LMFDB - Embedded newform 8023.2.a.c.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.43745 q^{2} -0.327529 q^{3} +3.94116 q^{4} -2.07610 q^{5} +0.798335 q^{6} -0.184041 q^{7} -4.73147 q^{8} -2.89272 q^{9} +O(q^{10})$	\(q-2.43745 q^{2} -0.327529 q^{3} +3.94116 q^{4} -2.07610 q^{5} +0.798335 q^{6} -0.184041 q^{7} -4.73147 q^{8} -2.89272 q^{9} +5.06038 q^{10} +6.19257 q^{11} -1.29084 q^{12} +5.93759 q^{13} +0.448592 q^{14} +0.679982 q^{15} +3.65040 q^{16} -1.22386 q^{17} +7.05087 q^{18} +6.79540 q^{19} -8.18222 q^{20} +0.0602789 q^{21} -15.0941 q^{22} +4.78804 q^{23} +1.54969 q^{24} -0.689820 q^{25} -14.4726 q^{26} +1.93004 q^{27} -0.725336 q^{28} -1.27393 q^{29} -1.65742 q^{30} -3.43925 q^{31} +0.565277 q^{32} -2.02824 q^{33} +2.98309 q^{34} +0.382088 q^{35} -11.4007 q^{36} +6.19766 q^{37} -16.5634 q^{38} -1.94473 q^{39} +9.82299 q^{40} -10.3441 q^{41} -0.146927 q^{42} -4.48759 q^{43} +24.4059 q^{44} +6.00558 q^{45} -11.6706 q^{46} -11.8515 q^{47} -1.19561 q^{48} -6.96613 q^{49} +1.68140 q^{50} +0.400848 q^{51} +23.4010 q^{52} -12.2832 q^{53} -4.70437 q^{54} -12.8564 q^{55} +0.870786 q^{56} -2.22569 q^{57} +3.10514 q^{58} +0.000567193 q^{59} +2.67991 q^{60} -3.47475 q^{61} +8.38300 q^{62} +0.532381 q^{63} -8.67863 q^{64} -12.3270 q^{65} +4.94374 q^{66} +0.649522 q^{67} -4.82341 q^{68} -1.56822 q^{69} -0.931320 q^{70} -1.00000 q^{71} +13.6868 q^{72} +14.5453 q^{73} -15.1065 q^{74} +0.225936 q^{75} +26.7817 q^{76} -1.13969 q^{77} +4.74019 q^{78} -10.4879 q^{79} -7.57858 q^{80} +8.04603 q^{81} +25.2132 q^{82} -13.4124 q^{83} +0.237569 q^{84} +2.54084 q^{85} +10.9383 q^{86} +0.417250 q^{87} -29.2999 q^{88} -0.0342642 q^{89} -14.6383 q^{90} -1.09276 q^{91} +18.8704 q^{92} +1.12645 q^{93} +28.8874 q^{94} -14.1079 q^{95} -0.185145 q^{96} -4.90882 q^{97} +16.9796 q^{98} -17.9134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.43745	−1.72354	−0.861768	−	0.507302i	$-0.830643\pi$
$2$	−2.43745	−1.72354	−0.861768	+	0.507302i	$0.830643\pi$
$3$	−0.327529	−0.189099	−0.0945495	−	0.995520i	$-0.530141\pi$
$3$	−0.327529	−0.189099	−0.0945495	+	0.995520i	$0.530141\pi$
$4$	3.94116	1.97058
$5$	−2.07610	−0.928459	−0.464229	−	0.885715i	$-0.653669\pi$
$5$	−2.07610	−0.928459	−0.464229	+	0.885715i	$0.653669\pi$
$6$	0.798335	0.325919
$7$	−0.184041	−0.0695611	−0.0347806	−	0.999395i	$-0.511073\pi$
$7$	−0.184041	−0.0695611	−0.0347806	+	0.999395i	$0.511073\pi$
$8$	−4.73147	−1.67283
$9$	−2.89272	−0.964242
$10$	5.06038	1.60023
$11$	6.19257	1.86713	0.933565	−	0.358409i	$-0.116681\pi$
$11$	6.19257	1.86713	0.933565	+	0.358409i	$0.116681\pi$
$12$	−1.29084	−0.372634
$13$	5.93759	1.64679	0.823396	−	0.567468i	$-0.192077\pi$
$13$	5.93759	1.64679	0.823396	+	0.567468i	$0.192077\pi$
$14$	0.448592	0.119891
$15$	0.679982	0.175571
$16$	3.65040	0.912600
$17$	−1.22386	−0.296829	−0.148414	−	0.988925i	$-0.547417\pi$
$17$	−1.22386	−0.296829	−0.148414	+	0.988925i	$0.547417\pi$
$18$	7.05087	1.66191
$19$	6.79540	1.55897	0.779485	−	0.626420i	$-0.215481\pi$
$19$	6.79540	1.55897	0.779485	+	0.626420i	$0.215481\pi$
$20$	−8.18222	−1.82960
$21$	0.0602789	0.0131539
$22$	−15.0941	−3.21806
$23$	4.78804	0.998375	0.499187	−	0.866494i	$-0.333632\pi$
$23$	4.78804	0.998375	0.499187	+	0.866494i	$0.333632\pi$
$24$	1.54969	0.316330
$25$	−0.689820	−0.137964
$26$	−14.4726	−2.83830
$27$	1.93004	0.371436
$28$	−0.725336	−0.137076
$29$	−1.27393	−0.236563	−0.118282	−	0.992980i	$-0.537739\pi$
$29$	−1.27393	−0.236563	−0.118282	+	0.992980i	$0.537739\pi$
$30$	−1.65742	−0.302602
$31$	−3.43925	−0.617708	−0.308854	−	0.951110i	$-0.599945\pi$
$31$	−3.43925	−0.617708	−0.308854	+	0.951110i	$0.599945\pi$
$32$	0.565277	0.0999278
$33$	−2.02824	−0.353072
$34$	2.98309	0.511595
$35$	0.382088	0.0645846
$36$	−11.4007	−1.90011
$37$	6.19766	1.01889	0.509444	−	0.860504i	$-0.329851\pi$
$37$	6.19766	1.01889	0.509444	+	0.860504i	$0.329851\pi$
$38$	−16.5634	−2.68694
$39$	−1.94473	−0.311406
$40$	9.82299	1.55315
$41$	−10.3441	−1.61548	−0.807738	−	0.589541i	$-0.799308\pi$
$41$	−10.3441	−1.61548	−0.807738	+	0.589541i	$0.799308\pi$
$42$	−0.146927	−0.0226713
$43$	−4.48759	−0.684351	−0.342176	−	0.939636i	$-0.611164\pi$
$43$	−4.48759	−0.684351	−0.342176	+	0.939636i	$0.611164\pi$
$44$	24.4059	3.67932
$45$	6.00558	0.895259
$46$	−11.6706	−1.72073
$47$	−11.8515	−1.72872	−0.864359	−	0.502876i	$-0.832275\pi$
$47$	−11.8515	−1.72872	−0.864359	+	0.502876i	$0.832275\pi$
$48$	−1.19561	−0.172572
$49$	−6.96613	−0.995161
$50$	1.68140	0.237786
$51$	0.400848	0.0561300
$52$	23.4010	3.24513
$53$	−12.2832	−1.68723	−0.843615	−	0.536949i	$-0.819577\pi$
$53$	−12.2832	−1.68723	−0.843615	+	0.536949i	$0.819577\pi$
$54$	−4.70437	−0.640183
$55$	−12.8564	−1.73355
$56$	0.870786	0.116364
$57$	−2.22569	−0.294800
$58$	3.10514	0.407725
$59$	0.000567193 0	7.38422e−5 0	3.69211e−5	−	1.00000i	$-0.499988\pi$
$59$	0.000567193 0	7.38422e−5 0	3.69211e−5		1.00000i	$0.499988\pi$
$60$	2.67991	0.345976
$61$	−3.47475	−0.444896	−0.222448	−	0.974945i	$-0.571405\pi$
$61$	−3.47475	−0.444896	−0.222448	+	0.974945i	$0.571405\pi$
$62$	8.38300	1.06464
$63$	0.532381	0.0670737
$64$	−8.67863	−1.08483
$65$	−12.3270	−1.52898
$66$	4.94374	0.608533
$67$	0.649522	0.0793517	0.0396759	−	0.999213i	$-0.487367\pi$
$67$	0.649522	0.0793517	0.0396759	+	0.999213i	$0.487367\pi$
$68$	−4.82341	−0.584924
$69$	−1.56822	−0.188792
$70$	−0.931320	−0.111314
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	13.6868	1.61301
$73$	14.5453	1.70239	0.851197	−	0.524846i	$-0.175877\pi$
$73$	14.5453	1.70239	0.851197	+	0.524846i	$0.175877\pi$
$74$	−15.1065	−1.75609
$75$	0.225936	0.0260888
$76$	26.7817	3.07207
$77$	−1.13969	−0.129880
$78$	4.74019	0.536720
$79$	−10.4879	−1.17999	−0.589993	−	0.807408i	$-0.700870\pi$
$79$	−10.4879	−1.17999	−0.589993	+	0.807408i	$0.700870\pi$
$80$	−7.57858	−0.847311
$81$	8.04603	0.894003
$82$	25.2132	2.78433
$83$	−13.4124	−1.47220	−0.736102	−	0.676871i	$-0.763336\pi$
$83$	−13.4124	−1.47220	−0.736102	+	0.676871i	$0.763336\pi$
$84$	0.237569	0.0259209
$85$	2.54084	0.275593
$86$	10.9383	1.17950
$87$	0.417250	0.0447339
$88$	−29.2999	−3.12338
$89$	−0.0342642	−0.00363200	−0.00181600	−	0.999998i	$-0.500578\pi$
$89$	−0.0342642	−0.00363200	−0.00181600	+	0.999998i	$0.500578\pi$
$90$	−14.6383	−1.54301
$91$	−1.09276	−0.114553
$92$	18.8704	1.96737
$93$	1.12645	0.116808
$94$	28.8874	2.97951
$95$	−14.1079	−1.44744
$96$	−0.185145	−0.0188962
$97$	−4.90882	−0.498415	−0.249208	−	0.968450i	$-0.580170\pi$
$97$	−4.90882	−0.498415	−0.249208	+	0.968450i	$0.580170\pi$
$98$	16.9796	1.71520
$99$	−17.9134	−1.80036
$100$	−2.71869	−0.271869
$101$	−8.16140	−0.812089	−0.406045	−	0.913853i	$-0.633092\pi$
$101$	−8.16140	−0.812089	−0.406045	+	0.913853i	$0.633092\pi$
$102$	−0.977047	−0.0967421
$103$	3.00531	0.296122	0.148061	−	0.988978i	$-0.452697\pi$
$103$	3.00531	0.296122	0.148061	+	0.988978i	$0.452697\pi$
$104$	−28.0935	−2.75480
$105$	−0.125145	−0.0122129
$106$	29.9397	2.90800
$107$	9.98915	0.965688	0.482844	−	0.875706i	$-0.339604\pi$
$107$	9.98915	0.965688	0.482844	+	0.875706i	$0.339604\pi$
$108$	7.60658	0.731944
$109$	−3.20416	−0.306903	−0.153452	−	0.988156i	$-0.549039\pi$
$109$	−3.20416	−0.306903	−0.153452	+	0.988156i	$0.549039\pi$
$110$	31.3367	2.98784
$111$	−2.02991	−0.192671
$112$	−0.671825	−0.0634815
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	5.42500	0.508098
$115$	−9.94043	−0.926950
$116$	−5.02077	−0.466166
$117$	−17.1758	−1.58790
$118$	−0.00138250	−0.000127270 0
$119$	0.225240	0.0206477
$120$	−3.21731	−0.293699
$121$	27.3479	2.48617
$122$	8.46952	0.766794
$123$	3.38799	0.305485
$124$	−13.5546	−1.21724
$125$	11.8126	1.05655
$126$	−1.29765	−0.115604
$127$	−6.73100	−0.597280	−0.298640	−	0.954366i	$-0.596533\pi$
$127$	−6.73100	−0.597280	−0.298640	+	0.954366i	$0.596533\pi$
$128$	20.0232	1.76981
$129$	1.46982	0.129410
$130$	30.0465	2.63525
$131$	12.1022	1.05738	0.528688	−	0.848816i	$-0.322684\pi$
$131$	12.1022	1.05738	0.528688	+	0.848816i	$0.322684\pi$
$132$	−7.99363	−0.695756
$133$	−1.25063	−0.108444
$134$	−1.58318	−0.136766
$135$	−4.00695	−0.344863
$136$	5.79063	0.496543
$137$	−18.3870	−1.57091	−0.785455	−	0.618919i	$-0.787571\pi$
$137$	−18.3870	−1.57091	−0.785455	+	0.618919i	$0.787571\pi$
$138$	3.82246	0.325389
$139$	17.1306	1.45300	0.726499	−	0.687168i	$-0.241146\pi$
$139$	17.1306	1.45300	0.726499	+	0.687168i	$0.241146\pi$
$140$	1.50587	0.127269
$141$	3.88171	0.326899
$142$	2.43745	0.204546
$143$	36.7689	3.07477
$144$	−10.5596	−0.879967
$145$	2.64481	0.219639
$146$	−35.4533	−2.93414
$147$	2.28161	0.188184
$148$	24.4259	2.00780
$149$	20.7798	1.70235	0.851173	−	0.524885i	$-0.175892\pi$
$149$	20.7798	1.70235	0.851173	+	0.524885i	$0.175892\pi$
$150$	−0.550707	−0.0449651
$151$	3.33021	0.271008	0.135504	−	0.990777i	$-0.456735\pi$
$151$	3.33021	0.271008	0.135504	+	0.990777i	$0.456735\pi$
$152$	−32.1522	−2.60789
$153$	3.54028	0.286215
$154$	2.77793	0.223852
$155$	7.14022	0.573516
$156$	−7.66449	−0.613651
$157$	−4.18589	−0.334071	−0.167035	−	0.985951i	$-0.553419\pi$
$157$	−4.18589	−0.334071	−0.167035	+	0.985951i	$0.553419\pi$
$158$	25.5638	2.03375
$159$	4.02311	0.319053
$160$	−1.17357	−0.0927788
$161$	−0.881197	−0.0694481
$162$	−19.6118	−1.54085
$163$	−9.81851	−0.769045	−0.384523	−	0.923116i	$-0.625634\pi$
$163$	−9.81851	−0.769045	−0.384523	+	0.923116i	$0.625634\pi$
$164$	−40.7677	−3.18342
$165$	4.21083	0.327813
$166$	32.6921	2.53740
$167$	18.9979	1.47010	0.735051	−	0.678012i	$-0.237158\pi$
$167$	18.9979	1.47010	0.735051	+	0.678012i	$0.237158\pi$
$168$	−0.285208	−0.0220042
$169$	22.2550	1.71192
$170$	−6.19318	−0.474995
$171$	−19.6572	−1.50322
$172$	−17.6863	−1.34857
$173$	−22.4767	−1.70887	−0.854436	−	0.519557i	$-0.826097\pi$
$173$	−22.4767	−1.70887	−0.854436	+	0.519557i	$0.826097\pi$
$174$	−1.01702	−0.0771004
$175$	0.126955	0.00959693
$176$	22.6053	1.70394
$177$	−0.000185772 0	−1.39635e−5 0
$178$	0.0835172	0.00625988
$179$	−4.58668	−0.342824	−0.171412	−	0.985199i	$-0.554833\pi$
$179$	−4.58668	−0.342824	−0.171412	+	0.985199i	$0.554833\pi$
$180$	23.6689	1.76418
$181$	−7.91386	−0.588233	−0.294116	−	0.955770i	$-0.595025\pi$
$181$	−7.91386	−0.588233	−0.294116	+	0.955770i	$0.595025\pi$
$182$	2.66355	0.197436
$183$	1.13808	0.0841293
$184$	−22.6544	−1.67011
$185$	−12.8669	−0.945997
$186$	−2.74567	−0.201323
$187$	−7.57881	−0.554217
$188$	−46.7086	−3.40657
$189$	−0.355207	−0.0258375
$190$	34.3873	2.49472
$191$	−0.843412	−0.0610271	−0.0305136	−	0.999534i	$-0.509714\pi$
$191$	−0.843412	−0.0610271	−0.0305136	+	0.999534i	$0.509714\pi$
$192$	2.84250	0.205140
$193$	−11.7935	−0.848914	−0.424457	−	0.905448i	$-0.639535\pi$
$193$	−11.7935	−0.848914	−0.424457	+	0.905448i	$0.639535\pi$
$194$	11.9650	0.859037
$195$	4.03745	0.289128
$196$	−27.4546	−1.96104
$197$	13.5337	0.964237	0.482118	−	0.876106i	$-0.339868\pi$
$197$	13.5337	0.964237	0.482118	+	0.876106i	$0.339868\pi$
$198$	43.6630	3.10299
$199$	−1.57055	−0.111333	−0.0556666	−	0.998449i	$-0.517728\pi$
$199$	−1.57055	−0.111333	−0.0556666	+	0.998449i	$0.517728\pi$
$200$	3.26386	0.230790
$201$	−0.212737	−0.0150053
$202$	19.8930	1.39967
$203$	0.234456	0.0164556
$204$	1.57981	0.110608
$205$	21.4753	1.49990
$206$	−7.32528	−0.510376
$207$	−13.8505	−0.962674
$208$	21.6746	1.50286
$209$	42.0809	2.91080
$210$	0.305034	0.0210494
$211$	−18.8975	−1.30096	−0.650479	−	0.759524i	$-0.725432\pi$
$211$	−18.8975	−1.30096	−0.650479	+	0.759524i	$0.725432\pi$
$212$	−48.4101	−3.32482
$213$	0.327529	0.0224419
$214$	−24.3480	−1.66440
$215$	9.31668	0.635392
$216$	−9.13191	−0.621348
$217$	0.632964	0.0429684
$218$	7.80998	0.528959
$219$	−4.76399	−0.321921
$220$	−50.6690	−3.41610
$221$	−7.26675	−0.488815
$222$	4.94781	0.332075
$223$	2.89326	0.193747	0.0968734	−	0.995297i	$-0.469116\pi$
$223$	2.89326	0.193747	0.0968734	+	0.995297i	$0.469116\pi$
$224$	−0.104034	−0.00695109
$225$	1.99546	0.133031
$226$	2.43745	0.162137
$227$	−19.3822	−1.28644	−0.643221	−	0.765680i	$-0.722402\pi$
$227$	−19.3822	−1.28644	−0.643221	+	0.765680i	$0.722402\pi$
$228$	−8.77179	−0.580926
$229$	5.47946	0.362093	0.181047	−	0.983475i	$-0.442052\pi$
$229$	5.47946	0.362093	0.181047	+	0.983475i	$0.442052\pi$
$230$	24.2293	1.59763
$231$	0.373281	0.0245601
$232$	6.02757	0.395729
$233$	−8.03005	−0.526066	−0.263033	−	0.964787i	$-0.584723\pi$
$233$	−8.03005	−0.526066	−0.263033	+	0.964787i	$0.584723\pi$
$234$	41.8652	2.73681
$235$	24.6048	1.60504
$236$	0.00223540	0.000145512 0
$237$	3.43511	0.223134
$238$	−0.549011	−0.0355871
$239$	11.2863	0.730048	0.365024	−	0.930998i	$-0.381061\pi$
$239$	11.2863	0.730048	0.365024	+	0.930998i	$0.381061\pi$
$240$	2.48221	0.160226
$241$	9.04283	0.582500	0.291250	−	0.956647i	$-0.405929\pi$
$241$	9.04283	0.582500	0.291250	+	0.956647i	$0.405929\pi$
$242$	−66.6591	−4.28501
$243$	−8.42542	−0.540491
$244$	−13.6945	−0.876702
$245$	14.4624	0.923966
$246$	−8.25805	−0.526514
$247$	40.3483	2.56730
$248$	16.2727	1.03332
$249$	4.39296	0.278392
$250$	−28.7927	−1.82101
$251$	−18.1978	−1.14863	−0.574317	−	0.818633i	$-0.694732\pi$
$251$	−18.1978	−1.14863	−0.574317	+	0.818633i	$0.694732\pi$
$252$	2.09820	0.132174
$253$	29.6502	1.86409
$254$	16.4065	1.02943
$255$	−0.832200	−0.0521144
$256$	−31.4482	−1.96551
$257$	−19.6031	−1.22281	−0.611404	−	0.791318i	$-0.709395\pi$
$257$	−19.6031	−1.22281	−0.611404	+	0.791318i	$0.709395\pi$
$258$	−3.58260	−0.223043
$259$	−1.14063	−0.0708751
$260$	−48.5827	−3.01297
$261$	3.68514	0.228104
$262$	−29.4985	−1.82243
$263$	−26.8647	−1.65655	−0.828275	−	0.560322i	$-0.810677\pi$
$263$	−26.8647	−1.65655	−0.828275	+	0.560322i	$0.810677\pi$
$264$	9.59658	0.590628
$265$	25.5012	1.56652
$266$	3.04836	0.186907
$267$	0.0112225	0.000686807 0
$268$	2.55987	0.156369
$269$	−12.7425	−0.776927	−0.388463	−	0.921464i	$-0.626994\pi$
$269$	−12.7425	−0.776927	−0.388463	+	0.921464i	$0.626994\pi$
$270$	9.76673	0.594384
$271$	−7.91223	−0.480634	−0.240317	−	0.970694i	$-0.577251\pi$
$271$	−7.91223	−0.480634	−0.240317	+	0.970694i	$0.577251\pi$
$272$	−4.46756	−0.270886
$273$	0.357911	0.0216618
$274$	44.8174	2.70752
$275$	−4.27176	−0.257597
$276$	−6.18060	−0.372028
$277$	−3.35145	−0.201369	−0.100685	−	0.994918i	$-0.532103\pi$
$277$	−3.35145	−0.201369	−0.100685	+	0.994918i	$0.532103\pi$
$278$	−41.7549	−2.50429
$279$	9.94880	0.595619
$280$	−1.80784	−0.108039
$281$	24.3984	1.45549	0.727743	−	0.685850i	$-0.240569\pi$
$281$	24.3984	1.45549	0.727743	+	0.685850i	$0.240569\pi$
$282$	−9.46146	−0.563422
$283$	−2.71240	−0.161236	−0.0806178	−	0.996745i	$-0.525689\pi$
$283$	−2.71240	−0.161236	−0.0806178	+	0.996745i	$0.525689\pi$
$284$	−3.94116	−0.233865
$285$	4.62075	0.273709
$286$	−89.6224	−5.29948
$287$	1.90374	0.112374
$288$	−1.63519	−0.0963545
$289$	−15.5022	−0.911893
$290$	−6.44658	−0.378556
$291$	1.60778	0.0942498
$292$	57.3252	3.35470
$293$	−3.00508	−0.175559	−0.0877793	−	0.996140i	$-0.527977\pi$
$293$	−3.00508	−0.175559	−0.0877793	+	0.996140i	$0.527977\pi$
$294$	−5.56130	−0.324342
$295$	−0.00117755	−6.85595e−5 0
$296$	−29.3240	−1.70442
$297$	11.9519	0.693519
$298$	−50.6497	−2.93406
$299$	28.4294	1.64411
$300$	0.890449	0.0514101
$301$	0.825903	0.0476042
$302$	−8.11721	−0.467093
$303$	2.67309	0.153565
$304$	24.8059	1.42272
$305$	7.21391	0.413068
$306$	−8.62925	−0.493301
$307$	−18.2840	−1.04353	−0.521763	−	0.853091i	$-0.674725\pi$
$307$	−18.2840	−1.04353	−0.521763	+	0.853091i	$0.674725\pi$
$308$	−4.49169	−0.255938
$309$	−0.984325	−0.0559963
$310$	−17.4039	−0.988476
$311$	−27.3112	−1.54868	−0.774339	−	0.632770i	$-0.781918\pi$
$311$	−27.3112	−1.54868	−0.774339	+	0.632770i	$0.781918\pi$
$312$	9.20144	0.520929
$313$	−1.40525	−0.0794293	−0.0397147	−	0.999211i	$-0.512645\pi$
$313$	−1.40525	−0.0794293	−0.0397147	+	0.999211i	$0.512645\pi$
$314$	10.2029	0.575783
$315$	−1.10528	−0.0622752
$316$	−41.3346	−2.32526
$317$	−15.9962	−0.898435	−0.449217	−	0.893422i	$-0.648297\pi$
$317$	−15.9962	−0.898435	−0.449217	+	0.893422i	$0.648297\pi$
$318$	−9.80612	−0.549900
$319$	−7.88891	−0.441694
$320$	18.0177	1.00722
$321$	−3.27174	−0.182610
$322$	2.14787	0.119696
$323$	−8.31659	−0.462747
$324$	31.7107	1.76170
$325$	−4.09587	−0.227198
$326$	23.9321	1.32548
$327$	1.04946	0.0580350
$328$	48.9428	2.70241
$329$	2.18116	0.120252
$330$	−10.2637	−0.564998
$331$	−27.7606	−1.52586	−0.762930	−	0.646481i	$-0.776240\pi$
$331$	−27.7606	−1.52586	−0.762930	+	0.646481i	$0.776240\pi$
$332$	−52.8604	−2.90109
$333$	−17.9281	−0.982455
$334$	−46.3064	−2.53378
$335$	−1.34847	−0.0736748
$336$	0.220042	0.0120043
$337$	−19.6789	−1.07198	−0.535989	−	0.844225i	$-0.680061\pi$
$337$	−19.6789	−1.07198	−0.535989	+	0.844225i	$0.680061\pi$
$338$	−54.2454	−2.95056
$339$	0.327529	0.0177889
$340$	10.0139	0.543078
$341$	−21.2978	−1.15334
$342$	47.9134	2.59086
$343$	2.57035	0.138786
$344$	21.2329	1.14480
$345$	3.25578	0.175285
$346$	54.7858	2.94530
$347$	7.03330	0.377567	0.188784	−	0.982019i	$-0.439545\pi$
$347$	7.03330	0.377567	0.188784	+	0.982019i	$0.439545\pi$
$348$	1.64445	0.0881516
$349$	22.4973	1.20425	0.602127	−	0.798400i	$-0.294320\pi$
$349$	22.4973	1.20425	0.602127	+	0.798400i	$0.294320\pi$
$350$	−0.309447	−0.0165407
$351$	11.4598	0.611677
$352$	3.50051	0.186578
$353$	−26.2014	−1.39456	−0.697279	−	0.716800i	$-0.745606\pi$
$353$	−26.2014	−1.39456	−0.697279	+	0.716800i	$0.745606\pi$
$354$	0.000452810 0	2.40666e−5 0
$355$	2.07610	0.110188
$356$	−0.135041	−0.00715714
$357$	−0.0737727	−0.00390446
$358$	11.1798	0.590870
$359$	−7.54083	−0.397990	−0.198995	−	0.980001i	$-0.563768\pi$
$359$	−7.54083	−0.397990	−0.198995	+	0.980001i	$0.563768\pi$
$360$	−28.4152	−1.49761
$361$	27.1774	1.43039
$362$	19.2896	1.01384
$363$	−8.95722	−0.470132
$364$	−4.30675	−0.225735
$365$	−30.1974	−1.58060
$366$	−2.77401	−0.145000
$367$	−15.4682	−0.807431	−0.403716	−	0.914885i	$-0.632281\pi$
$367$	−15.4682	−0.807431	−0.403716	+	0.914885i	$0.632281\pi$
$368$	17.4782	0.911116
$369$	29.9226	1.55771
$370$	31.3625	1.63046
$371$	2.26062	0.117366
$372$	4.43953	0.230179
$373$	19.9834	1.03470	0.517351	−	0.855773i	$-0.326918\pi$
$373$	19.9834	1.03470	0.517351	+	0.855773i	$0.326918\pi$
$374$	18.4730	0.955214
$375$	−3.86897	−0.199793
$376$	56.0749	2.89184
$377$	−7.56409	−0.389570
$378$	0.865799	0.0445319
$379$	8.52459	0.437879	0.218939	−	0.975738i	$-0.429740\pi$
$379$	8.52459	0.437879	0.218939	+	0.975738i	$0.429740\pi$
$380$	−55.6015	−2.85229
$381$	2.20460	0.112945
$382$	2.05577	0.105182
$383$	−23.9332	−1.22293	−0.611464	−	0.791272i	$-0.709419\pi$
$383$	−23.9332	−1.22293	−0.611464	+	0.791272i	$0.709419\pi$
$384$	−6.55817	−0.334670
$385$	2.36610	0.120588
$386$	28.7460	1.46314
$387$	12.9814	0.659880
$388$	−19.3464	−0.982166
$389$	0.337116	0.0170924	0.00854622	−	0.999963i	$-0.497280\pi$
$389$	0.337116	0.0170924	0.00854622	+	0.999963i	$0.497280\pi$
$390$	−9.84109	−0.498323
$391$	−5.85987	−0.296346
$392$	32.9600	1.66473
$393$	−3.96383	−0.199949
$394$	−32.9877	−1.66190
$395$	21.7740	1.09557
$396$	−70.5995	−3.54776
$397$	31.6081	1.58637	0.793183	−	0.608984i	$-0.208423\pi$
$397$	31.6081	1.58637	0.793183	+	0.608984i	$0.208423\pi$
$398$	3.82813	0.191887
$399$	0.409619	0.0205066
$400$	−2.51812	−0.125906
$401$	5.59058	0.279180	0.139590	−	0.990209i	$-0.455422\pi$
$401$	5.59058	0.279180	0.139590	+	0.990209i	$0.455422\pi$
$402$	0.518536	0.0258622
$403$	−20.4209	−1.01724
$404$	−32.1653	−1.60029
$405$	−16.7043	−0.830045
$406$	−0.571475	−0.0283618
$407$	38.3794	1.90240
$408$	−1.89660	−0.0938957
$409$	39.3861	1.94752	0.973759	−	0.227583i	$-0.0730823\pi$
$409$	39.3861	1.94752	0.973759	+	0.227583i	$0.0730823\pi$
$410$	−52.3451	−2.58514
$411$	6.02228	0.297057
$412$	11.8444	0.583531
$413$	−0.000104387 0	−5.13655e−6 0
$414$	33.7598	1.65920
$415$	27.8455	1.36688
$416$	3.35638	0.164560
$417$	−5.61076	−0.274760
$418$	−102.570	−5.01687
$419$	−37.0310	−1.80908	−0.904541	−	0.426386i	$-0.859787\pi$
$419$	−37.0310	−1.80908	−0.904541	+	0.426386i	$0.859787\pi$
$420$	−0.493215	−0.0240664
$421$	23.6758	1.15389	0.576943	−	0.816784i	$-0.304245\pi$
$421$	23.6758	1.15389	0.576943	+	0.816784i	$0.304245\pi$
$422$	46.0617	2.24225
$423$	34.2831	1.66690
$424$	58.1177	2.82244
$425$	0.844240	0.0409517
$426$	−0.798335	−0.0386795
$427$	0.639498	0.0309475
$428$	39.3688	1.90296
$429$	−12.0429	−0.581436
$430$	−22.7089	−1.09512
$431$	1.75821	0.0846901	0.0423450	−	0.999103i	$-0.486517\pi$
$431$	1.75821	0.0846901	0.0423450	+	0.999103i	$0.486517\pi$
$432$	7.04541	0.338972
$433$	−21.8231	−1.04875	−0.524375	−	0.851487i	$-0.675701\pi$
$433$	−21.8231	−1.04875	−0.524375	+	0.851487i	$0.675701\pi$
$434$	−1.54282	−0.0740577
$435$	−0.866251	−0.0415335
$436$	−12.6281	−0.604776
$437$	32.5366	1.55644
$438$	11.6120	0.554842
$439$	22.3437	1.06641	0.533204	−	0.845987i	$-0.320988\pi$
$439$	22.3437	1.06641	0.533204	+	0.845987i	$0.320988\pi$
$440$	60.8295	2.89993
$441$	20.1511	0.959576
$442$	17.7123	0.842490
$443$	−39.5121	−1.87727	−0.938637	−	0.344906i	$-0.887911\pi$
$443$	−39.5121	−1.87727	−0.938637	+	0.344906i	$0.887911\pi$
$444$	−8.00020	−0.379673
$445$	0.0711358	0.00337216
$446$	−7.05216	−0.333930
$447$	−6.80598	−0.321912
$448$	1.59723	0.0754619
$449$	13.9786	0.659690	0.329845	−	0.944035i	$-0.393003\pi$
$449$	13.9786	0.659690	0.329845	+	0.944035i	$0.393003\pi$
$450$	−4.86383	−0.229283
$451$	−64.0565	−3.01630
$452$	−3.94116	−0.185376
$453$	−1.09074	−0.0512474
$454$	47.2431	2.21723
$455$	2.26868	0.106357
$456$	10.5308	0.493149
$457$	32.9067	1.53931	0.769655	−	0.638460i	$-0.220428\pi$
$457$	32.9067	1.53931	0.769655	+	0.638460i	$0.220428\pi$
$458$	−13.3559	−0.624081
$459$	−2.36209	−0.110253
$460$	−39.1768	−1.82663
$461$	25.5739	1.19109	0.595547	−	0.803320i	$-0.296935\pi$
$461$	25.5739	1.19109	0.595547	+	0.803320i	$0.296935\pi$
$462$	−0.909853	−0.0423302
$463$	36.6531	1.70341	0.851706	−	0.524020i	$-0.175568\pi$
$463$	36.6531	1.70341	0.851706	+	0.524020i	$0.175568\pi$
$464$	−4.65036	−0.215888
$465$	−2.33863	−0.108451
$466$	19.5728	0.906694
$467$	37.0449	1.71424	0.857118	−	0.515120i	$-0.172253\pi$
$467$	37.0449	1.71424	0.857118	+	0.515120i	$0.172253\pi$
$468$	−67.6926	−3.12909
$469$	−0.119539	−0.00551980
$470$	−59.9730	−2.76635
$471$	1.37100	0.0631724
$472$	−0.00268366	−0.000123525 0
$473$	−27.7897	−1.27777
$474$	−8.37290	−0.384580
$475$	−4.68760	−0.215082
$476$	0.887707	0.0406880
$477$	35.5320	1.62690
$478$	−27.5097	−1.25826
$479$	6.38969	0.291952	0.145976	−	0.989288i	$-0.453368\pi$
$479$	6.38969	0.291952	0.145976	+	0.989288i	$0.453368\pi$
$480$	0.384378	0.0175444
$481$	36.7992	1.67790
$482$	−22.0414	−1.00396
$483$	0.288618	0.0131326
$484$	107.782	4.89919
$485$	10.1912	0.462758
$486$	20.5365	0.931556
$487$	−4.39420	−0.199120	−0.0995601	−	0.995032i	$-0.531744\pi$
$487$	−4.39420	−0.199120	−0.0995601	+	0.995032i	$0.531744\pi$
$488$	16.4407	0.744234
$489$	3.21585	0.145426
$490$	−35.2513	−1.59249
$491$	−35.4352	−1.59917	−0.799583	−	0.600555i	$-0.794946\pi$
$491$	−35.4352	−1.59917	−0.799583	+	0.600555i	$0.794946\pi$
$492$	13.3526	0.601982
$493$	1.55911	0.0702187
$494$	−98.3469	−4.42483
$495$	37.1899	1.67156
$496$	−12.5546	−0.563720
$497$	0.184041	0.00825539
$498$	−10.7076	−0.479819
$499$	−15.0927	−0.675642	−0.337821	−	0.941210i	$-0.609690\pi$
$499$	−15.0927	−0.675642	−0.337821	+	0.941210i	$0.609690\pi$
$500$	46.5554	2.08202
$501$	−6.22237	−0.277995
$502$	44.3562	1.97971
$503$	−15.3291	−0.683493	−0.341746	−	0.939792i	$-0.611018\pi$
$503$	−15.3291	−0.683493	−0.341746	+	0.939792i	$0.611018\pi$
$504$	−2.51894	−0.112203
$505$	16.9439	0.753992
$506$	−72.2709	−3.21283
$507$	−7.28915	−0.323722
$508$	−26.5279	−1.17699
$509$	10.3928	0.460653	0.230327	−	0.973113i	$-0.426021\pi$
$509$	10.3928	0.460653	0.230327	+	0.973113i	$0.426021\pi$
$510$	2.02844	0.0898210
$511$	−2.67693	−0.118420
$512$	36.6070	1.61782
$513$	13.1154	0.579058
$514$	47.7816	2.10756
$515$	−6.23931	−0.274937
$516$	5.79277	0.255013
$517$	−73.3911	−3.22774
$518$	2.78022	0.122156
$519$	7.36177	0.323146
$520$	58.3249	2.55771
$521$	20.3842	0.893049	0.446524	−	0.894772i	$-0.352662\pi$
$521$	20.3842	0.893049	0.446524	+	0.894772i	$0.352662\pi$
$522$	−8.98233	−0.393146
$523$	34.0338	1.48819	0.744097	−	0.668071i	$-0.232880\pi$
$523$	34.0338	1.48819	0.744097	+	0.668071i	$0.232880\pi$
$524$	47.6967	2.08364
$525$	−0.0415816	−0.00181477
$526$	65.4814	2.85512
$527$	4.20915	0.183353
$528$	−7.40390	−0.322213
$529$	−0.0747118	−0.00324834
$530$	−62.1578	−2.69996
$531$	−0.00164073	−7.12018e−5 0
$532$	−4.92895	−0.213697
$533$	−61.4190	−2.66035
$534$	−0.0273543	−0.00118374
$535$	−20.7384	−0.896601
$536$	−3.07319	−0.132742
$537$	1.50227	0.0648277
$538$	31.0593	1.33906
$539$	−43.1382	−1.85809
$540$	−15.7920	−0.679580
$541$	44.7146	1.92243	0.961216	−	0.275796i	$-0.0889413\pi$
$541$	44.7146	1.92243	0.961216	+	0.275796i	$0.0889413\pi$
$542$	19.2857	0.828390
$543$	2.59202	0.111234
$544$	−0.691817	−0.0296614
$545$	6.65215	0.284947
$546$	−0.872391	−0.0373349
$547$	−7.24815	−0.309909	−0.154954	−	0.987922i	$-0.549523\pi$
$547$	−7.24815	−0.309909	−0.154954	+	0.987922i	$0.549523\pi$
$548$	−72.4662	−3.09560
$549$	10.0515	0.428987
$550$	10.4122	0.443977
$551$	−8.65687	−0.368795
$552$	7.41998	0.315816
$553$	1.93022	0.0820812
$554$	8.16899	0.347067
$555$	4.21430	0.178887
$556$	67.5143	2.86325
$557$	3.01891	0.127915	0.0639577	−	0.997953i	$-0.479628\pi$
$557$	3.01891	0.127915	0.0639577	+	0.997953i	$0.479628\pi$
$558$	−24.2497	−1.02657
$559$	−26.6455	−1.12698
$560$	1.39477	0.0589399
$561$	2.48228	0.104802
$562$	−59.4698	−2.50858
$563$	−13.9953	−0.589830	−0.294915	−	0.955524i	$-0.595291\pi$
$563$	−13.9953	−0.589830	−0.294915	+	0.955524i	$0.595291\pi$
$564$	15.2984	0.644179
$565$	2.07610	0.0873421
$566$	6.61135	0.277896
$567$	−1.48080	−0.0621879
$568$	4.73147	0.198528
$569$	5.84200	0.244909	0.122455	−	0.992474i	$-0.460923\pi$
$569$	5.84200	0.244909	0.122455	+	0.992474i	$0.460923\pi$
$570$	−11.2628	−0.471748
$571$	14.3015	0.598499	0.299249	−	0.954175i	$-0.403264\pi$
$571$	14.3015	0.598499	0.299249	+	0.954175i	$0.403264\pi$
$572$	144.912	6.05908
$573$	0.276242	0.0115402
$574$	−4.64027	−0.193681
$575$	−3.30288	−0.137740
$576$	25.1049	1.04604
$577$	−23.1355	−0.963143	−0.481572	−	0.876407i	$-0.659934\pi$
$577$	−23.1355	−0.963143	−0.481572	+	0.876407i	$0.659934\pi$
$578$	37.7858	1.57168
$579$	3.86271	0.160529
$580$	10.4236	0.432816
$581$	2.46844	0.102408
$582$	−3.91888	−0.162443
$583$	−76.0646	−3.15028
$584$	−68.8205	−2.84781
$585$	35.6587	1.47430
$586$	7.32472	0.302582
$587$	0.156411	0.00645575	0.00322788	−	0.999995i	$-0.498973\pi$
$587$	0.156411	0.00645575	0.00322788	+	0.999995i	$0.498973\pi$
$588$	8.99218	0.370831
$589$	−23.3711	−0.962988
$590$	0.00287021	0.000118165 0
$591$	−4.43268	−0.182336
$592$	22.6239	0.929838
$593$	−35.9541	−1.47646	−0.738228	−	0.674551i	$-0.764337\pi$
$593$	−35.9541	−1.47646	−0.738228	+	0.674551i	$0.764337\pi$
$594$	−29.1321	−1.19531
$595$	−0.467621	−0.0191706
$596$	81.8964	3.35461
$597$	0.514400	0.0210530
$598$	−69.2952	−2.83369
$599$	34.5138	1.41019	0.705097	−	0.709111i	$-0.250903\pi$
$599$	34.5138	1.41019	0.705097	+	0.709111i	$0.250903\pi$
$600$	−1.06901	−0.0436421
$601$	29.9584	1.22203	0.611014	−	0.791620i	$-0.290762\pi$
$601$	29.9584	1.22203	0.611014	+	0.791620i	$0.290762\pi$
$602$	−2.01310	−0.0820477
$603$	−1.87889	−0.0765143
$604$	13.1249	0.534043
$605$	−56.7769	−2.30831
$606$	−6.51553	−0.264675
$607$	−24.0552	−0.976371	−0.488185	−	0.872740i	$-0.662341\pi$
$607$	−24.0552	−0.976371	−0.488185	+	0.872740i	$0.662341\pi$
$608$	3.84128	0.155785
$609$	−0.0767912	−0.00311174
$610$	−17.5835	−0.711937
$611$	−70.3693	−2.84684
$612$	13.9528	0.564008
$613$	−16.2217	−0.655188	−0.327594	−	0.944819i	$-0.606238\pi$
$613$	−16.2217	−0.655188	−0.327594	+	0.944819i	$0.606238\pi$
$614$	44.5664	1.79855
$615$	−7.03380	−0.283630
$616$	5.39240	0.217266
$617$	−33.8823	−1.36405	−0.682026	−	0.731328i	$-0.738901\pi$
$617$	−33.8823	−1.36405	−0.682026	+	0.731328i	$0.738901\pi$
$618$	2.39924	0.0965116
$619$	−6.46819	−0.259979	−0.129989	−	0.991515i	$-0.541494\pi$
$619$	−6.46819	−0.259979	−0.129989	+	0.991515i	$0.541494\pi$
$620$	28.1407	1.13016
$621$	9.24109	0.370832
$622$	66.5698	2.66920
$623$	0.00630603	0.000252646 0
$624$	−7.09905	−0.284189
$625$	−21.0750	−0.843002
$626$	3.42522	0.136899
$627$	−13.7827	−0.550429
$628$	−16.4973	−0.658312
$629$	−7.58504	−0.302435
$630$	2.69405	0.107334
$631$	1.74216	0.0693545	0.0346772	−	0.999399i	$-0.488960\pi$
$631$	1.74216	0.0693545	0.0346772	+	0.999399i	$0.488960\pi$
$632$	49.6234	1.97391
$633$	6.18948	0.246010
$634$	38.9899	1.54849
$635$	13.9742	0.554549
$636$	15.8557	0.628719
$637$	−41.3620	−1.63882
$638$	19.2288	0.761276
$639$	2.89272	0.114434
$640$	−41.5700	−1.64320
$641$	−16.6102	−0.656065	−0.328033	−	0.944666i	$-0.606386\pi$
$641$	−16.6102	−0.656065	−0.328033	+	0.944666i	$0.606386\pi$
$642$	7.97469	0.314736
$643$	48.7587	1.92286	0.961428	−	0.275056i	$-0.0886965\pi$
$643$	48.7587	1.92286	0.961428	+	0.275056i	$0.0886965\pi$
$644$	−3.47293	−0.136853
$645$	−3.05148	−0.120152
$646$	20.2713	0.797562
$647$	30.0439	1.18115	0.590574	−	0.806983i	$-0.298901\pi$
$647$	30.0439	1.18115	0.590574	+	0.806983i	$0.298901\pi$
$648$	−38.0695	−1.49551
$649$	0.00351238	0.000137873 0
$650$	9.98347	0.391584
$651$	−0.207314	−0.00812528
$652$	−38.6963	−1.51546
$653$	7.59203	0.297099	0.148550	−	0.988905i	$-0.452540\pi$
$653$	7.59203	0.297099	0.148550	+	0.988905i	$0.452540\pi$
$654$	−2.55799	−0.100025
$655$	−25.1254	−0.981730
$656$	−37.7601	−1.47428
$657$	−42.0754	−1.64152
$658$	−5.31648	−0.207258
$659$	−9.73993	−0.379414	−0.189707	−	0.981841i	$-0.560754\pi$
$659$	−9.73993	−0.379414	−0.189707	+	0.981841i	$0.560754\pi$
$660$	16.5956	0.645981
$661$	−17.2422	−0.670643	−0.335322	−	0.942104i	$-0.608845\pi$
$661$	−17.2422	−0.670643	−0.335322	+	0.942104i	$0.608845\pi$
$662$	67.6650	2.62988
$663$	2.38007	0.0924343
$664$	63.4604	2.46274
$665$	2.59644	0.100686
$666$	43.6989	1.69330
$667$	−6.09963	−0.236179
$668$	74.8737	2.89695
$669$	−0.947625	−0.0366373
$670$	3.28683	0.126981
$671$	−21.5176	−0.830678
$672$	0.0340743	0.00131444
$673$	42.6402	1.64366	0.821830	−	0.569732i	$-0.192953\pi$
$673$	42.6402	1.64366	0.821830	+	0.569732i	$0.192953\pi$
$674$	47.9663	1.84759
$675$	−1.33138	−0.0512448
$676$	87.7103	3.37347
$677$	32.6847	1.25618	0.628088	−	0.778142i	$-0.283838\pi$
$677$	32.6847	1.25618	0.628088	+	0.778142i	$0.283838\pi$
$678$	−0.798335	−0.0306599
$679$	0.903426	0.0346703
$680$	−12.0219	−0.461020
$681$	6.34823	0.243265
$682$	51.9123	1.98782
$683$	−47.4081	−1.81402	−0.907010	−	0.421109i	$-0.861641\pi$
$683$	−47.4081	−1.81402	−0.907010	+	0.421109i	$0.861641\pi$
$684$	−77.4721	−2.96222
$685$	38.1733	1.45853
$686$	−6.26509	−0.239202
$687$	−1.79468	−0.0684714
$688$	−16.3815	−0.624539
$689$	−72.9327	−2.77851
$690$	−7.93579	−0.302110
$691$	20.3203	0.773020	0.386510	−	0.922285i	$-0.373680\pi$
$691$	20.3203	0.773020	0.386510	+	0.922285i	$0.373680\pi$
$692$	−88.5842	−3.36747
$693$	3.29681	0.125235
$694$	−17.1433	−0.650751
$695$	−35.5648	−1.34905
$696$	−1.97420	−0.0748320
$697$	12.6597	0.479520
$698$	−54.8361	−2.07558
$699$	2.63007	0.0994786
$700$	0.500351	0.0189115
$701$	−21.0342	−0.794452	−0.397226	−	0.917721i	$-0.630027\pi$
$701$	−21.0342	−0.794452	−0.397226	+	0.917721i	$0.630027\pi$
$702$	−27.9326	−1.05425
$703$	42.1156	1.58842
$704$	−53.7430	−2.02552
$705$	−8.05880	−0.303512
$706$	63.8645	2.40357
$707$	1.50203	0.0564898
$708$	−0.000732157 0	−2.75161e−5 0
$709$	−39.8120	−1.49517	−0.747585	−	0.664166i	$-0.768787\pi$
$709$	−39.8120	−1.49517	−0.747585	+	0.664166i	$0.768787\pi$
$710$	−5.06038	−0.189913
$711$	30.3387	1.13779
$712$	0.162120	0.00607570
$713$	−16.4673	−0.616703
$714$	0.179817	0.00672949
$715$	−76.3359	−2.85480
$716$	−18.0768	−0.675562
$717$	−3.69658	−0.138051
$718$	18.3804	0.685950
$719$	13.3455	0.497705	0.248852	−	0.968541i	$-0.419947\pi$
$719$	13.3455	0.497705	0.248852	+	0.968541i	$0.419947\pi$
$720$	21.9228	0.817013
$721$	−0.553101	−0.0205986
$722$	−66.2436	−2.46533
$723$	−2.96179	−0.110150
$724$	−31.1898	−1.15916
$725$	0.878784	0.0326372
$726$	21.8328	0.810290
$727$	−12.0974	−0.448669	−0.224334	−	0.974512i	$-0.572021\pi$
$727$	−12.0974	−0.448669	−0.224334	+	0.974512i	$0.572021\pi$
$728$	5.17037	0.191627
$729$	−21.3785	−0.791797
$730$	73.6046	2.72423
$731$	5.49216	0.203135
$732$	4.48535	0.165783
$733$	−22.9649	−0.848226	−0.424113	−	0.905609i	$-0.639414\pi$
$733$	−22.9649	−0.848226	−0.424113	+	0.905609i	$0.639414\pi$
$734$	37.7028	1.39164
$735$	−4.73684	−0.174721
$736$	2.70657	0.0997654
$737$	4.02221	0.148160
$738$	−72.9349	−2.68477
$739$	14.5386	0.534811	0.267405	−	0.963584i	$-0.413834\pi$
$739$	14.5386	0.534811	0.267405	+	0.963584i	$0.413834\pi$
$740$	−50.7106	−1.86416
$741$	−13.2152	−0.485474
$742$	−5.51015	−0.202284
$743$	−19.3507	−0.709909	−0.354954	−	0.934884i	$-0.615504\pi$
$743$	−19.3507	−0.709909	−0.354954	+	0.934884i	$0.615504\pi$
$744$	−5.32978	−0.195399
$745$	−43.1409	−1.58056
$746$	−48.7086	−1.78335
$747$	38.7984	1.41956
$748$	−29.8693	−1.09213
$749$	−1.83842	−0.0671743
$750$	9.43043	0.344351
$751$	−17.3043	−0.631444	−0.315722	−	0.948852i	$-0.602247\pi$
$751$	−17.3043	−0.631444	−0.315722	+	0.948852i	$0.602247\pi$
$752$	−43.2627	−1.57763
$753$	5.96030	0.217205
$754$	18.4371	0.671439
$755$	−6.91383	−0.251620
$756$	−1.39993	−0.0509148
$757$	16.1487	0.586934	0.293467	−	0.955969i	$-0.405191\pi$
$757$	16.1487	0.586934	0.293467	+	0.955969i	$0.405191\pi$
$758$	−20.7783	−0.754700
$759$	−9.71131	−0.352498
$760$	66.7511	2.42132
$761$	−33.5310	−1.21550	−0.607749	−	0.794129i	$-0.707927\pi$
$761$	−33.5310	−1.21550	−0.607749	+	0.794129i	$0.707927\pi$
$762$	−5.37359	−0.194665
$763$	0.589698	0.0213485
$764$	−3.32402	−0.120259
$765$	−7.34996	−0.265738
$766$	58.3359	2.10776
$767$	0.00336776	0.000121603 0
$768$	10.3002	0.371676
$769$	47.4454	1.71093	0.855463	−	0.517863i	$-0.173272\pi$
$769$	47.4454	1.71093	0.855463	+	0.517863i	$0.173272\pi$
$770$	−5.76726	−0.207838
$771$	6.42059	0.231232
$772$	−46.4800	−1.67285
$773$	−39.9719	−1.43769	−0.718845	−	0.695171i	$-0.755329\pi$
$773$	−39.9719	−1.43769	−0.718845	+	0.695171i	$0.755329\pi$
$774$	−31.6414	−1.13733
$775$	2.37246	0.0852214
$776$	23.2259	0.833762
$777$	0.373588	0.0134024
$778$	−0.821702	−0.0294595
$779$	−70.2922	−2.51848
$780$	15.9122	0.569749
$781$	−6.19257	−0.221587
$782$	14.2831	0.510763
$783$	−2.45874	−0.0878681
$784$	−25.4291	−0.908184
$785$	8.69032	0.310171
$786$	9.66162	0.344619
$787$	−49.9378	−1.78009	−0.890046	−	0.455871i	$-0.849328\pi$
$787$	−49.9378	−1.78009	−0.890046	+	0.455871i	$0.849328\pi$
$788$	53.3384	1.90010
$789$	8.79897	0.313252
$790$	−53.0730	−1.88825
$791$	0.184041	0.00654376
$792$	84.7566	3.01170
$793$	−20.6316	−0.732650
$794$	−77.0431	−2.73416
$795$	−8.35237	−0.296228
$796$	−6.18978	−0.219391
$797$	−9.91488	−0.351203	−0.175601	−	0.984461i	$-0.556187\pi$
$797$	−9.91488	−0.351203	−0.175601	+	0.984461i	$0.556187\pi$
$798$	−0.998425	−0.0353439
$799$	14.5045	0.513133
$800$	−0.389939	−0.0137864
$801$	0.0991169	0.00350212
$802$	−13.6268	−0.481177
$803$	90.0725	3.17859
$804$	−0.838431	−0.0295692
$805$	1.82945	0.0644797
$806$	49.7748	1.75324
$807$	4.17355	0.146916
$808$	38.6154	1.35848
$809$	33.7817	1.18770	0.593851	−	0.804575i	$-0.297607\pi$
$809$	33.7817	1.18770	0.593851	+	0.804575i	$0.297607\pi$
$810$	40.7160	1.43061
$811$	−38.1556	−1.33983	−0.669913	−	0.742440i	$-0.733669\pi$
$811$	−38.1556	−1.33983	−0.669913	+	0.742440i	$0.733669\pi$
$812$	0.924029	0.0324271
$813$	2.59149	0.0908874
$814$	−93.5479	−3.27885
$815$	20.3842	0.714027
$816$	1.46326	0.0512242
$817$	−30.4950	−1.06688
$818$	−96.0016	−3.35662
$819$	3.16106	0.110456
$820$	84.6377	2.95568
$821$	−26.6886	−0.931440	−0.465720	−	0.884932i	$-0.654205\pi$
$821$	−26.6886	−0.931440	−0.465720	+	0.884932i	$0.654205\pi$
$822$	−14.6790	−0.511989
$823$	−54.1423	−1.88728	−0.943640	−	0.330972i	$-0.892623\pi$
$823$	−54.1423	−1.88728	−0.943640	+	0.330972i	$0.892623\pi$
$824$	−14.2195	−0.495360
$825$	1.39912	0.0487112
$826$	0.000254438 0	8.85303e−6 0
$827$	41.6673	1.44891	0.724456	−	0.689321i	$-0.242091\pi$
$827$	41.6673	1.44891	0.724456	+	0.689321i	$0.242091\pi$
$828$	−54.5869	−1.89702
$829$	−53.9328	−1.87316	−0.936582	−	0.350450i	$-0.886029\pi$
$829$	−53.9328	−1.87316	−0.936582	+	0.350450i	$0.886029\pi$
$830$	−67.8719	−2.35587
$831$	1.09770	0.0380787
$832$	−51.5301	−1.78649
$833$	8.52554	0.295392
$834$	13.6759	0.473559
$835$	−39.4415	−1.36493
$836$	165.848	5.73596
$837$	−6.63788	−0.229439
$838$	90.2612	3.11802
$839$	24.3030	0.839034	0.419517	−	0.907747i	$-0.362199\pi$
$839$	24.3030	0.839034	0.419517	+	0.907747i	$0.362199\pi$
$840$	0.592119	0.0204300
$841$	−27.3771	−0.944038
$842$	−57.7085	−1.98877
$843$	−7.99118	−0.275231
$844$	−74.4781	−2.56364
$845$	−46.2035	−1.58945
$846$	−83.5633	−2.87296
$847$	−5.03314	−0.172941
$848$	−44.8386	−1.53977
$849$	0.888391	0.0304895
$850$	−2.05779	−0.0705817
$851$	29.6746	1.01723
$852$	1.29084	0.0442235
$853$	−33.2930	−1.13993	−0.569965	−	0.821669i	$-0.693043\pi$
$853$	−33.2930	−1.13993	−0.569965	+	0.821669i	$0.693043\pi$
$854$	−1.55874	−0.0533391
$855$	40.8103	1.39568
$856$	−47.2634	−1.61543
$857$	4.61700	0.157714	0.0788569	−	0.996886i	$-0.474873\pi$
$857$	4.61700	0.157714	0.0788569	+	0.996886i	$0.474873\pi$
$858$	29.3539	1.00213
$859$	8.18929	0.279415	0.139708	−	0.990193i	$-0.455384\pi$
$859$	8.18929	0.279415	0.139708	+	0.990193i	$0.455384\pi$
$860$	36.7185	1.25209
$861$	−0.623531	−0.0212499
$862$	−4.28555	−0.145966
$863$	26.1352	0.889654	0.444827	−	0.895617i	$-0.353265\pi$
$863$	26.1352	0.889654	0.444827	+	0.895617i	$0.353265\pi$
$864$	1.09101	0.0371168
$865$	46.6638	1.58662
$866$	53.1926	1.80756
$867$	5.07741	0.172438
$868$	2.49461	0.0846726
$869$	−64.9473	−2.20319
$870$	2.11144	0.0715846
$871$	3.85660	0.130676
$872$	15.1604	0.513396
$873$	14.1999	0.480593
$874$	−79.3063	−2.68258
$875$	−2.17401	−0.0734950
$876$	−18.7756	−0.634370
$877$	26.4964	0.894718	0.447359	−	0.894354i	$-0.352365\pi$
$877$	26.4964	0.894718	0.447359	+	0.894354i	$0.352365\pi$
$878$	−54.4617	−1.83799
$879$	0.984250	0.0331979
$880$	−46.9309	−1.58204
$881$	−3.90597	−0.131595	−0.0657977	−	0.997833i	$-0.520959\pi$
$881$	−3.90597	−0.131595	−0.0657977	+	0.997833i	$0.520959\pi$
$882$	−49.1173	−1.65386
$883$	−24.9050	−0.838119	−0.419059	−	0.907959i	$-0.637640\pi$
$883$	−24.9050	−0.838119	−0.419059	+	0.907959i	$0.637640\pi$
$884$	−28.6394	−0.963248
$885$	0.000385681 0	1.29645e−5 0
$886$	96.3086	3.23555
$887$	22.7565	0.764088	0.382044	−	0.924144i	$-0.375220\pi$
$887$	22.7565	0.764088	0.382044	+	0.924144i	$0.375220\pi$
$888$	9.60447	0.322305
$889$	1.23878	0.0415474
$890$	−0.173390	−0.00581204
$891$	49.8256	1.66922
$892$	11.4028	0.381793
$893$	−80.5356	−2.69502
$894$	16.5892	0.554827
$895$	9.52239	0.318298
$896$	−3.68509	−0.123110
$897$	−9.31145	−0.310900
$898$	−34.0721	−1.13700
$899$	4.38137	0.146127
$900$	7.86442	0.262147
$901$	15.0329	0.500818
$902$	156.134	5.19871
$903$	−0.270507	−0.00900191
$904$	4.73147	0.157366
$905$	16.4299	0.546150
$906$	2.65862	0.0883268
$907$	−41.5772	−1.38055	−0.690273	−	0.723549i	$-0.742510\pi$
$907$	−41.5772	−1.38055	−0.690273	+	0.723549i	$0.742510\pi$
$908$	−76.3883	−2.53504
$909$	23.6087	0.783050
$910$	−5.52979	−0.183311
$911$	7.66058	0.253806	0.126903	−	0.991915i	$-0.459496\pi$
$911$	7.66058	0.253806	0.126903	+	0.991915i	$0.459496\pi$
$912$	−8.12465	−0.269034
$913$	−83.0573	−2.74880
$914$	−80.2083	−2.65306
$915$	−2.36277	−0.0781106
$916$	21.5954	0.713533
$917$	−2.22731	−0.0735522
$918$	5.75747	0.190025
$919$	45.2128	1.49143	0.745716	−	0.666264i	$-0.232107\pi$
$919$	45.2128	1.49143	0.745716	+	0.666264i	$0.232107\pi$
$920$	47.0328	1.55063
$921$	5.98855	0.197330
$922$	−62.3350	−2.05290
$923$	−5.93759	−0.195438
$924$	1.47116	0.0483976
$925$	−4.27527	−0.140570
$926$	−89.3399	−2.93589
$927$	−8.69352	−0.285533
$928$	−0.720124	−0.0236392
$929$	16.4780	0.540627	0.270314	−	0.962772i	$-0.412873\pi$
$929$	16.4780	0.540627	0.270314	+	0.962772i	$0.412873\pi$
$930$	5.70029	0.186920
$931$	−47.3376	−1.55143
$932$	−31.6477	−1.03665
$933$	8.94522	0.292853
$934$	−90.2951	−2.95455
$935$	15.7343	0.514568
$936$	81.2668	2.65629
$937$	−25.5293	−0.834006	−0.417003	−	0.908905i	$-0.636920\pi$
$937$	−25.5293	−0.834006	−0.417003	+	0.908905i	$0.636920\pi$
$938$	0.291370	0.00951357
$939$	0.460259	0.0150200
$940$	96.9715	3.16286
$941$	−5.57361	−0.181694	−0.0908472	−	0.995865i	$-0.528957\pi$
$941$	−5.57361	−0.181694	−0.0908472	+	0.995865i	$0.528957\pi$
$942$	−3.34175	−0.108880
$943$	−49.5279	−1.61285
$944$	0.00207048	6.73884e−5 0
$945$	0.737444	0.0239891
$946$	67.7360	2.20229
$947$	−5.41184	−0.175861	−0.0879306	−	0.996127i	$-0.528025\pi$
$947$	−5.41184	−0.175861	−0.0879306	+	0.996127i	$0.528025\pi$
$948$	13.5383	0.439703
$949$	86.3638	2.80349
$950$	11.4258	0.370701
$951$	5.23921	0.169893
$952$	−1.06572	−0.0345401
$953$	32.1253	1.04064	0.520320	−	0.853972i	$-0.325813\pi$
$953$	32.1253	1.04064	0.520320	+	0.853972i	$0.325813\pi$
$954$	−86.6073	−2.80402
$955$	1.75100	0.0566612
$956$	44.4809	1.43862
$957$	2.58385	0.0835239
$958$	−15.5745	−0.503190
$959$	3.38398	0.109274
$960$	−5.90131	−0.190464
$961$	−19.1716	−0.618437
$962$	−89.6961	−2.89192
$963$	−28.8959	−0.931156
$964$	35.6392	1.14786
$965$	24.4844	0.788182
$966$	−0.703490	−0.0226344
$967$	10.5398	0.338938	0.169469	−	0.985535i	$-0.445795\pi$
$967$	10.5398	0.338938	0.169469	+	0.985535i	$0.445795\pi$
$968$	−129.396	−4.15893
$969$	2.72392	0.0875050
$970$	−24.8405	−0.797580
$971$	17.8853	0.573968	0.286984	−	0.957935i	$-0.407347\pi$
$971$	17.8853	0.573968	0.286984	+	0.957935i	$0.407347\pi$
$972$	−33.2059	−1.06508
$973$	−3.15274	−0.101072
$974$	10.7106	0.343191
$975$	1.34152	0.0429629
$976$	−12.6842	−0.406012
$977$	59.1835	1.89345	0.946725	−	0.322044i	$-0.104370\pi$
$977$	59.1835	1.89345	0.946725	+	0.322044i	$0.104370\pi$
$978$	−7.83846	−0.250646
$979$	−0.212183	−0.00678141
$980$	56.9984	1.82075
$981$	9.26876	0.295929
$982$	86.3714	2.75622
$983$	−7.59683	−0.242301	−0.121151	−	0.992634i	$-0.538658\pi$
$983$	−7.59683	−0.242301	−0.121151	+	0.992634i	$0.538658\pi$
$984$	−16.0302	−0.511023
$985$	−28.0973	−0.895254
$986$	−3.80025	−0.121025
$987$	−0.714395	−0.0227394
$988$	159.019	5.05906
$989$	−21.4867	−0.683239
$990$	−90.6486	−2.88100
$991$	−4.38131	−0.139177	−0.0695885	−	0.997576i	$-0.522169\pi$
$991$	−4.38131	−0.139177	−0.0695885	+	0.997576i	$0.522169\pi$
$992$	−1.94413	−0.0617261
$993$	9.09240	0.288539
$994$	−0.448592	−0.0142285
$995$	3.26061	0.103368
$996$	17.3133	0.548594
$997$	−15.6397	−0.495315	−0.247658	−	0.968848i	$-0.579661\pi$
$997$	−15.6397	−0.495315	−0.247658	+	0.968848i	$0.579661\pi$
$998$	36.7877	1.16449
$999$	11.9617	0.378452

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.18	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-2.43745 q^{2} -0.327529 q^{3} +3.94116 q^{4} -2.07610 q^{5} +0.798335 q^{6} -0.184041 q^{7} -4.73147 q^{8} -2.89272 q^{9} +O(q^{10})\)	\(q-2.43745 q^{2} -0.327529 q^{3} +3.94116 q^{4} -2.07610 q^{5} +0.798335 q^{6} -0.184041 q^{7} -4.73147 q^{8} -2.89272 q^{9} +5.06038 q^{10} +6.19257 q^{11} -1.29084 q^{12} +5.93759 q^{13} +0.448592 q^{14} +0.679982 q^{15} +3.65040 q^{16} -1.22386 q^{17} +7.05087 q^{18} +6.79540 q^{19} -8.18222 q^{20} +0.0602789 q^{21} -15.0941 q^{22} +4.78804 q^{23} +1.54969 q^{24} -0.689820 q^{25} -14.4726 q^{26} +1.93004 q^{27} -0.725336 q^{28} -1.27393 q^{29} -1.65742 q^{30} -3.43925 q^{31} +0.565277 q^{32} -2.02824 q^{33} +2.98309 q^{34} +0.382088 q^{35} -11.4007 q^{36} +6.19766 q^{37} -16.5634 q^{38} -1.94473 q^{39} +9.82299 q^{40} -10.3441 q^{41} -0.146927 q^{42} -4.48759 q^{43} +24.4059 q^{44} +6.00558 q^{45} -11.6706 q^{46} -11.8515 q^{47} -1.19561 q^{48} -6.96613 q^{49} +1.68140 q^{50} +0.400848 q^{51} +23.4010 q^{52} -12.2832 q^{53} -4.70437 q^{54} -12.8564 q^{55} +0.870786 q^{56} -2.22569 q^{57} +3.10514 q^{58} +0.000567193 q^{59} +2.67991 q^{60} -3.47475 q^{61} +8.38300 q^{62} +0.532381 q^{63} -8.67863 q^{64} -12.3270 q^{65} +4.94374 q^{66} +0.649522 q^{67} -4.82341 q^{68} -1.56822 q^{69} -0.931320 q^{70} -1.00000 q^{71} +13.6868 q^{72} +14.5453 q^{73} -15.1065 q^{74} +0.225936 q^{75} +26.7817 q^{76} -1.13969 q^{77} +4.74019 q^{78} -10.4879 q^{79} -7.57858 q^{80} +8.04603 q^{81} +25.2132 q^{82} -13.4124 q^{83} +0.237569 q^{84} +2.54084 q^{85} +10.9383 q^{86} +0.417250 q^{87} -29.2999 q^{88} -0.0342642 q^{89} -14.6383 q^{90} -1.09276 q^{91} +18.8704 q^{92} +1.12645 q^{93} +28.8874 q^{94} -14.1079 q^{95} -0.185145 q^{96} -4.90882 q^{97} +16.9796 q^{98} -17.9134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 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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