LMFDB - Embedded newform 4015.2.a.b.1.12

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:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-0.182665 q^{2} +1.60195 q^{3} -1.96663 q^{4} +1.00000 q^{5} -0.292620 q^{6} -3.46851 q^{7} +0.724566 q^{8} -0.433762 q^{9} +O(q^{10})$	\(q-0.182665 q^{2} +1.60195 q^{3} -1.96663 q^{4} +1.00000 q^{5} -0.292620 q^{6} -3.46851 q^{7} +0.724566 q^{8} -0.433762 q^{9} -0.182665 q^{10} +1.00000 q^{11} -3.15044 q^{12} +0.962291 q^{13} +0.633577 q^{14} +1.60195 q^{15} +3.80091 q^{16} -0.973228 q^{17} +0.0792333 q^{18} +2.41069 q^{19} -1.96663 q^{20} -5.55638 q^{21} -0.182665 q^{22} +6.07442 q^{23} +1.16072 q^{24} +1.00000 q^{25} -0.175777 q^{26} -5.50071 q^{27} +6.82130 q^{28} +2.63177 q^{29} -0.292620 q^{30} -4.93131 q^{31} -2.14343 q^{32} +1.60195 q^{33} +0.177775 q^{34} -3.46851 q^{35} +0.853051 q^{36} -10.4845 q^{37} -0.440349 q^{38} +1.54154 q^{39} +0.724566 q^{40} -8.05986 q^{41} +1.01496 q^{42} +4.55659 q^{43} -1.96663 q^{44} -0.433762 q^{45} -1.10959 q^{46} +2.01190 q^{47} +6.08887 q^{48} +5.03059 q^{49} -0.182665 q^{50} -1.55906 q^{51} -1.89247 q^{52} +1.88393 q^{53} +1.00479 q^{54} +1.00000 q^{55} -2.51317 q^{56} +3.86180 q^{57} -0.480733 q^{58} +5.30971 q^{59} -3.15044 q^{60} +4.89858 q^{61} +0.900779 q^{62} +1.50451 q^{63} -7.21030 q^{64} +0.962291 q^{65} -0.292620 q^{66} -4.60552 q^{67} +1.91398 q^{68} +9.73091 q^{69} +0.633577 q^{70} -4.05808 q^{71} -0.314290 q^{72} -1.00000 q^{73} +1.91516 q^{74} +1.60195 q^{75} -4.74094 q^{76} -3.46851 q^{77} -0.281586 q^{78} -12.1868 q^{79} +3.80091 q^{80} -7.51056 q^{81} +1.47226 q^{82} -13.0501 q^{83} +10.9274 q^{84} -0.973228 q^{85} -0.832330 q^{86} +4.21596 q^{87} +0.724566 q^{88} -6.44087 q^{89} +0.0792333 q^{90} -3.33772 q^{91} -11.9462 q^{92} -7.89970 q^{93} -0.367504 q^{94} +2.41069 q^{95} -3.43366 q^{96} +6.21334 q^{97} -0.918914 q^{98} -0.433762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * 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 $

$2$	−0.182665	−0.129164	−0.0645819	−	0.997912i	$-0.520571\pi$
$2$	−0.182665	−0.129164	−0.0645819	+	0.997912i	$0.520571\pi$
$3$	1.60195	0.924885	0.462443	−	0.886649i	$-0.346973\pi$
$3$	1.60195	0.924885	0.462443	+	0.886649i	$0.346973\pi$
$4$	−1.96663	−0.983317
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.292620	−0.119462
$7$	−3.46851	−1.31097	−0.655487	−	0.755206i	$-0.727537\pi$
$7$	−3.46851	−1.31097	−0.655487	+	0.755206i	$0.727537\pi$
$8$	0.724566	0.256173
$9$	−0.433762	−0.144587
$10$	−0.182665	−0.0577638
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.15044	−0.909455
$13$	0.962291	0.266891	0.133446	−	0.991056i	$-0.457396\pi$
$13$	0.962291	0.266891	0.133446	+	0.991056i	$0.457396\pi$
$14$	0.633577	0.169331
$15$	1.60195	0.413621
$16$	3.80091	0.950228
$17$	−0.973228	−0.236043	−0.118021	−	0.993011i	$-0.537655\pi$
$17$	−0.973228	−0.236043	−0.118021	+	0.993011i	$0.537655\pi$
$18$	0.0792333	0.0186755
$19$	2.41069	0.553050	0.276525	−	0.961007i	$-0.410817\pi$
$19$	2.41069	0.553050	0.276525	+	0.961007i	$0.410817\pi$
$20$	−1.96663	−0.439753
$21$	−5.55638	−1.21250
$22$	−0.182665	−0.0389444
$23$	6.07442	1.26660	0.633302	−	0.773905i	$-0.281699\pi$
$23$	6.07442	1.26660	0.633302	+	0.773905i	$0.281699\pi$
$24$	1.16072	0.236930
$25$	1.00000	0.200000
$26$	−0.175777	−0.0344727
$27$	−5.50071	−1.05861
$28$	6.82130	1.28910
$29$	2.63177	0.488708	0.244354	−	0.969686i	$-0.421424\pi$
$29$	2.63177	0.488708	0.244354	+	0.969686i	$0.421424\pi$
$30$	−0.292620	−0.0534249
$31$	−4.93131	−0.885690	−0.442845	−	0.896598i	$-0.646031\pi$
$31$	−4.93131	−0.885690	−0.442845	+	0.896598i	$0.646031\pi$
$32$	−2.14343	−0.378908
$33$	1.60195	0.278863
$34$	0.177775	0.0304882
$35$	−3.46851	−0.586286
$36$	0.853051	0.142175
$37$	−10.4845	−1.72365	−0.861825	−	0.507207i	$-0.830678\pi$
$37$	−10.4845	−1.72365	−0.861825	+	0.507207i	$0.830678\pi$
$38$	−0.440349	−0.0714341
$39$	1.54154	0.246844
$40$	0.724566	0.114564
$41$	−8.05986	−1.25874	−0.629369	−	0.777107i	$-0.716687\pi$
$41$	−8.05986	−1.25874	−0.629369	+	0.777107i	$0.716687\pi$
$42$	1.01496	0.156611
$43$	4.55659	0.694873	0.347436	−	0.937704i	$-0.387052\pi$
$43$	4.55659	0.694873	0.347436	+	0.937704i	$0.387052\pi$
$44$	−1.96663	−0.296481
$45$	−0.433762	−0.0646615
$46$	−1.10959	−0.163600
$47$	2.01190	0.293466	0.146733	−	0.989176i	$-0.453124\pi$
$47$	2.01190	0.293466	0.146733	+	0.989176i	$0.453124\pi$
$48$	6.08887	0.878852
$49$	5.03059	0.718655
$50$	−0.182665	−0.0258328
$51$	−1.55906	−0.218312
$52$	−1.89247	−0.262439
$53$	1.88393	0.258778	0.129389	−	0.991594i	$-0.458698\pi$
$53$	1.88393	0.258778	0.129389	+	0.991594i	$0.458698\pi$
$54$	1.00479	0.136734
$55$	1.00000	0.134840
$56$	−2.51317	−0.335836
$57$	3.86180	0.511508
$58$	−0.480733	−0.0631234
$59$	5.30971	0.691266	0.345633	−	0.938370i	$-0.387664\pi$
$59$	5.30971	0.691266	0.345633	+	0.938370i	$0.387664\pi$
$60$	−3.15044	−0.406721
$61$	4.89858	0.627198	0.313599	−	0.949555i	$-0.398465\pi$
$61$	4.89858	0.627198	0.313599	+	0.949555i	$0.398465\pi$
$62$	0.900779	0.114399
$63$	1.50451	0.189551
$64$	−7.21030	−0.901287
$65$	0.962291	0.119358
$66$	−0.292620	−0.0360191
$67$	−4.60552	−0.562654	−0.281327	−	0.959612i	$-0.590775\pi$
$67$	−4.60552	−0.562654	−0.281327	+	0.959612i	$0.590775\pi$
$68$	1.91398	0.232105
$69$	9.73091	1.17146
$70$	0.633577	0.0757269
$71$	−4.05808	−0.481605	−0.240803	−	0.970574i	$-0.577411\pi$
$71$	−4.05808	−0.481605	−0.240803	+	0.970574i	$0.577411\pi$
$72$	−0.314290	−0.0370394
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	1.91516	0.222633
$75$	1.60195	0.184977
$76$	−4.74094	−0.543823
$77$	−3.46851	−0.395274
$78$	−0.281586	−0.0318833
$79$	−12.1868	−1.37113	−0.685563	−	0.728013i	$-0.740444\pi$
$79$	−12.1868	−1.37113	−0.685563	+	0.728013i	$0.740444\pi$
$80$	3.80091	0.424955
$81$	−7.51056	−0.834507
$82$	1.47226	0.162583
$83$	−13.0501	−1.43243	−0.716217	−	0.697877i	$-0.754128\pi$
$83$	−13.0501	−1.43243	−0.716217	+	0.697877i	$0.754128\pi$
$84$	10.9274	1.19227
$85$	−0.973228	−0.105561
$86$	−0.832330	−0.0897525
$87$	4.21596	0.451998
$88$	0.724566	0.0772390
$89$	−6.44087	−0.682731	−0.341366	−	0.939931i	$-0.610889\pi$
$89$	−6.44087	−0.682731	−0.341366	+	0.939931i	$0.610889\pi$
$90$	0.0792333	0.00835192
$91$	−3.33772	−0.349888
$92$	−11.9462	−1.24547
$93$	−7.89970	−0.819161
$94$	−0.367504	−0.0379052
$95$	2.41069	0.247331
$96$	−3.43366	−0.350446
$97$	6.21334	0.630869	0.315435	−	0.948947i	$-0.397850\pi$
$97$	6.21334	0.630869	0.315435	+	0.948947i	$0.397850\pi$
$98$	−0.918914	−0.0928243
$99$	−0.433762	−0.0435948
$100$	−1.96663	−0.196663
$101$	−4.40392	−0.438206	−0.219103	−	0.975702i	$-0.570313\pi$
$101$	−4.40392	−0.438206	−0.219103	+	0.975702i	$0.570313\pi$
$102$	0.284786	0.0281981
$103$	−14.0164	−1.38107	−0.690537	−	0.723297i	$-0.742626\pi$
$103$	−14.0164	−1.38107	−0.690537	+	0.723297i	$0.742626\pi$
$104$	0.697243	0.0683703
$105$	−5.55638	−0.542247
$106$	−0.344129	−0.0334248
$107$	2.12397	0.205332	0.102666	−	0.994716i	$-0.467263\pi$
$107$	2.12397	0.205332	0.102666	+	0.994716i	$0.467263\pi$
$108$	10.8179	1.04095
$109$	−11.1442	−1.06742	−0.533710	−	0.845668i	$-0.679203\pi$
$109$	−11.1442	−1.06742	−0.533710	+	0.845668i	$0.679203\pi$
$110$	−0.182665	−0.0174165
$111$	−16.7957	−1.59418
$112$	−13.1835	−1.24573
$113$	−2.26984	−0.213528	−0.106764	−	0.994284i	$-0.534049\pi$
$113$	−2.26984	−0.213528	−0.106764	+	0.994284i	$0.534049\pi$
$114$	−0.705416	−0.0660683
$115$	6.07442	0.566443
$116$	−5.17573	−0.480554
$117$	−0.417406	−0.0385892
$118$	−0.969900	−0.0892866
$119$	3.37566	0.309446
$120$	1.16072	0.105959
$121$	1.00000	0.0909091
$122$	−0.894800	−0.0810114
$123$	−12.9115	−1.16419
$124$	9.69808	0.870913
$125$	1.00000	0.0894427
$126$	−0.274822	−0.0244831
$127$	4.20796	0.373396	0.186698	−	0.982417i	$-0.440221\pi$
$127$	4.20796	0.373396	0.186698	+	0.982417i	$0.440221\pi$
$128$	5.60393	0.495322
$129$	7.29942	0.642678
$130$	−0.175777	−0.0154167
$131$	−11.5137	−1.00595	−0.502977	−	0.864300i	$-0.667762\pi$
$131$	−11.5137	−1.00595	−0.502977	+	0.864300i	$0.667762\pi$
$132$	−3.15044	−0.274211
$133$	−8.36151	−0.725035
$134$	0.841268	0.0726745
$135$	−5.50071	−0.473426
$136$	−0.705168	−0.0604677
$137$	7.02639	0.600305	0.300152	−	0.953891i	$-0.402962\pi$
$137$	7.02639	0.600305	0.300152	+	0.953891i	$0.402962\pi$
$138$	−1.77750	−0.151311
$139$	−16.7675	−1.42220	−0.711100	−	0.703091i	$-0.751803\pi$
$139$	−16.7675	−1.42220	−0.711100	+	0.703091i	$0.751803\pi$
$140$	6.82130	0.576505
$141$	3.22296	0.271422
$142$	0.741270	0.0622060
$143$	0.962291	0.0804708
$144$	−1.64869	−0.137391
$145$	2.63177	0.218557
$146$	0.182665	0.0151175
$147$	8.05874	0.664674
$148$	20.6193	1.69489
$149$	−4.62686	−0.379047	−0.189524	−	0.981876i	$-0.560694\pi$
$149$	−4.62686	−0.379047	−0.189524	+	0.981876i	$0.560694\pi$
$150$	−0.292620	−0.0238923
$151$	−19.1401	−1.55760	−0.778799	−	0.627274i	$-0.784171\pi$
$151$	−19.1401	−1.55760	−0.778799	+	0.627274i	$0.784171\pi$
$152$	1.74670	0.141676
$153$	0.422150	0.0341288
$154$	0.633577	0.0510551
$155$	−4.93131	−0.396092
$156$	−3.03164	−0.242726
$157$	11.3097	0.902610	0.451305	−	0.892370i	$-0.350959\pi$
$157$	11.3097	0.902610	0.451305	+	0.892370i	$0.350959\pi$
$158$	2.22611	0.177100
$159$	3.01796	0.239340
$160$	−2.14343	−0.169453
$161$	−21.0692	−1.66049
$162$	1.37192	0.107788
$163$	−24.0552	−1.88415	−0.942074	−	0.335405i	$-0.891127\pi$
$163$	−24.0552	−1.88415	−0.942074	+	0.335405i	$0.891127\pi$
$164$	15.8508	1.23774
$165$	1.60195	0.124711
$166$	2.38380	0.185019
$167$	3.29189	0.254734	0.127367	−	0.991856i	$-0.459347\pi$
$167$	3.29189	0.254734	0.127367	+	0.991856i	$0.459347\pi$
$168$	−4.02596	−0.310610
$169$	−12.0740	−0.928769
$170$	0.177775	0.0136347
$171$	−1.04567	−0.0799641
$172$	−8.96114	−0.683280
$173$	3.24197	0.246482	0.123241	−	0.992377i	$-0.460671\pi$
$173$	3.24197	0.246482	0.123241	+	0.992377i	$0.460671\pi$
$174$	−0.770110	−0.0583819
$175$	−3.46851	−0.262195
$176$	3.80091	0.286505
$177$	8.50588	0.639341
$178$	1.17652	0.0881842
$179$	22.0275	1.64641	0.823206	−	0.567743i	$-0.192183\pi$
$179$	22.0275	1.64641	0.823206	+	0.567743i	$0.192183\pi$
$180$	0.853051	0.0635827
$181$	15.5292	1.15428	0.577139	−	0.816646i	$-0.304169\pi$
$181$	15.5292	1.15428	0.577139	+	0.816646i	$0.304169\pi$
$182$	0.609685	0.0451929
$183$	7.84727	0.580087
$184$	4.40132	0.324470
$185$	−10.4845	−0.770839
$186$	1.44300	0.105806
$187$	−0.973228	−0.0711695
$188$	−3.95667	−0.288570
$189$	19.0793	1.38781
$190$	−0.440349	−0.0319463
$191$	16.1522	1.16873	0.584365	−	0.811491i	$-0.301344\pi$
$191$	16.1522	1.16873	0.584365	+	0.811491i	$0.301344\pi$
$192$	−11.5505	−0.833587
$193$	−9.06264	−0.652343	−0.326172	−	0.945311i	$-0.605759\pi$
$193$	−9.06264	−0.652343	−0.326172	+	0.945311i	$0.605759\pi$
$194$	−1.13496	−0.0814855
$195$	1.54154	0.110392
$196$	−9.89332	−0.706666
$197$	−22.8203	−1.62588	−0.812940	−	0.582347i	$-0.802134\pi$
$197$	−22.8203	−1.62588	−0.812940	+	0.582347i	$0.802134\pi$
$198$	0.0792333	0.00563087
$199$	−16.0897	−1.14057	−0.570283	−	0.821448i	$-0.693167\pi$
$199$	−16.0897	−1.14057	−0.570283	+	0.821448i	$0.693167\pi$
$200$	0.724566	0.0512346
$201$	−7.37780	−0.520390
$202$	0.804443	0.0566004
$203$	−9.12833	−0.640683
$204$	3.06610	0.214670
$205$	−8.05986	−0.562925
$206$	2.56030	0.178385
$207$	−2.63486	−0.183135
$208$	3.65758	0.253608
$209$	2.41069	0.166751
$210$	1.01496	0.0700387
$211$	7.97794	0.549224	0.274612	−	0.961555i	$-0.411451\pi$
$211$	7.97794	0.549224	0.274612	+	0.961555i	$0.411451\pi$
$212$	−3.70501	−0.254461
$213$	−6.50083	−0.445430
$214$	−0.387975	−0.0265215
$215$	4.55659	0.310757
$216$	−3.98563	−0.271188
$217$	17.1043	1.16112
$218$	2.03566	0.137872
$219$	−1.60195	−0.108250
$220$	−1.96663	−0.132590
$221$	−0.936529	−0.0629978
$222$	3.06799	0.205910
$223$	−3.41839	−0.228913	−0.114456	−	0.993428i	$-0.536513\pi$
$223$	−3.41839	−0.228913	−0.114456	+	0.993428i	$0.536513\pi$
$224$	7.43451	0.496739
$225$	−0.433762	−0.0289175
$226$	0.414620	0.0275801
$227$	−12.1397	−0.805741	−0.402871	−	0.915257i	$-0.631988\pi$
$227$	−12.1397	−0.805741	−0.402871	+	0.915257i	$0.631988\pi$
$228$	−7.59474	−0.502974
$229$	16.6891	1.10285	0.551423	−	0.834226i	$-0.314085\pi$
$229$	16.6891	1.10285	0.551423	+	0.834226i	$0.314085\pi$
$230$	−1.10959	−0.0731639
$231$	−5.55638	−0.365583
$232$	1.90689	0.125194
$233$	3.46254	0.226839	0.113419	−	0.993547i	$-0.463820\pi$
$233$	3.46254	0.226839	0.113419	+	0.993547i	$0.463820\pi$
$234$	0.0762455	0.00498432
$235$	2.01190	0.131242
$236$	−10.4423	−0.679733
$237$	−19.5227	−1.26813
$238$	−0.616615	−0.0399692
$239$	−1.88879	−0.122176	−0.0610879	−	0.998132i	$-0.519457\pi$
$239$	−1.88879	−0.122176	−0.0610879	+	0.998132i	$0.519457\pi$
$240$	6.08887	0.393035
$241$	−27.7387	−1.78681	−0.893405	−	0.449252i	$-0.851690\pi$
$241$	−27.7387	−1.78681	−0.893405	+	0.449252i	$0.851690\pi$
$242$	−0.182665	−0.0117422
$243$	4.47059	0.286789
$244$	−9.63370	−0.616735
$245$	5.03059	0.321392
$246$	2.35848	0.150371
$247$	2.31978	0.147604
$248$	−3.57306	−0.226890
$249$	−20.9056	−1.32484
$250$	−0.182665	−0.0115528
$251$	20.2914	1.28078	0.640392	−	0.768049i	$-0.278772\pi$
$251$	20.2914	1.28078	0.640392	+	0.768049i	$0.278772\pi$
$252$	−2.95882	−0.186388
$253$	6.07442	0.381896
$254$	−0.768649	−0.0482293
$255$	−1.55906	−0.0976322
$256$	13.3970	0.837310
$257$	−10.9697	−0.684271	−0.342136	−	0.939651i	$-0.611150\pi$
$257$	−10.9697	−0.684271	−0.342136	+	0.939651i	$0.611150\pi$
$258$	−1.33335	−0.0830107
$259$	36.3658	2.25966
$260$	−1.89247	−0.117366
$261$	−1.14156	−0.0706610
$262$	2.10315	0.129933
$263$	15.6112	0.962631	0.481315	−	0.876547i	$-0.340159\pi$
$263$	15.6112	0.962631	0.481315	+	0.876547i	$0.340159\pi$
$264$	1.16072	0.0714372
$265$	1.88393	0.115729
$266$	1.52736	0.0936483
$267$	−10.3179	−0.631448
$268$	9.05737	0.553267
$269$	20.4205	1.24506	0.622531	−	0.782595i	$-0.286104\pi$
$269$	20.4205	1.24506	0.622531	+	0.782595i	$0.286104\pi$
$270$	1.00479	0.0611495
$271$	−22.5860	−1.37200	−0.686001	−	0.727600i	$-0.740636\pi$
$271$	−22.5860	−1.37200	−0.686001	+	0.727600i	$0.740636\pi$
$272$	−3.69916	−0.224294
$273$	−5.34685	−0.323606
$274$	−1.28348	−0.0775377
$275$	1.00000	0.0603023
$276$	−19.1371	−1.15192
$277$	1.71132	0.102824	0.0514118	−	0.998678i	$-0.483628\pi$
$277$	1.71132	0.102824	0.0514118	+	0.998678i	$0.483628\pi$
$278$	3.06284	0.183697
$279$	2.13902	0.128060
$280$	−2.51317	−0.150191
$281$	22.8990	1.36604	0.683021	−	0.730399i	$-0.260666\pi$
$281$	22.8990	1.36604	0.683021	+	0.730399i	$0.260666\pi$
$282$	−0.588723	−0.0350579
$283$	−4.45860	−0.265036	−0.132518	−	0.991181i	$-0.542306\pi$
$283$	−4.45860	−0.265036	−0.132518	+	0.991181i	$0.542306\pi$
$284$	7.98076	0.473571
$285$	3.86180	0.228753
$286$	−0.175777	−0.0103939
$287$	27.9557	1.65017
$288$	0.929738	0.0547853
$289$	−16.0528	−0.944284
$290$	−0.480733	−0.0282296
$291$	9.95345	0.583481
$292$	1.96663	0.115089
$293$	6.09117	0.355850	0.177925	−	0.984044i	$-0.443062\pi$
$293$	6.09117	0.355850	0.177925	+	0.984044i	$0.443062\pi$
$294$	−1.47205	−0.0858518
$295$	5.30971	0.309143
$296$	−7.59675	−0.441552
$297$	−5.50071	−0.319184
$298$	0.845167	0.0489592
$299$	5.84536	0.338046
$300$	−3.15044	−0.181891
$301$	−15.8046	−0.910961
$302$	3.49623	0.201185
$303$	−7.05485	−0.405290
$304$	9.16282	0.525524
$305$	4.89858	0.280492
$306$	−0.0771121	−0.00440821
$307$	−13.5427	−0.772921	−0.386460	−	0.922306i	$-0.626302\pi$
$307$	−13.5427	−0.772921	−0.386460	+	0.922306i	$0.626302\pi$
$308$	6.82130	0.388679
$309$	−22.4535	−1.27733
$310$	0.900779	0.0511608
$311$	8.54169	0.484355	0.242178	−	0.970232i	$-0.422138\pi$
$311$	8.54169	0.484355	0.242178	+	0.970232i	$0.422138\pi$
$312$	1.11695	0.0632347
$313$	4.80470	0.271577	0.135789	−	0.990738i	$-0.456643\pi$
$313$	4.80470	0.271577	0.135789	+	0.990738i	$0.456643\pi$
$314$	−2.06589	−0.116585
$315$	1.50451	0.0847696
$316$	23.9670	1.34825
$317$	−4.22151	−0.237104	−0.118552	−	0.992948i	$-0.537825\pi$
$317$	−4.22151	−0.237104	−0.118552	+	0.992948i	$0.537825\pi$
$318$	−0.551277	−0.0309141
$319$	2.63177	0.147351
$320$	−7.21030	−0.403068
$321$	3.40249	0.189908
$322$	3.84861	0.214475
$323$	−2.34615	−0.130543
$324$	14.7705	0.820585
$325$	0.962291	0.0533783
$326$	4.39405	0.243364
$327$	−17.8524	−0.987241
$328$	−5.83990	−0.322454
$329$	−6.97830	−0.384726
$330$	−0.292620	−0.0161082
$331$	−1.63548	−0.0898942	−0.0449471	−	0.998989i	$-0.514312\pi$
$331$	−1.63548	−0.0898942	−0.0449471	+	0.998989i	$0.514312\pi$
$332$	25.6648	1.40854
$333$	4.54780	0.249218
$334$	−0.601315	−0.0329025
$335$	−4.60552	−0.251626
$336$	−21.1193	−1.15215
$337$	21.1591	1.15261	0.576305	−	0.817235i	$-0.304494\pi$
$337$	21.1591	1.15261	0.576305	+	0.817235i	$0.304494\pi$
$338$	2.20550	0.119963
$339$	−3.63616	−0.197489
$340$	1.91398	0.103800
$341$	−4.93131	−0.267045
$342$	0.191007	0.0103285
$343$	6.83093	0.368836
$344$	3.30155	0.178008
$345$	9.73091	0.523895
$346$	−0.592195	−0.0318366
$347$	−19.7377	−1.05957	−0.529787	−	0.848131i	$-0.677728\pi$
$347$	−19.7377	−1.05957	−0.529787	+	0.848131i	$0.677728\pi$
$348$	−8.29125	−0.444458
$349$	11.0357	0.590729	0.295365	−	0.955385i	$-0.404559\pi$
$349$	11.0357	0.590729	0.295365	+	0.955385i	$0.404559\pi$
$350$	0.633577	0.0338661
$351$	−5.29328	−0.282535
$352$	−2.14343	−0.114245
$353$	4.41812	0.235153	0.117576	−	0.993064i	$-0.462487\pi$
$353$	4.41812	0.235153	0.117576	+	0.993064i	$0.462487\pi$
$354$	−1.55373	−0.0825798
$355$	−4.05808	−0.215381
$356$	12.6668	0.671341
$357$	5.40763	0.286202
$358$	−4.02366	−0.212657
$359$	35.6209	1.88000	0.940001	−	0.341172i	$-0.110824\pi$
$359$	35.6209	1.88000	0.940001	+	0.341172i	$0.110824\pi$
$360$	−0.314290	−0.0165645
$361$	−13.1886	−0.694136
$362$	−2.83665	−0.149091
$363$	1.60195	0.0840805
$364$	6.56407	0.344051
$365$	−1.00000	−0.0523424
$366$	−1.43342	−0.0749262
$367$	−18.4423	−0.962681	−0.481341	−	0.876534i	$-0.659850\pi$
$367$	−18.4423	−0.962681	−0.481341	+	0.876534i	$0.659850\pi$
$368$	23.0884	1.20356
$369$	3.49606	0.181998
$370$	1.91516	0.0995646
$371$	−6.53445	−0.339252
$372$	15.5358	0.805495
$373$	−3.21895	−0.166671	−0.0833355	−	0.996522i	$-0.526557\pi$
$373$	−3.21895	−0.166671	−0.0833355	+	0.996522i	$0.526557\pi$
$374$	0.177775	0.00919253
$375$	1.60195	0.0827242
$376$	1.45775	0.0751779
$377$	2.53253	0.130432
$378$	−3.48512	−0.179255
$379$	3.62305	0.186104	0.0930518	−	0.995661i	$-0.470338\pi$
$379$	3.62305	0.186104	0.0930518	+	0.995661i	$0.470338\pi$
$380$	−4.74094	−0.243205
$381$	6.74094	0.345349
$382$	−2.95044	−0.150958
$383$	5.05248	0.258170	0.129085	−	0.991634i	$-0.458796\pi$
$383$	5.05248	0.258170	0.129085	+	0.991634i	$0.458796\pi$
$384$	8.97720	0.458116
$385$	−3.46851	−0.176772
$386$	1.65543	0.0842592
$387$	−1.97648	−0.100470
$388$	−12.2194	−0.620344
$389$	−27.4082	−1.38965	−0.694825	−	0.719179i	$-0.744518\pi$
$389$	−27.4082	−1.38965	−0.694825	+	0.719179i	$0.744518\pi$
$390$	−0.281586	−0.0142587
$391$	−5.91180	−0.298973
$392$	3.64499	0.184100
$393$	−18.4443	−0.930393
$394$	4.16848	0.210005
$395$	−12.1868	−0.613186
$396$	0.853051	0.0428674
$397$	−21.3526	−1.07166	−0.535828	−	0.844327i	$-0.680001\pi$
$397$	−21.3526	−1.07166	−0.535828	+	0.844327i	$0.680001\pi$
$398$	2.93902	0.147320
$399$	−13.3947	−0.670574
$400$	3.80091	0.190046
$401$	12.6620	0.632309	0.316154	−	0.948708i	$-0.397608\pi$
$401$	12.6620	0.632309	0.316154	+	0.948708i	$0.397608\pi$
$402$	1.34767	0.0672156
$403$	−4.74536	−0.236383
$404$	8.66089	0.430895
$405$	−7.51056	−0.373203
$406$	1.66743	0.0827531
$407$	−10.4845	−0.519700
$408$	−1.12964	−0.0559257
$409$	−23.8342	−1.17853	−0.589263	−	0.807941i	$-0.700582\pi$
$409$	−23.8342	−1.17853	−0.589263	+	0.807941i	$0.700582\pi$
$410$	1.47226	0.0727095
$411$	11.2559	0.555213
$412$	27.5650	1.35803
$413$	−18.4168	−0.906232
$414$	0.481297	0.0236544
$415$	−13.0501	−0.640604
$416$	−2.06260	−0.101127
$417$	−26.8607	−1.31537
$418$	−0.440349	−0.0215382
$419$	−3.48747	−0.170374	−0.0851871	−	0.996365i	$-0.527149\pi$
$419$	−3.48747	−0.170374	−0.0851871	+	0.996365i	$0.527149\pi$
$420$	10.9274	0.533201
$421$	26.5865	1.29575	0.647873	−	0.761748i	$-0.275659\pi$
$421$	26.5865	1.29575	0.647873	+	0.761748i	$0.275659\pi$
$422$	−1.45729	−0.0709399
$423$	−0.872686	−0.0424314
$424$	1.36504	0.0662920
$425$	−0.973228	−0.0472085
$426$	1.18748	0.0575334
$427$	−16.9908	−0.822242
$428$	−4.17707	−0.201906
$429$	1.54154	0.0744263
$430$	−0.832330	−0.0401385
$431$	−20.6833	−0.996280	−0.498140	−	0.867097i	$-0.665983\pi$
$431$	−20.6833	−0.996280	−0.498140	+	0.867097i	$0.665983\pi$
$432$	−20.9077	−1.00592
$433$	−23.9198	−1.14951	−0.574756	−	0.818325i	$-0.694903\pi$
$433$	−23.9198	−1.14951	−0.574756	+	0.818325i	$0.694903\pi$
$434$	−3.12437	−0.149974
$435$	4.21596	0.202140
$436$	21.9165	1.04961
$437$	14.6435	0.700496
$438$	0.292620	0.0139819
$439$	−5.40904	−0.258159	−0.129080	−	0.991634i	$-0.541202\pi$
$439$	−5.40904	−0.258159	−0.129080	+	0.991634i	$0.541202\pi$
$440$	0.724566	0.0345423
$441$	−2.18208	−0.103909
$442$	0.171071	0.00813703
$443$	26.7300	1.26998	0.634990	−	0.772520i	$-0.281004\pi$
$443$	26.7300	1.26998	0.634990	+	0.772520i	$0.281004\pi$
$444$	33.0310	1.56758
$445$	−6.44087	−0.305327
$446$	0.624422	0.0295672
$447$	−7.41199	−0.350575
$448$	25.0090	1.18156
$449$	7.96772	0.376020	0.188010	−	0.982167i	$-0.439796\pi$
$449$	7.96772	0.376020	0.188010	+	0.982167i	$0.439796\pi$
$450$	0.0792333	0.00373509
$451$	−8.05986	−0.379524
$452$	4.46393	0.209966
$453$	−30.6614	−1.44060
$454$	2.21750	0.104073
$455$	−3.33772	−0.156475
$456$	2.79813	0.131034
$457$	9.36258	0.437963	0.218982	−	0.975729i	$-0.429727\pi$
$457$	9.36258	0.437963	0.218982	+	0.975729i	$0.429727\pi$
$458$	−3.04852	−0.142448
$459$	5.35345	0.249877
$460$	−11.9462	−0.556993
$461$	−36.9208	−1.71957	−0.859787	−	0.510653i	$-0.829404\pi$
$461$	−36.9208	−1.71957	−0.859787	+	0.510653i	$0.829404\pi$
$462$	1.01496	0.0472201
$463$	22.1352	1.02871	0.514355	−	0.857577i	$-0.328031\pi$
$463$	22.1352	1.02871	0.514355	+	0.857577i	$0.328031\pi$
$464$	10.0031	0.464384
$465$	−7.89970	−0.366340
$466$	−0.632486	−0.0292994
$467$	6.60098	0.305457	0.152729	−	0.988268i	$-0.451194\pi$
$467$	6.60098	0.305457	0.152729	+	0.988268i	$0.451194\pi$
$468$	0.820884	0.0379454
$469$	15.9743	0.737625
$470$	−0.367504	−0.0169517
$471$	18.1175	0.834811
$472$	3.84724	0.177084
$473$	4.55659	0.209512
$474$	3.56612	0.163797
$475$	2.41069	0.110610
$476$	−6.63868	−0.304283
$477$	−0.817180	−0.0374161
$478$	0.345017	0.0157807
$479$	−33.3721	−1.52481	−0.762405	−	0.647100i	$-0.775982\pi$
$479$	−33.3721	−1.52481	−0.762405	+	0.647100i	$0.775982\pi$
$480$	−3.43366	−0.156724
$481$	−10.0892	−0.460027
$482$	5.06691	0.230791
$483$	−33.7518	−1.53576
$484$	−1.96663	−0.0893924
$485$	6.21334	0.282133
$486$	−0.816622	−0.0370427
$487$	23.0114	1.04275	0.521373	−	0.853329i	$-0.325420\pi$
$487$	23.0114	1.04275	0.521373	+	0.853329i	$0.325420\pi$
$488$	3.54934	0.160671
$489$	−38.5352	−1.74262
$490$	−0.918914	−0.0415123
$491$	−20.0630	−0.905429	−0.452714	−	0.891656i	$-0.649544\pi$
$491$	−20.0630	−0.905429	−0.452714	+	0.891656i	$0.649544\pi$
$492$	25.3921	1.14477
$493$	−2.56131	−0.115356
$494$	−0.423744	−0.0190651
$495$	−0.433762	−0.0194962
$496$	−18.7435	−0.841607
$497$	14.0755	0.631373
$498$	3.81872	0.171121
$499$	12.2233	0.547190	0.273595	−	0.961845i	$-0.411787\pi$
$499$	12.2233	0.547190	0.273595	+	0.961845i	$0.411787\pi$
$500$	−1.96663	−0.0879505
$501$	5.27344	0.235600
$502$	−3.70654	−0.165431
$503$	25.1170	1.11991	0.559955	−	0.828523i	$-0.310818\pi$
$503$	25.1170	1.11991	0.559955	+	0.828523i	$0.310818\pi$
$504$	1.09012	0.0485577
$505$	−4.40392	−0.195972
$506$	−1.10959	−0.0493271
$507$	−19.3419	−0.859005
$508$	−8.27552	−0.367167
$509$	37.2763	1.65224	0.826122	−	0.563491i	$-0.190542\pi$
$509$	37.2763	1.65224	0.826122	+	0.563491i	$0.190542\pi$
$510$	0.284786	0.0126106
$511$	3.46851	0.153438
$512$	−13.6550	−0.603472
$513$	−13.2605	−0.585465
$514$	2.00378	0.0883831
$515$	−14.0164	−0.617635
$516$	−14.3553	−0.631956
$517$	2.01190	0.0884832
$518$	−6.64277	−0.291866
$519$	5.19346	0.227968
$520$	0.697243	0.0305761
$521$	27.8662	1.22084	0.610420	−	0.792078i	$-0.291001\pi$
$521$	27.8662	1.22084	0.610420	+	0.792078i	$0.291001\pi$
$522$	0.208524	0.00912684
$523$	25.5957	1.11922	0.559611	−	0.828756i	$-0.310951\pi$
$523$	25.5957	1.11922	0.559611	+	0.828756i	$0.310951\pi$
$524$	22.6432	0.989172
$525$	−5.55638	−0.242500
$526$	−2.85163	−0.124337
$527$	4.79929	0.209060
$528$	6.08887	0.264984
$529$	13.8986	0.604287
$530$	−0.344129	−0.0149480
$531$	−2.30315	−0.0999483
$532$	16.4440	0.712939
$533$	−7.75593	−0.335946
$534$	1.88473	0.0815603
$535$	2.12397	0.0918272
$536$	−3.33700	−0.144137
$537$	35.2869	1.52274
$538$	−3.73012	−0.160817
$539$	5.03059	0.216683
$540$	10.8179	0.465527
$541$	−3.73085	−0.160402	−0.0802008	−	0.996779i	$-0.525556\pi$
$541$	−3.73085	−0.160402	−0.0802008	+	0.996779i	$0.525556\pi$
$542$	4.12568	0.177213
$543$	24.8770	1.06757
$544$	2.08604	0.0894384
$545$	−11.1442	−0.477365
$546$	0.976684	0.0417982
$547$	26.2872	1.12396	0.561980	−	0.827151i	$-0.310040\pi$
$547$	26.2872	1.12396	0.561980	+	0.827151i	$0.310040\pi$
$548$	−13.8183	−0.590290
$549$	−2.12482	−0.0906850
$550$	−0.182665	−0.00778887
$551$	6.34438	0.270280
$552$	7.05069	0.300097
$553$	42.2702	1.79751
$554$	−0.312600	−0.0132811
$555$	−16.7957	−0.712938
$556$	32.9755	1.39847
$557$	5.17985	0.219477	0.109739	−	0.993960i	$-0.464999\pi$
$557$	5.17985	0.219477	0.109739	+	0.993960i	$0.464999\pi$
$558$	−0.390724	−0.0165407
$559$	4.38476	0.185456
$560$	−13.1835	−0.557105
$561$	−1.55906	−0.0658236
$562$	−4.18286	−0.176443
$563$	−4.44556	−0.187358	−0.0936791	−	0.995602i	$-0.529863\pi$
$563$	−4.44556	−0.187358	−0.0936791	+	0.995602i	$0.529863\pi$
$564$	−6.33838	−0.266894
$565$	−2.26984	−0.0954927
$566$	0.814431	0.0342331
$567$	26.0505	1.09402
$568$	−2.94035	−0.123374
$569$	−42.0989	−1.76488	−0.882438	−	0.470428i	$-0.844099\pi$
$569$	−42.0989	−1.76488	−0.882438	+	0.470428i	$0.844099\pi$
$570$	−0.705416	−0.0295466
$571$	3.25794	0.136340	0.0681702	−	0.997674i	$-0.478284\pi$
$571$	3.25794	0.136340	0.0681702	+	0.997674i	$0.478284\pi$
$572$	−1.89247	−0.0791283
$573$	25.8749	1.08094
$574$	−5.10654	−0.213143
$575$	6.07442	0.253321
$576$	3.12756	0.130315
$577$	−27.8847	−1.16085	−0.580427	−	0.814312i	$-0.697114\pi$
$577$	−27.8847	−1.16085	−0.580427	+	0.814312i	$0.697114\pi$
$578$	2.93229	0.121967
$579$	−14.5179	−0.603343
$580$	−5.17573	−0.214910
$581$	45.2645	1.87789
$582$	−1.81815	−0.0753647
$583$	1.88393	0.0780246
$584$	−0.724566	−0.0299828
$585$	−0.417406	−0.0172576
$586$	−1.11265	−0.0459630
$587$	33.0330	1.36342	0.681708	−	0.731624i	$-0.261237\pi$
$587$	33.0330	1.36342	0.681708	+	0.731624i	$0.261237\pi$
$588$	−15.8486	−0.653585
$589$	−11.8879	−0.489831
$590$	−0.969900	−0.0399302
$591$	−36.5570	−1.50375
$592$	−39.8509	−1.63786
$593$	−39.9192	−1.63928	−0.819642	−	0.572876i	$-0.805828\pi$
$593$	−39.9192	−1.63928	−0.819642	+	0.572876i	$0.805828\pi$
$594$	1.00479	0.0412270
$595$	3.37566	0.138388
$596$	9.09934	0.372723
$597$	−25.7748	−1.05489
$598$	−1.06774	−0.0436633
$599$	16.8649	0.689082	0.344541	−	0.938771i	$-0.388035\pi$
$599$	16.8649	0.689082	0.344541	+	0.938771i	$0.388035\pi$
$600$	1.16072	0.0473861
$601$	−15.3461	−0.625981	−0.312990	−	0.949756i	$-0.601331\pi$
$601$	−15.3461	−0.625981	−0.312990	+	0.949756i	$0.601331\pi$
$602$	2.88695	0.117663
$603$	1.99770	0.0813527
$604$	37.6415	1.53161
$605$	1.00000	0.0406558
$606$	1.28868	0.0523489
$607$	37.3138	1.51452	0.757260	−	0.653113i	$-0.226537\pi$
$607$	37.3138	1.51452	0.757260	+	0.653113i	$0.226537\pi$
$608$	−5.16714	−0.209555
$609$	−14.6231	−0.592559
$610$	−0.894800	−0.0362294
$611$	1.93603	0.0783235
$612$	−0.830214	−0.0335594
$613$	−33.5470	−1.35495	−0.677476	−	0.735545i	$-0.736926\pi$
$613$	−33.5470	−1.35495	−0.677476	+	0.735545i	$0.736926\pi$
$614$	2.47378	0.0998334
$615$	−12.9115	−0.520641
$616$	−2.51317	−0.101258
$617$	−15.3505	−0.617988	−0.308994	−	0.951064i	$-0.599992\pi$
$617$	−15.3505	−0.617988	−0.308994	+	0.951064i	$0.599992\pi$
$618$	4.10147	0.164985
$619$	−37.7981	−1.51924	−0.759618	−	0.650370i	$-0.774614\pi$
$619$	−37.7981	−1.51924	−0.759618	+	0.650370i	$0.774614\pi$
$620$	9.69808	0.389484
$621$	−33.4136	−1.34084
$622$	−1.56027	−0.0625612
$623$	22.3403	0.895044
$624$	5.85926	0.234558
$625$	1.00000	0.0400000
$626$	−0.877651	−0.0350780
$627$	3.86180	0.154225
$628$	−22.2420	−0.887552
$629$	10.2039	0.406855
$630$	−0.274822	−0.0109492
$631$	28.0785	1.11779	0.558893	−	0.829240i	$-0.311226\pi$
$631$	28.0785	1.11779	0.558893	+	0.829240i	$0.311226\pi$
$632$	−8.83017	−0.351245
$633$	12.7802	0.507969
$634$	0.771124	0.0306252
$635$	4.20796	0.166988
$636$	−5.93523	−0.235347
$637$	4.84089	0.191803
$638$	−0.480733	−0.0190324
$639$	1.76024	0.0696341
$640$	5.60393	0.221515
$641$	32.6834	1.29092	0.645458	−	0.763796i	$-0.276667\pi$
$641$	32.6834	1.29092	0.645458	+	0.763796i	$0.276667\pi$
$642$	−0.621517	−0.0245293
$643$	7.79235	0.307300	0.153650	−	0.988125i	$-0.450897\pi$
$643$	7.79235	0.307300	0.153650	+	0.988125i	$0.450897\pi$
$644$	41.4354	1.63278
$645$	7.29942	0.287414
$646$	0.428560	0.0168615
$647$	−7.29004	−0.286601	−0.143301	−	0.989679i	$-0.545772\pi$
$647$	−7.29004	−0.286601	−0.143301	+	0.989679i	$0.545772\pi$
$648$	−5.44190	−0.213778
$649$	5.30971	0.208424
$650$	−0.175777	−0.00689455
$651$	27.4002	1.07390
$652$	47.3077	1.85271
$653$	−48.3319	−1.89137	−0.945686	−	0.325081i	$-0.894609\pi$
$653$	−48.3319	−1.89137	−0.945686	+	0.325081i	$0.894609\pi$
$654$	3.26102	0.127516
$655$	−11.5137	−0.449877
$656$	−30.6348	−1.19609
$657$	0.433762	0.0169227
$658$	1.27469	0.0496927
$659$	41.1840	1.60430	0.802150	−	0.597123i	$-0.203690\pi$
$659$	41.1840	1.60430	0.802150	+	0.597123i	$0.203690\pi$
$660$	−3.15044	−0.122631
$661$	−26.3829	−1.02618	−0.513088	−	0.858336i	$-0.671498\pi$
$661$	−26.3829	−1.02618	−0.513088	+	0.858336i	$0.671498\pi$
$662$	0.298746	0.0116111
$663$	−1.50027	−0.0582657
$664$	−9.45566	−0.366951
$665$	−8.36151	−0.324245
$666$	−0.830725	−0.0321900
$667$	15.9865	0.618999
$668$	−6.47395	−0.250485
$669$	−5.47609	−0.211718
$670$	0.841268	0.0325010
$671$	4.89858	0.189107
$672$	11.9097	0.459426
$673$	23.6237	0.910625	0.455313	−	0.890332i	$-0.349527\pi$
$673$	23.6237	0.910625	0.455313	+	0.890332i	$0.349527\pi$
$674$	−3.86503	−0.148875
$675$	−5.50071	−0.211722
$676$	23.7451	0.913274
$677$	43.3318	1.66538	0.832688	−	0.553743i	$-0.186801\pi$
$677$	43.3318	1.66538	0.832688	+	0.553743i	$0.186801\pi$
$678$	0.664200	0.0255084
$679$	−21.5511	−0.827054
$680$	−0.705168	−0.0270420
$681$	−19.4472	−0.745218
$682$	0.900779	0.0344926
$683$	−5.49554	−0.210281	−0.105140	−	0.994457i	$-0.533529\pi$
$683$	−5.49554	−0.210281	−0.105140	+	0.994457i	$0.533529\pi$
$684$	2.05644	0.0786300
$685$	7.02639	0.268464
$686$	−1.24777	−0.0476402
$687$	26.7350	1.02001
$688$	17.3192	0.660288
$689$	1.81289	0.0690657
$690$	−1.77750	−0.0676682
$691$	−7.61673	−0.289754	−0.144877	−	0.989450i	$-0.546279\pi$
$691$	−7.61673	−0.289754	−0.144877	+	0.989450i	$0.546279\pi$
$692$	−6.37576	−0.242370
$693$	1.50451	0.0571516
$694$	3.60539	0.136859
$695$	−16.7675	−0.636027
$696$	3.05474	0.115790
$697$	7.84408	0.297116
$698$	−2.01585	−0.0763009
$699$	5.54681	0.209800
$700$	6.82130	0.257821
$701$	−20.9263	−0.790376	−0.395188	−	0.918600i	$-0.629321\pi$
$701$	−20.9263	−0.790376	−0.395188	+	0.918600i	$0.629321\pi$
$702$	0.966899	0.0364932
$703$	−25.2750	−0.953264
$704$	−7.21030	−0.271748
$705$	3.22296	0.121384
$706$	−0.807037	−0.0303733
$707$	15.2750	0.574477
$708$	−16.7280	−0.628675
$709$	−42.8181	−1.60807	−0.804033	−	0.594584i	$-0.797317\pi$
$709$	−42.8181	−1.60807	−0.804033	+	0.594584i	$0.797317\pi$
$710$	0.741270	0.0278194
$711$	5.28619	0.198248
$712$	−4.66684	−0.174897
$713$	−29.9549	−1.12182
$714$	−0.987786	−0.0369669
$715$	0.962291	0.0359876
$716$	−43.3200	−1.61894
$717$	−3.02575	−0.112999
$718$	−6.50671	−0.242828
$719$	−0.417369	−0.0155652	−0.00778261	−	0.999970i	$-0.502477\pi$
$719$	−0.417369	−0.0155652	−0.00778261	+	0.999970i	$0.502477\pi$
$720$	−1.64869	−0.0614432
$721$	48.6160	1.81055
$722$	2.40910	0.0896572
$723$	−44.4360	−1.65259
$724$	−30.5403	−1.13502
$725$	2.63177	0.0977415
$726$	−0.292620	−0.0108602
$727$	−44.4491	−1.64853	−0.824264	−	0.566206i	$-0.808411\pi$
$727$	−44.4491	−1.64853	−0.824264	+	0.566206i	$0.808411\pi$
$728$	−2.41840	−0.0896318
$729$	29.6934	1.09975
$730$	0.182665	0.00676075
$731$	−4.43460	−0.164020
$732$	−15.4327	−0.570409
$733$	41.3985	1.52909	0.764544	−	0.644572i	$-0.222964\pi$
$733$	41.3985	1.52909	0.764544	+	0.644572i	$0.222964\pi$
$734$	3.36877	0.124344
$735$	8.05874	0.297251
$736$	−13.0201	−0.479927
$737$	−4.60552	−0.169646
$738$	−0.638609	−0.0235075
$739$	17.7880	0.654344	0.327172	−	0.944965i	$-0.393904\pi$
$739$	17.7880	0.654344	0.327172	+	0.944965i	$0.393904\pi$
$740$	20.6193	0.757979
$741$	3.71617	0.136517
$742$	1.19362	0.0438191
$743$	−0.535161	−0.0196332	−0.00981658	−	0.999952i	$-0.503125\pi$
$743$	−0.535161	−0.0196332	−0.00981658	+	0.999952i	$0.503125\pi$
$744$	−5.72386	−0.209847
$745$	−4.62686	−0.169515
$746$	0.587991	0.0215279
$747$	5.66064	0.207112
$748$	1.91398	0.0699822
$749$	−7.36702	−0.269185
$750$	−0.292620	−0.0106850
$751$	−26.8009	−0.977980	−0.488990	−	0.872290i	$-0.662634\pi$
$751$	−26.8009	−0.977980	−0.488990	+	0.872290i	$0.662634\pi$
$752$	7.64706	0.278859
$753$	32.5058	1.18458
$754$	−0.462605	−0.0168471
$755$	−19.1401	−0.696579
$756$	−37.5220	−1.36466
$757$	−10.2193	−0.371428	−0.185714	−	0.982604i	$-0.559460\pi$
$757$	−10.2193	−0.371428	−0.185714	+	0.982604i	$0.559460\pi$
$758$	−0.661806	−0.0240379
$759$	9.73091	0.353210
$760$	1.74670	0.0633596
$761$	−5.71513	−0.207173	−0.103587	−	0.994620i	$-0.533032\pi$
$761$	−5.71513	−0.207173	−0.103587	+	0.994620i	$0.533032\pi$
$762$	−1.23134	−0.0446066
$763$	38.6538	1.39936
$764$	−31.7654	−1.14923
$765$	0.422150	0.0152629
$766$	−0.922913	−0.0333462
$767$	5.10949	0.184493
$768$	21.4612	0.774415
$769$	−13.0582	−0.470892	−0.235446	−	0.971887i	$-0.575655\pi$
$769$	−13.0582	−0.470892	−0.235446	+	0.971887i	$0.575655\pi$
$770$	0.633577	0.0228325
$771$	−17.5729	−0.632872
$772$	17.8229	0.641460
$773$	19.5219	0.702153	0.351076	−	0.936347i	$-0.385816\pi$
$773$	19.5219	0.702153	0.351076	+	0.936347i	$0.385816\pi$
$774$	0.361033	0.0129771
$775$	−4.93131	−0.177138
$776$	4.50198	0.161612
$777$	58.2561	2.08993
$778$	5.00652	0.179492
$779$	−19.4298	−0.696145
$780$	−3.03164	−0.108550
$781$	−4.05808	−0.145210
$782$	1.07988	0.0386165
$783$	−14.4766	−0.517352
$784$	19.1208	0.682887
$785$	11.3097	0.403660
$786$	3.36914	0.120173
$787$	35.5202	1.26616	0.633080	−	0.774087i	$-0.281790\pi$
$787$	35.5202	1.26616	0.633080	+	0.774087i	$0.281790\pi$
$788$	44.8792	1.59876
$789$	25.0084	0.890323
$790$	2.22611	0.0792015
$791$	7.87296	0.279930
$792$	−0.314290	−0.0111678
$793$	4.71386	0.167394
$794$	3.90038	0.138419
$795$	3.01796	0.107036
$796$	31.6425	1.12154
$797$	−30.4314	−1.07793	−0.538967	−	0.842327i	$-0.681185\pi$
$797$	−30.4314	−1.07793	−0.538967	+	0.842327i	$0.681185\pi$
$798$	2.44675	0.0866139
$799$	−1.95804	−0.0692704
$800$	−2.14343	−0.0757816
$801$	2.79381	0.0987144
$802$	−2.31290	−0.0816714
$803$	−1.00000	−0.0352892
$804$	14.5094	0.511708
$805$	−21.0692	−0.742592
$806$	0.866812	0.0305321
$807$	32.7126	1.15154
$808$	−3.19093	−0.112256
$809$	−29.9735	−1.05381	−0.526906	−	0.849923i	$-0.676648\pi$
$809$	−29.9735	−1.05381	−0.526906	+	0.849923i	$0.676648\pi$
$810$	1.37192	0.0482043
$811$	−30.4167	−1.06808	−0.534038	−	0.845460i	$-0.679326\pi$
$811$	−30.4167	−1.06808	−0.534038	+	0.845460i	$0.679326\pi$
$812$	17.9521	0.629995
$813$	−36.1816	−1.26894
$814$	1.91516	0.0671264
$815$	−24.0552	−0.842617
$816$	−5.92586	−0.207447
$817$	10.9845	0.384299
$818$	4.35369	0.152223
$819$	1.44778	0.0505894
$820$	15.8508	0.553533
$821$	−30.1076	−1.05076	−0.525381	−	0.850867i	$-0.676077\pi$
$821$	−30.1076	−1.05076	−0.525381	+	0.850867i	$0.676077\pi$
$822$	−2.05606	−0.0717135
$823$	25.4311	0.886474	0.443237	−	0.896404i	$-0.353830\pi$
$823$	25.4311	0.886474	0.443237	+	0.896404i	$0.353830\pi$
$824$	−10.1558	−0.353793
$825$	1.60195	0.0557727
$826$	3.36411	0.117052
$827$	−21.5535	−0.749489	−0.374745	−	0.927128i	$-0.622270\pi$
$827$	−21.5535	−0.749489	−0.374745	+	0.927128i	$0.622270\pi$
$828$	5.18179	0.180080
$829$	−16.0132	−0.556162	−0.278081	−	0.960558i	$-0.589698\pi$
$829$	−16.0132	−0.556162	−0.278081	+	0.960558i	$0.589698\pi$
$830$	2.38380	0.0827429
$831$	2.74145	0.0951000
$832$	−6.93840	−0.240546
$833$	−4.89591	−0.169633
$834$	4.90651	0.169899
$835$	3.29189	0.113921
$836$	−4.74094	−0.163969
$837$	27.1257	0.937602
$838$	0.637040	0.0220062
$839$	−1.52948	−0.0528034	−0.0264017	−	0.999651i	$-0.508405\pi$
$839$	−1.52948	−0.0528034	−0.0264017	+	0.999651i	$0.508405\pi$
$840$	−4.02596	−0.138909
$841$	−22.0738	−0.761165
$842$	−4.85643	−0.167364
$843$	36.6831	1.26343
$844$	−15.6897	−0.540061
$845$	−12.0740	−0.415358
$846$	0.159409	0.00548061
$847$	−3.46851	−0.119180
$848$	7.16067	0.245898
$849$	−7.14244	−0.245128
$850$	0.177775	0.00609763
$851$	−63.6876	−2.18318
$852$	12.7848	0.437999
$853$	12.8050	0.438436	0.219218	−	0.975676i	$-0.429649\pi$
$853$	12.8050	0.438436	0.219218	+	0.975676i	$0.429649\pi$
$854$	3.10363	0.106204
$855$	−1.04567	−0.0357610
$856$	1.53896	0.0526004
$857$	2.42136	0.0827122	0.0413561	−	0.999144i	$-0.486832\pi$
$857$	2.42136	0.0827122	0.0413561	+	0.999144i	$0.486832\pi$
$858$	−0.281586	−0.00961318
$859$	5.22850	0.178394	0.0891971	−	0.996014i	$-0.471570\pi$
$859$	5.22850	0.178394	0.0891971	+	0.996014i	$0.471570\pi$
$860$	−8.96114	−0.305572
$861$	44.7836	1.52622
$862$	3.77812	0.128683
$863$	47.7365	1.62497	0.812484	−	0.582983i	$-0.198115\pi$
$863$	47.7365	1.62497	0.812484	+	0.582983i	$0.198115\pi$
$864$	11.7904	0.401117
$865$	3.24197	0.110230
$866$	4.36932	0.148475
$867$	−25.7158	−0.873354
$868$	−33.6379	−1.14175
$869$	−12.1868	−0.413410
$870$	−0.770110	−0.0261092
$871$	−4.43185	−0.150167
$872$	−8.07470	−0.273444
$873$	−2.69511	−0.0912157
$874$	−2.67487	−0.0904787
$875$	−3.46851	−0.117257
$876$	3.15044	0.106444
$877$	4.46612	0.150810	0.0754051	−	0.997153i	$-0.475975\pi$
$877$	4.46612	0.150810	0.0754051	+	0.997153i	$0.475975\pi$
$878$	0.988043	0.0333448
$879$	9.75774	0.329120
$880$	3.80091	0.128129
$881$	−7.59729	−0.255959	−0.127980	−	0.991777i	$-0.540849\pi$
$881$	−7.59729	−0.255959	−0.127980	+	0.991777i	$0.540849\pi$
$882$	0.398590	0.0134212
$883$	51.3190	1.72702	0.863510	−	0.504331i	$-0.168261\pi$
$883$	51.3190	1.72702	0.863510	+	0.504331i	$0.168261\pi$
$884$	1.84181	0.0619467
$885$	8.50588	0.285922
$886$	−4.88264	−0.164036
$887$	2.37763	0.0798332	0.0399166	−	0.999203i	$-0.487291\pi$
$887$	2.37763	0.0798332	0.0399166	+	0.999203i	$0.487291\pi$
$888$	−12.1696	−0.408385
$889$	−14.5954	−0.489513
$890$	1.17652	0.0394372
$891$	−7.51056	−0.251613
$892$	6.72273	0.225094
$893$	4.85006	0.162301
$894$	1.35391	0.0452816
$895$	22.0275	0.736298
$896$	−19.4373	−0.649354
$897$	9.36397	0.312654
$898$	−1.45543	−0.0485682
$899$	−12.9781	−0.432843
$900$	0.853051	0.0284350
$901$	−1.83350	−0.0610827
$902$	1.47226	0.0490208
$903$	−25.3181	−0.842534
$904$	−1.64465	−0.0547001
$905$	15.5292	0.516209
$906$	5.60078	0.186073
$907$	44.9504	1.49255	0.746277	−	0.665635i	$-0.231839\pi$
$907$	44.9504	1.49255	0.746277	+	0.665635i	$0.231839\pi$
$908$	23.8744	0.792299
$909$	1.91025	0.0633591
$910$	0.609685	0.0202109
$911$	15.3787	0.509518	0.254759	−	0.967005i	$-0.418004\pi$
$911$	15.3787	0.509518	0.254759	+	0.967005i	$0.418004\pi$
$912$	14.6784	0.486049
$913$	−13.0501	−0.431895
$914$	−1.71022	−0.0565690
$915$	7.84727	0.259423
$916$	−32.8213	−1.08445
$917$	39.9354	1.31878
$918$	−0.977889	−0.0322751
$919$	42.5035	1.40206	0.701030	−	0.713131i	$-0.252724\pi$
$919$	42.5035	1.40206	0.701030	+	0.713131i	$0.252724\pi$
$920$	4.40132	0.145107
$921$	−21.6947	−0.714863
$922$	6.74415	0.222107
$923$	−3.90505	−0.128536
$924$	10.9274	0.359484
$925$	−10.4845	−0.344730
$926$	−4.04333	−0.132872
$927$	6.07977	0.199686
$928$	−5.64101	−0.185175
$929$	6.72724	0.220714	0.110357	−	0.993892i	$-0.464801\pi$
$929$	6.72724	0.220714	0.110357	+	0.993892i	$0.464801\pi$
$930$	1.44300	0.0473179
$931$	12.1272	0.397452
$932$	−6.80955	−0.223054
$933$	13.6834	0.447973
$934$	−1.20577	−0.0394540
$935$	−0.973228	−0.0318280
$936$	−0.302438	−0.00988549
$937$	−27.8416	−0.909544	−0.454772	−	0.890608i	$-0.650279\pi$
$937$	−27.8416	−0.909544	−0.454772	+	0.890608i	$0.650279\pi$
$938$	−2.91795	−0.0952745
$939$	7.69687	0.251178
$940$	−3.95667	−0.129052
$941$	12.3109	0.401323	0.200661	−	0.979661i	$-0.435691\pi$
$941$	12.3109	0.401323	0.200661	+	0.979661i	$0.435691\pi$
$942$	−3.30944	−0.107827
$943$	−48.9590	−1.59432
$944$	20.1818	0.656860
$945$	19.0793	0.620649
$946$	−0.832330	−0.0270614
$947$	−37.6530	−1.22356	−0.611778	−	0.791029i	$-0.709546\pi$
$947$	−37.6530	−1.22356	−0.611778	+	0.791029i	$0.709546\pi$
$948$	38.3940	1.24698
$949$	−0.962291	−0.0312373
$950$	−0.440349	−0.0142868
$951$	−6.76264	−0.219294
$952$	2.44589	0.0792716
$953$	−45.9168	−1.48739	−0.743695	−	0.668519i	$-0.766929\pi$
$953$	−45.9168	−1.48739	−0.743695	+	0.668519i	$0.766929\pi$
$954$	0.149270	0.00483281
$955$	16.1522	0.522672
$956$	3.71456	0.120137
$957$	4.21596	0.136283
$958$	6.09593	0.196950
$959$	−24.3711	−0.786985
$960$	−11.5505	−0.372792
$961$	−6.68217	−0.215554
$962$	1.84294	0.0594189
$963$	−0.921298	−0.0296884
$964$	54.5519	1.75700
$965$	−9.06264	−0.291737
$966$	6.16528	0.198365
$967$	38.5376	1.23928	0.619642	−	0.784884i	$-0.287278\pi$
$967$	38.5376	1.23928	0.619642	+	0.784884i	$0.287278\pi$
$968$	0.724566	0.0232884
$969$	−3.75841	−0.120738
$970$	−1.13496	−0.0364414
$971$	39.9616	1.28243	0.641214	−	0.767362i	$-0.278431\pi$
$971$	39.9616	1.28243	0.641214	+	0.767362i	$0.278431\pi$
$972$	−8.79202	−0.282004
$973$	58.1583	1.86447
$974$	−4.20338	−0.134685
$975$	1.54154	0.0493688
$976$	18.6191	0.595982
$977$	52.5708	1.68189	0.840945	−	0.541121i	$-0.182000\pi$
$977$	52.5708	1.68189	0.840945	+	0.541121i	$0.182000\pi$
$978$	7.03904	0.225084
$979$	−6.44087	−0.205851
$980$	−9.89332	−0.316031
$981$	4.83393	0.154336
$982$	3.66481	0.116949
$983$	−9.77187	−0.311674	−0.155837	−	0.987783i	$-0.549808\pi$
$983$	−9.77187	−0.311674	−0.155837	+	0.987783i	$0.549808\pi$
$984$	−9.35521	−0.298233
$985$	−22.8203	−0.727116
$986$	0.467863	0.0148998
$987$	−11.1789	−0.355827
$988$	−4.56217	−0.145142
$989$	27.6786	0.880129
$990$	0.0792333	0.00251820
$991$	28.5534	0.907027	0.453514	−	0.891249i	$-0.350170\pi$
$991$	28.5534	0.907027	0.453514	+	0.891249i	$0.350170\pi$
$992$	10.5699	0.335595
$993$	−2.61996	−0.0831418
$994$	−2.57111	−0.0815505
$995$	−16.0897	−0.510077
$996$	41.1136	1.30273
$997$	−25.0582	−0.793600	−0.396800	−	0.917905i	$-0.629879\pi$
$997$	−25.0582	−0.793600	−0.396800	+	0.917905i	$0.629879\pi$
$998$	−2.23277	−0.0706772
$999$	57.6724	1.82468

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.b.1.12	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.b.1.12	✓	23	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)

\(f(q)\)	\(=\)	\(q-0.182665 q^{2} +1.60195 q^{3} -1.96663 q^{4} +1.00000 q^{5} -0.292620 q^{6} -3.46851 q^{7} +0.724566 q^{8} -0.433762 q^{9} +O(q^{10})\)	\(q-0.182665 q^{2} +1.60195 q^{3} -1.96663 q^{4} +1.00000 q^{5} -0.292620 q^{6} -3.46851 q^{7} +0.724566 q^{8} -0.433762 q^{9} -0.182665 q^{10} +1.00000 q^{11} -3.15044 q^{12} +0.962291 q^{13} +0.633577 q^{14} +1.60195 q^{15} +3.80091 q^{16} -0.973228 q^{17} +0.0792333 q^{18} +2.41069 q^{19} -1.96663 q^{20} -5.55638 q^{21} -0.182665 q^{22} +6.07442 q^{23} +1.16072 q^{24} +1.00000 q^{25} -0.175777 q^{26} -5.50071 q^{27} +6.82130 q^{28} +2.63177 q^{29} -0.292620 q^{30} -4.93131 q^{31} -2.14343 q^{32} +1.60195 q^{33} +0.177775 q^{34} -3.46851 q^{35} +0.853051 q^{36} -10.4845 q^{37} -0.440349 q^{38} +1.54154 q^{39} +0.724566 q^{40} -8.05986 q^{41} +1.01496 q^{42} +4.55659 q^{43} -1.96663 q^{44} -0.433762 q^{45} -1.10959 q^{46} +2.01190 q^{47} +6.08887 q^{48} +5.03059 q^{49} -0.182665 q^{50} -1.55906 q^{51} -1.89247 q^{52} +1.88393 q^{53} +1.00479 q^{54} +1.00000 q^{55} -2.51317 q^{56} +3.86180 q^{57} -0.480733 q^{58} +5.30971 q^{59} -3.15044 q^{60} +4.89858 q^{61} +0.900779 q^{62} +1.50451 q^{63} -7.21030 q^{64} +0.962291 q^{65} -0.292620 q^{66} -4.60552 q^{67} +1.91398 q^{68} +9.73091 q^{69} +0.633577 q^{70} -4.05808 q^{71} -0.314290 q^{72} -1.00000 q^{73} +1.91516 q^{74} +1.60195 q^{75} -4.74094 q^{76} -3.46851 q^{77} -0.281586 q^{78} -12.1868 q^{79} +3.80091 q^{80} -7.51056 q^{81} +1.47226 q^{82} -13.0501 q^{83} +10.9274 q^{84} -0.973228 q^{85} -0.832330 q^{86} +4.21596 q^{87} +0.724566 q^{88} -6.44087 q^{89} +0.0792333 q^{90} -3.33772 q^{91} -11.9462 q^{92} -7.89970 q^{93} -0.367504 q^{94} +2.41069 q^{95} -3.43366 q^{96} +6.21334 q^{97} -0.918914 q^{98} -0.433762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * q^99

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