LMFDB - Embedded newform 4015.2.a.h.1.10

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			1.10
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)

$f(q)$	$=$	$q-1.58931 q^{2} -0.358295 q^{3} +0.525917 q^{4} +1.00000 q^{5} +0.569443 q^{6} +2.77249 q^{7} +2.34278 q^{8} -2.87162 q^{9} +O(q^{10})$	\(q-1.58931 q^{2} -0.358295 q^{3} +0.525917 q^{4} +1.00000 q^{5} +0.569443 q^{6} +2.77249 q^{7} +2.34278 q^{8} -2.87162 q^{9} -1.58931 q^{10} +1.00000 q^{11} -0.188433 q^{12} +1.54440 q^{13} -4.40635 q^{14} -0.358295 q^{15} -4.77525 q^{16} +3.82023 q^{17} +4.56391 q^{18} +5.21934 q^{19} +0.525917 q^{20} -0.993369 q^{21} -1.58931 q^{22} +4.87751 q^{23} -0.839406 q^{24} +1.00000 q^{25} -2.45454 q^{26} +2.10377 q^{27} +1.45810 q^{28} -6.06529 q^{29} +0.569443 q^{30} +2.13802 q^{31} +2.90380 q^{32} -0.358295 q^{33} -6.07154 q^{34} +2.77249 q^{35} -1.51024 q^{36} +2.69997 q^{37} -8.29517 q^{38} -0.553352 q^{39} +2.34278 q^{40} -2.64072 q^{41} +1.57877 q^{42} +2.93477 q^{43} +0.525917 q^{44} -2.87162 q^{45} -7.75189 q^{46} +13.5437 q^{47} +1.71095 q^{48} +0.686693 q^{49} -1.58931 q^{50} -1.36877 q^{51} +0.812228 q^{52} -0.687193 q^{53} -3.34355 q^{54} +1.00000 q^{55} +6.49533 q^{56} -1.87006 q^{57} +9.63964 q^{58} -2.29624 q^{59} -0.188433 q^{60} -11.0870 q^{61} -3.39798 q^{62} -7.96155 q^{63} +4.93544 q^{64} +1.54440 q^{65} +0.569443 q^{66} -6.87347 q^{67} +2.00912 q^{68} -1.74759 q^{69} -4.40635 q^{70} +15.4683 q^{71} -6.72759 q^{72} +1.00000 q^{73} -4.29109 q^{74} -0.358295 q^{75} +2.74494 q^{76} +2.77249 q^{77} +0.879450 q^{78} +12.3392 q^{79} -4.77525 q^{80} +7.86110 q^{81} +4.19693 q^{82} -3.83901 q^{83} -0.522429 q^{84} +3.82023 q^{85} -4.66427 q^{86} +2.17316 q^{87} +2.34278 q^{88} -1.55274 q^{89} +4.56391 q^{90} +4.28184 q^{91} +2.56516 q^{92} -0.766041 q^{93} -21.5252 q^{94} +5.21934 q^{95} -1.04042 q^{96} +6.46974 q^{97} -1.09137 q^{98} -2.87162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.58931	−1.12381	−0.561907	−	0.827200i	$-0.689932\pi$
$2$	−1.58931	−1.12381	−0.561907	+	0.827200i	$0.689932\pi$
$3$	−0.358295	−0.206862	−0.103431	−	0.994637i	$-0.532982\pi$
$3$	−0.358295	−0.206862	−0.103431	+	0.994637i	$0.532982\pi$
$4$	0.525917	0.262958
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.569443	0.232474
$7$	2.77249	1.04790	0.523951	−	0.851748i	$-0.324457\pi$
$7$	2.77249	1.04790	0.523951	+	0.851748i	$0.324457\pi$
$8$	2.34278	0.828298
$9$	−2.87162	−0.957208
$10$	−1.58931	−0.502585
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.188433	−0.0543960
$13$	1.54440	0.428341	0.214170	−	0.976796i	$-0.431295\pi$
$13$	1.54440	0.428341	0.214170	+	0.976796i	$0.431295\pi$
$14$	−4.40635	−1.17765
$15$	−0.358295	−0.0925114
$16$	−4.77525	−1.19381
$17$	3.82023	0.926542	0.463271	−	0.886217i	$-0.346676\pi$
$17$	3.82023	0.926542	0.463271	+	0.886217i	$0.346676\pi$
$18$	4.56391	1.07572
$19$	5.21934	1.19740	0.598700	−	0.800974i	$-0.295684\pi$
$19$	5.21934	1.19740	0.598700	+	0.800974i	$0.295684\pi$
$20$	0.525917	0.117599
$21$	−0.993369	−0.216771
$22$	−1.58931	−0.338843
$23$	4.87751	1.01703	0.508516	−	0.861053i	$-0.330194\pi$
$23$	4.87751	1.01703	0.508516	+	0.861053i	$0.330194\pi$
$24$	−0.839406	−0.171343
$25$	1.00000	0.200000
$26$	−2.45454	−0.481375
$27$	2.10377	0.404871
$28$	1.45810	0.275555
$29$	−6.06529	−1.12630	−0.563148	−	0.826356i	$-0.690410\pi$
$29$	−6.06529	−1.12630	−0.563148	+	0.826356i	$0.690410\pi$
$30$	0.569443	0.103966
$31$	2.13802	0.383999	0.192000	−	0.981395i	$-0.438503\pi$
$31$	2.13802	0.383999	0.192000	+	0.981395i	$0.438503\pi$
$32$	2.90380	0.513324
$33$	−0.358295	−0.0623711
$34$	−6.07154	−1.04126
$35$	2.77249	0.468636
$36$	−1.51024	−0.251706
$37$	2.69997	0.443872	0.221936	−	0.975061i	$-0.428762\pi$
$37$	2.69997	0.443872	0.221936	+	0.975061i	$0.428762\pi$
$38$	−8.29517	−1.34565
$39$	−0.553352	−0.0886073
$40$	2.34278	0.370426
$41$	−2.64072	−0.412411	−0.206205	−	0.978509i	$-0.566111\pi$
$41$	−2.64072	−0.412411	−0.206205	+	0.978509i	$0.566111\pi$
$42$	1.57877	0.243610
$43$	2.93477	0.447548	0.223774	−	0.974641i	$-0.428162\pi$
$43$	2.93477	0.447548	0.223774	+	0.974641i	$0.428162\pi$
$44$	0.525917	0.0792849
$45$	−2.87162	−0.428077
$46$	−7.75189	−1.14295
$47$	13.5437	1.97555	0.987775	−	0.155888i	$-0.0498238\pi$
$47$	13.5437	1.97555	0.987775	+	0.155888i	$0.0498238\pi$
$48$	1.71095	0.246954
$49$	0.686693	0.0980990
$50$	−1.58931	−0.224763
$51$	−1.36877	−0.191666
$52$	0.812228	0.112636
$53$	−0.687193	−0.0943932	−0.0471966	−	0.998886i	$-0.515029\pi$
$53$	−0.687193	−0.0943932	−0.0471966	+	0.998886i	$0.515029\pi$
$54$	−3.34355	−0.455000
$55$	1.00000	0.134840
$56$	6.49533	0.867975
$57$	−1.87006	−0.247696
$58$	9.63964	1.26575
$59$	−2.29624	−0.298944	−0.149472	−	0.988766i	$-0.547757\pi$
$59$	−2.29624	−0.298944	−0.149472	+	0.988766i	$0.547757\pi$
$60$	−0.188433	−0.0243266
$61$	−11.0870	−1.41954	−0.709770	−	0.704434i	$-0.751201\pi$
$61$	−11.0870	−1.41954	−0.709770	+	0.704434i	$0.751201\pi$
$62$	−3.39798	−0.431544
$63$	−7.96155	−1.00306
$64$	4.93544	0.616930
$65$	1.54440	0.191560
$66$	0.569443	0.0700936
$67$	−6.87347	−0.839728	−0.419864	−	0.907587i	$-0.637922\pi$
$67$	−6.87347	−0.839728	−0.419864	+	0.907587i	$0.637922\pi$
$68$	2.00912	0.243642
$69$	−1.74759	−0.210385
$70$	−4.40635	−0.526660
$71$	15.4683	1.83576	0.917878	−	0.396864i	$-0.129901\pi$
$71$	15.4683	1.83576	0.917878	+	0.396864i	$0.129901\pi$
$72$	−6.72759	−0.792854
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−4.29109	−0.498830
$75$	−0.358295	−0.0413723
$76$	2.74494	0.314866
$77$	2.77249	0.315954
$78$	0.879450	0.0995781
$79$	12.3392	1.38827	0.694133	−	0.719847i	$-0.255788\pi$
$79$	12.3392	1.38827	0.694133	+	0.719847i	$0.255788\pi$
$80$	−4.77525	−0.533889
$81$	7.86110	0.873456
$82$	4.19693	0.463473
$83$	−3.83901	−0.421386	−0.210693	−	0.977552i	$-0.567572\pi$
$83$	−3.83901	−0.421386	−0.210693	+	0.977552i	$0.567572\pi$
$84$	−0.522429	−0.0570017
$85$	3.82023	0.414362
$86$	−4.66427	−0.502961
$87$	2.17316	0.232987
$88$	2.34278	0.249741
$89$	−1.55274	−0.164590	−0.0822952	−	0.996608i	$-0.526225\pi$
$89$	−1.55274	−0.164590	−0.0822952	+	0.996608i	$0.526225\pi$
$90$	4.56391	0.481079
$91$	4.28184	0.448859
$92$	2.56516	0.267437
$93$	−0.766041	−0.0794347
$94$	−21.5252	−2.22015
$95$	5.21934	0.535493
$96$	−1.04042	−0.106187
$97$	6.46974	0.656902	0.328451	−	0.944521i	$-0.393473\pi$
$97$	6.46974	0.656902	0.328451	+	0.944521i	$0.393473\pi$
$98$	−1.09137	−0.110245
$99$	−2.87162	−0.288609
$100$	0.525917	0.0525917
$101$	10.7012	1.06481	0.532405	−	0.846490i	$-0.321288\pi$
$101$	10.7012	1.06481	0.532405	+	0.846490i	$0.321288\pi$
$102$	2.17540	0.215397
$103$	0.663135	0.0653407	0.0326703	−	0.999466i	$-0.489599\pi$
$103$	0.663135	0.0653407	0.0326703	+	0.999466i	$0.489599\pi$
$104$	3.61820	0.354794
$105$	−0.993369	−0.0969428
$106$	1.09216	0.106080
$107$	−5.14402	−0.497291	−0.248646	−	0.968595i	$-0.579985\pi$
$107$	−5.14402	−0.497291	−0.248646	+	0.968595i	$0.579985\pi$
$108$	1.10641	0.106464
$109$	−19.0573	−1.82536	−0.912680	−	0.408675i	$-0.865991\pi$
$109$	−19.0573	−1.82536	−0.912680	+	0.408675i	$0.865991\pi$
$110$	−1.58931	−0.151535
$111$	−0.967385	−0.0918201
$112$	−13.2393	−1.25100
$113$	−17.0646	−1.60530	−0.802651	−	0.596449i	$-0.796578\pi$
$113$	−17.0646	−1.60530	−0.802651	+	0.596449i	$0.796578\pi$
$114$	2.97212	0.278364
$115$	4.87751	0.454830
$116$	−3.18984	−0.296169
$117$	−4.43495	−0.410011
$118$	3.64944	0.335958
$119$	10.5915	0.970926
$120$	−0.839406	−0.0766270
$121$	1.00000	0.0909091
$122$	17.6206	1.59530
$123$	0.946155	0.0853120
$124$	1.12442	0.100976
$125$	1.00000	0.0894427
$126$	12.6534	1.12725
$127$	−9.78783	−0.868529	−0.434265	−	0.900785i	$-0.642992\pi$
$127$	−9.78783	−0.868529	−0.434265	+	0.900785i	$0.642992\pi$
$128$	−13.6516	−1.20664
$129$	−1.05151	−0.0925805
$130$	−2.45454	−0.215278
$131$	−8.33503	−0.728235	−0.364117	−	0.931353i	$-0.618629\pi$
$131$	−8.33503	−0.728235	−0.364117	+	0.931353i	$0.618629\pi$
$132$	−0.188433	−0.0164010
$133$	14.4706	1.25476
$134$	10.9241	0.943698
$135$	2.10377	0.181064
$136$	8.94996	0.767453
$137$	7.43070	0.634848	0.317424	−	0.948284i	$-0.397182\pi$
$137$	7.43070	0.634848	0.317424	+	0.948284i	$0.397182\pi$
$138$	2.77746	0.236433
$139$	−6.67957	−0.566553	−0.283277	−	0.959038i	$-0.591421\pi$
$139$	−6.67957	−0.566553	−0.283277	+	0.959038i	$0.591421\pi$
$140$	1.45810	0.123232
$141$	−4.85263	−0.408665
$142$	−24.5841	−2.06305
$143$	1.54440	0.129150
$144$	13.7127	1.14273
$145$	−6.06529	−0.503695
$146$	−1.58931	−0.131533
$147$	−0.246039	−0.0202929
$148$	1.41996	0.116720
$149$	−8.40880	−0.688876	−0.344438	−	0.938809i	$-0.611930\pi$
$149$	−8.40880	−0.688876	−0.344438	+	0.938809i	$0.611930\pi$
$150$	0.569443	0.0464948
$151$	19.4962	1.58658	0.793288	−	0.608846i	$-0.208367\pi$
$151$	19.4962	1.58658	0.793288	+	0.608846i	$0.208367\pi$
$152$	12.2278	0.991803
$153$	−10.9703	−0.886894
$154$	−4.40635	−0.355074
$155$	2.13802	0.171730
$156$	−0.291017	−0.0233000
$157$	−2.51905	−0.201042	−0.100521	−	0.994935i	$-0.532051\pi$
$157$	−2.51905	−0.201042	−0.100521	+	0.994935i	$0.532051\pi$
$158$	−19.6108	−1.56015
$159$	0.246218	0.0195263
$160$	2.90380	0.229566
$161$	13.5228	1.06575
$162$	−12.4938	−0.981602
$163$	−18.1926	−1.42496	−0.712478	−	0.701694i	$-0.752427\pi$
$163$	−18.1926	−1.42496	−0.712478	+	0.701694i	$0.752427\pi$
$164$	−1.38880	−0.108447
$165$	−0.358295	−0.0278932
$166$	6.10139	0.473559
$167$	6.56752	0.508210	0.254105	−	0.967177i	$-0.418219\pi$
$167$	6.56752	0.508210	0.254105	+	0.967177i	$0.418219\pi$
$168$	−2.32724	−0.179551
$169$	−10.6148	−0.816524
$170$	−6.07154	−0.465666
$171$	−14.9880	−1.14616
$172$	1.54344	0.117687
$173$	−11.7823	−0.895791	−0.447896	−	0.894086i	$-0.647826\pi$
$173$	−11.7823	−0.895791	−0.447896	+	0.894086i	$0.647826\pi$
$174$	−3.45383	−0.261834
$175$	2.77249	0.209580
$176$	−4.77525	−0.359948
$177$	0.822730	0.0618402
$178$	2.46780	0.184969
$179$	0.760265	0.0568249	0.0284124	−	0.999596i	$-0.490955\pi$
$179$	0.760265	0.0568249	0.0284124	+	0.999596i	$0.490955\pi$
$180$	−1.51024	−0.112566
$181$	−1.51659	−0.112727	−0.0563635	−	0.998410i	$-0.517951\pi$
$181$	−1.51659	−0.112727	−0.0563635	+	0.998410i	$0.517951\pi$
$182$	−6.80519	−0.504434
$183$	3.97240	0.293648
$184$	11.4269	0.842405
$185$	2.69997	0.198506
$186$	1.21748	0.0892699
$187$	3.82023	0.279363
$188$	7.12285	0.519487
$189$	5.83269	0.424266
$190$	−8.29517	−0.601795
$191$	−20.5084	−1.48393	−0.741967	−	0.670436i	$-0.766107\pi$
$191$	−20.5084	−1.48393	−0.741967	+	0.670436i	$0.766107\pi$
$192$	−1.76834	−0.127619
$193$	18.9736	1.36575	0.682875	−	0.730535i	$-0.260729\pi$
$193$	18.9736	1.36575	0.682875	+	0.730535i	$0.260729\pi$
$194$	−10.2824	−0.738236
$195$	−0.553352	−0.0396264
$196$	0.361143	0.0257960
$197$	−18.7332	−1.33468	−0.667341	−	0.744752i	$-0.732568\pi$
$197$	−18.7332	−1.33468	−0.667341	+	0.744752i	$0.732568\pi$
$198$	4.56391	0.324343
$199$	−8.45384	−0.599277	−0.299639	−	0.954053i	$-0.596866\pi$
$199$	−8.45384	−0.599277	−0.299639	+	0.954053i	$0.596866\pi$
$200$	2.34278	0.165660
$201$	2.46273	0.173708
$202$	−17.0076	−1.19665
$203$	−16.8159	−1.18025
$204$	−0.719859	−0.0504002
$205$	−2.64072	−0.184436
$206$	−1.05393	−0.0734308
$207$	−14.0064	−0.973511
$208$	−7.37491	−0.511358
$209$	5.21934	0.361029
$210$	1.57877	0.108946
$211$	23.0640	1.58779	0.793895	−	0.608054i	$-0.208050\pi$
$211$	23.0640	1.58779	0.793895	+	0.608054i	$0.208050\pi$
$212$	−0.361406	−0.0248215
$213$	−5.54223	−0.379747
$214$	8.17546	0.558863
$215$	2.93477	0.200150
$216$	4.92868	0.335354
$217$	5.92763	0.402394
$218$	30.2881	2.05137
$219$	−0.358295	−0.0242113
$220$	0.525917	0.0354573
$221$	5.89998	0.396876
$222$	1.53748	0.103189
$223$	−1.18111	−0.0790930	−0.0395465	−	0.999218i	$-0.512591\pi$
$223$	−1.18111	−0.0790930	−0.0395465	+	0.999218i	$0.512591\pi$
$224$	8.05075	0.537914
$225$	−2.87162	−0.191442
$226$	27.1210	1.80406
$227$	22.7929	1.51282	0.756410	−	0.654098i	$-0.226952\pi$
$227$	22.7929	1.51282	0.756410	+	0.654098i	$0.226952\pi$
$228$	−0.983498	−0.0651337
$229$	5.05456	0.334014	0.167007	−	0.985956i	$-0.446590\pi$
$229$	5.05456	0.334014	0.167007	+	0.985956i	$0.446590\pi$
$230$	−7.75189	−0.511145
$231$	−0.993369	−0.0653589
$232$	−14.2096	−0.932908
$233$	17.1854	1.12586	0.562928	−	0.826506i	$-0.309675\pi$
$233$	17.1854	1.12586	0.562928	+	0.826506i	$0.309675\pi$
$234$	7.04852	0.460776
$235$	13.5437	0.883493
$236$	−1.20763	−0.0786100
$237$	−4.42106	−0.287179
$238$	−16.8333	−1.09114
$239$	30.0725	1.94523	0.972614	−	0.232427i	$-0.0746667\pi$
$239$	30.0725	1.94523	0.972614	+	0.232427i	$0.0746667\pi$
$240$	1.71095	0.110441
$241$	−22.8889	−1.47441	−0.737203	−	0.675672i	$-0.763854\pi$
$241$	−22.8889	−1.47441	−0.737203	+	0.675672i	$0.763854\pi$
$242$	−1.58931	−0.102165
$243$	−9.12791	−0.585556
$244$	−5.83082	−0.373280
$245$	0.686693	0.0438712
$246$	−1.50374	−0.0958748
$247$	8.06077	0.512895
$248$	5.00890	0.318066
$249$	1.37550	0.0871686
$250$	−1.58931	−0.100517
$251$	7.07469	0.446551	0.223275	−	0.974755i	$-0.428325\pi$
$251$	7.07469	0.446551	0.223275	+	0.974755i	$0.428325\pi$
$252$	−4.18711	−0.263763
$253$	4.87751	0.306646
$254$	15.5559	0.976066
$255$	−1.36877	−0.0857157
$256$	11.8257	0.739108
$257$	9.48611	0.591728	0.295864	−	0.955230i	$-0.404393\pi$
$257$	9.48611	0.591728	0.295864	+	0.955230i	$0.404393\pi$
$258$	1.67118	0.104043
$259$	7.48563	0.465134
$260$	0.812228	0.0503722
$261$	17.4172	1.07810
$262$	13.2470	0.818401
$263$	12.2124	0.753048	0.376524	−	0.926407i	$-0.377119\pi$
$263$	12.2124	0.753048	0.376524	+	0.926407i	$0.377119\pi$
$264$	−0.839406	−0.0516619
$265$	−0.687193	−0.0422139
$266$	−22.9983	−1.41011
$267$	0.556340	0.0340475
$268$	−3.61487	−0.220814
$269$	8.12364	0.495307	0.247654	−	0.968849i	$-0.420341\pi$
$269$	8.12364	0.495307	0.247654	+	0.968849i	$0.420341\pi$
$270$	−3.34355	−0.203482
$271$	13.2137	0.802677	0.401339	−	0.915930i	$-0.368545\pi$
$271$	13.2137	0.802677	0.401339	+	0.915930i	$0.368545\pi$
$272$	−18.2425	−1.10612
$273$	−1.53416	−0.0928517
$274$	−11.8097	−0.713451
$275$	1.00000	0.0603023
$276$	−0.919085	−0.0553224
$277$	16.6660	1.00137	0.500683	−	0.865631i	$-0.333082\pi$
$277$	16.6660	1.00137	0.500683	+	0.865631i	$0.333082\pi$
$278$	10.6159	0.636701
$279$	−6.13958	−0.367567
$280$	6.49533	0.388170
$281$	15.0661	0.898766	0.449383	−	0.893339i	$-0.351644\pi$
$281$	15.0661	0.898766	0.449383	+	0.893339i	$0.351644\pi$
$282$	7.71236	0.459264
$283$	−5.64685	−0.335671	−0.167835	−	0.985815i	$-0.553678\pi$
$283$	−5.64685	−0.335671	−0.167835	+	0.985815i	$0.553678\pi$
$284$	8.13506	0.482727
$285$	−1.87006	−0.110773
$286$	−2.45454	−0.145140
$287$	−7.32136	−0.432166
$288$	−8.33862	−0.491358
$289$	−2.40583	−0.141520
$290$	9.63964	0.566059
$291$	−2.31807	−0.135888
$292$	0.525917	0.0307769
$293$	21.0863	1.23187	0.615936	−	0.787796i	$-0.288778\pi$
$293$	21.0863	1.23187	0.615936	+	0.787796i	$0.288778\pi$
$294$	0.391032	0.0228055
$295$	−2.29624	−0.133692
$296$	6.32543	0.367658
$297$	2.10377	0.122073
$298$	13.3642	0.774168
$299$	7.53285	0.435636
$300$	−0.188433	−0.0108792
$301$	8.13661	0.468987
$302$	−30.9855	−1.78302
$303$	−3.83419	−0.220268
$304$	−24.9236	−1.42947
$305$	−11.0870	−0.634837
$306$	17.4352	0.996704
$307$	4.68925	0.267630	0.133815	−	0.991006i	$-0.457277\pi$
$307$	4.68925	0.267630	0.133815	+	0.991006i	$0.457277\pi$
$308$	1.45810	0.0830829
$309$	−0.237598	−0.0135165
$310$	−3.39798	−0.192992
$311$	18.5820	1.05369	0.526845	−	0.849961i	$-0.323375\pi$
$311$	18.5820	1.05369	0.526845	+	0.849961i	$0.323375\pi$
$312$	−1.29638	−0.0733932
$313$	22.0184	1.24456	0.622278	−	0.782796i	$-0.286207\pi$
$313$	22.0184	1.24456	0.622278	+	0.782796i	$0.286207\pi$
$314$	4.00357	0.225934
$315$	−7.96155	−0.448582
$316$	6.48938	0.365056
$317$	25.1735	1.41389	0.706943	−	0.707270i	$-0.250074\pi$
$317$	25.1735	1.41389	0.706943	+	0.707270i	$0.250074\pi$
$318$	−0.391317	−0.0219440
$319$	−6.06529	−0.339591
$320$	4.93544	0.275900
$321$	1.84308	0.102871
$322$	−21.4920	−1.19770
$323$	19.9391	1.10944
$324$	4.13429	0.229683
$325$	1.54440	0.0856681
$326$	28.9138	1.60139
$327$	6.82814	0.377597
$328$	−6.18662	−0.341599
$329$	37.5497	2.07018
$330$	0.569443	0.0313468
$331$	−3.08347	−0.169483	−0.0847413	−	0.996403i	$-0.527006\pi$
$331$	−3.08347	−0.169483	−0.0847413	+	0.996403i	$0.527006\pi$
$332$	−2.01900	−0.110807
$333$	−7.75329	−0.424878
$334$	−10.4378	−0.571134
$335$	−6.87347	−0.375538
$336$	4.74358	0.258783
$337$	−6.37803	−0.347433	−0.173717	−	0.984796i	$-0.555578\pi$
$337$	−6.37803	−0.347433	−0.173717	+	0.984796i	$0.555578\pi$
$338$	16.8703	0.917622
$339$	6.11416	0.332076
$340$	2.00912	0.108960
$341$	2.13802	0.115780
$342$	23.8206	1.28807
$343$	−17.5036	−0.945104
$344$	6.87552	0.370703
$345$	−1.74759	−0.0940869
$346$	18.7258	1.00670
$347$	−27.1949	−1.45990	−0.729948	−	0.683503i	$-0.760456\pi$
$347$	−27.1949	−1.45990	−0.729948	+	0.683503i	$0.760456\pi$
$348$	1.14290	0.0612660
$349$	4.95780	0.265385	0.132692	−	0.991157i	$-0.457638\pi$
$349$	4.95780	0.265385	0.132692	+	0.991157i	$0.457638\pi$
$350$	−4.40635	−0.235529
$351$	3.24908	0.173423
$352$	2.90380	0.154773
$353$	2.14290	0.114055	0.0570274	−	0.998373i	$-0.481838\pi$
$353$	2.14290	0.114055	0.0570274	+	0.998373i	$0.481838\pi$
$354$	−1.30758	−0.0694968
$355$	15.4683	0.820975
$356$	−0.816614	−0.0432804
$357$	−3.79490	−0.200847
$358$	−1.20830	−0.0638606
$359$	−23.9840	−1.26582	−0.632912	−	0.774223i	$-0.718141\pi$
$359$	−23.9840	−1.26582	−0.632912	+	0.774223i	$0.718141\pi$
$360$	−6.72759	−0.354575
$361$	8.24154	0.433765
$362$	2.41033	0.126684
$363$	−0.358295	−0.0188056
$364$	2.25189	0.118031
$365$	1.00000	0.0523424
$366$	−6.31339	−0.330006
$367$	8.11237	0.423462	0.211731	−	0.977328i	$-0.432090\pi$
$367$	8.11237	0.423462	0.211731	+	0.977328i	$0.432090\pi$
$368$	−23.2913	−1.21414
$369$	7.58315	0.394763
$370$	−4.29109	−0.223083
$371$	−1.90523	−0.0989148
$372$	−0.402874	−0.0208880
$373$	−34.6277	−1.79296	−0.896478	−	0.443089i	$-0.853883\pi$
$373$	−34.6277	−1.79296	−0.896478	+	0.443089i	$0.853883\pi$
$374$	−6.07154	−0.313952
$375$	−0.358295	−0.0185023
$376$	31.7299	1.63634
$377$	−9.36725	−0.482438
$378$	−9.26997	−0.476796
$379$	11.8174	0.607021	0.303510	−	0.952828i	$-0.401841\pi$
$379$	11.8174	0.607021	0.303510	+	0.952828i	$0.401841\pi$
$380$	2.74494	0.140812
$381$	3.50693	0.179665
$382$	32.5942	1.66767
$383$	25.3422	1.29492	0.647462	−	0.762098i	$-0.275830\pi$
$383$	25.3422	1.29492	0.647462	+	0.762098i	$0.275830\pi$
$384$	4.89129	0.249607
$385$	2.77249	0.141299
$386$	−30.1550	−1.53485
$387$	−8.42756	−0.428397
$388$	3.40254	0.172738
$389$	12.6873	0.643273	0.321637	−	0.946863i	$-0.395767\pi$
$389$	12.6873	0.643273	0.321637	+	0.946863i	$0.395767\pi$
$390$	0.879450	0.0445327
$391$	18.6332	0.942322
$392$	1.60877	0.0812552
$393$	2.98640	0.150644
$394$	29.7729	1.49994
$395$	12.3392	0.620851
$396$	−1.51024	−0.0758922
$397$	−3.57925	−0.179637	−0.0898186	−	0.995958i	$-0.528629\pi$
$397$	−3.57925	−0.179637	−0.0898186	+	0.995958i	$0.528629\pi$
$398$	13.4358	0.673476
$399$	−5.18473	−0.259561
$400$	−4.77525	−0.238762
$401$	−12.4739	−0.622917	−0.311459	−	0.950260i	$-0.600818\pi$
$401$	−12.4739	−0.622917	−0.311459	+	0.950260i	$0.600818\pi$
$402$	−3.91405	−0.195215
$403$	3.30196	0.164482
$404$	5.62795	0.280001
$405$	7.86110	0.390621
$406$	26.7258	1.32638
$407$	2.69997	0.133832
$408$	−3.20673	−0.158757
$409$	−3.57165	−0.176607	−0.0883035	−	0.996094i	$-0.528145\pi$
$409$	−3.57165	−0.176607	−0.0883035	+	0.996094i	$0.528145\pi$
$410$	4.19693	0.207271
$411$	−2.66238	−0.131326
$412$	0.348754	0.0171819
$413$	−6.36629	−0.313265
$414$	22.2605	1.09405
$415$	−3.83901	−0.188449
$416$	4.48464	0.219878
$417$	2.39325	0.117198
$418$	−8.29517	−0.405730
$419$	7.44269	0.363599	0.181799	−	0.983336i	$-0.441808\pi$
$419$	7.44269	0.363599	0.181799	+	0.983336i	$0.441808\pi$
$420$	−0.522429	−0.0254919
$421$	31.0592	1.51373	0.756867	−	0.653568i	$-0.226729\pi$
$421$	31.0592	1.51373	0.756867	+	0.653568i	$0.226729\pi$
$422$	−36.6559	−1.78438
$423$	−38.8924	−1.89101
$424$	−1.60994	−0.0781857
$425$	3.82023	0.185308
$426$	8.80834	0.426766
$427$	−30.7385	−1.48754
$428$	−2.70533	−0.130767
$429$	−0.553352	−0.0267161
$430$	−4.66427	−0.224931
$431$	18.5244	0.892290	0.446145	−	0.894961i	$-0.352797\pi$
$431$	18.5244	0.892290	0.446145	+	0.894961i	$0.352797\pi$
$432$	−10.0460	−0.483340
$433$	−35.8455	−1.72262	−0.861312	−	0.508077i	$-0.830357\pi$
$433$	−35.8455	−1.72262	−0.861312	+	0.508077i	$0.830357\pi$
$434$	−9.42086	−0.452216
$435$	2.17316	0.104195
$436$	−10.0226	−0.479994
$437$	25.4574	1.21779
$438$	0.569443	0.0272090
$439$	33.7428	1.61046	0.805228	−	0.592965i	$-0.202043\pi$
$439$	33.7428	1.61046	0.805228	+	0.592965i	$0.202043\pi$
$440$	2.34278	0.111688
$441$	−1.97192	−0.0939012
$442$	−9.37692	−0.446015
$443$	−27.4936	−1.30626	−0.653131	−	0.757245i	$-0.726545\pi$
$443$	−27.4936	−1.30626	−0.653131	+	0.757245i	$0.726545\pi$
$444$	−0.508764	−0.0241449
$445$	−1.55274	−0.0736071
$446$	1.87715	0.0888858
$447$	3.01283	0.142502
$448$	13.6835	0.646483
$449$	−13.0328	−0.615057	−0.307528	−	0.951539i	$-0.599502\pi$
$449$	−13.0328	−0.615057	−0.307528	+	0.951539i	$0.599502\pi$
$450$	4.56391	0.215145
$451$	−2.64072	−0.124346
$452$	−8.97456	−0.422128
$453$	−6.98538	−0.328202
$454$	−36.2251	−1.70013
$455$	4.28184	0.200736
$456$	−4.38115	−0.205166
$457$	0.283972	0.0132836	0.00664182	−	0.999978i	$-0.497886\pi$
$457$	0.283972	0.0132836	0.00664182	+	0.999978i	$0.497886\pi$
$458$	−8.03327	−0.375370
$459$	8.03690	0.375130
$460$	2.56516	0.119601
$461$	27.9712	1.30275	0.651374	−	0.758757i	$-0.274193\pi$
$461$	27.9712	1.30275	0.651374	+	0.758757i	$0.274193\pi$
$462$	1.57877	0.0734512
$463$	−24.2650	−1.12769	−0.563845	−	0.825880i	$-0.690679\pi$
$463$	−24.2650	−1.12769	−0.563845	+	0.825880i	$0.690679\pi$
$464$	28.9632	1.34458
$465$	−0.766041	−0.0355243
$466$	−27.3130	−1.26525
$467$	41.3041	1.91133	0.955663	−	0.294463i	$-0.0951408\pi$
$467$	41.3041	1.91133	0.955663	+	0.294463i	$0.0951408\pi$
$468$	−2.33241	−0.107816
$469$	−19.0566	−0.879953
$470$	−21.5252	−0.992882
$471$	0.902564	0.0415880
$472$	−5.37958	−0.247615
$473$	2.93477	0.134941
$474$	7.02646	0.322736
$475$	5.21934	0.239480
$476$	5.57027	0.255313
$477$	1.97336	0.0903539
$478$	−47.7946	−2.18607
$479$	−27.1543	−1.24071	−0.620357	−	0.784320i	$-0.713012\pi$
$479$	−27.1543	−1.24071	−0.620357	+	0.784320i	$0.713012\pi$
$480$	−1.04042	−0.0474883
$481$	4.16984	0.190128
$482$	36.3777	1.65696
$483$	−4.84517	−0.220463
$484$	0.525917	0.0239053
$485$	6.46974	0.293776
$486$	14.5071	0.658056
$487$	−4.87307	−0.220820	−0.110410	−	0.993886i	$-0.535216\pi$
$487$	−4.87307	−0.220820	−0.110410	+	0.993886i	$0.535216\pi$
$488$	−25.9743	−1.17580
$489$	6.51833	0.294769
$490$	−1.09137	−0.0493031
$491$	31.3247	1.41366	0.706831	−	0.707382i	$-0.250124\pi$
$491$	31.3247	1.41366	0.706831	+	0.707382i	$0.250124\pi$
$492$	0.497599	0.0224335
$493$	−23.1708	−1.04356
$494$	−12.8111	−0.576398
$495$	−2.87162	−0.129070
$496$	−10.2096	−0.458423
$497$	42.8858	1.92369
$498$	−2.18610	−0.0979613
$499$	27.7778	1.24351	0.621754	−	0.783213i	$-0.286421\pi$
$499$	27.7778	1.24351	0.621754	+	0.783213i	$0.286421\pi$
$500$	0.525917	0.0235197
$501$	−2.35311	−0.105129
$502$	−11.2439	−0.501840
$503$	−16.2552	−0.724782	−0.362391	−	0.932026i	$-0.618039\pi$
$503$	−16.2552	−0.724782	−0.362391	+	0.932026i	$0.618039\pi$
$504$	−18.6522	−0.830833
$505$	10.7012	0.476198
$506$	−7.75189	−0.344614
$507$	3.80323	0.168908
$508$	−5.14758	−0.228387
$509$	−2.33732	−0.103600	−0.0517999	−	0.998657i	$-0.516496\pi$
$509$	−2.33732	−0.103600	−0.0517999	+	0.998657i	$0.516496\pi$
$510$	2.17540	0.0963285
$511$	2.77249	0.122648
$512$	8.50834	0.376019
$513$	10.9803	0.484793
$514$	−15.0764	−0.664992
$515$	0.663135	0.0292212
$516$	−0.553008	−0.0243448
$517$	13.5437	0.595651
$518$	−11.8970	−0.522725
$519$	4.22154	0.185305
$520$	3.61820	0.158669
$521$	7.13712	0.312683	0.156341	−	0.987703i	$-0.450030\pi$
$521$	7.13712	0.312683	0.156341	+	0.987703i	$0.450030\pi$
$522$	−27.6814	−1.21158
$523$	−35.5719	−1.55545	−0.777726	−	0.628603i	$-0.783627\pi$
$523$	−35.5719	−1.55545	−0.777726	+	0.628603i	$0.783627\pi$
$524$	−4.38353	−0.191495
$525$	−0.993369	−0.0433542
$526$	−19.4093	−0.846286
$527$	8.16772	0.355791
$528$	1.71095	0.0744594
$529$	0.790109	0.0343526
$530$	1.09216	0.0474406
$531$	6.59393	0.286152
$532$	7.61031	0.329949
$533$	−4.07833	−0.176652
$534$	−0.884198	−0.0382630
$535$	−5.14402	−0.222395
$536$	−16.1030	−0.695545
$537$	−0.272399	−0.0117549
$538$	−12.9110	−0.556633
$539$	0.686693	0.0295780
$540$	1.10641	0.0476123
$541$	14.9080	0.640946	0.320473	−	0.947258i	$-0.396158\pi$
$541$	14.9080	0.640946	0.320473	+	0.947258i	$0.396158\pi$
$542$	−21.0008	−0.902060
$543$	0.543386	0.0233189
$544$	11.0932	0.475617
$545$	−19.0573	−0.816326
$546$	2.43826	0.104348
$547$	12.7017	0.543085	0.271542	−	0.962427i	$-0.412466\pi$
$547$	12.7017	0.543085	0.271542	+	0.962427i	$0.412466\pi$
$548$	3.90793	0.166939
$549$	31.8376	1.35879
$550$	−1.58931	−0.0677685
$551$	−31.6568	−1.34863
$552$	−4.09421	−0.174261
$553$	34.2102	1.45477
$554$	−26.4876	−1.12535
$555$	−0.967385	−0.0410632
$556$	−3.51290	−0.148980
$557$	30.5291	1.29356	0.646779	−	0.762677i	$-0.276116\pi$
$557$	30.5291	1.29356	0.646779	+	0.762677i	$0.276116\pi$
$558$	9.75772	0.413077
$559$	4.53247	0.191703
$560$	−13.2393	−0.559463
$561$	−1.36877	−0.0577895
$562$	−23.9447	−1.01005
$563$	13.9172	0.586540	0.293270	−	0.956030i	$-0.405256\pi$
$563$	13.9172	0.586540	0.293270	+	0.956030i	$0.405256\pi$
$564$	−2.55208	−0.107462
$565$	−17.0646	−0.717913
$566$	8.97462	0.377231
$567$	21.7948	0.915296
$568$	36.2389	1.52055
$569$	22.8833	0.959319	0.479659	−	0.877455i	$-0.340760\pi$
$569$	22.8833	0.959319	0.479659	+	0.877455i	$0.340760\pi$
$570$	2.97212	0.124488
$571$	−12.9138	−0.540425	−0.270212	−	0.962801i	$-0.587094\pi$
$571$	−12.9138	−0.540425	−0.270212	+	0.962801i	$0.587094\pi$
$572$	0.812228	0.0339610
$573$	7.34805	0.306969
$574$	11.6359	0.485674
$575$	4.87751	0.203406
$576$	−14.1727	−0.590531
$577$	−29.6690	−1.23514	−0.617569	−	0.786516i	$-0.711882\pi$
$577$	−29.6690	−1.23514	−0.617569	+	0.786516i	$0.711882\pi$
$578$	3.82362	0.159042
$579$	−6.79815	−0.282521
$580$	−3.18984	−0.132451
$581$	−10.6436	−0.441571
$582$	3.68415	0.152713
$583$	−0.687193	−0.0284606
$584$	2.34278	0.0969449
$585$	−4.43495	−0.183363
$586$	−33.5127	−1.38440
$587$	9.91066	0.409057	0.204528	−	0.978861i	$-0.434434\pi$
$587$	9.91066	0.409057	0.204528	+	0.978861i	$0.434434\pi$
$588$	−0.129396	−0.00533619
$589$	11.1590	0.459800
$590$	3.64944	0.150245
$591$	6.71200	0.276095
$592$	−12.8930	−0.529899
$593$	18.3040	0.751656	0.375828	−	0.926689i	$-0.377358\pi$
$593$	18.3040	0.751656	0.375828	+	0.926689i	$0.377358\pi$
$594$	−3.34355	−0.137188
$595$	10.5915	0.434211
$596$	−4.42233	−0.181146
$597$	3.02897	0.123967
$598$	−11.9721	−0.489574
$599$	13.3164	0.544095	0.272047	−	0.962284i	$-0.412299\pi$
$599$	13.3164	0.544095	0.272047	+	0.962284i	$0.412299\pi$
$600$	−0.839406	−0.0342686
$601$	32.7419	1.33557	0.667785	−	0.744354i	$-0.267243\pi$
$601$	32.7419	1.33557	0.667785	+	0.744354i	$0.267243\pi$
$602$	−12.9316	−0.527054
$603$	19.7380	0.803795
$604$	10.2534	0.417204
$605$	1.00000	0.0406558
$606$	6.09373	0.247541
$607$	8.71880	0.353885	0.176943	−	0.984221i	$-0.443379\pi$
$607$	8.71880	0.353885	0.176943	+	0.984221i	$0.443379\pi$
$608$	15.1559	0.614654
$609$	6.02507	0.244148
$610$	17.6206	0.713439
$611$	20.9169	0.846208
$612$	−5.76945	−0.233216
$613$	−15.2287	−0.615083	−0.307541	−	0.951535i	$-0.599506\pi$
$613$	−15.2287	−0.615083	−0.307541	+	0.951535i	$0.599506\pi$
$614$	−7.45269	−0.300766
$615$	0.946155	0.0381527
$616$	6.49533	0.261704
$617$	7.25939	0.292252	0.146126	−	0.989266i	$-0.453319\pi$
$617$	7.25939	0.292252	0.146126	+	0.989266i	$0.453319\pi$
$618$	0.377618	0.0151900
$619$	−33.0601	−1.32880	−0.664399	−	0.747378i	$-0.731313\pi$
$619$	−33.0601	−1.32880	−0.664399	+	0.747378i	$0.731313\pi$
$620$	1.12442	0.0451578
$621$	10.2612	0.411767
$622$	−29.5327	−1.18415
$623$	−4.30496	−0.172475
$624$	2.64239	0.105780
$625$	1.00000	0.0400000
$626$	−34.9942	−1.39865
$627$	−1.87006	−0.0746832
$628$	−1.32481	−0.0528658
$629$	10.3145	0.411266
$630$	12.6534	0.504123
$631$	2.09192	0.0832779	0.0416389	−	0.999133i	$-0.486742\pi$
$631$	2.09192	0.0832779	0.0416389	+	0.999133i	$0.486742\pi$
$632$	28.9080	1.14990
$633$	−8.26371	−0.328453
$634$	−40.0086	−1.58895
$635$	−9.78783	−0.388418
$636$	0.129490	0.00513461
$637$	1.06053	0.0420198
$638$	9.63964	0.381637
$639$	−44.4193	−1.75720
$640$	−13.6516	−0.539625
$641$	25.9614	1.02542	0.512708	−	0.858563i	$-0.328643\pi$
$641$	25.9614	1.02542	0.512708	+	0.858563i	$0.328643\pi$
$642$	−2.92923	−0.115607
$643$	−37.4967	−1.47873	−0.739364	−	0.673306i	$-0.764874\pi$
$643$	−37.4967	−1.47873	−0.739364	+	0.673306i	$0.764874\pi$
$644$	7.11189	0.280248
$645$	−1.05151	−0.0414033
$646$	−31.6895	−1.24681
$647$	−41.2807	−1.62291	−0.811456	−	0.584413i	$-0.801325\pi$
$647$	−41.2807	−1.62291	−0.811456	+	0.584413i	$0.801325\pi$
$648$	18.4168	0.723482
$649$	−2.29624	−0.0901352
$650$	−2.45454	−0.0962751
$651$	−2.12384	−0.0832398
$652$	−9.56781	−0.374704
$653$	−34.0475	−1.33238	−0.666190	−	0.745782i	$-0.732076\pi$
$653$	−34.0475	−1.33238	−0.666190	+	0.745782i	$0.732076\pi$
$654$	−10.8521	−0.424349
$655$	−8.33503	−0.325677
$656$	12.6101	0.492341
$657$	−2.87162	−0.112033
$658$	−59.6783	−2.32650
$659$	35.1215	1.36814	0.684071	−	0.729416i	$-0.260208\pi$
$659$	35.1215	1.36814	0.684071	+	0.729416i	$0.260208\pi$
$660$	−0.188433	−0.00733476
$661$	−38.9130	−1.51354	−0.756769	−	0.653682i	$-0.773223\pi$
$661$	−38.9130	−1.51354	−0.756769	+	0.653682i	$0.773223\pi$
$662$	4.90059	0.190467
$663$	−2.11393	−0.0820984
$664$	−8.99395	−0.349033
$665$	14.4706	0.561145
$666$	12.3224	0.477484
$667$	−29.5835	−1.14548
$668$	3.45397	0.133638
$669$	0.423186	0.0163613
$670$	10.9241	0.422035
$671$	−11.0870	−0.428007
$672$	−2.88454	−0.111274
$673$	11.2565	0.433904	0.216952	−	0.976182i	$-0.430388\pi$
$673$	11.2565	0.433904	0.216952	+	0.976182i	$0.430388\pi$
$674$	10.1367	0.390450
$675$	2.10377	0.0809743
$676$	−5.58251	−0.214712
$677$	21.3808	0.821731	0.410865	−	0.911696i	$-0.365227\pi$
$677$	21.3808	0.821731	0.410865	+	0.911696i	$0.365227\pi$
$678$	−9.71731	−0.373191
$679$	17.9373	0.688369
$680$	8.94996	0.343215
$681$	−8.16659	−0.312944
$682$	−3.39798	−0.130115
$683$	42.2983	1.61850	0.809249	−	0.587466i	$-0.199874\pi$
$683$	42.2983	1.61850	0.809249	+	0.587466i	$0.199874\pi$
$684$	−7.88244	−0.301393
$685$	7.43070	0.283912
$686$	27.8187	1.06212
$687$	−1.81102	−0.0690948
$688$	−14.0142	−0.534288
$689$	−1.06130	−0.0404324
$690$	2.77746	0.105736
$691$	42.3738	1.61197	0.805987	−	0.591933i	$-0.201635\pi$
$691$	42.3738	1.61197	0.805987	+	0.591933i	$0.201635\pi$
$692$	−6.19651	−0.235556
$693$	−7.96155	−0.302434
$694$	43.2211	1.64065
$695$	−6.67957	−0.253370
$696$	5.09124	0.192983
$697$	−10.0881	−0.382116
$698$	−7.87949	−0.298243
$699$	−6.15745	−0.232896
$700$	1.45810	0.0551109
$701$	17.5189	0.661681	0.330841	−	0.943687i	$-0.392668\pi$
$701$	17.5189	0.661681	0.330841	+	0.943687i	$0.392668\pi$
$702$	−5.16380	−0.194895
$703$	14.0921	0.531492
$704$	4.93544	0.186011
$705$	−4.85263	−0.182761
$706$	−3.40573	−0.128176
$707$	29.6690	1.11582
$708$	0.432687	0.0162614
$709$	−30.4570	−1.14384	−0.571918	−	0.820311i	$-0.693800\pi$
$709$	−30.4570	−1.14384	−0.571918	+	0.820311i	$0.693800\pi$
$710$	−24.5841	−0.922623
$711$	−35.4335	−1.32886
$712$	−3.63774	−0.136330
$713$	10.4282	0.390539
$714$	6.03128	0.225715
$715$	1.54440	0.0577574
$716$	0.399836	0.0149426
$717$	−10.7748	−0.402393
$718$	38.1180	1.42255
$719$	−11.3820	−0.424475	−0.212238	−	0.977218i	$-0.568075\pi$
$719$	−11.3820	−0.424475	−0.212238	+	0.977218i	$0.568075\pi$
$720$	13.7127	0.511043
$721$	1.83854	0.0684706
$722$	−13.0984	−0.487472
$723$	8.20098	0.304998
$724$	−0.797599	−0.0296425
$725$	−6.06529	−0.225259
$726$	0.569443	0.0211340
$727$	17.1104	0.634589	0.317294	−	0.948327i	$-0.397226\pi$
$727$	17.1104	0.634589	0.317294	+	0.948327i	$0.397226\pi$
$728$	10.0314	0.371789
$729$	−20.3128	−0.752327
$730$	−1.58931	−0.0588231
$731$	11.2115	0.414672
$732$	2.08915	0.0772173
$733$	−26.9184	−0.994254	−0.497127	−	0.867678i	$-0.665612\pi$
$733$	−26.9184	−0.994254	−0.497127	+	0.867678i	$0.665612\pi$
$734$	−12.8931	−0.475893
$735$	−0.246039	−0.00907527
$736$	14.1633	0.522067
$737$	−6.87347	−0.253188
$738$	−12.0520	−0.443640
$739$	−45.6317	−1.67859	−0.839294	−	0.543677i	$-0.817032\pi$
$739$	−45.6317	−1.67859	−0.839294	+	0.543677i	$0.817032\pi$
$740$	1.41996	0.0521987
$741$	−2.88813	−0.106098
$742$	3.02801	0.111162
$743$	53.7454	1.97173	0.985863	−	0.167554i	$-0.0535867\pi$
$743$	53.7454	1.97173	0.985863	+	0.167554i	$0.0535867\pi$
$744$	−1.79466	−0.0657956
$745$	−8.40880	−0.308075
$746$	55.0343	2.01495
$747$	11.0242	0.403354
$748$	2.00912	0.0734608
$749$	−14.2617	−0.521113
$750$	0.569443	0.0207931
$751$	2.61297	0.0953486	0.0476743	−	0.998863i	$-0.484819\pi$
$751$	2.61297	0.0953486	0.0476743	+	0.998863i	$0.484819\pi$
$752$	−64.6744	−2.35843
$753$	−2.53483	−0.0923742
$754$	14.8875	0.542171
$755$	19.4962	0.709538
$756$	3.06751	0.111564
$757$	28.3526	1.03049	0.515246	−	0.857042i	$-0.327701\pi$
$757$	28.3526	1.03049	0.515246	+	0.857042i	$0.327701\pi$
$758$	−18.7816	−0.682178
$759$	−1.74759	−0.0634334
$760$	12.2278	0.443548
$761$	−49.4215	−1.79153	−0.895763	−	0.444531i	$-0.853370\pi$
$761$	−49.4215	−1.79153	−0.895763	+	0.444531i	$0.853370\pi$
$762$	−5.57361	−0.201911
$763$	−52.8362	−1.91280
$764$	−10.7857	−0.390213
$765$	−10.9703	−0.396631
$766$	−40.2766	−1.45525
$767$	−3.54632	−0.128050
$768$	−4.23710	−0.152893
$769$	−5.00599	−0.180521	−0.0902603	−	0.995918i	$-0.528770\pi$
$769$	−5.00599	−0.180521	−0.0902603	+	0.995918i	$0.528770\pi$
$770$	−4.40635	−0.158794
$771$	−3.39883	−0.122406
$772$	9.97854	0.359135
$773$	−47.5925	−1.71178	−0.855892	−	0.517155i	$-0.826991\pi$
$773$	−47.5925	−1.71178	−0.855892	+	0.517155i	$0.826991\pi$
$774$	13.3940	0.481438
$775$	2.13802	0.0767998
$776$	15.1572	0.544111
$777$	−2.68206	−0.0962185
$778$	−20.1642	−0.722920
$779$	−13.7828	−0.493820
$780$	−0.291017	−0.0104201
$781$	15.4683	0.553501
$782$	−29.6140	−1.05900
$783$	−12.7600	−0.456005
$784$	−3.27913	−0.117112
$785$	−2.51905	−0.0899089
$786$	−4.74632	−0.169296
$787$	−46.7784	−1.66747	−0.833735	−	0.552164i	$-0.813802\pi$
$787$	−46.7784	−1.66747	−0.833735	+	0.552164i	$0.813802\pi$
$788$	−9.85209	−0.350966
$789$	−4.37563	−0.155777
$790$	−19.6108	−0.697722
$791$	−47.3114	−1.68220
$792$	−6.72759	−0.239054
$793$	−17.1227	−0.608046
$794$	5.68854	0.201879
$795$	0.246218	0.00873244
$796$	−4.44602	−0.157585
$797$	10.6258	0.376386	0.188193	−	0.982132i	$-0.439737\pi$
$797$	10.6258	0.376386	0.188193	+	0.982132i	$0.439737\pi$
$798$	8.24016	0.291699
$799$	51.7400	1.83043
$800$	2.90380	0.102665
$801$	4.45890	0.157547
$802$	19.8250	0.700043
$803$	1.00000	0.0352892
$804$	1.29519	0.0456779
$805$	13.5228	0.476618
$806$	−5.24785	−0.184848
$807$	−2.91066	−0.102460
$808$	25.0706	0.881980
$809$	−28.0198	−0.985124	−0.492562	−	0.870277i	$-0.663940\pi$
$809$	−28.0198	−0.985124	−0.492562	+	0.870277i	$0.663940\pi$
$810$	−12.4938	−0.438986
$811$	−39.8403	−1.39898	−0.699491	−	0.714641i	$-0.746590\pi$
$811$	−39.8403	−1.39898	−0.699491	+	0.714641i	$0.746590\pi$
$812$	−8.84378	−0.310356
$813$	−4.73441	−0.166043
$814$	−4.29109	−0.150403
$815$	−18.1926	−0.637260
$816$	6.53621	0.228813
$817$	15.3176	0.535894
$818$	5.67648	0.198473
$819$	−12.2958	−0.429652
$820$	−1.38880	−0.0484989
$821$	2.87142	0.100213	0.0501067	−	0.998744i	$-0.484044\pi$
$821$	2.87142	0.100213	0.0501067	+	0.998744i	$0.484044\pi$
$822$	4.23136	0.147586
$823$	10.1523	0.353886	0.176943	−	0.984221i	$-0.443379\pi$
$823$	10.1523	0.353886	0.176943	+	0.984221i	$0.443379\pi$
$824$	1.55358	0.0541215
$825$	−0.358295	−0.0124742
$826$	10.1180	0.352051
$827$	8.78411	0.305453	0.152727	−	0.988268i	$-0.451195\pi$
$827$	8.78411	0.305453	0.152727	+	0.988268i	$0.451195\pi$
$828$	−7.36619	−0.255993
$829$	−10.1027	−0.350881	−0.175440	−	0.984490i	$-0.556135\pi$
$829$	−10.1027	−0.350881	−0.175440	+	0.984490i	$0.556135\pi$
$830$	6.10139	0.211782
$831$	−5.97136	−0.207144
$832$	7.62232	0.264256
$833$	2.62333	0.0908929
$834$	−3.80363	−0.131709
$835$	6.56752	0.227278
$836$	2.74494	0.0949357
$837$	4.49790	0.155470
$838$	−11.8288	−0.408618
$839$	−29.0683	−1.00355	−0.501774	−	0.864999i	$-0.667319\pi$
$839$	−29.0683	−1.00355	−0.501774	+	0.864999i	$0.667319\pi$
$840$	−2.32724	−0.0802976
$841$	7.78770	0.268541
$842$	−49.3629	−1.70116
$843$	−5.39810	−0.185920
$844$	12.1297	0.417523
$845$	−10.6148	−0.365161
$846$	61.8122	2.12515
$847$	2.77249	0.0952638
$848$	3.28151	0.112688
$849$	2.02324	0.0694374
$850$	−6.07154	−0.208252
$851$	13.1691	0.451432
$852$	−2.91475	−0.0998578
$853$	−6.58834	−0.225580	−0.112790	−	0.993619i	$-0.535979\pi$
$853$	−6.58834	−0.225580	−0.112790	+	0.993619i	$0.535979\pi$
$854$	48.8530	1.67172
$855$	−14.9880	−0.512579
$856$	−12.0513	−0.411905
$857$	−22.5970	−0.771900	−0.385950	−	0.922520i	$-0.626126\pi$
$857$	−22.5970	−0.771900	−0.385950	+	0.922520i	$0.626126\pi$
$858$	0.879450	0.0300239
$859$	23.5812	0.804579	0.402290	−	0.915512i	$-0.368214\pi$
$859$	23.5812	0.804579	0.402290	+	0.915512i	$0.368214\pi$
$860$	1.54344	0.0526310
$861$	2.62321	0.0893986
$862$	−29.4411	−1.00277
$863$	−13.0857	−0.445443	−0.222721	−	0.974882i	$-0.571494\pi$
$863$	−13.0857	−0.445443	−0.222721	+	0.974882i	$0.571494\pi$
$864$	6.10894	0.207830
$865$	−11.7823	−0.400610
$866$	56.9697	1.93591
$867$	0.861998	0.0292750
$868$	3.11744	0.105813
$869$	12.3392	0.418578
$870$	−3.45383	−0.117096
$871$	−10.6154	−0.359690
$872$	−44.6471	−1.51194
$873$	−18.5787	−0.628792
$874$	−40.4598	−1.36857
$875$	2.77249	0.0937272
$876$	−0.188433	−0.00636657
$877$	−5.04783	−0.170453	−0.0852266	−	0.996362i	$-0.527161\pi$
$877$	−5.04783	−0.170453	−0.0852266	+	0.996362i	$0.527161\pi$
$878$	−53.6279	−1.80985
$879$	−7.55510	−0.254827
$880$	−4.77525	−0.160973
$881$	18.0015	0.606485	0.303242	−	0.952913i	$-0.401931\pi$
$881$	18.0015	0.606485	0.303242	+	0.952913i	$0.401931\pi$
$882$	3.13401	0.105527
$883$	6.77061	0.227849	0.113925	−	0.993489i	$-0.463658\pi$
$883$	6.77061	0.227849	0.113925	+	0.993489i	$0.463658\pi$
$884$	3.10290	0.104362
$885$	0.822730	0.0276558
$886$	43.6960	1.46800
$887$	−38.4285	−1.29030	−0.645152	−	0.764054i	$-0.723206\pi$
$887$	−38.4285	−1.29030	−0.645152	+	0.764054i	$0.723206\pi$
$888$	−2.26637	−0.0760544
$889$	−27.1366	−0.910134
$890$	2.46780	0.0827207
$891$	7.86110	0.263357
$892$	−0.621165	−0.0207982
$893$	70.6891	2.36552
$894$	−4.78833	−0.160146
$895$	0.760265	0.0254129
$896$	−37.8488	−1.26444
$897$	−2.69898	−0.0901164
$898$	20.7132	0.691210
$899$	−12.9677	−0.432497
$900$	−1.51024	−0.0503412
$901$	−2.62524	−0.0874593
$902$	4.19693	0.139742
$903$	−2.91531	−0.0970154
$904$	−39.9786	−1.32967
$905$	−1.51659	−0.0504131
$906$	11.1020	0.368838
$907$	10.3893	0.344971	0.172486	−	0.985012i	$-0.444820\pi$
$907$	10.3893	0.344971	0.172486	+	0.985012i	$0.444820\pi$
$908$	11.9872	0.397808
$909$	−30.7299	−1.01925
$910$	−6.80519	−0.225590
$911$	54.2046	1.79588	0.897939	−	0.440120i	$-0.145064\pi$
$911$	54.2046	1.79588	0.897939	+	0.440120i	$0.145064\pi$
$912$	8.93001	0.295702
$913$	−3.83901	−0.127053
$914$	−0.451320	−0.0149283
$915$	3.97240	0.131324
$916$	2.65828	0.0878319
$917$	−23.1088	−0.763119
$918$	−12.7732	−0.421577
$919$	20.4846	0.675724	0.337862	−	0.941196i	$-0.390296\pi$
$919$	20.4846	0.675724	0.337862	+	0.941196i	$0.390296\pi$
$920$	11.4269	0.376735
$921$	−1.68014	−0.0553623
$922$	−44.4550	−1.46405
$923$	23.8894	0.786329
$924$	−0.522429	−0.0171867
$925$	2.69997	0.0887744
$926$	38.5647	1.26731
$927$	−1.90428	−0.0625446
$928$	−17.6124	−0.578155
$929$	−18.6103	−0.610584	−0.305292	−	0.952259i	$-0.598754\pi$
$929$	−18.6103	−0.610584	−0.305292	+	0.952259i	$0.598754\pi$
$930$	1.21748	0.0399227
$931$	3.58409	0.117464
$932$	9.03811	0.296053
$933$	−6.65785	−0.217968
$934$	−65.6452	−2.14797
$935$	3.82023	0.124935
$936$	−10.3901	−0.339611
$937$	17.3476	0.566723	0.283361	−	0.959013i	$-0.408550\pi$
$937$	17.3476	0.566723	0.283361	+	0.959013i	$0.408550\pi$
$938$	30.2869	0.988904
$939$	−7.88910	−0.257451
$940$	7.12285	0.232322
$941$	27.9871	0.912352	0.456176	−	0.889890i	$-0.349219\pi$
$941$	27.9871	0.912352	0.456176	+	0.889890i	$0.349219\pi$
$942$	−1.43446	−0.0467371
$943$	−12.8801	−0.419435
$944$	10.9651	0.356883
$945$	5.83269	0.189737
$946$	−4.66427	−0.151648
$947$	27.3964	0.890263	0.445132	−	0.895465i	$-0.353157\pi$
$947$	27.3964	0.890263	0.445132	+	0.895465i	$0.353157\pi$
$948$	−2.32511	−0.0755161
$949$	1.54440	0.0501335
$950$	−8.29517	−0.269131
$951$	−9.01955	−0.292479
$952$	24.8137	0.804216
$953$	26.4846	0.857919	0.428959	−	0.903324i	$-0.358880\pi$
$953$	26.4846	0.857919	0.428959	+	0.903324i	$0.358880\pi$
$954$	−3.13629	−0.101541
$955$	−20.5084	−0.663636
$956$	15.8156	0.511514
$957$	2.17316	0.0702483
$958$	43.1567	1.39433
$959$	20.6015	0.665258
$960$	−1.76834	−0.0570730
$961$	−26.4289	−0.852545
$962$	−6.62718	−0.213669
$963$	14.7717	0.476011
$964$	−12.0377	−0.387707
$965$	18.9736	0.610782
$966$	7.70049	0.247759
$967$	1.40806	0.0452801	0.0226401	−	0.999744i	$-0.492793\pi$
$967$	1.40806	0.0452801	0.0226401	+	0.999744i	$0.492793\pi$
$968$	2.34278	0.0752998
$969$	−7.14408	−0.229501
$970$	−10.2824	−0.330149
$971$	−53.4940	−1.71670	−0.858352	−	0.513061i	$-0.828512\pi$
$971$	−53.4940	−1.71670	−0.858352	+	0.513061i	$0.828512\pi$
$972$	−4.80052	−0.153977
$973$	−18.5190	−0.593693
$974$	7.74484	0.248161
$975$	−0.553352	−0.0177215
$976$	52.9429	1.69466
$977$	−31.4776	−1.00706	−0.503529	−	0.863978i	$-0.667965\pi$
$977$	−31.4776	−1.00706	−0.503529	+	0.863978i	$0.667965\pi$
$978$	−10.3597	−0.331265
$979$	−1.55274	−0.0496259
$980$	0.361143	0.0115363
$981$	54.7255	1.74725
$982$	−49.7847	−1.58869
$983$	−14.8466	−0.473532	−0.236766	−	0.971567i	$-0.576087\pi$
$983$	−14.8466	−0.473532	−0.236766	+	0.971567i	$0.576087\pi$
$984$	2.21663	0.0706637
$985$	−18.7332	−0.596888
$986$	36.8257	1.17277
$987$	−13.4539	−0.428241
$988$	4.23930	0.134870
$989$	14.3144	0.455170
$990$	4.56391	0.145051
$991$	−8.68902	−0.276016	−0.138008	−	0.990431i	$-0.544070\pi$
$991$	−8.68902	−0.276016	−0.138008	+	0.990431i	$0.544070\pi$
$992$	6.20838	0.197116
$993$	1.10479	0.0350595
$994$	−68.1590	−2.16187
$995$	−8.45384	−0.268005
$996$	0.723397	0.0229217
$997$	−12.9670	−0.410669	−0.205335	−	0.978692i	$-0.565828\pi$
$997$	−12.9670	−0.410669	−0.205335	+	0.978692i	$0.565828\pi$
$998$	−44.1477	−1.39747
$999$	5.68012	0.179711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.10	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.58931 q^{2} -0.358295 q^{3} +0.525917 q^{4} +1.00000 q^{5} +0.569443 q^{6} +2.77249 q^{7} +2.34278 q^{8} -2.87162 q^{9} +O(q^{10})\)	\(q-1.58931 q^{2} -0.358295 q^{3} +0.525917 q^{4} +1.00000 q^{5} +0.569443 q^{6} +2.77249 q^{7} +2.34278 q^{8} -2.87162 q^{9} -1.58931 q^{10} +1.00000 q^{11} -0.188433 q^{12} +1.54440 q^{13} -4.40635 q^{14} -0.358295 q^{15} -4.77525 q^{16} +3.82023 q^{17} +4.56391 q^{18} +5.21934 q^{19} +0.525917 q^{20} -0.993369 q^{21} -1.58931 q^{22} +4.87751 q^{23} -0.839406 q^{24} +1.00000 q^{25} -2.45454 q^{26} +2.10377 q^{27} +1.45810 q^{28} -6.06529 q^{29} +0.569443 q^{30} +2.13802 q^{31} +2.90380 q^{32} -0.358295 q^{33} -6.07154 q^{34} +2.77249 q^{35} -1.51024 q^{36} +2.69997 q^{37} -8.29517 q^{38} -0.553352 q^{39} +2.34278 q^{40} -2.64072 q^{41} +1.57877 q^{42} +2.93477 q^{43} +0.525917 q^{44} -2.87162 q^{45} -7.75189 q^{46} +13.5437 q^{47} +1.71095 q^{48} +0.686693 q^{49} -1.58931 q^{50} -1.36877 q^{51} +0.812228 q^{52} -0.687193 q^{53} -3.34355 q^{54} +1.00000 q^{55} +6.49533 q^{56} -1.87006 q^{57} +9.63964 q^{58} -2.29624 q^{59} -0.188433 q^{60} -11.0870 q^{61} -3.39798 q^{62} -7.96155 q^{63} +4.93544 q^{64} +1.54440 q^{65} +0.569443 q^{66} -6.87347 q^{67} +2.00912 q^{68} -1.74759 q^{69} -4.40635 q^{70} +15.4683 q^{71} -6.72759 q^{72} +1.00000 q^{73} -4.29109 q^{74} -0.358295 q^{75} +2.74494 q^{76} +2.77249 q^{77} +0.879450 q^{78} +12.3392 q^{79} -4.77525 q^{80} +7.86110 q^{81} +4.19693 q^{82} -3.83901 q^{83} -0.522429 q^{84} +3.82023 q^{85} -4.66427 q^{86} +2.17316 q^{87} +2.34278 q^{88} -1.55274 q^{89} +4.56391 q^{90} +4.28184 q^{91} +2.56516 q^{92} -0.766041 q^{93} -21.5252 q^{94} +5.21934 q^{95} -1.04042 q^{96} +6.46974 q^{97} -1.09137 q^{98} -2.87162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 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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