LMFDB - Embedded newform 8026.2.a.c.1.7

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:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.97454 q^{3} +1.00000 q^{4} -1.53544 q^{5} +2.97454 q^{6} +2.95859 q^{7} -1.00000 q^{8} +5.84792 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.97454 q^{3} +1.00000 q^{4} -1.53544 q^{5} +2.97454 q^{6} +2.95859 q^{7} -1.00000 q^{8} +5.84792 q^{9} +1.53544 q^{10} +2.26074 q^{11} -2.97454 q^{12} -4.83704 q^{13} -2.95859 q^{14} +4.56724 q^{15} +1.00000 q^{16} -3.14206 q^{17} -5.84792 q^{18} -0.263091 q^{19} -1.53544 q^{20} -8.80045 q^{21} -2.26074 q^{22} -8.85129 q^{23} +2.97454 q^{24} -2.64242 q^{25} +4.83704 q^{26} -8.47126 q^{27} +2.95859 q^{28} -3.60256 q^{29} -4.56724 q^{30} -6.28055 q^{31} -1.00000 q^{32} -6.72467 q^{33} +3.14206 q^{34} -4.54273 q^{35} +5.84792 q^{36} -3.79919 q^{37} +0.263091 q^{38} +14.3880 q^{39} +1.53544 q^{40} +9.13540 q^{41} +8.80045 q^{42} +1.16297 q^{43} +2.26074 q^{44} -8.97913 q^{45} +8.85129 q^{46} -3.61093 q^{47} -2.97454 q^{48} +1.75323 q^{49} +2.64242 q^{50} +9.34619 q^{51} -4.83704 q^{52} -1.19918 q^{53} +8.47126 q^{54} -3.47123 q^{55} -2.95859 q^{56} +0.782577 q^{57} +3.60256 q^{58} -0.201132 q^{59} +4.56724 q^{60} +3.05370 q^{61} +6.28055 q^{62} +17.3016 q^{63} +1.00000 q^{64} +7.42698 q^{65} +6.72467 q^{66} -2.03601 q^{67} -3.14206 q^{68} +26.3286 q^{69} +4.54273 q^{70} -3.52574 q^{71} -5.84792 q^{72} +4.25600 q^{73} +3.79919 q^{74} +7.86001 q^{75} -0.263091 q^{76} +6.68859 q^{77} -14.3880 q^{78} -15.0798 q^{79} -1.53544 q^{80} +7.65439 q^{81} -9.13540 q^{82} +10.0626 q^{83} -8.80045 q^{84} +4.82444 q^{85} -1.16297 q^{86} +10.7160 q^{87} -2.26074 q^{88} +9.85513 q^{89} +8.97913 q^{90} -14.3108 q^{91} -8.85129 q^{92} +18.6818 q^{93} +3.61093 q^{94} +0.403961 q^{95} +2.97454 q^{96} -6.43258 q^{97} -1.75323 q^{98} +13.2206 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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
$3$	−2.97454	−1.71735	−0.858677	−	0.512517i	$-0.828713\pi$
$3$	−2.97454	−1.71735	−0.858677	+	0.512517i	$0.828713\pi$
$4$	1.00000	0.500000
$5$	−1.53544	−0.686670	−0.343335	−	0.939213i	$-0.611557\pi$
$5$	−1.53544	−0.686670	−0.343335	+	0.939213i	$0.611557\pi$
$6$	2.97454	1.21435
$7$	2.95859	1.11824	0.559120	−	0.829087i	$-0.311139\pi$
$7$	2.95859	1.11824	0.559120	+	0.829087i	$0.311139\pi$
$8$	−1.00000	−0.353553
$9$	5.84792	1.94931
$10$	1.53544	0.485549
$11$	2.26074	0.681639	0.340819	−	0.940129i	$-0.389296\pi$
$11$	2.26074	0.681639	0.340819	+	0.940129i	$0.389296\pi$
$12$	−2.97454	−0.858677
$13$	−4.83704	−1.34155	−0.670776	−	0.741660i	$-0.734039\pi$
$13$	−4.83704	−1.34155	−0.670776	+	0.741660i	$0.734039\pi$
$14$	−2.95859	−0.790716
$15$	4.56724	1.17926
$16$	1.00000	0.250000
$17$	−3.14206	−0.762061	−0.381030	−	0.924563i	$-0.624431\pi$
$17$	−3.14206	−0.762061	−0.381030	+	0.924563i	$0.624431\pi$
$18$	−5.84792	−1.37837
$19$	−0.263091	−0.0603573	−0.0301787	−	0.999545i	$-0.509608\pi$
$19$	−0.263091	−0.0603573	−0.0301787	+	0.999545i	$0.509608\pi$
$20$	−1.53544	−0.343335
$21$	−8.80045	−1.92042
$22$	−2.26074	−0.481991
$23$	−8.85129	−1.84562	−0.922811	−	0.385253i	$-0.874114\pi$
$23$	−8.85129	−1.84562	−0.922811	+	0.385253i	$0.874114\pi$
$24$	2.97454	0.607176
$25$	−2.64242	−0.528485
$26$	4.83704	0.948621
$27$	−8.47126	−1.63029
$28$	2.95859	0.559120
$29$	−3.60256	−0.668979	−0.334490	−	0.942399i	$-0.608564\pi$
$29$	−3.60256	−0.668979	−0.334490	+	0.942399i	$0.608564\pi$
$30$	−4.56724	−0.833859
$31$	−6.28055	−1.12802	−0.564010	−	0.825768i	$-0.690742\pi$
$31$	−6.28055	−1.12802	−0.564010	+	0.825768i	$0.690742\pi$
$32$	−1.00000	−0.176777
$33$	−6.72467	−1.17061
$34$	3.14206	0.538858
$35$	−4.54273	−0.767862
$36$	5.84792	0.974653
$37$	−3.79919	−0.624583	−0.312292	−	0.949986i	$-0.601097\pi$
$37$	−3.79919	−0.624583	−0.312292	+	0.949986i	$0.601097\pi$
$38$	0.263091	0.0426791
$39$	14.3880	2.30392
$40$	1.53544	0.242774
$41$	9.13540	1.42671	0.713355	−	0.700803i	$-0.247175\pi$
$41$	9.13540	1.42671	0.713355	+	0.700803i	$0.247175\pi$
$42$	8.80045	1.35794
$43$	1.16297	0.177351	0.0886753	−	0.996061i	$-0.471737\pi$
$43$	1.16297	0.177351	0.0886753	+	0.996061i	$0.471737\pi$
$44$	2.26074	0.340819
$45$	−8.97913	−1.33853
$46$	8.85129	1.30505
$47$	−3.61093	−0.526708	−0.263354	−	0.964699i	$-0.584829\pi$
$47$	−3.61093	−0.526708	−0.263354	+	0.964699i	$0.584829\pi$
$48$	−2.97454	−0.429339
$49$	1.75323	0.250462
$50$	2.64242	0.373695
$51$	9.34619	1.30873
$52$	−4.83704	−0.670776
$53$	−1.19918	−0.164720	−0.0823601	−	0.996603i	$-0.526246\pi$
$53$	−1.19918	−0.164720	−0.0823601	+	0.996603i	$0.526246\pi$
$54$	8.47126	1.15279
$55$	−3.47123	−0.468061
$56$	−2.95859	−0.395358
$57$	0.782577	0.103655
$58$	3.60256	0.473040
$59$	−0.201132	−0.0261852	−0.0130926	−	0.999914i	$-0.504168\pi$
$59$	−0.201132	−0.0261852	−0.0130926	+	0.999914i	$0.504168\pi$
$60$	4.56724	0.589628
$61$	3.05370	0.390987	0.195493	−	0.980705i	$-0.437369\pi$
$61$	3.05370	0.390987	0.195493	+	0.980705i	$0.437369\pi$
$62$	6.28055	0.797630
$63$	17.3016	2.17979
$64$	1.00000	0.125000
$65$	7.42698	0.921203
$66$	6.72467	0.827750
$67$	−2.03601	−0.248738	−0.124369	−	0.992236i	$-0.539691\pi$
$67$	−2.03601	−0.248738	−0.124369	+	0.992236i	$0.539691\pi$
$68$	−3.14206	−0.381030
$69$	26.3286	3.16959
$70$	4.54273	0.542960
$71$	−3.52574	−0.418428	−0.209214	−	0.977870i	$-0.567091\pi$
$71$	−3.52574	−0.418428	−0.209214	+	0.977870i	$0.567091\pi$
$72$	−5.84792	−0.689184
$73$	4.25600	0.498127	0.249063	−	0.968487i	$-0.419877\pi$
$73$	4.25600	0.498127	0.249063	+	0.968487i	$0.419877\pi$
$74$	3.79919	0.441647
$75$	7.86001	0.907595
$76$	−0.263091	−0.0301787
$77$	6.68859	0.762236
$78$	−14.3880	−1.62912
$79$	−15.0798	−1.69661	−0.848306	−	0.529506i	$-0.822377\pi$
$79$	−15.0798	−1.69661	−0.848306	+	0.529506i	$0.822377\pi$
$80$	−1.53544	−0.171667
$81$	7.65439	0.850487
$82$	−9.13540	−1.00884
$83$	10.0626	1.10451	0.552255	−	0.833675i	$-0.313767\pi$
$83$	10.0626	1.10451	0.552255	+	0.833675i	$0.313767\pi$
$84$	−8.80045	−0.960208
$85$	4.82444	0.523284
$86$	−1.16297	−0.125406
$87$	10.7160	1.14887
$88$	−2.26074	−0.240996
$89$	9.85513	1.04464	0.522321	−	0.852749i	$-0.325066\pi$
$89$	9.85513	1.04464	0.522321	+	0.852749i	$0.325066\pi$
$90$	8.97913	0.946483
$91$	−14.3108	−1.50018
$92$	−8.85129	−0.922811
$93$	18.6818	1.93721
$94$	3.61093	0.372439
$95$	0.403961	0.0414455
$96$	2.97454	0.303588
$97$	−6.43258	−0.653129	−0.326565	−	0.945175i	$-0.605891\pi$
$97$	−6.43258	−0.653129	−0.326565	+	0.945175i	$0.605891\pi$
$98$	−1.75323	−0.177103
$99$	13.2206	1.32872
$100$	−2.64242	−0.264242
$101$	16.4964	1.64145	0.820727	−	0.571320i	$-0.193569\pi$
$101$	16.4964	1.64145	0.820727	+	0.571320i	$0.193569\pi$
$102$	−9.34619	−0.925410
$103$	−14.1434	−1.39359	−0.696795	−	0.717270i	$-0.745391\pi$
$103$	−14.1434	−1.39359	−0.696795	+	0.717270i	$0.745391\pi$
$104$	4.83704	0.474310
$105$	13.5126	1.31869
$106$	1.19918	0.116475
$107$	−1.34614	−0.130137	−0.0650684	−	0.997881i	$-0.520727\pi$
$107$	−1.34614	−0.130137	−0.0650684	+	0.997881i	$0.520727\pi$
$108$	−8.47126	−0.815147
$109$	−7.82692	−0.749683	−0.374842	−	0.927089i	$-0.622303\pi$
$109$	−7.82692	−0.749683	−0.374842	+	0.927089i	$0.622303\pi$
$110$	3.47123	0.330969
$111$	11.3009	1.07263
$112$	2.95859	0.279560
$113$	−13.7055	−1.28931	−0.644653	−	0.764476i	$-0.722998\pi$
$113$	−13.7055	−1.28931	−0.644653	+	0.764476i	$0.722998\pi$
$114$	−0.782577	−0.0732951
$115$	13.5906	1.26733
$116$	−3.60256	−0.334490
$117$	−28.2866	−2.61510
$118$	0.201132	0.0185157
$119$	−9.29604	−0.852167
$120$	−4.56724	−0.416930
$121$	−5.88906	−0.535369
$122$	−3.05370	−0.276469
$123$	−27.1737	−2.45017
$124$	−6.28055	−0.564010
$125$	11.7345	1.04956
$126$	−17.3016	−1.54135
$127$	9.43557	0.837271	0.418636	−	0.908154i	$-0.362508\pi$
$127$	9.43557	0.837271	0.418636	+	0.908154i	$0.362508\pi$
$128$	−1.00000	−0.0883883
$129$	−3.45930	−0.304574
$130$	−7.42698	−0.651389
$131$	5.64623	0.493313	0.246657	−	0.969103i	$-0.420668\pi$
$131$	5.64623	0.493313	0.246657	+	0.969103i	$0.420668\pi$
$132$	−6.72467	−0.585307
$133$	−0.778379	−0.0674940
$134$	2.03601	0.175884
$135$	13.0071	1.11947
$136$	3.14206	0.269429
$137$	13.5632	1.15878	0.579390	−	0.815051i	$-0.303291\pi$
$137$	13.5632	1.15878	0.579390	+	0.815051i	$0.303291\pi$
$138$	−26.3286	−2.24124
$139$	−9.52432	−0.807843	−0.403921	−	0.914794i	$-0.632353\pi$
$139$	−9.52432	−0.807843	−0.403921	+	0.914794i	$0.632353\pi$
$140$	−4.54273	−0.383931
$141$	10.7409	0.904544
$142$	3.52574	0.295873
$143$	−10.9353	−0.914454
$144$	5.84792	0.487326
$145$	5.53152	0.459368
$146$	−4.25600	−0.352229
$147$	−5.21508	−0.430132
$148$	−3.79919	−0.312292
$149$	2.94318	0.241114	0.120557	−	0.992706i	$-0.461532\pi$
$149$	2.94318	0.241114	0.120557	+	0.992706i	$0.461532\pi$
$150$	−7.86001	−0.641767
$151$	−9.91628	−0.806976	−0.403488	−	0.914985i	$-0.632202\pi$
$151$	−9.91628	−0.806976	−0.403488	+	0.914985i	$0.632202\pi$
$152$	0.263091	0.0213395
$153$	−18.3745	−1.48549
$154$	−6.68859	−0.538982
$155$	9.64340	0.774577
$156$	14.3880	1.15196
$157$	−0.288245	−0.0230045	−0.0115022	−	0.999934i	$-0.503661\pi$
$157$	−0.288245	−0.0230045	−0.0115022	+	0.999934i	$0.503661\pi$
$158$	15.0798	1.19969
$159$	3.56702	0.282883
$160$	1.53544	0.121387
$161$	−26.1873	−2.06385
$162$	−7.65439	−0.601385
$163$	4.66918	0.365718	0.182859	−	0.983139i	$-0.441465\pi$
$163$	4.66918	0.365718	0.182859	+	0.983139i	$0.441465\pi$
$164$	9.13540	0.713355
$165$	10.3253	0.803826
$166$	−10.0626	−0.781006
$167$	−19.0904	−1.47726	−0.738628	−	0.674113i	$-0.764526\pi$
$167$	−19.0904	−1.47726	−0.738628	+	0.674113i	$0.764526\pi$
$168$	8.80045	0.678969
$169$	10.3969	0.799763
$170$	−4.82444	−0.370018
$171$	−1.53854	−0.117655
$172$	1.16297	0.0886753
$173$	−16.1537	−1.22814	−0.614072	−	0.789250i	$-0.710470\pi$
$173$	−16.1537	−1.22814	−0.614072	+	0.789250i	$0.710470\pi$
$174$	−10.7160	−0.812377
$175$	−7.81784	−0.590973
$176$	2.26074	0.170410
$177$	0.598277	0.0449693
$178$	−9.85513	−0.738673
$179$	5.65291	0.422518	0.211259	−	0.977430i	$-0.432244\pi$
$179$	5.65291	0.422518	0.211259	+	0.977430i	$0.432244\pi$
$180$	−8.97913	−0.669265
$181$	−3.27094	−0.243127	−0.121564	−	0.992584i	$-0.538791\pi$
$181$	−3.27094	−0.243127	−0.121564	+	0.992584i	$0.538791\pi$
$182$	14.3108	1.06079
$183$	−9.08338	−0.671463
$184$	8.85129	0.652526
$185$	5.83343	0.428882
$186$	−18.6818	−1.36981
$187$	−7.10337	−0.519450
$188$	−3.61093	−0.263354
$189$	−25.0630	−1.82306
$190$	−0.403961	−0.0293064
$191$	3.93182	0.284496	0.142248	−	0.989831i	$-0.454567\pi$
$191$	3.93182	0.284496	0.142248	+	0.989831i	$0.454567\pi$
$192$	−2.97454	−0.214669
$193$	−6.00551	−0.432286	−0.216143	−	0.976362i	$-0.569348\pi$
$193$	−6.00551	−0.432286	−0.216143	+	0.976362i	$0.569348\pi$
$194$	6.43258	0.461832
$195$	−22.0919	−1.58203
$196$	1.75323	0.125231
$197$	1.84429	0.131400	0.0657002	−	0.997839i	$-0.479072\pi$
$197$	1.84429	0.131400	0.0657002	+	0.997839i	$0.479072\pi$
$198$	−13.2206	−0.939548
$199$	−17.9639	−1.27343	−0.636715	−	0.771099i	$-0.719707\pi$
$199$	−17.9639	−1.27343	−0.636715	+	0.771099i	$0.719707\pi$
$200$	2.64242	0.186848
$201$	6.05620	0.427171
$202$	−16.4964	−1.16068
$203$	−10.6585	−0.748080
$204$	9.34619	0.654364
$205$	−14.0269	−0.979678
$206$	14.1434	0.985417
$207$	−51.7616	−3.59768
$208$	−4.83704	−0.335388
$209$	−0.594781	−0.0411419
$210$	−13.5126	−0.932455
$211$	14.5624	1.00252	0.501258	−	0.865298i	$-0.332871\pi$
$211$	14.5624	1.00252	0.501258	+	0.865298i	$0.332871\pi$
$212$	−1.19918	−0.0823601
$213$	10.4875	0.718589
$214$	1.34614	0.0920205
$215$	−1.78566	−0.121781
$216$	8.47126	0.576396
$217$	−18.5815	−1.26140
$218$	7.82692	0.530106
$219$	−12.6597	−0.855460
$220$	−3.47123	−0.234030
$221$	15.1982	1.02234
$222$	−11.3009	−0.758465
$223$	1.75474	0.117506	0.0587530	−	0.998273i	$-0.481288\pi$
$223$	1.75474	0.117506	0.0587530	+	0.998273i	$0.481288\pi$
$224$	−2.95859	−0.197679
$225$	−15.4527	−1.03018
$226$	13.7055	0.911677
$227$	21.9196	1.45485	0.727426	−	0.686186i	$-0.240717\pi$
$227$	21.9196	1.45485	0.727426	+	0.686186i	$0.240717\pi$
$228$	0.782577	0.0518274
$229$	8.38837	0.554319	0.277160	−	0.960824i	$-0.410607\pi$
$229$	8.38837	0.554319	0.277160	+	0.960824i	$0.410607\pi$
$230$	−13.5906	−0.896139
$231$	−19.8955	−1.30903
$232$	3.60256	0.236520
$233$	−24.3474	−1.59505	−0.797524	−	0.603287i	$-0.793858\pi$
$233$	−24.3474	−1.59505	−0.797524	+	0.603287i	$0.793858\pi$
$234$	28.2866	1.84915
$235$	5.54436	0.361674
$236$	−0.201132	−0.0130926
$237$	44.8556	2.91368
$238$	9.29604	0.602573
$239$	14.8808	0.962557	0.481278	−	0.876568i	$-0.340173\pi$
$239$	14.8808	0.962557	0.481278	+	0.876568i	$0.340173\pi$
$240$	4.56724	0.294814
$241$	−1.53633	−0.0989640	−0.0494820	−	0.998775i	$-0.515757\pi$
$241$	−1.53633	−0.0989640	−0.0494820	+	0.998775i	$0.515757\pi$
$242$	5.88906	0.378563
$243$	2.64546	0.169706
$244$	3.05370	0.195493
$245$	−2.69199	−0.171985
$246$	27.1737	1.73253
$247$	1.27258	0.0809725
$248$	6.28055	0.398815
$249$	−29.9316	−1.89683
$250$	−11.7345	−0.742154
$251$	20.0558	1.26591	0.632955	−	0.774188i	$-0.281842\pi$
$251$	20.0558	1.26591	0.632955	+	0.774188i	$0.281842\pi$
$252$	17.3016	1.08990
$253$	−20.0105	−1.25805
$254$	−9.43557	−0.592040
$255$	−14.3505	−0.898664
$256$	1.00000	0.0625000
$257$	3.72089	0.232103	0.116051	−	0.993243i	$-0.462976\pi$
$257$	3.72089	0.232103	0.116051	+	0.993243i	$0.462976\pi$
$258$	3.45930	0.215366
$259$	−11.2402	−0.698434
$260$	7.42698	0.460602
$261$	−21.0675	−1.30404
$262$	−5.64623	−0.348825
$263$	6.23898	0.384712	0.192356	−	0.981325i	$-0.438387\pi$
$263$	6.23898	0.384712	0.192356	+	0.981325i	$0.438387\pi$
$264$	6.72467	0.413875
$265$	1.84127	0.113108
$266$	0.778379	0.0477255
$267$	−29.3145	−1.79402
$268$	−2.03601	−0.124369
$269$	14.2782	0.870557	0.435279	−	0.900296i	$-0.356650\pi$
$269$	14.2782	0.870557	0.435279	+	0.900296i	$0.356650\pi$
$270$	−13.0071	−0.791588
$271$	8.12694	0.493676	0.246838	−	0.969057i	$-0.420608\pi$
$271$	8.12694	0.493676	0.246838	+	0.969057i	$0.420608\pi$
$272$	−3.14206	−0.190515
$273$	42.5681	2.57634
$274$	−13.5632	−0.819381
$275$	−5.97383	−0.360236
$276$	26.3286	1.58479
$277$	−10.2344	−0.614928	−0.307464	−	0.951560i	$-0.599480\pi$
$277$	−10.2344	−0.614928	−0.307464	+	0.951560i	$0.599480\pi$
$278$	9.52432	0.571231
$279$	−36.7281	−2.19885
$280$	4.54273	0.271480
$281$	4.58935	0.273778	0.136889	−	0.990586i	$-0.456290\pi$
$281$	4.58935	0.273778	0.136889	+	0.990586i	$0.456290\pi$
$282$	−10.7409	−0.639609
$283$	10.2135	0.607132	0.303566	−	0.952810i	$-0.401823\pi$
$283$	10.2135	0.607132	0.303566	+	0.952810i	$0.401823\pi$
$284$	−3.52574	−0.209214
$285$	−1.20160	−0.0711767
$286$	10.9353	0.646617
$287$	27.0279	1.59540
$288$	−5.84792	−0.344592
$289$	−7.12748	−0.419264
$290$	−5.53152	−0.324822
$291$	19.1340	1.12165
$292$	4.25600	0.249063
$293$	−22.7256	−1.32764	−0.663821	−	0.747892i	$-0.731066\pi$
$293$	−22.7256	−1.32764	−0.663821	+	0.747892i	$0.731066\pi$
$294$	5.21508	0.304149
$295$	0.308827	0.0179806
$296$	3.79919	0.220824
$297$	−19.1513	−1.11127
$298$	−2.94318	−0.170494
$299$	42.8140	2.47600
$300$	7.86001	0.453798
$301$	3.44074	0.198321
$302$	9.91628	0.570618
$303$	−49.0693	−2.81896
$304$	−0.263091	−0.0150893
$305$	−4.68878	−0.268479
$306$	18.3745	1.05040
$307$	−15.9284	−0.909084	−0.454542	−	0.890725i	$-0.650197\pi$
$307$	−15.9284	−0.909084	−0.454542	+	0.890725i	$0.650197\pi$
$308$	6.68859	0.381118
$309$	42.0702	2.39329
$310$	−9.64340	−0.547708
$311$	−13.3880	−0.759164	−0.379582	−	0.925158i	$-0.623932\pi$
$311$	−13.3880	−0.759164	−0.379582	+	0.925158i	$0.623932\pi$
$312$	−14.3880	−0.814559
$313$	−3.28866	−0.185886	−0.0929429	−	0.995671i	$-0.529627\pi$
$313$	−3.28866	−0.185886	−0.0929429	+	0.995671i	$0.529627\pi$
$314$	0.288245	0.0162666
$315$	−26.5655	−1.49680
$316$	−15.0798	−0.848306
$317$	−1.29486	−0.0727267	−0.0363633	−	0.999339i	$-0.511577\pi$
$317$	−1.29486	−0.0727267	−0.0363633	+	0.999339i	$0.511577\pi$
$318$	−3.56702	−0.200028
$319$	−8.14446	−0.456002
$320$	−1.53544	−0.0858337
$321$	4.00417	0.223491
$322$	26.1873	1.45936
$323$	0.826648	0.0459959
$324$	7.65439	0.425244
$325$	12.7815	0.708990
$326$	−4.66918	−0.258602
$327$	23.2815	1.28747
$328$	−9.13540	−0.504418
$329$	−10.6832	−0.588986
$330$	−10.3253	−0.568391
$331$	17.8412	0.980641	0.490320	−	0.871542i	$-0.336880\pi$
$331$	17.8412	0.980641	0.490320	+	0.871542i	$0.336880\pi$
$332$	10.0626	0.552255
$333$	−22.2174	−1.21750
$334$	19.0904	1.04458
$335$	3.12617	0.170801
$336$	−8.80045	−0.480104
$337$	−1.20582	−0.0656850	−0.0328425	−	0.999461i	$-0.510456\pi$
$337$	−1.20582	−0.0656850	−0.0328425	+	0.999461i	$0.510456\pi$
$338$	−10.3969	−0.565518
$339$	40.7676	2.21419
$340$	4.82444	0.261642
$341$	−14.1987	−0.768901
$342$	1.53854	0.0831946
$343$	−15.5230	−0.838164
$344$	−1.16297	−0.0627029
$345$	−40.4259	−2.17646
$346$	16.1537	0.868429
$347$	11.5032	0.617523	0.308762	−	0.951139i	$-0.400086\pi$
$347$	11.5032	0.617523	0.308762	+	0.951139i	$0.400086\pi$
$348$	10.7160	0.574437
$349$	23.2141	1.24262	0.621311	−	0.783564i	$-0.286601\pi$
$349$	23.2141	1.24262	0.621311	+	0.783564i	$0.286601\pi$
$350$	7.81784	0.417881
$351$	40.9758	2.18713
$352$	−2.26074	−0.120498
$353$	−12.8892	−0.686025	−0.343013	−	0.939331i	$-0.611447\pi$
$353$	−12.8892	−0.686025	−0.343013	+	0.939331i	$0.611447\pi$
$354$	−0.598277	−0.0317981
$355$	5.41356	0.287322
$356$	9.85513	0.522321
$357$	27.6515	1.46347
$358$	−5.65291	−0.298765
$359$	14.4667	0.763522	0.381761	−	0.924261i	$-0.375318\pi$
$359$	14.4667	0.763522	0.381761	+	0.924261i	$0.375318\pi$
$360$	8.97913	0.473242
$361$	−18.9308	−0.996357
$362$	3.27094	0.171917
$363$	17.5173	0.919418
$364$	−14.3108	−0.750089
$365$	−6.53483	−0.342048
$366$	9.08338	0.474796
$367$	4.89277	0.255401	0.127700	−	0.991813i	$-0.459240\pi$
$367$	4.89277	0.255401	0.127700	+	0.991813i	$0.459240\pi$
$368$	−8.85129	−0.461405
$369$	53.4231	2.78109
$370$	−5.83343	−0.303266
$371$	−3.54788	−0.184197
$372$	18.6818	0.968604
$373$	23.7327	1.22883	0.614416	−	0.788982i	$-0.289392\pi$
$373$	23.7327	1.22883	0.614416	+	0.788982i	$0.289392\pi$
$374$	7.10337	0.367307
$375$	−34.9047	−1.80247
$376$	3.61093	0.186219
$377$	17.4257	0.897471
$378$	25.0630	1.28910
$379$	18.7135	0.961249	0.480625	−	0.876926i	$-0.340410\pi$
$379$	18.7135	0.961249	0.480625	+	0.876926i	$0.340410\pi$
$380$	0.403961	0.0207228
$381$	−28.0665	−1.43789
$382$	−3.93182	−0.201169
$383$	17.8598	0.912592	0.456296	−	0.889828i	$-0.349176\pi$
$383$	17.8598	0.912592	0.456296	+	0.889828i	$0.349176\pi$
$384$	2.97454	0.151794
$385$	−10.2699	−0.523404
$386$	6.00551	0.305672
$387$	6.80093	0.345711
$388$	−6.43258	−0.326565
$389$	−12.8866	−0.653378	−0.326689	−	0.945132i	$-0.605933\pi$
$389$	−12.8866	−0.653378	−0.326689	+	0.945132i	$0.605933\pi$
$390$	22.0919	1.11867
$391$	27.8113	1.40648
$392$	−1.75323	−0.0885517
$393$	−16.7950	−0.847194
$394$	−1.84429	−0.0929141
$395$	23.1542	1.16501
$396$	13.2206	0.664361
$397$	−25.9858	−1.30419	−0.652095	−	0.758137i	$-0.726110\pi$
$397$	−25.9858	−1.30419	−0.652095	+	0.758137i	$0.726110\pi$
$398$	17.9639	0.900451
$399$	2.31532	0.115911
$400$	−2.64242	−0.132121
$401$	−29.3166	−1.46400	−0.732001	−	0.681303i	$-0.761414\pi$
$401$	−29.3166	−1.46400	−0.732001	+	0.681303i	$0.761414\pi$
$402$	−6.05620	−0.302056
$403$	30.3792	1.51330
$404$	16.4964	0.820727
$405$	−11.7529	−0.584004
$406$	10.6585	0.528972
$407$	−8.58898	−0.425740
$408$	−9.34619	−0.462705
$409$	5.93305	0.293370	0.146685	−	0.989183i	$-0.453140\pi$
$409$	5.93305	0.293370	0.146685	+	0.989183i	$0.453140\pi$
$410$	14.0269	0.692737
$411$	−40.3442	−1.99003
$412$	−14.1434	−0.696795
$413$	−0.595067	−0.0292814
$414$	51.7616	2.54394
$415$	−15.4505	−0.758434
$416$	4.83704	0.237155
$417$	28.3305	1.38735
$418$	0.594781	0.0290917
$419$	−6.56842	−0.320888	−0.160444	−	0.987045i	$-0.551293\pi$
$419$	−6.56842	−0.320888	−0.160444	+	0.987045i	$0.551293\pi$
$420$	13.5126	0.659346
$421$	−28.6517	−1.39640	−0.698198	−	0.715905i	$-0.746015\pi$
$421$	−28.6517	−1.39640	−0.698198	+	0.715905i	$0.746015\pi$
$422$	−14.5624	−0.708886
$423$	−21.1164	−1.02671
$424$	1.19918	0.0582374
$425$	8.30264	0.402737
$426$	−10.4875	−0.508119
$427$	9.03465	0.437217
$428$	−1.34614	−0.0650684
$429$	32.5275	1.57044
$430$	1.78566	0.0861124
$431$	−23.2400	−1.11943	−0.559717	−	0.828684i	$-0.689090\pi$
$431$	−23.2400	−1.11943	−0.559717	+	0.828684i	$0.689090\pi$
$432$	−8.47126	−0.407574
$433$	28.5938	1.37413	0.687066	−	0.726595i	$-0.258899\pi$
$433$	28.5938	1.37413	0.687066	+	0.726595i	$0.258899\pi$
$434$	18.5815	0.891942
$435$	−16.4538	−0.788897
$436$	−7.82692	−0.374842
$437$	2.32870	0.111397
$438$	12.6597	0.604902
$439$	7.41086	0.353701	0.176850	−	0.984238i	$-0.443409\pi$
$439$	7.41086	0.353701	0.176850	+	0.984238i	$0.443409\pi$
$440$	3.47123	0.165484
$441$	10.2528	0.488227
$442$	−15.1982	−0.722907
$443$	−22.8254	−1.08447	−0.542235	−	0.840227i	$-0.682422\pi$
$443$	−22.8254	−1.08447	−0.542235	+	0.840227i	$0.682422\pi$
$444$	11.3009	0.536315
$445$	−15.1320	−0.717324
$446$	−1.75474	−0.0830892
$447$	−8.75461	−0.414079
$448$	2.95859	0.139780
$449$	−10.6776	−0.503908	−0.251954	−	0.967739i	$-0.581073\pi$
$449$	−10.6776	−0.503908	−0.251954	+	0.967739i	$0.581073\pi$
$450$	15.4527	0.728446
$451$	20.6528	0.972501
$452$	−13.7055	−0.644653
$453$	29.4964	1.38586
$454$	−21.9196	−1.02874
$455$	21.9734	1.03013
$456$	−0.782577	−0.0366475
$457$	−15.1039	−0.706531	−0.353265	−	0.935523i	$-0.614929\pi$
$457$	−15.1039	−0.706531	−0.353265	+	0.935523i	$0.614929\pi$
$458$	−8.38837	−0.391963
$459$	26.6172	1.24238
$460$	13.5906	0.633666
$461$	−34.0907	−1.58776	−0.793880	−	0.608074i	$-0.791942\pi$
$461$	−34.0907	−1.58776	−0.793880	+	0.608074i	$0.791942\pi$
$462$	19.8955	0.925623
$463$	13.7867	0.640720	0.320360	−	0.947296i	$-0.396196\pi$
$463$	13.7867	0.640720	0.320360	+	0.947296i	$0.396196\pi$
$464$	−3.60256	−0.167245
$465$	−28.6847	−1.33022
$466$	24.3474	1.12787
$467$	30.9413	1.43179	0.715896	−	0.698207i	$-0.246019\pi$
$467$	30.9413	1.43179	0.715896	+	0.698207i	$0.246019\pi$
$468$	−28.2866	−1.30755
$469$	−6.02371	−0.278149
$470$	−5.54436	−0.255742
$471$	0.857399	0.0395069
$472$	0.201132	0.00925787
$473$	2.62916	0.120889
$474$	−44.8556	−2.06029
$475$	0.695199	0.0318979
$476$	−9.29604	−0.426084
$477$	−7.01271	−0.321090
$478$	−14.8808	−0.680630
$479$	19.8431	0.906655	0.453327	−	0.891344i	$-0.350237\pi$
$479$	19.8431	0.906655	0.453327	+	0.891344i	$0.350237\pi$
$480$	−4.56724	−0.208465
$481$	18.3768	0.837911
$482$	1.53633	0.0699781
$483$	77.8953	3.54436
$484$	−5.88906	−0.267684
$485$	9.87683	0.448484
$486$	−2.64546	−0.120000
$487$	−13.1744	−0.596987	−0.298494	−	0.954412i	$-0.596484\pi$
$487$	−13.1744	−0.596987	−0.298494	+	0.954412i	$0.596484\pi$
$488$	−3.05370	−0.138235
$489$	−13.8887	−0.628068
$490$	2.69199	0.121612
$491$	10.1503	0.458075	0.229038	−	0.973418i	$-0.426442\pi$
$491$	10.1503	0.458075	0.229038	+	0.973418i	$0.426442\pi$
$492$	−27.1737	−1.22508
$493$	11.3195	0.509803
$494$	−1.27258	−0.0572562
$495$	−20.2995	−0.912393
$496$	−6.28055	−0.282005
$497$	−10.4312	−0.467903
$498$	29.9316	1.34126
$499$	21.2570	0.951596	0.475798	−	0.879555i	$-0.342159\pi$
$499$	21.2570	0.951596	0.475798	+	0.879555i	$0.342159\pi$
$500$	11.7345	0.524782
$501$	56.7851	2.53697
$502$	−20.0558	−0.895134
$503$	−12.5364	−0.558971	−0.279486	−	0.960150i	$-0.590164\pi$
$503$	−12.5364	−0.558971	−0.279486	+	0.960150i	$0.590164\pi$
$504$	−17.3016	−0.770673
$505$	−25.3293	−1.12714
$506$	20.0105	0.889574
$507$	−30.9261	−1.37348
$508$	9.43557	0.418636
$509$	−9.16436	−0.406203	−0.203102	−	0.979158i	$-0.565102\pi$
$509$	−9.16436	−0.406203	−0.203102	+	0.979158i	$0.565102\pi$
$510$	14.3505	0.635451
$511$	12.5917	0.557025
$512$	−1.00000	−0.0441942
$513$	2.22872	0.0984002
$514$	−3.72089	−0.164121
$515$	21.7163	0.956936
$516$	−3.45930	−0.152287
$517$	−8.16336	−0.359024
$518$	11.2402	0.493868
$519$	48.0500	2.10916
$520$	−7.42698	−0.325695
$521$	−22.3389	−0.978685	−0.489342	−	0.872092i	$-0.662763\pi$
$521$	−22.3389	−0.978685	−0.489342	+	0.872092i	$0.662763\pi$
$522$	21.0675	0.922099
$523$	−10.9961	−0.480825	−0.240412	−	0.970671i	$-0.577283\pi$
$523$	−10.9961	−0.480825	−0.240412	+	0.970671i	$0.577283\pi$
$524$	5.64623	0.246657
$525$	23.2545	1.01491
$526$	−6.23898	−0.272032
$527$	19.7338	0.859619
$528$	−6.72467	−0.292654
$529$	55.3454	2.40632
$530$	−1.84127	−0.0799797
$531$	−1.17621	−0.0510430
$532$	−0.778379	−0.0337470
$533$	−44.1883	−1.91401
$534$	29.3145	1.26856
$535$	2.06692	0.0893609
$536$	2.03601	0.0879422
$537$	−16.8148	−0.725613
$538$	−14.2782	−0.615577
$539$	3.96361	0.170725
$540$	13.0071	0.559737
$541$	−2.96642	−0.127536	−0.0637682	−	0.997965i	$-0.520312\pi$
$541$	−2.96642	−0.127536	−0.0637682	+	0.997965i	$0.520312\pi$
$542$	−8.12694	−0.349082
$543$	9.72956	0.417535
$544$	3.14206	0.134715
$545$	12.0178	0.514785
$546$	−42.5681	−1.82175
$547$	17.2667	0.738269	0.369134	−	0.929376i	$-0.379654\pi$
$547$	17.2667	0.738269	0.369134	+	0.929376i	$0.379654\pi$
$548$	13.5632	0.579390
$549$	17.8578	0.762153
$550$	5.97383	0.254725
$551$	0.947803	0.0403778
$552$	−26.3286	−1.12062
$553$	−44.6150	−1.89722
$554$	10.2344	0.434820
$555$	−17.3518	−0.736543
$556$	−9.52432	−0.403921
$557$	−23.6211	−1.00086	−0.500429	−	0.865778i	$-0.666824\pi$
$557$	−23.6211	−1.00086	−0.500429	+	0.865778i	$0.666824\pi$
$558$	36.7281	1.55483
$559$	−5.62531	−0.237925
$560$	−4.54273	−0.191965
$561$	21.1293	0.892079
$562$	−4.58935	−0.193590
$563$	2.50221	0.105456	0.0527279	−	0.998609i	$-0.483208\pi$
$563$	2.50221	0.105456	0.0527279	+	0.998609i	$0.483208\pi$
$564$	10.7409	0.452272
$565$	21.0440	0.885327
$566$	−10.2135	−0.429307
$567$	22.6462	0.951050
$568$	3.52574	0.147937
$569$	36.3513	1.52392	0.761962	−	0.647621i	$-0.224236\pi$
$569$	36.3513	1.52392	0.761962	+	0.647621i	$0.224236\pi$
$570$	1.20160	0.0503295
$571$	46.9156	1.96336	0.981678	−	0.190547i	$-0.0610262\pi$
$571$	46.9156	1.96336	0.981678	+	0.190547i	$0.0610262\pi$
$572$	−10.9353	−0.457227
$573$	−11.6954	−0.488581
$574$	−27.0279	−1.12812
$575$	23.3889	0.975383
$576$	5.84792	0.243663
$577$	−3.70911	−0.154412	−0.0772062	−	0.997015i	$-0.524600\pi$
$577$	−3.70911	−0.154412	−0.0772062	+	0.997015i	$0.524600\pi$
$578$	7.12748	0.296464
$579$	17.8637	0.742388
$580$	5.53152	0.229684
$581$	29.7710	1.23511
$582$	−19.1340	−0.793129
$583$	−2.71104	−0.112280
$584$	−4.25600	−0.176114
$585$	43.4324	1.79571
$586$	22.7256	0.938784
$587$	32.8348	1.35524	0.677619	−	0.735413i	$-0.263012\pi$
$587$	32.8348	1.35524	0.677619	+	0.735413i	$0.263012\pi$
$588$	−5.21508	−0.215066
$589$	1.65236	0.0680842
$590$	−0.308827	−0.0127142
$591$	−5.48593	−0.225661
$592$	−3.79919	−0.156146
$593$	39.8647	1.63705	0.818523	−	0.574473i	$-0.194793\pi$
$593$	39.8647	1.63705	0.818523	+	0.574473i	$0.194793\pi$
$594$	19.1513	0.785788
$595$	14.2735	0.585157
$596$	2.94318	0.120557
$597$	53.4345	2.18693
$598$	−42.8140	−1.75080
$599$	11.6233	0.474917	0.237458	−	0.971398i	$-0.423686\pi$
$599$	11.6233	0.474917	0.237458	+	0.971398i	$0.423686\pi$
$600$	−7.86001	−0.320883
$601$	14.7108	0.600068	0.300034	−	0.953929i	$-0.403002\pi$
$601$	14.7108	0.600068	0.300034	+	0.953929i	$0.403002\pi$
$602$	−3.44074	−0.140234
$603$	−11.9064	−0.484866
$604$	−9.91628	−0.403488
$605$	9.04230	0.367622
$606$	49.0693	1.99330
$607$	34.5403	1.40195	0.700973	−	0.713188i	$-0.252749\pi$
$607$	34.5403	1.40195	0.700973	+	0.713188i	$0.252749\pi$
$608$	0.263091	0.0106698
$609$	31.7042	1.28472
$610$	4.68878	0.189843
$611$	17.4662	0.706606
$612$	−18.3745	−0.742745
$613$	16.7677	0.677239	0.338620	−	0.940923i	$-0.390040\pi$
$613$	16.7677	0.677239	0.338620	+	0.940923i	$0.390040\pi$
$614$	15.9284	0.642819
$615$	41.7235	1.68246
$616$	−6.68859	−0.269491
$617$	35.7033	1.43736	0.718680	−	0.695341i	$-0.244747\pi$
$617$	35.7033	1.43736	0.718680	+	0.695341i	$0.244747\pi$
$618$	−42.0702	−1.69231
$619$	25.0424	1.00654	0.503270	−	0.864130i	$-0.332130\pi$
$619$	25.0424	1.00654	0.503270	+	0.864130i	$0.332130\pi$
$620$	9.64340	0.387288
$621$	74.9816	3.00891
$622$	13.3880	0.536810
$623$	29.1572	1.16816
$624$	14.3880	0.575980
$625$	−4.80548	−0.192219
$626$	3.28866	0.131441
$627$	1.76920	0.0706552
$628$	−0.288245	−0.0115022
$629$	11.9373	0.475970
$630$	26.5655	1.05840
$631$	−30.1314	−1.19951	−0.599756	−	0.800183i	$-0.704736\pi$
$631$	−30.1314	−1.19951	−0.599756	+	0.800183i	$0.704736\pi$
$632$	15.0798	0.599843
$633$	−43.3165	−1.72168
$634$	1.29486	0.0514255
$635$	−14.4877	−0.574929
$636$	3.56702	0.141441
$637$	−8.48046	−0.336008
$638$	8.14446	0.322442
$639$	−20.6182	−0.815644
$640$	1.53544	0.0606936
$641$	−8.83369	−0.348910	−0.174455	−	0.984665i	$-0.555816\pi$
$641$	−8.83369	−0.348910	−0.174455	+	0.984665i	$0.555816\pi$
$642$	−4.00417	−0.158032
$643$	−45.8181	−1.80689	−0.903445	−	0.428704i	$-0.858970\pi$
$643$	−45.8181	−1.80689	−0.903445	+	0.428704i	$0.858970\pi$
$644$	−26.1873	−1.03192
$645$	5.31154	0.209142
$646$	−0.826648	−0.0325240
$647$	8.17625	0.321441	0.160721	−	0.987000i	$-0.448618\pi$
$647$	8.17625	0.321441	0.160721	+	0.987000i	$0.448618\pi$
$648$	−7.65439	−0.300693
$649$	−0.454708	−0.0178488
$650$	−12.7815	−0.501332
$651$	55.2716	2.16627
$652$	4.66918	0.182859
$653$	−6.76438	−0.264711	−0.132355	−	0.991202i	$-0.542254\pi$
$653$	−6.76438	−0.264711	−0.132355	+	0.991202i	$0.542254\pi$
$654$	−23.2815	−0.910380
$655$	−8.66945	−0.338743
$656$	9.13540	0.356677
$657$	24.8887	0.971001
$658$	10.6832	0.416476
$659$	−40.1969	−1.56585	−0.782925	−	0.622116i	$-0.786273\pi$
$659$	−40.1969	−1.56585	−0.782925	+	0.622116i	$0.786273\pi$
$660$	10.3253	0.401913
$661$	11.7887	0.458527	0.229263	−	0.973364i	$-0.426368\pi$
$661$	11.7887	0.458527	0.229263	+	0.973364i	$0.426368\pi$
$662$	−17.8412	−0.693418
$663$	−45.2078	−1.75573
$664$	−10.0626	−0.390503
$665$	1.19515	0.0463461
$666$	22.2174	0.860905
$667$	31.8873	1.23468
$668$	−19.0904	−0.738628
$669$	−5.21955	−0.201799
$670$	−3.12617	−0.120774
$671$	6.90363	0.266512
$672$	8.80045	0.339485
$673$	36.1069	1.39182	0.695910	−	0.718129i	$-0.255001\pi$
$673$	36.1069	1.39182	0.695910	+	0.718129i	$0.255001\pi$
$674$	1.20582	0.0464463
$675$	22.3847	0.861586
$676$	10.3969	0.399882
$677$	−5.94262	−0.228394	−0.114197	−	0.993458i	$-0.536429\pi$
$677$	−5.94262	−0.228394	−0.114197	+	0.993458i	$0.536429\pi$
$678$	−40.7676	−1.56567
$679$	−19.0313	−0.730355
$680$	−4.82444	−0.185009
$681$	−65.2007	−2.49850
$682$	14.1987	0.543695
$683$	9.91531	0.379399	0.189699	−	0.981842i	$-0.439249\pi$
$683$	9.91531	0.379399	0.189699	+	0.981842i	$0.439249\pi$
$684$	−1.53854	−0.0588274
$685$	−20.8254	−0.795699
$686$	15.5230	0.592671
$687$	−24.9516	−0.951962
$688$	1.16297	0.0443377
$689$	5.80048	0.220981
$690$	40.4259	1.53899
$691$	−45.4478	−1.72892	−0.864458	−	0.502704i	$-0.832338\pi$
$691$	−45.4478	−1.72892	−0.864458	+	0.502704i	$0.832338\pi$
$692$	−16.1537	−0.614072
$693$	39.1143	1.48583
$694$	−11.5032	−0.436655
$695$	14.6240	0.554721
$696$	−10.7160	−0.406188
$697$	−28.7039	−1.08724
$698$	−23.2141	−0.878666
$699$	72.4223	2.73926
$700$	−7.81784	−0.295487
$701$	−2.99171	−0.112995	−0.0564977	−	0.998403i	$-0.517993\pi$
$701$	−2.99171	−0.112995	−0.0564977	+	0.998403i	$0.517993\pi$
$702$	−40.9758	−1.54653
$703$	0.999535	0.0376982
$704$	2.26074	0.0852048
$705$	−16.4920	−0.621123
$706$	12.8892	0.485093
$707$	48.8061	1.83554
$708$	0.598277	0.0224846
$709$	27.4819	1.03210	0.516052	−	0.856557i	$-0.327401\pi$
$709$	27.4819	1.03210	0.516052	+	0.856557i	$0.327401\pi$
$710$	−5.41356	−0.203167
$711$	−88.1856	−3.30722
$712$	−9.85513	−0.369337
$713$	55.5909	2.08190
$714$	−27.6515	−1.03483
$715$	16.7905	0.627928
$716$	5.65291	0.211259
$717$	−44.2635	−1.65305
$718$	−14.4667	−0.539891
$719$	−7.13105	−0.265943	−0.132972	−	0.991120i	$-0.542452\pi$
$719$	−7.13105	−0.265943	−0.132972	+	0.991120i	$0.542452\pi$
$720$	−8.97913	−0.334632
$721$	−41.8445	−1.55837
$722$	18.9308	0.704531
$723$	4.56990	0.169956
$724$	−3.27094	−0.121564
$725$	9.51950	0.353545
$726$	−17.5173	−0.650127
$727$	−20.1777	−0.748351	−0.374176	−	0.927358i	$-0.622074\pi$
$727$	−20.1777	−0.748351	−0.374176	+	0.927358i	$0.622074\pi$
$728$	14.3108	0.530393
$729$	−30.8322	−1.14193
$730$	6.53483	0.241865
$731$	−3.65410	−0.135152
$732$	−9.08338	−0.335731
$733$	−17.3450	−0.640653	−0.320326	−	0.947307i	$-0.603793\pi$
$733$	−17.3450	−0.640653	−0.320326	+	0.947307i	$0.603793\pi$
$734$	−4.89277	−0.180596
$735$	8.00744	0.295359
$736$	8.85129	0.326263
$737$	−4.60288	−0.169549
$738$	−53.4231	−1.96653
$739$	5.36054	0.197191	0.0985954	−	0.995128i	$-0.468565\pi$
$739$	5.36054	0.197191	0.0985954	+	0.995128i	$0.468565\pi$
$740$	5.83343	0.214441
$741$	−3.78535	−0.139058
$742$	3.54788	0.130247
$743$	41.3408	1.51665	0.758324	−	0.651878i	$-0.226018\pi$
$743$	41.3408	1.51665	0.758324	+	0.651878i	$0.226018\pi$
$744$	−18.6818	−0.684907
$745$	−4.51907	−0.165566
$746$	−23.7327	−0.868915
$747$	58.8450	2.15303
$748$	−7.10337	−0.259725
$749$	−3.98269	−0.145524
$750$	34.9047	1.27454
$751$	−39.0920	−1.42649	−0.713244	−	0.700916i	$-0.752775\pi$
$751$	−39.0920	−1.42649	−0.713244	+	0.700916i	$0.752775\pi$
$752$	−3.61093	−0.131677
$753$	−59.6569	−2.17402
$754$	−17.4257	−0.634608
$755$	15.2259	0.554126
$756$	−25.0630	−0.911531
$757$	−23.3042	−0.847005	−0.423503	−	0.905895i	$-0.639200\pi$
$757$	−23.3042	−0.847005	−0.423503	+	0.905895i	$0.639200\pi$
$758$	−18.7135	−0.679706
$759$	59.5220	2.16051
$760$	−0.403961	−0.0146532
$761$	−12.4461	−0.451172	−0.225586	−	0.974223i	$-0.572430\pi$
$761$	−12.4461	−0.451172	−0.225586	+	0.974223i	$0.572430\pi$
$762$	28.0665	1.01674
$763$	−23.1566	−0.838326
$764$	3.93182	0.142248
$765$	28.2129	1.02004
$766$	−17.8598	−0.645300
$767$	0.972884	0.0351288
$768$	−2.97454	−0.107335
$769$	2.63214	0.0949175	0.0474588	−	0.998873i	$-0.484888\pi$
$769$	2.63214	0.0949175	0.0474588	+	0.998873i	$0.484888\pi$
$770$	10.2699	0.370103
$771$	−11.0679	−0.398602
$772$	−6.00551	−0.216143
$773$	2.14308	0.0770814	0.0385407	−	0.999257i	$-0.487729\pi$
$773$	2.14308	0.0770814	0.0385407	+	0.999257i	$0.487729\pi$
$774$	−6.80093	−0.244454
$775$	16.5959	0.596141
$776$	6.43258	0.230916
$777$	33.4346	1.19946
$778$	12.8866	0.462008
$779$	−2.40345	−0.0861124
$780$	−22.0919	−0.791016
$781$	−7.97077	−0.285217
$782$	−27.8113	−0.994528
$783$	30.5182	1.09063
$784$	1.75323	0.0626155
$785$	0.442584	0.0157965
$786$	16.7950	0.599056
$787$	29.8976	1.06573	0.532866	−	0.846199i	$-0.321115\pi$
$787$	29.8976	1.06573	0.532866	+	0.846199i	$0.321115\pi$
$788$	1.84429	0.0657002
$789$	−18.5581	−0.660686
$790$	−23.1542	−0.823788
$791$	−40.5489	−1.44175
$792$	−13.2206	−0.469774
$793$	−14.7709	−0.524529
$794$	25.9858	0.922202
$795$	−5.47694	−0.194247
$796$	−17.9639	−0.636715
$797$	19.2862	0.683151	0.341576	−	0.939854i	$-0.389039\pi$
$797$	19.2862	0.683151	0.341576	+	0.939854i	$0.389039\pi$
$798$	−2.31532	−0.0819615
$799$	11.3457	0.401383
$800$	2.64242	0.0934238
$801$	57.6320	2.03633
$802$	29.3166	1.03521
$803$	9.62170	0.339542
$804$	6.05620	0.213586
$805$	40.2090	1.41718
$806$	−30.3792	−1.07006
$807$	−42.4711	−1.49505
$808$	−16.4964	−0.580342
$809$	32.6295	1.14719	0.573597	−	0.819138i	$-0.305548\pi$
$809$	32.6295	1.14719	0.573597	+	0.819138i	$0.305548\pi$
$810$	11.7529	0.412953
$811$	−38.8355	−1.36370	−0.681849	−	0.731493i	$-0.738824\pi$
$811$	−38.8355	−1.36370	−0.681849	+	0.731493i	$0.738824\pi$
$812$	−10.6585	−0.374040
$813$	−24.1740	−0.847817
$814$	8.58898	0.301044
$815$	−7.16924	−0.251128
$816$	9.34619	0.327182
$817$	−0.305966	−0.0107044
$818$	−5.93305	−0.207444
$819$	−83.6883	−2.92431
$820$	−14.0269	−0.489839
$821$	9.81138	0.342420	0.171210	−	0.985235i	$-0.445232\pi$
$821$	9.81138	0.342420	0.171210	+	0.985235i	$0.445232\pi$
$822$	40.3442	1.40717
$823$	−31.0346	−1.08180	−0.540899	−	0.841088i	$-0.681916\pi$
$823$	−31.0346	−1.08180	−0.540899	+	0.841088i	$0.681916\pi$
$824$	14.1434	0.492709
$825$	17.7694	0.618652
$826$	0.595067	0.0207050
$827$	−3.27450	−0.113866	−0.0569328	−	0.998378i	$-0.518132\pi$
$827$	−3.27450	−0.113866	−0.0569328	+	0.998378i	$0.518132\pi$
$828$	−51.7616	−1.79884
$829$	31.4551	1.09248	0.546240	−	0.837628i	$-0.316058\pi$
$829$	31.4551	1.09248	0.546240	+	0.837628i	$0.316058\pi$
$830$	15.4505	0.536293
$831$	30.4428	1.05605
$832$	−4.83704	−0.167694
$833$	−5.50876	−0.190867
$834$	−28.3305	−0.981006
$835$	29.3121	1.01439
$836$	−0.594781	−0.0205709
$837$	53.2041	1.83900
$838$	6.56842	0.226902
$839$	−11.0417	−0.381201	−0.190601	−	0.981668i	$-0.561044\pi$
$839$	−11.0417	−0.381201	−0.190601	+	0.981668i	$0.561044\pi$
$840$	−13.5126	−0.466228
$841$	−16.0215	−0.552467
$842$	28.6517	0.987401
$843$	−13.6512	−0.470173
$844$	14.5624	0.501258
$845$	−15.9638	−0.549173
$846$	21.1164	0.725997
$847$	−17.4233	−0.598671
$848$	−1.19918	−0.0411801
$849$	−30.3806	−1.04266
$850$	−8.30264	−0.284778
$851$	33.6278	1.15274
$852$	10.4875	0.359295
$853$	10.4281	0.357053	0.178526	−	0.983935i	$-0.442867\pi$
$853$	10.4281	0.357053	0.178526	+	0.983935i	$0.442867\pi$
$854$	−9.03465	−0.309159
$855$	2.36233	0.0807900
$856$	1.34614	0.0460103
$857$	−1.19144	−0.0406989	−0.0203495	−	0.999793i	$-0.506478\pi$
$857$	−1.19144	−0.0406989	−0.0203495	+	0.999793i	$0.506478\pi$
$858$	−32.5275	−1.11047
$859$	−13.5705	−0.463020	−0.231510	−	0.972833i	$-0.574367\pi$
$859$	−13.5705	−0.463020	−0.231510	+	0.972833i	$0.574367\pi$
$860$	−1.78566	−0.0608907
$861$	−80.3956	−2.73988
$862$	23.2400	0.791559
$863$	2.17410	0.0740072	0.0370036	−	0.999315i	$-0.488219\pi$
$863$	2.17410	0.0740072	0.0370036	+	0.999315i	$0.488219\pi$
$864$	8.47126	0.288198
$865$	24.8031	0.843330
$866$	−28.5938	−0.971657
$867$	21.2010	0.720024
$868$	−18.5815	−0.630698
$869$	−34.0915	−1.15648
$870$	16.4538	0.557835
$871$	9.84825	0.333695
$872$	7.82692	0.265053
$873$	−37.6172	−1.27315
$874$	−2.32870	−0.0787694
$875$	34.7175	1.17367
$876$	−12.6597	−0.427730
$877$	−27.4594	−0.927237	−0.463619	−	0.886035i	$-0.653449\pi$
$877$	−27.4594	−0.927237	−0.463619	+	0.886035i	$0.653449\pi$
$878$	−7.41086	−0.250104
$879$	67.5982	2.28003
$880$	−3.47123	−0.117015
$881$	19.0342	0.641280	0.320640	−	0.947201i	$-0.396102\pi$
$881$	19.0342	0.641280	0.320640	+	0.947201i	$0.396102\pi$
$882$	−10.2528	−0.345229
$883$	32.2329	1.08472	0.542362	−	0.840145i	$-0.317530\pi$
$883$	32.2329	1.08472	0.542362	+	0.840145i	$0.317530\pi$
$884$	15.1982	0.511172
$885$	−0.918619	−0.0308790
$886$	22.8254	0.766835
$887$	53.8692	1.80875	0.904376	−	0.426737i	$-0.140337\pi$
$887$	53.8692	1.80875	0.904376	+	0.426737i	$0.140337\pi$
$888$	−11.3009	−0.379232
$889$	27.9159	0.936271
$890$	15.1320	0.507224
$891$	17.3046	0.579725
$892$	1.75474	0.0587530
$893$	0.950004	0.0317907
$894$	8.75461	0.292798
$895$	−8.67970	−0.290130
$896$	−2.95859	−0.0988394
$897$	−127.352	−4.25217
$898$	10.6776	0.356317
$899$	22.6261	0.754621
$900$	−15.4527	−0.515089
$901$	3.76789	0.125527
$902$	−20.6528	−0.687662
$903$	−10.2346	−0.340587
$904$	13.7055	0.455838
$905$	5.02233	0.166948
$906$	−29.4964	−0.979953
$907$	−3.76378	−0.124974	−0.0624871	−	0.998046i	$-0.519903\pi$
$907$	−3.76378	−0.124974	−0.0624871	+	0.998046i	$0.519903\pi$
$908$	21.9196	0.727426
$909$	96.4697	3.19970
$910$	−21.9734	−0.728410
$911$	20.8946	0.692268	0.346134	−	0.938185i	$-0.387494\pi$
$911$	20.8946	0.692268	0.346134	+	0.938185i	$0.387494\pi$
$912$	0.782577	0.0259137
$913$	22.7488	0.752877
$914$	15.1039	0.499593
$915$	13.9470	0.461073
$916$	8.38837	0.277160
$917$	16.7049	0.551643
$918$	−26.6172	−0.878498
$919$	1.13217	0.0373469	0.0186734	−	0.999826i	$-0.494056\pi$
$919$	1.13217	0.0373469	0.0186734	+	0.999826i	$0.494056\pi$
$920$	−13.5906	−0.448070
$921$	47.3799	1.56122
$922$	34.0907	1.12272
$923$	17.0541	0.561343
$924$	−19.8955	−0.654515
$925$	10.0391	0.330083
$926$	−13.7867	−0.453058
$927$	−82.7094	−2.71653
$928$	3.60256	0.118260
$929$	−31.1370	−1.02157	−0.510786	−	0.859708i	$-0.670646\pi$
$929$	−31.1370	−1.02157	−0.510786	+	0.859708i	$0.670646\pi$
$930$	28.6847	0.940609
$931$	−0.461261	−0.0151172
$932$	−24.3474	−0.797524
$933$	39.8232	1.30375
$934$	−30.9413	−1.01243
$935$	10.9068	0.356690
$936$	28.2866	0.924576
$937$	−14.6346	−0.478093	−0.239047	−	0.971008i	$-0.576835\pi$
$937$	−14.6346	−0.478093	−0.239047	+	0.971008i	$0.576835\pi$
$938$	6.02371	0.196681
$939$	9.78226	0.319232
$940$	5.54436	0.180837
$941$	57.2534	1.86641	0.933204	−	0.359347i	$-0.117001\pi$
$941$	57.2534	1.86641	0.933204	+	0.359347i	$0.117001\pi$
$942$	−0.857399	−0.0279356
$943$	−80.8601	−2.63317
$944$	−0.201132	−0.00654630
$945$	38.4827	1.25184
$946$	−2.62916	−0.0854815
$947$	−48.3801	−1.57214	−0.786071	−	0.618136i	$-0.787888\pi$
$947$	−48.3801	−1.57214	−0.786071	+	0.618136i	$0.787888\pi$
$948$	44.8556	1.45684
$949$	−20.5864	−0.668263
$950$	−0.695199	−0.0225552
$951$	3.85162	0.124897
$952$	9.29604	0.301287
$953$	8.92387	0.289072	0.144536	−	0.989500i	$-0.453831\pi$
$953$	8.92387	0.289072	0.144536	+	0.989500i	$0.453831\pi$
$954$	7.01271	0.227045
$955$	−6.03707	−0.195355
$956$	14.8808	0.481278
$957$	24.2261	0.783117
$958$	−19.8431	−0.641102
$959$	40.1278	1.29579
$960$	4.56724	0.147407
$961$	8.44525	0.272428
$962$	−18.3768	−0.592493
$963$	−7.87214	−0.253676
$964$	−1.53633	−0.0494820
$965$	9.22110	0.296838
$966$	−77.8953	−2.50624
$967$	−2.16174	−0.0695168	−0.0347584	−	0.999396i	$-0.511066\pi$
$967$	−2.16174	−0.0695168	−0.0347584	+	0.999396i	$0.511066\pi$
$968$	5.88906	0.189281
$969$	−2.45890	−0.0789913
$970$	−9.87683	−0.317126
$971$	−39.4708	−1.26668	−0.633339	−	0.773875i	$-0.718316\pi$
$971$	−39.4708	−1.26668	−0.633339	+	0.773875i	$0.718316\pi$
$972$	2.64546	0.0848531
$973$	−28.1785	−0.903362
$974$	13.1744	0.422134
$975$	−38.0191	−1.21759
$976$	3.05370	0.0977467
$977$	36.9843	1.18323	0.591617	−	0.806219i	$-0.298490\pi$
$977$	36.9843	1.18323	0.591617	+	0.806219i	$0.298490\pi$
$978$	13.8887	0.444111
$979$	22.2799	0.712068
$980$	−2.69199	−0.0859924
$981$	−45.7712	−1.46136
$982$	−10.1503	−0.323908
$983$	13.2316	0.422023	0.211011	−	0.977484i	$-0.432324\pi$
$983$	13.2316	0.422023	0.211011	+	0.977484i	$0.432324\pi$
$984$	27.1737	0.866265
$985$	−2.83180	−0.0902286
$986$	−11.3195	−0.360485
$987$	31.7778	1.01150
$988$	1.27258	0.0404863
$989$	−10.2938	−0.327322
$990$	20.2995	0.645159
$991$	8.60901	0.273474	0.136737	−	0.990607i	$-0.456338\pi$
$991$	8.60901	0.273474	0.136737	+	0.990607i	$0.456338\pi$
$992$	6.28055	0.199408
$993$	−53.0694	−1.68411
$994$	10.4312	0.330858
$995$	27.5826	0.874426
$996$	−29.9316	−0.948417
$997$	−7.91219	−0.250582	−0.125291	−	0.992120i	$-0.539986\pi$
$997$	−7.91219	−0.250582	−0.125291	+	0.992120i	$0.539986\pi$
$998$	−21.2570	−0.672880
$999$	32.1839	1.01825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.7	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.7	✓	86	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.97454 q^{3} +1.00000 q^{4} -1.53544 q^{5} +2.97454 q^{6} +2.95859 q^{7} -1.00000 q^{8} +5.84792 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.97454 q^{3} +1.00000 q^{4} -1.53544 q^{5} +2.97454 q^{6} +2.95859 q^{7} -1.00000 q^{8} +5.84792 q^{9} +1.53544 q^{10} +2.26074 q^{11} -2.97454 q^{12} -4.83704 q^{13} -2.95859 q^{14} +4.56724 q^{15} +1.00000 q^{16} -3.14206 q^{17} -5.84792 q^{18} -0.263091 q^{19} -1.53544 q^{20} -8.80045 q^{21} -2.26074 q^{22} -8.85129 q^{23} +2.97454 q^{24} -2.64242 q^{25} +4.83704 q^{26} -8.47126 q^{27} +2.95859 q^{28} -3.60256 q^{29} -4.56724 q^{30} -6.28055 q^{31} -1.00000 q^{32} -6.72467 q^{33} +3.14206 q^{34} -4.54273 q^{35} +5.84792 q^{36} -3.79919 q^{37} +0.263091 q^{38} +14.3880 q^{39} +1.53544 q^{40} +9.13540 q^{41} +8.80045 q^{42} +1.16297 q^{43} +2.26074 q^{44} -8.97913 q^{45} +8.85129 q^{46} -3.61093 q^{47} -2.97454 q^{48} +1.75323 q^{49} +2.64242 q^{50} +9.34619 q^{51} -4.83704 q^{52} -1.19918 q^{53} +8.47126 q^{54} -3.47123 q^{55} -2.95859 q^{56} +0.782577 q^{57} +3.60256 q^{58} -0.201132 q^{59} +4.56724 q^{60} +3.05370 q^{61} +6.28055 q^{62} +17.3016 q^{63} +1.00000 q^{64} +7.42698 q^{65} +6.72467 q^{66} -2.03601 q^{67} -3.14206 q^{68} +26.3286 q^{69} +4.54273 q^{70} -3.52574 q^{71} -5.84792 q^{72} +4.25600 q^{73} +3.79919 q^{74} +7.86001 q^{75} -0.263091 q^{76} +6.68859 q^{77} -14.3880 q^{78} -15.0798 q^{79} -1.53544 q^{80} +7.65439 q^{81} -9.13540 q^{82} +10.0626 q^{83} -8.80045 q^{84} +4.82444 q^{85} -1.16297 q^{86} +10.7160 q^{87} -2.26074 q^{88} +9.85513 q^{89} +8.97913 q^{90} -14.3108 q^{91} -8.85129 q^{92} +18.6818 q^{93} +3.61093 q^{94} +0.403961 q^{95} +2.97454 q^{96} -6.43258 q^{97} -1.75323 q^{98} +13.2206 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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