LMFDB - Embedded newform 8041.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28377 q^{2} +1.73431 q^{3} +3.21562 q^{4} -2.87299 q^{5} -3.96077 q^{6} +2.79436 q^{7} -2.77620 q^{8} +0.00783032 q^{9} +O(q^{10})$	\(q-2.28377 q^{2} +1.73431 q^{3} +3.21562 q^{4} -2.87299 q^{5} -3.96077 q^{6} +2.79436 q^{7} -2.77620 q^{8} +0.00783032 q^{9} +6.56126 q^{10} -1.00000 q^{11} +5.57688 q^{12} -4.38126 q^{13} -6.38169 q^{14} -4.98265 q^{15} -0.0910260 q^{16} +1.00000 q^{17} -0.0178827 q^{18} -4.69044 q^{19} -9.23844 q^{20} +4.84629 q^{21} +2.28377 q^{22} +0.581829 q^{23} -4.81479 q^{24} +3.25407 q^{25} +10.0058 q^{26} -5.18935 q^{27} +8.98561 q^{28} -1.03166 q^{29} +11.3793 q^{30} -2.80421 q^{31} +5.76029 q^{32} -1.73431 q^{33} -2.28377 q^{34} -8.02818 q^{35} +0.0251793 q^{36} +1.68905 q^{37} +10.7119 q^{38} -7.59847 q^{39} +7.97600 q^{40} +2.09395 q^{41} -11.0678 q^{42} -1.00000 q^{43} -3.21562 q^{44} -0.0224964 q^{45} -1.32877 q^{46} +8.21756 q^{47} -0.157867 q^{48} +0.808469 q^{49} -7.43156 q^{50} +1.73431 q^{51} -14.0885 q^{52} +5.24173 q^{53} +11.8513 q^{54} +2.87299 q^{55} -7.75772 q^{56} -8.13468 q^{57} +2.35607 q^{58} -13.4106 q^{59} -16.0223 q^{60} -13.6054 q^{61} +6.40418 q^{62} +0.0218808 q^{63} -12.9731 q^{64} +12.5873 q^{65} +3.96077 q^{66} +1.17184 q^{67} +3.21562 q^{68} +1.00907 q^{69} +18.3345 q^{70} -0.922665 q^{71} -0.0217386 q^{72} +4.29327 q^{73} -3.85741 q^{74} +5.64356 q^{75} -15.0827 q^{76} -2.79436 q^{77} +17.3532 q^{78} -6.63656 q^{79} +0.261517 q^{80} -9.02343 q^{81} -4.78211 q^{82} +0.299457 q^{83} +15.5838 q^{84} -2.87299 q^{85} +2.28377 q^{86} -1.78921 q^{87} +2.77620 q^{88} +6.55235 q^{89} +0.0513768 q^{90} -12.2428 q^{91} +1.87094 q^{92} -4.86337 q^{93} -18.7670 q^{94} +13.4756 q^{95} +9.99012 q^{96} +3.79961 q^{97} -1.84636 q^{98} -0.00783032 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) $ 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * 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 $

$2$	−2.28377	−1.61487	−0.807436	−	0.589955i	$-0.799145\pi$
$2$	−2.28377	−1.61487	−0.807436	+	0.589955i	$0.799145\pi$
$3$	1.73431	1.00130	0.500652	−	0.865649i	$-0.333094\pi$
$3$	1.73431	1.00130	0.500652	+	0.865649i	$0.333094\pi$
$4$	3.21562	1.60781
$5$	−2.87299	−1.28484	−0.642420	−	0.766353i	$-0.722070\pi$
$5$	−2.87299	−1.28484	−0.642420	+	0.766353i	$0.722070\pi$
$6$	−3.96077	−1.61698
$7$	2.79436	1.05617	0.528085	−	0.849191i	$-0.322910\pi$
$7$	2.79436	1.05617	0.528085	+	0.849191i	$0.322910\pi$
$8$	−2.77620	−0.981535
$9$	0.00783032	0.00261011
$10$	6.56126	2.07485
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.57688	1.60991
$13$	−4.38126	−1.21514	−0.607572	−	0.794265i	$-0.707856\pi$
$13$	−4.38126	−1.21514	−0.607572	+	0.794265i	$0.707856\pi$
$14$	−6.38169	−1.70558
$15$	−4.98265	−1.28652
$16$	−0.0910260	−0.0227565
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.0178827	−0.00421499
$19$	−4.69044	−1.07606	−0.538031	−	0.842925i	$-0.680832\pi$
$19$	−4.69044	−1.07606	−0.538031	+	0.842925i	$0.680832\pi$
$20$	−9.23844	−2.06578
$21$	4.84629	1.05755
$22$	2.28377	0.486902
$23$	0.581829	0.121320	0.0606599	−	0.998158i	$-0.480679\pi$
$23$	0.581829	0.121320	0.0606599	+	0.998158i	$0.480679\pi$
$24$	−4.81479	−0.982816
$25$	3.25407	0.650814
$26$	10.0058	1.96230
$27$	−5.18935	−0.998691
$28$	8.98561	1.69812
$29$	−1.03166	−0.191574	−0.0957869	−	0.995402i	$-0.530537\pi$
$29$	−1.03166	−0.191574	−0.0957869	+	0.995402i	$0.530537\pi$
$30$	11.3793	2.07756
$31$	−2.80421	−0.503651	−0.251826	−	0.967773i	$-0.581031\pi$
$31$	−2.80421	−0.503651	−0.251826	+	0.967773i	$0.581031\pi$
$32$	5.76029	1.01828
$33$	−1.73431	−0.301905
$34$	−2.28377	−0.391664
$35$	−8.02818	−1.35701
$36$	0.0251793	0.00419656
$37$	1.68905	0.277678	0.138839	−	0.990315i	$-0.455663\pi$
$37$	1.68905	0.277678	0.138839	+	0.990315i	$0.455663\pi$
$38$	10.7119	1.73770
$39$	−7.59847	−1.21673
$40$	7.97600	1.26112
$41$	2.09395	0.327020	0.163510	−	0.986542i	$-0.447718\pi$
$41$	2.09395	0.327020	0.163510	+	0.986542i	$0.447718\pi$
$42$	−11.0678	−1.70780
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−3.21562	−0.484773
$45$	−0.0224964	−0.00335357
$46$	−1.32877	−0.195916
$47$	8.21756	1.19865	0.599327	−	0.800504i	$-0.295435\pi$
$47$	8.21756	1.19865	0.599327	+	0.800504i	$0.295435\pi$
$48$	−0.157867	−0.0227862
$49$	0.808469	0.115496
$50$	−7.43156	−1.05098
$51$	1.73431	0.242852
$52$	−14.0885	−1.95372
$53$	5.24173	0.720007	0.360003	−	0.932951i	$-0.382776\pi$
$53$	5.24173	0.720007	0.360003	+	0.932951i	$0.382776\pi$
$54$	11.8513	1.61276
$55$	2.87299	0.387394
$56$	−7.75772	−1.03667
$57$	−8.13468	−1.07746
$58$	2.35607	0.309367
$59$	−13.4106	−1.74592	−0.872958	−	0.487795i	$-0.837801\pi$
$59$	−13.4106	−1.74592	−0.872958	+	0.487795i	$0.837801\pi$
$60$	−16.0223	−2.06847
$61$	−13.6054	−1.74199	−0.870997	−	0.491289i	$-0.836526\pi$
$61$	−13.6054	−1.74199	−0.870997	+	0.491289i	$0.836526\pi$
$62$	6.40418	0.813332
$63$	0.0218808	0.00275672
$64$	−12.9731	−1.62164
$65$	12.5873	1.56127
$66$	3.96077	0.487537
$67$	1.17184	0.143163	0.0715813	−	0.997435i	$-0.477195\pi$
$67$	1.17184	0.143163	0.0715813	+	0.997435i	$0.477195\pi$
$68$	3.21562	0.389951
$69$	1.00907	0.121478
$70$	18.3345	2.19140
$71$	−0.922665	−0.109500	−0.0547501	−	0.998500i	$-0.517436\pi$
$71$	−0.922665	−0.109500	−0.0547501	+	0.998500i	$0.517436\pi$
$72$	−0.0217386	−0.00256191
$73$	4.29327	0.502490	0.251245	−	0.967924i	$-0.419160\pi$
$73$	4.29327	0.502490	0.251245	+	0.967924i	$0.419160\pi$
$74$	−3.85741	−0.448415
$75$	5.64356	0.651663
$76$	−15.0827	−1.73010
$77$	−2.79436	−0.318447
$78$	17.3532	1.96486
$79$	−6.63656	−0.746671	−0.373336	−	0.927696i	$-0.621786\pi$
$79$	−6.63656	−0.746671	−0.373336	+	0.927696i	$0.621786\pi$
$80$	0.261517	0.0292384
$81$	−9.02343	−1.00260
$82$	−4.78211	−0.528095
$83$	0.299457	0.0328697	0.0164349	−	0.999865i	$-0.494768\pi$
$83$	0.299457	0.0328697	0.0164349	+	0.999865i	$0.494768\pi$
$84$	15.5838	1.70034
$85$	−2.87299	−0.311619
$86$	2.28377	0.246266
$87$	−1.78921	−0.191824
$88$	2.77620	0.295944
$89$	6.55235	0.694548	0.347274	−	0.937764i	$-0.387107\pi$
$89$	6.55235	0.694548	0.347274	+	0.937764i	$0.387107\pi$
$90$	0.0513768	0.00541559
$91$	−12.2428	−1.28340
$92$	1.87094	0.195059
$93$	−4.86337	−0.504308
$94$	−18.7670	−1.93567
$95$	13.4756	1.38257
$96$	9.99012	1.01961
$97$	3.79961	0.385792	0.192896	−	0.981219i	$-0.438212\pi$
$97$	3.79961	0.385792	0.192896	+	0.981219i	$0.438212\pi$
$98$	−1.84636	−0.186511
$99$	−0.00783032	−0.000786977 0
$100$	10.4639	1.04639
$101$	4.08848	0.406819	0.203410	−	0.979094i	$-0.434798\pi$
$101$	4.08848	0.406819	0.203410	+	0.979094i	$0.434798\pi$
$102$	−3.96077	−0.392175
$103$	12.6396	1.24541	0.622706	−	0.782456i	$-0.286033\pi$
$103$	12.6396	1.24541	0.622706	+	0.782456i	$0.286033\pi$
$104$	12.1633	1.19271
$105$	−13.9233	−1.35878
$106$	−11.9709	−1.16272
$107$	15.1397	1.46361	0.731806	−	0.681513i	$-0.238678\pi$
$107$	15.1397	1.46361	0.731806	+	0.681513i	$0.238678\pi$
$108$	−16.6870	−1.60571
$109$	−15.5437	−1.48881	−0.744407	−	0.667727i	$-0.767268\pi$
$109$	−15.5437	−1.48881	−0.744407	+	0.667727i	$0.767268\pi$
$110$	−6.56126	−0.625591
$111$	2.92934	0.278041
$112$	−0.254360	−0.0240347
$113$	9.68719	0.911294	0.455647	−	0.890160i	$-0.349408\pi$
$113$	9.68719	0.911294	0.455647	+	0.890160i	$0.349408\pi$
$114$	18.5778	1.73997
$115$	−1.67159	−0.155877
$116$	−3.31741	−0.308014
$117$	−0.0343067	−0.00317166
$118$	30.6269	2.81943
$119$	2.79436	0.256159
$120$	13.8329	1.26276
$121$	1.00000	0.0909091
$122$	31.0717	2.81310
$123$	3.63156	0.327447
$124$	−9.01728	−0.809776
$125$	5.01604	0.448648
$126$	−0.0499707	−0.00445175
$127$	6.87900	0.610412	0.305206	−	0.952286i	$-0.401275\pi$
$127$	6.87900	0.610412	0.305206	+	0.952286i	$0.401275\pi$
$128$	18.1071	1.60046
$129$	−1.73431	−0.152697
$130$	−28.7466	−2.52124
$131$	12.7181	1.11119	0.555593	−	0.831454i	$-0.312491\pi$
$131$	12.7181	1.11119	0.555593	+	0.831454i	$0.312491\pi$
$132$	−5.57688	−0.485405
$133$	−13.1068	−1.13650
$134$	−2.67621	−0.231189
$135$	14.9089	1.28316
$136$	−2.77620	−0.238057
$137$	2.76836	0.236517	0.118258	−	0.992983i	$-0.462269\pi$
$137$	2.76836	0.236517	0.118258	+	0.992983i	$0.462269\pi$
$138$	−2.30449	−0.196171
$139$	−2.95292	−0.250463	−0.125232	−	0.992128i	$-0.539967\pi$
$139$	−2.95292	−0.250463	−0.125232	+	0.992128i	$0.539967\pi$
$140$	−25.8156	−2.18181
$141$	14.2518	1.20022
$142$	2.10716	0.176829
$143$	4.38126	0.366380
$144$	−0.000712763 0	−5.93969e−5 0
$145$	2.96394	0.246142
$146$	−9.80486	−0.811456
$147$	1.40214	0.115646
$148$	5.43135	0.446454
$149$	−1.97940	−0.162159	−0.0810793	−	0.996708i	$-0.525837\pi$
$149$	−1.97940	−0.162159	−0.0810793	+	0.996708i	$0.525837\pi$
$150$	−12.8886	−1.05235
$151$	19.3816	1.57726	0.788628	−	0.614871i	$-0.210792\pi$
$151$	19.3816	1.57726	0.788628	+	0.614871i	$0.210792\pi$
$152$	13.0216	1.05619
$153$	0.00783032	0.000633044 0
$154$	6.38169	0.514252
$155$	8.05647	0.647111
$156$	−24.4338	−1.95627
$157$	−18.5880	−1.48348	−0.741740	−	0.670687i	$-0.765999\pi$
$157$	−18.5880	−1.48348	−0.741740	+	0.670687i	$0.765999\pi$
$158$	15.1564	1.20578
$159$	9.09078	0.720946
$160$	−16.5492	−1.30833
$161$	1.62584	0.128134
$162$	20.6075	1.61908
$163$	2.99676	0.234724	0.117362	−	0.993089i	$-0.462556\pi$
$163$	2.99676	0.234724	0.117362	+	0.993089i	$0.462556\pi$
$164$	6.73335	0.525786
$165$	4.98265	0.387899
$166$	−0.683893	−0.0530804
$167$	6.34232	0.490784	0.245392	−	0.969424i	$-0.421083\pi$
$167$	6.34232	0.490784	0.245392	+	0.969424i	$0.421083\pi$
$168$	−13.4543	−1.03802
$169$	6.19548	0.476575
$170$	6.56126	0.503225
$171$	−0.0367277	−0.00280864
$172$	−3.21562	−0.245189
$173$	4.14499	0.315138	0.157569	−	0.987508i	$-0.449634\pi$
$173$	4.14499	0.315138	0.157569	+	0.987508i	$0.449634\pi$
$174$	4.08615	0.309770
$175$	9.09305	0.687370
$176$	0.0910260	0.00686134
$177$	−23.2582	−1.74819
$178$	−14.9641	−1.12161
$179$	−16.2884	−1.21745	−0.608727	−	0.793380i	$-0.708320\pi$
$179$	−16.2884	−1.21745	−0.608727	+	0.793380i	$0.708320\pi$
$180$	−0.0723400	−0.00539190
$181$	10.9665	0.815133	0.407566	−	0.913176i	$-0.366378\pi$
$181$	10.9665	0.815133	0.407566	+	0.913176i	$0.366378\pi$
$182$	27.9599	2.07252
$183$	−23.5960	−1.74427
$184$	−1.61528	−0.119080
$185$	−4.85263	−0.356772
$186$	11.1068	0.814393
$187$	−1.00000	−0.0731272
$188$	26.4246	1.92721
$189$	−14.5009	−1.05479
$190$	−30.7752	−2.23267
$191$	0.642008	0.0464540	0.0232270	−	0.999730i	$-0.492606\pi$
$191$	0.642008	0.0464540	0.0232270	+	0.999730i	$0.492606\pi$
$192$	−22.4994	−1.62376
$193$	−4.55507	−0.327881	−0.163941	−	0.986470i	$-0.552421\pi$
$193$	−4.55507	−0.327881	−0.163941	+	0.986470i	$0.552421\pi$
$194$	−8.67744	−0.623004
$195$	21.8303	1.56330
$196$	2.59973	0.185695
$197$	6.06527	0.432133	0.216066	−	0.976379i	$-0.430677\pi$
$197$	6.06527	0.432133	0.216066	+	0.976379i	$0.430677\pi$
$198$	0.0178827	0.00127087
$199$	15.9315	1.12935	0.564677	−	0.825312i	$-0.309001\pi$
$199$	15.9315	1.12935	0.564677	+	0.825312i	$0.309001\pi$
$200$	−9.03395	−0.638797
$201$	2.03233	0.143349
$202$	−9.33717	−0.656961
$203$	−2.88282	−0.202334
$204$	5.57688	0.390460
$205$	−6.01590	−0.420169
$206$	−28.8659	−2.01118
$207$	0.00455591	0.000316658 0
$208$	0.398809	0.0276524
$209$	4.69044	0.324445
$210$	31.7978	2.19425
$211$	17.1452	1.18032	0.590161	−	0.807285i	$-0.299064\pi$
$211$	17.1452	1.18032	0.590161	+	0.807285i	$0.299064\pi$
$212$	16.8554	1.15763
$213$	−1.60019	−0.109643
$214$	−34.5757	−2.36354
$215$	2.87299	0.195936
$216$	14.4067	0.980250
$217$	−7.83599	−0.531942
$218$	35.4982	2.40424
$219$	7.44587	0.503145
$220$	9.23844	0.622856
$221$	−4.38126	−0.294716
$222$	−6.68995	−0.449000
$223$	−11.4383	−0.765967	−0.382983	−	0.923755i	$-0.625103\pi$
$223$	−11.4383	−0.765967	−0.382983	+	0.923755i	$0.625103\pi$
$224$	16.0963	1.07548
$225$	0.0254804	0.00169869
$226$	−22.1234	−1.47162
$227$	−20.4354	−1.35635	−0.678173	−	0.734903i	$-0.737228\pi$
$227$	−20.4354	−1.35635	−0.678173	+	0.734903i	$0.737228\pi$
$228$	−26.1580	−1.73236
$229$	−10.5633	−0.698045	−0.349023	−	0.937114i	$-0.613486\pi$
$229$	−10.5633	−0.698045	−0.349023	+	0.937114i	$0.613486\pi$
$230$	3.81753	0.251721
$231$	−4.84629	−0.318863
$232$	2.86408	0.188036
$233$	11.0875	0.726367	0.363183	−	0.931718i	$-0.381690\pi$
$233$	11.0875	0.726367	0.363183	+	0.931718i	$0.381690\pi$
$234$	0.0783488	0.00512182
$235$	−23.6090	−1.54008
$236$	−43.1235	−2.80710
$237$	−11.5098	−0.747645
$238$	−6.38169	−0.413664
$239$	−7.02393	−0.454341	−0.227170	−	0.973855i	$-0.572947\pi$
$239$	−7.02393	−0.454341	−0.227170	+	0.973855i	$0.572947\pi$
$240$	0.453551	0.0292766
$241$	7.52155	0.484505	0.242253	−	0.970213i	$-0.422114\pi$
$241$	7.52155	0.484505	0.242253	+	0.970213i	$0.422114\pi$
$242$	−2.28377	−0.146807
$243$	−0.0813749	−0.00522020
$244$	−43.7498	−2.80080
$245$	−2.32272	−0.148393
$246$	−8.29366	−0.528784
$247$	20.5501	1.30757
$248$	7.78506	0.494352
$249$	0.519352	0.0329126
$250$	−11.4555	−0.724509
$251$	14.1071	0.890429	0.445215	−	0.895424i	$-0.353127\pi$
$251$	14.1071	0.890429	0.445215	+	0.895424i	$0.353127\pi$
$252$	0.0703602	0.00443228
$253$	−0.581829	−0.0365793
$254$	−15.7101	−0.985738
$255$	−4.98265	−0.312026
$256$	−15.4063	−0.962894
$257$	−2.52365	−0.157421	−0.0787104	−	0.996898i	$-0.525080\pi$
$257$	−2.52365	−0.157421	−0.0787104	+	0.996898i	$0.525080\pi$
$258$	3.96077	0.246587
$259$	4.71983	0.293276
$260$	40.4761	2.51022
$261$	−0.00807820	−0.000500028 0
$262$	−29.0453	−1.79442
$263$	18.9966	1.17138	0.585689	−	0.810536i	$-0.300824\pi$
$263$	18.9966	1.17138	0.585689	+	0.810536i	$0.300824\pi$
$264$	4.81479	0.296330
$265$	−15.0594	−0.925093
$266$	29.9330	1.83531
$267$	11.3638	0.695454
$268$	3.76818	0.230178
$269$	−20.9993	−1.28035	−0.640174	−	0.768230i	$-0.721138\pi$
$269$	−20.9993	−1.28035	−0.640174	+	0.768230i	$0.721138\pi$
$270$	−34.0487	−2.07213
$271$	5.57550	0.338688	0.169344	−	0.985557i	$-0.445835\pi$
$271$	5.57550	0.338688	0.169344	+	0.985557i	$0.445835\pi$
$272$	−0.0910260	−0.00551926
$273$	−21.2329	−1.28507
$274$	−6.32230	−0.381944
$275$	−3.25407	−0.196228
$276$	3.24479	0.195314
$277$	−24.3315	−1.46194	−0.730968	−	0.682412i	$-0.760931\pi$
$277$	−24.3315	−1.46194	−0.730968	+	0.682412i	$0.760931\pi$
$278$	6.74380	0.404466
$279$	−0.0219579	−0.00131458
$280$	22.2878	1.33195
$281$	−9.26659	−0.552798	−0.276399	−	0.961043i	$-0.589141\pi$
$281$	−9.26659	−0.552798	−0.276399	+	0.961043i	$0.589141\pi$
$282$	−32.5479	−1.93820
$283$	13.6737	0.812815	0.406407	−	0.913692i	$-0.366781\pi$
$283$	13.6737	0.812815	0.406407	+	0.913692i	$0.366781\pi$
$284$	−2.96694	−0.176056
$285$	23.3709	1.38437
$286$	−10.0058	−0.591656
$287$	5.85126	0.345389
$288$	0.0451049	0.00265783
$289$	1.00000	0.0588235
$290$	−6.76896	−0.397487
$291$	6.58969	0.386295
$292$	13.8055	0.807908
$293$	16.9515	0.990316	0.495158	−	0.868803i	$-0.335110\pi$
$293$	16.9515	0.990316	0.495158	+	0.868803i	$0.335110\pi$
$294$	−3.20216	−0.186754
$295$	38.5286	2.24322
$296$	−4.68915	−0.272551
$297$	5.18935	0.301117
$298$	4.52050	0.261865
$299$	−2.54915	−0.147421
$300$	18.1476	1.04775
$301$	−2.79436	−0.161064
$302$	−44.2633	−2.54707
$303$	7.09069	0.407350
$304$	0.426952	0.0244874
$305$	39.0882	2.23818
$306$	−0.0178827	−0.00102228
$307$	30.0638	1.71583	0.857915	−	0.513792i	$-0.171760\pi$
$307$	30.0638	1.71583	0.857915	+	0.513792i	$0.171760\pi$
$308$	−8.98561	−0.512003
$309$	21.9209	1.24704
$310$	−18.3992	−1.04500
$311$	−15.9100	−0.902171	−0.451086	−	0.892481i	$-0.648963\pi$
$311$	−15.9100	−0.902171	−0.451086	+	0.892481i	$0.648963\pi$
$312$	21.0949	1.19426
$313$	1.23548	0.0698334	0.0349167	−	0.999390i	$-0.488883\pi$
$313$	1.23548	0.0698334	0.0349167	+	0.999390i	$0.488883\pi$
$314$	42.4507	2.39563
$315$	−0.0628632	−0.00354194
$316$	−21.3407	−1.20051
$317$	17.6783	0.992910	0.496455	−	0.868062i	$-0.334635\pi$
$317$	17.6783	0.992910	0.496455	+	0.868062i	$0.334635\pi$
$318$	−20.7613	−1.16423
$319$	1.03166	0.0577616
$320$	37.2717	2.08355
$321$	26.2570	1.46552
$322$	−3.71306	−0.206921
$323$	−4.69044	−0.260983
$324$	−29.0159	−1.61200
$325$	−14.2569	−0.790833
$326$	−6.84392	−0.379050
$327$	−26.9575	−1.49075
$328$	−5.81323	−0.320982
$329$	22.9629	1.26598
$330$	−11.3793	−0.626407
$331$	−30.7914	−1.69245	−0.846224	−	0.532828i	$-0.821129\pi$
$331$	−30.7914	−1.69245	−0.846224	+	0.532828i	$0.821129\pi$
$332$	0.962942	0.0528483
$333$	0.0132258	0.000724771 0
$334$	−14.4844	−0.792552
$335$	−3.36667	−0.183941
$336$	−0.441138	−0.0240661
$337$	32.4131	1.76565	0.882826	−	0.469699i	$-0.155638\pi$
$337$	32.4131	1.76565	0.882826	+	0.469699i	$0.155638\pi$
$338$	−14.1491	−0.769608
$339$	16.8006	0.912483
$340$	−9.23844	−0.501025
$341$	2.80421	0.151857
$342$	0.0838777	0.00453559
$343$	−17.3014	−0.934187
$344$	2.77620	0.149683
$345$	−2.89905	−0.156080
$346$	−9.46622	−0.508907
$347$	−19.0232	−1.02122	−0.510608	−	0.859813i	$-0.670580\pi$
$347$	−19.0232	−1.02122	−0.510608	+	0.859813i	$0.670580\pi$
$348$	−5.75342	−0.308416
$349$	−0.655787	−0.0351035	−0.0175517	−	0.999846i	$-0.505587\pi$
$349$	−0.655787	−0.0351035	−0.0175517	+	0.999846i	$0.505587\pi$
$350$	−20.7665	−1.11001
$351$	22.7359	1.21355
$352$	−5.76029	−0.307024
$353$	21.9574	1.16867	0.584336	−	0.811512i	$-0.301355\pi$
$353$	21.9574	1.16867	0.584336	+	0.811512i	$0.301355\pi$
$354$	53.1165	2.82311
$355$	2.65081	0.140690
$356$	21.0699	1.11670
$357$	4.84629	0.256493
$358$	37.1991	1.96603
$359$	3.55415	0.187581	0.0937904	−	0.995592i	$-0.470102\pi$
$359$	3.55415	0.187581	0.0937904	+	0.995592i	$0.470102\pi$
$360$	0.0624546	0.00329165
$361$	3.00025	0.157908
$362$	−25.0450	−1.31633
$363$	1.73431	0.0910277
$364$	−39.3683	−2.06346
$365$	−12.3345	−0.645619
$366$	53.8879	2.81676
$367$	−12.4822	−0.651568	−0.325784	−	0.945444i	$-0.605628\pi$
$367$	−12.4822	−0.651568	−0.325784	+	0.945444i	$0.605628\pi$
$368$	−0.0529616	−0.00276081
$369$	0.0163963	0.000853558 0
$370$	11.0823	0.576142
$371$	14.6473	0.760450
$372$	−15.6388	−0.810832
$373$	−8.19432	−0.424286	−0.212143	−	0.977239i	$-0.568044\pi$
$373$	−8.19432	−0.424286	−0.212143	+	0.977239i	$0.568044\pi$
$374$	2.28377	0.118091
$375$	8.69937	0.449233
$376$	−22.8136	−1.17652
$377$	4.51996	0.232790
$378$	33.1168	1.70335
$379$	9.45806	0.485828	0.242914	−	0.970048i	$-0.421897\pi$
$379$	9.45806	0.485828	0.242914	+	0.970048i	$0.421897\pi$
$380$	43.3324	2.22290
$381$	11.9303	0.611208
$382$	−1.46620	−0.0750173
$383$	5.05456	0.258276	0.129138	−	0.991627i	$-0.458779\pi$
$383$	5.05456	0.258276	0.129138	+	0.991627i	$0.458779\pi$
$384$	31.4034	1.60255
$385$	8.02818	0.409154
$386$	10.4027	0.529486
$387$	−0.00783032	−0.000398038 0
$388$	12.2181	0.620280
$389$	31.7305	1.60880	0.804401	−	0.594087i	$-0.202486\pi$
$389$	31.7305	1.60880	0.804401	+	0.594087i	$0.202486\pi$
$390$	−49.8555	−2.52453
$391$	0.581829	0.0294244
$392$	−2.24447	−0.113363
$393$	22.0571	1.11264
$394$	−13.8517	−0.697839
$395$	19.0668	0.959353
$396$	−0.0251793	−0.00126531
$397$	−9.35363	−0.469445	−0.234723	−	0.972062i	$-0.575418\pi$
$397$	−9.35363	−0.469445	−0.234723	+	0.972062i	$0.575418\pi$
$398$	−36.3840	−1.82376
$399$	−22.7313	−1.13799
$400$	−0.296205	−0.0148102
$401$	20.6862	1.03302	0.516511	−	0.856281i	$-0.327231\pi$
$401$	20.6862	1.03302	0.516511	+	0.856281i	$0.327231\pi$
$402$	−4.64137	−0.231491
$403$	12.2860	0.612009
$404$	13.1470	0.654088
$405$	25.9242	1.28818
$406$	6.58371	0.326744
$407$	−1.68905	−0.0837232
$408$	−4.81479	−0.238368
$409$	30.6090	1.51352	0.756758	−	0.653696i	$-0.226782\pi$
$409$	30.6090	1.51352	0.756758	+	0.653696i	$0.226782\pi$
$410$	13.7389	0.678518
$411$	4.80119	0.236825
$412$	40.6440	2.00239
$413$	−37.4742	−1.84399
$414$	−0.0104047	−0.000511362 0
$415$	−0.860338	−0.0422323
$416$	−25.2373	−1.23736
$417$	−5.12128	−0.250790
$418$	−10.7119	−0.523936
$419$	4.09445	0.200027	0.100014	−	0.994986i	$-0.468111\pi$
$419$	4.09445	0.200027	0.100014	+	0.994986i	$0.468111\pi$
$420$	−44.7722	−2.18466
$421$	−22.9353	−1.11780	−0.558899	−	0.829236i	$-0.688776\pi$
$421$	−22.9353	−1.11780	−0.558899	+	0.829236i	$0.688776\pi$
$422$	−39.1557	−1.90607
$423$	0.0643462	0.00312862
$424$	−14.5521	−0.706712
$425$	3.25407	0.157846
$426$	3.65446	0.177059
$427$	−38.0185	−1.83984
$428$	48.6836	2.35321
$429$	7.59847	0.366858
$430$	−6.56126	−0.316412
$431$	−18.2363	−0.878412	−0.439206	−	0.898386i	$-0.644740\pi$
$431$	−18.2363	−0.878412	−0.439206	+	0.898386i	$0.644740\pi$
$432$	0.472365	0.0227267
$433$	−9.39814	−0.451646	−0.225823	−	0.974168i	$-0.572507\pi$
$433$	−9.39814	−0.451646	−0.225823	+	0.974168i	$0.572507\pi$
$434$	17.8956	0.859017
$435$	5.14038	0.246463
$436$	−49.9825	−2.39373
$437$	−2.72904	−0.130548
$438$	−17.0047	−0.812515
$439$	0.138606	0.00661530	0.00330765	−	0.999995i	$-0.498947\pi$
$439$	0.138606	0.00661530	0.00330765	+	0.999995i	$0.498947\pi$
$440$	−7.97600	−0.380241
$441$	0.00633058	0.000301456 0
$442$	10.0058	0.475928
$443$	−34.9960	−1.66271	−0.831356	−	0.555741i	$-0.812435\pi$
$443$	−34.9960	−1.66271	−0.831356	+	0.555741i	$0.812435\pi$
$444$	9.41964	0.447037
$445$	−18.8248	−0.892383
$446$	26.1225	1.23694
$447$	−3.43289	−0.162370
$448$	−36.2517	−1.71273
$449$	−25.0367	−1.18155	−0.590776	−	0.806835i	$-0.701179\pi$
$449$	−25.0367	−1.18155	−0.590776	+	0.806835i	$0.701179\pi$
$450$	−0.0581915	−0.00274317
$451$	−2.09395	−0.0986003
$452$	31.1503	1.46519
$453$	33.6138	1.57931
$454$	46.6698	2.19032
$455$	35.1736	1.64896
$456$	22.5835	1.05757
$457$	28.8234	1.34830	0.674151	−	0.738594i	$-0.264510\pi$
$457$	28.8234	1.34830	0.674151	+	0.738594i	$0.264510\pi$
$458$	24.1243	1.12725
$459$	−5.18935	−0.242218
$460$	−5.37520	−0.250620
$461$	−18.0951	−0.842775	−0.421387	−	0.906881i	$-0.638457\pi$
$461$	−18.0951	−0.842775	−0.421387	+	0.906881i	$0.638457\pi$
$462$	11.0678	0.514922
$463$	7.63551	0.354852	0.177426	−	0.984134i	$-0.443223\pi$
$463$	7.63551	0.354852	0.177426	+	0.984134i	$0.443223\pi$
$464$	0.0939075	0.00435955
$465$	13.9724	0.647955
$466$	−25.3213	−1.17299
$467$	23.7762	1.10023	0.550115	−	0.835089i	$-0.314584\pi$
$467$	23.7762	1.10023	0.550115	+	0.835089i	$0.314584\pi$
$468$	−0.110317	−0.00509942
$469$	3.27454	0.151204
$470$	53.9175	2.48703
$471$	−32.2373	−1.48542
$472$	37.2306	1.71368
$473$	1.00000	0.0459800
$474$	26.2859	1.20735
$475$	−15.2630	−0.700316
$476$	8.98561	0.411855
$477$	0.0410444	0.00187929
$478$	16.0411	0.733702
$479$	7.99083	0.365110	0.182555	−	0.983196i	$-0.441563\pi$
$479$	7.99083	0.365110	0.182555	+	0.983196i	$0.441563\pi$
$480$	−28.7015	−1.31004
$481$	−7.40018	−0.337419
$482$	−17.1775	−0.782414
$483$	2.81972	0.128302
$484$	3.21562	0.146165
$485$	−10.9162	−0.495680
$486$	0.185842	0.00842995
$487$	29.5763	1.34023	0.670116	−	0.742257i	$-0.266244\pi$
$487$	29.5763	1.34023	0.670116	+	0.742257i	$0.266244\pi$
$488$	37.7713	1.70983
$489$	5.19731	0.235031
$490$	5.30458	0.239636
$491$	31.3014	1.41261	0.706306	−	0.707907i	$-0.250360\pi$
$491$	31.3014	1.41261	0.706306	+	0.707907i	$0.250360\pi$
$492$	11.6777	0.526472
$493$	−1.03166	−0.0464634
$494$	−46.9317	−2.11156
$495$	0.0224964	0.00101114
$496$	0.255256	0.0114613
$497$	−2.57826	−0.115651
$498$	−1.18608	−0.0531496
$499$	11.6246	0.520390	0.260195	−	0.965556i	$-0.416213\pi$
$499$	11.6246	0.520390	0.260195	+	0.965556i	$0.416213\pi$
$500$	16.1297	0.721341
$501$	10.9996	0.491424
$502$	−32.2173	−1.43793
$503$	1.20915	0.0539132	0.0269566	−	0.999637i	$-0.491418\pi$
$503$	1.20915	0.0539132	0.0269566	+	0.999637i	$0.491418\pi$
$504$	−0.0607454	−0.00270582
$505$	−11.7462	−0.522698
$506$	1.32877	0.0590709
$507$	10.7449	0.477197
$508$	22.1202	0.981427
$509$	1.15217	0.0510692	0.0255346	−	0.999674i	$-0.491871\pi$
$509$	1.15217	0.0510692	0.0255346	+	0.999674i	$0.491871\pi$
$510$	11.3793	0.503882
$511$	11.9970	0.530715
$512$	−1.02975	−0.0455089
$513$	24.3403	1.07465
$514$	5.76344	0.254214
$515$	−36.3133	−1.60016
$516$	−5.57688	−0.245509
$517$	−8.21756	−0.361408
$518$	−10.7790	−0.473603
$519$	7.18869	0.315549
$520$	−34.9450	−1.53244
$521$	−26.0177	−1.13986	−0.569928	−	0.821695i	$-0.693029\pi$
$521$	−26.0177	−1.13986	−0.569928	+	0.821695i	$0.693029\pi$
$522$	0.0184488	0.000807481 0
$523$	27.7646	1.21406	0.607032	−	0.794678i	$-0.292360\pi$
$523$	27.7646	1.21406	0.607032	+	0.794678i	$0.292360\pi$
$524$	40.8966	1.78658
$525$	15.7702	0.688267
$526$	−43.3838	−1.89162
$527$	−2.80421	−0.122153
$528$	0.157867	0.00687029
$529$	−22.6615	−0.985281
$530$	34.3923	1.49391
$531$	−0.105010	−0.00455703
$532$	−42.1465	−1.82728
$533$	−9.17415	−0.397377
$534$	−25.9524	−1.12307
$535$	−43.4962	−1.88051
$536$	−3.25325	−0.140519
$537$	−28.2492	−1.21904
$538$	47.9575	2.06760
$539$	−0.808469	−0.0348232
$540$	47.9415	2.06307
$541$	18.1340	0.779642	0.389821	−	0.920891i	$-0.372537\pi$
$541$	18.1340	0.779642	0.389821	+	0.920891i	$0.372537\pi$
$542$	−12.7332	−0.546937
$543$	19.0193	0.816196
$544$	5.76029	0.246970
$545$	44.6568	1.91289
$546$	48.4911	2.07523
$547$	−9.39581	−0.401736	−0.200868	−	0.979618i	$-0.564376\pi$
$547$	−9.39581	−0.401736	−0.200868	+	0.979618i	$0.564376\pi$
$548$	8.90199	0.380274
$549$	−0.106535	−0.00454679
$550$	7.43156	0.316883
$551$	4.83892	0.206145
$552$	−2.80139	−0.119235
$553$	−18.5450	−0.788612
$554$	55.5675	2.36084
$555$	−8.41596	−0.357238
$556$	−9.49547	−0.402698
$557$	40.1686	1.70200	0.851000	−	0.525166i	$-0.175997\pi$
$557$	40.1686	1.70200	0.851000	+	0.525166i	$0.175997\pi$
$558$	0.0501468	0.00212288
$559$	4.38126	0.185308
$560$	0.730773	0.0308808
$561$	−1.73431	−0.0732226
$562$	21.1628	0.892699
$563$	−18.5047	−0.779882	−0.389941	−	0.920840i	$-0.627505\pi$
$563$	−18.5047	−0.779882	−0.389941	+	0.920840i	$0.627505\pi$
$564$	45.8284	1.92972
$565$	−27.8312	−1.17087
$566$	−31.2275	−1.31259
$567$	−25.2147	−1.05892
$568$	2.56150	0.107478
$569$	−20.9268	−0.877297	−0.438649	−	0.898659i	$-0.644543\pi$
$569$	−20.9268	−0.877297	−0.438649	+	0.898659i	$0.644543\pi$
$570$	−53.3737	−2.23558
$571$	6.01928	0.251899	0.125950	−	0.992037i	$-0.459802\pi$
$571$	6.01928	0.251899	0.125950	+	0.992037i	$0.459802\pi$
$572$	14.0885	0.589069
$573$	1.11344	0.0465146
$574$	−13.3630	−0.557759
$575$	1.89331	0.0789566
$576$	−0.101584	−0.00423266
$577$	20.9242	0.871085	0.435542	−	0.900168i	$-0.356557\pi$
$577$	20.9242	0.871085	0.435542	+	0.900168i	$0.356557\pi$
$578$	−2.28377	−0.0949924
$579$	−7.89990	−0.328309
$580$	9.53090	0.395749
$581$	0.836793	0.0347160
$582$	−15.0494	−0.623816
$583$	−5.24173	−0.217090
$584$	−11.9190	−0.493211
$585$	0.0985628	0.00407507
$586$	−38.7133	−1.59923
$587$	−12.6579	−0.522447	−0.261223	−	0.965278i	$-0.584126\pi$
$587$	−12.6579	−0.522447	−0.261223	+	0.965278i	$0.584126\pi$
$588$	4.50874	0.185937
$589$	13.1530	0.541960
$590$	−87.9907	−3.62252
$591$	10.5191	0.432696
$592$	−0.153748	−0.00631899
$593$	35.5467	1.45973	0.729865	−	0.683591i	$-0.239583\pi$
$593$	35.5467	1.45973	0.729865	+	0.683591i	$0.239583\pi$
$594$	−11.8513	−0.486265
$595$	−8.02818	−0.329123
$596$	−6.36499	−0.260720
$597$	27.6302	1.13083
$598$	5.82168	0.238066
$599$	30.0960	1.22969	0.614845	−	0.788648i	$-0.289219\pi$
$599$	30.0960	1.22969	0.614845	+	0.788648i	$0.289219\pi$
$600$	−15.6677	−0.639630
$601$	−36.9707	−1.50807	−0.754033	−	0.656837i	$-0.771894\pi$
$601$	−36.9707	−1.50807	−0.754033	+	0.656837i	$0.771894\pi$
$602$	6.38169	0.260098
$603$	0.00917585	0.000373670 0
$604$	62.3240	2.53593
$605$	−2.87299	−0.116804
$606$	−16.1935	−0.657817
$607$	−26.5035	−1.07574	−0.537871	−	0.843027i	$-0.680771\pi$
$607$	−26.5035	−1.07574	−0.537871	+	0.843027i	$0.680771\pi$
$608$	−27.0183	−1.09574
$609$	−4.99971	−0.202598
$610$	−89.2686	−3.61438
$611$	−36.0033	−1.45654
$612$	0.0251793	0.00101781
$613$	19.6581	0.793982	0.396991	−	0.917823i	$-0.370054\pi$
$613$	19.6581	0.793982	0.396991	+	0.917823i	$0.370054\pi$
$614$	−68.6588	−2.77085
$615$	−10.4334	−0.420717
$616$	7.75772	0.312567
$617$	24.8619	1.00090	0.500450	−	0.865765i	$-0.333168\pi$
$617$	24.8619	1.00090	0.500450	+	0.865765i	$0.333168\pi$
$618$	−50.0624	−2.01380
$619$	−45.8990	−1.84484	−0.922419	−	0.386191i	$-0.873791\pi$
$619$	−45.8990	−1.84484	−0.922419	+	0.386191i	$0.873791\pi$
$620$	25.9066	1.04043
$621$	−3.01932	−0.121161
$622$	36.3348	1.45689
$623$	18.3097	0.733561
$624$	0.691658	0.0276885
$625$	−30.6814	−1.22726
$626$	−2.82155	−0.112772
$627$	8.13468	0.324868
$628$	−59.7718	−2.38515
$629$	1.68905	0.0673469
$630$	0.143565	0.00571978
$631$	−6.33493	−0.252190	−0.126095	−	0.992018i	$-0.540244\pi$
$631$	−6.33493	−0.252190	−0.126095	+	0.992018i	$0.540244\pi$
$632$	18.4244	0.732884
$633$	29.7350	1.18186
$634$	−40.3731	−1.60342
$635$	−19.7633	−0.784282
$636$	29.2325	1.15914
$637$	−3.54212	−0.140344
$638$	−2.35607	−0.0932776
$639$	−0.00722476	−0.000285807 0
$640$	−52.0216	−2.05633
$641$	−27.9829	−1.10526	−0.552628	−	0.833428i	$-0.686375\pi$
$641$	−27.9829	−1.10526	−0.552628	+	0.833428i	$0.686375\pi$
$642$	−59.9649	−2.36663
$643$	−8.30777	−0.327627	−0.163813	−	0.986491i	$-0.552379\pi$
$643$	−8.30777	−0.327627	−0.163813	+	0.986491i	$0.552379\pi$
$644$	5.22809	0.206016
$645$	4.98265	0.196192
$646$	10.7119	0.421454
$647$	5.85254	0.230087	0.115044	−	0.993360i	$-0.463299\pi$
$647$	5.85254	0.230087	0.115044	+	0.993360i	$0.463299\pi$
$648$	25.0509	0.984091
$649$	13.4106	0.526414
$650$	32.5596	1.27709
$651$	−13.5900	−0.532635
$652$	9.63644	0.377392
$653$	−15.7391	−0.615919	−0.307959	−	0.951399i	$-0.599646\pi$
$653$	−15.7391	−0.615919	−0.307959	+	0.951399i	$0.599646\pi$
$654$	61.5649	2.40738
$655$	−36.5390	−1.42770
$656$	−0.190604	−0.00744183
$657$	0.0336177	0.00131155
$658$	−52.4420	−2.04440
$659$	2.44016	0.0950553	0.0475277	−	0.998870i	$-0.484866\pi$
$659$	2.44016	0.0950553	0.0475277	+	0.998870i	$0.484866\pi$
$660$	16.0223	0.623668
$661$	−40.3469	−1.56931	−0.784656	−	0.619931i	$-0.787161\pi$
$661$	−40.3469	−1.56931	−0.784656	+	0.619931i	$0.787161\pi$
$662$	70.3205	2.73309
$663$	−7.59847	−0.295100
$664$	−0.831354	−0.0322628
$665$	37.6557	1.46023
$666$	−0.0302048	−0.00117041
$667$	−0.600248	−0.0232417
$668$	20.3945	0.789087
$669$	−19.8376	−0.766966
$670$	7.68871	0.297041
$671$	13.6054	0.525231
$672$	27.9160	1.07688
$673$	0.440284	0.0169717	0.00848586	−	0.999964i	$-0.497299\pi$
$673$	0.440284	0.0169717	0.00848586	+	0.999964i	$0.497299\pi$
$674$	−74.0241	−2.85130
$675$	−16.8865	−0.649962
$676$	19.9223	0.766243
$677$	46.0409	1.76950	0.884748	−	0.466070i	$-0.154331\pi$
$677$	46.0409	1.76950	0.884748	+	0.466070i	$0.154331\pi$
$678$	−38.3687	−1.47354
$679$	10.6175	0.407462
$680$	7.97600	0.305866
$681$	−35.4413	−1.35811
$682$	−6.40418	−0.245229
$683$	−33.7231	−1.29038	−0.645190	−	0.764022i	$-0.723222\pi$
$683$	−33.7231	−1.29038	−0.645190	+	0.764022i	$0.723222\pi$
$684$	−0.118102	−0.00451575
$685$	−7.95346	−0.303886
$686$	39.5125	1.50859
$687$	−18.3201	−0.698956
$688$	0.0910260	0.00347033
$689$	−22.9654	−0.874912
$690$	6.62078	0.252049
$691$	44.5620	1.69522	0.847608	−	0.530622i	$-0.178042\pi$
$691$	44.5620	1.69522	0.847608	+	0.530622i	$0.178042\pi$
$692$	13.3287	0.506682
$693$	−0.0218808	−0.000831182 0
$694$	43.4446	1.64913
$695$	8.48371	0.321805
$696$	4.96721	0.188282
$697$	2.09395	0.0793140
$698$	1.49767	0.0566876
$699$	19.2292	0.727314
$700$	29.2398	1.10516
$701$	35.7817	1.35146	0.675728	−	0.737151i	$-0.263829\pi$
$701$	35.7817	1.35146	0.675728	+	0.737151i	$0.263829\pi$
$702$	−51.9237	−1.95973
$703$	−7.92240	−0.298799
$704$	12.9731	0.488943
$705$	−40.9453	−1.54209
$706$	−50.1456	−1.88726
$707$	11.4247	0.429670
$708$	−74.7896	−2.81076
$709$	11.5245	0.432810	0.216405	−	0.976304i	$-0.430567\pi$
$709$	11.5245	0.432810	0.216405	+	0.976304i	$0.430567\pi$
$710$	−6.05384	−0.227197
$711$	−0.0519664	−0.00194889
$712$	−18.1907	−0.681724
$713$	−1.63157	−0.0611029
$714$	−11.0678	−0.414203
$715$	−12.5873	−0.470739
$716$	−52.3774	−1.95744
$717$	−12.1817	−0.454933
$718$	−8.11687	−0.302919
$719$	43.3249	1.61575	0.807873	−	0.589357i	$-0.200619\pi$
$719$	43.3249	1.61575	0.807873	+	0.589357i	$0.200619\pi$
$720$	0.00204776	7.63155e−5 0
$721$	35.3195	1.31537
$722$	−6.85189	−0.255001
$723$	13.0447	0.485137
$724$	35.2641	1.31058
$725$	−3.35708	−0.124679
$726$	−3.96077	−0.146998
$727$	−23.7335	−0.880225	−0.440113	−	0.897943i	$-0.645061\pi$
$727$	−23.7335	−0.880225	−0.440113	+	0.897943i	$0.645061\pi$
$728$	33.9886	1.25970
$729$	26.9292	0.997376
$730$	28.1693	1.04259
$731$	−1.00000	−0.0369863
$732$	−75.8757	−2.80445
$733$	30.4176	1.12350	0.561750	−	0.827307i	$-0.310128\pi$
$733$	30.4176	1.12350	0.561750	+	0.827307i	$0.310128\pi$
$734$	28.5066	1.05220
$735$	−4.02832	−0.148587
$736$	3.35150	0.123538
$737$	−1.17184	−0.0431651
$738$	−0.0374454	−0.00137839
$739$	−46.3908	−1.70651	−0.853257	−	0.521491i	$-0.825376\pi$
$739$	−46.3908	−1.70651	−0.853257	+	0.521491i	$0.825376\pi$
$740$	−15.6042	−0.573622
$741$	35.6402	1.30927
$742$	−33.4511	−1.22803
$743$	−11.9256	−0.437506	−0.218753	−	0.975780i	$-0.570199\pi$
$743$	−11.9256	−0.437506	−0.218753	+	0.975780i	$0.570199\pi$
$744$	13.5017	0.494996
$745$	5.68679	0.208348
$746$	18.7140	0.685167
$747$	0.00234485	8.57935e−5 0
$748$	−3.21562	−0.117575
$749$	42.3059	1.54582
$750$	−19.8674	−0.725454
$751$	−18.3907	−0.671087	−0.335543	−	0.942025i	$-0.608920\pi$
$751$	−18.3907	−0.671087	−0.335543	+	0.942025i	$0.608920\pi$
$752$	−0.748012	−0.0272772
$753$	24.4660	0.891591
$754$	−10.3226	−0.375925
$755$	−55.6833	−2.02652
$756$	−46.6295	−1.69590
$757$	8.51674	0.309546	0.154773	−	0.987950i	$-0.450535\pi$
$757$	8.51674	0.309546	0.154773	+	0.987950i	$0.450535\pi$
$758$	−21.6001	−0.784550
$759$	−1.00907	−0.0366270
$760$	−37.4110	−1.35704
$761$	−40.7953	−1.47883	−0.739415	−	0.673250i	$-0.764898\pi$
$761$	−40.7953	−1.47883	−0.739415	+	0.673250i	$0.764898\pi$
$762$	−27.2461	−0.987023
$763$	−43.4347	−1.57244
$764$	2.06445	0.0746893
$765$	−0.0224964	−0.000813360 0
$766$	−11.5435	−0.417083
$767$	58.7556	2.12154
$768$	−26.7193	−0.964150
$769$	37.3826	1.34805	0.674025	−	0.738708i	$-0.264564\pi$
$769$	37.3826	1.34805	0.674025	+	0.738708i	$0.264564\pi$
$770$	−18.3345	−0.660731
$771$	−4.37679	−0.157626
$772$	−14.6474	−0.527171
$773$	−20.9909	−0.754992	−0.377496	−	0.926011i	$-0.623215\pi$
$773$	−20.9909	−0.754992	−0.377496	+	0.926011i	$0.623215\pi$
$774$	0.0178827	0.000642780 0
$775$	−9.12510	−0.327783
$776$	−10.5485	−0.378668
$777$	8.18564	0.293658
$778$	−72.4654	−2.59801
$779$	−9.82155	−0.351894
$780$	70.1980	2.51349
$781$	0.922665	0.0330156
$782$	−1.32877	−0.0475166
$783$	5.35362	0.191323
$784$	−0.0735917	−0.00262828
$785$	53.4030	1.90603
$786$	−50.3735	−1.79676
$787$	6.57051	0.234213	0.117107	−	0.993119i	$-0.462638\pi$
$787$	6.57051	0.234213	0.117107	+	0.993119i	$0.462638\pi$
$788$	19.5036	0.694787
$789$	32.9459	1.17291
$790$	−43.5442	−1.54923
$791$	27.0695	0.962482
$792$	0.0217386	0.000772446 0
$793$	59.6089	2.11677
$794$	21.3616	0.758094
$795$	−26.1177	−0.926300
$796$	51.2297	1.81579
$797$	8.99337	0.318561	0.159281	−	0.987233i	$-0.449083\pi$
$797$	8.99337	0.318561	0.159281	+	0.987233i	$0.449083\pi$
$798$	51.9130	1.83770
$799$	8.21756	0.290716
$800$	18.7444	0.662714
$801$	0.0513070	0.00181284
$802$	−47.2427	−1.66820
$803$	−4.29327	−0.151506
$804$	6.53519	0.230478
$805$	−4.67103	−0.164632
$806$	−28.0584	−0.988316
$807$	−36.4192	−1.28202
$808$	−11.3504	−0.399307
$809$	10.0212	0.352328	0.176164	−	0.984361i	$-0.443631\pi$
$809$	10.0212	0.352328	0.176164	+	0.984361i	$0.443631\pi$
$810$	−59.2050	−2.08025
$811$	42.8069	1.50315	0.751577	−	0.659646i	$-0.229294\pi$
$811$	42.8069	1.50315	0.751577	+	0.659646i	$0.229294\pi$
$812$	−9.27006	−0.325315
$813$	9.66965	0.339129
$814$	3.85741	0.135202
$815$	−8.60966	−0.301583
$816$	−0.157867	−0.00552646
$817$	4.69044	0.164098
$818$	−69.9039	−2.44413
$819$	−0.0958654	−0.00334981
$820$	−19.3448	−0.675551
$821$	−24.3191	−0.848741	−0.424371	−	0.905489i	$-0.639505\pi$
$821$	−24.3191	−0.848741	−0.424371	+	0.905489i	$0.639505\pi$
$822$	−10.9648	−0.382442
$823$	6.68230	0.232930	0.116465	−	0.993195i	$-0.462844\pi$
$823$	6.68230	0.232930	0.116465	+	0.993195i	$0.462844\pi$
$824$	−35.0900	−1.22242
$825$	−5.64356	−0.196484
$826$	85.5826	2.97780
$827$	29.7514	1.03456	0.517279	−	0.855817i	$-0.326945\pi$
$827$	29.7514	1.03456	0.517279	+	0.855817i	$0.326945\pi$
$828$	0.0146501	0.000509126 0
$829$	−22.0187	−0.764742	−0.382371	−	0.924009i	$-0.624892\pi$
$829$	−22.0187	−0.764742	−0.382371	+	0.924009i	$0.624892\pi$
$830$	1.96482	0.0681998
$831$	−42.1983	−1.46384
$832$	56.8387	1.97053
$833$	0.808469	0.0280118
$834$	11.6958	0.404994
$835$	−18.2214	−0.630578
$836$	15.0827	0.521645
$837$	14.5520	0.502992
$838$	−9.35080	−0.323018
$839$	34.7265	1.19889	0.599447	−	0.800415i	$-0.295387\pi$
$839$	34.7265	1.19889	0.599447	+	0.800415i	$0.295387\pi$
$840$	38.6540	1.33369
$841$	−27.9357	−0.963300
$842$	52.3790	1.80510
$843$	−16.0711	−0.553519
$844$	55.1324	1.89773
$845$	−17.7995	−0.612323
$846$	−0.146952	−0.00505232
$847$	2.79436	0.0960155
$848$	−0.477133	−0.0163848
$849$	23.7144	0.813875
$850$	−7.43156	−0.254900
$851$	0.982740	0.0336879
$852$	−5.14559	−0.176285
$853$	50.6296	1.73352	0.866762	−	0.498722i	$-0.166197\pi$
$853$	50.6296	1.73352	0.866762	+	0.498722i	$0.166197\pi$
$854$	86.8255	2.97111
$855$	0.105518	0.00360865
$856$	−42.0309	−1.43659
$857$	0.788044	0.0269191	0.0134595	−	0.999909i	$-0.495716\pi$
$857$	0.788044	0.0269191	0.0134595	+	0.999909i	$0.495716\pi$
$858$	−17.3532	−0.592428
$859$	−45.5952	−1.55569	−0.777843	−	0.628458i	$-0.783686\pi$
$859$	−45.5952	−1.55569	−0.777843	+	0.628458i	$0.783686\pi$
$860$	9.23844	0.315028
$861$	10.1479	0.345839
$862$	41.6476	1.41852
$863$	53.4443	1.81926	0.909632	−	0.415415i	$-0.136364\pi$
$863$	53.4443	1.81926	0.909632	+	0.415415i	$0.136364\pi$
$864$	−29.8921	−1.01695
$865$	−11.9085	−0.404901
$866$	21.4632	0.729350
$867$	1.73431	0.0589002
$868$	−25.1976	−0.855261
$869$	6.63656	0.225130
$870$	−11.7395	−0.398005
$871$	−5.13412	−0.173963
$872$	43.1524	1.46132
$873$	0.0297521	0.00100696
$874$	6.23250	0.210818
$875$	14.0166	0.473849
$876$	23.9431	0.808962
$877$	47.4945	1.60378	0.801888	−	0.597474i	$-0.203829\pi$
$877$	47.4945	1.60378	0.801888	+	0.597474i	$0.203829\pi$
$878$	−0.316544	−0.0106829
$879$	29.3991	0.991607
$880$	−0.261517	−0.00881572
$881$	6.86714	0.231360	0.115680	−	0.993287i	$-0.463095\pi$
$881$	6.86714	0.231360	0.115680	+	0.993287i	$0.463095\pi$
$882$	−0.0144576	−0.000486813 0
$883$	36.8660	1.24064	0.620319	−	0.784349i	$-0.287003\pi$
$883$	36.8660	1.24064	0.620319	+	0.784349i	$0.287003\pi$
$884$	−14.0885	−0.473847
$885$	66.8206	2.24615
$886$	79.9230	2.68506
$887$	−15.0633	−0.505776	−0.252888	−	0.967496i	$-0.581380\pi$
$887$	−15.0633	−0.505776	−0.252888	+	0.967496i	$0.581380\pi$
$888$	−8.13244	−0.272907
$889$	19.2224	0.644699
$890$	42.9917	1.44108
$891$	9.02343	0.302296
$892$	−36.7813	−1.23153
$893$	−38.5440	−1.28983
$894$	7.83994	0.262207
$895$	46.7965	1.56423
$896$	50.5979	1.69036
$897$	−4.42101	−0.147613
$898$	57.1781	1.90806
$899$	2.89298	0.0964864
$900$	0.0819353	0.00273118
$901$	5.24173	0.174627
$902$	4.78211	0.159227
$903$	−4.84629	−0.161275
$904$	−26.8936	−0.894468
$905$	−31.5066	−1.04732
$906$	−76.7662	−2.55039
$907$	9.29239	0.308549	0.154274	−	0.988028i	$-0.450696\pi$
$907$	9.29239	0.308549	0.154274	+	0.988028i	$0.450696\pi$
$908$	−65.7125	−2.18075
$909$	0.0320141	0.00106184
$910$	−80.3285	−2.66286
$911$	1.94664	0.0644949	0.0322474	−	0.999480i	$-0.489734\pi$
$911$	1.94664	0.0644949	0.0322474	+	0.999480i	$0.489734\pi$
$912$	0.740467	0.0245193
$913$	−0.299457	−0.00991060
$914$	−65.8261	−2.17733
$915$	67.7910	2.24110
$916$	−33.9677	−1.12232
$917$	35.5390	1.17360
$918$	11.8513	0.391151
$919$	−7.27125	−0.239856	−0.119928	−	0.992783i	$-0.538266\pi$
$919$	−7.27125	−0.239856	−0.119928	+	0.992783i	$0.538266\pi$
$920$	4.64067	0.152998
$921$	52.1399	1.71807
$922$	41.3252	1.36097
$923$	4.04244	0.133059
$924$	−15.5838	−0.512671
$925$	5.49629	0.180717
$926$	−17.4378	−0.573041
$927$	0.0989718	0.00325066
$928$	−5.94263	−0.195076
$929$	45.2231	1.48372	0.741861	−	0.670554i	$-0.233943\pi$
$929$	45.2231	1.48372	0.741861	+	0.670554i	$0.233943\pi$
$930$	−31.9098	−1.04636
$931$	−3.79208	−0.124280
$932$	35.6532	1.16786
$933$	−27.5928	−0.903348
$934$	−54.2994	−1.77673
$935$	2.87299	0.0939568
$936$	0.0952423	0.00311309
$937$	6.17005	0.201567	0.100783	−	0.994908i	$-0.467865\pi$
$937$	6.17005	0.201567	0.100783	+	0.994908i	$0.467865\pi$
$938$	−7.47830	−0.244175
$939$	2.14270	0.0699245
$940$	−75.9175	−2.47616
$941$	−13.8366	−0.451060	−0.225530	−	0.974236i	$-0.572411\pi$
$941$	−13.8366	−0.451060	−0.225530	+	0.974236i	$0.572411\pi$
$942$	73.6226	2.39875
$943$	1.21832	0.0396740
$944$	1.22072	0.0397309
$945$	41.6610	1.35523
$946$	−2.28377	−0.0742519
$947$	−41.3518	−1.34375	−0.671877	−	0.740663i	$-0.734512\pi$
$947$	−41.3518	−1.34375	−0.671877	+	0.740663i	$0.734512\pi$
$948$	−37.0113	−1.20207
$949$	−18.8100	−0.610597
$950$	34.8573	1.13092
$951$	30.6596	0.994205
$952$	−7.75772	−0.251429
$953$	7.95711	0.257756	0.128878	−	0.991660i	$-0.458862\pi$
$953$	7.95711	0.257756	0.128878	+	0.991660i	$0.458862\pi$
$954$	−0.0937361	−0.00303482
$955$	−1.84448	−0.0596860
$956$	−22.5863	−0.730493
$957$	1.78921	0.0578370
$958$	−18.2492	−0.589606
$959$	7.73580	0.249802
$960$	64.6406	2.08627
$961$	−23.1364	−0.746335
$962$	16.9003	0.544889
$963$	0.118549	0.00382018
$964$	24.1864	0.778993
$965$	13.0867	0.421275
$966$	−6.43959	−0.207190
$967$	17.5074	0.562999	0.281499	−	0.959561i	$-0.409168\pi$
$967$	17.5074	0.562999	0.281499	+	0.959561i	$0.409168\pi$
$968$	−2.77620	−0.0892305
$969$	−8.13468	−0.261324
$970$	24.9302	0.800460
$971$	14.1319	0.453513	0.226757	−	0.973951i	$-0.427188\pi$
$971$	14.1319	0.453513	0.226757	+	0.973951i	$0.427188\pi$
$972$	−0.261671	−0.00839309
$973$	−8.25153	−0.264532
$974$	−67.5456	−2.16430
$975$	−24.7259	−0.791864
$976$	1.23845	0.0396417
$977$	16.3254	0.522295	0.261148	−	0.965299i	$-0.415899\pi$
$977$	16.3254	0.522295	0.261148	+	0.965299i	$0.415899\pi$
$978$	−11.8695	−0.379544
$979$	−6.55235	−0.209414
$980$	−7.46900	−0.238588
$981$	−0.121712	−0.00388596
$982$	−71.4853	−2.28119
$983$	24.5511	0.783058	0.391529	−	0.920166i	$-0.371946\pi$
$983$	24.5511	0.783058	0.391529	+	0.920166i	$0.371946\pi$
$984$	−10.0819	−0.321400
$985$	−17.4255	−0.555221
$986$	2.35607	0.0750325
$987$	39.8247	1.26763
$988$	66.0812	2.10232
$989$	−0.581829	−0.0185011
$990$	−0.0513768	−0.00163286
$991$	5.64683	0.179378	0.0896888	−	0.995970i	$-0.471413\pi$
$991$	5.64683	0.179378	0.0896888	+	0.995970i	$0.471413\pi$
$992$	−16.1531	−0.512860
$993$	−53.4018	−1.69465
$994$	5.88817	0.186761
$995$	−45.7711	−1.45104
$996$	1.67004	0.0529172
$997$	49.1883	1.55781	0.778905	−	0.627142i	$-0.215775\pi$
$997$	49.1883	1.55781	0.778905	+	0.627142i	$0.215775\pi$
$998$	−26.5480	−0.840363
$999$	−8.76508	−0.277315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.5	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.5	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28377 q^{2} +1.73431 q^{3} +3.21562 q^{4} -2.87299 q^{5} -3.96077 q^{6} +2.79436 q^{7} -2.77620 q^{8} +0.00783032 q^{9} +O(q^{10})\)	\(q-2.28377 q^{2} +1.73431 q^{3} +3.21562 q^{4} -2.87299 q^{5} -3.96077 q^{6} +2.79436 q^{7} -2.77620 q^{8} +0.00783032 q^{9} +6.56126 q^{10} -1.00000 q^{11} +5.57688 q^{12} -4.38126 q^{13} -6.38169 q^{14} -4.98265 q^{15} -0.0910260 q^{16} +1.00000 q^{17} -0.0178827 q^{18} -4.69044 q^{19} -9.23844 q^{20} +4.84629 q^{21} +2.28377 q^{22} +0.581829 q^{23} -4.81479 q^{24} +3.25407 q^{25} +10.0058 q^{26} -5.18935 q^{27} +8.98561 q^{28} -1.03166 q^{29} +11.3793 q^{30} -2.80421 q^{31} +5.76029 q^{32} -1.73431 q^{33} -2.28377 q^{34} -8.02818 q^{35} +0.0251793 q^{36} +1.68905 q^{37} +10.7119 q^{38} -7.59847 q^{39} +7.97600 q^{40} +2.09395 q^{41} -11.0678 q^{42} -1.00000 q^{43} -3.21562 q^{44} -0.0224964 q^{45} -1.32877 q^{46} +8.21756 q^{47} -0.157867 q^{48} +0.808469 q^{49} -7.43156 q^{50} +1.73431 q^{51} -14.0885 q^{52} +5.24173 q^{53} +11.8513 q^{54} +2.87299 q^{55} -7.75772 q^{56} -8.13468 q^{57} +2.35607 q^{58} -13.4106 q^{59} -16.0223 q^{60} -13.6054 q^{61} +6.40418 q^{62} +0.0218808 q^{63} -12.9731 q^{64} +12.5873 q^{65} +3.96077 q^{66} +1.17184 q^{67} +3.21562 q^{68} +1.00907 q^{69} +18.3345 q^{70} -0.922665 q^{71} -0.0217386 q^{72} +4.29327 q^{73} -3.85741 q^{74} +5.64356 q^{75} -15.0827 q^{76} -2.79436 q^{77} +17.3532 q^{78} -6.63656 q^{79} +0.261517 q^{80} -9.02343 q^{81} -4.78211 q^{82} +0.299457 q^{83} +15.5838 q^{84} -2.87299 q^{85} +2.28377 q^{86} -1.78921 q^{87} +2.77620 q^{88} +6.55235 q^{89} +0.0513768 q^{90} -12.2428 q^{91} +1.87094 q^{92} -4.86337 q^{93} -18.7670 q^{94} +13.4756 q^{95} +9.99012 q^{96} +3.79961 q^{97} -1.84636 q^{98} -0.00783032 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9} + 7 q^{10} - 66 q^{11} + 12 q^{12} + 12 q^{13} + 13 q^{14} + 35 q^{15} + 58 q^{16} + 66 q^{17} + 37 q^{18} + 24 q^{19} + 17 q^{20} + 16 q^{21} - 12 q^{22} + 25 q^{23} + 22 q^{24} + 56 q^{25} + 36 q^{26} + 17 q^{28} + 29 q^{29} + 28 q^{30} + 37 q^{31} + 62 q^{32} + 12 q^{34} + 40 q^{35} + 107 q^{36} - 34 q^{37} + 22 q^{38} + 61 q^{39} + 37 q^{40} + 41 q^{41} + 19 q^{42} - 66 q^{43} - 66 q^{44} + 10 q^{45} + 43 q^{46} + 61 q^{47} + 29 q^{48} + 33 q^{49} + 59 q^{50} + 51 q^{52} - 35 q^{53} - 37 q^{54} - 6 q^{55} + 37 q^{56} - 7 q^{57} + 17 q^{58} + 48 q^{59} - 56 q^{60} + q^{61} + 37 q^{62} + 43 q^{63} + 68 q^{64} + 41 q^{65} - 7 q^{66} + 10 q^{67} + 66 q^{68} + 18 q^{69} + 77 q^{70} + 84 q^{71} + 83 q^{72} + 5 q^{73} + 36 q^{74} + 14 q^{75} + 14 q^{76} - 13 q^{77} + 41 q^{78} + 58 q^{79} + 25 q^{80} + 78 q^{81} - 28 q^{82} + 47 q^{83} + 44 q^{84} + 6 q^{85} - 12 q^{86} + 101 q^{87} - 30 q^{88} + 53 q^{89} + q^{90} + 2 q^{91} + 34 q^{92} - 3 q^{93} + 17 q^{94} + 91 q^{95} + 27 q^{96} - 28 q^{97} + 87 q^{98} - 58 q^{99}+O(q^{100}) \) 66 * q + 12 * q^2 + 66 * q^4 + 6 * q^5 + 7 * q^6 + 13 * q^7 + 30 * q^8 + 58 * q^9 + 7 * q^10 - 66 * q^11 + 12 * q^12 + 12 * q^13 + 13 * q^14 + 35 * q^15 + 58 * q^16 + 66 * q^17 + 37 * q^18 + 24 * q^19 + 17 * q^20 + 16 * q^21 - 12 * q^22 + 25 * q^23 + 22 * q^24 + 56 * q^25 + 36 * q^26 + 17 * q^28 + 29 * q^29 + 28 * q^30 + 37 * q^31 + 62 * q^32 + 12 * q^34 + 40 * q^35 + 107 * q^36 - 34 * q^37 + 22 * q^38 + 61 * q^39 + 37 * q^40 + 41 * q^41 + 19 * q^42 - 66 * q^43 - 66 * q^44 + 10 * q^45 + 43 * q^46 + 61 * q^47 + 29 * q^48 + 33 * q^49 + 59 * q^50 + 51 * q^52 - 35 * q^53 - 37 * q^54 - 6 * q^55 + 37 * q^56 - 7 * q^57 + 17 * q^58 + 48 * q^59 - 56 * q^60 + q^61 + 37 * q^62 + 43 * q^63 + 68 * q^64 + 41 * q^65 - 7 * q^66 + 10 * q^67 + 66 * q^68 + 18 * q^69 + 77 * q^70 + 84 * q^71 + 83 * q^72 + 5 * q^73 + 36 * q^74 + 14 * q^75 + 14 * q^76 - 13 * q^77 + 41 * q^78 + 58 * q^79 + 25 * q^80 + 78 * q^81 - 28 * q^82 + 47 * q^83 + 44 * q^84 + 6 * q^85 - 12 * q^86 + 101 * q^87 - 30 * q^88 + 53 * q^89 + q^90 + 2 * q^91 + 34 * q^92 - 3 * q^93 + 17 * q^94 + 91 * q^95 + 27 * q^96 - 28 * q^97 + 87 * q^98 - 58 * q^99

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