LMFDB - Embedded newform 4021.2.a.b.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66021 q^{2} -2.13808 q^{3} +5.07674 q^{4} +4.04432 q^{5} +5.68776 q^{6} +2.33919 q^{7} -8.18478 q^{8} +1.57140 q^{9} +O(q^{10})$	\(q-2.66021 q^{2} -2.13808 q^{3} +5.07674 q^{4} +4.04432 q^{5} +5.68776 q^{6} +2.33919 q^{7} -8.18478 q^{8} +1.57140 q^{9} -10.7588 q^{10} -3.14973 q^{11} -10.8545 q^{12} +1.72817 q^{13} -6.22274 q^{14} -8.64709 q^{15} +11.6198 q^{16} -6.63688 q^{17} -4.18025 q^{18} -1.77322 q^{19} +20.5320 q^{20} -5.00138 q^{21} +8.37894 q^{22} -1.54350 q^{23} +17.4997 q^{24} +11.3565 q^{25} -4.59730 q^{26} +3.05447 q^{27} +11.8754 q^{28} +0.189248 q^{29} +23.0031 q^{30} -8.15368 q^{31} -14.5415 q^{32} +6.73437 q^{33} +17.6555 q^{34} +9.46043 q^{35} +7.97756 q^{36} +11.9757 q^{37} +4.71714 q^{38} -3.69497 q^{39} -33.1019 q^{40} +1.47390 q^{41} +13.3047 q^{42} +3.08573 q^{43} -15.9903 q^{44} +6.35523 q^{45} +4.10603 q^{46} -9.23978 q^{47} -24.8440 q^{48} -1.52820 q^{49} -30.2108 q^{50} +14.1902 q^{51} +8.77345 q^{52} +1.50625 q^{53} -8.12555 q^{54} -12.7385 q^{55} -19.1457 q^{56} +3.79129 q^{57} -0.503440 q^{58} -7.45713 q^{59} -43.8990 q^{60} +7.89048 q^{61} +21.6905 q^{62} +3.67579 q^{63} +15.4441 q^{64} +6.98927 q^{65} -17.9149 q^{66} -3.28501 q^{67} -33.6937 q^{68} +3.30012 q^{69} -25.1668 q^{70} -2.32869 q^{71} -12.8615 q^{72} -11.6972 q^{73} -31.8579 q^{74} -24.2812 q^{75} -9.00216 q^{76} -7.36780 q^{77} +9.82940 q^{78} +1.37540 q^{79} +46.9941 q^{80} -11.2449 q^{81} -3.92089 q^{82} +3.32612 q^{83} -25.3907 q^{84} -26.8417 q^{85} -8.20871 q^{86} -0.404627 q^{87} +25.7798 q^{88} +4.27515 q^{89} -16.9063 q^{90} +4.04251 q^{91} -7.83593 q^{92} +17.4332 q^{93} +24.5798 q^{94} -7.17147 q^{95} +31.0910 q^{96} -3.21236 q^{97} +4.06533 q^{98} -4.94947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.66021	−1.88106	−0.940528	−	0.339717i	$-0.889669\pi$
$2$	−2.66021	−1.88106	−0.940528	+	0.339717i	$0.889669\pi$
$3$	−2.13808	−1.23442	−0.617211	−	0.786798i	$-0.711738\pi$
$3$	−2.13808	−1.23442	−0.617211	+	0.786798i	$0.711738\pi$
$4$	5.07674	2.53837
$5$	4.04432	1.80868	0.904338	−	0.426817i	$-0.140365\pi$
$5$	4.04432	1.80868	0.904338	+	0.426817i	$0.140365\pi$
$6$	5.68776	2.32202
$7$	2.33919	0.884130	0.442065	−	0.896983i	$-0.354246\pi$
$7$	2.33919	0.884130	0.442065	+	0.896983i	$0.354246\pi$
$8$	−8.18478	−2.89376
$9$	1.57140	0.523799
$10$	−10.7588	−3.40222
$11$	−3.14973	−0.949678	−0.474839	−	0.880073i	$-0.657494\pi$
$11$	−3.14973	−0.949678	−0.474839	+	0.880073i	$0.657494\pi$
$12$	−10.8545	−3.13342
$13$	1.72817	0.479308	0.239654	−	0.970858i	$-0.422966\pi$
$13$	1.72817	0.479308	0.239654	+	0.970858i	$0.422966\pi$
$14$	−6.22274	−1.66310
$15$	−8.64709	−2.23267
$16$	11.6198	2.90495
$17$	−6.63688	−1.60968	−0.804840	−	0.593493i	$-0.797749\pi$
$17$	−6.63688	−1.60968	−0.804840	+	0.593493i	$0.797749\pi$
$18$	−4.18025	−0.985294
$19$	−1.77322	−0.406804	−0.203402	−	0.979095i	$-0.565200\pi$
$19$	−1.77322	−0.406804	−0.203402	+	0.979095i	$0.565200\pi$
$20$	20.5320	4.59108
$21$	−5.00138	−1.09139
$22$	8.37894	1.78640
$23$	−1.54350	−0.321841	−0.160921	−	0.986967i	$-0.551446\pi$
$23$	−1.54350	−0.321841	−0.160921	+	0.986967i	$0.551446\pi$
$24$	17.4997	3.57212
$25$	11.3565	2.27131
$26$	−4.59730	−0.901604
$27$	3.05447	0.587834
$28$	11.8754	2.24425
$29$	0.189248	0.0351424	0.0175712	−	0.999846i	$-0.494407\pi$
$29$	0.189248	0.0351424	0.0175712	+	0.999846i	$0.494407\pi$
$30$	23.0031	4.19977
$31$	−8.15368	−1.46444	−0.732222	−	0.681066i	$-0.761517\pi$
$31$	−8.15368	−1.46444	−0.732222	+	0.681066i	$0.761517\pi$
$32$	−14.5415	−2.57061
$33$	6.73437	1.17230
$34$	17.6555	3.02789
$35$	9.46043	1.59910
$36$	7.97756	1.32959
$37$	11.9757	1.96879	0.984397	−	0.175962i	$-0.0563036\pi$
$37$	11.9757	1.96879	0.984397	+	0.175962i	$0.0563036\pi$
$38$	4.71714	0.765221
$39$	−3.69497	−0.591668
$40$	−33.1019	−5.23387
$41$	1.47390	0.230184	0.115092	−	0.993355i	$-0.463284\pi$
$41$	1.47390	0.230184	0.115092	+	0.993355i	$0.463284\pi$
$42$	13.3047	2.05296
$43$	3.08573	0.470570	0.235285	−	0.971926i	$-0.424398\pi$
$43$	3.08573	0.470570	0.235285	+	0.971926i	$0.424398\pi$
$44$	−15.9903	−2.41063
$45$	6.35523	0.947382
$46$	4.10603	0.605402
$47$	−9.23978	−1.34776	−0.673880	−	0.738841i	$-0.735373\pi$
$47$	−9.23978	−1.34776	−0.673880	+	0.738841i	$0.735373\pi$
$48$	−24.8440	−3.58593
$49$	−1.52820	−0.218314
$50$	−30.2108	−4.27245
$51$	14.1902	1.98702
$52$	8.77345	1.21666
$53$	1.50625	0.206899	0.103450	−	0.994635i	$-0.467012\pi$
$53$	1.50625	0.206899	0.103450	+	0.994635i	$0.467012\pi$
$54$	−8.12555	−1.10575
$55$	−12.7385	−1.71766
$56$	−19.1457	−2.55846
$57$	3.79129	0.502168
$58$	−0.503440	−0.0661049
$59$	−7.45713	−0.970836	−0.485418	−	0.874282i	$-0.661333\pi$
$59$	−7.45713	−0.970836	−0.485418	+	0.874282i	$0.661333\pi$
$60$	−43.8990	−5.66734
$61$	7.89048	1.01027	0.505136	−	0.863040i	$-0.331442\pi$
$61$	7.89048	1.01027	0.505136	+	0.863040i	$0.331442\pi$
$62$	21.6905	2.75470
$63$	3.67579	0.463106
$64$	15.4441	1.93051
$65$	6.98927	0.866912
$66$	−17.9149	−2.20517
$67$	−3.28501	−0.401328	−0.200664	−	0.979660i	$-0.564310\pi$
$67$	−3.28501	−0.401328	−0.200664	+	0.979660i	$0.564310\pi$
$68$	−33.6937	−4.08596
$69$	3.30012	0.397288
$70$	−25.1668	−3.00800
$71$	−2.32869	−0.276365	−0.138182	−	0.990407i	$-0.544126\pi$
$71$	−2.32869	−0.276365	−0.138182	+	0.990407i	$0.544126\pi$
$72$	−12.8615	−1.51574
$73$	−11.6972	−1.36905	−0.684525	−	0.728989i	$-0.739990\pi$
$73$	−11.6972	−1.36905	−0.684525	+	0.728989i	$0.739990\pi$
$74$	−31.8579	−3.70341
$75$	−24.2812	−2.80375
$76$	−9.00216	−1.03262
$77$	−7.36780	−0.839639
$78$	9.82940	1.11296
$79$	1.37540	0.154745	0.0773723	−	0.997002i	$-0.475347\pi$
$79$	1.37540	0.154745	0.0773723	+	0.997002i	$0.475347\pi$
$80$	46.9941	5.25410
$81$	−11.2449	−1.24943
$82$	−3.92089	−0.432989
$83$	3.32612	0.365089	0.182545	−	0.983198i	$-0.441567\pi$
$83$	3.32612	0.365089	0.182545	+	0.983198i	$0.441567\pi$
$84$	−25.3907	−2.77035
$85$	−26.8417	−2.91139
$86$	−8.20871	−0.885168
$87$	−0.404627	−0.0433806
$88$	25.7798	2.74814
$89$	4.27515	0.453165	0.226582	−	0.973992i	$-0.427245\pi$
$89$	4.27515	0.453165	0.226582	+	0.973992i	$0.427245\pi$
$90$	−16.9063	−1.78208
$91$	4.04251	0.423770
$92$	−7.83593	−0.816952
$93$	17.4332	1.80774
$94$	24.5798	2.53521
$95$	−7.17147	−0.735777
$96$	31.0910	3.17321
$97$	−3.21236	−0.326165	−0.163083	−	0.986612i	$-0.552144\pi$
$97$	−3.21236	−0.326165	−0.163083	+	0.986612i	$0.552144\pi$
$98$	4.06533	0.410660
$99$	−4.94947	−0.497440
$100$	57.6542	5.76542
$101$	−4.52042	−0.449798	−0.224899	−	0.974382i	$-0.572205\pi$
$101$	−4.52042	−0.449798	−0.224899	+	0.974382i	$0.572205\pi$
$102$	−37.7489	−3.73770
$103$	−4.81080	−0.474022	−0.237011	−	0.971507i	$-0.576168\pi$
$103$	−4.81080	−0.474022	−0.237011	+	0.971507i	$0.576168\pi$
$104$	−14.1447	−1.38700
$105$	−20.2272	−1.97397
$106$	−4.00694	−0.389188
$107$	19.2527	1.86123	0.930616	−	0.365998i	$-0.119272\pi$
$107$	19.2527	1.86123	0.930616	+	0.365998i	$0.119272\pi$
$108$	15.5068	1.49214
$109$	9.14820	0.876239	0.438119	−	0.898917i	$-0.355645\pi$
$109$	9.14820	0.876239	0.438119	+	0.898917i	$0.355645\pi$
$110$	33.8871	3.23101
$111$	−25.6050	−2.43032
$112$	27.1809	2.56835
$113$	−7.12936	−0.670674	−0.335337	−	0.942098i	$-0.608850\pi$
$113$	−7.12936	−0.670674	−0.335337	+	0.942098i	$0.608850\pi$
$114$	−10.0856	−0.944606
$115$	−6.24240	−0.582107
$116$	0.960761	0.0892044
$117$	2.71564	0.251061
$118$	19.8376	1.82620
$119$	−15.5249	−1.42317
$120$	70.7745	6.46080
$121$	−1.07922	−0.0981114
$122$	−20.9904	−1.90038
$123$	−3.15132	−0.284145
$124$	−41.3941	−3.71730
$125$	25.7079	2.29938
$126$	−9.77839	−0.871128
$127$	−17.6797	−1.56882	−0.784408	−	0.620245i	$-0.787033\pi$
$127$	−17.6797	−1.56882	−0.784408	+	0.620245i	$0.787033\pi$
$128$	−12.0014	−1.06078
$129$	−6.59755	−0.580882
$130$	−18.5929	−1.63071
$131$	−2.11082	−0.184423	−0.0922117	−	0.995739i	$-0.529394\pi$
$131$	−2.11082	−0.184423	−0.0922117	+	0.995739i	$0.529394\pi$
$132$	34.1886	2.97574
$133$	−4.14789	−0.359668
$134$	8.73883	0.754920
$135$	12.3533	1.06320
$136$	54.3214	4.65802
$137$	−20.7527	−1.77303	−0.886513	−	0.462704i	$-0.846879\pi$
$137$	−20.7527	−1.77303	−0.886513	+	0.462704i	$0.846879\pi$
$138$	−8.77904	−0.747321
$139$	−17.4632	−1.48121	−0.740604	−	0.671942i	$-0.765460\pi$
$139$	−17.4632	−1.48121	−0.740604	+	0.671942i	$0.765460\pi$
$140$	48.0281	4.05912
$141$	19.7554	1.66370
$142$	6.19482	0.519858
$143$	−5.44326	−0.455188
$144$	18.2593	1.52161
$145$	0.765379	0.0635613
$146$	31.1170	2.57526
$147$	3.26741	0.269491
$148$	60.7975	4.99752
$149$	−12.5529	−1.02838	−0.514188	−	0.857678i	$-0.671906\pi$
$149$	−12.5529	−1.02838	−0.514188	+	0.857678i	$0.671906\pi$
$150$	64.5932	5.27401
$151$	5.78366	0.470668	0.235334	−	0.971915i	$-0.424382\pi$
$151$	5.78366	0.470668	0.235334	+	0.971915i	$0.424382\pi$
$152$	14.5134	1.17719
$153$	−10.4292	−0.843148
$154$	19.5999	1.57941
$155$	−32.9761	−2.64871
$156$	−18.7584	−1.50187
$157$	23.6984	1.89134	0.945668	−	0.325135i	$-0.105410\pi$
$157$	23.6984	1.89134	0.945668	+	0.325135i	$0.105410\pi$
$158$	−3.65886	−0.291083
$159$	−3.22048	−0.255401
$160$	−58.8107	−4.64939
$161$	−3.61053	−0.284550
$162$	29.9138	2.35025
$163$	6.08103	0.476303	0.238152	−	0.971228i	$-0.423459\pi$
$163$	6.08103	0.476303	0.238152	+	0.971228i	$0.423459\pi$
$164$	7.48260	0.584293
$165$	27.2360	2.12032
$166$	−8.84820	−0.686753
$167$	15.3576	1.18841	0.594203	−	0.804315i	$-0.297467\pi$
$167$	15.3576	1.18841	0.594203	+	0.804315i	$0.297467\pi$
$168$	40.9352	3.15822
$169$	−10.0134	−0.770264
$170$	71.4046	5.47648
$171$	−2.78643	−0.213083
$172$	15.6655	1.19448
$173$	11.1757	0.849675	0.424837	−	0.905270i	$-0.360331\pi$
$173$	11.1757	0.849675	0.424837	+	0.905270i	$0.360331\pi$
$174$	1.07640	0.0816013
$175$	26.5651	2.00813
$176$	−36.5991	−2.75876
$177$	15.9440	1.19842
$178$	−11.3728	−0.852428
$179$	0.422569	0.0315843	0.0157922	−	0.999875i	$-0.494973\pi$
$179$	0.422569	0.0315843	0.0157922	+	0.999875i	$0.494973\pi$
$180$	32.2638	2.40480
$181$	−25.7629	−1.91494	−0.957470	−	0.288533i	$-0.906832\pi$
$181$	−25.7629	−1.91494	−0.957470	+	0.288533i	$0.906832\pi$
$182$	−10.7539	−0.797135
$183$	−16.8705	−1.24710
$184$	12.6332	0.931331
$185$	48.4336	3.56091
$186$	−46.3762	−3.40047
$187$	20.9043	1.52868
$188$	−46.9079	−3.42111
$189$	7.14499	0.519722
$190$	19.0776	1.38404
$191$	−18.9484	−1.37106	−0.685530	−	0.728045i	$-0.740429\pi$
$191$	−18.9484	−1.37106	−0.685530	+	0.728045i	$0.740429\pi$
$192$	−33.0207	−2.38306
$193$	6.14937	0.442641	0.221321	−	0.975201i	$-0.428963\pi$
$193$	6.14937	0.442641	0.221321	+	0.975201i	$0.428963\pi$
$194$	8.54556	0.613535
$195$	−14.9436	−1.07014
$196$	−7.75825	−0.554161
$197$	−0.867762	−0.0618255	−0.0309127	−	0.999522i	$-0.509841\pi$
$197$	−0.867762	−0.0618255	−0.0309127	+	0.999522i	$0.509841\pi$
$198$	13.1666	0.935712
$199$	−13.9620	−0.989743	−0.494871	−	0.868966i	$-0.664785\pi$
$199$	−13.9620	−0.989743	−0.494871	+	0.868966i	$0.664785\pi$
$200$	−92.9507	−6.57261
$201$	7.02362	0.495408
$202$	12.0253	0.846096
$203$	0.442686	0.0310705
$204$	72.0398	5.04380
$205$	5.96092	0.416329
$206$	12.7978	0.891662
$207$	−2.42545	−0.168580
$208$	20.0809	1.39236
$209$	5.58515	0.386333
$210$	53.8086	3.71315
$211$	−15.1336	−1.04184	−0.520919	−	0.853606i	$-0.674411\pi$
$211$	−15.1336	−1.04184	−0.520919	+	0.853606i	$0.674411\pi$
$212$	7.64682	0.525186
$213$	4.97894	0.341151
$214$	−51.2164	−3.50108
$215$	12.4797	0.851109
$216$	−25.0002	−1.70105
$217$	−19.0730	−1.29476
$218$	−24.3362	−1.64825
$219$	25.0095	1.68999
$220$	−64.6700	−4.36005
$221$	−11.4696	−0.771531
$222$	68.1149	4.57157
$223$	10.3437	0.692663	0.346332	−	0.938112i	$-0.387427\pi$
$223$	10.3437	0.692663	0.346332	+	0.938112i	$0.387427\pi$
$224$	−34.0154	−2.27275
$225$	17.8456	1.18971
$226$	18.9656	1.26157
$227$	−16.9718	−1.12645	−0.563227	−	0.826302i	$-0.690440\pi$
$227$	−16.9718	−1.12645	−0.563227	+	0.826302i	$0.690440\pi$
$228$	19.2474	1.27469
$229$	0.739614	0.0488751	0.0244375	−	0.999701i	$-0.492221\pi$
$229$	0.739614	0.0488751	0.0244375	+	0.999701i	$0.492221\pi$
$230$	16.6061	1.09498
$231$	15.7530	1.03647
$232$	−1.54895	−0.101694
$233$	−5.99310	−0.392621	−0.196310	−	0.980542i	$-0.562896\pi$
$233$	−5.99310	−0.392621	−0.196310	+	0.980542i	$0.562896\pi$
$234$	−7.22417	−0.472259
$235$	−37.3686	−2.43766
$236$	−37.8579	−2.46434
$237$	−2.94072	−0.191020
$238$	41.2996	2.67705
$239$	−16.6237	−1.07530	−0.537648	−	0.843169i	$-0.680687\pi$
$239$	−16.6237	−1.07530	−0.537648	+	0.843169i	$0.680687\pi$
$240$	−100.477	−6.48578
$241$	16.0149	1.03161	0.515804	−	0.856706i	$-0.327493\pi$
$241$	16.0149	1.03161	0.515804	+	0.856706i	$0.327493\pi$
$242$	2.87097	0.184553
$243$	14.8791	0.954495
$244$	40.0579	2.56444
$245$	−6.18052	−0.394859
$246$	8.38318	0.534492
$247$	−3.06442	−0.194984
$248$	66.7361	4.23775
$249$	−7.11152	−0.450675
$250$	−68.3885	−4.32527
$251$	12.6982	0.801505	0.400752	−	0.916186i	$-0.368749\pi$
$251$	12.6982	0.801505	0.400752	+	0.916186i	$0.368749\pi$
$252$	18.6610	1.17553
$253$	4.86159	0.305646
$254$	47.0317	2.95103
$255$	57.3897	3.59388
$256$	1.03818	0.0648861
$257$	−6.95206	−0.433657	−0.216829	−	0.976210i	$-0.569571\pi$
$257$	−6.95206	−0.433657	−0.216829	+	0.976210i	$0.569571\pi$
$258$	17.5509	1.09267
$259$	28.0134	1.74067
$260$	35.4827	2.20054
$261$	0.297383	0.0184076
$262$	5.61524	0.346911
$263$	5.73792	0.353815	0.176908	−	0.984227i	$-0.443391\pi$
$263$	5.73792	0.353815	0.176908	+	0.984227i	$0.443391\pi$
$264$	−55.1193	−3.39236
$265$	6.09175	0.374213
$266$	11.0343	0.676555
$267$	−9.14061	−0.559397
$268$	−16.6771	−1.01872
$269$	−14.2866	−0.871068	−0.435534	−	0.900172i	$-0.643441\pi$
$269$	−14.2866	−0.871068	−0.435534	+	0.900172i	$0.643441\pi$
$270$	−32.8623	−1.99994
$271$	−4.31543	−0.262144	−0.131072	−	0.991373i	$-0.541842\pi$
$271$	−4.31543	−0.262144	−0.131072	+	0.991373i	$0.541842\pi$
$272$	−77.1191	−4.67603
$273$	−8.64322	−0.523112
$274$	55.2067	3.33516
$275$	−35.7700	−2.15701
$276$	16.7539	1.00846
$277$	5.84085	0.350942	0.175471	−	0.984485i	$-0.443855\pi$
$277$	5.84085	0.350942	0.175471	+	0.984485i	$0.443855\pi$
$278$	46.4558	2.78623
$279$	−12.8127	−0.767074
$280$	−77.4315	−4.62742
$281$	−25.9111	−1.54573	−0.772863	−	0.634573i	$-0.781176\pi$
$281$	−25.9111	−1.54573	−0.772863	+	0.634573i	$0.781176\pi$
$282$	−52.5536	−3.12952
$283$	5.97138	0.354962	0.177481	−	0.984124i	$-0.443205\pi$
$283$	5.97138	0.354962	0.177481	+	0.984124i	$0.443205\pi$
$284$	−11.8222	−0.701516
$285$	15.3332	0.908259
$286$	14.4802	0.856234
$287$	3.44773	0.203513
$288$	−22.8505	−1.34648
$289$	27.0481	1.59107
$290$	−2.03607	−0.119562
$291$	6.86828	0.402626
$292$	−59.3835	−3.47515
$293$	26.3974	1.54215	0.771077	−	0.636742i	$-0.219718\pi$
$293$	26.3974	1.54215	0.771077	+	0.636742i	$0.219718\pi$
$294$	−8.69201	−0.506928
$295$	−30.1590	−1.75593
$296$	−98.0185	−5.69721
$297$	−9.62076	−0.558253
$298$	33.3934	1.93443
$299$	−2.66742	−0.154261
$300$	−123.269	−7.11696
$301$	7.21811	0.416045
$302$	−15.3858	−0.885352
$303$	9.66503	0.555241
$304$	−20.6044	−1.18174
$305$	31.9116	1.82726
$306$	27.7438	1.58601
$307$	8.78852	0.501588	0.250794	−	0.968041i	$-0.419308\pi$
$307$	8.78852	0.501588	0.250794	+	0.968041i	$0.419308\pi$
$308$	−37.4044	−2.13131
$309$	10.2859	0.585144
$310$	87.7235	4.98236
$311$	−3.75433	−0.212888	−0.106444	−	0.994319i	$-0.533947\pi$
$311$	−3.75433	−0.212888	−0.106444	+	0.994319i	$0.533947\pi$
$312$	30.2425	1.71214
$313$	7.13821	0.403476	0.201738	−	0.979440i	$-0.435341\pi$
$313$	7.13821	0.403476	0.201738	+	0.979440i	$0.435341\pi$
$314$	−63.0427	−3.55771
$315$	14.8661	0.837609
$316$	6.98254	0.392799
$317$	8.60956	0.483561	0.241780	−	0.970331i	$-0.422269\pi$
$317$	8.60956	0.483561	0.241780	+	0.970331i	$0.422269\pi$
$318$	8.56717	0.480423
$319$	−0.596079	−0.0333740
$320$	62.4607	3.49166
$321$	−41.1639	−2.29755
$322$	9.60479	0.535254
$323$	11.7686	0.654824
$324$	−57.0874	−3.17152
$325$	19.6260	1.08866
$326$	−16.1768	−0.895952
$327$	−19.5596	−1.08165
$328$	−12.0635	−0.666097
$329$	−21.6136	−1.19160
$330$	−72.4535	−3.98843
$331$	−23.6671	−1.30086	−0.650431	−	0.759565i	$-0.725412\pi$
$331$	−23.6671	−1.30086	−0.650431	+	0.759565i	$0.725412\pi$
$332$	16.8859	0.926731
$333$	18.8186	1.03125
$334$	−40.8545	−2.23546
$335$	−13.2856	−0.725872
$336$	−58.1149	−3.17043
$337$	−14.3357	−0.780918	−0.390459	−	0.920620i	$-0.627684\pi$
$337$	−14.3357	−0.780918	−0.390459	+	0.920620i	$0.627684\pi$
$338$	26.6379	1.44891
$339$	15.2432	0.827895
$340$	−136.268	−7.39017
$341$	25.6819	1.39075
$342$	7.41249	0.400822
$343$	−19.9491	−1.07715
$344$	−25.2560	−1.36171
$345$	13.3468	0.718566
$346$	−29.7298	−1.59829
$347$	−6.53708	−0.350929	−0.175464	−	0.984486i	$-0.556143\pi$
$347$	−6.53708	−0.350929	−0.175464	+	0.984486i	$0.556143\pi$
$348$	−2.05419	−0.110116
$349$	−3.95131	−0.211509	−0.105754	−	0.994392i	$-0.533726\pi$
$349$	−3.95131	−0.211509	−0.105754	+	0.994392i	$0.533726\pi$
$350$	−70.6688	−3.77741
$351$	5.27864	0.281753
$352$	45.8019	2.44125
$353$	−23.3528	−1.24294	−0.621472	−	0.783437i	$-0.713465\pi$
$353$	−23.3528	−1.24294	−0.621472	+	0.783437i	$0.713465\pi$
$354$	−42.4143	−2.25430
$355$	−9.41798	−0.499854
$356$	21.7038	1.15030
$357$	33.1935	1.75679
$358$	−1.12412	−0.0594118
$359$	10.6896	0.564176	0.282088	−	0.959389i	$-0.408973\pi$
$359$	10.6896	0.564176	0.282088	+	0.959389i	$0.408973\pi$
$360$	−52.0161	−2.74149
$361$	−15.8557	−0.834510
$362$	68.5348	3.60211
$363$	2.30747	0.121111
$364$	20.5228	1.07569
$365$	−47.3071	−2.47617
$366$	44.8791	2.34587
$367$	12.3842	0.646448	0.323224	−	0.946322i	$-0.395233\pi$
$367$	12.3842	0.646448	0.323224	+	0.946322i	$0.395233\pi$
$368$	−17.9351	−0.934932
$369$	2.31608	0.120570
$370$	−128.844	−6.69827
$371$	3.52340	0.182926
$372$	88.5040	4.58872
$373$	−18.4412	−0.954847	−0.477424	−	0.878673i	$-0.658429\pi$
$373$	−18.4412	−0.954847	−0.477424	+	0.878673i	$0.658429\pi$
$374$	−55.6100	−2.87553
$375$	−54.9656	−2.83841
$376$	75.6255	3.90009
$377$	0.327052	0.0168440
$378$	−19.0072	−0.977625
$379$	24.2020	1.24317	0.621586	−	0.783346i	$-0.286489\pi$
$379$	24.2020	1.24317	0.621586	+	0.783346i	$0.286489\pi$
$380$	−36.4076	−1.86767
$381$	37.8006	1.93658
$382$	50.4068	2.57904
$383$	15.8156	0.808141	0.404070	−	0.914728i	$-0.367595\pi$
$383$	15.8156	0.808141	0.404070	+	0.914728i	$0.367595\pi$
$384$	25.6600	1.30946
$385$	−29.7978	−1.51863
$386$	−16.3586	−0.832633
$387$	4.84891	0.246484
$388$	−16.3083	−0.827928
$389$	4.57181	0.231800	0.115900	−	0.993261i	$-0.463025\pi$
$389$	4.57181	0.231800	0.115900	+	0.993261i	$0.463025\pi$
$390$	39.7532	2.01298
$391$	10.2440	0.518061
$392$	12.5079	0.631747
$393$	4.51311	0.227656
$394$	2.30843	0.116297
$395$	5.56256	0.279883
$396$	−25.1271	−1.26269
$397$	−21.2172	−1.06486	−0.532431	−	0.846473i	$-0.678721\pi$
$397$	−21.2172	−1.06486	−0.532431	+	0.846473i	$0.678721\pi$
$398$	37.1420	1.86176
$399$	8.86853	0.443982
$400$	131.960	6.59802
$401$	−13.4954	−0.673929	−0.336965	−	0.941517i	$-0.609400\pi$
$401$	−13.4954	−0.673929	−0.336965	+	0.941517i	$0.609400\pi$
$402$	−18.6843	−0.931890
$403$	−14.0909	−0.701920
$404$	−22.9490	−1.14175
$405$	−45.4780	−2.25982
$406$	−1.17764	−0.0584453
$407$	−37.7202	−1.86972
$408$	−116.144	−5.74996
$409$	−29.1835	−1.44303	−0.721516	−	0.692398i	$-0.756554\pi$
$409$	−29.1835	−1.44303	−0.721516	+	0.692398i	$0.756554\pi$
$410$	−15.8573	−0.783137
$411$	44.3711	2.18866
$412$	−24.4232	−1.20324
$413$	−17.4436	−0.858345
$414$	6.45220	0.317108
$415$	13.4519	0.660328
$416$	−25.1302	−1.23211
$417$	37.3377	1.82844
$418$	−14.8577	−0.726714
$419$	−30.2180	−1.47624	−0.738122	−	0.674667i	$-0.764287\pi$
$419$	−30.2180	−1.47624	−0.738122	+	0.674667i	$0.764287\pi$
$420$	−102.688	−5.01066
$421$	11.8536	0.577708	0.288854	−	0.957373i	$-0.406726\pi$
$421$	11.8536	0.577708	0.288854	+	0.957373i	$0.406726\pi$
$422$	40.2586	1.95976
$423$	−14.5193	−0.705955
$424$	−12.3283	−0.598715
$425$	−75.3719	−3.65608
$426$	−13.2450	−0.641724
$427$	18.4573	0.893212
$428$	97.7410	4.72449
$429$	11.6381	0.561894
$430$	−33.1987	−1.60098
$431$	1.66962	0.0804230	0.0402115	−	0.999191i	$-0.487197\pi$
$431$	1.66962	0.0804230	0.0402115	+	0.999191i	$0.487197\pi$
$432$	35.4923	1.70762
$433$	11.1734	0.536960	0.268480	−	0.963285i	$-0.413479\pi$
$433$	11.1734	0.536960	0.268480	+	0.963285i	$0.413479\pi$
$434$	50.7383	2.43551
$435$	−1.63644	−0.0784614
$436$	46.4430	2.22422
$437$	2.73696	0.130926
$438$	−66.5306	−3.17896
$439$	39.6909	1.89434	0.947171	−	0.320728i	$-0.103928\pi$
$439$	39.6909	1.89434	0.947171	+	0.320728i	$0.103928\pi$
$440$	104.262	4.97049
$441$	−2.40140	−0.114352
$442$	30.5117	1.45129
$443$	−39.2821	−1.86635	−0.933173	−	0.359426i	$-0.882972\pi$
$443$	−39.2821	−1.86635	−0.933173	+	0.359426i	$0.882972\pi$
$444$	−129.990	−6.16906
$445$	17.2901	0.819628
$446$	−27.5164	−1.30294
$447$	26.8392	1.26945
$448$	36.1266	1.70682
$449$	−32.2782	−1.52330	−0.761650	−	0.647988i	$-0.775610\pi$
$449$	−32.2782	−1.52330	−0.761650	+	0.647988i	$0.775610\pi$
$450$	−47.4731	−2.23791
$451$	−4.64238	−0.218601
$452$	−36.1939	−1.70242
$453$	−12.3659	−0.581003
$454$	45.1485	2.11892
$455$	16.3492	0.766463
$456$	−31.0308	−1.45315
$457$	13.8476	0.647764	0.323882	−	0.946097i	$-0.395012\pi$
$457$	13.8476	0.647764	0.323882	+	0.946097i	$0.395012\pi$
$458$	−1.96753	−0.0919367
$459$	−20.2722	−0.946224
$460$	−31.6910	−1.47760
$461$	37.3842	1.74115	0.870577	−	0.492032i	$-0.163746\pi$
$461$	37.3842	1.74115	0.870577	+	0.492032i	$0.163746\pi$
$462$	−41.9063	−1.94966
$463$	29.9635	1.39252	0.696261	−	0.717788i	$-0.254845\pi$
$463$	29.9635	1.39252	0.696261	+	0.717788i	$0.254845\pi$
$464$	2.19902	0.102087
$465$	70.5057	3.26962
$466$	15.9429	0.738542
$467$	−37.2066	−1.72172	−0.860858	−	0.508845i	$-0.830073\pi$
$467$	−37.2066	−1.72172	−0.860858	+	0.508845i	$0.830073\pi$
$468$	13.7866	0.637284
$469$	−7.68426	−0.354826
$470$	99.4085	4.58537
$471$	−50.6691	−2.33471
$472$	61.0350	2.80936
$473$	−9.71922	−0.446890
$474$	7.82294	0.359320
$475$	−20.1376	−0.923977
$476$	−78.8159	−3.61252
$477$	2.36691	0.108373
$478$	44.2225	2.02269
$479$	−29.7028	−1.35716	−0.678578	−	0.734528i	$-0.737403\pi$
$479$	−29.7028	−1.35716	−0.678578	+	0.734528i	$0.737403\pi$
$480$	125.742	5.73932
$481$	20.6960	0.943658
$482$	−42.6030	−1.94051
$483$	7.71961	0.351255
$484$	−5.47894	−0.249043
$485$	−12.9918	−0.589928
$486$	−39.5816	−1.79546
$487$	−31.3136	−1.41895	−0.709476	−	0.704729i	$-0.751069\pi$
$487$	−31.3136	−1.41895	−0.709476	+	0.704729i	$0.751069\pi$
$488$	−64.5818	−2.92348
$489$	−13.0017	−0.587959
$490$	16.4415	0.742751
$491$	−3.51205	−0.158497	−0.0792483	−	0.996855i	$-0.525252\pi$
$491$	−3.51205	−0.158497	−0.0792483	+	0.996855i	$0.525252\pi$
$492$	−15.9984	−0.721264
$493$	−1.25601	−0.0565680
$494$	8.15201	0.366776
$495$	−20.0172	−0.899708
$496$	−94.7440	−4.25413
$497$	−5.44725	−0.244343
$498$	18.9182	0.847744
$499$	−38.6225	−1.72898	−0.864490	−	0.502651i	$-0.832358\pi$
$499$	−38.6225	−1.72898	−0.864490	+	0.502651i	$0.832358\pi$
$500$	130.512	5.83668
$501$	−32.8358	−1.46700
$502$	−33.7800	−1.50767
$503$	2.22646	0.0992729	0.0496364	−	0.998767i	$-0.484194\pi$
$503$	2.22646	0.0992729	0.0496364	+	0.998767i	$0.484194\pi$
$504$	−30.0855	−1.34012
$505$	−18.2820	−0.813540
$506$	−12.9329	−0.574937
$507$	21.4095	0.950831
$508$	−89.7550	−3.98223
$509$	31.5584	1.39880	0.699401	−	0.714729i	$-0.253450\pi$
$509$	31.5584	1.39880	0.699401	+	0.714729i	$0.253450\pi$
$510$	−152.669	−6.76029
$511$	−27.3619	−1.21042
$512$	21.2410	0.938730
$513$	−5.41625	−0.239133
$514$	18.4940	0.815733
$515$	−19.4564	−0.857352
$516$	−33.4940	−1.47449
$517$	29.1028	1.27994
$518$	−74.5217	−3.27430
$519$	−23.8946	−1.04886
$520$	−57.2056	−2.50863
$521$	43.3834	1.90066	0.950332	−	0.311239i	$-0.100744\pi$
$521$	43.3834	1.90066	0.950332	+	0.311239i	$0.100744\pi$
$522$	−0.791103	−0.0346256
$523$	32.1805	1.40715	0.703577	−	0.710619i	$-0.251585\pi$
$523$	32.1805	1.40715	0.703577	+	0.710619i	$0.251585\pi$
$524$	−10.7161	−0.468134
$525$	−56.7983	−2.47888
$526$	−15.2641	−0.665546
$527$	54.1150	2.35729
$528$	78.2519	3.40548
$529$	−20.6176	−0.896418
$530$	−16.2054	−0.703916
$531$	−11.7181	−0.508522
$532$	−21.0578	−0.912970
$533$	2.54714	0.110329
$534$	24.3160	1.05226
$535$	77.8642	3.36636
$536$	26.8871	1.16135
$537$	−0.903488	−0.0389884
$538$	38.0054	1.63853
$539$	4.81340	0.207328
$540$	62.7143	2.69879
$541$	34.9821	1.50400	0.751998	−	0.659165i	$-0.229090\pi$
$541$	34.9821	1.50400	0.751998	+	0.659165i	$0.229090\pi$
$542$	11.4800	0.493107
$543$	55.0832	2.36384
$544$	96.5105	4.13785
$545$	36.9983	1.58483
$546$	22.9928	0.984002
$547$	43.5995	1.86418	0.932089	−	0.362229i	$-0.117984\pi$
$547$	43.5995	1.86418	0.932089	+	0.362229i	$0.117984\pi$
$548$	−105.356	−4.50059
$549$	12.3991	0.529179
$550$	95.1558	4.05746
$551$	−0.335578	−0.0142961
$552$	−27.0108	−1.14966
$553$	3.21732	0.136814
$554$	−15.5379	−0.660142
$555$	−103.555	−4.39567
$556$	−88.6559	−3.75985
$557$	−15.7817	−0.668692	−0.334346	−	0.942450i	$-0.608515\pi$
$557$	−15.7817	−0.668692	−0.334346	+	0.942450i	$0.608515\pi$
$558$	34.0844	1.44291
$559$	5.33267	0.225548
$560$	109.928	4.64531
$561$	−44.6952	−1.88703
$562$	68.9290	2.90760
$563$	−9.36490	−0.394683	−0.197342	−	0.980335i	$-0.563231\pi$
$563$	−9.36490	−0.394683	−0.197342	+	0.980335i	$0.563231\pi$
$564$	100.293	4.22310
$565$	−28.8334	−1.21303
$566$	−15.8852	−0.667703
$567$	−26.3039	−1.10466
$568$	19.0598	0.799732
$569$	7.60343	0.318752	0.159376	−	0.987218i	$-0.449052\pi$
$569$	7.60343	0.318752	0.159376	+	0.987218i	$0.449052\pi$
$570$	−40.7895	−1.70849
$571$	−10.9967	−0.460200	−0.230100	−	0.973167i	$-0.573905\pi$
$571$	−10.9967	−0.460200	−0.230100	+	0.973167i	$0.573905\pi$
$572$	−27.6340	−1.15543
$573$	40.5133	1.69247
$574$	−9.17169	−0.382819
$575$	−17.5288	−0.731001
$576$	24.2687	1.01120
$577$	16.9256	0.704622	0.352311	−	0.935883i	$-0.385396\pi$
$577$	16.9256	0.704622	0.352311	+	0.935883i	$0.385396\pi$
$578$	−71.9538	−2.99288
$579$	−13.1479	−0.546407
$580$	3.88563	0.161342
$581$	7.78043	0.322787
$582$	−18.2711	−0.757362
$583$	−4.74427	−0.196487
$584$	95.7387	3.96170
$585$	10.9829	0.454087
$586$	−70.2228	−2.90088
$587$	45.8644	1.89302	0.946512	−	0.322668i	$-0.104580\pi$
$587$	45.8644	1.89302	0.946512	+	0.322668i	$0.104580\pi$
$588$	16.5878	0.684068
$589$	14.4583	0.595742
$590$	80.2295	3.30300
$591$	1.85535	0.0763188
$592$	139.155	5.71924
$593$	−24.4954	−1.00591	−0.502953	−	0.864314i	$-0.667753\pi$
$593$	−24.4954	−1.00591	−0.502953	+	0.864314i	$0.667753\pi$
$594$	25.5933	1.05010
$595$	−62.7877	−2.57405
$596$	−63.7279	−2.61039
$597$	29.8520	1.22176
$598$	7.09592	0.290174
$599$	16.3267	0.667090	0.333545	−	0.942734i	$-0.391755\pi$
$599$	16.3267	0.667090	0.333545	+	0.942734i	$0.391755\pi$
$600$	198.736	8.11338
$601$	−12.5982	−0.513891	−0.256945	−	0.966426i	$-0.582716\pi$
$601$	−12.5982	−0.513891	−0.256945	+	0.966426i	$0.582716\pi$
$602$	−19.2017	−0.782604
$603$	−5.16205	−0.210215
$604$	29.3621	1.19473
$605$	−4.36473	−0.177452
$606$	−25.7110	−1.04444
$607$	−7.85460	−0.318808	−0.159404	−	0.987213i	$-0.550957\pi$
$607$	−7.85460	−0.318808	−0.159404	+	0.987213i	$0.550957\pi$
$608$	25.7853	1.04573
$609$	−0.946500	−0.0383541
$610$	−84.8918	−3.43717
$611$	−15.9679	−0.645991
$612$	−52.9461	−2.14022
$613$	23.4340	0.946491	0.473245	−	0.880931i	$-0.343082\pi$
$613$	23.4340	0.946491	0.473245	+	0.880931i	$0.343082\pi$
$614$	−23.3794	−0.943514
$615$	−12.7449	−0.513926
$616$	60.3038	2.42971
$617$	46.8048	1.88429	0.942145	−	0.335205i	$-0.108806\pi$
$617$	46.8048	1.88429	0.942145	+	0.335205i	$0.108806\pi$
$618$	−27.3627	−1.10069
$619$	−31.1652	−1.25263	−0.626317	−	0.779568i	$-0.715438\pi$
$619$	−31.1652	−1.25263	−0.626317	+	0.779568i	$0.715438\pi$
$620$	−167.411	−6.72339
$621$	−4.71457	−0.189189
$622$	9.98731	0.400455
$623$	10.0004	0.400657
$624$	−42.9347	−1.71876
$625$	47.1883	1.88753
$626$	−18.9892	−0.758960
$627$	−11.9415	−0.476898
$628$	120.310	4.80091
$629$	−79.4813	−3.16913
$630$	−39.5470	−1.57559
$631$	−6.47666	−0.257832	−0.128916	−	0.991656i	$-0.541150\pi$
$631$	−6.47666	−0.257832	−0.128916	+	0.991656i	$0.541150\pi$
$632$	−11.2573	−0.447793
$633$	32.3568	1.28607
$634$	−22.9033	−0.909605
$635$	−71.5022	−2.83748
$636$	−16.3495	−0.648301
$637$	−2.64098	−0.104639
$638$	1.58570	0.0627783
$639$	−3.65930	−0.144760
$640$	−48.5375	−1.91861
$641$	11.2584	0.444681	0.222341	−	0.974969i	$-0.428630\pi$
$641$	11.2584	0.444681	0.222341	+	0.974969i	$0.428630\pi$
$642$	109.505	4.32181
$643$	−37.5719	−1.48169	−0.740846	−	0.671675i	$-0.765575\pi$
$643$	−37.5719	−1.48169	−0.740846	+	0.671675i	$0.765575\pi$
$644$	−18.3297	−0.722292
$645$	−26.6826	−1.05063
$646$	−31.3071	−1.23176
$647$	−28.5661	−1.12305	−0.561525	−	0.827459i	$-0.689785\pi$
$647$	−28.5661	−1.12305	−0.561525	+	0.827459i	$0.689785\pi$
$648$	92.0370	3.61556
$649$	23.4879	0.921982
$650$	−52.2094	−2.04782
$651$	40.7797	1.59828
$652$	30.8718	1.20903
$653$	−30.1161	−1.17853	−0.589267	−	0.807938i	$-0.700584\pi$
$653$	−30.1161	−1.17853	−0.589267	+	0.807938i	$0.700584\pi$
$654$	52.0327	2.03464
$655$	−8.53684	−0.333562
$656$	17.1264	0.668673
$657$	−18.3809	−0.717106
$658$	57.4967	2.24146
$659$	−25.5507	−0.995315	−0.497658	−	0.867374i	$-0.665806\pi$
$659$	−25.5507	−0.995315	−0.497658	+	0.867374i	$0.665806\pi$
$660$	138.270	5.38215
$661$	15.3314	0.596323	0.298162	−	0.954515i	$-0.403627\pi$
$661$	15.3314	0.596323	0.298162	+	0.954515i	$0.403627\pi$
$662$	62.9596	2.44699
$663$	24.5230	0.952396
$664$	−27.2236	−1.05648
$665$	−16.7754	−0.650523
$666$	−50.0614	−1.93984
$667$	−0.292104	−0.0113103
$668$	77.9665	3.01661
$669$	−22.1156	−0.855039
$670$	35.3427	1.36541
$671$	−24.8529	−0.959434
$672$	72.7278	2.80553
$673$	−9.47206	−0.365121	−0.182561	−	0.983195i	$-0.558439\pi$
$673$	−9.47206	−0.365121	−0.182561	+	0.983195i	$0.558439\pi$
$674$	38.1361	1.46895
$675$	34.6882	1.33515
$676$	−50.8356	−1.95521
$677$	45.6464	1.75433	0.877166	−	0.480187i	$-0.159431\pi$
$677$	45.6464	1.75433	0.877166	+	0.480187i	$0.159431\pi$
$678$	−40.5501	−1.55732
$679$	−7.51431	−0.288373
$680$	219.693	8.42484
$681$	36.2870	1.39052
$682$	−68.3193	−2.61608
$683$	−47.7559	−1.82733	−0.913664	−	0.406471i	$-0.866759\pi$
$683$	−47.7559	−1.82733	−0.913664	+	0.406471i	$0.866759\pi$
$684$	−14.1460	−0.540884
$685$	−83.9307	−3.20683
$686$	53.0688	2.02617
$687$	−1.58136	−0.0603325
$688$	35.8556	1.36698
$689$	2.60305	0.0991683
$690$	−35.5052	−1.35166
$691$	15.7630	0.599652	0.299826	−	0.953994i	$-0.403071\pi$
$691$	15.7630	0.599652	0.299826	+	0.953994i	$0.403071\pi$
$692$	56.7362	2.15679
$693$	−11.5777	−0.439802
$694$	17.3900	0.660116
$695$	−70.6267	−2.67902
$696$	3.31178	0.125533
$697$	−9.78208	−0.370523
$698$	10.5113	0.397859
$699$	12.8137	0.484660
$700$	134.864	5.09738
$701$	42.7491	1.61461	0.807305	−	0.590134i	$-0.200925\pi$
$701$	42.7491	1.61461	0.807305	+	0.590134i	$0.200925\pi$
$702$	−14.0423	−0.529993
$703$	−21.2355	−0.800914
$704$	−48.6446	−1.83336
$705$	79.8972	3.00910
$706$	62.1234	2.33804
$707$	−10.5741	−0.397680
$708$	80.9433	3.04204
$709$	−12.3285	−0.463007	−0.231504	−	0.972834i	$-0.574365\pi$
$709$	−12.3285	−0.463007	−0.231504	+	0.972834i	$0.574365\pi$
$710$	25.0538	0.940254
$711$	2.16130	0.0810550
$712$	−34.9911	−1.31135
$713$	12.5852	0.471319
$714$	−88.3019	−3.30461
$715$	−22.0143	−0.823287
$716$	2.14527	0.0801726
$717$	35.5428	1.32737
$718$	−28.4366	−1.06125
$719$	38.4135	1.43258	0.716291	−	0.697802i	$-0.245838\pi$
$719$	38.4135	1.43258	0.716291	+	0.697802i	$0.245838\pi$
$720$	73.8464	2.75209
$721$	−11.2534	−0.419097
$722$	42.1795	1.56976
$723$	−34.2411	−1.27344
$724$	−130.791	−4.86082
$725$	2.14920	0.0798193
$726$	−6.13837	−0.227816
$727$	13.4958	0.500533	0.250267	−	0.968177i	$-0.419482\pi$
$727$	13.4958	0.500533	0.250267	+	0.968177i	$0.419482\pi$
$728$	−33.0871	−1.22629
$729$	1.92196	0.0711836
$730$	125.847	4.65781
$731$	−20.4796	−0.757467
$732$	−85.6471	−3.16561
$733$	7.19266	0.265667	0.132833	−	0.991138i	$-0.457592\pi$
$733$	7.19266	0.265667	0.132833	+	0.991138i	$0.457592\pi$
$734$	−32.9445	−1.21600
$735$	13.2145	0.487423
$736$	22.4448	0.827328
$737$	10.3469	0.381132
$738$	−6.16126	−0.226799
$739$	27.9601	1.02853	0.514264	−	0.857632i	$-0.328065\pi$
$739$	27.9601	1.02853	0.514264	+	0.857632i	$0.328065\pi$
$740$	245.885	9.03890
$741$	6.55198	0.240693
$742$	−9.37299	−0.344093
$743$	−5.27971	−0.193694	−0.0968469	−	0.995299i	$-0.530876\pi$
$743$	−5.27971	−0.193694	−0.0968469	+	0.995299i	$0.530876\pi$
$744$	−142.687	−5.23117
$745$	−50.7680	−1.86000
$746$	49.0574	1.79612
$747$	5.22666	0.191233
$748$	106.126	3.88035
$749$	45.0358	1.64557
$750$	146.220	5.33921
$751$	40.6736	1.48420	0.742100	−	0.670289i	$-0.233830\pi$
$751$	40.6736	1.48420	0.742100	+	0.670289i	$0.233830\pi$
$752$	−107.364	−3.91517
$753$	−27.1498	−0.989395
$754$	−0.870028	−0.0316846
$755$	23.3910	0.851285
$756$	36.2732	1.31924
$757$	−51.8456	−1.88436	−0.942181	−	0.335105i	$-0.891228\pi$
$757$	−51.8456	−1.88436	−0.942181	+	0.335105i	$0.891228\pi$
$758$	−64.3824	−2.33847
$759$	−10.3945	−0.377296
$760$	58.6968	2.12916
$761$	39.6071	1.43575	0.717877	−	0.696169i	$-0.245114\pi$
$761$	39.6071	1.43575	0.717877	+	0.696169i	$0.245114\pi$
$762$	−100.558	−3.64282
$763$	21.3994	0.774709
$764$	−96.1961	−3.48025
$765$	−42.1789	−1.52498
$766$	−42.0729	−1.52016
$767$	−12.8872	−0.465329
$768$	−2.21971	−0.0800968
$769$	7.22279	0.260461	0.130230	−	0.991484i	$-0.458428\pi$
$769$	7.22279	0.260461	0.130230	+	0.991484i	$0.458428\pi$
$770$	79.2684	2.85664
$771$	14.8641	0.535316
$772$	31.2187	1.12359
$773$	−43.3356	−1.55867	−0.779337	−	0.626605i	$-0.784444\pi$
$773$	−43.3356	−1.55867	−0.779337	+	0.626605i	$0.784444\pi$
$774$	−12.8991	−0.463650
$775$	−92.5976	−3.32620
$776$	26.2924	0.943843
$777$	−59.8950	−2.14872
$778$	−12.1620	−0.436028
$779$	−2.61354	−0.0936399
$780$	−75.8649	−2.71640
$781$	7.33474	0.262458
$782$	−27.2512	−0.974502
$783$	0.578052	0.0206579
$784$	−17.7573	−0.634190
$785$	95.8438	3.42081
$786$	−12.0058	−0.428234
$787$	19.3636	0.690239	0.345120	−	0.938559i	$-0.387838\pi$
$787$	19.3636	0.690239	0.345120	+	0.938559i	$0.387838\pi$
$788$	−4.40540	−0.156936
$789$	−12.2681	−0.436757
$790$	−14.7976	−0.526475
$791$	−16.6769	−0.592963
$792$	40.5103	1.43947
$793$	13.6361	0.484231
$794$	56.4424	2.00306
$795$	−13.0247	−0.461937
$796$	−70.8816	−2.51233
$797$	22.7057	0.804276	0.402138	−	0.915579i	$-0.368267\pi$
$797$	22.7057	0.804276	0.402138	+	0.915579i	$0.368267\pi$
$798$	−23.5922	−0.835155
$799$	61.3232	2.16946
$800$	−165.142	−5.83864
$801$	6.71795	0.237367
$802$	35.9007	1.26770
$803$	36.8429	1.30016
$804$	35.6571	1.25753
$805$	−14.6022	−0.514658
$806$	37.4849	1.32035
$807$	30.5459	1.07527
$808$	36.9986	1.30161
$809$	−16.1717	−0.568567	−0.284284	−	0.958740i	$-0.591756\pi$
$809$	−16.1717	−0.568567	−0.284284	+	0.958740i	$0.591756\pi$
$810$	120.981	4.25085
$811$	−39.4947	−1.38685	−0.693424	−	0.720530i	$-0.743899\pi$
$811$	−39.4947	−1.38685	−0.693424	+	0.720530i	$0.743899\pi$
$812$	2.24740	0.0788683
$813$	9.22674	0.323596
$814$	100.344	3.51705
$815$	24.5936	0.861478
$816$	164.887	5.77220
$817$	−5.47168	−0.191430
$818$	77.6343	2.71442
$819$	6.35238	0.221970
$820$	30.2620	1.05680
$821$	21.6844	0.756790	0.378395	−	0.925644i	$-0.376476\pi$
$821$	21.6844	0.756790	0.378395	+	0.925644i	$0.376476\pi$
$822$	−118.036	−4.11700
$823$	−28.0537	−0.977890	−0.488945	−	0.872314i	$-0.662618\pi$
$823$	−28.0537	−0.977890	−0.488945	+	0.872314i	$0.662618\pi$
$824$	39.3753	1.37170
$825$	76.4792	2.66266
$826$	46.4038	1.61460
$827$	−29.4739	−1.02491	−0.512454	−	0.858714i	$-0.671264\pi$
$827$	−29.4739	−1.02491	−0.512454	+	0.858714i	$0.671264\pi$
$828$	−12.3133	−0.427918
$829$	−39.2577	−1.36348	−0.681738	−	0.731596i	$-0.738776\pi$
$829$	−39.2577	−1.36348	−0.681738	+	0.731596i	$0.738776\pi$
$830$	−35.7850	−1.24211
$831$	−12.4882	−0.433211
$832$	26.6899	0.925307
$833$	10.1425	0.351415
$834$	−99.3263	−3.43939
$835$	62.1111	2.14944
$836$	28.3543	0.980656
$837$	−24.9052	−0.860850
$838$	80.3863	2.77690
$839$	−52.7711	−1.82186	−0.910931	−	0.412558i	$-0.864635\pi$
$839$	−52.7711	−1.82186	−0.910931	+	0.412558i	$0.864635\pi$
$840$	165.555	5.71219
$841$	−28.9642	−0.998765
$842$	−31.5331	−1.08670
$843$	55.4000	1.90808
$844$	−76.8292	−2.64457
$845$	−40.4976	−1.39316
$846$	38.6246	1.32794
$847$	−2.52451	−0.0867432
$848$	17.5023	0.601030
$849$	−12.7673	−0.438173
$850$	200.505	6.87728
$851$	−18.4845	−0.633640
$852$	25.2767	0.865967
$853$	−39.2539	−1.34403	−0.672014	−	0.740538i	$-0.734571\pi$
$853$	−39.2539	−1.34403	−0.672014	+	0.740538i	$0.734571\pi$
$854$	−49.1004	−1.68018
$855$	−11.2692	−0.385399
$856$	−157.579	−5.38595
$857$	−23.1870	−0.792052	−0.396026	−	0.918239i	$-0.629611\pi$
$857$	−23.1870	−0.792052	−0.396026	+	0.918239i	$0.629611\pi$
$858$	−30.9599	−1.05695
$859$	−4.35817	−0.148699	−0.0743495	−	0.997232i	$-0.523688\pi$
$859$	−4.35817	−0.148699	−0.0743495	+	0.997232i	$0.523688\pi$
$860$	63.3562	2.16043
$861$	−7.37152	−0.251221
$862$	−4.44156	−0.151280
$863$	−12.6637	−0.431077	−0.215539	−	0.976495i	$-0.569151\pi$
$863$	−12.6637	−0.431077	−0.215539	+	0.976495i	$0.569151\pi$
$864$	−44.4168	−1.51109
$865$	45.1982	1.53679
$866$	−29.7237	−1.01005
$867$	−57.8311	−1.96405
$868$	−96.8286	−3.28658
$869$	−4.33213	−0.146958
$870$	4.35329	0.147590
$871$	−5.67705	−0.192360
$872$	−74.8760	−2.53562
$873$	−5.04788	−0.170845
$874$	−7.28089	−0.246280
$875$	60.1356	2.03295
$876$	126.967	4.28981
$877$	−55.9946	−1.89080	−0.945401	−	0.325910i	$-0.894329\pi$
$877$	−55.9946	−1.89080	−0.945401	+	0.325910i	$0.894329\pi$
$878$	−105.586	−3.56336
$879$	−56.4399	−1.90367
$880$	−148.019	−4.98971
$881$	−26.2654	−0.884904	−0.442452	−	0.896792i	$-0.645891\pi$
$881$	−26.2654	−0.884904	−0.442452	+	0.896792i	$0.645891\pi$
$882$	6.38824	0.215103
$883$	23.1704	0.779745	0.389873	−	0.920869i	$-0.372519\pi$
$883$	23.1704	0.779745	0.389873	+	0.920869i	$0.372519\pi$
$884$	−58.2283	−1.95843
$885$	64.4825	2.16756
$886$	104.499	3.51070
$887$	−36.2980	−1.21877	−0.609384	−	0.792875i	$-0.708583\pi$
$887$	−36.2980	−1.21877	−0.609384	+	0.792875i	$0.708583\pi$
$888$	209.572	7.03276
$889$	−41.3561	−1.38704
$890$	−45.9953	−1.54177
$891$	35.4184	1.18656
$892$	52.5121	1.75823
$893$	16.3841	0.548274
$894$	−71.3979	−2.38790
$895$	1.70901	0.0571258
$896$	−28.0735	−0.937871
$897$	5.70317	0.190423
$898$	85.8668	2.86541
$899$	−1.54307	−0.0514642
$900$	90.5975	3.01992
$901$	−9.99678	−0.333041
$902$	12.3497	0.411201
$903$	−15.4329	−0.513575
$904$	58.3522	1.94077
$905$	−104.193	−3.46351
$906$	32.8961	1.09290
$907$	−32.6893	−1.08543	−0.542715	−	0.839917i	$-0.682604\pi$
$907$	−32.6893	−1.08543	−0.542715	+	0.839917i	$0.682604\pi$
$908$	−86.1611	−2.85936
$909$	−7.10337	−0.235604
$910$	−43.4924	−1.44176
$911$	11.6397	0.385639	0.192820	−	0.981234i	$-0.438237\pi$
$911$	11.6397	0.385639	0.192820	+	0.981234i	$0.438237\pi$
$912$	44.0539	1.45877
$913$	−10.4764	−0.346717
$914$	−36.8376	−1.21848
$915$	−68.2297	−2.25560
$916$	3.75483	0.124063
$917$	−4.93761	−0.163054
$918$	53.9283	1.77990
$919$	−28.8366	−0.951233	−0.475617	−	0.879653i	$-0.657775\pi$
$919$	−28.8366	−0.951233	−0.475617	+	0.879653i	$0.657775\pi$
$920$	51.0927	1.68447
$921$	−18.7906	−0.619171
$922$	−99.4498	−3.27521
$923$	−4.02437	−0.132464
$924$	79.9737	2.63094
$925$	136.003	4.47174
$926$	−79.7094	−2.61941
$927$	−7.55967	−0.248292
$928$	−2.75196	−0.0903374
$929$	−11.0511	−0.362575	−0.181287	−	0.983430i	$-0.558026\pi$
$929$	−11.0511	−0.362575	−0.181287	+	0.983430i	$0.558026\pi$
$930$	−187.560	−6.15034
$931$	2.70983	0.0888110
$932$	−30.4254	−0.996616
$933$	8.02706	0.262794
$934$	98.9775	3.23864
$935$	84.5439	2.76488
$936$	−22.2269	−0.726508
$937$	4.52086	0.147690	0.0738450	−	0.997270i	$-0.476473\pi$
$937$	4.52086	0.147690	0.0738450	+	0.997270i	$0.476473\pi$
$938$	20.4418	0.667448
$939$	−15.2621	−0.498059
$940$	−189.711	−6.18768
$941$	12.5858	0.410286	0.205143	−	0.978732i	$-0.434234\pi$
$941$	12.5858	0.410286	0.205143	+	0.978732i	$0.434234\pi$
$942$	134.791	4.39171
$943$	−2.27496	−0.0740829
$944$	−86.6502	−2.82023
$945$	28.8966	0.940008
$946$	25.8552	0.840625
$947$	−9.27941	−0.301540	−0.150770	−	0.988569i	$-0.548175\pi$
$947$	−9.27941	−0.301540	−0.150770	+	0.988569i	$0.548175\pi$
$948$	−14.9293	−0.484880
$949$	−20.2147	−0.656196
$950$	53.5704	1.73805
$951$	−18.4079	−0.596918
$952$	127.068	4.11829
$953$	−7.15296	−0.231707	−0.115853	−	0.993266i	$-0.536960\pi$
$953$	−7.15296	−0.231707	−0.115853	+	0.993266i	$0.536960\pi$
$954$	−6.29649	−0.203856
$955$	−76.6335	−2.47980
$956$	−84.3941	−2.72950
$957$	1.27447	0.0411976
$958$	79.0158	2.55289
$959$	−48.5446	−1.56759
$960$	−133.546	−4.31019
$961$	35.4826	1.14460
$962$	−55.0559	−1.77507
$963$	30.2537	0.974910
$964$	81.3033	2.61860
$965$	24.8700	0.800595
$966$	−20.5358	−0.660729
$967$	5.12907	0.164940	0.0824698	−	0.996594i	$-0.473719\pi$
$967$	5.12907	0.164940	0.0824698	+	0.996594i	$0.473719\pi$
$968$	8.83322	0.283910
$969$	−25.1623	−0.808330
$970$	34.5610	1.10969
$971$	−20.3638	−0.653504	−0.326752	−	0.945110i	$-0.605954\pi$
$971$	−20.3638	−0.653504	−0.326752	+	0.945110i	$0.605954\pi$
$972$	75.5373	2.42286
$973$	−40.8497	−1.30958
$974$	83.3008	2.66913
$975$	−41.9620	−1.34386
$976$	91.6857	2.93479
$977$	32.2746	1.03256	0.516278	−	0.856421i	$-0.327317\pi$
$977$	32.2746	1.03256	0.516278	+	0.856421i	$0.327317\pi$
$978$	34.5874	1.10598
$979$	−13.4655	−0.430361
$980$	−31.3769	−1.00230
$981$	14.3754	0.458973
$982$	9.34280	0.298141
$983$	−44.2023	−1.40983	−0.704917	−	0.709290i	$-0.749016\pi$
$983$	−44.2023	−1.40983	−0.704917	+	0.709290i	$0.749016\pi$
$984$	25.7928	0.822245
$985$	−3.50951	−0.111822
$986$	3.34127	0.106408
$987$	46.2116	1.47093
$988$	−15.5573	−0.494942
$989$	−4.76282	−0.151449
$990$	53.2501	1.69240
$991$	44.9779	1.42877	0.714385	−	0.699753i	$-0.246707\pi$
$991$	44.9779	1.42877	0.714385	+	0.699753i	$0.246707\pi$
$992$	118.567	3.76451
$993$	50.6022	1.60581
$994$	14.4908	0.459622
$995$	−56.4670	−1.79012
$996$	−36.1033	−1.14398
$997$	50.4690	1.59837	0.799184	−	0.601087i	$-0.205265\pi$
$997$	50.4690	1.59837	0.799184	+	0.601087i	$0.205265\pi$
$998$	102.744	3.25231
$999$	36.5795	1.15732

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.6	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.6	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66021 q^{2} -2.13808 q^{3} +5.07674 q^{4} +4.04432 q^{5} +5.68776 q^{6} +2.33919 q^{7} -8.18478 q^{8} +1.57140 q^{9} +O(q^{10})\)	\(q-2.66021 q^{2} -2.13808 q^{3} +5.07674 q^{4} +4.04432 q^{5} +5.68776 q^{6} +2.33919 q^{7} -8.18478 q^{8} +1.57140 q^{9} -10.7588 q^{10} -3.14973 q^{11} -10.8545 q^{12} +1.72817 q^{13} -6.22274 q^{14} -8.64709 q^{15} +11.6198 q^{16} -6.63688 q^{17} -4.18025 q^{18} -1.77322 q^{19} +20.5320 q^{20} -5.00138 q^{21} +8.37894 q^{22} -1.54350 q^{23} +17.4997 q^{24} +11.3565 q^{25} -4.59730 q^{26} +3.05447 q^{27} +11.8754 q^{28} +0.189248 q^{29} +23.0031 q^{30} -8.15368 q^{31} -14.5415 q^{32} +6.73437 q^{33} +17.6555 q^{34} +9.46043 q^{35} +7.97756 q^{36} +11.9757 q^{37} +4.71714 q^{38} -3.69497 q^{39} -33.1019 q^{40} +1.47390 q^{41} +13.3047 q^{42} +3.08573 q^{43} -15.9903 q^{44} +6.35523 q^{45} +4.10603 q^{46} -9.23978 q^{47} -24.8440 q^{48} -1.52820 q^{49} -30.2108 q^{50} +14.1902 q^{51} +8.77345 q^{52} +1.50625 q^{53} -8.12555 q^{54} -12.7385 q^{55} -19.1457 q^{56} +3.79129 q^{57} -0.503440 q^{58} -7.45713 q^{59} -43.8990 q^{60} +7.89048 q^{61} +21.6905 q^{62} +3.67579 q^{63} +15.4441 q^{64} +6.98927 q^{65} -17.9149 q^{66} -3.28501 q^{67} -33.6937 q^{68} +3.30012 q^{69} -25.1668 q^{70} -2.32869 q^{71} -12.8615 q^{72} -11.6972 q^{73} -31.8579 q^{74} -24.2812 q^{75} -9.00216 q^{76} -7.36780 q^{77} +9.82940 q^{78} +1.37540 q^{79} +46.9941 q^{80} -11.2449 q^{81} -3.92089 q^{82} +3.32612 q^{83} -25.3907 q^{84} -26.8417 q^{85} -8.20871 q^{86} -0.404627 q^{87} +25.7798 q^{88} +4.27515 q^{89} -16.9063 q^{90} +4.04251 q^{91} -7.83593 q^{92} +17.4332 q^{93} +24.5798 q^{94} -7.17147 q^{95} +31.0910 q^{96} -3.21236 q^{97} +4.06533 q^{98} -4.94947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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