LMFDB - Embedded newform 8043.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49955 q^{2} +1.00000 q^{3} +4.24777 q^{4} +0.613091 q^{5} -2.49955 q^{6} -1.00000 q^{7} -5.61841 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49955 q^{2} +1.00000 q^{3} +4.24777 q^{4} +0.613091 q^{5} -2.49955 q^{6} -1.00000 q^{7} -5.61841 q^{8} +1.00000 q^{9} -1.53245 q^{10} -2.20359 q^{11} +4.24777 q^{12} -6.08698 q^{13} +2.49955 q^{14} +0.613091 q^{15} +5.54798 q^{16} -4.83549 q^{17} -2.49955 q^{18} -2.02467 q^{19} +2.60427 q^{20} -1.00000 q^{21} +5.50799 q^{22} +3.36534 q^{23} -5.61841 q^{24} -4.62412 q^{25} +15.2147 q^{26} +1.00000 q^{27} -4.24777 q^{28} +2.93697 q^{29} -1.53245 q^{30} +8.74164 q^{31} -2.63065 q^{32} -2.20359 q^{33} +12.0866 q^{34} -0.613091 q^{35} +4.24777 q^{36} +1.17510 q^{37} +5.06077 q^{38} -6.08698 q^{39} -3.44459 q^{40} -3.39861 q^{41} +2.49955 q^{42} +1.86214 q^{43} -9.36034 q^{44} +0.613091 q^{45} -8.41185 q^{46} +4.86025 q^{47} +5.54798 q^{48} +1.00000 q^{49} +11.5582 q^{50} -4.83549 q^{51} -25.8561 q^{52} -0.596697 q^{53} -2.49955 q^{54} -1.35100 q^{55} +5.61841 q^{56} -2.02467 q^{57} -7.34111 q^{58} -3.43361 q^{59} +2.60427 q^{60} -9.06180 q^{61} -21.8502 q^{62} -1.00000 q^{63} -4.52051 q^{64} -3.73187 q^{65} +5.50799 q^{66} -4.26657 q^{67} -20.5400 q^{68} +3.36534 q^{69} +1.53245 q^{70} +0.0483515 q^{71} -5.61841 q^{72} +4.78042 q^{73} -2.93723 q^{74} -4.62412 q^{75} -8.60032 q^{76} +2.20359 q^{77} +15.2147 q^{78} -8.43434 q^{79} +3.40141 q^{80} +1.00000 q^{81} +8.49502 q^{82} +12.1613 q^{83} -4.24777 q^{84} -2.96459 q^{85} -4.65452 q^{86} +2.93697 q^{87} +12.3807 q^{88} -5.56821 q^{89} -1.53245 q^{90} +6.08698 q^{91} +14.2952 q^{92} +8.74164 q^{93} -12.1485 q^{94} -1.24131 q^{95} -2.63065 q^{96} +0.138665 q^{97} -2.49955 q^{98} -2.20359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9} + 18 q^{10} + 8 q^{11} + 45 q^{12} + 23 q^{13} - 7 q^{14} + 17 q^{15} + 37 q^{16} + 15 q^{17} + 7 q^{18} + 15 q^{19} + 53 q^{20} - 41 q^{21} + 13 q^{22} + 44 q^{23} + 12 q^{24} + 58 q^{25} + 9 q^{26} + 41 q^{27} - 45 q^{28} + 21 q^{29} + 18 q^{30} + 39 q^{31} + 61 q^{32} + 8 q^{33} + 9 q^{34} - 17 q^{35} + 45 q^{36} + 11 q^{37} + 44 q^{38} + 23 q^{39} + 24 q^{40} + 17 q^{41} - 7 q^{42} + 7 q^{43} + 30 q^{44} + 17 q^{45} - 12 q^{46} + 36 q^{47} + 37 q^{48} + 41 q^{49} + 28 q^{50} + 15 q^{51} + 58 q^{52} + 26 q^{53} + 7 q^{54} + 32 q^{55} - 12 q^{56} + 15 q^{57} - 4 q^{58} + 33 q^{59} + 53 q^{60} + 59 q^{61} - q^{62} - 41 q^{63} + 16 q^{64} + 72 q^{65} + 13 q^{66} + 12 q^{67} + 52 q^{68} + 44 q^{69} - 18 q^{70} + 33 q^{71} + 12 q^{72} + 18 q^{73} + 42 q^{74} + 58 q^{75} + 7 q^{76} - 8 q^{77} + 9 q^{78} + 22 q^{79} + 69 q^{80} + 41 q^{81} + 41 q^{82} + 32 q^{83} - 45 q^{84} - 44 q^{85} + 11 q^{86} + 21 q^{87} + 52 q^{88} + 63 q^{89} + 18 q^{90} - 23 q^{91} + 52 q^{92} + 39 q^{93} + 17 q^{94} + 37 q^{95} + 61 q^{96} + 8 q^{97} + 7 q^{98} + 8 q^{99}+O(q^{100}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9 + 18 * q^10 + 8 * q^11 + 45 * q^12 + 23 * q^13 - 7 * q^14 + 17 * q^15 + 37 * q^16 + 15 * q^17 + 7 * q^18 + 15 * q^19 + 53 * q^20 - 41 * q^21 + 13 * q^22 + 44 * q^23 + 12 * q^24 + 58 * q^25 + 9 * q^26 + 41 * q^27 - 45 * q^28 + 21 * q^29 + 18 * q^30 + 39 * q^31 + 61 * q^32 + 8 * q^33 + 9 * q^34 - 17 * q^35 + 45 * q^36 + 11 * q^37 + 44 * q^38 + 23 * q^39 + 24 * q^40 + 17 * q^41 - 7 * q^42 + 7 * q^43 + 30 * q^44 + 17 * q^45 - 12 * q^46 + 36 * q^47 + 37 * q^48 + 41 * q^49 + 28 * q^50 + 15 * q^51 + 58 * q^52 + 26 * q^53 + 7 * q^54 + 32 * q^55 - 12 * q^56 + 15 * q^57 - 4 * q^58 + 33 * q^59 + 53 * q^60 + 59 * q^61 - q^62 - 41 * q^63 + 16 * q^64 + 72 * q^65 + 13 * q^66 + 12 * q^67 + 52 * q^68 + 44 * q^69 - 18 * q^70 + 33 * q^71 + 12 * q^72 + 18 * q^73 + 42 * q^74 + 58 * q^75 + 7 * q^76 - 8 * q^77 + 9 * q^78 + 22 * q^79 + 69 * q^80 + 41 * q^81 + 41 * q^82 + 32 * q^83 - 45 * q^84 - 44 * q^85 + 11 * q^86 + 21 * q^87 + 52 * q^88 + 63 * q^89 + 18 * q^90 - 23 * q^91 + 52 * q^92 + 39 * q^93 + 17 * q^94 + 37 * q^95 + 61 * q^96 + 8 * q^97 + 7 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.49955	−1.76745	−0.883725	−	0.468006i	$-0.844973\pi$
$2$	−2.49955	−1.76745	−0.883725	+	0.468006i	$0.844973\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.24777	2.12388
$5$	0.613091	0.274183	0.137091	−	0.990558i	$-0.456225\pi$
$5$	0.613091	0.274183	0.137091	+	0.990558i	$0.456225\pi$
$6$	−2.49955	−1.02044
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−5.61841	−1.98641
$9$	1.00000	0.333333
$10$	−1.53245	−0.484604
$11$	−2.20359	−0.664408	−0.332204	−	0.943208i	$-0.607792\pi$
$11$	−2.20359	−0.664408	−0.332204	+	0.943208i	$0.607792\pi$
$12$	4.24777	1.22622
$13$	−6.08698	−1.68823	−0.844113	−	0.536166i	$-0.819872\pi$
$13$	−6.08698	−1.68823	−0.844113	+	0.536166i	$0.819872\pi$
$14$	2.49955	0.668034
$15$	0.613091	0.158299
$16$	5.54798	1.38699
$17$	−4.83549	−1.17278	−0.586389	−	0.810030i	$-0.699451\pi$
$17$	−4.83549	−1.17278	−0.586389	+	0.810030i	$0.699451\pi$
$18$	−2.49955	−0.589150
$19$	−2.02467	−0.464491	−0.232246	−	0.972657i	$-0.574607\pi$
$19$	−2.02467	−0.464491	−0.232246	+	0.972657i	$0.574607\pi$
$20$	2.60427	0.582331
$21$	−1.00000	−0.218218
$22$	5.50799	1.17431
$23$	3.36534	0.701722	0.350861	−	0.936428i	$-0.385889\pi$
$23$	3.36534	0.701722	0.350861	+	0.936428i	$0.385889\pi$
$24$	−5.61841	−1.14685
$25$	−4.62412	−0.924824
$26$	15.2147	2.98386
$27$	1.00000	0.192450
$28$	−4.24777	−0.802752
$29$	2.93697	0.545382	0.272691	−	0.962102i	$-0.412086\pi$
$29$	2.93697	0.545382	0.272691	+	0.962102i	$0.412086\pi$
$30$	−1.53245	−0.279786
$31$	8.74164	1.57005	0.785023	−	0.619467i	$-0.212651\pi$
$31$	8.74164	1.57005	0.785023	+	0.619467i	$0.212651\pi$
$32$	−2.63065	−0.465037
$33$	−2.20359	−0.383596
$34$	12.0866	2.07283
$35$	−0.613091	−0.103631
$36$	4.24777	0.707961
$37$	1.17510	0.193186	0.0965929	−	0.995324i	$-0.469205\pi$
$37$	1.17510	0.193186	0.0965929	+	0.995324i	$0.469205\pi$
$38$	5.06077	0.820965
$39$	−6.08698	−0.974697
$40$	−3.44459	−0.544638
$41$	−3.39861	−0.530774	−0.265387	−	0.964142i	$-0.585500\pi$
$41$	−3.39861	−0.530774	−0.265387	+	0.964142i	$0.585500\pi$
$42$	2.49955	0.385689
$43$	1.86214	0.283974	0.141987	−	0.989869i	$-0.454651\pi$
$43$	1.86214	0.283974	0.141987	+	0.989869i	$0.454651\pi$
$44$	−9.36034	−1.41112
$45$	0.613091	0.0913942
$46$	−8.41185	−1.24026
$47$	4.86025	0.708941	0.354470	−	0.935067i	$-0.384661\pi$
$47$	4.86025	0.708941	0.354470	+	0.935067i	$0.384661\pi$
$48$	5.54798	0.800782
$49$	1.00000	0.142857
$50$	11.5582	1.63458
$51$	−4.83549	−0.677103
$52$	−25.8561	−3.58559
$53$	−0.596697	−0.0819626	−0.0409813	−	0.999160i	$-0.513048\pi$
$53$	−0.596697	−0.0819626	−0.0409813	+	0.999160i	$0.513048\pi$
$54$	−2.49955	−0.340146
$55$	−1.35100	−0.182169
$56$	5.61841	0.750791
$57$	−2.02467	−0.268174
$58$	−7.34111	−0.963935
$59$	−3.43361	−0.447017	−0.223509	−	0.974702i	$-0.571751\pi$
$59$	−3.43361	−0.447017	−0.223509	+	0.974702i	$0.571751\pi$
$60$	2.60427	0.336209
$61$	−9.06180	−1.16024	−0.580122	−	0.814529i	$-0.696995\pi$
$61$	−9.06180	−1.16024	−0.580122	+	0.814529i	$0.696995\pi$
$62$	−21.8502	−2.77498
$63$	−1.00000	−0.125988
$64$	−4.52051	−0.565064
$65$	−3.73187	−0.462882
$66$	5.50799	0.677987
$67$	−4.26657	−0.521245	−0.260622	−	0.965441i	$-0.583928\pi$
$67$	−4.26657	−0.521245	−0.260622	+	0.965441i	$0.583928\pi$
$68$	−20.5400	−2.49084
$69$	3.36534	0.405140
$70$	1.53245	0.183163
$71$	0.0483515	0.00573827	0.00286913	−	0.999996i	$-0.499087\pi$
$71$	0.0483515	0.00573827	0.00286913	+	0.999996i	$0.499087\pi$
$72$	−5.61841	−0.662136
$73$	4.78042	0.559506	0.279753	−	0.960072i	$-0.409747\pi$
$73$	4.78042	0.559506	0.279753	+	0.960072i	$0.409747\pi$
$74$	−2.93723	−0.341447
$75$	−4.62412	−0.533947
$76$	−8.60032	−0.986524
$77$	2.20359	0.251122
$78$	15.2147	1.72273
$79$	−8.43434	−0.948937	−0.474469	−	0.880272i	$-0.657360\pi$
$79$	−8.43434	−0.948937	−0.474469	+	0.880272i	$0.657360\pi$
$80$	3.40141	0.380290
$81$	1.00000	0.111111
$82$	8.49502	0.938118
$83$	12.1613	1.33488	0.667438	−	0.744665i	$-0.267391\pi$
$83$	12.1613	1.33488	0.667438	+	0.744665i	$0.267391\pi$
$84$	−4.24777	−0.463469
$85$	−2.96459	−0.321555
$86$	−4.65452	−0.501910
$87$	2.93697	0.314876
$88$	12.3807	1.31978
$89$	−5.56821	−0.590229	−0.295114	−	0.955462i	$-0.595358\pi$
$89$	−5.56821	−0.590229	−0.295114	+	0.955462i	$0.595358\pi$
$90$	−1.53245	−0.161535
$91$	6.08698	0.638089
$92$	14.2952	1.49038
$93$	8.74164	0.906466
$94$	−12.1485	−1.25302
$95$	−1.24131	−0.127355
$96$	−2.63065	−0.268489
$97$	0.138665	0.0140793	0.00703965	−	0.999975i	$-0.497759\pi$
$97$	0.138665	0.0140793	0.00703965	+	0.999975i	$0.497759\pi$
$98$	−2.49955	−0.252493
$99$	−2.20359	−0.221469
$100$	−19.6422	−1.96422
$101$	−2.95992	−0.294523	−0.147262	−	0.989098i	$-0.547046\pi$
$101$	−2.95992	−0.294523	−0.147262	+	0.989098i	$0.547046\pi$
$102$	12.0866	1.19675
$103$	−4.58781	−0.452050	−0.226025	−	0.974121i	$-0.572573\pi$
$103$	−4.58781	−0.452050	−0.226025	+	0.974121i	$0.572573\pi$
$104$	34.1992	3.35350
$105$	−0.613091	−0.0598315
$106$	1.49148	0.144865
$107$	5.03568	0.486818	0.243409	−	0.969924i	$-0.421734\pi$
$107$	5.03568	0.486818	0.243409	+	0.969924i	$0.421734\pi$
$108$	4.24777	0.408741
$109$	−5.46094	−0.523063	−0.261531	−	0.965195i	$-0.584227\pi$
$109$	−5.46094	−0.523063	−0.261531	+	0.965195i	$0.584227\pi$
$110$	3.37690	0.321975
$111$	1.17510	0.111536
$112$	−5.54798	−0.524235
$113$	7.60379	0.715304	0.357652	−	0.933855i	$-0.383577\pi$
$113$	7.60379	0.715304	0.357652	+	0.933855i	$0.383577\pi$
$114$	5.06077	0.473984
$115$	2.06326	0.192400
$116$	12.4756	1.15833
$117$	−6.08698	−0.562742
$118$	8.58248	0.790081
$119$	4.83549	0.443268
$120$	−3.44459	−0.314447
$121$	−6.14419	−0.558562
$122$	22.6504	2.05067
$123$	−3.39861	−0.306443
$124$	37.1324	3.33459
$125$	−5.90046	−0.527753
$126$	2.49955	0.222678
$127$	−11.1824	−0.992275	−0.496137	−	0.868244i	$-0.665249\pi$
$127$	−11.1824	−0.992275	−0.496137	+	0.868244i	$0.665249\pi$
$128$	16.5606	1.46376
$129$	1.86214	0.163952
$130$	9.32802	0.818121
$131$	−12.9842	−1.13444	−0.567218	−	0.823568i	$-0.691980\pi$
$131$	−12.9842	−1.13444	−0.567218	+	0.823568i	$0.691980\pi$
$132$	−9.36034	−0.814713
$133$	2.02467	0.175561
$134$	10.6645	0.921274
$135$	0.613091	0.0527665
$136$	27.1677	2.32961
$137$	9.08018	0.775772	0.387886	−	0.921707i	$-0.373205\pi$
$137$	9.08018	0.775772	0.387886	+	0.921707i	$0.373205\pi$
$138$	−8.41185	−0.716064
$139$	−10.7228	−0.909500	−0.454750	−	0.890619i	$-0.650271\pi$
$139$	−10.7228	−0.909500	−0.454750	+	0.890619i	$0.650271\pi$
$140$	−2.60427	−0.220101
$141$	4.86025	0.409307
$142$	−0.120857	−0.0101421
$143$	13.4132	1.12167
$144$	5.54798	0.462331
$145$	1.80063	0.149534
$146$	−11.9489	−0.988899
$147$	1.00000	0.0824786
$148$	4.99157	0.410304
$149$	−1.81787	−0.148925	−0.0744627	−	0.997224i	$-0.523724\pi$
$149$	−1.81787	−0.148925	−0.0744627	+	0.997224i	$0.523724\pi$
$150$	11.5582	0.943726
$151$	−13.6364	−1.10971	−0.554855	−	0.831947i	$-0.687226\pi$
$151$	−13.6364	−1.10971	−0.554855	+	0.831947i	$0.687226\pi$
$152$	11.3754	0.922668
$153$	−4.83549	−0.390926
$154$	−5.50799	−0.443847
$155$	5.35942	0.430479
$156$	−25.8561	−2.07014
$157$	0.553736	0.0441929	0.0220965	−	0.999756i	$-0.492966\pi$
$157$	0.553736	0.0441929	0.0220965	+	0.999756i	$0.492966\pi$
$158$	21.0821	1.67720
$159$	−0.596697	−0.0473211
$160$	−1.61283	−0.127505
$161$	−3.36534	−0.265226
$162$	−2.49955	−0.196383
$163$	14.8683	1.16457	0.582287	−	0.812983i	$-0.302158\pi$
$163$	14.8683	1.16457	0.582287	+	0.812983i	$0.302158\pi$
$164$	−14.4365	−1.12730
$165$	−1.35100	−0.105175
$166$	−30.3978	−2.35933
$167$	23.0991	1.78746	0.893730	−	0.448605i	$-0.148079\pi$
$167$	23.0991	1.78746	0.893730	+	0.448605i	$0.148079\pi$
$168$	5.61841	0.433470
$169$	24.0514	1.85011
$170$	7.41015	0.568333
$171$	−2.02467	−0.154830
$172$	7.90994	0.603127
$173$	4.12999	0.313997	0.156999	−	0.987599i	$-0.449818\pi$
$173$	4.12999	0.313997	0.156999	+	0.987599i	$0.449818\pi$
$174$	−7.34111	−0.556528
$175$	4.62412	0.349551
$176$	−12.2255	−0.921530
$177$	−3.43361	−0.258086
$178$	13.9180	1.04320
$179$	22.0984	1.65171	0.825854	−	0.563884i	$-0.190693\pi$
$179$	22.0984	1.65171	0.825854	+	0.563884i	$0.190693\pi$
$180$	2.60427	0.194110
$181$	−10.8343	−0.805304	−0.402652	−	0.915353i	$-0.631912\pi$
$181$	−10.8343	−0.805304	−0.402652	+	0.915353i	$0.631912\pi$
$182$	−15.2147	−1.12779
$183$	−9.06180	−0.669867
$184$	−18.9079	−1.39391
$185$	0.720445	0.0529682
$186$	−21.8502	−1.60213
$187$	10.6554	0.779202
$188$	20.6452	1.50571
$189$	−1.00000	−0.0727393
$190$	3.10271	0.225094
$191$	3.79700	0.274741	0.137371	−	0.990520i	$-0.456135\pi$
$191$	3.79700	0.274741	0.137371	+	0.990520i	$0.456135\pi$
$192$	−4.52051	−0.326240
$193$	−21.3639	−1.53781	−0.768904	−	0.639364i	$-0.779198\pi$
$193$	−21.3639	−1.53781	−0.768904	+	0.639364i	$0.779198\pi$
$194$	−0.346601	−0.0248845
$195$	−3.73187	−0.267245
$196$	4.24777	0.303412
$197$	1.98598	0.141495	0.0707477	−	0.997494i	$-0.477461\pi$
$197$	1.98598	0.141495	0.0707477	+	0.997494i	$0.477461\pi$
$198$	5.50799	0.391436
$199$	10.3843	0.736123	0.368061	−	0.929802i	$-0.380022\pi$
$199$	10.3843	0.736123	0.368061	+	0.929802i	$0.380022\pi$
$200$	25.9802	1.83708
$201$	−4.26657	−0.300941
$202$	7.39848	0.520556
$203$	−2.93697	−0.206135
$204$	−20.5400	−1.43809
$205$	−2.08366	−0.145529
$206$	11.4675	0.798977
$207$	3.36534	0.233907
$208$	−33.7705	−2.34156
$209$	4.46154	0.308611
$210$	1.53245	0.105749
$211$	15.1658	1.04406	0.522029	−	0.852928i	$-0.325175\pi$
$211$	15.1658	1.04406	0.522029	+	0.852928i	$0.325175\pi$
$212$	−2.53463	−0.174079
$213$	0.0483515	0.00331299
$214$	−12.5869	−0.860426
$215$	1.14166	0.0778607
$216$	−5.61841	−0.382284
$217$	−8.74164	−0.593421
$218$	13.6499	0.924488
$219$	4.78042	0.323031
$220$	−5.73874	−0.386905
$221$	29.4335	1.97991
$222$	−2.93723	−0.197134
$223$	6.49252	0.434771	0.217385	−	0.976086i	$-0.430247\pi$
$223$	6.49252	0.434771	0.217385	+	0.976086i	$0.430247\pi$
$224$	2.63065	0.175768
$225$	−4.62412	−0.308275
$226$	−19.0061	−1.26427
$227$	14.7063	0.976092	0.488046	−	0.872818i	$-0.337710\pi$
$227$	14.7063	0.976092	0.488046	+	0.872818i	$0.337710\pi$
$228$	−8.60032	−0.569570
$229$	−10.2142	−0.674972	−0.337486	−	0.941330i	$-0.609577\pi$
$229$	−10.2142	−0.674972	−0.337486	+	0.941330i	$0.609577\pi$
$230$	−5.15723	−0.340058
$231$	2.20359	0.144986
$232$	−16.5011	−1.08335
$233$	2.55265	0.167230	0.0836148	−	0.996498i	$-0.473353\pi$
$233$	2.55265	0.167230	0.0836148	+	0.996498i	$0.473353\pi$
$234$	15.2147	0.994619
$235$	2.97978	0.194379
$236$	−14.5851	−0.949412
$237$	−8.43434	−0.547869
$238$	−12.0866	−0.783455
$239$	−11.5507	−0.747154	−0.373577	−	0.927599i	$-0.621869\pi$
$239$	−11.5507	−0.747154	−0.373577	+	0.927599i	$0.621869\pi$
$240$	3.40141	0.219560
$241$	23.1144	1.48893	0.744465	−	0.667661i	$-0.232705\pi$
$241$	23.1144	1.48893	0.744465	+	0.667661i	$0.232705\pi$
$242$	15.3577	0.987232
$243$	1.00000	0.0641500
$244$	−38.4924	−2.46422
$245$	0.613091	0.0391689
$246$	8.49502	0.541622
$247$	12.3241	0.784166
$248$	−49.1141	−3.11875
$249$	12.1613	0.770691
$250$	14.7485	0.932778
$251$	6.88417	0.434525	0.217263	−	0.976113i	$-0.430287\pi$
$251$	6.88417	0.434525	0.217263	+	0.976113i	$0.430287\pi$
$252$	−4.24777	−0.267584
$253$	−7.41584	−0.466230
$254$	27.9509	1.75380
$255$	−2.96459	−0.185650
$256$	−32.3530	−2.02206
$257$	12.9127	0.805475	0.402737	−	0.915316i	$-0.368059\pi$
$257$	12.9127	0.805475	0.402737	+	0.915316i	$0.368059\pi$
$258$	−4.65452	−0.289778
$259$	−1.17510	−0.0730174
$260$	−15.8521	−0.983107
$261$	2.93697	0.181794
$262$	32.4547	2.00506
$263$	6.47426	0.399220	0.199610	−	0.979875i	$-0.436032\pi$
$263$	6.47426	0.399220	0.199610	+	0.979875i	$0.436032\pi$
$264$	12.3807	0.761978
$265$	−0.365829	−0.0224727
$266$	−5.06077	−0.310296
$267$	−5.56821	−0.340769
$268$	−18.1234	−1.10706
$269$	11.5336	0.703216	0.351608	−	0.936147i	$-0.385635\pi$
$269$	11.5336	0.703216	0.351608	+	0.936147i	$0.385635\pi$
$270$	−1.53245	−0.0932621
$271$	−1.91592	−0.116384	−0.0581920	−	0.998305i	$-0.518534\pi$
$271$	−1.91592	−0.116384	−0.0581920	+	0.998305i	$0.518534\pi$
$272$	−26.8272	−1.62664
$273$	6.08698	0.368401
$274$	−22.6964	−1.37114
$275$	10.1897	0.614460
$276$	14.2952	0.860469
$277$	8.53365	0.512738	0.256369	−	0.966579i	$-0.417474\pi$
$277$	8.53365	0.512738	0.256369	+	0.966579i	$0.417474\pi$
$278$	26.8023	1.60750
$279$	8.74164	0.523348
$280$	3.44459	0.205854
$281$	9.86916	0.588745	0.294372	−	0.955691i	$-0.404889\pi$
$281$	9.86916	0.588745	0.294372	+	0.955691i	$0.404889\pi$
$282$	−12.1485	−0.723430
$283$	30.6416	1.82146	0.910728	−	0.413006i	$-0.135521\pi$
$283$	30.6416	1.82146	0.910728	+	0.413006i	$0.135521\pi$
$284$	0.205386	0.0121874
$285$	−1.24131	−0.0735286
$286$	−33.5271	−1.98250
$287$	3.39861	0.200614
$288$	−2.63065	−0.155012
$289$	6.38193	0.375407
$290$	−4.50077	−0.264294
$291$	0.138665	0.00812869
$292$	20.3061	1.18833
$293$	8.95188	0.522974	0.261487	−	0.965207i	$-0.415787\pi$
$293$	8.95188	0.522974	0.261487	+	0.965207i	$0.415787\pi$
$294$	−2.49955	−0.145777
$295$	−2.10511	−0.122564
$296$	−6.60221	−0.383746
$297$	−2.20359	−0.127865
$298$	4.54385	0.263218
$299$	−20.4848	−1.18467
$300$	−19.6422	−1.13404
$301$	−1.86214	−0.107332
$302$	34.0848	1.96136
$303$	−2.95992	−0.170043
$304$	−11.2328	−0.644247
$305$	−5.55571	−0.318119
$306$	12.0866	0.690942
$307$	10.5109	0.599886	0.299943	−	0.953957i	$-0.403032\pi$
$307$	10.5109	0.599886	0.299943	+	0.953957i	$0.403032\pi$
$308$	9.36034	0.533355
$309$	−4.58781	−0.260991
$310$	−13.3962	−0.760850
$311$	20.0770	1.13846	0.569230	−	0.822178i	$-0.307241\pi$
$311$	20.0770	1.13846	0.569230	+	0.822178i	$0.307241\pi$
$312$	34.1992	1.93615
$313$	20.1457	1.13870	0.569352	−	0.822094i	$-0.307194\pi$
$313$	20.1457	1.13870	0.569352	+	0.822094i	$0.307194\pi$
$314$	−1.38409	−0.0781088
$315$	−0.613091	−0.0345438
$316$	−35.8271	−2.01543
$317$	11.3279	0.636238	0.318119	−	0.948051i	$-0.396949\pi$
$317$	11.3279	0.636238	0.318119	+	0.948051i	$0.396949\pi$
$318$	1.49148	0.0836378
$319$	−6.47188	−0.362356
$320$	−2.77148	−0.154931
$321$	5.03568	0.281064
$322$	8.41185	0.468774
$323$	9.79026	0.544745
$324$	4.24777	0.235987
$325$	28.1469	1.56131
$326$	−37.1641	−2.05833
$327$	−5.46094	−0.301990
$328$	19.0948	1.05433
$329$	−4.86025	−0.267954
$330$	3.37690	0.185892
$331$	23.8819	1.31267	0.656334	−	0.754471i	$-0.272106\pi$
$331$	23.8819	1.31267	0.656334	+	0.754471i	$0.272106\pi$
$332$	51.6583	2.83512
$333$	1.17510	0.0643953
$334$	−57.7374	−3.15925
$335$	−2.61580	−0.142916
$336$	−5.54798	−0.302667
$337$	−7.34306	−0.400002	−0.200001	−	0.979796i	$-0.564095\pi$
$337$	−7.34306	−0.400002	−0.200001	+	0.979796i	$0.564095\pi$
$338$	−60.1177	−3.26997
$339$	7.60379	0.412981
$340$	−12.5929	−0.682945
$341$	−19.2630	−1.04315
$342$	5.06077	0.273655
$343$	−1.00000	−0.0539949
$344$	−10.4623	−0.564088
$345$	2.06326	0.111082
$346$	−10.3231	−0.554975
$347$	−2.74780	−0.147510	−0.0737548	−	0.997276i	$-0.523498\pi$
$347$	−2.74780	−0.147510	−0.0737548	+	0.997276i	$0.523498\pi$
$348$	12.4756	0.668760
$349$	−19.9097	−1.06574	−0.532870	−	0.846197i	$-0.678886\pi$
$349$	−19.9097	−1.06574	−0.532870	+	0.846197i	$0.678886\pi$
$350$	−11.5582	−0.617813
$351$	−6.08698	−0.324899
$352$	5.79687	0.308974
$353$	−18.5654	−0.988135	−0.494067	−	0.869424i	$-0.664490\pi$
$353$	−18.5654	−0.988135	−0.494067	+	0.869424i	$0.664490\pi$
$354$	8.58248	0.456154
$355$	0.0296439	0.00157333
$356$	−23.6524	−1.25358
$357$	4.83549	0.255921
$358$	−55.2360	−2.91931
$359$	31.0940	1.64108	0.820539	−	0.571591i	$-0.193673\pi$
$359$	31.0940	1.64108	0.820539	+	0.571591i	$0.193673\pi$
$360$	−3.44459	−0.181546
$361$	−14.9007	−0.784248
$362$	27.0808	1.42334
$363$	−6.14419	−0.322486
$364$	25.8561	1.35523
$365$	2.93083	0.153407
$366$	22.6504	1.18396
$367$	27.9348	1.45818	0.729092	−	0.684416i	$-0.239943\pi$
$367$	27.9348	1.45818	0.729092	+	0.684416i	$0.239943\pi$
$368$	18.6708	0.973285
$369$	−3.39861	−0.176925
$370$	−1.80079	−0.0936187
$371$	0.596697	0.0309790
$372$	37.1324	1.92523
$373$	28.6014	1.48092	0.740461	−	0.672099i	$-0.234607\pi$
$373$	28.6014	1.48092	0.740461	+	0.672099i	$0.234607\pi$
$374$	−26.6338	−1.37720
$375$	−5.90046	−0.304698
$376$	−27.3069	−1.40825
$377$	−17.8773	−0.920727
$378$	2.49955	0.128563
$379$	−22.7932	−1.17081	−0.585403	−	0.810742i	$-0.699064\pi$
$379$	−22.7932	−1.17081	−0.585403	+	0.810742i	$0.699064\pi$
$380$	−5.27278	−0.270488
$381$	−11.1824	−0.572890
$382$	−9.49081	−0.485592
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	16.5606	0.845102
$385$	1.35100	0.0688534
$386$	53.4002	2.71800
$387$	1.86214	0.0946580
$388$	0.589017	0.0299028
$389$	−9.17752	−0.465319	−0.232659	−	0.972558i	$-0.574743\pi$
$389$	−9.17752	−0.465319	−0.232659	+	0.972558i	$0.574743\pi$
$390$	9.32802	0.472342
$391$	−16.2731	−0.822964
$392$	−5.61841	−0.283772
$393$	−12.9842	−0.654967
$394$	−4.96407	−0.250086
$395$	−5.17102	−0.260182
$396$	−9.36034	−0.470375
$397$	28.7208	1.44145	0.720727	−	0.693219i	$-0.243808\pi$
$397$	28.7208	1.44145	0.720727	+	0.693219i	$0.243808\pi$
$398$	−25.9561	−1.30106
$399$	2.02467	0.101360
$400$	−25.6545	−1.28273
$401$	−28.3495	−1.41571	−0.707853	−	0.706360i	$-0.750336\pi$
$401$	−28.3495	−1.41571	−0.707853	+	0.706360i	$0.750336\pi$
$402$	10.6645	0.531898
$403$	−53.2102	−2.65059
$404$	−12.5731	−0.625533
$405$	0.613091	0.0304647
$406$	7.34111	0.364333
$407$	−2.58945	−0.128354
$408$	27.1677	1.34500
$409$	−24.8223	−1.22738	−0.613692	−	0.789546i	$-0.710316\pi$
$409$	−24.8223	−1.22738	−0.613692	+	0.789546i	$0.710316\pi$
$410$	5.20822	0.257215
$411$	9.08018	0.447892
$412$	−19.4879	−0.960102
$413$	3.43361	0.168957
$414$	−8.41185	−0.413420
$415$	7.45598	0.366000
$416$	16.0127	0.785088
$417$	−10.7228	−0.525100
$418$	−11.1519	−0.545456
$419$	11.6107	0.567220	0.283610	−	0.958940i	$-0.408468\pi$
$419$	11.6107	0.567220	0.283610	+	0.958940i	$0.408468\pi$
$420$	−2.60427	−0.127075
$421$	−33.1025	−1.61332	−0.806659	−	0.591017i	$-0.798727\pi$
$421$	−33.1025	−1.61332	−0.806659	+	0.591017i	$0.798727\pi$
$422$	−37.9078	−1.84532
$423$	4.86025	0.236314
$424$	3.35249	0.162811
$425$	22.3599	1.08461
$426$	−0.120857	−0.00585555
$427$	9.06180	0.438531
$428$	21.3904	1.03394
$429$	13.4132	0.647596
$430$	−2.85365	−0.137615
$431$	−14.1693	−0.682512	−0.341256	−	0.939970i	$-0.610852\pi$
$431$	−14.1693	−0.682512	−0.341256	+	0.939970i	$0.610852\pi$
$432$	5.54798	0.266927
$433$	8.08874	0.388720	0.194360	−	0.980930i	$-0.437737\pi$
$433$	8.08874	0.388720	0.194360	+	0.980930i	$0.437737\pi$
$434$	21.8502	1.04884
$435$	1.80063	0.0863336
$436$	−23.1968	−1.11092
$437$	−6.81371	−0.325944
$438$	−11.9489	−0.570941
$439$	35.2615	1.68294	0.841470	−	0.540304i	$-0.181691\pi$
$439$	35.2615	1.68294	0.841470	+	0.540304i	$0.181691\pi$
$440$	7.59048	0.361862
$441$	1.00000	0.0476190
$442$	−73.5707	−3.49940
$443$	−2.63761	−0.125317	−0.0626584	−	0.998035i	$-0.519958\pi$
$443$	−2.63761	−0.125317	−0.0626584	+	0.998035i	$0.519958\pi$
$444$	4.99157	0.236889
$445$	−3.41382	−0.161830
$446$	−16.2284	−0.768436
$447$	−1.81787	−0.0859821
$448$	4.52051	0.213574
$449$	−16.4904	−0.778229	−0.389115	−	0.921189i	$-0.627219\pi$
$449$	−16.4904	−0.778229	−0.389115	+	0.921189i	$0.627219\pi$
$450$	11.5582	0.544860
$451$	7.48916	0.352651
$452$	32.2991	1.51922
$453$	−13.6364	−0.640692
$454$	−36.7592	−1.72519
$455$	3.73187	0.174953
$456$	11.3754	0.532703
$457$	13.2885	0.621610	0.310805	−	0.950474i	$-0.399401\pi$
$457$	13.2885	0.621610	0.310805	+	0.950474i	$0.399401\pi$
$458$	25.5309	1.19298
$459$	−4.83549	−0.225701
$460$	8.76424	0.408635
$461$	12.3430	0.574869	0.287434	−	0.957800i	$-0.407198\pi$
$461$	12.3430	0.574869	0.287434	+	0.957800i	$0.407198\pi$
$462$	−5.50799	−0.256255
$463$	−26.5543	−1.23408	−0.617041	−	0.786931i	$-0.711669\pi$
$463$	−26.5543	−1.23408	−0.617041	+	0.786931i	$0.711669\pi$
$464$	16.2942	0.756441
$465$	5.35942	0.248537
$466$	−6.38048	−0.295570
$467$	38.7198	1.79174	0.895869	−	0.444319i	$-0.146554\pi$
$467$	38.7198	1.79174	0.895869	+	0.444319i	$0.146554\pi$
$468$	−25.8561	−1.19520
$469$	4.26657	0.197012
$470$	−7.44811	−0.343556
$471$	0.553736	0.0255148
$472$	19.2914	0.887958
$473$	−4.10340	−0.188675
$474$	21.0821	0.968332
$475$	9.36231	0.429572
$476$	20.5400	0.941450
$477$	−0.596697	−0.0273209
$478$	28.8716	1.32056
$479$	18.8960	0.863379	0.431689	−	0.902022i	$-0.357918\pi$
$479$	18.8960	0.863379	0.431689	+	0.902022i	$0.357918\pi$
$480$	−1.61283	−0.0736151
$481$	−7.15284	−0.326141
$482$	−57.7757	−2.63161
$483$	−3.36534	−0.153128
$484$	−26.0991	−1.18632
$485$	0.0850143	0.00386030
$486$	−2.49955	−0.113382
$487$	−10.5988	−0.480276	−0.240138	−	0.970739i	$-0.577193\pi$
$487$	−10.5988	−0.480276	−0.240138	+	0.970739i	$0.577193\pi$
$488$	50.9129	2.30472
$489$	14.8683	0.672367
$490$	−1.53245	−0.0692292
$491$	24.1109	1.08811	0.544055	−	0.839050i	$-0.316888\pi$
$491$	24.1109	1.08811	0.544055	+	0.839050i	$0.316888\pi$
$492$	−14.4365	−0.650848
$493$	−14.2017	−0.639611
$494$	−30.8048	−1.38597
$495$	−1.35100	−0.0607230
$496$	48.4984	2.17764
$497$	−0.0483515	−0.00216886
$498$	−30.3978	−1.36216
$499$	−11.6015	−0.519355	−0.259678	−	0.965695i	$-0.583616\pi$
$499$	−11.6015	−0.519355	−0.259678	+	0.965695i	$0.583616\pi$
$500$	−25.0638	−1.12089
$501$	23.0991	1.03199
$502$	−17.2074	−0.768002
$503$	−3.74712	−0.167076	−0.0835380	−	0.996505i	$-0.526622\pi$
$503$	−3.74712	−0.167076	−0.0835380	+	0.996505i	$0.526622\pi$
$504$	5.61841	0.250264
$505$	−1.81470	−0.0807532
$506$	18.5363	0.824038
$507$	24.0514	1.06816
$508$	−47.5001	−2.10748
$509$	−11.6113	−0.514663	−0.257331	−	0.966323i	$-0.582843\pi$
$509$	−11.6113	−0.514663	−0.257331	+	0.966323i	$0.582843\pi$
$510$	7.41015	0.328127
$511$	−4.78042	−0.211473
$512$	47.7468	2.11013
$513$	−2.02467	−0.0893913
$514$	−32.2761	−1.42364
$515$	−2.81274	−0.123944
$516$	7.90994	0.348216
$517$	−10.7100	−0.471026
$518$	2.93723	0.129055
$519$	4.12999	0.181286
$520$	20.9672	0.919472
$521$	29.0230	1.27152	0.635760	−	0.771887i	$-0.280687\pi$
$521$	29.0230	1.27152	0.635760	+	0.771887i	$0.280687\pi$
$522$	−7.34111	−0.321312
$523$	25.6157	1.12010	0.560048	−	0.828460i	$-0.310783\pi$
$523$	25.6157	1.12010	0.560048	+	0.828460i	$0.310783\pi$
$524$	−55.1539	−2.40941
$525$	4.62412	0.201813
$526$	−16.1828	−0.705602
$527$	−42.2701	−1.84131
$528$	−12.2255	−0.532045
$529$	−11.6745	−0.507586
$530$	0.914410	0.0397194
$531$	−3.43361	−0.149006
$532$	8.60032	0.372871
$533$	20.6873	0.896067
$534$	13.9180	0.602292
$535$	3.08733	0.133477
$536$	23.9713	1.03540
$537$	22.0984	0.953614
$538$	−28.8289	−1.24290
$539$	−2.20359	−0.0949154
$540$	2.60427	0.112070
$541$	−17.3153	−0.744441	−0.372221	−	0.928144i	$-0.621404\pi$
$541$	−17.3153	−0.744441	−0.372221	+	0.928144i	$0.621404\pi$
$542$	4.78895	0.205703
$543$	−10.8343	−0.464943
$544$	12.7205	0.545385
$545$	−3.34805	−0.143415
$546$	−15.2147	−0.651131
$547$	39.0733	1.67066	0.835328	−	0.549752i	$-0.185278\pi$
$547$	39.0733	1.67066	0.835328	+	0.549752i	$0.185278\pi$
$548$	38.5705	1.64765
$549$	−9.06180	−0.386748
$550$	−25.4696	−1.08603
$551$	−5.94639	−0.253325
$552$	−18.9079	−0.804772
$553$	8.43434	0.358665
$554$	−21.3303	−0.906239
$555$	0.720445	0.0305812
$556$	−45.5481	−1.93167
$557$	−2.83220	−0.120004	−0.0600020	−	0.998198i	$-0.519111\pi$
$557$	−2.83220	−0.120004	−0.0600020	+	0.998198i	$0.519111\pi$
$558$	−21.8502	−0.924993
$559$	−11.3348	−0.479412
$560$	−3.40141	−0.143736
$561$	10.6554	0.449873
$562$	−24.6685	−1.04058
$563$	−25.2870	−1.06572	−0.532859	−	0.846204i	$-0.678882\pi$
$563$	−25.2870	−1.06572	−0.532859	+	0.846204i	$0.678882\pi$
$564$	20.6452	0.869320
$565$	4.66181	0.196124
$566$	−76.5904	−3.21934
$567$	−1.00000	−0.0419961
$568$	−0.271658	−0.0113985
$569$	12.9423	0.542569	0.271285	−	0.962499i	$-0.412552\pi$
$569$	12.9423	0.542569	0.271285	+	0.962499i	$0.412552\pi$
$570$	3.10271	0.129958
$571$	11.8279	0.494983	0.247491	−	0.968890i	$-0.420394\pi$
$571$	11.8279	0.494983	0.247491	+	0.968890i	$0.420394\pi$
$572$	56.9762	2.38230
$573$	3.79700	0.158622
$574$	−8.49502	−0.354575
$575$	−15.5617	−0.648970
$576$	−4.52051	−0.188355
$577$	40.0839	1.66871	0.834357	−	0.551225i	$-0.185839\pi$
$577$	40.0839	1.66871	0.834357	+	0.551225i	$0.185839\pi$
$578$	−15.9520	−0.663514
$579$	−21.3639	−0.887854
$580$	7.64865	0.317593
$581$	−12.1613	−0.504536
$582$	−0.346601	−0.0143671
$583$	1.31488	0.0544566
$584$	−26.8584	−1.11141
$585$	−3.73187	−0.154294
$586$	−22.3757	−0.924331
$587$	−12.9594	−0.534892	−0.267446	−	0.963573i	$-0.586180\pi$
$587$	−12.9594	−0.534892	−0.267446	+	0.963573i	$0.586180\pi$
$588$	4.24777	0.175175
$589$	−17.6989	−0.729272
$590$	5.26184	0.216626
$591$	1.98598	0.0816924
$592$	6.51945	0.267948
$593$	−17.3737	−0.713451	−0.356726	−	0.934209i	$-0.616107\pi$
$593$	−17.3737	−0.713451	−0.356726	+	0.934209i	$0.616107\pi$
$594$	5.50799	0.225996
$595$	2.96459	0.121536
$596$	−7.72186	−0.316300
$597$	10.3843	0.425001
$598$	51.2028	2.09384
$599$	34.2356	1.39883	0.699414	−	0.714717i	$-0.253444\pi$
$599$	34.2356	1.39883	0.699414	+	0.714717i	$0.253444\pi$
$600$	25.9802	1.06064
$601$	−3.92753	−0.160207	−0.0801036	−	0.996787i	$-0.525525\pi$
$601$	−3.92753	−0.160207	−0.0801036	+	0.996787i	$0.525525\pi$
$602$	4.65452	0.189704
$603$	−4.26657	−0.173748
$604$	−57.9240	−2.35690
$605$	−3.76694	−0.153148
$606$	7.39848	0.300543
$607$	4.27927	0.173690	0.0868451	−	0.996222i	$-0.472321\pi$
$607$	4.27927	0.173690	0.0868451	+	0.996222i	$0.472321\pi$
$608$	5.32619	0.216006
$609$	−2.93697	−0.119012
$610$	13.8868	0.562259
$611$	−29.5843	−1.19685
$612$	−20.5400	−0.830281
$613$	33.0601	1.33528	0.667642	−	0.744482i	$-0.267304\pi$
$613$	33.0601	1.33528	0.667642	+	0.744482i	$0.267304\pi$
$614$	−26.2724	−1.06027
$615$	−2.08366	−0.0840212
$616$	−12.3807	−0.498832
$617$	1.16973	0.0470914	0.0235457	−	0.999723i	$-0.492504\pi$
$617$	1.16973	0.0470914	0.0235457	+	0.999723i	$0.492504\pi$
$618$	11.4675	0.461289
$619$	28.3915	1.14115	0.570576	−	0.821245i	$-0.306720\pi$
$619$	28.3915	1.14115	0.570576	+	0.821245i	$0.306720\pi$
$620$	22.7656	0.914287
$621$	3.36534	0.135047
$622$	−50.1835	−2.01217
$623$	5.56821	0.223086
$624$	−33.7705	−1.35190
$625$	19.5031	0.780123
$626$	−50.3553	−2.01260
$627$	4.46154	0.178177
$628$	2.35214	0.0938606
$629$	−5.68220	−0.226564
$630$	1.53245	0.0610544
$631$	−31.9723	−1.27280	−0.636399	−	0.771360i	$-0.719577\pi$
$631$	−31.9723	−1.27280	−0.636399	+	0.771360i	$0.719577\pi$
$632$	47.3876	1.88498
$633$	15.1658	0.602787
$634$	−28.3147	−1.12452
$635$	−6.85581	−0.272064
$636$	−2.53463	−0.100505
$637$	−6.08698	−0.241175
$638$	16.1768	0.640446
$639$	0.0483515	0.00191276
$640$	10.1531	0.401337
$641$	41.9668	1.65759	0.828795	−	0.559552i	$-0.189027\pi$
$641$	41.9668	1.65759	0.828795	+	0.559552i	$0.189027\pi$
$642$	−12.5869	−0.496767
$643$	−7.49337	−0.295510	−0.147755	−	0.989024i	$-0.547205\pi$
$643$	−7.49337	−0.295510	−0.147755	+	0.989024i	$0.547205\pi$
$644$	−14.2952	−0.563309
$645$	1.14166	0.0449529
$646$	−24.4713	−0.962810
$647$	−47.0238	−1.84870	−0.924348	−	0.381550i	$-0.875390\pi$
$647$	−47.0238	−1.84870	−0.924348	+	0.381550i	$0.875390\pi$
$648$	−5.61841	−0.220712
$649$	7.56626	0.297002
$650$	−70.3548	−2.75954
$651$	−8.74164	−0.342612
$652$	63.1570	2.47342
$653$	4.76086	0.186307	0.0931535	−	0.995652i	$-0.470305\pi$
$653$	4.76086	0.186307	0.0931535	+	0.995652i	$0.470305\pi$
$654$	13.6499	0.533753
$655$	−7.96050	−0.311043
$656$	−18.8554	−0.736181
$657$	4.78042	0.186502
$658$	12.1485	0.473596
$659$	−14.0224	−0.546234	−0.273117	−	0.961981i	$-0.588055\pi$
$659$	−14.0224	−0.546234	−0.273117	+	0.961981i	$0.588055\pi$
$660$	−5.73874	−0.223380
$661$	8.46620	0.329297	0.164648	−	0.986352i	$-0.447351\pi$
$661$	8.46620	0.329297	0.164648	+	0.986352i	$0.447351\pi$
$662$	−59.6940	−2.32007
$663$	29.4335	1.14310
$664$	−68.3271	−2.65161
$665$	1.24131	0.0481358
$666$	−2.93723	−0.113816
$667$	9.88391	0.382706
$668$	98.1194	3.79636
$669$	6.49252	0.251015
$670$	6.53832	0.252597
$671$	19.9685	0.770875
$672$	2.63065	0.101479
$673$	−11.5687	−0.445942	−0.222971	−	0.974825i	$-0.571576\pi$
$673$	−11.5687	−0.445942	−0.222971	+	0.974825i	$0.571576\pi$
$674$	18.3544	0.706984
$675$	−4.62412	−0.177982
$676$	102.165	3.92941
$677$	−19.5838	−0.752667	−0.376334	−	0.926484i	$-0.622815\pi$
$677$	−19.5838	−0.752667	−0.376334	+	0.926484i	$0.622815\pi$
$678$	−19.0061	−0.729924
$679$	−0.138665	−0.00532148
$680$	16.6563	0.638739
$681$	14.7063	0.563547
$682$	48.1489	1.84372
$683$	−25.9817	−0.994160	−0.497080	−	0.867705i	$-0.665595\pi$
$683$	−25.9817	−0.994160	−0.497080	+	0.867705i	$0.665595\pi$
$684$	−8.60032	−0.328841
$685$	5.56697	0.212703
$686$	2.49955	0.0954334
$687$	−10.2142	−0.389696
$688$	10.3311	0.393870
$689$	3.63208	0.138371
$690$	−5.15723	−0.196332
$691$	13.3173	0.506614	0.253307	−	0.967386i	$-0.418482\pi$
$691$	13.3173	0.506614	0.253307	+	0.967386i	$0.418482\pi$
$692$	17.5432	0.666893
$693$	2.20359	0.0837075
$694$	6.86827	0.260716
$695$	−6.57408	−0.249369
$696$	−16.5011	−0.625472
$697$	16.4340	0.622480
$698$	49.7652	1.88364
$699$	2.55265	0.0965500
$700$	19.6422	0.742404
$701$	1.88596	0.0712319	0.0356159	−	0.999366i	$-0.488661\pi$
$701$	1.88596	0.0712319	0.0356159	+	0.999366i	$0.488661\pi$
$702$	15.2147	0.574243
$703$	−2.37920	−0.0897331
$704$	9.96135	0.375433
$705$	2.97978	0.112225
$706$	46.4051	1.74648
$707$	2.95992	0.111319
$708$	−14.5851	−0.548143
$709$	3.03409	0.113948	0.0569738	−	0.998376i	$-0.481855\pi$
$709$	3.03409	0.113948	0.0569738	+	0.998376i	$0.481855\pi$
$710$	−0.0740964	−0.00278079
$711$	−8.43434	−0.316312
$712$	31.2845	1.17244
$713$	29.4186	1.10174
$714$	−12.0866	−0.452328
$715$	8.22352	0.307542
$716$	93.8686	3.50803
$717$	−11.5507	−0.431369
$718$	−77.7211	−2.90052
$719$	0.508314	0.0189569	0.00947846	−	0.999955i	$-0.496983\pi$
$719$	0.508314	0.0189569	0.00947846	+	0.999955i	$0.496983\pi$
$720$	3.40141	0.126763
$721$	4.58781	0.170859
$722$	37.2451	1.38612
$723$	23.1144	0.859634
$724$	−46.0214	−1.71037
$725$	−13.5809	−0.504382
$726$	15.3577	0.569978
$727$	14.8707	0.551523	0.275761	−	0.961226i	$-0.411070\pi$
$727$	14.8707	0.551523	0.275761	+	0.961226i	$0.411070\pi$
$728$	−34.1992	−1.26751
$729$	1.00000	0.0370370
$730$	−7.32577	−0.271139
$731$	−9.00436	−0.333038
$732$	−38.4924	−1.42272
$733$	−8.99177	−0.332118	−0.166059	−	0.986116i	$-0.553104\pi$
$733$	−8.99177	−0.332118	−0.166059	+	0.986116i	$0.553104\pi$
$734$	−69.8245	−2.57727
$735$	0.613091	0.0226142
$736$	−8.85303	−0.326327
$737$	9.40178	0.346319
$738$	8.49502	0.312706
$739$	39.3761	1.44847	0.724237	−	0.689551i	$-0.242192\pi$
$739$	39.3761	1.44847	0.724237	+	0.689551i	$0.242192\pi$
$740$	3.06028	0.112498
$741$	12.3241	0.452738
$742$	−1.49148	−0.0547538
$743$	−14.4402	−0.529758	−0.264879	−	0.964282i	$-0.585332\pi$
$743$	−14.4402	−0.529758	−0.264879	+	0.964282i	$0.585332\pi$
$744$	−49.1141	−1.80061
$745$	−1.11452	−0.0408327
$746$	−71.4906	−2.61746
$747$	12.1613	0.444959
$748$	45.2618	1.65493
$749$	−5.03568	−0.184000
$750$	14.7485	0.538539
$751$	44.9324	1.63961	0.819804	−	0.572645i	$-0.194083\pi$
$751$	44.9324	1.63961	0.819804	+	0.572645i	$0.194083\pi$
$752$	26.9646	0.983297
$753$	6.88417	0.250873
$754$	44.6852	1.62734
$755$	−8.36032	−0.304263
$756$	−4.24777	−0.154490
$757$	15.8527	0.576175	0.288088	−	0.957604i	$-0.406981\pi$
$757$	15.8527	0.576175	0.288088	+	0.957604i	$0.406981\pi$
$758$	56.9727	2.06934
$759$	−7.41584	−0.269178
$760$	6.97416	0.252980
$761$	−0.744282	−0.0269802	−0.0134901	−	0.999909i	$-0.504294\pi$
$761$	−0.744282	−0.0269802	−0.0134901	+	0.999909i	$0.504294\pi$
$762$	27.9509	1.01256
$763$	5.46094	0.197699
$764$	16.1288	0.583518
$765$	−2.96459	−0.107185
$766$	2.49955	0.0903125
$767$	20.9003	0.754666
$768$	−32.3530	−1.16744
$769$	−8.21400	−0.296204	−0.148102	−	0.988972i	$-0.547316\pi$
$769$	−8.21400	−0.296204	−0.148102	+	0.988972i	$0.547316\pi$
$770$	−3.37690	−0.121695
$771$	12.9127	0.465041
$772$	−90.7489	−3.26612
$773$	−0.861755	−0.0309952	−0.0154976	−	0.999880i	$-0.504933\pi$
$773$	−0.861755	−0.0309952	−0.0154976	+	0.999880i	$0.504933\pi$
$774$	−4.65452	−0.167303
$775$	−40.4224	−1.45202
$776$	−0.779077	−0.0279672
$777$	−1.17510	−0.0421566
$778$	22.9397	0.822428
$779$	6.88107	0.246540
$780$	−15.8521	−0.567597
$781$	−0.106547	−0.00381255
$782$	40.6754	1.45455
$783$	2.93697	0.104959
$784$	5.54798	0.198142
$785$	0.339490	0.0121169
$786$	32.4547	1.15762
$787$	−32.0073	−1.14094	−0.570468	−	0.821320i	$-0.693238\pi$
$787$	−32.0073	−1.14094	−0.570468	+	0.821320i	$0.693238\pi$
$788$	8.43599	0.300520
$789$	6.47426	0.230490
$790$	12.9252	0.459859
$791$	−7.60379	−0.270360
$792$	12.3807	0.439928
$793$	55.1590	1.95875
$794$	−71.7890	−2.54770
$795$	−0.365829	−0.0129746
$796$	44.1100	1.56344
$797$	−33.0185	−1.16958	−0.584788	−	0.811186i	$-0.698822\pi$
$797$	−33.0185	−1.16958	−0.584788	+	0.811186i	$0.698822\pi$
$798$	−5.06077	−0.179149
$799$	−23.5017	−0.831430
$800$	12.1644	0.430078
$801$	−5.56821	−0.196743
$802$	70.8610	2.50219
$803$	−10.5341	−0.371740
$804$	−18.1234	−0.639163
$805$	−2.06326	−0.0727204
$806$	133.002	4.68479
$807$	11.5336	0.406002
$808$	16.6301	0.585043
$809$	−21.5525	−0.757746	−0.378873	−	0.925449i	$-0.623688\pi$
$809$	−21.5525	−0.757746	−0.378873	+	0.925449i	$0.623688\pi$
$810$	−1.53245	−0.0538449
$811$	27.8004	0.976205	0.488103	−	0.872786i	$-0.337689\pi$
$811$	27.8004	0.976205	0.488103	+	0.872786i	$0.337689\pi$
$812$	−12.4756	−0.437806
$813$	−1.91592	−0.0671943
$814$	6.47246	0.226860
$815$	9.11561	0.319306
$816$	−26.8272	−0.939139
$817$	−3.77022	−0.131903
$818$	62.0446	2.16934
$819$	6.08698	0.212696
$820$	−8.85089	−0.309087
$821$	42.6920	1.48996	0.744981	−	0.667086i	$-0.232459\pi$
$821$	42.6920	1.48996	0.744981	+	0.667086i	$0.232459\pi$
$822$	−22.6964	−0.791627
$823$	−42.7350	−1.48965	−0.744824	−	0.667261i	$-0.767467\pi$
$823$	−42.7350	−1.48965	−0.744824	+	0.667261i	$0.767467\pi$
$824$	25.7762	0.897956
$825$	10.1897	0.354759
$826$	−8.58248	−0.298623
$827$	−39.0685	−1.35855	−0.679273	−	0.733886i	$-0.737705\pi$
$827$	−39.0685	−1.35855	−0.679273	+	0.733886i	$0.737705\pi$
$828$	14.2952	0.496792
$829$	−0.756809	−0.0262851	−0.0131425	−	0.999914i	$-0.504184\pi$
$829$	−0.756809	−0.0262851	−0.0131425	+	0.999914i	$0.504184\pi$
$830$	−18.6366	−0.646886
$831$	8.53365	0.296029
$832$	27.5163	0.953955
$833$	−4.83549	−0.167540
$834$	26.8023	0.928088
$835$	14.1618	0.490090
$836$	18.9516	0.655454
$837$	8.74164	0.302155
$838$	−29.0216	−1.00253
$839$	−23.7787	−0.820931	−0.410466	−	0.911876i	$-0.634634\pi$
$839$	−23.7787	−0.820931	−0.410466	+	0.911876i	$0.634634\pi$
$840$	3.44459	0.118850
$841$	−20.3742	−0.702559
$842$	82.7415	2.85146
$843$	9.86916	0.339912
$844$	64.4208	2.21746
$845$	14.7457	0.507267
$846$	−12.1485	−0.417673
$847$	6.14419	0.211117
$848$	−3.31046	−0.113682
$849$	30.6416	1.05162
$850$	−55.8897	−1.91700
$851$	3.95463	0.135563
$852$	0.205386	0.00703640
$853$	−35.6118	−1.21932	−0.609662	−	0.792662i	$-0.708695\pi$
$853$	−35.6118	−1.21932	−0.609662	+	0.792662i	$0.708695\pi$
$854$	−22.6504	−0.775082
$855$	−1.24131	−0.0424518
$856$	−28.2925	−0.967018
$857$	28.8851	0.986697	0.493349	−	0.869832i	$-0.335773\pi$
$857$	28.8851	0.986697	0.493349	+	0.869832i	$0.335773\pi$
$858$	−33.5271	−1.14459
$859$	49.3235	1.68290	0.841448	−	0.540338i	$-0.181704\pi$
$859$	49.3235	1.68290	0.841448	+	0.540338i	$0.181704\pi$
$860$	4.84951	0.165367
$861$	3.39861	0.115824
$862$	35.4170	1.20631
$863$	−10.0120	−0.340813	−0.170407	−	0.985374i	$-0.554508\pi$
$863$	−10.0120	−0.340813	−0.170407	+	0.985374i	$0.554508\pi$
$864$	−2.63065	−0.0894965
$865$	2.53206	0.0860926
$866$	−20.2182	−0.687043
$867$	6.38193	0.216742
$868$	−37.1324	−1.26036
$869$	18.5858	0.630481
$870$	−4.50077	−0.152590
$871$	25.9706	0.879979
$872$	30.6818	1.03902
$873$	0.138665	0.00469310
$874$	17.0312	0.576090
$875$	5.90046	0.199472
$876$	20.3061	0.686080
$877$	−11.8757	−0.401012	−0.200506	−	0.979692i	$-0.564259\pi$
$877$	−11.8757	−0.401012	−0.200506	+	0.979692i	$0.564259\pi$
$878$	−88.1380	−2.97451
$879$	8.95188	0.301939
$880$	−7.49532	−0.252667
$881$	−8.13763	−0.274164	−0.137082	−	0.990560i	$-0.543772\pi$
$881$	−8.13763	−0.274164	−0.137082	+	0.990560i	$0.543772\pi$
$882$	−2.49955	−0.0841643
$883$	−19.5707	−0.658607	−0.329303	−	0.944224i	$-0.606814\pi$
$883$	−19.5707	−0.658607	−0.329303	+	0.944224i	$0.606814\pi$
$884$	125.027	4.20510
$885$	−2.10511	−0.0707626
$886$	6.59285	0.221491
$887$	−20.6306	−0.692708	−0.346354	−	0.938104i	$-0.612580\pi$
$887$	−20.6306	−0.692708	−0.346354	+	0.938104i	$0.612580\pi$
$888$	−6.60221	−0.221556
$889$	11.1824	0.375045
$890$	8.53302	0.286027
$891$	−2.20359	−0.0738231
$892$	27.5787	0.923402
$893$	−9.84041	−0.329297
$894$	4.54385	0.151969
$895$	13.5483	0.452870
$896$	−16.5606	−0.553249
$897$	−20.4848	−0.683967
$898$	41.2186	1.37548
$899$	25.6739	0.856274
$900$	−19.6422	−0.654739
$901$	2.88532	0.0961239
$902$	−18.7195	−0.623293
$903$	−1.86214	−0.0619682
$904$	−42.7212	−1.42089
$905$	−6.64238	−0.220800
$906$	34.0848	1.13239
$907$	−9.31008	−0.309136	−0.154568	−	0.987982i	$-0.549399\pi$
$907$	−9.31008	−0.309136	−0.154568	+	0.987982i	$0.549399\pi$
$908$	62.4689	2.07310
$909$	−2.95992	−0.0981745
$910$	−9.32802	−0.309221
$911$	24.5542	0.813516	0.406758	−	0.913536i	$-0.366659\pi$
$911$	24.5542	0.813516	0.406758	+	0.913536i	$0.366659\pi$
$912$	−11.2328	−0.371956
$913$	−26.7985	−0.886902
$914$	−33.2153	−1.09866
$915$	−5.55571	−0.183666
$916$	−43.3875	−1.43356
$917$	12.9842	0.428777
$918$	12.0866	0.398916
$919$	−25.5671	−0.843381	−0.421691	−	0.906740i	$-0.638563\pi$
$919$	−25.5671	−0.843381	−0.421691	+	0.906740i	$0.638563\pi$
$920$	−11.5922	−0.382185
$921$	10.5109	0.346344
$922$	−30.8519	−1.01605
$923$	−0.294315	−0.00968749
$924$	9.36034	0.307932
$925$	−5.43382	−0.178663
$926$	66.3739	2.18118
$927$	−4.58781	−0.150683
$928$	−7.72614	−0.253623
$929$	55.3937	1.81741	0.908703	−	0.417442i	$-0.137073\pi$
$929$	55.3937	1.81741	0.908703	+	0.417442i	$0.137073\pi$
$930$	−13.3962	−0.439277
$931$	−2.02467	−0.0663559
$932$	10.8430	0.355176
$933$	20.0770	0.657291
$934$	−96.7821	−3.16681
$935$	6.53275	0.213644
$936$	34.1992	1.11783
$937$	−13.7107	−0.447909	−0.223954	−	0.974600i	$-0.571897\pi$
$937$	−13.7107	−0.447909	−0.223954	+	0.974600i	$0.571897\pi$
$938$	−10.6645	−0.348209
$939$	20.1457	0.657431
$940$	12.6574	0.412839
$941$	55.1798	1.79881	0.899405	−	0.437116i	$-0.144000\pi$
$941$	55.1798	1.79881	0.899405	+	0.437116i	$0.144000\pi$
$942$	−1.38409	−0.0450961
$943$	−11.4375	−0.372456
$944$	−19.0496	−0.620011
$945$	−0.613091	−0.0199438
$946$	10.2567	0.333473
$947$	−6.55466	−0.212998	−0.106499	−	0.994313i	$-0.533964\pi$
$947$	−6.55466	−0.212998	−0.106499	+	0.994313i	$0.533964\pi$
$948$	−35.8271	−1.16361
$949$	−29.0983	−0.944572
$950$	−23.4016	−0.759248
$951$	11.3279	0.367332
$952$	−27.1677	−0.880511
$953$	39.2543	1.27157	0.635785	−	0.771866i	$-0.280676\pi$
$953$	39.2543	1.27157	0.635785	+	0.771866i	$0.280676\pi$
$954$	1.49148	0.0482883
$955$	2.32791	0.0753293
$956$	−49.0647	−1.58687
$957$	−6.47188	−0.209206
$958$	−47.2315	−1.52598
$959$	−9.08018	−0.293214
$960$	−2.77148	−0.0894492
$961$	45.4163	1.46504
$962$	17.8789	0.576439
$963$	5.03568	0.162273
$964$	98.1846	3.16231
$965$	−13.0980	−0.421640
$966$	8.41185	0.270647
$967$	32.0126	1.02946	0.514728	−	0.857353i	$-0.327893\pi$
$967$	32.0126	1.02946	0.514728	+	0.857353i	$0.327893\pi$
$968$	34.5205	1.10953
$969$	9.79026	0.314509
$970$	−0.212498	−0.00682289
$971$	34.7609	1.11553	0.557765	−	0.829999i	$-0.311659\pi$
$971$	34.7609	1.11553	0.557765	+	0.829999i	$0.311659\pi$
$972$	4.24777	0.136247
$973$	10.7228	0.343759
$974$	26.4922	0.848865
$975$	28.1469	0.901424
$976$	−50.2747	−1.60925
$977$	−4.01148	−0.128338	−0.0641692	−	0.997939i	$-0.520440\pi$
$977$	−4.01148	−0.128338	−0.0641692	+	0.997939i	$0.520440\pi$
$978$	−37.1641	−1.18838
$979$	12.2701	0.392153
$980$	2.60427	0.0831902
$981$	−5.46094	−0.174354
$982$	−60.2665	−1.92318
$983$	48.7890	1.55613	0.778063	−	0.628186i	$-0.216202\pi$
$983$	48.7890	1.55613	0.778063	+	0.628186i	$0.216202\pi$
$984$	19.0948	0.608720
$985$	1.21759	0.0387956
$986$	35.4979	1.13048
$987$	−4.86025	−0.154704
$988$	52.3500	1.66548
$989$	6.26675	0.199271
$990$	3.37690	0.107325
$991$	12.8125	0.407002	0.203501	−	0.979075i	$-0.434768\pi$
$991$	12.8125	0.407002	0.203501	+	0.979075i	$0.434768\pi$
$992$	−22.9962	−0.730130
$993$	23.8819	0.757869
$994$	0.120857	0.00383336
$995$	6.36651	0.201832
$996$	51.6583	1.63686
$997$	41.1019	1.30171	0.650855	−	0.759202i	$-0.274410\pi$
$997$	41.1019	1.30171	0.650855	+	0.759202i	$0.274410\pi$
$998$	28.9986	0.917935
$999$	1.17510	0.0371786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.p.1.3	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.p.1.3	✓	41	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49955 q^{2} +1.00000 q^{3} +4.24777 q^{4} +0.613091 q^{5} -2.49955 q^{6} -1.00000 q^{7} -5.61841 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49955 q^{2} +1.00000 q^{3} +4.24777 q^{4} +0.613091 q^{5} -2.49955 q^{6} -1.00000 q^{7} -5.61841 q^{8} +1.00000 q^{9} -1.53245 q^{10} -2.20359 q^{11} +4.24777 q^{12} -6.08698 q^{13} +2.49955 q^{14} +0.613091 q^{15} +5.54798 q^{16} -4.83549 q^{17} -2.49955 q^{18} -2.02467 q^{19} +2.60427 q^{20} -1.00000 q^{21} +5.50799 q^{22} +3.36534 q^{23} -5.61841 q^{24} -4.62412 q^{25} +15.2147 q^{26} +1.00000 q^{27} -4.24777 q^{28} +2.93697 q^{29} -1.53245 q^{30} +8.74164 q^{31} -2.63065 q^{32} -2.20359 q^{33} +12.0866 q^{34} -0.613091 q^{35} +4.24777 q^{36} +1.17510 q^{37} +5.06077 q^{38} -6.08698 q^{39} -3.44459 q^{40} -3.39861 q^{41} +2.49955 q^{42} +1.86214 q^{43} -9.36034 q^{44} +0.613091 q^{45} -8.41185 q^{46} +4.86025 q^{47} +5.54798 q^{48} +1.00000 q^{49} +11.5582 q^{50} -4.83549 q^{51} -25.8561 q^{52} -0.596697 q^{53} -2.49955 q^{54} -1.35100 q^{55} +5.61841 q^{56} -2.02467 q^{57} -7.34111 q^{58} -3.43361 q^{59} +2.60427 q^{60} -9.06180 q^{61} -21.8502 q^{62} -1.00000 q^{63} -4.52051 q^{64} -3.73187 q^{65} +5.50799 q^{66} -4.26657 q^{67} -20.5400 q^{68} +3.36534 q^{69} +1.53245 q^{70} +0.0483515 q^{71} -5.61841 q^{72} +4.78042 q^{73} -2.93723 q^{74} -4.62412 q^{75} -8.60032 q^{76} +2.20359 q^{77} +15.2147 q^{78} -8.43434 q^{79} +3.40141 q^{80} +1.00000 q^{81} +8.49502 q^{82} +12.1613 q^{83} -4.24777 q^{84} -2.96459 q^{85} -4.65452 q^{86} +2.93697 q^{87} +12.3807 q^{88} -5.56821 q^{89} -1.53245 q^{90} +6.08698 q^{91} +14.2952 q^{92} +8.74164 q^{93} -12.1485 q^{94} -1.24131 q^{95} -2.63065 q^{96} +0.138665 q^{97} -2.49955 q^{98} -2.20359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9} + 18 q^{10} + 8 q^{11} + 45 q^{12} + 23 q^{13} - 7 q^{14} + 17 q^{15} + 37 q^{16} + 15 q^{17} + 7 q^{18} + 15 q^{19} + 53 q^{20} - 41 q^{21} + 13 q^{22} + 44 q^{23} + 12 q^{24} + 58 q^{25} + 9 q^{26} + 41 q^{27} - 45 q^{28} + 21 q^{29} + 18 q^{30} + 39 q^{31} + 61 q^{32} + 8 q^{33} + 9 q^{34} - 17 q^{35} + 45 q^{36} + 11 q^{37} + 44 q^{38} + 23 q^{39} + 24 q^{40} + 17 q^{41} - 7 q^{42} + 7 q^{43} + 30 q^{44} + 17 q^{45} - 12 q^{46} + 36 q^{47} + 37 q^{48} + 41 q^{49} + 28 q^{50} + 15 q^{51} + 58 q^{52} + 26 q^{53} + 7 q^{54} + 32 q^{55} - 12 q^{56} + 15 q^{57} - 4 q^{58} + 33 q^{59} + 53 q^{60} + 59 q^{61} - q^{62} - 41 q^{63} + 16 q^{64} + 72 q^{65} + 13 q^{66} + 12 q^{67} + 52 q^{68} + 44 q^{69} - 18 q^{70} + 33 q^{71} + 12 q^{72} + 18 q^{73} + 42 q^{74} + 58 q^{75} + 7 q^{76} - 8 q^{77} + 9 q^{78} + 22 q^{79} + 69 q^{80} + 41 q^{81} + 41 q^{82} + 32 q^{83} - 45 q^{84} - 44 q^{85} + 11 q^{86} + 21 q^{87} + 52 q^{88} + 63 q^{89} + 18 q^{90} - 23 q^{91} + 52 q^{92} + 39 q^{93} + 17 q^{94} + 37 q^{95} + 61 q^{96} + 8 q^{97} + 7 q^{98} + 8 q^{99}+O(q^{100}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9 + 18 * q^10 + 8 * q^11 + 45 * q^12 + 23 * q^13 - 7 * q^14 + 17 * q^15 + 37 * q^16 + 15 * q^17 + 7 * q^18 + 15 * q^19 + 53 * q^20 - 41 * q^21 + 13 * q^22 + 44 * q^23 + 12 * q^24 + 58 * q^25 + 9 * q^26 + 41 * q^27 - 45 * q^28 + 21 * q^29 + 18 * q^30 + 39 * q^31 + 61 * q^32 + 8 * q^33 + 9 * q^34 - 17 * q^35 + 45 * q^36 + 11 * q^37 + 44 * q^38 + 23 * q^39 + 24 * q^40 + 17 * q^41 - 7 * q^42 + 7 * q^43 + 30 * q^44 + 17 * q^45 - 12 * q^46 + 36 * q^47 + 37 * q^48 + 41 * q^49 + 28 * q^50 + 15 * q^51 + 58 * q^52 + 26 * q^53 + 7 * q^54 + 32 * q^55 - 12 * q^56 + 15 * q^57 - 4 * q^58 + 33 * q^59 + 53 * q^60 + 59 * q^61 - q^62 - 41 * q^63 + 16 * q^64 + 72 * q^65 + 13 * q^66 + 12 * q^67 + 52 * q^68 + 44 * q^69 - 18 * q^70 + 33 * q^71 + 12 * q^72 + 18 * q^73 + 42 * q^74 + 58 * q^75 + 7 * q^76 - 8 * q^77 + 9 * q^78 + 22 * q^79 + 69 * q^80 + 41 * q^81 + 41 * q^82 + 32 * q^83 - 45 * q^84 - 44 * q^85 + 11 * q^86 + 21 * q^87 + 52 * q^88 + 63 * q^89 + 18 * q^90 - 23 * q^91 + 52 * q^92 + 39 * q^93 + 17 * q^94 + 37 * q^95 + 61 * q^96 + 8 * q^97 + 7 * q^98 + 8 * q^99

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