LMFDB - Embedded newform 6026.2.a.k.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.41881 q^{3} +1.00000 q^{4} -3.09594 q^{5} -2.41881 q^{6} +0.393889 q^{7} +1.00000 q^{8} +2.85065 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.41881 q^{3} +1.00000 q^{4} -3.09594 q^{5} -2.41881 q^{6} +0.393889 q^{7} +1.00000 q^{8} +2.85065 q^{9} -3.09594 q^{10} +5.36126 q^{11} -2.41881 q^{12} -7.02322 q^{13} +0.393889 q^{14} +7.48850 q^{15} +1.00000 q^{16} +6.31365 q^{17} +2.85065 q^{18} -4.68307 q^{19} -3.09594 q^{20} -0.952743 q^{21} +5.36126 q^{22} -1.00000 q^{23} -2.41881 q^{24} +4.58485 q^{25} -7.02322 q^{26} +0.361240 q^{27} +0.393889 q^{28} -10.2128 q^{29} +7.48850 q^{30} +6.38589 q^{31} +1.00000 q^{32} -12.9679 q^{33} +6.31365 q^{34} -1.21946 q^{35} +2.85065 q^{36} -2.46937 q^{37} -4.68307 q^{38} +16.9879 q^{39} -3.09594 q^{40} -5.74013 q^{41} -0.952743 q^{42} +0.439070 q^{43} +5.36126 q^{44} -8.82546 q^{45} -1.00000 q^{46} +5.93764 q^{47} -2.41881 q^{48} -6.84485 q^{49} +4.58485 q^{50} -15.2715 q^{51} -7.02322 q^{52} +2.54808 q^{53} +0.361240 q^{54} -16.5982 q^{55} +0.393889 q^{56} +11.3275 q^{57} -10.2128 q^{58} +3.48987 q^{59} +7.48850 q^{60} +8.18751 q^{61} +6.38589 q^{62} +1.12284 q^{63} +1.00000 q^{64} +21.7435 q^{65} -12.9679 q^{66} -9.38594 q^{67} +6.31365 q^{68} +2.41881 q^{69} -1.21946 q^{70} +7.41856 q^{71} +2.85065 q^{72} -11.2530 q^{73} -2.46937 q^{74} -11.0899 q^{75} -4.68307 q^{76} +2.11174 q^{77} +16.9879 q^{78} +9.61616 q^{79} -3.09594 q^{80} -9.42573 q^{81} -5.74013 q^{82} -14.9494 q^{83} -0.952743 q^{84} -19.5467 q^{85} +0.439070 q^{86} +24.7029 q^{87} +5.36126 q^{88} -13.8969 q^{89} -8.82546 q^{90} -2.76637 q^{91} -1.00000 q^{92} -15.4463 q^{93} +5.93764 q^{94} +14.4985 q^{95} -2.41881 q^{96} -10.3992 q^{97} -6.84485 q^{98} +15.2831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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
$3$	−2.41881	−1.39650	−0.698251	−	0.715853i	$-0.746038\pi$
$3$	−2.41881	−1.39650	−0.698251	+	0.715853i	$0.746038\pi$
$4$	1.00000	0.500000
$5$	−3.09594	−1.38455	−0.692273	−	0.721635i	$-0.743391\pi$
$5$	−3.09594	−1.38455	−0.692273	+	0.721635i	$0.743391\pi$
$6$	−2.41881	−0.987476
$7$	0.393889	0.148876	0.0744380	−	0.997226i	$-0.476284\pi$
$7$	0.393889	0.148876	0.0744380	+	0.997226i	$0.476284\pi$
$8$	1.00000	0.353553
$9$	2.85065	0.950218
$10$	−3.09594	−0.979022
$11$	5.36126	1.61648	0.808241	−	0.588852i	$-0.200420\pi$
$11$	5.36126	1.61648	0.808241	+	0.588852i	$0.200420\pi$
$12$	−2.41881	−0.698251
$13$	−7.02322	−1.94789	−0.973945	−	0.226783i	$-0.927179\pi$
$13$	−7.02322	−1.94789	−0.973945	+	0.226783i	$0.927179\pi$
$14$	0.393889	0.105271
$15$	7.48850	1.93352
$16$	1.00000	0.250000
$17$	6.31365	1.53129	0.765643	−	0.643266i	$-0.222421\pi$
$17$	6.31365	1.53129	0.765643	+	0.643266i	$0.222421\pi$
$18$	2.85065	0.671906
$19$	−4.68307	−1.07437	−0.537185	−	0.843465i	$-0.680512\pi$
$19$	−4.68307	−1.07437	−0.537185	+	0.843465i	$0.680512\pi$
$20$	−3.09594	−0.692273
$21$	−0.952743	−0.207906
$22$	5.36126	1.14303
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.41881	−0.493738
$25$	4.58485	0.916970
$26$	−7.02322	−1.37737
$27$	0.361240	0.0695206
$28$	0.393889	0.0744380
$29$	−10.2128	−1.89647	−0.948235	−	0.317568i	$-0.897134\pi$
$29$	−10.2128	−1.89647	−0.948235	+	0.317568i	$0.897134\pi$
$30$	7.48850	1.36721
$31$	6.38589	1.14694	0.573470	−	0.819227i	$-0.305597\pi$
$31$	6.38589	1.14694	0.573470	+	0.819227i	$0.305597\pi$
$32$	1.00000	0.176777
$33$	−12.9679	−2.25742
$34$	6.31365	1.08278
$35$	−1.21946	−0.206126
$36$	2.85065	0.475109
$37$	−2.46937	−0.405963	−0.202981	−	0.979183i	$-0.565063\pi$
$37$	−2.46937	−0.405963	−0.202981	+	0.979183i	$0.565063\pi$
$38$	−4.68307	−0.759694
$39$	16.9879	2.72023
$40$	−3.09594	−0.489511
$41$	−5.74013	−0.896457	−0.448228	−	0.893919i	$-0.647945\pi$
$41$	−5.74013	−0.896457	−0.448228	+	0.893919i	$0.647945\pi$
$42$	−0.952743	−0.147011
$43$	0.439070	0.0669576	0.0334788	−	0.999439i	$-0.489341\pi$
$43$	0.439070	0.0669576	0.0334788	+	0.999439i	$0.489341\pi$
$44$	5.36126	0.808241
$45$	−8.82546	−1.31562
$46$	−1.00000	−0.147442
$47$	5.93764	0.866093	0.433047	−	0.901372i	$-0.357439\pi$
$47$	5.93764	0.866093	0.433047	+	0.901372i	$0.357439\pi$
$48$	−2.41881	−0.349126
$49$	−6.84485	−0.977836
$50$	4.58485	0.648396
$51$	−15.2715	−2.13844
$52$	−7.02322	−0.973945
$53$	2.54808	0.350005	0.175003	−	0.984568i	$-0.444007\pi$
$53$	2.54808	0.350005	0.175003	+	0.984568i	$0.444007\pi$
$54$	0.361240	0.0491585
$55$	−16.5982	−2.23809
$56$	0.393889	0.0526356
$57$	11.3275	1.50036
$58$	−10.2128	−1.34101
$59$	3.48987	0.454342	0.227171	−	0.973855i	$-0.427052\pi$
$59$	3.48987	0.454342	0.227171	+	0.973855i	$0.427052\pi$
$60$	7.48850	0.966761
$61$	8.18751	1.04830	0.524151	−	0.851625i	$-0.324383\pi$
$61$	8.18751	1.04830	0.524151	+	0.851625i	$0.324383\pi$
$62$	6.38589	0.811008
$63$	1.12284	0.141465
$64$	1.00000	0.125000
$65$	21.7435	2.69695
$66$	−12.9679	−1.59624
$67$	−9.38594	−1.14667	−0.573337	−	0.819319i	$-0.694352\pi$
$67$	−9.38594	−1.14667	−0.573337	+	0.819319i	$0.694352\pi$
$68$	6.31365	0.765643
$69$	2.41881	0.291191
$70$	−1.21946	−0.145753
$71$	7.41856	0.880421	0.440210	−	0.897895i	$-0.354904\pi$
$71$	7.41856	0.880421	0.440210	+	0.897895i	$0.354904\pi$
$72$	2.85065	0.335953
$73$	−11.2530	−1.31707	−0.658533	−	0.752552i	$-0.728823\pi$
$73$	−11.2530	−1.31707	−0.658533	+	0.752552i	$0.728823\pi$
$74$	−2.46937	−0.287059
$75$	−11.0899	−1.28055
$76$	−4.68307	−0.537185
$77$	2.11174	0.240655
$78$	16.9879	1.92350
$79$	9.61616	1.08190	0.540951	−	0.841054i	$-0.318064\pi$
$79$	9.61616	1.08190	0.540951	+	0.841054i	$0.318064\pi$
$80$	−3.09594	−0.346137
$81$	−9.42573	−1.04730
$82$	−5.74013	−0.633891
$83$	−14.9494	−1.64091	−0.820457	−	0.571708i	$-0.806281\pi$
$83$	−14.9494	−1.64091	−0.820457	+	0.571708i	$0.806281\pi$
$84$	−0.952743	−0.103953
$85$	−19.5467	−2.12014
$86$	0.439070	0.0473462
$87$	24.7029	2.64843
$88$	5.36126	0.571513
$89$	−13.8969	−1.47307	−0.736536	−	0.676399i	$-0.763540\pi$
$89$	−13.8969	−1.47307	−0.736536	+	0.676399i	$0.763540\pi$
$90$	−8.82546	−0.930285
$91$	−2.76637	−0.289994
$92$	−1.00000	−0.104257
$93$	−15.4463	−1.60170
$94$	5.93764	0.612420
$95$	14.4985	1.48751
$96$	−2.41881	−0.246869
$97$	−10.3992	−1.05587	−0.527937	−	0.849283i	$-0.677034\pi$
$97$	−10.3992	−1.05587	−0.527937	+	0.849283i	$0.677034\pi$
$98$	−6.84485	−0.691434
$99$	15.2831	1.53601
$100$	4.58485	0.458485
$101$	14.7464	1.46732	0.733659	−	0.679518i	$-0.237811\pi$
$101$	14.7464	1.46732	0.733659	+	0.679518i	$0.237811\pi$
$102$	−15.2715	−1.51211
$103$	−13.3431	−1.31473	−0.657366	−	0.753571i	$-0.728330\pi$
$103$	−13.3431	−1.31473	−0.657366	+	0.753571i	$0.728330\pi$
$104$	−7.02322	−0.688683
$105$	2.94964	0.287855
$106$	2.54808	0.247491
$107$	9.15480	0.885028	0.442514	−	0.896762i	$-0.354087\pi$
$107$	9.15480	0.885028	0.442514	+	0.896762i	$0.354087\pi$
$108$	0.361240	0.0347603
$109$	−7.30663	−0.699848	−0.349924	−	0.936778i	$-0.613793\pi$
$109$	−7.30663	−0.699848	−0.349924	+	0.936778i	$0.613793\pi$
$110$	−16.5982	−1.58257
$111$	5.97296	0.566928
$112$	0.393889	0.0372190
$113$	16.0090	1.50600	0.753002	−	0.658018i	$-0.228605\pi$
$113$	16.0090	1.50600	0.753002	+	0.658018i	$0.228605\pi$
$114$	11.3275	1.06091
$115$	3.09594	0.288698
$116$	−10.2128	−0.948235
$117$	−20.0208	−1.85092
$118$	3.48987	0.321268
$119$	2.48688	0.227972
$120$	7.48850	0.683603
$121$	17.7431	1.61301
$122$	8.18751	0.741262
$123$	13.8843	1.25190
$124$	6.38589	0.573470
$125$	1.28528	0.114959
$126$	1.12284	0.100031
$127$	9.66881	0.857968	0.428984	−	0.903312i	$-0.358872\pi$
$127$	9.66881	0.857968	0.428984	+	0.903312i	$0.358872\pi$
$128$	1.00000	0.0883883
$129$	−1.06203	−0.0935064
$130$	21.7435	1.90703
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−12.9679	−1.12871
$133$	−1.84461	−0.159948
$134$	−9.38594	−0.810821
$135$	−1.11838	−0.0962546
$136$	6.31365	0.541391
$137$	−12.1370	−1.03693	−0.518465	−	0.855099i	$-0.673496\pi$
$137$	−12.1370	−1.03693	−0.518465	+	0.855099i	$0.673496\pi$
$138$	2.41881	0.205903
$139$	−1.90943	−0.161955	−0.0809777	−	0.996716i	$-0.525804\pi$
$139$	−1.90943	−0.161955	−0.0809777	+	0.996716i	$0.525804\pi$
$140$	−1.21946	−0.103063
$141$	−14.3620	−1.20950
$142$	7.41856	0.622552
$143$	−37.6533	−3.14873
$144$	2.85065	0.237555
$145$	31.6182	2.62575
$146$	−11.2530	−0.931306
$147$	16.5564	1.36555
$148$	−2.46937	−0.202981
$149$	18.8253	1.54223	0.771116	−	0.636694i	$-0.219699\pi$
$149$	18.8253	1.54223	0.771116	+	0.636694i	$0.219699\pi$
$150$	−11.0899	−0.905486
$151$	14.6322	1.19075	0.595376	−	0.803447i	$-0.297003\pi$
$151$	14.6322	1.19075	0.595376	+	0.803447i	$0.297003\pi$
$152$	−4.68307	−0.379847
$153$	17.9980	1.45506
$154$	2.11174	0.170169
$155$	−19.7703	−1.58799
$156$	16.9879	1.36012
$157$	−17.3043	−1.38104	−0.690518	−	0.723315i	$-0.742617\pi$
$157$	−17.3043	−1.38104	−0.690518	+	0.723315i	$0.742617\pi$
$158$	9.61616	0.765020
$159$	−6.16332	−0.488783
$160$	−3.09594	−0.244756
$161$	−0.393889	−0.0310428
$162$	−9.42573	−0.740556
$163$	19.7917	1.55020	0.775101	−	0.631837i	$-0.217699\pi$
$163$	19.7917	1.55020	0.775101	+	0.631837i	$0.217699\pi$
$164$	−5.74013	−0.448228
$165$	40.1478	3.12550
$166$	−14.9494	−1.16030
$167$	21.6092	1.67217	0.836084	−	0.548601i	$-0.184839\pi$
$167$	21.6092	1.67217	0.836084	+	0.548601i	$0.184839\pi$
$168$	−0.952743	−0.0735057
$169$	36.3256	2.79428
$170$	−19.5467	−1.49916
$171$	−13.3498	−1.02088
$172$	0.439070	0.0334788
$173$	−3.55588	−0.270348	−0.135174	−	0.990822i	$-0.543159\pi$
$173$	−3.55588	−0.270348	−0.135174	+	0.990822i	$0.543159\pi$
$174$	24.7029	1.87272
$175$	1.80592	0.136515
$176$	5.36126	0.404120
$177$	−8.44133	−0.634489
$178$	−13.8969	−1.04162
$179$	6.92272	0.517428	0.258714	−	0.965954i	$-0.416701\pi$
$179$	6.92272	0.517428	0.258714	+	0.965954i	$0.416701\pi$
$180$	−8.82546	−0.657811
$181$	−8.78060	−0.652657	−0.326328	−	0.945256i	$-0.605812\pi$
$181$	−8.78060	−0.652657	−0.326328	+	0.945256i	$0.605812\pi$
$182$	−2.76637	−0.205057
$183$	−19.8040	−1.46396
$184$	−1.00000	−0.0737210
$185$	7.64504	0.562074
$186$	−15.4463	−1.13257
$187$	33.8492	2.47530
$188$	5.93764	0.433047
$189$	0.142288	0.0103500
$190$	14.4985	1.05183
$191$	26.3687	1.90797	0.953984	−	0.299856i	$-0.0969387\pi$
$191$	26.3687	1.90797	0.953984	+	0.299856i	$0.0969387\pi$
$192$	−2.41881	−0.174563
$193$	4.37051	0.314596	0.157298	−	0.987551i	$-0.449722\pi$
$193$	4.37051	0.314596	0.157298	+	0.987551i	$0.449722\pi$
$194$	−10.3992	−0.746616
$195$	−52.5934	−3.76629
$196$	−6.84485	−0.488918
$197$	−0.881103	−0.0627760	−0.0313880	−	0.999507i	$-0.509993\pi$
$197$	−0.881103	−0.0627760	−0.0313880	+	0.999507i	$0.509993\pi$
$198$	15.2831	1.08612
$199$	13.9664	0.990054	0.495027	−	0.868878i	$-0.335158\pi$
$199$	13.9664	0.990054	0.495027	+	0.868878i	$0.335158\pi$
$200$	4.58485	0.324198
$201$	22.7028	1.60133
$202$	14.7464	1.03755
$203$	−4.02271	−0.282339
$204$	−15.2715	−1.06922
$205$	17.7711	1.24119
$206$	−13.3431	−0.929656
$207$	−2.85065	−0.198134
$208$	−7.02322	−0.486973
$209$	−25.1072	−1.73670
$210$	2.94964	0.203544
$211$	4.26942	0.293919	0.146960	−	0.989143i	$-0.453051\pi$
$211$	4.26942	0.293919	0.146960	+	0.989143i	$0.453051\pi$
$212$	2.54808	0.175003
$213$	−17.9441	−1.22951
$214$	9.15480	0.625809
$215$	−1.35934	−0.0927059
$216$	0.361240	0.0245793
$217$	2.51533	0.170752
$218$	−7.30663	−0.494867
$219$	27.2189	1.83928
$220$	−16.5982	−1.11905
$221$	−44.3422	−2.98278
$222$	5.97296	0.400878
$223$	−6.55478	−0.438940	−0.219470	−	0.975619i	$-0.570433\pi$
$223$	−6.55478	−0.438940	−0.219470	+	0.975619i	$0.570433\pi$
$224$	0.393889	0.0263178
$225$	13.0698	0.871321
$226$	16.0090	1.06491
$227$	19.3305	1.28301	0.641507	−	0.767117i	$-0.278310\pi$
$227$	19.3305	1.28301	0.641507	+	0.767117i	$0.278310\pi$
$228$	11.3275	0.750179
$229$	20.7934	1.37406	0.687032	−	0.726627i	$-0.258913\pi$
$229$	20.7934	1.37406	0.687032	+	0.726627i	$0.258913\pi$
$230$	3.09594	0.204140
$231$	−5.10791	−0.336076
$232$	−10.2128	−0.670504
$233$	9.08742	0.595337	0.297668	−	0.954669i	$-0.403791\pi$
$233$	9.08742	0.595337	0.297668	+	0.954669i	$0.403791\pi$
$234$	−20.0208	−1.30880
$235$	−18.3826	−1.19915
$236$	3.48987	0.227171
$237$	−23.2597	−1.51088
$238$	2.48688	0.161200
$239$	7.68838	0.497320	0.248660	−	0.968591i	$-0.420010\pi$
$239$	7.68838	0.497320	0.248660	+	0.968591i	$0.420010\pi$
$240$	7.48850	0.483381
$241$	16.1849	1.04256	0.521280	−	0.853386i	$-0.325455\pi$
$241$	16.1849	1.04256	0.521280	+	0.853386i	$0.325455\pi$
$242$	17.7431	1.14057
$243$	21.7154	1.39304
$244$	8.18751	0.524151
$245$	21.1913	1.35386
$246$	13.8843	0.885230
$247$	32.8902	2.09275
$248$	6.38589	0.405504
$249$	36.1599	2.29154
$250$	1.28528	0.0812883
$251$	−21.3661	−1.34862	−0.674309	−	0.738449i	$-0.735559\pi$
$251$	−21.3661	−1.34862	−0.674309	+	0.738449i	$0.735559\pi$
$252$	1.12284	0.0707323
$253$	−5.36126	−0.337060
$254$	9.66881	0.606675
$255$	47.2798	2.96078
$256$	1.00000	0.0625000
$257$	29.4553	1.83737	0.918686	−	0.394988i	$-0.129251\pi$
$257$	29.4553	1.83737	0.918686	+	0.394988i	$0.129251\pi$
$258$	−1.06203	−0.0661190
$259$	−0.972659	−0.0604381
$260$	21.7435	1.34847
$261$	−29.1132	−1.80206
$262$	−1.00000	−0.0617802
$263$	22.6447	1.39633	0.698166	−	0.715936i	$-0.254000\pi$
$263$	22.6447	1.39633	0.698166	+	0.715936i	$0.254000\pi$
$264$	−12.9679	−0.798119
$265$	−7.88870	−0.484599
$266$	−1.84461	−0.113100
$267$	33.6141	2.05715
$268$	−9.38594	−0.573337
$269$	−4.88361	−0.297759	−0.148879	−	0.988855i	$-0.547567\pi$
$269$	−4.88361	−0.297759	−0.148879	+	0.988855i	$0.547567\pi$
$270$	−1.11838	−0.0680623
$271$	−23.4304	−1.42329	−0.711646	−	0.702538i	$-0.752050\pi$
$271$	−23.4304	−1.42329	−0.711646	+	0.702538i	$0.752050\pi$
$272$	6.31365	0.382821
$273$	6.69133	0.404977
$274$	−12.1370	−0.733221
$275$	24.5806	1.48227
$276$	2.41881	0.145595
$277$	−16.9480	−1.01830	−0.509152	−	0.860677i	$-0.670041\pi$
$277$	−16.9480	−1.01830	−0.509152	+	0.860677i	$0.670041\pi$
$278$	−1.90943	−0.114520
$279$	18.2040	1.08984
$280$	−1.21946	−0.0728765
$281$	−11.6493	−0.694940	−0.347470	−	0.937691i	$-0.612959\pi$
$281$	−11.6493	−0.694940	−0.347470	+	0.937691i	$0.612959\pi$
$282$	−14.3620	−0.855246
$283$	6.47542	0.384924	0.192462	−	0.981304i	$-0.438353\pi$
$283$	6.47542	0.384924	0.192462	+	0.981304i	$0.438353\pi$
$284$	7.41856	0.440210
$285$	−35.0691	−2.07732
$286$	−37.6533	−2.22649
$287$	−2.26097	−0.133461
$288$	2.85065	0.167976
$289$	22.8622	1.34484
$290$	31.6182	1.85669
$291$	25.1536	1.47453
$292$	−11.2530	−0.658533
$293$	19.0392	1.11228	0.556141	−	0.831088i	$-0.312282\pi$
$293$	19.0392	1.11228	0.556141	+	0.831088i	$0.312282\pi$
$294$	16.5564	0.965590
$295$	−10.8044	−0.629057
$296$	−2.46937	−0.143530
$297$	1.93670	0.112379
$298$	18.8253	1.09052
$299$	7.02322	0.406163
$300$	−11.0899	−0.640275
$301$	0.172945	0.00996838
$302$	14.6322	0.841988
$303$	−35.6687	−2.04911
$304$	−4.68307	−0.268592
$305$	−25.3480	−1.45142
$306$	17.9980	1.02888
$307$	−13.5785	−0.774968	−0.387484	−	0.921876i	$-0.626656\pi$
$307$	−13.5785	−0.774968	−0.387484	+	0.921876i	$0.626656\pi$
$308$	2.11174	0.120328
$309$	32.2744	1.83603
$310$	−19.7703	−1.12288
$311$	12.7239	0.721509	0.360754	−	0.932661i	$-0.382519\pi$
$311$	12.7239	0.721509	0.360754	+	0.932661i	$0.382519\pi$
$312$	16.9879	0.961748
$313$	5.05187	0.285549	0.142774	−	0.989755i	$-0.454398\pi$
$313$	5.05187	0.285549	0.142774	+	0.989755i	$0.454398\pi$
$314$	−17.3043	−0.976540
$315$	−3.47625	−0.195864
$316$	9.61616	0.540951
$317$	7.97222	0.447764	0.223882	−	0.974616i	$-0.428127\pi$
$317$	7.97222	0.447764	0.223882	+	0.974616i	$0.428127\pi$
$318$	−6.16332	−0.345622
$319$	−54.7535	−3.06561
$320$	−3.09594	−0.173068
$321$	−22.1437	−1.23594
$322$	−0.393889	−0.0219506
$323$	−29.5673	−1.64517
$324$	−9.42573	−0.523652
$325$	−32.2004	−1.78616
$326$	19.7917	1.09616
$327$	17.6734	0.977340
$328$	−5.74013	−0.316945
$329$	2.33877	0.128940
$330$	40.1478	2.21006
$331$	10.1790	0.559490	0.279745	−	0.960074i	$-0.409750\pi$
$331$	10.1790	0.559490	0.279745	+	0.960074i	$0.409750\pi$
$332$	−14.9494	−0.820457
$333$	−7.03933	−0.385753
$334$	21.6092	1.18240
$335$	29.0583	1.58762
$336$	−0.952743	−0.0519764
$337$	0.241214	0.0131398	0.00656988	−	0.999978i	$-0.497909\pi$
$337$	0.241214	0.0131398	0.00656988	+	0.999978i	$0.497909\pi$
$338$	36.3256	1.97585
$339$	−38.7229	−2.10314
$340$	−19.5467	−1.06007
$341$	34.2364	1.85401
$342$	−13.3498	−0.721875
$343$	−5.45333	−0.294452
$344$	0.439070	0.0236731
$345$	−7.48850	−0.403167
$346$	−3.55588	−0.191165
$347$	−16.8959	−0.907017	−0.453509	−	0.891252i	$-0.649828\pi$
$347$	−16.8959	−0.907017	−0.453509	+	0.891252i	$0.649828\pi$
$348$	24.7029	1.32421
$349$	16.7877	0.898626	0.449313	−	0.893374i	$-0.351669\pi$
$349$	16.7877	0.898626	0.449313	+	0.893374i	$0.351669\pi$
$350$	1.80592	0.0965305
$351$	−2.53707	−0.135419
$352$	5.36126	0.285756
$353$	5.69541	0.303136	0.151568	−	0.988447i	$-0.451568\pi$
$353$	5.69541	0.303136	0.151568	+	0.988447i	$0.451568\pi$
$354$	−8.44133	−0.448652
$355$	−22.9674	−1.21898
$356$	−13.8969	−0.736536
$357$	−6.01529	−0.318363
$358$	6.92272	0.365877
$359$	−17.1022	−0.902622	−0.451311	−	0.892367i	$-0.649044\pi$
$359$	−17.1022	−0.902622	−0.451311	+	0.892367i	$0.649044\pi$
$360$	−8.82546	−0.465142
$361$	2.93111	0.154269
$362$	−8.78060	−0.461498
$363$	−42.9173	−2.25258
$364$	−2.76637	−0.144997
$365$	34.8387	1.82354
$366$	−19.8040	−1.03517
$367$	−2.59258	−0.135332	−0.0676658	−	0.997708i	$-0.521555\pi$
$367$	−2.59258	−0.135332	−0.0676658	+	0.997708i	$0.521555\pi$
$368$	−1.00000	−0.0521286
$369$	−16.3631	−0.851830
$370$	7.64504	0.397447
$371$	1.00366	0.0521074
$372$	−15.4463	−0.800851
$373$	15.3331	0.793916	0.396958	−	0.917837i	$-0.370066\pi$
$373$	15.3331	0.793916	0.396958	+	0.917837i	$0.370066\pi$
$374$	33.8492	1.75030
$375$	−3.10885	−0.160540
$376$	5.93764	0.306210
$377$	71.7268	3.69412
$378$	0.142288	0.00731852
$379$	4.12700	0.211990	0.105995	−	0.994367i	$-0.466197\pi$
$379$	4.12700	0.211990	0.105995	+	0.994367i	$0.466197\pi$
$380$	14.4985	0.743757
$381$	−23.3870	−1.19815
$382$	26.3687	1.34914
$383$	−8.84464	−0.451940	−0.225970	−	0.974134i	$-0.572555\pi$
$383$	−8.84464	−0.451940	−0.225970	+	0.974134i	$0.572555\pi$
$384$	−2.41881	−0.123435
$385$	−6.53783	−0.333199
$386$	4.37051	0.222453
$387$	1.25164	0.0636243
$388$	−10.3992	−0.527937
$389$	−11.7131	−0.593879	−0.296939	−	0.954896i	$-0.595966\pi$
$389$	−11.7131	−0.593879	−0.296939	+	0.954896i	$0.595966\pi$
$390$	−52.5934	−2.66317
$391$	−6.31365	−0.319295
$392$	−6.84485	−0.345717
$393$	2.41881	0.122013
$394$	−0.881103	−0.0443893
$395$	−29.7711	−1.49794
$396$	15.2831	0.768005
$397$	9.73273	0.488472	0.244236	−	0.969716i	$-0.421463\pi$
$397$	9.73273	0.488472	0.244236	+	0.969716i	$0.421463\pi$
$398$	13.9664	0.700074
$399$	4.46176	0.223367
$400$	4.58485	0.229242
$401$	−35.1737	−1.75649	−0.878246	−	0.478210i	$-0.841286\pi$
$401$	−35.1737	−1.75649	−0.878246	+	0.478210i	$0.841286\pi$
$402$	22.7028	1.13231
$403$	−44.8495	−2.23411
$404$	14.7464	0.733659
$405$	29.1815	1.45004
$406$	−4.02271	−0.199644
$407$	−13.2390	−0.656231
$408$	−15.2715	−0.756054
$409$	−15.2179	−0.752475	−0.376238	−	0.926523i	$-0.622782\pi$
$409$	−15.2179	−0.752475	−0.376238	+	0.926523i	$0.622782\pi$
$410$	17.7711	0.877651
$411$	29.3570	1.44808
$412$	−13.3431	−0.657366
$413$	1.37462	0.0676406
$414$	−2.85065	−0.140102
$415$	46.2826	2.27192
$416$	−7.02322	−0.344342
$417$	4.61854	0.226171
$418$	−25.1072	−1.22803
$419$	−8.41787	−0.411240	−0.205620	−	0.978632i	$-0.565921\pi$
$419$	−8.41787	−0.411240	−0.205620	+	0.978632i	$0.565921\pi$
$420$	2.94964	0.143928
$421$	6.62581	0.322922	0.161461	−	0.986879i	$-0.448379\pi$
$421$	6.62581	0.322922	0.161461	+	0.986879i	$0.448379\pi$
$422$	4.26942	0.207832
$423$	16.9261	0.822977
$424$	2.54808	0.123746
$425$	28.9471	1.40414
$426$	−17.9441	−0.869394
$427$	3.22497	0.156067
$428$	9.15480	0.442514
$429$	91.0763	4.39721
$430$	−1.35934	−0.0655530
$431$	22.9118	1.10362	0.551812	−	0.833968i	$-0.313936\pi$
$431$	22.9118	1.10362	0.551812	+	0.833968i	$0.313936\pi$
$432$	0.361240	0.0173802
$433$	25.2565	1.21375	0.606875	−	0.794798i	$-0.292423\pi$
$433$	25.2565	1.21375	0.606875	+	0.794798i	$0.292423\pi$
$434$	2.51533	0.120740
$435$	−76.4786	−3.66687
$436$	−7.30663	−0.349924
$437$	4.68307	0.224021
$438$	27.2189	1.30057
$439$	33.1873	1.58395	0.791973	−	0.610557i	$-0.209054\pi$
$439$	33.1873	1.58395	0.791973	+	0.610557i	$0.209054\pi$
$440$	−16.5982	−0.791286
$441$	−19.5123	−0.929157
$442$	−44.3422	−2.10914
$443$	−8.56351	−0.406865	−0.203432	−	0.979089i	$-0.565210\pi$
$443$	−8.56351	−0.406865	−0.203432	+	0.979089i	$0.565210\pi$
$444$	5.97296	0.283464
$445$	43.0241	2.03954
$446$	−6.55478	−0.310378
$447$	−45.5350	−2.15373
$448$	0.393889	0.0186095
$449$	−2.62420	−0.123844	−0.0619219	−	0.998081i	$-0.519723\pi$
$449$	−2.62420	−0.123844	−0.0619219	+	0.998081i	$0.519723\pi$
$450$	13.0698	0.616117
$451$	−30.7743	−1.44911
$452$	16.0090	0.753002
$453$	−35.3925	−1.66289
$454$	19.3305	0.907228
$455$	8.56451	0.401510
$456$	11.3275	0.530457
$457$	18.4948	0.865150	0.432575	−	0.901598i	$-0.357605\pi$
$457$	18.4948	0.865150	0.432575	+	0.901598i	$0.357605\pi$
$458$	20.7934	0.971610
$459$	2.28074	0.106456
$460$	3.09594	0.144349
$461$	11.9614	0.557096	0.278548	−	0.960422i	$-0.410147\pi$
$461$	11.9614	0.557096	0.278548	+	0.960422i	$0.410147\pi$
$462$	−5.10791	−0.237641
$463$	12.1198	0.563253	0.281627	−	0.959524i	$-0.409126\pi$
$463$	12.1198	0.563253	0.281627	+	0.959524i	$0.409126\pi$
$464$	−10.2128	−0.474118
$465$	47.8207	2.21763
$466$	9.08742	0.420967
$467$	−7.16148	−0.331394	−0.165697	−	0.986177i	$-0.552987\pi$
$467$	−7.16148	−0.331394	−0.165697	+	0.986177i	$0.552987\pi$
$468$	−20.0208	−0.925460
$469$	−3.69702	−0.170712
$470$	−18.3826	−0.847925
$471$	41.8559	1.92862
$472$	3.48987	0.160634
$473$	2.35397	0.108236
$474$	−23.2597	−1.06835
$475$	−21.4712	−0.985164
$476$	2.48688	0.113986
$477$	7.26369	0.332581
$478$	7.68838	0.351659
$479$	12.9329	0.590920	0.295460	−	0.955355i	$-0.404527\pi$
$479$	12.9329	0.590920	0.295460	+	0.955355i	$0.404527\pi$
$480$	7.48850	0.341802
$481$	17.3430	0.790771
$482$	16.1849	0.737201
$483$	0.952743	0.0433513
$484$	17.7431	0.806507
$485$	32.1952	1.46191
$486$	21.7154	0.985029
$487$	−28.1383	−1.27507	−0.637535	−	0.770422i	$-0.720046\pi$
$487$	−28.1383	−1.27507	−0.637535	+	0.770422i	$0.720046\pi$
$488$	8.18751	0.370631
$489$	−47.8723	−2.16486
$490$	21.1913	0.957323
$491$	−7.65932	−0.345660	−0.172830	−	0.984952i	$-0.555291\pi$
$491$	−7.65932	−0.345660	−0.172830	+	0.984952i	$0.555291\pi$
$492$	13.8843	0.625952
$493$	−64.4801	−2.90404
$494$	32.8902	1.47980
$495$	−47.3156	−2.12668
$496$	6.38589	0.286735
$497$	2.92209	0.131074
$498$	36.1599	1.62036
$499$	20.3495	0.910970	0.455485	−	0.890243i	$-0.349466\pi$
$499$	20.3495	0.910970	0.455485	+	0.890243i	$0.349466\pi$
$500$	1.28528	0.0574795
$501$	−52.2686	−2.33519
$502$	−21.3661	−0.953617
$503$	2.46318	0.109828	0.0549138	−	0.998491i	$-0.482512\pi$
$503$	2.46318	0.109828	0.0549138	+	0.998491i	$0.482512\pi$
$504$	1.12284	0.0500153
$505$	−45.6539	−2.03157
$506$	−5.36126	−0.238337
$507$	−87.8648	−3.90221
$508$	9.66881	0.428984
$509$	16.3907	0.726503	0.363252	−	0.931691i	$-0.381667\pi$
$509$	16.3907	0.726503	0.363252	+	0.931691i	$0.381667\pi$
$510$	47.2798	2.09358
$511$	−4.43244	−0.196079
$512$	1.00000	0.0441942
$513$	−1.69171	−0.0746908
$514$	29.4553	1.29922
$515$	41.3094	1.82031
$516$	−1.06203	−0.0467532
$517$	31.8332	1.40002
$518$	−0.972659	−0.0427362
$519$	8.60100	0.377542
$520$	21.7435	0.953514
$521$	40.2834	1.76485	0.882424	−	0.470455i	$-0.155910\pi$
$521$	40.2834	1.76485	0.882424	+	0.470455i	$0.155910\pi$
$522$	−29.1132	−1.27425
$523$	−16.6956	−0.730050	−0.365025	−	0.930998i	$-0.618940\pi$
$523$	−16.6956	−0.730050	−0.365025	+	0.930998i	$0.618940\pi$
$524$	−1.00000	−0.0436852
$525$	−4.36818	−0.190643
$526$	22.6447	0.987356
$527$	40.3183	1.75629
$528$	−12.9679	−0.564355
$529$	1.00000	0.0434783
$530$	−7.88870	−0.342663
$531$	9.94840	0.431724
$532$	−1.84461	−0.0799739
$533$	40.3142	1.74620
$534$	33.6141	1.45462
$535$	−28.3427	−1.22536
$536$	−9.38594	−0.405411
$537$	−16.7448	−0.722590
$538$	−4.88361	−0.210547
$539$	−36.6971	−1.58065
$540$	−1.11838	−0.0481273
$541$	18.5032	0.795516	0.397758	−	0.917490i	$-0.369788\pi$
$541$	18.5032	0.795516	0.397758	+	0.917490i	$0.369788\pi$
$542$	−23.4304	−1.00642
$543$	21.2386	0.911437
$544$	6.31365	0.270696
$545$	22.6209	0.968973
$546$	6.69133	0.286362
$547$	−10.4734	−0.447810	−0.223905	−	0.974611i	$-0.571880\pi$
$547$	−10.4734	−0.447810	−0.223905	+	0.974611i	$0.571880\pi$
$548$	−12.1370	−0.518465
$549$	23.3398	0.996116
$550$	24.5806	1.04812
$551$	47.8273	2.03751
$552$	2.41881	0.102951
$553$	3.78770	0.161069
$554$	−16.9480	−0.720050
$555$	−18.4919	−0.784938
$556$	−1.90943	−0.0809777
$557$	−39.3988	−1.66938	−0.834691	−	0.550719i	$-0.814353\pi$
$557$	−39.3988	−1.66938	−0.834691	+	0.550719i	$0.814353\pi$
$558$	18.2040	0.770635
$559$	−3.08369	−0.130426
$560$	−1.21946	−0.0515314
$561$	−81.8748	−3.45675
$562$	−11.6493	−0.491397
$563$	−29.4638	−1.24175	−0.620875	−	0.783909i	$-0.713223\pi$
$563$	−29.4638	−1.24175	−0.620875	+	0.783909i	$0.713223\pi$
$564$	−14.3620	−0.604750
$565$	−49.5631	−2.08513
$566$	6.47542	0.272182
$567$	−3.71269	−0.155918
$568$	7.41856	0.311276
$569$	−10.3090	−0.432176	−0.216088	−	0.976374i	$-0.569330\pi$
$569$	−10.3090	−0.432176	−0.216088	+	0.976374i	$0.569330\pi$
$570$	−35.0691	−1.46888
$571$	2.26743	0.0948888	0.0474444	−	0.998874i	$-0.484892\pi$
$571$	2.26743	0.0948888	0.0474444	+	0.998874i	$0.484892\pi$
$572$	−37.6533	−1.57436
$573$	−63.7808	−2.66448
$574$	−2.26097	−0.0943711
$575$	−4.58485	−0.191201
$576$	2.85065	0.118777
$577$	−9.98010	−0.415477	−0.207739	−	0.978184i	$-0.566610\pi$
$577$	−9.98010	−0.415477	−0.207739	+	0.978184i	$0.566610\pi$
$578$	22.8622	0.950942
$579$	−10.5714	−0.439334
$580$	31.6182	1.31288
$581$	−5.88842	−0.244293
$582$	25.1536	1.04265
$583$	13.6609	0.565777
$584$	−11.2530	−0.465653
$585$	61.9831	2.56269
$586$	19.0392	0.786502
$587$	16.8726	0.696408	0.348204	−	0.937419i	$-0.386792\pi$
$587$	16.8726	0.696408	0.348204	+	0.937419i	$0.386792\pi$
$588$	16.5564	0.682775
$589$	−29.9055	−1.23224
$590$	−10.8044	−0.444811
$591$	2.13122	0.0876668
$592$	−2.46937	−0.101491
$593$	−9.09803	−0.373612	−0.186806	−	0.982397i	$-0.559814\pi$
$593$	−9.09803	−0.373612	−0.186806	+	0.982397i	$0.559814\pi$
$594$	1.93670	0.0794638
$595$	−7.69922	−0.315637
$596$	18.8253	0.771116
$597$	−33.7822	−1.38261
$598$	7.02322	0.287201
$599$	−11.8970	−0.486099	−0.243049	−	0.970014i	$-0.578148\pi$
$599$	−11.8970	−0.486099	−0.243049	+	0.970014i	$0.578148\pi$
$600$	−11.0899	−0.452743
$601$	−5.81941	−0.237379	−0.118689	−	0.992931i	$-0.537869\pi$
$601$	−5.81941	−0.237379	−0.118689	+	0.992931i	$0.537869\pi$
$602$	0.172945	0.00704871
$603$	−26.7561	−1.08959
$604$	14.6322	0.595376
$605$	−54.9317	−2.23329
$606$	−35.6687	−1.44894
$607$	−25.9777	−1.05440	−0.527202	−	0.849740i	$-0.676759\pi$
$607$	−25.9777	−1.05440	−0.527202	+	0.849740i	$0.676759\pi$
$608$	−4.68307	−0.189923
$609$	9.73018	0.394287
$610$	−25.3480	−1.02631
$611$	−41.7013	−1.68705
$612$	17.9980	0.727528
$613$	−30.4742	−1.23084	−0.615420	−	0.788199i	$-0.711014\pi$
$613$	−30.4742	−1.23084	−0.615420	+	0.788199i	$0.711014\pi$
$614$	−13.5785	−0.547985
$615$	−42.9849	−1.73332
$616$	2.11174	0.0850845
$617$	−15.7643	−0.634647	−0.317324	−	0.948317i	$-0.602784\pi$
$617$	−15.7643	−0.634647	−0.317324	+	0.948317i	$0.602784\pi$
$618$	32.2744	1.29827
$619$	4.62518	0.185902	0.0929508	−	0.995671i	$-0.470370\pi$
$619$	4.62518	0.185902	0.0929508	+	0.995671i	$0.470370\pi$
$620$	−19.7703	−0.793995
$621$	−0.361240	−0.0144961
$622$	12.7239	0.510184
$623$	−5.47385	−0.219305
$624$	16.9879	0.680058
$625$	−26.9034	−1.07614
$626$	5.05187	0.201913
$627$	60.7295	2.42530
$628$	−17.3043	−0.690518
$629$	−15.5908	−0.621645
$630$	−3.47625	−0.138497
$631$	13.2680	0.528189	0.264095	−	0.964497i	$-0.414927\pi$
$631$	13.2680	0.528189	0.264095	+	0.964497i	$0.414927\pi$
$632$	9.61616	0.382510
$633$	−10.3269	−0.410459
$634$	7.97222	0.316617
$635$	−29.9341	−1.18790
$636$	−6.16332	−0.244392
$637$	48.0729	1.90472
$638$	−54.7535	−2.16771
$639$	21.1477	0.836592
$640$	−3.09594	−0.122378
$641$	−26.9886	−1.06598	−0.532992	−	0.846120i	$-0.678932\pi$
$641$	−26.9886	−1.06598	−0.532992	+	0.846120i	$0.678932\pi$
$642$	−22.1437	−0.873944
$643$	23.7322	0.935907	0.467953	−	0.883753i	$-0.344992\pi$
$643$	23.7322	0.935907	0.467953	+	0.883753i	$0.344992\pi$
$644$	−0.393889	−0.0155214
$645$	3.28798	0.129464
$646$	−29.5673	−1.16331
$647$	0.532319	0.0209276	0.0104638	−	0.999945i	$-0.496669\pi$
$647$	0.532319	0.0209276	0.0104638	+	0.999945i	$0.496669\pi$
$648$	−9.42573	−0.370278
$649$	18.7101	0.734435
$650$	−32.2004	−1.26300
$651$	−6.08411	−0.238455
$652$	19.7917	0.775101
$653$	48.5454	1.89973	0.949864	−	0.312663i	$-0.101221\pi$
$653$	48.5454	1.89973	0.949864	+	0.312663i	$0.101221\pi$
$654$	17.6734	0.691083
$655$	3.09594	0.120968
$656$	−5.74013	−0.224114
$657$	−32.0784	−1.25150
$658$	2.33877	0.0911747
$659$	−24.2419	−0.944329	−0.472165	−	0.881510i	$-0.656527\pi$
$659$	−24.2419	−0.944329	−0.472165	+	0.881510i	$0.656527\pi$
$660$	40.1478	1.56275
$661$	20.9311	0.814125	0.407062	−	0.913400i	$-0.366553\pi$
$661$	20.9311	0.814125	0.407062	+	0.913400i	$0.366553\pi$
$662$	10.1790	0.395619
$663$	107.255	4.16545
$664$	−14.9494	−0.580151
$665$	5.71080	0.221455
$666$	−7.03933	−0.272769
$667$	10.2128	0.395441
$668$	21.6092	0.836084
$669$	15.8548	0.612981
$670$	29.0583	1.12262
$671$	43.8954	1.69456
$672$	−0.952743	−0.0367529
$673$	0.404007	0.0155733	0.00778666	−	0.999970i	$-0.497521\pi$
$673$	0.404007	0.0155733	0.00778666	+	0.999970i	$0.497521\pi$
$674$	0.241214	0.00929122
$675$	1.65623	0.0637483
$676$	36.3256	1.39714
$677$	−15.0590	−0.578764	−0.289382	−	0.957214i	$-0.593450\pi$
$677$	−15.0590	−0.578764	−0.289382	+	0.957214i	$0.593450\pi$
$678$	−38.7229	−1.48714
$679$	−4.09611	−0.157194
$680$	−19.5467	−0.749581
$681$	−46.7570	−1.79173
$682$	34.2364	1.31098
$683$	−6.65023	−0.254464	−0.127232	−	0.991873i	$-0.540609\pi$
$683$	−6.65023	−0.254464	−0.127232	+	0.991873i	$0.540609\pi$
$684$	−13.3498	−0.510442
$685$	37.5753	1.43568
$686$	−5.45333	−0.208209
$687$	−50.2953	−1.91888
$688$	0.439070	0.0167394
$689$	−17.8957	−0.681772
$690$	−7.48850	−0.285082
$691$	2.73093	0.103889	0.0519447	−	0.998650i	$-0.483458\pi$
$691$	2.73093	0.103889	0.0519447	+	0.998650i	$0.483458\pi$
$692$	−3.55588	−0.135174
$693$	6.01985	0.228675
$694$	−16.8959	−0.641358
$695$	5.91147	0.224235
$696$	24.7029	0.936360
$697$	−36.2412	−1.37273
$698$	16.7877	0.635424
$699$	−21.9808	−0.831389
$700$	1.80592	0.0682574
$701$	0.463589	0.0175095	0.00875476	−	0.999962i	$-0.497213\pi$
$701$	0.463589	0.0175095	0.00875476	+	0.999962i	$0.497213\pi$
$702$	−2.53707	−0.0957554
$703$	11.5642	0.436154
$704$	5.36126	0.202060
$705$	44.4640	1.67461
$706$	5.69541	0.214350
$707$	5.80843	0.218448
$708$	−8.44133	−0.317245
$709$	−6.24881	−0.234679	−0.117339	−	0.993092i	$-0.537437\pi$
$709$	−6.24881	−0.234679	−0.117339	+	0.993092i	$0.537437\pi$
$710$	−22.9674	−0.861952
$711$	27.4123	1.02804
$712$	−13.8969	−0.520809
$713$	−6.38589	−0.239153
$714$	−6.01529	−0.225117
$715$	116.572	4.35956
$716$	6.92272	0.258714
$717$	−18.5968	−0.694509
$718$	−17.1022	−0.638250
$719$	−16.2009	−0.604190	−0.302095	−	0.953278i	$-0.597686\pi$
$719$	−16.2009	−0.604190	−0.302095	+	0.953278i	$0.597686\pi$
$720$	−8.82546	−0.328905
$721$	−5.25569	−0.195732
$722$	2.93111	0.109085
$723$	−39.1482	−1.45594
$724$	−8.78060	−0.326328
$725$	−46.8242	−1.73901
$726$	−42.9173	−1.59281
$727$	−12.1087	−0.449087	−0.224544	−	0.974464i	$-0.572089\pi$
$727$	−12.1087	−0.449087	−0.224544	+	0.974464i	$0.572089\pi$
$728$	−2.76637	−0.102528
$729$	−24.2482	−0.898081
$730$	34.8387	1.28944
$731$	2.77214	0.102531
$732$	−19.8040	−0.731979
$733$	25.7619	0.951539	0.475769	−	0.879570i	$-0.342170\pi$
$733$	25.7619	0.951539	0.475769	+	0.879570i	$0.342170\pi$
$734$	−2.59258	−0.0956939
$735$	−51.2577	−1.89067
$736$	−1.00000	−0.0368605
$737$	−50.3205	−1.85358
$738$	−16.3631	−0.602334
$739$	48.6161	1.78837	0.894186	−	0.447696i	$-0.147755\pi$
$739$	48.6161	1.78837	0.894186	+	0.447696i	$0.147755\pi$
$740$	7.64504	0.281037
$741$	−79.5552	−2.92253
$742$	1.00366	0.0368455
$743$	−16.2782	−0.597188	−0.298594	−	0.954380i	$-0.596518\pi$
$743$	−16.2782	−0.597188	−0.298594	+	0.954380i	$0.596518\pi$
$744$	−15.4463	−0.566287
$745$	−58.2822	−2.13529
$746$	15.3331	0.561383
$747$	−42.6157	−1.55923
$748$	33.8492	1.23765
$749$	3.60597	0.131759
$750$	−3.10885	−0.113519
$751$	−35.0316	−1.27832	−0.639161	−	0.769073i	$-0.720718\pi$
$751$	−35.0316	−1.27832	−0.639161	+	0.769073i	$0.720718\pi$
$752$	5.93764	0.216523
$753$	51.6807	1.88335
$754$	71.7268	2.61214
$755$	−45.3004	−1.64865
$756$	0.142288	0.00517498
$757$	33.0877	1.20259	0.601297	−	0.799025i	$-0.294651\pi$
$757$	33.0877	1.20259	0.601297	+	0.799025i	$0.294651\pi$
$758$	4.12700	0.149899
$759$	12.9679	0.470705
$760$	14.4985	0.525916
$761$	4.34750	0.157597	0.0787983	−	0.996891i	$-0.474892\pi$
$761$	4.34750	0.157597	0.0787983	+	0.996891i	$0.474892\pi$
$762$	−23.3870	−0.847223
$763$	−2.87800	−0.104191
$764$	26.3687	0.953984
$765$	−55.7209	−2.01459
$766$	−8.84464	−0.319570
$767$	−24.5101	−0.885008
$768$	−2.41881	−0.0872814
$769$	20.0324	0.722386	0.361193	−	0.932491i	$-0.382370\pi$
$769$	20.0324	0.722386	0.361193	+	0.932491i	$0.382370\pi$
$770$	−6.53783	−0.235607
$771$	−71.2469	−2.56590
$772$	4.37051	0.157298
$773$	43.3755	1.56011	0.780054	−	0.625713i	$-0.215192\pi$
$773$	43.3755	1.56011	0.780054	+	0.625713i	$0.215192\pi$
$774$	1.25164	0.0449892
$775$	29.2783	1.05171
$776$	−10.3992	−0.373308
$777$	2.35268	0.0844019
$778$	−11.7131	−0.419936
$779$	26.8814	0.963126
$780$	−52.5934	−1.88315
$781$	39.7728	1.42318
$782$	−6.31365	−0.225776
$783$	−3.68927	−0.131844
$784$	−6.84485	−0.244459
$785$	53.5732	1.91211
$786$	2.41881	0.0862762
$787$	53.6923	1.91392	0.956962	−	0.290214i	$-0.0937265\pi$
$787$	53.6923	1.91392	0.956962	+	0.290214i	$0.0937265\pi$
$788$	−0.881103	−0.0313880
$789$	−54.7733	−1.94998
$790$	−29.7711	−1.05921
$791$	6.30579	0.224208
$792$	15.2831	0.543062
$793$	−57.5027	−2.04198
$794$	9.73273	0.345402
$795$	19.0813	0.676743
$796$	13.9664	0.495027
$797$	−33.6274	−1.19114	−0.595571	−	0.803303i	$-0.703074\pi$
$797$	−33.6274	−1.19114	−0.595571	+	0.803303i	$0.703074\pi$
$798$	4.46176	0.157945
$799$	37.4882	1.32624
$800$	4.58485	0.162099
$801$	−39.6153	−1.39974
$802$	−35.1737	−1.24203
$803$	−60.3303	−2.12901
$804$	22.7028	0.800667
$805$	1.21946	0.0429802
$806$	−44.8495	−1.57976
$807$	11.8125	0.415821
$808$	14.7464	0.518775
$809$	5.55594	0.195336	0.0976682	−	0.995219i	$-0.468862\pi$
$809$	5.55594	0.195336	0.0976682	+	0.995219i	$0.468862\pi$
$810$	29.1815	1.02533
$811$	−14.9975	−0.526634	−0.263317	−	0.964709i	$-0.584816\pi$
$811$	−14.9975	−0.526634	−0.263317	+	0.964709i	$0.584816\pi$
$812$	−4.02271	−0.141169
$813$	56.6736	1.98763
$814$	−13.2390	−0.464026
$815$	−61.2738	−2.14633
$816$	−15.2715	−0.534611
$817$	−2.05620	−0.0719372
$818$	−15.2179	−0.532080
$819$	−7.88596	−0.275558
$820$	17.7711	0.620593
$821$	−9.69178	−0.338246	−0.169123	−	0.985595i	$-0.554093\pi$
$821$	−9.69178	−0.338246	−0.169123	+	0.985595i	$0.554093\pi$
$822$	29.3570	1.02394
$823$	24.0738	0.839160	0.419580	−	0.907718i	$-0.362177\pi$
$823$	24.0738	0.839160	0.419580	+	0.907718i	$0.362177\pi$
$824$	−13.3431	−0.464828
$825$	−59.4558	−2.06999
$826$	1.37462	0.0478291
$827$	17.1365	0.595896	0.297948	−	0.954582i	$-0.403698\pi$
$827$	17.1365	0.595896	0.297948	+	0.954582i	$0.403698\pi$
$828$	−2.85065	−0.0990671
$829$	−21.9227	−0.761408	−0.380704	−	0.924697i	$-0.624318\pi$
$829$	−21.9227	−0.761408	−0.380704	+	0.924697i	$0.624318\pi$
$830$	46.2826	1.60649
$831$	40.9939	1.42206
$832$	−7.02322	−0.243486
$833$	−43.2160	−1.49735
$834$	4.61854	0.159927
$835$	−66.9008	−2.31520
$836$	−25.1072	−0.868349
$837$	2.30684	0.0797359
$838$	−8.41787	−0.290790
$839$	15.0329	0.518994	0.259497	−	0.965744i	$-0.416443\pi$
$839$	15.0329	0.518994	0.259497	+	0.965744i	$0.416443\pi$
$840$	2.94964	0.101772
$841$	75.3014	2.59660
$842$	6.62581	0.228341
$843$	28.1775	0.970485
$844$	4.26942	0.146960
$845$	−112.462	−3.86881
$846$	16.9261	0.581933
$847$	6.98883	0.240139
$848$	2.54808	0.0875013
$849$	−15.6628	−0.537547
$850$	28.9471	0.992879
$851$	2.46937	0.0846491
$852$	−17.9441	−0.614755
$853$	−46.3103	−1.58563	−0.792817	−	0.609459i	$-0.791386\pi$
$853$	−46.3103	−1.58563	−0.792817	+	0.609459i	$0.791386\pi$
$854$	3.22497	0.110356
$855$	41.3302	1.41346
$856$	9.15480	0.312905
$857$	−44.1378	−1.50772	−0.753859	−	0.657036i	$-0.771810\pi$
$857$	−44.1378	−1.50772	−0.753859	+	0.657036i	$0.771810\pi$
$858$	91.0763	3.10930
$859$	−19.7067	−0.672383	−0.336192	−	0.941794i	$-0.609139\pi$
$859$	−19.7067	−0.672383	−0.336192	+	0.941794i	$0.609139\pi$
$860$	−1.35934	−0.0463530
$861$	5.46887	0.186378
$862$	22.9118	0.780380
$863$	−34.3546	−1.16945	−0.584723	−	0.811233i	$-0.698797\pi$
$863$	−34.3546	−1.16945	−0.584723	+	0.811233i	$0.698797\pi$
$864$	0.361240	0.0122896
$865$	11.0088	0.374310
$866$	25.2565	0.858250
$867$	−55.2994	−1.87807
$868$	2.51533	0.0853758
$869$	51.5548	1.74888
$870$	−76.4786	−2.59287
$871$	65.9195	2.23360
$872$	−7.30663	−0.247434
$873$	−29.6444	−1.00331
$874$	4.68307	0.158407
$875$	0.506258	0.0171146
$876$	27.2189	0.919642
$877$	36.6044	1.23604	0.618022	−	0.786161i	$-0.287934\pi$
$877$	36.6044	1.23604	0.618022	+	0.786161i	$0.287934\pi$
$878$	33.1873	1.12002
$879$	−46.0522	−1.55330
$880$	−16.5982	−0.559524
$881$	27.2630	0.918515	0.459258	−	0.888303i	$-0.348116\pi$
$881$	27.2630	0.918515	0.459258	+	0.888303i	$0.348116\pi$
$882$	−19.5123	−0.657013
$883$	28.6143	0.962947	0.481473	−	0.876461i	$-0.340102\pi$
$883$	28.6143	0.962947	0.481473	+	0.876461i	$0.340102\pi$
$884$	−44.3422	−1.49139
$885$	26.1339	0.878480
$886$	−8.56351	−0.287697
$887$	−26.1131	−0.876793	−0.438396	−	0.898782i	$-0.644453\pi$
$887$	−26.1131	−0.876793	−0.438396	+	0.898782i	$0.644453\pi$
$888$	5.97296	0.200439
$889$	3.80844	0.127731
$890$	43.0241	1.44217
$891$	−50.5338	−1.69295
$892$	−6.55478	−0.219470
$893$	−27.8063	−0.930504
$894$	−45.5350	−1.52292
$895$	−21.4323	−0.716404
$896$	0.393889	0.0131589
$897$	−16.9879	−0.567208
$898$	−2.62420	−0.0875708
$899$	−65.2178	−2.17514
$900$	13.0698	0.435661
$901$	16.0877	0.535958
$902$	−30.7743	−1.02467
$903$	−0.418321	−0.0139209
$904$	16.0090	0.532453
$905$	27.1842	0.903634
$906$	−35.3925	−1.17584
$907$	16.6373	0.552433	0.276216	−	0.961095i	$-0.410919\pi$
$907$	16.6373	0.552433	0.276216	+	0.961095i	$0.410919\pi$
$908$	19.3305	0.641507
$909$	42.0368	1.39427
$910$	8.56451	0.283911
$911$	−20.6089	−0.682804	−0.341402	−	0.939917i	$-0.610902\pi$
$911$	−20.6089	−0.682804	−0.341402	+	0.939917i	$0.610902\pi$
$912$	11.3275	0.375090
$913$	−80.1479	−2.65251
$914$	18.4948	0.611753
$915$	61.3122	2.02692
$916$	20.7934	0.687032
$917$	−0.393889	−0.0130074
$918$	2.28074	0.0752757
$919$	28.4740	0.939272	0.469636	−	0.882860i	$-0.344385\pi$
$919$	28.4740	0.939272	0.469636	+	0.882860i	$0.344385\pi$
$920$	3.09594	0.102070
$921$	32.8439	1.08224
$922$	11.9614	0.393926
$923$	−52.1022	−1.71496
$924$	−5.10791	−0.168038
$925$	−11.3217	−0.372256
$926$	12.1198	0.398280
$927$	−38.0365	−1.24928
$928$	−10.2128	−0.335252
$929$	−18.9623	−0.622132	−0.311066	−	0.950388i	$-0.600686\pi$
$929$	−18.9623	−0.622132	−0.311066	+	0.950388i	$0.600686\pi$
$930$	47.8207	1.56810
$931$	32.0549	1.05056
$932$	9.08742	0.297668
$933$	−30.7768	−1.00759
$934$	−7.16148	−0.234331
$935$	−104.795	−3.42716
$936$	−20.0208	−0.654399
$937$	−32.2500	−1.05356	−0.526781	−	0.850001i	$-0.676601\pi$
$937$	−32.2500	−1.05356	−0.526781	+	0.850001i	$0.676601\pi$
$938$	−3.69702	−0.120712
$939$	−12.2195	−0.398769
$940$	−18.3826	−0.599573
$941$	39.7076	1.29443	0.647215	−	0.762308i	$-0.275934\pi$
$941$	39.7076	1.29443	0.647215	+	0.762308i	$0.275934\pi$
$942$	41.8559	1.36374
$943$	5.74013	0.186924
$944$	3.48987	0.113585
$945$	−0.440516	−0.0143300
$946$	2.35397	0.0765342
$947$	32.2226	1.04709	0.523546	−	0.851997i	$-0.324609\pi$
$947$	32.2226	1.04709	0.523546	+	0.851997i	$0.324609\pi$
$948$	−23.2597	−0.755439
$949$	79.0324	2.56550
$950$	−21.4712	−0.696616
$951$	−19.2833	−0.625304
$952$	2.48688	0.0806002
$953$	−20.7657	−0.672666	−0.336333	−	0.941743i	$-0.609187\pi$
$953$	−20.7657	−0.672666	−0.336333	+	0.941743i	$0.609187\pi$
$954$	7.26369	0.235171
$955$	−81.6358	−2.64167
$956$	7.68838	0.248660
$957$	132.439	4.28113
$958$	12.9329	0.417844
$959$	−4.78061	−0.154374
$960$	7.48850	0.241690
$961$	9.77955	0.315469
$962$	17.3430	0.559160
$963$	26.0972	0.840969
$964$	16.1849	0.521280
$965$	−13.5308	−0.435573
$966$	0.952743	0.0306540
$967$	45.5374	1.46438	0.732191	−	0.681099i	$-0.238498\pi$
$967$	45.5374	1.46438	0.732191	+	0.681099i	$0.238498\pi$
$968$	17.7431	0.570286
$969$	71.5176	2.29748
$970$	32.1952	1.03373
$971$	−4.06455	−0.130438	−0.0652188	−	0.997871i	$-0.520775\pi$
$971$	−4.06455	−0.130438	−0.0652188	+	0.997871i	$0.520775\pi$
$972$	21.7154	0.696521
$973$	−0.752102	−0.0241113
$974$	−28.1383	−0.901610
$975$	77.8867	2.49437
$976$	8.18751	0.262076
$977$	43.9567	1.40630	0.703149	−	0.711042i	$-0.251777\pi$
$977$	43.9567	1.40630	0.703149	+	0.711042i	$0.251777\pi$
$978$	−47.8723	−1.53079
$979$	−74.5051	−2.38119
$980$	21.1913	0.676930
$981$	−20.8287	−0.665008
$982$	−7.65932	−0.244419
$983$	−3.69467	−0.117842	−0.0589208	−	0.998263i	$-0.518766\pi$
$983$	−3.69467	−0.117842	−0.0589208	+	0.998263i	$0.518766\pi$
$984$	13.8843	0.442615
$985$	2.72784	0.0869163
$986$	−64.4801	−2.05347
$987$	−5.65704	−0.180066
$988$	32.8902	1.04638
$989$	−0.439070	−0.0139616
$990$	−47.3156	−1.50379
$991$	16.3852	0.520494	0.260247	−	0.965542i	$-0.416196\pi$
$991$	16.3852	0.520494	0.260247	+	0.965542i	$0.416196\pi$
$992$	6.38589	0.202752
$993$	−24.6212	−0.781329
$994$	2.92209	0.0926830
$995$	−43.2392	−1.37078
$996$	36.1599	1.14577
$997$	33.8256	1.07127	0.535634	−	0.844450i	$-0.320073\pi$
$997$	33.8256	1.07127	0.535634	+	0.844450i	$0.320073\pi$
$998$	20.3495	0.644153
$999$	−0.892036	−0.0282228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.7	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.7	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.41881 q^{3} +1.00000 q^{4} -3.09594 q^{5} -2.41881 q^{6} +0.393889 q^{7} +1.00000 q^{8} +2.85065 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.41881 q^{3} +1.00000 q^{4} -3.09594 q^{5} -2.41881 q^{6} +0.393889 q^{7} +1.00000 q^{8} +2.85065 q^{9} -3.09594 q^{10} +5.36126 q^{11} -2.41881 q^{12} -7.02322 q^{13} +0.393889 q^{14} +7.48850 q^{15} +1.00000 q^{16} +6.31365 q^{17} +2.85065 q^{18} -4.68307 q^{19} -3.09594 q^{20} -0.952743 q^{21} +5.36126 q^{22} -1.00000 q^{23} -2.41881 q^{24} +4.58485 q^{25} -7.02322 q^{26} +0.361240 q^{27} +0.393889 q^{28} -10.2128 q^{29} +7.48850 q^{30} +6.38589 q^{31} +1.00000 q^{32} -12.9679 q^{33} +6.31365 q^{34} -1.21946 q^{35} +2.85065 q^{36} -2.46937 q^{37} -4.68307 q^{38} +16.9879 q^{39} -3.09594 q^{40} -5.74013 q^{41} -0.952743 q^{42} +0.439070 q^{43} +5.36126 q^{44} -8.82546 q^{45} -1.00000 q^{46} +5.93764 q^{47} -2.41881 q^{48} -6.84485 q^{49} +4.58485 q^{50} -15.2715 q^{51} -7.02322 q^{52} +2.54808 q^{53} +0.361240 q^{54} -16.5982 q^{55} +0.393889 q^{56} +11.3275 q^{57} -10.2128 q^{58} +3.48987 q^{59} +7.48850 q^{60} +8.18751 q^{61} +6.38589 q^{62} +1.12284 q^{63} +1.00000 q^{64} +21.7435 q^{65} -12.9679 q^{66} -9.38594 q^{67} +6.31365 q^{68} +2.41881 q^{69} -1.21946 q^{70} +7.41856 q^{71} +2.85065 q^{72} -11.2530 q^{73} -2.46937 q^{74} -11.0899 q^{75} -4.68307 q^{76} +2.11174 q^{77} +16.9879 q^{78} +9.61616 q^{79} -3.09594 q^{80} -9.42573 q^{81} -5.74013 q^{82} -14.9494 q^{83} -0.952743 q^{84} -19.5467 q^{85} +0.439070 q^{86} +24.7029 q^{87} +5.36126 q^{88} -13.8969 q^{89} -8.82546 q^{90} -2.76637 q^{91} -1.00000 q^{92} -15.4463 q^{93} +5.93764 q^{94} +14.4985 q^{95} -2.41881 q^{96} -10.3992 q^{97} -6.84485 q^{98} +15.2831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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