LMFDB - Embedded newform 8023.2.a.c.1.2

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:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.78025 q^{2} -2.83508 q^{3} +5.72982 q^{4} -1.35792 q^{5} +7.88223 q^{6} +4.56765 q^{7} -10.3698 q^{8} +5.03765 q^{9} +O(q^{10})$	\(q-2.78025 q^{2} -2.83508 q^{3} +5.72982 q^{4} -1.35792 q^{5} +7.88223 q^{6} +4.56765 q^{7} -10.3698 q^{8} +5.03765 q^{9} +3.77538 q^{10} -2.32075 q^{11} -16.2445 q^{12} +0.925145 q^{13} -12.6992 q^{14} +3.84982 q^{15} +17.3712 q^{16} +6.55335 q^{17} -14.0060 q^{18} +3.74303 q^{19} -7.78066 q^{20} -12.9496 q^{21} +6.45229 q^{22} -3.65314 q^{23} +29.3993 q^{24} -3.15604 q^{25} -2.57214 q^{26} -5.77690 q^{27} +26.1718 q^{28} +6.80696 q^{29} -10.7035 q^{30} +0.567710 q^{31} -27.5566 q^{32} +6.57951 q^{33} -18.2200 q^{34} -6.20253 q^{35} +28.8648 q^{36} -0.527535 q^{37} -10.4066 q^{38} -2.62285 q^{39} +14.0815 q^{40} -10.2683 q^{41} +36.0033 q^{42} +2.28995 q^{43} -13.2975 q^{44} -6.84076 q^{45} +10.1567 q^{46} +6.93053 q^{47} -49.2486 q^{48} +13.8635 q^{49} +8.77459 q^{50} -18.5793 q^{51} +5.30091 q^{52} -6.32497 q^{53} +16.0613 q^{54} +3.15141 q^{55} -47.3659 q^{56} -10.6118 q^{57} -18.9251 q^{58} +4.25528 q^{59} +22.0588 q^{60} +13.6294 q^{61} -1.57838 q^{62} +23.0103 q^{63} +41.8720 q^{64} -1.25628 q^{65} -18.2927 q^{66} +0.248824 q^{67} +37.5495 q^{68} +10.3569 q^{69} +17.2446 q^{70} -1.00000 q^{71} -52.2397 q^{72} -4.69109 q^{73} +1.46668 q^{74} +8.94761 q^{75} +21.4469 q^{76} -10.6004 q^{77} +7.29220 q^{78} -10.4399 q^{79} -23.5887 q^{80} +1.26500 q^{81} +28.5486 q^{82} -12.1304 q^{83} -74.1991 q^{84} -8.89896 q^{85} -6.36666 q^{86} -19.2982 q^{87} +24.0659 q^{88} -11.0175 q^{89} +19.0190 q^{90} +4.22574 q^{91} -20.9318 q^{92} -1.60950 q^{93} -19.2686 q^{94} -5.08275 q^{95} +78.1250 q^{96} -11.9944 q^{97} -38.5440 q^{98} -11.6912 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.78025	−1.96594	−0.982969	−	0.183774i	$-0.941169\pi$
$2$	−2.78025	−1.96594	−0.982969	+	0.183774i	$0.941169\pi$
$3$	−2.83508	−1.63683	−0.818416	−	0.574626i	$-0.805147\pi$
$3$	−2.83508	−1.63683	−0.818416	+	0.574626i	$0.805147\pi$
$4$	5.72982	2.86491
$5$	−1.35792	−0.607283	−0.303641	−	0.952786i	$-0.598202\pi$
$5$	−1.35792	−0.607283	−0.303641	+	0.952786i	$0.598202\pi$
$6$	7.88223	3.21791
$7$	4.56765	1.72641	0.863206	−	0.504853i	$-0.168453\pi$
$7$	4.56765	1.72641	0.863206	+	0.504853i	$0.168453\pi$
$8$	−10.3698	−3.66629
$9$	5.03765	1.67922
$10$	3.77538	1.19388
$11$	−2.32075	−0.699734	−0.349867	−	0.936799i	$-0.613773\pi$
$11$	−2.32075	−0.699734	−0.349867	+	0.936799i	$0.613773\pi$
$12$	−16.2445	−4.68937
$13$	0.925145	0.256589	0.128294	−	0.991736i	$-0.459050\pi$
$13$	0.925145	0.256589	0.128294	+	0.991736i	$0.459050\pi$
$14$	−12.6992	−3.39402
$15$	3.84982	0.994019
$16$	17.3712	4.34279
$17$	6.55335	1.58942	0.794711	−	0.606988i	$-0.207623\pi$
$17$	6.55335	1.58942	0.794711	+	0.606988i	$0.207623\pi$
$18$	−14.0060	−3.30124
$19$	3.74303	0.858709	0.429355	−	0.903136i	$-0.358741\pi$
$19$	3.74303	0.858709	0.429355	+	0.903136i	$0.358741\pi$
$20$	−7.78066	−1.73981
$21$	−12.9496	−2.82584
$22$	6.45229	1.37563
$23$	−3.65314	−0.761732	−0.380866	−	0.924630i	$-0.624374\pi$
$23$	−3.65314	−0.761732	−0.380866	+	0.924630i	$0.624374\pi$
$24$	29.3993	6.00110
$25$	−3.15604	−0.631208
$26$	−2.57214	−0.504438
$27$	−5.77690	−1.11177
$28$	26.1718	4.94601
$29$	6.80696	1.26402	0.632010	−	0.774960i	$-0.282230\pi$
$29$	6.80696	1.26402	0.632010	+	0.774960i	$0.282230\pi$
$30$	−10.7035	−1.95418
$31$	0.567710	0.101964	0.0509819	−	0.998700i	$-0.483765\pi$
$31$	0.567710	0.101964	0.0509819	+	0.998700i	$0.483765\pi$
$32$	−27.5566	−4.87136
$33$	6.57951	1.14535
$34$	−18.2200	−3.12470
$35$	−6.20253	−1.04842
$36$	28.8648	4.81081
$37$	−0.527535	−0.0867262	−0.0433631	−	0.999059i	$-0.513807\pi$
$37$	−0.527535	−0.0867262	−0.0433631	+	0.999059i	$0.513807\pi$
$38$	−10.4066	−1.68817
$39$	−2.62285	−0.419993
$40$	14.0815	2.22648
$41$	−10.2683	−1.60364	−0.801821	−	0.597564i	$-0.796135\pi$
$41$	−10.2683	−1.60364	−0.801821	+	0.597564i	$0.796135\pi$
$42$	36.0033	5.55543
$43$	2.28995	0.349215	0.174607	−	0.984638i	$-0.444134\pi$
$43$	2.28995	0.349215	0.174607	+	0.984638i	$0.444134\pi$
$44$	−13.2975	−2.00467
$45$	−6.84076	−1.01976
$46$	10.1567	1.49752
$47$	6.93053	1.01092	0.505461	−	0.862850i	$-0.331323\pi$
$47$	6.93053	1.01092	0.505461	+	0.862850i	$0.331323\pi$
$48$	−49.2486	−7.10842
$49$	13.8635	1.98050
$50$	8.77459	1.24092
$51$	−18.5793	−2.60162
$52$	5.30091	0.735104
$53$	−6.32497	−0.868802	−0.434401	−	0.900720i	$-0.643040\pi$
$53$	−6.32497	−0.868802	−0.434401	+	0.900720i	$0.643040\pi$
$54$	16.0613	2.18566
$55$	3.15141	0.424936
$56$	−47.3659	−6.32953
$57$	−10.6118	−1.40556
$58$	−18.9251	−2.48498
$59$	4.25528	0.553990	0.276995	−	0.960871i	$-0.410661\pi$
$59$	4.25528	0.553990	0.276995	+	0.960871i	$0.410661\pi$
$60$	22.0588	2.84777
$61$	13.6294	1.74506	0.872532	−	0.488557i	$-0.162477\pi$
$61$	13.6294	1.74506	0.872532	+	0.488557i	$0.162477\pi$
$62$	−1.57838	−0.200454
$63$	23.0103	2.89902
$64$	41.8720	5.23400
$65$	−1.25628	−0.155822
$66$	−18.2927	−2.25168
$67$	0.248824	0.0303986	0.0151993	−	0.999884i	$-0.495162\pi$
$67$	0.248824	0.0303986	0.0151993	+	0.999884i	$0.495162\pi$
$68$	37.5495	4.55355
$69$	10.3569	1.24683
$70$	17.2446	2.06113
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−52.2397	−6.15650
$73$	−4.69109	−0.549050	−0.274525	−	0.961580i	$-0.588521\pi$
$73$	−4.69109	−0.549050	−0.274525	+	0.961580i	$0.588521\pi$
$74$	1.46668	0.170498
$75$	8.94761	1.03318
$76$	21.4469	2.46012
$77$	−10.6004	−1.20803
$78$	7.29220	0.825680
$79$	−10.4399	−1.17458	−0.587292	−	0.809375i	$-0.699806\pi$
$79$	−10.4399	−1.17458	−0.587292	+	0.809375i	$0.699806\pi$
$80$	−23.5887	−2.63730
$81$	1.26500	0.140555
$82$	28.5486	3.15266
$83$	−12.1304	−1.33148	−0.665741	−	0.746183i	$-0.731884\pi$
$83$	−12.1304	−1.33148	−0.665741	+	0.746183i	$0.731884\pi$
$84$	−74.1991	−8.09579
$85$	−8.89896	−0.965228
$86$	−6.36666	−0.686534
$87$	−19.2982	−2.06899
$88$	24.0659	2.56543
$89$	−11.0175	−1.16785	−0.583927	−	0.811806i	$-0.698484\pi$
$89$	−11.0175	−1.16785	−0.583927	+	0.811806i	$0.698484\pi$
$90$	19.0190	2.00478
$91$	4.22574	0.442978
$92$	−20.9318	−2.18229
$93$	−1.60950	−0.166898
$94$	−19.2686	−1.98741
$95$	−5.08275	−0.521479
$96$	78.1250	7.97360
$97$	−11.9944	−1.21784	−0.608922	−	0.793230i	$-0.708398\pi$
$97$	−11.9944	−1.21784	−0.608922	+	0.793230i	$0.708398\pi$
$98$	−38.5440	−3.89353
$99$	−11.6912	−1.17501
$100$	−18.0835	−1.80835
$101$	1.99744	0.198753	0.0993765	−	0.995050i	$-0.468315\pi$
$101$	1.99744	0.198753	0.0993765	+	0.995050i	$0.468315\pi$
$102$	51.6551	5.11461
$103$	−13.4220	−1.32251	−0.661253	−	0.750163i	$-0.729975\pi$
$103$	−13.4220	−1.32251	−0.661253	+	0.750163i	$0.729975\pi$
$104$	−9.59360	−0.940730
$105$	17.5846	1.71609
$106$	17.5850	1.70801
$107$	9.86660	0.953840	0.476920	−	0.878947i	$-0.341753\pi$
$107$	9.86660	0.953840	0.476920	+	0.878947i	$0.341753\pi$
$108$	−33.1006	−3.18511
$109$	2.21647	0.212299	0.106149	−	0.994350i	$-0.466148\pi$
$109$	2.21647	0.212299	0.106149	+	0.994350i	$0.466148\pi$
$110$	−8.76172	−0.835397
$111$	1.49560	0.141956
$112$	79.3455	7.49744
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	29.5034	2.76325
$115$	4.96069	0.462587
$116$	39.0026	3.62130
$117$	4.66056	0.430869
$118$	−11.8308	−1.08911
$119$	29.9334	2.74399
$120$	−39.9220	−3.64437
$121$	−5.61410	−0.510373
$122$	−37.8932	−3.43068
$123$	29.1115	2.62489
$124$	3.25288	0.292117
$125$	11.0753	0.990604
$126$	−63.9744	−5.69929
$127$	−22.0617	−1.95766	−0.978828	−	0.204686i	$-0.934383\pi$
$127$	−22.0617	−1.95766	−0.978828	+	0.204686i	$0.934383\pi$
$128$	−61.3017	−5.41835
$129$	−6.49219	−0.571606
$130$	3.49277	0.306336
$131$	−4.10331	−0.358508	−0.179254	−	0.983803i	$-0.557368\pi$
$131$	−4.10331	−0.358508	−0.179254	+	0.983803i	$0.557368\pi$
$132$	37.6994	3.28131
$133$	17.0969	1.48249
$134$	−0.691793	−0.0597618
$135$	7.84460	0.675156
$136$	−67.9572	−5.82728
$137$	−11.1980	−0.956713	−0.478357	−	0.878166i	$-0.658767\pi$
$137$	−11.1980	−0.956713	−0.478357	+	0.878166i	$0.658767\pi$
$138$	−28.7949	−2.45118
$139$	1.30155	0.110396	0.0551980	−	0.998475i	$-0.482421\pi$
$139$	1.30155	0.110396	0.0551980	+	0.998475i	$0.482421\pi$
$140$	−35.5394	−3.00363
$141$	−19.6486	−1.65471
$142$	2.78025	0.233314
$143$	−2.14703	−0.179544
$144$	87.5099	7.29249
$145$	−9.24334	−0.767617
$146$	13.0424	1.07940
$147$	−39.3040	−3.24174
$148$	−3.02268	−0.248463
$149$	−5.33309	−0.436904	−0.218452	−	0.975848i	$-0.570101\pi$
$149$	−5.33309	−0.436904	−0.218452	+	0.975848i	$0.570101\pi$
$150$	−24.8766	−2.03117
$151$	−2.88788	−0.235013	−0.117506	−	0.993072i	$-0.537490\pi$
$151$	−2.88788	−0.235013	−0.117506	+	0.993072i	$0.537490\pi$
$152$	−38.8146	−3.14828
$153$	33.0135	2.66899
$154$	29.4718	2.37491
$155$	−0.770908	−0.0619208
$156$	−15.0285	−1.20324
$157$	−16.0035	−1.27722	−0.638608	−	0.769532i	$-0.720490\pi$
$157$	−16.0035	−1.27722	−0.638608	+	0.769532i	$0.720490\pi$
$158$	29.0257	2.30916
$159$	17.9318	1.42208
$160$	37.4198	2.95829
$161$	−16.6863	−1.31506
$162$	−3.51702	−0.276323
$163$	−23.6542	−1.85274	−0.926371	−	0.376612i	$-0.877089\pi$
$163$	−23.6542	−1.85274	−0.926371	+	0.376612i	$0.877089\pi$
$164$	−58.8356	−4.59429
$165$	−8.93449	−0.695549
$166$	33.7255	2.61761
$167$	−8.49400	−0.657285	−0.328643	−	0.944454i	$-0.606591\pi$
$167$	−8.49400	−0.657285	−0.328643	+	0.944454i	$0.606591\pi$
$168$	134.286	10.3604
$169$	−12.1441	−0.934162
$170$	24.7414	1.89758
$171$	18.8561	1.44196
$172$	13.1210	1.00047
$173$	−1.96994	−0.149772	−0.0748859	−	0.997192i	$-0.523859\pi$
$173$	−1.96994	−0.149772	−0.0748859	+	0.997192i	$0.523859\pi$
$174$	53.6540	4.06750
$175$	−14.4157	−1.08972
$176$	−40.3142	−3.03880
$177$	−12.0640	−0.906789
$178$	30.6315	2.29593
$179$	3.32473	0.248502	0.124251	−	0.992251i	$-0.460347\pi$
$179$	3.32473	0.248502	0.124251	+	0.992251i	$0.460347\pi$
$180$	−39.1963	−2.92152
$181$	−9.24568	−0.687226	−0.343613	−	0.939111i	$-0.611651\pi$
$181$	−9.24568	−0.687226	−0.343613	+	0.939111i	$0.611651\pi$
$182$	−11.7486	−0.870867
$183$	−38.6403	−2.85638
$184$	37.8825	2.79273
$185$	0.716353	0.0526673
$186$	4.47482	0.328110
$187$	−15.2087	−1.11217
$188$	39.7107	2.89620
$189$	−26.3869	−1.91936
$190$	14.1313	1.02520
$191$	4.13653	0.299309	0.149655	−	0.988738i	$-0.452184\pi$
$191$	4.13653	0.299309	0.149655	+	0.988738i	$0.452184\pi$
$192$	−118.710	−8.56718
$193$	−2.78974	−0.200810	−0.100405	−	0.994947i	$-0.532014\pi$
$193$	−2.78974	−0.200810	−0.100405	+	0.994947i	$0.532014\pi$
$194$	33.3474	2.39420
$195$	3.56164	0.255054
$196$	79.4351	5.67394
$197$	−21.1019	−1.50345	−0.751726	−	0.659476i	$-0.770778\pi$
$197$	−21.1019	−1.50345	−0.751726	+	0.659476i	$0.770778\pi$
$198$	32.5044	2.30999
$199$	6.71402	0.475944	0.237972	−	0.971272i	$-0.423517\pi$
$199$	6.71402	0.475944	0.237972	+	0.971272i	$0.423517\pi$
$200$	32.7276	2.31419
$201$	−0.705434	−0.0497574
$202$	−5.55340	−0.390736
$203$	31.0918	2.18222
$204$	−106.456	−7.45339
$205$	13.9436	0.973864
$206$	37.3165	2.59996
$207$	−18.4033	−1.27911
$208$	16.0708	1.11431
$209$	−8.68664	−0.600868
$210$	−48.8898	−3.37372
$211$	−10.2201	−0.703580	−0.351790	−	0.936079i	$-0.614427\pi$
$211$	−10.2201	−0.703580	−0.351790	+	0.936079i	$0.614427\pi$
$212$	−36.2409	−2.48904
$213$	2.83508	0.194256
$214$	−27.4317	−1.87519
$215$	−3.10959	−0.212072
$216$	59.9056	4.07606
$217$	2.59310	0.176031
$218$	−6.16234	−0.417366
$219$	13.2996	0.898702
$220$	18.0570	1.21740
$221$	6.06280	0.407828
$222$	−4.15815	−0.279077
$223$	1.64166	0.109933	0.0549667	−	0.998488i	$-0.482495\pi$
$223$	1.64166	0.109933	0.0549667	+	0.998488i	$0.482495\pi$
$224$	−125.869	−8.40997
$225$	−15.8990	−1.05994
$226$	2.78025	0.184940
$227$	14.4635	0.959977	0.479988	−	0.877275i	$-0.340641\pi$
$227$	14.4635	0.959977	0.479988	+	0.877275i	$0.340641\pi$
$228$	−60.8035	−4.02681
$229$	17.4257	1.15152	0.575760	−	0.817619i	$-0.304706\pi$
$229$	17.4257	1.15152	0.575760	+	0.817619i	$0.304706\pi$
$230$	−13.7920	−0.909416
$231$	30.0529	1.97734
$232$	−70.5871	−4.63427
$233$	−9.64829	−0.632081	−0.316040	−	0.948746i	$-0.602354\pi$
$233$	−9.64829	−0.632081	−0.316040	+	0.948746i	$0.602354\pi$
$234$	−12.9575	−0.847061
$235$	−9.41114	−0.613915
$236$	24.3820	1.58713
$237$	29.5980	1.92260
$238$	−83.2226	−5.39452
$239$	12.4640	0.806232	0.403116	−	0.915149i	$-0.367927\pi$
$239$	12.4640	0.806232	0.403116	+	0.915149i	$0.367927\pi$
$240$	66.8759	4.31682
$241$	−20.0926	−1.29428	−0.647139	−	0.762372i	$-0.724035\pi$
$241$	−20.0926	−1.29428	−0.647139	+	0.762372i	$0.724035\pi$
$242$	15.6086	1.00336
$243$	13.7443	0.881700
$244$	78.0939	4.99945
$245$	−18.8255	−1.20272
$246$	−80.9373	−5.16037
$247$	3.46284	0.220335
$248$	−5.88706	−0.373829
$249$	34.3905	2.17941
$250$	−30.7921	−1.94747
$251$	9.05151	0.571327	0.285663	−	0.958330i	$-0.407786\pi$
$251$	9.05151	0.571327	0.285663	+	0.958330i	$0.407786\pi$
$252$	131.845	8.30543
$253$	8.47804	0.533010
$254$	61.3370	3.84863
$255$	25.2292	1.57992
$256$	86.6903	5.41814
$257$	7.75143	0.483521	0.241761	−	0.970336i	$-0.422275\pi$
$257$	7.75143	0.483521	0.241761	+	0.970336i	$0.422275\pi$
$258$	18.0500	1.12374
$259$	−2.40960	−0.149725
$260$	−7.19824	−0.446416
$261$	34.2911	2.12257
$262$	11.4083	0.704804
$263$	−7.97762	−0.491921	−0.245961	−	0.969280i	$-0.579103\pi$
$263$	−7.97762	−0.491921	−0.245961	+	0.969280i	$0.579103\pi$
$264$	−68.2285	−4.19917
$265$	8.58884	0.527608
$266$	−47.5336	−2.91447
$267$	31.2355	1.91158
$268$	1.42571	0.0870893
$269$	9.21856	0.562065	0.281033	−	0.959698i	$-0.409323\pi$
$269$	9.21856	0.562065	0.281033	+	0.959698i	$0.409323\pi$
$270$	−21.8100	−1.32731
$271$	13.6676	0.830246	0.415123	−	0.909765i	$-0.363739\pi$
$271$	13.6676	0.830246	0.415123	+	0.909765i	$0.363739\pi$
$272$	113.839	6.90253
$273$	−11.9803	−0.725080
$274$	31.1334	1.88084
$275$	7.32439	0.441677
$276$	59.3433	3.57205
$277$	20.2242	1.21515	0.607576	−	0.794262i	$-0.292142\pi$
$277$	20.2242	1.21515	0.607576	+	0.794262i	$0.292142\pi$
$278$	−3.61864	−0.217032
$279$	2.85993	0.171219
$280$	64.3193	3.84381
$281$	30.7000	1.83141	0.915705	−	0.401851i	$-0.131633\pi$
$281$	30.7000	1.83141	0.915705	+	0.401851i	$0.131633\pi$
$282$	54.6280	3.25305
$283$	32.8524	1.95287	0.976436	−	0.215805i	$-0.0692377\pi$
$283$	32.8524	1.95287	0.976436	+	0.215805i	$0.0692377\pi$
$284$	−5.72982	−0.340002
$285$	14.4100	0.853574
$286$	5.96930	0.352972
$287$	−46.9021	−2.76855
$288$	−138.821	−8.18008
$289$	25.9464	1.52626
$290$	25.6988	1.50909
$291$	34.0049	1.99341
$292$	−26.8791	−1.57298
$293$	−24.4695	−1.42952	−0.714761	−	0.699369i	$-0.753464\pi$
$293$	−24.4695	−1.42952	−0.714761	+	0.699369i	$0.753464\pi$
$294$	109.275	6.37305
$295$	−5.77835	−0.336429
$296$	5.47045	0.317964
$297$	13.4068	0.777940
$298$	14.8274	0.858926
$299$	−3.37968	−0.195452
$300$	51.2682	2.95997
$301$	10.4597	0.602888
$302$	8.02905	0.462020
$303$	−5.66290	−0.325325
$304$	65.0207	3.72920
$305$	−18.5077	−1.05975
$306$	−91.7860	−5.24706
$307$	−5.00753	−0.285795	−0.142897	−	0.989738i	$-0.545642\pi$
$307$	−5.00753	−0.285795	−0.142897	+	0.989738i	$0.545642\pi$
$308$	−60.7384	−3.46089
$309$	38.0523	2.16472
$310$	2.14332	0.121732
$311$	13.2735	0.752669	0.376334	−	0.926484i	$-0.377184\pi$
$311$	13.2735	0.752669	0.376334	+	0.926484i	$0.377184\pi$
$312$	27.1986	1.53982
$313$	−13.5598	−0.766445	−0.383222	−	0.923656i	$-0.625186\pi$
$313$	−13.5598	−0.766445	−0.383222	+	0.923656i	$0.625186\pi$
$314$	44.4937	2.51093
$315$	−31.2462	−1.76052
$316$	−59.8189	−3.36507
$317$	−18.2361	−1.02424	−0.512121	−	0.858913i	$-0.671140\pi$
$317$	−18.2361	−1.02424	−0.512121	+	0.858913i	$0.671140\pi$
$318$	−49.8549	−2.79572
$319$	−15.7973	−0.884478
$320$	−56.8590	−3.17852
$321$	−27.9726	−1.56128
$322$	46.3921	2.58533
$323$	24.5294	1.36485
$324$	7.24820	0.402678
$325$	−2.91979	−0.161961
$326$	65.7648	3.64237
$327$	−6.28385	−0.347498
$328$	106.481	5.87942
$329$	31.6563	1.74527
$330$	24.8401	1.36741
$331$	−14.7073	−0.808387	−0.404193	−	0.914674i	$-0.632448\pi$
$331$	−14.7073	−0.808387	−0.404193	+	0.914674i	$0.632448\pi$
$332$	−69.5048	−3.81457
$333$	−2.65754	−0.145632
$334$	23.6155	1.29218
$335$	−0.337884	−0.0184606
$336$	−224.950	−12.2721
$337$	32.8557	1.78977	0.894883	−	0.446300i	$-0.147259\pi$
$337$	32.8557	1.78977	0.894883	+	0.446300i	$0.147259\pi$
$338$	33.7637	1.83650
$339$	2.83508	0.153980
$340$	−50.9894	−2.76529
$341$	−1.31752	−0.0713475
$342$	−52.4247	−2.83480
$343$	31.3499	1.69274
$344$	−23.7465	−1.28032
$345$	−14.0639	−0.757177
$346$	5.47694	0.294442
$347$	35.1785	1.88848	0.944240	−	0.329258i	$-0.106799\pi$
$347$	35.1785	1.88848	0.944240	+	0.329258i	$0.106799\pi$
$348$	−110.575	−5.92746
$349$	30.8581	1.65180	0.825898	−	0.563820i	$-0.190669\pi$
$349$	30.8581	1.65180	0.825898	+	0.563820i	$0.190669\pi$
$350$	40.0793	2.14233
$351$	−5.34447	−0.285267
$352$	63.9521	3.40866
$353$	19.6728	1.04708	0.523538	−	0.852003i	$-0.324612\pi$
$353$	19.6728	1.04708	0.523538	+	0.852003i	$0.324612\pi$
$354$	33.5411	1.78269
$355$	1.35792	0.0720712
$356$	−63.1283	−3.34579
$357$	−84.8636	−4.49146
$358$	−9.24360	−0.488539
$359$	−25.3106	−1.33584	−0.667921	−	0.744232i	$-0.732816\pi$
$359$	−25.3106	−1.33584	−0.667921	+	0.744232i	$0.732816\pi$
$360$	70.9376	3.73874
$361$	−4.98975	−0.262618
$362$	25.7053	1.35104
$363$	15.9164	0.835394
$364$	24.2127	1.26909
$365$	6.37014	0.333428
$366$	107.430	5.61545
$367$	−32.0745	−1.67427	−0.837137	−	0.546994i	$-0.815772\pi$
$367$	−32.0745	−1.67427	−0.837137	+	0.546994i	$0.815772\pi$
$368$	−63.4593	−3.30804
$369$	−51.7283	−2.69287
$370$	−1.99164	−0.103541
$371$	−28.8903	−1.49991
$372$	−9.22215	−0.478146
$373$	−18.1022	−0.937298	−0.468649	−	0.883384i	$-0.655259\pi$
$373$	−18.1022	−0.937298	−0.468649	+	0.883384i	$0.655259\pi$
$374$	42.2841	2.18646
$375$	−31.3993	−1.62145
$376$	−71.8685	−3.70633
$377$	6.29742	0.324334
$378$	73.3623	3.77335
$379$	−17.8823	−0.918553	−0.459276	−	0.888293i	$-0.651891\pi$
$379$	−17.8823	−0.918553	−0.459276	+	0.888293i	$0.651891\pi$
$380$	−29.1232	−1.49399
$381$	62.5465	3.20435
$382$	−11.5006	−0.588423
$383$	30.5204	1.55952	0.779759	−	0.626080i	$-0.215342\pi$
$383$	30.5204	1.55952	0.779759	+	0.626080i	$0.215342\pi$
$384$	173.795	8.86893
$385$	14.3946	0.733614
$386$	7.75620	0.394780
$387$	11.5360	0.586408
$388$	−68.7255	−3.48901
$389$	−34.2585	−1.73697	−0.868486	−	0.495713i	$-0.834907\pi$
$389$	−34.2585	−1.73697	−0.868486	+	0.495713i	$0.834907\pi$
$390$	−9.90227	−0.501421
$391$	−23.9403	−1.21071
$392$	−143.762	−7.26107
$393$	11.6332	0.586817
$394$	58.6688	2.95569
$395$	14.1766	0.713304
$396$	−66.9882	−3.36628
$397$	−30.0695	−1.50915	−0.754573	−	0.656216i	$-0.772156\pi$
$397$	−30.0695	−1.50915	−0.754573	+	0.656216i	$0.772156\pi$
$398$	−18.6667	−0.935677
$399$	−48.4709	−2.42658
$400$	−54.8241	−2.74120
$401$	−27.4334	−1.36996	−0.684980	−	0.728562i	$-0.740189\pi$
$401$	−27.4334	−1.36996	−0.684980	+	0.728562i	$0.740189\pi$
$402$	1.96129	0.0978200
$403$	0.525214	0.0261628
$404$	11.4450	0.569409
$405$	−1.71777	−0.0853568
$406$	−86.4432	−4.29010
$407$	1.22428	0.0606852
$408$	192.664	9.53828
$409$	10.2227	0.505481	0.252740	−	0.967534i	$-0.418668\pi$
$409$	10.2227	0.505481	0.252740	+	0.967534i	$0.418668\pi$
$410$	−38.7668	−1.91456
$411$	31.7473	1.56598
$412$	−76.9054	−3.78886
$413$	19.4366	0.956415
$414$	51.1657	2.51466
$415$	16.4721	0.808586
$416$	−25.4938	−1.24994
$417$	−3.68999	−0.180700
$418$	24.1511	1.18127
$419$	−36.6206	−1.78903	−0.894516	−	0.447036i	$-0.852480\pi$
$419$	−36.6206	−1.78903	−0.894516	+	0.447036i	$0.852480\pi$
$420$	100.757	4.91643
$421$	26.5902	1.29593	0.647965	−	0.761670i	$-0.275620\pi$
$421$	26.5902	1.29593	0.647965	+	0.761670i	$0.275620\pi$
$422$	28.4145	1.38319
$423$	34.9136	1.69756
$424$	65.5890	3.18528
$425$	−20.6826	−1.00326
$426$	−7.88223	−0.381895
$427$	62.2543	3.01270
$428$	56.5338	2.73267
$429$	6.08700	0.293883
$430$	8.64544	0.416920
$431$	−20.4152	−0.983367	−0.491684	−	0.870774i	$-0.663618\pi$
$431$	−20.4152	−0.983367	−0.491684	+	0.870774i	$0.663618\pi$
$432$	−100.352	−4.82817
$433$	−24.3286	−1.16916	−0.584578	−	0.811337i	$-0.698740\pi$
$433$	−24.3286	−1.16916	−0.584578	+	0.811337i	$0.698740\pi$
$434$	−7.20949	−0.346067
$435$	26.2056	1.25646
$436$	12.6999	0.608217
$437$	−13.6738	−0.654107
$438$	−36.9762	−1.76679
$439$	14.7695	0.704909	0.352454	−	0.935829i	$-0.385347\pi$
$439$	14.7695	0.704909	0.352454	+	0.935829i	$0.385347\pi$
$440$	−32.6796	−1.55794
$441$	69.8393	3.32568
$442$	−16.8561	−0.801764
$443$	−9.08687	−0.431730	−0.215865	−	0.976423i	$-0.569257\pi$
$443$	−9.08687	−0.431730	−0.215865	+	0.976423i	$0.569257\pi$
$444$	8.56952	0.406692
$445$	14.9609	0.709217
$446$	−4.56422	−0.216122
$447$	15.1197	0.715138
$448$	191.257	9.03604
$449$	−25.8193	−1.21849	−0.609245	−	0.792982i	$-0.708527\pi$
$449$	−25.8193	−1.21849	−0.609245	+	0.792982i	$0.708527\pi$
$450$	44.2034	2.08377
$451$	23.8302	1.12212
$452$	−5.72982	−0.269508
$453$	8.18736	0.384676
$454$	−40.2122	−1.88725
$455$	−5.73824	−0.269013
$456$	110.042	5.15320
$457$	−28.4982	−1.33309	−0.666545	−	0.745465i	$-0.732227\pi$
$457$	−28.4982	−1.33309	−0.666545	+	0.745465i	$0.732227\pi$
$458$	−48.4478	−2.26382
$459$	−37.8581	−1.76706
$460$	28.4238	1.32527
$461$	16.1738	0.753288	0.376644	−	0.926358i	$-0.377078\pi$
$461$	16.1738	0.753288	0.376644	+	0.926358i	$0.377078\pi$
$462$	−83.5548	−3.88732
$463$	3.84579	0.178729	0.0893646	−	0.995999i	$-0.471516\pi$
$463$	3.84579	0.178729	0.0893646	+	0.995999i	$0.471516\pi$
$464$	118.245	5.48938
$465$	2.18558	0.101354
$466$	26.8247	1.24263
$467$	−19.6041	−0.907170	−0.453585	−	0.891213i	$-0.649855\pi$
$467$	−19.6041	−0.907170	−0.453585	+	0.891213i	$0.649855\pi$
$468$	26.7041	1.23440
$469$	1.13654	0.0524805
$470$	26.1654	1.20692
$471$	45.3711	2.09059
$472$	−44.1266	−2.03109
$473$	−5.31442	−0.244357
$474$	−82.2899	−3.77970
$475$	−11.8131	−0.542024
$476$	171.513	7.86129
$477$	−31.8630	−1.45891
$478$	−34.6532	−1.58500
$479$	−19.6463	−0.897663	−0.448832	−	0.893616i	$-0.648160\pi$
$479$	−19.6463	−0.897663	−0.448832	+	0.893616i	$0.648160\pi$
$480$	−106.088	−4.84223
$481$	−0.488046	−0.0222530
$482$	55.8625	2.54447
$483$	47.3069	2.15254
$484$	−32.1678	−1.46217
$485$	16.2875	0.739575
$486$	−38.2128	−1.73337
$487$	−8.52740	−0.386413	−0.193207	−	0.981158i	$-0.561889\pi$
$487$	−8.52740	−0.386413	−0.193207	+	0.981158i	$0.561889\pi$
$488$	−141.335	−6.39791
$489$	67.0615	3.03263
$490$	52.3398	2.36447
$491$	40.5401	1.82955	0.914774	−	0.403965i	$-0.132368\pi$
$491$	40.5401	1.82955	0.914774	+	0.403965i	$0.132368\pi$
$492$	166.803	7.52008
$493$	44.6084	2.00906
$494$	−9.62758	−0.433165
$495$	15.8757	0.713560
$496$	9.86179	0.442807
$497$	−4.56765	−0.204887
$498$	−95.6145	−4.28459
$499$	11.9027	0.532837	0.266419	−	0.963857i	$-0.414160\pi$
$499$	11.9027	0.532837	0.266419	+	0.963857i	$0.414160\pi$
$500$	63.4594	2.83799
$501$	24.0811	1.07587
$502$	−25.1655	−1.12319
$503$	13.4961	0.601763	0.300882	−	0.953662i	$-0.402719\pi$
$503$	13.4961	0.601763	0.300882	+	0.953662i	$0.402719\pi$
$504$	−238.613	−10.6287
$505$	−2.71238	−0.120699
$506$	−23.5711	−1.04786
$507$	34.4295	1.52907
$508$	−126.409	−5.60850
$509$	41.5708	1.84259	0.921296	−	0.388862i	$-0.127132\pi$
$509$	41.5708	1.84259	0.921296	+	0.388862i	$0.127132\pi$
$510$	−70.1437	−3.10601
$511$	−21.4273	−0.947886
$512$	−118.418	−5.23337
$513$	−21.6231	−0.954683
$514$	−21.5510	−0.950572
$515$	18.2260	0.803135
$516$	−37.1991	−1.63760
$517$	−16.0841	−0.707376
$518$	6.69929	0.294350
$519$	5.58493	0.245151
$520$	13.0274	0.571289
$521$	16.4250	0.719593	0.359797	−	0.933031i	$-0.382846\pi$
$521$	16.4250	0.719593	0.359797	+	0.933031i	$0.382846\pi$
$522$	−95.3380	−4.17283
$523$	−8.56429	−0.374490	−0.187245	−	0.982313i	$-0.559956\pi$
$523$	−8.56429	−0.374490	−0.187245	+	0.982313i	$0.559956\pi$
$524$	−23.5112	−1.02709
$525$	40.8696	1.78370
$526$	22.1798	0.967086
$527$	3.72041	0.162063
$528$	114.294	4.97400
$529$	−9.65457	−0.419764
$530$	−23.8792	−1.03724
$531$	21.4366	0.930270
$532$	97.9618	4.24718
$533$	−9.49968	−0.411477
$534$	−86.8425	−3.75804
$535$	−13.3981	−0.579251
$536$	−2.58026	−0.111450
$537$	−9.42586	−0.406756
$538$	−25.6299	−1.10499
$539$	−32.1737	−1.38582
$540$	44.9481	1.93426
$541$	19.5921	0.842331	0.421165	−	0.906984i	$-0.361621\pi$
$541$	19.5921	0.842331	0.421165	+	0.906984i	$0.361621\pi$
$542$	−37.9993	−1.63221
$543$	26.2122	1.12487
$544$	−180.588	−7.74265
$545$	−3.00979	−0.128925
$546$	33.3083	1.42546
$547$	31.2971	1.33817	0.669084	−	0.743187i	$-0.266687\pi$
$547$	31.2971	1.33817	0.669084	+	0.743187i	$0.266687\pi$
$548$	−64.1627	−2.74090
$549$	68.6601	2.93034
$550$	−20.3637	−0.868310
$551$	25.4786	1.08543
$552$	−107.400	−4.57123
$553$	−47.6860	−2.02781
$554$	−56.2283	−2.38891
$555$	−2.03091	−0.0862075
$556$	7.45764	0.316274
$557$	−38.7702	−1.64274	−0.821372	−	0.570393i	$-0.806791\pi$
$557$	−38.7702	−1.64274	−0.821372	+	0.570393i	$0.806791\pi$
$558$	−7.95133	−0.336607
$559$	2.11854	0.0896046
$560$	−107.745	−4.55307
$561$	43.1179	1.82044
$562$	−85.3539	−3.60044
$563$	−18.9163	−0.797228	−0.398614	−	0.917119i	$-0.630509\pi$
$563$	−18.9163	−0.797228	−0.398614	+	0.917119i	$0.630509\pi$
$564$	−112.583	−4.74059
$565$	1.35792	0.0571283
$566$	−91.3381	−3.83923
$567$	5.77807	0.242656
$568$	10.3698	0.435109
$569$	43.1626	1.80947	0.904736	−	0.425974i	$-0.140068\pi$
$569$	43.1626	1.80947	0.904736	+	0.425974i	$0.140068\pi$
$570$	−40.0634	−1.67807
$571$	18.6071	0.778682	0.389341	−	0.921094i	$-0.372703\pi$
$571$	18.6071	0.778682	0.389341	+	0.921094i	$0.372703\pi$
$572$	−12.3021	−0.514377
$573$	−11.7274	−0.489918
$574$	130.400	5.44279
$575$	11.5295	0.480811
$576$	210.937	8.78903
$577$	−8.60942	−0.358415	−0.179207	−	0.983811i	$-0.557353\pi$
$577$	−8.60942	−0.358415	−0.179207	+	0.983811i	$0.557353\pi$
$578$	−72.1377	−3.00053
$579$	7.90913	0.328692
$580$	−52.9626	−2.19915
$581$	−55.4074	−2.29869
$582$	−94.5424	−3.91891
$583$	14.6787	0.607930
$584$	48.6458	2.01298
$585$	−6.32869	−0.261659
$586$	68.0314	2.81035
$587$	−8.58617	−0.354389	−0.177195	−	0.984176i	$-0.556702\pi$
$587$	−8.58617	−0.354389	−0.177195	+	0.984176i	$0.556702\pi$
$588$	−225.205	−9.28728
$589$	2.12495	0.0875572
$590$	16.0653	0.661397
$591$	59.8256	2.46090
$592$	−9.16390	−0.376634
$593$	−15.3209	−0.629152	−0.314576	−	0.949232i	$-0.601862\pi$
$593$	−15.3209	−0.629152	−0.314576	+	0.949232i	$0.601862\pi$
$594$	−37.2742	−1.52938
$595$	−40.6474	−1.66638
$596$	−30.5577	−1.25169
$597$	−19.0348	−0.779041
$598$	9.39638	0.384246
$599$	−12.4253	−0.507682	−0.253841	−	0.967246i	$-0.581694\pi$
$599$	−12.4253	−0.507682	−0.253841	+	0.967246i	$0.581694\pi$
$600$	−92.7853	−3.78794
$601$	34.8496	1.42154	0.710771	−	0.703423i	$-0.248346\pi$
$601$	34.8496	1.42154	0.710771	+	0.703423i	$0.248346\pi$
$602$	−29.0807	−1.18524
$603$	1.25349	0.0510459
$604$	−16.5470	−0.673289
$605$	7.62353	0.309940
$606$	15.7443	0.639569
$607$	−19.7067	−0.799872	−0.399936	−	0.916543i	$-0.630968\pi$
$607$	−19.7067	−0.799872	−0.399936	+	0.916543i	$0.630968\pi$
$608$	−103.145	−4.18308
$609$	−88.1477	−3.57192
$610$	51.4561	2.08340
$611$	6.41174	0.259391
$612$	189.161	7.64640
$613$	14.5960	0.589525	0.294763	−	0.955571i	$-0.404759\pi$
$613$	14.5960	0.589525	0.294763	+	0.955571i	$0.404759\pi$
$614$	13.9222	0.561854
$615$	−39.5312	−1.59405
$616$	109.924	4.42898
$617$	3.43056	0.138109	0.0690545	−	0.997613i	$-0.478002\pi$
$617$	3.43056	0.138109	0.0690545	+	0.997613i	$0.478002\pi$
$618$	−105.795	−4.25570
$619$	−35.7460	−1.43675	−0.718376	−	0.695655i	$-0.755114\pi$
$619$	−35.7460	−1.43675	−0.718376	+	0.695655i	$0.755114\pi$
$620$	−4.41716	−0.177397
$621$	21.1038	0.846868
$622$	−36.9036	−1.47970
$623$	−50.3242	−2.01619
$624$	−45.5621	−1.82394
$625$	0.740785	0.0296314
$626$	37.6997	1.50678
$627$	24.6273	0.983519
$628$	−91.6970	−3.65911
$629$	−3.45712	−0.137844
$630$	86.8724	3.46108
$631$	4.08984	0.162814	0.0814069	−	0.996681i	$-0.474059\pi$
$631$	4.08984	0.162814	0.0814069	+	0.996681i	$0.474059\pi$
$632$	108.260	4.30637
$633$	28.9747	1.15164
$634$	50.7011	2.01360
$635$	29.9581	1.18885
$636$	102.746	4.07414
$637$	12.8257	0.508173
$638$	43.9204	1.73883
$639$	−5.03765	−0.199287
$640$	83.2431	3.29047
$641$	12.1121	0.478398	0.239199	−	0.970971i	$-0.423115\pi$
$641$	12.1121	0.478398	0.239199	+	0.970971i	$0.423115\pi$
$642$	77.7709	3.06937
$643$	35.7414	1.40950	0.704752	−	0.709453i	$-0.251058\pi$
$643$	35.7414	1.40950	0.704752	+	0.709453i	$0.251058\pi$
$644$	−95.6093	−3.76754
$645$	8.81591	0.347126
$646$	−68.1979	−2.68321
$647$	5.27768	0.207487	0.103743	−	0.994604i	$-0.466918\pi$
$647$	5.27768	0.207487	0.103743	+	0.994604i	$0.466918\pi$
$648$	−13.1178	−0.515317
$649$	−9.87546	−0.387646
$650$	8.11777	0.318405
$651$	−7.35165	−0.288134
$652$	−135.534	−5.30794
$653$	−20.9329	−0.819166	−0.409583	−	0.912273i	$-0.634326\pi$
$653$	−20.9329	−0.819166	−0.409583	+	0.912273i	$0.634326\pi$
$654$	17.4707	0.683158
$655$	5.57199	0.217716
$656$	−178.373	−6.96429
$657$	−23.6321	−0.921975
$658$	−88.0125	−3.43108
$659$	−22.1436	−0.862594	−0.431297	−	0.902210i	$-0.641944\pi$
$659$	−22.1436	−0.862594	−0.431297	+	0.902210i	$0.641944\pi$
$660$	−51.1930	−1.99268
$661$	−13.7208	−0.533679	−0.266839	−	0.963741i	$-0.585979\pi$
$661$	−13.7208	−0.533679	−0.266839	+	0.963741i	$0.585979\pi$
$662$	40.8901	1.58924
$663$	−17.1885	−0.667546
$664$	125.790	4.88160
$665$	−23.2162	−0.900287
$666$	7.38863	0.286304
$667$	−24.8668	−0.962845
$668$	−48.6691	−1.88306
$669$	−4.65422	−0.179943
$670$	0.939403	0.0362923
$671$	−31.6304	−1.22108
$672$	356.848	13.7657
$673$	12.8606	0.495739	0.247870	−	0.968793i	$-0.420270\pi$
$673$	12.8606	0.495739	0.247870	+	0.968793i	$0.420270\pi$
$674$	−91.3474	−3.51857
$675$	18.2321	0.701755
$676$	−69.5835	−2.67629
$677$	−26.5452	−1.02022	−0.510108	−	0.860111i	$-0.670394\pi$
$677$	−26.5452	−1.02022	−0.510108	+	0.860111i	$0.670394\pi$
$678$	−7.88223	−0.302715
$679$	−54.7861	−2.10250
$680$	92.2808	3.53881
$681$	−41.0051	−1.57132
$682$	3.66303	0.140265
$683$	33.0229	1.26359	0.631793	−	0.775137i	$-0.282319\pi$
$683$	33.0229	1.26359	0.631793	+	0.775137i	$0.282319\pi$
$684$	108.042	4.13108
$685$	15.2061	0.580995
$686$	−87.1608	−3.32782
$687$	−49.4031	−1.88485
$688$	39.7792	1.51657
$689$	−5.85151	−0.222925
$690$	39.1013	1.48856
$691$	−13.5117	−0.514011	−0.257005	−	0.966410i	$-0.582736\pi$
$691$	−13.5117	−0.514011	−0.257005	+	0.966410i	$0.582736\pi$
$692$	−11.2874	−0.429083
$693$	−53.4012	−2.02854
$694$	−97.8052	−3.71263
$695$	−1.76741	−0.0670415
$696$	200.120	7.58552
$697$	−67.2919	−2.54886
$698$	−85.7933	−3.24733
$699$	27.3536	1.03461
$700$	−82.5993	−3.12196
$701$	6.34428	0.239620	0.119810	−	0.992797i	$-0.461771\pi$
$701$	6.34428	0.239620	0.119810	+	0.992797i	$0.461771\pi$
$702$	14.8590	0.560817
$703$	−1.97458	−0.0744726
$704$	−97.1746	−3.66241
$705$	26.6813	1.00488
$706$	−54.6953	−2.05848
$707$	9.12363	0.343129
$708$	−69.1247	−2.59787
$709$	−6.33194	−0.237801	−0.118900	−	0.992906i	$-0.537937\pi$
$709$	−6.33194	−0.237801	−0.118900	+	0.992906i	$0.537937\pi$
$710$	−3.77538	−0.141687
$711$	−52.5927	−1.97238
$712$	114.250	4.28169
$713$	−2.07392	−0.0776691
$714$	235.942	8.82992
$715$	2.91551	0.109034
$716$	19.0501	0.711936
$717$	−35.3365	−1.31967
$718$	70.3699	2.62618
$719$	−12.5088	−0.466499	−0.233250	−	0.972417i	$-0.574936\pi$
$719$	−12.5088	−0.466499	−0.233250	+	0.972417i	$0.574936\pi$
$720$	−118.832	−4.42860
$721$	−61.3069	−2.28319
$722$	13.8728	0.516291
$723$	56.9640	2.11852
$724$	−52.9761	−1.96884
$725$	−21.4830	−0.797860
$726$	−44.2516	−1.64233
$727$	42.7515	1.58557	0.792783	−	0.609504i	$-0.208631\pi$
$727$	42.7515	1.58557	0.792783	+	0.609504i	$0.208631\pi$
$728$	−43.8203	−1.62409
$729$	−42.7613	−1.58375
$730$	−17.7106	−0.655499
$731$	15.0069	0.555049
$732$	−221.402	−8.18325
$733$	15.8530	0.585543	0.292772	−	0.956182i	$-0.405422\pi$
$733$	15.8530	0.585543	0.292772	+	0.956182i	$0.405422\pi$
$734$	89.1752	3.29152
$735$	53.3718	1.96865
$736$	100.668	3.71067
$737$	−0.577458	−0.0212709
$738$	143.818	5.29400
$739$	25.2962	0.930535	0.465268	−	0.885170i	$-0.345958\pi$
$739$	25.2962	0.930535	0.465268	+	0.885170i	$0.345958\pi$
$740$	4.10457	0.150887
$741$	−9.81742	−0.360652
$742$	80.3224	2.94873
$743$	22.9640	0.842467	0.421233	−	0.906952i	$-0.361597\pi$
$743$	22.9640	0.842467	0.421233	+	0.906952i	$0.361597\pi$
$744$	16.6903	0.611895
$745$	7.24194	0.265324
$746$	50.3288	1.84267
$747$	−61.1086	−2.23585
$748$	−87.1432	−3.18627
$749$	45.0672	1.64672
$750$	87.2980	3.18767
$751$	−0.0225246	−0.000821935 0	−0.000410967	−	1.00000i	$-0.500131\pi$
$751$	−0.0225246	−0.000821935 0	−0.000410967		1.00000i	$0.500131\pi$
$752$	120.391	4.39022
$753$	−25.6617	−0.935165
$754$	−17.5084	−0.637619
$755$	3.92153	0.142719
$756$	−151.192	−5.49880
$757$	−13.9006	−0.505227	−0.252613	−	0.967567i	$-0.581290\pi$
$757$	−13.9006	−0.505227	−0.252613	+	0.967567i	$0.581290\pi$
$758$	49.7174	1.80582
$759$	−24.0359	−0.872447
$760$	52.7073	1.91189
$761$	28.5594	1.03528	0.517639	−	0.855599i	$-0.326811\pi$
$761$	28.5594	1.03528	0.517639	+	0.855599i	$0.326811\pi$
$762$	−173.895	−6.29956
$763$	10.1240	0.366515
$764$	23.7016	0.857493
$765$	−44.8299	−1.62083
$766$	−84.8544	−3.06591
$767$	3.93675	0.142148
$768$	−245.773	−8.86858
$769$	−16.7698	−0.604736	−0.302368	−	0.953191i	$-0.597777\pi$
$769$	−16.7698	−0.604736	−0.302368	+	0.953191i	$0.597777\pi$
$770$	−40.0205	−1.44224
$771$	−21.9759	−0.791443
$772$	−15.9847	−0.575303
$773$	−47.5970	−1.71195	−0.855973	−	0.517020i	$-0.827041\pi$
$773$	−47.5970	−1.71195	−0.855973	+	0.517020i	$0.827041\pi$
$774$	−32.0730	−1.15284
$775$	−1.79172	−0.0643603
$776$	124.380	4.46497
$777$	6.83139	0.245075
$778$	95.2472	3.41478
$779$	−38.4346	−1.37706
$780$	20.4075	0.730707
$781$	2.32075	0.0830431
$782$	66.5602	2.38019
$783$	−39.3231	−1.40529
$784$	240.825	8.60088
$785$	21.7315	0.775631
$786$	−32.3433	−1.15365
$787$	−14.7359	−0.525276	−0.262638	−	0.964894i	$-0.584593\pi$
$787$	−14.7359	−0.525276	−0.262638	+	0.964894i	$0.584593\pi$
$788$	−120.910	−4.30725
$789$	22.6172	0.805192
$790$	−39.4147	−1.40231
$791$	−4.56765	−0.162407
$792$	121.235	4.30791
$793$	12.6091	0.447764
$794$	83.6009	2.96689
$795$	−24.3500	−0.863606
$796$	38.4701	1.36354
$797$	40.4274	1.43201	0.716007	−	0.698093i	$-0.245968\pi$
$797$	40.4274	1.43201	0.716007	+	0.698093i	$0.245968\pi$
$798$	134.761	4.77050
$799$	45.4182	1.60678
$800$	86.9697	3.07484
$801$	−55.5024	−1.96108
$802$	76.2719	2.69325
$803$	10.8869	0.384189
$804$	−4.04201	−0.142551
$805$	22.6587	0.798615
$806$	−1.46023	−0.0514344
$807$	−26.1353	−0.920007
$808$	−20.7132	−0.728687
$809$	9.41337	0.330956	0.165478	−	0.986213i	$-0.447083\pi$
$809$	9.41337	0.330956	0.165478	+	0.986213i	$0.447083\pi$
$810$	4.77584	0.167806
$811$	−12.6653	−0.444739	−0.222369	−	0.974962i	$-0.571379\pi$
$811$	−12.6653	−0.444739	−0.222369	+	0.974962i	$0.571379\pi$
$812$	178.150	6.25186
$813$	−38.7486	−1.35897
$814$	−3.40381	−0.119303
$815$	32.1207	1.12514
$816$	−322.743	−11.2983
$817$	8.57136	0.299874
$818$	−28.4217	−0.993743
$819$	21.2878	0.743857
$820$	79.8943	2.79003
$821$	−10.3521	−0.361291	−0.180646	−	0.983548i	$-0.557819\pi$
$821$	−10.3521	−0.361291	−0.180646	+	0.983548i	$0.557819\pi$
$822$	−88.2656	−3.07862
$823$	−39.6681	−1.38274	−0.691371	−	0.722500i	$-0.742993\pi$
$823$	−39.6681	−1.38274	−0.691371	+	0.722500i	$0.742993\pi$
$824$	139.184	4.84869
$825$	−20.7652	−0.722952
$826$	−54.0388	−1.88025
$827$	−26.4575	−0.920018	−0.460009	−	0.887914i	$-0.652154\pi$
$827$	−26.4575	−0.920018	−0.460009	+	0.887914i	$0.652154\pi$
$828$	−105.447	−3.66455
$829$	−15.9603	−0.554322	−0.277161	−	0.960823i	$-0.589394\pi$
$829$	−15.9603	−0.554322	−0.277161	+	0.960823i	$0.589394\pi$
$830$	−45.7968	−1.58963
$831$	−57.3370	−1.98900
$832$	38.7377	1.34299
$833$	90.8522	3.14784
$834$	10.2591	0.355244
$835$	11.5342	0.399158
$836$	−49.7729	−1.72143
$837$	−3.27961	−0.113360
$838$	101.815	3.51712
$839$	30.8623	1.06548	0.532742	−	0.846278i	$-0.321162\pi$
$839$	30.8623	1.06548	0.532742	+	0.846278i	$0.321162\pi$
$840$	−182.350	−6.29167
$841$	17.3347	0.597747
$842$	−73.9276	−2.54772
$843$	−87.0369	−2.99771
$844$	−58.5593	−2.01569
$845$	16.4908	0.567300
$846$	−97.0687	−3.33729
$847$	−25.6433	−0.881113
$848$	−109.872	−3.77303
$849$	−93.1391	−3.19652
$850$	57.5030	1.97234
$851$	1.92716	0.0660621
$852$	16.2445	0.556526
$853$	53.2145	1.82203	0.911015	−	0.412373i	$-0.135300\pi$
$853$	53.2145	1.82203	0.911015	+	0.412373i	$0.135300\pi$
$854$	−173.083	−5.92277
$855$	−25.6051	−0.875677
$856$	−102.315	−3.49706
$857$	−8.79570	−0.300455	−0.150228	−	0.988651i	$-0.548001\pi$
$857$	−8.79570	−0.300455	−0.150228	+	0.988651i	$0.548001\pi$
$858$	−16.9234	−0.577756
$859$	−33.0621	−1.12806	−0.564032	−	0.825753i	$-0.690750\pi$
$859$	−33.0621	−1.12806	−0.564032	+	0.825753i	$0.690750\pi$
$860$	−17.8174	−0.607567
$861$	132.971	4.53164
$862$	56.7596	1.93324
$863$	24.2564	0.825697	0.412849	−	0.910800i	$-0.364534\pi$
$863$	24.2564	0.825697	0.412849	+	0.910800i	$0.364534\pi$
$864$	159.192	5.41581
$865$	2.67503	0.0909538
$866$	67.6396	2.29849
$867$	−73.5601	−2.49823
$868$	14.8580	0.504314
$869$	24.2285	0.821896
$870$	−72.8581	−2.47012
$871$	0.230198	0.00779995
$872$	−22.9844	−0.778350
$873$	−60.4235	−2.04503
$874$	38.0166	1.28593
$875$	50.5881	1.71019
$876$	76.2042	2.57470
$877$	−6.35434	−0.214571	−0.107285	−	0.994228i	$-0.534216\pi$
$877$	−6.35434	−0.214571	−0.107285	+	0.994228i	$0.534216\pi$
$878$	−41.0629	−1.38581
$879$	69.3728	2.33989
$880$	54.7437	1.84541
$881$	5.62464	0.189499	0.0947495	−	0.995501i	$-0.469795\pi$
$881$	5.62464	0.189499	0.0947495	+	0.995501i	$0.469795\pi$
$882$	−194.171	−6.53808
$883$	−25.9219	−0.872341	−0.436170	−	0.899864i	$-0.643665\pi$
$883$	−25.9219	−0.872341	−0.436170	+	0.899864i	$0.643665\pi$
$884$	34.7387	1.16839
$885$	16.3821	0.550677
$886$	25.2638	0.848754
$887$	−20.1048	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$887$	−20.1048	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$888$	−15.5091	−0.520453
$889$	−100.770	−3.37972
$890$	−41.5952	−1.39428
$891$	−2.93575	−0.0983513
$892$	9.40639	0.314949
$893$	25.9412	0.868088
$894$	−42.0367	−1.40592
$895$	−4.51473	−0.150911
$896$	−280.005	−9.35431
$897$	9.58165	0.319922
$898$	71.7843	2.39547
$899$	3.86438	0.128884
$900$	−91.0986	−3.03662
$901$	−41.4498	−1.38089
$902$	−66.2542	−2.20602
$903$	−29.6541	−0.986827
$904$	10.3698	0.344896
$905$	12.5549	0.417340
$906$	−22.7630	−0.756249
$907$	33.1419	1.10046	0.550229	−	0.835014i	$-0.314540\pi$
$907$	33.1419	1.10046	0.550229	+	0.835014i	$0.314540\pi$
$908$	82.8732	2.75025
$909$	10.0624	0.333750
$910$	15.9538	0.528862
$911$	−50.2957	−1.66637	−0.833185	−	0.552994i	$-0.813485\pi$
$911$	−50.2957	−1.66637	−0.833185	+	0.552994i	$0.813485\pi$
$912$	−184.339	−6.10407
$913$	28.1516	0.931683
$914$	79.2323	2.62077
$915$	52.4707	1.73463
$916$	99.8459	3.29900
$917$	−18.7425	−0.618932
$918$	105.255	3.47394
$919$	−17.9589	−0.592410	−0.296205	−	0.955124i	$-0.595721\pi$
$919$	−17.9589	−0.592410	−0.296205	+	0.955124i	$0.595721\pi$
$920$	−51.4416	−1.69598
$921$	14.1967	0.467798
$922$	−44.9672	−1.48092
$923$	−0.925145	−0.0304515
$924$	172.198	5.66489
$925$	1.66492	0.0547423
$926$	−10.6923	−0.351370
$927$	−67.6152	−2.22078
$928$	−187.577	−6.15750
$929$	5.28059	0.173251	0.0866253	−	0.996241i	$-0.472392\pi$
$929$	5.28059	0.173251	0.0866253	+	0.996241i	$0.472392\pi$
$930$	−6.07648	−0.199255
$931$	51.8913	1.70067
$932$	−55.2830	−1.81085
$933$	−37.6313	−1.23199
$934$	54.5044	1.78344
$935$	20.6523	0.675402
$936$	−48.3293	−1.57969
$937$	−13.4700	−0.440045	−0.220023	−	0.975495i	$-0.570613\pi$
$937$	−13.4700	−0.440045	−0.220023	+	0.975495i	$0.570613\pi$
$938$	−3.15987	−0.103173
$939$	38.4430	1.25454
$940$	−53.9241	−1.75881
$941$	−17.2245	−0.561502	−0.280751	−	0.959781i	$-0.590583\pi$
$941$	−17.2245	−0.561502	−0.280751	+	0.959781i	$0.590583\pi$
$942$	−126.143	−4.10996
$943$	37.5116	1.22155
$944$	73.9192	2.40586
$945$	35.8314	1.16560
$946$	14.7754	0.480391
$947$	−12.2776	−0.398968	−0.199484	−	0.979901i	$-0.563927\pi$
$947$	−12.2776	−0.398968	−0.199484	+	0.979901i	$0.563927\pi$
$948$	169.591	5.50806
$949$	−4.33993	−0.140880
$950$	32.8435	1.06559
$951$	51.7008	1.67651
$952$	−310.405	−10.0603
$953$	51.1836	1.65800	0.828999	−	0.559250i	$-0.188911\pi$
$953$	51.1836	1.65800	0.828999	+	0.559250i	$0.188911\pi$
$954$	88.5873	2.86812
$955$	−5.61710	−0.181765
$956$	71.4167	2.30978
$957$	44.7865	1.44774
$958$	54.6218	1.76475
$959$	−51.1488	−1.65168
$960$	161.200	5.20270
$961$	−30.6777	−0.989603
$962$	1.35689	0.0437480
$963$	49.7045	1.60171
$964$	−115.127	−3.70799
$965$	3.78826	0.121948
$966$	−131.525	−4.23175
$967$	−27.4749	−0.883534	−0.441767	−	0.897130i	$-0.645648\pi$
$967$	−27.4749	−0.883534	−0.441767	+	0.897130i	$0.645648\pi$
$968$	58.2173	1.87118
$969$	−69.5426	−2.23403
$970$	−45.2833	−1.45396
$971$	41.9208	1.34530	0.672651	−	0.739960i	$-0.265156\pi$
$971$	41.9208	1.34530	0.672651	+	0.739960i	$0.265156\pi$
$972$	78.7526	2.52599
$973$	5.94503	0.190589
$974$	23.7084	0.759665
$975$	8.27783	0.265103
$976$	236.758	7.57845
$977$	−41.6747	−1.33329	−0.666646	−	0.745375i	$-0.732271\pi$
$977$	−41.6747	−1.33329	−0.666646	+	0.745375i	$0.732271\pi$
$978$	−186.448	−5.96195
$979$	25.5689	0.817186
$980$	−107.867	−3.44568
$981$	11.1658	0.356496
$982$	−112.712	−3.59678
$983$	−20.9423	−0.667955	−0.333977	−	0.942581i	$-0.608391\pi$
$983$	−20.9423	−0.667955	−0.333977	+	0.942581i	$0.608391\pi$
$984$	−301.881	−9.62363
$985$	28.6549	0.913020
$986$	−124.023	−3.94969
$987$	−89.7479	−2.85671
$988$	19.8414	0.631240
$989$	−8.36552	−0.266008
$990$	−44.1385	−1.40281
$991$	−30.0934	−0.955950	−0.477975	−	0.878374i	$-0.658629\pi$
$991$	−30.0934	−0.955950	−0.477975	+	0.878374i	$0.658629\pi$
$992$	−15.6442	−0.496703
$993$	41.6963	1.32319
$994$	12.6992	0.402796
$995$	−9.11714	−0.289033
$996$	197.051	6.24382
$997$	−43.6776	−1.38328	−0.691642	−	0.722241i	$-0.743112\pi$
$997$	−43.6776	−1.38328	−0.691642	+	0.722241i	$0.743112\pi$
$998$	−33.0925	−1.04752
$999$	3.04752	0.0964192

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.2	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.2	✓	158	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)

\(f(q)\)	\(=\)	\(q-2.78025 q^{2} -2.83508 q^{3} +5.72982 q^{4} -1.35792 q^{5} +7.88223 q^{6} +4.56765 q^{7} -10.3698 q^{8} +5.03765 q^{9} +O(q^{10})\)	\(q-2.78025 q^{2} -2.83508 q^{3} +5.72982 q^{4} -1.35792 q^{5} +7.88223 q^{6} +4.56765 q^{7} -10.3698 q^{8} +5.03765 q^{9} +3.77538 q^{10} -2.32075 q^{11} -16.2445 q^{12} +0.925145 q^{13} -12.6992 q^{14} +3.84982 q^{15} +17.3712 q^{16} +6.55335 q^{17} -14.0060 q^{18} +3.74303 q^{19} -7.78066 q^{20} -12.9496 q^{21} +6.45229 q^{22} -3.65314 q^{23} +29.3993 q^{24} -3.15604 q^{25} -2.57214 q^{26} -5.77690 q^{27} +26.1718 q^{28} +6.80696 q^{29} -10.7035 q^{30} +0.567710 q^{31} -27.5566 q^{32} +6.57951 q^{33} -18.2200 q^{34} -6.20253 q^{35} +28.8648 q^{36} -0.527535 q^{37} -10.4066 q^{38} -2.62285 q^{39} +14.0815 q^{40} -10.2683 q^{41} +36.0033 q^{42} +2.28995 q^{43} -13.2975 q^{44} -6.84076 q^{45} +10.1567 q^{46} +6.93053 q^{47} -49.2486 q^{48} +13.8635 q^{49} +8.77459 q^{50} -18.5793 q^{51} +5.30091 q^{52} -6.32497 q^{53} +16.0613 q^{54} +3.15141 q^{55} -47.3659 q^{56} -10.6118 q^{57} -18.9251 q^{58} +4.25528 q^{59} +22.0588 q^{60} +13.6294 q^{61} -1.57838 q^{62} +23.0103 q^{63} +41.8720 q^{64} -1.25628 q^{65} -18.2927 q^{66} +0.248824 q^{67} +37.5495 q^{68} +10.3569 q^{69} +17.2446 q^{70} -1.00000 q^{71} -52.2397 q^{72} -4.69109 q^{73} +1.46668 q^{74} +8.94761 q^{75} +21.4469 q^{76} -10.6004 q^{77} +7.29220 q^{78} -10.4399 q^{79} -23.5887 q^{80} +1.26500 q^{81} +28.5486 q^{82} -12.1304 q^{83} -74.1991 q^{84} -8.89896 q^{85} -6.36666 q^{86} -19.2982 q^{87} +24.0659 q^{88} -11.0175 q^{89} +19.0190 q^{90} +4.22574 q^{91} -20.9318 q^{92} -1.60950 q^{93} -19.2686 q^{94} -5.08275 q^{95} +78.1250 q^{96} -11.9944 q^{97} -38.5440 q^{98} -11.6912 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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