LMFDB - Embedded newform 8026.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.52707 q^{3} +1.00000 q^{4} -2.67563 q^{5} -2.52707 q^{6} -1.45299 q^{7} +1.00000 q^{8} +3.38607 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.52707 q^{3} +1.00000 q^{4} -2.67563 q^{5} -2.52707 q^{6} -1.45299 q^{7} +1.00000 q^{8} +3.38607 q^{9} -2.67563 q^{10} -2.13623 q^{11} -2.52707 q^{12} +1.79444 q^{13} -1.45299 q^{14} +6.76150 q^{15} +1.00000 q^{16} -3.37091 q^{17} +3.38607 q^{18} -3.49848 q^{19} -2.67563 q^{20} +3.67181 q^{21} -2.13623 q^{22} +4.68412 q^{23} -2.52707 q^{24} +2.15900 q^{25} +1.79444 q^{26} -0.975613 q^{27} -1.45299 q^{28} +2.31775 q^{29} +6.76150 q^{30} +0.0984331 q^{31} +1.00000 q^{32} +5.39840 q^{33} -3.37091 q^{34} +3.88767 q^{35} +3.38607 q^{36} +6.46076 q^{37} -3.49848 q^{38} -4.53466 q^{39} -2.67563 q^{40} +7.96643 q^{41} +3.67181 q^{42} -0.0587343 q^{43} -2.13623 q^{44} -9.05986 q^{45} +4.68412 q^{46} -7.92463 q^{47} -2.52707 q^{48} -4.88881 q^{49} +2.15900 q^{50} +8.51851 q^{51} +1.79444 q^{52} +8.63311 q^{53} -0.975613 q^{54} +5.71577 q^{55} -1.45299 q^{56} +8.84089 q^{57} +2.31775 q^{58} +11.6833 q^{59} +6.76150 q^{60} -6.89946 q^{61} +0.0984331 q^{62} -4.91993 q^{63} +1.00000 q^{64} -4.80125 q^{65} +5.39840 q^{66} -3.12393 q^{67} -3.37091 q^{68} -11.8371 q^{69} +3.88767 q^{70} +11.5427 q^{71} +3.38607 q^{72} -5.45707 q^{73} +6.46076 q^{74} -5.45594 q^{75} -3.49848 q^{76} +3.10393 q^{77} -4.53466 q^{78} +13.2661 q^{79} -2.67563 q^{80} -7.69276 q^{81} +7.96643 q^{82} -3.11817 q^{83} +3.67181 q^{84} +9.01930 q^{85} -0.0587343 q^{86} -5.85711 q^{87} -2.13623 q^{88} -11.1759 q^{89} -9.05986 q^{90} -2.60731 q^{91} +4.68412 q^{92} -0.248747 q^{93} -7.92463 q^{94} +9.36064 q^{95} -2.52707 q^{96} -10.6411 q^{97} -4.88881 q^{98} -7.23343 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.52707	−1.45900	−0.729501	−	0.683979i	$-0.760248\pi$
$3$	−2.52707	−1.45900	−0.729501	+	0.683979i	$0.760248\pi$
$4$	1.00000	0.500000
$5$	−2.67563	−1.19658	−0.598289	−	0.801280i	$-0.704153\pi$
$5$	−2.67563	−1.19658	−0.598289	+	0.801280i	$0.704153\pi$
$6$	−2.52707	−1.03167
$7$	−1.45299	−0.549180	−0.274590	−	0.961561i	$-0.588542\pi$
$7$	−1.45299	−0.549180	−0.274590	+	0.961561i	$0.588542\pi$
$8$	1.00000	0.353553
$9$	3.38607	1.12869
$10$	−2.67563	−0.846109
$11$	−2.13623	−0.644099	−0.322049	−	0.946723i	$-0.604372\pi$
$11$	−2.13623	−0.644099	−0.322049	+	0.946723i	$0.604372\pi$
$12$	−2.52707	−0.729501
$13$	1.79444	0.497687	0.248844	−	0.968544i	$-0.419949\pi$
$13$	1.79444	0.497687	0.248844	+	0.968544i	$0.419949\pi$
$14$	−1.45299	−0.388329
$15$	6.76150	1.74581
$16$	1.00000	0.250000
$17$	−3.37091	−0.817565	−0.408783	−	0.912632i	$-0.634047\pi$
$17$	−3.37091	−0.817565	−0.408783	+	0.912632i	$0.634047\pi$
$18$	3.38607	0.798103
$19$	−3.49848	−0.802606	−0.401303	−	0.915945i	$-0.631443\pi$
$19$	−3.49848	−0.802606	−0.401303	+	0.915945i	$0.631443\pi$
$20$	−2.67563	−0.598289
$21$	3.67181	0.801255
$22$	−2.13623	−0.455446
$23$	4.68412	0.976707	0.488354	−	0.872646i	$-0.337598\pi$
$23$	4.68412	0.976707	0.488354	+	0.872646i	$0.337598\pi$
$24$	−2.52707	−0.515835
$25$	2.15900	0.431800
$26$	1.79444	0.351918
$27$	−0.975613	−0.187757
$28$	−1.45299	−0.274590
$29$	2.31775	0.430395	0.215198	−	0.976570i	$-0.430960\pi$
$29$	2.31775	0.430395	0.215198	+	0.976570i	$0.430960\pi$
$30$	6.76150	1.23447
$31$	0.0984331	0.0176791	0.00883955	−	0.999961i	$-0.497186\pi$
$31$	0.0984331	0.0176791	0.00883955	+	0.999961i	$0.497186\pi$
$32$	1.00000	0.176777
$33$	5.39840	0.939742
$34$	−3.37091	−0.578106
$35$	3.88767	0.657137
$36$	3.38607	0.564344
$37$	6.46076	1.06214	0.531071	−	0.847327i	$-0.321790\pi$
$37$	6.46076	1.06214	0.531071	+	0.847327i	$0.321790\pi$
$38$	−3.49848	−0.567528
$39$	−4.53466	−0.726127
$40$	−2.67563	−0.423054
$41$	7.96643	1.24415	0.622074	−	0.782959i	$-0.286290\pi$
$41$	7.96643	1.24415	0.622074	+	0.782959i	$0.286290\pi$
$42$	3.67181	0.566573
$43$	−0.0587343	−0.00895690	−0.00447845	−	0.999990i	$-0.501426\pi$
$43$	−0.0587343	−0.00895690	−0.00447845	+	0.999990i	$0.501426\pi$
$44$	−2.13623	−0.322049
$45$	−9.05986	−1.35056
$46$	4.68412	0.690636
$47$	−7.92463	−1.15593	−0.577963	−	0.816063i	$-0.696152\pi$
$47$	−7.92463	−1.15593	−0.577963	+	0.816063i	$0.696152\pi$
$48$	−2.52707	−0.364751
$49$	−4.88881	−0.698401
$50$	2.15900	0.305329
$51$	8.51851	1.19283
$52$	1.79444	0.248844
$53$	8.63311	1.18585	0.592925	−	0.805258i	$-0.297973\pi$
$53$	8.63311	1.18585	0.592925	+	0.805258i	$0.297973\pi$
$54$	−0.975613	−0.132764
$55$	5.71577	0.770714
$56$	−1.45299	−0.194164
$57$	8.84089	1.17100
$58$	2.31775	0.304336
$59$	11.6833	1.52103	0.760517	−	0.649318i	$-0.224945\pi$
$59$	11.6833	1.52103	0.760517	+	0.649318i	$0.224945\pi$
$60$	6.76150	0.872905
$61$	−6.89946	−0.883386	−0.441693	−	0.897166i	$-0.645622\pi$
$61$	−6.89946	−0.883386	−0.441693	+	0.897166i	$0.645622\pi$
$62$	0.0984331	0.0125010
$63$	−4.91993	−0.619853
$64$	1.00000	0.125000
$65$	−4.80125	−0.595522
$66$	5.39840	0.664498
$67$	−3.12393	−0.381649	−0.190825	−	0.981624i	$-0.561116\pi$
$67$	−3.12393	−0.381649	−0.190825	+	0.981624i	$0.561116\pi$
$68$	−3.37091	−0.408783
$69$	−11.8371	−1.42502
$70$	3.88767	0.464666
$71$	11.5427	1.36986	0.684932	−	0.728607i	$-0.259832\pi$
$71$	11.5427	1.36986	0.684932	+	0.728607i	$0.259832\pi$
$72$	3.38607	0.399052
$73$	−5.45707	−0.638702	−0.319351	−	0.947637i	$-0.603465\pi$
$73$	−5.45707	−0.638702	−0.319351	+	0.947637i	$0.603465\pi$
$74$	6.46076	0.751048
$75$	−5.45594	−0.629997
$76$	−3.49848	−0.401303
$77$	3.10393	0.353726
$78$	−4.53466	−0.513449
$79$	13.2661	1.49255	0.746275	−	0.665637i	$-0.231840\pi$
$79$	13.2661	1.49255	0.746275	+	0.665637i	$0.231840\pi$
$80$	−2.67563	−0.299145
$81$	−7.69276	−0.854751
$82$	7.96643	0.879745
$83$	−3.11817	−0.342264	−0.171132	−	0.985248i	$-0.554742\pi$
$83$	−3.11817	−0.342264	−0.171132	+	0.985248i	$0.554742\pi$
$84$	3.67181	0.400628
$85$	9.01930	0.978281
$86$	−0.0587343	−0.00633348
$87$	−5.85711	−0.627948
$88$	−2.13623	−0.227723
$89$	−11.1759	−1.18465	−0.592324	−	0.805700i	$-0.701789\pi$
$89$	−11.1759	−1.18465	−0.592324	+	0.805700i	$0.701789\pi$
$90$	−9.05986	−0.954993
$91$	−2.60731	−0.273320
$92$	4.68412	0.488354
$93$	−0.248747	−0.0257938
$94$	−7.92463	−0.817363
$95$	9.36064	0.960381
$96$	−2.52707	−0.257918
$97$	−10.6411	−1.08044	−0.540221	−	0.841523i	$-0.681660\pi$
$97$	−10.6411	−1.08044	−0.540221	+	0.841523i	$0.681660\pi$
$98$	−4.88881	−0.493844
$99$	−7.23343	−0.726987
$100$	2.15900	0.215900
$101$	4.72395	0.470051	0.235026	−	0.971989i	$-0.424483\pi$
$101$	4.72395	0.470051	0.235026	+	0.971989i	$0.424483\pi$
$102$	8.51851	0.843458
$103$	11.5992	1.14291	0.571454	−	0.820634i	$-0.306380\pi$
$103$	11.5992	1.14291	0.571454	+	0.820634i	$0.306380\pi$
$104$	1.79444	0.175959
$105$	−9.82441	−0.958765
$106$	8.63311	0.838522
$107$	15.7147	1.51920	0.759600	−	0.650390i	$-0.225395\pi$
$107$	15.7147	1.51920	0.759600	+	0.650390i	$0.225395\pi$
$108$	−0.975613	−0.0938784
$109$	−15.3432	−1.46961	−0.734806	−	0.678277i	$-0.762727\pi$
$109$	−15.3432	−1.46961	−0.734806	+	0.678277i	$0.762727\pi$
$110$	5.71577	0.544977
$111$	−16.3268	−1.54967
$112$	−1.45299	−0.137295
$113$	−5.56933	−0.523918	−0.261959	−	0.965079i	$-0.584369\pi$
$113$	−5.56933	−0.523918	−0.261959	+	0.965079i	$0.584369\pi$
$114$	8.84089	0.828025
$115$	−12.5330	−1.16871
$116$	2.31775	0.215198
$117$	6.07608	0.561734
$118$	11.6833	1.07553
$119$	4.89791	0.448990
$120$	6.76150	0.617237
$121$	−6.43651	−0.585137
$122$	−6.89946	−0.624648
$123$	−20.1317	−1.81521
$124$	0.0984331	0.00883955
$125$	7.60147	0.679896
$126$	−4.91993	−0.438302
$127$	18.1983	1.61483	0.807417	−	0.589981i	$-0.200865\pi$
$127$	18.1983	1.61483	0.807417	+	0.589981i	$0.200865\pi$
$128$	1.00000	0.0883883
$129$	0.148426	0.0130681
$130$	−4.80125	−0.421097
$131$	−6.18210	−0.540133	−0.270066	−	0.962842i	$-0.587046\pi$
$131$	−6.18210	−0.540133	−0.270066	+	0.962842i	$0.587046\pi$
$132$	5.39840	0.469871
$133$	5.08327	0.440775
$134$	−3.12393	−0.269867
$135$	2.61038	0.224666
$136$	−3.37091	−0.289053
$137$	4.69661	0.401258	0.200629	−	0.979667i	$-0.435701\pi$
$137$	4.69661	0.401258	0.200629	+	0.979667i	$0.435701\pi$
$138$	−11.8371	−1.00764
$139$	−5.48504	−0.465235	−0.232617	−	0.972568i	$-0.574729\pi$
$139$	−5.48504	−0.465235	−0.232617	+	0.972568i	$0.574729\pi$
$140$	3.88767	0.328568
$141$	20.0261	1.68650
$142$	11.5427	0.968640
$143$	−3.83334	−0.320560
$144$	3.38607	0.282172
$145$	−6.20144	−0.515002
$146$	−5.45707	−0.451630
$147$	12.3543	1.01897
$148$	6.46076	0.531071
$149$	−5.55014	−0.454685	−0.227343	−	0.973815i	$-0.573004\pi$
$149$	−5.55014	−0.454685	−0.227343	+	0.973815i	$0.573004\pi$
$150$	−5.45594	−0.445475
$151$	19.2123	1.56348	0.781739	−	0.623606i	$-0.214333\pi$
$151$	19.2123	1.56348	0.781739	+	0.623606i	$0.214333\pi$
$152$	−3.49848	−0.283764
$153$	−11.4141	−0.922776
$154$	3.10393	0.250122
$155$	−0.263370	−0.0211544
$156$	−4.53466	−0.363063
$157$	10.4855	0.836835	0.418417	−	0.908255i	$-0.362585\pi$
$157$	10.4855	0.836835	0.418417	+	0.908255i	$0.362585\pi$
$158$	13.2661	1.05539
$159$	−21.8165	−1.73016
$160$	−2.67563	−0.211527
$161$	−6.80600	−0.536388
$162$	−7.69276	−0.604400
$163$	−13.8562	−1.08530	−0.542649	−	0.839960i	$-0.682579\pi$
$163$	−13.8562	−1.08530	−0.542649	+	0.839960i	$0.682579\pi$
$164$	7.96643	0.622074
$165$	−14.4441	−1.12447
$166$	−3.11817	−0.242017
$167$	−17.4271	−1.34855	−0.674274	−	0.738481i	$-0.735543\pi$
$167$	−17.4271	−1.34855	−0.674274	+	0.738481i	$0.735543\pi$
$168$	3.67181	0.283286
$169$	−9.78000	−0.752307
$170$	9.01930	0.691749
$171$	−11.8461	−0.905892
$172$	−0.0587343	−0.00447845
$173$	5.74012	0.436414	0.218207	−	0.975903i	$-0.429979\pi$
$173$	5.74012	0.436414	0.218207	+	0.975903i	$0.429979\pi$
$174$	−5.85711	−0.444026
$175$	−3.13701	−0.237136
$176$	−2.13623	−0.161025
$177$	−29.5244	−2.21919
$178$	−11.1759	−0.837672
$179$	−9.28037	−0.693647	−0.346824	−	0.937930i	$-0.612740\pi$
$179$	−9.28037	−0.693647	−0.346824	+	0.937930i	$0.612740\pi$
$180$	−9.05986	−0.675282
$181$	20.8857	1.55242	0.776212	−	0.630473i	$-0.217139\pi$
$181$	20.8857	1.55242	0.776212	+	0.630473i	$0.217139\pi$
$182$	−2.60731	−0.193266
$183$	17.4354	1.28886
$184$	4.68412	0.345318
$185$	−17.2866	−1.27094
$186$	−0.248747	−0.0182390
$187$	7.20104	0.526593
$188$	−7.92463	−0.577963
$189$	1.41756	0.103112
$190$	9.36064	0.679092
$191$	4.66462	0.337520	0.168760	−	0.985657i	$-0.446024\pi$
$191$	4.66462	0.337520	0.168760	+	0.985657i	$0.446024\pi$
$192$	−2.52707	−0.182375
$193$	−16.6020	−1.19504	−0.597520	−	0.801854i	$-0.703847\pi$
$193$	−16.6020	−1.19504	−0.597520	+	0.801854i	$0.703847\pi$
$194$	−10.6411	−0.763989
$195$	12.1331	0.868868
$196$	−4.88881	−0.349201
$197$	−10.5694	−0.753036	−0.376518	−	0.926409i	$-0.622879\pi$
$197$	−10.5694	−0.753036	−0.376518	+	0.926409i	$0.622879\pi$
$198$	−7.23343	−0.514057
$199$	1.47509	0.104566	0.0522832	−	0.998632i	$-0.483350\pi$
$199$	1.47509	0.104566	0.0522832	+	0.998632i	$0.483350\pi$
$200$	2.15900	0.152664
$201$	7.89439	0.556827
$202$	4.72395	0.332376
$203$	−3.36768	−0.236365
$204$	8.51851	0.596415
$205$	−21.3152	−1.48872
$206$	11.5992	0.808157
$207$	15.8607	1.10240
$208$	1.79444	0.124422
$209$	7.47357	0.516958
$210$	−9.82441	−0.677949
$211$	−6.28681	−0.432802	−0.216401	−	0.976305i	$-0.569432\pi$
$211$	−6.28681	−0.432802	−0.216401	+	0.976305i	$0.569432\pi$
$212$	8.63311	0.592925
$213$	−29.1691	−1.99863
$214$	15.7147	1.07424
$215$	0.157151	0.0107176
$216$	−0.975613	−0.0663821
$217$	−0.143023	−0.00970901
$218$	−15.3432	−1.03917
$219$	13.7904	0.931868
$220$	5.71577	0.385357
$221$	−6.04888	−0.406892
$222$	−16.3268	−1.09578
$223$	−4.81806	−0.322641	−0.161321	−	0.986902i	$-0.551575\pi$
$223$	−4.81806	−0.322641	−0.161321	+	0.986902i	$0.551575\pi$
$224$	−1.45299	−0.0970822
$225$	7.31051	0.487368
$226$	−5.56933	−0.370466
$227$	−18.5733	−1.23275	−0.616377	−	0.787451i	$-0.711400\pi$
$227$	−18.5733	−1.23275	−0.616377	+	0.787451i	$0.711400\pi$
$228$	8.84089	0.585502
$229$	13.9245	0.920156	0.460078	−	0.887878i	$-0.347821\pi$
$229$	13.9245	0.920156	0.460078	+	0.887878i	$0.347821\pi$
$230$	−12.5330	−0.826400
$231$	−7.84385	−0.516087
$232$	2.31775	0.152168
$233$	−21.8200	−1.42948	−0.714739	−	0.699392i	$-0.753454\pi$
$233$	−21.8200	−1.42948	−0.714739	+	0.699392i	$0.753454\pi$
$234$	6.07608	0.397206
$235$	21.2034	1.38316
$236$	11.6833	0.760517
$237$	−33.5243	−2.17764
$238$	4.89791	0.317484
$239$	7.74419	0.500930	0.250465	−	0.968126i	$-0.419416\pi$
$239$	7.74419	0.500930	0.250465	+	0.968126i	$0.419416\pi$
$240$	6.76150	0.436453
$241$	30.8856	1.98952	0.994760	−	0.102240i	$-0.0326009\pi$
$241$	30.8856	1.98952	0.994760	+	0.102240i	$0.0326009\pi$
$242$	−6.43651	−0.413754
$243$	22.3669	1.43484
$244$	−6.89946	−0.441693
$245$	13.0806	0.835692
$246$	−20.1317	−1.28355
$247$	−6.27780	−0.399447
$248$	0.0984331	0.00625050
$249$	7.87983	0.499364
$250$	7.60147	0.480759
$251$	−3.81717	−0.240938	−0.120469	−	0.992717i	$-0.538440\pi$
$251$	−3.81717	−0.240938	−0.120469	+	0.992717i	$0.538440\pi$
$252$	−4.91993	−0.309927
$253$	−10.0064	−0.629096
$254$	18.1983	1.14186
$255$	−22.7924	−1.42731
$256$	1.00000	0.0625000
$257$	−19.9622	−1.24521	−0.622603	−	0.782538i	$-0.713925\pi$
$257$	−19.9622	−1.24521	−0.622603	+	0.782538i	$0.713925\pi$
$258$	0.148426	0.00924057
$259$	−9.38745	−0.583307
$260$	−4.80125	−0.297761
$261$	7.84806	0.485782
$262$	−6.18210	−0.381932
$263$	−12.3016	−0.758548	−0.379274	−	0.925285i	$-0.623826\pi$
$263$	−12.3016	−0.758548	−0.379274	+	0.925285i	$0.623826\pi$
$264$	5.39840	0.332249
$265$	−23.0990	−1.41896
$266$	5.08327	0.311675
$267$	28.2423	1.72840
$268$	−3.12393	−0.190825
$269$	−7.12032	−0.434134	−0.217067	−	0.976157i	$-0.569649\pi$
$269$	−7.12032	−0.434134	−0.217067	+	0.976157i	$0.569649\pi$
$270$	2.61038	0.158863
$271$	2.45119	0.148899	0.0744497	−	0.997225i	$-0.476280\pi$
$271$	2.45119	0.148899	0.0744497	+	0.997225i	$0.476280\pi$
$272$	−3.37091	−0.204391
$273$	6.58883	0.398774
$274$	4.69661	0.283732
$275$	−4.61213	−0.278122
$276$	−11.8371	−0.712509
$277$	2.94040	0.176672	0.0883358	−	0.996091i	$-0.471845\pi$
$277$	2.94040	0.176672	0.0883358	+	0.996091i	$0.471845\pi$
$278$	−5.48504	−0.328971
$279$	0.333301	0.0199542
$280$	3.88767	0.232333
$281$	−9.82520	−0.586122	−0.293061	−	0.956094i	$-0.594674\pi$
$281$	−9.82520	−0.586122	−0.293061	+	0.956094i	$0.594674\pi$
$282$	20.0261	1.19253
$283$	−12.3801	−0.735922	−0.367961	−	0.929841i	$-0.619944\pi$
$283$	−12.3801	−0.735922	−0.367961	+	0.929841i	$0.619944\pi$
$284$	11.5427	0.684932
$285$	−23.6550	−1.40120
$286$	−3.83334	−0.226670
$287$	−11.5752	−0.683261
$288$	3.38607	0.199526
$289$	−5.63699	−0.331587
$290$	−6.20144	−0.364161
$291$	26.8908	1.57637
$292$	−5.45707	−0.319351
$293$	6.06734	0.354458	0.177229	−	0.984170i	$-0.443287\pi$
$293$	6.06734	0.354458	0.177229	+	0.984170i	$0.443287\pi$
$294$	12.3543	0.720520
$295$	−31.2602	−1.82004
$296$	6.46076	0.375524
$297$	2.08414	0.120934
$298$	−5.55014	−0.321511
$299$	8.40536	0.486095
$300$	−5.45594	−0.314999
$301$	0.0853406	0.00491895
$302$	19.2123	1.10555
$303$	−11.9377	−0.685806
$304$	−3.49848	−0.200652
$305$	18.4604	1.05704
$306$	−11.4141	−0.652501
$307$	−2.74779	−0.156825	−0.0784124	−	0.996921i	$-0.524985\pi$
$307$	−2.74779	−0.156825	−0.0784124	+	0.996921i	$0.524985\pi$
$308$	3.10393	0.176863
$309$	−29.3120	−1.66750
$310$	−0.263370	−0.0149584
$311$	−31.6371	−1.79397	−0.896987	−	0.442057i	$-0.854249\pi$
$311$	−31.6371	−1.79397	−0.896987	+	0.442057i	$0.854249\pi$
$312$	−4.53466	−0.256725
$313$	−9.15614	−0.517536	−0.258768	−	0.965940i	$-0.583316\pi$
$313$	−9.15614	−0.517536	−0.258768	+	0.965940i	$0.583316\pi$
$314$	10.4855	0.591731
$315$	13.1639	0.741703
$316$	13.2661	0.746275
$317$	−16.1584	−0.907545	−0.453772	−	0.891118i	$-0.649922\pi$
$317$	−16.1584	−0.907545	−0.453772	+	0.891118i	$0.649922\pi$
$318$	−21.8165	−1.22341
$319$	−4.95126	−0.277217
$320$	−2.67563	−0.149572
$321$	−39.7122	−2.21652
$322$	−6.80600	−0.379284
$323$	11.7930	0.656183
$324$	−7.69276	−0.427375
$325$	3.87419	0.214901
$326$	−13.8562	−0.767422
$327$	38.7733	2.14417
$328$	7.96643	0.439872
$329$	11.5144	0.634811
$330$	−14.4441	−0.795123
$331$	−18.5202	−1.01796	−0.508982	−	0.860777i	$-0.669978\pi$
$331$	−18.5202	−1.01796	−0.508982	+	0.860777i	$0.669978\pi$
$332$	−3.11817	−0.171132
$333$	21.8766	1.19883
$334$	−17.4271	−0.953568
$335$	8.35850	0.456673
$336$	3.67181	0.200314
$337$	24.7604	1.34879	0.674393	−	0.738373i	$-0.264405\pi$
$337$	24.7604	1.34879	0.674393	+	0.738373i	$0.264405\pi$
$338$	−9.78000	−0.531962
$339$	14.0741	0.764398
$340$	9.01930	0.489140
$341$	−0.210276	−0.0113871
$342$	−11.8461	−0.640563
$343$	17.2744	0.932728
$344$	−0.0587343	−0.00316674
$345$	31.6717	1.70515
$346$	5.74012	0.308591
$347$	−6.68956	−0.359114	−0.179557	−	0.983748i	$-0.557466\pi$
$347$	−6.68956	−0.359114	−0.179557	+	0.983748i	$0.557466\pi$
$348$	−5.85711	−0.313974
$349$	2.95283	0.158061	0.0790306	−	0.996872i	$-0.474818\pi$
$349$	2.95283	0.158061	0.0790306	+	0.996872i	$0.474818\pi$
$350$	−3.13701	−0.167680
$351$	−1.75068	−0.0934442
$352$	−2.13623	−0.113862
$353$	−17.4897	−0.930881	−0.465440	−	0.885079i	$-0.654104\pi$
$353$	−17.4897	−0.930881	−0.465440	+	0.885079i	$0.654104\pi$
$354$	−29.5244	−1.56921
$355$	−30.8839	−1.63915
$356$	−11.1759	−0.592324
$357$	−12.3773	−0.655078
$358$	−9.28037	−0.490483
$359$	−16.3563	−0.863253	−0.431626	−	0.902052i	$-0.642060\pi$
$359$	−16.3563	−0.863253	−0.431626	+	0.902052i	$0.642060\pi$
$360$	−9.05986	−0.477497
$361$	−6.76064	−0.355823
$362$	20.8857	1.09773
$363$	16.2655	0.853716
$364$	−2.60731	−0.136660
$365$	14.6011	0.764257
$366$	17.4354	0.911363
$367$	−14.4739	−0.755529	−0.377765	−	0.925902i	$-0.623307\pi$
$367$	−14.4739	−0.755529	−0.377765	+	0.925902i	$0.623307\pi$
$368$	4.68412	0.244177
$369$	26.9749	1.40425
$370$	−17.2866	−0.898688
$371$	−12.5439	−0.651245
$372$	−0.248747	−0.0128969
$373$	15.1901	0.786512	0.393256	−	0.919429i	$-0.371349\pi$
$373$	15.1901	0.786512	0.393256	+	0.919429i	$0.371349\pi$
$374$	7.20104	0.372357
$375$	−19.2094	−0.991970
$376$	−7.92463	−0.408681
$377$	4.15906	0.214202
$378$	1.41756	0.0729114
$379$	5.80196	0.298027	0.149013	−	0.988835i	$-0.452390\pi$
$379$	5.80196	0.298027	0.149013	+	0.988835i	$0.452390\pi$
$380$	9.36064	0.480191
$381$	−45.9882	−2.35605
$382$	4.66462	0.238663
$383$	−18.9473	−0.968164	−0.484082	−	0.875023i	$-0.660846\pi$
$383$	−18.9473	−0.968164	−0.484082	+	0.875023i	$0.660846\pi$
$384$	−2.52707	−0.128959
$385$	−8.30498	−0.423261
$386$	−16.6020	−0.845021
$387$	−0.198878	−0.0101095
$388$	−10.6411	−0.540221
$389$	−8.39479	−0.425633	−0.212816	−	0.977092i	$-0.568264\pi$
$389$	−8.39479	−0.425633	−0.212816	+	0.977092i	$0.568264\pi$
$390$	12.1331	0.614382
$391$	−15.7897	−0.798522
$392$	−4.88881	−0.246922
$393$	15.6226	0.788055
$394$	−10.5694	−0.532477
$395$	−35.4951	−1.78595
$396$	−7.23343	−0.363493
$397$	24.6726	1.23828	0.619141	−	0.785280i	$-0.287481\pi$
$397$	24.6726	1.23828	0.619141	+	0.785280i	$0.287481\pi$
$398$	1.47509	0.0739396
$399$	−12.8458	−0.643092
$400$	2.15900	0.107950
$401$	−10.6258	−0.530629	−0.265314	−	0.964162i	$-0.585476\pi$
$401$	−10.6258	−0.530629	−0.265314	+	0.964162i	$0.585476\pi$
$402$	7.89439	0.393736
$403$	0.176632	0.00879866
$404$	4.72395	0.235026
$405$	20.5830	1.02278
$406$	−3.36768	−0.167135
$407$	−13.8017	−0.684125
$408$	8.51851	0.421729
$409$	−19.3072	−0.954681	−0.477341	−	0.878718i	$-0.658399\pi$
$409$	−19.3072	−0.954681	−0.477341	+	0.878718i	$0.658399\pi$
$410$	−21.3152	−1.05268
$411$	−11.8686	−0.585437
$412$	11.5992	0.571454
$413$	−16.9757	−0.835322
$414$	15.8607	0.779513
$415$	8.34308	0.409546
$416$	1.79444	0.0879795
$417$	13.8611	0.678779
$418$	7.47357	0.365544
$419$	−11.7811	−0.575543	−0.287771	−	0.957699i	$-0.592914\pi$
$419$	−11.7811	−0.575543	−0.287771	+	0.957699i	$0.592914\pi$
$420$	−9.82441	−0.479382
$421$	−4.44918	−0.216840	−0.108420	−	0.994105i	$-0.534579\pi$
$421$	−4.44918	−0.216840	−0.108420	+	0.994105i	$0.534579\pi$
$422$	−6.28681	−0.306037
$423$	−26.8333	−1.30468
$424$	8.63311	0.419261
$425$	−7.27779	−0.353025
$426$	−29.1691	−1.41325
$427$	10.0249	0.485138
$428$	15.7147	0.759600
$429$	9.68709	0.467697
$430$	0.157151	0.00757851
$431$	1.19495	0.0575586	0.0287793	−	0.999586i	$-0.490838\pi$
$431$	1.19495	0.0575586	0.0287793	+	0.999586i	$0.490838\pi$
$432$	−0.975613	−0.0469392
$433$	−27.5909	−1.32593	−0.662967	−	0.748649i	$-0.730703\pi$
$433$	−27.5909	−1.32593	−0.662967	+	0.748649i	$0.730703\pi$
$434$	−0.143023	−0.00686531
$435$	15.6715	0.751389
$436$	−15.3432	−0.734806
$437$	−16.3873	−0.783911
$438$	13.7904	0.658930
$439$	−24.0920	−1.14985	−0.574925	−	0.818206i	$-0.694969\pi$
$439$	−24.0920	−1.14985	−0.574925	+	0.818206i	$0.694969\pi$
$440$	5.71577	0.272489
$441$	−16.5538	−0.788277
$442$	−6.04888	−0.287716
$443$	9.12247	0.433422	0.216711	−	0.976236i	$-0.430467\pi$
$443$	9.12247	0.433422	0.216711	+	0.976236i	$0.430467\pi$
$444$	−16.3268	−0.774834
$445$	29.9027	1.41752
$446$	−4.81806	−0.228142
$447$	14.0256	0.663387
$448$	−1.45299	−0.0686475
$449$	7.46012	0.352065	0.176032	−	0.984384i	$-0.443674\pi$
$449$	7.46012	0.352065	0.176032	+	0.984384i	$0.443674\pi$
$450$	7.31051	0.344621
$451$	−17.0182	−0.801354
$452$	−5.56933	−0.261959
$453$	−48.5508	−2.28112
$454$	−18.5733	−0.871689
$455$	6.97619	0.327049
$456$	8.84089	0.414013
$457$	15.2758	0.714573	0.357287	−	0.933995i	$-0.383702\pi$
$457$	15.2758	0.714573	0.357287	+	0.933995i	$0.383702\pi$
$458$	13.9245	0.650649
$459$	3.28870	0.153503
$460$	−12.5330	−0.584353
$461$	−31.0667	−1.44692	−0.723459	−	0.690367i	$-0.757449\pi$
$461$	−31.0667	−1.44692	−0.723459	+	0.690367i	$0.757449\pi$
$462$	−7.84385	−0.364929
$463$	25.5352	1.18672	0.593362	−	0.804936i	$-0.297800\pi$
$463$	25.5352	1.18672	0.593362	+	0.804936i	$0.297800\pi$
$464$	2.31775	0.107599
$465$	0.665555	0.0308644
$466$	−21.8200	−1.01079
$467$	21.4190	0.991153	0.495577	−	0.868564i	$-0.334957\pi$
$467$	21.4190	0.991153	0.495577	+	0.868564i	$0.334957\pi$
$468$	6.07608	0.280867
$469$	4.53906	0.209594
$470$	21.2034	0.978039
$471$	−26.4976	−1.22094
$472$	11.6833	0.537767
$473$	0.125470	0.00576913
$474$	−33.5243	−1.53982
$475$	−7.55322	−0.346565
$476$	4.89791	0.224495
$477$	29.2323	1.33845
$478$	7.74419	0.354211
$479$	−4.85774	−0.221956	−0.110978	−	0.993823i	$-0.535398\pi$
$479$	−4.85774	−0.221956	−0.110978	+	0.993823i	$0.535398\pi$
$480$	6.76150	0.308619
$481$	11.5934	0.528615
$482$	30.8856	1.40680
$483$	17.1992	0.782592
$484$	−6.43651	−0.292568
$485$	28.4717	1.29283
$486$	22.3669	1.01459
$487$	3.58778	0.162578	0.0812890	−	0.996691i	$-0.474096\pi$
$487$	3.58778	0.162578	0.0812890	+	0.996691i	$0.474096\pi$
$488$	−6.89946	−0.312324
$489$	35.0154	1.58345
$490$	13.0806	0.590923
$491$	−43.5048	−1.96334	−0.981672	−	0.190579i	$-0.938964\pi$
$491$	−43.5048	−1.96334	−0.981672	+	0.190579i	$0.938964\pi$
$492$	−20.1317	−0.907607
$493$	−7.81292	−0.351876
$494$	−6.27780	−0.282452
$495$	19.3540	0.869897
$496$	0.0984331	0.00441977
$497$	−16.7714	−0.752302
$498$	7.87983	0.353104
$499$	26.3214	1.17831	0.589155	−	0.808020i	$-0.299461\pi$
$499$	26.3214	1.17831	0.589155	+	0.808020i	$0.299461\pi$
$500$	7.60147	0.339948
$501$	44.0394	1.96754
$502$	−3.81717	−0.170369
$503$	13.0522	0.581968	0.290984	−	0.956728i	$-0.406017\pi$
$503$	13.0522	0.581968	0.290984	+	0.956728i	$0.406017\pi$
$504$	−4.91993	−0.219151
$505$	−12.6396	−0.562453
$506$	−10.0064	−0.444838
$507$	24.7147	1.09762
$508$	18.1983	0.807417
$509$	−24.6512	−1.09265	−0.546323	−	0.837574i	$-0.683973\pi$
$509$	−24.6512	−1.09265	−0.546323	+	0.837574i	$0.683973\pi$
$510$	−22.7924	−1.00926
$511$	7.92909	0.350762
$512$	1.00000	0.0441942
$513$	3.41316	0.150695
$514$	−19.9622	−0.880494
$515$	−31.0353	−1.36758
$516$	0.148426	0.00653407
$517$	16.9289	0.744530
$518$	−9.38745	−0.412461
$519$	−14.5057	−0.636729
$520$	−4.80125	−0.210549
$521$	−41.1032	−1.80077	−0.900383	−	0.435099i	$-0.856713\pi$
$521$	−41.1032	−1.80077	−0.900383	+	0.435099i	$0.856713\pi$
$522$	7.84806	0.343500
$523$	36.8873	1.61297	0.806485	−	0.591255i	$-0.201367\pi$
$523$	36.8873	1.61297	0.806485	+	0.591255i	$0.201367\pi$
$524$	−6.18210	−0.270066
$525$	7.92744	0.345982
$526$	−12.3016	−0.536374
$527$	−0.331809	−0.0144538
$528$	5.39840	0.234935
$529$	−1.05899	−0.0460430
$530$	−23.0990	−1.00336
$531$	39.5604	1.71677
$532$	5.08327	0.220388
$533$	14.2953	0.619196
$534$	28.2423	1.22217
$535$	−42.0468	−1.81784
$536$	−3.12393	−0.134933
$537$	23.4521	1.01203
$538$	−7.12032	−0.306979
$539$	10.4436	0.449839
$540$	2.61038	0.112333
$541$	17.8316	0.766642	0.383321	−	0.923615i	$-0.374780\pi$
$541$	17.8316	0.766642	0.383321	+	0.923615i	$0.374780\pi$
$542$	2.45119	0.105288
$543$	−52.7796	−2.26499
$544$	−3.37091	−0.144526
$545$	41.0528	1.75851
$546$	6.58883	0.281976
$547$	12.8024	0.547392	0.273696	−	0.961816i	$-0.411754\pi$
$547$	12.8024	0.547392	0.273696	+	0.961816i	$0.411754\pi$
$548$	4.69661	0.200629
$549$	−23.3620	−0.997067
$550$	−4.61213	−0.196662
$551$	−8.10860	−0.345438
$552$	−11.8371	−0.503820
$553$	−19.2755	−0.819679
$554$	2.94040	0.124926
$555$	43.6844	1.85430
$556$	−5.48504	−0.232617
$557$	−27.8098	−1.17834	−0.589169	−	0.808010i	$-0.700545\pi$
$557$	−27.8098	−1.17834	−0.589169	+	0.808010i	$0.700545\pi$
$558$	0.333301	0.0141097
$559$	−0.105395	−0.00445773
$560$	3.88767	0.164284
$561$	−18.1975	−0.768300
$562$	−9.82520	−0.414451
$563$	−24.8209	−1.04607	−0.523037	−	0.852310i	$-0.675201\pi$
$563$	−24.8209	−1.04607	−0.523037	+	0.852310i	$0.675201\pi$
$564$	20.0261	0.843249
$565$	14.9015	0.626909
$566$	−12.3801	−0.520375
$567$	11.1775	0.469412
$568$	11.5427	0.484320
$569$	1.70775	0.0715925	0.0357963	−	0.999359i	$-0.488603\pi$
$569$	1.70775	0.0715925	0.0357963	+	0.999359i	$0.488603\pi$
$570$	−23.6550	−0.990797
$571$	20.6703	0.865025	0.432512	−	0.901628i	$-0.357627\pi$
$571$	20.6703	0.865025	0.432512	+	0.901628i	$0.357627\pi$
$572$	−3.83334	−0.160280
$573$	−11.7878	−0.492443
$574$	−11.5752	−0.483138
$575$	10.1130	0.421742
$576$	3.38607	0.141086
$577$	13.1818	0.548767	0.274383	−	0.961620i	$-0.411526\pi$
$577$	13.1818	0.548767	0.274383	+	0.961620i	$0.411526\pi$
$578$	−5.63699	−0.234468
$579$	41.9544	1.74357
$580$	−6.20144	−0.257501
$581$	4.53068	0.187964
$582$	26.8908	1.11466
$583$	−18.4423	−0.763804
$584$	−5.45707	−0.225815
$585$	−16.2573	−0.672159
$586$	6.06734	0.250639
$587$	36.1472	1.49196	0.745978	−	0.665971i	$-0.231982\pi$
$587$	36.1472	1.49196	0.745978	+	0.665971i	$0.231982\pi$
$588$	12.3543	0.509485
$589$	−0.344366	−0.0141894
$590$	−31.2602	−1.28696
$591$	26.7095	1.09868
$592$	6.46076	0.265536
$593$	−6.65321	−0.273214	−0.136607	−	0.990625i	$-0.543620\pi$
$593$	−6.65321	−0.273214	−0.136607	+	0.990625i	$0.543620\pi$
$594$	2.08414	0.0855132
$595$	−13.1050	−0.537252
$596$	−5.55014	−0.227343
$597$	−3.72765	−0.152563
$598$	8.40536	0.343721
$599$	−12.4623	−0.509195	−0.254598	−	0.967047i	$-0.581943\pi$
$599$	−12.4623	−0.509195	−0.254598	+	0.967047i	$0.581943\pi$
$600$	−5.45594	−0.222738
$601$	5.18412	0.211464	0.105732	−	0.994395i	$-0.466281\pi$
$601$	5.18412	0.211464	0.105732	+	0.994395i	$0.466281\pi$
$602$	0.0853406	0.00347822
$603$	−10.5778	−0.430763
$604$	19.2123	0.781739
$605$	17.2217	0.700162
$606$	−11.9377	−0.484938
$607$	−19.1387	−0.776818	−0.388409	−	0.921487i	$-0.626975\pi$
$607$	−19.1387	−0.776818	−0.388409	+	0.921487i	$0.626975\pi$
$608$	−3.49848	−0.141882
$609$	8.51034	0.344857
$610$	18.4604	0.747440
$611$	−14.2202	−0.575289
$612$	−11.4141	−0.461388
$613$	8.13101	0.328409	0.164204	−	0.986426i	$-0.447494\pi$
$613$	8.13101	0.328409	0.164204	+	0.986426i	$0.447494\pi$
$614$	−2.74779	−0.110892
$615$	53.8650	2.17205
$616$	3.10393	0.125061
$617$	14.8889	0.599405	0.299703	−	0.954033i	$-0.403113\pi$
$617$	14.8889	0.599405	0.299703	+	0.954033i	$0.403113\pi$
$618$	−29.3120	−1.17910
$619$	42.4128	1.70471	0.852357	−	0.522961i	$-0.175173\pi$
$619$	42.4128	1.70471	0.852357	+	0.522961i	$0.175173\pi$
$620$	−0.263370	−0.0105772
$621$	−4.56989	−0.183383
$622$	−31.6371	−1.26853
$623$	16.2386	0.650585
$624$	−4.53466	−0.181532
$625$	−31.1337	−1.24535
$626$	−9.15614	−0.365953
$627$	−18.8862	−0.754242
$628$	10.4855	0.418417
$629$	−21.7786	−0.868371
$630$	13.1639	0.524463
$631$	−1.86692	−0.0743208	−0.0371604	−	0.999309i	$-0.511831\pi$
$631$	−1.86692	−0.0743208	−0.0371604	+	0.999309i	$0.511831\pi$
$632$	13.2661	0.527696
$633$	15.8872	0.631459
$634$	−16.1584	−0.641731
$635$	−48.6918	−1.93228
$636$	−21.8165	−0.865079
$637$	−8.77266	−0.347585
$638$	−4.95126	−0.196022
$639$	39.0842	1.54615
$640$	−2.67563	−0.105764
$641$	36.3726	1.43663	0.718315	−	0.695718i	$-0.244914\pi$
$641$	36.3726	1.43663	0.718315	+	0.695718i	$0.244914\pi$
$642$	−39.7122	−1.56731
$643$	20.6574	0.814650	0.407325	−	0.913283i	$-0.366462\pi$
$643$	20.6574	0.814650	0.407325	+	0.913283i	$0.366462\pi$
$644$	−6.80600	−0.268194
$645$	−0.397132	−0.0156371
$646$	11.7930	0.463991
$647$	−33.9417	−1.33438	−0.667192	−	0.744885i	$-0.732504\pi$
$647$	−33.9417	−1.33438	−0.667192	+	0.744885i	$0.732504\pi$
$648$	−7.69276	−0.302200
$649$	−24.9582	−0.979696
$650$	3.87419	0.151958
$651$	0.361428	0.0141655
$652$	−13.8562	−0.542649
$653$	−13.1720	−0.515458	−0.257729	−	0.966217i	$-0.582974\pi$
$653$	−13.1720	−0.515458	−0.257729	+	0.966217i	$0.582974\pi$
$654$	38.7733	1.51616
$655$	16.5410	0.646311
$656$	7.96643	0.311037
$657$	−18.4780	−0.720895
$658$	11.5144	0.448879
$659$	21.7453	0.847078	0.423539	−	0.905878i	$-0.360788\pi$
$659$	21.7453	0.847078	0.423539	+	0.905878i	$0.360788\pi$
$660$	−14.4441	−0.562237
$661$	−19.1430	−0.744576	−0.372288	−	0.928117i	$-0.621427\pi$
$661$	−19.1430	−0.744576	−0.372288	+	0.928117i	$0.621427\pi$
$662$	−18.5202	−0.719809
$663$	15.2859	0.593656
$664$	−3.11817	−0.121009
$665$	−13.6010	−0.527422
$666$	21.8766	0.847699
$667$	10.8566	0.420370
$668$	−17.4271	−0.674274
$669$	12.1756	0.470735
$670$	8.35850	0.322917
$671$	14.7389	0.568988
$672$	3.67181	0.141643
$673$	21.1176	0.814025	0.407013	−	0.913423i	$-0.366571\pi$
$673$	21.1176	0.814025	0.407013	+	0.913423i	$0.366571\pi$
$674$	24.7604	0.953735
$675$	−2.10635	−0.0810734
$676$	−9.78000	−0.376154
$677$	21.5660	0.828848	0.414424	−	0.910084i	$-0.363983\pi$
$677$	21.5660	0.828848	0.414424	+	0.910084i	$0.363983\pi$
$678$	14.0741	0.540511
$679$	15.4615	0.593358
$680$	9.01930	0.345874
$681$	46.9360	1.79859
$682$	−0.210276	−0.00805188
$683$	28.9997	1.10964	0.554822	−	0.831969i	$-0.312786\pi$
$683$	28.9997	1.10964	0.554822	+	0.831969i	$0.312786\pi$
$684$	−11.8461	−0.452946
$685$	−12.5664	−0.480137
$686$	17.2744	0.659538
$687$	−35.1881	−1.34251
$688$	−0.0587343	−0.00223922
$689$	15.4916	0.590182
$690$	31.6717	1.20572
$691$	−20.8933	−0.794820	−0.397410	−	0.917641i	$-0.630091\pi$
$691$	−20.8933	−0.794820	−0.397410	+	0.917641i	$0.630091\pi$
$692$	5.74012	0.218207
$693$	10.5101	0.399247
$694$	−6.68956	−0.253932
$695$	14.6759	0.556690
$696$	−5.85711	−0.222013
$697$	−26.8541	−1.01717
$698$	2.95283	0.111766
$699$	55.1406	2.08561
$700$	−3.13701	−0.118568
$701$	−8.30724	−0.313760	−0.156880	−	0.987618i	$-0.550144\pi$
$701$	−8.30724	−0.313760	−0.156880	+	0.987618i	$0.550144\pi$
$702$	−1.75068	−0.0660750
$703$	−22.6028	−0.852482
$704$	−2.13623	−0.0805123
$705$	−53.5823	−2.01803
$706$	−17.4897	−0.658232
$707$	−6.86388	−0.258143
$708$	−29.5244	−1.10960
$709$	−43.9673	−1.65123	−0.825614	−	0.564235i	$-0.809171\pi$
$709$	−43.9673	−1.65123	−0.825614	+	0.564235i	$0.809171\pi$
$710$	−30.8839	−1.15905
$711$	44.9198	1.68462
$712$	−11.1759	−0.418836
$713$	0.461073	0.0172673
$714$	−12.3773	−0.463210
$715$	10.2566	0.383575
$716$	−9.28037	−0.346824
$717$	−19.5701	−0.730859
$718$	−16.3563	−0.610412
$719$	−6.33868	−0.236393	−0.118196	−	0.992990i	$-0.537711\pi$
$719$	−6.33868	−0.236393	−0.118196	+	0.992990i	$0.537711\pi$
$720$	−9.05986	−0.337641
$721$	−16.8536	−0.627662
$722$	−6.76064	−0.251605
$723$	−78.0501	−2.90271
$724$	20.8857	0.776212
$725$	5.00402	0.185845
$726$	16.2655	0.603669
$727$	26.1776	0.970875	0.485437	−	0.874271i	$-0.338660\pi$
$727$	26.1776	0.970875	0.485437	+	0.874271i	$0.338660\pi$
$728$	−2.60731	−0.0966332
$729$	−33.4445	−1.23869
$730$	14.6011	0.540411
$731$	0.197988	0.00732285
$732$	17.4354	0.644431
$733$	−21.1943	−0.782828	−0.391414	−	0.920215i	$-0.628014\pi$
$733$	−21.1943	−0.782828	−0.391414	+	0.920215i	$0.628014\pi$
$734$	−14.4739	−0.534240
$735$	−33.0557	−1.21928
$736$	4.68412	0.172659
$737$	6.67345	0.245820
$738$	26.9749	0.992958
$739$	28.9007	1.06313	0.531564	−	0.847018i	$-0.321604\pi$
$739$	28.9007	1.06313	0.531564	+	0.847018i	$0.321604\pi$
$740$	−17.2866	−0.635468
$741$	15.8644	0.582794
$742$	−12.5439	−0.460500
$743$	−42.0778	−1.54368	−0.771842	−	0.635815i	$-0.780664\pi$
$743$	−42.0778	−1.54368	−0.771842	+	0.635815i	$0.780664\pi$
$744$	−0.248747	−0.00911950
$745$	14.8501	0.544067
$746$	15.1901	0.556148
$747$	−10.5583	−0.386309
$748$	7.20104	0.263296
$749$	−22.8334	−0.834314
$750$	−19.2094	−0.701429
$751$	30.2742	1.10472	0.552361	−	0.833605i	$-0.313727\pi$
$751$	30.2742	1.10472	0.552361	+	0.833605i	$0.313727\pi$
$752$	−7.92463	−0.288981
$753$	9.64625	0.351529
$754$	4.15906	0.151464
$755$	−51.4051	−1.87082
$756$	1.41756	0.0515562
$757$	30.6031	1.11229	0.556144	−	0.831086i	$-0.312280\pi$
$757$	30.6031	1.11229	0.556144	+	0.831086i	$0.312280\pi$
$758$	5.80196	0.210737
$759$	25.2868	0.917852
$760$	9.36064	0.339546
$761$	−23.7666	−0.861539	−0.430769	−	0.902462i	$-0.641758\pi$
$761$	−23.7666	−0.861539	−0.430769	+	0.902462i	$0.641758\pi$
$762$	−45.9882	−1.66598
$763$	22.2936	0.807082
$764$	4.66462	0.168760
$765$	30.5399	1.10417
$766$	−18.9473	−0.684595
$767$	20.9649	0.756999
$768$	−2.52707	−0.0911877
$769$	−51.5305	−1.85824	−0.929118	−	0.369782i	$-0.879432\pi$
$769$	−51.5305	−1.85824	−0.929118	+	0.369782i	$0.879432\pi$
$770$	−8.30498	−0.299291
$771$	50.4458	1.81676
$772$	−16.6020	−0.597520
$773$	6.42948	0.231252	0.115626	−	0.993293i	$-0.463113\pi$
$773$	6.42948	0.231252	0.115626	+	0.993293i	$0.463113\pi$
$774$	−0.198878	−0.00714853
$775$	0.212517	0.00763383
$776$	−10.6411	−0.381994
$777$	23.7227	0.851047
$778$	−8.39479	−0.300968
$779$	−27.8704	−0.998560
$780$	12.1331	0.434434
$781$	−24.6578	−0.882327
$782$	−15.7897	−0.564640
$783$	−2.26123	−0.0808097
$784$	−4.88881	−0.174600
$785$	−28.0553	−1.00134
$786$	15.6226	0.557239
$787$	−34.3533	−1.22456	−0.612281	−	0.790640i	$-0.709748\pi$
$787$	−34.3533	−1.22456	−0.612281	+	0.790640i	$0.709748\pi$
$788$	−10.5694	−0.376518
$789$	31.0869	1.10672
$790$	−35.4951	−1.26286
$791$	8.09220	0.287725
$792$	−7.23343	−0.257029
$793$	−12.3807	−0.439650
$794$	24.6726	0.875598
$795$	58.3728	2.07027
$796$	1.47509	0.0522832
$797$	−53.8752	−1.90836	−0.954179	−	0.299236i	$-0.903268\pi$
$797$	−53.8752	−1.90836	−0.954179	+	0.299236i	$0.903268\pi$
$798$	−12.8458	−0.454735
$799$	26.7132	0.945044
$800$	2.15900	0.0763322
$801$	−37.8425	−1.33710
$802$	−10.6258	−0.375211
$803$	11.6576	0.411387
$804$	7.89439	0.278414
$805$	18.2103	0.641830
$806$	0.176632	0.00622159
$807$	17.9935	0.633402
$808$	4.72395	0.166188
$809$	−6.02093	−0.211685	−0.105842	−	0.994383i	$-0.533754\pi$
$809$	−6.02093	−0.211685	−0.105842	+	0.994383i	$0.533754\pi$
$810$	20.5830	0.723212
$811$	−35.8529	−1.25896	−0.629482	−	0.777015i	$-0.716733\pi$
$811$	−35.8529	−1.25896	−0.629482	+	0.777015i	$0.716733\pi$
$812$	−3.36768	−0.118182
$813$	−6.19433	−0.217245
$814$	−13.8017	−0.483749
$815$	37.0740	1.29864
$816$	8.51851	0.298207
$817$	0.205481	0.00718886
$818$	−19.3072	−0.675061
$819$	−8.82851	−0.308493
$820$	−21.3152	−0.744360
$821$	39.7491	1.38725	0.693627	−	0.720334i	$-0.256012\pi$
$821$	39.7491	1.38725	0.693627	+	0.720334i	$0.256012\pi$
$822$	−11.8686	−0.413966
$823$	36.7529	1.28113	0.640564	−	0.767905i	$-0.278701\pi$
$823$	36.7529	1.28113	0.640564	+	0.767905i	$0.278701\pi$
$824$	11.5992	0.404079
$825$	11.6552	0.405780
$826$	−16.9757	−0.590662
$827$	39.2395	1.36449	0.682246	−	0.731123i	$-0.261003\pi$
$827$	39.2395	1.36449	0.682246	+	0.731123i	$0.261003\pi$
$828$	15.8607	0.551199
$829$	51.7041	1.79576	0.897879	−	0.440242i	$-0.145107\pi$
$829$	51.7041	1.79576	0.897879	+	0.440242i	$0.145107\pi$
$830$	8.34308	0.289592
$831$	−7.43059	−0.257764
$832$	1.79444	0.0622109
$833$	16.4797	0.570988
$834$	13.8611	0.479969
$835$	46.6284	1.61364
$836$	7.47357	0.258479
$837$	−0.0960326	−0.00331937
$838$	−11.7811	−0.406970
$839$	52.6697	1.81836	0.909180	−	0.416404i	$-0.136710\pi$
$839$	52.6697	1.81836	0.909180	+	0.416404i	$0.136710\pi$
$840$	−9.82441	−0.338974
$841$	−23.6280	−0.814760
$842$	−4.44918	−0.153329
$843$	24.8289	0.855154
$844$	−6.28681	−0.216401
$845$	26.1677	0.900195
$846$	−26.8333	−0.922548
$847$	9.35220	0.321346
$848$	8.63311	0.296462
$849$	31.2854	1.07371
$850$	−7.27779	−0.249626
$851$	30.2630	1.03740
$852$	−29.1691	−0.999317
$853$	55.3195	1.89410	0.947052	−	0.321080i	$-0.104046\pi$
$853$	55.3195	1.89410	0.947052	+	0.321080i	$0.104046\pi$
$854$	10.0249	0.343044
$855$	31.6957	1.08397
$856$	15.7147	0.537118
$857$	8.94011	0.305388	0.152694	−	0.988273i	$-0.451205\pi$
$857$	8.94011	0.305388	0.152694	+	0.988273i	$0.451205\pi$
$858$	9.68709	0.330712
$859$	−20.4719	−0.698494	−0.349247	−	0.937031i	$-0.613563\pi$
$859$	−20.4719	−0.698494	−0.349247	+	0.937031i	$0.613563\pi$
$860$	0.157151	0.00535882
$861$	29.2512	0.996879
$862$	1.19495	0.0407000
$863$	−5.50462	−0.187379	−0.0936897	−	0.995601i	$-0.529866\pi$
$863$	−5.50462	−0.187379	−0.0936897	+	0.995601i	$0.529866\pi$
$864$	−0.975613	−0.0331910
$865$	−15.3585	−0.522203
$866$	−27.5909	−0.937577
$867$	14.2450	0.483787
$868$	−0.143023	−0.00485450
$869$	−28.3394	−0.961350
$870$	15.6715	0.531312
$871$	−5.60570	−0.189942
$872$	−15.3432	−0.519587
$873$	−36.0316	−1.21948
$874$	−16.3873	−0.554309
$875$	−11.0449	−0.373385
$876$	13.7904	0.465934
$877$	26.4102	0.891809	0.445904	−	0.895081i	$-0.352882\pi$
$877$	26.4102	0.891809	0.445904	+	0.895081i	$0.352882\pi$
$878$	−24.0920	−0.813067
$879$	−15.3326	−0.517154
$880$	5.71577	0.192679
$881$	34.5206	1.16303	0.581515	−	0.813536i	$-0.302460\pi$
$881$	34.5206	1.16303	0.581515	+	0.813536i	$0.302460\pi$
$882$	−16.5538	−0.557396
$883$	28.0663	0.944507	0.472254	−	0.881463i	$-0.343441\pi$
$883$	28.0663	0.944507	0.472254	+	0.881463i	$0.343441\pi$
$884$	−6.04888	−0.203446
$885$	78.9965	2.65544
$886$	9.12247	0.306476
$887$	47.9757	1.61087	0.805433	−	0.592686i	$-0.201933\pi$
$887$	47.9757	1.61087	0.805433	+	0.592686i	$0.201933\pi$
$888$	−16.3268	−0.547891
$889$	−26.4420	−0.886835
$890$	29.9027	1.00234
$891$	16.4335	0.550544
$892$	−4.81806	−0.161321
$893$	27.7241	0.927753
$894$	14.0256	0.469086
$895$	24.8308	0.830004
$896$	−1.45299	−0.0485411
$897$	−21.2409	−0.709213
$898$	7.46012	0.248947
$899$	0.228143	0.00760900
$900$	7.31051	0.243684
$901$	−29.1014	−0.969509
$902$	−17.0182	−0.566643
$903$	−0.215661	−0.00717676
$904$	−5.56933	−0.185233
$905$	−55.8825	−1.85760
$906$	−48.5508	−1.61299
$907$	14.4782	0.480741	0.240371	−	0.970681i	$-0.422731\pi$
$907$	14.4782	0.480741	0.240371	+	0.970681i	$0.422731\pi$
$908$	−18.5733	−0.616377
$909$	15.9956	0.530541
$910$	6.97619	0.231258
$911$	−10.7742	−0.356966	−0.178483	−	0.983943i	$-0.557119\pi$
$911$	−10.7742	−0.356966	−0.178483	+	0.983943i	$0.557119\pi$
$912$	8.84089	0.292751
$913$	6.66114	0.220452
$914$	15.2758	0.505279
$915$	−46.6507	−1.54222
$916$	13.9245	0.460078
$917$	8.98256	0.296630
$918$	3.28870	0.108543
$919$	−4.96704	−0.163847	−0.0819237	−	0.996639i	$-0.526106\pi$
$919$	−4.96704	−0.163847	−0.0819237	+	0.996639i	$0.526106\pi$
$920$	−12.5330	−0.413200
$921$	6.94385	0.228808
$922$	−31.0667	−1.02313
$923$	20.7126	0.681763
$924$	−7.84385	−0.258044
$925$	13.9488	0.458633
$926$	25.5352	0.839140
$927$	39.2758	1.28999
$928$	2.31775	0.0760839
$929$	33.5923	1.10213	0.551064	−	0.834463i	$-0.314222\pi$
$929$	33.5923	1.10213	0.551064	+	0.834463i	$0.314222\pi$
$930$	0.665555	0.0218244
$931$	17.1034	0.560541
$932$	−21.8200	−0.714739
$933$	79.9490	2.61741
$934$	21.4190	0.700851
$935$	−19.2673	−0.630109
$936$	6.07608	0.198603
$937$	9.59836	0.313565	0.156782	−	0.987633i	$-0.449888\pi$
$937$	9.59836	0.313565	0.156782	+	0.987633i	$0.449888\pi$
$938$	4.53906	0.148206
$939$	23.1382	0.755086
$940$	21.2034	0.691578
$941$	−45.8950	−1.49614	−0.748068	−	0.663622i	$-0.769018\pi$
$941$	−45.8950	−1.49614	−0.748068	+	0.663622i	$0.769018\pi$
$942$	−26.4976	−0.863338
$943$	37.3157	1.21517
$944$	11.6833	0.380259
$945$	−3.79287	−0.123382
$946$	0.125470	0.00407939
$947$	−46.5132	−1.51148	−0.755738	−	0.654874i	$-0.772722\pi$
$947$	−46.5132	−1.51148	−0.755738	+	0.654874i	$0.772722\pi$
$948$	−33.5243	−1.08882
$949$	−9.79237	−0.317874
$950$	−7.55322	−0.245059
$951$	40.8333	1.32411
$952$	4.89791	0.158742
$953$	−44.8872	−1.45404	−0.727019	−	0.686618i	$-0.759095\pi$
$953$	−44.8872	−1.45404	−0.727019	+	0.686618i	$0.759095\pi$
$954$	29.2323	0.946430
$955$	−12.4808	−0.403870
$956$	7.74419	0.250465
$957$	12.5122	0.404460
$958$	−4.85774	−0.156946
$959$	−6.82414	−0.220363
$960$	6.76150	0.218226
$961$	−30.9903	−0.999687
$962$	11.5934	0.373787
$963$	53.2111	1.71470
$964$	30.8856	0.994760
$965$	44.4209	1.42996
$966$	17.1992	0.553376
$967$	37.8285	1.21648	0.608241	−	0.793753i	$-0.291876\pi$
$967$	37.8285	1.21648	0.608241	+	0.793753i	$0.291876\pi$
$968$	−6.43651	−0.206877
$969$	−29.8018	−0.957372
$970$	28.4717	0.914172
$971$	−33.5383	−1.07629	−0.538147	−	0.842851i	$-0.680876\pi$
$971$	−33.5383	−1.07629	−0.538147	+	0.842851i	$0.680876\pi$
$972$	22.3669	0.717420
$973$	7.96973	0.255498
$974$	3.58778	0.114960
$975$	−9.79033	−0.313542
$976$	−6.89946	−0.220846
$977$	−45.1678	−1.44504	−0.722522	−	0.691348i	$-0.757017\pi$
$977$	−45.1678	−1.44504	−0.722522	+	0.691348i	$0.757017\pi$
$978$	35.0154	1.11967
$979$	23.8744	0.763030
$980$	13.0806	0.417846
$981$	−51.9531	−1.65873
$982$	−43.5048	−1.38829
$983$	−6.19036	−0.197442	−0.0987209	−	0.995115i	$-0.531475\pi$
$983$	−6.19036	−0.197442	−0.0987209	+	0.995115i	$0.531475\pi$
$984$	−20.1317	−0.641775
$985$	28.2797	0.901067
$986$	−7.81292	−0.248814
$987$	−29.0977	−0.926191
$988$	−6.27780	−0.199723
$989$	−0.275119	−0.00874827
$990$	19.3540	0.615110
$991$	35.7352	1.13516	0.567582	−	0.823317i	$-0.307879\pi$
$991$	35.7352	1.13516	0.567582	+	0.823317i	$0.307879\pi$
$992$	0.0984331	0.00312525
$993$	46.8018	1.48521
$994$	−16.7714	−0.531958
$995$	−3.94680	−0.125122
$996$	7.87983	0.249682
$997$	22.7702	0.721138	0.360569	−	0.932732i	$-0.382582\pi$
$997$	22.7702	0.721138	0.360569	+	0.932732i	$0.382582\pi$
$998$	26.3214	0.833190
$999$	−6.30320	−0.199425

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.9	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.9	✓	71	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.52707 q^{3} +1.00000 q^{4} -2.67563 q^{5} -2.52707 q^{6} -1.45299 q^{7} +1.00000 q^{8} +3.38607 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.52707 q^{3} +1.00000 q^{4} -2.67563 q^{5} -2.52707 q^{6} -1.45299 q^{7} +1.00000 q^{8} +3.38607 q^{9} -2.67563 q^{10} -2.13623 q^{11} -2.52707 q^{12} +1.79444 q^{13} -1.45299 q^{14} +6.76150 q^{15} +1.00000 q^{16} -3.37091 q^{17} +3.38607 q^{18} -3.49848 q^{19} -2.67563 q^{20} +3.67181 q^{21} -2.13623 q^{22} +4.68412 q^{23} -2.52707 q^{24} +2.15900 q^{25} +1.79444 q^{26} -0.975613 q^{27} -1.45299 q^{28} +2.31775 q^{29} +6.76150 q^{30} +0.0984331 q^{31} +1.00000 q^{32} +5.39840 q^{33} -3.37091 q^{34} +3.88767 q^{35} +3.38607 q^{36} +6.46076 q^{37} -3.49848 q^{38} -4.53466 q^{39} -2.67563 q^{40} +7.96643 q^{41} +3.67181 q^{42} -0.0587343 q^{43} -2.13623 q^{44} -9.05986 q^{45} +4.68412 q^{46} -7.92463 q^{47} -2.52707 q^{48} -4.88881 q^{49} +2.15900 q^{50} +8.51851 q^{51} +1.79444 q^{52} +8.63311 q^{53} -0.975613 q^{54} +5.71577 q^{55} -1.45299 q^{56} +8.84089 q^{57} +2.31775 q^{58} +11.6833 q^{59} +6.76150 q^{60} -6.89946 q^{61} +0.0984331 q^{62} -4.91993 q^{63} +1.00000 q^{64} -4.80125 q^{65} +5.39840 q^{66} -3.12393 q^{67} -3.37091 q^{68} -11.8371 q^{69} +3.88767 q^{70} +11.5427 q^{71} +3.38607 q^{72} -5.45707 q^{73} +6.46076 q^{74} -5.45594 q^{75} -3.49848 q^{76} +3.10393 q^{77} -4.53466 q^{78} +13.2661 q^{79} -2.67563 q^{80} -7.69276 q^{81} +7.96643 q^{82} -3.11817 q^{83} +3.67181 q^{84} +9.01930 q^{85} -0.0587343 q^{86} -5.85711 q^{87} -2.13623 q^{88} -11.1759 q^{89} -9.05986 q^{90} -2.60731 q^{91} +4.68412 q^{92} -0.248747 q^{93} -7.92463 q^{94} +9.36064 q^{95} -2.52707 q^{96} -10.6411 q^{97} -4.88881 q^{98} -7.23343 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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