LMFDB - Embedded newform 8023.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51204 q^{2} +1.13882 q^{3} +4.31034 q^{4} +2.43582 q^{5} -2.86077 q^{6} -2.08264 q^{7} -5.80366 q^{8} -1.70308 q^{9} +O(q^{10})$	\(q-2.51204 q^{2} +1.13882 q^{3} +4.31034 q^{4} +2.43582 q^{5} -2.86077 q^{6} -2.08264 q^{7} -5.80366 q^{8} -1.70308 q^{9} -6.11887 q^{10} +6.22712 q^{11} +4.90871 q^{12} -2.54545 q^{13} +5.23167 q^{14} +2.77396 q^{15} +5.95835 q^{16} -0.549314 q^{17} +4.27821 q^{18} +4.43449 q^{19} +10.4992 q^{20} -2.37176 q^{21} -15.6428 q^{22} +1.19478 q^{23} -6.60935 q^{24} +0.933205 q^{25} +6.39427 q^{26} -5.35598 q^{27} -8.97688 q^{28} -9.16846 q^{29} -6.96831 q^{30} -2.41432 q^{31} -3.36028 q^{32} +7.09159 q^{33} +1.37990 q^{34} -5.07293 q^{35} -7.34086 q^{36} +6.83404 q^{37} -11.1396 q^{38} -2.89882 q^{39} -14.1367 q^{40} +3.03198 q^{41} +5.95795 q^{42} +9.94256 q^{43} +26.8410 q^{44} -4.14840 q^{45} -3.00132 q^{46} -3.01764 q^{47} +6.78551 q^{48} -2.66261 q^{49} -2.34425 q^{50} -0.625571 q^{51} -10.9718 q^{52} +1.01655 q^{53} +13.4544 q^{54} +15.1681 q^{55} +12.0869 q^{56} +5.05010 q^{57} +23.0315 q^{58} -7.79149 q^{59} +11.9567 q^{60} +6.41808 q^{61} +6.06486 q^{62} +3.54691 q^{63} -3.47555 q^{64} -6.20026 q^{65} -17.8143 q^{66} +6.59793 q^{67} -2.36773 q^{68} +1.36064 q^{69} +12.7434 q^{70} +1.00000 q^{71} +9.88412 q^{72} -0.685923 q^{73} -17.1674 q^{74} +1.06276 q^{75} +19.1142 q^{76} -12.9688 q^{77} +7.28195 q^{78} +9.54563 q^{79} +14.5135 q^{80} -0.990265 q^{81} -7.61645 q^{82} +15.9005 q^{83} -10.2231 q^{84} -1.33803 q^{85} -24.9761 q^{86} -10.4412 q^{87} -36.1401 q^{88} -0.0927770 q^{89} +10.4209 q^{90} +5.30126 q^{91} +5.14989 q^{92} -2.74948 q^{93} +7.58043 q^{94} +10.8016 q^{95} -3.82676 q^{96} +6.37467 q^{97} +6.68859 q^{98} -10.6053 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * 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 $

$2$	−2.51204	−1.77628	−0.888140	−	0.459573i	$-0.848002\pi$
$2$	−2.51204	−1.77628	−0.888140	+	0.459573i	$0.848002\pi$
$3$	1.13882	0.657500	0.328750	−	0.944417i	$-0.393373\pi$
$3$	1.13882	0.657500	0.328750	+	0.944417i	$0.393373\pi$
$4$	4.31034	2.15517
$5$	2.43582	1.08933	0.544665	−	0.838654i	$-0.316657\pi$
$5$	2.43582	1.08933	0.544665	+	0.838654i	$0.316657\pi$
$6$	−2.86077	−1.16790
$7$	−2.08264	−0.787164	−0.393582	−	0.919290i	$-0.628764\pi$
$7$	−2.08264	−0.787164	−0.393582	+	0.919290i	$0.628764\pi$
$8$	−5.80366	−2.05191
$9$	−1.70308	−0.567694
$10$	−6.11887	−1.93496
$11$	6.22712	1.87755	0.938774	−	0.344534i	$-0.111963\pi$
$11$	6.22712	1.87755	0.938774	+	0.344534i	$0.111963\pi$
$12$	4.90871	1.41702
$13$	−2.54545	−0.705981	−0.352991	−	0.935627i	$-0.614835\pi$
$13$	−2.54545	−0.705981	−0.352991	+	0.935627i	$0.614835\pi$
$14$	5.23167	1.39822
$15$	2.77396	0.716235
$16$	5.95835	1.48959
$17$	−0.549314	−0.133228	−0.0666141	−	0.997779i	$-0.521220\pi$
$17$	−0.549314	−0.133228	−0.0666141	+	0.997779i	$0.521220\pi$
$18$	4.27821	1.00838
$19$	4.43449	1.01734	0.508671	−	0.860961i	$-0.330137\pi$
$19$	4.43449	1.01734	0.508671	+	0.860961i	$0.330137\pi$
$20$	10.4992	2.34769
$21$	−2.37176	−0.517560
$22$	−15.6428	−3.33505
$23$	1.19478	0.249128	0.124564	−	0.992212i	$-0.460247\pi$
$23$	1.19478	0.249128	0.124564	+	0.992212i	$0.460247\pi$
$24$	−6.60935	−1.34913
$25$	0.933205	0.186641
$26$	6.39427	1.25402
$27$	−5.35598	−1.03076
$28$	−8.97688	−1.69647
$29$	−9.16846	−1.70254	−0.851270	−	0.524728i	$-0.824167\pi$
$29$	−9.16846	−1.70254	−0.851270	+	0.524728i	$0.824167\pi$
$30$	−6.96831	−1.27223
$31$	−2.41432	−0.433624	−0.216812	−	0.976213i	$-0.569566\pi$
$31$	−2.41432	−0.433624	−0.216812	+	0.976213i	$0.569566\pi$
$32$	−3.36028	−0.594019
$33$	7.09159	1.23449
$34$	1.37990	0.236650
$35$	−5.07293	−0.857481
$36$	−7.34086	−1.22348
$37$	6.83404	1.12351	0.561754	−	0.827304i	$-0.310127\pi$
$37$	6.83404	1.12351	0.561754	+	0.827304i	$0.310127\pi$
$38$	−11.1396	−1.80708
$39$	−2.89882	−0.464183
$40$	−14.1367	−2.23520
$41$	3.03198	0.473515	0.236758	−	0.971569i	$-0.423915\pi$
$41$	3.03198	0.473515	0.236758	+	0.971569i	$0.423915\pi$
$42$	5.95795	0.919331
$43$	9.94256	1.51623	0.758113	−	0.652123i	$-0.226121\pi$
$43$	9.94256	1.51623	0.758113	+	0.652123i	$0.226121\pi$
$44$	26.8410	4.04643
$45$	−4.14840	−0.618406
$46$	−3.00132	−0.442521
$47$	−3.01764	−0.440168	−0.220084	−	0.975481i	$-0.570633\pi$
$47$	−3.01764	−0.440168	−0.220084	+	0.975481i	$0.570633\pi$
$48$	6.78551	0.979404
$49$	−2.66261	−0.380373
$50$	−2.34425	−0.331527
$51$	−0.625571	−0.0875975
$52$	−10.9718	−1.52151
$53$	1.01655	0.139634	0.0698168	−	0.997560i	$-0.477759\pi$
$53$	1.01655	0.139634	0.0698168	+	0.997560i	$0.477759\pi$
$54$	13.4544	1.83092
$55$	15.1681	2.04527
$56$	12.0869	1.61519
$57$	5.05010	0.668902
$58$	23.0315	3.02419
$59$	−7.79149	−1.01437	−0.507183	−	0.861838i	$-0.669313\pi$
$59$	−7.79149	−1.01437	−0.507183	+	0.861838i	$0.669313\pi$
$60$	11.9567	1.54361
$61$	6.41808	0.821750	0.410875	−	0.911692i	$-0.365223\pi$
$61$	6.41808	0.821750	0.410875	+	0.911692i	$0.365223\pi$
$62$	6.06486	0.770238
$63$	3.54691	0.446868
$64$	−3.47555	−0.434443
$65$	−6.20026	−0.769047
$66$	−17.8143	−2.19279
$67$	6.59793	0.806065	0.403033	−	0.915186i	$-0.367956\pi$
$67$	6.59793	0.806065	0.403033	+	0.915186i	$0.367956\pi$
$68$	−2.36773	−0.287129
$69$	1.36064	0.163802
$70$	12.7434	1.52313
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	9.88412	1.16485
$73$	−0.685923	−0.0802812	−0.0401406	−	0.999194i	$-0.512781\pi$
$73$	−0.685923	−0.0802812	−0.0401406	+	0.999194i	$0.512781\pi$
$74$	−17.1674	−1.99567
$75$	1.06276	0.122716
$76$	19.1142	2.19254
$77$	−12.9688	−1.47794
$78$	7.28195	0.824518
$79$	9.54563	1.07397	0.536984	−	0.843593i	$-0.319564\pi$
$79$	9.54563	1.07397	0.536984	+	0.843593i	$0.319564\pi$
$80$	14.5135	1.62265
$81$	−0.990265	−0.110029
$82$	−7.61645	−0.841096
$83$	15.9005	1.74531	0.872655	−	0.488337i	$-0.162396\pi$
$83$	15.9005	1.74531	0.872655	+	0.488337i	$0.162396\pi$
$84$	−10.2231	−1.11543
$85$	−1.33803	−0.145129
$86$	−24.9761	−2.69324
$87$	−10.4412	−1.11942
$88$	−36.1401	−3.85255
$89$	−0.0927770	−0.00983435	−0.00491717	−	0.999988i	$-0.501565\pi$
$89$	−0.0927770	−0.00983435	−0.00491717	+	0.999988i	$0.501565\pi$
$90$	10.4209	1.09846
$91$	5.30126	0.555723
$92$	5.14989	0.536913
$93$	−2.74948	−0.285108
$94$	7.58043	0.781862
$95$	10.8016	1.10822
$96$	−3.82676	−0.390568
$97$	6.37467	0.647250	0.323625	−	0.946185i	$-0.395098\pi$
$97$	6.37467	0.647250	0.323625	+	0.946185i	$0.395098\pi$
$98$	6.68859	0.675650
$99$	−10.6053	−1.06587
$100$	4.02243	0.402243
$101$	−3.01636	−0.300139	−0.150070	−	0.988675i	$-0.547950\pi$
$101$	−3.01636	−0.300139	−0.150070	+	0.988675i	$0.547950\pi$
$102$	1.57146	0.155598
$103$	−7.90484	−0.778887	−0.389444	−	0.921050i	$-0.627333\pi$
$103$	−7.90484	−0.778887	−0.389444	+	0.921050i	$0.627333\pi$
$104$	14.7729	1.44861
$105$	−5.77717	−0.563794
$106$	−2.55361	−0.248028
$107$	9.64073	0.932004	0.466002	−	0.884784i	$-0.345694\pi$
$107$	9.64073	0.932004	0.466002	+	0.884784i	$0.345694\pi$
$108$	−23.0861	−2.22146
$109$	−9.82610	−0.941170	−0.470585	−	0.882355i	$-0.655957\pi$
$109$	−9.82610	−0.941170	−0.470585	+	0.882355i	$0.655957\pi$
$110$	−38.1029	−3.63297
$111$	7.78276	0.738707
$112$	−12.4091	−1.17255
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−12.6860	−1.18816
$115$	2.91026	0.271383
$116$	−39.5192	−3.66926
$117$	4.33511	0.400781
$118$	19.5725	1.80180
$119$	1.14402	0.104872
$120$	−16.0992	−1.46965
$121$	27.7770	2.52519
$122$	−16.1225	−1.45966
$123$	3.45289	0.311336
$124$	−10.4065	−0.934534
$125$	−9.90597	−0.886017
$126$	−8.90996	−0.793763
$127$	15.3618	1.36314	0.681568	−	0.731755i	$-0.261298\pi$
$127$	15.3618	1.36314	0.681568	+	0.731755i	$0.261298\pi$
$128$	15.4513	1.36571
$129$	11.3228	0.996918
$130$	15.5753	1.36604
$131$	3.18483	0.278260	0.139130	−	0.990274i	$-0.455569\pi$
$131$	3.18483	0.278260	0.139130	+	0.990274i	$0.455569\pi$
$132$	30.5672	2.66053
$133$	−9.23544	−0.800815
$134$	−16.5743	−1.43180
$135$	−13.0462	−1.12284
$136$	3.18803	0.273371
$137$	−9.17945	−0.784254	−0.392127	−	0.919911i	$-0.628261\pi$
$137$	−9.17945	−0.784254	−0.392127	+	0.919911i	$0.628261\pi$
$138$	−3.41798	−0.290958
$139$	−1.85509	−0.157347	−0.0786734	−	0.996900i	$-0.525068\pi$
$139$	−1.85509	−0.157347	−0.0786734	+	0.996900i	$0.525068\pi$
$140$	−21.8660	−1.84802
$141$	−3.43656	−0.289410
$142$	−2.51204	−0.210806
$143$	−15.8508	−1.32551
$144$	−10.1476	−0.845630
$145$	−22.3327	−1.85463
$146$	1.72307	0.142602
$147$	−3.03225	−0.250095
$148$	29.4570	2.42135
$149$	−19.1436	−1.56830	−0.784151	−	0.620570i	$-0.786901\pi$
$149$	−19.1436	−1.56830	−0.784151	+	0.620570i	$0.786901\pi$
$150$	−2.66968	−0.217979
$151$	−14.8031	−1.20466	−0.602331	−	0.798247i	$-0.705761\pi$
$151$	−14.8031	−1.20466	−0.602331	+	0.798247i	$0.705761\pi$
$152$	−25.7363	−2.08749
$153$	0.935526	0.0756328
$154$	32.5782	2.62523
$155$	−5.88083	−0.472360
$156$	−12.4949	−1.00039
$157$	4.22845	0.337467	0.168733	−	0.985662i	$-0.446032\pi$
$157$	4.22845	0.337467	0.168733	+	0.985662i	$0.446032\pi$
$158$	−23.9790	−1.90767
$159$	1.15767	0.0918090
$160$	−8.18503	−0.647083
$161$	−2.48829	−0.196105
$162$	2.48758	0.195443
$163$	23.3681	1.83033	0.915165	−	0.403080i	$-0.132060\pi$
$163$	23.3681	1.83033	0.915165	+	0.403080i	$0.132060\pi$
$164$	13.0689	1.02051
$165$	17.2738	1.34476
$166$	−39.9428	−3.10016
$167$	1.25174	0.0968624	0.0484312	−	0.998827i	$-0.484578\pi$
$167$	1.25174	0.0968624	0.0484312	+	0.998827i	$0.484578\pi$
$168$	13.7649	1.06198
$169$	−6.52067	−0.501590
$170$	3.36118	0.257791
$171$	−7.55230	−0.577539
$172$	42.8558	3.26773
$173$	10.5751	0.804010	0.402005	−	0.915638i	$-0.368313\pi$
$173$	10.5751	0.804010	0.402005	+	0.915638i	$0.368313\pi$
$174$	26.2288	1.98840
$175$	−1.94353	−0.146917
$176$	37.1034	2.79677
$177$	−8.87313	−0.666946
$178$	0.233060	0.0174686
$179$	22.7160	1.69787	0.848936	−	0.528495i	$-0.177244\pi$
$179$	22.7160	1.69787	0.848936	+	0.528495i	$0.177244\pi$
$180$	−17.8810	−1.33277
$181$	−3.56244	−0.264794	−0.132397	−	0.991197i	$-0.542267\pi$
$181$	−3.56244	−0.264794	−0.132397	+	0.991197i	$0.542267\pi$
$182$	−13.3170	−0.987119
$183$	7.30905	0.540301
$184$	−6.93408	−0.511187
$185$	16.6465	1.22387
$186$	6.90680	0.506431
$187$	−3.42064	−0.250142
$188$	−13.0071	−0.948637
$189$	11.1546	0.811376
$190$	−27.1341	−1.96851
$191$	22.9476	1.66043	0.830213	−	0.557446i	$-0.188218\pi$
$191$	22.9476	1.66043	0.830213	+	0.557446i	$0.188218\pi$
$192$	−3.95803	−0.285646
$193$	−0.842590	−0.0606510	−0.0303255	−	0.999540i	$-0.509654\pi$
$193$	−0.842590	−0.0606510	−0.0303255	+	0.999540i	$0.509654\pi$
$194$	−16.0134	−1.14970
$195$	−7.06099	−0.505648
$196$	−11.4768	−0.819769
$197$	9.60084	0.684031	0.342016	−	0.939694i	$-0.388890\pi$
$197$	9.60084	0.684031	0.342016	+	0.939694i	$0.388890\pi$
$198$	26.6409	1.89329
$199$	−3.27124	−0.231892	−0.115946	−	0.993256i	$-0.536990\pi$
$199$	−3.27124	−0.231892	−0.115946	+	0.993256i	$0.536990\pi$
$200$	−5.41601	−0.382969
$201$	7.51387	0.529988
$202$	7.57722	0.533132
$203$	19.0946	1.34018
$204$	−2.69642	−0.188787
$205$	7.38534	0.515815
$206$	19.8573	1.38352
$207$	−2.03480	−0.141429
$208$	−15.1667	−1.05162
$209$	27.6141	1.91011
$210$	14.5125	1.00146
$211$	16.0742	1.10659	0.553296	−	0.832985i	$-0.313370\pi$
$211$	16.0742	1.10659	0.553296	+	0.832985i	$0.313370\pi$
$212$	4.38167	0.300934
$213$	1.13882	0.0780309
$214$	−24.2179	−1.65550
$215$	24.2183	1.65167
$216$	31.0843	2.11502
$217$	5.02815	0.341333
$218$	24.6835	1.67178
$219$	−0.781145	−0.0527849
$220$	65.3798	4.40790
$221$	1.39825	0.0940566
$222$	−19.5506	−1.31215
$223$	14.8685	0.995667	0.497833	−	0.867273i	$-0.334129\pi$
$223$	14.8685	0.995667	0.497833	+	0.867273i	$0.334129\pi$
$224$	6.99825	0.467590
$225$	−1.58932	−0.105955
$226$	2.51204	0.167098
$227$	7.42297	0.492680	0.246340	−	0.969184i	$-0.420772\pi$
$227$	7.42297	0.492680	0.246340	+	0.969184i	$0.420772\pi$
$228$	21.7676	1.44160
$229$	−12.7723	−0.844019	−0.422010	−	0.906591i	$-0.638675\pi$
$229$	−12.7723	−0.844019	−0.422010	+	0.906591i	$0.638675\pi$
$230$	−7.31068	−0.482052
$231$	−14.7692	−0.971743
$232$	53.2106	3.49345
$233$	14.4669	0.947755	0.473878	−	0.880591i	$-0.342854\pi$
$233$	14.4669	0.947755	0.473878	+	0.880591i	$0.342854\pi$
$234$	−10.8900	−0.711900
$235$	−7.35042	−0.479488
$236$	−33.5840	−2.18613
$237$	10.8708	0.706133
$238$	−2.87383	−0.186283
$239$	3.70722	0.239800	0.119900	−	0.992786i	$-0.461743\pi$
$239$	3.70722	0.239800	0.119900	+	0.992786i	$0.461743\pi$
$240$	16.5283	1.06689
$241$	13.2945	0.856371	0.428186	−	0.903691i	$-0.359153\pi$
$241$	13.2945	0.856371	0.428186	+	0.903691i	$0.359153\pi$
$242$	−69.7770	−4.48544
$243$	14.9402	0.958414
$244$	27.6641	1.77101
$245$	−6.48564	−0.414352
$246$	−8.67378	−0.553020
$247$	−11.2878	−0.718224
$248$	14.0119	0.889755
$249$	18.1079	1.14754
$250$	24.8842	1.57381
$251$	17.5926	1.11044	0.555219	−	0.831704i	$-0.312635\pi$
$251$	17.5926	1.11044	0.555219	+	0.831704i	$0.312635\pi$
$252$	15.2884	0.963077
$253$	7.44002	0.467750
$254$	−38.5893	−2.42131
$255$	−1.52378	−0.0954226
$256$	−31.8631	−1.99144
$257$	21.6915	1.35308	0.676540	−	0.736406i	$-0.263479\pi$
$257$	21.6915	1.35308	0.676540	+	0.736406i	$0.263479\pi$
$258$	−28.4434	−1.77081
$259$	−14.2328	−0.884385
$260$	−26.7252	−1.65743
$261$	15.6146	0.966522
$262$	−8.00042	−0.494268
$263$	−1.23708	−0.0762813	−0.0381407	−	0.999272i	$-0.512143\pi$
$263$	−1.23708	−0.0762813	−0.0381407	+	0.999272i	$0.512143\pi$
$264$	−41.1572	−2.53305
$265$	2.47612	0.152107
$266$	23.1998	1.42247
$267$	−0.105657	−0.00646608
$268$	28.4393	1.73721
$269$	11.5548	0.704508	0.352254	−	0.935904i	$-0.385415\pi$
$269$	11.5548	0.704508	0.352254	+	0.935904i	$0.385415\pi$
$270$	32.7725	1.99447
$271$	−10.0263	−0.609054	−0.304527	−	0.952504i	$-0.598498\pi$
$271$	−10.0263	−0.609054	−0.304527	+	0.952504i	$0.598498\pi$
$272$	−3.27300	−0.198455
$273$	6.03719	0.365388
$274$	23.0591	1.39305
$275$	5.81118	0.350427
$276$	5.86482	0.353020
$277$	7.87496	0.473161	0.236580	−	0.971612i	$-0.423973\pi$
$277$	7.87496	0.473161	0.236580	+	0.971612i	$0.423973\pi$
$278$	4.66006	0.279492
$279$	4.11178	0.246166
$280$	29.4416	1.75947
$281$	−5.01931	−0.299427	−0.149713	−	0.988729i	$-0.547835\pi$
$281$	−5.01931	−0.299427	−0.149713	+	0.988729i	$0.547835\pi$
$282$	8.63277	0.514074
$283$	−17.8732	−1.06245	−0.531226	−	0.847230i	$-0.678269\pi$
$283$	−17.8732	−1.06245	−0.531226	+	0.847230i	$0.678269\pi$
$284$	4.31034	0.255772
$285$	12.3011	0.728656
$286$	39.8179	2.35448
$287$	−6.31452	−0.372734
$288$	5.72283	0.337221
$289$	−16.6983	−0.982250
$290$	56.1006	3.29434
$291$	7.25963	0.425567
$292$	−2.95656	−0.173020
$293$	18.8000	1.09831	0.549154	−	0.835721i	$-0.314950\pi$
$293$	18.8000	1.09831	0.549154	+	0.835721i	$0.314950\pi$
$294$	7.61712	0.444240
$295$	−18.9787	−1.10498
$296$	−39.6624	−2.30533
$297$	−33.3523	−1.93530
$298$	48.0894	2.78574
$299$	−3.04125	−0.175880
$300$	4.58084	0.264475
$301$	−20.7068	−1.19352
$302$	37.1860	2.13982
$303$	−3.43510	−0.197342
$304$	26.4223	1.51542
$305$	15.6333	0.895158
$306$	−2.35008	−0.134345
$307$	−0.802812	−0.0458189	−0.0229094	−	0.999738i	$-0.507293\pi$
$307$	−0.802812	−0.0458189	−0.0229094	+	0.999738i	$0.507293\pi$
$308$	−55.9001	−3.18521
$309$	−9.00222	−0.512118
$310$	14.7729	0.839043
$311$	−16.3003	−0.924303	−0.462151	−	0.886801i	$-0.652922\pi$
$311$	−16.3003	−0.924303	−0.462151	+	0.886801i	$0.652922\pi$
$312$	16.8238	0.952459
$313$	−30.8858	−1.74577	−0.872883	−	0.487929i	$-0.837752\pi$
$313$	−30.8858	−1.74577	−0.872883	+	0.487929i	$0.837752\pi$
$314$	−10.6220	−0.599435
$315$	8.63961	0.486787
$316$	41.1449	2.31458
$317$	5.79183	0.325301	0.162651	−	0.986684i	$-0.447996\pi$
$317$	5.79183	0.325301	0.162651	+	0.986684i	$0.447996\pi$
$318$	−2.90811	−0.163079
$319$	−57.0931	−3.19660
$320$	−8.46579	−0.473252
$321$	10.9791	0.612793
$322$	6.25068	0.348337
$323$	−2.43593	−0.135539
$324$	−4.26838	−0.237132
$325$	−2.37543	−0.131765
$326$	−58.7015	−3.25118
$327$	−11.1902	−0.618819
$328$	−17.5966	−0.971609
$329$	6.28465	0.346484
$330$	−43.3925	−2.38868
$331$	−18.0663	−0.993014	−0.496507	−	0.868033i	$-0.665384\pi$
$331$	−18.0663	−0.993014	−0.496507	+	0.868033i	$0.665384\pi$
$332$	68.5367	3.76144
$333$	−11.6389	−0.637809
$334$	−3.14442	−0.172055
$335$	16.0713	0.878071
$336$	−14.1318	−0.770951
$337$	4.17157	0.227240	0.113620	−	0.993524i	$-0.463755\pi$
$337$	4.17157	0.227240	0.113620	+	0.993524i	$0.463755\pi$
$338$	16.3802	0.890965
$339$	−1.13882	−0.0618524
$340$	−5.76735	−0.312779
$341$	−15.0342	−0.814150
$342$	18.9717	1.02587
$343$	20.1237	1.08658
$344$	−57.7033	−3.11115
$345$	3.31427	0.178434
$346$	−26.5651	−1.42815
$347$	−4.57022	−0.245342	−0.122671	−	0.992447i	$-0.539146\pi$
$347$	−4.57022	−0.245342	−0.122671	+	0.992447i	$0.539146\pi$
$348$	−45.0053	−2.41254
$349$	−10.2034	−0.546176	−0.273088	−	0.961989i	$-0.588045\pi$
$349$	−10.2034	−0.546176	−0.273088	+	0.961989i	$0.588045\pi$
$350$	4.88222	0.260966
$351$	13.6334	0.727696
$352$	−20.9249	−1.11530
$353$	20.8976	1.11227	0.556133	−	0.831093i	$-0.312284\pi$
$353$	20.8976	1.11227	0.556133	+	0.831093i	$0.312284\pi$
$354$	22.2897	1.18468
$355$	2.43582	0.129280
$356$	−0.399901	−0.0211947
$357$	1.30284	0.0689535
$358$	−57.0634	−3.01590
$359$	6.59011	0.347812	0.173906	−	0.984762i	$-0.444361\pi$
$359$	6.59011	0.347812	0.173906	+	0.984762i	$0.444361\pi$
$360$	24.0759	1.26891
$361$	0.664710	0.0349848
$362$	8.94899	0.470348
$363$	31.6331	1.66031
$364$	22.8502	1.19768
$365$	−1.67078	−0.0874528
$366$	−18.3606	−0.959725
$367$	14.5746	0.760790	0.380395	−	0.924824i	$-0.375788\pi$
$367$	14.5746	0.760790	0.380395	+	0.924824i	$0.375788\pi$
$368$	7.11890	0.371098
$369$	−5.16371	−0.268812
$370$	−41.8166	−2.17394
$371$	−2.11710	−0.109914
$372$	−11.8512	−0.614456
$373$	−12.1919	−0.631270	−0.315635	−	0.948881i	$-0.602218\pi$
$373$	−12.1919	−0.631270	−0.315635	+	0.948881i	$0.602218\pi$
$374$	8.59279	0.444322
$375$	−11.2811	−0.582556
$376$	17.5134	0.903183
$377$	23.3379	1.20196
$378$	−28.0207	−1.44123
$379$	−12.1581	−0.624518	−0.312259	−	0.949997i	$-0.601086\pi$
$379$	−12.1581	−0.624518	−0.312259	+	0.949997i	$0.601086\pi$
$380$	46.5586	2.38841
$381$	17.4943	0.896261
$382$	−57.6452	−2.94938
$383$	4.92879	0.251849	0.125925	−	0.992040i	$-0.459810\pi$
$383$	4.92879	0.251849	0.125925	+	0.992040i	$0.459810\pi$
$384$	17.5963	0.897955
$385$	−31.5897	−1.60996
$386$	2.11662	0.107733
$387$	−16.9330	−0.860753
$388$	27.4770	1.39493
$389$	−10.6987	−0.542444	−0.271222	−	0.962517i	$-0.587428\pi$
$389$	−10.6987	−0.542444	−0.271222	+	0.962517i	$0.587428\pi$
$390$	17.7375	0.898173
$391$	−0.656307	−0.0331909
$392$	15.4529	0.780490
$393$	3.62696	0.182956
$394$	−24.1177	−1.21503
$395$	23.2514	1.16991
$396$	−45.7124	−2.29714
$397$	−17.1441	−0.860439	−0.430219	−	0.902724i	$-0.641564\pi$
$397$	−17.1441	−0.860439	−0.430219	+	0.902724i	$0.641564\pi$
$398$	8.21749	0.411905
$399$	−10.5175	−0.526535
$400$	5.56036	0.278018
$401$	−13.7479	−0.686537	−0.343268	−	0.939237i	$-0.611534\pi$
$401$	−13.7479	−0.686537	−0.343268	+	0.939237i	$0.611534\pi$
$402$	−18.8751	−0.941406
$403$	6.14553	0.306131
$404$	−13.0016	−0.646851
$405$	−2.41210	−0.119858
$406$	−47.9663	−2.38053
$407$	42.5564	2.10944
$408$	3.63060	0.179742
$409$	28.5276	1.41060	0.705299	−	0.708910i	$-0.250813\pi$
$409$	28.5276	1.41060	0.705299	+	0.708910i	$0.250813\pi$
$410$	−18.5523	−0.916231
$411$	−10.4538	−0.515647
$412$	−34.0726	−1.67863
$413$	16.2269	0.798472
$414$	5.11150	0.251217
$415$	38.7308	1.90122
$416$	8.55343	0.419367
$417$	−2.11262	−0.103456
$418$	−69.3677	−3.39289
$419$	7.70474	0.376401	0.188201	−	0.982131i	$-0.439734\pi$
$419$	7.70474	0.376401	0.188201	+	0.982131i	$0.439734\pi$
$420$	−24.9016	−1.21507
$421$	−3.45866	−0.168565	−0.0842825	−	0.996442i	$-0.526860\pi$
$421$	−3.45866	−0.168565	−0.0842825	+	0.996442i	$0.526860\pi$
$422$	−40.3789	−1.96562
$423$	5.13929	0.249881
$424$	−5.89970	−0.286515
$425$	−0.512622	−0.0248658
$426$	−2.86077	−0.138605
$427$	−13.3665	−0.646852
$428$	41.5548	2.00863
$429$	−18.0513	−0.871525
$430$	−60.8372	−2.93383
$431$	22.1191	1.06544	0.532719	−	0.846292i	$-0.321170\pi$
$431$	22.1191	1.06544	0.532719	+	0.846292i	$0.321170\pi$
$432$	−31.9128	−1.53541
$433$	−26.0250	−1.25068	−0.625340	−	0.780353i	$-0.715040\pi$
$433$	−26.0250	−1.25068	−0.625340	+	0.780353i	$0.715040\pi$
$434$	−12.6309	−0.606303
$435$	−25.4330	−1.21942
$436$	−42.3538	−2.02838
$437$	5.29823	0.253448
$438$	1.96227	0.0937607
$439$	39.7875	1.89896	0.949478	−	0.313834i	$-0.101614\pi$
$439$	39.7875	1.89896	0.949478	+	0.313834i	$0.101614\pi$
$440$	−88.0307	−4.19670
$441$	4.53465	0.215936
$442$	−3.51246	−0.167071
$443$	15.1490	0.719749	0.359875	−	0.933001i	$-0.382819\pi$
$443$	15.1490	0.719749	0.359875	+	0.933001i	$0.382819\pi$
$444$	33.5463	1.59204
$445$	−0.225988	−0.0107129
$446$	−37.3502	−1.76858
$447$	−21.8011	−1.03116
$448$	7.23831	0.341978
$449$	−18.6450	−0.879912	−0.439956	−	0.898019i	$-0.645006\pi$
$449$	−18.6450	−0.879912	−0.439956	+	0.898019i	$0.645006\pi$
$450$	3.99244	0.188206
$451$	18.8805	0.889048
$452$	−4.31034	−0.202741
$453$	−16.8581	−0.792064
$454$	−18.6468	−0.875137
$455$	12.9129	0.605366
$456$	−29.3091	−1.37252
$457$	18.6502	0.872421	0.436210	−	0.899845i	$-0.356320\pi$
$457$	18.6502	0.872421	0.436210	+	0.899845i	$0.356320\pi$
$458$	32.0846	1.49921
$459$	2.94211	0.137326
$460$	12.5442	0.584876
$461$	−25.3418	−1.18029	−0.590144	−	0.807298i	$-0.700929\pi$
$461$	−25.3418	−1.18029	−0.590144	+	0.807298i	$0.700929\pi$
$462$	37.1009	1.72609
$463$	19.2873	0.896357	0.448179	−	0.893944i	$-0.352073\pi$
$463$	19.2873	0.896357	0.448179	+	0.893944i	$0.352073\pi$
$464$	−54.6289	−2.53608
$465$	−6.69723	−0.310577
$466$	−36.3413	−1.68348
$467$	3.69170	0.170831	0.0854157	−	0.996345i	$-0.472778\pi$
$467$	3.69170	0.170831	0.0854157	+	0.996345i	$0.472778\pi$
$468$	18.6858	0.863752
$469$	−13.7411	−0.634505
$470$	18.4645	0.851706
$471$	4.81545	0.221884
$472$	45.2192	2.08138
$473$	61.9135	2.84679
$474$	−27.3078	−1.25429
$475$	4.13829	0.189878
$476$	4.93112	0.226018
$477$	−1.73126	−0.0792691
$478$	−9.31268	−0.425952
$479$	−24.9840	−1.14155	−0.570774	−	0.821107i	$-0.693357\pi$
$479$	−24.9840	−1.14155	−0.570774	+	0.821107i	$0.693357\pi$
$480$	−9.32130	−0.425457
$481$	−17.3957	−0.793176
$482$	−33.3962	−1.52115
$483$	−2.83372	−0.128939
$484$	119.728	5.44220
$485$	15.5275	0.705069
$486$	−37.5304	−1.70241
$487$	24.4930	1.10988	0.554942	−	0.831889i	$-0.312740\pi$
$487$	24.4930	1.10988	0.554942	+	0.831889i	$0.312740\pi$
$488$	−37.2484	−1.68615
$489$	26.6121	1.20344
$490$	16.2922	0.736006
$491$	−22.4990	−1.01537	−0.507683	−	0.861544i	$-0.669498\pi$
$491$	−22.4990	−1.01537	−0.507683	+	0.861544i	$0.669498\pi$
$492$	14.8831	0.670983
$493$	5.03636	0.226826
$494$	28.3554	1.27577
$495$	−25.8326	−1.16109
$496$	−14.3853	−0.645921
$497$	−2.08264	−0.0934191
$498$	−45.4877	−2.03835
$499$	−2.21148	−0.0989993	−0.0494997	−	0.998774i	$-0.515763\pi$
$499$	−2.21148	−0.0989993	−0.0494997	+	0.998774i	$0.515763\pi$
$500$	−42.6981	−1.90952
$501$	1.42551	0.0636870
$502$	−44.1934	−1.97245
$503$	−9.18749	−0.409650	−0.204825	−	0.978799i	$-0.565662\pi$
$503$	−9.18749	−0.409650	−0.204825	+	0.978799i	$0.565662\pi$
$504$	−20.5850	−0.916931
$505$	−7.34731	−0.326951
$506$	−18.6896	−0.830855
$507$	−7.42589	−0.329796
$508$	66.2144	2.93779
$509$	−15.8751	−0.703652	−0.351826	−	0.936065i	$-0.614439\pi$
$509$	−15.8751	−0.703652	−0.351826	+	0.936065i	$0.614439\pi$
$510$	3.82779	0.169497
$511$	1.42853	0.0631945
$512$	49.1388	2.17165
$513$	−23.7510	−1.04863
$514$	−54.4899	−2.40345
$515$	−19.2547	−0.848466
$516$	48.8052	2.14853
$517$	−18.7912	−0.826436
$518$	35.7534	1.57092
$519$	12.0432	0.528636
$520$	35.9842	1.57801
$521$	30.2459	1.32510	0.662549	−	0.749018i	$-0.269475\pi$
$521$	30.2459	1.32510	0.662549	+	0.749018i	$0.269475\pi$
$522$	−39.2246	−1.71681
$523$	−10.2307	−0.447359	−0.223679	−	0.974663i	$-0.571807\pi$
$523$	−10.2307	−0.447359	−0.223679	+	0.974663i	$0.571807\pi$
$524$	13.7277	0.599698
$525$	−2.21334	−0.0965979
$526$	3.10758	0.135497
$527$	1.32622	0.0577709
$528$	42.2542	1.83888
$529$	−21.5725	−0.937935
$530$	−6.22012	−0.270185
$531$	13.2696	0.575850
$532$	−39.8079	−1.72589
$533$	−7.71775	−0.334293
$534$	0.265414	0.0114856
$535$	23.4831	1.01526
$536$	−38.2922	−1.65397
$537$	25.8695	1.11635
$538$	−29.0261	−1.25140
$539$	−16.5804	−0.714169
$540$	−56.2335	−2.41990
$541$	−21.2942	−0.915509	−0.457754	−	0.889079i	$-0.651346\pi$
$541$	−21.2942	−0.915509	−0.457754	+	0.889079i	$0.651346\pi$
$542$	25.1864	1.08185
$543$	−4.05699	−0.174102
$544$	1.84585	0.0791401
$545$	−23.9346	−1.02524
$546$	−15.1657	−0.649031
$547$	7.54051	0.322409	0.161205	−	0.986921i	$-0.448462\pi$
$547$	7.54051	0.322409	0.161205	+	0.986921i	$0.448462\pi$
$548$	−39.5666	−1.69020
$549$	−10.9305	−0.466503
$550$	−14.5979	−0.622457
$551$	−40.6574	−1.73207
$552$	−7.89669	−0.336105
$553$	−19.8801	−0.845388
$554$	−19.7822	−0.840466
$555$	18.9574	0.804696
$556$	−7.99608	−0.339109
$557$	2.99409	0.126864	0.0634319	−	0.997986i	$-0.479795\pi$
$557$	2.99409	0.126864	0.0634319	+	0.997986i	$0.479795\pi$
$558$	−10.3290	−0.437259
$559$	−25.3083	−1.07043
$560$	−30.2263	−1.27729
$561$	−3.89551	−0.164468
$562$	12.6087	0.531866
$563$	2.04427	0.0861556	0.0430778	−	0.999072i	$-0.486284\pi$
$563$	2.04427	0.0861556	0.0430778	+	0.999072i	$0.486284\pi$
$564$	−14.8127	−0.623729
$565$	−2.43582	−0.102476
$566$	44.8982	1.88721
$567$	2.06236	0.0866112
$568$	−5.80366	−0.243516
$569$	2.20924	0.0926163	0.0463082	−	0.998927i	$-0.485254\pi$
$569$	2.20924	0.0926163	0.0463082	+	0.998927i	$0.485254\pi$
$570$	−30.9009	−1.29430
$571$	19.9566	0.835160	0.417580	−	0.908640i	$-0.362878\pi$
$571$	19.9566	0.835160	0.417580	+	0.908640i	$0.362878\pi$
$572$	−68.3225	−2.85671
$573$	26.1332	1.09173
$574$	15.8623	0.662080
$575$	1.11497	0.0464975
$576$	5.91914	0.246631
$577$	−11.6554	−0.485222	−0.242611	−	0.970124i	$-0.578004\pi$
$577$	−11.6554	−0.485222	−0.242611	+	0.970124i	$0.578004\pi$
$578$	41.9467	1.74475
$579$	−0.959561	−0.0398780
$580$	−96.2615	−3.99704
$581$	−33.1151	−1.37384
$582$	−18.2365	−0.755926
$583$	6.33016	0.262169
$584$	3.98087	0.164729
$585$	10.5595	0.436583
$586$	−47.2263	−1.95090
$587$	−13.3673	−0.551728	−0.275864	−	0.961197i	$-0.588964\pi$
$587$	−13.3673	−0.551728	−0.275864	+	0.961197i	$0.588964\pi$
$588$	−13.0700	−0.538998
$589$	−10.7063	−0.441144
$590$	47.6751	1.96275
$591$	10.9337	0.449750
$592$	40.7196	1.67356
$593$	−26.5093	−1.08861	−0.544303	−	0.838888i	$-0.683206\pi$
$593$	−26.5093	−1.08861	−0.544303	+	0.838888i	$0.683206\pi$
$594$	83.7823	3.43763
$595$	2.78663	0.114241
$596$	−82.5153	−3.37996
$597$	−3.72537	−0.152469
$598$	7.63973	0.312412
$599$	23.1795	0.947089	0.473545	−	0.880770i	$-0.342974\pi$
$599$	23.1795	0.947089	0.473545	+	0.880770i	$0.342974\pi$
$600$	−6.16787	−0.251802
$601$	22.4643	0.916336	0.458168	−	0.888866i	$-0.348506\pi$
$601$	22.4643	0.916336	0.458168	+	0.888866i	$0.348506\pi$
$602$	52.0162	2.12002
$603$	−11.2368	−0.457598
$604$	−63.8065	−2.59625
$605$	67.6598	2.75076
$606$	8.62912	0.350534
$607$	17.0610	0.692485	0.346243	−	0.938145i	$-0.387457\pi$
$607$	17.0610	0.692485	0.346243	+	0.938145i	$0.387457\pi$
$608$	−14.9011	−0.604321
$609$	21.7454	0.881166
$610$	−39.2714	−1.59005
$611$	7.68126	0.310750
$612$	4.03244	0.163002
$613$	18.5757	0.750267	0.375133	−	0.926971i	$-0.377597\pi$
$613$	18.5757	0.750267	0.375133	+	0.926971i	$0.377597\pi$
$614$	2.01669	0.0813872
$615$	8.41060	0.339148
$616$	75.2668	3.03259
$617$	−20.7126	−0.833858	−0.416929	−	0.908939i	$-0.636894\pi$
$617$	−20.7126	−0.833858	−0.416929	+	0.908939i	$0.636894\pi$
$618$	22.6139	0.909665
$619$	29.5961	1.18957	0.594785	−	0.803885i	$-0.297237\pi$
$619$	29.5961	1.18957	0.594785	+	0.803885i	$0.297237\pi$
$620$	−25.3484	−1.01802
$621$	−6.39920	−0.256791
$622$	40.9469	1.64182
$623$	0.193221	0.00774124
$624$	−17.2722	−0.691441
$625$	−28.7952	−1.15181
$626$	77.5862	3.10097
$627$	31.4476	1.25590
$628$	18.2260	0.727298
$629$	−3.75403	−0.149683
$630$	−21.7030	−0.864670
$631$	−23.0089	−0.915969	−0.457985	−	0.888960i	$-0.651429\pi$
$631$	−23.0089	−0.915969	−0.457985	+	0.888960i	$0.651429\pi$
$632$	−55.3996	−2.20368
$633$	18.3056	0.727584
$634$	−14.5493	−0.577826
$635$	37.4184	1.48491
$636$	4.98994	0.197864
$637$	6.77756	0.268537
$638$	143.420	5.67805
$639$	−1.70308	−0.0673729
$640$	37.6365	1.48771
$641$	−19.0627	−0.752930	−0.376465	−	0.926431i	$-0.622861\pi$
$641$	−19.0627	−0.752930	−0.376465	+	0.926431i	$0.622861\pi$
$642$	−27.5799	−1.08849
$643$	−17.4093	−0.686555	−0.343277	−	0.939234i	$-0.611537\pi$
$643$	−17.4093	−0.686555	−0.343277	+	0.939234i	$0.611537\pi$
$644$	−10.7254	−0.422639
$645$	27.5803	1.08597
$646$	6.11914	0.240754
$647$	−48.4182	−1.90352	−0.951758	−	0.306850i	$-0.900725\pi$
$647$	−48.4182	−1.90352	−0.951758	+	0.306850i	$0.900725\pi$
$648$	5.74717	0.225770
$649$	−48.5186	−1.90452
$650$	5.96717	0.234052
$651$	5.72617	0.224426
$652$	100.724	3.94467
$653$	14.2327	0.556969	0.278485	−	0.960441i	$-0.410168\pi$
$653$	14.2327	0.556969	0.278485	+	0.960441i	$0.410168\pi$
$654$	28.1102	1.09920
$655$	7.75767	0.303117
$656$	18.0656	0.705343
$657$	1.16818	0.0455752
$658$	−15.7873	−0.615453
$659$	−5.40820	−0.210674	−0.105337	−	0.994437i	$-0.533592\pi$
$659$	−5.40820	−0.210674	−0.105337	+	0.994437i	$0.533592\pi$
$660$	74.4560	2.89820
$661$	42.4670	1.65178	0.825888	−	0.563835i	$-0.190674\pi$
$661$	42.4670	1.65178	0.825888	+	0.563835i	$0.190674\pi$
$662$	45.3833	1.76387
$663$	1.59236	0.0618422
$664$	−92.2814	−3.58121
$665$	−22.4959	−0.872352
$666$	29.2374	1.13293
$667$	−10.9543	−0.424150
$668$	5.39542	0.208755
$669$	16.9326	0.654651
$670$	−40.3718	−1.55970
$671$	39.9661	1.54288
$672$	7.96977	0.307441
$673$	44.0183	1.69678	0.848391	−	0.529371i	$-0.177572\pi$
$673$	44.0183	1.69678	0.848391	+	0.529371i	$0.177572\pi$
$674$	−10.4791	−0.403641
$675$	−4.99822	−0.192382
$676$	−28.1063	−1.08101
$677$	48.2615	1.85484	0.927421	−	0.374020i	$-0.122021\pi$
$677$	48.2615	1.85484	0.927421	+	0.374020i	$0.122021\pi$
$678$	2.86077	0.109867
$679$	−13.2761	−0.509492
$680$	7.76546	0.297792
$681$	8.45345	0.323937
$682$	37.7666	1.44616
$683$	−2.63464	−0.100812	−0.0504058	−	0.998729i	$-0.516051\pi$
$683$	−2.63464	−0.100812	−0.0504058	+	0.998729i	$0.516051\pi$
$684$	−32.5530	−1.24469
$685$	−22.3595	−0.854311
$686$	−50.5516	−1.93007
$687$	−14.5454	−0.554943
$688$	59.2413	2.25855
$689$	−2.58757	−0.0985787
$690$	−8.32557	−0.316949
$691$	25.3093	0.962812	0.481406	−	0.876498i	$-0.340126\pi$
$691$	25.3093	0.962812	0.481406	+	0.876498i	$0.340126\pi$
$692$	45.5823	1.73278
$693$	22.0870	0.839016
$694$	11.4806	0.435796
$695$	−4.51867	−0.171403
$696$	60.5975	2.29694
$697$	−1.66551	−0.0630856
$698$	25.6314	0.970162
$699$	16.4752	0.623149
$700$	−8.37727	−0.316631
$701$	7.76930	0.293442	0.146721	−	0.989178i	$-0.453128\pi$
$701$	7.76930	0.293442	0.146721	+	0.989178i	$0.453128\pi$
$702$	−34.2476	−1.29259
$703$	30.3055	1.14299
$704$	−21.6426	−0.815688
$705$	−8.37083	−0.315264
$706$	−52.4956	−1.97570
$707$	6.28200	0.236259
$708$	−38.2462	−1.43738
$709$	−39.1716	−1.47112	−0.735560	−	0.677460i	$-0.763081\pi$
$709$	−39.1716	−1.47112	−0.735560	+	0.677460i	$0.763081\pi$
$710$	−6.11887	−0.229637
$711$	−16.2570	−0.609685
$712$	0.538447	0.0201791
$713$	−2.88457	−0.108028
$714$	−3.27278	−0.122481
$715$	−38.6097	−1.44392
$716$	97.9136	3.65920
$717$	4.22187	0.157668
$718$	−16.5546	−0.617812
$719$	31.0558	1.15818	0.579092	−	0.815262i	$-0.303407\pi$
$719$	31.0558	1.15818	0.579092	+	0.815262i	$0.303407\pi$
$720$	−24.7176	−0.921171
$721$	16.4629	0.613112
$722$	−1.66978	−0.0621427
$723$	15.1400	0.563064
$724$	−15.3553	−0.570676
$725$	−8.55605	−0.317764
$726$	−79.4637	−2.94917
$727$	−45.5261	−1.68847	−0.844234	−	0.535975i	$-0.819944\pi$
$727$	−45.5261	−1.68847	−0.844234	+	0.535975i	$0.819944\pi$
$728$	−30.7667	−1.14029
$729$	19.9850	0.740187
$730$	4.19707	0.155341
$731$	−5.46158	−0.202004
$732$	31.5045	1.16444
$733$	−48.9008	−1.80619	−0.903096	−	0.429438i	$-0.858712\pi$
$733$	−48.9008	−1.80619	−0.903096	+	0.429438i	$0.858712\pi$
$734$	−36.6121	−1.35138
$735$	−7.38600	−0.272437
$736$	−4.01478	−0.147987
$737$	41.0861	1.51343
$738$	12.9714	0.477485
$739$	−51.9020	−1.90925	−0.954623	−	0.297818i	$-0.903741\pi$
$739$	−51.9020	−1.90925	−0.954623	+	0.297818i	$0.903741\pi$
$740$	71.7519	2.63765
$741$	−12.8548	−0.472232
$742$	5.31824	0.195239
$743$	−9.23857	−0.338930	−0.169465	−	0.985536i	$-0.554204\pi$
$743$	−9.23857	−0.338930	−0.169465	+	0.985536i	$0.554204\pi$
$744$	15.9571	0.585014
$745$	−46.6303	−1.70840
$746$	30.6264	1.12131
$747$	−27.0799	−0.990802
$748$	−14.7441	−0.539099
$749$	−20.0782	−0.733640
$750$	28.3387	1.03478
$751$	15.8040	0.576697	0.288348	−	0.957526i	$-0.406894\pi$
$751$	15.8040	0.576697	0.288348	+	0.957526i	$0.406894\pi$
$752$	−17.9802	−0.655669
$753$	20.0349	0.730112
$754$	−58.6256	−2.13502
$755$	−36.0577	−1.31227
$756$	48.0800	1.74865
$757$	−43.2644	−1.57247	−0.786236	−	0.617926i	$-0.787973\pi$
$757$	−43.2644	−1.57247	−0.786236	+	0.617926i	$0.787973\pi$
$758$	30.5415	1.10932
$759$	8.47286	0.307545
$760$	−62.6889	−2.27397
$761$	30.1233	1.09197	0.545985	−	0.837795i	$-0.316156\pi$
$761$	30.1233	1.09197	0.545985	+	0.837795i	$0.316156\pi$
$762$	−43.9464	−1.59201
$763$	20.4642	0.740855
$764$	98.9118	3.57850
$765$	2.27877	0.0823891
$766$	−12.3813	−0.447355
$767$	19.8329	0.716124
$768$	−36.2864	−1.30937
$769$	29.6541	1.06935	0.534676	−	0.845057i	$-0.320434\pi$
$769$	29.6541	1.06935	0.534676	+	0.845057i	$0.320434\pi$
$770$	79.3547	2.85974
$771$	24.7028	0.889650
$772$	−3.63185	−0.130713
$773$	40.1400	1.44373	0.721867	−	0.692032i	$-0.243284\pi$
$773$	40.1400	1.44373	0.721867	+	0.692032i	$0.243284\pi$
$774$	42.5363	1.52894
$775$	−2.25305	−0.0809320
$776$	−36.9965	−1.32810
$777$	−16.2087	−0.581483
$778$	26.8755	0.963532
$779$	13.4453	0.481727
$780$	−30.4353	−1.08976
$781$	6.22712	0.222824
$782$	1.64867	0.0589563
$783$	49.1061	1.75491
$784$	−15.8648	−0.566600
$785$	10.2997	0.367613
$786$	−9.11106	−0.324981
$787$	30.4722	1.08622	0.543109	−	0.839662i	$-0.317247\pi$
$787$	30.4722	1.08622	0.543109	+	0.839662i	$0.317247\pi$
$788$	41.3829	1.47420
$789$	−1.40881	−0.0501550
$790$	−58.4085	−2.07808
$791$	2.08264	0.0740501
$792$	61.5496	2.18707
$793$	−16.3369	−0.580140
$794$	43.0667	1.52838
$795$	2.81987	0.100010
$796$	−14.1002	−0.499767
$797$	29.3240	1.03871	0.519354	−	0.854559i	$-0.326173\pi$
$797$	29.3240	1.03871	0.519354	+	0.854559i	$0.326173\pi$
$798$	26.4205	0.935274
$799$	1.65763	0.0586428
$800$	−3.13583	−0.110868
$801$	0.158007	0.00558290
$802$	34.5352	1.21948
$803$	−4.27133	−0.150732
$804$	32.3873	1.14221
$805$	−6.06101	−0.213623
$806$	−15.4378	−0.543773
$807$	13.1589	0.463214
$808$	17.5060	0.615858
$809$	−6.65013	−0.233806	−0.116903	−	0.993143i	$-0.537297\pi$
$809$	−6.65013	−0.233806	−0.116903	+	0.993143i	$0.537297\pi$
$810$	6.05930	0.212902
$811$	40.1322	1.40923	0.704616	−	0.709588i	$-0.251119\pi$
$811$	40.1322	1.40923	0.704616	+	0.709588i	$0.251119\pi$
$812$	82.3042	2.88831
$813$	−11.4182	−0.400453
$814$	−106.903	−3.74696
$815$	56.9204	1.99383
$816$	−3.72737	−0.130484
$817$	44.0902	1.54252
$818$	−71.6624	−2.50562
$819$	−9.02848	−0.315481
$820$	31.8333	1.11167
$821$	22.1760	0.773948	0.386974	−	0.922091i	$-0.373520\pi$
$821$	22.1760	0.773948	0.386974	+	0.922091i	$0.373520\pi$
$822$	26.2603	0.915933
$823$	−3.50926	−0.122325	−0.0611626	−	0.998128i	$-0.519481\pi$
$823$	−3.50926	−0.122325	−0.0611626	+	0.998128i	$0.519481\pi$
$824$	45.8770	1.59820
$825$	6.61790	0.230406
$826$	−40.7625	−1.41831
$827$	36.9152	1.28367	0.641834	−	0.766844i	$-0.278174\pi$
$827$	36.9152	1.28367	0.641834	+	0.766844i	$0.278174\pi$
$828$	−8.77069	−0.304803
$829$	−50.0506	−1.73833	−0.869164	−	0.494524i	$-0.835342\pi$
$829$	−50.0506	−1.73833	−0.869164	+	0.494524i	$0.835342\pi$
$830$	−97.2933	−3.37710
$831$	8.96819	0.311103
$832$	8.84683	0.306709
$833$	1.46261	0.0506764
$834$	5.30699	0.183766
$835$	3.04901	0.105515
$836$	119.026	4.11661
$837$	12.9310	0.446962
$838$	−19.3546	−0.668594
$839$	45.3330	1.56507	0.782535	−	0.622606i	$-0.213926\pi$
$839$	45.3330	1.56507	0.782535	+	0.622606i	$0.213926\pi$
$840$	33.5287	1.15685
$841$	55.0606	1.89864
$842$	8.68830	0.299418
$843$	−5.71611	−0.196873
$844$	69.2851	2.38489
$845$	−15.8832	−0.546398
$846$	−12.9101	−0.443858
$847$	−57.8496	−1.98773
$848$	6.05695	0.207996
$849$	−20.3544	−0.698562
$850$	1.28773	0.0441687
$851$	8.16514	0.279898
$852$	4.90871	0.168170
$853$	−30.9417	−1.05942	−0.529712	−	0.848178i	$-0.677700\pi$
$853$	−30.9417	−1.05942	−0.529712	+	0.848178i	$0.677700\pi$
$854$	33.5773	1.14899
$855$	−18.3960	−0.629131
$856$	−55.9515	−1.91238
$857$	−10.4401	−0.356628	−0.178314	−	0.983974i	$-0.557064\pi$
$857$	−10.4401	−0.356628	−0.178314	+	0.983974i	$0.557064\pi$
$858$	45.3456	1.54807
$859$	38.2283	1.30433	0.652167	−	0.758076i	$-0.273860\pi$
$859$	38.2283	1.30433	0.652167	+	0.758076i	$0.273860\pi$
$860$	104.389	3.55963
$861$	−7.19112	−0.245073
$862$	−55.5640	−1.89252
$863$	−23.0543	−0.784779	−0.392389	−	0.919799i	$-0.628351\pi$
$863$	−23.0543	−0.784779	−0.392389	+	0.919799i	$0.628351\pi$
$864$	17.9976	0.612290
$865$	25.7590	0.875832
$866$	65.3757	2.22156
$867$	−19.0164	−0.645829
$868$	21.6730	0.735631
$869$	59.4418	2.01643
$870$	63.8886	2.16603
$871$	−16.7947	−0.569067
$872$	57.0274	1.93119
$873$	−10.8566	−0.367440
$874$	−13.3093	−0.450195
$875$	20.6306	0.697440
$876$	−3.36700	−0.113760
$877$	5.60858	0.189388	0.0946941	−	0.995506i	$-0.469813\pi$
$877$	5.60858	0.189388	0.0946941	+	0.995506i	$0.469813\pi$
$878$	−99.9479	−3.37308
$879$	21.4099	0.722137
$880$	90.3770	3.04661
$881$	12.6899	0.427533	0.213767	−	0.976885i	$-0.431427\pi$
$881$	12.6899	0.427533	0.213767	+	0.976885i	$0.431427\pi$
$882$	−11.3912	−0.383562
$883$	−35.8920	−1.20786	−0.603932	−	0.797036i	$-0.706400\pi$
$883$	−35.8920	−1.20786	−0.603932	+	0.797036i	$0.706400\pi$
$884$	6.02694	0.202708
$885$	−21.6133	−0.726524
$886$	−38.0548	−1.27848
$887$	35.2874	1.18484	0.592418	−	0.805631i	$-0.298173\pi$
$887$	35.2874	1.18484	0.592418	+	0.805631i	$0.298173\pi$
$888$	−45.1685	−1.51576
$889$	−31.9930	−1.07301
$890$	0.567690	0.0190290
$891$	−6.16650	−0.206586
$892$	64.0882	2.14583
$893$	−13.3817	−0.447801
$894$	54.7653	1.83163
$895$	55.3320	1.84954
$896$	−32.1794	−1.07504
$897$	−3.46344	−0.115641
$898$	46.8370	1.56297
$899$	22.1356	0.738262
$900$	−6.85053	−0.228351
$901$	−0.558403	−0.0186031
$902$	−47.4285	−1.57920
$903$	−23.5813	−0.784738
$904$	5.80366	0.193027
$905$	−8.67745	−0.288448
$906$	42.3483	1.40693
$907$	29.7342	0.987308	0.493654	−	0.869658i	$-0.335661\pi$
$907$	29.7342	0.987308	0.493654	+	0.869658i	$0.335661\pi$
$908$	31.9955	1.06181
$909$	5.13712	0.170387
$910$	−32.4377	−1.07530
$911$	−18.4954	−0.612781	−0.306390	−	0.951906i	$-0.599121\pi$
$911$	−18.4954	−0.612781	−0.306390	+	0.951906i	$0.599121\pi$
$912$	30.0903	0.996388
$913$	99.0146	3.27690
$914$	−46.8501	−1.54966
$915$	17.8035	0.588566
$916$	−55.0531	−1.81901
$917$	−6.63285	−0.219036
$918$	−7.39070	−0.243929
$919$	0.120182	0.00396445	0.00198222	−	0.999998i	$-0.499369\pi$
$919$	0.120182	0.00396445	0.00198222	+	0.999998i	$0.499369\pi$
$920$	−16.8902	−0.556852
$921$	−0.914261	−0.0301259
$922$	63.6597	2.09652
$923$	−2.54545	−0.0837846
$924$	−63.6604	−2.09427
$925$	6.37755	0.209693
$926$	−48.4505	−1.59218
$927$	13.4626	0.442170
$928$	30.8086	1.01134
$929$	−9.55684	−0.313550	−0.156775	−	0.987634i	$-0.550110\pi$
$929$	−9.55684	−0.313550	−0.156775	+	0.987634i	$0.550110\pi$
$930$	16.8237	0.551671
$931$	−11.8073	−0.386970
$932$	62.3571	2.04257
$933$	−18.5631	−0.607729
$934$	−9.27369	−0.303445
$935$	−8.33206	−0.272487
$936$	−25.1595	−0.822365
$937$	54.1782	1.76992	0.884962	−	0.465663i	$-0.154184\pi$
$937$	54.1782	1.76992	0.884962	+	0.465663i	$0.154184\pi$
$938$	34.5182	1.12706
$939$	−35.1734	−1.14784
$940$	−31.6828	−1.03338
$941$	−6.01029	−0.195930	−0.0979650	−	0.995190i	$-0.531233\pi$
$941$	−6.01029	−0.195930	−0.0979650	+	0.995190i	$0.531233\pi$
$942$	−12.0966	−0.394129
$943$	3.62254	0.117966
$944$	−46.4245	−1.51099
$945$	27.1705	0.883856
$946$	−155.529	−5.05669
$947$	13.9539	0.453442	0.226721	−	0.973960i	$-0.427199\pi$
$947$	13.9539	0.453442	0.226721	+	0.973960i	$0.427199\pi$
$948$	46.8568	1.52184
$949$	1.74598	0.0566771
$950$	−10.3955	−0.337276
$951$	6.59586	0.213886
$952$	−6.63952	−0.215188
$953$	−40.1650	−1.30107	−0.650537	−	0.759475i	$-0.725456\pi$
$953$	−40.1650	−1.30107	−0.650537	+	0.759475i	$0.725456\pi$
$954$	4.34900	0.140804
$955$	55.8961	1.80875
$956$	15.9794	0.516810
$957$	−65.0189	−2.10176
$958$	62.7608	2.02771
$959$	19.1175	0.617336
$960$	−9.64104	−0.311163
$961$	−25.1711	−0.811970
$962$	43.6987	1.40890
$963$	−16.4190	−0.529093
$964$	57.3036	1.84563
$965$	−2.05240	−0.0660689
$966$	7.11841	0.229031
$967$	−36.3859	−1.17009	−0.585046	−	0.811000i	$-0.698924\pi$
$967$	−36.3859	−1.17009	−0.585046	+	0.811000i	$0.698924\pi$
$968$	−161.209	−5.18144
$969$	−2.77409	−0.0891166
$970$	−39.0058	−1.25240
$971$	10.0831	0.323581	0.161790	−	0.986825i	$-0.448273\pi$
$971$	10.0831	0.323581	0.161790	+	0.986825i	$0.448273\pi$
$972$	64.3973	2.06555
$973$	3.86349	0.123858
$974$	−61.5274	−1.97147
$975$	−2.70519	−0.0866355
$976$	38.2411	1.22407
$977$	−30.5937	−0.978780	−0.489390	−	0.872065i	$-0.662781\pi$
$977$	−30.5937	−0.978780	−0.489390	+	0.872065i	$0.662781\pi$
$978$	−66.8507	−2.13765
$979$	−0.577734	−0.0184645
$980$	−27.9553	−0.893000
$981$	16.7347	0.534296
$982$	56.5184	1.80358
$983$	32.0776	1.02312	0.511558	−	0.859249i	$-0.329068\pi$
$983$	32.0776	1.02312	0.511558	+	0.859249i	$0.329068\pi$
$984$	−20.0394	−0.638832
$985$	23.3859	0.745136
$986$	−12.6515	−0.402907
$987$	7.15711	0.227813
$988$	−48.6542	−1.54790
$989$	11.8791	0.377735
$990$	64.8924	2.06242
$991$	−43.8235	−1.39210	−0.696049	−	0.717994i	$-0.745060\pi$
$991$	−43.8235	−1.39210	−0.696049	+	0.717994i	$0.745060\pi$
$992$	8.11278	0.257581
$993$	−20.5743	−0.652906
$994$	5.23167	0.165939
$995$	−7.96815	−0.252607
$996$	78.0512	2.47315
$997$	−41.4030	−1.31125	−0.655623	−	0.755088i	$-0.727594\pi$
$997$	−41.4030	−1.31125	−0.655623	+	0.755088i	$0.727594\pi$
$998$	5.55532	0.175851
$999$	−36.6029	−1.15807

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.9	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.9	✓	165	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51204 q^{2} +1.13882 q^{3} +4.31034 q^{4} +2.43582 q^{5} -2.86077 q^{6} -2.08264 q^{7} -5.80366 q^{8} -1.70308 q^{9} +O(q^{10})\)	\(q-2.51204 q^{2} +1.13882 q^{3} +4.31034 q^{4} +2.43582 q^{5} -2.86077 q^{6} -2.08264 q^{7} -5.80366 q^{8} -1.70308 q^{9} -6.11887 q^{10} +6.22712 q^{11} +4.90871 q^{12} -2.54545 q^{13} +5.23167 q^{14} +2.77396 q^{15} +5.95835 q^{16} -0.549314 q^{17} +4.27821 q^{18} +4.43449 q^{19} +10.4992 q^{20} -2.37176 q^{21} -15.6428 q^{22} +1.19478 q^{23} -6.60935 q^{24} +0.933205 q^{25} +6.39427 q^{26} -5.35598 q^{27} -8.97688 q^{28} -9.16846 q^{29} -6.96831 q^{30} -2.41432 q^{31} -3.36028 q^{32} +7.09159 q^{33} +1.37990 q^{34} -5.07293 q^{35} -7.34086 q^{36} +6.83404 q^{37} -11.1396 q^{38} -2.89882 q^{39} -14.1367 q^{40} +3.03198 q^{41} +5.95795 q^{42} +9.94256 q^{43} +26.8410 q^{44} -4.14840 q^{45} -3.00132 q^{46} -3.01764 q^{47} +6.78551 q^{48} -2.66261 q^{49} -2.34425 q^{50} -0.625571 q^{51} -10.9718 q^{52} +1.01655 q^{53} +13.4544 q^{54} +15.1681 q^{55} +12.0869 q^{56} +5.05010 q^{57} +23.0315 q^{58} -7.79149 q^{59} +11.9567 q^{60} +6.41808 q^{61} +6.06486 q^{62} +3.54691 q^{63} -3.47555 q^{64} -6.20026 q^{65} -17.8143 q^{66} +6.59793 q^{67} -2.36773 q^{68} +1.36064 q^{69} +12.7434 q^{70} +1.00000 q^{71} +9.88412 q^{72} -0.685923 q^{73} -17.1674 q^{74} +1.06276 q^{75} +19.1142 q^{76} -12.9688 q^{77} +7.28195 q^{78} +9.54563 q^{79} +14.5135 q^{80} -0.990265 q^{81} -7.61645 q^{82} +15.9005 q^{83} -10.2231 q^{84} -1.33803 q^{85} -24.9761 q^{86} -10.4412 q^{87} -36.1401 q^{88} -0.0927770 q^{89} +10.4209 q^{90} +5.30126 q^{91} +5.14989 q^{92} -2.74948 q^{93} +7.58043 q^{94} +10.8016 q^{95} -3.82676 q^{96} +6.37467 q^{97} +6.68859 q^{98} -10.6053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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