LMFDB - Embedded newform 4033.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$85$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26706 q^{2} -2.69699 q^{3} +3.13957 q^{4} -3.90758 q^{5} +6.11425 q^{6} -4.79951 q^{7} -2.58348 q^{8} +4.27377 q^{9} +O(q^{10})$	\(q-2.26706 q^{2} -2.69699 q^{3} +3.13957 q^{4} -3.90758 q^{5} +6.11425 q^{6} -4.79951 q^{7} -2.58348 q^{8} +4.27377 q^{9} +8.85872 q^{10} -1.38285 q^{11} -8.46740 q^{12} +2.27493 q^{13} +10.8808 q^{14} +10.5387 q^{15} -0.422238 q^{16} +2.73391 q^{17} -9.68891 q^{18} -4.28446 q^{19} -12.2681 q^{20} +12.9442 q^{21} +3.13500 q^{22} +6.13686 q^{23} +6.96762 q^{24} +10.2692 q^{25} -5.15740 q^{26} -3.43536 q^{27} -15.0684 q^{28} -9.75536 q^{29} -23.8919 q^{30} +1.51721 q^{31} +6.12419 q^{32} +3.72953 q^{33} -6.19794 q^{34} +18.7545 q^{35} +13.4178 q^{36} +1.00000 q^{37} +9.71313 q^{38} -6.13547 q^{39} +10.0951 q^{40} -1.14774 q^{41} -29.3454 q^{42} -8.75122 q^{43} -4.34154 q^{44} -16.7001 q^{45} -13.9126 q^{46} +12.5748 q^{47} +1.13877 q^{48} +16.0353 q^{49} -23.2809 q^{50} -7.37334 q^{51} +7.14230 q^{52} -9.73727 q^{53} +7.78817 q^{54} +5.40358 q^{55} +12.3994 q^{56} +11.5551 q^{57} +22.1160 q^{58} -2.87631 q^{59} +33.0870 q^{60} -9.93731 q^{61} -3.43960 q^{62} -20.5120 q^{63} -13.0395 q^{64} -8.88946 q^{65} -8.45507 q^{66} +2.26696 q^{67} +8.58330 q^{68} -16.5511 q^{69} -42.5175 q^{70} -5.98115 q^{71} -11.0412 q^{72} -16.5196 q^{73} -2.26706 q^{74} -27.6959 q^{75} -13.4514 q^{76} +6.63698 q^{77} +13.9095 q^{78} -6.45107 q^{79} +1.64993 q^{80} -3.55618 q^{81} +2.60200 q^{82} +7.49907 q^{83} +40.6394 q^{84} -10.6830 q^{85} +19.8396 q^{86} +26.3101 q^{87} +3.57255 q^{88} +0.279679 q^{89} +37.8602 q^{90} -10.9185 q^{91} +19.2671 q^{92} -4.09190 q^{93} -28.5079 q^{94} +16.7418 q^{95} -16.5169 q^{96} -12.6937 q^{97} -36.3530 q^{98} -5.90997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) $ 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.26706	−1.60305	−0.801527	−	0.597958i	$-0.795979\pi$
$2$	−2.26706	−1.60305	−0.801527	+	0.597958i	$0.795979\pi$
$3$	−2.69699	−1.55711	−0.778555	−	0.627576i	$-0.784047\pi$
$3$	−2.69699	−1.55711	−0.778555	+	0.627576i	$0.784047\pi$
$4$	3.13957	1.56979
$5$	−3.90758	−1.74752	−0.873761	−	0.486355i	$-0.838326\pi$
$5$	−3.90758	−1.74752	−0.873761	+	0.486355i	$0.838326\pi$
$6$	6.11425	2.49613
$7$	−4.79951	−1.81404	−0.907022	−	0.421083i	$-0.861650\pi$
$7$	−4.79951	−1.81404	−0.907022	+	0.421083i	$0.861650\pi$
$8$	−2.58348	−0.913397
$9$	4.27377	1.42459
$10$	8.85872	2.80137
$11$	−1.38285	−0.416944	−0.208472	−	0.978028i	$-0.566849\pi$
$11$	−1.38285	−0.416944	−0.208472	+	0.978028i	$0.566849\pi$
$12$	−8.46740	−2.44433
$13$	2.27493	0.630952	0.315476	−	0.948934i	$-0.397836\pi$
$13$	2.27493	0.630952	0.315476	+	0.948934i	$0.397836\pi$
$14$	10.8808	2.90801
$15$	10.5387	2.72108
$16$	−0.422238	−0.105559
$17$	2.73391	0.663071	0.331535	−	0.943443i	$-0.392433\pi$
$17$	2.73391	0.663071	0.331535	+	0.943443i	$0.392433\pi$
$18$	−9.68891	−2.28370
$19$	−4.28446	−0.982921	−0.491461	−	0.870900i	$-0.663537\pi$
$19$	−4.28446	−0.982921	−0.491461	+	0.870900i	$0.663537\pi$
$20$	−12.2681	−2.74323
$21$	12.9442	2.82467
$22$	3.13500	0.668384
$23$	6.13686	1.27962	0.639812	−	0.768532i	$-0.279012\pi$
$23$	6.13686	1.27962	0.639812	+	0.768532i	$0.279012\pi$
$24$	6.96762	1.42226
$25$	10.2692	2.05383
$26$	−5.15740	−1.01145
$27$	−3.43536	−0.661135
$28$	−15.0684	−2.84766
$29$	−9.75536	−1.81152	−0.905762	−	0.423787i	$-0.860701\pi$
$29$	−9.75536	−1.81152	−0.905762	+	0.423787i	$0.860701\pi$
$30$	−23.8919	−4.36205
$31$	1.51721	0.272498	0.136249	−	0.990675i	$-0.456495\pi$
$31$	1.51721	0.272498	0.136249	+	0.990675i	$0.456495\pi$
$32$	6.12419	1.08261
$33$	3.72953	0.649228
$34$	−6.19794	−1.06294
$35$	18.7545	3.17008
$36$	13.4178	2.23630
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	9.71313	1.57568
$39$	−6.13547	−0.982461
$40$	10.0951	1.59618
$41$	−1.14774	−0.179247	−0.0896236	−	0.995976i	$-0.528566\pi$
$41$	−1.14774	−0.179247	−0.0896236	+	0.995976i	$0.528566\pi$
$42$	−29.3454	−4.52809
$43$	−8.75122	−1.33455	−0.667274	−	0.744812i	$-0.732539\pi$
$43$	−8.75122	−1.33455	−0.667274	+	0.744812i	$0.732539\pi$
$44$	−4.34154	−0.654512
$45$	−16.7001	−2.48951
$46$	−13.9126	−2.05131
$47$	12.5748	1.83423	0.917113	−	0.398626i	$-0.130513\pi$
$47$	12.5748	1.83423	0.917113	+	0.398626i	$0.130513\pi$
$48$	1.13877	0.164368
$49$	16.0353	2.29076
$50$	−23.2809	−3.29241
$51$	−7.37334	−1.03247
$52$	7.14230	0.990459
$53$	−9.73727	−1.33752	−0.668758	−	0.743480i	$-0.733174\pi$
$53$	−9.73727	−1.33752	−0.668758	+	0.743480i	$0.733174\pi$
$54$	7.78817	1.05984
$55$	5.40358	0.728619
$56$	12.3994	1.65694
$57$	11.5551	1.53052
$58$	22.1160	2.90397
$59$	−2.87631	−0.374463	−0.187232	−	0.982316i	$-0.559951\pi$
$59$	−2.87631	−0.374463	−0.187232	+	0.982316i	$0.559951\pi$
$60$	33.0870	4.27152
$61$	−9.93731	−1.27234	−0.636171	−	0.771548i	$-0.719483\pi$
$61$	−9.93731	−1.27234	−0.636171	+	0.771548i	$0.719483\pi$
$62$	−3.43960	−0.436830
$63$	−20.5120	−2.58427
$64$	−13.0395	−1.62993
$65$	−8.88946	−1.10260
$66$	−8.45507	−1.04075
$67$	2.26696	0.276953	0.138476	−	0.990366i	$-0.455779\pi$
$67$	2.26696	0.276953	0.138476	+	0.990366i	$0.455779\pi$
$68$	8.58330	1.04088
$69$	−16.5511	−1.99251
$70$	−42.5175	−5.08182
$71$	−5.98115	−0.709832	−0.354916	−	0.934898i	$-0.615490\pi$
$71$	−5.98115	−0.709832	−0.354916	+	0.934898i	$0.615490\pi$
$72$	−11.0412	−1.30122
$73$	−16.5196	−1.93347	−0.966736	−	0.255775i	$-0.917669\pi$
$73$	−16.5196	−1.93347	−0.966736	+	0.255775i	$0.917669\pi$
$74$	−2.26706	−0.263541
$75$	−27.6959	−3.19805
$76$	−13.4514	−1.54298
$77$	6.63698	0.756355
$78$	13.9095	1.57494
$79$	−6.45107	−0.725802	−0.362901	−	0.931828i	$-0.618214\pi$
$79$	−6.45107	−0.725802	−0.362901	+	0.931828i	$0.618214\pi$
$80$	1.64993	0.184468
$81$	−3.55618	−0.395131
$82$	2.60200	0.287343
$83$	7.49907	0.823130	0.411565	−	0.911380i	$-0.364982\pi$
$83$	7.49907	0.823130	0.411565	+	0.911380i	$0.364982\pi$
$84$	40.6394	4.43412
$85$	−10.6830	−1.15873
$86$	19.8396	2.13935
$87$	26.3101	2.82074
$88$	3.57255	0.380835
$89$	0.279679	0.0296460	0.0148230	−	0.999890i	$-0.495282\pi$
$89$	0.279679	0.0296460	0.0148230	+	0.999890i	$0.495282\pi$
$90$	37.8602	3.99081
$91$	−10.9185	−1.14457
$92$	19.2671	2.00873
$93$	−4.09190	−0.424310
$94$	−28.5079	−2.94037
$95$	16.7418	1.71768
$96$	−16.5169	−1.68575
$97$	−12.6937	−1.28885	−0.644426	−	0.764666i	$-0.722904\pi$
$97$	−12.6937	−1.28885	−0.644426	+	0.764666i	$0.722904\pi$
$98$	−36.3530	−3.67221
$99$	−5.90997	−0.593975
$100$	32.2408	3.22408
$101$	−8.19444	−0.815377	−0.407689	−	0.913121i	$-0.633665\pi$
$101$	−8.19444	−0.815377	−0.407689	+	0.913121i	$0.633665\pi$
$102$	16.7158	1.65511
$103$	4.51496	0.444872	0.222436	−	0.974947i	$-0.428599\pi$
$103$	4.51496	0.444872	0.222436	+	0.974947i	$0.428599\pi$
$104$	−5.87723	−0.576309
$105$	−50.5807	−4.93617
$106$	22.0750	2.14411
$107$	14.8383	1.43447	0.717237	−	0.696830i	$-0.245407\pi$
$107$	14.8383	1.43447	0.717237	+	0.696830i	$0.245407\pi$
$108$	−10.7856	−1.03784
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	−12.2503	−1.16802
$111$	−2.69699	−0.255987
$112$	2.02654	0.191490
$113$	11.4853	1.08045	0.540224	−	0.841521i	$-0.318339\pi$
$113$	11.4853	1.08045	0.540224	+	0.841521i	$0.318339\pi$
$114$	−26.1962	−2.45350
$115$	−23.9803	−2.23617
$116$	−30.6276	−2.84370
$117$	9.72253	0.898848
$118$	6.52077	0.600285
$119$	−13.1214	−1.20284
$120$	−27.2265	−2.48543
$121$	−9.08774	−0.826158
$122$	22.5285	2.03963
$123$	3.09545	0.279108
$124$	4.76338	0.427764
$125$	−20.5897	−1.84160
$126$	46.5020	4.14273
$127$	2.27602	0.201964	0.100982	−	0.994888i	$-0.467802\pi$
$127$	2.27602	0.201964	0.100982	+	0.994888i	$0.467802\pi$
$128$	17.3129	1.53026
$129$	23.6020	2.07804
$130$	20.1530	1.76753
$131$	−2.27581	−0.198838	−0.0994191	−	0.995046i	$-0.531698\pi$
$131$	−2.27581	−0.198838	−0.0994191	+	0.995046i	$0.531698\pi$
$132$	11.7091	1.01915
$133$	20.5633	1.78306
$134$	−5.13933	−0.443971
$135$	13.4239	1.15535
$136$	−7.06299	−0.605647
$137$	−6.84896	−0.585146	−0.292573	−	0.956243i	$-0.594511\pi$
$137$	−6.84896	−0.585146	−0.292573	+	0.956243i	$0.594511\pi$
$138$	37.5223	3.19411
$139$	−5.59110	−0.474231	−0.237115	−	0.971481i	$-0.576202\pi$
$139$	−5.59110	−0.474231	−0.237115	+	0.971481i	$0.576202\pi$
$140$	58.8810	4.97635
$141$	−33.9142	−2.85609
$142$	13.5596	1.13790
$143$	−3.14588	−0.263071
$144$	−1.80455	−0.150379
$145$	38.1198	3.16568
$146$	37.4510	3.09946
$147$	−43.2471	−3.56696
$148$	3.13957	0.258071
$149$	−14.4316	−1.18228	−0.591141	−	0.806568i	$-0.701322\pi$
$149$	−14.4316	−1.18228	−0.591141	+	0.806568i	$0.701322\pi$
$150$	62.7883	5.12664
$151$	11.3800	0.926089	0.463044	−	0.886335i	$-0.346757\pi$
$151$	11.3800	0.926089	0.463044	+	0.886335i	$0.346757\pi$
$152$	11.0688	0.897798
$153$	11.6841	0.944605
$154$	−15.0465	−1.21248
$155$	−5.92860	−0.476197
$156$	−19.2627	−1.54225
$157$	−12.5949	−1.00518	−0.502592	−	0.864524i	$-0.667620\pi$
$157$	−12.5949	−1.00518	−0.502592	+	0.864524i	$0.667620\pi$
$158$	14.6250	1.16350
$159$	26.2614	2.08266
$160$	−23.9308	−1.89189
$161$	−29.4539	−2.32129
$162$	8.06208	0.633417
$163$	−12.9150	−1.01158	−0.505791	−	0.862656i	$-0.668799\pi$
$163$	−12.9150	−1.01158	−0.505791	+	0.862656i	$0.668799\pi$
$164$	−3.60342	−0.281380
$165$	−14.5734	−1.13454
$166$	−17.0009	−1.31952
$167$	−12.9607	−1.00293	−0.501463	−	0.865179i	$-0.667205\pi$
$167$	−12.9607	−1.00293	−0.501463	+	0.865179i	$0.667205\pi$
$168$	−33.4412	−2.58004
$169$	−7.82470	−0.601900
$170$	24.2190	1.85751
$171$	−18.3108	−1.40026
$172$	−27.4751	−2.09495
$173$	−2.25143	−0.171173	−0.0855866	−	0.996331i	$-0.527276\pi$
$173$	−2.25143	−0.171173	−0.0855866	+	0.996331i	$0.527276\pi$
$174$	−59.6467	−4.52180
$175$	−49.2870	−3.72575
$176$	0.583890	0.0440124
$177$	7.75738	0.583080
$178$	−0.634051	−0.0475241
$179$	−6.45763	−0.482666	−0.241333	−	0.970442i	$-0.577585\pi$
$179$	−6.45763	−0.482666	−0.241333	+	0.970442i	$0.577585\pi$
$180$	−52.4312	−3.90799
$181$	−22.4584	−1.66932	−0.834661	−	0.550763i	$-0.814337\pi$
$181$	−22.4584	−1.66932	−0.834661	+	0.550763i	$0.814337\pi$
$182$	24.7530	1.83482
$183$	26.8009	1.98118
$184$	−15.8544	−1.16880
$185$	−3.90758	−0.287291
$186$	9.27658	0.680192
$187$	−3.78058	−0.276463
$188$	39.4796	2.87934
$189$	16.4880	1.19933
$190$	−37.9548	−2.75353
$191$	16.7988	1.21552	0.607758	−	0.794122i	$-0.292069\pi$
$191$	16.7988	1.21552	0.607758	+	0.794122i	$0.292069\pi$
$192$	35.1673	2.53798
$193$	−9.77320	−0.703490	−0.351745	−	0.936096i	$-0.614412\pi$
$193$	−9.77320	−0.703490	−0.351745	+	0.936096i	$0.614412\pi$
$194$	28.7775	2.06610
$195$	23.9748	1.71687
$196$	50.3439	3.59599
$197$	−25.1556	−1.79226	−0.896132	−	0.443788i	$-0.853634\pi$
$197$	−25.1556	−1.79226	−0.896132	+	0.443788i	$0.853634\pi$
$198$	13.3983	0.952174
$199$	18.5202	1.31286	0.656431	−	0.754386i	$-0.272065\pi$
$199$	18.5202	1.31286	0.656431	+	0.754386i	$0.272065\pi$
$200$	−26.5302	−1.87597
$201$	−6.11397	−0.431246
$202$	18.5773	1.30709
$203$	46.8209	3.28618
$204$	−23.1491	−1.62076
$205$	4.48489	0.313238
$206$	−10.2357	−0.713154
$207$	26.2275	1.82294
$208$	−0.960561	−0.0666029
$209$	5.92474	0.409823
$210$	114.669	7.91295
$211$	6.59359	0.453922	0.226961	−	0.973904i	$-0.427121\pi$
$211$	6.59359	0.453922	0.226961	+	0.973904i	$0.427121\pi$
$212$	−30.5708	−2.09961
$213$	16.1311	1.10529
$214$	−33.6394	−2.29954
$215$	34.1961	2.33215
$216$	8.87517	0.603879
$217$	−7.28185	−0.494324
$218$	2.26706	0.153545
$219$	44.5532	3.01063
$220$	16.9649	1.14378
$221$	6.21945	0.418365
$222$	6.11425	0.410362
$223$	−12.3053	−0.824024	−0.412012	−	0.911178i	$-0.635174\pi$
$223$	−12.3053	−0.824024	−0.412012	+	0.911178i	$0.635174\pi$
$224$	−29.3931	−1.96391
$225$	43.8881	2.92587
$226$	−26.0379	−1.73202
$227$	−6.59178	−0.437512	−0.218756	−	0.975780i	$-0.570200\pi$
$227$	−6.59178	−0.437512	−0.218756	+	0.975780i	$0.570200\pi$
$228$	36.2782	2.40258
$229$	1.40131	0.0926015	0.0463007	−	0.998928i	$-0.485257\pi$
$229$	1.40131	0.0926015	0.0463007	+	0.998928i	$0.485257\pi$
$230$	54.3647	3.58470
$231$	−17.8999	−1.17773
$232$	25.2027	1.65464
$233$	−9.92219	−0.650024	−0.325012	−	0.945710i	$-0.605368\pi$
$233$	−9.92219	−0.650024	−0.325012	+	0.945710i	$0.605368\pi$
$234$	−22.0416	−1.44090
$235$	−49.1371	−3.20535
$236$	−9.03037	−0.587827
$237$	17.3985	1.13015
$238$	29.7471	1.92822
$239$	−3.63292	−0.234994	−0.117497	−	0.993073i	$-0.537487\pi$
$239$	−3.63292	−0.234994	−0.117497	+	0.993073i	$0.537487\pi$
$240$	−4.44985	−0.287236
$241$	−8.95515	−0.576852	−0.288426	−	0.957502i	$-0.593132\pi$
$241$	−8.95515	−0.576852	−0.288426	+	0.957502i	$0.593132\pi$
$242$	20.6025	1.32438
$243$	19.8971	1.27640
$244$	−31.1989	−1.99730
$245$	−62.6592	−4.00315
$246$	−7.01758	−0.447425
$247$	−9.74683	−0.620176
$248$	−3.91967	−0.248899
$249$	−20.2250	−1.28170
$250$	46.6782	2.95219
$251$	−6.07033	−0.383156	−0.191578	−	0.981477i	$-0.561360\pi$
$251$	−6.07033	−0.383156	−0.191578	+	0.981477i	$0.561360\pi$
$252$	−64.3989	−4.05675
$253$	−8.48633	−0.533531
$254$	−5.15988	−0.323759
$255$	28.8119	1.80427
$256$	−13.1704	−0.823151
$257$	23.5738	1.47049	0.735246	−	0.677800i	$-0.237067\pi$
$257$	23.5738	1.47049	0.735246	+	0.677800i	$0.237067\pi$
$258$	−53.5071	−3.33121
$259$	−4.79951	−0.298227
$260$	−27.9091	−1.73085
$261$	−41.6922	−2.58068
$262$	5.15940	0.318749
$263$	1.47912	0.0912067	0.0456034	−	0.998960i	$-0.485479\pi$
$263$	1.47912	0.0912067	0.0456034	+	0.998960i	$0.485479\pi$
$264$	−9.63515	−0.593003
$265$	38.0492	2.33734
$266$	−46.6182	−2.85835
$267$	−0.754294	−0.0461620
$268$	7.11727	0.434757
$269$	29.2441	1.78304	0.891522	−	0.452978i	$-0.149638\pi$
$269$	29.2441	1.78304	0.891522	+	0.452978i	$0.149638\pi$
$270$	−30.4329	−1.85209
$271$	−5.60187	−0.340289	−0.170145	−	0.985419i	$-0.554424\pi$
$271$	−5.60187	−0.340289	−0.170145	+	0.985419i	$0.554424\pi$
$272$	−1.15436	−0.0699934
$273$	29.4472	1.78223
$274$	15.5270	0.938021
$275$	−14.2007	−0.856334
$276$	−51.9632	−3.12782
$277$	−1.94784	−0.117034	−0.0585171	−	0.998286i	$-0.518637\pi$
$277$	−1.94784	−0.117034	−0.0585171	+	0.998286i	$0.518637\pi$
$278$	12.6754	0.760218
$279$	6.48420	0.388199
$280$	−48.4517	−2.89554
$281$	−26.9135	−1.60553	−0.802763	−	0.596298i	$-0.796638\pi$
$281$	−26.9135	−1.60553	−0.802763	+	0.596298i	$0.796638\pi$
$282$	76.8856	4.57847
$283$	−5.39817	−0.320888	−0.160444	−	0.987045i	$-0.551293\pi$
$283$	−5.39817	−0.320888	−0.160444	+	0.987045i	$0.551293\pi$
$284$	−18.7782	−1.11428
$285$	−45.1527	−2.67461
$286$	7.13190	0.421718
$287$	5.50860	0.325162
$288$	26.1734	1.54228
$289$	−9.52574	−0.560337
$290$	−86.4200	−5.07476
$291$	34.2349	2.00689
$292$	−51.8644	−3.03514
$293$	−9.20631	−0.537838	−0.268919	−	0.963163i	$-0.586666\pi$
$293$	−9.20631	−0.537838	−0.268919	+	0.963163i	$0.586666\pi$
$294$	98.0438	5.71803
$295$	11.2394	0.654383
$296$	−2.58348	−0.150162
$297$	4.75057	0.275656
$298$	32.7173	1.89526
$299$	13.9609	0.807381
$300$	−86.9532	−5.02025
$301$	42.0015	2.42093
$302$	−25.7991	−1.48457
$303$	22.1003	1.26963
$304$	1.80906	0.103757
$305$	38.8308	2.22345
$306$	−26.4886	−1.51425
$307$	−16.1861	−0.923791	−0.461896	−	0.886934i	$-0.652831\pi$
$307$	−16.1861	−0.923791	−0.461896	+	0.886934i	$0.652831\pi$
$308$	20.8373	1.18731
$309$	−12.1768	−0.692715
$310$	13.4405	0.763370
$311$	29.3232	1.66277	0.831384	−	0.555698i	$-0.187549\pi$
$311$	29.3232	1.66277	0.831384	+	0.555698i	$0.187549\pi$
$312$	15.8508	0.897377
$313$	27.9445	1.57952	0.789758	−	0.613418i	$-0.210206\pi$
$313$	27.9445	1.57952	0.789758	+	0.613418i	$0.210206\pi$
$314$	28.5535	1.61137
$315$	80.1523	4.51607
$316$	−20.2536	−1.13935
$317$	12.3817	0.695426	0.347713	−	0.937601i	$-0.386958\pi$
$317$	12.3817	0.695426	0.347713	+	0.937601i	$0.386958\pi$
$318$	−59.5361	−3.33862
$319$	13.4902	0.755304
$320$	50.9527	2.84834
$321$	−40.0188	−2.23363
$322$	66.7738	3.72116
$323$	−11.7133	−0.651746
$324$	−11.1649	−0.620271
$325$	23.3616	1.29587
$326$	29.2791	1.62162
$327$	2.69699	0.149144
$328$	2.96516	0.163724
$329$	−60.3530	−3.32737
$330$	33.0389	1.81873
$331$	−18.6325	−1.02414	−0.512068	−	0.858945i	$-0.671120\pi$
$331$	−18.6325	−1.02414	−0.512068	+	0.858945i	$0.671120\pi$
$332$	23.5439	1.29214
$333$	4.27377	0.234201
$334$	29.3826	1.60775
$335$	−8.85831	−0.483981
$336$	−5.46555	−0.298170
$337$	−26.0497	−1.41902	−0.709510	−	0.704695i	$-0.751084\pi$
$337$	−26.0497	−1.41902	−0.709510	+	0.704695i	$0.751084\pi$
$338$	17.7391	0.964879
$339$	−30.9758	−1.68238
$340$	−33.5399	−1.81896
$341$	−2.09806	−0.113617
$342$	41.5117	2.24470
$343$	−43.3650	−2.34149
$344$	22.6086	1.21897
$345$	64.6746	3.48196
$346$	5.10414	0.274400
$347$	−33.6303	−1.80537	−0.902686	−	0.430301i	$-0.858408\pi$
$347$	−33.6303	−1.80537	−0.902686	+	0.430301i	$0.858408\pi$
$348$	82.6025	4.42796
$349$	28.4304	1.52184	0.760921	−	0.648844i	$-0.224747\pi$
$349$	28.4304	1.52184	0.760921	+	0.648844i	$0.224747\pi$
$350$	111.737	5.97258
$351$	−7.81520	−0.417144
$352$	−8.46882	−0.451390
$353$	−6.04422	−0.321701	−0.160851	−	0.986979i	$-0.551424\pi$
$353$	−6.04422	−0.321701	−0.160851	+	0.986979i	$0.551424\pi$
$354$	−17.5865	−0.934710
$355$	23.3718	1.24045
$356$	0.878073	0.0465378
$357$	35.3884	1.87295
$358$	14.6399	0.773740
$359$	−15.0125	−0.792328	−0.396164	−	0.918180i	$-0.629659\pi$
$359$	−15.0125	−0.792328	−0.396164	+	0.918180i	$0.629659\pi$
$360$	43.1443	2.27391
$361$	−0.643441	−0.0338653
$362$	50.9147	2.67602
$363$	24.5096	1.28642
$364$	−34.2795	−1.79674
$365$	64.5516	3.37879
$366$	−60.7592	−3.17593
$367$	−5.74743	−0.300013	−0.150007	−	0.988685i	$-0.547930\pi$
$367$	−5.74743	−0.300013	−0.150007	+	0.988685i	$0.547930\pi$
$368$	−2.59121	−0.135076
$369$	−4.90519	−0.255354
$370$	8.85872	0.460543
$371$	46.7341	2.42631
$372$	−12.8468	−0.666075
$373$	5.73024	0.296700	0.148350	−	0.988935i	$-0.452604\pi$
$373$	5.73024	0.296700	0.148350	+	0.988935i	$0.452604\pi$
$374$	8.57081	0.443186
$375$	55.5303	2.86757
$376$	−32.4868	−1.67538
$377$	−22.1927	−1.14298
$378$	−37.3794	−1.92259
$379$	2.33628	0.120007	0.0600034	−	0.998198i	$-0.480889\pi$
$379$	2.33628	0.120007	0.0600034	+	0.998198i	$0.480889\pi$
$380$	52.5622	2.69638
$381$	−6.13841	−0.314480
$382$	−38.0838	−1.94854
$383$	38.8560	1.98545	0.992724	−	0.120415i	$-0.0384226\pi$
$383$	38.8560	1.98545	0.992724	+	0.120415i	$0.0384226\pi$
$384$	−46.6927	−2.38278
$385$	−25.9345	−1.32175
$386$	22.1564	1.12773
$387$	−37.4007	−1.90119
$388$	−39.8528	−2.02322
$389$	25.0339	1.26927	0.634633	−	0.772813i	$-0.281151\pi$
$389$	25.0339	1.26927	0.634633	+	0.772813i	$0.281151\pi$
$390$	−54.3524	−2.75224
$391$	16.7776	0.848481
$392$	−41.4268	−2.09237
$393$	6.13784	0.309613
$394$	57.0293	2.87310
$395$	25.2081	1.26836
$396$	−18.5548	−0.932413
$397$	0.770024	0.0386464	0.0193232	−	0.999813i	$-0.493849\pi$
$397$	0.770024	0.0386464	0.0193232	+	0.999813i	$0.493849\pi$
$398$	−41.9864	−2.10459
$399$	−55.4590	−2.77642
$400$	−4.33603	−0.216802
$401$	−28.2063	−1.40856	−0.704279	−	0.709923i	$-0.748730\pi$
$401$	−28.2063	−1.40856	−0.704279	+	0.709923i	$0.748730\pi$
$402$	13.8607	0.691311
$403$	3.45154	0.171933
$404$	−25.7270	−1.27997
$405$	13.8961	0.690501
$406$	−106.146	−5.26793
$407$	−1.38285	−0.0685452
$408$	19.0488	0.943059
$409$	−39.6979	−1.96294	−0.981469	−	0.191623i	$-0.938625\pi$
$409$	−39.6979	−1.96294	−0.981469	+	0.191623i	$0.938625\pi$
$410$	−10.1675	−0.502138
$411$	18.4716	0.911136
$412$	14.1750	0.698354
$413$	13.8049	0.679293
$414$	−59.4595	−2.92227
$415$	−29.3032	−1.43844
$416$	13.9321	0.683078
$417$	15.0792	0.738429
$418$	−13.4318	−0.656969
$419$	13.0860	0.639293	0.319646	−	0.947537i	$-0.396436\pi$
$419$	13.0860	0.639293	0.319646	+	0.947537i	$0.396436\pi$
$420$	−158.802	−7.74872
$421$	16.8470	0.821071	0.410536	−	0.911845i	$-0.365342\pi$
$421$	16.8470	0.821071	0.410536	+	0.911845i	$0.365342\pi$
$422$	−14.9481	−0.727662
$423$	53.7420	2.61302
$424$	25.1560	1.22168
$425$	28.0750	1.36184
$426$	−36.5702	−1.77183
$427$	47.6942	2.30808
$428$	46.5859	2.25181
$429$	8.48441	0.409631
$430$	−77.5246	−3.73857
$431$	−2.56848	−0.123719	−0.0618597	−	0.998085i	$-0.519703\pi$
$431$	−2.56848	−0.123719	−0.0618597	+	0.998085i	$0.519703\pi$
$432$	1.45054	0.0697891
$433$	9.02113	0.433528	0.216764	−	0.976224i	$-0.430450\pi$
$433$	9.02113	0.433528	0.216764	+	0.976224i	$0.430450\pi$
$434$	16.5084	0.792429
$435$	−102.809	−4.92931
$436$	−3.13957	−0.150358
$437$	−26.2931	−1.25777
$438$	−101.005	−4.82620
$439$	−15.5195	−0.740704	−0.370352	−	0.928891i	$-0.620763\pi$
$439$	−15.5195	−0.740704	−0.370352	+	0.928891i	$0.620763\pi$
$440$	−13.9600	−0.665518
$441$	68.5312	3.26339
$442$	−14.0999	−0.670663
$443$	−2.47284	−0.117488	−0.0587440	−	0.998273i	$-0.518710\pi$
$443$	−2.47284	−0.117488	−0.0587440	+	0.998273i	$0.518710\pi$
$444$	−8.46740	−0.401845
$445$	−1.09287	−0.0518070
$446$	27.8969	1.32096
$447$	38.9219	1.84094
$448$	62.5830	2.95677
$449$	0.118434	0.00558924	0.00279462	−	0.999996i	$-0.499110\pi$
$449$	0.118434	0.00558924	0.00279462	+	0.999996i	$0.499110\pi$
$450$	−99.4971	−4.69034
$451$	1.58715	0.0747360
$452$	36.0590	1.69607
$453$	−30.6917	−1.44202
$454$	14.9440	0.701356
$455$	42.6651	2.00017
$456$	−29.8525	−1.39797
$457$	−36.8279	−1.72274	−0.861369	−	0.507979i	$-0.830393\pi$
$457$	−36.8279	−1.72274	−0.861369	+	0.507979i	$0.830393\pi$
$458$	−3.17687	−0.148445
$459$	−9.39196	−0.438379
$460$	−75.2877	−3.51031
$461$	0.785039	0.0365629	0.0182815	−	0.999833i	$-0.494181\pi$
$461$	0.785039	0.0365629	0.0182815	+	0.999833i	$0.494181\pi$
$462$	40.5802	1.88796
$463$	11.4484	0.532055	0.266027	−	0.963965i	$-0.414289\pi$
$463$	11.4484	0.532055	0.266027	+	0.963965i	$0.414289\pi$
$464$	4.11908	0.191224
$465$	15.9894	0.741491
$466$	22.4942	1.04202
$467$	37.9401	1.75566	0.877829	−	0.478974i	$-0.158991\pi$
$467$	37.9401	1.75566	0.877829	+	0.478974i	$0.158991\pi$
$468$	30.5246	1.41100
$469$	−10.8803	−0.502405
$470$	111.397	5.13836
$471$	33.9684	1.56518
$472$	7.43087	0.342034
$473$	12.1016	0.556432
$474$	−39.4435	−1.81170
$475$	−43.9978	−2.01876
$476$	−41.1956	−1.88820
$477$	−41.6149	−1.90541
$478$	8.23605	0.376708
$479$	−29.8738	−1.36497	−0.682484	−	0.730901i	$-0.739100\pi$
$479$	−29.8738	−1.36497	−0.682484	+	0.730901i	$0.739100\pi$
$480$	64.5411	2.94589
$481$	2.27493	0.103728
$482$	20.3019	0.924725
$483$	79.4370	3.61451
$484$	−28.5316	−1.29689
$485$	49.6017	2.25230
$486$	−45.1079	−2.04614
$487$	−0.0302710	−0.00137171	−0.000685855	−	1.00000i	$-0.500218\pi$
$487$	−0.0302710	−0.00137171	−0.000685855		1.00000i	$0.500218\pi$
$488$	25.6728	1.16215
$489$	34.8317	1.57514
$490$	142.052	6.41726
$491$	−25.4346	−1.14785	−0.573923	−	0.818909i	$-0.694579\pi$
$491$	−25.4346	−1.14785	−0.573923	+	0.818909i	$0.694579\pi$
$492$	9.71839	0.438139
$493$	−26.6703	−1.20117
$494$	22.0967	0.994176
$495$	23.0937	1.03798
$496$	−0.640622	−0.0287648
$497$	28.7066	1.28767
$498$	45.8512	2.05464
$499$	1.05251	0.0471169	0.0235584	−	0.999722i	$-0.492500\pi$
$499$	1.05251	0.0471169	0.0235584	+	0.999722i	$0.492500\pi$
$500$	−64.6429	−2.89092
$501$	34.9548	1.56167
$502$	13.7618	0.614219
$503$	13.6643	0.609259	0.304630	−	0.952471i	$-0.401467\pi$
$503$	13.6643	0.609259	0.304630	+	0.952471i	$0.401467\pi$
$504$	52.9923	2.36047
$505$	32.0204	1.42489
$506$	19.2390	0.855280
$507$	21.1032	0.937224
$508$	7.14572	0.317040
$509$	−6.02784	−0.267179	−0.133590	−	0.991037i	$-0.542650\pi$
$509$	−6.02784	−0.267179	−0.133590	+	0.991037i	$0.542650\pi$
$510$	−65.3184	−2.89235
$511$	79.2860	3.50740
$512$	−4.76755	−0.210698
$513$	14.7186	0.649844
$514$	−53.4432	−2.35728
$515$	−17.6426	−0.777424
$516$	74.1001	3.26207
$517$	−17.3891	−0.764770
$518$	10.8808	0.478074
$519$	6.07210	0.266535
$520$	22.9657	1.00711
$521$	4.47223	0.195932	0.0979661	−	0.995190i	$-0.468766\pi$
$521$	4.47223	0.195932	0.0979661	+	0.995190i	$0.468766\pi$
$522$	94.5188	4.13697
$523$	−15.2839	−0.668316	−0.334158	−	0.942517i	$-0.608452\pi$
$523$	−15.2839	−0.668316	−0.334158	+	0.942517i	$0.608452\pi$
$524$	−7.14506	−0.312133
$525$	132.927	5.80140
$526$	−3.35327	−0.146209
$527$	4.14791	0.180686
$528$	−1.57475	−0.0685321
$529$	14.6610	0.637436
$530$	−86.2598	−3.74689
$531$	−12.2927	−0.533457
$532$	64.5599	2.79903
$533$	−2.61103	−0.113096
$534$	1.71003	0.0740003
$535$	−57.9819	−2.50677
$536$	−5.85663	−0.252968
$537$	17.4162	0.751564
$538$	−66.2982	−2.85832
$539$	−22.1743	−0.955117
$540$	42.1454	1.81365
$541$	15.9178	0.684362	0.342181	−	0.939634i	$-0.388834\pi$
$541$	15.9178	0.684362	0.342181	+	0.939634i	$0.388834\pi$
$542$	12.6998	0.545503
$543$	60.5703	2.59932
$544$	16.7430	0.717850
$545$	3.90758	0.167382
$546$	−66.7587	−2.85701
$547$	−43.0374	−1.84015	−0.920073	−	0.391747i	$-0.871871\pi$
$547$	−43.0374	−1.84015	−0.920073	+	0.391747i	$0.871871\pi$
$548$	−21.5028	−0.918553
$549$	−42.4698	−1.81257
$550$	32.1938	1.37275
$551$	41.7964	1.78059
$552$	42.7593	1.81996
$553$	30.9620	1.31664
$554$	4.41587	0.187612
$555$	10.5387	0.447344
$556$	−17.5536	−0.744441
$557$	28.7849	1.21966	0.609829	−	0.792533i	$-0.291238\pi$
$557$	28.7849	1.21966	0.609829	+	0.792533i	$0.291238\pi$
$558$	−14.7001	−0.622304
$559$	−19.9084	−0.842035
$560$	−7.91885	−0.334632
$561$	10.1962	0.430484
$562$	61.0146	2.57375
$563$	−5.09060	−0.214543	−0.107272	−	0.994230i	$-0.534211\pi$
$563$	−5.09060	−0.214543	−0.107272	+	0.994230i	$0.534211\pi$
$564$	−106.476	−4.48345
$565$	−44.8798	−1.88811
$566$	12.2380	0.514401
$567$	17.0679	0.716785
$568$	15.4522	0.648358
$569$	44.7274	1.87507	0.937536	−	0.347889i	$-0.113101\pi$
$569$	44.7274	1.87507	0.937536	+	0.347889i	$0.113101\pi$
$570$	102.364	4.28755
$571$	36.7979	1.53994	0.769972	−	0.638077i	$-0.220270\pi$
$571$	36.7979	1.53994	0.769972	+	0.638077i	$0.220270\pi$
$572$	−9.87670	−0.412966
$573$	−45.3061	−1.89269
$574$	−12.4883	−0.521253
$575$	63.0205	2.62814
$576$	−55.7277	−2.32199
$577$	−21.9204	−0.912556	−0.456278	−	0.889837i	$-0.650818\pi$
$577$	−21.9204	−0.912556	−0.456278	+	0.889837i	$0.650818\pi$
$578$	21.5954	0.898252
$579$	26.3583	1.09541
$580$	119.680	4.96944
$581$	−35.9919	−1.49319
$582$	−77.6126	−3.21715
$583$	13.4652	0.557670
$584$	42.6780	1.76603
$585$	−37.9916	−1.57076
$586$	20.8713	0.862185
$587$	−21.2708	−0.877938	−0.438969	−	0.898502i	$-0.644656\pi$
$587$	−21.2708	−0.877938	−0.438969	+	0.898502i	$0.644656\pi$
$588$	−135.777	−5.59936
$589$	−6.50040	−0.267844
$590$	−25.4804	−1.04901
$591$	67.8445	2.79075
$592$	−0.422238	−0.0173539
$593$	15.9520	0.655070	0.327535	−	0.944839i	$-0.393782\pi$
$593$	15.9520	0.655070	0.327535	+	0.944839i	$0.393782\pi$
$594$	−10.7698	−0.441892
$595$	51.2730	2.10199
$596$	−45.3090	−1.85593
$597$	−49.9489	−2.04427
$598$	−31.6503	−1.29428
$599$	−30.0794	−1.22901	−0.614506	−	0.788912i	$-0.710645\pi$
$599$	−30.0794	−1.22901	−0.614506	+	0.788912i	$0.710645\pi$
$600$	71.5517	2.92109
$601$	−20.3443	−0.829861	−0.414930	−	0.909853i	$-0.636194\pi$
$601$	−20.3443	−0.829861	−0.414930	+	0.909853i	$0.636194\pi$
$602$	−95.2201	−3.88088
$603$	9.68846	0.394545
$604$	35.7282	1.45376
$605$	35.5110	1.44373
$606$	−50.1029	−2.03529
$607$	−20.3111	−0.824402	−0.412201	−	0.911093i	$-0.635240\pi$
$607$	−20.3111	−0.824402	−0.412201	+	0.911093i	$0.635240\pi$
$608$	−26.2388	−1.06413
$609$	−126.276	−5.11695
$610$	−88.0319	−3.56431
$611$	28.6068	1.15731
$612$	36.6831	1.48283
$613$	36.1412	1.45973	0.729864	−	0.683592i	$-0.239583\pi$
$613$	36.1412	1.45973	0.729864	+	0.683592i	$0.239583\pi$
$614$	36.6950	1.48089
$615$	−12.0957	−0.487747
$616$	−17.1465	−0.690852
$617$	−13.2986	−0.535383	−0.267691	−	0.963505i	$-0.586261\pi$
$617$	−13.2986	−0.535383	−0.267691	+	0.963505i	$0.586261\pi$
$618$	27.6056	1.11046
$619$	−7.63434	−0.306850	−0.153425	−	0.988160i	$-0.549030\pi$
$619$	−7.63434	−0.306850	−0.153425	+	0.988160i	$0.549030\pi$
$620$	−18.6133	−0.747527
$621$	−21.0823	−0.846004
$622$	−66.4776	−2.66551
$623$	−1.34232	−0.0537791
$624$	2.59063	0.103708
$625$	29.1101	1.16440
$626$	−63.3519	−2.53205
$627$	−15.9790	−0.638140
$628$	−39.5427	−1.57792
$629$	2.73391	0.109008
$630$	−181.710	−7.23951
$631$	−35.6061	−1.41746	−0.708729	−	0.705481i	$-0.750731\pi$
$631$	−35.6061	−1.41746	−0.708729	+	0.705481i	$0.750731\pi$
$632$	16.6662	0.662945
$633$	−17.7829	−0.706806
$634$	−28.0701	−1.11481
$635$	−8.89373	−0.352937
$636$	82.4494	3.26933
$637$	36.4791	1.44536
$638$	−30.5830	−1.21079
$639$	−25.5621	−1.01122
$640$	−67.6514	−2.67416
$641$	−17.9187	−0.707745	−0.353873	−	0.935294i	$-0.615135\pi$
$641$	−17.9187	−0.707745	−0.353873	+	0.935294i	$0.615135\pi$
$642$	90.7251	3.58064
$643$	7.99908	0.315453	0.157726	−	0.987483i	$-0.449584\pi$
$643$	7.99908	0.315453	0.157726	+	0.987483i	$0.449584\pi$
$644$	−92.4726	−3.64393
$645$	−92.2266	−3.63142
$646$	26.5548	1.04479
$647$	−18.6325	−0.732521	−0.366260	−	0.930512i	$-0.619362\pi$
$647$	−18.6325	−0.732521	−0.366260	+	0.930512i	$0.619362\pi$
$648$	9.18731	0.360912
$649$	3.97749	0.156130
$650$	−52.9623	−2.07735
$651$	19.6391	0.769717
$652$	−40.5476	−1.58797
$653$	−1.83131	−0.0716648	−0.0358324	−	0.999358i	$-0.511408\pi$
$653$	−1.83131	−0.0716648	−0.0358324	+	0.999358i	$0.511408\pi$
$654$	−6.11425	−0.239086
$655$	8.89290	0.347474
$656$	0.484620	0.0189212
$657$	−70.6010	−2.75441
$658$	136.824	5.33395
$659$	−6.29243	−0.245118	−0.122559	−	0.992461i	$-0.539110\pi$
$659$	−6.29243	−0.245118	−0.122559	+	0.992461i	$0.539110\pi$
$660$	−45.7543	−1.78098
$661$	21.7758	0.846979	0.423489	−	0.905901i	$-0.360805\pi$
$661$	21.7758	0.846979	0.423489	+	0.905901i	$0.360805\pi$
$662$	42.2411	1.64175
$663$	−16.7738	−0.651441
$664$	−19.3737	−0.751845
$665$	−80.3527	−3.11594
$666$	−9.68891	−0.375438
$667$	−59.8672	−2.31807
$668$	−40.6909	−1.57438
$669$	33.1873	1.28310
$670$	20.0823	0.775849
$671$	13.7418	0.530495
$672$	79.2731	3.05802
$673$	3.07068	0.118366	0.0591831	−	0.998247i	$-0.481150\pi$
$673$	3.07068	0.118366	0.0591831	+	0.998247i	$0.481150\pi$
$674$	59.0564	2.27477
$675$	−35.2783	−1.35786
$676$	−24.5662	−0.944854
$677$	−3.24960	−0.124892	−0.0624462	−	0.998048i	$-0.519890\pi$
$677$	−3.24960	−0.124892	−0.0624462	+	0.998048i	$0.519890\pi$
$678$	70.2242	2.69694
$679$	60.9237	2.33804
$680$	27.5992	1.05838
$681$	17.7780	0.681254
$682$	4.75644	0.182134
$683$	−40.0227	−1.53143	−0.765714	−	0.643182i	$-0.777614\pi$
$683$	−40.0227	−1.53143	−0.765714	+	0.643182i	$0.777614\pi$
$684$	−57.4880	−2.19811
$685$	26.7628	1.02256
$686$	98.3110	3.75353
$687$	−3.77934	−0.144191
$688$	3.69510	0.140874
$689$	−22.1516	−0.843909
$690$	−146.621	−5.58178
$691$	4.10442	0.156139	0.0780697	−	0.996948i	$-0.475124\pi$
$691$	4.10442	0.156139	0.0780697	+	0.996948i	$0.475124\pi$
$692$	−7.06853	−0.268705
$693$	28.3650	1.07750
$694$	76.2421	2.89411
$695$	21.8477	0.828729
$696$	−67.9716	−2.57646
$697$	−3.13782	−0.118854
$698$	−64.4534	−2.43960
$699$	26.7601	1.01216
$700$	−154.740	−5.84862
$701$	−41.9022	−1.58262	−0.791312	−	0.611413i	$-0.790602\pi$
$701$	−41.9022	−1.58262	−0.791312	+	0.611413i	$0.790602\pi$
$702$	17.7175	0.668705
$703$	−4.28446	−0.161591
$704$	18.0316	0.679590
$705$	132.522	4.99109
$706$	13.7026	0.515705
$707$	39.3293	1.47913
$708$	24.3548	0.915311
$709$	−11.0237	−0.414004	−0.207002	−	0.978340i	$-0.566371\pi$
$709$	−11.0237	−0.414004	−0.207002	+	0.978340i	$0.566371\pi$
$710$	−52.9853	−1.98850
$711$	−27.5704	−1.03397
$712$	−0.722545	−0.0270785
$713$	9.31088	0.348695
$714$	−80.2277	−3.00245
$715$	12.2928	0.459723
$716$	−20.2742	−0.757682
$717$	9.79796	0.365911
$718$	34.0342	1.27015
$719$	−28.1282	−1.04900	−0.524502	−	0.851409i	$-0.675749\pi$
$719$	−28.1282	−1.04900	−0.524502	+	0.851409i	$0.675749\pi$
$720$	7.05142	0.262791
$721$	−21.6696	−0.807018
$722$	1.45872	0.0542880
$723$	24.1520	0.898222
$724$	−70.5099	−2.62048
$725$	−100.179	−3.72057
$726$	−55.5647	−2.06220
$727$	−12.6327	−0.468522	−0.234261	−	0.972174i	$-0.575267\pi$
$727$	−12.6327	−0.468522	−0.234261	+	0.972174i	$0.575267\pi$
$728$	28.2078	1.04545
$729$	−42.9937	−1.59236
$730$	−146.343	−5.41638
$731$	−23.9250	−0.884900
$732$	84.1432	3.11002
$733$	29.0669	1.07361	0.536805	−	0.843707i	$-0.319631\pi$
$733$	29.0669	1.07361	0.536805	+	0.843707i	$0.319631\pi$
$734$	13.0298	0.480938
$735$	168.991	6.23334
$736$	37.5833	1.38534
$737$	−3.13485	−0.115474
$738$	11.1204	0.409346
$739$	23.0222	0.846887	0.423444	−	0.905922i	$-0.360821\pi$
$739$	23.0222	0.846887	0.423444	+	0.905922i	$0.360821\pi$
$740$	−12.2681	−0.450985
$741$	26.2871	0.965682
$742$	−105.949	−3.88952
$743$	−37.0672	−1.35986	−0.679931	−	0.733276i	$-0.737990\pi$
$743$	−37.0672	−1.35986	−0.679931	+	0.733276i	$0.737990\pi$
$744$	10.5713	0.387563
$745$	56.3926	2.06607
$746$	−12.9908	−0.475627
$747$	32.0493	1.17262
$748$	−11.8694	−0.433988
$749$	−71.2166	−2.60220
$750$	−125.891	−4.59688
$751$	−1.41819	−0.0517505	−0.0258753	−	0.999665i	$-0.508237\pi$
$751$	−1.41819	−0.0517505	−0.0258753	+	0.999665i	$0.508237\pi$
$752$	−5.30957	−0.193620
$753$	16.3716	0.596615
$754$	50.3123	1.83227
$755$	−44.4681	−1.61836
$756$	51.7654	1.88269
$757$	−0.0199105	−0.000723659 0	−0.000361830	−	1.00000i	$-0.500115\pi$
$757$	−0.0199105	−0.000723659 0	−0.000361830		1.00000i	$0.500115\pi$
$758$	−5.29650	−0.192378
$759$	22.8876	0.830767
$760$	−43.2522	−1.56892
$761$	21.1444	0.766484	0.383242	−	0.923648i	$-0.374808\pi$
$761$	21.1444	0.766484	0.383242	+	0.923648i	$0.374808\pi$
$762$	13.9162	0.504129
$763$	4.79951	0.173754
$764$	52.7409	1.90810
$765$	−45.6566	−1.65072
$766$	−88.0889	−3.18278
$767$	−6.54339	−0.236268
$768$	35.5205	1.28174
$769$	−7.28020	−0.262531	−0.131265	−	0.991347i	$-0.541904\pi$
$769$	−7.28020	−0.262531	−0.131265	+	0.991347i	$0.541904\pi$
$770$	58.7952	2.11883
$771$	−63.5783	−2.28972
$772$	−30.6836	−1.10433
$773$	−18.8747	−0.678877	−0.339438	−	0.940628i	$-0.610237\pi$
$773$	−18.8747	−0.678877	−0.339438	+	0.940628i	$0.610237\pi$
$774$	84.7897	3.04770
$775$	15.5805	0.559667
$776$	32.7939	1.17723
$777$	12.9442	0.464372
$778$	−56.7533	−2.03470
$779$	4.91745	0.176186
$780$	75.2706	2.69512
$781$	8.27101	0.295960
$782$	−38.0359	−1.36016
$783$	33.5131	1.19766
$784$	−6.77071	−0.241811
$785$	49.2157	1.75658
$786$	−13.9149	−0.496327
$787$	−34.8376	−1.24183	−0.620914	−	0.783879i	$-0.713238\pi$
$787$	−34.8376	−1.24183	−0.620914	+	0.783879i	$0.713238\pi$
$788$	−78.9778	−2.81347
$789$	−3.98919	−0.142019
$790$	−57.1482	−2.03324
$791$	−55.1239	−1.95998
$792$	15.2683	0.542535
$793$	−22.6067	−0.802786
$794$	−1.74569	−0.0619523
$795$	−102.618	−3.63950
$796$	58.1455	2.06091
$797$	15.4218	0.546270	0.273135	−	0.961976i	$-0.411939\pi$
$797$	15.4218	0.546270	0.273135	+	0.961976i	$0.411939\pi$
$798$	125.729	4.45076
$799$	34.3784	1.21622
$800$	62.8904	2.22351
$801$	1.19529	0.0422334
$802$	63.9455	2.25800
$803$	22.8441	0.806150
$804$	−19.1952	−0.676964
$805$	115.093	4.05651
$806$	−7.82485	−0.275618
$807$	−78.8711	−2.77639
$808$	21.1701	0.744763
$809$	−25.0283	−0.879947	−0.439973	−	0.898011i	$-0.645012\pi$
$809$	−25.0283	−0.879947	−0.439973	+	0.898011i	$0.645012\pi$
$810$	−31.5032	−1.10691
$811$	−46.7655	−1.64216	−0.821080	−	0.570813i	$-0.806628\pi$
$811$	−46.7655	−1.64216	−0.821080	+	0.570813i	$0.806628\pi$
$812$	146.998	5.15860
$813$	15.1082	0.529868
$814$	3.13500	0.109882
$815$	50.4664	1.76776
$816$	3.11330	0.108987
$817$	37.4942	1.31176
$818$	89.9977	3.14670
$819$	−46.6634	−1.63055
$820$	14.0806	0.491717
$821$	−4.93802	−0.172338	−0.0861690	−	0.996281i	$-0.527463\pi$
$821$	−4.93802	−0.172338	−0.0861690	+	0.996281i	$0.527463\pi$
$822$	−41.8762	−1.46060
$823$	−10.0634	−0.350788	−0.175394	−	0.984498i	$-0.556120\pi$
$823$	−10.0634	−0.350788	−0.175394	+	0.984498i	$0.556120\pi$
$824$	−11.6643	−0.406345
$825$	38.2992	1.33341
$826$	−31.2965	−1.08894
$827$	−8.66040	−0.301152	−0.150576	−	0.988598i	$-0.548113\pi$
$827$	−8.66040	−0.301152	−0.150576	+	0.988598i	$0.548113\pi$
$828$	82.3432	2.86162
$829$	−34.4007	−1.19478	−0.597392	−	0.801949i	$-0.703797\pi$
$829$	−34.4007	−1.19478	−0.597392	+	0.801949i	$0.703797\pi$
$830$	66.4322	2.30590
$831$	5.25331	0.182235
$832$	−29.6638	−1.02841
$833$	43.8390	1.51893
$834$	−34.1854	−1.18374
$835$	50.6448	1.75264
$836$	18.6012	0.643334
$837$	−5.21215	−0.180158
$838$	−29.6668	−1.02482
$839$	15.1294	0.522324	0.261162	−	0.965295i	$-0.415894\pi$
$839$	15.1294	0.522324	0.261162	+	0.965295i	$0.415894\pi$
$840$	130.674	4.50868
$841$	66.1670	2.28162
$842$	−38.1931	−1.31622
$843$	72.5856	2.49998
$844$	20.7011	0.712560
$845$	30.5756	1.05183
$846$	−121.836	−4.18882
$847$	43.6167	1.49869
$848$	4.11145	0.141188
$849$	14.5588	0.499658
$850$	−63.6478	−2.18310
$851$	6.13686	0.210369
$852$	50.6448	1.73506
$853$	2.12121	0.0726288	0.0363144	−	0.999340i	$-0.488438\pi$
$853$	2.12121	0.0726288	0.0363144	+	0.999340i	$0.488438\pi$
$854$	−108.126	−3.69999
$855$	71.5509	2.44699
$856$	−38.3344	−1.31024
$857$	−25.4613	−0.869742	−0.434871	−	0.900493i	$-0.643206\pi$
$857$	−25.4613	−0.869742	−0.434871	+	0.900493i	$0.643206\pi$
$858$	−19.2347	−0.656661
$859$	−15.7319	−0.536765	−0.268383	−	0.963312i	$-0.586489\pi$
$859$	−15.7319	−0.536765	−0.268383	+	0.963312i	$0.586489\pi$
$860$	107.361	3.66098
$861$	−14.8567	−0.506313
$862$	5.82290	0.198329
$863$	−3.88810	−0.132353	−0.0661763	−	0.997808i	$-0.521080\pi$
$863$	−3.88810	−0.132353	−0.0661763	+	0.997808i	$0.521080\pi$
$864$	−21.0388	−0.715755
$865$	8.79765	0.299129
$866$	−20.4515	−0.694969
$867$	25.6908	0.872507
$868$	−22.8619	−0.775982
$869$	8.92084	0.302619
$870$	233.074	7.90196
$871$	5.15717	0.174744
$872$	2.58348	0.0874876
$873$	−54.2501	−1.83609
$874$	59.6081	2.01627
$875$	98.8205	3.34074
$876$	139.878	4.72604
$877$	9.84333	0.332386	0.166193	−	0.986093i	$-0.446853\pi$
$877$	9.84333	0.332386	0.166193	+	0.986093i	$0.446853\pi$
$878$	35.1836	1.18739
$879$	24.8294	0.837473
$880$	−2.28160	−0.0769126
$881$	−27.6161	−0.930410	−0.465205	−	0.885203i	$-0.654019\pi$
$881$	−27.6161	−0.930410	−0.465205	+	0.885203i	$0.654019\pi$
$882$	−155.364	−5.23139
$883$	18.4095	0.619529	0.309765	−	0.950813i	$-0.399750\pi$
$883$	18.4095	0.619529	0.309765	+	0.950813i	$0.399750\pi$
$884$	19.5264	0.656744
$885$	−30.3126	−1.01895
$886$	5.60607	0.188340
$887$	−23.9276	−0.803412	−0.401706	−	0.915769i	$-0.631583\pi$
$887$	−23.9276	−0.803412	−0.401706	+	0.915769i	$0.631583\pi$
$888$	6.96762	0.233818
$889$	−10.9238	−0.366372
$890$	2.47760	0.0830494
$891$	4.91765	0.164748
$892$	−38.6334	−1.29354
$893$	−53.8763	−1.80290
$894$	−88.2384	−2.95113
$895$	25.2337	0.843470
$896$	−83.0932	−2.77595
$897$	−37.6525	−1.25718
$898$	−0.268497	−0.00895985
$899$	−14.8009	−0.493637
$900$	137.790	4.59300
$901$	−26.6208	−0.886868
$902$	−3.59817	−0.119806
$903$	−113.278	−3.76965
$904$	−29.6721	−0.986878
$905$	87.7581	2.91718
$906$	69.5800	2.31164
$907$	33.0950	1.09890	0.549451	−	0.835526i	$-0.314837\pi$
$907$	33.0950	1.09890	0.549451	+	0.835526i	$0.314837\pi$
$908$	−20.6954	−0.686800
$909$	−35.0212	−1.16158
$910$	−96.7243	−3.20638
$911$	−44.7060	−1.48118	−0.740588	−	0.671959i	$-0.765453\pi$
$911$	−44.7060	−1.48118	−0.740588	+	0.671959i	$0.765453\pi$
$912$	−4.87902	−0.161561
$913$	−10.3701	−0.343199
$914$	83.4912	2.76164
$915$	−104.726	−3.46215
$916$	4.39953	0.145364
$917$	10.9228	0.360701
$918$	21.2922	0.702746
$919$	−18.3157	−0.604179	−0.302090	−	0.953280i	$-0.597684\pi$
$919$	−18.3157	−0.604179	−0.302090	+	0.953280i	$0.597684\pi$
$920$	61.9525	2.04251
$921$	43.6539	1.43844
$922$	−1.77973	−0.0586124
$923$	−13.6067	−0.447869
$924$	−56.1980	−1.84878
$925$	10.2692	0.337648
$926$	−25.9543	−0.852913
$927$	19.2959	0.633761
$928$	−59.7437	−1.96118
$929$	8.47775	0.278146	0.139073	−	0.990282i	$-0.455588\pi$
$929$	8.47775	0.278146	0.139073	+	0.990282i	$0.455588\pi$
$930$	−36.2490	−1.18865
$931$	−68.7025	−2.25163
$932$	−31.1514	−1.02040
$933$	−79.0846	−2.58911
$934$	−86.0126	−2.81442
$935$	14.7729	0.483126
$936$	−25.1179	−0.821005
$937$	−48.0495	−1.56971	−0.784855	−	0.619680i	$-0.787263\pi$
$937$	−48.0495	−1.56971	−0.784855	+	0.619680i	$0.787263\pi$
$938$	24.6663	0.805382
$939$	−75.3661	−2.45948
$940$	−154.269	−5.03172
$941$	36.3086	1.18363	0.591813	−	0.806076i	$-0.298413\pi$
$941$	36.3086	1.18363	0.591813	+	0.806076i	$0.298413\pi$
$942$	−77.0085	−2.50907
$943$	−7.04353	−0.229369
$944$	1.21449	0.0395281
$945$	−64.4283	−2.09585
$946$	−27.4351	−0.891991
$947$	4.69074	0.152429	0.0762144	−	0.997091i	$-0.475717\pi$
$947$	4.69074	0.152429	0.0762144	+	0.997091i	$0.475717\pi$
$948$	54.6238	1.77410
$949$	−37.5809	−1.21993
$950$	99.7458	3.23618
$951$	−33.3934	−1.08285
$952$	33.8989	1.09867
$953$	58.8275	1.90561	0.952805	−	0.303582i	$-0.0981828\pi$
$953$	58.8275	1.90561	0.952805	+	0.303582i	$0.0981828\pi$
$954$	94.3435	3.05448
$955$	−65.6425	−2.12414
$956$	−11.4058	−0.368890
$957$	−36.3829	−1.17609
$958$	67.7257	2.18812
$959$	32.8716	1.06148
$960$	−137.419	−4.43518
$961$	−28.6981	−0.925745
$962$	−5.15740	−0.166281
$963$	63.4156	2.04354
$964$	−28.1153	−0.905533
$965$	38.1895	1.22937
$966$	−180.089	−5.79426
$967$	−28.7247	−0.923725	−0.461862	−	0.886952i	$-0.652819\pi$
$967$	−28.7247	−0.923725	−0.461862	+	0.886952i	$0.652819\pi$
$968$	23.4780	0.754610
$969$	31.5907	1.01484
$970$	−112.450	−3.61056
$971$	41.6689	1.33722	0.668609	−	0.743614i	$-0.266890\pi$
$971$	41.6689	1.33722	0.668609	+	0.743614i	$0.266890\pi$
$972$	62.4683	2.00367
$973$	26.8345	0.860276
$974$	0.0686262	0.00219893
$975$	−63.0062	−2.01781
$976$	4.19591	0.134308
$977$	−53.4803	−1.71099	−0.855493	−	0.517814i	$-0.826746\pi$
$977$	−53.4803	−1.71099	−0.855493	+	0.517814i	$0.826746\pi$
$978$	−78.9656	−2.52504
$979$	−0.386754	−0.0123607
$980$	−196.723	−6.28408
$981$	−4.27377	−0.136451
$982$	57.6617	1.84006
$983$	−6.75920	−0.215585	−0.107793	−	0.994173i	$-0.534378\pi$
$983$	−6.75920	−0.215585	−0.107793	+	0.994173i	$0.534378\pi$
$984$	−7.99703	−0.254936
$985$	98.2976	3.13202
$986$	60.4632	1.92554
$987$	162.772	5.18108
$988$	−30.6009	−0.973543
$989$	−53.7050	−1.70772
$990$	−52.3548	−1.66395
$991$	−58.2238	−1.84954	−0.924770	−	0.380525i	$-0.875743\pi$
$991$	−58.2238	−1.84954	−0.924770	+	0.380525i	$0.875743\pi$
$992$	9.29167	0.295011
$993$	50.2518	1.59469
$994$	−65.0796	−2.06420
$995$	−72.3691	−2.29426
$996$	−63.4977	−2.01200
$997$	39.0144	1.23560	0.617800	−	0.786336i	$-0.288024\pi$
$997$	39.0144	1.23560	0.617800	+	0.786336i	$0.288024\pi$
$998$	−2.38611	−0.0755310
$999$	−3.43536	−0.108690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.f.1.10	✓	85

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.f.1.10	✓	85	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.26706 q^{2} -2.69699 q^{3} +3.13957 q^{4} -3.90758 q^{5} +6.11425 q^{6} -4.79951 q^{7} -2.58348 q^{8} +4.27377 q^{9} +O(q^{10})\)	\(q-2.26706 q^{2} -2.69699 q^{3} +3.13957 q^{4} -3.90758 q^{5} +6.11425 q^{6} -4.79951 q^{7} -2.58348 q^{8} +4.27377 q^{9} +8.85872 q^{10} -1.38285 q^{11} -8.46740 q^{12} +2.27493 q^{13} +10.8808 q^{14} +10.5387 q^{15} -0.422238 q^{16} +2.73391 q^{17} -9.68891 q^{18} -4.28446 q^{19} -12.2681 q^{20} +12.9442 q^{21} +3.13500 q^{22} +6.13686 q^{23} +6.96762 q^{24} +10.2692 q^{25} -5.15740 q^{26} -3.43536 q^{27} -15.0684 q^{28} -9.75536 q^{29} -23.8919 q^{30} +1.51721 q^{31} +6.12419 q^{32} +3.72953 q^{33} -6.19794 q^{34} +18.7545 q^{35} +13.4178 q^{36} +1.00000 q^{37} +9.71313 q^{38} -6.13547 q^{39} +10.0951 q^{40} -1.14774 q^{41} -29.3454 q^{42} -8.75122 q^{43} -4.34154 q^{44} -16.7001 q^{45} -13.9126 q^{46} +12.5748 q^{47} +1.13877 q^{48} +16.0353 q^{49} -23.2809 q^{50} -7.37334 q^{51} +7.14230 q^{52} -9.73727 q^{53} +7.78817 q^{54} +5.40358 q^{55} +12.3994 q^{56} +11.5551 q^{57} +22.1160 q^{58} -2.87631 q^{59} +33.0870 q^{60} -9.93731 q^{61} -3.43960 q^{62} -20.5120 q^{63} -13.0395 q^{64} -8.88946 q^{65} -8.45507 q^{66} +2.26696 q^{67} +8.58330 q^{68} -16.5511 q^{69} -42.5175 q^{70} -5.98115 q^{71} -11.0412 q^{72} -16.5196 q^{73} -2.26706 q^{74} -27.6959 q^{75} -13.4514 q^{76} +6.63698 q^{77} +13.9095 q^{78} -6.45107 q^{79} +1.64993 q^{80} -3.55618 q^{81} +2.60200 q^{82} +7.49907 q^{83} +40.6394 q^{84} -10.6830 q^{85} +19.8396 q^{86} +26.3101 q^{87} +3.57255 q^{88} +0.279679 q^{89} +37.8602 q^{90} -10.9185 q^{91} +19.2671 q^{92} -4.09190 q^{93} -28.5079 q^{94} +16.7418 q^{95} -16.5169 q^{96} -12.6937 q^{97} -36.3530 q^{98} -5.90997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9	\( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 85 * q + 11 * q^2 + 21 * q^3 + 93 * q^4 + 12 * q^5 + 4 * q^6 + 17 * q^7 + 30 * q^8 + 98 * q^9 + 9 * q^10 + 37 * q^11 + 44 * q^12 + 14 * q^13 + 26 * q^14 + 27 * q^15 + 85 * q^16 + 34 * q^17 + 3 * q^18 + 15 * q^19 + 15 * q^20 + 17 * q^21 + q^22 + 72 * q^23 + 15 * q^24 + 85 * q^25 + 33 * q^26 + 69 * q^27 + 7 * q^28 + 19 * q^29 - 9 * q^30 + 23 * q^31 + 51 * q^32 + 32 * q^33 + 49 * q^34 + 40 * q^35 + 121 * q^36 + 85 * q^37 + 84 * q^38 + 39 * q^39 + 22 * q^40 + 55 * q^41 - 28 * q^42 + 78 * q^44 + 28 * q^45 + 17 * q^46 + 184 * q^47 + 97 * q^48 + 88 * q^49 + 26 * q^50 + 27 * q^51 + 73 * q^52 + 64 * q^53 + 31 * q^54 + 39 * q^55 + 68 * q^56 - 33 * q^57 + 28 * q^58 + 60 * q^59 - 22 * q^60 + 7 * q^61 + 70 * q^62 + 28 * q^63 + 102 * q^64 + 17 * q^65 - 15 * q^66 + 82 * q^67 + 92 * q^68 + 22 * q^69 - 41 * q^70 + 113 * q^71 - 19 * q^73 + 11 * q^74 + 45 * q^75 + 34 * q^76 + 64 * q^77 + 29 * q^78 + 23 * q^79 + 54 * q^80 + 149 * q^81 + 4 * q^82 + 100 * q^83 - 49 * q^84 - 5 * q^85 - 24 * q^86 + 65 * q^87 + 14 * q^88 + 84 * q^89 - 21 * q^90 + 32 * q^91 + 95 * q^92 + 19 * q^93 - 47 * q^94 + 102 * q^95 + 29 * q^96 + 7 * q^97 + 26 * q^98 + 107 * q^99

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