LMFDB - Embedded newform 8041.2.a.f.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.13623 q^{2} -2.11060 q^{3} +2.56346 q^{4} +3.94938 q^{5} +4.50873 q^{6} -1.45786 q^{7} -1.20369 q^{8} +1.45464 q^{9} +O(q^{10})$	\(q-2.13623 q^{2} -2.11060 q^{3} +2.56346 q^{4} +3.94938 q^{5} +4.50873 q^{6} -1.45786 q^{7} -1.20369 q^{8} +1.45464 q^{9} -8.43678 q^{10} -1.00000 q^{11} -5.41045 q^{12} -6.16904 q^{13} +3.11432 q^{14} -8.33558 q^{15} -2.55558 q^{16} +1.00000 q^{17} -3.10745 q^{18} +4.81217 q^{19} +10.1241 q^{20} +3.07696 q^{21} +2.13623 q^{22} +2.82042 q^{23} +2.54051 q^{24} +10.5976 q^{25} +13.1785 q^{26} +3.26163 q^{27} -3.73717 q^{28} -1.46184 q^{29} +17.8067 q^{30} +1.97541 q^{31} +7.86667 q^{32} +2.11060 q^{33} -2.13623 q^{34} -5.75765 q^{35} +3.72892 q^{36} -1.52393 q^{37} -10.2799 q^{38} +13.0204 q^{39} -4.75382 q^{40} +8.31271 q^{41} -6.57309 q^{42} -1.00000 q^{43} -2.56346 q^{44} +5.74494 q^{45} -6.02505 q^{46} -11.1405 q^{47} +5.39381 q^{48} -4.87464 q^{49} -22.6389 q^{50} -2.11060 q^{51} -15.8141 q^{52} -6.70960 q^{53} -6.96759 q^{54} -3.94938 q^{55} +1.75481 q^{56} -10.1566 q^{57} +3.12282 q^{58} +4.50874 q^{59} -21.3680 q^{60} +8.19162 q^{61} -4.21992 q^{62} -2.12067 q^{63} -11.6938 q^{64} -24.3639 q^{65} -4.50873 q^{66} -2.49997 q^{67} +2.56346 q^{68} -5.95278 q^{69} +12.2996 q^{70} -3.16783 q^{71} -1.75093 q^{72} -3.42048 q^{73} +3.25546 q^{74} -22.3674 q^{75} +12.3358 q^{76} +1.45786 q^{77} -27.8145 q^{78} +10.8713 q^{79} -10.0930 q^{80} -11.2479 q^{81} -17.7578 q^{82} -2.83772 q^{83} +7.88769 q^{84} +3.94938 q^{85} +2.13623 q^{86} +3.08536 q^{87} +1.20369 q^{88} -9.91450 q^{89} -12.2725 q^{90} +8.99360 q^{91} +7.23003 q^{92} -4.16930 q^{93} +23.7986 q^{94} +19.0051 q^{95} -16.6034 q^{96} +13.2965 q^{97} +10.4133 q^{98} -1.45464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.13623	−1.51054	−0.755270	−	0.655414i	$-0.772494\pi$
$2$	−2.13623	−1.51054	−0.755270	+	0.655414i	$0.772494\pi$
$3$	−2.11060	−1.21856	−0.609278	−	0.792956i	$-0.708541\pi$
$3$	−2.11060	−1.21856	−0.609278	+	0.792956i	$0.708541\pi$
$4$	2.56346	1.28173
$5$	3.94938	1.76622	0.883109	−	0.469168i	$-0.155446\pi$
$5$	3.94938	1.76622	0.883109	+	0.469168i	$0.155446\pi$
$6$	4.50873	1.84068
$7$	−1.45786	−0.551019	−0.275510	−	0.961298i	$-0.588847\pi$
$7$	−1.45786	−0.551019	−0.275510	+	0.961298i	$0.588847\pi$
$8$	−1.20369	−0.425568
$9$	1.45464	0.484881
$10$	−8.43678	−2.66794
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−5.41045	−1.56186
$13$	−6.16904	−1.71098	−0.855492	−	0.517816i	$-0.826745\pi$
$13$	−6.16904	−1.71098	−0.855492	+	0.517816i	$0.826745\pi$
$14$	3.11432	0.832337
$15$	−8.33558	−2.15224
$16$	−2.55558	−0.638895
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.10745	−0.732432
$19$	4.81217	1.10399	0.551994	−	0.833848i	$-0.313867\pi$
$19$	4.81217	1.10399	0.551994	+	0.833848i	$0.313867\pi$
$20$	10.1241	2.26382
$21$	3.07696	0.671448
$22$	2.13623	0.455445
$23$	2.82042	0.588097	0.294049	−	0.955790i	$-0.404997\pi$
$23$	2.82042	0.588097	0.294049	+	0.955790i	$0.404997\pi$
$24$	2.54051	0.518578
$25$	10.5976	2.11953
$26$	13.1785	2.58451
$27$	3.26163	0.627702
$28$	−3.73717	−0.706259
$29$	−1.46184	−0.271457	−0.135728	−	0.990746i	$-0.543337\pi$
$29$	−1.46184	−0.271457	−0.135728	+	0.990746i	$0.543337\pi$
$30$	17.8067	3.25104
$31$	1.97541	0.354794	0.177397	−	0.984139i	$-0.443232\pi$
$31$	1.97541	0.354794	0.177397	+	0.984139i	$0.443232\pi$
$32$	7.86667	1.39064
$33$	2.11060	0.367409
$34$	−2.13623	−0.366360
$35$	−5.75765	−0.973220
$36$	3.72892	0.621487
$37$	−1.52393	−0.250533	−0.125266	−	0.992123i	$-0.539979\pi$
$37$	−1.52393	−0.250533	−0.125266	+	0.992123i	$0.539979\pi$
$38$	−10.2799	−1.66762
$39$	13.0204	2.08493
$40$	−4.75382	−0.751645
$41$	8.31271	1.29823	0.649113	−	0.760692i	$-0.275140\pi$
$41$	8.31271	1.29823	0.649113	+	0.760692i	$0.275140\pi$
$42$	−6.57309	−1.01425
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−2.56346	−0.386457
$45$	5.74494	0.856405
$46$	−6.02505	−0.888345
$47$	−11.1405	−1.62501	−0.812503	−	0.582957i	$-0.801896\pi$
$47$	−11.1405	−1.62501	−0.812503	+	0.582957i	$0.801896\pi$
$48$	5.39381	0.778530
$49$	−4.87464	−0.696378
$50$	−22.6389	−3.20163
$51$	−2.11060	−0.295543
$52$	−15.8141	−2.19302
$53$	−6.70960	−0.921635	−0.460817	−	0.887495i	$-0.652444\pi$
$53$	−6.70960	−0.921635	−0.460817	+	0.887495i	$0.652444\pi$
$54$	−6.96759	−0.948169
$55$	−3.94938	−0.532535
$56$	1.75481	0.234496
$57$	−10.1566	−1.34527
$58$	3.12282	0.410047
$59$	4.50874	0.586987	0.293494	−	0.955961i	$-0.405182\pi$
$59$	4.50874	0.586987	0.293494	+	0.955961i	$0.405182\pi$
$60$	−21.3680	−2.75859
$61$	8.19162	1.04883	0.524415	−	0.851463i	$-0.324284\pi$
$61$	8.19162	1.04883	0.524415	+	0.851463i	$0.324284\pi$
$62$	−4.21992	−0.535930
$63$	−2.12067	−0.267179
$64$	−11.6938	−1.46173
$65$	−24.3639	−3.02197
$66$	−4.50873	−0.554986
$67$	−2.49997	−0.305420	−0.152710	−	0.988271i	$-0.548800\pi$
$67$	−2.49997	−0.305420	−0.152710	+	0.988271i	$0.548800\pi$
$68$	2.56346	0.310866
$69$	−5.95278	−0.716630
$70$	12.2996	1.47009
$71$	−3.16783	−0.375952	−0.187976	−	0.982174i	$-0.560193\pi$
$71$	−3.16783	−0.375952	−0.187976	+	0.982174i	$0.560193\pi$
$72$	−1.75093	−0.206350
$73$	−3.42048	−0.400337	−0.200169	−	0.979761i	$-0.564149\pi$
$73$	−3.42048	−0.400337	−0.200169	+	0.979761i	$0.564149\pi$
$74$	3.25546	0.378440
$75$	−22.3674	−2.58276
$76$	12.3358	1.41502
$77$	1.45786	0.166139
$78$	−27.8145	−3.14937
$79$	10.8713	1.22311	0.611557	−	0.791201i	$-0.290544\pi$
$79$	10.8713	1.22311	0.611557	+	0.791201i	$0.290544\pi$
$80$	−10.0930	−1.12843
$81$	−11.2479	−1.24977
$82$	−17.7578	−1.96102
$83$	−2.83772	−0.311480	−0.155740	−	0.987798i	$-0.549776\pi$
$83$	−2.83772	−0.311480	−0.155740	+	0.987798i	$0.549776\pi$
$84$	7.88769	0.860617
$85$	3.94938	0.428371
$86$	2.13623	0.230355
$87$	3.08536	0.330786
$88$	1.20369	0.128313
$89$	−9.91450	−1.05094	−0.525468	−	0.850814i	$-0.676110\pi$
$89$	−9.91450	−1.05094	−0.525468	+	0.850814i	$0.676110\pi$
$90$	−12.2725	−1.29363
$91$	8.99360	0.942786
$92$	7.23003	0.753783
$93$	−4.16930	−0.432336
$94$	23.7986	2.45464
$95$	19.0051	1.94988
$96$	−16.6034	−1.69458
$97$	13.2965	1.35006	0.675028	−	0.737792i	$-0.264132\pi$
$97$	13.2965	1.35006	0.675028	+	0.737792i	$0.264132\pi$
$98$	10.4133	1.05191
$99$	−1.45464	−0.146197
$100$	27.1666	2.71666
$101$	14.3790	1.43077	0.715384	−	0.698731i	$-0.246252\pi$
$101$	14.3790	1.43077	0.715384	+	0.698731i	$0.246252\pi$
$102$	4.50873	0.446430
$103$	12.4798	1.22967	0.614834	−	0.788656i	$-0.289223\pi$
$103$	12.4798	1.22967	0.614834	+	0.788656i	$0.289223\pi$
$104$	7.42560	0.728140
$105$	12.1521	1.18592
$106$	14.3332	1.39217
$107$	10.6170	1.02639	0.513194	−	0.858272i	$-0.328462\pi$
$107$	10.6170	1.02639	0.513194	+	0.858272i	$0.328462\pi$
$108$	8.36108	0.804546
$109$	−3.39730	−0.325403	−0.162701	−	0.986675i	$-0.552021\pi$
$109$	−3.39730	−0.325403	−0.162701	+	0.986675i	$0.552021\pi$
$110$	8.43678	0.804415
$111$	3.21641	0.305289
$112$	3.72568	0.352044
$113$	−11.7125	−1.10182	−0.550908	−	0.834566i	$-0.685719\pi$
$113$	−11.7125	−1.10182	−0.550908	+	0.834566i	$0.685719\pi$
$114$	21.6967	2.03209
$115$	11.1389	1.03871
$116$	−3.74737	−0.347935
$117$	−8.97375	−0.829624
$118$	−9.63168	−0.886668
$119$	−1.45786	−0.133642
$120$	10.0334	0.915922
$121$	1.00000	0.0909091
$122$	−17.4992	−1.58430
$123$	−17.5448	−1.58196
$124$	5.06389	0.454750
$125$	22.1072	1.97733
$126$	4.53022	0.403584
$127$	−9.38147	−0.832471	−0.416235	−	0.909257i	$-0.636651\pi$
$127$	−9.38147	−0.832471	−0.416235	+	0.909257i	$0.636651\pi$
$128$	9.24734	0.817357
$129$	2.11060	0.185828
$130$	52.0468	4.56481
$131$	−10.6117	−0.927148	−0.463574	−	0.886058i	$-0.653433\pi$
$131$	−10.6117	−0.927148	−0.463574	+	0.886058i	$0.653433\pi$
$132$	5.41045	0.470920
$133$	−7.01547	−0.608318
$134$	5.34050	0.461349
$135$	12.8814	1.10866
$136$	−1.20369	−0.103215
$137$	−19.5783	−1.67269	−0.836346	−	0.548203i	$-0.815312\pi$
$137$	−19.5783	−1.67269	−0.836346	+	0.548203i	$0.815312\pi$
$138$	12.7165	1.08250
$139$	21.0190	1.78281	0.891405	−	0.453207i	$-0.149720\pi$
$139$	21.0190	1.78281	0.891405	+	0.453207i	$0.149720\pi$
$140$	−14.7595	−1.24741
$141$	23.5131	1.98016
$142$	6.76720	0.567891
$143$	6.16904	0.515881
$144$	−3.71746	−0.309788
$145$	−5.77337	−0.479452
$146$	7.30693	0.604726
$147$	10.2884	0.848576
$148$	−3.90655	−0.321116
$149$	17.6195	1.44345	0.721725	−	0.692180i	$-0.243350\pi$
$149$	17.6195	1.44345	0.721725	+	0.692180i	$0.243350\pi$
$150$	47.7818	3.90137
$151$	−18.0016	−1.46495	−0.732474	−	0.680795i	$-0.761635\pi$
$151$	−18.0016	−1.46495	−0.732474	+	0.680795i	$0.761635\pi$
$152$	−5.79235	−0.469821
$153$	1.45464	0.117601
$154$	−3.11432	−0.250959
$155$	7.80164	0.626643
$156$	33.3773	2.67232
$157$	−18.7032	−1.49268	−0.746338	−	0.665567i	$-0.768190\pi$
$157$	−18.7032	−1.49268	−0.746338	+	0.665567i	$0.768190\pi$
$158$	−23.2235	−1.84756
$159$	14.1613	1.12306
$160$	31.0685	2.45618
$161$	−4.11177	−0.324053
$162$	24.0282	1.88783
$163$	9.77317	0.765494	0.382747	−	0.923853i	$-0.374978\pi$
$163$	9.77317	0.765494	0.382747	+	0.923853i	$0.374978\pi$
$164$	21.3093	1.66398
$165$	8.33558	0.648924
$166$	6.06201	0.470503
$167$	6.39257	0.494672	0.247336	−	0.968930i	$-0.420445\pi$
$167$	6.39257	0.494672	0.247336	+	0.968930i	$0.420445\pi$
$168$	−3.70370	−0.285747
$169$	25.0571	1.92747
$170$	−8.43678	−0.647071
$171$	6.99999	0.535302
$172$	−2.56346	−0.195462
$173$	−0.00260403	−0.000197980 0	−9.89902e−5	−	1.00000i	$-0.500032\pi$
$173$	−0.00260403	−0.000197980 0	−9.89902e−5		1.00000i	$0.500032\pi$
$174$	−6.59104	−0.499665
$175$	−15.4499	−1.16790
$176$	2.55558	0.192634
$177$	−9.51615	−0.715278
$178$	21.1796	1.58748
$179$	−10.2764	−0.768095	−0.384048	−	0.923313i	$-0.625470\pi$
$179$	−10.2764	−0.768095	−0.384048	+	0.923313i	$0.625470\pi$
$180$	14.7270	1.09768
$181$	−12.5577	−0.933405	−0.466702	−	0.884414i	$-0.654558\pi$
$181$	−12.5577	−0.933405	−0.466702	+	0.884414i	$0.654558\pi$
$182$	−19.2124	−1.42412
$183$	−17.2893	−1.27806
$184$	−3.39490	−0.250275
$185$	−6.01859	−0.442496
$186$	8.90657	0.653061
$187$	−1.00000	−0.0731272
$188$	−28.5582	−2.08282
$189$	−4.75501	−0.345876
$190$	−40.5992	−2.94538
$191$	−17.3262	−1.25368	−0.626839	−	0.779149i	$-0.715652\pi$
$191$	−17.3262	−1.25368	−0.626839	+	0.779149i	$0.715652\pi$
$192$	24.6810	1.78120
$193$	−4.48958	−0.323167	−0.161584	−	0.986859i	$-0.551660\pi$
$193$	−4.48958	−0.323167	−0.161584	+	0.986859i	$0.551660\pi$
$194$	−28.4043	−2.03931
$195$	51.4225	3.68244
$196$	−12.4960	−0.892570
$197$	−9.34856	−0.666058	−0.333029	−	0.942917i	$-0.608071\pi$
$197$	−9.34856	−0.666058	−0.333029	+	0.942917i	$0.608071\pi$
$198$	3.10745	0.220837
$199$	−18.1306	−1.28525	−0.642623	−	0.766183i	$-0.722154\pi$
$199$	−18.1306	−1.28525	−0.642623	+	0.766183i	$0.722154\pi$
$200$	−12.7562	−0.902002
$201$	5.27644	0.372171
$202$	−30.7169	−2.16123
$203$	2.13116	0.149578
$204$	−5.41045	−0.378808
$205$	32.8301	2.29295
$206$	−26.6596	−1.85746
$207$	4.10270	0.285157
$208$	15.7655	1.09314
$209$	−4.81217	−0.332865
$210$	−25.9597	−1.79139
$211$	13.0122	0.895798	0.447899	−	0.894084i	$-0.352172\pi$
$211$	13.0122	0.895798	0.447899	+	0.894084i	$0.352172\pi$
$212$	−17.1998	−1.18129
$213$	6.68603	0.458119
$214$	−22.6804	−1.55040
$215$	−3.94938	−0.269346
$216$	−3.92599	−0.267130
$217$	−2.87987	−0.195498
$218$	7.25741	0.491534
$219$	7.21928	0.487834
$220$	−10.1241	−0.682567
$221$	−6.16904	−0.414975
$222$	−6.87099	−0.461151
$223$	28.8942	1.93490	0.967450	−	0.253061i	$-0.0814374\pi$
$223$	28.8942	1.93490	0.967450	+	0.253061i	$0.0814374\pi$
$224$	−11.4685	−0.766272
$225$	15.4158	1.02772
$226$	25.0205	1.66434
$227$	24.1434	1.60245	0.801227	−	0.598360i	$-0.204181\pi$
$227$	24.1434	1.60245	0.801227	+	0.598360i	$0.204181\pi$
$228$	−26.0360	−1.72428
$229$	−8.42196	−0.556539	−0.278269	−	0.960503i	$-0.589761\pi$
$229$	−8.42196	−0.556539	−0.278269	+	0.960503i	$0.589761\pi$
$230$	−23.7952	−1.56901
$231$	−3.07696	−0.202449
$232$	1.75960	0.115523
$233$	18.6986	1.22498	0.612492	−	0.790477i	$-0.290167\pi$
$233$	18.6986	1.22498	0.612492	+	0.790477i	$0.290167\pi$
$234$	19.1700	1.25318
$235$	−43.9980	−2.87012
$236$	11.5580	0.752361
$237$	−22.9449	−1.49043
$238$	3.11432	0.201871
$239$	11.8938	0.769344	0.384672	−	0.923053i	$-0.374315\pi$
$239$	11.8938	0.769344	0.384672	+	0.923053i	$0.374315\pi$
$240$	21.3022	1.37505
$241$	16.1507	1.04036	0.520179	−	0.854057i	$-0.325865\pi$
$241$	16.1507	1.04036	0.520179	+	0.854057i	$0.325865\pi$
$242$	−2.13623	−0.137322
$243$	13.9550	0.895216
$244$	20.9989	1.34432
$245$	−19.2518	−1.22995
$246$	37.4797	2.38962
$247$	−29.6865	−1.88891
$248$	−2.37777	−0.150989
$249$	5.98929	0.379556
$250$	−47.2259	−2.98683
$251$	−1.82378	−0.115116	−0.0575580	−	0.998342i	$-0.518331\pi$
$251$	−1.82378	−0.115116	−0.0575580	+	0.998342i	$0.518331\pi$
$252$	−5.43625	−0.342452
$253$	−2.82042	−0.177318
$254$	20.0409	1.25748
$255$	−8.33558	−0.521994
$256$	3.63326	0.227079
$257$	6.37540	0.397687	0.198843	−	0.980031i	$-0.436281\pi$
$257$	6.37540	0.397687	0.198843	+	0.980031i	$0.436281\pi$
$258$	−4.50873	−0.280701
$259$	2.22168	0.138048
$260$	−62.4560	−3.87336
$261$	−2.12646	−0.131624
$262$	22.6690	1.40049
$263$	4.46188	0.275131	0.137566	−	0.990493i	$-0.456072\pi$
$263$	4.46188	0.275131	0.137566	+	0.990493i	$0.456072\pi$
$264$	−2.54051	−0.156357
$265$	−26.4988	−1.62781
$266$	14.9866	0.918889
$267$	20.9256	1.28062
$268$	−6.40858	−0.391466
$269$	−3.00741	−0.183365	−0.0916826	−	0.995788i	$-0.529225\pi$
$269$	−3.00741	−0.183365	−0.0916826	+	0.995788i	$0.529225\pi$
$270$	−27.5177	−1.67467
$271$	−4.99275	−0.303288	−0.151644	−	0.988435i	$-0.548457\pi$
$271$	−4.99275	−0.303288	−0.151644	+	0.988435i	$0.548457\pi$
$272$	−2.55558	−0.154955
$273$	−18.9819	−1.14884
$274$	41.8238	2.52667
$275$	−10.5976	−0.639061
$276$	−15.2597	−0.918528
$277$	4.59840	0.276291	0.138146	−	0.990412i	$-0.455886\pi$
$277$	4.59840	0.276291	0.138146	+	0.990412i	$0.455886\pi$
$278$	−44.9014	−2.69301
$279$	2.87351	0.172033
$280$	6.93041	0.414171
$281$	−16.4429	−0.980899	−0.490450	−	0.871470i	$-0.663167\pi$
$281$	−16.4429	−0.980899	−0.490450	+	0.871470i	$0.663167\pi$
$282$	−50.2294	−2.99112
$283$	16.7621	0.996403	0.498201	−	0.867061i	$-0.333994\pi$
$283$	16.7621	0.996403	0.498201	+	0.867061i	$0.333994\pi$
$284$	−8.12061	−0.481870
$285$	−40.1122	−2.37604
$286$	−13.1785	−0.779259
$287$	−12.1188	−0.715348
$288$	11.4432	0.674297
$289$	1.00000	0.0588235
$290$	12.3332	0.724232
$291$	−28.0636	−1.64512
$292$	−8.76829	−0.513125
$293$	−22.8775	−1.33652	−0.668259	−	0.743929i	$-0.732960\pi$
$293$	−22.8775	−1.33652	−0.668259	+	0.743929i	$0.732960\pi$
$294$	−21.9784	−1.28181
$295$	17.8067	1.03675
$296$	1.83434	0.106619
$297$	−3.26163	−0.189259
$298$	−37.6393	−2.18039
$299$	−17.3993	−1.00623
$300$	−57.3380	−3.31041
$301$	1.45786	0.0840297
$302$	38.4555	2.21286
$303$	−30.3485	−1.74347
$304$	−12.2979	−0.705332
$305$	32.3519	1.85246
$306$	−3.10745	−0.177641
$307$	8.37269	0.477855	0.238927	−	0.971037i	$-0.423204\pi$
$307$	8.37269	0.477855	0.238927	+	0.971037i	$0.423204\pi$
$308$	3.73717	0.212945
$309$	−26.3398	−1.49842
$310$	−16.6661	−0.946569
$311$	30.1008	1.70686	0.853429	−	0.521210i	$-0.174519\pi$
$311$	30.1008	1.70686	0.853429	+	0.521210i	$0.174519\pi$
$312$	−15.6725	−0.887280
$313$	−12.6376	−0.714321	−0.357161	−	0.934043i	$-0.616255\pi$
$313$	−12.6376	−0.714321	−0.357161	+	0.934043i	$0.616255\pi$
$314$	39.9542	2.25475
$315$	−8.37532	−0.471896
$316$	27.8681	1.56770
$317$	−7.90503	−0.443990	−0.221995	−	0.975048i	$-0.571257\pi$
$317$	−7.90503	−0.443990	−0.221995	+	0.975048i	$0.571257\pi$
$318$	−30.2517	−1.69643
$319$	1.46184	0.0818473
$320$	−46.1834	−2.58173
$321$	−22.4084	−1.25071
$322$	8.78368	0.489495
$323$	4.81217	0.267756
$324$	−28.8337	−1.60187
$325$	−65.3772	−3.62648
$326$	−20.8777	−1.15631
$327$	7.17036	0.396522
$328$	−10.0059	−0.552483
$329$	16.2413	0.895410
$330$	−17.8067	−0.980226
$331$	6.55382	0.360231	0.180115	−	0.983646i	$-0.442353\pi$
$331$	6.55382	0.360231	0.180115	+	0.983646i	$0.442353\pi$
$332$	−7.27439	−0.399234
$333$	−2.21678	−0.121479
$334$	−13.6560	−0.747221
$335$	−9.87334	−0.539438
$336$	−7.86343	−0.428985
$337$	−24.8257	−1.35234	−0.676171	−	0.736744i	$-0.736362\pi$
$337$	−24.8257	−1.35234	−0.676171	+	0.736744i	$0.736362\pi$
$338$	−53.5276	−2.91152
$339$	24.7204	1.34263
$340$	10.1241	0.549057
$341$	−1.97541	−0.106974
$342$	−14.9536	−0.808596
$343$	17.3116	0.934737
$344$	1.20369	0.0648985
$345$	−23.5098	−1.26572
$346$	0.00556279	0.000299057 0
$347$	5.46900	0.293591	0.146796	−	0.989167i	$-0.453104\pi$
$347$	5.46900	0.293591	0.146796	+	0.989167i	$0.453104\pi$
$348$	7.90922	0.423979
$349$	30.6995	1.64331	0.821653	−	0.569988i	$-0.193052\pi$
$349$	30.6995	1.64331	0.821653	+	0.569988i	$0.193052\pi$
$350$	33.0044	1.76416
$351$	−20.1212	−1.07399
$352$	−7.86667	−0.419295
$353$	−7.37199	−0.392371	−0.196186	−	0.980567i	$-0.562856\pi$
$353$	−7.37199	−0.392371	−0.196186	+	0.980567i	$0.562856\pi$
$354$	20.3287	1.08046
$355$	−12.5110	−0.664013
$356$	−25.4155	−1.34702
$357$	3.07696	0.162850
$358$	21.9528	1.16024
$359$	−12.7451	−0.672661	−0.336330	−	0.941744i	$-0.609186\pi$
$359$	−12.7451	−0.672661	−0.336330	+	0.941744i	$0.609186\pi$
$360$	−6.91511	−0.364458
$361$	4.15697	0.218788
$362$	26.8260	1.40995
$363$	−2.11060	−0.110778
$364$	23.0548	1.20840
$365$	−13.5088	−0.707083
$366$	36.9338	1.93056
$367$	19.4376	1.01463	0.507316	−	0.861760i	$-0.330638\pi$
$367$	19.4376	1.01463	0.507316	+	0.861760i	$0.330638\pi$
$368$	−7.20780	−0.375732
$369$	12.0920	0.629485
$370$	12.8571	0.668407
$371$	9.78166	0.507839
$372$	−10.6879	−0.554139
$373$	−0.540065	−0.0279635	−0.0139818	−	0.999902i	$-0.504451\pi$
$373$	−0.540065	−0.0279635	−0.0139818	+	0.999902i	$0.504451\pi$
$374$	2.13623	0.110462
$375$	−46.6595	−2.40948
$376$	13.4097	0.691550
$377$	9.01815	0.464459
$378$	10.1578	0.522460
$379$	12.5104	0.642614	0.321307	−	0.946975i	$-0.395878\pi$
$379$	12.5104	0.642614	0.321307	+	0.946975i	$0.395878\pi$
$380$	48.7189	2.49923
$381$	19.8006	1.01441
$382$	37.0127	1.89373
$383$	28.8132	1.47229	0.736144	−	0.676825i	$-0.236645\pi$
$383$	28.8132	1.47229	0.736144	+	0.676825i	$0.236645\pi$
$384$	−19.5175	−0.995996
$385$	5.75765	0.293437
$386$	9.59077	0.488157
$387$	−1.45464	−0.0739436
$388$	34.0851	1.73041
$389$	−27.8051	−1.40977	−0.704887	−	0.709319i	$-0.749002\pi$
$389$	−27.8051	−1.40977	−0.704887	+	0.709319i	$0.749002\pi$
$390$	−109.850	−5.56248
$391$	2.82042	0.142635
$392$	5.86755	0.296356
$393$	22.3971	1.12978
$394$	19.9707	1.00611
$395$	42.9348	2.16028
$396$	−3.72892	−0.187386
$397$	−12.6556	−0.635167	−0.317584	−	0.948230i	$-0.602871\pi$
$397$	−12.6556	−0.635167	−0.317584	+	0.948230i	$0.602871\pi$
$398$	38.7311	1.94142
$399$	14.8069	0.741271
$400$	−27.0831	−1.35415
$401$	32.8010	1.63800	0.819001	−	0.573792i	$-0.194528\pi$
$401$	32.8010	1.63800	0.819001	+	0.573792i	$0.194528\pi$
$402$	−11.2717	−0.562180
$403$	−12.1864	−0.607046
$404$	36.8602	1.83386
$405$	−44.4224	−2.20737
$406$	−4.55264	−0.225944
$407$	1.52393	0.0755385
$408$	2.54051	0.125774
$409$	−36.4352	−1.80161	−0.900803	−	0.434227i	$-0.857021\pi$
$409$	−36.4352	−1.80161	−0.900803	+	0.434227i	$0.857021\pi$
$410$	−70.1324	−3.46359
$411$	41.3221	2.03827
$412$	31.9915	1.57611
$413$	−6.57311	−0.323441
$414$	−8.76429	−0.430741
$415$	−11.2072	−0.550141
$416$	−48.5298	−2.37937
$417$	−44.3628	−2.17246
$418$	10.2799	0.502806
$419$	14.3655	0.701803	0.350901	−	0.936412i	$-0.385875\pi$
$419$	14.3655	0.701803	0.350901	+	0.936412i	$0.385875\pi$
$420$	31.1515	1.52004
$421$	23.5165	1.14613	0.573063	−	0.819511i	$-0.305755\pi$
$421$	23.5165	1.14613	0.573063	+	0.819511i	$0.305755\pi$
$422$	−27.7971	−1.35314
$423$	−16.2054	−0.787935
$424$	8.07626	0.392218
$425$	10.5976	0.514060
$426$	−14.2829	−0.692007
$427$	−11.9422	−0.577926
$428$	27.2164	1.31556
$429$	−13.0204	−0.628631
$430$	8.43678	0.406858
$431$	20.9272	1.00803	0.504013	−	0.863696i	$-0.331856\pi$
$431$	20.9272	1.00803	0.504013	+	0.863696i	$0.331856\pi$
$432$	−8.33537	−0.401036
$433$	30.9105	1.48546	0.742731	−	0.669590i	$-0.233530\pi$
$433$	30.9105	1.48546	0.742731	+	0.669590i	$0.233530\pi$
$434$	6.15205	0.295308
$435$	12.1853	0.584240
$436$	−8.70887	−0.417079
$437$	13.5723	0.649252
$438$	−15.4220	−0.736893
$439$	29.1262	1.39012	0.695060	−	0.718952i	$-0.255378\pi$
$439$	29.1262	1.39012	0.695060	+	0.718952i	$0.255378\pi$
$440$	4.75382	0.226630
$441$	−7.09087	−0.337660
$442$	13.1785	0.626836
$443$	−16.6029	−0.788830	−0.394415	−	0.918932i	$-0.629053\pi$
$443$	−16.6029	−0.788830	−0.394415	+	0.918932i	$0.629053\pi$
$444$	8.24516	0.391298
$445$	−39.1562	−1.85618
$446$	−61.7246	−2.92275
$447$	−37.1879	−1.75893
$448$	17.0480	0.805441
$449$	31.2967	1.47698	0.738492	−	0.674263i	$-0.235538\pi$
$449$	31.2967	1.47698	0.738492	+	0.674263i	$0.235538\pi$
$450$	−32.9316	−1.55241
$451$	−8.31271	−0.391430
$452$	−30.0245	−1.41223
$453$	37.9942	1.78512
$454$	−51.5758	−2.42057
$455$	35.5192	1.66516
$456$	12.2253	0.572504
$457$	−1.40508	−0.0657269	−0.0328635	−	0.999460i	$-0.510463\pi$
$457$	−1.40508	−0.0657269	−0.0328635	+	0.999460i	$0.510463\pi$
$458$	17.9912	0.840674
$459$	3.26163	0.152240
$460$	28.5542	1.33135
$461$	−29.4750	−1.37279	−0.686393	−	0.727231i	$-0.740807\pi$
$461$	−29.4750	−1.37279	−0.686393	+	0.727231i	$0.740807\pi$
$462$	6.57309	0.305808
$463$	−28.0392	−1.30309	−0.651545	−	0.758610i	$-0.725879\pi$
$463$	−28.0392	−1.30309	−0.651545	+	0.758610i	$0.725879\pi$
$464$	3.73585	0.173432
$465$	−16.4662	−0.763600
$466$	−39.9444	−1.85039
$467$	15.4877	0.716683	0.358342	−	0.933591i	$-0.383342\pi$
$467$	15.4877	0.716683	0.358342	+	0.933591i	$0.383342\pi$
$468$	−23.0039	−1.06336
$469$	3.64461	0.168292
$470$	93.9898	4.33542
$471$	39.4750	1.81891
$472$	−5.42711	−0.249803
$473$	1.00000	0.0459800
$474$	49.0156	2.25136
$475$	50.9976	2.33993
$476$	−3.73717	−0.171293
$477$	−9.76007	−0.446883
$478$	−25.4078	−1.16213
$479$	6.29190	0.287484	0.143742	−	0.989615i	$-0.454086\pi$
$479$	6.29190	0.287484	0.143742	+	0.989615i	$0.454086\pi$
$480$	−65.5733	−2.99300
$481$	9.40120	0.428658
$482$	−34.5016	−1.57150
$483$	8.67831	0.394877
$484$	2.56346	0.116521
$485$	52.5130	2.38449
$486$	−29.8111	−1.35226
$487$	−26.0912	−1.18231	−0.591153	−	0.806559i	$-0.701327\pi$
$487$	−26.0912	−1.18231	−0.591153	+	0.806559i	$0.701327\pi$
$488$	−9.86015	−0.446348
$489$	−20.6273	−0.932797
$490$	41.1263	1.85790
$491$	−12.7432	−0.575092	−0.287546	−	0.957767i	$-0.592839\pi$
$491$	−12.7432	−0.575092	−0.287546	+	0.957767i	$0.592839\pi$
$492$	−44.9755	−2.02765
$493$	−1.46184	−0.0658380
$494$	63.4170	2.85327
$495$	−5.74494	−0.258216
$496$	−5.04831	−0.226676
$497$	4.61825	0.207157
$498$	−12.7945	−0.573335
$499$	−12.9649	−0.580390	−0.290195	−	0.956968i	$-0.593720\pi$
$499$	−12.9649	−0.580390	−0.290195	+	0.956968i	$0.593720\pi$
$500$	56.6710	2.53440
$501$	−13.4922	−0.602785
$502$	3.89601	0.173887
$503$	19.1605	0.854323	0.427161	−	0.904175i	$-0.359514\pi$
$503$	19.1605	0.854323	0.427161	+	0.904175i	$0.359514\pi$
$504$	2.55262	0.113703
$505$	56.7884	2.52705
$506$	6.02505	0.267846
$507$	−52.8856	−2.34873
$508$	−24.0491	−1.06700
$509$	42.3105	1.87538	0.937691	−	0.347471i	$-0.112960\pi$
$509$	42.3105	1.87538	0.937691	+	0.347471i	$0.112960\pi$
$510$	17.8067	0.788493
$511$	4.98659	0.220594
$512$	−26.2561	−1.16037
$513$	15.6955	0.692975
$514$	−13.6193	−0.600722
$515$	49.2874	2.17186
$516$	5.41045	0.238182
$517$	11.1405	0.489958
$518$	−4.74601	−0.208528
$519$	0.00549606	0.000241250 0
$520$	29.3265	1.28605
$521$	−34.7841	−1.52392	−0.761958	−	0.647626i	$-0.775762\pi$
$521$	−34.7841	−1.52392	−0.761958	+	0.647626i	$0.775762\pi$
$522$	4.54259	0.198824
$523$	6.18139	0.270293	0.135147	−	0.990826i	$-0.456849\pi$
$523$	6.18139	0.270293	0.135147	+	0.990826i	$0.456849\pi$
$524$	−27.2027	−1.18836
$525$	32.6085	1.42315
$526$	−9.53158	−0.415597
$527$	1.97541	0.0860501
$528$	−5.39381	−0.234736
$529$	−15.0453	−0.654142
$530$	56.6074	2.45887
$531$	6.55860	0.284619
$532$	−17.9839	−0.779701
$533$	−51.2814	−2.22125
$534$	−44.7018	−1.93443
$535$	41.9308	1.81283
$536$	3.00918	0.129977
$537$	21.6894	0.935968
$538$	6.42452	0.276981
$539$	4.87464	0.209966
$540$	33.0211	1.42100
$541$	−13.9031	−0.597740	−0.298870	−	0.954294i	$-0.596610\pi$
$541$	−13.9031	−0.597740	−0.298870	+	0.954294i	$0.596610\pi$
$542$	10.6656	0.458128
$543$	26.5043	1.13741
$544$	7.86667	0.337281
$545$	−13.4173	−0.574732
$546$	40.5497	1.73537
$547$	−14.2350	−0.608644	−0.304322	−	0.952569i	$-0.598430\pi$
$547$	−14.2350	−0.608644	−0.304322	+	0.952569i	$0.598430\pi$
$548$	−50.1884	−2.14394
$549$	11.9159	0.508558
$550$	22.6389	0.965327
$551$	−7.03462	−0.299685
$552$	7.16528	0.304975
$553$	−15.8488	−0.673959
$554$	−9.82322	−0.417349
$555$	12.7029	0.539206
$556$	53.8815	2.28509
$557$	18.1584	0.769396	0.384698	−	0.923043i	$-0.374306\pi$
$557$	18.1584	0.769396	0.384698	+	0.923043i	$0.374306\pi$
$558$	−6.13847	−0.259862
$559$	6.16904	0.260923
$560$	14.7141	0.621786
$561$	2.11060	0.0891097
$562$	35.1257	1.48169
$563$	−20.2847	−0.854897	−0.427449	−	0.904040i	$-0.640588\pi$
$563$	−20.2847	−0.854897	−0.427449	+	0.904040i	$0.640588\pi$
$564$	60.2751	2.53804
$565$	−46.2570	−1.94605
$566$	−35.8076	−1.50511
$567$	16.3979	0.688648
$568$	3.81307	0.159993
$569$	24.1660	1.01309	0.506545	−	0.862213i	$-0.330922\pi$
$569$	24.1660	1.01309	0.506545	+	0.862213i	$0.330922\pi$
$570$	85.6888	3.58911
$571$	−28.7549	−1.20336	−0.601678	−	0.798738i	$-0.705501\pi$
$571$	−28.7549	−1.20336	−0.601678	+	0.798738i	$0.705501\pi$
$572$	15.8141	0.661222
$573$	36.5687	1.52768
$574$	25.8884	1.08056
$575$	29.8897	1.24649
$576$	−17.0104	−0.708765
$577$	15.0121	0.624961	0.312480	−	0.949924i	$-0.398840\pi$
$577$	15.0121	0.624961	0.312480	+	0.949924i	$0.398840\pi$
$578$	−2.13623	−0.0888553
$579$	9.47572	0.393798
$580$	−14.7998	−0.614529
$581$	4.13700	0.171631
$582$	59.9503	2.48502
$583$	6.70960	0.277883
$584$	4.11719	0.170371
$585$	−35.4408	−1.46530
$586$	48.8715	2.01886
$587$	−38.3549	−1.58307	−0.791537	−	0.611121i	$-0.790719\pi$
$587$	−38.3549	−1.58307	−0.791537	+	0.611121i	$0.790719\pi$
$588$	26.3740	1.08765
$589$	9.50599	0.391688
$590$	−38.0392	−1.56605
$591$	19.7311	0.811629
$592$	3.89453	0.160064
$593$	−29.0021	−1.19097	−0.595486	−	0.803366i	$-0.703041\pi$
$593$	−29.0021	−1.19097	−0.595486	+	0.803366i	$0.703041\pi$
$594$	6.96759	0.285884
$595$	−5.75765	−0.236041
$596$	45.1671	1.85012
$597$	38.2665	1.56615
$598$	37.1688	1.51994
$599$	40.8675	1.66980	0.834901	−	0.550400i	$-0.185525\pi$
$599$	40.8675	1.66980	0.834901	+	0.550400i	$0.185525\pi$
$600$	26.9233	1.09914
$601$	16.9156	0.690002	0.345001	−	0.938602i	$-0.387879\pi$
$601$	16.9156	0.690002	0.345001	+	0.938602i	$0.387879\pi$
$602$	−3.11432	−0.126930
$603$	−3.63656	−0.148092
$604$	−46.1464	−1.87767
$605$	3.94938	0.160565
$606$	64.8312	2.63359
$607$	−5.03899	−0.204526	−0.102263	−	0.994757i	$-0.532608\pi$
$607$	−5.03899	−0.204526	−0.102263	+	0.994757i	$0.532608\pi$
$608$	37.8558	1.53525
$609$	−4.49803	−0.182269
$610$	−69.1109	−2.79822
$611$	68.7261	2.78036
$612$	3.72892	0.150733
$613$	−16.3439	−0.660123	−0.330061	−	0.943959i	$-0.607069\pi$
$613$	−16.3439	−0.660123	−0.330061	+	0.943959i	$0.607069\pi$
$614$	−17.8860	−0.721819
$615$	−69.2912	−2.79409
$616$	−1.75481	−0.0707032
$617$	35.1486	1.41503	0.707514	−	0.706699i	$-0.249817\pi$
$617$	35.1486	1.41503	0.707514	+	0.706699i	$0.249817\pi$
$618$	56.2679	2.26343
$619$	12.4938	0.502168	0.251084	−	0.967965i	$-0.419213\pi$
$619$	12.4938	0.502168	0.251084	+	0.967965i	$0.419213\pi$
$620$	19.9992	0.803188
$621$	9.19916	0.369150
$622$	−64.3020	−2.57828
$623$	14.4540	0.579086
$624$	−33.2747	−1.33205
$625$	34.3216	1.37286
$626$	26.9968	1.07901
$627$	10.1566	0.405615
$628$	−47.9449	−1.91321
$629$	−1.52393	−0.0607631
$630$	17.8916	0.712818
$631$	23.7373	0.944969	0.472484	−	0.881339i	$-0.343357\pi$
$631$	23.7373	0.944969	0.472484	+	0.881339i	$0.343357\pi$
$632$	−13.0856	−0.520517
$633$	−27.4636	−1.09158
$634$	16.8869	0.670666
$635$	−37.0510	−1.47032
$636$	36.3020	1.43947
$637$	30.0719	1.19149
$638$	−3.12282	−0.123634
$639$	−4.60806	−0.182292
$640$	36.5213	1.44363
$641$	33.2439	1.31306	0.656528	−	0.754302i	$-0.272025\pi$
$641$	33.2439	1.31306	0.656528	+	0.754302i	$0.272025\pi$
$642$	47.8693	1.88925
$643$	−19.7871	−0.780327	−0.390163	−	0.920746i	$-0.627582\pi$
$643$	−19.7871	−0.780327	−0.390163	+	0.920746i	$0.627582\pi$
$644$	−10.5404	−0.415349
$645$	8.33558	0.328213
$646$	−10.2799	−0.404457
$647$	−28.5574	−1.12271	−0.561354	−	0.827576i	$-0.689719\pi$
$647$	−28.5574	−1.12271	−0.561354	+	0.827576i	$0.689719\pi$
$648$	13.5390	0.531862
$649$	−4.50874	−0.176983
$650$	139.661	5.47794
$651$	6.07826	0.238226
$652$	25.0532	0.981158
$653$	−4.04800	−0.158411	−0.0792053	−	0.996858i	$-0.525238\pi$
$653$	−4.04800	−0.158411	−0.0792053	+	0.996858i	$0.525238\pi$
$654$	−15.3175	−0.598962
$655$	−41.9096	−1.63754
$656$	−21.2438	−0.829430
$657$	−4.97558	−0.194116
$658$	−34.6950	−1.35255
$659$	−0.880013	−0.0342804	−0.0171402	−	0.999853i	$-0.505456\pi$
$659$	−0.880013	−0.0342804	−0.0171402	+	0.999853i	$0.505456\pi$
$660$	21.3680	0.831747
$661$	−47.4829	−1.84687	−0.923435	−	0.383755i	$-0.874631\pi$
$661$	−47.4829	−1.84687	−0.923435	+	0.383755i	$0.874631\pi$
$662$	−14.0004	−0.544143
$663$	13.0204	0.505670
$664$	3.41572	0.132556
$665$	−27.7068	−1.07442
$666$	4.73554	0.183498
$667$	−4.12300	−0.159643
$668$	16.3871	0.634036
$669$	−60.9842	−2.35779
$670$	21.0917	0.814843
$671$	−8.19162	−0.316234
$672$	24.2055	0.933746
$673$	−49.0376	−1.89026	−0.945131	−	0.326692i	$-0.894066\pi$
$673$	−49.0376	−1.89026	−0.945131	+	0.326692i	$0.894066\pi$
$674$	53.0333	2.04277
$675$	34.5656	1.33043
$676$	64.2329	2.47050
$677$	27.7849	1.06786	0.533930	−	0.845529i	$-0.320715\pi$
$677$	27.7849	1.06786	0.533930	+	0.845529i	$0.320715\pi$
$678$	−52.8083	−2.02809
$679$	−19.3844	−0.743907
$680$	−4.75382	−0.182301
$681$	−50.9571	−1.95268
$682$	4.21992	0.161589
$683$	10.1600	0.388762	0.194381	−	0.980926i	$-0.437730\pi$
$683$	10.1600	0.388762	0.194381	+	0.980926i	$0.437730\pi$
$684$	17.9442	0.686114
$685$	−77.3224	−2.95434
$686$	−36.9814	−1.41196
$687$	17.7754	0.678174
$688$	2.55558	0.0974306
$689$	41.3918	1.57690
$690$	50.2222	1.91193
$691$	26.4757	1.00718	0.503592	−	0.863942i	$-0.332011\pi$
$691$	26.4757	1.00718	0.503592	+	0.863942i	$0.332011\pi$
$692$	−0.00667533	−0.000253758 0
$693$	2.12067	0.0805574
$694$	−11.6830	−0.443481
$695$	83.0122	3.14883
$696$	−3.71381	−0.140772
$697$	8.31271	0.314866
$698$	−65.5810	−2.48228
$699$	−39.4652	−1.49271
$700$	−39.6052	−1.49693
$701$	38.5126	1.45460	0.727300	−	0.686319i	$-0.240775\pi$
$701$	38.5126	1.45460	0.727300	+	0.686319i	$0.240775\pi$
$702$	42.9834	1.62230
$703$	−7.33342	−0.276585
$704$	11.6938	0.440728
$705$	92.8624	3.49740
$706$	15.7482	0.592693
$707$	−20.9626	−0.788381
$708$	−24.3943	−0.916794
$709$	−38.8249	−1.45810	−0.729050	−	0.684461i	$-0.760038\pi$
$709$	−38.8249	−1.45810	−0.729050	+	0.684461i	$0.760038\pi$
$710$	26.7263	1.00302
$711$	15.8138	0.593064
$712$	11.9340	0.447244
$713$	5.57147	0.208653
$714$	−6.57309	−0.245992
$715$	24.3639	0.911159
$716$	−26.3432	−0.984492
$717$	−25.1030	−0.937490
$718$	27.2264	1.01608
$719$	−11.5605	−0.431134	−0.215567	−	0.976489i	$-0.569160\pi$
$719$	−11.5605	−0.431134	−0.215567	+	0.976489i	$0.569160\pi$
$720$	−14.6817	−0.547153
$721$	−18.1938	−0.677571
$722$	−8.88023	−0.330488
$723$	−34.0877	−1.26774
$724$	−32.1911	−1.19637
$725$	−15.4920	−0.575360
$726$	4.50873	0.167334
$727$	6.21048	0.230334	0.115167	−	0.993346i	$-0.463260\pi$
$727$	6.21048	0.230334	0.115167	+	0.993346i	$0.463260\pi$
$728$	−10.8255	−0.401219
$729$	4.29030	0.158900
$730$	28.8579	1.06808
$731$	−1.00000	−0.0369863
$732$	−44.3204	−1.63813
$733$	25.4706	0.940777	0.470388	−	0.882459i	$-0.344114\pi$
$733$	25.4706	0.940777	0.470388	+	0.882459i	$0.344114\pi$
$734$	−41.5230	−1.53264
$735$	40.6330	1.49877
$736$	22.1873	0.817834
$737$	2.49997	0.0920876
$738$	−25.8313	−0.950863
$739$	14.4038	0.529852	0.264926	−	0.964269i	$-0.414653\pi$
$739$	14.4038	0.529852	0.264926	+	0.964269i	$0.414653\pi$
$740$	−15.4284	−0.567161
$741$	62.6564	2.30174
$742$	−20.8958	−0.767111
$743$	−16.0691	−0.589517	−0.294759	−	0.955572i	$-0.595239\pi$
$743$	−16.0691	−0.589517	−0.294759	+	0.955572i	$0.595239\pi$
$744$	5.01853	0.183988
$745$	69.5863	2.54945
$746$	1.15370	0.0422400
$747$	−4.12786	−0.151031
$748$	−2.56346	−0.0937295
$749$	−15.4782	−0.565560
$750$	99.6752	3.63962
$751$	35.6554	1.30108	0.650542	−	0.759470i	$-0.274542\pi$
$751$	35.6554	1.30108	0.650542	+	0.759470i	$0.274542\pi$
$752$	28.4704	1.03821
$753$	3.84928	0.140275
$754$	−19.2648	−0.701583
$755$	−71.0952	−2.58742
$756$	−12.1893	−0.443320
$757$	−3.95975	−0.143920	−0.0719598	−	0.997408i	$-0.522925\pi$
$757$	−3.95975	−0.143920	−0.0719598	+	0.997408i	$0.522925\pi$
$758$	−26.7250	−0.970694
$759$	5.95278	0.216072
$760$	−22.8762	−0.829807
$761$	24.1194	0.874327	0.437164	−	0.899382i	$-0.355983\pi$
$761$	24.1194	0.874327	0.437164	+	0.899382i	$0.355983\pi$
$762$	−42.2985	−1.53231
$763$	4.95279	0.179303
$764$	−44.4150	−1.60688
$765$	5.74494	0.207709
$766$	−61.5516	−2.22395
$767$	−27.8146	−1.00433
$768$	−7.66837	−0.276709
$769$	14.2219	0.512853	0.256427	−	0.966564i	$-0.417455\pi$
$769$	14.2219	0.512853	0.256427	+	0.966564i	$0.417455\pi$
$770$	−12.2996	−0.443248
$771$	−13.4559	−0.484604
$772$	−11.5089	−0.414214
$773$	9.93764	0.357432	0.178716	−	0.983901i	$-0.442806\pi$
$773$	9.93764	0.357432	0.178716	+	0.983901i	$0.442806\pi$
$774$	3.10745	0.111695
$775$	20.9346	0.751994
$776$	−16.0048	−0.574540
$777$	−4.68908	−0.168220
$778$	59.3980	2.12952
$779$	40.0021	1.43323
$780$	131.820	4.71991
$781$	3.16783	0.113354
$782$	−6.02505	−0.215455
$783$	−4.76799	−0.170394
$784$	12.4575	0.444912
$785$	−73.8660	−2.63639
$786$	−47.8452	−1.70658
$787$	29.8329	1.06343	0.531714	−	0.846924i	$-0.321548\pi$
$787$	29.8329	1.06343	0.531714	+	0.846924i	$0.321548\pi$
$788$	−23.9647	−0.853707
$789$	−9.41725	−0.335263
$790$	−91.7185	−3.26320
$791$	17.0751	0.607122
$792$	1.75093	0.0622168
$793$	−50.5345	−1.79453
$794$	27.0353	0.959446
$795$	55.9284	1.98358
$796$	−46.4772	−1.64734
$797$	30.9781	1.09730	0.548650	−	0.836052i	$-0.315142\pi$
$797$	30.9781	1.09730	0.548650	+	0.836052i	$0.315142\pi$
$798$	−31.6308	−1.11972
$799$	−11.1405	−0.394122
$800$	83.3681	2.94751
$801$	−14.4221	−0.509578
$802$	−70.0703	−2.47427
$803$	3.42048	0.120706
$804$	13.5260	0.477024
$805$	−16.2390	−0.572348
$806$	26.0329	0.916968
$807$	6.34746	0.223441
$808$	−17.3079	−0.608889
$809$	−20.9860	−0.737830	−0.368915	−	0.929463i	$-0.620271\pi$
$809$	−20.9860	−0.737830	−0.368915	+	0.929463i	$0.620271\pi$
$810$	94.8964	3.33432
$811$	3.63708	0.127715	0.0638575	−	0.997959i	$-0.479660\pi$
$811$	3.63708	0.127715	0.0638575	+	0.997959i	$0.479660\pi$
$812$	5.46315	0.191719
$813$	10.5377	0.369573
$814$	−3.25546	−0.114104
$815$	38.5980	1.35203
$816$	5.39381	0.188821
$817$	−4.81217	−0.168356
$818$	77.8339	2.72140
$819$	13.0825	0.457139
$820$	84.1587	2.93895
$821$	−15.5684	−0.543341	−0.271670	−	0.962390i	$-0.587576\pi$
$821$	−15.5684	−0.543341	−0.271670	+	0.962390i	$0.587576\pi$
$822$	−88.2734	−3.07889
$823$	−4.49007	−0.156514	−0.0782569	−	0.996933i	$-0.524935\pi$
$823$	−4.49007	−0.156514	−0.0782569	+	0.996933i	$0.524935\pi$
$824$	−15.0217	−0.523307
$825$	22.3674	0.778732
$826$	14.0416	0.488571
$827$	−39.9219	−1.38822	−0.694110	−	0.719869i	$-0.744202\pi$
$827$	−39.9219	−1.38822	−0.694110	+	0.719869i	$0.744202\pi$
$828$	10.5171	0.365495
$829$	37.7875	1.31241	0.656207	−	0.754581i	$-0.272160\pi$
$829$	37.7875	1.31241	0.656207	+	0.754581i	$0.272160\pi$
$830$	23.9412	0.831011
$831$	−9.70539	−0.336676
$832$	72.1398	2.50100
$833$	−4.87464	−0.168896
$834$	94.7690	3.28158
$835$	25.2467	0.873698
$836$	−12.3358	−0.426643
$837$	6.44306	0.222705
$838$	−30.6881	−1.06010
$839$	36.9274	1.27488	0.637438	−	0.770502i	$-0.279994\pi$
$839$	36.9274	1.27488	0.637438	+	0.770502i	$0.279994\pi$
$840$	−14.6273	−0.504691
$841$	−26.8630	−0.926311
$842$	−50.2367	−1.73127
$843$	34.7044	1.19528
$844$	33.3564	1.14817
$845$	98.9600	3.40433
$846$	34.6185	1.19021
$847$	−1.45786	−0.0500927
$848$	17.1469	0.588828
$849$	−35.3781	−1.21417
$850$	−22.6389	−0.776509
$851$	−4.29812	−0.147338
$852$	17.1394	0.587186
$853$	24.4766	0.838062	0.419031	−	0.907972i	$-0.362370\pi$
$853$	24.4766	0.838062	0.419031	+	0.907972i	$0.362370\pi$
$854$	25.5113	0.872980
$855$	27.6456	0.945461
$856$	−12.7796	−0.436798
$857$	14.4630	0.494047	0.247023	−	0.969010i	$-0.420548\pi$
$857$	14.4630	0.494047	0.247023	+	0.969010i	$0.420548\pi$
$858$	27.8145	0.949572
$859$	11.1369	0.379986	0.189993	−	0.981785i	$-0.439153\pi$
$859$	11.1369	0.379986	0.189993	+	0.981785i	$0.439153\pi$
$860$	−10.1241	−0.345229
$861$	25.5779	0.871692
$862$	−44.7051	−1.52266
$863$	29.2404	0.995354	0.497677	−	0.867362i	$-0.334186\pi$
$863$	29.2404	0.995354	0.497677	+	0.867362i	$0.334186\pi$
$864$	25.6582	0.872910
$865$	−0.0102843	−0.000349676 0
$866$	−66.0318	−2.24385
$867$	−2.11060	−0.0716798
$868$	−7.38244	−0.250576
$869$	−10.8713	−0.368782
$870$	−26.0305	−0.882517
$871$	15.4224	0.522569
$872$	4.08929	0.138481
$873$	19.3417	0.654616
$874$	−28.9935	−0.980721
$875$	−32.2292	−1.08954
$876$	18.5064	0.625272
$877$	36.8410	1.24403	0.622016	−	0.783004i	$-0.286314\pi$
$877$	36.8410	1.24403	0.622016	+	0.783004i	$0.286314\pi$
$878$	−62.2203	−2.09983
$879$	48.2853	1.62862
$880$	10.0930	0.340234
$881$	15.1660	0.510955	0.255477	−	0.966815i	$-0.417767\pi$
$881$	15.1660	0.510955	0.255477	+	0.966815i	$0.417767\pi$
$882$	15.1477	0.510049
$883$	−19.4906	−0.655910	−0.327955	−	0.944693i	$-0.606359\pi$
$883$	−19.4906	−0.655910	−0.327955	+	0.944693i	$0.606359\pi$
$884$	−15.8141	−0.531886
$885$	−37.5829	−1.26334
$886$	35.4677	1.19156
$887$	−24.1343	−0.810350	−0.405175	−	0.914239i	$-0.632789\pi$
$887$	−24.1343	−0.810350	−0.405175	+	0.914239i	$0.632789\pi$
$888$	−3.87156	−0.129921
$889$	13.6769	0.458708
$890$	83.6465	2.80384
$891$	11.2479	0.376820
$892$	74.0693	2.48002
$893$	−53.6099	−1.79399
$894$	79.4417	2.65693
$895$	−40.5855	−1.35662
$896$	−13.4813	−0.450379
$897$	36.7229	1.22614
$898$	−66.8569	−2.23104
$899$	−2.88773	−0.0963112
$900$	39.5178	1.31726
$901$	−6.70960	−0.223529
$902$	17.7578	0.591271
$903$	−3.07696	−0.102395
$904$	14.0982	0.468898
$905$	−49.5951	−1.64860
$906$	−81.1642	−2.69650
$907$	−55.8286	−1.85376	−0.926879	−	0.375360i	$-0.877519\pi$
$907$	−55.8286	−1.85376	−0.926879	+	0.375360i	$0.877519\pi$
$908$	61.8908	2.05392
$909$	20.9164	0.693752
$910$	−75.8770	−2.51530
$911$	52.1276	1.72706	0.863531	−	0.504295i	$-0.168248\pi$
$911$	52.1276	1.72706	0.863531	+	0.504295i	$0.168248\pi$
$912$	25.9559	0.859487
$913$	2.83772	0.0939147
$914$	3.00157	0.0992832
$915$	−68.2819	−2.25733
$916$	−21.5894	−0.713334
$917$	15.4704	0.510876
$918$	−6.96759	−0.229965
$919$	26.8283	0.884985	0.442493	−	0.896772i	$-0.354094\pi$
$919$	26.8283	0.884985	0.442493	+	0.896772i	$0.354094\pi$
$920$	−13.4078	−0.442040
$921$	−17.6714	−0.582293
$922$	62.9652	2.07365
$923$	19.5425	0.643248
$924$	−7.88769	−0.259486
$925$	−16.1501	−0.531011
$926$	59.8980	1.96837
$927$	18.1536	0.596243
$928$	−11.4998	−0.377500
$929$	37.7067	1.23712	0.618558	−	0.785739i	$-0.287717\pi$
$929$	37.7067	1.23712	0.618558	+	0.785739i	$0.287717\pi$
$930$	35.1755	1.15345
$931$	−23.4576	−0.768792
$932$	47.9331	1.57010
$933$	−63.5307	−2.07990
$934$	−33.0851	−1.08258
$935$	−3.94938	−0.129159
$936$	10.8016	0.353061
$937$	52.2970	1.70847	0.854235	−	0.519887i	$-0.174026\pi$
$937$	52.2970	1.70847	0.854235	+	0.519887i	$0.174026\pi$
$938$	−7.78570	−0.254212
$939$	26.6730	0.870441
$940$	−112.787	−3.67872
$941$	2.06219	0.0672254	0.0336127	−	0.999435i	$-0.489299\pi$
$941$	2.06219	0.0672254	0.0336127	+	0.999435i	$0.489299\pi$
$942$	−84.3275	−2.74754
$943$	23.4453	0.763483
$944$	−11.5224	−0.375023
$945$	−18.7793	−0.610892
$946$	−2.13623	−0.0694547
$947$	2.74661	0.0892527	0.0446264	−	0.999004i	$-0.485790\pi$
$947$	2.74661	0.0892527	0.0446264	+	0.999004i	$0.485790\pi$
$948$	−58.8185	−1.91034
$949$	21.1011	0.684971
$950$	−108.942	−3.53456
$951$	16.6844	0.541028
$952$	1.75481	0.0568736
$953$	−25.2827	−0.818988	−0.409494	−	0.912313i	$-0.634295\pi$
$953$	−25.2827	−0.818988	−0.409494	+	0.912313i	$0.634295\pi$
$954$	20.8497	0.675035
$955$	−68.4277	−2.21427
$956$	30.4893	0.986093
$957$	−3.08536	−0.0997356
$958$	−13.4409	−0.434257
$959$	28.5425	0.921685
$960$	97.4749	3.14599
$961$	−27.0978	−0.874121
$962$	−20.0831	−0.647505
$963$	15.4440	0.497676
$964$	41.4018	1.33346
$965$	−17.7311	−0.570784
$966$	−18.5388	−0.596478
$967$	28.8363	0.927313	0.463656	−	0.886015i	$-0.346537\pi$
$967$	28.8363	0.927313	0.463656	+	0.886015i	$0.346537\pi$
$968$	−1.20369	−0.0386880
$969$	−10.1566	−0.326276
$970$	−112.180	−3.60187
$971$	13.7664	0.441785	0.220893	−	0.975298i	$-0.429103\pi$
$971$	13.7664	0.441785	0.220893	+	0.975298i	$0.429103\pi$
$972$	35.7732	1.14743
$973$	−30.6428	−0.982363
$974$	55.7368	1.78592
$975$	137.985	4.41907
$976$	−20.9343	−0.670092
$977$	4.62404	0.147936	0.0739681	−	0.997261i	$-0.476434\pi$
$977$	4.62404	0.147936	0.0739681	+	0.997261i	$0.476434\pi$
$978$	44.0645	1.40903
$979$	9.91450	0.316869
$980$	−49.3514	−1.57647
$981$	−4.94186	−0.157782
$982$	27.2224	0.868700
$983$	22.3882	0.714071	0.357036	−	0.934091i	$-0.383787\pi$
$983$	22.3882	0.714071	0.357036	+	0.934091i	$0.383787\pi$
$984$	21.1185	0.673232
$985$	−36.9211	−1.17640
$986$	3.12282	0.0994509
$987$	−34.2789	−1.09111
$988$	−76.1002	−2.42107
$989$	−2.82042	−0.0896840
$990$	12.2725	0.390046
$991$	8.99300	0.285672	0.142836	−	0.989746i	$-0.454378\pi$
$991$	8.99300	0.285672	0.142836	+	0.989746i	$0.454378\pi$
$992$	15.5399	0.493392
$993$	−13.8325	−0.438961
$994$	−9.86563	−0.312919
$995$	−71.6048	−2.27002
$996$	15.3533	0.486489
$997$	30.3356	0.960738	0.480369	−	0.877067i	$-0.340503\pi$
$997$	30.3356	0.960738	0.480369	+	0.877067i	$0.340503\pi$
$998$	27.6960	0.876702
$999$	−4.97051	−0.157260

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.f.1.9	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.f.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.13623 q^{2} -2.11060 q^{3} +2.56346 q^{4} +3.94938 q^{5} +4.50873 q^{6} -1.45786 q^{7} -1.20369 q^{8} +1.45464 q^{9} +O(q^{10})\)	\(q-2.13623 q^{2} -2.11060 q^{3} +2.56346 q^{4} +3.94938 q^{5} +4.50873 q^{6} -1.45786 q^{7} -1.20369 q^{8} +1.45464 q^{9} -8.43678 q^{10} -1.00000 q^{11} -5.41045 q^{12} -6.16904 q^{13} +3.11432 q^{14} -8.33558 q^{15} -2.55558 q^{16} +1.00000 q^{17} -3.10745 q^{18} +4.81217 q^{19} +10.1241 q^{20} +3.07696 q^{21} +2.13623 q^{22} +2.82042 q^{23} +2.54051 q^{24} +10.5976 q^{25} +13.1785 q^{26} +3.26163 q^{27} -3.73717 q^{28} -1.46184 q^{29} +17.8067 q^{30} +1.97541 q^{31} +7.86667 q^{32} +2.11060 q^{33} -2.13623 q^{34} -5.75765 q^{35} +3.72892 q^{36} -1.52393 q^{37} -10.2799 q^{38} +13.0204 q^{39} -4.75382 q^{40} +8.31271 q^{41} -6.57309 q^{42} -1.00000 q^{43} -2.56346 q^{44} +5.74494 q^{45} -6.02505 q^{46} -11.1405 q^{47} +5.39381 q^{48} -4.87464 q^{49} -22.6389 q^{50} -2.11060 q^{51} -15.8141 q^{52} -6.70960 q^{53} -6.96759 q^{54} -3.94938 q^{55} +1.75481 q^{56} -10.1566 q^{57} +3.12282 q^{58} +4.50874 q^{59} -21.3680 q^{60} +8.19162 q^{61} -4.21992 q^{62} -2.12067 q^{63} -11.6938 q^{64} -24.3639 q^{65} -4.50873 q^{66} -2.49997 q^{67} +2.56346 q^{68} -5.95278 q^{69} +12.2996 q^{70} -3.16783 q^{71} -1.75093 q^{72} -3.42048 q^{73} +3.25546 q^{74} -22.3674 q^{75} +12.3358 q^{76} +1.45786 q^{77} -27.8145 q^{78} +10.8713 q^{79} -10.0930 q^{80} -11.2479 q^{81} -17.7578 q^{82} -2.83772 q^{83} +7.88769 q^{84} +3.94938 q^{85} +2.13623 q^{86} +3.08536 q^{87} +1.20369 q^{88} -9.91450 q^{89} -12.2725 q^{90} +8.99360 q^{91} +7.23003 q^{92} -4.16930 q^{93} +23.7986 q^{94} +19.0051 q^{95} -16.6034 q^{96} +13.2965 q^{97} +10.4133 q^{98} -1.45464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 12 q^{2} + 66 q^{4} + 6 q^{5} + 7 q^{6} + 13 q^{7} + 30 q^{8} + 58 q^{9}+O(q^{10}) \) 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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