LMFDB - Embedded newform 4001.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71370 q^{2} +0.987518 q^{3} +5.36416 q^{4} +1.22965 q^{5} -2.67983 q^{6} +4.88451 q^{7} -9.12930 q^{8} -2.02481 q^{9} +O(q^{10})$	\(q-2.71370 q^{2} +0.987518 q^{3} +5.36416 q^{4} +1.22965 q^{5} -2.67983 q^{6} +4.88451 q^{7} -9.12930 q^{8} -2.02481 q^{9} -3.33689 q^{10} +2.42166 q^{11} +5.29720 q^{12} -6.22353 q^{13} -13.2551 q^{14} +1.21430 q^{15} +14.0459 q^{16} +4.92849 q^{17} +5.49472 q^{18} -2.22202 q^{19} +6.59601 q^{20} +4.82355 q^{21} -6.57166 q^{22} -6.90022 q^{23} -9.01535 q^{24} -3.48797 q^{25} +16.8888 q^{26} -4.96209 q^{27} +26.2013 q^{28} -5.43580 q^{29} -3.29524 q^{30} -8.91237 q^{31} -19.8576 q^{32} +2.39144 q^{33} -13.3744 q^{34} +6.00622 q^{35} -10.8614 q^{36} -0.474942 q^{37} +6.02988 q^{38} -6.14584 q^{39} -11.2258 q^{40} +4.08409 q^{41} -13.0896 q^{42} -9.27719 q^{43} +12.9902 q^{44} -2.48980 q^{45} +18.7251 q^{46} +10.5019 q^{47} +13.8705 q^{48} +16.8585 q^{49} +9.46530 q^{50} +4.86697 q^{51} -33.3840 q^{52} +4.69151 q^{53} +13.4656 q^{54} +2.97779 q^{55} -44.5922 q^{56} -2.19428 q^{57} +14.7511 q^{58} +1.75863 q^{59} +6.51368 q^{60} -10.7437 q^{61} +24.1855 q^{62} -9.89021 q^{63} +25.7958 q^{64} -7.65273 q^{65} -6.48964 q^{66} -15.9579 q^{67} +26.4372 q^{68} -6.81409 q^{69} -16.2991 q^{70} -9.84488 q^{71} +18.4851 q^{72} -13.3382 q^{73} +1.28885 q^{74} -3.44443 q^{75} -11.9192 q^{76} +11.8287 q^{77} +16.6780 q^{78} -4.81901 q^{79} +17.2714 q^{80} +1.17427 q^{81} -11.0830 q^{82} +1.44886 q^{83} +25.8743 q^{84} +6.06030 q^{85} +25.1755 q^{86} -5.36795 q^{87} -22.1081 q^{88} -11.3574 q^{89} +6.75656 q^{90} -30.3989 q^{91} -37.0139 q^{92} -8.80113 q^{93} -28.4990 q^{94} -2.73229 q^{95} -19.6097 q^{96} +4.86746 q^{97} -45.7488 q^{98} -4.90340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * 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 $

$2$	−2.71370	−1.91887	−0.959437	−	0.281923i	$-0.909028\pi$
$2$	−2.71370	−1.91887	−0.959437	+	0.281923i	$0.909028\pi$
$3$	0.987518	0.570144	0.285072	−	0.958506i	$-0.407983\pi$
$3$	0.987518	0.570144	0.285072	+	0.958506i	$0.407983\pi$
$4$	5.36416	2.68208
$5$	1.22965	0.549914	0.274957	−	0.961456i	$-0.411336\pi$
$5$	1.22965	0.549914	0.274957	+	0.961456i	$0.411336\pi$
$6$	−2.67983	−1.09403
$7$	4.88451	1.84617	0.923087	−	0.384592i	$-0.125658\pi$
$7$	4.88451	1.84617	0.923087	+	0.384592i	$0.125658\pi$
$8$	−9.12930	−3.22770
$9$	−2.02481	−0.674936
$10$	−3.33689	−1.05522
$11$	2.42166	0.730159	0.365080	−	0.930976i	$-0.381042\pi$
$11$	2.42166	0.730159	0.365080	+	0.930976i	$0.381042\pi$
$12$	5.29720	1.52917
$13$	−6.22353	−1.72610	−0.863048	−	0.505123i	$-0.831447\pi$
$13$	−6.22353	−1.72610	−0.863048	+	0.505123i	$0.831447\pi$
$14$	−13.2551	−3.54257
$15$	1.21430	0.313530
$16$	14.0459	3.51146
$17$	4.92849	1.19533	0.597667	−	0.801744i	$-0.296094\pi$
$17$	4.92849	1.19533	0.597667	+	0.801744i	$0.296094\pi$
$18$	5.49472	1.29512
$19$	−2.22202	−0.509766	−0.254883	−	0.966972i	$-0.582037\pi$
$19$	−2.22202	−0.509766	−0.254883	+	0.966972i	$0.582037\pi$
$20$	6.59601	1.47491
$21$	4.82355	1.05258
$22$	−6.57166	−1.40108
$23$	−6.90022	−1.43880	−0.719398	−	0.694598i	$-0.755582\pi$
$23$	−6.90022	−1.43880	−0.719398	+	0.694598i	$0.755582\pi$
$24$	−9.01535	−1.84025
$25$	−3.48797	−0.697594
$26$	16.8888	3.31216
$27$	−4.96209	−0.954954
$28$	26.2013	4.95158
$29$	−5.43580	−1.00940	−0.504701	−	0.863294i	$-0.668397\pi$
$29$	−5.43580	−1.00940	−0.504701	+	0.863294i	$0.668397\pi$
$30$	−3.29524	−0.601625
$31$	−8.91237	−1.60071	−0.800355	−	0.599527i	$-0.795355\pi$
$31$	−8.91237	−1.60071	−0.800355	+	0.599527i	$0.795355\pi$
$32$	−19.8576	−3.51036
$33$	2.39144	0.416296
$34$	−13.3744	−2.29370
$35$	6.00622	1.01524
$36$	−10.8614	−1.81023
$37$	−0.474942	−0.0780800	−0.0390400	−	0.999238i	$-0.512430\pi$
$37$	−0.474942	−0.0780800	−0.0390400	+	0.999238i	$0.512430\pi$
$38$	6.02988	0.978176
$39$	−6.14584	−0.984122
$40$	−11.2258	−1.77496
$41$	4.08409	0.637827	0.318914	−	0.947784i	$-0.396682\pi$
$41$	4.08409	0.637827	0.318914	+	0.947784i	$0.396682\pi$
$42$	−13.0896	−2.01978
$43$	−9.27719	−1.41476	−0.707379	−	0.706834i	$-0.750123\pi$
$43$	−9.27719	−1.41476	−0.707379	+	0.706834i	$0.750123\pi$
$44$	12.9902	1.95834
$45$	−2.48980	−0.371157
$46$	18.7251	2.76087
$47$	10.5019	1.53186	0.765930	−	0.642924i	$-0.222279\pi$
$47$	10.5019	1.53186	0.765930	+	0.642924i	$0.222279\pi$
$48$	13.8705	2.00204
$49$	16.8585	2.40836
$50$	9.46530	1.33860
$51$	4.86697	0.681513
$52$	−33.3840	−4.62952
$53$	4.69151	0.644429	0.322214	−	0.946667i	$-0.395573\pi$
$53$	4.69151	0.644429	0.322214	+	0.946667i	$0.395573\pi$
$54$	13.4656	1.83244
$55$	2.97779	0.401525
$56$	−44.5922	−5.95888
$57$	−2.19428	−0.290640
$58$	14.7511	1.93692
$59$	1.75863	0.228955	0.114477	−	0.993426i	$-0.463481\pi$
$59$	1.75863	0.228955	0.114477	+	0.993426i	$0.463481\pi$
$60$	6.51368	0.840913
$61$	−10.7437	−1.37559	−0.687796	−	0.725904i	$-0.741421\pi$
$61$	−10.7437	−1.37559	−0.687796	+	0.725904i	$0.741421\pi$
$62$	24.1855	3.07156
$63$	−9.89021	−1.24605
$64$	25.7958	3.22448
$65$	−7.65273	−0.949205
$66$	−6.48964	−0.798819
$67$	−15.9579	−1.94956	−0.974781	−	0.223164i	$-0.928361\pi$
$67$	−15.9579	−1.94956	−0.974781	+	0.223164i	$0.928361\pi$
$68$	26.4372	3.20598
$69$	−6.81409	−0.820321
$70$	−16.2991	−1.94811
$71$	−9.84488	−1.16837	−0.584186	−	0.811620i	$-0.698586\pi$
$71$	−9.84488	−1.16837	−0.584186	+	0.811620i	$0.698586\pi$
$72$	18.4851	2.17849
$73$	−13.3382	−1.56112	−0.780559	−	0.625083i	$-0.785065\pi$
$73$	−13.3382	−1.56112	−0.780559	+	0.625083i	$0.785065\pi$
$74$	1.28885	0.149826
$75$	−3.44443	−0.397729
$76$	−11.9192	−1.36723
$77$	11.8287	1.34800
$78$	16.6780	1.88841
$79$	−4.81901	−0.542182	−0.271091	−	0.962554i	$-0.587384\pi$
$79$	−4.81901	−0.542182	−0.271091	+	0.962554i	$0.587384\pi$
$80$	17.2714	1.93100
$81$	1.17427	0.130475
$82$	−11.0830	−1.22391
$83$	1.44886	0.159033	0.0795164	−	0.996834i	$-0.474662\pi$
$83$	1.44886	0.159033	0.0795164	+	0.996834i	$0.474662\pi$
$84$	25.8743	2.82311
$85$	6.06030	0.657332
$86$	25.1755	2.71474
$87$	−5.36795	−0.575504
$88$	−22.1081	−2.35673
$89$	−11.3574	−1.20389	−0.601944	−	0.798539i	$-0.705607\pi$
$89$	−11.3574	−1.20389	−0.601944	+	0.798539i	$0.705607\pi$
$90$	6.75656	0.712204
$91$	−30.3989	−3.18667
$92$	−37.0139	−3.85896
$93$	−8.80113	−0.912634
$94$	−28.4990	−2.93945
$95$	−2.73229	−0.280327
$96$	−19.6097	−2.00141
$97$	4.86746	0.494216	0.247108	−	0.968988i	$-0.420520\pi$
$97$	4.86746	0.494216	0.247108	+	0.968988i	$0.420520\pi$
$98$	−45.7488	−4.62133
$99$	−4.90340	−0.492811
$100$	−18.7100	−1.87100
$101$	−5.02269	−0.499776	−0.249888	−	0.968275i	$-0.580394\pi$
$101$	−5.02269	−0.499776	−0.249888	+	0.968275i	$0.580394\pi$
$102$	−13.2075	−1.30774
$103$	−6.50676	−0.641130	−0.320565	−	0.947227i	$-0.603873\pi$
$103$	−6.50676	−0.641130	−0.320565	+	0.947227i	$0.603873\pi$
$104$	56.8164	5.57131
$105$	5.93125	0.578831
$106$	−12.7314	−1.23658
$107$	1.79880	0.173897	0.0869484	−	0.996213i	$-0.472288\pi$
$107$	1.79880	0.173897	0.0869484	+	0.996213i	$0.472288\pi$
$108$	−26.6174	−2.56126
$109$	−1.12103	−0.107375	−0.0536877	−	0.998558i	$-0.517098\pi$
$109$	−1.12103	−0.107375	−0.0536877	+	0.998558i	$0.517098\pi$
$110$	−8.08082	−0.770476
$111$	−0.469014	−0.0445168
$112$	68.6072	6.48277
$113$	6.02167	0.566471	0.283235	−	0.959050i	$-0.408592\pi$
$113$	6.02167	0.566471	0.283235	+	0.959050i	$0.408592\pi$
$114$	5.95462	0.557701
$115$	−8.48483	−0.791215
$116$	−29.1585	−2.70729
$117$	12.6014	1.16500
$118$	−4.77240	−0.439335
$119$	24.0733	2.20680
$120$	−11.0857	−1.01198
$121$	−5.13555	−0.466868
$122$	29.1552	2.63959
$123$	4.03311	0.363653
$124$	−47.8074	−4.29323
$125$	−10.4372	−0.933531
$126$	26.8390	2.39101
$127$	6.26743	0.556145	0.278072	−	0.960560i	$-0.410305\pi$
$127$	6.26743	0.556145	0.278072	+	0.960560i	$0.410305\pi$
$128$	−30.2869	−2.67701
$129$	−9.16139	−0.806615
$130$	20.7672	1.82140
$131$	0.631631	0.0551859	0.0275929	−	0.999619i	$-0.491216\pi$
$131$	0.631631	0.0551859	0.0275929	+	0.999619i	$0.491216\pi$
$132$	12.8280	1.11654
$133$	−10.8535	−0.941116
$134$	43.3048	3.74096
$135$	−6.10161	−0.525143
$136$	−44.9937	−3.85818
$137$	−16.7603	−1.43193	−0.715967	−	0.698135i	$-0.754014\pi$
$137$	−16.7603	−1.43193	−0.715967	+	0.698135i	$0.754014\pi$
$138$	18.4914	1.57409
$139$	22.1669	1.88017	0.940086	−	0.340939i	$-0.110745\pi$
$139$	22.1669	1.88017	0.940086	+	0.340939i	$0.110745\pi$
$140$	32.2183	2.72295
$141$	10.3708	0.873380
$142$	26.7160	2.24196
$143$	−15.0713	−1.26032
$144$	−28.4402	−2.37001
$145$	−6.68410	−0.555085
$146$	36.1958	2.99559
$147$	16.6481	1.37311
$148$	−2.54766	−0.209417
$149$	−12.1101	−0.992094	−0.496047	−	0.868296i	$-0.665216\pi$
$149$	−12.1101	−0.992094	−0.496047	+	0.868296i	$0.665216\pi$
$150$	9.34715	0.763192
$151$	−7.88838	−0.641947	−0.320974	−	0.947088i	$-0.604010\pi$
$151$	−7.88838	−0.641947	−0.320974	+	0.947088i	$0.604010\pi$
$152$	20.2855	1.64537
$153$	−9.97925	−0.806775
$154$	−32.0994	−2.58664
$155$	−10.9591	−0.880253
$156$	−32.9673	−2.63949
$157$	14.5597	1.16199	0.580996	−	0.813906i	$-0.302663\pi$
$157$	14.5597	1.16199	0.580996	+	0.813906i	$0.302663\pi$
$158$	13.0773	1.04038
$159$	4.63295	0.367417
$160$	−24.4178	−1.93040
$161$	−33.7042	−2.65627
$162$	−3.18662	−0.250365
$163$	6.02199	0.471678	0.235839	−	0.971792i	$-0.424216\pi$
$163$	6.02199	0.471678	0.235839	+	0.971792i	$0.424216\pi$
$164$	21.9077	1.71070
$165$	2.94062	0.228927
$166$	−3.93176	−0.305164
$167$	18.1174	1.40197	0.700983	−	0.713178i	$-0.252745\pi$
$167$	18.1174	1.40197	0.700983	+	0.713178i	$0.252745\pi$
$168$	−44.0356	−3.39742
$169$	25.7323	1.97940
$170$	−16.4458	−1.26134
$171$	4.49916	0.344059
$172$	−49.7643	−3.79449
$173$	−17.6588	−1.34257	−0.671287	−	0.741197i	$-0.734258\pi$
$173$	−17.6588	−1.34257	−0.671287	+	0.741197i	$0.734258\pi$
$174$	14.5670	1.10432
$175$	−17.0370	−1.28788
$176$	34.0143	2.56393
$177$	1.73668	0.130537
$178$	30.8207	2.31011
$179$	24.4361	1.82644	0.913219	−	0.407470i	$-0.133589\pi$
$179$	24.4361	1.82644	0.913219	+	0.407470i	$0.133589\pi$
$180$	−13.3557	−0.995472
$181$	15.4318	1.14703	0.573517	−	0.819194i	$-0.305579\pi$
$181$	15.4318	1.14703	0.573517	+	0.819194i	$0.305579\pi$
$182$	82.4934	6.11482
$183$	−10.6096	−0.784285
$184$	62.9942	4.64400
$185$	−0.584011	−0.0429373
$186$	23.8836	1.75123
$187$	11.9352	0.872785
$188$	56.3338	4.10857
$189$	−24.2374	−1.76301
$190$	7.41462	0.537913
$191$	17.1045	1.23764	0.618820	−	0.785533i	$-0.287611\pi$
$191$	17.1045	1.23764	0.618820	+	0.785533i	$0.287611\pi$
$192$	25.4738	1.83842
$193$	8.40942	0.605323	0.302662	−	0.953098i	$-0.402125\pi$
$193$	8.40942	0.605323	0.302662	+	0.953098i	$0.402125\pi$
$194$	−13.2088	−0.948338
$195$	−7.55721	−0.541183
$196$	90.4315	6.45940
$197$	3.49911	0.249301	0.124651	−	0.992201i	$-0.460219\pi$
$197$	3.49911	0.249301	0.124651	+	0.992201i	$0.460219\pi$
$198$	13.3064	0.945642
$199$	−11.4759	−0.813503	−0.406751	−	0.913539i	$-0.633338\pi$
$199$	−11.4759	−0.813503	−0.406751	+	0.913539i	$0.633338\pi$
$200$	31.8427	2.25162
$201$	−15.7587	−1.11153
$202$	13.6301	0.959007
$203$	−26.5512	−1.86353
$204$	26.1072	1.82787
$205$	5.02198	0.350750
$206$	17.6574	1.23025
$207$	13.9716	0.971095
$208$	−87.4147	−6.06112
$209$	−5.38098	−0.372210
$210$	−16.0956	−1.11070
$211$	5.77399	0.397498	0.198749	−	0.980050i	$-0.436312\pi$
$211$	5.77399	0.397498	0.198749	+	0.980050i	$0.436312\pi$
$212$	25.1660	1.72841
$213$	−9.72199	−0.666140
$214$	−4.88141	−0.333686
$215$	−11.4077	−0.777996
$216$	45.3004	3.08230
$217$	−43.5326	−2.95519
$218$	3.04214	0.206040
$219$	−13.1717	−0.890061
$220$	15.9733	1.07692
$221$	−30.6726	−2.06326
$222$	1.27276	0.0854222
$223$	−16.1124	−1.07896	−0.539482	−	0.841997i	$-0.681380\pi$
$223$	−16.1124	−1.07896	−0.539482	+	0.841997i	$0.681380\pi$
$224$	−96.9948	−6.48073
$225$	7.06247	0.470831
$226$	−16.3410	−1.08699
$227$	26.0572	1.72947	0.864737	−	0.502225i	$-0.167485\pi$
$227$	26.0572	1.72947	0.864737	+	0.502225i	$0.167485\pi$
$228$	−11.7705	−0.779518
$229$	20.3468	1.34456	0.672278	−	0.740299i	$-0.265316\pi$
$229$	20.3468	1.34456	0.672278	+	0.740299i	$0.265316\pi$
$230$	23.0253	1.51824
$231$	11.6810	0.768554
$232$	49.6250	3.25804
$233$	10.0270	0.656893	0.328447	−	0.944523i	$-0.393475\pi$
$233$	10.0270	0.656893	0.328447	+	0.944523i	$0.393475\pi$
$234$	−34.1965	−2.23550
$235$	12.9136	0.842391
$236$	9.43359	0.614074
$237$	−4.75886	−0.309121
$238$	−65.3276	−4.23456
$239$	−29.5170	−1.90930	−0.954649	−	0.297734i	$-0.903769\pi$
$239$	−29.5170	−1.90930	−0.954649	+	0.297734i	$0.903769\pi$
$240$	17.0558	1.10095
$241$	7.19247	0.463308	0.231654	−	0.972798i	$-0.425586\pi$
$241$	7.19247	0.463308	0.231654	+	0.972798i	$0.425586\pi$
$242$	13.9363	0.895860
$243$	16.0459	1.02934
$244$	−57.6309	−3.68944
$245$	20.7300	1.32439
$246$	−10.9446	−0.697805
$247$	13.8288	0.879904
$248$	81.3637	5.16660
$249$	1.43077	0.0906716
$250$	28.3234	1.79133
$251$	−12.7693	−0.805990	−0.402995	−	0.915202i	$-0.632031\pi$
$251$	−12.7693	−0.805990	−0.402995	+	0.915202i	$0.632031\pi$
$252$	−53.0526	−3.34200
$253$	−16.7100	−1.05055
$254$	−17.0079	−1.06717
$255$	5.98466	0.374774
$256$	30.5977	1.91236
$257$	1.72620	0.107677	0.0538386	−	0.998550i	$-0.482854\pi$
$257$	1.72620	0.107677	0.0538386	+	0.998550i	$0.482854\pi$
$258$	24.8612	1.54779
$259$	−2.31986	−0.144149
$260$	−41.0505	−2.54584
$261$	11.0064	0.681282
$262$	−1.71406	−0.105895
$263$	3.56745	0.219979	0.109989	−	0.993933i	$-0.464918\pi$
$263$	3.56745	0.219979	0.109989	+	0.993933i	$0.464918\pi$
$264$	−21.8321	−1.34368
$265$	5.76890	0.354381
$266$	29.4531	1.80588
$267$	−11.2157	−0.686389
$268$	−85.6004	−5.22888
$269$	−19.4247	−1.18434	−0.592172	−	0.805811i	$-0.701729\pi$
$269$	−19.4247	−1.18434	−0.592172	+	0.805811i	$0.701729\pi$
$270$	16.5579	1.00768
$271$	−6.42907	−0.390538	−0.195269	−	0.980750i	$-0.562558\pi$
$271$	−6.42907	−0.390538	−0.195269	+	0.980750i	$0.562558\pi$
$272$	69.2249	4.19738
$273$	−30.0195	−1.81686
$274$	45.4825	2.74770
$275$	−8.44669	−0.509355
$276$	−36.5519	−2.20016
$277$	12.3940	0.744681	0.372340	−	0.928096i	$-0.378555\pi$
$277$	12.3940	0.744681	0.372340	+	0.928096i	$0.378555\pi$
$278$	−60.1542	−3.60781
$279$	18.0458	1.08038
$280$	−54.8326	−3.27688
$281$	7.28442	0.434552	0.217276	−	0.976110i	$-0.430283\pi$
$281$	7.28442	0.434552	0.217276	+	0.976110i	$0.430283\pi$
$282$	−28.1433	−1.67591
$283$	6.48146	0.385283	0.192641	−	0.981269i	$-0.438295\pi$
$283$	6.48146	0.385283	0.192641	+	0.981269i	$0.438295\pi$
$284$	−52.8095	−3.13367
$285$	−2.69819	−0.159827
$286$	40.8989	2.41840
$287$	19.9488	1.17754
$288$	40.2078	2.36927
$289$	7.29004	0.428826
$290$	18.1386	1.06514
$291$	4.80671	0.281774
$292$	−71.5481	−4.18704
$293$	11.8682	0.693345	0.346673	−	0.937986i	$-0.387311\pi$
$293$	11.8682	0.693345	0.346673	+	0.937986i	$0.387311\pi$
$294$	−45.1778	−2.63482
$295$	2.16250	0.125905
$296$	4.33589	0.252018
$297$	−12.0165	−0.697269
$298$	32.8630	1.90370
$299$	42.9437	2.48350
$300$	−18.4765	−1.06674
$301$	−45.3146	−2.61189
$302$	21.4067	1.23182
$303$	−4.95999	−0.284944
$304$	−31.2101	−1.79002
$305$	−13.2110	−0.756458
$306$	27.0807	1.54810
$307$	16.4308	0.937758	0.468879	−	0.883262i	$-0.344658\pi$
$307$	16.4308	0.937758	0.468879	+	0.883262i	$0.344658\pi$
$308$	63.4507	3.61544
$309$	−6.42554	−0.365536
$310$	29.7396	1.68910
$311$	17.5392	0.994555	0.497277	−	0.867592i	$-0.334333\pi$
$311$	17.5392	0.994555	0.497277	+	0.867592i	$0.334333\pi$
$312$	56.1073	3.17645
$313$	15.7327	0.889264	0.444632	−	0.895713i	$-0.353334\pi$
$313$	15.7327	0.889264	0.444632	+	0.895713i	$0.353334\pi$
$314$	−39.5107	−2.22972
$315$	−12.1615	−0.685220
$316$	−25.8499	−1.45417
$317$	−12.9524	−0.727477	−0.363738	−	0.931501i	$-0.618500\pi$
$317$	−12.9524	−0.727477	−0.363738	+	0.931501i	$0.618500\pi$
$318$	−12.5724	−0.705027
$319$	−13.1637	−0.737024
$320$	31.7197	1.77319
$321$	1.77635	0.0991462
$322$	91.4631	5.09704
$323$	−10.9512	−0.609341
$324$	6.29898	0.349944
$325$	21.7075	1.20411
$326$	−16.3418	−0.905091
$327$	−1.10704	−0.0612194
$328$	−37.2849	−2.05871
$329$	51.2967	2.82808
$330$	−7.97995	−0.439282
$331$	8.54262	0.469545	0.234772	−	0.972050i	$-0.424566\pi$
$331$	8.54262	0.469545	0.234772	+	0.972050i	$0.424566\pi$
$332$	7.77190	0.426538
$333$	0.961667	0.0526990
$334$	−49.1651	−2.69020
$335$	−19.6225	−1.07209
$336$	67.7508	3.69611
$337$	15.9113	0.866744	0.433372	−	0.901215i	$-0.357324\pi$
$337$	15.9113	0.866744	0.433372	+	0.901215i	$0.357324\pi$
$338$	−69.8296	−3.79823
$339$	5.94650	0.322970
$340$	32.5084	1.76302
$341$	−21.5828	−1.16877
$342$	−12.2094	−0.660206
$343$	48.1539	2.60007
$344$	84.6943	4.56641
$345$	−8.37892	−0.451106
$346$	47.9207	2.57623
$347$	13.7057	0.735761	0.367880	−	0.929873i	$-0.380084\pi$
$347$	13.7057	0.735761	0.367880	+	0.929873i	$0.380084\pi$
$348$	−28.7945	−1.54355
$349$	21.9493	1.17492	0.587461	−	0.809253i	$-0.300128\pi$
$349$	21.9493	1.17492	0.587461	+	0.809253i	$0.300128\pi$
$350$	46.2334	2.47128
$351$	30.8817	1.64834
$352$	−48.0884	−2.56312
$353$	6.24516	0.332396	0.166198	−	0.986092i	$-0.446851\pi$
$353$	6.24516	0.332396	0.166198	+	0.986092i	$0.446851\pi$
$354$	−4.71283	−0.250484
$355$	−12.1057	−0.642505
$356$	−60.9231	−3.22892
$357$	23.7728	1.25819
$358$	−66.3121	−3.50470
$359$	2.18370	0.115251	0.0576256	−	0.998338i	$-0.481647\pi$
$359$	2.18370	0.115251	0.0576256	+	0.998338i	$0.481647\pi$
$360$	22.7301	1.19798
$361$	−14.0626	−0.740139
$362$	−41.8771	−2.20101
$363$	−5.07144	−0.266182
$364$	−163.064	−8.54690
$365$	−16.4013	−0.858481
$366$	28.7913	1.50494
$367$	−27.1703	−1.41828	−0.709140	−	0.705068i	$-0.750917\pi$
$367$	−27.1703	−1.41828	−0.709140	+	0.705068i	$0.750917\pi$
$368$	−96.9195	−5.05228
$369$	−8.26949	−0.430493
$370$	1.58483	0.0823913
$371$	22.9158	1.18973
$372$	−47.2106	−2.44776
$373$	−13.0521	−0.675813	−0.337906	−	0.941180i	$-0.609719\pi$
$373$	−13.0521	−0.675813	−0.337906	+	0.941180i	$0.609719\pi$
$374$	−32.3884	−1.67476
$375$	−10.3069	−0.532247
$376$	−95.8750	−4.94438
$377$	33.8298	1.74232
$378$	65.7730	3.38300
$379$	14.4165	0.740525	0.370262	−	0.928927i	$-0.379268\pi$
$379$	14.4165	0.740525	0.370262	+	0.928927i	$0.379268\pi$
$380$	−14.6565	−0.751860
$381$	6.18920	0.317082
$382$	−46.4165	−2.37488
$383$	−9.10153	−0.465066	−0.232533	−	0.972588i	$-0.574701\pi$
$383$	−9.10153	−0.465066	−0.232533	+	0.972588i	$0.574701\pi$
$384$	−29.9088	−1.52628
$385$	14.5451	0.741285
$386$	−22.8206	−1.16154
$387$	18.7845	0.954871
$388$	26.1098	1.32553
$389$	3.92081	0.198793	0.0993964	−	0.995048i	$-0.468309\pi$
$389$	3.92081	0.198793	0.0993964	+	0.995048i	$0.468309\pi$
$390$	20.5080	1.03846
$391$	−34.0077	−1.71984
$392$	−153.906	−7.77344
$393$	0.623747	0.0314639
$394$	−9.49552	−0.478377
$395$	−5.92568	−0.298153
$396$	−26.3026	−1.32176
$397$	13.4456	0.674816	0.337408	−	0.941359i	$-0.390450\pi$
$397$	13.4456	0.674816	0.337408	+	0.941359i	$0.390450\pi$
$398$	31.1420	1.56101
$399$	−10.7180	−0.536571
$400$	−48.9915	−2.44958
$401$	−5.99211	−0.299231	−0.149616	−	0.988744i	$-0.547804\pi$
$401$	−5.99211	−0.299231	−0.149616	+	0.988744i	$0.547804\pi$
$402$	42.7643	2.13289
$403$	55.4664	2.76298
$404$	−26.9425	−1.34044
$405$	1.44394	0.0717500
$406$	72.0520	3.57588
$407$	−1.15015	−0.0570108
$408$	−44.4321	−2.19972
$409$	−26.1382	−1.29245	−0.646226	−	0.763146i	$-0.723654\pi$
$409$	−26.1382	−1.29245	−0.646226	+	0.763146i	$0.723654\pi$
$410$	−13.6281	−0.673046
$411$	−16.5511	−0.816408
$412$	−34.9033	−1.71956
$413$	8.59007	0.422690
$414$	−37.9148	−1.86341
$415$	1.78158	0.0874544
$416$	123.584	6.05922
$417$	21.8902	1.07197
$418$	14.6023	0.714224
$419$	10.8330	0.529227	0.264614	−	0.964354i	$-0.414756\pi$
$419$	10.8330	0.529227	0.264614	+	0.964354i	$0.414756\pi$
$420$	31.8162	1.55247
$421$	−8.53368	−0.415906	−0.207953	−	0.978139i	$-0.566680\pi$
$421$	−8.53368	−0.415906	−0.207953	+	0.978139i	$0.566680\pi$
$422$	−15.6689	−0.762748
$423$	−21.2643	−1.03391
$424$	−42.8302	−2.08002
$425$	−17.1904	−0.833859
$426$	26.3826	1.27824
$427$	−52.4778	−2.53958
$428$	9.64906	0.466405
$429$	−14.8832	−0.718566
$430$	30.9569	1.49288
$431$	31.4354	1.51419	0.757096	−	0.653304i	$-0.226618\pi$
$431$	31.4354	1.51419	0.757096	+	0.653304i	$0.226618\pi$
$432$	−69.6968	−3.35329
$433$	−0.703063	−0.0337871	−0.0168935	−	0.999857i	$-0.505378\pi$
$433$	−0.703063	−0.0337871	−0.0168935	+	0.999857i	$0.505378\pi$
$434$	118.134	5.67063
$435$	−6.60067	−0.316478
$436$	−6.01339	−0.287989
$437$	15.3324	0.733449
$438$	35.7440	1.70792
$439$	−35.4279	−1.69088	−0.845440	−	0.534070i	$-0.820662\pi$
$439$	−35.4279	−1.69088	−0.845440	+	0.534070i	$0.820662\pi$
$440$	−27.1851	−1.29600
$441$	−34.1352	−1.62549
$442$	83.2362	3.95914
$443$	−3.69379	−0.175497	−0.0877487	−	0.996143i	$-0.527967\pi$
$443$	−3.69379	−0.175497	−0.0877487	+	0.996143i	$0.527967\pi$
$444$	−2.51586	−0.119398
$445$	−13.9656	−0.662035
$446$	43.7241	2.07040
$447$	−11.9589	−0.565636
$448$	126.000	5.95294
$449$	−25.2829	−1.19317	−0.596587	−	0.802549i	$-0.703477\pi$
$449$	−25.2829	−1.19317	−0.596587	+	0.802549i	$0.703477\pi$
$450$	−19.1654	−0.903466
$451$	9.89028	0.465715
$452$	32.3012	1.51932
$453$	−7.78992	−0.366002
$454$	−70.7112	−3.31864
$455$	−37.3799	−1.75240
$456$	20.0323	0.938097
$457$	−23.5593	−1.10206	−0.551029	−	0.834486i	$-0.685765\pi$
$457$	−23.5593	−1.10206	−0.551029	+	0.834486i	$0.685765\pi$
$458$	−55.2151	−2.58003
$459$	−24.4556	−1.14149
$460$	−45.5140	−2.12210
$461$	9.57076	0.445755	0.222877	−	0.974846i	$-0.428455\pi$
$461$	9.57076	0.445755	0.222877	+	0.974846i	$0.428455\pi$
$462$	−31.6987	−1.47476
$463$	1.85558	0.0862362	0.0431181	−	0.999070i	$-0.486271\pi$
$463$	1.85558	0.0862362	0.0431181	+	0.999070i	$0.486271\pi$
$464$	−76.3504	−3.54448
$465$	−10.8223	−0.501871
$466$	−27.2103	−1.26050
$467$	−8.10755	−0.375173	−0.187586	−	0.982248i	$-0.560066\pi$
$467$	−8.10755	−0.375173	−0.187586	+	0.982248i	$0.560066\pi$
$468$	67.5961	3.12463
$469$	−77.9464	−3.59923
$470$	−35.0437	−1.61644
$471$	14.3780	0.662503
$472$	−16.0551	−0.738996
$473$	−22.4662	−1.03300
$474$	12.9141	0.593165
$475$	7.75033	0.355610
$476$	129.133	5.91880
$477$	−9.49942	−0.434948
$478$	80.1003	3.66370
$479$	−7.96985	−0.364152	−0.182076	−	0.983284i	$-0.558282\pi$
$479$	−7.96985	−0.364152	−0.182076	+	0.983284i	$0.558282\pi$
$480$	−24.1130	−1.10060
$481$	2.95581	0.134774
$482$	−19.5182	−0.889030
$483$	−33.2835	−1.51445
$484$	−27.5479	−1.25218
$485$	5.98526	0.271777
$486$	−43.5437	−1.97518
$487$	−10.3638	−0.469629	−0.234815	−	0.972040i	$-0.575448\pi$
$487$	−10.3638	−0.469629	−0.234815	+	0.972040i	$0.575448\pi$
$488$	98.0826	4.43999
$489$	5.94682	0.268924
$490$	−56.2549	−2.54134
$491$	30.1818	1.36208	0.681042	−	0.732244i	$-0.261527\pi$
$491$	30.1818	1.36208	0.681042	+	0.732244i	$0.261527\pi$
$492$	21.6342	0.975346
$493$	−26.7903	−1.20657
$494$	−37.5271	−1.68843
$495$	−6.02945	−0.271004
$496$	−125.182	−5.62083
$497$	−48.0875	−2.15702
$498$	−3.88269	−0.173987
$499$	−11.6950	−0.523540	−0.261770	−	0.965130i	$-0.584306\pi$
$499$	−11.6950	−0.523540	−0.261770	+	0.965130i	$0.584306\pi$
$500$	−55.9868	−2.50380
$501$	17.8912	0.799322
$502$	34.6520	1.54659
$503$	2.76414	0.123247	0.0616234	−	0.998099i	$-0.480372\pi$
$503$	2.76414	0.123247	0.0616234	+	0.998099i	$0.480372\pi$
$504$	90.2907	4.02187
$505$	−6.17613	−0.274834
$506$	45.3459	2.01587
$507$	25.4111	1.12855
$508$	33.6195	1.49162
$509$	10.5400	0.467176	0.233588	−	0.972336i	$-0.424953\pi$
$509$	10.5400	0.467176	0.233588	+	0.972336i	$0.424953\pi$
$510$	−16.2405	−0.719144
$511$	−65.1506	−2.88209
$512$	−22.4593	−0.992571
$513$	11.0258	0.486803
$514$	−4.68437	−0.206619
$515$	−8.00101	−0.352567
$516$	−49.1431	−2.16341
$517$	25.4321	1.11850
$518$	6.29540	0.276604
$519$	−17.4384	−0.765461
$520$	69.8641	3.06374
$521$	−16.5444	−0.724825	−0.362413	−	0.932018i	$-0.618047\pi$
$521$	−16.5444	−0.724825	−0.362413	+	0.932018i	$0.618047\pi$
$522$	−29.8682	−1.30729
$523$	−5.04694	−0.220687	−0.110344	−	0.993893i	$-0.535195\pi$
$523$	−5.04694	−0.220687	−0.110344	+	0.993893i	$0.535195\pi$
$524$	3.38817	0.148013
$525$	−16.8244	−0.734276
$526$	−9.68099	−0.422111
$527$	−43.9246	−1.91338
$528$	33.5898	1.46181
$529$	24.6131	1.07013
$530$	−15.6551	−0.680012
$531$	−3.56090	−0.154530
$532$	−58.2197	−2.52415
$533$	−25.4174	−1.10095
$534$	30.4360	1.31709
$535$	2.21189	0.0956284
$536$	145.684	6.29259
$537$	24.1311	1.04133
$538$	52.7127	2.27261
$539$	40.8256	1.75848
$540$	−32.7300	−1.40847
$541$	35.6268	1.53172	0.765858	−	0.643009i	$-0.222314\pi$
$541$	35.6268	1.53172	0.765858	+	0.643009i	$0.222314\pi$
$542$	17.4465	0.749393
$543$	15.2391	0.653974
$544$	−97.8680	−4.19606
$545$	−1.37847	−0.0590473
$546$	81.4637	3.48633
$547$	−0.836477	−0.0357652	−0.0178826	−	0.999840i	$-0.505693\pi$
$547$	−0.836477	−0.0357652	−0.0178826	+	0.999840i	$0.505693\pi$
$548$	−89.9051	−3.84056
$549$	21.7540	0.928436
$550$	22.9218	0.977388
$551$	12.0784	0.514558
$552$	62.2079	2.64775
$553$	−23.5385	−1.00096
$554$	−33.6335	−1.42895
$555$	−0.576721	−0.0244804
$556$	118.907	5.04277
$557$	−32.5206	−1.37794	−0.688971	−	0.724789i	$-0.741937\pi$
$557$	−32.5206	−1.37794	−0.688971	+	0.724789i	$0.741937\pi$
$558$	−48.9710	−2.07311
$559$	57.7368	2.44201
$560$	84.3626	3.56497
$561$	11.7862	0.497613
$562$	−19.7677	−0.833851
$563$	5.95336	0.250904	0.125452	−	0.992100i	$-0.459962\pi$
$563$	5.95336	0.250904	0.125452	+	0.992100i	$0.459962\pi$
$564$	55.6307	2.34247
$565$	7.40452	0.311510
$566$	−17.5887	−0.739309
$567$	5.73575	0.240879
$568$	89.8769	3.77115
$569$	−12.2244	−0.512472	−0.256236	−	0.966614i	$-0.582482\pi$
$569$	−12.2244	−0.512472	−0.256236	+	0.966614i	$0.582482\pi$
$570$	7.32207	0.306688
$571$	18.0505	0.755389	0.377695	−	0.925930i	$-0.376717\pi$
$571$	18.0505	0.755389	0.377695	+	0.925930i	$0.376717\pi$
$572$	−80.8447	−3.38029
$573$	16.8910	0.705633
$574$	−54.1350	−2.25955
$575$	24.0678	1.00370
$576$	−52.2316	−2.17632
$577$	−27.1100	−1.12860	−0.564302	−	0.825568i	$-0.690855\pi$
$577$	−27.1100	−1.12860	−0.564302	+	0.825568i	$0.690855\pi$
$578$	−19.7830	−0.822862
$579$	8.30445	0.345121
$580$	−35.8546	−1.48878
$581$	7.07697	0.293602
$582$	−13.0440	−0.540689
$583$	11.3613	0.470536
$584$	121.768	5.03881
$585$	15.4953	0.640652
$586$	−32.2066	−1.33044
$587$	39.6649	1.63715	0.818574	−	0.574402i	$-0.194765\pi$
$587$	39.6649	1.63715	0.818574	+	0.574402i	$0.194765\pi$
$588$	89.3028	3.68278
$589$	19.8034	0.815987
$590$	−5.86836	−0.241597
$591$	3.45543	0.142137
$592$	−6.67097	−0.274175
$593$	−22.7285	−0.933346	−0.466673	−	0.884430i	$-0.654548\pi$
$593$	−22.7285	−0.933346	−0.466673	+	0.884430i	$0.654548\pi$
$594$	32.6092	1.33797
$595$	29.6016	1.21355
$596$	−64.9602	−2.66087
$597$	−11.3326	−0.463814
$598$	−116.536	−4.76552
$599$	−31.5692	−1.28988	−0.644940	−	0.764233i	$-0.723118\pi$
$599$	−31.5692	−1.28988	−0.644940	+	0.764233i	$0.723118\pi$
$600$	31.4453	1.28375
$601$	−9.66054	−0.394062	−0.197031	−	0.980397i	$-0.563130\pi$
$601$	−9.66054	−0.394062	−0.197031	+	0.980397i	$0.563130\pi$
$602$	122.970	5.01188
$603$	32.3116	1.31583
$604$	−42.3145	−1.72175
$605$	−6.31490	−0.256737
$606$	13.4599	0.546772
$607$	22.8939	0.929233	0.464617	−	0.885512i	$-0.346192\pi$
$607$	22.8939	0.929233	0.464617	+	0.885512i	$0.346192\pi$
$608$	44.1239	1.78946
$609$	−26.2198	−1.06248
$610$	35.8506	1.45155
$611$	−65.3588	−2.64414
$612$	−53.5303	−2.16383
$613$	−21.4250	−0.865349	−0.432675	−	0.901550i	$-0.642430\pi$
$613$	−21.4250	−0.865349	−0.432675	+	0.901550i	$0.642430\pi$
$614$	−44.5883	−1.79944
$615$	4.95930	0.199978
$616$	−107.987	−4.35093
$617$	8.03271	0.323385	0.161692	−	0.986841i	$-0.448305\pi$
$617$	8.03271	0.323385	0.161692	+	0.986841i	$0.448305\pi$
$618$	17.4370	0.701418
$619$	11.3762	0.457250	0.228625	−	0.973515i	$-0.426577\pi$
$619$	11.3762	0.457250	0.228625	+	0.973515i	$0.426577\pi$
$620$	−58.7861	−2.36091
$621$	34.2395	1.37398
$622$	−47.5960	−1.90843
$623$	−55.4756	−2.22258
$624$	−86.3236	−3.45571
$625$	4.60579	0.184232
$626$	−42.6938	−1.70639
$627$	−5.31381	−0.212213
$628$	78.1006	3.11655
$629$	−2.34075	−0.0933318
$630$	33.0025	1.31485
$631$	−25.2057	−1.00342	−0.501711	−	0.865035i	$-0.667296\pi$
$631$	−25.2057	−1.00342	−0.501711	+	0.865035i	$0.667296\pi$
$632$	43.9942	1.75000
$633$	5.70192	0.226631
$634$	35.1488	1.39594
$635$	7.70672	0.305832
$636$	24.8519	0.985441
$637$	−104.919	−4.15705
$638$	35.7222	1.41426
$639$	19.9340	0.788577
$640$	−37.2421	−1.47212
$641$	−37.6847	−1.48845	−0.744227	−	0.667926i	$-0.767182\pi$
$641$	−37.6847	−1.48845	−0.744227	+	0.667926i	$0.767182\pi$
$642$	−4.82048	−0.190249
$643$	45.0596	1.77698	0.888489	−	0.458899i	$-0.151756\pi$
$643$	45.0596	1.77698	0.888489	+	0.458899i	$0.151756\pi$
$644$	−180.795	−7.12431
$645$	−11.2653	−0.443569
$646$	29.7182	1.16925
$647$	41.1255	1.61681	0.808404	−	0.588628i	$-0.200332\pi$
$647$	41.1255	1.61681	0.808404	+	0.588628i	$0.200332\pi$
$648$	−10.7203	−0.421133
$649$	4.25882	0.167173
$650$	−58.9075	−2.31054
$651$	−42.9892	−1.68488
$652$	32.3029	1.26508
$653$	−38.9220	−1.52313	−0.761567	−	0.648086i	$-0.775570\pi$
$653$	−38.9220	−1.52313	−0.761567	+	0.648086i	$0.775570\pi$
$654$	3.00417	0.117472
$655$	0.776683	0.0303475
$656$	57.3645	2.23971
$657$	27.0073	1.05365
$658$	−139.204	−5.42672
$659$	−5.90765	−0.230129	−0.115065	−	0.993358i	$-0.536708\pi$
$659$	−5.90765	−0.230129	−0.115065	+	0.993358i	$0.536708\pi$
$660$	15.7739	0.614000
$661$	−10.6580	−0.414547	−0.207273	−	0.978283i	$-0.566459\pi$
$661$	−10.6580	−0.414547	−0.207273	+	0.978283i	$0.566459\pi$
$662$	−23.1821	−0.900997
$663$	−30.2897	−1.17636
$664$	−13.2271	−0.513310
$665$	−13.3459	−0.517533
$666$	−2.60967	−0.101123
$667$	37.5082	1.45232
$668$	97.1845	3.76018
$669$	−15.9112	−0.615164
$670$	53.2496	2.05721
$671$	−26.0177	−1.00440
$672$	−95.7841	−3.69495
$673$	20.5007	0.790245	0.395122	−	0.918629i	$-0.370702\pi$
$673$	20.5007	0.790245	0.395122	+	0.918629i	$0.370702\pi$
$674$	−43.1785	−1.66317
$675$	17.3076	0.666171
$676$	138.032	5.30892
$677$	23.4608	0.901673	0.450836	−	0.892607i	$-0.351126\pi$
$677$	23.4608	0.901673	0.450836	+	0.892607i	$0.351126\pi$
$678$	−16.1370	−0.619738
$679$	23.7752	0.912408
$680$	−55.3263	−2.12167
$681$	25.7319	0.986049
$682$	58.5691	2.24273
$683$	−43.0468	−1.64714	−0.823569	−	0.567215i	$-0.808021\pi$
$683$	−43.0468	−1.64714	−0.823569	+	0.567215i	$0.808021\pi$
$684$	24.1342	0.922794
$685$	−20.6093	−0.787441
$686$	−130.675	−4.98920
$687$	20.0929	0.766590
$688$	−130.306	−4.96787
$689$	−29.1978	−1.11235
$690$	22.7379	0.865616
$691$	−44.7416	−1.70205	−0.851026	−	0.525123i	$-0.824019\pi$
$691$	−44.7416	−1.70205	−0.851026	+	0.525123i	$0.824019\pi$
$692$	−94.7246	−3.60089
$693$	−23.9508	−0.909814
$694$	−37.1931	−1.41183
$695$	27.2574	1.03393
$696$	49.0056	1.85755
$697$	20.1284	0.762417
$698$	−59.5639	−2.25453
$699$	9.90188	0.374523
$700$	−91.3894	−3.45419
$701$	−37.2303	−1.40617	−0.703084	−	0.711106i	$-0.748194\pi$
$701$	−37.2303	−1.40617	−0.703084	+	0.711106i	$0.748194\pi$
$702$	−83.8036	−3.16296
$703$	1.05533	0.0398025
$704$	62.4688	2.35438
$705$	12.7524	0.480284
$706$	−16.9475	−0.637826
$707$	−24.5334	−0.922673
$708$	9.31584	0.350111
$709$	−15.2594	−0.573078	−0.286539	−	0.958069i	$-0.592505\pi$
$709$	−15.2594	−0.573078	−0.286539	+	0.958069i	$0.592505\pi$
$710$	32.8513	1.23289
$711$	9.75758	0.365938
$712$	103.686	3.88578
$713$	61.4974	2.30309
$714$	−64.5122	−2.41431
$715$	−18.5323	−0.693070
$716$	131.079	4.89865
$717$	−29.1486	−1.08857
$718$	−5.92590	−0.221153
$719$	−32.6056	−1.21598	−0.607992	−	0.793943i	$-0.708025\pi$
$719$	−32.6056	−1.21598	−0.607992	+	0.793943i	$0.708025\pi$
$720$	−34.9713	−1.30330
$721$	−31.7824	−1.18364
$722$	38.1618	1.42023
$723$	7.10270	0.264152
$724$	82.7784	3.07643
$725$	18.9599	0.704153
$726$	13.7624	0.510769
$727$	9.48099	0.351630	0.175815	−	0.984423i	$-0.443744\pi$
$727$	9.48099	0.351630	0.175815	+	0.984423i	$0.443744\pi$
$728$	277.521	10.2856
$729$	12.3228	0.456399
$730$	44.5080	1.64732
$731$	−45.7226	−1.69111
$732$	−56.9116	−2.10351
$733$	48.6187	1.79577	0.897886	−	0.440228i	$-0.145102\pi$
$733$	48.6187	1.79577	0.897886	+	0.440228i	$0.145102\pi$
$734$	73.7321	2.72150
$735$	20.4712	0.755092
$736$	137.022	5.05069
$737$	−38.6445	−1.42349
$738$	22.4409	0.826061
$739$	−15.2079	−0.559433	−0.279716	−	0.960083i	$-0.590240\pi$
$739$	−15.2079	−0.559433	−0.279716	+	0.960083i	$0.590240\pi$
$740$	−3.13272	−0.115161
$741$	13.6562	0.501672
$742$	−62.1865	−2.28294
$743$	26.3997	0.968511	0.484255	−	0.874927i	$-0.339091\pi$
$743$	26.3997	0.968511	0.484255	+	0.874927i	$0.339091\pi$
$744$	80.3482	2.94571
$745$	−14.8911	−0.545567
$746$	35.4195	1.29680
$747$	−2.93366	−0.107337
$748$	64.0220	2.34088
$749$	8.78628	0.321044
$750$	27.9699	1.02132
$751$	−22.3026	−0.813834	−0.406917	−	0.913465i	$-0.633396\pi$
$751$	−22.3026	−0.813834	−0.406917	+	0.913465i	$0.633396\pi$
$752$	147.508	5.37907
$753$	−12.6099	−0.459530
$754$	−91.8039	−3.34330
$755$	−9.69991	−0.353016
$756$	−130.013	−4.72853
$757$	7.26085	0.263900	0.131950	−	0.991256i	$-0.457876\pi$
$757$	7.26085	0.263900	0.131950	+	0.991256i	$0.457876\pi$
$758$	−39.1220	−1.42097
$759$	−16.5014	−0.598964
$760$	24.9439	0.904812
$761$	9.18742	0.333044	0.166522	−	0.986038i	$-0.446746\pi$
$761$	9.18742	0.333044	0.166522	+	0.986038i	$0.446746\pi$
$762$	−16.7956	−0.608441
$763$	−5.47570	−0.198233
$764$	91.7514	3.31945
$765$	−12.2709	−0.443657
$766$	24.6988	0.892404
$767$	−10.9449	−0.395198
$768$	30.2158	1.09032
$769$	−42.0254	−1.51548	−0.757738	−	0.652559i	$-0.773695\pi$
$769$	−42.0254	−1.51548	−0.757738	+	0.652559i	$0.773695\pi$
$770$	−39.4709	−1.42243
$771$	1.70465	0.0613915
$772$	45.1094	1.62352
$773$	2.41306	0.0867919	0.0433959	−	0.999058i	$-0.486182\pi$
$773$	2.41306	0.0867919	0.0433959	+	0.999058i	$0.486182\pi$
$774$	−50.9755	−1.83228
$775$	31.0861	1.11665
$776$	−44.4365	−1.59518
$777$	−2.29091	−0.0821858
$778$	−10.6399	−0.381458
$779$	−9.07491	−0.325142
$780$	−40.5381	−1.45150
$781$	−23.8410	−0.853098
$782$	92.2866	3.30016
$783$	26.9729	0.963933
$784$	236.792	8.45685
$785$	17.9033	0.638996
$786$	−1.69266	−0.0603752
$787$	27.3293	0.974185	0.487093	−	0.873350i	$-0.338057\pi$
$787$	27.3293	0.974185	0.487093	+	0.873350i	$0.338057\pi$
$788$	18.7698	0.668645
$789$	3.52292	0.125419
$790$	16.0805	0.572119
$791$	29.4129	1.04580
$792$	44.7647	1.59064
$793$	66.8638	2.37440
$794$	−36.4873	−1.29489
$795$	5.69689	0.202048
$796$	−61.5583	−2.18188
$797$	14.7500	0.522470	0.261235	−	0.965275i	$-0.415870\pi$
$797$	14.7500	0.522470	0.261235	+	0.965275i	$0.415870\pi$
$798$	29.0854	1.02961
$799$	51.7585	1.83108
$800$	69.2627	2.44881
$801$	22.9967	0.812547
$802$	16.2608	0.574188
$803$	−32.3006	−1.13986
$804$	−84.5319	−2.98121
$805$	−41.4443	−1.46072
$806$	−150.519	−5.30180
$807$	−19.1822	−0.675247
$808$	45.8536	1.61313
$809$	22.1939	0.780297	0.390149	−	0.920752i	$-0.372424\pi$
$809$	22.1939	0.780297	0.390149	+	0.920752i	$0.372424\pi$
$810$	−3.91842	−0.137679
$811$	28.4065	0.997488	0.498744	−	0.866749i	$-0.333795\pi$
$811$	28.4065	0.997488	0.498744	+	0.866749i	$0.333795\pi$
$812$	−142.425	−4.99813
$813$	−6.34882	−0.222663
$814$	3.12116	0.109397
$815$	7.40491	0.259383
$816$	68.3608	2.39311
$817$	20.6141	0.721195
$818$	70.9313	2.48005
$819$	61.5519	2.15080
$820$	26.9387	0.940740
$821$	−50.0471	−1.74665	−0.873327	−	0.487134i	$-0.838042\pi$
$821$	−50.0471	−1.74665	−0.873327	+	0.487134i	$0.838042\pi$
$822$	44.9148	1.56658
$823$	−11.4825	−0.400256	−0.200128	−	0.979770i	$-0.564136\pi$
$823$	−11.4825	−0.400256	−0.200128	+	0.979770i	$0.564136\pi$
$824$	59.4022	2.06937
$825$	−8.34126	−0.290405
$826$	−23.3109	−0.811089
$827$	−12.5044	−0.434821	−0.217411	−	0.976080i	$-0.569761\pi$
$827$	−12.5044	−0.434821	−0.217411	+	0.976080i	$0.569761\pi$
$828$	74.9460	2.60455
$829$	−36.3271	−1.26169	−0.630845	−	0.775908i	$-0.717292\pi$
$829$	−36.3271	−1.26169	−0.630845	+	0.775908i	$0.717292\pi$
$830$	−4.83468	−0.167814
$831$	12.2393	0.424575
$832$	−160.541	−5.56576
$833$	83.0869	2.87879
$834$	−59.4034	−2.05697
$835$	22.2780	0.770961
$836$	−28.8644	−0.998296
$837$	44.2240	1.52860
$838$	−29.3975	−1.01552
$839$	−0.672749	−0.0232259	−0.0116129	−	0.999933i	$-0.503697\pi$
$839$	−0.672749	−0.0232259	−0.0116129	+	0.999933i	$0.503697\pi$
$840$	−54.1482	−1.86829
$841$	0.547880	0.0188924
$842$	23.1578	0.798071
$843$	7.19350	0.247757
$844$	30.9726	1.06612
$845$	31.6416	1.08850
$846$	57.7050	1.98394
$847$	−25.0846	−0.861919
$848$	65.8963	2.26289
$849$	6.40056	0.219667
$850$	46.6497	1.60007
$851$	3.27721	0.112341
$852$	−52.1503	−1.78664
$853$	57.4362	1.96658	0.983289	−	0.182050i	$-0.0582732\pi$
$853$	57.4362	1.96658	0.983289	+	0.182050i	$0.0582732\pi$
$854$	142.409	4.87313
$855$	5.53237	0.189203
$856$	−16.4218	−0.561286
$857$	19.5926	0.669270	0.334635	−	0.942348i	$-0.391387\pi$
$857$	19.5926	0.669270	0.334635	+	0.942348i	$0.391387\pi$
$858$	40.3884	1.37884
$859$	−51.8707	−1.76981	−0.884903	−	0.465775i	$-0.845776\pi$
$859$	−51.8707	−1.76981	−0.884903	+	0.465775i	$0.845776\pi$
$860$	−61.1925	−2.08665
$861$	19.6998	0.671367
$862$	−85.3063	−2.90554
$863$	17.0557	0.580582	0.290291	−	0.956938i	$-0.406248\pi$
$863$	17.0557	0.580582	0.290291	+	0.956938i	$0.406248\pi$
$864$	98.5352	3.35224
$865$	−21.7141	−0.738301
$866$	1.90790	0.0648331
$867$	7.19904	0.244492
$868$	−233.516	−7.92604
$869$	−11.6700	−0.395879
$870$	17.9122	0.607282
$871$	99.3141	3.36513
$872$	10.2342	0.346575
$873$	−9.85568	−0.333564
$874$	−41.6075	−1.40740
$875$	−50.9807	−1.72346
$876$	−70.6551	−2.38721
$877$	29.0922	0.982373	0.491186	−	0.871054i	$-0.336563\pi$
$877$	29.0922	0.982373	0.491186	+	0.871054i	$0.336563\pi$
$878$	96.1406	3.24459
$879$	11.7200	0.395307
$880$	41.8256	1.40994
$881$	16.0523	0.540815	0.270407	−	0.962746i	$-0.412842\pi$
$881$	16.0523	0.540815	0.270407	+	0.962746i	$0.412842\pi$
$882$	92.6326	3.11910
$883$	−46.1994	−1.55473	−0.777367	−	0.629047i	$-0.783445\pi$
$883$	−46.1994	−1.55473	−0.777367	+	0.629047i	$0.783445\pi$
$884$	−164.533	−5.53383
$885$	2.13551	0.0717842
$886$	10.0238	0.336757
$887$	0.992227	0.0333157	0.0166579	−	0.999861i	$-0.494697\pi$
$887$	0.992227	0.0333157	0.0166579	+	0.999861i	$0.494697\pi$
$888$	4.28177	0.143687
$889$	30.6134	1.02674
$890$	37.8985	1.27036
$891$	2.84369	0.0952674
$892$	−86.4292	−2.89386
$893$	−23.3354	−0.780889
$894$	32.4528	1.08539
$895$	30.0477	1.00438
$896$	−147.937	−4.94222
$897$	42.4077	1.41595
$898$	68.6101	2.28955
$899$	48.4458	1.61576
$900$	37.8842	1.26281
$901$	23.1221	0.770308
$902$	−26.8392	−0.893649
$903$	−44.7489	−1.48915
$904$	−54.9736	−1.82839
$905$	18.9756	0.630770
$906$	21.1395	0.702312
$907$	−44.2353	−1.46881	−0.734404	−	0.678713i	$-0.762538\pi$
$907$	−44.2353	−1.46881	−0.734404	+	0.678713i	$0.762538\pi$
$908$	139.775	4.63858
$909$	10.1700	0.337317
$910$	101.438	3.36263
$911$	−43.2497	−1.43293	−0.716463	−	0.697625i	$-0.754240\pi$
$911$	−43.2497	−1.43293	−0.716463	+	0.697625i	$0.754240\pi$
$912$	−30.8206	−1.02057
$913$	3.50865	0.116119
$914$	63.9329	2.11471
$915$	−13.0461	−0.431290
$916$	109.144	3.60620
$917$	3.08521	0.101883
$918$	66.3651	2.19038
$919$	−29.6854	−0.979231	−0.489615	−	0.871938i	$-0.662863\pi$
$919$	−29.6854	−0.979231	−0.489615	+	0.871938i	$0.662863\pi$
$920$	77.4606	2.55380
$921$	16.2258	0.534657
$922$	−25.9722	−0.855347
$923$	61.2698	2.01672
$924$	62.6587	2.06132
$925$	1.65658	0.0544682
$926$	−5.03549	−0.165476
$927$	13.1749	0.432722
$928$	107.942	3.54337
$929$	10.2860	0.337472	0.168736	−	0.985661i	$-0.446032\pi$
$929$	10.2860	0.337472	0.168736	+	0.985661i	$0.446032\pi$
$930$	29.3684	0.963027
$931$	−37.4598	−1.22770
$932$	53.7866	1.76184
$933$	17.3202	0.567039
$934$	22.0014	0.719909
$935$	14.6760	0.479957
$936$	−115.042	−3.76028
$937$	−25.9748	−0.848560	−0.424280	−	0.905531i	$-0.639473\pi$
$937$	−25.9748	−0.848560	−0.424280	+	0.905531i	$0.639473\pi$
$938$	211.523	6.90647
$939$	15.5363	0.507008
$940$	69.2707	2.25936
$941$	−7.36967	−0.240244	−0.120122	−	0.992759i	$-0.538329\pi$
$941$	−7.36967	−0.240244	−0.120122	+	0.992759i	$0.538329\pi$
$942$	−39.0175	−1.27126
$943$	−28.1811	−0.917703
$944$	24.7015	0.803966
$945$	−29.8034	−0.969505
$946$	60.9666	1.98219
$947$	−19.2184	−0.624513	−0.312257	−	0.949998i	$-0.601085\pi$
$947$	−19.2184	−0.624513	−0.312257	+	0.949998i	$0.601085\pi$
$948$	−25.5273	−0.829088
$949$	83.0106	2.69464
$950$	−21.0321	−0.682370
$951$	−12.7907	−0.414766
$952$	−219.772	−7.12286
$953$	18.3623	0.594812	0.297406	−	0.954751i	$-0.403878\pi$
$953$	18.3623	0.594812	0.297406	+	0.954751i	$0.403878\pi$
$954$	25.7785	0.834611
$955$	21.0325	0.680596
$956$	−158.334	−5.12089
$957$	−12.9994	−0.420210
$958$	21.6278	0.698762
$959$	−81.8662	−2.64360
$960$	31.3238	1.01097
$961$	48.4304	1.56227
$962$	−8.02119	−0.258613
$963$	−3.64223	−0.117369
$964$	38.5815	1.24263
$965$	10.3406	0.332876
$966$	90.3215	2.90605
$967$	−2.74833	−0.0883804	−0.0441902	−	0.999023i	$-0.514071\pi$
$967$	−2.74833	−0.0883804	−0.0441902	+	0.999023i	$0.514071\pi$
$968$	46.8839	1.50691
$969$	−10.8145	−0.347412
$970$	−16.2422	−0.521505
$971$	−40.9324	−1.31358	−0.656792	−	0.754072i	$-0.728087\pi$
$971$	−40.9324	−1.31358	−0.656792	+	0.754072i	$0.728087\pi$
$972$	86.0726	2.76078
$973$	108.275	3.47112
$974$	28.1243	0.901160
$975$	21.4365	0.686518
$976$	−150.905	−4.83034
$977$	−25.6759	−0.821446	−0.410723	−	0.911760i	$-0.634724\pi$
$977$	−25.6759	−0.821446	−0.410723	+	0.911760i	$0.634724\pi$
$978$	−16.1379	−0.516032
$979$	−27.5039	−0.879029
$980$	111.199	3.55211
$981$	2.26987	0.0724715
$982$	−81.9042	−2.61367
$983$	2.17519	0.0693779	0.0346890	−	0.999398i	$-0.488956\pi$
$983$	2.17519	0.0693779	0.0346890	+	0.999398i	$0.488956\pi$
$984$	−36.8195	−1.17376
$985$	4.30266	0.137094
$986$	72.7007	2.31526
$987$	50.6564	1.61241
$988$	74.1797	2.35997
$989$	64.0147	2.03555
$990$	16.3621	0.520022
$991$	−22.1646	−0.704081	−0.352040	−	0.935985i	$-0.614512\pi$
$991$	−22.1646	−0.704081	−0.352040	+	0.935985i	$0.614512\pi$
$992$	176.978	5.61907
$993$	8.43599	0.267708
$994$	130.495	4.13904
$995$	−14.1113	−0.447357
$996$	7.67489	0.243188
$997$	11.6103	0.367702	0.183851	−	0.982954i	$-0.441144\pi$
$997$	11.6103	0.367702	0.183851	+	0.982954i	$0.441144\pi$
$998$	31.7367	1.00461
$999$	2.35670	0.0745628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.a.1.1	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.a.1.1	✓	149	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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71370 q^{2} +0.987518 q^{3} +5.36416 q^{4} +1.22965 q^{5} -2.67983 q^{6} +4.88451 q^{7} -9.12930 q^{8} -2.02481 q^{9} +O(q^{10})\)	\(q-2.71370 q^{2} +0.987518 q^{3} +5.36416 q^{4} +1.22965 q^{5} -2.67983 q^{6} +4.88451 q^{7} -9.12930 q^{8} -2.02481 q^{9} -3.33689 q^{10} +2.42166 q^{11} +5.29720 q^{12} -6.22353 q^{13} -13.2551 q^{14} +1.21430 q^{15} +14.0459 q^{16} +4.92849 q^{17} +5.49472 q^{18} -2.22202 q^{19} +6.59601 q^{20} +4.82355 q^{21} -6.57166 q^{22} -6.90022 q^{23} -9.01535 q^{24} -3.48797 q^{25} +16.8888 q^{26} -4.96209 q^{27} +26.2013 q^{28} -5.43580 q^{29} -3.29524 q^{30} -8.91237 q^{31} -19.8576 q^{32} +2.39144 q^{33} -13.3744 q^{34} +6.00622 q^{35} -10.8614 q^{36} -0.474942 q^{37} +6.02988 q^{38} -6.14584 q^{39} -11.2258 q^{40} +4.08409 q^{41} -13.0896 q^{42} -9.27719 q^{43} +12.9902 q^{44} -2.48980 q^{45} +18.7251 q^{46} +10.5019 q^{47} +13.8705 q^{48} +16.8585 q^{49} +9.46530 q^{50} +4.86697 q^{51} -33.3840 q^{52} +4.69151 q^{53} +13.4656 q^{54} +2.97779 q^{55} -44.5922 q^{56} -2.19428 q^{57} +14.7511 q^{58} +1.75863 q^{59} +6.51368 q^{60} -10.7437 q^{61} +24.1855 q^{62} -9.89021 q^{63} +25.7958 q^{64} -7.65273 q^{65} -6.48964 q^{66} -15.9579 q^{67} +26.4372 q^{68} -6.81409 q^{69} -16.2991 q^{70} -9.84488 q^{71} +18.4851 q^{72} -13.3382 q^{73} +1.28885 q^{74} -3.44443 q^{75} -11.9192 q^{76} +11.8287 q^{77} +16.6780 q^{78} -4.81901 q^{79} +17.2714 q^{80} +1.17427 q^{81} -11.0830 q^{82} +1.44886 q^{83} +25.8743 q^{84} +6.06030 q^{85} +25.1755 q^{86} -5.36795 q^{87} -22.1081 q^{88} -11.3574 q^{89} +6.75656 q^{90} -30.3989 q^{91} -37.0139 q^{92} -8.80113 q^{93} -28.4990 q^{94} -2.73229 q^{95} -19.6097 q^{96} +4.86746 q^{97} -45.7488 q^{98} -4.90340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9	\( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 149 * q - 6 * q^2 - 28 * q^3 + 116 * q^4 - 19 * q^5 - 31 * q^6 - 47 * q^7 - 15 * q^8 + 115 * q^9 - 48 * q^10 - 31 * q^11 - 61 * q^12 - 54 * q^13 - 44 * q^14 - 65 * q^15 + 58 * q^16 - 26 * q^17 - 23 * q^18 - 86 * q^19 - 52 * q^20 - 30 * q^21 - 56 * q^22 - 63 * q^23 - 90 * q^24 + 92 * q^25 - 38 * q^26 - 103 * q^27 - 77 * q^28 - 51 * q^29 - 22 * q^30 - 256 * q^31 - 21 * q^32 - 36 * q^33 - 124 * q^34 - 50 * q^35 + 45 * q^36 - 42 * q^37 - 14 * q^38 - 119 * q^39 - 131 * q^40 - 55 * q^41 - 5 * q^42 - 55 * q^43 - 54 * q^44 - 68 * q^45 - 59 * q^46 - 82 * q^47 - 89 * q^48 + 30 * q^49 + 13 * q^50 - 83 * q^51 - 126 * q^52 - 23 * q^53 - 83 * q^54 - 244 * q^55 - 94 * q^56 - 14 * q^57 - 60 * q^58 - 93 * q^59 - 70 * q^60 - 139 * q^61 - 10 * q^62 - 120 * q^63 - 45 * q^64 - 37 * q^65 - 28 * q^66 - 110 * q^67 - 27 * q^68 - 79 * q^69 - 78 * q^70 - 123 * q^71 - 74 * q^73 - 25 * q^74 - 146 * q^75 - 192 * q^76 - q^77 + 26 * q^78 - 273 * q^79 - 51 * q^80 + 41 * q^81 - 120 * q^82 - 27 * q^83 - 14 * q^84 - 71 * q^85 + 3 * q^86 - 98 * q^87 - 143 * q^88 - 70 * q^89 - 24 * q^90 - 256 * q^91 - 47 * q^92 + 16 * q^93 - 151 * q^94 - 83 * q^95 - 137 * q^96 - 108 * q^97 + 17 * q^98 - 131 * q^99

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