LMFDB - Embedded newform 8002.2.a.e.1.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, 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("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.730818 q^{3} +1.00000 q^{4} +4.20821 q^{5} +0.730818 q^{6} +4.20254 q^{7} -1.00000 q^{8} -2.46590 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.730818 q^{3} +1.00000 q^{4} +4.20821 q^{5} +0.730818 q^{6} +4.20254 q^{7} -1.00000 q^{8} -2.46590 q^{9} -4.20821 q^{10} -4.30363 q^{11} -0.730818 q^{12} -3.98181 q^{13} -4.20254 q^{14} -3.07544 q^{15} +1.00000 q^{16} +4.97753 q^{17} +2.46590 q^{18} +0.292843 q^{19} +4.20821 q^{20} -3.07129 q^{21} +4.30363 q^{22} +2.11769 q^{23} +0.730818 q^{24} +12.7091 q^{25} +3.98181 q^{26} +3.99458 q^{27} +4.20254 q^{28} -3.80342 q^{29} +3.07544 q^{30} -1.14507 q^{31} -1.00000 q^{32} +3.14517 q^{33} -4.97753 q^{34} +17.6852 q^{35} -2.46590 q^{36} -0.610692 q^{37} -0.292843 q^{38} +2.90998 q^{39} -4.20821 q^{40} +2.12764 q^{41} +3.07129 q^{42} +3.68546 q^{43} -4.30363 q^{44} -10.3771 q^{45} -2.11769 q^{46} -1.73674 q^{47} -0.730818 q^{48} +10.6613 q^{49} -12.7091 q^{50} -3.63767 q^{51} -3.98181 q^{52} -4.66241 q^{53} -3.99458 q^{54} -18.1106 q^{55} -4.20254 q^{56} -0.214015 q^{57} +3.80342 q^{58} +6.48533 q^{59} -3.07544 q^{60} -1.39282 q^{61} +1.14507 q^{62} -10.3631 q^{63} +1.00000 q^{64} -16.7563 q^{65} -3.14517 q^{66} -9.49023 q^{67} +4.97753 q^{68} -1.54765 q^{69} -17.6852 q^{70} +4.53305 q^{71} +2.46590 q^{72} +7.20743 q^{73} +0.610692 q^{74} -9.28801 q^{75} +0.292843 q^{76} -18.0862 q^{77} -2.90998 q^{78} +6.92468 q^{79} +4.20821 q^{80} +4.47840 q^{81} -2.12764 q^{82} +4.56015 q^{83} -3.07129 q^{84} +20.9465 q^{85} -3.68546 q^{86} +2.77961 q^{87} +4.30363 q^{88} +14.1013 q^{89} +10.3771 q^{90} -16.7337 q^{91} +2.11769 q^{92} +0.836840 q^{93} +1.73674 q^{94} +1.23235 q^{95} +0.730818 q^{96} -3.12656 q^{97} -10.6613 q^{98} +10.6123 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * 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
$3$	−0.730818	−0.421938	−0.210969	−	0.977493i	$-0.567662\pi$
$3$	−0.730818	−0.421938	−0.210969	+	0.977493i	$0.567662\pi$
$4$	1.00000	0.500000
$5$	4.20821	1.88197	0.940985	−	0.338448i	$-0.109902\pi$
$5$	4.20821	1.88197	0.940985	+	0.338448i	$0.109902\pi$
$6$	0.730818	0.298355
$7$	4.20254	1.58841	0.794205	−	0.607650i	$-0.207888\pi$
$7$	4.20254	1.58841	0.794205	+	0.607650i	$0.207888\pi$
$8$	−1.00000	−0.353553
$9$	−2.46590	−0.821968
$10$	−4.20821	−1.33075
$11$	−4.30363	−1.29759	−0.648797	−	0.760962i	$-0.724728\pi$
$11$	−4.30363	−1.29759	−0.648797	+	0.760962i	$0.724728\pi$
$12$	−0.730818	−0.210969
$13$	−3.98181	−1.10435	−0.552177	−	0.833727i	$-0.686203\pi$
$13$	−3.98181	−1.10435	−0.552177	+	0.833727i	$0.686203\pi$
$14$	−4.20254	−1.12318
$15$	−3.07544	−0.794075
$16$	1.00000	0.250000
$17$	4.97753	1.20723	0.603614	−	0.797277i	$-0.293727\pi$
$17$	4.97753	1.20723	0.603614	+	0.797277i	$0.293727\pi$
$18$	2.46590	0.581219
$19$	0.292843	0.0671828	0.0335914	−	0.999436i	$-0.489306\pi$
$19$	0.292843	0.0671828	0.0335914	+	0.999436i	$0.489306\pi$
$20$	4.20821	0.940985
$21$	−3.07129	−0.670211
$22$	4.30363	0.917537
$23$	2.11769	0.441569	0.220784	−	0.975323i	$-0.429138\pi$
$23$	2.11769	0.441569	0.220784	+	0.975323i	$0.429138\pi$
$24$	0.730818	0.149178
$25$	12.7091	2.54181
$26$	3.98181	0.780897
$27$	3.99458	0.768758
$28$	4.20254	0.794205
$29$	−3.80342	−0.706277	−0.353138	−	0.935571i	$-0.614886\pi$
$29$	−3.80342	−0.706277	−0.353138	+	0.935571i	$0.614886\pi$
$30$	3.07544	0.561496
$31$	−1.14507	−0.205661	−0.102831	−	0.994699i	$-0.532790\pi$
$31$	−1.14507	−0.205661	−0.102831	+	0.994699i	$0.532790\pi$
$32$	−1.00000	−0.176777
$33$	3.14517	0.547504
$34$	−4.97753	−0.853639
$35$	17.6852	2.98934
$36$	−2.46590	−0.410984
$37$	−0.610692	−0.100397	−0.0501986	−	0.998739i	$-0.515985\pi$
$37$	−0.610692	−0.100397	−0.0501986	+	0.998739i	$0.515985\pi$
$38$	−0.292843	−0.0475054
$39$	2.90998	0.465969
$40$	−4.20821	−0.665377
$41$	2.12764	0.332281	0.166141	−	0.986102i	$-0.446869\pi$
$41$	2.12764	0.332281	0.166141	+	0.986102i	$0.446869\pi$
$42$	3.07129	0.473910
$43$	3.68546	0.562028	0.281014	−	0.959704i	$-0.409329\pi$
$43$	3.68546	0.562028	0.281014	+	0.959704i	$0.409329\pi$
$44$	−4.30363	−0.648797
$45$	−10.3771	−1.54692
$46$	−2.11769	−0.312236
$47$	−1.73674	−0.253329	−0.126665	−	0.991946i	$-0.540427\pi$
$47$	−1.73674	−0.253329	−0.126665	+	0.991946i	$0.540427\pi$
$48$	−0.730818	−0.105485
$49$	10.6613	1.52305
$50$	−12.7091	−1.79733
$51$	−3.63767	−0.509376
$52$	−3.98181	−0.552177
$53$	−4.66241	−0.640432	−0.320216	−	0.947345i	$-0.603755\pi$
$53$	−4.66241	−0.640432	−0.320216	+	0.947345i	$0.603755\pi$
$54$	−3.99458	−0.543594
$55$	−18.1106	−2.44203
$56$	−4.20254	−0.561588
$57$	−0.214015	−0.0283470
$58$	3.80342	0.499413
$59$	6.48533	0.844318	0.422159	−	0.906522i	$-0.361272\pi$
$59$	6.48533	0.844318	0.422159	+	0.906522i	$0.361272\pi$
$60$	−3.07544	−0.397037
$61$	−1.39282	−0.178332	−0.0891660	−	0.996017i	$-0.528420\pi$
$61$	−1.39282	−0.178332	−0.0891660	+	0.996017i	$0.528420\pi$
$62$	1.14507	0.145424
$63$	−10.3631	−1.30562
$64$	1.00000	0.125000
$65$	−16.7563	−2.07836
$66$	−3.14517	−0.387144
$67$	−9.49023	−1.15942	−0.579708	−	0.814824i	$-0.696833\pi$
$67$	−9.49023	−1.15942	−0.579708	+	0.814824i	$0.696833\pi$
$68$	4.97753	0.603614
$69$	−1.54765	−0.186315
$70$	−17.6852	−2.11378
$71$	4.53305	0.537975	0.268987	−	0.963144i	$-0.413311\pi$
$71$	4.53305	0.537975	0.268987	+	0.963144i	$0.413311\pi$
$72$	2.46590	0.290610
$73$	7.20743	0.843566	0.421783	−	0.906697i	$-0.361404\pi$
$73$	7.20743	0.843566	0.421783	+	0.906697i	$0.361404\pi$
$74$	0.610692	0.0709915
$75$	−9.28801	−1.07249
$76$	0.292843	0.0335914
$77$	−18.0862	−2.06111
$78$	−2.90998	−0.329490
$79$	6.92468	0.779087	0.389544	−	0.921008i	$-0.372633\pi$
$79$	6.92468	0.779087	0.389544	+	0.921008i	$0.372633\pi$
$80$	4.20821	0.470493
$81$	4.47840	0.497600
$82$	−2.12764	−0.234958
$83$	4.56015	0.500541	0.250271	−	0.968176i	$-0.419480\pi$
$83$	4.56015	0.500541	0.250271	+	0.968176i	$0.419480\pi$
$84$	−3.07129	−0.335105
$85$	20.9465	2.27197
$86$	−3.68546	−0.397413
$87$	2.77961	0.298005
$88$	4.30363	0.458769
$89$	14.1013	1.49474	0.747369	−	0.664409i	$-0.231317\pi$
$89$	14.1013	1.49474	0.747369	+	0.664409i	$0.231317\pi$
$90$	10.3771	1.09384
$91$	−16.7337	−1.75417
$92$	2.11769	0.220784
$93$	0.836840	0.0867763
$94$	1.73674	0.179131
$95$	1.23235	0.126436
$96$	0.730818	0.0745888
$97$	−3.12656	−0.317454	−0.158727	−	0.987323i	$-0.550739\pi$
$97$	−3.12656	−0.317454	−0.158727	+	0.987323i	$0.550739\pi$
$98$	−10.6613	−1.07696
$99$	10.6123	1.06658
$100$	12.7091	1.27091
$101$	−1.87471	−0.186540	−0.0932702	−	0.995641i	$-0.529732\pi$
$101$	−1.87471	−0.186540	−0.0932702	+	0.995641i	$0.529732\pi$
$102$	3.63767	0.360183
$103$	3.16643	0.311997	0.155999	−	0.987757i	$-0.450140\pi$
$103$	3.16643	0.311997	0.155999	+	0.987757i	$0.450140\pi$
$104$	3.98181	0.390448
$105$	−12.9246	−1.26132
$106$	4.66241	0.452854
$107$	15.8421	1.53152	0.765758	−	0.643129i	$-0.222364\pi$
$107$	15.8421	1.53152	0.765758	+	0.643129i	$0.222364\pi$
$108$	3.99458	0.384379
$109$	−6.73060	−0.644675	−0.322337	−	0.946625i	$-0.604469\pi$
$109$	−6.73060	−0.644675	−0.322337	+	0.946625i	$0.604469\pi$
$110$	18.1106	1.72678
$111$	0.446305	0.0423614
$112$	4.20254	0.397102
$113$	−8.20510	−0.771871	−0.385935	−	0.922526i	$-0.626121\pi$
$113$	−8.20510	−0.771871	−0.385935	+	0.922526i	$0.626121\pi$
$114$	0.214015	0.0200443
$115$	8.91169	0.831020
$116$	−3.80342	−0.353138
$117$	9.81876	0.907745
$118$	−6.48533	−0.597023
$119$	20.9183	1.91757
$120$	3.07544	0.280748
$121$	7.52125	0.683750
$122$	1.39282	0.126100
$123$	−1.55492	−0.140202
$124$	−1.14507	−0.102831
$125$	32.4414	2.90165
$126$	10.3631	0.923214
$127$	12.7349	1.13004	0.565021	−	0.825077i	$-0.308868\pi$
$127$	12.7349	1.13004	0.565021	+	0.825077i	$0.308868\pi$
$128$	−1.00000	−0.0883883
$129$	−2.69340	−0.237141
$130$	16.7563	1.46962
$131$	−14.1615	−1.23730	−0.618649	−	0.785667i	$-0.712320\pi$
$131$	−14.1615	−1.23730	−0.618649	+	0.785667i	$0.712320\pi$
$132$	3.14517	0.273752
$133$	1.23068	0.106714
$134$	9.49023	0.819831
$135$	16.8101	1.44678
$136$	−4.97753	−0.426820
$137$	12.8583	1.09856	0.549281	−	0.835638i	$-0.314902\pi$
$137$	12.8583	1.09856	0.549281	+	0.835638i	$0.314902\pi$
$138$	1.54765	0.131744
$139$	18.3891	1.55974	0.779871	−	0.625940i	$-0.215285\pi$
$139$	18.3891	1.55974	0.779871	+	0.625940i	$0.215285\pi$
$140$	17.6852	1.49467
$141$	1.26924	0.106889
$142$	−4.53305	−0.380405
$143$	17.1362	1.43300
$144$	−2.46590	−0.205492
$145$	−16.0056	−1.32919
$146$	−7.20743	−0.596491
$147$	−7.79148	−0.642631
$148$	−0.610692	−0.0501986
$149$	8.29894	0.679876	0.339938	−	0.940448i	$-0.389594\pi$
$149$	8.29894	0.679876	0.339938	+	0.940448i	$0.389594\pi$
$150$	9.28801	0.758363
$151$	−4.00226	−0.325699	−0.162850	−	0.986651i	$-0.552069\pi$
$151$	−4.00226	−0.325699	−0.162850	+	0.986651i	$0.552069\pi$
$152$	−0.292843	−0.0237527
$153$	−12.2741	−0.992303
$154$	18.0862	1.45743
$155$	−4.81871	−0.387048
$156$	2.90998	0.232985
$157$	−5.24816	−0.418849	−0.209425	−	0.977825i	$-0.567159\pi$
$157$	−5.24816	−0.418849	−0.209425	+	0.977825i	$0.567159\pi$
$158$	−6.92468	−0.550898
$159$	3.40738	0.270222
$160$	−4.20821	−0.332688
$161$	8.89967	0.701392
$162$	−4.47840	−0.351856
$163$	−7.52173	−0.589148	−0.294574	−	0.955629i	$-0.595178\pi$
$163$	−7.52173	−0.589148	−0.294574	+	0.955629i	$0.595178\pi$
$164$	2.12764	0.166141
$165$	13.2356	1.03039
$166$	−4.56015	−0.353936
$167$	−15.6056	−1.20760	−0.603798	−	0.797137i	$-0.706347\pi$
$167$	−15.6056	−1.20760	−0.603798	+	0.797137i	$0.706347\pi$
$168$	3.07129	0.236955
$169$	2.85479	0.219600
$170$	−20.9465	−1.60652
$171$	−0.722123	−0.0552221
$172$	3.68546	0.281014
$173$	20.2959	1.54307	0.771533	−	0.636190i	$-0.219490\pi$
$173$	20.2959	1.54307	0.771533	+	0.636190i	$0.219490\pi$
$174$	−2.77961	−0.210721
$175$	53.4103	4.03744
$176$	−4.30363	−0.324398
$177$	−4.73960	−0.356250
$178$	−14.1013	−1.05694
$179$	2.08953	0.156179	0.0780893	−	0.996946i	$-0.475118\pi$
$179$	2.08953	0.156179	0.0780893	+	0.996946i	$0.475118\pi$
$180$	−10.3771	−0.773460
$181$	0.321744	0.0239150	0.0119575	−	0.999929i	$-0.496194\pi$
$181$	0.321744	0.0239150	0.0119575	+	0.999929i	$0.496194\pi$
$182$	16.7337	1.24038
$183$	1.01790	0.0752451
$184$	−2.11769	−0.156118
$185$	−2.56992	−0.188944
$186$	−0.836840	−0.0613601
$187$	−21.4215	−1.56649
$188$	−1.73674	−0.126665
$189$	16.7874	1.22110
$190$	−1.23235	−0.0894037
$191$	22.0060	1.59230	0.796148	−	0.605102i	$-0.206868\pi$
$191$	22.0060	1.59230	0.796148	+	0.605102i	$0.206868\pi$
$192$	−0.730818	−0.0527423
$193$	15.6403	1.12581	0.562906	−	0.826521i	$-0.309683\pi$
$193$	15.6403	1.12581	0.562906	+	0.826521i	$0.309683\pi$
$194$	3.12656	0.224474
$195$	12.2458	0.876940
$196$	10.6613	0.761523
$197$	−3.98375	−0.283830	−0.141915	−	0.989879i	$-0.545326\pi$
$197$	−3.98375	−0.283830	−0.141915	+	0.989879i	$0.545326\pi$
$198$	−10.6123	−0.754187
$199$	2.16747	0.153648	0.0768239	−	0.997045i	$-0.475522\pi$
$199$	2.16747	0.153648	0.0768239	+	0.997045i	$0.475522\pi$
$200$	−12.7091	−0.898666
$201$	6.93563	0.489202
$202$	1.87471	0.131904
$203$	−15.9840	−1.12186
$204$	−3.63767	−0.254688
$205$	8.95355	0.625343
$206$	−3.16643	−0.220615
$207$	−5.22202	−0.362956
$208$	−3.98181	−0.276089
$209$	−1.26029	−0.0871760
$210$	12.9246	0.891885
$211$	11.2801	0.776553	0.388276	−	0.921543i	$-0.373071\pi$
$211$	11.2801	0.776553	0.388276	+	0.921543i	$0.373071\pi$
$212$	−4.66241	−0.320216
$213$	−3.31284	−0.226992
$214$	−15.8421	−1.08295
$215$	15.5092	1.05772
$216$	−3.99458	−0.271797
$217$	−4.81221	−0.326674
$218$	6.73060	0.455854
$219$	−5.26732	−0.355933
$220$	−18.1106	−1.22102
$221$	−19.8196	−1.33321
$222$	−0.446305	−0.0299540
$223$	14.0294	0.939479	0.469739	−	0.882805i	$-0.344348\pi$
$223$	14.0294	0.939479	0.469739	+	0.882805i	$0.344348\pi$
$224$	−4.20254	−0.280794
$225$	−31.3393	−2.08929
$226$	8.20510	0.545795
$227$	−12.3724	−0.821182	−0.410591	−	0.911820i	$-0.634678\pi$
$227$	−12.3724	−0.821182	−0.410591	+	0.911820i	$0.634678\pi$
$228$	−0.214015	−0.0141735
$229$	−10.2501	−0.677345	−0.338673	−	0.940904i	$-0.609978\pi$
$229$	−10.2501	−0.677345	−0.338673	+	0.940904i	$0.609978\pi$
$230$	−8.91169	−0.587620
$231$	13.2177	0.869661
$232$	3.80342	0.249707
$233$	−5.83236	−0.382091	−0.191045	−	0.981581i	$-0.561188\pi$
$233$	−5.83236	−0.382091	−0.191045	+	0.981581i	$0.561188\pi$
$234$	−9.81876	−0.641872
$235$	−7.30856	−0.476758
$236$	6.48533	0.422159
$237$	−5.06068	−0.328726
$238$	−20.9183	−1.35593
$239$	−14.5058	−0.938305	−0.469152	−	0.883117i	$-0.655441\pi$
$239$	−14.5058	−0.938305	−0.469152	+	0.883117i	$0.655441\pi$
$240$	−3.07544	−0.198519
$241$	10.8803	0.700865	0.350432	−	0.936588i	$-0.386035\pi$
$241$	10.8803	0.700865	0.350432	+	0.936588i	$0.386035\pi$
$242$	−7.52125	−0.483484
$243$	−15.2566	−0.978714
$244$	−1.39282	−0.0891660
$245$	44.8651	2.86633
$246$	1.55492	0.0991378
$247$	−1.16604	−0.0741936
$248$	1.14507	0.0727122
$249$	−3.33264	−0.211197
$250$	−32.4414	−2.05177
$251$	26.4807	1.67145	0.835724	−	0.549149i	$-0.185048\pi$
$251$	26.4807	1.67145	0.835724	+	0.549149i	$0.185048\pi$
$252$	−10.3631	−0.652811
$253$	−9.11376	−0.572977
$254$	−12.7349	−0.799060
$255$	−15.3081	−0.958630
$256$	1.00000	0.0625000
$257$	1.55227	0.0968281	0.0484141	−	0.998827i	$-0.484583\pi$
$257$	1.55227	0.0968281	0.0484141	+	0.998827i	$0.484583\pi$
$258$	2.69340	0.167684
$259$	−2.56646	−0.159472
$260$	−16.7563	−1.03918
$261$	9.37886	0.580537
$262$	14.1615	0.874902
$263$	0.388973	0.0239851	0.0119926	−	0.999928i	$-0.496183\pi$
$263$	0.388973	0.0239851	0.0119926	+	0.999928i	$0.496183\pi$
$264$	−3.14517	−0.193572
$265$	−19.6204	−1.20527
$266$	−1.23068	−0.0754580
$267$	−10.3055	−0.630687
$268$	−9.49023	−0.579708
$269$	27.2863	1.66368	0.831839	−	0.555018i	$-0.187289\pi$
$269$	27.2863	1.66368	0.831839	+	0.555018i	$0.187289\pi$
$270$	−16.8101	−1.02303
$271$	−0.702103	−0.0426497	−0.0213249	−	0.999773i	$-0.506788\pi$
$271$	−0.702103	−0.0426497	−0.0213249	+	0.999773i	$0.506788\pi$
$272$	4.97753	0.301807
$273$	12.2293	0.740150
$274$	−12.8583	−0.776800
$275$	−54.6951	−3.29824
$276$	−1.54765	−0.0931574
$277$	−5.82878	−0.350217	−0.175109	−	0.984549i	$-0.556028\pi$
$277$	−5.82878	−0.350217	−0.175109	+	0.984549i	$0.556028\pi$
$278$	−18.3891	−1.10290
$279$	2.82364	0.169047
$280$	−17.6852	−1.05689
$281$	6.15785	0.367347	0.183673	−	0.982987i	$-0.441201\pi$
$281$	6.15785	0.367347	0.183673	+	0.982987i	$0.441201\pi$
$282$	−1.26924	−0.0755821
$283$	21.6190	1.28511	0.642557	−	0.766238i	$-0.277873\pi$
$283$	21.6190	1.28511	0.642557	+	0.766238i	$0.277873\pi$
$284$	4.53305	0.268987
$285$	−0.900620	−0.0533482
$286$	−17.1362	−1.01329
$287$	8.94147	0.527798
$288$	2.46590	0.145305
$289$	7.77581	0.457400
$290$	16.0056	0.939881
$291$	2.28495	0.133946
$292$	7.20743	0.421783
$293$	−3.84858	−0.224836	−0.112418	−	0.993661i	$-0.535860\pi$
$293$	−3.84858	−0.224836	−0.112418	+	0.993661i	$0.535860\pi$
$294$	7.79148	0.454409
$295$	27.2917	1.58898
$296$	0.610692	0.0354958
$297$	−17.1912	−0.997535
$298$	−8.29894	−0.480745
$299$	−8.43223	−0.487649
$300$	−9.28801	−0.536244
$301$	15.4883	0.892730
$302$	4.00226	0.230304
$303$	1.37007	0.0787085
$304$	0.292843	0.0167957
$305$	−5.86127	−0.335616
$306$	12.2741	0.701664
$307$	−4.34060	−0.247731	−0.123865	−	0.992299i	$-0.539529\pi$
$307$	−4.34060	−0.247731	−0.123865	+	0.992299i	$0.539529\pi$
$308$	−18.0862	−1.03056
$309$	−2.31408	−0.131643
$310$	4.81871	0.273685
$311$	19.7205	1.11825	0.559123	−	0.829085i	$-0.311138\pi$
$311$	19.7205	1.11825	0.559123	+	0.829085i	$0.311138\pi$
$312$	−2.90998	−0.164745
$313$	7.69081	0.434711	0.217355	−	0.976093i	$-0.430257\pi$
$313$	7.69081	0.434711	0.217355	+	0.976093i	$0.430257\pi$
$314$	5.24816	0.296171
$315$	−43.6100	−2.45714
$316$	6.92468	0.389544
$317$	−21.5365	−1.20961	−0.604805	−	0.796374i	$-0.706749\pi$
$317$	−21.5365	−1.20961	−0.604805	+	0.796374i	$0.706749\pi$
$318$	−3.40738	−0.191076
$319$	16.3685	0.916460
$320$	4.20821	0.235246
$321$	−11.5777	−0.646205
$322$	−8.89967	−0.495959
$323$	1.45763	0.0811049
$324$	4.47840	0.248800
$325$	−50.6050	−2.80706
$326$	7.52173	0.416590
$327$	4.91885	0.272013
$328$	−2.12764	−0.117479
$329$	−7.29870	−0.402391
$330$	−13.2356	−0.728593
$331$	23.5206	1.29281	0.646404	−	0.762995i	$-0.276272\pi$
$331$	23.5206	1.29281	0.646404	+	0.762995i	$0.276272\pi$
$332$	4.56015	0.250271
$333$	1.50591	0.0825233
$334$	15.6056	0.853899
$335$	−39.9369	−2.18199
$336$	−3.07129	−0.167553
$337$	−28.8652	−1.57239	−0.786195	−	0.617978i	$-0.787952\pi$
$337$	−28.8652	−1.57239	−0.786195	+	0.617978i	$0.787952\pi$
$338$	−2.85479	−0.155280
$339$	5.99644	0.325682
$340$	20.9465	1.13598
$341$	4.92797	0.266865
$342$	0.722123	0.0390479
$343$	15.3868	0.830810
$344$	−3.68546	−0.198707
$345$	−6.51283	−0.350639
$346$	−20.2959	−1.09111
$347$	−17.7594	−0.953373	−0.476686	−	0.879073i	$-0.658162\pi$
$347$	−17.7594	−0.953373	−0.476686	+	0.879073i	$0.658162\pi$
$348$	2.77961	0.149003
$349$	−9.59553	−0.513637	−0.256819	−	0.966460i	$-0.582674\pi$
$349$	−9.59553	−0.513637	−0.256819	+	0.966460i	$0.582674\pi$
$350$	−53.4103	−2.85490
$351$	−15.9057	−0.848981
$352$	4.30363	0.229384
$353$	15.5290	0.826523	0.413261	−	0.910612i	$-0.364390\pi$
$353$	15.5290	0.826523	0.413261	+	0.910612i	$0.364390\pi$
$354$	4.73960	0.251907
$355$	19.0761	1.01245
$356$	14.1013	0.747369
$357$	−15.2874	−0.809097
$358$	−2.08953	−0.110435
$359$	−20.9408	−1.10521	−0.552606	−	0.833443i	$-0.686367\pi$
$359$	−20.9408	−1.10521	−0.552606	+	0.833443i	$0.686367\pi$
$360$	10.3771	0.546919
$361$	−18.9142	−0.995486
$362$	−0.321744	−0.0169105
$363$	−5.49667	−0.288500
$364$	−16.7337	−0.877084
$365$	30.3304	1.58757
$366$	−1.01790	−0.0532063
$367$	24.4775	1.27772	0.638858	−	0.769325i	$-0.279407\pi$
$367$	24.4775	1.27772	0.638858	+	0.769325i	$0.279407\pi$
$368$	2.11769	0.110392
$369$	−5.24655	−0.273124
$370$	2.56992	0.133604
$371$	−19.5940	−1.01727
$372$	0.836840	0.0433882
$373$	−24.0142	−1.24341	−0.621705	−	0.783252i	$-0.713560\pi$
$373$	−24.0142	−1.24341	−0.621705	+	0.783252i	$0.713560\pi$
$374$	21.4215	1.10768
$375$	−23.7088	−1.22431
$376$	1.73674	0.0895654
$377$	15.1445	0.779980
$378$	−16.7874	−0.863450
$379$	−17.4272	−0.895176	−0.447588	−	0.894240i	$-0.647717\pi$
$379$	−17.4272	−0.895176	−0.447588	+	0.894240i	$0.647717\pi$
$380$	1.23235	0.0632180
$381$	−9.30691	−0.476808
$382$	−22.0060	−1.12592
$383$	7.90840	0.404101	0.202050	−	0.979375i	$-0.435240\pi$
$383$	7.90840	0.404101	0.202050	+	0.979375i	$0.435240\pi$
$384$	0.730818	0.0372944
$385$	−76.1105	−3.87895
$386$	−15.6403	−0.796069
$387$	−9.08800	−0.461969
$388$	−3.12656	−0.158727
$389$	−13.8731	−0.703393	−0.351696	−	0.936114i	$-0.614395\pi$
$389$	−13.8731	−0.703393	−0.351696	+	0.936114i	$0.614395\pi$
$390$	−12.2458	−0.620091
$391$	10.5409	0.533075
$392$	−10.6613	−0.538478
$393$	10.3495	0.522063
$394$	3.98375	0.200698
$395$	29.1405	1.46622
$396$	10.6123	0.533290
$397$	−33.5263	−1.68264	−0.841318	−	0.540540i	$-0.818220\pi$
$397$	−33.5263	−1.68264	−0.841318	+	0.540540i	$0.818220\pi$
$398$	−2.16747	−0.108645
$399$	−0.899406	−0.0450266
$400$	12.7091	0.635453
$401$	−29.8260	−1.48944	−0.744719	−	0.667378i	$-0.767416\pi$
$401$	−29.8260	−1.48944	−0.744719	+	0.667378i	$0.767416\pi$
$402$	−6.93563	−0.345918
$403$	4.55946	0.227123
$404$	−1.87471	−0.0932702
$405$	18.8461	0.936469
$406$	15.9840	0.793273
$407$	2.62819	0.130275
$408$	3.63767	0.180091
$409$	−22.1405	−1.09478	−0.547389	−	0.836878i	$-0.684378\pi$
$409$	−22.1405	−1.09478	−0.547389	+	0.836878i	$0.684378\pi$
$410$	−8.95355	−0.442184
$411$	−9.39710	−0.463525
$412$	3.16643	0.155999
$413$	27.2548	1.34112
$414$	5.22202	0.256648
$415$	19.1901	0.942003
$416$	3.98181	0.195224
$417$	−13.4391	−0.658115
$418$	1.26029	0.0616427
$419$	−5.56629	−0.271931	−0.135966	−	0.990714i	$-0.543414\pi$
$419$	−5.56629	−0.271931	−0.135966	+	0.990714i	$0.543414\pi$
$420$	−12.9246	−0.630658
$421$	27.0685	1.31924	0.659620	−	0.751599i	$-0.270717\pi$
$421$	27.0685	1.31924	0.659620	+	0.751599i	$0.270717\pi$
$422$	−11.2801	−0.549106
$423$	4.28263	0.208229
$424$	4.66241	0.226427
$425$	63.2597	3.06855
$426$	3.31284	0.160508
$427$	−5.85337	−0.283264
$428$	15.8421	0.765758
$429$	−12.5235	−0.604639
$430$	−15.5092	−0.747920
$431$	19.7598	0.951798	0.475899	−	0.879500i	$-0.342123\pi$
$431$	19.7598	0.951798	0.475899	+	0.879500i	$0.342123\pi$
$432$	3.99458	0.192189
$433$	−35.7270	−1.71693	−0.858464	−	0.512874i	$-0.828581\pi$
$433$	−35.7270	−1.71693	−0.858464	+	0.512874i	$0.828581\pi$
$434$	4.81221	0.230994
$435$	11.6972	0.560837
$436$	−6.73060	−0.322337
$437$	0.620150	0.0296658
$438$	5.26732	0.251682
$439$	9.58956	0.457685	0.228842	−	0.973463i	$-0.426506\pi$
$439$	9.58956	0.457685	0.228842	+	0.973463i	$0.426506\pi$
$440$	18.1106	0.863389
$441$	−26.2898	−1.25189
$442$	19.8196	0.942721
$443$	22.9128	1.08862	0.544311	−	0.838884i	$-0.316791\pi$
$443$	22.9128	1.08862	0.544311	+	0.838884i	$0.316791\pi$
$444$	0.446305	0.0211807
$445$	59.3414	2.81305
$446$	−14.0294	−0.664312
$447$	−6.06502	−0.286866
$448$	4.20254	0.198551
$449$	−35.1115	−1.65701	−0.828507	−	0.559979i	$-0.810809\pi$
$449$	−35.1115	−1.65701	−0.828507	+	0.559979i	$0.810809\pi$
$450$	31.3393	1.47735
$451$	−9.15656	−0.431166
$452$	−8.20510	−0.385935
$453$	2.92493	0.137425
$454$	12.3724	0.580663
$455$	−70.4190	−3.30129
$456$	0.214015	0.0100222
$457$	22.8081	1.06692	0.533459	−	0.845826i	$-0.320892\pi$
$457$	22.8081	1.06692	0.533459	+	0.845826i	$0.320892\pi$
$458$	10.2501	0.478956
$459$	19.8832	0.928066
$460$	8.91169	0.415510
$461$	17.6143	0.820379	0.410189	−	0.912000i	$-0.365463\pi$
$461$	17.6143	0.820379	0.410189	+	0.912000i	$0.365463\pi$
$462$	−13.2177	−0.614943
$463$	36.1455	1.67982	0.839912	−	0.542722i	$-0.182606\pi$
$463$	36.1455	1.67982	0.839912	+	0.542722i	$0.182606\pi$
$464$	−3.80342	−0.176569
$465$	3.52160	0.163310
$466$	5.83236	0.270179
$467$	−27.3860	−1.26727	−0.633637	−	0.773631i	$-0.718439\pi$
$467$	−27.3860	−1.26727	−0.633637	+	0.773631i	$0.718439\pi$
$468$	9.81876	0.453872
$469$	−39.8830	−1.84163
$470$	7.30856	0.337119
$471$	3.83545	0.176728
$472$	−6.48533	−0.298512
$473$	−15.8609	−0.729283
$474$	5.06068	0.232445
$475$	3.72176	0.170766
$476$	20.9183	0.958787
$477$	11.4971	0.526414
$478$	14.5058	0.663482
$479$	15.9699	0.729683	0.364841	−	0.931070i	$-0.381123\pi$
$479$	15.9699	0.729683	0.364841	+	0.931070i	$0.381123\pi$
$480$	3.07544	0.140374
$481$	2.43166	0.110874
$482$	−10.8803	−0.495586
$483$	−6.50404	−0.295944
$484$	7.52125	0.341875
$485$	−13.1572	−0.597439
$486$	15.2566	0.692055
$487$	7.45609	0.337867	0.168934	−	0.985627i	$-0.445968\pi$
$487$	7.45609	0.337867	0.168934	+	0.985627i	$0.445968\pi$
$488$	1.39282	0.0630499
$489$	5.49702	0.248584
$490$	−44.8651	−2.02680
$491$	23.1563	1.04503	0.522514	−	0.852631i	$-0.324994\pi$
$491$	23.1563	1.04503	0.522514	+	0.852631i	$0.324994\pi$
$492$	−1.55492	−0.0701010
$493$	−18.9316	−0.852637
$494$	1.16604	0.0524628
$495$	44.6590	2.00727
$496$	−1.14507	−0.0514153
$497$	19.0503	0.854524
$498$	3.33264	0.149339
$499$	−14.0712	−0.629911	−0.314956	−	0.949106i	$-0.601990\pi$
$499$	−14.0712	−0.629911	−0.314956	+	0.949106i	$0.601990\pi$
$500$	32.4414	1.45082
$501$	11.4048	0.509531
$502$	−26.4807	−1.18189
$503$	16.8698	0.752187	0.376094	−	0.926582i	$-0.377267\pi$
$503$	16.8698	0.752187	0.376094	+	0.926582i	$0.377267\pi$
$504$	10.3631	0.461607
$505$	−7.88917	−0.351064
$506$	9.11376	0.405156
$507$	−2.08634	−0.0926574
$508$	12.7349	0.565021
$509$	20.2659	0.898270	0.449135	−	0.893464i	$-0.351732\pi$
$509$	20.2659	0.898270	0.449135	+	0.893464i	$0.351732\pi$
$510$	15.3081	0.677854
$511$	30.2895	1.33993
$512$	−1.00000	−0.0441942
$513$	1.16979	0.0516473
$514$	−1.55227	−0.0684678
$515$	13.3250	0.587169
$516$	−2.69340	−0.118570
$517$	7.47428	0.328718
$518$	2.56646	0.112764
$519$	−14.8326	−0.651078
$520$	16.7563	0.734812
$521$	6.64985	0.291335	0.145668	−	0.989334i	$-0.453467\pi$
$521$	6.64985	0.291335	0.145668	+	0.989334i	$0.453467\pi$
$522$	−9.37886	−0.410502
$523$	−35.6405	−1.55845	−0.779224	−	0.626745i	$-0.784387\pi$
$523$	−35.6405	−1.55845	−0.779224	+	0.626745i	$0.784387\pi$
$524$	−14.1615	−0.618649
$525$	−39.0332	−1.70355
$526$	−0.388973	−0.0169600
$527$	−5.69964	−0.248280
$528$	3.14517	0.136876
$529$	−18.5154	−0.805017
$530$	19.6204	0.852257
$531$	−15.9922	−0.694003
$532$	1.23068	0.0533569
$533$	−8.47184	−0.366956
$534$	10.3055	0.445963
$535$	66.6670	2.88227
$536$	9.49023	0.409915
$537$	−1.52707	−0.0658977
$538$	−27.2863	−1.17640
$539$	−45.8824	−1.97629
$540$	16.8101	0.723390
$541$	11.4432	0.491983	0.245991	−	0.969272i	$-0.420887\pi$
$541$	11.4432	0.491983	0.245991	+	0.969272i	$0.420887\pi$
$542$	0.702103	0.0301579
$543$	−0.235136	−0.0100907
$544$	−4.97753	−0.213410
$545$	−28.3238	−1.21326
$546$	−12.2293	−0.523365
$547$	−40.3551	−1.72546	−0.862730	−	0.505665i	$-0.831247\pi$
$547$	−40.3551	−1.72546	−0.862730	+	0.505665i	$0.831247\pi$
$548$	12.8583	0.549281
$549$	3.43456	0.146583
$550$	54.6951	2.33221
$551$	−1.11380	−0.0474496
$552$	1.54765	0.0658722
$553$	29.1012	1.23751
$554$	5.82878	0.247641
$555$	1.87815	0.0797229
$556$	18.3891	0.779871
$557$	29.9562	1.26928	0.634642	−	0.772806i	$-0.281148\pi$
$557$	29.9562	1.26928	0.634642	+	0.772806i	$0.281148\pi$
$558$	−2.82364	−0.119534
$559$	−14.6748	−0.620678
$560$	17.6852	0.747335
$561$	15.6552	0.660963
$562$	−6.15785	−0.259753
$563$	31.1981	1.31484	0.657422	−	0.753523i	$-0.271647\pi$
$563$	31.1981	1.31484	0.657422	+	0.753523i	$0.271647\pi$
$564$	1.26924	0.0534446
$565$	−34.5288	−1.45264
$566$	−21.6190	−0.908713
$567$	18.8206	0.790393
$568$	−4.53305	−0.190203
$569$	30.0027	1.25778	0.628890	−	0.777495i	$-0.283510\pi$
$569$	30.0027	1.25778	0.628890	+	0.777495i	$0.283510\pi$
$570$	0.900620	0.0377228
$571$	−43.0451	−1.80138	−0.900691	−	0.434461i	$-0.856939\pi$
$571$	−43.0451	−1.80138	−0.900691	+	0.434461i	$0.856939\pi$
$572$	17.1362	0.716502
$573$	−16.0824	−0.671850
$574$	−8.94147	−0.373210
$575$	26.9139	1.12239
$576$	−2.46590	−0.102746
$577$	13.9529	0.580869	0.290434	−	0.956895i	$-0.406200\pi$
$577$	13.9529	0.580869	0.290434	+	0.956895i	$0.406200\pi$
$578$	−7.77581	−0.323431
$579$	−11.4302	−0.475023
$580$	−16.0056	−0.664596
$581$	19.1642	0.795064
$582$	−2.28495	−0.0947141
$583$	20.0653	0.831020
$584$	−7.20743	−0.298246
$585$	41.3194	1.70835
$586$	3.84858	0.158983
$587$	−26.2651	−1.08408	−0.542038	−	0.840354i	$-0.682347\pi$
$587$	−26.2651	−1.08408	−0.542038	+	0.840354i	$0.682347\pi$
$588$	−7.79148	−0.321315
$589$	−0.335327	−0.0138169
$590$	−27.2917	−1.12358
$591$	2.91139	0.119759
$592$	−0.610692	−0.0250993
$593$	13.9887	0.574449	0.287224	−	0.957863i	$-0.407268\pi$
$593$	13.9887	0.574449	0.287224	+	0.957863i	$0.407268\pi$
$594$	17.1912	0.705364
$595$	88.0285	3.60882
$596$	8.29894	0.339938
$597$	−1.58403	−0.0648298
$598$	8.43223	0.344820
$599$	45.9150	1.87604	0.938019	−	0.346584i	$-0.112659\pi$
$599$	45.9150	1.87604	0.938019	+	0.346584i	$0.112659\pi$
$600$	9.28801	0.379182
$601$	2.95809	0.120663	0.0603315	−	0.998178i	$-0.480784\pi$
$601$	2.95809	0.120663	0.0603315	+	0.998178i	$0.480784\pi$
$602$	−15.4883	−0.631255
$603$	23.4020	0.953003
$604$	−4.00226	−0.162850
$605$	31.6510	1.28680
$606$	−1.37007	−0.0556553
$607$	−31.1067	−1.26258	−0.631292	−	0.775545i	$-0.717475\pi$
$607$	−31.1067	−1.26258	−0.631292	+	0.775545i	$0.717475\pi$
$608$	−0.292843	−0.0118763
$609$	11.6814	0.473354
$610$	5.86127	0.237316
$611$	6.91535	0.279765
$612$	−12.2741	−0.496152
$613$	−31.6530	−1.27845	−0.639227	−	0.769018i	$-0.720745\pi$
$613$	−31.6530	−1.27845	−0.639227	+	0.769018i	$0.720745\pi$
$614$	4.34060	0.175172
$615$	−6.54342	−0.263856
$616$	18.0862	0.728713
$617$	20.6985	0.833292	0.416646	−	0.909069i	$-0.363206\pi$
$617$	20.6985	0.833292	0.416646	+	0.909069i	$0.363206\pi$
$618$	2.31408	0.0930860
$619$	40.5535	1.62998	0.814990	−	0.579474i	$-0.196742\pi$
$619$	40.5535	1.62998	0.814990	+	0.579474i	$0.196742\pi$
$620$	−4.81871	−0.193524
$621$	8.45929	0.339460
$622$	−19.7205	−0.790720
$623$	59.2614	2.37426
$624$	2.90998	0.116492
$625$	72.9749	2.91900
$626$	−7.69081	−0.307387
$627$	0.921041	0.0367829
$628$	−5.24816	−0.209425
$629$	−3.03974	−0.121202
$630$	43.6100	1.73746
$631$	41.6176	1.65677	0.828384	−	0.560160i	$-0.189260\pi$
$631$	41.6176	1.65677	0.828384	+	0.560160i	$0.189260\pi$
$632$	−6.92468	−0.275449
$633$	−8.24369	−0.327657
$634$	21.5365	0.855323
$635$	53.5913	2.12671
$636$	3.40738	0.135111
$637$	−42.4513	−1.68198
$638$	−16.3685	−0.648035
$639$	−11.1781	−0.442198
$640$	−4.20821	−0.166344
$641$	12.7556	0.503815	0.251908	−	0.967751i	$-0.418942\pi$
$641$	12.7556	0.503815	0.251908	+	0.967751i	$0.418942\pi$
$642$	11.5777	0.456936
$643$	16.4151	0.647349	0.323675	−	0.946168i	$-0.395082\pi$
$643$	16.4151	0.647349	0.323675	+	0.946168i	$0.395082\pi$
$644$	8.89967	0.350696
$645$	−11.3344	−0.446292
$646$	−1.45763	−0.0573499
$647$	−15.6737	−0.616198	−0.308099	−	0.951354i	$-0.599693\pi$
$647$	−15.6737	−0.616198	−0.308099	+	0.951354i	$0.599693\pi$
$648$	−4.47840	−0.175928
$649$	−27.9105	−1.09558
$650$	50.6050	1.98489
$651$	3.51685	0.137836
$652$	−7.52173	−0.294574
$653$	2.02137	0.0791022	0.0395511	−	0.999218i	$-0.487407\pi$
$653$	2.02137	0.0791022	0.0395511	+	0.999218i	$0.487407\pi$
$654$	−4.91885	−0.192342
$655$	−59.5948	−2.32856
$656$	2.12764	0.0830703
$657$	−17.7728	−0.693385
$658$	7.29870	0.284533
$659$	1.44175	0.0561627	0.0280814	−	0.999606i	$-0.491060\pi$
$659$	1.44175	0.0561627	0.0280814	+	0.999606i	$0.491060\pi$
$660$	13.2356	0.515193
$661$	−35.9318	−1.39759	−0.698793	−	0.715324i	$-0.746279\pi$
$661$	−35.9318	−1.39759	−0.698793	+	0.715324i	$0.746279\pi$
$662$	−23.5206	−0.914154
$663$	14.4845	0.562531
$664$	−4.56015	−0.176968
$665$	5.17898	0.200832
$666$	−1.50591	−0.0583528
$667$	−8.05446	−0.311870
$668$	−15.6056	−0.603798
$669$	−10.2529	−0.396402
$670$	39.9369	1.54290
$671$	5.99417	0.231403
$672$	3.07129	0.118478
$673$	−14.8783	−0.573518	−0.286759	−	0.958003i	$-0.592578\pi$
$673$	−14.8783	−0.573518	−0.286759	+	0.958003i	$0.592578\pi$
$674$	28.8652	1.11185
$675$	50.7674	1.95404
$676$	2.85479	0.109800
$677$	−15.3773	−0.590996	−0.295498	−	0.955343i	$-0.595486\pi$
$677$	−15.3773	−0.590996	−0.295498	+	0.955343i	$0.595486\pi$
$678$	−5.99644	−0.230292
$679$	−13.1395	−0.504247
$680$	−20.9465	−0.803262
$681$	9.04194	0.346488
$682$	−4.92797	−0.188702
$683$	−32.0920	−1.22797	−0.613984	−	0.789318i	$-0.710434\pi$
$683$	−32.0920	−1.22797	−0.613984	+	0.789318i	$0.710434\pi$
$684$	−0.722123	−0.0276111
$685$	54.1106	2.06746
$686$	−15.3868	−0.587471
$687$	7.49096	0.285798
$688$	3.68546	0.140507
$689$	18.5648	0.707264
$690$	6.51283	0.247939
$691$	−12.2559	−0.466235	−0.233117	−	0.972449i	$-0.574893\pi$
$691$	−12.2559	−0.466235	−0.233117	+	0.972449i	$0.574893\pi$
$692$	20.2959	0.771533
$693$	44.5988	1.69417
$694$	17.7594	0.674136
$695$	77.3852	2.93539
$696$	−2.77961	−0.105361
$697$	10.5904	0.401139
$698$	9.59553	0.363196
$699$	4.26240	0.161219
$700$	53.4103	2.01872
$701$	−38.5816	−1.45721	−0.728603	−	0.684936i	$-0.759830\pi$
$701$	−38.5816	−1.45721	−0.728603	+	0.684936i	$0.759830\pi$
$702$	15.9057	0.600320
$703$	−0.178837	−0.00674496
$704$	−4.30363	−0.162199
$705$	5.34123	0.201162
$706$	−15.5290	−0.584440
$707$	−7.87853	−0.296303
$708$	−4.73960	−0.178125
$709$	36.6877	1.37784	0.688918	−	0.724839i	$-0.258086\pi$
$709$	36.6877	1.37784	0.688918	+	0.724839i	$0.258086\pi$
$710$	−19.0761	−0.715912
$711$	−17.0756	−0.640385
$712$	−14.1013	−0.528470
$713$	−2.42491	−0.0908136
$714$	15.2874	0.572118
$715$	72.1129	2.69687
$716$	2.08953	0.0780893
$717$	10.6011	0.395907
$718$	20.9408	0.781503
$719$	−27.1376	−1.01206	−0.506031	−	0.862515i	$-0.668888\pi$
$719$	−27.1376	−1.01206	−0.506031	+	0.862515i	$0.668888\pi$
$720$	−10.3771	−0.386730
$721$	13.3070	0.495579
$722$	18.9142	0.703915
$723$	−7.95155	−0.295722
$724$	0.321744	0.0119575
$725$	−48.3379	−1.79522
$726$	5.49667	0.204000
$727$	−41.9422	−1.55555	−0.777775	−	0.628543i	$-0.783652\pi$
$727$	−41.9422	−1.55555	−0.777775	+	0.628543i	$0.783652\pi$
$728$	16.7337	0.620192
$729$	−2.28537	−0.0846433
$730$	−30.3304	−1.12258
$731$	18.3445	0.678496
$732$	1.01790	0.0376225
$733$	−23.2701	−0.859500	−0.429750	−	0.902948i	$-0.641398\pi$
$733$	−23.2701	−0.859500	−0.429750	+	0.902948i	$0.641398\pi$
$734$	−24.4775	−0.903481
$735$	−32.7882	−1.20941
$736$	−2.11769	−0.0780591
$737$	40.8424	1.50445
$738$	5.24655	0.193128
$739$	9.99729	0.367756	0.183878	−	0.982949i	$-0.441135\pi$
$739$	9.99729	0.367756	0.183878	+	0.982949i	$0.441135\pi$
$740$	−2.56992	−0.0944722
$741$	0.852166	0.0313051
$742$	19.5940	0.719317
$743$	19.5666	0.717830	0.358915	−	0.933370i	$-0.383147\pi$
$743$	19.5666	0.717830	0.358915	+	0.933370i	$0.383147\pi$
$744$	−0.836840	−0.0306801
$745$	34.9237	1.27951
$746$	24.0142	0.879223
$747$	−11.2449	−0.411429
$748$	−21.4215	−0.783246
$749$	66.5771	2.43267
$750$	23.7088	0.865721
$751$	12.8295	0.468156	0.234078	−	0.972218i	$-0.424793\pi$
$751$	12.8295	0.468156	0.234078	+	0.972218i	$0.424793\pi$
$752$	−1.73674	−0.0633323
$753$	−19.3526	−0.705248
$754$	−15.1445	−0.551529
$755$	−16.8424	−0.612957
$756$	16.7874	0.610551
$757$	24.1194	0.876636	0.438318	−	0.898820i	$-0.355574\pi$
$757$	24.1194	0.876636	0.438318	+	0.898820i	$0.355574\pi$
$758$	17.4272	0.632985
$759$	6.66050	0.241761
$760$	−1.23235	−0.0447019
$761$	6.16461	0.223467	0.111734	−	0.993738i	$-0.464360\pi$
$761$	6.16461	0.223467	0.111734	+	0.993738i	$0.464360\pi$
$762$	9.30691	0.337154
$763$	−28.2856	−1.02401
$764$	22.0060	0.796148
$765$	−51.6521	−1.86749
$766$	−7.90840	−0.285742
$767$	−25.8233	−0.932427
$768$	−0.730818	−0.0263711
$769$	27.1683	0.979712	0.489856	−	0.871803i	$-0.337049\pi$
$769$	27.1683	0.979712	0.489856	+	0.871803i	$0.337049\pi$
$770$	76.1105	2.74283
$771$	−1.13443	−0.0408555
$772$	15.6403	0.562906
$773$	−35.2206	−1.26680	−0.633398	−	0.773826i	$-0.718340\pi$
$773$	−35.2206	−1.26680	−0.633398	+	0.773826i	$0.718340\pi$
$774$	9.08800	0.326661
$775$	−14.5528	−0.522752
$776$	3.12656	0.112237
$777$	1.87561	0.0672872
$778$	13.8731	0.497374
$779$	0.623063	0.0223236
$780$	12.2458	0.438470
$781$	−19.5086	−0.698072
$782$	−10.5409	−0.376941
$783$	−15.1931	−0.542956
$784$	10.6613	0.380761
$785$	−22.0854	−0.788262
$786$	−10.3495	−0.369155
$787$	−18.3080	−0.652611	−0.326305	−	0.945264i	$-0.605804\pi$
$787$	−18.3080	−0.652611	−0.326305	+	0.945264i	$0.605804\pi$
$788$	−3.98375	−0.141915
$789$	−0.284269	−0.0101202
$790$	−29.1405	−1.03677
$791$	−34.4822	−1.22605
$792$	−10.6123	−0.377093
$793$	5.54593	0.196942
$794$	33.5263	1.18980
$795$	14.3390	0.508551
$796$	2.16747	0.0768239
$797$	−35.6465	−1.26266	−0.631332	−	0.775513i	$-0.717492\pi$
$797$	−35.6465	−1.26266	−0.631332	+	0.775513i	$0.717492\pi$
$798$	0.899406	0.0318386
$799$	−8.64466	−0.305826
$800$	−12.7091	−0.449333
$801$	−34.7725	−1.22863
$802$	29.8260	1.05319
$803$	−31.0181	−1.09461
$804$	6.93563	0.244601
$805$	37.4517	1.32000
$806$	−4.55946	−0.160600
$807$	−19.9413	−0.701969
$808$	1.87471	0.0659520
$809$	7.80137	0.274282	0.137141	−	0.990552i	$-0.456209\pi$
$809$	7.80137	0.274282	0.137141	+	0.990552i	$0.456209\pi$
$810$	−18.8461	−0.662183
$811$	−21.4429	−0.752963	−0.376481	−	0.926424i	$-0.622866\pi$
$811$	−21.4429	−0.752963	−0.376481	+	0.926424i	$0.622866\pi$
$812$	−15.9840	−0.560928
$813$	0.513110	0.0179955
$814$	−2.62819	−0.0921181
$815$	−31.6531	−1.10876
$816$	−3.63767	−0.127344
$817$	1.07926	0.0377586
$818$	22.1405	0.774125
$819$	41.2637	1.44187
$820$	8.95355	0.312672
$821$	−19.3833	−0.676481	−0.338241	−	0.941060i	$-0.609832\pi$
$821$	−19.3833	−0.676481	−0.338241	+	0.941060i	$0.609832\pi$
$822$	9.39710	0.327761
$823$	1.43383	0.0499801	0.0249900	−	0.999688i	$-0.492045\pi$
$823$	1.43383	0.0499801	0.0249900	+	0.999688i	$0.492045\pi$
$824$	−3.16643	−0.110308
$825$	39.9722	1.39165
$826$	−27.2548	−0.948317
$827$	39.9390	1.38882	0.694408	−	0.719581i	$-0.255666\pi$
$827$	39.9390	1.38882	0.694408	+	0.719581i	$0.255666\pi$
$828$	−5.22202	−0.181478
$829$	−16.9656	−0.589239	−0.294619	−	0.955615i	$-0.595193\pi$
$829$	−16.9656	−0.589239	−0.294619	+	0.955615i	$0.595193\pi$
$830$	−19.1901	−0.666097
$831$	4.25978	0.147770
$832$	−3.98181	−0.138044
$833$	53.0670	1.83866
$834$	13.4391	0.465357
$835$	−65.6716	−2.27266
$836$	−1.26029	−0.0435880
$837$	−4.57409	−0.158104
$838$	5.56629	0.192284
$839$	9.13151	0.315255	0.157627	−	0.987499i	$-0.449616\pi$
$839$	9.13151	0.315255	0.157627	+	0.987499i	$0.449616\pi$
$840$	12.9246	0.445943
$841$	−14.5340	−0.501173
$842$	−27.0685	−0.932843
$843$	−4.50027	−0.154997
$844$	11.2801	0.388276
$845$	12.0136	0.413280
$846$	−4.28263	−0.147240
$847$	31.6083	1.08607
$848$	−4.66241	−0.160108
$849$	−15.7995	−0.542239
$850$	−63.2597	−2.16979
$851$	−1.29326	−0.0443323
$852$	−3.31284	−0.113496
$853$	26.4130	0.904365	0.452182	−	0.891926i	$-0.350646\pi$
$853$	26.4130	0.904365	0.452182	+	0.891926i	$0.350646\pi$
$854$	5.85337	0.200298
$855$	−3.03885	−0.103926
$856$	−15.8421	−0.541473
$857$	−24.1843	−0.826120	−0.413060	−	0.910704i	$-0.635540\pi$
$857$	−24.1843	−0.826120	−0.413060	+	0.910704i	$0.635540\pi$
$858$	12.5235	0.427544
$859$	−3.59352	−0.122609	−0.0613047	−	0.998119i	$-0.519526\pi$
$859$	−3.59352	−0.122609	−0.0613047	+	0.998119i	$0.519526\pi$
$860$	15.5092	0.528860
$861$	−6.53459	−0.222698
$862$	−19.7598	−0.673023
$863$	26.1086	0.888746	0.444373	−	0.895842i	$-0.353426\pi$
$863$	26.1086	0.888746	0.444373	+	0.895842i	$0.353426\pi$
$864$	−3.99458	−0.135898
$865$	85.4093	2.90400
$866$	35.7270	1.21405
$867$	−5.68270	−0.192995
$868$	−4.81221	−0.163337
$869$	−29.8013	−1.01094
$870$	−11.6972	−0.396571
$871$	37.7883	1.28041
$872$	6.73060	0.227927
$873$	7.70980	0.260937
$874$	−0.620150	−0.0209769
$875$	136.336	4.60900
$876$	−5.26732	−0.177966
$877$	5.68476	0.191961	0.0959803	−	0.995383i	$-0.469401\pi$
$877$	5.68476	0.191961	0.0959803	+	0.995383i	$0.469401\pi$
$878$	−9.58956	−0.323632
$879$	2.81261	0.0948670
$880$	−18.1106	−0.610508
$881$	21.2589	0.716232	0.358116	−	0.933677i	$-0.383419\pi$
$881$	21.2589	0.716232	0.358116	+	0.933677i	$0.383419\pi$
$882$	26.2898	0.885223
$883$	31.6959	1.06665	0.533326	−	0.845910i	$-0.320942\pi$
$883$	31.6959	1.06665	0.533326	+	0.845910i	$0.320942\pi$
$884$	−19.8196	−0.666604
$885$	−19.9452	−0.670452
$886$	−22.9128	−0.769772
$887$	−31.7798	−1.06706	−0.533531	−	0.845781i	$-0.679135\pi$
$887$	−31.7798	−1.06706	−0.533531	+	0.845781i	$0.679135\pi$
$888$	−0.446305	−0.0149770
$889$	53.5190	1.79497
$890$	−59.3414	−1.98913
$891$	−19.2734	−0.645683
$892$	14.0294	0.469739
$893$	−0.508591	−0.0170194
$894$	6.06502	0.202845
$895$	8.79318	0.293924
$896$	−4.20254	−0.140397
$897$	6.16243	0.205758
$898$	35.1115	1.17169
$899$	4.35519	0.145254
$900$	−31.3393	−1.04464
$901$	−23.2073	−0.773147
$902$	9.15656	0.304880
$903$	−11.3191	−0.376677
$904$	8.20510	0.272898
$905$	1.35397	0.0450074
$906$	−2.92493	−0.0971742
$907$	40.7553	1.35326	0.676629	−	0.736324i	$-0.263440\pi$
$907$	40.7553	1.35326	0.676629	+	0.736324i	$0.263440\pi$
$908$	−12.3724	−0.410591
$909$	4.62285	0.153330
$910$	70.4190	2.33437
$911$	−45.3067	−1.50108	−0.750539	−	0.660826i	$-0.770206\pi$
$911$	−45.3067	−1.50108	−0.750539	+	0.660826i	$0.770206\pi$
$912$	−0.214015	−0.00708674
$913$	−19.6252	−0.649499
$914$	−22.8081	−0.754425
$915$	4.28353	0.141609
$916$	−10.2501	−0.338673
$917$	−59.5144	−1.96534
$918$	−19.8832	−0.656242
$919$	−6.10517	−0.201391	−0.100695	−	0.994917i	$-0.532107\pi$
$919$	−6.10517	−0.201391	−0.100695	+	0.994917i	$0.532107\pi$
$920$	−8.91169	−0.293810
$921$	3.17219	0.104527
$922$	−17.6143	−0.580095
$923$	−18.0498	−0.594115
$924$	13.2177	0.434831
$925$	−7.76132	−0.255191
$926$	−36.1455	−1.18782
$927$	−7.80810	−0.256452
$928$	3.80342	0.124853
$929$	−36.7092	−1.20439	−0.602195	−	0.798349i	$-0.705707\pi$
$929$	−36.7092	−1.20439	−0.602195	+	0.798349i	$0.705707\pi$
$930$	−3.52160	−0.115478
$931$	3.12209	0.102322
$932$	−5.83236	−0.191045
$933$	−14.4121	−0.471831
$934$	27.3860	0.896098
$935$	−90.1461	−2.94809
$936$	−9.81876	−0.320936
$937$	36.0057	1.17626	0.588128	−	0.808768i	$-0.299865\pi$
$937$	36.0057	1.17626	0.588128	+	0.808768i	$0.299865\pi$
$938$	39.8830	1.30223
$939$	−5.62059	−0.183421
$940$	−7.30856	−0.238379
$941$	46.1695	1.50508	0.752542	−	0.658544i	$-0.228827\pi$
$941$	46.1695	1.50508	0.752542	+	0.658544i	$0.228827\pi$
$942$	−3.83545	−0.124966
$943$	4.50567	0.146725
$944$	6.48533	0.211080
$945$	70.6449	2.29808
$946$	15.8609	0.515681
$947$	−23.0216	−0.748103	−0.374051	−	0.927408i	$-0.622032\pi$
$947$	−23.0216	−0.748103	−0.374051	+	0.927408i	$0.622032\pi$
$948$	−5.06068	−0.164363
$949$	−28.6986	−0.931597
$950$	−3.72176	−0.120750
$951$	15.7393	0.510380
$952$	−20.9183	−0.677965
$953$	−40.4173	−1.30925	−0.654623	−	0.755956i	$-0.727173\pi$
$953$	−40.4173	−1.30925	−0.654623	+	0.755956i	$0.727173\pi$
$954$	−11.4971	−0.372231
$955$	92.6058	2.99665
$956$	−14.5058	−0.469152
$957$	−11.9624	−0.386690
$958$	−15.9699	−0.515964
$959$	54.0376	1.74496
$960$	−3.07544	−0.0992594
$961$	−29.6888	−0.957703
$962$	−2.43166	−0.0783998
$963$	−39.0652	−1.25886
$964$	10.8803	0.350432
$965$	65.8177	2.11875
$966$	6.50404	0.209264
$967$	−11.9584	−0.384557	−0.192279	−	0.981340i	$-0.561588\pi$
$967$	−11.9584	−0.384557	−0.192279	+	0.981340i	$0.561588\pi$
$968$	−7.52125	−0.241742
$969$	−1.06527	−0.0342213
$970$	13.1572	0.422453
$971$	−18.8594	−0.605225	−0.302613	−	0.953114i	$-0.597859\pi$
$971$	−18.8594	−0.605225	−0.302613	+	0.953114i	$0.597859\pi$
$972$	−15.2566	−0.489357
$973$	77.2808	2.47751
$974$	−7.45609	−0.238908
$975$	36.9831	1.18441
$976$	−1.39282	−0.0445830
$977$	−20.4971	−0.655762	−0.327881	−	0.944719i	$-0.606334\pi$
$977$	−20.4971	−0.655762	−0.327881	+	0.944719i	$0.606334\pi$
$978$	−5.49702	−0.175775
$979$	−60.6869	−1.93956
$980$	44.8651	1.43316
$981$	16.5970	0.529902
$982$	−23.1563	−0.738946
$983$	−21.5153	−0.686231	−0.343116	−	0.939293i	$-0.611482\pi$
$983$	−21.5153	−0.686231	−0.343116	+	0.939293i	$0.611482\pi$
$984$	1.55492	0.0495689
$985$	−16.7645	−0.534160
$986$	18.9316	0.602906
$987$	5.33403	0.169784
$988$	−1.16604	−0.0370968
$989$	7.80466	0.248174
$990$	−44.6590	−1.41936
$991$	8.55827	0.271863	0.135931	−	0.990718i	$-0.456597\pi$
$991$	8.55827	0.271863	0.135931	+	0.990718i	$0.456597\pi$
$992$	1.14507	0.0363561
$993$	−17.1893	−0.545485
$994$	−19.0503	−0.604240
$995$	9.12117	0.289161
$996$	−3.33264	−0.105599
$997$	46.6609	1.47777	0.738883	−	0.673834i	$-0.235354\pi$
$997$	46.6609	1.47777	0.738883	+	0.673834i	$0.235354\pi$
$998$	14.0712	0.445415
$999$	−2.43946	−0.0771811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.29	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.29	✓	77	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.730818 q^{3} +1.00000 q^{4} +4.20821 q^{5} +0.730818 q^{6} +4.20254 q^{7} -1.00000 q^{8} -2.46590 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.730818 q^{3} +1.00000 q^{4} +4.20821 q^{5} +0.730818 q^{6} +4.20254 q^{7} -1.00000 q^{8} -2.46590 q^{9} -4.20821 q^{10} -4.30363 q^{11} -0.730818 q^{12} -3.98181 q^{13} -4.20254 q^{14} -3.07544 q^{15} +1.00000 q^{16} +4.97753 q^{17} +2.46590 q^{18} +0.292843 q^{19} +4.20821 q^{20} -3.07129 q^{21} +4.30363 q^{22} +2.11769 q^{23} +0.730818 q^{24} +12.7091 q^{25} +3.98181 q^{26} +3.99458 q^{27} +4.20254 q^{28} -3.80342 q^{29} +3.07544 q^{30} -1.14507 q^{31} -1.00000 q^{32} +3.14517 q^{33} -4.97753 q^{34} +17.6852 q^{35} -2.46590 q^{36} -0.610692 q^{37} -0.292843 q^{38} +2.90998 q^{39} -4.20821 q^{40} +2.12764 q^{41} +3.07129 q^{42} +3.68546 q^{43} -4.30363 q^{44} -10.3771 q^{45} -2.11769 q^{46} -1.73674 q^{47} -0.730818 q^{48} +10.6613 q^{49} -12.7091 q^{50} -3.63767 q^{51} -3.98181 q^{52} -4.66241 q^{53} -3.99458 q^{54} -18.1106 q^{55} -4.20254 q^{56} -0.214015 q^{57} +3.80342 q^{58} +6.48533 q^{59} -3.07544 q^{60} -1.39282 q^{61} +1.14507 q^{62} -10.3631 q^{63} +1.00000 q^{64} -16.7563 q^{65} -3.14517 q^{66} -9.49023 q^{67} +4.97753 q^{68} -1.54765 q^{69} -17.6852 q^{70} +4.53305 q^{71} +2.46590 q^{72} +7.20743 q^{73} +0.610692 q^{74} -9.28801 q^{75} +0.292843 q^{76} -18.0862 q^{77} -2.90998 q^{78} +6.92468 q^{79} +4.20821 q^{80} +4.47840 q^{81} -2.12764 q^{82} +4.56015 q^{83} -3.07129 q^{84} +20.9465 q^{85} -3.68546 q^{86} +2.77961 q^{87} +4.30363 q^{88} +14.1013 q^{89} +10.3771 q^{90} -16.7337 q^{91} +2.11769 q^{92} +0.836840 q^{93} +1.73674 q^{94} +1.23235 q^{95} +0.730818 q^{96} -3.12656 q^{97} -10.6613 q^{98} +10.6123 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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