.934644i	$-0.615718\pi$
$31$	−3.95962	−0.711169	−0.355584	+	0.934644i	$0.615718\pi$
$32$	−10.5781	−1.86996
$33$	−2.09619	−0.364900
$34$	−17.8707	−3.06479
$35$	−14.5398	−2.45767
$36$	−13.2197	−2.20328
$37$	−7.21708	−1.18648	−0.593240	−	0.805026i	$-0.702151\pi$
$37$	−7.21708	−1.18648	−0.593240	+	0.805026i	$0.702151\pi$
$38$	−14.7954	−2.40013
$39$	−0.516414	−0.0826925
$40$	29.4280	4.65297
$41$	−9.50552	−1.48451	−0.742256	−	0.670116i	$-0.766244\pi$
$41$	−9.50552	−1.48451	−0.742256	+	0.670116i	$0.766244\pi$
$42$	−4.94777	−0.763458
$43$	−5.45391	−0.831714	−0.415857	−	0.909430i	$-0.636518\pi$
$43$	−5.45391	−0.831714	−0.415857	+	0.909430i	$0.636518\pi$
$44$	−19.6319	−2.95963
$45$	10.8456	1.61676
$46$	12.4417	1.83443
$47$	9.77351	1.42561	0.712806	−	0.701361i	$-0.247424\pi$
$47$	9.77351	1.42561	0.712806	+	0.701361i	$0.247424\pi$
$48$	5.01885	0.724409
$49$	6.42734	0.918192
$50$	−28.0929	−3.97294
$51$	3.52957	0.494239
$52$	−4.83649	−0.670700
$53$	2.55531	0.350999	0.175500	−	0.984479i	$-0.443846\pi$
$53$	2.55531	0.350999	0.175500	+	0.984479i	$0.443846\pi$
$54$	7.74142	1.05347
$55$	16.1063	2.17177
$56$	−27.1765	−3.63161
$57$	2.92219	0.387054
$58$	−6.72423	−0.882935
$59$	1.66855	0.217227	0.108614	−	0.994084i	$-0.465359\pi$
$59$	1.66855	0.217227	0.108614	+	0.994084i	$0.465359\pi$
$60$	−9.91039	−1.27943
$61$	6.44218	0.824837	0.412418	−	0.910995i	$-0.364684\pi$
$61$	6.44218	0.824837	0.412418	+	0.910995i	$0.364684\pi$
$62$	10.3531	1.31484
$63$	−10.0158	−1.26187
$64$	8.22091	1.02761
$65$	3.96792	0.492159
$66$	5.48085	0.674646
$67$	−12.3003	−1.50272	−0.751362	−	0.659890i	$-0.770603\pi$
$67$	−12.3003	−1.50272	−0.751362	+	0.659890i	$0.770603\pi$
$68$	33.0563	4.00867
$69$	−2.45732	−0.295826
$70$	38.0167	4.54386
$71$	11.6516	1.38279	0.691397	−	0.722475i	$-0.256996\pi$
$71$	11.6516	1.38279	0.691397	+	0.722475i	$0.256996\pi$
$72$	20.2716	2.38903
$73$	9.66772	1.13152	0.565761	−	0.824570i	$-0.308583\pi$
$73$	9.66772	1.13152	0.565761	+	0.824570i	$0.308583\pi$
$74$	18.8703	2.19362
$75$	5.54854	0.640690
$76$	27.3678	3.13931
$77$	−14.8740	−1.69505
$78$	1.35025	0.152886
$79$	17.0304	1.91606	0.958032	−	0.286661i	$-0.0925453\pi$
$79$	17.0304	1.91606	0.958032	+	0.286661i	$0.0925453\pi$
$80$	−38.5628	−4.31145
$81$	6.67097	0.741219
$82$	24.8538	2.74464
$83$	−5.34508	−0.586699	−0.293350	−	0.956005i	$-0.594770\pi$
$83$	−5.34508	−0.586699	−0.293350	+	0.956005i	$0.594770\pi$
$84$	9.15216	0.998583
$85$	−27.1198	−2.94156
$86$	14.2602	1.53771
$87$	1.32808	0.142385
$88$	30.1044	3.20914
$89$	1.55773	0.165119	0.0825597	−	0.996586i	$-0.473690\pi$
$89$	1.55773	0.165119	0.0825597	+	0.996586i	$0.473690\pi$
$90$	−28.3576	−2.98915
$91$	−3.66433	−0.384127
$92$	−23.0140	−2.39938
$93$	−2.04480	−0.212036
$94$	−25.5545	−2.63574
$95$	−22.4529	−2.30362
$96$	−5.46268	−0.557533
$97$	−8.63999	−0.877258	−0.438629	−	0.898668i	$-0.644536\pi$
$97$	−8.63999	−0.877258	−0.438629	+	0.898668i	$0.644536\pi$
$98$	−16.8054	−1.69760
$99$	11.0949	1.11508
$100$	51.9649	5.19649
$101$	2.63471	0.262163	0.131082	−	0.991372i	$-0.458155\pi$
$101$	2.63471	0.262163	0.131082	+	0.991372i	$0.458155\pi$
$102$	−9.22867	−0.913774
$103$	−4.04364	−0.398432	−0.199216	−	0.979956i	$-0.563839\pi$
$103$	−4.04364	−0.398432	−0.199216	+	0.979956i	$0.563839\pi$
$104$	7.41648	0.727246
$105$	−7.50854	−0.732759
$106$	−6.68130	−0.648945
$107$	6.85131	0.662342	0.331171	−	0.943571i	$-0.392556\pi$
$107$	6.85131	0.662342	0.331171	+	0.943571i	$0.392556\pi$
$108$	−14.3197	−1.37792
$109$	−8.75770	−0.838835	−0.419418	−	0.907793i	$-0.637766\pi$
$109$	−8.75770	−0.838835	−0.419418	+	0.907793i	$0.637766\pi$
$110$	−42.1126	−4.01528
$111$	−3.72700	−0.353751
$112$	35.6124	3.36506
$113$	5.02085	0.472322	0.236161	−	0.971714i	$-0.424111\pi$
$113$	5.02085	0.472322	0.236161	+	0.971714i	$0.424111\pi$
$114$	−7.64056	−0.715604
$115$	18.8810	1.76066
$116$	12.4382	1.15486
$117$	2.73332	0.252695
$118$	−4.36272	−0.401620
$119$	25.0449	2.29586
$120$	15.1970	1.38729
$121$	5.47652	0.497866
$122$	−16.8442	−1.52500
$123$	−4.90879	−0.442610
$124$	−19.1507	−1.71978
$125$	−22.7931	−2.03868
$126$	26.1880	2.33301
$127$	11.8635	1.05272	0.526359	−	0.850262i	$-0.323557\pi$
$127$	11.8635	1.05272	0.526359	+	0.850262i	$0.323557\pi$
$128$	−0.338753	−0.0299419
$129$	−2.81648	−0.247977
$130$	−10.3748	−0.909929
$131$	−16.0397	−1.40140	−0.700699	−	0.713457i	$-0.747129\pi$
$131$	−16.0397	−1.40140	−0.700699	+	0.713457i	$0.747129\pi$
$132$	−10.1382	−0.882418
$133$	20.7351	1.79796
$134$	32.1613	2.77831
$135$	11.7481	1.01111
$136$	−50.6900	−4.34663
$137$	−11.3458	−0.969334	−0.484667	−	0.874699i	$-0.661059\pi$
$137$	−11.3458	−0.969334	−0.484667	+	0.874699i	$0.661059\pi$
$138$	6.42506	0.546938
$139$	6.10627	0.517927	0.258963	−	0.965887i	$-0.416619\pi$
$139$	6.10627	0.517927	0.258963	+	0.965887i	$0.416619\pi$
$140$	−70.3214	−5.94325
$141$	5.04718	0.425049
$142$	−30.4651	−2.55658
$143$	4.05913	0.339441
$144$	−26.5642	−2.21368
$145$	−10.2044	−0.847432
$146$	−25.2779	−2.09201
$147$	3.31917	0.273761
$148$	−34.9053	−2.86920
$149$	3.37099	0.276162	0.138081	−	0.990421i	$-0.455907\pi$
$149$	3.37099	0.276162	0.138081	+	0.990421i	$0.455907\pi$
$150$	−14.5076	−1.18454
$151$	−5.03260	−0.409547	−0.204773	−	0.978809i	$-0.565646\pi$
$151$	−5.03260	−0.409547	−0.204773	+	0.978809i	$0.565646\pi$
$152$	−41.9670	−3.40397
$153$	−18.6816	−1.51032
$154$	38.8906	3.13389
$155$	15.7114	1.26197
$156$	−2.49763	−0.199971
$157$	−0.156318	−0.0124755	−0.00623775	−	0.999981i	$-0.501986\pi$
$157$	−0.156318	−0.0124755	−0.00623775	+	0.999981i	$0.501986\pi$
$158$	−44.5287	−3.54251
$159$	1.31960	0.104651
$160$	41.9730	3.31826
$161$	−17.4364	−1.37418
$162$	−17.4424	−1.37040
$163$	16.1465	1.26469	0.632347	−	0.774685i	$-0.282092\pi$
$163$	16.1465	1.26469	0.632347	+	0.774685i	$0.282092\pi$
$164$	−45.9733	−3.58991
$165$	8.31751	0.647517
$166$	13.9756	1.08472
$167$	17.1965	1.33071	0.665354	−	0.746528i	$-0.268281\pi$
$167$	17.1965	1.33071	0.665354	+	0.746528i	$0.268281\pi$
$168$	−14.0343	−1.08277
$169$	1.00000	0.0769231
$170$	70.9093	5.43849
$171$	−15.4668	−1.18277
$172$	−26.3778	−2.01129
$173$	6.29881	0.478890	0.239445	−	0.970910i	$-0.423035\pi$
$173$	6.29881	0.478890	0.239445	+	0.970910i	$0.423035\pi$
$174$	−3.47249	−0.263249
$175$	39.3709	2.97616
$176$	−39.4493	−2.97360
$177$	0.861665	0.0647667
$178$	−4.07295	−0.305281
$179$	−16.7790	−1.25412	−0.627062	−	0.778969i	$-0.715743\pi$
$179$	−16.7790	−1.25412	−0.627062	+	0.778969i	$0.715743\pi$
$180$	52.4545	3.90973
$181$	−12.8676	−0.956438	−0.478219	−	0.878241i	$-0.658717\pi$
$181$	−12.8676	−0.956438	−0.478219	+	0.878241i	$0.658717\pi$
$182$	9.58102	0.710192
$183$	3.32683	0.245927
$184$	35.2907	2.60167
$185$	28.6367	2.10542
$186$	5.34648	0.392023
$187$	−27.7432	−2.02879
$188$	47.2695	3.44748
$189$	−10.8492	−0.789166
$190$	58.7069	4.25905
$191$	1.64260	0.118854	0.0594272	−	0.998233i	$-0.481073\pi$
$191$	1.64260	0.118854	0.0594272	+	0.998233i	$0.481073\pi$
$192$	4.24540	0.306385
$193$	−10.0442	−0.722999	−0.361499	−	0.932372i	$-0.617735\pi$
$193$	−10.0442	−0.722999	−0.361499	+	0.932372i	$0.617735\pi$
$194$	22.5907	1.62192
$195$	2.04909	0.146738
$196$	31.0858	2.22041
$197$	−5.42575	−0.386569	−0.193284	−	0.981143i	$-0.561914\pi$
$197$	−5.42575	−0.386569	−0.193284	+	0.981143i	$0.561914\pi$
$198$	−29.0094	−2.06161
$199$	20.1230	1.42648	0.713239	−	0.700921i	$-0.247227\pi$
$199$	20.1230	1.42648	0.713239	+	0.700921i	$0.247227\pi$
$200$	−79.6853	−5.63460
$201$	−6.35206	−0.448040
$202$	−6.88889	−0.484701
$203$	9.42370	0.661414
$204$	17.0708	1.19519
$205$	37.7171	2.63428
$206$	10.5728	0.736640
$207$	13.0063	0.903998
$208$	−9.71866	−0.673868
$209$	−22.9691	−1.58880
$210$	19.6323	1.35476
$211$	−5.86848	−0.404003	−0.202001	−	0.979385i	$-0.564745\pi$
$211$	−5.86848	−0.404003	−0.202001	+	0.979385i	$0.564745\pi$
$212$	12.3587	0.848802
$213$	6.01707	0.412283
$214$	−17.9139	−1.22457
$215$	21.6407	1.47588
$216$	21.9585	1.49408
$217$	−14.5094	−0.984960
$218$	22.8985	1.55088
$219$	4.99255	0.337365
$220$	77.8978	5.25187
$221$	−6.83477	−0.459757
$222$	9.74487	0.654033
$223$	−13.8753	−0.929161	−0.464581	−	0.885531i	$-0.653795\pi$
$223$	−13.8753	−0.929161	−0.464581	+	0.885531i	$0.653795\pi$
$224$	−38.7617	−2.58987
$225$	−29.3677	−1.95785
$226$	−13.1279	−0.873253
$227$	−1.13422	−0.0752811	−0.0376405	−	0.999291i	$-0.511984\pi$
$227$	−1.13422	−0.0752811	−0.0376405	+	0.999291i	$0.511984\pi$
$228$	14.1331	0.935990
$229$	6.71154	0.443511	0.221756	−	0.975102i	$-0.428821\pi$
$229$	6.71154	0.443511	0.221756	+	0.975102i	$0.428821\pi$
$230$	−49.3676	−3.25520
$231$	−7.68115	−0.505382
$232$	−19.0732	−1.25222
$233$	−4.49394	−0.294408	−0.147204	−	0.989106i	$-0.547027\pi$
$233$	−4.49394	−0.294408	−0.147204	+	0.989106i	$0.547027\pi$
$234$	−7.14672	−0.467195
$235$	−38.7804	−2.52976
$236$	8.06995	0.525309
$237$	8.79472	0.571278
$238$	−65.4841	−4.24470
$239$	−15.9542	−1.03199	−0.515997	−	0.856590i	$-0.672578\pi$
$239$	−15.9542	−1.03199	−0.515997	+	0.856590i	$0.672578\pi$
$240$	−19.9144	−1.28547
$241$	24.6518	1.58796	0.793980	−	0.607944i	$-0.208006\pi$
$241$	24.6518	1.58796	0.793980	+	0.607944i	$0.208006\pi$
$242$	−14.3193	−0.920479
$243$	12.3273	0.790796
$244$	31.1575	1.99466
$245$	−25.5032	−1.62934
$246$	12.8348	0.818320
$247$	−5.65862	−0.360049
$248$	29.3664	1.86477
$249$	−2.76028	−0.174925
$250$	59.5964	3.76921
$251$	29.1834	1.84204	0.921019	−	0.389518i	$-0.127358\pi$
$251$	29.1834	1.84204	0.921019	+	0.389518i	$0.127358\pi$
$252$	−48.4412	−3.05151
$253$	19.3150	1.21433
$254$	−31.0192	−1.94632
$255$	−14.0051	−0.877030
$256$	−15.5561	−0.972256
$257$	−28.7805	−1.79528	−0.897641	−	0.440728i	$-0.854720\pi$
$257$	−28.7805	−1.79528	−0.897641	+	0.440728i	$0.854720\pi$
$258$	7.36416	0.458472
$259$	−26.4458	−1.64326
$260$	19.1908	1.19016
$261$	−7.02937	−0.435107
$262$	41.9386	2.59098
$263$	22.3088	1.37562	0.687810	−	0.725890i	$-0.258572\pi$
$263$	22.3088	1.37562	0.687810	+	0.725890i	$0.258572\pi$
$264$	15.5464	0.956813
$265$	−10.1393	−0.622850
$266$	−54.2153	−3.32415
$267$	0.804435	0.0492306
$268$	−59.4904	−3.63395
$269$	10.8353	0.660638	0.330319	−	0.943869i	$-0.392844\pi$
$269$	10.8353	0.660638	0.330319	+	0.943869i	$0.392844\pi$
$270$	−30.7173	−1.86940
$271$	−32.4903	−1.97364	−0.986822	−	0.161812i	$-0.948266\pi$
$271$	−32.4903	−1.97364	−0.986822	+	0.161812i	$0.948266\pi$
$272$	66.4248	4.02760
$273$	−1.89231	−0.114528
$274$	29.6654	1.79215
$275$	−43.6127	−2.62994
$276$	−11.8848	−0.715380
$277$	−30.5687	−1.83670	−0.918349	−	0.395772i	$-0.870477\pi$
$277$	−30.5687	−1.83670	−0.918349	+	0.395772i	$0.870477\pi$
$278$	−15.9659	−0.957569
$279$	10.8229	0.647950
$280$	107.834	6.44431
$281$	18.5659	1.10755	0.553774	−	0.832667i	$-0.313187\pi$
$281$	18.5659	1.10755	0.553774	+	0.832667i	$0.313187\pi$
$282$	−13.1967	−0.785852
$283$	−5.44527	−0.323688	−0.161844	−	0.986816i	$-0.551744\pi$
$283$	−5.44527	−0.323688	−0.161844	+	0.986816i	$0.551744\pi$
$284$	56.3530	3.34393
$285$	−11.5950	−0.686829
$286$	−10.6133	−0.627576
$287$	−34.8314	−2.05603
$288$	28.9133	1.70373
$289$	29.7141	1.74789
$290$	26.6812	1.56677
$291$	−4.46181	−0.261556
$292$	46.7578	2.73630
$293$	−2.81750	−0.164600	−0.0823000	−	0.996608i	$-0.526227\pi$
$293$	−2.81750	−0.164600	−0.0823000	+	0.996608i	$0.526227\pi$
$294$	−8.67853	−0.506142
$295$	−6.62068	−0.385471
$296$	53.5253	3.11109
$297$	12.0181	0.697363
$298$	−8.81401	−0.510582
$299$	4.75842	0.275186
$300$	26.8354	1.54935
$301$	−19.9850	−1.15191
$302$	13.1586	0.757191
$303$	1.36060	0.0781645
$304$	54.9941	3.15413
$305$	−25.5620	−1.46368
$306$	48.8462	2.79235
$307$	−16.7456	−0.955721	−0.477860	−	0.878436i	$-0.658588\pi$
$307$	−16.7456	−0.955721	−0.477860	+	0.878436i	$0.658588\pi$
$308$	−71.9380	−4.09905
$309$	−2.08819	−0.118793
$310$	−41.0802	−2.33320
$311$	−29.3352	−1.66344	−0.831722	−	0.555192i	$-0.812645\pi$
$311$	−29.3352	−1.66344	−0.831722	+	0.555192i	$0.812645\pi$
$312$	3.82998	0.216830
$313$	20.3749	1.15166	0.575830	−	0.817570i	$-0.304679\pi$
$313$	20.3749	1.15166	0.575830	+	0.817570i	$0.304679\pi$
$314$	0.408719	0.0230653
$315$	39.7418	2.23920
$316$	82.3671	4.63351
$317$	−2.12437	−0.119316	−0.0596582	−	0.998219i	$-0.519001\pi$
$317$	−2.12437	−0.119316	−0.0596582	+	0.998219i	$0.519001\pi$
$318$	−3.45032	−0.193484
$319$	−10.4390	−0.584472
$320$	−32.6199	−1.82351
$321$	3.53812	0.197478
$322$	45.5905	2.54066
$323$	38.6754	2.15195
$324$	32.2641	1.79245
$325$	−10.7444	−0.595989
$326$	−42.2178	−2.33823
$327$	−4.52260	−0.250100
$328$	70.4975	3.89257
$329$	35.8134	1.97446
$330$	−21.7475	−1.19716
$331$	−6.61479	−0.363581	−0.181791	−	0.983337i	$-0.558189\pi$
$331$	−6.61479	−0.363581	−0.181791	+	0.983337i	$0.558189\pi$
$332$	−25.8514	−1.41878
$333$	19.7265	1.08101
$334$	−44.9632	−2.46028
$335$	48.8066	2.66659
$336$	18.3908	1.00330
$337$	−11.7420	−0.639628	−0.319814	−	0.947480i	$-0.603621\pi$
$337$	−11.7420	−0.639628	−0.319814	+	0.947480i	$0.603621\pi$
$338$	−2.61467	−0.142219
$339$	2.59284	0.140824
$340$	−131.165	−7.11340
$341$	16.0726	0.870380
$342$	40.4405	2.18677
$343$	−2.09841	−0.113303
$344$	40.4488	2.18086
$345$	9.75042	0.524945
$346$	−16.4693	−0.885395
$347$	−28.2984	−1.51914	−0.759568	−	0.650428i	$-0.774590\pi$
$347$	−28.2984	−1.51914	−0.759568	+	0.650428i	$0.774590\pi$
$348$	6.42325	0.344322
$349$	−17.7809	−0.951788	−0.475894	−	0.879503i	$-0.657875\pi$
$349$	−17.7809	−0.951788	−0.475894	+	0.879503i	$0.657875\pi$
$350$	−102.942	−5.50247
$351$	2.96077	0.158034
$352$	42.9379	2.28860
$353$	−13.1955	−0.702324	−0.351162	−	0.936315i	$-0.614213\pi$
$353$	−13.1955	−0.702324	−0.351162	+	0.936315i	$0.614213\pi$
$354$	−2.25297	−0.119744
$355$	−46.2327	−2.45377
$356$	7.53396	0.399299
$357$	12.9335	0.684516
$358$	43.8716	2.31869
$359$	−27.6771	−1.46074	−0.730372	−	0.683050i	$-0.760653\pi$
$359$	−27.6771	−1.46074	−0.730372	+	0.683050i	$0.760653\pi$
$360$	−80.4359	−4.23935
$361$	13.0199	0.685260
$362$	33.6444	1.76831
$363$	2.82815	0.148440
$364$	−17.7225	−0.928912
$365$	−38.3607	−2.00789
$366$	−8.69857	−0.454681
$367$	−4.14855	−0.216552	−0.108276	−	0.994121i	$-0.534533\pi$
$367$	−4.14855	−0.216552	−0.108276	+	0.994121i	$0.534533\pi$
$368$	−46.2454	−2.41071
$369$	25.9816	1.35255
$370$	−74.8756	−3.89260
$371$	9.36352	0.486130
$372$	−9.88968	−0.512756
$373$	20.9763	1.08611	0.543057	−	0.839696i	$-0.317267\pi$
$373$	20.9763	1.08611	0.543057	+	0.839696i	$0.317267\pi$
$374$	72.5393	3.75092
$375$	−11.7707	−0.607835
$376$	−72.4850	−3.73813
$377$	−2.57174	−0.132451
$378$	28.3672	1.45905
$379$	−0.158477	−0.00814039	−0.00407020	−	0.999992i	$-0.501296\pi$
$379$	−0.158477	−0.00814039	−0.00407020	+	0.999992i	$0.501296\pi$
$380$	−108.593	−5.57072
$381$	6.12650	0.313870
$382$	−4.29486	−0.219744
$383$	−1.59774	−0.0816405	−0.0408203	−	0.999167i	$-0.512997\pi$
$383$	−1.59774	−0.0816405	−0.0408203	+	0.999167i	$0.512997\pi$
$384$	−0.174937	−0.00892722
$385$	59.0188	3.00788
$386$	26.2623	1.33672
$387$	14.9073	0.757779
$388$	−41.7872	−2.12142
$389$	−21.5650	−1.09339	−0.546694	−	0.837333i	$-0.684114\pi$
$389$	−21.5650	−1.09339	−0.546694	+	0.837333i	$0.684114\pi$
$390$	−5.35769	−0.271297
$391$	−32.5227	−1.64474
$392$	−47.6683	−2.40761
$393$	−8.28315	−0.417830
$394$	14.1865	0.714707
$395$	−67.5750	−3.40007
$396$	53.6603	2.69653
$397$	−12.3672	−0.620691	−0.310345	−	0.950624i	$-0.600445\pi$
$397$	−12.3672	−0.620691	−0.310345	+	0.950624i	$0.600445\pi$
$398$	−52.6149	−2.63734
$399$	10.7079	0.536065
$400$	104.421	5.22103
$401$	27.7093	1.38374	0.691869	−	0.722023i	$-0.256788\pi$
$401$	27.7093	1.38374	0.691869	+	0.722023i	$0.256788\pi$
$402$	16.6085	0.828359
$403$	3.95962	0.197243
$404$	12.7427	0.633975
$405$	−26.4698	−1.31530
$406$	−24.6398	−1.22285
$407$	29.2950	1.45210
$408$	−26.1770	−1.29596
$409$	−3.32364	−0.164344	−0.0821718	−	0.996618i	$-0.526186\pi$
$409$	−3.32364	−0.164344	−0.0821718	+	0.996618i	$0.526186\pi$
$410$	−98.6177	−4.87038
$411$	−5.85911	−0.289009
$412$	−19.5570	−0.963505
$413$	6.11414	0.300857
$414$	−34.0071	−1.67136
$415$	21.2088	1.04110
$416$	10.5781	0.518634
$417$	3.15336	0.154421
$418$	60.0564	2.93746
$419$	20.8682	1.01948	0.509738	−	0.860329i	$-0.329742\pi$
$419$	20.8682	1.01948	0.509738	+	0.860329i	$0.329742\pi$
$420$	−36.3150	−1.77199
$421$	−17.3042	−0.843355	−0.421677	−	0.906746i	$-0.638559\pi$
$421$	−17.3042	−0.843355	−0.421677	+	0.906746i	$0.638559\pi$
$422$	15.3441	0.746940
$423$	−26.7141	−1.29888
$424$	−18.9514	−0.920363
$425$	73.4352	3.56213
$426$	−15.7326	−0.762248
$427$	23.6063	1.14239
$428$	33.1363	1.60170
$429$	2.09619	0.101205
$430$	−56.5832	−2.72868
$431$	17.8907	0.861765	0.430883	−	0.902408i	$-0.358202\pi$
$431$	17.8907	0.861765	0.430883	+	0.902408i	$0.358202\pi$
$432$	−28.7747	−1.38442
$433$	5.75906	0.276763	0.138381	−	0.990379i	$-0.455810\pi$
$433$	5.75906	0.276763	0.138381	+	0.990379i	$0.455810\pi$
$434$	37.9372	1.82104
$435$	−5.26971	−0.252663
$436$	−42.3565	−2.02851
$437$	−26.9261	−1.28805
$438$	−13.0539	−0.623738
$439$	4.41924	0.210919	0.105460	−	0.994424i	$-0.466369\pi$
$439$	4.41924	0.210919	0.105460	+	0.994424i	$0.466369\pi$
$440$	−119.452	−5.69465
$441$	−17.5680	−0.836570
$442$	17.8707	0.850021
$443$	34.4181	1.63525	0.817627	−	0.575748i	$-0.195289\pi$
$443$	34.4181	1.63525	0.817627	+	0.575748i	$0.195289\pi$
$444$	−18.0256	−0.855457
$445$	−6.18095	−0.293005
$446$	36.2794	1.71788
$447$	1.74083	0.0823383
$448$	30.1242	1.42323
$449$	8.81167	0.415848	0.207924	−	0.978145i	$-0.433329\pi$
$449$	8.81167	0.415848	0.207924	+	0.978145i	$0.433329\pi$
$450$	76.7868	3.61977
$451$	38.5841	1.81686
$452$	24.2833	1.14219
$453$	−2.59890	−0.122107
$454$	2.96562	0.139183
$455$	14.5398	0.681635
$456$	−21.6724	−1.01490
$457$	22.7634	1.06483	0.532413	−	0.846485i	$-0.321285\pi$
$457$	22.7634	1.06483	0.532413	+	0.846485i	$0.321285\pi$
$458$	−17.5485	−0.819985
$459$	−20.2362	−0.944543
$460$	91.3178	4.25771
$461$	−29.0577	−1.35335	−0.676675	−	0.736282i	$-0.736580\pi$
$461$	−29.0577	−1.35335	−0.676675	+	0.736282i	$0.736580\pi$
$462$	20.0837	0.934376
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	24.9938	1.16031
$465$	8.11361	0.376260
$466$	11.7502	0.544316
$467$	−30.8878	−1.42932	−0.714658	−	0.699474i	$-0.753418\pi$
$467$	−30.8878	−1.42932	−0.714658	+	0.699474i	$0.753418\pi$
$468$	13.2197	0.611079
$469$	−45.0725	−2.08125
$470$	101.398	4.67714
$471$	−0.0807246	−0.00371960
$472$	−12.3748	−0.569596
$473$	22.1381	1.01791
$474$	−22.9953	−1.05621
$475$	60.7982	2.78961
$476$	121.129	5.55196
$477$	−6.98448	−0.319797
$478$	41.7150	1.90800
$479$	−28.7693	−1.31450	−0.657251	−	0.753672i	$-0.728281\pi$
$479$	−28.7693	−1.31450	−0.657251	+	0.753672i	$0.728281\pi$
$480$	21.6755	0.989345
$481$	7.21708	0.329070
$482$	−64.4562	−2.93590
$483$	−9.00442	−0.409715
$484$	26.4871	1.20396
$485$	34.2827	1.55670
$486$	−32.2318	−1.46206
$487$	8.93341	0.404811	0.202406	−	0.979302i	$-0.435124\pi$
$487$	8.93341	0.404811	0.202406	+	0.979302i	$0.435124\pi$
$488$	−47.7783	−2.16282
$489$	8.33830	0.377071
$490$	66.6823	3.01240
$491$	−26.5992	−1.20041	−0.600203	−	0.799847i	$-0.704914\pi$
$491$	−26.5992	−1.20041	−0.600203	+	0.799847i	$0.704914\pi$
$492$	−23.7413	−1.07034
$493$	17.5772	0.791638
$494$	14.7954	0.665677
$495$	−44.0235	−1.97871
$496$	−38.4822	−1.72790
$497$	42.6954	1.91515
$498$	7.21721	0.323411
$499$	−11.8209	−0.529178	−0.264589	−	0.964361i	$-0.585236\pi$
$499$	−11.8209	−0.529178	−0.264589	+	0.964361i	$0.585236\pi$
$500$	−110.239	−4.93002
$501$	8.88054	0.396753
$502$	−76.3048	−3.40565
$503$	−36.4015	−1.62306	−0.811531	−	0.584309i	$-0.801366\pi$
$503$	−36.4015	−1.62306	−0.811531	+	0.584309i	$0.801366\pi$
$504$	74.2819	3.30878
$505$	−10.4543	−0.465210
$506$	−50.5024	−2.24511
$507$	0.516414	0.0229348
$508$	57.3778	2.54573
$509$	12.5810	0.557642	0.278821	−	0.960343i	$-0.410056\pi$
$509$	12.5810	0.557642	0.278821	+	0.960343i	$0.410056\pi$
$510$	36.6186	1.62150
$511$	35.4258	1.56714
$512$	41.3515	1.82750
$513$	−16.7538	−0.739700
$514$	75.2516	3.31920
$515$	16.0448	0.707019
$516$	−13.6219	−0.599669
$517$	−39.6719	−1.74477
$518$	69.1469	3.03814
$519$	3.25280	0.142782
$520$	−29.4280	−1.29050
$521$	22.4443	0.983303	0.491651	−	0.870792i	$-0.336393\pi$
$521$	22.4443	0.983303	0.491651	+	0.870792i	$0.336393\pi$
$522$	18.3795	0.804447
$523$	−17.0484	−0.745476	−0.372738	−	0.927937i	$-0.621581\pi$
$523$	−17.0484	−0.745476	−0.372738	+	0.927937i	$0.621581\pi$
$524$	−77.5761	−3.38893
$525$	20.3317	0.887348
$526$	−58.3302	−2.54332
$527$	−27.0631	−1.17889
$528$	−20.3722	−0.886585
$529$	−0.357457	−0.0155416
$530$	26.5108	1.15156
$531$	−4.56069	−0.197917
$532$	100.285	4.34790
$533$	9.50552	0.411730
$534$	−2.10333	−0.0910201
$535$	−27.1854	−1.17533
$536$	91.2251	3.94032
$537$	−8.66494	−0.373920
$538$	−28.3306	−1.22142
$539$	−26.0894	−1.12375
$540$	56.8194	2.44512
$541$	−27.9361	−1.20107	−0.600534	−	0.799599i	$-0.705045\pi$
$541$	−27.9361	−1.20107	−0.600534	+	0.799599i	$0.705045\pi$
$542$	84.9513	3.64897
$543$	−6.64499	−0.285164
$544$	−72.2989	−3.09979
$545$	34.7498	1.48852
$546$	4.94777	0.211745
$547$	26.0637	1.11440	0.557201	−	0.830378i	$-0.311875\pi$
$547$	26.0637	1.11440	0.557201	+	0.830378i	$0.311875\pi$
$548$	−54.8737	−2.34409
$549$	−17.6085	−0.751513
$550$	114.033	4.86237
$551$	14.5525	0.619956
$552$	18.2246	0.775692
$553$	62.4049	2.65373
$554$	79.9271	3.39578
$555$	14.7884	0.627734
$556$	29.5329	1.25247
$557$	40.3163	1.70826	0.854128	−	0.520063i	$-0.174092\pi$
$557$	40.3163	1.70826	0.854128	+	0.520063i	$0.174092\pi$
$558$	−28.2983	−1.19796
$559$	5.45391	0.230676
$560$	−141.307	−5.97131
$561$	−14.3270	−0.604886
$562$	−48.5437	−2.04769
$563$	−14.1869	−0.597906	−0.298953	−	0.954268i	$-0.596637\pi$
$563$	−14.1869	−0.597906	−0.298953	+	0.954268i	$0.596637\pi$
$564$	24.4106	1.02787
$565$	−19.9223	−0.838138
$566$	14.2376	0.598450
$567$	24.4446	1.02658
$568$	−86.4140	−3.62585
$569$	3.21884	0.134941	0.0674704	−	0.997721i	$-0.478507\pi$
$569$	3.21884	0.134941	0.0674704	+	0.997721i	$0.478507\pi$
$570$	30.3171	1.26984
$571$	−19.3074	−0.807991	−0.403996	−	0.914761i	$-0.632379\pi$
$571$	−19.3074	−0.807991	−0.403996	+	0.914761i	$0.632379\pi$
$572$	19.6319	0.820852
$573$	0.848263	0.0354367
$574$	91.0725	3.80129
$575$	−51.1261	−2.13211
$576$	−22.4703	−0.936265
$577$	−33.3699	−1.38921	−0.694603	−	0.719393i	$-0.744420\pi$
$577$	−33.3699	−1.38921	−0.694603	+	0.719393i	$0.744420\pi$
$578$	−77.6926	−3.23159
$579$	−5.18698	−0.215563
$580$	−49.3536	−2.04930
$581$	−19.5862	−0.812571
$582$	11.6662	0.483578
$583$	−10.3723	−0.429579
$584$	−71.7005	−2.96699
$585$	−10.8456	−0.448409
$586$	7.36682	0.304321
$587$	−15.6739	−0.646932	−0.323466	−	0.946240i	$-0.604848\pi$
$587$	−15.6739	−0.646932	−0.323466	+	0.946240i	$0.604848\pi$
$588$	16.0531	0.662020
$589$	−22.4060	−0.923222
$590$	17.3109	0.712678
$591$	−2.80193	−0.115256
$592$	−70.1403	−2.88275
$593$	−18.7228	−0.768853	−0.384427	−	0.923156i	$-0.625601\pi$
$593$	−18.7228	−0.768853	−0.384427	+	0.923156i	$0.625601\pi$
$594$	−31.4234	−1.28932
$595$	−99.3760	−4.07402
$596$	16.3037	0.667828
$597$	10.3918	0.425307
$598$	−12.4417	−0.508778
$599$	21.6083	0.882891	0.441446	−	0.897288i	$-0.354466\pi$
$599$	21.6083	0.882891	0.441446	+	0.897288i	$0.354466\pi$
$600$	−41.1506	−1.67997
$601$	−23.6929	−0.966453	−0.483226	−	0.875495i	$-0.660535\pi$
$601$	−23.6929	−0.966453	−0.483226	+	0.875495i	$0.660535\pi$
$602$	52.2540	2.12972
$603$	33.6207	1.36914
$604$	−24.3401	−0.990385
$605$	−21.7304	−0.883465
$606$	−3.55752	−0.144514
$607$	−5.78819	−0.234935	−0.117468	−	0.993077i	$-0.537478\pi$
$607$	−5.78819	−0.234935	−0.117468	+	0.993077i	$0.537478\pi$
$608$	−59.8574	−2.42754
$609$	4.86653	0.197202
$610$	66.8362	2.70612
$611$	−9.77351	−0.395394
$612$	−90.3534	−3.65232
$613$	−0.444274	−0.0179441	−0.00897204	−	0.999960i	$-0.502856\pi$
$613$	−0.444274	−0.0179441	−0.00897204	+	0.999960i	$0.502856\pi$
$614$	43.7841	1.76698
$615$	19.4776	0.785414
$616$	110.313	4.44463
$617$	34.8303	1.40221	0.701107	−	0.713056i	$-0.252690\pi$
$617$	34.8303	1.40221	0.701107	+	0.713056i	$0.252690\pi$
$618$	5.45993	0.219631
$619$	−0.879306	−0.0353423	−0.0176711	−	0.999844i	$-0.505625\pi$
$619$	−0.879306	−0.0353423	−0.0176711	+	0.999844i	$0.505625\pi$
$620$	75.9882	3.05176
$621$	14.0886	0.565355
$622$	76.7017	3.07546
$623$	5.70805	0.228688
$624$	−5.01885	−0.200915
$625$	36.7193	1.46877
$626$	−53.2737	−2.12924
$627$	−11.8615	−0.473705
$628$	−0.756028	−0.0301688
$629$	−49.3271	−1.96680
$630$	−103.912	−4.13994
$631$	−29.6761	−1.18139	−0.590693	−	0.806897i	$-0.701145\pi$
$631$	−29.6761	−1.18139	−0.590693	+	0.806897i	$0.701145\pi$
$632$	−126.305	−5.02415
$633$	−3.03056	−0.120454
$634$	5.55452	0.220598
$635$	−47.0735	−1.86805
$636$	6.38223	0.253072
$637$	−6.42734	−0.254661
$638$	27.2945	1.08060
$639$	−31.8476	−1.25987
$640$	1.34414	0.0531320
$641$	−7.53264	−0.297521	−0.148761	−	0.988873i	$-0.547528\pi$
$641$	−7.53264	−0.297521	−0.148761	+	0.988873i	$0.547528\pi$
$642$	−9.25100	−0.365108
$643$	10.4189	0.410883	0.205441	−	0.978669i	$-0.434137\pi$
$643$	10.4189	0.410883	0.205441	+	0.978669i	$0.434137\pi$
$644$	−84.3311	−3.32311
$645$	11.1755	0.440037
$646$	−101.123	−3.97864
$647$	−3.41329	−0.134190	−0.0670952	−	0.997747i	$-0.521373\pi$
$647$	−3.41329	−0.134190	−0.0670952	+	0.997747i	$0.521373\pi$
$648$	−49.4751	−1.94357
$649$	−6.77287	−0.265859
$650$	28.0929	1.10189
$651$	−7.49285	−0.293668
$652$	78.0925	3.05834
$653$	14.4692	0.566223	0.283112	−	0.959087i	$-0.408633\pi$
$653$	14.4692	0.566223	0.283112	+	0.959087i	$0.408633\pi$
$654$	11.8251	0.462398
$655$	63.6443	2.48679
$656$	−92.3809	−3.60687
$657$	−26.4249	−1.03094
$658$	−93.6401	−3.65047
$659$	−40.9706	−1.59599	−0.797995	−	0.602664i	$-0.794106\pi$
$659$	−40.9706	−1.59599	−0.797995	+	0.602664i	$0.794106\pi$
$660$	40.2276	1.56586
$661$	−37.2666	−1.44950	−0.724751	−	0.689010i	$-0.758045\pi$
$661$	−37.2666	−1.44950	−0.724751	+	0.689010i	$0.758045\pi$
$662$	17.2955	0.672207
$663$	−3.52957	−0.137077
$664$	39.6417	1.53840
$665$	−82.2750	−3.19049
$666$	−51.5784	−1.99862
$667$	−12.2374	−0.473834
$668$	83.1709	3.21798
$669$	−7.16542	−0.277031
$670$	−127.613	−4.93013
$671$	−26.1496	−1.00950
$672$	−20.0171	−0.772176
$673$	−23.2471	−0.896108	−0.448054	−	0.894007i	$-0.647883\pi$
$673$	−23.2471	−0.896108	−0.448054	+	0.894007i	$0.647883\pi$
$674$	30.7015	1.18258
$675$	−31.8115	−1.22443
$676$	4.83649	0.186019
$677$	−22.3348	−0.858395	−0.429198	−	0.903211i	$-0.641204\pi$
$677$	−22.3348	−0.858395	−0.429198	+	0.903211i	$0.641204\pi$
$678$	−6.77942	−0.260362
$679$	−31.6598	−1.21499
$680$	201.133	7.71312
$681$	−0.585729	−0.0224452
$682$	−42.0245	−1.60920
$683$	−20.3051	−0.776952	−0.388476	−	0.921459i	$-0.626998\pi$
$683$	−20.3051	−0.776952	−0.388476	+	0.921459i	$0.626998\pi$
$684$	−74.8050	−2.86024
$685$	45.0190	1.72009
$686$	5.48663	0.209481
$687$	3.46594	0.132234
$688$	−53.0047	−2.02079
$689$	−2.55531	−0.0973497
$690$	−25.4941	−0.970544
$691$	13.9532	0.530806	0.265403	−	0.964138i	$-0.414495\pi$
$691$	13.9532	0.530806	0.265403	+	0.964138i	$0.414495\pi$
$692$	30.4641	1.15807
$693$	40.6554	1.54437
$694$	73.9909	2.80866
$695$	−24.2292	−0.919064
$696$	−9.84968	−0.373351
$697$	−64.9681	−2.46084
$698$	46.4911	1.75971
$699$	−2.32073	−0.0877782
$700$	190.417	7.19708
$701$	−43.1435	−1.62951	−0.814753	−	0.579808i	$-0.803128\pi$
$701$	−43.1435	−1.62951	−0.814753	+	0.579808i	$0.803128\pi$
$702$	−7.74142	−0.292181
$703$	−40.8387	−1.54026
$704$	−33.3697	−1.25767
$705$	−20.0268	−0.754252
$706$	34.5018	1.29849
$707$	9.65445	0.363093
$708$	4.16744	0.156622
$709$	−19.8621	−0.745936	−0.372968	−	0.927844i	$-0.621660\pi$
$709$	−19.8621	−0.745936	−0.372968	+	0.927844i	$0.621660\pi$
$710$	120.883	4.53666
$711$	−46.5493	−1.74574
$712$	−11.5529	−0.432963
$713$	18.8415	0.705621
$714$	−33.8169	−1.26557
$715$	−16.1063	−0.602341
$716$	−81.1517	−3.03278
$717$	−8.23900	−0.307691
$718$	72.3666	2.70070
$719$	−47.3389	−1.76544	−0.882722	−	0.469896i	$-0.844291\pi$
$719$	−47.3389	−1.76544	−0.882722	+	0.469896i	$0.844291\pi$
$720$	105.404	3.92819
$721$	−14.8172	−0.551823
$722$	−34.0428	−1.26694
$723$	12.7305	0.473453
$724$	−62.2338	−2.31290
$725$	27.6316	1.02621
$726$	−7.39469	−0.274443
$727$	−22.3110	−0.827468	−0.413734	−	0.910398i	$-0.635776\pi$
$727$	−22.3110	−0.827468	−0.413734	+	0.910398i	$0.635776\pi$
$728$	27.1765	1.00723
$729$	−13.6469	−0.505441
$730$	100.301	3.71229
$731$	−37.2763	−1.37871
$732$	16.0902	0.594711
$733$	−15.5210	−0.573282	−0.286641	−	0.958038i	$-0.592539\pi$
$733$	−15.5210	−0.573282	−0.286641	+	0.958038i	$0.592539\pi$
$734$	10.8471	0.400373
$735$	−13.1702	−0.485790
$736$	50.3350	1.85537
$737$	49.9286	1.83914
$738$	−67.9332	−2.50066
$739$	51.9562	1.91124	0.955619	−	0.294604i	$-0.0951879\pi$
$739$	51.9562	1.91124	0.955619	+	0.294604i	$0.0951879\pi$
$740$	138.501	5.09141
$741$	−2.92219	−0.107349
$742$	−24.4825	−0.898781
$743$	−42.2515	−1.55006	−0.775029	−	0.631925i	$-0.782265\pi$
$743$	−42.2515	−1.55006	−0.775029	+	0.631925i	$0.782265\pi$
$744$	15.1653	0.555985
$745$	−13.3758	−0.490051
$746$	−54.8462	−2.00806
$747$	14.6098	0.534545
$748$	−134.180	−4.90610
$749$	25.1055	0.917335
$750$	30.7764	1.12380
$751$	−45.8553	−1.67328	−0.836642	−	0.547750i	$-0.815485\pi$
$751$	−45.8553	−1.67328	−0.836642	+	0.547750i	$0.815485\pi$
$752$	94.9853	3.46376
$753$	15.0707	0.549207
$754$	6.72423	0.244882
$755$	19.9689	0.726743
$756$	−52.4722	−1.90840
$757$	22.9495	0.834115	0.417057	−	0.908880i	$-0.363061\pi$
$757$	22.9495	0.834115	0.417057	+	0.908880i	$0.363061\pi$
$758$	0.414364	0.0150504
$759$	9.97456	0.362053
$760$	166.522	6.04037
$761$	−16.2527	−0.589162	−0.294581	−	0.955627i	$-0.595180\pi$
$761$	−16.2527	−0.589162	−0.294581	+	0.955627i	$0.595180\pi$
$762$	−16.0188	−0.580298
$763$	−32.0911	−1.16178
$764$	7.94443	0.287419
$765$	74.1270	2.68007
$766$	4.17755	0.150941
$767$	−1.66855	−0.0602480
$768$	−8.03339	−0.289880
$769$	−27.4349	−0.989327	−0.494663	−	0.869085i	$-0.664709\pi$
$769$	−27.4349	−0.989327	−0.494663	+	0.869085i	$0.664709\pi$
$770$	−154.315	−5.56111
$771$	−14.8627	−0.535267
$772$	−48.5788	−1.74839
$773$	−1.99609	−0.0717944	−0.0358972	−	0.999355i	$-0.511429\pi$
$773$	−1.99609	−0.0717944	−0.0358972	+	0.999355i	$0.511429\pi$
$774$	−38.9776	−1.40102
$775$	−42.5435	−1.52821
$776$	64.0783	2.30028
$777$	−13.6570	−0.489941
$778$	56.3852	2.02151
$779$	−53.7881	−1.92716
$780$	9.91039	0.354849
$781$	−47.2954	−1.69236
$782$	85.0361	3.04088
$783$	−7.61431	−0.272113
$784$	62.4651	2.23090
$785$	0.620255	0.0221378
$786$	21.6577	0.772504
$787$	−17.9730	−0.640669	−0.320334	−	0.947305i	$-0.603795\pi$
$787$	−17.9730	−0.640669	−0.320334	+	0.947305i	$0.603795\pi$
$788$	−26.2416	−0.934818
$789$	11.5206	0.410144
$790$	176.686	6.28621
$791$	18.3981	0.654161
$792$	−82.2850	−2.92387
$793$	−6.44218	−0.228768
$794$	32.3361	1.14756
$795$	−5.23606	−0.185704
$796$	97.3245	3.44957
$797$	52.9183	1.87446	0.937231	−	0.348709i	$-0.113380\pi$
$797$	52.9183	1.87446	0.937231	+	0.348709i	$0.113380\pi$
$798$	−27.9976	−0.991103
$799$	66.7997	2.36320
$800$	−113.655	−4.01830
$801$	−4.25778	−0.150441
$802$	−72.4507	−2.55832
$803$	−39.2425	−1.38484
$804$	−30.7217	−1.08347
$805$	69.1863	2.43850
$806$	−10.3531	−0.364672
$807$	5.59549	0.196971
$808$	−19.5403	−0.687424
$809$	−15.8035	−0.555622	−0.277811	−	0.960636i	$-0.589609\pi$
$809$	−15.8035	−0.555622	−0.277811	+	0.960636i	$0.589609\pi$
$810$	69.2098	2.43179
$811$	38.7452	1.36053	0.680263	−	0.732968i	$-0.261865\pi$
$811$	38.7452	1.36053	0.680263	+	0.732968i	$0.261865\pi$
$812$	45.5776	1.59946
$813$	−16.7784	−0.588446
$814$	−76.5968	−2.68472
$815$	−64.0681	−2.24421
$816$	34.3027	1.20084
$817$	−30.8616	−1.07971
$818$	8.69022	0.303847
$819$	10.0158	0.349980
$820$	182.418	6.37032
$821$	−46.5438	−1.62439	−0.812194	−	0.583387i	$-0.801727\pi$
$821$	−46.5438	−1.62439	−0.812194	+	0.583387i	$0.801727\pi$
$822$	15.3196	0.534334
$823$	−33.7574	−1.17671	−0.588355	−	0.808603i	$-0.700224\pi$
$823$	−33.7574	−1.17671	−0.588355	+	0.808603i	$0.700224\pi$
$824$	29.9896	1.04474
$825$	−22.5222	−0.784123
$826$	−15.9864	−0.556240
$827$	−19.1147	−0.664682	−0.332341	−	0.943159i	$-0.607838\pi$
$827$	−19.1147	−0.664682	−0.332341	+	0.943159i	$0.607838\pi$
$828$	62.9047	2.18609
$829$	42.3630	1.47133	0.735664	−	0.677347i	$-0.236870\pi$
$829$	42.3630	1.47133	0.735664	+	0.677347i	$0.236870\pi$
$830$	−55.4541	−1.92484
$831$	−15.7861	−0.547615
$832$	−8.22091	−0.285009
$833$	43.9294	1.52206
$834$	−8.24500	−0.285501
$835$	−68.2344	−2.36135
$836$	−111.090	−3.84211
$837$	11.7235	0.405224
$838$	−54.5633	−1.88486
$839$	−12.1013	−0.417782	−0.208891	−	0.977939i	$-0.566985\pi$
$839$	−12.1013	−0.417782	−0.208891	+	0.977939i	$0.566985\pi$
$840$	55.6870	1.92138
$841$	−22.3862	−0.771937
$842$	45.2447	1.55924
$843$	9.58770	0.330218
$844$	−28.3828	−0.976977
$845$	−3.96792	−0.136500
$846$	69.8485	2.40144
$847$	20.0678	0.689538
$848$	24.8342	0.852810
$849$	−2.81202	−0.0965082
$850$	−192.009	−6.58584
$851$	34.3419	1.17722
$852$	29.1015	0.997000
$853$	20.1866	0.691175	0.345587	−	0.938387i	$-0.387680\pi$
$853$	20.1866	0.691175	0.345587	+	0.938387i	$0.387680\pi$
$854$	−61.7226	−2.11210
$855$	61.3709	2.09884
$856$	−50.8126	−1.73674
$857$	50.6130	1.72891	0.864454	−	0.502712i	$-0.167664\pi$
$857$	50.6130	1.72891	0.864454	+	0.502712i	$0.167664\pi$
$858$	−5.48085	−0.187113
$859$	−9.30923	−0.317627	−0.158813	−	0.987309i	$-0.550767\pi$
$859$	−9.30923	−0.317627	−0.158813	+	0.987309i	$0.550767\pi$
$860$	104.665	3.56904
$861$	−17.9874	−0.613010
$862$	−46.7783	−1.59327
$863$	40.5687	1.38097	0.690487	−	0.723345i	$-0.257396\pi$
$863$	40.5687	1.38097	0.690487	+	0.723345i	$0.257396\pi$
$864$	31.3193	1.06550
$865$	−24.9932	−0.849793
$866$	−15.0580	−0.511693
$867$	15.3448	0.521137
$868$	−70.1744	−2.38187
$869$	−69.1284	−2.34502
$870$	13.7785	0.467137
$871$	12.3003	0.416781
$872$	64.9513	2.19953
$873$	23.6158	0.799274
$874$	70.4027	2.38141
$875$	−83.5215	−2.82354
$876$	24.1464	0.815832
$877$	35.6136	1.20259	0.601293	−	0.799028i	$-0.294652\pi$
$877$	35.6136	1.20259	0.601293	+	0.799028i	$0.294652\pi$
$878$	−11.5549	−0.389958
$879$	−1.45500	−0.0490758
$880$	156.531	5.27667
$881$	−29.6146	−0.997741	−0.498871	−	0.866676i	$-0.666252\pi$
$881$	−29.6146	−0.997741	−0.498871	+	0.866676i	$0.666252\pi$
$882$	45.9344	1.54669
$883$	45.8761	1.54385	0.771927	−	0.635712i	$-0.219293\pi$
$883$	45.8761	1.54385	0.771927	+	0.635712i	$0.219293\pi$
$884$	−33.0563	−1.11180
$885$	−3.41901	−0.114929
$886$	−89.9920	−3.02334
$887$	−10.4274	−0.350117	−0.175059	−	0.984558i	$-0.556011\pi$
$887$	−10.4274	−0.350117	−0.175059	+	0.984558i	$0.556011\pi$
$888$	27.6412	0.927579
$889$	43.4719	1.45800
$890$	16.1611	0.541723
$891$	−27.0783	−0.907157
$892$	−67.1079	−2.24694
$893$	55.3045	1.85070
$894$	−4.55168	−0.152231
$895$	66.5778	2.22545
$896$	−1.24131	−0.0414691
$897$	2.45732	0.0820474
$898$	−23.0396	−0.768841
$899$	−10.1831	−0.339625
$900$	−142.037	−4.73455
$901$	17.4650	0.581843
$902$	−100.885	−3.35909
$903$	−10.3205	−0.343445
$904$	−37.2371	−1.23849
$905$	51.0574	1.69720
$906$	6.79527	0.225758
$907$	21.2084	0.704213	0.352107	−	0.935960i	$-0.385465\pi$
$907$	21.2084	0.704213	0.352107	+	0.935960i	$0.385465\pi$
$908$	−5.48566	−0.182048
$909$	−7.20149	−0.238858
$910$	−38.0167	−1.26024
$911$	6.90102	0.228641	0.114320	−	0.993444i	$-0.463531\pi$
$911$	6.90102	0.228641	0.114320	+	0.993444i	$0.463531\pi$
$912$	28.3998	0.940410
$913$	21.6964	0.718045
$914$	−59.5187	−1.96870
$915$	−13.2006	−0.436398
$916$	32.4603	1.07252
$917$	−58.7750	−1.94092
$918$	52.9109	1.74632
$919$	28.6539	0.945204	0.472602	−	0.881276i	$-0.343315\pi$
$919$	28.6539	0.945204	0.472602	+	0.881276i	$0.343315\pi$
$920$	−140.031	−4.61667
$921$	−8.64766	−0.284950
$922$	75.9761	2.50214
$923$	−11.6516	−0.383518
$924$	−37.1498	−1.22214
$925$	−77.5428	−2.54959
$926$	2.61467	0.0859233
$927$	11.0525	0.363013
$928$	−27.2041	−0.893017
$929$	−29.6861	−0.973969	−0.486984	−	0.873411i	$-0.661903\pi$
$929$	−29.6861	−0.973969	−0.486984	+	0.873411i	$0.661903\pi$
$930$	−21.2144	−0.695648
$931$	36.3699	1.19197
$932$	−21.7349	−0.711950
$933$	−15.1491	−0.495959
$934$	80.7613	2.64259
$935$	110.083	3.60009
$936$	−20.2716	−0.662598
$937$	−18.2151	−0.595062	−0.297531	−	0.954712i	$-0.596163\pi$
$937$	−18.2151	−0.595062	−0.297531	+	0.954712i	$0.596163\pi$
$938$	117.850	3.84793
$939$	10.5219	0.343369
$940$	−187.561	−6.11757
$941$	27.0873	0.883020	0.441510	−	0.897256i	$-0.354443\pi$
$941$	27.0873	0.883020	0.441510	+	0.897256i	$0.354443\pi$
$942$	0.211068	0.00687697
$943$	45.2312	1.47293
$944$	16.2161	0.527789
$945$	43.0489	1.40038
$946$	−57.8839	−1.88197
$947$	34.7395	1.12888	0.564441	−	0.825474i	$-0.309092\pi$
$947$	34.7395	1.12888	0.564441	+	0.825474i	$0.309092\pi$
$948$	42.5356	1.38149
$949$	−9.66772	−0.313828
$950$	−158.967	−5.15757
$951$	−1.09705	−0.0355744
$952$	−185.745	−6.02003
$953$	48.4186	1.56843	0.784215	−	0.620489i	$-0.213066\pi$
$953$	48.4186	1.56843	0.784215	+	0.620489i	$0.213066\pi$
$954$	18.2621	0.591257
$955$	−6.51770	−0.210908
$956$	−77.1625	−2.49561
$957$	−5.39085	−0.174261
$958$	75.2221	2.43032
$959$	−41.5747	−1.34252
$960$	−16.8454	−0.543682
$961$	−15.3214	−0.494239
$962$	−18.8703	−0.608402
$963$	−18.7268	−0.603463
$964$	119.228	3.84007
$965$	39.8546	1.28297
$966$	23.5436	0.757502
$967$	26.8726	0.864166	0.432083	−	0.901834i	$-0.357779\pi$
$967$	26.8726	0.864166	0.432083	+	0.901834i	$0.357779\pi$
$968$	−40.6165	−1.30546
$969$	19.9725	0.641609
$970$	−89.6380	−2.87810
$971$	50.6696	1.62607	0.813033	−	0.582217i	$-0.197815\pi$
$971$	50.6696	1.62607	0.813033	+	0.582217i	$0.197815\pi$
$972$	59.6208	1.91234
$973$	22.3754	0.717322
$974$	−23.3579	−0.748435
$975$	−5.54854	−0.177695
$976$	62.6093	2.00408
$977$	−51.9373	−1.66162	−0.830811	−	0.556555i	$-0.812123\pi$
$977$	−51.9373	−1.66162	−0.830811	+	0.556555i	$0.812123\pi$
$978$	−21.8019	−0.697147
$979$	−6.32304	−0.202085
$980$	−123.346	−3.94014
$981$	23.9376	0.764267
$982$	69.5482	2.21937
$983$	−46.3978	−1.47986	−0.739929	−	0.672685i	$-0.765141\pi$
$983$	−46.3978	−1.47986	−0.739929	+	0.672685i	$0.765141\pi$
$984$	36.4059	1.16058
$985$	21.5289	0.685968
$986$	−45.9586	−1.46362
$987$	18.4945	0.588688
$988$	−27.3678	−0.870687
$989$	25.9520	0.825226
$990$	115.107	3.65834
$991$	−37.9464	−1.20541	−0.602703	−	0.797965i	$-0.705910\pi$
$991$	−37.9464	−1.20541	−0.602703	+	0.797965i	$0.705910\pi$
$992$	41.8853	1.32986
$993$	−3.41597	−0.108403
$994$	−111.634	−3.54083
$995$	−79.8462	−2.53129
$996$	−13.3501	−0.423013
$997$	−45.8252	−1.45130	−0.725649	−	0.688065i	$-0.758461\pi$
$997$	−45.8252	−1.45130	−0.725649	+	0.688065i	$0.758461\pi$
$998$	30.9078	0.978370
$999$	21.3681	0.676056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.6	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.6	✓	108	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61467 q^{2} +0.516414 q^{3} +4.83649 q^{4} -3.96792 q^{5} -1.35025 q^{6} +3.66433 q^{7} -7.41648 q^{8} -2.73332 q^{9} +O(q^{10})\)	\(q-2.61467 q^{2} +0.516414 q^{3} +4.83649 q^{4} -3.96792 q^{5} -1.35025 q^{6} +3.66433 q^{7} -7.41648 q^{8} -2.73332 q^{9} +10.3748 q^{10} -4.05913 q^{11} +2.49763 q^{12} -1.00000 q^{13} -9.58102 q^{14} -2.04909 q^{15} +9.71866 q^{16} +6.83477 q^{17} +7.14672 q^{18} +5.65862 q^{19} -19.1908 q^{20} +1.89231 q^{21} +10.6133 q^{22} -4.75842 q^{23} -3.82998 q^{24} +10.7444 q^{25} +2.61467 q^{26} -2.96077 q^{27} +17.7225 q^{28} +2.57174 q^{29} +5.35769 q^{30} -3.95962 q^{31} -10.5781 q^{32} -2.09619 q^{33} -17.8707 q^{34} -14.5398 q^{35} -13.2197 q^{36} -7.21708 q^{37} -14.7954 q^{38} -0.516414 q^{39} +29.4280 q^{40} -9.50552 q^{41} -4.94777 q^{42} -5.45391 q^{43} -19.6319 q^{44} +10.8456 q^{45} +12.4417 q^{46} +9.77351 q^{47} +5.01885 q^{48} +6.42734 q^{49} -28.0929 q^{50} +3.52957 q^{51} -4.83649 q^{52} +2.55531 q^{53} +7.74142 q^{54} +16.1063 q^{55} -27.1765 q^{56} +2.92219 q^{57} -6.72423 q^{58} +1.66855 q^{59} -9.91039 q^{60} +6.44218 q^{61} +10.3531 q^{62} -10.0158 q^{63} +8.22091 q^{64} +3.96792 q^{65} +5.48085 q^{66} -12.3003 q^{67} +33.0563 q^{68} -2.45732 q^{69} +38.0167 q^{70} +11.6516 q^{71} +20.2716 q^{72} +9.66772 q^{73} +18.8703 q^{74} +5.54854 q^{75} +27.3678 q^{76} -14.8740 q^{77} +1.35025 q^{78} +17.0304 q^{79} -38.5628 q^{80} +6.67097 q^{81} +24.8538 q^{82} -5.34508 q^{83} +9.15216 q^{84} -27.1198 q^{85} +14.2602 q^{86} +1.32808 q^{87} +30.1044 q^{88} +1.55773 q^{89} -28.3576 q^{90} -3.66433 q^{91} -23.0140 q^{92} -2.04480 q^{93} -25.5545 q^{94} -22.4529 q^{95} -5.46268 q^{96} -8.63999 q^{97} -16.8054 q^{98} +11.0949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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