LMFDB - Embedded newform 4015.2.a.h.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.503541 q^{2} +0.0692183 q^{3} -1.74645 q^{4} +1.00000 q^{5} +0.0348542 q^{6} -2.92313 q^{7} -1.88649 q^{8} -2.99521 q^{9} +O(q^{10})$	\(q+0.503541 q^{2} +0.0692183 q^{3} -1.74645 q^{4} +1.00000 q^{5} +0.0348542 q^{6} -2.92313 q^{7} -1.88649 q^{8} -2.99521 q^{9} +0.503541 q^{10} +1.00000 q^{11} -0.120886 q^{12} +5.73426 q^{13} -1.47192 q^{14} +0.0692183 q^{15} +2.54297 q^{16} +0.148278 q^{17} -1.50821 q^{18} -4.90526 q^{19} -1.74645 q^{20} -0.202334 q^{21} +0.503541 q^{22} -6.36870 q^{23} -0.130579 q^{24} +1.00000 q^{25} +2.88743 q^{26} -0.414978 q^{27} +5.10510 q^{28} -1.48132 q^{29} +0.0348542 q^{30} +6.03969 q^{31} +5.05347 q^{32} +0.0692183 q^{33} +0.0746642 q^{34} -2.92313 q^{35} +5.23097 q^{36} -6.02102 q^{37} -2.47000 q^{38} +0.396915 q^{39} -1.88649 q^{40} +1.06629 q^{41} -0.101884 q^{42} +0.407031 q^{43} -1.74645 q^{44} -2.99521 q^{45} -3.20690 q^{46} -3.78321 q^{47} +0.176020 q^{48} +1.54472 q^{49} +0.503541 q^{50} +0.0102636 q^{51} -10.0146 q^{52} +0.702635 q^{53} -0.208958 q^{54} +1.00000 q^{55} +5.51446 q^{56} -0.339533 q^{57} -0.745903 q^{58} +4.46036 q^{59} -0.120886 q^{60} -2.17639 q^{61} +3.04123 q^{62} +8.75540 q^{63} -2.54131 q^{64} +5.73426 q^{65} +0.0348542 q^{66} +4.71801 q^{67} -0.258960 q^{68} -0.440831 q^{69} -1.47192 q^{70} +6.20880 q^{71} +5.65043 q^{72} +1.00000 q^{73} -3.03183 q^{74} +0.0692183 q^{75} +8.56677 q^{76} -2.92313 q^{77} +0.199863 q^{78} -7.70643 q^{79} +2.54297 q^{80} +8.95690 q^{81} +0.536922 q^{82} +15.6514 q^{83} +0.353366 q^{84} +0.148278 q^{85} +0.204957 q^{86} -0.102534 q^{87} -1.88649 q^{88} +3.63060 q^{89} -1.50821 q^{90} -16.7620 q^{91} +11.1226 q^{92} +0.418057 q^{93} -1.90500 q^{94} -4.90526 q^{95} +0.349792 q^{96} +17.1806 q^{97} +0.777827 q^{98} -2.99521 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	0.503541	0.356057	0.178029	−	0.984025i	$-0.443028\pi$
$2$	0.503541	0.356057	0.178029	+	0.984025i	$0.443028\pi$
$3$	0.0692183	0.0399632	0.0199816	−	0.999800i	$-0.493639\pi$
$3$	0.0692183	0.0399632	0.0199816	+	0.999800i	$0.493639\pi$
$4$	−1.74645	−0.873223
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0348542	0.0142292
$7$	−2.92313	−1.10484	−0.552421	−	0.833566i	$-0.686296\pi$
$7$	−2.92313	−1.10484	−0.552421	+	0.833566i	$0.686296\pi$
$8$	−1.88649	−0.666975
$9$	−2.99521	−0.998403
$10$	0.503541	0.159234
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.120886	−0.0348968
$13$	5.73426	1.59040	0.795198	−	0.606350i	$-0.207367\pi$
$13$	5.73426	1.59040	0.795198	+	0.606350i	$0.207367\pi$
$14$	−1.47192	−0.393387
$15$	0.0692183	0.0178721
$16$	2.54297	0.635742
$17$	0.148278	0.0359628	0.0179814	−	0.999838i	$-0.494276\pi$
$17$	0.148278	0.0359628	0.0179814	+	0.999838i	$0.494276\pi$
$18$	−1.50821	−0.355488
$19$	−4.90526	−1.12534	−0.562671	−	0.826681i	$-0.690226\pi$
$19$	−4.90526	−1.12534	−0.562671	+	0.826681i	$0.690226\pi$
$20$	−1.74645	−0.390517
$21$	−0.202334	−0.0441530
$22$	0.503541	0.107355
$23$	−6.36870	−1.32797	−0.663983	−	0.747747i	$-0.731135\pi$
$23$	−6.36870	−1.32797	−0.663983	+	0.747747i	$0.731135\pi$
$24$	−0.130579	−0.0266544
$25$	1.00000	0.200000
$26$	2.88743	0.566272
$27$	−0.414978	−0.0798625
$28$	5.10510	0.964773
$29$	−1.48132	−0.275073	−0.137537	−	0.990497i	$-0.543918\pi$
$29$	−1.48132	−0.275073	−0.137537	+	0.990497i	$0.543918\pi$
$30$	0.0348542	0.00636348
$31$	6.03969	1.08476	0.542381	−	0.840133i	$-0.317523\pi$
$31$	6.03969	1.08476	0.542381	+	0.840133i	$0.317523\pi$
$32$	5.05347	0.893335
$33$	0.0692183	0.0120494
$34$	0.0746642	0.0128048
$35$	−2.92313	−0.494100
$36$	5.23097	0.871829
$37$	−6.02102	−0.989850	−0.494925	−	0.868936i	$-0.664804\pi$
$37$	−6.02102	−0.989850	−0.494925	+	0.868936i	$0.664804\pi$
$38$	−2.47000	−0.400686
$39$	0.396915	0.0635573
$40$	−1.88649	−0.298280
$41$	1.06629	0.166527	0.0832635	−	0.996528i	$-0.473466\pi$
$41$	1.06629	0.166527	0.0832635	+	0.996528i	$0.473466\pi$
$42$	−0.101884	−0.0157210
$43$	0.407031	0.0620717	0.0310358	−	0.999518i	$-0.490119\pi$
$43$	0.407031	0.0620717	0.0310358	+	0.999518i	$0.490119\pi$
$44$	−1.74645	−0.263287
$45$	−2.99521	−0.446499
$46$	−3.20690	−0.472832
$47$	−3.78321	−0.551838	−0.275919	−	0.961181i	$-0.588982\pi$
$47$	−3.78321	−0.551838	−0.275919	+	0.961181i	$0.588982\pi$
$48$	0.176020	0.0254063
$49$	1.54472	0.220674
$50$	0.503541	0.0712114
$51$	0.0102636	0.00143719
$52$	−10.0146	−1.38877
$53$	0.702635	0.0965143	0.0482572	−	0.998835i	$-0.484633\pi$
$53$	0.702635	0.0965143	0.0482572	+	0.998835i	$0.484633\pi$
$54$	−0.208958	−0.0284356
$55$	1.00000	0.134840
$56$	5.51446	0.736901
$57$	−0.339533	−0.0449723
$58$	−0.745903	−0.0979418
$59$	4.46036	0.580690	0.290345	−	0.956922i	$-0.406230\pi$
$59$	4.46036	0.580690	0.290345	+	0.956922i	$0.406230\pi$
$60$	−0.120886	−0.0156063
$61$	−2.17639	−0.278658	−0.139329	−	0.990246i	$-0.544495\pi$
$61$	−2.17639	−0.278658	−0.139329	+	0.990246i	$0.544495\pi$
$62$	3.04123	0.386237
$63$	8.75540	1.10308
$64$	−2.54131	−0.317664
$65$	5.73426	0.711247
$66$	0.0348542	0.00429026
$67$	4.71801	0.576396	0.288198	−	0.957571i	$-0.406944\pi$
$67$	4.71801	0.576396	0.288198	+	0.957571i	$0.406944\pi$
$68$	−0.258960	−0.0314035
$69$	−0.440831	−0.0530698
$70$	−1.47192	−0.175928
$71$	6.20880	0.736849	0.368424	−	0.929658i	$-0.379897\pi$
$71$	6.20880	0.736849	0.368424	+	0.929658i	$0.379897\pi$
$72$	5.65043	0.665909
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−3.03183	−0.352443
$75$	0.0692183	0.00799264
$76$	8.56677	0.982676
$77$	−2.92313	−0.333122
$78$	0.199863	0.0226300
$79$	−7.70643	−0.867041	−0.433520	−	0.901144i	$-0.642729\pi$
$79$	−7.70643	−0.867041	−0.433520	+	0.901144i	$0.642729\pi$
$80$	2.54297	0.284313
$81$	8.95690	0.995211
$82$	0.536922	0.0592931
$83$	15.6514	1.71797	0.858984	−	0.512002i	$-0.171096\pi$
$83$	15.6514	1.71797	0.858984	+	0.512002i	$0.171096\pi$
$84$	0.353366	0.0385554
$85$	0.148278	0.0160830
$86$	0.204957	0.0221011
$87$	−0.102534	−0.0109928
$88$	−1.88649	−0.201100
$89$	3.63060	0.384842	0.192421	−	0.981312i	$-0.438366\pi$
$89$	3.63060	0.384842	0.192421	+	0.981312i	$0.438366\pi$
$90$	−1.50821	−0.158979
$91$	−16.7620	−1.75714
$92$	11.1226	1.15961
$93$	0.418057	0.0433505
$94$	−1.90500	−0.196486
$95$	−4.90526	−0.503269
$96$	0.349792	0.0357005
$97$	17.1806	1.74443	0.872215	−	0.489122i	$-0.162683\pi$
$97$	17.1806	1.74443	0.872215	+	0.489122i	$0.162683\pi$
$98$	0.777827	0.0785724
$99$	−2.99521	−0.301030
$100$	−1.74645	−0.174645
$101$	12.4499	1.23882	0.619408	−	0.785070i	$-0.287373\pi$
$101$	12.4499	1.23882	0.619408	+	0.785070i	$0.287373\pi$
$102$	0.00516813	0.000511721 0
$103$	12.1754	1.19967	0.599837	−	0.800122i	$-0.295232\pi$
$103$	12.1754	1.19967	0.599837	+	0.800122i	$0.295232\pi$
$104$	−10.8176	−1.06075
$105$	−0.202334	−0.0197458
$106$	0.353805	0.0343646
$107$	2.78463	0.269200	0.134600	−	0.990900i	$-0.457025\pi$
$107$	2.78463	0.269200	0.134600	+	0.990900i	$0.457025\pi$
$108$	0.724737	0.0697378
$109$	2.97959	0.285393	0.142696	−	0.989767i	$-0.454423\pi$
$109$	2.97959	0.285393	0.142696	+	0.989767i	$0.454423\pi$
$110$	0.503541	0.0480107
$111$	−0.416765	−0.0395576
$112$	−7.43344	−0.702394
$113$	5.56265	0.523290	0.261645	−	0.965164i	$-0.415735\pi$
$113$	5.56265	0.523290	0.261645	+	0.965164i	$0.415735\pi$
$114$	−0.170969	−0.0160127
$115$	−6.36870	−0.593885
$116$	2.58704	0.240200
$117$	−17.1753	−1.58786
$118$	2.24598	0.206759
$119$	−0.433438	−0.0397332
$120$	−0.130579	−0.0119202
$121$	1.00000	0.0909091
$122$	−1.09590	−0.0992181
$123$	0.0738069	0.00665495
$124$	−10.5480	−0.947239
$125$	1.00000	0.0894427
$126$	4.40870	0.392758
$127$	9.87999	0.876708	0.438354	−	0.898802i	$-0.355562\pi$
$127$	9.87999	0.876708	0.438354	+	0.898802i	$0.355562\pi$
$128$	−11.3866	−1.00644
$129$	0.0281740	0.00248058
$130$	2.88743	0.253245
$131$	−0.0462060	−0.00403703	−0.00201852	−	0.999998i	$-0.500643\pi$
$131$	−0.0462060	−0.00403703	−0.00201852	+	0.999998i	$0.500643\pi$
$132$	−0.120886	−0.0105218
$133$	14.3387	1.24333
$134$	2.37571	0.205230
$135$	−0.414978	−0.0357156
$136$	−0.279726	−0.0239863
$137$	13.6843	1.16913	0.584564	−	0.811348i	$-0.301266\pi$
$137$	13.6843	1.16913	0.584564	+	0.811348i	$0.301266\pi$
$138$	−0.221976	−0.0188959
$139$	1.26747	0.107505	0.0537526	−	0.998554i	$-0.482882\pi$
$139$	1.26747	0.107505	0.0537526	+	0.998554i	$0.482882\pi$
$140$	5.10510	0.431460
$141$	−0.261867	−0.0220532
$142$	3.12638	0.262360
$143$	5.73426	0.479523
$144$	−7.61672	−0.634727
$145$	−1.48132	−0.123017
$146$	0.503541	0.0416733
$147$	0.106923	0.00881882
$148$	10.5154	0.864360
$149$	13.6738	1.12020	0.560099	−	0.828426i	$-0.310763\pi$
$149$	13.6738	1.12020	0.560099	+	0.828426i	$0.310763\pi$
$150$	0.0348542	0.00284583
$151$	−1.73480	−0.141176	−0.0705882	−	0.997506i	$-0.522488\pi$
$151$	−1.73480	−0.141176	−0.0705882	+	0.997506i	$0.522488\pi$
$152$	9.25371	0.750575
$153$	−0.444125	−0.0359054
$154$	−1.47192	−0.118611
$155$	6.03969	0.485120
$156$	−0.693191	−0.0554997
$157$	4.58342	0.365797	0.182898	−	0.983132i	$-0.441452\pi$
$157$	4.58342	0.365797	0.182898	+	0.983132i	$0.441452\pi$
$158$	−3.88050	−0.308716
$159$	0.0486352	0.00385702
$160$	5.05347	0.399512
$161$	18.6166	1.46719
$162$	4.51017	0.354352
$163$	−19.5809	−1.53370	−0.766848	−	0.641829i	$-0.778176\pi$
$163$	−19.5809	−1.53370	−0.766848	+	0.641829i	$0.778176\pi$
$164$	−1.86222	−0.145415
$165$	0.0692183	0.00538863
$166$	7.88114	0.611695
$167$	−1.67099	−0.129305	−0.0646524	−	0.997908i	$-0.520594\pi$
$167$	−1.67099	−0.129305	−0.0646524	+	0.997908i	$0.520594\pi$
$168$	0.381701	0.0294489
$169$	19.8817	1.52936
$170$	0.0746642	0.00572648
$171$	14.6923	1.12355
$172$	−0.710858	−0.0542024
$173$	−16.9382	−1.28778	−0.643892	−	0.765116i	$-0.722681\pi$
$173$	−16.9382	−1.28778	−0.643892	+	0.765116i	$0.722681\pi$
$174$	−0.0516301	−0.00391407
$175$	−2.92313	−0.220968
$176$	2.54297	0.191684
$177$	0.308739	0.0232062
$178$	1.82815	0.137026
$179$	2.65541	0.198475	0.0992374	−	0.995064i	$-0.468360\pi$
$179$	2.65541	0.198475	0.0992374	+	0.995064i	$0.468360\pi$
$180$	5.23097	0.389894
$181$	−10.5568	−0.784679	−0.392340	−	0.919820i	$-0.628334\pi$
$181$	−10.5568	−0.784679	−0.392340	+	0.919820i	$0.628334\pi$
$182$	−8.44035	−0.625641
$183$	−0.150646	−0.0111360
$184$	12.0145	0.885720
$185$	−6.02102	−0.442674
$186$	0.210509	0.0154353
$187$	0.148278	0.0108432
$188$	6.60717	0.481878
$189$	1.21304	0.0882354
$190$	−2.47000	−0.179192
$191$	7.27263	0.526229	0.263114	−	0.964765i	$-0.415250\pi$
$191$	7.27263	0.526229	0.263114	+	0.964765i	$0.415250\pi$
$192$	−0.175905	−0.0126949
$193$	21.0373	1.51430	0.757150	−	0.653241i	$-0.226591\pi$
$193$	21.0373	1.51430	0.757150	+	0.653241i	$0.226591\pi$
$194$	8.65116	0.621117
$195$	0.396915	0.0284237
$196$	−2.69776	−0.192697
$197$	11.8782	0.846284	0.423142	−	0.906063i	$-0.360927\pi$
$197$	11.8782	0.846284	0.423142	+	0.906063i	$0.360927\pi$
$198$	−1.50821	−0.107184
$199$	23.6215	1.67448	0.837241	−	0.546835i	$-0.184167\pi$
$199$	23.6215	1.67448	0.837241	+	0.546835i	$0.184167\pi$
$200$	−1.88649	−0.133395
$201$	0.326572	0.0230346
$202$	6.26905	0.441089
$203$	4.33008	0.303912
$204$	−0.0179248	−0.00125499
$205$	1.06629	0.0744731
$206$	6.13079	0.427153
$207$	19.0756	1.32585
$208$	14.5820	1.01108
$209$	−4.90526	−0.339304
$210$	−0.101884	−0.00703063
$211$	23.0822	1.58904	0.794521	−	0.607237i	$-0.207722\pi$
$211$	23.0822	1.58904	0.794521	+	0.607237i	$0.207722\pi$
$212$	−1.22711	−0.0842786
$213$	0.429762	0.0294468
$214$	1.40217	0.0958507
$215$	0.407031	0.0277593
$216$	0.782851	0.0532663
$217$	−17.6548	−1.19849
$218$	1.50034	0.101616
$219$	0.0692183	0.00467734
$220$	−1.74645	−0.117745
$221$	0.850266	0.0571951
$222$	−0.209858	−0.0140847
$223$	−9.46907	−0.634096	−0.317048	−	0.948410i	$-0.602692\pi$
$223$	−9.46907	−0.634096	−0.317048	+	0.948410i	$0.602692\pi$
$224$	−14.7720	−0.986993
$225$	−2.99521	−0.199681
$226$	2.80102	0.186321
$227$	−14.7932	−0.981860	−0.490930	−	0.871199i	$-0.663343\pi$
$227$	−14.7932	−0.981860	−0.490930	+	0.871199i	$0.663343\pi$
$228$	0.592977	0.0392708
$229$	−10.3786	−0.685840	−0.342920	−	0.939365i	$-0.611416\pi$
$229$	−10.3786	−0.685840	−0.342920	+	0.939365i	$0.611416\pi$
$230$	−3.20690	−0.211457
$231$	−0.202334	−0.0133126
$232$	2.79448	0.183467
$233$	−6.44758	−0.422395	−0.211198	−	0.977443i	$-0.567736\pi$
$233$	−6.44758	−0.422395	−0.211198	+	0.977443i	$0.567736\pi$
$234$	−8.64846	−0.565368
$235$	−3.78321	−0.246789
$236$	−7.78979	−0.507072
$237$	−0.533425	−0.0346497
$238$	−0.218254	−0.0141473
$239$	−14.5254	−0.939568	−0.469784	−	0.882781i	$-0.655668\pi$
$239$	−14.5254	−0.939568	−0.469784	+	0.882781i	$0.655668\pi$
$240$	0.176020	0.0113620
$241$	3.36384	0.216684	0.108342	−	0.994114i	$-0.465446\pi$
$241$	3.36384	0.216684	0.108342	+	0.994114i	$0.465446\pi$
$242$	0.503541	0.0323688
$243$	1.86491	0.119634
$244$	3.80094	0.243330
$245$	1.54472	0.0986883
$246$	0.0371648	0.00236954
$247$	−28.1280	−1.78974
$248$	−11.3938	−0.723508
$249$	1.08337	0.0686555
$250$	0.503541	0.0318467
$251$	−25.7115	−1.62289	−0.811447	−	0.584426i	$-0.801320\pi$
$251$	−25.7115	−1.62289	−0.811447	+	0.584426i	$0.801320\pi$
$252$	−15.2908	−0.963232
$253$	−6.36870	−0.400397
$254$	4.97498	0.312158
$255$	0.0102636	0.000642730 0
$256$	−0.650989	−0.0406868
$257$	12.9607	0.808469	0.404234	−	0.914655i	$-0.367538\pi$
$257$	12.9607	0.808469	0.404234	+	0.914655i	$0.367538\pi$
$258$	0.0141868	0.000883229 0
$259$	17.6003	1.09363
$260$	−10.0146	−0.621077
$261$	4.43685	0.274634
$262$	−0.0232666	−0.00143741
$263$	−29.5752	−1.82368	−0.911842	−	0.410542i	$-0.865339\pi$
$263$	−29.5752	−1.82368	−0.911842	+	0.410542i	$0.865339\pi$
$264$	−0.130579	−0.00803661
$265$	0.702635	0.0431625
$266$	7.22013	0.442695
$267$	0.251303	0.0153795
$268$	−8.23975	−0.503323
$269$	22.6119	1.37867	0.689336	−	0.724442i	$-0.257902\pi$
$269$	22.6119	1.37867	0.689336	+	0.724442i	$0.257902\pi$
$270$	−0.208958	−0.0127168
$271$	−25.5167	−1.55003	−0.775015	−	0.631943i	$-0.782258\pi$
$271$	−25.5167	−1.55003	−0.775015	+	0.631943i	$0.782258\pi$
$272$	0.377067	0.0228631
$273$	−1.16024	−0.0702207
$274$	6.89060	0.416276
$275$	1.00000	0.0603023
$276$	0.769887	0.0463418
$277$	18.5524	1.11471	0.557353	−	0.830275i	$-0.311817\pi$
$277$	18.5524	1.11471	0.557353	+	0.830275i	$0.311817\pi$
$278$	0.638221	0.0382780
$279$	−18.0901	−1.08303
$280$	5.51446	0.329552
$281$	14.8603	0.886491	0.443245	−	0.896400i	$-0.353827\pi$
$281$	14.8603	0.886491	0.443245	+	0.896400i	$0.353827\pi$
$282$	−0.131861	−0.00785219
$283$	6.14254	0.365136	0.182568	−	0.983193i	$-0.441559\pi$
$283$	6.14254	0.365136	0.182568	+	0.983193i	$0.441559\pi$
$284$	−10.8433	−0.643433
$285$	−0.339533	−0.0201122
$286$	2.88743	0.170737
$287$	−3.11692	−0.183986
$288$	−15.1362	−0.891908
$289$	−16.9780	−0.998707
$290$	−0.745903	−0.0438009
$291$	1.18921	0.0697130
$292$	−1.74645	−0.102203
$293$	−11.8885	−0.694535	−0.347268	−	0.937766i	$-0.612890\pi$
$293$	−11.8885	−0.694535	−0.347268	+	0.937766i	$0.612890\pi$
$294$	0.0538399	0.00314000
$295$	4.46036	0.259692
$296$	11.3586	0.660205
$297$	−0.414978	−0.0240795
$298$	6.88530	0.398855
$299$	−36.5198	−2.11199
$300$	−0.120886	−0.00697936
$301$	−1.18981	−0.0685793
$302$	−0.873545	−0.0502669
$303$	0.861763	0.0495070
$304$	−12.4739	−0.715428
$305$	−2.17639	−0.124620
$306$	−0.223635	−0.0127844
$307$	−32.7128	−1.86702	−0.933508	−	0.358557i	$-0.883269\pi$
$307$	−32.7128	−1.86702	−0.933508	+	0.358557i	$0.883269\pi$
$308$	5.10510	0.290890
$309$	0.842758	0.0479428
$310$	3.04123	0.172730
$311$	−16.1358	−0.914978	−0.457489	−	0.889215i	$-0.651251\pi$
$311$	−16.1358	−0.914978	−0.457489	+	0.889215i	$0.651251\pi$
$312$	−0.748776	−0.0423911
$313$	12.1415	0.686280	0.343140	−	0.939284i	$-0.388510\pi$
$313$	12.1415	0.686280	0.343140	+	0.939284i	$0.388510\pi$
$314$	2.30794	0.130244
$315$	8.75540	0.493311
$316$	13.4589	0.757120
$317$	6.37854	0.358255	0.179127	−	0.983826i	$-0.442673\pi$
$317$	6.37854	0.358255	0.179127	+	0.983826i	$0.442673\pi$
$318$	0.0244898	0.00137332
$319$	−1.48132	−0.0829377
$320$	−2.54131	−0.142064
$321$	0.192747	0.0107581
$322$	9.37421	0.522404
$323$	−0.727343	−0.0404705
$324$	−15.6428	−0.869042
$325$	5.73426	0.318079
$326$	−9.85979	−0.546083
$327$	0.206242	0.0114052
$328$	−2.01155	−0.111069
$329$	11.0588	0.609693
$330$	0.0348542	0.00191866
$331$	−6.05625	−0.332882	−0.166441	−	0.986051i	$-0.553227\pi$
$331$	−6.05625	−0.332882	−0.166441	+	0.986051i	$0.553227\pi$
$332$	−27.3344	−1.50017
$333$	18.0342	0.988269
$334$	−0.841410	−0.0460399
$335$	4.71801	0.257772
$336$	−0.514530	−0.0280699
$337$	−26.4455	−1.44058	−0.720288	−	0.693675i	$-0.755991\pi$
$337$	−26.4455	−1.44058	−0.720288	+	0.693675i	$0.755991\pi$
$338$	10.0112	0.544540
$339$	0.385037	0.0209123
$340$	−0.258960	−0.0140441
$341$	6.03969	0.327068
$342$	7.39816	0.400046
$343$	15.9465	0.861032
$344$	−0.767860	−0.0414002
$345$	−0.440831	−0.0237335
$346$	−8.52905	−0.458525
$347$	−27.9460	−1.50022	−0.750111	−	0.661312i	$-0.770000\pi$
$347$	−27.9460	−1.50022	−0.750111	+	0.661312i	$0.770000\pi$
$348$	0.179070	0.00959917
$349$	34.5706	1.85052	0.925261	−	0.379331i	$-0.123846\pi$
$349$	34.5706	1.85052	0.925261	+	0.379331i	$0.123846\pi$
$350$	−1.47192	−0.0786773
$351$	−2.37959	−0.127013
$352$	5.05347	0.269351
$353$	1.60102	0.0852139	0.0426070	−	0.999092i	$-0.486434\pi$
$353$	1.60102	0.0852139	0.0426070	+	0.999092i	$0.486434\pi$
$354$	0.155463	0.00826274
$355$	6.20880	0.329529
$356$	−6.34064	−0.336053
$357$	−0.0300018	−0.00158786
$358$	1.33711	0.0706684
$359$	4.41178	0.232845	0.116422	−	0.993200i	$-0.462857\pi$
$359$	4.41178	0.232845	0.116422	+	0.993200i	$0.462857\pi$
$360$	5.65043	0.297804
$361$	5.06154	0.266397
$362$	−5.31577	−0.279391
$363$	0.0692183	0.00363302
$364$	29.2739	1.53437
$365$	1.00000	0.0523424
$366$	−0.0758562	−0.00396507
$367$	−24.5704	−1.28256	−0.641282	−	0.767305i	$-0.721597\pi$
$367$	−24.5704	−1.28256	−0.641282	+	0.767305i	$0.721597\pi$
$368$	−16.1954	−0.844245
$369$	−3.19377	−0.166261
$370$	−3.03183	−0.157617
$371$	−2.05390	−0.106633
$372$	−0.730114	−0.0378547
$373$	34.2164	1.77166	0.885830	−	0.464010i	$-0.153590\pi$
$373$	34.2164	1.77166	0.885830	+	0.464010i	$0.153590\pi$
$374$	0.0746642	0.00386080
$375$	0.0692183	0.00357442
$376$	7.13698	0.368062
$377$	−8.49424	−0.437476
$378$	0.610813	0.0314168
$379$	9.46370	0.486118	0.243059	−	0.970012i	$-0.421849\pi$
$379$	9.46370	0.486118	0.243059	+	0.970012i	$0.421849\pi$
$380$	8.56677	0.439466
$381$	0.683876	0.0350360
$382$	3.66206	0.187368
$383$	31.9424	1.63218	0.816090	−	0.577925i	$-0.196137\pi$
$383$	31.9424	1.63218	0.816090	+	0.577925i	$0.196137\pi$
$384$	−0.788160	−0.0402206
$385$	−2.92313	−0.148977
$386$	10.5932	0.539177
$387$	−1.21914	−0.0619726
$388$	−30.0051	−1.52328
$389$	−27.7993	−1.40948	−0.704741	−	0.709465i	$-0.748937\pi$
$389$	−27.7993	−1.40948	−0.704741	+	0.709465i	$0.748937\pi$
$390$	0.199863	0.0101205
$391$	−0.944341	−0.0477574
$392$	−2.91409	−0.147184
$393$	−0.00319830	−0.000161333 0
$394$	5.98114	0.301325
$395$	−7.70643	−0.387752
$396$	5.23097	0.262866
$397$	22.9262	1.15063	0.575316	−	0.817931i	$-0.304879\pi$
$397$	22.9262	1.15063	0.575316	+	0.817931i	$0.304879\pi$
$398$	11.8944	0.596211
$399$	0.992501	0.0496872
$400$	2.54297	0.127148
$401$	−4.82523	−0.240960	−0.120480	−	0.992716i	$-0.538443\pi$
$401$	−4.82523	−0.240960	−0.120480	+	0.992716i	$0.538443\pi$
$402$	0.164442	0.00820164
$403$	34.6332	1.72520
$404$	−21.7432	−1.08176
$405$	8.95690	0.445072
$406$	2.18037	0.108210
$407$	−6.02102	−0.298451
$408$	−0.0193621	−0.000958567 0
$409$	6.11712	0.302472	0.151236	−	0.988498i	$-0.451675\pi$
$409$	6.11712	0.302472	0.151236	+	0.988498i	$0.451675\pi$
$410$	0.536922	0.0265167
$411$	0.947203	0.0467221
$412$	−21.2636	−1.04758
$413$	−13.0382	−0.641570
$414$	9.60534	0.472077
$415$	15.6514	0.768299
$416$	28.9779	1.42076
$417$	0.0877319	0.00429625
$418$	−2.47000	−0.120811
$419$	24.3574	1.18994	0.594968	−	0.803750i	$-0.297165\pi$
$419$	24.3574	1.18994	0.594968	+	0.803750i	$0.297165\pi$
$420$	0.353366	0.0172425
$421$	−23.4906	−1.14486	−0.572430	−	0.819954i	$-0.693999\pi$
$421$	−23.4906	−1.14486	−0.572430	+	0.819954i	$0.693999\pi$
$422$	11.6228	0.565790
$423$	11.3315	0.550956
$424$	−1.32551	−0.0643726
$425$	0.148278	0.00719256
$426$	0.216403	0.0104847
$427$	6.36187	0.307872
$428$	−4.86321	−0.235072
$429$	0.396915	0.0191632
$430$	0.204957	0.00988390
$431$	29.6527	1.42832	0.714160	−	0.699982i	$-0.246809\pi$
$431$	29.6527	1.42832	0.714160	+	0.699982i	$0.246809\pi$
$432$	−1.05528	−0.0507720
$433$	31.5416	1.51579	0.757895	−	0.652376i	$-0.226228\pi$
$433$	31.5416	1.51579	0.757895	+	0.652376i	$0.226228\pi$
$434$	−8.88993	−0.426730
$435$	−0.102534	−0.00491613
$436$	−5.20369	−0.249212
$437$	31.2401	1.49442
$438$	0.0348542	0.00166540
$439$	22.1450	1.05692	0.528462	−	0.848957i	$-0.322769\pi$
$439$	22.1450	1.05692	0.528462	+	0.848957i	$0.322769\pi$
$440$	−1.88649	−0.0899348
$441$	−4.62675	−0.220321
$442$	0.428144	0.0203647
$443$	−19.8277	−0.942043	−0.471021	−	0.882122i	$-0.656115\pi$
$443$	−19.8277	−0.942043	−0.471021	+	0.882122i	$0.656115\pi$
$444$	0.727857	0.0345426
$445$	3.63060	0.172107
$446$	−4.76806	−0.225774
$447$	0.946474	0.0447667
$448$	7.42860	0.350968
$449$	−26.1829	−1.23565	−0.617823	−	0.786318i	$-0.711985\pi$
$449$	−26.1829	−1.23565	−0.617823	+	0.786318i	$0.711985\pi$
$450$	−1.50821	−0.0710977
$451$	1.06629	0.0502098
$452$	−9.71488	−0.456949
$453$	−0.120080	−0.00564186
$454$	−7.44899	−0.349598
$455$	−16.7620	−0.785815
$456$	0.640526	0.0299954
$457$	−19.3732	−0.906241	−0.453120	−	0.891449i	$-0.649689\pi$
$457$	−19.3732	−0.906241	−0.453120	+	0.891449i	$0.649689\pi$
$458$	−5.22607	−0.244198
$459$	−0.0615323	−0.00287208
$460$	11.1226	0.518594
$461$	30.2137	1.40719	0.703595	−	0.710601i	$-0.251577\pi$
$461$	30.2137	1.40719	0.703595	+	0.710601i	$0.251577\pi$
$462$	−0.101884	−0.00474005
$463$	−6.26645	−0.291227	−0.145613	−	0.989342i	$-0.546516\pi$
$463$	−6.26645	−0.291227	−0.145613	+	0.989342i	$0.546516\pi$
$464$	−3.76694	−0.174876
$465$	0.418057	0.0193869
$466$	−3.24662	−0.150397
$467$	21.4366	0.991968	0.495984	−	0.868332i	$-0.334807\pi$
$467$	21.4366	0.991968	0.495984	+	0.868332i	$0.334807\pi$
$468$	29.9957	1.38655
$469$	−13.7914	−0.636826
$470$	−1.90500	−0.0878711
$471$	0.317256	0.0146184
$472$	−8.41443	−0.387305
$473$	0.407031	0.0187153
$474$	−0.268601	−0.0123373
$475$	−4.90526	−0.225069
$476$	0.756976	0.0346959
$477$	−2.10454	−0.0963602
$478$	−7.31412	−0.334540
$479$	−8.25086	−0.376991	−0.188496	−	0.982074i	$-0.560361\pi$
$479$	−8.25086	−0.376991	−0.188496	+	0.982074i	$0.560361\pi$
$480$	0.349792	0.0159658
$481$	−34.5261	−1.57425
$482$	1.69383	0.0771519
$483$	1.28861	0.0586337
$484$	−1.74645	−0.0793839
$485$	17.1806	0.780133
$486$	0.939061	0.0425967
$487$	−2.22229	−0.100701	−0.0503507	−	0.998732i	$-0.516034\pi$
$487$	−2.22229	−0.100701	−0.0503507	+	0.998732i	$0.516034\pi$
$488$	4.10573	0.185858
$489$	−1.35536	−0.0612913
$490$	0.777827	0.0351387
$491$	41.6526	1.87976	0.939879	−	0.341509i	$-0.110938\pi$
$491$	41.6526	1.87976	0.939879	+	0.341509i	$0.110938\pi$
$492$	−0.128900	−0.00581125
$493$	−0.219647	−0.00989240
$494$	−14.1636	−0.637250
$495$	−2.99521	−0.134625
$496$	15.3588	0.689628
$497$	−18.1491	−0.814100
$498$	0.545519	0.0244453
$499$	4.61368	0.206537	0.103268	−	0.994654i	$-0.467070\pi$
$499$	4.61368	0.206537	0.103268	+	0.994654i	$0.467070\pi$
$500$	−1.74645	−0.0781035
$501$	−0.115663	−0.00516743
$502$	−12.9468	−0.577843
$503$	−6.36777	−0.283925	−0.141962	−	0.989872i	$-0.545341\pi$
$503$	−6.36777	−0.283925	−0.141962	+	0.989872i	$0.545341\pi$
$504$	−16.5170	−0.735724
$505$	12.4499	0.554015
$506$	−3.20690	−0.142564
$507$	1.37618	0.0611181
$508$	−17.2549	−0.765562
$509$	−2.36511	−0.104832	−0.0524158	−	0.998625i	$-0.516692\pi$
$509$	−2.36511	−0.104832	−0.0524158	+	0.998625i	$0.516692\pi$
$510$	0.00516813	0.000228849 0
$511$	−2.92313	−0.129312
$512$	22.4454	0.991955
$513$	2.03557	0.0898727
$514$	6.52626	0.287861
$515$	12.1754	0.536511
$516$	−0.0492044	−0.00216610
$517$	−3.78321	−0.166385
$518$	8.86245	0.389394
$519$	−1.17243	−0.0514640
$520$	−10.8176	−0.474384
$521$	−22.6602	−0.992762	−0.496381	−	0.868105i	$-0.665338\pi$
$521$	−22.6602	−0.992762	−0.496381	+	0.868105i	$0.665338\pi$
$522$	2.23413	0.0977854
$523$	−8.73652	−0.382021	−0.191011	−	0.981588i	$-0.561176\pi$
$523$	−8.73652	−0.382021	−0.191011	+	0.981588i	$0.561176\pi$
$524$	0.0806963	0.00352523
$525$	−0.202334	−0.00883059
$526$	−14.8923	−0.649335
$527$	0.895556	0.0390110
$528$	0.176020	0.00766028
$529$	17.5604	0.763496
$530$	0.353805	0.0153683
$531$	−13.3597	−0.579763
$532$	−25.0418	−1.08570
$533$	6.11440	0.264844
$534$	0.126542	0.00547599
$535$	2.78463	0.120390
$536$	−8.90047	−0.384442
$537$	0.183803	0.00793168
$538$	11.3860	0.490886
$539$	1.54472	0.0665356
$540$	0.724737	0.0311877
$541$	−1.05163	−0.0452131	−0.0226065	−	0.999744i	$-0.507196\pi$
$541$	−1.05163	−0.0452131	−0.0226065	+	0.999744i	$0.507196\pi$
$542$	−12.8487	−0.551899
$543$	−0.730722	−0.0313583
$544$	0.749320	0.0321268
$545$	2.97959	0.127632
$546$	−0.584226	−0.0250026
$547$	31.6544	1.35345	0.676723	−	0.736238i	$-0.263399\pi$
$547$	31.6544	1.35345	0.676723	+	0.736238i	$0.263399\pi$
$548$	−23.8989	−1.02091
$549$	6.51873	0.278213
$550$	0.503541	0.0214711
$551$	7.26623	0.309552
$552$	0.831622	0.0353962
$553$	22.5269	0.957942
$554$	9.34190	0.396899
$555$	−0.416765	−0.0176907
$556$	−2.21356	−0.0938760
$557$	7.01070	0.297053	0.148526	−	0.988908i	$-0.452547\pi$
$557$	7.01070	0.297053	0.148526	+	0.988908i	$0.452547\pi$
$558$	−9.10913	−0.385620
$559$	2.33402	0.0987186
$560$	−7.43344	−0.314120
$561$	0.0102636	0.000433328 0
$562$	7.48276	0.315641
$563$	−17.9652	−0.757144	−0.378572	−	0.925572i	$-0.623585\pi$
$563$	−17.9652	−0.757144	−0.378572	+	0.925572i	$0.623585\pi$
$564$	0.457337	0.0192574
$565$	5.56265	0.234023
$566$	3.09302	0.130009
$567$	−26.1822	−1.09955
$568$	−11.7128	−0.491459
$569$	13.8524	0.580725	0.290362	−	0.956917i	$-0.406224\pi$
$569$	13.8524	0.580725	0.290362	+	0.956917i	$0.406224\pi$
$570$	−0.170969	−0.00716110
$571$	31.3483	1.31189	0.655943	−	0.754811i	$-0.272271\pi$
$571$	31.3483	1.31189	0.655943	+	0.754811i	$0.272271\pi$
$572$	−10.0146	−0.418730
$573$	0.503398	0.0210298
$574$	−1.56950	−0.0655095
$575$	−6.36870	−0.265593
$576$	7.61176	0.317157
$577$	−45.8827	−1.91012	−0.955061	−	0.296410i	$-0.904210\pi$
$577$	−45.8827	−1.91012	−0.955061	+	0.296410i	$0.904210\pi$
$578$	−8.54912	−0.355597
$579$	1.45617	0.0605163
$580$	2.58704	0.107421
$581$	−45.7513	−1.89808
$582$	0.598818	0.0248218
$583$	0.702635	0.0291002
$584$	−1.88649	−0.0780635
$585$	−17.1753	−0.710111
$586$	−5.98636	−0.247294
$587$	−7.47689	−0.308604	−0.154302	−	0.988024i	$-0.549313\pi$
$587$	−7.47689	−0.308604	−0.154302	+	0.988024i	$0.549313\pi$
$588$	−0.186734	−0.00770080
$589$	−29.6262	−1.22073
$590$	2.24598	0.0924654
$591$	0.822185	0.0338202
$592$	−15.3113	−0.629290
$593$	−9.67487	−0.397299	−0.198650	−	0.980071i	$-0.563656\pi$
$593$	−9.67487	−0.397299	−0.198650	+	0.980071i	$0.563656\pi$
$594$	−0.208958	−0.00857366
$595$	−0.433438	−0.0177692
$596$	−23.8805	−0.978183
$597$	1.63504	0.0669176
$598$	−18.3892	−0.751990
$599$	36.6763	1.49855	0.749276	−	0.662257i	$-0.230401\pi$
$599$	36.6763	1.49855	0.749276	+	0.662257i	$0.230401\pi$
$600$	−0.130579	−0.00533088
$601$	1.06165	0.0433056	0.0216528	−	0.999766i	$-0.493107\pi$
$601$	1.06165	0.0433056	0.0216528	+	0.999766i	$0.493107\pi$
$602$	−0.599116	−0.0244182
$603$	−14.1314	−0.575476
$604$	3.02974	0.123279
$605$	1.00000	0.0406558
$606$	0.433933	0.0176273
$607$	−12.9975	−0.527553	−0.263776	−	0.964584i	$-0.584968\pi$
$607$	−12.9975	−0.527553	−0.263776	+	0.964584i	$0.584968\pi$
$608$	−24.7885	−1.00531
$609$	0.299721	0.0121453
$610$	−1.09590	−0.0443717
$611$	−21.6939	−0.877641
$612$	0.775640	0.0313534
$613$	−9.18222	−0.370866	−0.185433	−	0.982657i	$-0.559369\pi$
$613$	−9.18222	−0.370866	−0.185433	+	0.982657i	$0.559369\pi$
$614$	−16.4722	−0.664764
$615$	0.0738069	0.00297618
$616$	5.51446	0.222184
$617$	2.00272	0.0806265	0.0403133	−	0.999187i	$-0.487164\pi$
$617$	2.00272	0.0806265	0.0403133	+	0.999187i	$0.487164\pi$
$618$	0.424363	0.0170704
$619$	5.49082	0.220695	0.110347	−	0.993893i	$-0.464804\pi$
$619$	5.49082	0.220695	0.110347	+	0.993893i	$0.464804\pi$
$620$	−10.5480	−0.423618
$621$	2.64287	0.106055
$622$	−8.12504	−0.325784
$623$	−10.6127	−0.425190
$624$	1.00934	0.0404061
$625$	1.00000	0.0400000
$626$	6.11375	0.244355
$627$	−0.339533	−0.0135597
$628$	−8.00469	−0.319422
$629$	−0.892788	−0.0355978
$630$	4.40870	0.175647
$631$	−35.3593	−1.40763	−0.703815	−	0.710383i	$-0.748522\pi$
$631$	−35.3593	−1.40763	−0.703815	+	0.710383i	$0.748522\pi$
$632$	14.5381	0.578294
$633$	1.59771	0.0635031
$634$	3.21186	0.127559
$635$	9.87999	0.392076
$636$	−0.0849387	−0.00336804
$637$	8.85779	0.350959
$638$	−0.745903	−0.0295306
$639$	−18.5966	−0.735672
$640$	−11.3866	−0.450094
$641$	28.8580	1.13982	0.569911	−	0.821706i	$-0.306978\pi$
$641$	28.8580	1.13982	0.569911	+	0.821706i	$0.306978\pi$
$642$	0.0970561	0.00383050
$643$	22.9963	0.906887	0.453443	−	0.891285i	$-0.350195\pi$
$643$	22.9963	0.906887	0.453443	+	0.891285i	$0.350195\pi$
$644$	−32.5129	−1.28119
$645$	0.0281740	0.00110935
$646$	−0.366247	−0.0144098
$647$	−22.7153	−0.893029	−0.446515	−	0.894776i	$-0.647335\pi$
$647$	−22.7153	−0.893029	−0.446515	+	0.894776i	$0.647335\pi$
$648$	−16.8971	−0.663781
$649$	4.46036	0.175085
$650$	2.88743	0.113254
$651$	−1.22204	−0.0478954
$652$	34.1970	1.33926
$653$	26.5444	1.03876	0.519382	−	0.854542i	$-0.326162\pi$
$653$	26.5444	1.03876	0.519382	+	0.854542i	$0.326162\pi$
$654$	0.103851	0.00406090
$655$	−0.0462060	−0.00180542
$656$	2.71155	0.105868
$657$	−2.99521	−0.116854
$658$	5.56857	0.217085
$659$	24.4136	0.951018	0.475509	−	0.879711i	$-0.342264\pi$
$659$	24.4136	0.951018	0.475509	+	0.879711i	$0.342264\pi$
$660$	−0.120886	−0.00470548
$661$	10.6242	0.413233	0.206616	−	0.978422i	$-0.433755\pi$
$661$	10.6242	0.413233	0.206616	+	0.978422i	$0.433755\pi$
$662$	−3.04957	−0.118525
$663$	0.0588539	0.00228570
$664$	−29.5263	−1.14584
$665$	14.3387	0.556032
$666$	9.08097	0.351880
$667$	9.43406	0.365288
$668$	2.91829	0.112912
$669$	−0.655432	−0.0253405
$670$	2.37571	0.0917816
$671$	−2.17639	−0.0840185
$672$	−1.02249	−0.0394434
$673$	49.2143	1.89707	0.948535	−	0.316672i	$-0.102565\pi$
$673$	49.2143	1.89707	0.948535	+	0.316672i	$0.102565\pi$
$674$	−13.3164	−0.512928
$675$	−0.414978	−0.0159725
$676$	−34.7223	−1.33547
$677$	−7.71267	−0.296422	−0.148211	−	0.988956i	$-0.547351\pi$
$677$	−7.71267	−0.296422	−0.148211	+	0.988956i	$0.547351\pi$
$678$	0.193882	0.00744599
$679$	−50.2213	−1.92732
$680$	−0.279726	−0.0107270
$681$	−1.02396	−0.0392383
$682$	3.04123	0.116455
$683$	−25.3815	−0.971195	−0.485597	−	0.874183i	$-0.661398\pi$
$683$	−25.3815	−0.971195	−0.485597	+	0.874183i	$0.661398\pi$
$684$	−25.6593	−0.981106
$685$	13.6843	0.522850
$686$	8.02973	0.306576
$687$	−0.718391	−0.0274083
$688$	1.03507	0.0394616
$689$	4.02909	0.153496
$690$	−0.221976	−0.00845049
$691$	−3.74986	−0.142651	−0.0713256	−	0.997453i	$-0.522723\pi$
$691$	−3.74986	−0.142651	−0.0713256	+	0.997453i	$0.522723\pi$
$692$	29.5816	1.12452
$693$	8.75540	0.332590
$694$	−14.0720	−0.534164
$695$	1.26747	0.0480778
$696$	0.193429	0.00733192
$697$	0.158108	0.00598877
$698$	17.4077	0.658892
$699$	−0.446290	−0.0168802
$700$	5.10510	0.192955
$701$	2.89554	0.109363	0.0546816	−	0.998504i	$-0.482586\pi$
$701$	2.89554	0.109363	0.0546816	+	0.998504i	$0.482586\pi$
$702$	−1.19822	−0.0452239
$703$	29.5347	1.11392
$704$	−2.54131	−0.0957793
$705$	−0.261867	−0.00986248
$706$	0.806181	0.0303410
$707$	−36.3928	−1.36869
$708$	−0.539196	−0.0202642
$709$	−20.6188	−0.774356	−0.387178	−	0.922005i	$-0.626550\pi$
$709$	−20.6188	−0.774356	−0.387178	+	0.922005i	$0.626550\pi$
$710$	3.12638	0.117331
$711$	23.0824	0.865656
$712$	−6.84908	−0.256680
$713$	−38.4650	−1.44053
$714$	−0.0151071	−0.000565370 0
$715$	5.73426	0.214449
$716$	−4.63753	−0.173313
$717$	−1.00542	−0.0375481
$718$	2.22151	0.0829060
$719$	−5.36575	−0.200109	−0.100054	−	0.994982i	$-0.531902\pi$
$719$	−5.36575	−0.200109	−0.100054	+	0.994982i	$0.531902\pi$
$720$	−7.61672	−0.283859
$721$	−35.5902	−1.32545
$722$	2.54869	0.0948525
$723$	0.232839	0.00865938
$724$	18.4368	0.685200
$725$	−1.48132	−0.0550147
$726$	0.0348542	0.00129356
$727$	−24.7930	−0.919520	−0.459760	−	0.888043i	$-0.652065\pi$
$727$	−24.7930	−0.919520	−0.459760	+	0.888043i	$0.652065\pi$
$728$	31.6213	1.17196
$729$	−26.7416	−0.990430
$730$	0.503541	0.0186369
$731$	0.0603539	0.00223227
$732$	0.263095	0.00972426
$733$	−39.2809	−1.45087	−0.725436	−	0.688289i	$-0.758362\pi$
$733$	−39.2809	−1.45087	−0.725436	+	0.688289i	$0.758362\pi$
$734$	−12.3722	−0.456666
$735$	0.106923	0.00394390
$736$	−32.1840	−1.18632
$737$	4.71801	0.173790
$738$	−1.60819	−0.0591984
$739$	24.7129	0.909078	0.454539	−	0.890727i	$-0.349804\pi$
$739$	24.7129	0.909078	0.454539	+	0.890727i	$0.349804\pi$
$740$	10.5154	0.386554
$741$	−1.94697	−0.0715238
$742$	−1.03422	−0.0379674
$743$	−5.78402	−0.212195	−0.106098	−	0.994356i	$-0.533836\pi$
$743$	−5.78402	−0.212195	−0.106098	+	0.994356i	$0.533836\pi$
$744$	−0.788660	−0.0289137
$745$	13.6738	0.500968
$746$	17.2294	0.630812
$747$	−46.8793	−1.71523
$748$	−0.258960	−0.00946853
$749$	−8.13985	−0.297423
$750$	0.0348542	0.00127270
$751$	37.6508	1.37390	0.686948	−	0.726707i	$-0.258950\pi$
$751$	37.6508	1.37390	0.686948	+	0.726707i	$0.258950\pi$
$752$	−9.62058	−0.350827
$753$	−1.77970	−0.0648560
$754$	−4.27720	−0.155766
$755$	−1.73480	−0.0631360
$756$	−2.11850	−0.0770492
$757$	37.3917	1.35902	0.679512	−	0.733664i	$-0.262192\pi$
$757$	37.3917	1.35902	0.679512	+	0.733664i	$0.262192\pi$
$758$	4.76536	0.173086
$759$	−0.440831	−0.0160011
$760$	9.25371	0.335667
$761$	6.93789	0.251498	0.125749	−	0.992062i	$-0.459867\pi$
$761$	6.93789	0.251498	0.125749	+	0.992062i	$0.459867\pi$
$762$	0.344359	0.0124748
$763$	−8.70974	−0.315314
$764$	−12.7013	−0.459515
$765$	−0.444125	−0.0160574
$766$	16.0843	0.581149
$767$	25.5769	0.923527
$768$	−0.0450603	−0.00162597
$769$	−8.74815	−0.315466	−0.157733	−	0.987482i	$-0.550419\pi$
$769$	−8.74815	−0.315466	−0.157733	+	0.987482i	$0.550419\pi$
$770$	−1.47192	−0.0530442
$771$	0.897120	0.0323090
$772$	−36.7406	−1.32232
$773$	−45.8116	−1.64773	−0.823864	−	0.566788i	$-0.808186\pi$
$773$	−45.8116	−1.64773	−0.823864	+	0.566788i	$0.808186\pi$
$774$	−0.613889	−0.0220658
$775$	6.03969	0.216952
$776$	−32.4111	−1.16349
$777$	1.21826	0.0437048
$778$	−13.9981	−0.501856
$779$	−5.23044	−0.187400
$780$	−0.693191	−0.0248202
$781$	6.20880	0.222168
$782$	−0.475514	−0.0170044
$783$	0.614713	0.0219681
$784$	3.92816	0.140292
$785$	4.58342	0.163589
$786$	−0.00161047	−5.74437e−5 0
$787$	2.08207	0.0742179	0.0371089	−	0.999311i	$-0.488185\pi$
$787$	2.08207	0.0742179	0.0371089	+	0.999311i	$0.488185\pi$
$788$	−20.7446	−0.738994
$789$	−2.04714	−0.0728802
$790$	−3.88050	−0.138062
$791$	−16.2604	−0.578153
$792$	5.65043	0.200779
$793$	−12.4800	−0.443176
$794$	11.5443	0.409691
$795$	0.0486352	0.00172491
$796$	−41.2536	−1.46220
$797$	23.1135	0.818722	0.409361	−	0.912372i	$-0.365752\pi$
$797$	23.1135	0.818722	0.409361	+	0.912372i	$0.365752\pi$
$798$	0.499765	0.0176915
$799$	−0.560968	−0.0198456
$800$	5.05347	0.178667
$801$	−10.8744	−0.384228
$802$	−2.42970	−0.0857957
$803$	1.00000	0.0352892
$804$	−0.570341	−0.0201144
$805$	18.6166	0.656148
$806$	17.4392	0.614270
$807$	1.56516	0.0550961
$808$	−23.4867	−0.826258
$809$	−7.46910	−0.262600	−0.131300	−	0.991343i	$-0.541915\pi$
$809$	−7.46910	−0.262600	−0.131300	+	0.991343i	$0.541915\pi$
$810$	4.51017	0.158471
$811$	2.00979	0.0705732	0.0352866	−	0.999377i	$-0.488766\pi$
$811$	2.00979	0.0705732	0.0352866	+	0.999377i	$0.488766\pi$
$812$	−7.56226	−0.265383
$813$	−1.76622	−0.0619441
$814$	−3.03183	−0.106266
$815$	−19.5809	−0.685889
$816$	0.0260999	0.000913681 0
$817$	−1.99659	−0.0698519
$818$	3.08022	0.107697
$819$	50.2057	1.75433
$820$	−1.86222	−0.0650317
$821$	51.5046	1.79752	0.898762	−	0.438437i	$-0.144468\pi$
$821$	51.5046	1.79752	0.898762	+	0.438437i	$0.144468\pi$
$822$	0.476955	0.0166357
$823$	−11.1764	−0.389586	−0.194793	−	0.980844i	$-0.562403\pi$
$823$	−11.1764	−0.389586	−0.194793	+	0.980844i	$0.562403\pi$
$824$	−22.9687	−0.800152
$825$	0.0692183	0.00240987
$826$	−6.56529	−0.228436
$827$	−51.5815	−1.79367	−0.896833	−	0.442370i	$-0.854138\pi$
$827$	−51.5815	−1.79367	−0.896833	+	0.442370i	$0.854138\pi$
$828$	−33.3145	−1.15776
$829$	−3.50380	−0.121692	−0.0608460	−	0.998147i	$-0.519380\pi$
$829$	−3.50380	−0.121692	−0.0608460	+	0.998147i	$0.519380\pi$
$830$	7.88114	0.273558
$831$	1.28417	0.0445472
$832$	−14.5725	−0.505212
$833$	0.229048	0.00793604
$834$	0.0441766	0.00152971
$835$	−1.67099	−0.0578268
$836$	8.56677	0.296288
$837$	−2.50634	−0.0866318
$838$	12.2649	0.423685
$839$	−4.04675	−0.139709	−0.0698547	−	0.997557i	$-0.522254\pi$
$839$	−4.04675	−0.139709	−0.0698547	+	0.997557i	$0.522254\pi$
$840$	0.381701	0.0131699
$841$	−26.8057	−0.924335
$842$	−11.8285	−0.407636
$843$	1.02860	0.0354270
$844$	−40.3118	−1.38759
$845$	19.8817	0.683951
$846$	5.70587	0.196172
$847$	−2.92313	−0.100440
$848$	1.78678	0.0613583
$849$	0.425176	0.0145920
$850$	0.0746642	0.00256096
$851$	38.3461	1.31449
$852$	−0.750556	−0.0257136
$853$	−12.0050	−0.411044	−0.205522	−	0.978652i	$-0.565889\pi$
$853$	−12.0050	−0.411044	−0.205522	+	0.978652i	$0.565889\pi$
$854$	3.20346	0.109620
$855$	14.6923	0.502465
$856$	−5.25317	−0.179550
$857$	4.73993	0.161913	0.0809565	−	0.996718i	$-0.474203\pi$
$857$	4.73993	0.161913	0.0809565	+	0.996718i	$0.474203\pi$
$858$	0.199863	0.00682321
$859$	42.0669	1.43530	0.717651	−	0.696403i	$-0.245217\pi$
$859$	42.0669	1.43530	0.717651	+	0.696403i	$0.245217\pi$
$860$	−0.710858	−0.0242401
$861$	−0.215748	−0.00735266
$862$	14.9313	0.508564
$863$	28.5115	0.970541	0.485271	−	0.874364i	$-0.338721\pi$
$863$	28.5115	0.970541	0.485271	+	0.874364i	$0.338721\pi$
$864$	−2.09708	−0.0713440
$865$	−16.9382	−0.575915
$866$	15.8825	0.539708
$867$	−1.17519	−0.0399115
$868$	30.8332	1.04655
$869$	−7.70643	−0.261423
$870$	−0.0516301	−0.00175042
$871$	27.0543	0.916698
$872$	−5.62096	−0.190350
$873$	−51.4596	−1.74164
$874$	15.7307	0.532098
$875$	−2.92313	−0.0988200
$876$	−0.120886	−0.00408436
$877$	30.6410	1.03467	0.517337	−	0.855782i	$-0.326923\pi$
$877$	30.6410	1.03467	0.517337	+	0.855782i	$0.326923\pi$
$878$	11.1509	0.376326
$879$	−0.822903	−0.0277558
$880$	2.54297	0.0857235
$881$	−0.352856	−0.0118880	−0.00594402	−	0.999982i	$-0.501892\pi$
$881$	−0.352856	−0.0118880	−0.00594402	+	0.999982i	$0.501892\pi$
$882$	−2.32976	−0.0784469
$883$	−22.9728	−0.773097	−0.386548	−	0.922269i	$-0.626333\pi$
$883$	−22.9728	−0.773097	−0.386548	+	0.922269i	$0.626333\pi$
$884$	−1.48494	−0.0499441
$885$	0.308739	0.0103781
$886$	−9.98406	−0.335421
$887$	−7.48394	−0.251286	−0.125643	−	0.992076i	$-0.540099\pi$
$887$	−7.48394	−0.251286	−0.125643	+	0.992076i	$0.540099\pi$
$888$	0.786222	0.0263839
$889$	−28.8806	−0.968623
$890$	1.82815	0.0612798
$891$	8.95690	0.300068
$892$	16.5372	0.553707
$893$	18.5576	0.621007
$894$	0.476588	0.0159395
$895$	2.65541	0.0887606
$896$	33.2845	1.11196
$897$	−2.52784	−0.0844020
$898$	−13.1841	−0.439960
$899$	−8.94669	−0.298389
$900$	5.23097	0.174366
$901$	0.104186	0.00347093
$902$	0.536922	0.0178775
$903$	−0.0823564	−0.00274065
$904$	−10.4939	−0.349021
$905$	−10.5568	−0.350919
$906$	−0.0604653	−0.00200882
$907$	−35.5524	−1.18050	−0.590249	−	0.807222i	$-0.700970\pi$
$907$	−35.5524	−1.18050	−0.590249	+	0.807222i	$0.700970\pi$
$908$	25.8356	0.857383
$909$	−37.2902	−1.23684
$910$	−8.44035	−0.279795
$911$	50.4252	1.67066	0.835331	−	0.549747i	$-0.185276\pi$
$911$	50.4252	1.67066	0.835331	+	0.549747i	$0.185276\pi$
$912$	−0.863423	−0.0285908
$913$	15.6514	0.517987
$914$	−9.75520	−0.322673
$915$	−0.150646	−0.00498019
$916$	18.1257	0.598891
$917$	0.135066	0.00446028
$918$	−0.0309840	−0.00102262
$919$	−10.0332	−0.330964	−0.165482	−	0.986213i	$-0.552918\pi$
$919$	−10.0332	−0.330964	−0.165482	+	0.986213i	$0.552918\pi$
$920$	12.0145	0.396106
$921$	−2.26432	−0.0746119
$922$	15.2138	0.501040
$923$	35.6028	1.17188
$924$	0.353366	0.0116249
$925$	−6.02102	−0.197970
$926$	−3.15542	−0.103693
$927$	−36.4678	−1.19776
$928$	−7.48578	−0.245733
$929$	−25.9326	−0.850821	−0.425410	−	0.905001i	$-0.639870\pi$
$929$	−25.9326	−0.850821	−0.425410	+	0.905001i	$0.639870\pi$
$930$	0.210509	0.00690286
$931$	−7.57723	−0.248334
$932$	11.2604	0.368845
$933$	−1.11689	−0.0365654
$934$	10.7942	0.353197
$935$	0.148278	0.00484922
$936$	32.4010	1.05906
$937$	−5.36428	−0.175243	−0.0876217	−	0.996154i	$-0.527927\pi$
$937$	−5.36428	−0.175243	−0.0876217	+	0.996154i	$0.527927\pi$
$938$	−6.94452	−0.226746
$939$	0.840415	0.0274259
$940$	6.60717	0.215502
$941$	16.7528	0.546124	0.273062	−	0.961996i	$-0.411964\pi$
$941$	16.7528	0.546124	0.273062	+	0.961996i	$0.411964\pi$
$942$	0.159751	0.00520498
$943$	−6.79090	−0.221142
$944$	11.3426	0.369169
$945$	1.21304	0.0394601
$946$	0.204957	0.00666372
$947$	−25.8379	−0.839617	−0.419809	−	0.907613i	$-0.637903\pi$
$947$	−25.8379	−0.839617	−0.419809	+	0.907613i	$0.637903\pi$
$948$	0.931599	0.0302569
$949$	5.73426	0.186142
$950$	−2.47000	−0.0801373
$951$	0.441512	0.0143170
$952$	0.817675	0.0265010
$953$	5.62062	0.182070	0.0910349	−	0.995848i	$-0.470983\pi$
$953$	5.62062	0.182070	0.0910349	+	0.995848i	$0.470983\pi$
$954$	−1.05972	−0.0343097
$955$	7.27263	0.235337
$956$	25.3678	0.820453
$957$	−0.102534	−0.00331445
$958$	−4.15464	−0.134230
$959$	−40.0010	−1.29170
$960$	−0.175905	−0.00567731
$961$	5.47790	0.176707
$962$	−17.3853	−0.560524
$963$	−8.34055	−0.268770
$964$	−5.87477	−0.189214
$965$	21.0373	0.677216
$966$	0.648866	0.0208769
$967$	−37.2610	−1.19823	−0.599117	−	0.800662i	$-0.704481\pi$
$967$	−37.2610	−1.19823	−0.599117	+	0.800662i	$0.704481\pi$
$968$	−1.88649	−0.0606340
$969$	−0.0503454	−0.00161733
$970$	8.65116	0.277772
$971$	−49.2881	−1.58173	−0.790866	−	0.611990i	$-0.790369\pi$
$971$	−49.2881	−1.58173	−0.790866	+	0.611990i	$0.790369\pi$
$972$	−3.25697	−0.104467
$973$	−3.70498	−0.118776
$974$	−1.11901	−0.0358555
$975$	0.396915	0.0127115
$976$	−5.53448	−0.177154
$977$	13.0956	0.418967	0.209483	−	0.977812i	$-0.432822\pi$
$977$	13.0956	0.418967	0.209483	+	0.977812i	$0.432822\pi$
$978$	−0.682477	−0.0218232
$979$	3.63060	0.116034
$980$	−2.69776	−0.0861769
$981$	−8.92449	−0.284937
$982$	20.9738	0.669301
$983$	14.7098	0.469170	0.234585	−	0.972096i	$-0.424627\pi$
$983$	14.7098	0.469170	0.234585	+	0.972096i	$0.424627\pi$
$984$	−0.139236	−0.00443868
$985$	11.8782	0.378469
$986$	−0.110601	−0.00352226
$987$	0.765473	0.0243653
$988$	49.1240	1.56284
$989$	−2.59226	−0.0824291
$990$	−1.50821	−0.0479341
$991$	24.4908	0.777976	0.388988	−	0.921243i	$-0.372825\pi$
$991$	24.4908	0.777976	0.388988	+	0.921243i	$0.372825\pi$
$992$	30.5214	0.969055
$993$	−0.419203	−0.0133030
$994$	−9.13884	−0.289866
$995$	23.6215	0.748851
$996$	−1.89204	−0.0599516
$997$	41.1570	1.30346	0.651728	−	0.758453i	$-0.274044\pi$
$997$	41.1570	1.30346	0.651728	+	0.758453i	$0.274044\pi$
$998$	2.32318	0.0735389
$999$	2.49859	0.0790519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.20	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.20	✓	37	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.503541 q^{2} +0.0692183 q^{3} -1.74645 q^{4} +1.00000 q^{5} +0.0348542 q^{6} -2.92313 q^{7} -1.88649 q^{8} -2.99521 q^{9} +O(q^{10})\)	\(q+0.503541 q^{2} +0.0692183 q^{3} -1.74645 q^{4} +1.00000 q^{5} +0.0348542 q^{6} -2.92313 q^{7} -1.88649 q^{8} -2.99521 q^{9} +0.503541 q^{10} +1.00000 q^{11} -0.120886 q^{12} +5.73426 q^{13} -1.47192 q^{14} +0.0692183 q^{15} +2.54297 q^{16} +0.148278 q^{17} -1.50821 q^{18} -4.90526 q^{19} -1.74645 q^{20} -0.202334 q^{21} +0.503541 q^{22} -6.36870 q^{23} -0.130579 q^{24} +1.00000 q^{25} +2.88743 q^{26} -0.414978 q^{27} +5.10510 q^{28} -1.48132 q^{29} +0.0348542 q^{30} +6.03969 q^{31} +5.05347 q^{32} +0.0692183 q^{33} +0.0746642 q^{34} -2.92313 q^{35} +5.23097 q^{36} -6.02102 q^{37} -2.47000 q^{38} +0.396915 q^{39} -1.88649 q^{40} +1.06629 q^{41} -0.101884 q^{42} +0.407031 q^{43} -1.74645 q^{44} -2.99521 q^{45} -3.20690 q^{46} -3.78321 q^{47} +0.176020 q^{48} +1.54472 q^{49} +0.503541 q^{50} +0.0102636 q^{51} -10.0146 q^{52} +0.702635 q^{53} -0.208958 q^{54} +1.00000 q^{55} +5.51446 q^{56} -0.339533 q^{57} -0.745903 q^{58} +4.46036 q^{59} -0.120886 q^{60} -2.17639 q^{61} +3.04123 q^{62} +8.75540 q^{63} -2.54131 q^{64} +5.73426 q^{65} +0.0348542 q^{66} +4.71801 q^{67} -0.258960 q^{68} -0.440831 q^{69} -1.47192 q^{70} +6.20880 q^{71} +5.65043 q^{72} +1.00000 q^{73} -3.03183 q^{74} +0.0692183 q^{75} +8.56677 q^{76} -2.92313 q^{77} +0.199863 q^{78} -7.70643 q^{79} +2.54297 q^{80} +8.95690 q^{81} +0.536922 q^{82} +15.6514 q^{83} +0.353366 q^{84} +0.148278 q^{85} +0.204957 q^{86} -0.102534 q^{87} -1.88649 q^{88} +3.63060 q^{89} -1.50821 q^{90} -16.7620 q^{91} +11.1226 q^{92} +0.418057 q^{93} -1.90500 q^{94} -4.90526 q^{95} +0.349792 q^{96} +17.1806 q^{97} +0.777827 q^{98} -2.99521 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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