LMFDB - Embedded newform 4031.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22708 q^{2} +1.27662 q^{3} +2.95990 q^{4} +0.197788 q^{5} -2.84313 q^{6} -3.89763 q^{7} -2.13778 q^{8} -1.37025 q^{9} +O(q^{10})$	\(q-2.22708 q^{2} +1.27662 q^{3} +2.95990 q^{4} +0.197788 q^{5} -2.84313 q^{6} -3.89763 q^{7} -2.13778 q^{8} -1.37025 q^{9} -0.440491 q^{10} -6.01342 q^{11} +3.77866 q^{12} -1.84502 q^{13} +8.68035 q^{14} +0.252500 q^{15} -1.15879 q^{16} -2.02964 q^{17} +3.05166 q^{18} -3.74689 q^{19} +0.585434 q^{20} -4.97578 q^{21} +13.3924 q^{22} +9.19269 q^{23} -2.72912 q^{24} -4.96088 q^{25} +4.10902 q^{26} -5.57913 q^{27} -11.5366 q^{28} +1.00000 q^{29} -0.562339 q^{30} -10.5604 q^{31} +6.85628 q^{32} -7.67684 q^{33} +4.52017 q^{34} -0.770906 q^{35} -4.05580 q^{36} +9.29928 q^{37} +8.34465 q^{38} -2.35539 q^{39} -0.422827 q^{40} +4.47505 q^{41} +11.0815 q^{42} -5.94938 q^{43} -17.7991 q^{44} -0.271019 q^{45} -20.4729 q^{46} -5.60197 q^{47} -1.47933 q^{48} +8.19153 q^{49} +11.0483 q^{50} -2.59107 q^{51} -5.46108 q^{52} +0.649739 q^{53} +12.4252 q^{54} -1.18938 q^{55} +8.33227 q^{56} -4.78335 q^{57} -2.22708 q^{58} -10.3232 q^{59} +0.747375 q^{60} -0.0261499 q^{61} +23.5190 q^{62} +5.34072 q^{63} -12.9519 q^{64} -0.364924 q^{65} +17.0970 q^{66} -9.09858 q^{67} -6.00753 q^{68} +11.7356 q^{69} +1.71687 q^{70} -14.3940 q^{71} +2.92929 q^{72} +11.9439 q^{73} -20.7103 q^{74} -6.33315 q^{75} -11.0904 q^{76} +23.4381 q^{77} +5.24564 q^{78} +8.70138 q^{79} -0.229195 q^{80} -3.01168 q^{81} -9.96631 q^{82} -11.6590 q^{83} -14.7278 q^{84} -0.401439 q^{85} +13.2498 q^{86} +1.27662 q^{87} +12.8554 q^{88} +10.7770 q^{89} +0.603582 q^{90} +7.19121 q^{91} +27.2095 q^{92} -13.4816 q^{93} +12.4761 q^{94} -0.741092 q^{95} +8.75285 q^{96} +7.81069 q^{97} -18.2432 q^{98} +8.23988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) $ 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * 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 $

$2$	−2.22708	−1.57479	−0.787393	−	0.616452i	$-0.788570\pi$
$2$	−2.22708	−1.57479	−0.787393	+	0.616452i	$0.788570\pi$
$3$	1.27662	0.737055	0.368528	−	0.929617i	$-0.379862\pi$
$3$	1.27662	0.737055	0.368528	+	0.929617i	$0.379862\pi$
$4$	2.95990	1.47995
$5$	0.197788	0.0884536	0.0442268	−	0.999022i	$-0.485918\pi$
$5$	0.197788	0.0884536	0.0442268	+	0.999022i	$0.485918\pi$
$6$	−2.84313	−1.16070
$7$	−3.89763	−1.47317	−0.736583	−	0.676347i	$-0.763562\pi$
$7$	−3.89763	−1.47317	−0.736583	+	0.676347i	$0.763562\pi$
$8$	−2.13778	−0.755819
$9$	−1.37025	−0.456749
$10$	−0.440491	−0.139295
$11$	−6.01342	−1.81312	−0.906558	−	0.422082i	$-0.861299\pi$
$11$	−6.01342	−1.81312	−0.906558	+	0.422082i	$0.861299\pi$
$12$	3.77866	1.09081
$13$	−1.84502	−0.511717	−0.255858	−	0.966714i	$-0.582358\pi$
$13$	−1.84502	−0.511717	−0.255858	+	0.966714i	$0.582358\pi$
$14$	8.68035	2.31992
$15$	0.252500	0.0651952
$16$	−1.15879	−0.289698
$17$	−2.02964	−0.492260	−0.246130	−	0.969237i	$-0.579159\pi$
$17$	−2.02964	−0.492260	−0.246130	+	0.969237i	$0.579159\pi$
$18$	3.05166	0.719282
$19$	−3.74689	−0.859597	−0.429798	−	0.902925i	$-0.641415\pi$
$19$	−3.74689	−0.859597	−0.429798	+	0.902925i	$0.641415\pi$
$20$	0.585434	0.130907
$21$	−4.97578	−1.08581
$22$	13.3924	2.85527
$23$	9.19269	1.91681	0.958405	−	0.285413i	$-0.0921308\pi$
$23$	9.19269	1.91681	0.958405	+	0.285413i	$0.0921308\pi$
$24$	−2.72912	−0.557080
$25$	−4.96088	−0.992176
$26$	4.10902	0.805844
$27$	−5.57913	−1.07370
$28$	−11.5366	−2.18021
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.562339	−0.102668
$31$	−10.5604	−1.89671	−0.948355	−	0.317212i	$-0.897253\pi$
$31$	−10.5604	−1.89671	−0.948355	+	0.317212i	$0.897253\pi$
$32$	6.85628	1.21203
$33$	−7.67684	−1.33637
$34$	4.52017	0.775203
$35$	−0.770906	−0.130307
$36$	−4.05580	−0.675966
$37$	9.29928	1.52879	0.764396	−	0.644747i	$-0.223037\pi$
$37$	9.29928	1.52879	0.764396	+	0.644747i	$0.223037\pi$
$38$	8.34465	1.35368
$39$	−2.35539	−0.377164
$40$	−0.422827	−0.0668549
$41$	4.47505	0.698885	0.349443	−	0.936958i	$-0.386371\pi$
$41$	4.47505	0.698885	0.349443	+	0.936958i	$0.386371\pi$
$42$	11.0815	1.70991
$43$	−5.94938	−0.907272	−0.453636	−	0.891187i	$-0.649873\pi$
$43$	−5.94938	−0.907272	−0.453636	+	0.891187i	$0.649873\pi$
$44$	−17.7991	−2.68332
$45$	−0.271019	−0.0404011
$46$	−20.4729	−3.01856
$47$	−5.60197	−0.817132	−0.408566	−	0.912729i	$-0.633971\pi$
$47$	−5.60197	−0.817132	−0.408566	+	0.912729i	$0.633971\pi$
$48$	−1.47933	−0.213523
$49$	8.19153	1.17022
$50$	11.0483	1.56246
$51$	−2.59107	−0.362823
$52$	−5.46108	−0.757315
$53$	0.649739	0.0892485	0.0446242	−	0.999004i	$-0.485791\pi$
$53$	0.649739	0.0892485	0.0446242	+	0.999004i	$0.485791\pi$
$54$	12.4252	1.69086
$55$	−1.18938	−0.160377
$56$	8.33227	1.11345
$57$	−4.78335	−0.633570
$58$	−2.22708	−0.292430
$59$	−10.3232	−1.34397	−0.671985	−	0.740565i	$-0.734558\pi$
$59$	−10.3232	−1.34397	−0.671985	+	0.740565i	$0.734558\pi$
$60$	0.747375	0.0964857
$61$	−0.0261499	−0.00334815	−0.00167408	−	0.999999i	$-0.500533\pi$
$61$	−0.0261499	−0.00334815	−0.00167408	+	0.999999i	$0.500533\pi$
$62$	23.5190	2.98691
$63$	5.34072	0.672868
$64$	−12.9519	−1.61899
$65$	−0.364924	−0.0452632
$66$	17.0970	2.10449
$67$	−9.09858	−1.11157	−0.555784	−	0.831327i	$-0.687582\pi$
$67$	−9.09858	−1.11157	−0.555784	+	0.831327i	$0.687582\pi$
$68$	−6.00753	−0.728520
$69$	11.7356	1.41279
$70$	1.71687	0.205205
$71$	−14.3940	−1.70826	−0.854128	−	0.520063i	$-0.825909\pi$
$71$	−14.3940	−1.70826	−0.854128	+	0.520063i	$0.825909\pi$
$72$	2.92929	0.345220
$73$	11.9439	1.39793	0.698966	−	0.715155i	$-0.253644\pi$
$73$	11.9439	1.39793	0.698966	+	0.715155i	$0.253644\pi$
$74$	−20.7103	−2.40752
$75$	−6.33315	−0.731289
$76$	−11.0904	−1.27216
$77$	23.4381	2.67102
$78$	5.24564	0.593952
$79$	8.70138	0.978982	0.489491	−	0.872008i	$-0.337183\pi$
$79$	8.70138	0.978982	0.489491	+	0.872008i	$0.337183\pi$
$80$	−0.229195	−0.0256248
$81$	−3.01168	−0.334631
$82$	−9.96631	−1.10059
$83$	−11.6590	−1.27974	−0.639872	−	0.768481i	$-0.721013\pi$
$83$	−11.6590	−1.27974	−0.639872	+	0.768481i	$0.721013\pi$
$84$	−14.7278	−1.60694
$85$	−0.401439	−0.0435421
$86$	13.2498	1.42876
$87$	1.27662	0.136868
$88$	12.8554	1.37039
$89$	10.7770	1.14236	0.571180	−	0.820825i	$-0.306486\pi$
$89$	10.7770	1.14236	0.571180	+	0.820825i	$0.306486\pi$
$90$	0.603582	0.0636231
$91$	7.19121	0.753844
$92$	27.2095	2.83678
$93$	−13.4816	−1.39798
$94$	12.4761	1.28681
$95$	−0.741092	−0.0760344
$96$	8.75285	0.893334
$97$	7.81069	0.793055	0.396528	−	0.918023i	$-0.370215\pi$
$97$	7.81069	0.793055	0.396528	+	0.918023i	$0.370215\pi$
$98$	−18.2432	−1.84284
$99$	8.23988	0.828139
$100$	−14.6837	−1.46837
$101$	1.58154	0.157369	0.0786845	−	0.996900i	$-0.474928\pi$
$101$	1.58154	0.157369	0.0786845	+	0.996900i	$0.474928\pi$
$102$	5.77053	0.571368
$103$	18.8209	1.85447	0.927237	−	0.374474i	$-0.122177\pi$
$103$	18.8209	1.85447	0.927237	+	0.374474i	$0.122177\pi$
$104$	3.94425	0.386765
$105$	−0.984152	−0.0960434
$106$	−1.44702	−0.140547
$107$	−6.93052	−0.669999	−0.334999	−	0.942218i	$-0.608736\pi$
$107$	−6.93052	−0.669999	−0.334999	+	0.942218i	$0.608736\pi$
$108$	−16.5137	−1.58903
$109$	9.94959	0.952998	0.476499	−	0.879175i	$-0.341906\pi$
$109$	9.94959	0.952998	0.476499	+	0.879175i	$0.341906\pi$
$110$	2.64886	0.252559
$111$	11.8716	1.12680
$112$	4.51654	0.426773
$113$	−11.6270	−1.09378	−0.546890	−	0.837205i	$-0.684188\pi$
$113$	−11.6270	−1.09378	−0.546890	+	0.837205i	$0.684188\pi$
$114$	10.6529	0.997737
$115$	1.81821	0.169549
$116$	2.95990	0.274820
$117$	2.52814	0.233726
$118$	22.9907	2.11646
$119$	7.91078	0.725180
$120$	−0.539789	−0.0492758
$121$	25.1613	2.28739
$122$	0.0582381	0.00527263
$123$	5.71293	0.515117
$124$	−31.2578	−2.80704
$125$	−1.97015	−0.176215
$126$	−11.8942	−1.05962
$127$	17.5969	1.56147	0.780736	−	0.624861i	$-0.214845\pi$
$127$	17.5969	1.56147	0.780736	+	0.624861i	$0.214845\pi$
$128$	15.1325	1.33753
$129$	−7.59508	−0.668709
$130$	0.812715	0.0712798
$131$	−12.6627	−1.10634	−0.553172	−	0.833067i	$-0.686583\pi$
$131$	−12.6627	−1.10634	−0.553172	+	0.833067i	$0.686583\pi$
$132$	−22.7227	−1.97776
$133$	14.6040	1.26633
$134$	20.2633	1.75048
$135$	−1.10349	−0.0949731
$136$	4.33892	0.372059
$137$	−8.32780	−0.711492	−0.355746	−	0.934583i	$-0.615773\pi$
$137$	−8.32780	−0.711492	−0.355746	+	0.934583i	$0.615773\pi$
$138$	−26.1361	−2.22485
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−2.28180	−0.192848
$141$	−7.15158	−0.602271
$142$	32.0567	2.69014
$143$	11.0949	0.927802
$144$	1.58783	0.132319
$145$	0.197788	0.0164254
$146$	−26.6002	−2.20144
$147$	10.4574	0.862516
$148$	27.5249	2.26254
$149$	11.2336	0.920289	0.460145	−	0.887844i	$-0.347798\pi$
$149$	11.2336	0.920289	0.460145	+	0.887844i	$0.347798\pi$
$150$	14.1044	1.15162
$151$	3.39366	0.276172	0.138086	−	0.990420i	$-0.455905\pi$
$151$	3.39366	0.276172	0.138086	+	0.990420i	$0.455905\pi$
$152$	8.01003	0.649699
$153$	2.78111	0.224839
$154$	−52.1986	−4.20628
$155$	−2.08873	−0.167771
$156$	−6.97171	−0.558183
$157$	−4.26295	−0.340221	−0.170110	−	0.985425i	$-0.554412\pi$
$157$	−4.26295	−0.340221	−0.170110	+	0.985425i	$0.554412\pi$
$158$	−19.3787	−1.54169
$159$	0.829468	0.0657811
$160$	1.35609	0.107208
$161$	−35.8297	−2.82378
$162$	6.70726	0.526972
$163$	−7.83711	−0.613850	−0.306925	−	0.951734i	$-0.599300\pi$
$163$	−7.83711	−0.613850	−0.306925	+	0.951734i	$0.599300\pi$
$164$	13.2457	1.03432
$165$	−1.51839	−0.118206
$166$	25.9656	2.01532
$167$	19.8647	1.53717	0.768587	−	0.639745i	$-0.220960\pi$
$167$	19.8647	1.53717	0.768587	+	0.639745i	$0.220960\pi$
$168$	10.6371	0.820672
$169$	−9.59590	−0.738146
$170$	0.894037	0.0685695
$171$	5.13417	0.392620
$172$	−17.6096	−1.34272
$173$	11.1060	0.844374	0.422187	−	0.906509i	$-0.361263\pi$
$173$	11.1060	0.844374	0.422187	+	0.906509i	$0.361263\pi$
$174$	−2.84313	−0.215537
$175$	19.3357	1.46164
$176$	6.96830	0.525255
$177$	−13.1788	−0.990580
$178$	−24.0013	−1.79897
$179$	12.0790	0.902829	0.451414	−	0.892314i	$-0.350920\pi$
$179$	12.0790	0.902829	0.451414	+	0.892314i	$0.350920\pi$
$180$	−0.802189	−0.0597917
$181$	−10.7628	−0.799993	−0.399996	−	0.916517i	$-0.630989\pi$
$181$	−10.7628	−0.799993	−0.399996	+	0.916517i	$0.630989\pi$
$182$	−16.0154	−1.18714
$183$	−0.0333835	−0.00246778
$184$	−19.6519	−1.44876
$185$	1.83929	0.135227
$186$	30.0247	2.20152
$187$	12.2051	0.892523
$188$	−16.5813	−1.20931
$189$	21.7454	1.58175
$190$	1.65047	0.119738
$191$	−25.1146	−1.81723	−0.908615	−	0.417635i	$-0.862859\pi$
$191$	−25.1146	−1.81723	−0.908615	+	0.417635i	$0.862859\pi$
$192$	−16.5347	−1.19329
$193$	−0.932560	−0.0671272	−0.0335636	−	0.999437i	$-0.510686\pi$
$193$	−0.932560	−0.0671272	−0.0335636	+	0.999437i	$0.510686\pi$
$194$	−17.3951	−1.24889
$195$	−0.465868	−0.0333615
$196$	24.2461	1.73186
$197$	17.6068	1.25443	0.627216	−	0.778845i	$-0.284194\pi$
$197$	17.6068	1.25443	0.627216	+	0.778845i	$0.284194\pi$
$198$	−18.3509	−1.30414
$199$	10.7579	0.762608	0.381304	−	0.924450i	$-0.375475\pi$
$199$	10.7579	0.762608	0.381304	+	0.924450i	$0.375475\pi$
$200$	10.6053	0.749905
$201$	−11.6154	−0.819288
$202$	−3.52222	−0.247822
$203$	−3.89763	−0.273560
$204$	−7.66931	−0.536959
$205$	0.885112	0.0618189
$206$	−41.9156	−2.92040
$207$	−12.5963	−0.875501
$208$	2.13799	0.148243
$209$	22.5317	1.55855
$210$	2.19179	0.151248
$211$	0.992456	0.0683235	0.0341617	−	0.999416i	$-0.489124\pi$
$211$	0.992456	0.0683235	0.0341617	+	0.999416i	$0.489124\pi$
$212$	1.92316	0.132083
$213$	−18.3757	−1.25908
$214$	15.4348	1.05510
$215$	−1.17672	−0.0802515
$216$	11.9270	0.811526
$217$	41.1607	2.79417
$218$	−22.1586	−1.50077
$219$	15.2478	1.03035
$220$	−3.52046	−0.237349
$221$	3.74473	0.251897
$222$	−26.4391	−1.77448
$223$	−3.63277	−0.243268	−0.121634	−	0.992575i	$-0.538813\pi$
$223$	−3.63277	−0.243268	−0.121634	+	0.992575i	$0.538813\pi$
$224$	−26.7232	−1.78552
$225$	6.79763	0.453176
$226$	25.8944	1.72247
$227$	−20.8629	−1.38472	−0.692358	−	0.721554i	$-0.743428\pi$
$227$	−20.8629	−1.38472	−0.692358	+	0.721554i	$0.743428\pi$
$228$	−14.1582	−0.937652
$229$	0.576114	0.0380707	0.0190353	−	0.999819i	$-0.493941\pi$
$229$	0.576114	0.0380707	0.0190353	+	0.999819i	$0.493941\pi$
$230$	−4.04930	−0.267003
$231$	29.9215	1.96869
$232$	−2.13778	−0.140352
$233$	−13.5819	−0.889781	−0.444890	−	0.895585i	$-0.646757\pi$
$233$	−13.5819	−0.889781	−0.444890	+	0.895585i	$0.646757\pi$
$234$	−5.63037	−0.368069
$235$	−1.10800	−0.0722783
$236$	−30.5557	−1.98901
$237$	11.1083	0.721564
$238$	−17.6180	−1.14200
$239$	−10.9792	−0.710183	−0.355091	−	0.934832i	$-0.615550\pi$
$239$	−10.9792	−0.710183	−0.355091	+	0.934832i	$0.615550\pi$
$240$	−0.292595	−0.0188869
$241$	−2.11954	−0.136532	−0.0682659	−	0.997667i	$-0.521747\pi$
$241$	−2.11954	−0.136532	−0.0682659	+	0.997667i	$0.521747\pi$
$242$	−56.0362	−3.60215
$243$	12.8926	0.827064
$244$	−0.0774012	−0.00495510
$245$	1.62019	0.103510
$246$	−12.7232	−0.811199
$247$	6.91310	0.439870
$248$	22.5759	1.43357
$249$	−14.8841	−0.943242
$250$	4.38768	0.277501
$251$	21.6475	1.36638	0.683190	−	0.730240i	$-0.260592\pi$
$251$	21.6475	1.36638	0.683190	+	0.730240i	$0.260592\pi$
$252$	15.8080	0.995810
$253$	−55.2796	−3.47540
$254$	−39.1897	−2.45898
$255$	−0.512484	−0.0320930
$256$	−7.79740	−0.487337
$257$	7.77031	0.484699	0.242349	−	0.970189i	$-0.422082\pi$
$257$	7.77031	0.484699	0.242349	+	0.970189i	$0.422082\pi$
$258$	16.9149	1.05307
$259$	−36.2452	−2.25217
$260$	−1.08014	−0.0669873
$261$	−1.37025	−0.0848162
$262$	28.2009	1.74226
$263$	28.3544	1.74841	0.874204	−	0.485558i	$-0.161384\pi$
$263$	28.3544	1.74841	0.874204	+	0.485558i	$0.161384\pi$
$264$	16.4114	1.01005
$265$	0.128511	0.00789435
$266$	−32.5244	−1.99420
$267$	13.7581	0.841982
$268$	−26.9309	−1.64507
$269$	−13.0884	−0.798015	−0.399008	−	0.916948i	$-0.630645\pi$
$269$	−13.0884	−0.798015	−0.399008	+	0.916948i	$0.630645\pi$
$270$	2.45756	0.149562
$271$	5.49464	0.333776	0.166888	−	0.985976i	$-0.446628\pi$
$271$	5.49464	0.333776	0.166888	+	0.985976i	$0.446628\pi$
$272$	2.35193	0.142606
$273$	9.18043	0.555625
$274$	18.5467	1.12045
$275$	29.8319	1.79893
$276$	34.7361	2.09087
$277$	−14.2587	−0.856723	−0.428362	−	0.903607i	$-0.640909\pi$
$277$	−14.2587	−0.856723	−0.428362	+	0.903607i	$0.640909\pi$
$278$	2.22708	0.133572
$279$	14.4704	0.866321
$280$	1.64803	0.0984884
$281$	−23.1679	−1.38208	−0.691042	−	0.722815i	$-0.742848\pi$
$281$	−23.1679	−1.38208	−0.691042	+	0.722815i	$0.742848\pi$
$282$	15.9272	0.948448
$283$	5.77145	0.343077	0.171539	−	0.985177i	$-0.445126\pi$
$283$	5.77145	0.343077	0.171539	+	0.985177i	$0.445126\pi$
$284$	−42.6049	−2.52813
$285$	−0.946091	−0.0560416
$286$	−24.7093	−1.46109
$287$	−17.4421	−1.02957
$288$	−9.39480	−0.553594
$289$	−12.8806	−0.757680
$290$	−0.440491	−0.0258665
$291$	9.97126	0.584526
$292$	35.3529	2.06887
$293$	−26.6758	−1.55842	−0.779209	−	0.626764i	$-0.784379\pi$
$293$	−26.6758	−1.55842	−0.779209	+	0.626764i	$0.784379\pi$
$294$	−23.2896	−1.35828
$295$	−2.04181	−0.118879
$296$	−19.8798	−1.15549
$297$	33.5497	1.94675
$298$	−25.0181	−1.44926
$299$	−16.9607	−0.980863
$300$	−18.7455	−1.08227
$301$	23.1885	1.33656
$302$	−7.55796	−0.434911
$303$	2.01902	0.115990
$304$	4.34187	0.249023
$305$	−0.00517215	−0.000296156 0
$306$	−6.19376	−0.354074
$307$	−33.1088	−1.88962	−0.944811	−	0.327617i	$-0.893755\pi$
$307$	−33.1088	−1.88962	−0.944811	+	0.327617i	$0.893755\pi$
$308$	69.3745	3.95298
$309$	24.0270	1.36685
$310$	4.65178	0.264203
$311$	21.1503	1.19932	0.599662	−	0.800253i	$-0.295302\pi$
$311$	21.1503	1.19932	0.599662	+	0.800253i	$0.295302\pi$
$312$	5.03529	0.285067
$313$	0.349266	0.0197417	0.00987085	−	0.999951i	$-0.496858\pi$
$313$	0.349266	0.0197417	0.00987085	+	0.999951i	$0.496858\pi$
$314$	9.49395	0.535775
$315$	1.05633	0.0595176
$316$	25.7552	1.44884
$317$	−16.8619	−0.947059	−0.473529	−	0.880778i	$-0.657020\pi$
$317$	−16.8619	−0.947059	−0.473529	+	0.880778i	$0.657020\pi$
$318$	−1.84729	−0.103591
$319$	−6.01342	−0.336687
$320$	−2.56174	−0.143206
$321$	−8.84762	−0.493826
$322$	79.7958	4.44685
$323$	7.60484	0.423145
$324$	−8.91426	−0.495237
$325$	9.15293	0.507713
$326$	17.4539	0.966682
$327$	12.7018	0.702412
$328$	−9.56666	−0.528231
$329$	21.8344	1.20377
$330$	3.38158	0.186150
$331$	26.0057	1.42940	0.714702	−	0.699429i	$-0.246562\pi$
$331$	26.0057	1.42940	0.714702	+	0.699429i	$0.246562\pi$
$332$	−34.5096	−1.89396
$333$	−12.7423	−0.698275
$334$	−44.2403	−2.42072
$335$	−1.79959	−0.0983223
$336$	5.76589	0.314555
$337$	5.57857	0.303884	0.151942	−	0.988389i	$-0.451447\pi$
$337$	5.57857	0.303884	0.151942	+	0.988389i	$0.451447\pi$
$338$	21.3709	1.16242
$339$	−14.8433	−0.806176
$340$	−1.18822	−0.0644402
$341$	63.5043	3.43895
$342$	−11.4342	−0.618293
$343$	−4.64414	−0.250760
$344$	12.7184	0.685733
$345$	2.32116	0.124967
$346$	−24.7340	−1.32971
$347$	26.5736	1.42655	0.713273	−	0.700886i	$-0.247212\pi$
$347$	26.5736	1.42655	0.713273	+	0.700886i	$0.247212\pi$
$348$	3.77866	0.202557
$349$	26.2365	1.40441	0.702204	−	0.711976i	$-0.252199\pi$
$349$	26.2365	1.40441	0.702204	+	0.711976i	$0.252199\pi$
$350$	−43.0622	−2.30177
$351$	10.2936	0.549433
$352$	−41.2297	−2.19755
$353$	−12.8662	−0.684801	−0.342401	−	0.939554i	$-0.611240\pi$
$353$	−12.8662	−0.684801	−0.342401	+	0.939554i	$0.611240\pi$
$354$	29.3503	1.55995
$355$	−2.84697	−0.151101
$356$	31.8988	1.69064
$357$	10.0990	0.534498
$358$	−26.9010	−1.42176
$359$	23.0362	1.21581	0.607903	−	0.794011i	$-0.292011\pi$
$359$	23.0362	1.21581	0.607903	+	0.794011i	$0.292011\pi$
$360$	0.579378	0.0305359
$361$	−4.96078	−0.261094
$362$	23.9697	1.25982
$363$	32.1213	1.68593
$364$	21.2853	1.11565
$365$	2.36237	0.123652
$366$	0.0743477	0.00388622
$367$	−14.0643	−0.734150	−0.367075	−	0.930191i	$-0.619641\pi$
$367$	−14.0643	−0.734150	−0.367075	+	0.930191i	$0.619641\pi$
$368$	−10.6524	−0.555295
$369$	−6.13193	−0.319215
$370$	−4.09625	−0.212954
$371$	−2.53244	−0.131478
$372$	−39.9043	−2.06894
$373$	−10.0096	−0.518278	−0.259139	−	0.965840i	$-0.583439\pi$
$373$	−10.0096	−0.518278	−0.259139	+	0.965840i	$0.583439\pi$
$374$	−27.1817	−1.40553
$375$	−2.51512	−0.129880
$376$	11.9758	0.617603
$377$	−1.84502	−0.0950234
$378$	−48.4288	−2.49091
$379$	−26.7655	−1.37485	−0.687427	−	0.726254i	$-0.741260\pi$
$379$	−26.7655	−1.37485	−0.687427	+	0.726254i	$0.741260\pi$
$380$	−2.19356	−0.112527
$381$	22.4645	1.15089
$382$	55.9324	2.86175
$383$	−37.5837	−1.92044	−0.960219	−	0.279248i	$-0.909915\pi$
$383$	−37.5837	−1.92044	−0.960219	+	0.279248i	$0.909915\pi$
$384$	19.3184	0.985836
$385$	4.63578	0.236261
$386$	2.07689	0.105711
$387$	8.15212	0.414396
$388$	23.1189	1.17368
$389$	−26.5968	−1.34851	−0.674255	−	0.738498i	$-0.735535\pi$
$389$	−26.5968	−1.34851	−0.674255	+	0.738498i	$0.735535\pi$
$390$	1.03753	0.0525372
$391$	−18.6578	−0.943568
$392$	−17.5117	−0.884473
$393$	−16.1654	−0.815437
$394$	−39.2118	−1.97546
$395$	1.72103	0.0865945
$396$	24.3892	1.22560
$397$	−18.9438	−0.950764	−0.475382	−	0.879780i	$-0.657690\pi$
$397$	−18.9438	−0.950764	−0.475382	+	0.879780i	$0.657690\pi$
$398$	−23.9588	−1.20094
$399$	18.6437	0.933354
$400$	5.74862	0.287431
$401$	−2.56699	−0.128189	−0.0640946	−	0.997944i	$-0.520416\pi$
$401$	−2.56699	−0.128189	−0.0640946	+	0.997944i	$0.520416\pi$
$402$	25.8685	1.29020
$403$	19.4842	0.970578
$404$	4.68120	0.232898
$405$	−0.595674	−0.0295993
$406$	8.68035	0.430799
$407$	−55.9205	−2.77188
$408$	5.53914	0.274228
$409$	28.1765	1.39324	0.696620	−	0.717440i	$-0.254686\pi$
$409$	28.1765	1.39324	0.696620	+	0.717440i	$0.254686\pi$
$410$	−1.97122	−0.0973516
$411$	−10.6314	−0.524409
$412$	55.7079	2.74453
$413$	40.2361	1.97989
$414$	28.0529	1.37873
$415$	−2.30602	−0.113198
$416$	−12.6500	−0.620216
$417$	−1.27662	−0.0625162
$418$	−50.1799	−2.45438
$419$	−18.5185	−0.904689	−0.452345	−	0.891843i	$-0.649412\pi$
$419$	−18.5185	−0.904689	−0.452345	+	0.891843i	$0.649412\pi$
$420$	−2.91299	−0.142139
$421$	14.0289	0.683729	0.341864	−	0.939749i	$-0.388942\pi$
$421$	14.0289	0.683729	0.341864	+	0.939749i	$0.388942\pi$
$422$	−2.21028	−0.107595
$423$	7.67609	0.373224
$424$	−1.38900	−0.0674557
$425$	10.0688	0.488408
$426$	40.9241	1.98278
$427$	0.101923	0.00493239
$428$	−20.5136	−0.991565
$429$	14.1639	0.683841
$430$	2.62065	0.126379
$431$	0.542361	0.0261246	0.0130623	−	0.999915i	$-0.495842\pi$
$431$	0.542361	0.0261246	0.0130623	+	0.999915i	$0.495842\pi$
$432$	6.46505	0.311050
$433$	34.5726	1.66145	0.830727	−	0.556680i	$-0.187925\pi$
$433$	34.5726	1.66145	0.830727	+	0.556680i	$0.187925\pi$
$434$	−91.6682	−4.40022
$435$	0.252500	0.0121064
$436$	29.4498	1.41039
$437$	−34.4441	−1.64768
$438$	−33.9582	−1.62259
$439$	−15.3871	−0.734386	−0.367193	−	0.930145i	$-0.619681\pi$
$439$	−15.3871	−0.734386	−0.367193	+	0.930145i	$0.619681\pi$
$440$	2.54264	0.121216
$441$	−11.2244	−0.534496
$442$	−8.33982	−0.396685
$443$	−11.9589	−0.568183	−0.284091	−	0.958797i	$-0.591692\pi$
$443$	−11.9589	−0.568183	−0.284091	+	0.958797i	$0.591692\pi$
$444$	35.1388	1.66762
$445$	2.13156	0.101046
$446$	8.09048	0.383095
$447$	14.3410	0.678304
$448$	50.4818	2.38504
$449$	5.09326	0.240366	0.120183	−	0.992752i	$-0.461652\pi$
$449$	5.09326	0.240366	0.120183	+	0.992752i	$0.461652\pi$
$450$	−15.1389	−0.713655
$451$	−26.9104	−1.26716
$452$	−34.4149	−1.61874
$453$	4.33240	0.203554
$454$	46.4633	2.18063
$455$	1.42234	0.0666802
$456$	10.2257	0.478864
$457$	−2.64347	−0.123657	−0.0618283	−	0.998087i	$-0.519693\pi$
$457$	−2.64347	−0.123657	−0.0618283	+	0.998087i	$0.519693\pi$
$458$	−1.28305	−0.0599531
$459$	11.3236	0.528542
$460$	5.38171	0.250924
$461$	8.20121	0.381968	0.190984	−	0.981593i	$-0.438832\pi$
$461$	8.20121	0.381968	0.190984	+	0.981593i	$0.438832\pi$
$462$	−66.6377	−3.10026
$463$	13.4453	0.624856	0.312428	−	0.949941i	$-0.398858\pi$
$463$	13.4453	0.624856	0.312428	+	0.949941i	$0.398858\pi$
$464$	−1.15879	−0.0537955
$465$	−2.66651	−0.123656
$466$	30.2481	1.40121
$467$	18.8675	0.873086	0.436543	−	0.899683i	$-0.356203\pi$
$467$	18.8675	0.873086	0.436543	+	0.899683i	$0.356203\pi$
$468$	7.48303	0.345903
$469$	35.4629	1.63753
$470$	2.46762	0.113823
$471$	−5.44216	−0.250761
$472$	22.0688	1.01580
$473$	35.7761	1.64499
$474$	−24.7392	−1.13631
$475$	18.5879	0.852871
$476$	23.4151	1.07323
$477$	−0.890303	−0.0407642
$478$	24.4515	1.11839
$479$	16.4168	0.750102	0.375051	−	0.927004i	$-0.377625\pi$
$479$	16.4168	0.750102	0.375051	+	0.927004i	$0.377625\pi$
$480$	1.73121	0.0790186
$481$	−17.1574	−0.782309
$482$	4.72040	0.215008
$483$	−45.7409	−2.08128
$484$	74.4748	3.38522
$485$	1.54486	0.0701486
$486$	−28.7130	−1.30245
$487$	29.4601	1.33497	0.667483	−	0.744625i	$-0.267372\pi$
$487$	29.4601	1.33497	0.667483	+	0.744625i	$0.267372\pi$
$488$	0.0559027	0.00253060
$489$	−10.0050	−0.452441
$490$	−3.60829	−0.163006
$491$	3.94071	0.177842	0.0889209	−	0.996039i	$-0.471658\pi$
$491$	3.94071	0.177842	0.0889209	+	0.996039i	$0.471658\pi$
$492$	16.9097	0.762348
$493$	−2.02964	−0.0914103
$494$	−15.3960	−0.692701
$495$	1.62975	0.0732519
$496$	12.2373	0.549472
$497$	56.1026	2.51654
$498$	33.1482	1.48540
$499$	38.3242	1.71562	0.857812	−	0.513963i	$-0.171823\pi$
$499$	38.3242	1.71562	0.857812	+	0.513963i	$0.171823\pi$
$500$	−5.83143	−0.260790
$501$	25.3596	1.13298
$502$	−48.2109	−2.15176
$503$	5.96826	0.266112	0.133056	−	0.991109i	$-0.457521\pi$
$503$	5.96826	0.266112	0.133056	+	0.991109i	$0.457521\pi$
$504$	−11.4173	−0.508566
$505$	0.312810	0.0139198
$506$	123.112	5.47300
$507$	−12.2503	−0.544055
$508$	52.0850	2.31090
$509$	9.61206	0.426047	0.213023	−	0.977047i	$-0.431669\pi$
$509$	9.61206	0.426047	0.213023	+	0.977047i	$0.431669\pi$
$510$	1.14134	0.0505396
$511$	−46.5531	−2.05939
$512$	−12.8995	−0.570081
$513$	20.9044	0.922953
$514$	−17.3051	−0.763297
$515$	3.72255	0.164035
$516$	−22.4807	−0.989657
$517$	33.6870	1.48155
$518$	80.7210	3.54668
$519$	14.1781	0.622350
$520$	0.780126	0.0342108
$521$	17.3943	0.762060	0.381030	−	0.924563i	$-0.375569\pi$
$521$	17.3943	0.762060	0.381030	+	0.924563i	$0.375569\pi$
$522$	3.05166	0.133567
$523$	−37.5479	−1.64185	−0.820927	−	0.571034i	$-0.806543\pi$
$523$	−37.5479	−1.64185	−0.820927	+	0.571034i	$0.806543\pi$
$524$	−37.4803	−1.63733
$525$	24.6843	1.07731
$526$	−63.1477	−2.75337
$527$	21.4339	0.933673
$528$	8.89585	0.387142
$529$	61.5056	2.67416
$530$	−0.286204	−0.0124319
$531$	14.1454	0.613857
$532$	43.2264	1.87410
$533$	−8.25656	−0.357631
$534$	−30.6404	−1.32594
$535$	−1.37078	−0.0592638
$536$	19.4507	0.840144
$537$	15.4203	0.665435
$538$	29.1490	1.25670
$539$	−49.2591	−2.12174
$540$	−3.26621	−0.140555
$541$	−23.1395	−0.994846	−0.497423	−	0.867508i	$-0.665720\pi$
$541$	−23.1395	−0.994846	−0.497423	+	0.867508i	$0.665720\pi$
$542$	−12.2370	−0.525625
$543$	−13.7400	−0.589639
$544$	−13.9158	−0.596634
$545$	1.96791	0.0842961
$546$	−20.4456	−0.874990
$547$	34.6418	1.48118	0.740588	−	0.671960i	$-0.234547\pi$
$547$	34.6418	1.48118	0.740588	+	0.671960i	$0.234547\pi$
$548$	−24.6495	−1.05297
$549$	0.0358319	0.00152927
$550$	−66.4381	−2.83293
$551$	−3.74689	−0.159623
$552$	−25.0880	−1.06782
$553$	−33.9148	−1.44220
$554$	31.7554	1.34916
$555$	2.34807	0.0996700
$556$	−2.95990	−0.125528
$557$	39.8496	1.68848	0.844242	−	0.535962i	$-0.180051\pi$
$557$	39.8496	1.68848	0.844242	+	0.535962i	$0.180051\pi$
$558$	−32.2268	−1.36427
$559$	10.9767	0.464266
$560$	0.893318	0.0377496
$561$	15.5812	0.657839
$562$	51.5969	2.17649
$563$	5.34298	0.225180	0.112590	−	0.993642i	$-0.464085\pi$
$563$	5.34298	0.225180	0.112590	+	0.993642i	$0.464085\pi$
$564$	−21.1680	−0.891332
$565$	−2.29969	−0.0967488
$566$	−12.8535	−0.540273
$567$	11.7384	0.492967
$568$	30.7712	1.29113
$569$	10.6779	0.447642	0.223821	−	0.974630i	$-0.428147\pi$
$569$	10.6779	0.447642	0.223821	+	0.974630i	$0.428147\pi$
$570$	2.10702	0.0882535
$571$	38.3789	1.60611	0.803054	−	0.595906i	$-0.203207\pi$
$571$	38.3789	1.60611	0.803054	+	0.595906i	$0.203207\pi$
$572$	32.8398	1.37310
$573$	−32.0618	−1.33940
$574$	38.8450	1.62136
$575$	−45.6038	−1.90181
$576$	17.7473	0.739473
$577$	−26.0198	−1.08322	−0.541610	−	0.840630i	$-0.682185\pi$
$577$	−26.0198	−1.08322	−0.541610	+	0.840630i	$0.682185\pi$
$578$	28.6861	1.19318
$579$	−1.19052	−0.0494764
$580$	0.585434	0.0243088
$581$	45.4426	1.88528
$582$	−22.2068	−0.920503
$583$	−3.90715	−0.161818
$584$	−25.5335	−1.05658
$585$	0.500036	0.0206739
$586$	59.4093	2.45418
$587$	−13.9119	−0.574206	−0.287103	−	0.957900i	$-0.592692\pi$
$587$	−13.9119	−0.574206	−0.287103	+	0.957900i	$0.592692\pi$
$588$	30.9530	1.27648
$589$	39.5688	1.63040
$590$	4.54729	0.187209
$591$	22.4772	0.924586
$592$	−10.7759	−0.442888
$593$	−10.5891	−0.434843	−0.217421	−	0.976078i	$-0.569765\pi$
$593$	−10.5891	−0.434843	−0.217421	+	0.976078i	$0.569765\pi$
$594$	−74.7180	−3.06572
$595$	1.56466	0.0641448
$596$	33.2502	1.36198
$597$	13.7337	0.562084
$598$	37.7729	1.54465
$599$	−11.3996	−0.465774	−0.232887	−	0.972504i	$-0.574817\pi$
$599$	−11.3996	−0.465774	−0.232887	+	0.972504i	$0.574817\pi$
$600$	13.5389	0.552722
$601$	35.0000	1.42768	0.713839	−	0.700309i	$-0.246955\pi$
$601$	35.0000	1.42768	0.713839	+	0.700309i	$0.246955\pi$
$602$	−51.6427	−2.10480
$603$	12.4673	0.507708
$604$	10.0449	0.408721
$605$	4.97660	0.202328
$606$	−4.49652	−0.182659
$607$	23.0383	0.935094	0.467547	−	0.883968i	$-0.345138\pi$
$607$	23.0383	0.935094	0.467547	+	0.883968i	$0.345138\pi$
$608$	−25.6898	−1.04186
$609$	−4.97578	−0.201629
$610$	0.0115188	0.000466383 0
$611$	10.3358	0.418140
$612$	8.23180	0.332751
$613$	−9.97279	−0.402797	−0.201399	−	0.979509i	$-0.564549\pi$
$613$	−9.97279	−0.402797	−0.201399	+	0.979509i	$0.564549\pi$
$614$	73.7362	2.97575
$615$	1.12995	0.0455640
$616$	−50.1055	−2.01881
$617$	−7.10698	−0.286116	−0.143058	−	0.989714i	$-0.545694\pi$
$617$	−7.10698	−0.286116	−0.143058	+	0.989714i	$0.545694\pi$
$618$	−53.5102	−2.15250
$619$	−35.4420	−1.42453	−0.712267	−	0.701909i	$-0.752331\pi$
$619$	−35.4420	−1.42453	−0.712267	+	0.701909i	$0.752331\pi$
$620$	−6.18243	−0.248292
$621$	−51.2873	−2.05809
$622$	−47.1035	−1.88868
$623$	−42.0048	−1.68289
$624$	2.72940	0.109263
$625$	24.4147	0.976589
$626$	−0.777845	−0.0310889
$627$	28.7643	1.14874
$628$	−12.6179	−0.503510
$629$	−18.8742	−0.752563
$630$	−2.35254	−0.0937274
$631$	−9.35596	−0.372455	−0.186227	−	0.982507i	$-0.559626\pi$
$631$	−9.35596	−0.372455	−0.186227	+	0.982507i	$0.559626\pi$
$632$	−18.6016	−0.739933
$633$	1.26699	0.0503582
$634$	37.5529	1.49141
$635$	3.48046	0.138118
$636$	2.45514	0.0973527
$637$	−15.1135	−0.598820
$638$	13.3924	0.530210
$639$	19.7234	0.780245
$640$	2.99302	0.118310
$641$	21.5640	0.851725	0.425863	−	0.904788i	$-0.359971\pi$
$641$	21.5640	0.851725	0.425863	+	0.904788i	$0.359971\pi$
$642$	19.7044	0.777670
$643$	−10.7277	−0.423060	−0.211530	−	0.977371i	$-0.567845\pi$
$643$	−10.7277	−0.423060	−0.211530	+	0.977371i	$0.567845\pi$
$644$	−106.052	−4.17905
$645$	−1.50222	−0.0591498
$646$	−16.9366	−0.666362
$647$	−34.9553	−1.37423	−0.687117	−	0.726546i	$-0.741124\pi$
$647$	−34.9553	−1.37423	−0.687117	+	0.726546i	$0.741124\pi$
$648$	6.43830	0.252920
$649$	62.0779	2.43677
$650$	−20.3843	−0.799539
$651$	52.5464	2.05946
$652$	−23.1971	−0.908467
$653$	1.64437	0.0643492	0.0321746	−	0.999482i	$-0.489757\pi$
$653$	1.64437	0.0643492	0.0321746	+	0.999482i	$0.489757\pi$
$654$	−28.2880	−1.10615
$655$	−2.50453	−0.0978602
$656$	−5.18564	−0.202465
$657$	−16.3662	−0.638505
$658$	−48.6271	−1.89568
$659$	−16.7029	−0.650653	−0.325326	−	0.945602i	$-0.605474\pi$
$659$	−16.7029	−0.650653	−0.325326	+	0.945602i	$0.605474\pi$
$660$	−4.49428	−0.174940
$661$	−7.33782	−0.285408	−0.142704	−	0.989765i	$-0.545580\pi$
$661$	−7.33782	−0.285408	−0.142704	+	0.989765i	$0.545580\pi$
$662$	−57.9169	−2.25101
$663$	4.78058	0.185662
$664$	24.9244	0.967255
$665$	2.88850	0.112011
$666$	28.3782	1.09963
$667$	9.19269	0.355943
$668$	58.7975	2.27494
$669$	−4.63766	−0.179302
$670$	4.00784	0.154837
$671$	0.157251	0.00607059
$672$	−34.1154	−1.31603
$673$	16.3219	0.629162	0.314581	−	0.949231i	$-0.398136\pi$
$673$	16.3219	0.629162	0.314581	+	0.949231i	$0.398136\pi$
$674$	−12.4239	−0.478552
$675$	27.6774	1.06530
$676$	−28.4029	−1.09242
$677$	−18.9833	−0.729586	−0.364793	−	0.931089i	$-0.618860\pi$
$677$	−18.9833	−0.729586	−0.364793	+	0.931089i	$0.618860\pi$
$678$	33.0572	1.26955
$679$	−30.4432	−1.16830
$680$	0.858187	0.0329100
$681$	−26.6339	−1.02061
$682$	−141.429	−5.41561
$683$	−45.5880	−1.74438	−0.872189	−	0.489170i	$-0.837300\pi$
$683$	−45.5880	−1.74438	−0.872189	+	0.489170i	$0.837300\pi$
$684$	15.1966	0.581058
$685$	−1.64714	−0.0629341
$686$	10.3429	0.394893
$687$	0.735477	0.0280602
$688$	6.89408	0.262834
$689$	−1.19878	−0.0456699
$690$	−5.16941	−0.196796
$691$	−24.0183	−0.913698	−0.456849	−	0.889544i	$-0.651022\pi$
$691$	−24.0183	−0.913698	−0.456849	+	0.889544i	$0.651022\pi$
$692$	32.8727	1.24963
$693$	−32.1160	−1.21999
$694$	−59.1816	−2.24650
$695$	−0.197788	−0.00750254
$696$	−2.72912	−0.103447
$697$	−9.08273	−0.344033
$698$	−58.4309	−2.21164
$699$	−17.3389	−0.655818
$700$	57.2317	2.16315
$701$	−36.1809	−1.36653	−0.683267	−	0.730169i	$-0.739441\pi$
$701$	−36.1809	−1.36653	−0.683267	+	0.730169i	$0.739441\pi$
$702$	−22.9248	−0.865239
$703$	−34.8434	−1.31414
$704$	77.8854	2.93542
$705$	−1.41450	−0.0532731
$706$	28.6542	1.07842
$707$	−6.16425	−0.231831
$708$	−39.0080	−1.46601
$709$	6.66086	0.250154	0.125077	−	0.992147i	$-0.460082\pi$
$709$	6.66086	0.250154	0.125077	+	0.992147i	$0.460082\pi$
$710$	6.34044	0.237952
$711$	−11.9230	−0.447149
$712$	−23.0388	−0.863417
$713$	−97.0788	−3.63563
$714$	−22.4914	−0.841720
$715$	2.19444	0.0820674
$716$	35.7527	1.33614
$717$	−14.0162	−0.523444
$718$	−51.3036	−1.91463
$719$	29.4584	1.09861	0.549306	−	0.835621i	$-0.314892\pi$
$719$	29.4584	1.09861	0.549306	+	0.835621i	$0.314892\pi$
$720$	0.314054	0.0117041
$721$	−73.3568	−2.73195
$722$	11.0481	0.411167
$723$	−2.70585	−0.100631
$724$	−31.8568	−1.18395
$725$	−4.96088	−0.184242
$726$	−71.5368	−2.65498
$727$	−9.45800	−0.350778	−0.175389	−	0.984499i	$-0.556118\pi$
$727$	−9.45800	−0.350778	−0.175389	+	0.984499i	$0.556118\pi$
$728$	−15.3732	−0.569769
$729$	25.4940	0.944222
$730$	−5.26120	−0.194726
$731$	12.0751	0.446613
$732$	−0.0988117	−0.00365219
$733$	−43.6346	−1.61168	−0.805840	−	0.592134i	$-0.798286\pi$
$733$	−43.6346	−1.61168	−0.805840	+	0.592134i	$0.798286\pi$
$734$	31.3223	1.15613
$735$	2.06836	0.0762926
$736$	63.0277	2.32323
$737$	54.7136	2.01540
$738$	13.6563	0.502696
$739$	−1.69593	−0.0623856	−0.0311928	−	0.999513i	$-0.509931\pi$
$739$	−1.69593	−0.0623856	−0.0311928	+	0.999513i	$0.509931\pi$
$740$	5.44411	0.200130
$741$	8.82538	0.324209
$742$	5.63996	0.207049
$743$	40.8480	1.49857	0.749283	−	0.662249i	$-0.230398\pi$
$743$	40.8480	1.49857	0.749283	+	0.662249i	$0.230398\pi$
$744$	28.8207	1.05662
$745$	2.22187	0.0814029
$746$	22.2922	0.816177
$747$	15.9758	0.584522
$748$	36.1258	1.32089
$749$	27.0126	0.987019
$750$	5.60139	0.204534
$751$	27.2623	0.994816	0.497408	−	0.867517i	$-0.334285\pi$
$751$	27.2623	0.994816	0.497408	+	0.867517i	$0.334285\pi$
$752$	6.49151	0.236721
$753$	27.6356	1.00710
$754$	4.10902	0.149642
$755$	0.671226	0.0244284
$756$	64.3642	2.34090
$757$	−35.8139	−1.30168	−0.650839	−	0.759216i	$-0.725583\pi$
$757$	−35.8139	−1.30168	−0.650839	+	0.759216i	$0.725583\pi$
$758$	59.6091	2.16510
$759$	−70.5709	−2.56156
$760$	1.58429	0.0574682
$761$	−39.8057	−1.44296	−0.721479	−	0.692437i	$-0.756537\pi$
$761$	−39.8057	−1.44296	−0.721479	+	0.692437i	$0.756537\pi$
$762$	−50.0303	−1.81241
$763$	−38.7798	−1.40392
$764$	−74.3368	−2.68941
$765$	0.550071	0.0198878
$766$	83.7021	3.02428
$767$	19.0466	0.687732
$768$	−9.95429	−0.359195
$769$	13.4658	0.485590	0.242795	−	0.970078i	$-0.421936\pi$
$769$	13.4658	0.485590	0.242795	+	0.970078i	$0.421936\pi$
$770$	−10.3243	−0.372061
$771$	9.91972	0.357250
$772$	−2.76029	−0.0993449
$773$	−25.1159	−0.903355	−0.451678	−	0.892181i	$-0.649174\pi$
$773$	−25.1159	−0.903355	−0.451678	+	0.892181i	$0.649174\pi$
$774$	−18.1555	−0.652584
$775$	52.3890	1.88187
$776$	−16.6975	−0.599406
$777$	−46.2712	−1.65997
$778$	59.2333	2.12362
$779$	−16.7675	−0.600759
$780$	−1.37892	−0.0493733
$781$	86.5573	3.09727
$782$	41.5526	1.48592
$783$	−5.57913	−0.199382
$784$	−9.49227	−0.339009
$785$	−0.843162	−0.0300937
$786$	36.0017	1.28414
$787$	−7.37127	−0.262757	−0.131379	−	0.991332i	$-0.541940\pi$
$787$	−7.37127	−0.262757	−0.131379	+	0.991332i	$0.541940\pi$
$788$	52.1144	1.85650
$789$	36.1978	1.28867
$790$	−3.83288	−0.136368
$791$	45.3179	1.61132
$792$	−17.6150	−0.625923
$793$	0.0482472	0.00171331
$794$	42.1895	1.49725
$795$	0.164059	0.00581857
$796$	31.8423	1.12862
$797$	35.7577	1.26660	0.633301	−	0.773905i	$-0.281699\pi$
$797$	35.7577	1.26660	0.633301	+	0.773905i	$0.281699\pi$
$798$	−41.5212	−1.46983
$799$	11.3700	0.402241
$800$	−34.0132	−1.20255
$801$	−14.7672	−0.521772
$802$	5.71689	0.201870
$803$	−71.8240	−2.53461
$804$	−34.3805	−1.21251
$805$	−7.08670	−0.249773
$806$	−43.3930	−1.52845
$807$	−16.7089	−0.588182
$808$	−3.38098	−0.118942
$809$	−18.8088	−0.661281	−0.330641	−	0.943757i	$-0.607265\pi$
$809$	−18.8088	−0.661281	−0.330641	+	0.943757i	$0.607265\pi$
$810$	1.32662	0.0466126
$811$	−16.3888	−0.575487	−0.287744	−	0.957707i	$-0.592905\pi$
$811$	−16.3888	−0.575487	−0.287744	+	0.957707i	$0.592905\pi$
$812$	−11.5366	−0.404855
$813$	7.01456	0.246011
$814$	124.540	4.36511
$815$	−1.55009	−0.0542973
$816$	3.00251	0.105109
$817$	22.2917	0.779888
$818$	−62.7515	−2.19405
$819$	−9.85374	−0.344318
$820$	2.61984	0.0914889
$821$	0.114680	0.00400237	0.00200119	−	0.999998i	$-0.499363\pi$
$821$	0.114680	0.00400237	0.00200119	+	0.999998i	$0.499363\pi$
$822$	23.6771	0.825832
$823$	11.0442	0.384975	0.192487	−	0.981299i	$-0.438345\pi$
$823$	11.0442	0.384975	0.192487	+	0.981299i	$0.438345\pi$
$824$	−40.2348	−1.40165
$825$	38.0839	1.32591
$826$	−89.6092	−3.11790
$827$	−9.53001	−0.331391	−0.165695	−	0.986177i	$-0.552987\pi$
$827$	−9.53001	−0.331391	−0.165695	+	0.986177i	$0.552987\pi$
$828$	−37.2837	−1.29570
$829$	−13.5650	−0.471132	−0.235566	−	0.971858i	$-0.575694\pi$
$829$	−13.5650	−0.471132	−0.235566	+	0.971858i	$0.575694\pi$
$830$	5.13570	0.178263
$831$	−18.2029	−0.631453
$832$	23.8966	0.828465
$833$	−16.6258	−0.576051
$834$	2.84313	0.0984497
$835$	3.92900	0.135969
$836$	66.6915	2.30657
$837$	58.9181	2.03651
$838$	41.2423	1.42469
$839$	3.47989	0.120139	0.0600695	−	0.998194i	$-0.480868\pi$
$839$	3.47989	0.120139	0.0600695	+	0.998194i	$0.480868\pi$
$840$	2.10390	0.0725914
$841$	1.00000	0.0344828
$842$	−31.2436	−1.07673
$843$	−29.5766	−1.01867
$844$	2.93757	0.101115
$845$	−1.89796	−0.0652917
$846$	−17.0953	−0.587748
$847$	−98.0693	−3.36970
$848$	−0.752911	−0.0258551
$849$	7.36794	0.252867
$850$	−22.4240	−0.769138
$851$	85.4855	2.93040
$852$	−54.3901	−1.86337
$853$	40.2840	1.37930	0.689648	−	0.724145i	$-0.257765\pi$
$853$	40.2840	1.37930	0.689648	+	0.724145i	$0.257765\pi$
$854$	−0.226990	−0.00776745
$855$	1.01548	0.0347287
$856$	14.8159	0.506397
$857$	−26.4524	−0.903595	−0.451798	−	0.892120i	$-0.649217\pi$
$857$	−26.4524	−0.903595	−0.451798	+	0.892120i	$0.649217\pi$
$858$	−31.5443	−1.07690
$859$	−18.4467	−0.629395	−0.314697	−	0.949192i	$-0.601903\pi$
$859$	−18.4467	−0.629395	−0.314697	+	0.949192i	$0.601903\pi$
$860$	−3.48297	−0.118768
$861$	−22.2669	−0.758853
$862$	−1.20788	−0.0411406
$863$	−11.9906	−0.408166	−0.204083	−	0.978954i	$-0.565421\pi$
$863$	−11.9906	−0.408166	−0.204083	+	0.978954i	$0.565421\pi$
$864$	−38.2521	−1.30136
$865$	2.19664	0.0746879
$866$	−76.9961	−2.61643
$867$	−16.4436	−0.558453
$868$	121.831	4.13523
$869$	−52.3251	−1.77501
$870$	−0.562339	−0.0190651
$871$	16.7871	0.568808
$872$	−21.2700	−0.720294
$873$	−10.7026	−0.362227
$874$	76.7098	2.59475
$875$	7.67890	0.259594
$876$	45.1321	1.52487
$877$	−6.34334	−0.214199	−0.107100	−	0.994248i	$-0.534156\pi$
$877$	−6.34334	−0.214199	−0.107100	+	0.994248i	$0.534156\pi$
$878$	34.2683	1.15650
$879$	−34.0548	−1.14864
$880$	1.37825	0.0464607
$881$	−43.5595	−1.46756	−0.733778	−	0.679390i	$-0.762245\pi$
$881$	−43.5595	−1.46756	−0.733778	+	0.679390i	$0.762245\pi$
$882$	24.9977	0.841717
$883$	−16.0600	−0.540462	−0.270231	−	0.962795i	$-0.587100\pi$
$883$	−16.0600	−0.540462	−0.270231	+	0.962795i	$0.587100\pi$
$884$	11.0840	0.372796
$885$	−2.60661	−0.0876204
$886$	26.6334	0.894766
$887$	−7.31635	−0.245659	−0.122829	−	0.992428i	$-0.539197\pi$
$887$	−7.31635	−0.245659	−0.122829	+	0.992428i	$0.539197\pi$
$888$	−25.3789	−0.851660
$889$	−68.5862	−2.30031
$890$	−4.74717	−0.159126
$891$	18.1105	0.606724
$892$	−10.7526	−0.360025
$893$	20.9900	0.702404
$894$	−31.9385	−1.06818
$895$	2.38909	0.0798585
$896$	−58.9807	−1.97041
$897$	−21.6523	−0.722951
$898$	−11.3431	−0.378524
$899$	−10.5604	−0.352210
$900$	20.1203	0.670677
$901$	−1.31873	−0.0439334
$902$	59.9316	1.99550
$903$	29.6028	0.985120
$904$	24.8560	0.826699
$905$	−2.12876	−0.0707622
$906$	−9.64862	−0.320554
$907$	−9.94414	−0.330190	−0.165095	−	0.986278i	$-0.552793\pi$
$907$	−9.94414	−0.330190	−0.165095	+	0.986278i	$0.552793\pi$
$908$	−61.7520	−2.04931
$909$	−2.16710	−0.0718781
$910$	−3.16766	−0.105007
$911$	−3.21195	−0.106417	−0.0532083	−	0.998583i	$-0.516945\pi$
$911$	−3.21195	−0.106417	−0.0532083	+	0.998583i	$0.516945\pi$
$912$	5.54290	0.183544
$913$	70.1107	2.32032
$914$	5.88724	0.194732
$915$	−0.00660286	−0.000218284 0
$916$	1.70524	0.0563427
$917$	49.3545	1.62983
$918$	−25.2187	−0.832340
$919$	−50.6294	−1.67011	−0.835054	−	0.550168i	$-0.814564\pi$
$919$	−50.6294	−1.67011	−0.835054	+	0.550168i	$0.814564\pi$
$920$	−3.88692	−0.128148
$921$	−42.2673	−1.39276
$922$	−18.2648	−0.601518
$923$	26.5573	0.874143
$924$	88.5646	2.91356
$925$	−46.1326	−1.51683
$926$	−29.9438	−0.984015
$927$	−25.7892	−0.847030
$928$	6.85628	0.225068
$929$	−16.6999	−0.547905	−0.273953	−	0.961743i	$-0.588331\pi$
$929$	−16.6999	−0.547905	−0.273953	+	0.961743i	$0.588331\pi$
$930$	5.93854	0.194732
$931$	−30.6928	−1.00592
$932$	−40.2011	−1.31683
$933$	27.0009	0.883968
$934$	−42.0196	−1.37492
$935$	2.41402	0.0789469
$936$	−5.40459	−0.176655
$937$	−2.85543	−0.0932827	−0.0466414	−	0.998912i	$-0.514852\pi$
$937$	−2.85543	−0.0932827	−0.0466414	+	0.998912i	$0.514852\pi$
$938$	−78.9789	−2.57875
$939$	0.445879	0.0145507
$940$	−3.27958	−0.106968
$941$	47.0039	1.53228	0.766141	−	0.642673i	$-0.222174\pi$
$941$	47.0039	1.53228	0.766141	+	0.642673i	$0.222174\pi$
$942$	12.1201	0.394896
$943$	41.1378	1.33963
$944$	11.9625	0.389345
$945$	4.30099	0.139911
$946$	−79.6764	−2.59050
$947$	−6.29758	−0.204644	−0.102322	−	0.994751i	$-0.532627\pi$
$947$	−6.29758	−0.204644	−0.102322	+	0.994751i	$0.532627\pi$
$948$	32.8796	1.06788
$949$	−22.0368	−0.715346
$950$	−41.3968	−1.34309
$951$	−21.5262	−0.698035
$952$	−16.9115	−0.548105
$953$	−41.8193	−1.35466	−0.677330	−	0.735679i	$-0.736863\pi$
$953$	−41.8193	−1.35466	−0.677330	+	0.735679i	$0.736863\pi$
$954$	1.98278	0.0641948
$955$	−4.96738	−0.160741
$956$	−32.4972	−1.05104
$957$	−7.67684	−0.248157
$958$	−36.5616	−1.18125
$959$	32.4587	1.04815
$960$	−3.27036	−0.105550
$961$	80.5227	2.59751
$962$	38.2109	1.23197
$963$	9.49653	0.306021
$964$	−6.27364	−0.202060
$965$	−0.184450	−0.00593764
$966$	101.869	3.27757
$967$	−50.0057	−1.60808	−0.804038	−	0.594578i	$-0.797319\pi$
$967$	−50.0057	−1.60808	−0.804038	+	0.594578i	$0.797319\pi$
$968$	−53.7892	−1.72885
$969$	9.70847	0.311881
$970$	−3.44054	−0.110469
$971$	41.2139	1.32262	0.661309	−	0.750114i	$-0.270001\pi$
$971$	41.2139	1.32262	0.661309	+	0.750114i	$0.270001\pi$
$972$	38.1609	1.22401
$973$	3.89763	0.124952
$974$	−65.6102	−2.10229
$975$	11.6848	0.374213
$976$	0.0303023	0.000969953 0
$977$	6.42622	0.205593	0.102797	−	0.994702i	$-0.467221\pi$
$977$	6.42622	0.205593	0.102797	+	0.994702i	$0.467221\pi$
$978$	22.2820	0.712498
$979$	−64.8067	−2.07123
$980$	4.79560	0.153190
$981$	−13.6334	−0.435281
$982$	−8.77629	−0.280063
$983$	−5.46749	−0.174386	−0.0871929	−	0.996191i	$-0.527790\pi$
$983$	−5.46749	−0.174386	−0.0871929	+	0.996191i	$0.527790\pi$
$984$	−12.2130	−0.389335
$985$	3.48242	0.110959
$986$	4.52017	0.143952
$987$	27.8742	0.887246
$988$	20.4621	0.650986
$989$	−54.6908	−1.73907
$990$	−3.62959	−0.115356
$991$	−3.81704	−0.121252	−0.0606261	−	0.998161i	$-0.519310\pi$
$991$	−3.81704	−0.121252	−0.0606261	+	0.998161i	$0.519310\pi$
$992$	−72.4053	−2.29887
$993$	33.1994	1.05355
$994$	−124.945	−3.96302
$995$	2.12779	0.0674554
$996$	−44.0555	−1.39595
$997$	6.87594	0.217763	0.108882	−	0.994055i	$-0.465273\pi$
$997$	6.87594	0.217763	0.108882	+	0.994055i	$0.465273\pi$
$998$	−85.3511	−2.70174
$999$	−51.8819	−1.64147

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.12	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.12	✓	98	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22708 q^{2} +1.27662 q^{3} +2.95990 q^{4} +0.197788 q^{5} -2.84313 q^{6} -3.89763 q^{7} -2.13778 q^{8} -1.37025 q^{9} +O(q^{10})\)	\(q-2.22708 q^{2} +1.27662 q^{3} +2.95990 q^{4} +0.197788 q^{5} -2.84313 q^{6} -3.89763 q^{7} -2.13778 q^{8} -1.37025 q^{9} -0.440491 q^{10} -6.01342 q^{11} +3.77866 q^{12} -1.84502 q^{13} +8.68035 q^{14} +0.252500 q^{15} -1.15879 q^{16} -2.02964 q^{17} +3.05166 q^{18} -3.74689 q^{19} +0.585434 q^{20} -4.97578 q^{21} +13.3924 q^{22} +9.19269 q^{23} -2.72912 q^{24} -4.96088 q^{25} +4.10902 q^{26} -5.57913 q^{27} -11.5366 q^{28} +1.00000 q^{29} -0.562339 q^{30} -10.5604 q^{31} +6.85628 q^{32} -7.67684 q^{33} +4.52017 q^{34} -0.770906 q^{35} -4.05580 q^{36} +9.29928 q^{37} +8.34465 q^{38} -2.35539 q^{39} -0.422827 q^{40} +4.47505 q^{41} +11.0815 q^{42} -5.94938 q^{43} -17.7991 q^{44} -0.271019 q^{45} -20.4729 q^{46} -5.60197 q^{47} -1.47933 q^{48} +8.19153 q^{49} +11.0483 q^{50} -2.59107 q^{51} -5.46108 q^{52} +0.649739 q^{53} +12.4252 q^{54} -1.18938 q^{55} +8.33227 q^{56} -4.78335 q^{57} -2.22708 q^{58} -10.3232 q^{59} +0.747375 q^{60} -0.0261499 q^{61} +23.5190 q^{62} +5.34072 q^{63} -12.9519 q^{64} -0.364924 q^{65} +17.0970 q^{66} -9.09858 q^{67} -6.00753 q^{68} +11.7356 q^{69} +1.71687 q^{70} -14.3940 q^{71} +2.92929 q^{72} +11.9439 q^{73} -20.7103 q^{74} -6.33315 q^{75} -11.0904 q^{76} +23.4381 q^{77} +5.24564 q^{78} +8.70138 q^{79} -0.229195 q^{80} -3.01168 q^{81} -9.96631 q^{82} -11.6590 q^{83} -14.7278 q^{84} -0.401439 q^{85} +13.2498 q^{86} +1.27662 q^{87} +12.8554 q^{88} +10.7770 q^{89} +0.603582 q^{90} +7.19121 q^{91} +27.2095 q^{92} -13.4816 q^{93} +12.4761 q^{94} -0.741092 q^{95} +8.75285 q^{96} +7.81069 q^{97} -18.2432 q^{98} +8.23988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

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