LMFDB - Embedded newform 8049.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46430 q^{2} -1.00000 q^{3} +4.07278 q^{4} -0.321627 q^{5} +2.46430 q^{6} +1.46780 q^{7} -5.10794 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.46430 q^{2} -1.00000 q^{3} +4.07278 q^{4} -0.321627 q^{5} +2.46430 q^{6} +1.46780 q^{7} -5.10794 q^{8} +1.00000 q^{9} +0.792584 q^{10} -5.99744 q^{11} -4.07278 q^{12} -6.52698 q^{13} -3.61709 q^{14} +0.321627 q^{15} +4.44195 q^{16} +4.94520 q^{17} -2.46430 q^{18} -4.63933 q^{19} -1.30991 q^{20} -1.46780 q^{21} +14.7795 q^{22} +3.59421 q^{23} +5.10794 q^{24} -4.89656 q^{25} +16.0844 q^{26} -1.00000 q^{27} +5.97801 q^{28} -7.81884 q^{29} -0.792584 q^{30} -3.29042 q^{31} -0.730412 q^{32} +5.99744 q^{33} -12.1865 q^{34} -0.472082 q^{35} +4.07278 q^{36} -11.1710 q^{37} +11.4327 q^{38} +6.52698 q^{39} +1.64285 q^{40} +3.34324 q^{41} +3.61709 q^{42} +2.35938 q^{43} -24.4262 q^{44} -0.321627 q^{45} -8.85722 q^{46} -6.60069 q^{47} -4.44195 q^{48} -4.84557 q^{49} +12.0666 q^{50} -4.94520 q^{51} -26.5829 q^{52} +0.322499 q^{53} +2.46430 q^{54} +1.92893 q^{55} -7.49742 q^{56} +4.63933 q^{57} +19.2680 q^{58} +7.70260 q^{59} +1.30991 q^{60} -8.01891 q^{61} +8.10859 q^{62} +1.46780 q^{63} -7.08394 q^{64} +2.09925 q^{65} -14.7795 q^{66} +2.23388 q^{67} +20.1407 q^{68} -3.59421 q^{69} +1.16335 q^{70} -4.95517 q^{71} -5.10794 q^{72} -1.95278 q^{73} +27.5287 q^{74} +4.89656 q^{75} -18.8949 q^{76} -8.80302 q^{77} -16.0844 q^{78} -13.0918 q^{79} -1.42865 q^{80} +1.00000 q^{81} -8.23874 q^{82} -15.3969 q^{83} -5.97801 q^{84} -1.59051 q^{85} -5.81421 q^{86} +7.81884 q^{87} +30.6345 q^{88} +9.39428 q^{89} +0.792584 q^{90} -9.58029 q^{91} +14.6384 q^{92} +3.29042 q^{93} +16.2661 q^{94} +1.49213 q^{95} +0.730412 q^{96} -3.78794 q^{97} +11.9409 q^{98} -5.99744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.46430	−1.74252	−0.871262	−	0.490819i	$-0.836698\pi$
$2$	−2.46430	−1.74252	−0.871262	+	0.490819i	$0.836698\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.07278	2.03639
$5$	−0.321627	−0.143836	−0.0719179	−	0.997411i	$-0.522912\pi$
$5$	−0.321627	−0.143836	−0.0719179	+	0.997411i	$0.522912\pi$
$6$	2.46430	1.00605
$7$	1.46780	0.554775	0.277388	−	0.960758i	$-0.410531\pi$
$7$	1.46780	0.554775	0.277388	+	0.960758i	$0.410531\pi$
$8$	−5.10794	−1.80593
$9$	1.00000	0.333333
$10$	0.792584	0.250637
$11$	−5.99744	−1.80830	−0.904148	−	0.427220i	$-0.859493\pi$
$11$	−5.99744	−1.80830	−0.904148	+	0.427220i	$0.859493\pi$
$12$	−4.07278	−1.17571
$13$	−6.52698	−1.81026	−0.905130	−	0.425135i	$-0.860226\pi$
$13$	−6.52698	−1.81026	−0.905130	+	0.425135i	$0.860226\pi$
$14$	−3.61709	−0.966709
$15$	0.321627	0.0830436
$16$	4.44195	1.11049
$17$	4.94520	1.19939	0.599693	−	0.800230i	$-0.295289\pi$
$17$	4.94520	1.19939	0.599693	+	0.800230i	$0.295289\pi$
$18$	−2.46430	−0.580841
$19$	−4.63933	−1.06434	−0.532168	−	0.846639i	$-0.678622\pi$
$19$	−4.63933	−1.06434	−0.532168	+	0.846639i	$0.678622\pi$
$20$	−1.30991	−0.292905
$21$	−1.46780	−0.320300
$22$	14.7795	3.15100
$23$	3.59421	0.749446	0.374723	−	0.927137i	$-0.377738\pi$
$23$	3.59421	0.749446	0.374723	+	0.927137i	$0.377738\pi$
$24$	5.10794	1.04265
$25$	−4.89656	−0.979311
$26$	16.0844	3.15442
$27$	−1.00000	−0.192450
$28$	5.97801	1.12974
$29$	−7.81884	−1.45192	−0.725961	−	0.687736i	$-0.758605\pi$
$29$	−7.81884	−1.45192	−0.725961	+	0.687736i	$0.758605\pi$
$30$	−0.792584	−0.144705
$31$	−3.29042	−0.590978	−0.295489	−	0.955346i	$-0.595483\pi$
$31$	−3.29042	−0.590978	−0.295489	+	0.955346i	$0.595483\pi$
$32$	−0.730412	−0.129120
$33$	5.99744	1.04402
$34$	−12.1865	−2.08996
$35$	−0.472082	−0.0797965
$36$	4.07278	0.678796
$37$	−11.1710	−1.83650	−0.918251	−	0.395999i	$-0.870398\pi$
$37$	−11.1710	−1.83650	−0.918251	+	0.395999i	$0.870398\pi$
$38$	11.4327	1.85463
$39$	6.52698	1.04515
$40$	1.64285	0.259757
$41$	3.34324	0.522126	0.261063	−	0.965322i	$-0.415927\pi$
$41$	3.34324	0.522126	0.261063	+	0.965322i	$0.415927\pi$
$42$	3.61709	0.558129
$43$	2.35938	0.359802	0.179901	−	0.983685i	$-0.442422\pi$
$43$	2.35938	0.359802	0.179901	+	0.983685i	$0.442422\pi$
$44$	−24.4262	−3.68239
$45$	−0.321627	−0.0479453
$46$	−8.85722	−1.30593
$47$	−6.60069	−0.962809	−0.481404	−	0.876499i	$-0.659873\pi$
$47$	−6.60069	−0.962809	−0.481404	+	0.876499i	$0.659873\pi$
$48$	−4.44195	−0.641140
$49$	−4.84557	−0.692225
$50$	12.0666	1.70647
$51$	−4.94520	−0.692466
$52$	−26.5829	−3.68639
$53$	0.322499	0.0442986	0.0221493	−	0.999755i	$-0.492949\pi$
$53$	0.322499	0.0442986	0.0221493	+	0.999755i	$0.492949\pi$
$54$	2.46430	0.335349
$55$	1.92893	0.260098
$56$	−7.49742	−1.00188
$57$	4.63933	0.614494
$58$	19.2680	2.53001
$59$	7.70260	1.00279	0.501396	−	0.865218i	$-0.332820\pi$
$59$	7.70260	1.00279	0.501396	+	0.865218i	$0.332820\pi$
$60$	1.30991	0.169109
$61$	−8.01891	−1.02672	−0.513358	−	0.858174i	$-0.671599\pi$
$61$	−8.01891	−1.02672	−0.513358	+	0.858174i	$0.671599\pi$
$62$	8.10859	1.02979
$63$	1.46780	0.184925
$64$	−7.08394	−0.885493
$65$	2.09925	0.260380
$66$	−14.7795	−1.81923
$67$	2.23388	0.272912	0.136456	−	0.990646i	$-0.456429\pi$
$67$	2.23388	0.272912	0.136456	+	0.990646i	$0.456429\pi$
$68$	20.1407	2.44242
$69$	−3.59421	−0.432693
$70$	1.16335	0.139047
$71$	−4.95517	−0.588070	−0.294035	−	0.955795i	$-0.594998\pi$
$71$	−4.95517	−0.588070	−0.294035	+	0.955795i	$0.594998\pi$
$72$	−5.10794	−0.601977
$73$	−1.95278	−0.228556	−0.114278	−	0.993449i	$-0.536455\pi$
$73$	−1.95278	−0.228556	−0.114278	+	0.993449i	$0.536455\pi$
$74$	27.5287	3.20015
$75$	4.89656	0.565406
$76$	−18.8949	−2.16740
$77$	−8.80302	−1.00320
$78$	−16.0844	−1.82120
$79$	−13.0918	−1.47294	−0.736469	−	0.676471i	$-0.763508\pi$
$79$	−13.0918	−1.47294	−0.736469	+	0.676471i	$0.763508\pi$
$80$	−1.42865	−0.159728
$81$	1.00000	0.111111
$82$	−8.23874	−0.909816
$83$	−15.3969	−1.69002	−0.845012	−	0.534747i	$-0.820407\pi$
$83$	−15.3969	−1.69002	−0.845012	+	0.534747i	$0.820407\pi$
$84$	−5.97801	−0.652254
$85$	−1.59051	−0.172515
$86$	−5.81421	−0.626963
$87$	7.81884	0.838267
$88$	30.6345	3.26565
$89$	9.39428	0.995792	0.497896	−	0.867237i	$-0.334106\pi$
$89$	9.39428	0.995792	0.497896	+	0.867237i	$0.334106\pi$
$90$	0.792584	0.0835457
$91$	−9.58029	−1.00429
$92$	14.6384	1.52616
$93$	3.29042	0.341201
$94$	16.2661	1.67772
$95$	1.49213	0.153089
$96$	0.730412	0.0745473
$97$	−3.78794	−0.384607	−0.192304	−	0.981335i	$-0.561596\pi$
$97$	−3.78794	−0.384607	−0.192304	+	0.981335i	$0.561596\pi$
$98$	11.9409	1.20622
$99$	−5.99744	−0.602765
$100$	−19.9426	−1.99426
$101$	−15.5816	−1.55043	−0.775213	−	0.631700i	$-0.782358\pi$
$101$	−15.5816	−1.55043	−0.775213	+	0.631700i	$0.782358\pi$
$102$	12.1865	1.20664
$103$	−3.94180	−0.388397	−0.194199	−	0.980962i	$-0.562211\pi$
$103$	−3.94180	−0.388397	−0.194199	+	0.980962i	$0.562211\pi$
$104$	33.3394	3.26920
$105$	0.472082	0.0460705
$106$	−0.794734	−0.0771914
$107$	−9.73338	−0.940961	−0.470481	−	0.882410i	$-0.655919\pi$
$107$	−9.73338	−0.940961	−0.470481	+	0.882410i	$0.655919\pi$
$108$	−4.07278	−0.391903
$109$	0.0109671	0.00105046	0.000525230	−	1.00000i	$-0.499833\pi$
$109$	0.0109671	0.00105046	0.000525230		1.00000i	$0.499833\pi$
$110$	−4.75347	−0.453226
$111$	11.1710	1.06030
$112$	6.51988	0.616071
$113$	4.47460	0.420935	0.210468	−	0.977601i	$-0.432501\pi$
$113$	4.47460	0.420935	0.210468	+	0.977601i	$0.432501\pi$
$114$	−11.4327	−1.07077
$115$	−1.15599	−0.107797
$116$	−31.8444	−2.95667
$117$	−6.52698	−0.603420
$118$	−18.9815	−1.74739
$119$	7.25855	0.665390
$120$	−1.64285	−0.149971
$121$	24.9692	2.26993
$122$	19.7610	1.78908
$123$	−3.34324	−0.301449
$124$	−13.4012	−1.20346
$125$	3.18299	0.284696
$126$	−3.61709	−0.322236
$127$	−13.8517	−1.22914	−0.614571	−	0.788862i	$-0.710671\pi$
$127$	−13.8517	−1.22914	−0.614571	+	0.788862i	$0.710671\pi$
$128$	18.9178	1.67211
$129$	−2.35938	−0.207732
$130$	−5.17318	−0.453718
$131$	0.428458	0.0374345	0.0187173	−	0.999825i	$-0.494042\pi$
$131$	0.428458	0.0374345	0.0187173	+	0.999825i	$0.494042\pi$
$132$	24.4262	2.12603
$133$	−6.80959	−0.590467
$134$	−5.50495	−0.475555
$135$	0.321627	0.0276812
$136$	−25.2598	−2.16601
$137$	18.7848	1.60489	0.802447	−	0.596724i	$-0.203531\pi$
$137$	18.7848	1.60489	0.802447	+	0.596724i	$0.203531\pi$
$138$	8.85722	0.753977
$139$	−1.00003	−0.0848216	−0.0424108	−	0.999100i	$-0.513504\pi$
$139$	−1.00003	−0.0848216	−0.0424108	+	0.999100i	$0.513504\pi$
$140$	−1.92269	−0.162497
$141$	6.60069	0.555878
$142$	12.2110	1.02473
$143$	39.1452	3.27348
$144$	4.44195	0.370162
$145$	2.51474	0.208838
$146$	4.81224	0.398264
$147$	4.84557	0.399656
$148$	−45.4970	−3.73983
$149$	1.48176	0.121391	0.0606954	−	0.998156i	$-0.480668\pi$
$149$	1.48176	0.121391	0.0606954	+	0.998156i	$0.480668\pi$
$150$	−12.0666	−0.985233
$151$	23.2288	1.89034	0.945168	−	0.326585i	$-0.105898\pi$
$151$	23.2288	1.89034	0.945168	+	0.326585i	$0.105898\pi$
$152$	23.6974	1.92211
$153$	4.94520	0.399796
$154$	21.6933	1.74809
$155$	1.05829	0.0850037
$156$	26.5829	2.12834
$157$	11.3397	0.905006	0.452503	−	0.891763i	$-0.350531\pi$
$157$	11.3397	0.905006	0.452503	+	0.891763i	$0.350531\pi$
$158$	32.2620	2.56663
$159$	−0.322499	−0.0255758
$160$	0.234920	0.0185720
$161$	5.27558	0.415774
$162$	−2.46430	−0.193614
$163$	−11.3244	−0.886995	−0.443497	−	0.896276i	$-0.646262\pi$
$163$	−11.3244	−0.886995	−0.443497	+	0.896276i	$0.646262\pi$
$164$	13.6162	1.06325
$165$	−1.92893	−0.150167
$166$	37.9425	2.94491
$167$	20.9123	1.61824	0.809120	−	0.587644i	$-0.199944\pi$
$167$	20.9123	1.61824	0.809120	+	0.587644i	$0.199944\pi$
$168$	7.49742	0.578438
$169$	29.6015	2.27704
$170$	3.91949	0.300611
$171$	−4.63933	−0.354778
$172$	9.60921	0.732696
$173$	21.1493	1.60795	0.803975	−	0.594664i	$-0.202715\pi$
$173$	21.1493	1.60795	0.803975	+	0.594664i	$0.202715\pi$
$174$	−19.2680	−1.46070
$175$	−7.18715	−0.543298
$176$	−26.6403	−2.00809
$177$	−7.70260	−0.578963
$178$	−23.1503	−1.73519
$179$	−1.29249	−0.0966051	−0.0483026	−	0.998833i	$-0.515381\pi$
$179$	−1.29249	−0.0966051	−0.0483026	+	0.998833i	$0.515381\pi$
$180$	−1.30991	−0.0976351
$181$	2.34310	0.174161	0.0870806	−	0.996201i	$-0.472246\pi$
$181$	2.34310	0.174161	0.0870806	+	0.996201i	$0.472246\pi$
$182$	23.6087	1.74999
$183$	8.01891	0.592775
$184$	−18.3590	−1.35345
$185$	3.59289	0.264155
$186$	−8.10859	−0.594551
$187$	−29.6585	−2.16885
$188$	−26.8831	−1.96065
$189$	−1.46780	−0.106767
$190$	−3.67706	−0.266762
$191$	−1.84871	−0.133768	−0.0668839	−	0.997761i	$-0.521306\pi$
$191$	−1.84871	−0.133768	−0.0668839	+	0.997761i	$0.521306\pi$
$192$	7.08394	0.511239
$193$	−20.7223	−1.49162	−0.745811	−	0.666158i	$-0.767938\pi$
$193$	−20.7223	−1.49162	−0.745811	+	0.666158i	$0.767938\pi$
$194$	9.33463	0.670187
$195$	−2.09925	−0.150330
$196$	−19.7349	−1.40964
$197$	−22.4062	−1.59638	−0.798188	−	0.602408i	$-0.794208\pi$
$197$	−22.4062	−1.59638	−0.798188	+	0.602408i	$0.794208\pi$
$198$	14.7795	1.05033
$199$	−2.12878	−0.150905	−0.0754525	−	0.997149i	$-0.524040\pi$
$199$	−2.12878	−0.150905	−0.0754525	+	0.997149i	$0.524040\pi$
$200$	25.0113	1.76857
$201$	−2.23388	−0.157566
$202$	38.3977	2.70165
$203$	−11.4765	−0.805490
$204$	−20.1407	−1.41013
$205$	−1.07527	−0.0751004
$206$	9.71378	0.676791
$207$	3.59421	0.249815
$208$	−28.9925	−2.01027
$209$	27.8241	1.92463
$210$	−1.16335	−0.0802790
$211$	−14.7262	−1.01379	−0.506896	−	0.862007i	$-0.669207\pi$
$211$	−14.7262	−1.01379	−0.506896	+	0.862007i	$0.669207\pi$
$212$	1.31347	0.0902092
$213$	4.95517	0.339523
$214$	23.9860	1.63965
$215$	−0.758838	−0.0517523
$216$	5.10794	0.347551
$217$	−4.82967	−0.327860
$218$	−0.0270263	−0.00183045
$219$	1.95278	0.131957
$220$	7.85612	0.529659
$221$	−32.2772	−2.17120
$222$	−27.5287	−1.84761
$223$	3.61514	0.242088	0.121044	−	0.992647i	$-0.461376\pi$
$223$	3.61514	0.242088	0.121044	+	0.992647i	$0.461376\pi$
$224$	−1.07210	−0.0716324
$225$	−4.89656	−0.326437
$226$	−11.0268	−0.733489
$227$	−16.3522	−1.08533	−0.542667	−	0.839948i	$-0.682585\pi$
$227$	−16.3522	−1.08533	−0.542667	+	0.839948i	$0.682585\pi$
$228$	18.8949	1.25135
$229$	24.0892	1.59186	0.795928	−	0.605391i	$-0.206983\pi$
$229$	24.0892	1.59186	0.795928	+	0.605391i	$0.206983\pi$
$230$	2.84872	0.187839
$231$	8.80302	0.579196
$232$	39.9381	2.62207
$233$	−27.1548	−1.77897	−0.889484	−	0.456967i	$-0.848936\pi$
$233$	−27.1548	−1.77897	−0.889484	+	0.456967i	$0.848936\pi$
$234$	16.0844	1.05147
$235$	2.12296	0.138486
$236$	31.3709	2.04207
$237$	13.0918	0.850401
$238$	−17.8872	−1.15946
$239$	−13.3824	−0.865635	−0.432818	−	0.901482i	$-0.642481\pi$
$239$	−13.3824	−0.865635	−0.432818	+	0.901482i	$0.642481\pi$
$240$	1.42865	0.0922188
$241$	−1.36066	−0.0876475	−0.0438238	−	0.999039i	$-0.513954\pi$
$241$	−1.36066	−0.0876475	−0.0438238	+	0.999039i	$0.513954\pi$
$242$	−61.5317	−3.95541
$243$	−1.00000	−0.0641500
$244$	−32.6592	−2.09079
$245$	1.55846	0.0995666
$246$	8.23874	0.525283
$247$	30.2808	1.92672
$248$	16.8073	1.06726
$249$	15.3969	0.975736
$250$	−7.84386	−0.496089
$251$	23.7729	1.50053	0.750267	−	0.661135i	$-0.229925\pi$
$251$	23.7729	1.50053	0.750267	+	0.661135i	$0.229925\pi$
$252$	5.97801	0.376579
$253$	−21.5561	−1.35522
$254$	34.1348	2.14181
$255$	1.59051	0.0996014
$256$	−32.4512	−2.02820
$257$	−1.44934	−0.0904076	−0.0452038	−	0.998978i	$-0.514394\pi$
$257$	−1.44934	−0.0904076	−0.0452038	+	0.998978i	$0.514394\pi$
$258$	5.81421	0.361977
$259$	−16.3968	−1.01885
$260$	8.54978	0.530235
$261$	−7.81884	−0.483974
$262$	−1.05585	−0.0652305
$263$	−29.3197	−1.80793	−0.903966	−	0.427604i	$-0.859358\pi$
$263$	−29.3197	−1.80793	−0.903966	+	0.427604i	$0.859358\pi$
$264$	−30.6345	−1.88543
$265$	−0.103724	−0.00637173
$266$	16.7809	1.02890
$267$	−9.39428	−0.574921
$268$	9.09809	0.555754
$269$	−19.0547	−1.16179	−0.580894	−	0.813979i	$-0.697297\pi$
$269$	−19.0547	−1.16179	−0.580894	+	0.813979i	$0.697297\pi$
$270$	−0.792584	−0.0482351
$271$	14.7890	0.898370	0.449185	−	0.893439i	$-0.351714\pi$
$271$	14.7890	0.898370	0.449185	+	0.893439i	$0.351714\pi$
$272$	21.9663	1.33190
$273$	9.58029	0.579825
$274$	−46.2914	−2.79656
$275$	29.3668	1.77088
$276$	−14.6384	−0.881130
$277$	13.2333	0.795112	0.397556	−	0.917578i	$-0.369858\pi$
$277$	13.2333	0.795112	0.397556	+	0.917578i	$0.369858\pi$
$278$	2.46438	0.147804
$279$	−3.29042	−0.196993
$280$	2.41137	0.144107
$281$	−10.3504	−0.617451	−0.308725	−	0.951151i	$-0.599902\pi$
$281$	−10.3504	−0.617451	−0.308725	+	0.951151i	$0.599902\pi$
$282$	−16.2661	−0.968630
$283$	−3.29398	−0.195807	−0.0979035	−	0.995196i	$-0.531214\pi$
$283$	−3.29398	−0.195807	−0.0979035	+	0.995196i	$0.531214\pi$
$284$	−20.1813	−1.19754
$285$	−1.49213	−0.0883862
$286$	−96.4655	−5.70412
$287$	4.90719	0.289662
$288$	−0.730412	−0.0430399
$289$	7.45499	0.438529
$290$	−6.19709	−0.363905
$291$	3.78794	0.222053
$292$	−7.95323	−0.465428
$293$	3.06333	0.178962	0.0894809	−	0.995989i	$-0.471479\pi$
$293$	3.06333	0.178962	0.0894809	+	0.995989i	$0.471479\pi$
$294$	−11.9409	−0.696410
$295$	−2.47736	−0.144237
$296$	57.0608	3.31659
$297$	5.99744	0.348007
$298$	−3.65151	−0.211526
$299$	−23.4594	−1.35669
$300$	19.9426	1.15139
$301$	3.46309	0.199609
$302$	−57.2428	−3.29395
$303$	15.5816	0.895139
$304$	−20.6077	−1.18193
$305$	2.57909	0.147679
$306$	−12.1865	−0.696653
$307$	18.4339	1.05208	0.526039	−	0.850460i	$-0.323676\pi$
$307$	18.4339	1.05208	0.526039	+	0.850460i	$0.323676\pi$
$308$	−35.8527	−2.04290
$309$	3.94180	0.224241
$310$	−2.60794	−0.148121
$311$	−21.5724	−1.22326	−0.611628	−	0.791145i	$-0.709485\pi$
$311$	−21.5724	−1.22326	−0.611628	+	0.791145i	$0.709485\pi$
$312$	−33.3394	−1.88747
$313$	−19.3334	−1.09279	−0.546395	−	0.837528i	$-0.684000\pi$
$313$	−19.3334	−1.09279	−0.546395	+	0.837528i	$0.684000\pi$
$314$	−27.9444	−1.57699
$315$	−0.472082	−0.0265988
$316$	−53.3198	−2.99947
$317$	8.04892	0.452072	0.226036	−	0.974119i	$-0.427423\pi$
$317$	8.04892	0.452072	0.226036	+	0.974119i	$0.427423\pi$
$318$	0.794734	0.0445665
$319$	46.8930	2.62550
$320$	2.27838	0.127366
$321$	9.73338	0.543264
$322$	−13.0006	−0.724495
$323$	−22.9424	−1.27655
$324$	4.07278	0.226265
$325$	31.9597	1.77281
$326$	27.9067	1.54561
$327$	−0.0109671	−0.000606483 0
$328$	−17.0771	−0.942922
$329$	−9.68847	−0.534142
$330$	4.75347	0.261670
$331$	−5.58624	−0.307047	−0.153524	−	0.988145i	$-0.549062\pi$
$331$	−5.58624	−0.307047	−0.153524	+	0.988145i	$0.549062\pi$
$332$	−62.7079	−3.44154
$333$	−11.1710	−0.612167
$334$	−51.5341	−2.81982
$335$	−0.718475	−0.0392545
$336$	−6.51988	−0.355688
$337$	−17.0134	−0.926777	−0.463389	−	0.886155i	$-0.653367\pi$
$337$	−17.0134	−0.926777	−0.463389	+	0.886155i	$0.653367\pi$
$338$	−72.9470	−3.96779
$339$	−4.47460	−0.243027
$340$	−6.47778	−0.351307
$341$	19.7341	1.06866
$342$	11.4327	0.618210
$343$	−17.3869	−0.938804
$344$	−12.0516	−0.649776
$345$	1.15599	0.0622367
$346$	−52.1182	−2.80189
$347$	25.8480	1.38759	0.693796	−	0.720172i	$-0.255937\pi$
$347$	25.8480	1.38759	0.693796	+	0.720172i	$0.255937\pi$
$348$	31.8444	1.70704
$349$	18.3447	0.981971	0.490985	−	0.871168i	$-0.336637\pi$
$349$	18.3447	0.981971	0.490985	+	0.871168i	$0.336637\pi$
$350$	17.7113	0.946709
$351$	6.52698	0.348385
$352$	4.38060	0.233487
$353$	4.53265	0.241248	0.120624	−	0.992698i	$-0.461510\pi$
$353$	4.53265	0.241248	0.120624	+	0.992698i	$0.461510\pi$
$354$	18.9815	1.00886
$355$	1.59371	0.0845855
$356$	38.2608	2.02782
$357$	−7.25855	−0.384163
$358$	3.18508	0.168337
$359$	−9.72869	−0.513461	−0.256730	−	0.966483i	$-0.582645\pi$
$359$	−9.72869	−0.513461	−0.256730	+	0.966483i	$0.582645\pi$
$360$	1.64285	0.0865857
$361$	2.52338	0.132810
$362$	−5.77410	−0.303480
$363$	−24.9692	−1.31055
$364$	−39.0184	−2.04512
$365$	0.628066	0.0328745
$366$	−19.7610	−1.03292
$367$	−1.91511	−0.0999681	−0.0499840	−	0.998750i	$-0.515917\pi$
$367$	−1.91511	−0.0999681	−0.0499840	+	0.998750i	$0.515917\pi$
$368$	15.9653	0.832250
$369$	3.34324	0.174042
$370$	−8.85396	−0.460296
$371$	0.473363	0.0245758
$372$	13.4012	0.694818
$373$	3.64810	0.188891	0.0944457	−	0.995530i	$-0.469892\pi$
$373$	3.64810	0.188891	0.0944457	+	0.995530i	$0.469892\pi$
$374$	73.0875	3.77926
$375$	−3.18299	−0.164369
$376$	33.7159	1.73877
$377$	51.0334	2.62835
$378$	3.61709	0.186043
$379$	−2.51174	−0.129019	−0.0645097	−	0.997917i	$-0.520548\pi$
$379$	−2.51174	−0.129019	−0.0645097	+	0.997917i	$0.520548\pi$
$380$	6.07712	0.311749
$381$	13.8517	0.709645
$382$	4.55577	0.233094
$383$	9.87655	0.504668	0.252334	−	0.967640i	$-0.418802\pi$
$383$	9.87655	0.504668	0.252334	+	0.967640i	$0.418802\pi$
$384$	−18.9178	−0.965394
$385$	2.83128	0.144296
$386$	51.0659	2.59919
$387$	2.35938	0.119934
$388$	−15.4274	−0.783210
$389$	−4.13084	−0.209442	−0.104721	−	0.994502i	$-0.533395\pi$
$389$	−4.13084	−0.209442	−0.104721	+	0.994502i	$0.533395\pi$
$390$	5.17318	0.261954
$391$	17.7741	0.898875
$392$	24.7509	1.25011
$393$	−0.428458	−0.0216128
$394$	55.2156	2.78172
$395$	4.21066	0.211861
$396$	−24.4262	−1.22746
$397$	−34.6198	−1.73752	−0.868759	−	0.495236i	$-0.835082\pi$
$397$	−34.6198	−1.73752	−0.868759	+	0.495236i	$0.835082\pi$
$398$	5.24595	0.262956
$399$	6.80959	0.340906
$400$	−21.7502	−1.08751
$401$	−37.5562	−1.87547	−0.937733	−	0.347356i	$-0.887079\pi$
$401$	−37.5562	−1.87547	−0.937733	+	0.347356i	$0.887079\pi$
$402$	5.50495	0.274562
$403$	21.4765	1.06982
$404$	−63.4603	−3.15727
$405$	−0.321627	−0.0159818
$406$	28.2815	1.40358
$407$	66.9974	3.32094
$408$	25.2598	1.25055
$409$	−13.3257	−0.658913	−0.329457	−	0.944171i	$-0.606866\pi$
$409$	−13.3257	−0.658913	−0.329457	+	0.944171i	$0.606866\pi$
$410$	2.64980	0.130864
$411$	−18.7848	−0.926586
$412$	−16.0541	−0.790927
$413$	11.3058	0.556324
$414$	−8.85722	−0.435309
$415$	4.95204	0.243086
$416$	4.76739	0.233740
$417$	1.00003	0.0489718
$418$	−68.5669	−3.35372
$419$	−23.0685	−1.12697	−0.563485	−	0.826126i	$-0.690540\pi$
$419$	−23.0685	−1.12697	−0.563485	+	0.826126i	$0.690540\pi$
$420$	1.92269	0.0938175
$421$	13.9857	0.681623	0.340811	−	0.940132i	$-0.389298\pi$
$421$	13.9857	0.681623	0.340811	+	0.940132i	$0.389298\pi$
$422$	36.2897	1.76656
$423$	−6.60069	−0.320936
$424$	−1.64730	−0.0800002
$425$	−24.2144	−1.17457
$426$	−12.2110	−0.591626
$427$	−11.7701	−0.569597
$428$	−39.6419	−1.91616
$429$	−39.1452	−1.88995
$430$	1.87001	0.0901797
$431$	32.9723	1.58822	0.794110	−	0.607774i	$-0.207937\pi$
$431$	32.9723	1.58822	0.794110	+	0.607774i	$0.207937\pi$
$432$	−4.44195	−0.213713
$433$	−6.69904	−0.321935	−0.160968	−	0.986960i	$-0.551462\pi$
$433$	−6.69904	−0.321935	−0.160968	+	0.986960i	$0.551462\pi$
$434$	11.9018	0.571303
$435$	−2.51474	−0.120573
$436$	0.0446666	0.00213914
$437$	−16.6747	−0.797661
$438$	−4.81224	−0.229938
$439$	12.0620	0.575687	0.287843	−	0.957678i	$-0.407062\pi$
$439$	12.0620	0.575687	0.287843	+	0.957678i	$0.407062\pi$
$440$	−9.85288	−0.469718
$441$	−4.84557	−0.230742
$442$	79.5408	3.78337
$443$	5.31672	0.252605	0.126302	−	0.991992i	$-0.459689\pi$
$443$	5.31672	0.252605	0.126302	+	0.991992i	$0.459689\pi$
$444$	45.4970	2.15919
$445$	−3.02145	−0.143230
$446$	−8.90878	−0.421843
$447$	−1.48176	−0.0700850
$448$	−10.3978	−0.491249
$449$	−28.9786	−1.36759	−0.683793	−	0.729676i	$-0.739671\pi$
$449$	−28.9786	−1.36759	−0.683793	+	0.729676i	$0.739671\pi$
$450$	12.0666	0.568824
$451$	−20.0508	−0.944158
$452$	18.2240	0.857187
$453$	−23.2288	−1.09139
$454$	40.2967	1.89122
$455$	3.08127	0.144452
$456$	−23.6974	−1.10973
$457$	−2.84103	−0.132898	−0.0664489	−	0.997790i	$-0.521167\pi$
$457$	−2.84103	−0.132898	−0.0664489	+	0.997790i	$0.521167\pi$
$458$	−59.3629	−2.77385
$459$	−4.94520	−0.230822
$460$	−4.70811	−0.219517
$461$	−2.47930	−0.115472	−0.0577362	−	0.998332i	$-0.518388\pi$
$461$	−2.47930	−0.115472	−0.0577362	+	0.998332i	$0.518388\pi$
$462$	−21.6933	−1.00926
$463$	19.6653	0.913925	0.456963	−	0.889486i	$-0.348937\pi$
$463$	19.6653	0.913925	0.456963	+	0.889486i	$0.348937\pi$
$464$	−34.7309	−1.61234
$465$	−1.05829	−0.0490769
$466$	66.9175	3.09989
$467$	−25.9656	−1.20154	−0.600772	−	0.799420i	$-0.705140\pi$
$467$	−25.9656	−1.20154	−0.600772	+	0.799420i	$0.705140\pi$
$468$	−26.5829	−1.22880
$469$	3.27888	0.151405
$470$	−5.23160	−0.241316
$471$	−11.3397	−0.522505
$472$	−39.3444	−1.81097
$473$	−14.1502	−0.650628
$474$	−32.2620	−1.48184
$475$	22.7167	1.04232
$476$	29.5624	1.35499
$477$	0.322499	0.0147662
$478$	32.9782	1.50839
$479$	18.3689	0.839297	0.419649	−	0.907687i	$-0.362153\pi$
$479$	18.3689	0.839297	0.419649	+	0.907687i	$0.362153\pi$
$480$	−0.234920	−0.0107226
$481$	72.9130	3.32455
$482$	3.35306	0.152728
$483$	−5.27558	−0.240047
$484$	101.694	4.62246
$485$	1.21830	0.0553203
$486$	2.46430	0.111783
$487$	−37.9130	−1.71800	−0.859002	−	0.511972i	$-0.828915\pi$
$487$	−37.9130	−1.71800	−0.859002	+	0.511972i	$0.828915\pi$
$488$	40.9601	1.85418
$489$	11.3244	0.512107
$490$	−3.84052	−0.173497
$491$	21.2442	0.958736	0.479368	−	0.877614i	$-0.340866\pi$
$491$	21.2442	0.958736	0.479368	+	0.877614i	$0.340866\pi$
$492$	−13.6162	−0.613868
$493$	−38.6657	−1.74142
$494$	−74.6211	−3.35736
$495$	1.92893	0.0866992
$496$	−14.6159	−0.656273
$497$	−7.27318	−0.326247
$498$	−37.9425	−1.70024
$499$	5.29572	0.237069	0.118534	−	0.992950i	$-0.462180\pi$
$499$	5.29572	0.237069	0.118534	+	0.992950i	$0.462180\pi$
$500$	12.9636	0.579751
$501$	−20.9123	−0.934291
$502$	−58.5836	−2.61471
$503$	34.7321	1.54863	0.774315	−	0.632801i	$-0.218095\pi$
$503$	34.7321	1.54863	0.774315	+	0.632801i	$0.218095\pi$
$504$	−7.49742	−0.333962
$505$	5.01145	0.223007
$506$	53.1206	2.36150
$507$	−29.6015	−1.31465
$508$	−56.4149	−2.50301
$509$	−7.44209	−0.329865	−0.164932	−	0.986305i	$-0.552741\pi$
$509$	−7.44209	−0.329865	−0.164932	+	0.986305i	$0.552741\pi$
$510$	−3.91949	−0.173558
$511$	−2.86628	−0.126797
$512$	42.1340	1.86208
$513$	4.63933	0.204831
$514$	3.57162	0.157537
$515$	1.26779	0.0558654
$516$	−9.60921	−0.423022
$517$	39.5872	1.74104
$518$	40.4066	1.77536
$519$	−21.1493	−0.928350
$520$	−10.7228	−0.470228
$521$	0.380847	0.0166852	0.00834260	−	0.999965i	$-0.497344\pi$
$521$	0.380847	0.0166852	0.00834260	+	0.999965i	$0.497344\pi$
$522$	19.2680	0.843336
$523$	−21.9797	−0.961105	−0.480553	−	0.876966i	$-0.659564\pi$
$523$	−21.9797	−0.961105	−0.480553	+	0.876966i	$0.659564\pi$
$524$	1.74501	0.0762312
$525$	7.18715	0.313673
$526$	72.2526	3.15036
$527$	−16.2718	−0.708811
$528$	26.6403	1.15937
$529$	−10.0816	−0.438331
$530$	0.255608	0.0111029
$531$	7.70260	0.334264
$532$	−27.7339	−1.20242
$533$	−21.8212	−0.945183
$534$	23.1503	1.00181
$535$	3.13051	0.135344
$536$	−11.4105	−0.492859
$537$	1.29249	0.0557750
$538$	46.9566	2.02444
$539$	29.0610	1.25175
$540$	1.30991	0.0563697
$541$	20.6855	0.889338	0.444669	−	0.895695i	$-0.353321\pi$
$541$	20.6855	0.889338	0.444669	+	0.895695i	$0.353321\pi$
$542$	−36.4446	−1.56543
$543$	−2.34310	−0.100552
$544$	−3.61203	−0.154865
$545$	−0.00352732	−0.000151094 0
$546$	−23.6087	−1.01036
$547$	−33.1941	−1.41928	−0.709638	−	0.704566i	$-0.751142\pi$
$547$	−33.1941	−1.41928	−0.709638	+	0.704566i	$0.751142\pi$
$548$	76.5063	3.26819
$549$	−8.01891	−0.342239
$550$	−72.3686	−3.08581
$551$	36.2742	1.54533
$552$	18.3590	0.781412
$553$	−19.2160	−0.817149
$554$	−32.6108	−1.38550
$555$	−3.59289	−0.152510
$556$	−4.07290	−0.172730
$557$	22.6155	0.958249	0.479125	−	0.877747i	$-0.340954\pi$
$557$	22.6155	0.958249	0.479125	+	0.877747i	$0.340954\pi$
$558$	8.10859	0.343264
$559$	−15.3996	−0.651334
$560$	−2.09697	−0.0886130
$561$	29.6585	1.25218
$562$	25.5064	1.07592
$563$	−44.1814	−1.86202	−0.931011	−	0.364990i	$-0.881072\pi$
$563$	−44.1814	−1.86202	−0.931011	+	0.364990i	$0.881072\pi$
$564$	26.8831	1.13198
$565$	−1.43915	−0.0605455
$566$	8.11736	0.341198
$567$	1.46780	0.0616417
$568$	25.3107	1.06201
$569$	−1.99873	−0.0837913	−0.0418956	−	0.999122i	$-0.513340\pi$
$569$	−1.99873	−0.0837913	−0.0418956	+	0.999122i	$0.513340\pi$
$570$	3.67706	0.154015
$571$	29.1796	1.22113	0.610565	−	0.791966i	$-0.290942\pi$
$571$	29.1796	1.22113	0.610565	+	0.791966i	$0.290942\pi$
$572$	159.429	6.66608
$573$	1.84871	0.0772309
$574$	−12.0928	−0.504743
$575$	−17.5993	−0.733941
$576$	−7.08394	−0.295164
$577$	−11.1726	−0.465122	−0.232561	−	0.972582i	$-0.574710\pi$
$577$	−11.1726	−0.465122	−0.232561	+	0.972582i	$0.574710\pi$
$578$	−18.3713	−0.764146
$579$	20.7223	0.861188
$580$	10.2420	0.425276
$581$	−22.5995	−0.937583
$582$	−9.33463	−0.386933
$583$	−1.93417	−0.0801050
$584$	9.97468	0.412755
$585$	2.09925	0.0867933
$586$	−7.54897	−0.311845
$587$	9.16569	0.378309	0.189154	−	0.981947i	$-0.439425\pi$
$587$	9.16569	0.378309	0.189154	+	0.981947i	$0.439425\pi$
$588$	19.7349	0.813855
$589$	15.2654	0.628998
$590$	6.10496	0.251337
$591$	22.4062	0.921668
$592$	−49.6210	−2.03941
$593$	25.3229	1.03989	0.519944	−	0.854200i	$-0.325953\pi$
$593$	25.3229	1.03989	0.519944	+	0.854200i	$0.325953\pi$
$594$	−14.7795	−0.606410
$595$	−2.33454	−0.0957069
$596$	6.03489	0.247199
$597$	2.12878	0.0871251
$598$	57.8110	2.36407
$599$	38.3019	1.56497	0.782486	−	0.622668i	$-0.213951\pi$
$599$	38.3019	1.56497	0.782486	+	0.622668i	$0.213951\pi$
$600$	−25.0113	−1.02108
$601$	19.3111	0.787714	0.393857	−	0.919172i	$-0.371140\pi$
$601$	19.3111	0.787714	0.393857	+	0.919172i	$0.371140\pi$
$602$	−8.53409	−0.347823
$603$	2.23388	0.0909706
$604$	94.6058	3.84946
$605$	−8.03077	−0.326497
$606$	−38.3977	−1.55980
$607$	−34.0177	−1.38074	−0.690368	−	0.723459i	$-0.742551\pi$
$607$	−34.0177	−1.38074	−0.690368	+	0.723459i	$0.742551\pi$
$608$	3.38862	0.137427
$609$	11.4765	0.465050
$610$	−6.35566	−0.257333
$611$	43.0826	1.74293
$612$	20.1407	0.814139
$613$	31.0031	1.25221	0.626103	−	0.779741i	$-0.284649\pi$
$613$	31.0031	1.25221	0.626103	+	0.779741i	$0.284649\pi$
$614$	−45.4267	−1.83327
$615$	1.07527	0.0433592
$616$	44.9653	1.81170
$617$	−22.2191	−0.894506	−0.447253	−	0.894407i	$-0.647598\pi$
$617$	−22.2191	−0.894506	−0.447253	+	0.894407i	$0.647598\pi$
$618$	−9.71378	−0.390745
$619$	−48.0071	−1.92957	−0.964783	−	0.263046i	$-0.915273\pi$
$619$	−48.0071	−1.92957	−0.964783	+	0.263046i	$0.915273\pi$
$620$	4.31017	0.173101
$621$	−3.59421	−0.144231
$622$	53.1608	2.13155
$623$	13.7889	0.552441
$624$	28.9925	1.16063
$625$	23.4590	0.938362
$626$	47.6433	1.90421
$627$	−27.8241	−1.11119
$628$	46.1840	1.84294
$629$	−55.2428	−2.20268
$630$	1.16335	0.0463491
$631$	42.1933	1.67969	0.839844	−	0.542828i	$-0.182646\pi$
$631$	42.1933	1.67969	0.839844	+	0.542828i	$0.182646\pi$
$632$	66.8719	2.66002
$633$	14.7262	0.585313
$634$	−19.8349	−0.787746
$635$	4.45508	0.176794
$636$	−1.31347	−0.0520823
$637$	31.6270	1.25311
$638$	−115.558	−4.57500
$639$	−4.95517	−0.196023
$640$	−6.08446	−0.240509
$641$	−10.5534	−0.416835	−0.208417	−	0.978040i	$-0.566831\pi$
$641$	−10.5534	−0.416835	−0.208417	+	0.978040i	$0.566831\pi$
$642$	−23.9860	−0.946651
$643$	13.0615	0.515096	0.257548	−	0.966266i	$-0.417085\pi$
$643$	13.0615	0.515096	0.257548	+	0.966266i	$0.417085\pi$
$644$	21.4862	0.846677
$645$	0.758838	0.0298792
$646$	56.5370	2.22442
$647$	46.1953	1.81613	0.908063	−	0.418835i	$-0.137561\pi$
$647$	46.1953	1.81613	0.908063	+	0.418835i	$0.137561\pi$
$648$	−5.10794	−0.200659
$649$	−46.1958	−1.81335
$650$	−78.7584	−3.08916
$651$	4.82967	0.189290
$652$	−46.1217	−1.80627
$653$	−35.3532	−1.38348	−0.691739	−	0.722148i	$-0.743155\pi$
$653$	−35.3532	−1.38348	−0.691739	+	0.722148i	$0.743155\pi$
$654$	0.0270263	0.00105681
$655$	−0.137803	−0.00538442
$656$	14.8505	0.579814
$657$	−1.95278	−0.0761852
$658$	23.8753	0.930756
$659$	40.7589	1.58774	0.793871	−	0.608086i	$-0.208063\pi$
$659$	40.7589	1.58774	0.793871	+	0.608086i	$0.208063\pi$
$660$	−7.85612	−0.305799
$661$	24.3463	0.946959	0.473480	−	0.880805i	$-0.342998\pi$
$661$	24.3463	0.946959	0.473480	+	0.880805i	$0.342998\pi$
$662$	13.7662	0.535037
$663$	32.2772	1.25354
$664$	78.6462	3.05207
$665$	2.19015	0.0849302
$666$	27.5287	1.06672
$667$	−28.1026	−1.08814
$668$	85.1709	3.29536
$669$	−3.61514	−0.139769
$670$	1.77054	0.0684018
$671$	48.0929	1.85661
$672$	1.07210	0.0413570
$673$	−37.1070	−1.43037	−0.715185	−	0.698935i	$-0.753658\pi$
$673$	−37.1070	−1.43037	−0.715185	+	0.698935i	$0.753658\pi$
$674$	41.9260	1.61493
$675$	4.89656	0.188469
$676$	120.560	4.63694
$677$	−33.2086	−1.27631	−0.638155	−	0.769908i	$-0.720302\pi$
$677$	−33.2086	−1.27631	−0.638155	+	0.769908i	$0.720302\pi$
$678$	11.0268	0.423480
$679$	−5.55993	−0.213371
$680$	8.12421	0.311549
$681$	16.3522	0.626618
$682$	−48.6308	−1.86217
$683$	9.43812	0.361140	0.180570	−	0.983562i	$-0.442206\pi$
$683$	9.43812	0.361140	0.180570	+	0.983562i	$0.442206\pi$
$684$	−18.8949	−0.722466
$685$	−6.04169	−0.230841
$686$	42.8465	1.63589
$687$	−24.0892	−0.919059
$688$	10.4802	0.399555
$689$	−2.10494	−0.0801920
$690$	−2.84872	−0.108449
$691$	45.3478	1.72511	0.862556	−	0.505962i	$-0.168862\pi$
$691$	45.3478	1.72511	0.862556	+	0.505962i	$0.168862\pi$
$692$	86.1362	3.27441
$693$	−8.80302	−0.334399
$694$	−63.6971	−2.41791
$695$	0.321637	0.0122004
$696$	−39.9381	−1.51385
$697$	16.5330	0.626231
$698$	−45.2069	−1.71111
$699$	27.1548	1.02709
$700$	−29.2716	−1.10636
$701$	21.6360	0.817179	0.408590	−	0.912718i	$-0.366021\pi$
$701$	21.6360	0.817179	0.408590	+	0.912718i	$0.366021\pi$
$702$	−16.0844	−0.607068
$703$	51.8260	1.95465
$704$	42.4855	1.60123
$705$	−2.12296	−0.0799551
$706$	−11.1698	−0.420381
$707$	−22.8706	−0.860138
$708$	−31.3709	−1.17899
$709$	−20.6815	−0.776709	−0.388355	−	0.921510i	$-0.626956\pi$
$709$	−20.6815	−0.776709	−0.388355	+	0.921510i	$0.626956\pi$
$710$	−3.92739	−0.147392
$711$	−13.0918	−0.490979
$712$	−47.9854	−1.79833
$713$	−11.8265	−0.442906
$714$	17.8872	0.669413
$715$	−12.5901	−0.470844
$716$	−5.26402	−0.196726
$717$	13.3824	0.499775
$718$	23.9744	0.894717
$719$	1.00953	0.0376490	0.0188245	−	0.999823i	$-0.494008\pi$
$719$	1.00953	0.0376490	0.0188245	+	0.999823i	$0.494008\pi$
$720$	−1.42865	−0.0532426
$721$	−5.78576	−0.215473
$722$	−6.21837	−0.231424
$723$	1.36066	0.0506033
$724$	9.54292	0.354660
$725$	38.2854	1.42188
$726$	61.5317	2.28366
$727$	−22.2990	−0.827024	−0.413512	−	0.910499i	$-0.635698\pi$
$727$	−22.2990	−0.827024	−0.413512	+	0.910499i	$0.635698\pi$
$728$	48.9355	1.81367
$729$	1.00000	0.0370370
$730$	−1.54774	−0.0572845
$731$	11.6676	0.431541
$732$	32.6592	1.20712
$733$	−26.4761	−0.977917	−0.488959	−	0.872307i	$-0.662623\pi$
$733$	−26.4761	−0.977917	−0.488959	+	0.872307i	$0.662623\pi$
$734$	4.71941	0.174197
$735$	−1.55846	−0.0574848
$736$	−2.62526	−0.0967682
$737$	−13.3975	−0.493505
$738$	−8.23874	−0.303272
$739$	39.6665	1.45916	0.729578	−	0.683897i	$-0.239716\pi$
$739$	39.6665	1.45916	0.729578	+	0.683897i	$0.239716\pi$
$740$	14.6330	0.537921
$741$	−30.2808	−1.11239
$742$	−1.16651	−0.0428239
$743$	25.7854	0.945976	0.472988	−	0.881069i	$-0.343175\pi$
$743$	25.7854	0.945976	0.472988	+	0.881069i	$0.343175\pi$
$744$	−16.8073	−0.616185
$745$	−0.476574	−0.0174603
$746$	−8.99001	−0.329148
$747$	−15.3969	−0.563341
$748$	−120.792	−4.41661
$749$	−14.2866	−0.522022
$750$	7.84386	0.286417
$751$	13.2313	0.482818	0.241409	−	0.970423i	$-0.422390\pi$
$751$	13.2313	0.482818	0.241409	+	0.970423i	$0.422390\pi$
$752$	−29.3199	−1.06919
$753$	−23.7729	−0.866334
$754$	−125.762	−4.57997
$755$	−7.47101	−0.271898
$756$	−5.97801	−0.217418
$757$	37.9945	1.38094	0.690468	−	0.723363i	$-0.257405\pi$
$757$	37.9945	1.38094	0.690468	+	0.723363i	$0.257405\pi$
$758$	6.18969	0.224819
$759$	21.5561	0.782436
$760$	−7.62172	−0.276469
$761$	11.4385	0.414644	0.207322	−	0.978273i	$-0.433525\pi$
$761$	11.4385	0.414644	0.207322	+	0.978273i	$0.433525\pi$
$762$	−34.1348	−1.23657
$763$	0.0160975	0.000582769 0
$764$	−7.52937	−0.272403
$765$	−1.59051	−0.0575049
$766$	−24.3388	−0.879396
$767$	−50.2747	−1.81532
$768$	32.4512	1.17098
$769$	−44.2315	−1.59503	−0.797514	−	0.603300i	$-0.793852\pi$
$769$	−44.2315	−1.59503	−0.797514	+	0.603300i	$0.793852\pi$
$770$	−6.97713	−0.251438
$771$	1.44934	0.0521969
$772$	−84.3972	−3.03752
$773$	12.5330	0.450781	0.225390	−	0.974269i	$-0.427634\pi$
$773$	12.5330	0.450781	0.225390	+	0.974269i	$0.427634\pi$
$774$	−5.81421	−0.208988
$775$	16.1117	0.578751
$776$	19.3486	0.694574
$777$	16.3968	0.588231
$778$	10.1796	0.364958
$779$	−15.5104	−0.555717
$780$	−8.54978	−0.306131
$781$	29.7183	1.06340
$782$	−43.8007	−1.56631
$783$	7.81884	0.279422
$784$	−21.5238	−0.768706
$785$	−3.64715	−0.130172
$786$	1.05585	0.0376609
$787$	−35.9984	−1.28320	−0.641602	−	0.767038i	$-0.721730\pi$
$787$	−35.9984	−1.28320	−0.641602	+	0.767038i	$0.721730\pi$
$788$	−91.2554	−3.25084
$789$	29.3197	1.04381
$790$	−10.3763	−0.369173
$791$	6.56781	0.233524
$792$	30.6345	1.08855
$793$	52.3393	1.85862
$794$	85.3135	3.02766
$795$	0.103724	0.00367872
$796$	−8.67003	−0.307301
$797$	−24.4225	−0.865090	−0.432545	−	0.901612i	$-0.642384\pi$
$797$	−24.4225	−0.865090	−0.432545	+	0.901612i	$0.642384\pi$
$798$	−16.7809	−0.594037
$799$	−32.6417	−1.15478
$800$	3.57650	0.126448
$801$	9.39428	0.331931
$802$	92.5497	3.26804
$803$	11.7117	0.413296
$804$	−9.09809	−0.320865
$805$	−1.69677	−0.0598031
$806$	−52.9247	−1.86419
$807$	19.0547	0.670758
$808$	79.5898	2.79996
$809$	−31.3863	−1.10348	−0.551741	−	0.834016i	$-0.686036\pi$
$809$	−31.3863	−1.10348	−0.551741	+	0.834016i	$0.686036\pi$
$810$	0.792584	0.0278486
$811$	0.377565	0.0132581	0.00662904	−	0.999978i	$-0.497890\pi$
$811$	0.377565	0.0132581	0.00662904	+	0.999978i	$0.497890\pi$
$812$	−46.7411	−1.64029
$813$	−14.7890	−0.518674
$814$	−165.102	−5.78681
$815$	3.64222	0.127582
$816$	−21.9663	−0.768975
$817$	−10.9459	−0.382950
$818$	32.8385	1.14817
$819$	−9.58029	−0.334762
$820$	−4.37935	−0.152933
$821$	53.0864	1.85273	0.926365	−	0.376628i	$-0.122916\pi$
$821$	53.0864	1.85273	0.926365	+	0.376628i	$0.122916\pi$
$822$	46.2914	1.61460
$823$	−35.9304	−1.25245	−0.626227	−	0.779641i	$-0.715402\pi$
$823$	−35.9304	−1.25245	−0.626227	+	0.779641i	$0.715402\pi$
$824$	20.1345	0.701418
$825$	−29.3668	−1.02242
$826$	−27.8610	−0.969408
$827$	−19.6738	−0.684125	−0.342062	−	0.939677i	$-0.611125\pi$
$827$	−19.6738	−0.684125	−0.342062	+	0.939677i	$0.611125\pi$
$828$	14.6384	0.508721
$829$	−7.57338	−0.263035	−0.131517	−	0.991314i	$-0.541985\pi$
$829$	−7.57338	−0.263035	−0.131517	+	0.991314i	$0.541985\pi$
$830$	−12.2033	−0.423583
$831$	−13.2333	−0.459058
$832$	46.2368	1.60297
$833$	−23.9623	−0.830245
$834$	−2.46438	−0.0853344
$835$	−6.72594	−0.232761
$836$	113.321	3.91930
$837$	3.29042	0.113734
$838$	56.8477	1.96377
$839$	17.3936	0.600492	0.300246	−	0.953862i	$-0.402931\pi$
$839$	17.3936	0.600492	0.300246	+	0.953862i	$0.402931\pi$
$840$	−2.41137	−0.0832001
$841$	32.1342	1.10808
$842$	−34.4650	−1.18774
$843$	10.3504	0.356485
$844$	−59.9764	−2.06447
$845$	−9.52063	−0.327520
$846$	16.2661	0.559239
$847$	36.6498	1.25930
$848$	1.43252	0.0491930
$849$	3.29398	0.113049
$850$	59.6717	2.04672
$851$	−40.1510	−1.37636
$852$	20.1813	0.691400
$853$	−25.4958	−0.872959	−0.436480	−	0.899714i	$-0.643775\pi$
$853$	−25.4958	−0.872959	−0.436480	+	0.899714i	$0.643775\pi$
$854$	29.0051	0.992535
$855$	1.49213	0.0510298
$856$	49.7175	1.69931
$857$	41.4523	1.41598	0.707992	−	0.706220i	$-0.249601\pi$
$857$	41.4523	1.41598	0.707992	+	0.706220i	$0.249601\pi$
$858$	96.4655	3.29328
$859$	56.5406	1.92914	0.964569	−	0.263829i	$-0.0849855\pi$
$859$	56.5406	1.92914	0.964569	+	0.263829i	$0.0849855\pi$
$860$	−3.09058	−0.105388
$861$	−4.90719	−0.167237
$862$	−81.2537	−2.76751
$863$	−32.8578	−1.11849	−0.559246	−	0.829002i	$-0.688909\pi$
$863$	−32.8578	−1.11849	−0.559246	+	0.829002i	$0.688909\pi$
$864$	0.730412	0.0248491
$865$	−6.80217	−0.231281
$866$	16.5085	0.560980
$867$	−7.45499	−0.253185
$868$	−19.6702	−0.667649
$869$	78.5170	2.66351
$870$	6.19709	0.210101
$871$	−14.5805	−0.494041
$872$	−0.0560194	−0.00189706
$873$	−3.78794	−0.128202
$874$	41.0916	1.38994
$875$	4.67199	0.157942
$876$	7.95323	0.268715
$877$	13.3676	0.451391	0.225695	−	0.974198i	$-0.427535\pi$
$877$	13.3676	0.451391	0.225695	+	0.974198i	$0.427535\pi$
$878$	−29.7243	−1.00315
$879$	−3.06333	−0.103324
$880$	8.56823	0.288835
$881$	−42.1713	−1.42079	−0.710394	−	0.703804i	$-0.751483\pi$
$881$	−42.1713	−1.42079	−0.710394	+	0.703804i	$0.751483\pi$
$882$	11.9409	0.402072
$883$	−4.53319	−0.152554	−0.0762771	−	0.997087i	$-0.524303\pi$
$883$	−4.53319	−0.152554	−0.0762771	+	0.997087i	$0.524303\pi$
$884$	−131.458	−4.42141
$885$	2.47736	0.0832755
$886$	−13.1020	−0.440170
$887$	54.9728	1.84581	0.922903	−	0.385034i	$-0.125810\pi$
$887$	54.9728	1.84581	0.922903	+	0.385034i	$0.125810\pi$
$888$	−57.0608	−1.91484
$889$	−20.3315	−0.681897
$890$	7.44576	0.249582
$891$	−5.99744	−0.200922
$892$	14.7236	0.492984
$893$	30.6228	1.02475
$894$	3.65151	0.122125
$895$	0.415699	0.0138953
$896$	27.7675	0.927646
$897$	23.4594	0.783286
$898$	71.4120	2.38305
$899$	25.7273	0.858053
$900$	−19.9426	−0.664752
$901$	1.59482	0.0531312
$902$	49.4113	1.64522
$903$	−3.46309	−0.115244
$904$	−22.8560	−0.760179
$905$	−0.753603	−0.0250506
$906$	57.2428	1.90177
$907$	12.0467	0.400003	0.200002	−	0.979796i	$-0.435905\pi$
$907$	12.0467	0.400003	0.200002	+	0.979796i	$0.435905\pi$
$908$	−66.5989	−2.21016
$909$	−15.5816	−0.516809
$910$	−7.59318	−0.251712
$911$	0.937976	0.0310765	0.0155383	−	0.999879i	$-0.495054\pi$
$911$	0.937976	0.0310765	0.0155383	+	0.999879i	$0.495054\pi$
$912$	20.6077	0.682388
$913$	92.3417	3.05606
$914$	7.00115	0.231577
$915$	−2.57909	−0.0852622
$916$	98.1097	3.24164
$917$	0.628889	0.0207677
$918$	12.1865	0.402213
$919$	1.81484	0.0598659	0.0299330	−	0.999552i	$-0.490471\pi$
$919$	1.81484	0.0598659	0.0299330	+	0.999552i	$0.490471\pi$
$920$	5.90475	0.194674
$921$	−18.4339	−0.607418
$922$	6.10973	0.201213
$923$	32.3423	1.06456
$924$	35.8527	1.17947
$925$	54.6995	1.79851
$926$	−48.4613	−1.59254
$927$	−3.94180	−0.129466
$928$	5.71097	0.187472
$929$	16.3024	0.534865	0.267433	−	0.963577i	$-0.413825\pi$
$929$	16.3024	0.534865	0.267433	+	0.963577i	$0.413825\pi$
$930$	2.60794	0.0855177
$931$	22.4802	0.736759
$932$	−110.595	−3.62267
$933$	21.5724	0.706247
$934$	63.9870	2.09372
$935$	9.53896	0.311957
$936$	33.3394	1.08973
$937$	−33.7036	−1.10105	−0.550525	−	0.834819i	$-0.685572\pi$
$937$	−33.7036	−1.10105	−0.550525	+	0.834819i	$0.685572\pi$
$938$	−8.08015	−0.263826
$939$	19.3334	0.630922
$940$	8.64632	0.282012
$941$	11.1039	0.361978	0.180989	−	0.983485i	$-0.442070\pi$
$941$	11.1039	0.361978	0.180989	+	0.983485i	$0.442070\pi$
$942$	27.9444	0.910478
$943$	12.0163	0.391305
$944$	34.2145	1.11359
$945$	0.472082	0.0153568
$946$	34.8704	1.13373
$947$	39.6673	1.28902	0.644508	−	0.764598i	$-0.277062\pi$
$947$	39.6673	1.28902	0.644508	+	0.764598i	$0.277062\pi$
$948$	53.3198	1.73175
$949$	12.7458	0.413745
$950$	−55.9809	−1.81626
$951$	−8.04892	−0.261004
$952$	−37.0762	−1.20165
$953$	13.6218	0.441253	0.220627	−	0.975358i	$-0.429190\pi$
$953$	13.6218	0.441253	0.220627	+	0.975358i	$0.429190\pi$
$954$	−0.794734	−0.0257305
$955$	0.594594	0.0192406
$956$	−54.5035	−1.76277
$957$	−46.8930	−1.51583
$958$	−45.2665	−1.46250
$959$	27.5723	0.890355
$960$	−2.27838	−0.0735345
$961$	−20.1731	−0.650745
$962$	−179.679	−5.79310
$963$	−9.73338	−0.313654
$964$	−5.54164	−0.178484
$965$	6.66483	0.214549
$966$	13.0006	0.418288
$967$	42.8959	1.37944	0.689720	−	0.724076i	$-0.257734\pi$
$967$	42.8959	1.37944	0.689720	+	0.724076i	$0.257734\pi$
$968$	−127.541	−4.09934
$969$	22.9424	0.737016
$970$	−3.00226	−0.0963969
$971$	24.6875	0.792260	0.396130	−	0.918195i	$-0.370353\pi$
$971$	24.6875	0.792260	0.396130	+	0.918195i	$0.370353\pi$
$972$	−4.07278	−0.130634
$973$	−1.46784	−0.0470569
$974$	93.4291	2.99366
$975$	−31.9597	−1.02353
$976$	−35.6196	−1.14015
$977$	−3.39883	−0.108738	−0.0543691	−	0.998521i	$-0.517315\pi$
$977$	−3.39883	−0.108738	−0.0543691	+	0.998521i	$0.517315\pi$
$978$	−27.9067	−0.892358
$979$	−56.3416	−1.80069
$980$	6.34728	0.202756
$981$	0.0109671	0.000350153 0
$982$	−52.3520	−1.67062
$983$	−20.3599	−0.649380	−0.324690	−	0.945821i	$-0.605260\pi$
$983$	−20.3599	−0.649380	−0.324690	+	0.945821i	$0.605260\pi$
$984$	17.0771	0.544396
$985$	7.20643	0.229616
$986$	95.2839	3.03446
$987$	9.68847	0.308387
$988$	123.327	3.92356
$989$	8.48011	0.269652
$990$	−4.75347	−0.151075
$991$	−29.8895	−0.949473	−0.474736	−	0.880128i	$-0.657457\pi$
$991$	−29.8895	−0.949473	−0.474736	+	0.880128i	$0.657457\pi$
$992$	2.40336	0.0763069
$993$	5.58624	0.177274
$994$	17.9233	0.568493
$995$	0.684671	0.0217055
$996$	62.7079	1.98698
$997$	−26.0159	−0.823930	−0.411965	−	0.911200i	$-0.635157\pi$
$997$	−26.0159	−0.823930	−0.411965	+	0.911200i	$0.635157\pi$
$998$	−13.0502	−0.413098
$999$	11.1710	0.353435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.9	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.9	✓	119	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46430 q^{2} -1.00000 q^{3} +4.07278 q^{4} -0.321627 q^{5} +2.46430 q^{6} +1.46780 q^{7} -5.10794 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.46430 q^{2} -1.00000 q^{3} +4.07278 q^{4} -0.321627 q^{5} +2.46430 q^{6} +1.46780 q^{7} -5.10794 q^{8} +1.00000 q^{9} +0.792584 q^{10} -5.99744 q^{11} -4.07278 q^{12} -6.52698 q^{13} -3.61709 q^{14} +0.321627 q^{15} +4.44195 q^{16} +4.94520 q^{17} -2.46430 q^{18} -4.63933 q^{19} -1.30991 q^{20} -1.46780 q^{21} +14.7795 q^{22} +3.59421 q^{23} +5.10794 q^{24} -4.89656 q^{25} +16.0844 q^{26} -1.00000 q^{27} +5.97801 q^{28} -7.81884 q^{29} -0.792584 q^{30} -3.29042 q^{31} -0.730412 q^{32} +5.99744 q^{33} -12.1865 q^{34} -0.472082 q^{35} +4.07278 q^{36} -11.1710 q^{37} +11.4327 q^{38} +6.52698 q^{39} +1.64285 q^{40} +3.34324 q^{41} +3.61709 q^{42} +2.35938 q^{43} -24.4262 q^{44} -0.321627 q^{45} -8.85722 q^{46} -6.60069 q^{47} -4.44195 q^{48} -4.84557 q^{49} +12.0666 q^{50} -4.94520 q^{51} -26.5829 q^{52} +0.322499 q^{53} +2.46430 q^{54} +1.92893 q^{55} -7.49742 q^{56} +4.63933 q^{57} +19.2680 q^{58} +7.70260 q^{59} +1.30991 q^{60} -8.01891 q^{61} +8.10859 q^{62} +1.46780 q^{63} -7.08394 q^{64} +2.09925 q^{65} -14.7795 q^{66} +2.23388 q^{67} +20.1407 q^{68} -3.59421 q^{69} +1.16335 q^{70} -4.95517 q^{71} -5.10794 q^{72} -1.95278 q^{73} +27.5287 q^{74} +4.89656 q^{75} -18.8949 q^{76} -8.80302 q^{77} -16.0844 q^{78} -13.0918 q^{79} -1.42865 q^{80} +1.00000 q^{81} -8.23874 q^{82} -15.3969 q^{83} -5.97801 q^{84} -1.59051 q^{85} -5.81421 q^{86} +7.81884 q^{87} +30.6345 q^{88} +9.39428 q^{89} +0.792584 q^{90} -9.58029 q^{91} +14.6384 q^{92} +3.29042 q^{93} +16.2661 q^{94} +1.49213 q^{95} +0.730412 q^{96} -3.78794 q^{97} +11.9409 q^{98} -5.99744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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