LMFDB - Embedded newform 4033.2.a.d.1.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.38
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.377677 q^{2} +1.85274 q^{3} -1.85736 q^{4} +2.49022 q^{5} -0.699737 q^{6} +0.226815 q^{7} +1.45684 q^{8} +0.432641 q^{9} +O(q^{10})$	\(q-0.377677 q^{2} +1.85274 q^{3} -1.85736 q^{4} +2.49022 q^{5} -0.699737 q^{6} +0.226815 q^{7} +1.45684 q^{8} +0.432641 q^{9} -0.940501 q^{10} -4.54883 q^{11} -3.44120 q^{12} -2.16683 q^{13} -0.0856628 q^{14} +4.61374 q^{15} +3.16451 q^{16} -0.658360 q^{17} -0.163399 q^{18} -0.672840 q^{19} -4.62524 q^{20} +0.420229 q^{21} +1.71799 q^{22} +5.23197 q^{23} +2.69914 q^{24} +1.20122 q^{25} +0.818362 q^{26} -4.75665 q^{27} -0.421277 q^{28} +2.07402 q^{29} -1.74250 q^{30} -9.51352 q^{31} -4.10884 q^{32} -8.42780 q^{33} +0.248648 q^{34} +0.564820 q^{35} -0.803570 q^{36} -1.00000 q^{37} +0.254116 q^{38} -4.01457 q^{39} +3.62785 q^{40} -1.19166 q^{41} -0.158711 q^{42} +0.139820 q^{43} +8.44882 q^{44} +1.07737 q^{45} -1.97600 q^{46} +4.67375 q^{47} +5.86300 q^{48} -6.94856 q^{49} -0.453673 q^{50} -1.21977 q^{51} +4.02458 q^{52} -10.8142 q^{53} +1.79648 q^{54} -11.3276 q^{55} +0.330432 q^{56} -1.24660 q^{57} -0.783309 q^{58} +9.32072 q^{59} -8.56937 q^{60} +4.09125 q^{61} +3.59304 q^{62} +0.0981294 q^{63} -4.77720 q^{64} -5.39589 q^{65} +3.18299 q^{66} -3.29597 q^{67} +1.22281 q^{68} +9.69347 q^{69} -0.213320 q^{70} +1.56936 q^{71} +0.630288 q^{72} -11.4729 q^{73} +0.377677 q^{74} +2.22555 q^{75} +1.24971 q^{76} -1.03174 q^{77} +1.51621 q^{78} +16.8021 q^{79} +7.88033 q^{80} -10.1107 q^{81} +0.450061 q^{82} -7.21407 q^{83} -0.780516 q^{84} -1.63946 q^{85} -0.0528067 q^{86} +3.84261 q^{87} -6.62691 q^{88} -14.0062 q^{89} -0.406900 q^{90} -0.491469 q^{91} -9.71765 q^{92} -17.6261 q^{93} -1.76517 q^{94} -1.67552 q^{95} -7.61260 q^{96} -4.57926 q^{97} +2.62431 q^{98} -1.96801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + 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 $

$2$	−0.377677	−0.267058	−0.133529	−	0.991045i	$-0.542631\pi$
$2$	−0.377677	−0.267058	−0.133529	+	0.991045i	$0.542631\pi$
$3$	1.85274	1.06968	0.534840	−	0.844954i	$-0.320372\pi$
$3$	1.85274	1.06968	0.534840	+	0.844954i	$0.320372\pi$
$4$	−1.85736	−0.928680
$5$	2.49022	1.11366	0.556831	−	0.830626i	$-0.312017\pi$
$5$	2.49022	1.11366	0.556831	+	0.830626i	$0.312017\pi$
$6$	−0.699737	−0.285667
$7$	0.226815	0.0857280	0.0428640	−	0.999081i	$-0.486352\pi$
$7$	0.226815	0.0857280	0.0428640	+	0.999081i	$0.486352\pi$
$8$	1.45684	0.515070
$9$	0.432641	0.144214
$10$	−0.940501	−0.297413
$11$	−4.54883	−1.37152	−0.685762	−	0.727826i	$-0.740531\pi$
$11$	−4.54883	−1.37152	−0.685762	+	0.727826i	$0.740531\pi$
$12$	−3.44120	−0.993390
$13$	−2.16683	−0.600970	−0.300485	−	0.953787i	$-0.597149\pi$
$13$	−2.16683	−0.600970	−0.300485	+	0.953787i	$0.597149\pi$
$14$	−0.0856628	−0.0228944
$15$	4.61374	1.19126
$16$	3.16451	0.791126
$17$	−0.658360	−0.159676	−0.0798379	−	0.996808i	$-0.525440\pi$
$17$	−0.658360	−0.159676	−0.0798379	+	0.996808i	$0.525440\pi$
$18$	−0.163399	−0.0385134
$19$	−0.672840	−0.154360	−0.0771801	−	0.997017i	$-0.524592\pi$
$19$	−0.672840	−0.154360	−0.0771801	+	0.997017i	$0.524592\pi$
$20$	−4.62524	−1.03424
$21$	0.420229	0.0917014
$22$	1.71799	0.366277
$23$	5.23197	1.09094	0.545470	−	0.838130i	$-0.316351\pi$
$23$	5.23197	1.09094	0.545470	+	0.838130i	$0.316351\pi$
$24$	2.69914	0.550959
$25$	1.20122	0.240244
$26$	0.818362	0.160494
$27$	−4.75665	−0.915417
$28$	−0.421277	−0.0796138
$29$	2.07402	0.385135	0.192568	−	0.981284i	$-0.438319\pi$
$29$	2.07402	0.385135	0.192568	+	0.981284i	$0.438319\pi$
$30$	−1.74250	−0.318136
$31$	−9.51352	−1.70868	−0.854340	−	0.519715i	$-0.826038\pi$
$31$	−9.51352	−1.70868	−0.854340	+	0.519715i	$0.826038\pi$
$32$	−4.10884	−0.726347
$33$	−8.42780	−1.46709
$34$	0.248648	0.0426427
$35$	0.564820	0.0954720
$36$	−0.803570	−0.133928
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	0.254116	0.0412231
$39$	−4.01457	−0.642845
$40$	3.62785	0.573614
$41$	−1.19166	−0.186105	−0.0930527	−	0.995661i	$-0.529663\pi$
$41$	−1.19166	−0.186105	−0.0930527	+	0.995661i	$0.529663\pi$
$42$	−0.158711	−0.0244896
$43$	0.139820	0.0213223	0.0106611	−	0.999943i	$-0.496606\pi$
$43$	0.139820	0.0213223	0.0106611	+	0.999943i	$0.496606\pi$
$44$	8.44882	1.27371
$45$	1.07737	0.160605
$46$	−1.97600	−0.291345
$47$	4.67375	0.681736	0.340868	−	0.940111i	$-0.389279\pi$
$47$	4.67375	0.681736	0.340868	+	0.940111i	$0.389279\pi$
$48$	5.86300	0.846251
$49$	−6.94856	−0.992651
$50$	−0.453673	−0.0641591
$51$	−1.21977	−0.170802
$52$	4.02458	0.558109
$53$	−10.8142	−1.48545	−0.742723	−	0.669599i	$-0.766466\pi$
$53$	−10.8142	−1.48545	−0.742723	+	0.669599i	$0.766466\pi$
$54$	1.79648	0.244470
$55$	−11.3276	−1.52741
$56$	0.330432	0.0441559
$57$	−1.24660	−0.165116
$58$	−0.783309	−0.102854
$59$	9.32072	1.21345	0.606727	−	0.794910i	$-0.292482\pi$
$59$	9.32072	1.21345	0.606727	+	0.794910i	$0.292482\pi$
$60$	−8.56937	−1.10630
$61$	4.09125	0.523831	0.261915	−	0.965091i	$-0.415646\pi$
$61$	4.09125	0.523831	0.261915	+	0.965091i	$0.415646\pi$
$62$	3.59304	0.456317
$63$	0.0981294	0.0123631
$64$	−4.77720	−0.597150
$65$	−5.39589	−0.669278
$66$	3.18299	0.391799
$67$	−3.29597	−0.402667	−0.201334	−	0.979523i	$-0.564528\pi$
$67$	−3.29597	−0.402667	−0.201334	+	0.979523i	$0.564528\pi$
$68$	1.22281	0.148288
$69$	9.69347	1.16696
$70$	−0.213320	−0.0254966
$71$	1.56936	0.186248	0.0931242	−	0.995655i	$-0.470315\pi$
$71$	1.56936	0.186248	0.0931242	+	0.995655i	$0.470315\pi$
$72$	0.630288	0.0742801
$73$	−11.4729	−1.34280	−0.671402	−	0.741094i	$-0.734308\pi$
$73$	−11.4729	−1.34280	−0.671402	+	0.741094i	$0.734308\pi$
$74$	0.377677	0.0439041
$75$	2.22555	0.256984
$76$	1.24971	0.143351
$77$	−1.03174	−0.117578
$78$	1.51621	0.171677
$79$	16.8021	1.89038	0.945192	−	0.326516i	$-0.105875\pi$
$79$	16.8021	1.89038	0.945192	+	0.326516i	$0.105875\pi$
$80$	7.88033	0.881048
$81$	−10.1107	−1.12342
$82$	0.450061	0.0497010
$83$	−7.21407	−0.791847	−0.395924	−	0.918283i	$-0.629575\pi$
$83$	−7.21407	−0.791847	−0.395924	+	0.918283i	$0.629575\pi$
$84$	−0.780516	−0.0851613
$85$	−1.63946	−0.177825
$86$	−0.0528067	−0.00569429
$87$	3.84261	0.411971
$88$	−6.62691	−0.706431
$89$	−14.0062	−1.48465	−0.742326	−	0.670039i	$-0.766277\pi$
$89$	−14.0062	−1.48465	−0.742326	+	0.670039i	$0.766277\pi$
$90$	−0.406900	−0.0428910
$91$	−0.491469	−0.0515200
$92$	−9.71765	−1.01313
$93$	−17.6261	−1.82774
$94$	−1.76517	−0.182063
$95$	−1.67552	−0.171905
$96$	−7.61260	−0.776958
$97$	−4.57926	−0.464953	−0.232477	−	0.972602i	$-0.574683\pi$
$97$	−4.57926	−0.464953	−0.232477	+	0.972602i	$0.574683\pi$
$98$	2.62431	0.265096
$99$	−1.96801	−0.197793
$100$	−2.23110	−0.223110
$101$	−5.85890	−0.582983	−0.291491	−	0.956573i	$-0.594151\pi$
$101$	−5.85890	−0.582983	−0.291491	+	0.956573i	$0.594151\pi$
$102$	0.460679	0.0456140
$103$	−13.1655	−1.29723	−0.648617	−	0.761115i	$-0.724652\pi$
$103$	−13.1655	−1.29723	−0.648617	+	0.761115i	$0.724652\pi$
$104$	−3.15672	−0.309542
$105$	1.04646	0.102124
$106$	4.08428	0.396700
$107$	−7.47254	−0.722397	−0.361199	−	0.932489i	$-0.617632\pi$
$107$	−7.47254	−0.722397	−0.361199	+	0.932489i	$0.617632\pi$
$108$	8.83480	0.850129
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	4.27818	0.407909
$111$	−1.85274	−0.175854
$112$	0.717757	0.0678217
$113$	−2.23709	−0.210448	−0.105224	−	0.994449i	$-0.533556\pi$
$113$	−2.23709	−0.210448	−0.105224	+	0.994449i	$0.533556\pi$
$114$	0.470811	0.0440955
$115$	13.0288	1.21494
$116$	−3.85220	−0.357667
$117$	−0.937459	−0.0866681
$118$	−3.52022	−0.324063
$119$	−0.149326	−0.0136887
$120$	6.72146	0.613583
$121$	9.69186	0.881079
$122$	−1.54517	−0.139893
$123$	−2.20783	−0.199073
$124$	17.6700	1.58682
$125$	−9.45982	−0.846112
$126$	−0.0370613	−0.00330168
$127$	−12.4969	−1.10892	−0.554459	−	0.832211i	$-0.687075\pi$
$127$	−12.4969	−1.10892	−0.554459	+	0.832211i	$0.687075\pi$
$128$	10.0219	0.885820
$129$	0.259049	0.0228080
$130$	2.03791	0.178736
$131$	−14.2388	−1.24405	−0.622026	−	0.782997i	$-0.713690\pi$
$131$	−14.2388	−1.24405	−0.622026	+	0.782997i	$0.713690\pi$
$132$	15.6534	1.36246
$133$	−0.152610	−0.0132330
$134$	1.24481	0.107536
$135$	−11.8451	−1.01947
$136$	−0.959123	−0.0822441
$137$	7.89171	0.674234	0.337117	−	0.941463i	$-0.390548\pi$
$137$	7.89171	0.674234	0.337117	+	0.941463i	$0.390548\pi$
$138$	−3.66100	−0.311645
$139$	−16.9313	−1.43609	−0.718046	−	0.695996i	$-0.754963\pi$
$139$	−16.9313	−1.43609	−0.718046	+	0.695996i	$0.754963\pi$
$140$	−1.04907	−0.0886630
$141$	8.65924	0.729239
$142$	−0.592710	−0.0497392
$143$	9.85654	0.824245
$144$	1.36910	0.114091
$145$	5.16477	0.428911
$146$	4.33306	0.358607
$147$	−12.8739	−1.06182
$148$	1.85736	0.152674
$149$	13.4007	1.09783	0.548913	−	0.835879i	$-0.315042\pi$
$149$	13.4007	1.09783	0.548913	+	0.835879i	$0.315042\pi$
$150$	−0.840538	−0.0686297
$151$	−2.53521	−0.206313	−0.103156	−	0.994665i	$-0.532894\pi$
$151$	−2.53521	−0.206313	−0.103156	+	0.994665i	$0.532894\pi$
$152$	−0.980219	−0.0795062
$153$	−0.284834	−0.0230274
$154$	0.389666	0.0314002
$155$	−23.6908	−1.90289
$156$	7.45650	0.596998
$157$	9.26904	0.739750	0.369875	−	0.929081i	$-0.379400\pi$
$157$	9.26904	0.739750	0.369875	+	0.929081i	$0.379400\pi$
$158$	−6.34577	−0.504842
$159$	−20.0359	−1.58895
$160$	−10.2319	−0.808905
$161$	1.18669	0.0935241
$162$	3.81860	0.300017
$163$	−0.792509	−0.0620741	−0.0310371	−	0.999518i	$-0.509881\pi$
$163$	−0.792509	−0.0620741	−0.0310371	+	0.999518i	$0.509881\pi$
$164$	2.21333	0.172832
$165$	−20.9871	−1.63384
$166$	2.72459	0.211469
$167$	6.15317	0.476147	0.238073	−	0.971247i	$-0.423484\pi$
$167$	6.15317	0.476147	0.238073	+	0.971247i	$0.423484\pi$
$168$	0.612205	0.0472326
$169$	−8.30485	−0.638835
$170$	0.619188	0.0474896
$171$	−0.291098	−0.0222608
$172$	−0.259695	−0.0198016
$173$	15.4067	1.17135	0.585674	−	0.810546i	$-0.300830\pi$
$173$	15.4067	1.17135	0.585674	+	0.810546i	$0.300830\pi$
$174$	−1.45127	−0.110020
$175$	0.272455	0.0205956
$176$	−14.3948	−1.08505
$177$	17.2689	1.29801
$178$	5.28982	0.396488
$179$	15.9171	1.18970	0.594850	−	0.803837i	$-0.297212\pi$
$179$	15.9171	1.18970	0.594850	+	0.803837i	$0.297212\pi$
$180$	−2.00107	−0.149151
$181$	18.0379	1.34074	0.670372	−	0.742025i	$-0.266135\pi$
$181$	18.0379	1.34074	0.670372	+	0.742025i	$0.266135\pi$
$182$	0.185617	0.0137588
$183$	7.58001	0.560331
$184$	7.62213	0.561911
$185$	−2.49022	−0.183085
$186$	6.65697	0.488113
$187$	2.99477	0.218999
$188$	−8.68083	−0.633115
$189$	−1.07888	−0.0784768
$190$	0.632807	0.0459087
$191$	20.8286	1.50711	0.753553	−	0.657388i	$-0.228339\pi$
$191$	20.8286	1.50711	0.753553	+	0.657388i	$0.228339\pi$
$192$	−8.85090	−0.638758
$193$	21.2934	1.53273	0.766366	−	0.642405i	$-0.222063\pi$
$193$	21.2934	1.53273	0.766366	+	0.642405i	$0.222063\pi$
$194$	1.72948	0.124170
$195$	−9.99718	−0.715913
$196$	12.9060	0.921855
$197$	8.09657	0.576857	0.288428	−	0.957501i	$-0.406867\pi$
$197$	8.09657	0.576857	0.288428	+	0.957501i	$0.406867\pi$
$198$	0.743273	0.0528221
$199$	20.4465	1.44941	0.724706	−	0.689058i	$-0.241976\pi$
$199$	20.4465	1.44941	0.724706	+	0.689058i	$0.241976\pi$
$200$	1.74998	0.123742
$201$	−6.10657	−0.430725
$202$	2.21277	0.155690
$203$	0.470418	0.0330169
$204$	2.26555	0.158620
$205$	−2.96749	−0.207259
$206$	4.97231	0.346437
$207$	2.26356	0.157329
$208$	−6.85694	−0.475443
$209$	3.06064	0.211709
$210$	−0.395226	−0.0272732
$211$	−12.7435	−0.877302	−0.438651	−	0.898658i	$-0.644544\pi$
$211$	−12.7435	−0.877302	−0.438651	+	0.898658i	$0.644544\pi$
$212$	20.0859	1.37950
$213$	2.90761	0.199226
$214$	2.82221	0.192922
$215$	0.348182	0.0237458
$216$	−6.92966	−0.471504
$217$	−2.15781	−0.146482
$218$	0.377677	0.0255795
$219$	−21.2563	−1.43637
$220$	21.0395	1.41848
$221$	1.42655	0.0959603
$222$	0.699737	0.0469633
$223$	14.1813	0.949651	0.474826	−	0.880080i	$-0.342511\pi$
$223$	14.1813	0.949651	0.474826	+	0.880080i	$0.342511\pi$
$224$	−0.931945	−0.0622682
$225$	0.519697	0.0346465
$226$	0.844899	0.0562019
$227$	−2.29255	−0.152162	−0.0760808	−	0.997102i	$-0.524241\pi$
$227$	−2.29255	−0.152162	−0.0760808	+	0.997102i	$0.524241\pi$
$228$	2.31538	0.153340
$229$	−14.1017	−0.931870	−0.465935	−	0.884819i	$-0.654282\pi$
$229$	−14.1017	−0.931870	−0.465935	+	0.884819i	$0.654282\pi$
$230$	−4.92067	−0.324460
$231$	−1.91155	−0.125771
$232$	3.02150	0.198372
$233$	10.1568	0.665396	0.332698	−	0.943033i	$-0.392041\pi$
$233$	10.1568	0.665396	0.332698	+	0.943033i	$0.392041\pi$
$234$	0.354057	0.0231454
$235$	11.6387	0.759224
$236$	−17.3119	−1.12691
$237$	31.1299	2.02210
$238$	0.0563970	0.00365567
$239$	−26.7097	−1.72771	−0.863854	−	0.503742i	$-0.831956\pi$
$239$	−26.7097	−1.72771	−0.863854	+	0.503742i	$0.831956\pi$
$240$	14.6002	0.942438
$241$	−21.3430	−1.37482	−0.687412	−	0.726268i	$-0.741253\pi$
$241$	−21.3430	−1.37482	−0.687412	+	0.726268i	$0.741253\pi$
$242$	−3.66040	−0.235299
$243$	−4.46263	−0.286278
$244$	−7.59892	−0.486471
$245$	−17.3035	−1.10548
$246$	0.833846	0.0531641
$247$	1.45793	0.0927658
$248$	−13.8597	−0.880089
$249$	−13.3658	−0.847022
$250$	3.57276	0.225961
$251$	−20.6745	−1.30497	−0.652483	−	0.757803i	$-0.726273\pi$
$251$	−20.6745	−1.30497	−0.652483	+	0.757803i	$0.726273\pi$
$252$	−0.182262	−0.0114814
$253$	−23.7993	−1.49625
$254$	4.71978	0.296146
$255$	−3.03750	−0.190216
$256$	5.76934	0.360584
$257$	17.6555	1.10132	0.550658	−	0.834731i	$-0.314377\pi$
$257$	17.6555	1.10132	0.550658	+	0.834731i	$0.314377\pi$
$258$	−0.0978369	−0.00609106
$259$	−0.226815	−0.0140936
$260$	10.0221	0.621545
$261$	0.897305	0.0555418
$262$	5.37768	0.332234
$263$	−20.1452	−1.24221	−0.621104	−	0.783728i	$-0.713316\pi$
$263$	−20.1452	−1.24221	−0.621104	+	0.783728i	$0.713316\pi$
$264$	−12.2779	−0.755654
$265$	−26.9298	−1.65429
$266$	0.0576374	0.00353398
$267$	−25.9498	−1.58810
$268$	6.12181	0.373949
$269$	6.65101	0.405519	0.202760	−	0.979229i	$-0.435009\pi$
$269$	6.65101	0.405519	0.202760	+	0.979229i	$0.435009\pi$
$270$	4.47363	0.272257
$271$	−11.4212	−0.693786	−0.346893	−	0.937905i	$-0.612763\pi$
$271$	−11.4212	−0.693786	−0.346893	+	0.937905i	$0.612763\pi$
$272$	−2.08338	−0.126324
$273$	−0.910564	−0.0551098
$274$	−2.98052	−0.180060
$275$	−5.46415	−0.329500
$276$	−18.0043	−1.08373
$277$	−16.7676	−1.00747	−0.503733	−	0.863860i	$-0.668040\pi$
$277$	−16.7676	−1.00747	−0.503733	+	0.863860i	$0.668040\pi$
$278$	6.39456	0.383520
$279$	−4.11594	−0.246415
$280$	0.822851	0.0491748
$281$	27.6632	1.65025	0.825125	−	0.564950i	$-0.191105\pi$
$281$	27.6632	1.65025	0.825125	+	0.564950i	$0.191105\pi$
$282$	−3.27040	−0.194749
$283$	−10.9029	−0.648109	−0.324054	−	0.946038i	$-0.605046\pi$
$283$	−10.9029	−0.648109	−0.324054	+	0.946038i	$0.605046\pi$
$284$	−2.91486	−0.172965
$285$	−3.10431	−0.183883
$286$	−3.72259	−0.220121
$287$	−0.270285	−0.0159544
$288$	−1.77765	−0.104749
$289$	−16.5666	−0.974504
$290$	−1.95062	−0.114544
$291$	−8.48417	−0.497351
$292$	21.3093	1.24703
$293$	−23.9204	−1.39744	−0.698722	−	0.715393i	$-0.746247\pi$
$293$	−23.9204	−1.39744	−0.698722	+	0.715393i	$0.746247\pi$
$294$	4.86216	0.283567
$295$	23.2107	1.35138
$296$	−1.45684	−0.0846769
$297$	21.6372	1.25552
$298$	−5.06113	−0.293183
$299$	−11.3368	−0.655623
$300$	−4.13364	−0.238656
$301$	0.0317131	0.00182792
$302$	0.957492	0.0550975
$303$	−10.8550	−0.623604
$304$	−2.12921	−0.122118
$305$	10.1881	0.583370
$306$	0.107575	0.00614966
$307$	−23.0431	−1.31514	−0.657570	−	0.753394i	$-0.728416\pi$
$307$	−23.0431	−1.31514	−0.657570	+	0.753394i	$0.728416\pi$
$308$	1.91632	0.109192
$309$	−24.3922	−1.38762
$310$	8.94748	0.508183
$311$	31.4664	1.78429	0.892147	−	0.451744i	$-0.149198\pi$
$311$	31.4664	1.78429	0.892147	+	0.451744i	$0.149198\pi$
$312$	−5.84857	−0.331110
$313$	−2.31780	−0.131010	−0.0655050	−	0.997852i	$-0.520866\pi$
$313$	−2.31780	−0.131010	−0.0655050	+	0.997852i	$0.520866\pi$
$314$	−3.50071	−0.197556
$315$	0.244364	0.0137684
$316$	−31.2075	−1.75556
$317$	14.5642	0.818007	0.409003	−	0.912533i	$-0.365876\pi$
$317$	14.5642	0.818007	0.409003	+	0.912533i	$0.365876\pi$
$318$	7.56711	0.424342
$319$	−9.43435	−0.528222
$320$	−11.8963	−0.665023
$321$	−13.8447	−0.772734
$322$	−0.448185	−0.0249764
$323$	0.442971	0.0246476
$324$	18.7793	1.04329
$325$	−2.60284	−0.144379
$326$	0.299313	0.0165774
$327$	−1.85274	−0.102457
$328$	−1.73605	−0.0958572
$329$	1.06008	0.0584439
$330$	7.92635	0.436331
$331$	19.3723	1.06480	0.532400	−	0.846493i	$-0.321290\pi$
$331$	19.3723	1.06480	0.532400	+	0.846493i	$0.321290\pi$
$332$	13.3991	0.735372
$333$	−0.432641	−0.0237086
$334$	−2.32391	−0.127159
$335$	−8.20771	−0.448435
$336$	1.32982	0.0725474
$337$	−8.00060	−0.435821	−0.217910	−	0.975969i	$-0.569924\pi$
$337$	−8.00060	−0.435821	−0.217910	+	0.975969i	$0.569924\pi$
$338$	3.13655	0.170606
$339$	−4.14475	−0.225112
$340$	3.04507	0.165142
$341$	43.2754	2.34350
$342$	0.109941	0.00594494
$343$	−3.16374	−0.170826
$344$	0.203694	0.0109825
$345$	24.1389	1.29960
$346$	−5.81876	−0.312818
$347$	33.7462	1.81159	0.905796	−	0.423713i	$-0.139274\pi$
$347$	33.7462	1.81159	0.905796	+	0.423713i	$0.139274\pi$
$348$	−7.13711	−0.382589
$349$	4.79087	0.256450	0.128225	−	0.991745i	$-0.459072\pi$
$349$	4.79087	0.256450	0.128225	+	0.991745i	$0.459072\pi$
$350$	−0.102900	−0.00550023
$351$	10.3068	0.550138
$352$	18.6904	0.996202
$353$	−23.7635	−1.26480	−0.632402	−	0.774640i	$-0.717931\pi$
$353$	−23.7635	−1.26480	−0.632402	+	0.774640i	$0.717931\pi$
$354$	−6.52205	−0.346643
$355$	3.90805	0.207418
$356$	26.0145	1.37877
$357$	−0.276662	−0.0146425
$358$	−6.01152	−0.317719
$359$	−17.3921	−0.917919	−0.458959	−	0.888457i	$-0.651778\pi$
$359$	−17.3921	−0.917919	−0.458959	+	0.888457i	$0.651778\pi$
$360$	1.56956	0.0827230
$361$	−18.5473	−0.976173
$362$	−6.81249	−0.358057
$363$	17.9565	0.942471
$364$	0.912835	0.0478455
$365$	−28.5701	−1.49543
$366$	−2.86280	−0.149641
$367$	−22.8218	−1.19129	−0.595645	−	0.803248i	$-0.703103\pi$
$367$	−22.8218	−1.19129	−0.595645	+	0.803248i	$0.703103\pi$
$368$	16.5566	0.863072
$369$	−0.515559	−0.0268389
$370$	0.940501	0.0488943
$371$	−2.45282	−0.127344
$372$	32.7380	1.69738
$373$	8.36932	0.433347	0.216673	−	0.976244i	$-0.430479\pi$
$373$	8.36932	0.433347	0.216673	+	0.976244i	$0.430479\pi$
$374$	−1.13106	−0.0584855
$375$	−17.5266	−0.905068
$376$	6.80889	0.351142
$377$	−4.49404	−0.231455
$378$	0.407468	0.0209579
$379$	−20.7198	−1.06431	−0.532153	−	0.846648i	$-0.678617\pi$
$379$	−20.7198	−1.06431	−0.532153	+	0.846648i	$0.678617\pi$
$380$	3.11205	0.159645
$381$	−23.1534	−1.18619
$382$	−7.86649	−0.402485
$383$	−25.1742	−1.28634	−0.643170	−	0.765723i	$-0.722381\pi$
$383$	−25.1742	−1.28634	−0.643170	+	0.765723i	$0.722381\pi$
$384$	18.5680	0.947543
$385$	−2.56927	−0.130942
$386$	−8.04203	−0.409328
$387$	0.0604917	0.00307496
$388$	8.50533	0.431793
$389$	−10.2855	−0.521494	−0.260747	−	0.965407i	$-0.583969\pi$
$389$	−10.2855	−0.521494	−0.260747	+	0.965407i	$0.583969\pi$
$390$	3.77571	0.191190
$391$	−3.44452	−0.174197
$392$	−10.1229	−0.511284
$393$	−26.3808	−1.33074
$394$	−3.05789	−0.154054
$395$	41.8410	2.10525
$396$	3.65531	0.183686
$397$	−24.6994	−1.23963	−0.619813	−	0.784749i	$-0.712792\pi$
$397$	−24.6994	−1.23963	−0.619813	+	0.784749i	$0.712792\pi$
$398$	−7.72217	−0.387077
$399$	−0.282747	−0.0141550
$400$	3.80127	0.190063
$401$	15.9994	0.798971	0.399485	−	0.916740i	$-0.369189\pi$
$401$	15.9994	0.798971	0.399485	+	0.916740i	$0.369189\pi$
$402$	2.30631	0.115029
$403$	20.6142	1.02687
$404$	10.8821	0.541404
$405$	−25.1780	−1.25111
$406$	−0.177666	−0.00881742
$407$	4.54883	0.225477
$408$	−1.77700	−0.0879748
$409$	−15.5958	−0.771160	−0.385580	−	0.922674i	$-0.625999\pi$
$409$	−15.5958	−0.771160	−0.385580	+	0.922674i	$0.625999\pi$
$410$	1.12075	0.0553501
$411$	14.6213	0.721214
$412$	24.4531	1.20472
$413$	2.11408	0.104027
$414$	−0.854897	−0.0420159
$415$	−17.9647	−0.881850
$416$	8.90314	0.436513
$417$	−31.3692	−1.53616
$418$	−1.15593	−0.0565385
$419$	5.22881	0.255444	0.127722	−	0.991810i	$-0.459233\pi$
$419$	5.22881	0.255444	0.127722	+	0.991810i	$0.459233\pi$
$420$	−1.94366	−0.0948409
$421$	34.8850	1.70019	0.850095	−	0.526629i	$-0.176544\pi$
$421$	34.8850	1.70019	0.850095	+	0.526629i	$0.176544\pi$
$422$	4.81295	0.234291
$423$	2.02206	0.0983157
$424$	−15.7545	−0.765108
$425$	−0.790835	−0.0383611
$426$	−1.09814	−0.0532049
$427$	0.927956	0.0449069
$428$	13.8792	0.670876
$429$	18.2616	0.881678
$430$	−0.131500	−0.00634151
$431$	28.7949	1.38700	0.693502	−	0.720455i	$-0.256067\pi$
$431$	28.7949	1.38700	0.693502	+	0.720455i	$0.256067\pi$
$432$	−15.0524	−0.724210
$433$	3.16453	0.152078	0.0760389	−	0.997105i	$-0.475773\pi$
$433$	3.16453	0.152078	0.0760389	+	0.997105i	$0.475773\pi$
$434$	0.814956	0.0391191
$435$	9.56897	0.458797
$436$	1.85736	0.0889514
$437$	−3.52028	−0.168398
$438$	8.02803	0.383594
$439$	1.04588	0.0499172	0.0249586	−	0.999688i	$-0.492055\pi$
$439$	1.04588	0.0499172	0.0249586	+	0.999688i	$0.492055\pi$
$440$	−16.5025	−0.786725
$441$	−3.00623	−0.143154
$442$	−0.538777	−0.0256270
$443$	−25.5667	−1.21471	−0.607355	−	0.794430i	$-0.707770\pi$
$443$	−25.5667	−1.21471	−0.607355	+	0.794430i	$0.707770\pi$
$444$	3.44120	0.163312
$445$	−34.8785	−1.65340
$446$	−5.35596	−0.253612
$447$	24.8280	1.17432
$448$	−1.08354	−0.0511924
$449$	28.5334	1.34657	0.673286	−	0.739382i	$-0.264882\pi$
$449$	28.5334	1.34657	0.673286	+	0.739382i	$0.264882\pi$
$450$	−0.196278	−0.00925262
$451$	5.42064	0.255248
$452$	4.15509	0.195439
$453$	−4.69709	−0.220688
$454$	0.865843	0.0406360
$455$	−1.22387	−0.0573758
$456$	−1.81609	−0.0850462
$457$	37.9625	1.77581	0.887905	−	0.460028i	$-0.152161\pi$
$457$	37.9625	1.77581	0.887905	+	0.460028i	$0.152161\pi$
$458$	5.32591	0.248863
$459$	3.13158	0.146170
$460$	−24.1991	−1.12829
$461$	−24.0405	−1.11968	−0.559838	−	0.828602i	$-0.689137\pi$
$461$	−24.0405	−1.11968	−0.559838	+	0.828602i	$0.689137\pi$
$462$	0.721949	0.0335881
$463$	14.2924	0.664226	0.332113	−	0.943240i	$-0.392238\pi$
$463$	14.2924	0.664226	0.332113	+	0.943240i	$0.392238\pi$
$464$	6.56324	0.304691
$465$	−43.8929	−2.03548
$466$	−3.83600	−0.177699
$467$	−29.9806	−1.38734	−0.693669	−	0.720294i	$-0.744007\pi$
$467$	−29.9806	−1.38734	−0.693669	+	0.720294i	$0.744007\pi$
$468$	1.74120	0.0804869
$469$	−0.747575	−0.0345198
$470$	−4.39567	−0.202757
$471$	17.1731	0.791295
$472$	13.5788	0.625013
$473$	−0.636015	−0.0292440
$474$	−11.7571	−0.540019
$475$	−0.808229	−0.0370841
$476$	0.277352	0.0127124
$477$	−4.67867	−0.214222
$478$	10.0877	0.461399
$479$	−21.8732	−0.999414	−0.499707	−	0.866195i	$-0.666559\pi$
$479$	−21.8732	−0.999414	−0.499707	+	0.866195i	$0.666559\pi$
$480$	−18.9571	−0.865269
$481$	2.16683	0.0987989
$482$	8.06077	0.367158
$483$	2.19862	0.100041
$484$	−18.0013	−0.818240
$485$	−11.4034	−0.517801
$486$	1.68544	0.0764529
$487$	36.7531	1.66544	0.832720	−	0.553694i	$-0.186782\pi$
$487$	36.7531	1.66544	0.832720	+	0.553694i	$0.186782\pi$
$488$	5.96028	0.269809
$489$	−1.46831	−0.0663994
$490$	6.53513	0.295227
$491$	19.3499	0.873249	0.436625	−	0.899644i	$-0.356174\pi$
$491$	19.3499	0.873249	0.436625	+	0.899644i	$0.356174\pi$
$492$	4.10073	0.184875
$493$	−1.36545	−0.0614967
$494$	−0.550627	−0.0247739
$495$	−4.90079	−0.220274
$496$	−30.1056	−1.35178
$497$	0.355953	0.0159667
$498$	5.04795	0.226204
$499$	−10.9423	−0.489844	−0.244922	−	0.969543i	$-0.578762\pi$
$499$	−10.9423	−0.489844	−0.244922	+	0.969543i	$0.578762\pi$
$500$	17.5703	0.785767
$501$	11.4002	0.509324
$502$	7.80831	0.348502
$503$	−23.7632	−1.05955	−0.529775	−	0.848138i	$-0.677724\pi$
$503$	−23.7632	−1.05955	−0.529775	+	0.848138i	$0.677724\pi$
$504$	0.142959	0.00636788
$505$	−14.5900	−0.649246
$506$	8.98847	0.399586
$507$	−15.3867	−0.683348
$508$	23.2112	1.02983
$509$	4.87543	0.216100	0.108050	−	0.994145i	$-0.465539\pi$
$509$	4.87543	0.216100	0.108050	+	0.994145i	$0.465539\pi$
$510$	1.14719	0.0507986
$511$	−2.60223	−0.115116
$512$	−22.2228	−0.982117
$513$	3.20046	0.141304
$514$	−6.66806	−0.294116
$515$	−32.7850	−1.44468
$516$	−0.481147	−0.0211813
$517$	−21.2601	−0.935018
$518$	0.0856628	0.00376381
$519$	28.5446	1.25297
$520$	−7.86093	−0.344725
$521$	−0.972100	−0.0425885	−0.0212942	−	0.999773i	$-0.506779\pi$
$521$	−0.972100	−0.0425885	−0.0212942	+	0.999773i	$0.506779\pi$
$522$	−0.338892	−0.0148329
$523$	2.68235	0.117291	0.0586456	−	0.998279i	$-0.481322\pi$
$523$	2.68235	0.117291	0.0586456	+	0.998279i	$0.481322\pi$
$524$	26.4466	1.15533
$525$	0.504787	0.0220307
$526$	7.60840	0.331742
$527$	6.26332	0.272835
$528$	−26.6698	−1.16065
$529$	4.37348	0.190151
$530$	10.1708	0.441790
$531$	4.03252	0.174997
$532$	0.283452	0.0122892
$533$	2.58211	0.111844
$534$	9.80065	0.424115
$535$	−18.6083	−0.804507
$536$	−4.80169	−0.207402
$537$	29.4902	1.27260
$538$	−2.51194	−0.108297
$539$	31.6078	1.36144
$540$	22.0006	0.946757
$541$	15.8006	0.679321	0.339661	−	0.940548i	$-0.389688\pi$
$541$	15.8006	0.679321	0.339661	+	0.940548i	$0.389688\pi$
$542$	4.31351	0.185281
$543$	33.4195	1.43417
$544$	2.70509	0.115980
$545$	−2.49022	−0.106670
$546$	0.343899	0.0147175
$547$	6.15167	0.263027	0.131513	−	0.991314i	$-0.458016\pi$
$547$	6.15167	0.263027	0.131513	+	0.991314i	$0.458016\pi$
$548$	−14.6577	−0.626148
$549$	1.77004	0.0755435
$550$	2.06368	0.0879958
$551$	−1.39548	−0.0594495
$552$	14.1218	0.601064
$553$	3.81096	0.162059
$554$	6.33273	0.269052
$555$	−4.61374	−0.195842
$556$	31.4475	1.33367
$557$	39.6137	1.67849	0.839243	−	0.543756i	$-0.182998\pi$
$557$	39.6137	1.67849	0.839243	+	0.543756i	$0.182998\pi$
$558$	1.55450	0.0658071
$559$	−0.302965	−0.0128141
$560$	1.78738	0.0755304
$561$	5.54852	0.234259
$562$	−10.4478	−0.440713
$563$	−26.8673	−1.13232	−0.566160	−	0.824295i	$-0.691572\pi$
$563$	−26.8673	−1.13232	−0.566160	+	0.824295i	$0.691572\pi$
$564$	−16.0833	−0.677230
$565$	−5.57086	−0.234368
$566$	4.11777	0.173083
$567$	−2.29327	−0.0963082
$568$	2.28630	0.0959309
$569$	−10.4423	−0.437766	−0.218883	−	0.975751i	$-0.570241\pi$
$569$	−10.4423	−0.437766	−0.218883	+	0.975751i	$0.570241\pi$
$570$	1.17243	0.0491075
$571$	3.86403	0.161705	0.0808523	−	0.996726i	$-0.474236\pi$
$571$	3.86403	0.161705	0.0808523	+	0.996726i	$0.474236\pi$
$572$	−18.3071	−0.765460
$573$	38.5900	1.61212
$574$	0.102081	0.00426076
$575$	6.28474	0.262092
$576$	−2.06681	−0.0861171
$577$	35.0754	1.46021	0.730104	−	0.683336i	$-0.239471\pi$
$577$	35.0754	1.46021	0.730104	+	0.683336i	$0.239471\pi$
$578$	6.25681	0.260249
$579$	39.4511	1.63953
$580$	−9.59283	−0.398321
$581$	−1.63626	−0.0678834
$582$	3.20428	0.132822
$583$	49.1920	2.03732
$584$	−16.7142	−0.691638
$585$	−2.33448	−0.0965190
$586$	9.03419	0.373199
$587$	−25.5186	−1.05326	−0.526632	−	0.850093i	$-0.676546\pi$
$587$	−25.5186	−1.05326	−0.526632	+	0.850093i	$0.676546\pi$
$588$	23.9114	0.986089
$589$	6.40108	0.263752
$590$	−8.76615	−0.360897
$591$	15.0008	0.617052
$592$	−3.16451	−0.130060
$593$	17.9300	0.736295	0.368148	−	0.929767i	$-0.379992\pi$
$593$	17.9300	0.736295	0.368148	+	0.929767i	$0.379992\pi$
$594$	−8.17187	−0.335296
$595$	−0.371855	−0.0152446
$596$	−24.8899	−1.01953
$597$	37.8820	1.55041
$598$	4.28164	0.175089
$599$	12.0902	0.493991	0.246996	−	0.969017i	$-0.420557\pi$
$599$	12.0902	0.493991	0.246996	+	0.969017i	$0.420557\pi$
$600$	3.24226	0.132365
$601$	−30.5264	−1.24520	−0.622599	−	0.782541i	$-0.713923\pi$
$601$	−30.5264	−1.24520	−0.622599	+	0.782541i	$0.713923\pi$
$602$	−0.0119773	−0.000488160 0
$603$	−1.42597	−0.0580701
$604$	4.70880	0.191598
$605$	24.1349	0.981224
$606$	4.09969	0.166539
$607$	−32.0003	−1.29885	−0.649425	−	0.760425i	$-0.724991\pi$
$607$	−32.0003	−1.29885	−0.649425	+	0.760425i	$0.724991\pi$
$608$	2.76459	0.112119
$609$	0.871561	0.0353175
$610$	−3.84782	−0.155794
$611$	−10.1272	−0.409703
$612$	0.529038	0.0213851
$613$	38.0683	1.53757	0.768783	−	0.639510i	$-0.220863\pi$
$613$	38.0683	1.53757	0.768783	+	0.639510i	$0.220863\pi$
$614$	8.70286	0.351219
$615$	−5.49799	−0.221700
$616$	−1.50308	−0.0605609
$617$	17.0559	0.686645	0.343322	−	0.939218i	$-0.388448\pi$
$617$	17.0559	0.686645	0.343322	+	0.939218i	$0.388448\pi$
$618$	9.21239	0.370576
$619$	−19.3695	−0.778526	−0.389263	−	0.921127i	$-0.627270\pi$
$619$	−19.3695	−0.778526	−0.389263	+	0.921127i	$0.627270\pi$
$620$	44.0024	1.76718
$621$	−24.8866	−0.998665
$622$	−11.8841	−0.476511
$623$	−3.17681	−0.127276
$624$	−12.7041	−0.508572
$625$	−29.5632	−1.18253
$626$	0.875382	0.0349873
$627$	5.67056	0.226460
$628$	−17.2159	−0.686991
$629$	0.658360	0.0262505
$630$	−0.0922909	−0.00367696
$631$	−15.8716	−0.631840	−0.315920	−	0.948786i	$-0.602313\pi$
$631$	−15.8716	−0.631840	−0.315920	+	0.948786i	$0.602313\pi$
$632$	24.4779	0.973679
$633$	−23.6105	−0.938431
$634$	−5.50056	−0.218455
$635$	−31.1200	−1.23496
$636$	37.2139	1.47563
$637$	15.0563	0.596553
$638$	3.56314	0.141066
$639$	0.678968	0.0268596
$640$	24.9568	0.986505
$641$	−9.61351	−0.379711	−0.189855	−	0.981812i	$-0.560802\pi$
$641$	−9.61351	−0.379711	−0.189855	+	0.981812i	$0.560802\pi$
$642$	5.22881	0.206365
$643$	47.3872	1.86877	0.934385	−	0.356264i	$-0.115950\pi$
$643$	47.3872	1.86877	0.934385	+	0.356264i	$0.115950\pi$
$644$	−2.20411	−0.0868540
$645$	0.645090	0.0254004
$646$	−0.167300	−0.00658233
$647$	26.7777	1.05274	0.526370	−	0.850255i	$-0.323553\pi$
$647$	26.7777	1.05274	0.526370	+	0.850255i	$0.323553\pi$
$648$	−14.7297	−0.578638
$649$	−42.3984	−1.66428
$650$	0.983033	0.0385577
$651$	−3.99786	−0.156688
$652$	1.47197	0.0576470
$653$	26.4912	1.03668	0.518340	−	0.855175i	$-0.326550\pi$
$653$	26.4912	1.03668	0.518340	+	0.855175i	$0.326550\pi$
$654$	0.699737	0.0273619
$655$	−35.4579	−1.38545
$656$	−3.77100	−0.147233
$657$	−4.96366	−0.193651
$658$	−0.400367	−0.0156079
$659$	1.79171	0.0697950	0.0348975	−	0.999391i	$-0.488890\pi$
$659$	1.79171	0.0697950	0.0348975	+	0.999391i	$0.488890\pi$
$660$	38.9806	1.51732
$661$	49.8395	1.93853	0.969267	−	0.246012i	$-0.0791202\pi$
$661$	49.8395	1.93853	0.969267	+	0.246012i	$0.0791202\pi$
$662$	−7.31649	−0.284364
$663$	2.64303	0.102647
$664$	−10.5097	−0.407856
$665$	−0.380034	−0.0147371
$666$	0.163399	0.00633157
$667$	10.8512	0.420160
$668$	−11.4286	−0.442188
$669$	26.2743	1.01582
$670$	3.09987	0.119758
$671$	−18.6104	−0.718446
$672$	−1.72665	−0.0666070
$673$	−26.3444	−1.01550	−0.507751	−	0.861504i	$-0.669523\pi$
$673$	−26.3444	−1.01550	−0.507751	+	0.861504i	$0.669523\pi$
$674$	3.02165	0.116389
$675$	−5.71378	−0.219923
$676$	15.4251	0.593273
$677$	9.13671	0.351152	0.175576	−	0.984466i	$-0.443821\pi$
$677$	9.13671	0.351152	0.175576	+	0.984466i	$0.443821\pi$
$678$	1.56538	0.0601180
$679$	−1.03864	−0.0398595
$680$	−2.38843	−0.0915922
$681$	−4.24749	−0.162764
$682$	−16.3441	−0.625850
$683$	−46.8104	−1.79115	−0.895574	−	0.444912i	$-0.853235\pi$
$683$	−46.8104	−1.79115	−0.895574	+	0.444912i	$0.853235\pi$
$684$	0.540674	0.0206732
$685$	19.6521	0.750869
$686$	1.19487	0.0456205
$687$	−26.1269	−0.996802
$688$	0.442460	0.0168686
$689$	23.4325	0.892709
$690$	−9.11672	−0.347068
$691$	−25.5821	−0.973191	−0.486595	−	0.873627i	$-0.661761\pi$
$691$	−25.5821	−0.973191	−0.486595	+	0.873627i	$0.661761\pi$
$692$	−28.6158	−1.08781
$693$	−0.446374	−0.0169564
$694$	−12.7452	−0.483801
$695$	−42.1627	−1.59932
$696$	5.59806	0.212194
$697$	0.784538	0.0297165
$698$	−1.80940	−0.0684869
$699$	18.8180	0.711760
$700$	−0.506046	−0.0191267
$701$	45.5713	1.72121	0.860603	−	0.509277i	$-0.170087\pi$
$701$	45.5713	1.72121	0.860603	+	0.509277i	$0.170087\pi$
$702$	−3.89266	−0.146919
$703$	0.672840	0.0253766
$704$	21.7307	0.819005
$705$	21.5634	0.812126
$706$	8.97494	0.337776
$707$	−1.32889	−0.0499779
$708$	−32.0745	−1.20543
$709$	28.1711	1.05799	0.528993	−	0.848626i	$-0.322570\pi$
$709$	28.1711	1.05799	0.528993	+	0.848626i	$0.322570\pi$
$710$	−1.47598	−0.0553926
$711$	7.26928	0.272619
$712$	−20.4047	−0.764699
$713$	−49.7745	−1.86407
$714$	0.104489	0.00391040
$715$	24.5450	0.917931
$716$	−29.5638	−1.10485
$717$	−49.4862	−1.84809
$718$	6.56859	0.245138
$719$	−27.0643	−1.00933	−0.504664	−	0.863316i	$-0.668383\pi$
$719$	−27.0643	−1.00933	−0.504664	+	0.863316i	$0.668383\pi$
$720$	3.40935	0.127059
$721$	−2.98613	−0.111209
$722$	7.00489	0.260695
$723$	−39.5430	−1.47062
$724$	−33.5028	−1.24512
$725$	2.49135	0.0925264
$726$	−6.78176	−0.251695
$727$	−30.2808	−1.12305	−0.561527	−	0.827459i	$-0.689786\pi$
$727$	−30.2808	−1.12305	−0.561527	+	0.827459i	$0.689786\pi$
$728$	−0.715990	−0.0265364
$729$	22.0641	0.817190
$730$	10.7903	0.399367
$731$	−0.0920516	−0.00340465
$732$	−14.0788	−0.520368
$733$	39.4557	1.45733	0.728666	−	0.684870i	$-0.240141\pi$
$733$	39.4557	1.45733	0.728666	+	0.684870i	$0.240141\pi$
$734$	8.61929	0.318144
$735$	−32.0588	−1.18251
$736$	−21.4973	−0.792401
$737$	14.9928	0.552268
$738$	0.194715	0.00716756
$739$	0.790588	0.0290823	0.0145411	−	0.999894i	$-0.495371\pi$
$739$	0.790588	0.0290823	0.0145411	+	0.999894i	$0.495371\pi$
$740$	4.62524	0.170027
$741$	2.70116	0.0992297
$742$	0.926376	0.0340083
$743$	49.6300	1.82075	0.910374	−	0.413786i	$-0.135794\pi$
$743$	49.6300	1.82075	0.910374	+	0.413786i	$0.135794\pi$
$744$	−25.6783	−0.941413
$745$	33.3707	1.22261
$746$	−3.16090	−0.115729
$747$	−3.12110	−0.114195
$748$	−5.56236	−0.203380
$749$	−1.69488	−0.0619297
$750$	6.61939	0.241706
$751$	43.5572	1.58942	0.794712	−	0.606987i	$-0.207622\pi$
$751$	43.5572	1.58942	0.794712	+	0.606987i	$0.207622\pi$
$752$	14.7901	0.539340
$753$	−38.3045	−1.39590
$754$	1.69730	0.0618119
$755$	−6.31325	−0.229763
$756$	2.00386	0.0728799
$757$	6.70499	0.243697	0.121849	−	0.992549i	$-0.461118\pi$
$757$	6.70499	0.243697	0.121849	+	0.992549i	$0.461118\pi$
$758$	7.82541	0.284232
$759$	−44.0940	−1.60051
$760$	−2.44096	−0.0885431
$761$	−16.4816	−0.597457	−0.298728	−	0.954338i	$-0.596562\pi$
$761$	−16.4816	−0.597457	−0.298728	+	0.954338i	$0.596562\pi$
$762$	8.74453	0.316781
$763$	−0.226815	−0.00821125
$764$	−38.6862	−1.39962
$765$	−0.709300	−0.0256448
$766$	9.50771	0.343528
$767$	−20.1964	−0.729250
$768$	10.6891	0.385709
$769$	30.7289	1.10811	0.554057	−	0.832479i	$-0.313079\pi$
$769$	30.7289	1.10811	0.554057	+	0.832479i	$0.313079\pi$
$770$	0.970355	0.0349692
$771$	32.7109	1.17806
$772$	−39.5495	−1.42342
$773$	−18.3585	−0.660311	−0.330155	−	0.943927i	$-0.607101\pi$
$773$	−18.3585	−0.660311	−0.330155	+	0.943927i	$0.607101\pi$
$774$	−0.0228463	−0.000821194 0
$775$	−11.4278	−0.410500
$776$	−6.67123	−0.239483
$777$	−0.420229	−0.0150756
$778$	3.88459	0.139269
$779$	0.801794	0.0287272
$780$	18.5684	0.664854
$781$	−7.13874	−0.255444
$782$	1.30092	0.0465207
$783$	−9.86536	−0.352559
$784$	−21.9887	−0.785312
$785$	23.0820	0.823832
$786$	9.96343	0.355384
$787$	8.55875	0.305087	0.152543	−	0.988297i	$-0.451254\pi$
$787$	8.55875	0.305087	0.152543	+	0.988297i	$0.451254\pi$
$788$	−15.0382	−0.535715
$789$	−37.3238	−1.32876
$790$	−15.8024	−0.562224
$791$	−0.507406	−0.0180413
$792$	−2.86707	−0.101877
$793$	−8.86503	−0.314807
$794$	9.32840	0.331053
$795$	−49.8939	−1.76955
$796$	−37.9764	−1.34604
$797$	26.2953	0.931428	0.465714	−	0.884935i	$-0.345797\pi$
$797$	26.2953	0.931428	0.465714	+	0.884935i	$0.345797\pi$
$798$	0.106787	0.00378022
$799$	−3.07701	−0.108857
$800$	−4.93562	−0.174500
$801$	−6.05965	−0.214107
$802$	−6.04260	−0.213372
$803$	52.1884	1.84169
$804$	11.3421	0.400005
$805$	2.95512	0.104154
$806$	−7.78551	−0.274233
$807$	12.3226	0.433775
$808$	−8.53547	−0.300277
$809$	13.8535	0.487064	0.243532	−	0.969893i	$-0.421694\pi$
$809$	13.8535	0.487064	0.243532	+	0.969893i	$0.421694\pi$
$810$	9.50917	0.334118
$811$	27.1981	0.955054	0.477527	−	0.878617i	$-0.341533\pi$
$811$	27.1981	0.955054	0.477527	+	0.878617i	$0.341533\pi$
$812$	−0.873735	−0.0306621
$813$	−21.1604	−0.742129
$814$	−1.71799	−0.0602155
$815$	−1.97353	−0.0691296
$816$	−3.85997	−0.135126
$817$	−0.0940762	−0.00329131
$818$	5.89016	0.205945
$819$	−0.212630	−0.00742988
$820$	5.51170	0.192477
$821$	1.22346	0.0426991	0.0213495	−	0.999772i	$-0.493204\pi$
$821$	1.22346	0.0426991	0.0213495	+	0.999772i	$0.493204\pi$
$822$	−5.52212	−0.192606
$823$	9.77394	0.340698	0.170349	−	0.985384i	$-0.445510\pi$
$823$	9.77394	0.340698	0.170349	+	0.985384i	$0.445510\pi$
$824$	−19.1800	−0.668166
$825$	−10.1236	−0.352460
$826$	−0.798439	−0.0277812
$827$	40.5525	1.41015	0.705074	−	0.709133i	$-0.250914\pi$
$827$	40.5525	1.41015	0.705074	+	0.709133i	$0.250914\pi$
$828$	−4.20425	−0.146108
$829$	17.3786	0.603583	0.301791	−	0.953374i	$-0.402415\pi$
$829$	17.3786	0.603583	0.301791	+	0.953374i	$0.402415\pi$
$830$	6.78484	0.235505
$831$	−31.0659	−1.07766
$832$	10.3514	0.358869
$833$	4.57465	0.158502
$834$	11.8474	0.410243
$835$	15.3228	0.530267
$836$	−5.68470	−0.196610
$837$	45.2525	1.56415
$838$	−1.97480	−0.0682184
$839$	−42.8610	−1.47973	−0.739863	−	0.672758i	$-0.765110\pi$
$839$	−42.8610	−1.47973	−0.739863	+	0.672758i	$0.765110\pi$
$840$	1.52453	0.0526012
$841$	−24.6985	−0.851671
$842$	−13.1753	−0.454050
$843$	51.2527	1.76524
$844$	23.6693	0.814733
$845$	−20.6810	−0.711446
$846$	−0.763685	−0.0262560
$847$	2.19826	0.0755331
$848$	−34.2216	−1.17518
$849$	−20.2002	−0.693268
$850$	0.298680	0.0102447
$851$	−5.23197	−0.179350
$852$	−5.40047	−0.185017
$853$	−22.4908	−0.770070	−0.385035	−	0.922902i	$-0.625811\pi$
$853$	−22.4908	−0.770070	−0.385035	+	0.922902i	$0.625811\pi$
$854$	−0.350468	−0.0119928
$855$	−0.724900	−0.0247911
$856$	−10.8863	−0.372085
$857$	12.4173	0.424165	0.212083	−	0.977252i	$-0.431975\pi$
$857$	12.4173	0.424165	0.212083	+	0.977252i	$0.431975\pi$
$858$	−6.89699	−0.235459
$859$	−6.70217	−0.228675	−0.114338	−	0.993442i	$-0.536475\pi$
$859$	−6.70217	−0.228675	−0.114338	+	0.993442i	$0.536475\pi$
$860$	−0.646699	−0.0220523
$861$	−0.500768	−0.0170661
$862$	−10.8752	−0.370411
$863$	43.4477	1.47898	0.739488	−	0.673170i	$-0.235068\pi$
$863$	43.4477	1.47898	0.739488	+	0.673170i	$0.235068\pi$
$864$	19.5443	0.664910
$865$	38.3661	1.30449
$866$	−1.19517	−0.0406136
$867$	−30.6935	−1.04241
$868$	4.00783	0.136035
$869$	−76.4299	−2.59271
$870$	−3.61398	−0.122525
$871$	7.14181	0.241991
$872$	−1.45684	−0.0493347
$873$	−1.98118	−0.0670526
$874$	1.32953	0.0449720
$875$	−2.14563	−0.0725354
$876$	39.4806	1.33393
$877$	29.3134	0.989842	0.494921	−	0.868938i	$-0.335197\pi$
$877$	29.3134	0.989842	0.494921	+	0.868938i	$0.335197\pi$
$878$	−0.395005	−0.0133308
$879$	−44.3182	−1.49482
$880$	−35.8463	−1.20838
$881$	−53.2109	−1.79272	−0.896360	−	0.443327i	$-0.853798\pi$
$881$	−53.2109	−1.79272	−0.896360	+	0.443327i	$0.853798\pi$
$882$	1.13539	0.0382304
$883$	−8.49052	−0.285729	−0.142864	−	0.989742i	$-0.545631\pi$
$883$	−8.49052	−0.285729	−0.142864	+	0.989742i	$0.545631\pi$
$884$	−2.64962	−0.0891164
$885$	43.0033	1.44554
$886$	9.65596	0.324398
$887$	36.4757	1.22473	0.612367	−	0.790574i	$-0.290218\pi$
$887$	36.4757	1.22473	0.612367	+	0.790574i	$0.290218\pi$
$888$	−2.69914	−0.0905772
$889$	−2.83448	−0.0950653
$890$	13.1728	0.441554
$891$	45.9921	1.54079
$892$	−26.3398	−0.881922
$893$	−3.14469	−0.105233
$894$	−9.37696	−0.313612
$895$	39.6371	1.32492
$896$	2.27312	0.0759396
$897$	−21.0041	−0.701306
$898$	−10.7764	−0.359613
$899$	−19.7312	−0.658073
$900$	−0.965264	−0.0321755
$901$	7.11964	0.237190
$902$	−2.04725	−0.0681661
$903$	0.0587562	0.00195528
$904$	−3.25908	−0.108395
$905$	44.9183	1.49314
$906$	1.77398	0.0589366
$907$	−40.5088	−1.34507	−0.672536	−	0.740065i	$-0.734795\pi$
$907$	−40.5088	−1.34507	−0.672536	+	0.740065i	$0.734795\pi$
$908$	4.25808	0.141310
$909$	−2.53480	−0.0840741
$910$	0.462227	0.0153227
$911$	−52.2206	−1.73015	−0.865074	−	0.501645i	$-0.832728\pi$
$911$	−52.2206	−1.73015	−0.865074	+	0.501645i	$0.832728\pi$
$912$	−3.94486	−0.130627
$913$	32.8156	1.08604
$914$	−14.3376	−0.474244
$915$	18.8759	0.624019
$916$	26.1920	0.865409
$917$	−3.22958	−0.106650
$918$	−1.18273	−0.0390359
$919$	−14.2721	−0.470794	−0.235397	−	0.971899i	$-0.575639\pi$
$919$	−14.2721	−0.470794	−0.235397	+	0.971899i	$0.575639\pi$
$920$	18.9808	0.625779
$921$	−42.6929	−1.40678
$922$	9.07953	0.299019
$923$	−3.40053	−0.111930
$924$	3.55044	0.116801
$925$	−1.20122	−0.0394959
$926$	−5.39793	−0.177387
$927$	−5.69593	−0.187079
$928$	−8.52180	−0.279742
$929$	−27.4779	−0.901522	−0.450761	−	0.892645i	$-0.648847\pi$
$929$	−27.4779	−0.901522	−0.450761	+	0.892645i	$0.648847\pi$
$930$	16.5774	0.543593
$931$	4.67527	0.153226
$932$	−18.8649	−0.617940
$933$	58.2990	1.90862
$934$	11.3230	0.370500
$935$	7.45765	0.243891
$936$	−1.36573	−0.0446401
$937$	13.4984	0.440973	0.220486	−	0.975390i	$-0.429236\pi$
$937$	13.4984	0.440973	0.220486	+	0.975390i	$0.429236\pi$
$938$	0.282342	0.00921880
$939$	−4.29429	−0.140139
$940$	−21.6172	−0.705076
$941$	−12.1747	−0.396884	−0.198442	−	0.980113i	$-0.563588\pi$
$941$	−12.1747	−0.396884	−0.198442	+	0.980113i	$0.563588\pi$
$942$	−6.48590	−0.211322
$943$	−6.23470	−0.203030
$944$	29.4955	0.959995
$945$	−2.68665	−0.0873967
$946$	0.240209	0.00780985
$947$	−40.7419	−1.32394	−0.661968	−	0.749532i	$-0.730278\pi$
$947$	−40.7419	−1.32394	−0.661968	+	0.749532i	$0.730278\pi$
$948$	−57.8194	−1.87789
$949$	24.8599	0.806985
$950$	0.305250	0.00990361
$951$	26.9836	0.875005
$952$	−0.217543	−0.00705062
$953$	29.6307	0.959833	0.479917	−	0.877314i	$-0.340667\pi$
$953$	29.6307	0.959833	0.479917	+	0.877314i	$0.340667\pi$
$954$	1.76703	0.0572096
$955$	51.8679	1.67841
$956$	49.6096	1.60449
$957$	−17.4794	−0.565028
$958$	8.26103	0.266902
$959$	1.78996	0.0578007
$960$	−22.0407	−0.711361
$961$	59.5072	1.91959
$962$	−0.818362	−0.0263851
$963$	−3.23293	−0.104180
$964$	39.6416	1.27677
$965$	53.0253	1.70695
$966$	−0.830370	−0.0267167
$967$	33.2095	1.06794	0.533972	−	0.845502i	$-0.320699\pi$
$967$	33.2095	1.06794	0.533972	+	0.845502i	$0.320699\pi$
$968$	14.1195	0.453817
$969$	0.820710	0.0263650
$970$	4.30680	0.138283
$971$	−28.6569	−0.919643	−0.459822	−	0.888011i	$-0.652087\pi$
$971$	−28.6569	−0.919643	−0.459822	+	0.888011i	$0.652087\pi$
$972$	8.28872	0.265861
$973$	−3.84026	−0.123113
$974$	−13.8808	−0.444770
$975$	−4.82238	−0.154440
$976$	12.9468	0.414416
$977$	34.5151	1.10423	0.552117	−	0.833766i	$-0.313820\pi$
$977$	34.5151	1.10423	0.552117	+	0.833766i	$0.313820\pi$
$978$	0.554548	0.0177325
$979$	63.7117	2.03624
$980$	32.1388	1.02664
$981$	−0.432641	−0.0138132
$982$	−7.30802	−0.233208
$983$	−17.5864	−0.560919	−0.280460	−	0.959866i	$-0.590487\pi$
$983$	−17.5864	−0.560919	−0.280460	+	0.959866i	$0.590487\pi$
$984$	−3.21644	−0.102537
$985$	20.1623	0.642424
$986$	0.515699	0.0164232
$987$	1.96404	0.0625162
$988$	−2.70790	−0.0861498
$989$	0.731531	0.0232613
$990$	1.85092	0.0588260
$991$	18.9380	0.601584	0.300792	−	0.953690i	$-0.402749\pi$
$991$	18.9380	0.601584	0.300792	+	0.953690i	$0.402749\pi$
$992$	39.0895	1.24109
$993$	35.8919	1.13899
$994$	−0.134436	−0.00426404
$995$	50.9163	1.61416
$996$	24.8251	0.786613
$997$	−15.9422	−0.504894	−0.252447	−	0.967611i	$-0.581235\pi$
$997$	−15.9422	−0.504894	−0.252447	+	0.967611i	$0.581235\pi$
$998$	4.13265	0.130817
$999$	4.75665	0.150494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.38	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.38	✓	79	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-0.377677 q^{2} +1.85274 q^{3} -1.85736 q^{4} +2.49022 q^{5} -0.699737 q^{6} +0.226815 q^{7} +1.45684 q^{8} +0.432641 q^{9} +O(q^{10})\)	\(q-0.377677 q^{2} +1.85274 q^{3} -1.85736 q^{4} +2.49022 q^{5} -0.699737 q^{6} +0.226815 q^{7} +1.45684 q^{8} +0.432641 q^{9} -0.940501 q^{10} -4.54883 q^{11} -3.44120 q^{12} -2.16683 q^{13} -0.0856628 q^{14} +4.61374 q^{15} +3.16451 q^{16} -0.658360 q^{17} -0.163399 q^{18} -0.672840 q^{19} -4.62524 q^{20} +0.420229 q^{21} +1.71799 q^{22} +5.23197 q^{23} +2.69914 q^{24} +1.20122 q^{25} +0.818362 q^{26} -4.75665 q^{27} -0.421277 q^{28} +2.07402 q^{29} -1.74250 q^{30} -9.51352 q^{31} -4.10884 q^{32} -8.42780 q^{33} +0.248648 q^{34} +0.564820 q^{35} -0.803570 q^{36} -1.00000 q^{37} +0.254116 q^{38} -4.01457 q^{39} +3.62785 q^{40} -1.19166 q^{41} -0.158711 q^{42} +0.139820 q^{43} +8.44882 q^{44} +1.07737 q^{45} -1.97600 q^{46} +4.67375 q^{47} +5.86300 q^{48} -6.94856 q^{49} -0.453673 q^{50} -1.21977 q^{51} +4.02458 q^{52} -10.8142 q^{53} +1.79648 q^{54} -11.3276 q^{55} +0.330432 q^{56} -1.24660 q^{57} -0.783309 q^{58} +9.32072 q^{59} -8.56937 q^{60} +4.09125 q^{61} +3.59304 q^{62} +0.0981294 q^{63} -4.77720 q^{64} -5.39589 q^{65} +3.18299 q^{66} -3.29597 q^{67} +1.22281 q^{68} +9.69347 q^{69} -0.213320 q^{70} +1.56936 q^{71} +0.630288 q^{72} -11.4729 q^{73} +0.377677 q^{74} +2.22555 q^{75} +1.24971 q^{76} -1.03174 q^{77} +1.51621 q^{78} +16.8021 q^{79} +7.88033 q^{80} -10.1107 q^{81} +0.450061 q^{82} -7.21407 q^{83} -0.780516 q^{84} -1.63946 q^{85} -0.0528067 q^{86} +3.84261 q^{87} -6.62691 q^{88} -14.0062 q^{89} -0.406900 q^{90} -0.491469 q^{91} -9.71765 q^{92} -17.6261 q^{93} -1.76517 q^{94} -1.67552 q^{95} -7.61260 q^{96} -4.57926 q^{97} +2.62431 q^{98} -1.96801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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