LMFDB - Embedded newform 8005.2.a.f.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8005,2,Mod(1,8005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8005 = 5 \cdot 1601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8005.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:	$63.9202468180$
Analytic rank:	$1$
Dimension:	$127$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17575 q^{2} +0.162649 q^{3} +2.73390 q^{4} -1.00000 q^{5} -0.353884 q^{6} -3.43107 q^{7} -1.59678 q^{8} -2.97355 q^{9} +O(q^{10})$	\(q-2.17575 q^{2} +0.162649 q^{3} +2.73390 q^{4} -1.00000 q^{5} -0.353884 q^{6} -3.43107 q^{7} -1.59678 q^{8} -2.97355 q^{9} +2.17575 q^{10} +1.06447 q^{11} +0.444666 q^{12} +6.71561 q^{13} +7.46515 q^{14} -0.162649 q^{15} -1.99359 q^{16} -2.21251 q^{17} +6.46970 q^{18} -4.88112 q^{19} -2.73390 q^{20} -0.558059 q^{21} -2.31602 q^{22} -7.28570 q^{23} -0.259715 q^{24} +1.00000 q^{25} -14.6115 q^{26} -0.971591 q^{27} -9.38019 q^{28} +6.62417 q^{29} +0.353884 q^{30} +4.71348 q^{31} +7.53113 q^{32} +0.173134 q^{33} +4.81388 q^{34} +3.43107 q^{35} -8.12938 q^{36} +2.18751 q^{37} +10.6201 q^{38} +1.09229 q^{39} +1.59678 q^{40} +0.419535 q^{41} +1.21420 q^{42} -0.104432 q^{43} +2.91015 q^{44} +2.97355 q^{45} +15.8519 q^{46} -2.46202 q^{47} -0.324256 q^{48} +4.77222 q^{49} -2.17575 q^{50} -0.359863 q^{51} +18.3598 q^{52} +5.66987 q^{53} +2.11394 q^{54} -1.06447 q^{55} +5.47867 q^{56} -0.793909 q^{57} -14.4126 q^{58} -8.68626 q^{59} -0.444666 q^{60} +4.16869 q^{61} -10.2554 q^{62} +10.2024 q^{63} -12.3987 q^{64} -6.71561 q^{65} -0.376698 q^{66} -5.88179 q^{67} -6.04879 q^{68} -1.18501 q^{69} -7.46515 q^{70} -8.73545 q^{71} +4.74811 q^{72} +13.1641 q^{73} -4.75948 q^{74} +0.162649 q^{75} -13.3445 q^{76} -3.65226 q^{77} -2.37655 q^{78} -0.535503 q^{79} +1.99359 q^{80} +8.76261 q^{81} -0.912805 q^{82} +6.93634 q^{83} -1.52568 q^{84} +2.21251 q^{85} +0.227218 q^{86} +1.07741 q^{87} -1.69972 q^{88} +13.3049 q^{89} -6.46970 q^{90} -23.0417 q^{91} -19.9184 q^{92} +0.766642 q^{93} +5.35675 q^{94} +4.88112 q^{95} +1.22493 q^{96} +12.0368 q^{97} -10.3832 q^{98} -3.16524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) $ 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.17575	−1.53849	−0.769245	−	0.638954i	$-0.779367\pi$
$2$	−2.17575	−1.53849	−0.769245	+	0.638954i	$0.779367\pi$
$3$	0.162649	0.0939054	0.0469527	−	0.998897i	$-0.485049\pi$
$3$	0.162649	0.0939054	0.0469527	+	0.998897i	$0.485049\pi$
$4$	2.73390	1.36695
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.353884	−0.144473
$7$	−3.43107	−1.29682	−0.648411	−	0.761291i	$-0.724566\pi$
$7$	−3.43107	−1.29682	−0.648411	+	0.761291i	$0.724566\pi$
$8$	−1.59678	−0.564549
$9$	−2.97355	−0.991182
$10$	2.17575	0.688033
$11$	1.06447	0.320949	0.160474	−	0.987040i	$-0.448698\pi$
$11$	1.06447	0.320949	0.160474	+	0.987040i	$0.448698\pi$
$12$	0.444666	0.128364
$13$	6.71561	1.86258	0.931288	−	0.364283i	$-0.118686\pi$
$13$	6.71561	1.86258	0.931288	+	0.364283i	$0.118686\pi$
$14$	7.46515	1.99515
$15$	−0.162649	−0.0419958
$16$	−1.99359	−0.498398
$17$	−2.21251	−0.536613	−0.268306	−	0.963334i	$-0.586464\pi$
$17$	−2.21251	−0.536613	−0.268306	+	0.963334i	$0.586464\pi$
$18$	6.46970	1.52492
$19$	−4.88112	−1.11981	−0.559903	−	0.828558i	$-0.689161\pi$
$19$	−4.88112	−1.11981	−0.559903	+	0.828558i	$0.689161\pi$
$20$	−2.73390	−0.611319
$21$	−0.558059	−0.121779
$22$	−2.31602	−0.493776
$23$	−7.28570	−1.51917	−0.759586	−	0.650407i	$-0.774599\pi$
$23$	−7.28570	−1.51917	−0.759586	+	0.650407i	$0.774599\pi$
$24$	−0.259715	−0.0530142
$25$	1.00000	0.200000
$26$	−14.6115	−2.86555
$27$	−0.971591	−0.186983
$28$	−9.38019	−1.77269
$29$	6.62417	1.23008	0.615039	−	0.788497i	$-0.289140\pi$
$29$	6.62417	1.23008	0.615039	+	0.788497i	$0.289140\pi$
$30$	0.353884	0.0646101
$31$	4.71348	0.846566	0.423283	−	0.905998i	$-0.360878\pi$
$31$	4.71348	0.846566	0.423283	+	0.905998i	$0.360878\pi$
$32$	7.53113	1.33133
$33$	0.173134	0.0301388
$34$	4.81388	0.825573
$35$	3.43107	0.579956
$36$	−8.12938	−1.35490
$37$	2.18751	0.359624	0.179812	−	0.983701i	$-0.442451\pi$
$37$	2.18751	0.359624	0.179812	+	0.983701i	$0.442451\pi$
$38$	10.6201	1.72281
$39$	1.09229	0.174906
$40$	1.59678	0.252474
$41$	0.419535	0.0655204	0.0327602	−	0.999463i	$-0.489570\pi$
$41$	0.419535	0.0655204	0.0327602	+	0.999463i	$0.489570\pi$
$42$	1.21420	0.187355
$43$	−0.104432	−0.0159257	−0.00796285	−	0.999968i	$-0.502535\pi$
$43$	−0.104432	−0.0159257	−0.00796285	+	0.999968i	$0.502535\pi$
$44$	2.91015	0.438721
$45$	2.97355	0.443270
$46$	15.8519	2.33723
$47$	−2.46202	−0.359123	−0.179561	−	0.983747i	$-0.557468\pi$
$47$	−2.46202	−0.359123	−0.179561	+	0.983747i	$0.557468\pi$
$48$	−0.324256	−0.0468023
$49$	4.77222	0.681746
$50$	−2.17575	−0.307698
$51$	−0.359863	−0.0503909
$52$	18.3598	2.54605
$53$	5.66987	0.778817	0.389409	−	0.921065i	$-0.372679\pi$
$53$	5.66987	0.778817	0.389409	+	0.921065i	$0.372679\pi$
$54$	2.11394	0.287671
$55$	−1.06447	−0.143533
$56$	5.47867	0.732119
$57$	−0.793909	−0.105156
$58$	−14.4126	−1.89246
$59$	−8.68626	−1.13085	−0.565427	−	0.824798i	$-0.691289\pi$
$59$	−8.68626	−1.13085	−0.565427	+	0.824798i	$0.691289\pi$
$60$	−0.444666	−0.0574061
$61$	4.16869	0.533746	0.266873	−	0.963732i	$-0.414010\pi$
$61$	4.16869	0.533746	0.266873	+	0.963732i	$0.414010\pi$
$62$	−10.2554	−1.30243
$63$	10.2024	1.28539
$64$	−12.3987	−1.54984
$65$	−6.71561	−0.832969
$66$	−0.376698	−0.0463683
$67$	−5.88179	−0.718574	−0.359287	−	0.933227i	$-0.616980\pi$
$67$	−5.88179	−0.718574	−0.359287	+	0.933227i	$0.616980\pi$
$68$	−6.04879	−0.733523
$69$	−1.18501	−0.142659
$70$	−7.46515	−0.892256
$71$	−8.73545	−1.03671	−0.518353	−	0.855167i	$-0.673455\pi$
$71$	−8.73545	−1.03671	−0.518353	+	0.855167i	$0.673455\pi$
$72$	4.74811	0.559570
$73$	13.1641	1.54074	0.770369	−	0.637599i	$-0.220072\pi$
$73$	13.1641	1.54074	0.770369	+	0.637599i	$0.220072\pi$
$74$	−4.75948	−0.553278
$75$	0.162649	0.0187811
$76$	−13.3445	−1.53072
$77$	−3.65226	−0.416213
$78$	−2.37655	−0.269091
$79$	−0.535503	−0.0602488	−0.0301244	−	0.999546i	$-0.509590\pi$
$79$	−0.535503	−0.0602488	−0.0301244	+	0.999546i	$0.509590\pi$
$80$	1.99359	0.222890
$81$	8.76261	0.973623
$82$	−0.912805	−0.100802
$83$	6.93634	0.761362	0.380681	−	0.924706i	$-0.375690\pi$
$83$	6.93634	0.761362	0.380681	+	0.924706i	$0.375690\pi$
$84$	−1.52568	−0.166465
$85$	2.21251	0.239981
$86$	0.227218	0.0245015
$87$	1.07741	0.115511
$88$	−1.69972	−0.181191
$89$	13.3049	1.41032	0.705161	−	0.709047i	$-0.250875\pi$
$89$	13.3049	1.41032	0.705161	+	0.709047i	$0.250875\pi$
$90$	−6.46970	−0.681966
$91$	−23.0417	−2.41543
$92$	−19.9184	−2.07663
$93$	0.766642	0.0794971
$94$	5.35675	0.552507
$95$	4.88112	0.500792
$96$	1.22493	0.125019
$97$	12.0368	1.22215	0.611074	−	0.791574i	$-0.290738\pi$
$97$	12.0368	1.22215	0.611074	+	0.791574i	$0.290738\pi$
$98$	−10.3832	−1.04886
$99$	−3.16524	−0.318119
$100$	2.73390	0.273390
$101$	4.73383	0.471034	0.235517	−	0.971870i	$-0.424322\pi$
$101$	4.73383	0.471034	0.235517	+	0.971870i	$0.424322\pi$
$102$	0.782972	0.0775258
$103$	−0.555876	−0.0547721	−0.0273860	−	0.999625i	$-0.508718\pi$
$103$	−0.555876	−0.0547721	−0.0273860	+	0.999625i	$0.508718\pi$
$104$	−10.7234	−1.05151
$105$	0.558059	0.0544610
$106$	−12.3362	−1.19820
$107$	−9.55677	−0.923888	−0.461944	−	0.886909i	$-0.652848\pi$
$107$	−9.55677	−0.923888	−0.461944	+	0.886909i	$0.652848\pi$
$108$	−2.65623	−0.255596
$109$	−12.7932	−1.22536	−0.612681	−	0.790330i	$-0.709909\pi$
$109$	−12.7932	−1.22536	−0.612681	+	0.790330i	$0.709909\pi$
$110$	2.31602	0.220824
$111$	0.355796	0.0337707
$112$	6.84014	0.646333
$113$	−6.97004	−0.655686	−0.327843	−	0.944732i	$-0.606322\pi$
$113$	−6.97004	−0.655686	−0.327843	+	0.944732i	$0.606322\pi$
$114$	1.72735	0.161781
$115$	7.28570	0.679395
$116$	18.1098	1.68145
$117$	−19.9692	−1.84615
$118$	18.8992	1.73981
$119$	7.59128	0.695891
$120$	0.259715	0.0237087
$121$	−9.86691	−0.896992
$122$	−9.07004	−0.821163
$123$	0.0682370	0.00615272
$124$	12.8862	1.15721
$125$	−1.00000	−0.0894427
$126$	−22.1980	−1.97755
$127$	6.01513	0.533756	0.266878	−	0.963730i	$-0.414008\pi$
$127$	6.01513	0.533756	0.266878	+	0.963730i	$0.414008\pi$
$128$	11.9142	1.05308
$129$	−0.0169857	−0.00149551
$130$	14.6115	1.28151
$131$	−5.36136	−0.468424	−0.234212	−	0.972186i	$-0.575251\pi$
$131$	−5.36136	−0.468424	−0.234212	+	0.972186i	$0.575251\pi$
$132$	0.473332	0.0411983
$133$	16.7474	1.45219
$134$	12.7973	1.10552
$135$	0.971591	0.0836212
$136$	3.53290	0.302944
$137$	18.2877	1.56242	0.781212	−	0.624266i	$-0.214602\pi$
$137$	18.2877	1.56242	0.781212	+	0.624266i	$0.214602\pi$
$138$	2.57829	0.219479
$139$	4.20436	0.356609	0.178304	−	0.983975i	$-0.442939\pi$
$139$	4.20436	0.356609	0.178304	+	0.983975i	$0.442939\pi$
$140$	9.38019	0.792771
$141$	−0.400445	−0.0337236
$142$	19.0062	1.59496
$143$	7.14855	0.597792
$144$	5.92803	0.494003
$145$	−6.62417	−0.550108
$146$	−28.6417	−2.37041
$147$	0.776196	0.0640196
$148$	5.98043	0.491589
$149$	−2.32469	−0.190446	−0.0952230	−	0.995456i	$-0.530356\pi$
$149$	−2.32469	−0.190446	−0.0952230	+	0.995456i	$0.530356\pi$
$150$	−0.353884	−0.0288945
$151$	−19.5165	−1.58823	−0.794113	−	0.607770i	$-0.792064\pi$
$151$	−19.5165	−1.58823	−0.794113	+	0.607770i	$0.792064\pi$
$152$	7.79409	0.632185
$153$	6.57900	0.531881
$154$	7.94641	0.640340
$155$	−4.71348	−0.378596
$156$	2.98621	0.239088
$157$	13.7527	1.09758	0.548791	−	0.835960i	$-0.315088\pi$
$157$	13.7527	1.09758	0.548791	+	0.835960i	$0.315088\pi$
$158$	1.16512	0.0926922
$159$	0.922199	0.0731352
$160$	−7.53113	−0.595388
$161$	24.9977	1.97010
$162$	−19.0653	−1.49791
$163$	1.62280	0.127107	0.0635537	−	0.997978i	$-0.479757\pi$
$163$	1.62280	0.127107	0.0635537	+	0.997978i	$0.479757\pi$
$164$	1.14697	0.0895631
$165$	−0.173134	−0.0134785
$166$	−15.0918	−1.17135
$167$	−4.52655	−0.350275	−0.175138	−	0.984544i	$-0.556037\pi$
$167$	−4.52655	−0.350275	−0.175138	+	0.984544i	$0.556037\pi$
$168$	0.891101	0.0687499
$169$	32.0995	2.46919
$170$	−4.81388	−0.369208
$171$	14.5142	1.10993
$172$	−0.285506	−0.0217696
$173$	14.6807	1.11615	0.558077	−	0.829789i	$-0.311540\pi$
$173$	14.6807	1.11615	0.558077	+	0.829789i	$0.311540\pi$
$174$	−2.34419	−0.177712
$175$	−3.43107	−0.259364
$176$	−2.12211	−0.159960
$177$	−1.41281	−0.106193
$178$	−28.9483	−2.16977
$179$	22.7492	1.70036	0.850179	−	0.526494i	$-0.176494\pi$
$179$	22.7492	1.70036	0.850179	+	0.526494i	$0.176494\pi$
$180$	8.12938	0.605928
$181$	13.3206	0.990109	0.495055	−	0.868862i	$-0.335148\pi$
$181$	13.3206	0.990109	0.495055	+	0.868862i	$0.335148\pi$
$182$	50.1331	3.71611
$183$	0.678033	0.0501217
$184$	11.6337	0.857647
$185$	−2.18751	−0.160829
$186$	−1.66802	−0.122305
$187$	−2.35515	−0.172225
$188$	−6.73092	−0.490903
$189$	3.33359	0.242483
$190$	−10.6201	−0.770463
$191$	−14.1296	−1.02238	−0.511192	−	0.859467i	$-0.670796\pi$
$191$	−14.1296	−1.02238	−0.511192	+	0.859467i	$0.670796\pi$
$192$	−2.01664	−0.145538
$193$	12.3952	0.892229	0.446114	−	0.894976i	$-0.352807\pi$
$193$	12.3952	0.892229	0.446114	+	0.894976i	$0.352807\pi$
$194$	−26.1890	−1.88026
$195$	−1.09229	−0.0782204
$196$	13.0468	0.931912
$197$	−11.8432	−0.843795	−0.421898	−	0.906643i	$-0.638636\pi$
$197$	−11.8432	−0.843795	−0.421898	+	0.906643i	$0.638636\pi$
$198$	6.88678	0.489422
$199$	18.7265	1.32749	0.663745	−	0.747959i	$-0.268966\pi$
$199$	18.7265	1.32749	0.663745	+	0.747959i	$0.268966\pi$
$200$	−1.59678	−0.112910
$201$	−0.956666	−0.0674780
$202$	−10.2996	−0.724680
$203$	−22.7280	−1.59519
$204$	−0.983829	−0.0688818
$205$	−0.419535	−0.0293016
$206$	1.20945	0.0842663
$207$	21.6643	1.50578
$208$	−13.3882	−0.928304
$209$	−5.19579	−0.359400
$210$	−1.21420	−0.0837877
$211$	−6.14337	−0.422927	−0.211464	−	0.977386i	$-0.567823\pi$
$211$	−6.14337	−0.422927	−0.211464	+	0.977386i	$0.567823\pi$
$212$	15.5009	1.06460
$213$	−1.42081	−0.0973524
$214$	20.7932	1.42139
$215$	0.104432	0.00712219
$216$	1.55142	0.105561
$217$	−16.1723	−1.09784
$218$	27.8348	1.88521
$219$	2.14112	0.144684
$220$	−2.91015	−0.196202
$221$	−14.8584	−0.999483
$222$	−0.774125	−0.0519558
$223$	−9.14791	−0.612589	−0.306295	−	0.951937i	$-0.599089\pi$
$223$	−9.14791	−0.612589	−0.306295	+	0.951937i	$0.599089\pi$
$224$	−25.8398	−1.72650
$225$	−2.97355	−0.198236
$226$	15.1651	1.00877
$227$	13.3181	0.883956	0.441978	−	0.897026i	$-0.354277\pi$
$227$	13.3181	0.883956	0.441978	+	0.897026i	$0.354277\pi$
$228$	−2.17047	−0.143743
$229$	12.9814	0.857832	0.428916	−	0.903344i	$-0.358896\pi$
$229$	12.9814	0.857832	0.428916	+	0.903344i	$0.358896\pi$
$230$	−15.8519	−1.04524
$231$	−0.594036	−0.0390847
$232$	−10.5774	−0.694439
$233$	−5.09081	−0.333510	−0.166755	−	0.985998i	$-0.553329\pi$
$233$	−5.09081	−0.333510	−0.166755	+	0.985998i	$0.553329\pi$
$234$	43.4480	2.84029
$235$	2.46202	0.160605
$236$	−23.7474	−1.54582
$237$	−0.0870990	−0.00565769
$238$	−16.5167	−1.07062
$239$	−24.2481	−1.56848	−0.784239	−	0.620459i	$-0.786947\pi$
$239$	−24.2481	−1.56848	−0.784239	+	0.620459i	$0.786947\pi$
$240$	0.324256	0.0209306
$241$	−27.1229	−1.74714	−0.873569	−	0.486701i	$-0.838200\pi$
$241$	−27.1229	−1.74714	−0.873569	+	0.486701i	$0.838200\pi$
$242$	21.4680	1.38001
$243$	4.34000	0.278411
$244$	11.3968	0.729605
$245$	−4.77222	−0.304886
$246$	−0.148467	−0.00946589
$247$	−32.7797	−2.08572
$248$	−7.52641	−0.477928
$249$	1.12819	0.0714960
$250$	2.17575	0.137607
$251$	18.9902	1.19865	0.599326	−	0.800505i	$-0.295435\pi$
$251$	18.9902	1.19865	0.599326	+	0.800505i	$0.295435\pi$
$252$	27.8924	1.75706
$253$	−7.75538	−0.487577
$254$	−13.0874	−0.821179
$255$	0.359863	0.0225355
$256$	−1.12504	−0.0703148
$257$	−10.4158	−0.649719	−0.324860	−	0.945762i	$-0.605317\pi$
$257$	−10.4158	−0.649719	−0.324860	+	0.945762i	$0.605317\pi$
$258$	0.0369567	0.00230083
$259$	−7.50549	−0.466369
$260$	−18.3598	−1.13863
$261$	−19.6973	−1.21923
$262$	11.6650	0.720666
$263$	−3.69922	−0.228103	−0.114052	−	0.993475i	$-0.536383\pi$
$263$	−3.69922	−0.228103	−0.114052	+	0.993475i	$0.536383\pi$
$264$	−0.276458	−0.0170148
$265$	−5.66987	−0.348298
$266$	−36.4383	−2.23417
$267$	2.16404	0.132437
$268$	−16.0802	−0.982255
$269$	−26.2760	−1.60208	−0.801038	−	0.598614i	$-0.795718\pi$
$269$	−26.2760	−1.60208	−0.801038	+	0.598614i	$0.795718\pi$
$270$	−2.11394	−0.128650
$271$	−3.29168	−0.199955	−0.0999777	−	0.994990i	$-0.531877\pi$
$271$	−3.29168	−0.199955	−0.0999777	+	0.994990i	$0.531877\pi$
$272$	4.41084	0.267447
$273$	−3.74771	−0.226822
$274$	−39.7895	−2.40377
$275$	1.06447	0.0641898
$276$	−3.23970	−0.195007
$277$	−16.4558	−0.988732	−0.494366	−	0.869254i	$-0.664600\pi$
$277$	−16.4558	−0.988732	−0.494366	+	0.869254i	$0.664600\pi$
$278$	−9.14764	−0.548639
$279$	−14.0157	−0.839101
$280$	−5.47867	−0.327413
$281$	−25.7796	−1.53788	−0.768942	−	0.639319i	$-0.779216\pi$
$281$	−25.7796	−1.53788	−0.768942	+	0.639319i	$0.779216\pi$
$282$	0.871270	0.0518834
$283$	−1.56486	−0.0930214	−0.0465107	−	0.998918i	$-0.514810\pi$
$283$	−1.56486	−0.0930214	−0.0465107	+	0.998918i	$0.514810\pi$
$284$	−23.8818	−1.41713
$285$	0.793909	0.0470271
$286$	−15.5535	−0.919696
$287$	−1.43945	−0.0849682
$288$	−22.3942	−1.31959
$289$	−12.1048	−0.712047
$290$	14.4126	0.846335
$291$	1.95777	0.114766
$292$	35.9892	2.10611
$293$	10.3346	0.603755	0.301878	−	0.953347i	$-0.402387\pi$
$293$	10.3346	0.603755	0.301878	+	0.953347i	$0.402387\pi$
$294$	−1.68881	−0.0984935
$295$	8.68626	0.505734
$296$	−3.49298	−0.203025
$297$	−1.03423	−0.0600119
$298$	5.05795	0.292999
$299$	−48.9279	−2.82957
$300$	0.444666	0.0256728
$301$	0.358313	0.0206528
$302$	42.4630	2.44347
$303$	0.769953	0.0442326
$304$	9.73095	0.558108
$305$	−4.16869	−0.238699
$306$	−14.3143	−0.818293
$307$	−2.81889	−0.160883	−0.0804414	−	0.996759i	$-0.525633\pi$
$307$	−2.81889	−0.160883	−0.0804414	+	0.996759i	$0.525633\pi$
$308$	−9.98490	−0.568943
$309$	−0.0904127	−0.00514340
$310$	10.2554	0.582466
$311$	−18.4018	−1.04347	−0.521734	−	0.853108i	$-0.674715\pi$
$311$	−18.4018	−1.04347	−0.521734	+	0.853108i	$0.674715\pi$
$312$	−1.74415	−0.0987430
$313$	−20.1947	−1.14147	−0.570735	−	0.821134i	$-0.693342\pi$
$313$	−20.1947	−1.14147	−0.570735	+	0.821134i	$0.693342\pi$
$314$	−29.9224	−1.68862
$315$	−10.2024	−0.574842
$316$	−1.46401	−0.0823571
$317$	12.8060	0.719258	0.359629	−	0.933095i	$-0.382903\pi$
$317$	12.8060	0.719258	0.359629	+	0.933095i	$0.382903\pi$
$318$	−2.00648	−0.112518
$319$	7.05121	0.394792
$320$	12.3987	0.693108
$321$	−1.55440	−0.0867581
$322$	−54.3888	−3.03097
$323$	10.7995	0.600902
$324$	23.9561	1.33089
$325$	6.71561	0.372515
$326$	−3.53081	−0.195553
$327$	−2.08079	−0.115068
$328$	−0.669907	−0.0369894
$329$	8.44736	0.465718
$330$	0.376698	0.0207365
$331$	−15.8774	−0.872699	−0.436349	−	0.899777i	$-0.643729\pi$
$331$	−15.8774	−0.872699	−0.436349	+	0.899777i	$0.643729\pi$
$332$	18.9633	1.04074
$333$	−6.50466	−0.356453
$334$	9.84866	0.538895
$335$	5.88179	0.321356
$336$	1.11254	0.0606942
$337$	24.2785	1.32253	0.661266	−	0.750152i	$-0.270020\pi$
$337$	24.2785	1.32253	0.661266	+	0.750152i	$0.270020\pi$
$338$	−69.8405	−3.79882
$339$	−1.13367	−0.0615725
$340$	6.04879	0.328041
$341$	5.01734	0.271704
$342$	−31.5794	−1.70762
$343$	7.64367	0.412719
$344$	0.166755	0.00899083
$345$	1.18501	0.0637988
$346$	−31.9416	−1.71719
$347$	−6.48385	−0.348071	−0.174036	−	0.984739i	$-0.555681\pi$
$347$	−6.48385	−0.348071	−0.174036	+	0.984739i	$0.555681\pi$
$348$	2.94554	0.157898
$349$	14.2340	0.761930	0.380965	−	0.924590i	$-0.375592\pi$
$349$	14.2340	0.761930	0.380965	+	0.924590i	$0.375592\pi$
$350$	7.46515	0.399029
$351$	−6.52483	−0.348270
$352$	8.01664	0.427288
$353$	33.8294	1.80056	0.900278	−	0.435316i	$-0.143363\pi$
$353$	33.8294	1.80056	0.900278	+	0.435316i	$0.143363\pi$
$354$	3.07393	0.163377
$355$	8.73545	0.463629
$356$	36.3744	1.92784
$357$	1.23471	0.0653479
$358$	−49.4967	−2.61598
$359$	8.48384	0.447760	0.223880	−	0.974617i	$-0.428128\pi$
$359$	8.48384	0.447760	0.223880	+	0.974617i	$0.428128\pi$
$360$	−4.74811	−0.250247
$361$	4.82531	0.253964
$362$	−28.9822	−1.52327
$363$	−1.60484	−0.0842324
$364$	−62.9938	−3.30177
$365$	−13.1641	−0.689039
$366$	−1.47523	−0.0771117
$367$	24.3034	1.26863	0.634313	−	0.773077i	$-0.281283\pi$
$367$	24.3034	1.26863	0.634313	+	0.773077i	$0.281283\pi$
$368$	14.5247	0.757152
$369$	−1.24751	−0.0649426
$370$	4.75948	0.247434
$371$	−19.4537	−1.00999
$372$	2.09592	0.108669
$373$	31.3760	1.62459	0.812293	−	0.583249i	$-0.198219\pi$
$373$	31.3760	1.62459	0.812293	+	0.583249i	$0.198219\pi$
$374$	5.12421	0.264967
$375$	−0.162649	−0.00839916
$376$	3.93132	0.202742
$377$	44.4854	2.29111
$378$	−7.25308	−0.373058
$379$	23.5681	1.21061	0.605307	−	0.795992i	$-0.293050\pi$
$379$	23.5681	1.21061	0.605307	+	0.795992i	$0.293050\pi$
$380$	13.3445	0.684558
$381$	0.978355	0.0501226
$382$	30.7426	1.57293
$383$	16.9664	0.866941	0.433470	−	0.901168i	$-0.357289\pi$
$383$	16.9664	0.866941	0.433470	+	0.901168i	$0.357289\pi$
$384$	1.93784	0.0988899
$385$	3.65226	0.186136
$386$	−26.9690	−1.37268
$387$	0.310533	0.0157853
$388$	32.9073	1.67061
$389$	−20.4303	−1.03586	−0.517929	−	0.855424i	$-0.673297\pi$
$389$	−20.4303	−1.03586	−0.517929	+	0.855424i	$0.673297\pi$
$390$	2.37655	0.120341
$391$	16.1197	0.815208
$392$	−7.62021	−0.384879
$393$	−0.872020	−0.0439876
$394$	25.7679	1.29817
$395$	0.535503	0.0269441
$396$	−8.65345	−0.434852
$397$	−21.8412	−1.09618	−0.548088	−	0.836421i	$-0.684644\pi$
$397$	−21.8412	−1.09618	−0.548088	+	0.836421i	$0.684644\pi$
$398$	−40.7443	−2.04233
$399$	2.72395	0.136368
$400$	−1.99359	−0.0996796
$401$	10.3686	0.517783	0.258892	−	0.965906i	$-0.416643\pi$
$401$	10.3686	0.517783	0.258892	+	0.965906i	$0.416643\pi$
$402$	2.08147	0.103814
$403$	31.6539	1.57679
$404$	12.9418	0.643879
$405$	−8.76261	−0.435417
$406$	49.4505	2.45418
$407$	2.32853	0.115421
$408$	0.574623	0.0284481
$409$	13.2482	0.655081	0.327541	−	0.944837i	$-0.393780\pi$
$409$	13.2482	0.655081	0.327541	+	0.944837i	$0.393780\pi$
$410$	0.912805	0.0450802
$411$	2.97448	0.146720
$412$	−1.51971	−0.0748707
$413$	29.8031	1.46652
$414$	−47.1363	−2.31662
$415$	−6.93634	−0.340492
$416$	50.5762	2.47970
$417$	0.683834	0.0334875
$418$	11.3048	0.552933
$419$	−23.1533	−1.13111	−0.565555	−	0.824710i	$-0.691338\pi$
$419$	−23.1533	−1.13111	−0.565555	+	0.824710i	$0.691338\pi$
$420$	1.52568	0.0744455
$421$	2.89928	0.141302	0.0706512	−	0.997501i	$-0.477492\pi$
$421$	2.89928	0.141302	0.0706512	+	0.997501i	$0.477492\pi$
$422$	13.3665	0.650669
$423$	7.32094	0.355956
$424$	−9.05357	−0.439680
$425$	−2.21251	−0.107323
$426$	3.09133	0.149776
$427$	−14.3031	−0.692174
$428$	−26.1273	−1.26291
$429$	1.16270	0.0561359
$430$	−0.227218	−0.0109574
$431$	−38.4029	−1.84980	−0.924901	−	0.380207i	$-0.875853\pi$
$431$	−38.4029	−1.84980	−0.924901	+	0.380207i	$0.875853\pi$
$432$	1.93696	0.0931918
$433$	−5.43070	−0.260983	−0.130491	−	0.991449i	$-0.541655\pi$
$433$	−5.43070	−0.260983	−0.130491	+	0.991449i	$0.541655\pi$
$434$	35.1868	1.68902
$435$	−1.07741	−0.0516581
$436$	−34.9752	−1.67501
$437$	35.5623	1.70118
$438$	−4.65855	−0.222594
$439$	23.5726	1.12506	0.562529	−	0.826778i	$-0.309829\pi$
$439$	23.5726	1.12506	0.562529	+	0.826778i	$0.309829\pi$
$440$	1.69972	0.0810312
$441$	−14.1904	−0.675734
$442$	32.3282	1.53769
$443$	−11.2897	−0.536390	−0.268195	−	0.963365i	$-0.586427\pi$
$443$	−11.2897	−0.536390	−0.268195	+	0.963365i	$0.586427\pi$
$444$	0.972711	0.0461628
$445$	−13.3049	−0.630715
$446$	19.9036	0.942462
$447$	−0.378109	−0.0178839
$448$	42.5408	2.00986
$449$	−31.0831	−1.46690	−0.733452	−	0.679741i	$-0.762092\pi$
$449$	−31.0831	−1.46690	−0.733452	+	0.679741i	$0.762092\pi$
$450$	6.46970	0.304985
$451$	0.446581	0.0210287
$452$	−19.0554	−0.896291
$453$	−3.17433	−0.149143
$454$	−28.9770	−1.35996
$455$	23.0417	1.08021
$456$	1.26770	0.0593656
$457$	−39.8390	−1.86359	−0.931794	−	0.362988i	$-0.881757\pi$
$457$	−39.8390	−1.86359	−0.931794	+	0.362988i	$0.881757\pi$
$458$	−28.2442	−1.31977
$459$	2.14966	0.100337
$460$	19.9184	0.928698
$461$	−17.3898	−0.809922	−0.404961	−	0.914334i	$-0.632715\pi$
$461$	−17.3898	−0.809922	−0.404961	+	0.914334i	$0.632715\pi$
$462$	1.29247	0.0601314
$463$	−9.38678	−0.436241	−0.218120	−	0.975922i	$-0.569993\pi$
$463$	−9.38678	−0.436241	−0.218120	+	0.975922i	$0.569993\pi$
$464$	−13.2059	−0.613068
$465$	−0.766642	−0.0355522
$466$	11.0763	0.513102
$467$	−25.1099	−1.16195	−0.580973	−	0.813923i	$-0.697328\pi$
$467$	−25.1099	−1.16195	−0.580973	+	0.813923i	$0.697328\pi$
$468$	−54.5938	−2.52360
$469$	20.1808	0.931863
$470$	−5.35675	−0.247089
$471$	2.23685	0.103069
$472$	13.8701	0.638423
$473$	−0.111164	−0.00511134
$474$	0.189506	0.00870430
$475$	−4.88112	−0.223961
$476$	20.7538	0.951248
$477$	−16.8596	−0.771949
$478$	52.7578	2.41309
$479$	−37.7412	−1.72444	−0.862220	−	0.506534i	$-0.830926\pi$
$479$	−37.7412	−1.72444	−0.862220	+	0.506534i	$0.830926\pi$
$480$	−1.22493	−0.0559102
$481$	14.6905	0.669828
$482$	59.0127	2.68795
$483$	4.06585	0.185003
$484$	−26.9751	−1.22614
$485$	−12.0368	−0.546561
$486$	−9.44277	−0.428333
$487$	30.6801	1.39025	0.695124	−	0.718890i	$-0.255349\pi$
$487$	30.6801	1.39025	0.695124	+	0.718890i	$0.255349\pi$
$488$	−6.65650	−0.301326
$489$	0.263947	0.0119361
$490$	10.3832	0.469064
$491$	−15.3167	−0.691232	−0.345616	−	0.938376i	$-0.612330\pi$
$491$	−15.3167	−0.691232	−0.345616	+	0.938376i	$0.612330\pi$
$492$	0.186553	0.00841046
$493$	−14.6561	−0.660076
$494$	71.3205	3.20886
$495$	3.16524	0.142267
$496$	−9.39675	−0.421927
$497$	29.9719	1.34442
$498$	−2.45466	−0.109996
$499$	30.4144	1.36154	0.680768	−	0.732500i	$-0.261646\pi$
$499$	30.4144	1.36154	0.680768	+	0.732500i	$0.261646\pi$
$500$	−2.73390	−0.122264
$501$	−0.736239	−0.0328927
$502$	−41.3180	−1.84411
$503$	−23.0089	−1.02592	−0.512959	−	0.858413i	$-0.671451\pi$
$503$	−23.0089	−1.02592	−0.512959	+	0.858413i	$0.671451\pi$
$504$	−16.2911	−0.725663
$505$	−4.73383	−0.210653
$506$	16.8738	0.750132
$507$	5.22095	0.231870
$508$	16.4448	0.729618
$509$	33.1599	1.46979	0.734894	−	0.678182i	$-0.237232\pi$
$509$	33.1599	1.46979	0.734894	+	0.678182i	$0.237232\pi$
$510$	−0.782972	−0.0346706
$511$	−45.1668	−1.99806
$512$	−21.3807	−0.944901
$513$	4.74245	0.209384
$514$	22.6622	0.999586
$515$	0.555876	0.0244948
$516$	−0.0464373	−0.00204429
$517$	−2.62074	−0.115260
$518$	16.3301	0.717503
$519$	2.38780	0.104813
$520$	10.7234	0.470252
$521$	1.94204	0.0850824	0.0425412	−	0.999095i	$-0.486455\pi$
$521$	1.94204	0.0850824	0.0425412	+	0.999095i	$0.486455\pi$
$522$	42.8564	1.87577
$523$	7.72435	0.337762	0.168881	−	0.985636i	$-0.445985\pi$
$523$	7.72435	0.337762	0.168881	+	0.985636i	$0.445985\pi$
$524$	−14.6574	−0.640313
$525$	−0.558059	−0.0243557
$526$	8.04858	0.350935
$527$	−10.4286	−0.454278
$528$	−0.345159	−0.0150211
$529$	30.0814	1.30789
$530$	12.3362	0.535852
$531$	25.8290	1.12088
$532$	45.7858	1.98507
$533$	2.81744	0.122037
$534$	−4.70841	−0.203753
$535$	9.55677	0.413175
$536$	9.39194	0.405670
$537$	3.70014	0.159673
$538$	57.1701	2.46478
$539$	5.07987	0.218805
$540$	2.65623	0.114306
$541$	−28.8861	−1.24191	−0.620956	−	0.783845i	$-0.713255\pi$
$541$	−28.8861	−1.24191	−0.620956	+	0.783845i	$0.713255\pi$
$542$	7.16188	0.307629
$543$	2.16658	0.0929766
$544$	−16.6627	−0.714408
$545$	12.7932	0.547999
$546$	8.15410	0.348963
$547$	4.22583	0.180683	0.0903416	−	0.995911i	$-0.471204\pi$
$547$	4.22583	0.180683	0.0903416	+	0.995911i	$0.471204\pi$
$548$	49.9968	2.13576
$549$	−12.3958	−0.529040
$550$	−2.31602	−0.0987553
$551$	−32.3334	−1.37745
$552$	1.89221	0.0805377
$553$	1.83735	0.0781320
$554$	35.8037	1.52115
$555$	−0.355796	−0.0151027
$556$	11.4943	0.487466
$557$	−1.01455	−0.0429879	−0.0214940	−	0.999769i	$-0.506842\pi$
$557$	−1.01455	−0.0429879	−0.0214940	+	0.999769i	$0.506842\pi$
$558$	30.4948	1.29095
$559$	−0.701324	−0.0296628
$560$	−6.84014	−0.289049
$561$	−0.383062	−0.0161729
$562$	56.0901	2.36602
$563$	5.21440	0.219761	0.109880	−	0.993945i	$-0.464953\pi$
$563$	5.21440	0.219761	0.109880	+	0.993945i	$0.464953\pi$
$564$	−1.09478	−0.0460985
$565$	6.97004	0.293232
$566$	3.40475	0.143112
$567$	−30.0651	−1.26262
$568$	13.9486	0.585271
$569$	−34.7248	−1.45574	−0.727870	−	0.685715i	$-0.759490\pi$
$569$	−34.7248	−1.45574	−0.727870	+	0.685715i	$0.759490\pi$
$570$	−1.72735	−0.0723507
$571$	−8.98538	−0.376026	−0.188013	−	0.982167i	$-0.560205\pi$
$571$	−8.98538	−0.376026	−0.188013	+	0.982167i	$0.560205\pi$
$572$	19.5434	0.817151
$573$	−2.29817	−0.0960074
$574$	3.13189	0.130723
$575$	−7.28570	−0.303834
$576$	36.8681	1.53617
$577$	−40.1008	−1.66942	−0.834709	−	0.550691i	$-0.814364\pi$
$577$	−40.1008	−1.66942	−0.834709	+	0.550691i	$0.814364\pi$
$578$	26.3370	1.09548
$579$	2.01607	0.0837851
$580$	−18.1098	−0.751969
$581$	−23.7990	−0.987351
$582$	−4.25961	−0.176567
$583$	6.03539	0.249960
$584$	−21.0202	−0.869821
$585$	19.9692	0.825624
$586$	−22.4856	−0.928871
$587$	23.8256	0.983387	0.491694	−	0.870768i	$-0.336378\pi$
$587$	23.8256	0.983387	0.491694	+	0.870768i	$0.336378\pi$
$588$	2.12204	0.0875116
$589$	−23.0070	−0.947989
$590$	−18.8992	−0.778066
$591$	−1.92629	−0.0792370
$592$	−4.36100	−0.179236
$593$	34.7922	1.42874	0.714372	−	0.699766i	$-0.246713\pi$
$593$	34.7922	1.42874	0.714372	+	0.699766i	$0.246713\pi$
$594$	2.25022	0.0923277
$595$	−7.59128	−0.311212
$596$	−6.35547	−0.260330
$597$	3.04585	0.124659
$598$	106.455	4.35327
$599$	−41.2594	−1.68581	−0.842907	−	0.538060i	$-0.819157\pi$
$599$	−41.2594	−1.68581	−0.842907	+	0.538060i	$0.819157\pi$
$600$	−0.259715	−0.0106028
$601$	16.5235	0.674006	0.337003	−	0.941504i	$-0.390587\pi$
$601$	16.5235	0.674006	0.337003	+	0.941504i	$0.390587\pi$
$602$	−0.779599	−0.0317741
$603$	17.4898	0.712238
$604$	−53.3560	−2.17103
$605$	9.86691	0.401147
$606$	−1.67523	−0.0680514
$607$	17.8164	0.723145	0.361573	−	0.932344i	$-0.382240\pi$
$607$	17.8164	0.723145	0.361573	+	0.932344i	$0.382240\pi$
$608$	−36.7603	−1.49083
$609$	−3.69668	−0.149797
$610$	9.07004	0.367235
$611$	−16.5340	−0.668894
$612$	17.9863	0.727055
$613$	3.83268	0.154801	0.0774003	−	0.997000i	$-0.475338\pi$
$613$	3.83268	0.154801	0.0774003	+	0.997000i	$0.475338\pi$
$614$	6.13322	0.247517
$615$	−0.0682370	−0.00275158
$616$	5.83187	0.234973
$617$	−29.5729	−1.19056	−0.595280	−	0.803518i	$-0.702959\pi$
$617$	−29.5729	−1.19056	−0.595280	+	0.803518i	$0.702959\pi$
$618$	0.196716	0.00791306
$619$	−8.36070	−0.336045	−0.168022	−	0.985783i	$-0.553738\pi$
$619$	−8.36070	−0.336045	−0.168022	+	0.985783i	$0.553738\pi$
$620$	−12.8862	−0.517521
$621$	7.07872	0.284059
$622$	40.0377	1.60536
$623$	−45.6502	−1.82894
$624$	−2.17758	−0.0871728
$625$	1.00000	0.0400000
$626$	43.9386	1.75614
$627$	−0.845090	−0.0337496
$628$	37.5984	1.50034
$629$	−4.83989	−0.192979
$630$	22.1980	0.884388
$631$	−25.7313	−1.02435	−0.512173	−	0.858882i	$-0.671159\pi$
$631$	−25.7313	−1.02435	−0.512173	+	0.858882i	$0.671159\pi$
$632$	0.855083	0.0340134
$633$	−0.999213	−0.0397152
$634$	−27.8627	−1.10657
$635$	−6.01513	−0.238703
$636$	2.52120	0.0999721
$637$	32.0484	1.26980
$638$	−15.3417	−0.607383
$639$	25.9752	1.02756
$640$	−11.9142	−0.470951
$641$	−33.1111	−1.30781	−0.653905	−	0.756577i	$-0.726870\pi$
$641$	−33.1111	−1.30781	−0.653905	+	0.756577i	$0.726870\pi$
$642$	3.38199	0.133476
$643$	41.4766	1.63568	0.817838	−	0.575448i	$-0.195172\pi$
$643$	41.4766	1.63568	0.817838	+	0.575448i	$0.195172\pi$
$644$	68.3412	2.69302
$645$	0.0169857	0.000668812 0
$646$	−23.4971	−0.924481
$647$	−21.9409	−0.862586	−0.431293	−	0.902212i	$-0.641942\pi$
$647$	−21.9409	−0.862586	−0.431293	+	0.902212i	$0.641942\pi$
$648$	−13.9920	−0.549658
$649$	−9.24624	−0.362947
$650$	−14.6115	−0.573111
$651$	−2.63040	−0.103094
$652$	4.43657	0.173749
$653$	21.4816	0.840641	0.420320	−	0.907376i	$-0.361918\pi$
$653$	21.4816	0.840641	0.420320	+	0.907376i	$0.361918\pi$
$654$	4.52729	0.177031
$655$	5.36136	0.209486
$656$	−0.836381	−0.0326552
$657$	−39.1439	−1.52715
$658$	−18.3794	−0.716503
$659$	−22.0923	−0.860592	−0.430296	−	0.902688i	$-0.641591\pi$
$659$	−22.0923	−0.860592	−0.430296	+	0.902688i	$0.641591\pi$
$660$	−0.473332	−0.0184244
$661$	−30.4567	−1.18463	−0.592314	−	0.805707i	$-0.701786\pi$
$661$	−30.4567	−1.18463	−0.592314	+	0.805707i	$0.701786\pi$
$662$	34.5452	1.34264
$663$	−2.41670	−0.0938568
$664$	−11.0758	−0.429826
$665$	−16.7474	−0.649438
$666$	14.1525	0.548399
$667$	−48.2617	−1.86870
$668$	−12.3751	−0.478809
$669$	−1.48790	−0.0575254
$670$	−12.7973	−0.494403
$671$	4.43743	0.171305
$672$	−4.20282	−0.162127
$673$	7.58717	0.292464	0.146232	−	0.989250i	$-0.453285\pi$
$673$	7.58717	0.292464	0.146232	+	0.989250i	$0.453285\pi$
$674$	−52.8239	−2.03470
$675$	−0.971591	−0.0373966
$676$	87.7568	3.37526
$677$	−38.5231	−1.48056	−0.740281	−	0.672298i	$-0.765307\pi$
$677$	−38.5231	−1.48056	−0.740281	+	0.672298i	$0.765307\pi$
$678$	2.46659	0.0947287
$679$	−41.2989	−1.58491
$680$	−3.53290	−0.135481
$681$	2.16618	0.0830082
$682$	−10.9165	−0.418014
$683$	12.4381	0.475931	0.237965	−	0.971274i	$-0.423520\pi$
$683$	12.4381	0.475931	0.237965	+	0.971274i	$0.423520\pi$
$684$	39.6804	1.51722
$685$	−18.2877	−0.698737
$686$	−16.6307	−0.634964
$687$	2.11140	0.0805551
$688$	0.208194	0.00793733
$689$	38.0767	1.45061
$690$	−2.57829	−0.0981538
$691$	6.75663	0.257034	0.128517	−	0.991707i	$-0.458978\pi$
$691$	6.75663	0.257034	0.128517	+	0.991707i	$0.458978\pi$
$692$	40.1356	1.52573
$693$	10.8602	0.412543
$694$	14.1072	0.535504
$695$	−4.20436	−0.159480
$696$	−1.72040	−0.0652116
$697$	−0.928226	−0.0351591
$698$	−30.9697	−1.17222
$699$	−0.828015	−0.0313184
$700$	−9.38019	−0.354538
$701$	8.98729	0.339445	0.169723	−	0.985492i	$-0.445713\pi$
$701$	8.98729	0.339445	0.169723	+	0.985492i	$0.445713\pi$
$702$	14.1964	0.535809
$703$	−10.6775	−0.402709
$704$	−13.1980	−0.497418
$705$	0.400445	0.0150816
$706$	−73.6043	−2.77014
$707$	−16.2421	−0.610847
$708$	−3.86249	−0.145161
$709$	−2.24163	−0.0841861	−0.0420931	−	0.999114i	$-0.513403\pi$
$709$	−2.24163	−0.0841861	−0.0420931	+	0.999114i	$0.513403\pi$
$710$	−19.0062	−0.713289
$711$	1.59234	0.0597175
$712$	−21.2451	−0.796195
$713$	−34.3410	−1.28608
$714$	−2.68643	−0.100537
$715$	−7.14855	−0.267341
$716$	62.1941	2.32430
$717$	−3.94393	−0.147289
$718$	−18.4587	−0.688874
$719$	30.6210	1.14197	0.570985	−	0.820960i	$-0.306561\pi$
$719$	30.6210	1.14197	0.570985	+	0.820960i	$0.306561\pi$
$720$	−5.92803	−0.220925
$721$	1.90725	0.0710296
$722$	−10.4987	−0.390721
$723$	−4.41151	−0.164066
$724$	36.4171	1.35343
$725$	6.62417	0.246016
$726$	3.49174	0.129591
$727$	−11.1710	−0.414311	−0.207155	−	0.978308i	$-0.566421\pi$
$727$	−11.1710	−0.414311	−0.207155	+	0.978308i	$0.566421\pi$
$728$	36.7927	1.36363
$729$	−25.5819	−0.947479
$730$	28.6417	1.06008
$731$	0.231057	0.00854594
$732$	1.85368	0.0685138
$733$	−48.5787	−1.79429	−0.897147	−	0.441733i	$-0.854364\pi$
$733$	−48.5787	−1.79429	−0.897147	+	0.441733i	$0.854364\pi$
$734$	−52.8781	−1.95177
$735$	−0.776196	−0.0286304
$736$	−54.8695	−2.02252
$737$	−6.26097	−0.230626
$738$	2.71427	0.0999135
$739$	43.5285	1.60122	0.800612	−	0.599183i	$-0.204508\pi$
$739$	43.5285	1.60122	0.800612	+	0.599183i	$0.204508\pi$
$740$	−5.98043	−0.219845
$741$	−5.33159	−0.195861
$742$	42.3265	1.55385
$743$	−31.0788	−1.14017	−0.570085	−	0.821586i	$-0.693090\pi$
$743$	−31.0788	−1.14017	−0.570085	+	0.821586i	$0.693090\pi$
$744$	−1.22416	−0.0448800
$745$	2.32469	0.0851701
$746$	−68.2664	−2.49941
$747$	−20.6255	−0.754648
$748$	−6.43873	−0.235423
$749$	32.7899	1.19812
$750$	0.353884	0.0129220
$751$	4.18828	0.152832	0.0764162	−	0.997076i	$-0.475652\pi$
$751$	4.18828	0.152832	0.0764162	+	0.997076i	$0.475652\pi$
$752$	4.90827	0.178986
$753$	3.08874	0.112560
$754$	−96.7892	−3.52485
$755$	19.5165	0.710276
$756$	9.11371	0.331462
$757$	−11.9071	−0.432772	−0.216386	−	0.976308i	$-0.569427\pi$
$757$	−11.9071	−0.432772	−0.216386	+	0.976308i	$0.569427\pi$
$758$	−51.2784	−1.86252
$759$	−1.26140	−0.0457861
$760$	−7.79409	−0.282722
$761$	19.9974	0.724906	0.362453	−	0.932002i	$-0.381939\pi$
$761$	19.9974	0.724906	0.362453	+	0.932002i	$0.381939\pi$
$762$	−2.12866	−0.0771131
$763$	43.8942	1.58908
$764$	−38.6290	−1.39755
$765$	−6.57900	−0.237864
$766$	−36.9146	−1.33378
$767$	−58.3336	−2.10630
$768$	−0.182986	−0.00660294
$769$	0.411437	0.0148368	0.00741839	−	0.999972i	$-0.497639\pi$
$769$	0.411437	0.0148368	0.00741839	+	0.999972i	$0.497639\pi$
$770$	−7.94641	−0.286369
$771$	−1.69412	−0.0610121
$772$	33.8873	1.21963
$773$	−18.4830	−0.664789	−0.332394	−	0.943141i	$-0.607856\pi$
$773$	−18.4830	−0.664789	−0.332394	+	0.943141i	$0.607856\pi$
$774$	−0.675642	−0.0242855
$775$	4.71348	0.169313
$776$	−19.2201	−0.689962
$777$	−1.22076	−0.0437945
$778$	44.4513	1.59366
$779$	−2.04780	−0.0733701
$780$	−2.98621	−0.106923
$781$	−9.29859	−0.332730
$782$	−35.0725	−1.25419
$783$	−6.43599	−0.230003
$784$	−9.51385	−0.339780
$785$	−13.7527	−0.490853
$786$	1.89730	0.0676744
$787$	−15.0679	−0.537111	−0.268556	−	0.963264i	$-0.586546\pi$
$787$	−15.0679	−0.537111	−0.268556	+	0.963264i	$0.586546\pi$
$788$	−32.3782	−1.15343
$789$	−0.601674	−0.0214201
$790$	−1.16512	−0.0414532
$791$	23.9147	0.850308
$792$	5.05421	0.179593
$793$	27.9953	0.994143
$794$	47.5210	1.68646
$795$	−0.922199	−0.0327070
$796$	51.1965	1.81461
$797$	−46.8772	−1.66048	−0.830238	−	0.557409i	$-0.811796\pi$
$797$	−46.8772	−1.66048	−0.830238	+	0.557409i	$0.811796\pi$
$798$	−5.92665	−0.209801
$799$	5.44725	0.192710
$800$	7.53113	0.266266
$801$	−39.5629	−1.39789
$802$	−22.5595	−0.796604
$803$	14.0127	0.494498
$804$	−2.61543	−0.0922391
$805$	−24.9977	−0.881053
$806$	−68.8711	−2.42588
$807$	−4.27376	−0.150444
$808$	−7.55891	−0.265921
$809$	−21.7369	−0.764228	−0.382114	−	0.924115i	$-0.624804\pi$
$809$	−21.7369	−0.764228	−0.382114	+	0.924115i	$0.624804\pi$
$810$	19.0653	0.669885
$811$	3.33670	0.117168	0.0585838	−	0.998282i	$-0.481342\pi$
$811$	3.33670	0.117168	0.0585838	+	0.998282i	$0.481342\pi$
$812$	−62.1360	−2.18055
$813$	−0.535388	−0.0187769
$814$	−5.06631	−0.177574
$815$	−1.62280	−0.0568442
$816$	0.717419	0.0251147
$817$	0.509744	0.0178337
$818$	−28.8248	−1.00784
$819$	68.5156	2.39413
$820$	−1.14697	−0.0400538
$821$	−29.2013	−1.01913	−0.509567	−	0.860431i	$-0.670194\pi$
$821$	−29.2013	−1.01913	−0.509567	+	0.860431i	$0.670194\pi$
$822$	−6.47172	−0.225727
$823$	38.7491	1.35071	0.675354	−	0.737494i	$-0.263991\pi$
$823$	38.7491	1.35071	0.675354	+	0.737494i	$0.263991\pi$
$824$	0.887614	0.0309215
$825$	0.173134	0.00602777
$826$	−64.8443	−2.25622
$827$	−41.5242	−1.44394	−0.721969	−	0.691926i	$-0.756763\pi$
$827$	−41.5242	−1.44394	−0.721969	+	0.691926i	$0.756763\pi$
$828$	59.2282	2.05832
$829$	16.6981	0.579948	0.289974	−	0.957034i	$-0.406353\pi$
$829$	16.6981	0.579948	0.289974	+	0.957034i	$0.406353\pi$
$830$	15.0918	0.523843
$831$	−2.67651	−0.0928473
$832$	−83.2649	−2.88669
$833$	−10.5586	−0.365833
$834$	−1.48785	−0.0515202
$835$	4.52655	0.156648
$836$	−14.2048	−0.491282
$837$	−4.57957	−0.158293
$838$	50.3758	1.74020
$839$	−36.4088	−1.25697	−0.628486	−	0.777821i	$-0.716325\pi$
$839$	−36.4088	−1.25697	−0.628486	+	0.777821i	$0.716325\pi$
$840$	−0.891101	−0.0307459
$841$	14.8797	0.513092
$842$	−6.30812	−0.217392
$843$	−4.19303	−0.144416
$844$	−16.7954	−0.578120
$845$	−32.0995	−1.10426
$846$	−15.9285	−0.547635
$847$	33.8540	1.16324
$848$	−11.3034	−0.388161
$849$	−0.254523	−0.00873522
$850$	4.81388	0.165115
$851$	−15.9375	−0.546332
$852$	−3.88436	−0.133076
$853$	5.24941	0.179736	0.0898682	−	0.995954i	$-0.471355\pi$
$853$	5.24941	0.179736	0.0898682	+	0.995954i	$0.471355\pi$
$854$	31.1199	1.06490
$855$	−14.5142	−0.496376
$856$	15.2601	0.521580
$857$	19.0827	0.651853	0.325926	−	0.945395i	$-0.394324\pi$
$857$	19.0827	0.651853	0.325926	+	0.945395i	$0.394324\pi$
$858$	−2.52976	−0.0863645
$859$	−31.6727	−1.08066	−0.540329	−	0.841454i	$-0.681700\pi$
$859$	−31.6727	−1.08066	−0.540329	+	0.841454i	$0.681700\pi$
$860$	0.285506	0.00973568
$861$	−0.234126	−0.00797898
$862$	83.5552	2.84590
$863$	−10.1097	−0.344139	−0.172069	−	0.985085i	$-0.555045\pi$
$863$	−10.1097	−0.344139	−0.172069	+	0.985085i	$0.555045\pi$
$864$	−7.31718	−0.248935
$865$	−14.6807	−0.499159
$866$	11.8159	0.401519
$867$	−1.96883	−0.0668650
$868$	−44.2133	−1.50070
$869$	−0.570025	−0.0193368
$870$	2.34419	0.0794754
$871$	−39.4998	−1.33840
$872$	20.4279	0.691777
$873$	−35.7918	−1.21137
$874$	−77.3749	−2.61724
$875$	3.43107	0.115991
$876$	5.85361	0.197775
$877$	25.4725	0.860146	0.430073	−	0.902794i	$-0.358488\pi$
$877$	25.4725	0.860146	0.430073	+	0.902794i	$0.358488\pi$
$878$	−51.2881	−1.73089
$879$	1.68092	0.0566959
$880$	2.12211	0.0715364
$881$	9.81920	0.330817	0.165409	−	0.986225i	$-0.447106\pi$
$881$	9.81920	0.330817	0.165409	+	0.986225i	$0.447106\pi$
$882$	30.8748	1.03961
$883$	−34.5948	−1.16421	−0.582103	−	0.813115i	$-0.697770\pi$
$883$	−34.5948	−1.16421	−0.582103	+	0.813115i	$0.697770\pi$
$884$	−40.6213	−1.36624
$885$	1.41281	0.0474911
$886$	24.5636	0.825230
$887$	42.5668	1.42925	0.714626	−	0.699507i	$-0.246597\pi$
$887$	42.5668	1.42925	0.714626	+	0.699507i	$0.246597\pi$
$888$	−0.568130	−0.0190652
$889$	−20.6383	−0.692187
$890$	28.9483	0.970349
$891$	9.32751	0.312483
$892$	−25.0095	−0.837379
$893$	12.0174	0.402148
$894$	0.822671	0.0275142
$895$	−22.7492	−0.760423
$896$	−40.8785	−1.36566
$897$	−7.95808	−0.265712
$898$	67.6292	2.25682
$899$	31.2229	1.04134
$900$	−8.12938	−0.270979
$901$	−12.5447	−0.417923
$902$	−0.971650	−0.0323524
$903$	0.0582792	0.00193941
$904$	11.1297	0.370167
$905$	−13.3206	−0.442790
$906$	6.90656	0.229455
$907$	−35.3512	−1.17382	−0.586909	−	0.809653i	$-0.699656\pi$
$907$	−35.3512	−1.17382	−0.586909	+	0.809653i	$0.699656\pi$
$908$	36.4104	1.20832
$909$	−14.0763	−0.466880
$910$	−50.1331	−1.66190
$911$	−15.7738	−0.522611	−0.261305	−	0.965256i	$-0.584153\pi$
$911$	−15.7738	−0.522611	−0.261305	+	0.965256i	$0.584153\pi$
$912$	1.58273	0.0524094
$913$	7.38350	0.244358
$914$	86.6797	2.86711
$915$	−0.678033	−0.0224151
$916$	35.4897	1.17261
$917$	18.3952	0.607463
$918$	−4.67712	−0.154368
$919$	45.9635	1.51620	0.758098	−	0.652141i	$-0.226129\pi$
$919$	45.9635	1.51620	0.758098	+	0.652141i	$0.226129\pi$
$920$	−11.6337	−0.383551
$921$	−0.458490	−0.0151078
$922$	37.8358	1.24606
$923$	−58.6639	−1.93095
$924$	−1.62403	−0.0534268
$925$	2.18751	0.0719249
$926$	20.4233	0.671152
$927$	1.65292	0.0542891
$928$	49.8875	1.63764
$929$	−26.5431	−0.870850	−0.435425	−	0.900225i	$-0.643402\pi$
$929$	−26.5431	−0.870850	−0.435425	+	0.900225i	$0.643402\pi$
$930$	1.66802	0.0546967
$931$	−23.2938	−0.763422
$932$	−13.9178	−0.455892
$933$	−2.99303	−0.0979873
$934$	54.6329	1.78764
$935$	2.35515	0.0770215
$936$	31.8865	1.04224
$937$	15.0040	0.490161	0.245080	−	0.969503i	$-0.421186\pi$
$937$	15.0040	0.490161	0.245080	+	0.969503i	$0.421186\pi$
$938$	−43.9084	−1.43366
$939$	−3.28464	−0.107190
$940$	6.73092	0.219539
$941$	−6.52129	−0.212588	−0.106294	−	0.994335i	$-0.533898\pi$
$941$	−6.52129	−0.212588	−0.106294	+	0.994335i	$0.533898\pi$
$942$	−4.86684	−0.158570
$943$	−3.05660	−0.0995368
$944$	17.3169	0.563616
$945$	−3.33359	−0.108442
$946$	0.241866	0.00786374
$947$	0.853061	0.0277208	0.0138604	−	0.999904i	$-0.495588\pi$
$947$	0.853061	0.0277208	0.0138604	+	0.999904i	$0.495588\pi$
$948$	−0.238120	−0.00773378
$949$	88.4048	2.86974
$950$	10.6201	0.344562
$951$	2.08289	0.0675422
$952$	−12.1216	−0.392864
$953$	−14.0426	−0.454883	−0.227442	−	0.973792i	$-0.573036\pi$
$953$	−14.0426	−0.454883	−0.227442	+	0.973792i	$0.573036\pi$
$954$	36.6824	1.18764
$955$	14.1296	0.457224
$956$	−66.2918	−2.14403
$957$	1.14687	0.0370731
$958$	82.1155	2.65303
$959$	−62.7463	−2.02618
$960$	2.01664	0.0650866
$961$	−8.78312	−0.283326
$962$	−31.9628	−1.03052
$963$	28.4175	0.915741
$964$	−74.1512	−2.38825
$965$	−12.3952	−0.399017
$966$	−8.84629	−0.284625
$967$	−52.2191	−1.67925	−0.839626	−	0.543165i	$-0.817226\pi$
$967$	−52.2191	−1.67925	−0.839626	+	0.543165i	$0.817226\pi$
$968$	15.7553	0.506396
$969$	1.75653	0.0564280
$970$	26.1890	0.840878
$971$	30.6810	0.984600	0.492300	−	0.870426i	$-0.336156\pi$
$971$	30.6810	0.984600	0.492300	+	0.870426i	$0.336156\pi$
$972$	11.8651	0.380574
$973$	−14.4254	−0.462458
$974$	−66.7523	−2.13888
$975$	1.09229	0.0349812
$976$	−8.31067	−0.266018
$977$	32.2596	1.03208	0.516039	−	0.856565i	$-0.327406\pi$
$977$	32.2596	1.03208	0.516039	+	0.856565i	$0.327406\pi$
$978$	−0.574283	−0.0183635
$979$	14.1627	0.452641
$980$	−13.0468	−0.416764
$981$	38.0410	1.21456
$982$	33.3253	1.06345
$983$	−38.4275	−1.22565	−0.612824	−	0.790219i	$-0.709967\pi$
$983$	−38.4275	−1.22565	−0.612824	+	0.790219i	$0.709967\pi$
$984$	−0.108960	−0.00347351
$985$	11.8432	0.377357
$986$	31.8880	1.01552
$987$	1.37396	0.0437335
$988$	−89.6164	−2.85108
$989$	0.760858	0.0241939
$990$	−6.88678	−0.218876
$991$	−42.7374	−1.35760	−0.678799	−	0.734324i	$-0.737499\pi$
$991$	−42.7374	−1.35760	−0.678799	+	0.734324i	$0.737499\pi$
$992$	35.4978	1.12706
$993$	−2.58244	−0.0819512
$994$	−65.2114	−2.06838
$995$	−18.7265	−0.593672
$996$	3.08435	0.0977315
$997$	26.1784	0.829080	0.414540	−	0.910031i	$-0.363943\pi$
$997$	26.1784	0.829080	0.414540	+	0.910031i	$0.363943\pi$
$998$	−66.1742	−2.09471
$999$	−2.12537	−0.0672436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8005.2.a.f.1.16	✓	127

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8005.2.a.f.1.16	✓	127	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:	\( N \)	\(=\)	\( 8005 = 5 \cdot 1601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17575 q^{2} +0.162649 q^{3} +2.73390 q^{4} -1.00000 q^{5} -0.353884 q^{6} -3.43107 q^{7} -1.59678 q^{8} -2.97355 q^{9} +O(q^{10})\)	\(q-2.17575 q^{2} +0.162649 q^{3} +2.73390 q^{4} -1.00000 q^{5} -0.353884 q^{6} -3.43107 q^{7} -1.59678 q^{8} -2.97355 q^{9} +2.17575 q^{10} +1.06447 q^{11} +0.444666 q^{12} +6.71561 q^{13} +7.46515 q^{14} -0.162649 q^{15} -1.99359 q^{16} -2.21251 q^{17} +6.46970 q^{18} -4.88112 q^{19} -2.73390 q^{20} -0.558059 q^{21} -2.31602 q^{22} -7.28570 q^{23} -0.259715 q^{24} +1.00000 q^{25} -14.6115 q^{26} -0.971591 q^{27} -9.38019 q^{28} +6.62417 q^{29} +0.353884 q^{30} +4.71348 q^{31} +7.53113 q^{32} +0.173134 q^{33} +4.81388 q^{34} +3.43107 q^{35} -8.12938 q^{36} +2.18751 q^{37} +10.6201 q^{38} +1.09229 q^{39} +1.59678 q^{40} +0.419535 q^{41} +1.21420 q^{42} -0.104432 q^{43} +2.91015 q^{44} +2.97355 q^{45} +15.8519 q^{46} -2.46202 q^{47} -0.324256 q^{48} +4.77222 q^{49} -2.17575 q^{50} -0.359863 q^{51} +18.3598 q^{52} +5.66987 q^{53} +2.11394 q^{54} -1.06447 q^{55} +5.47867 q^{56} -0.793909 q^{57} -14.4126 q^{58} -8.68626 q^{59} -0.444666 q^{60} +4.16869 q^{61} -10.2554 q^{62} +10.2024 q^{63} -12.3987 q^{64} -6.71561 q^{65} -0.376698 q^{66} -5.88179 q^{67} -6.04879 q^{68} -1.18501 q^{69} -7.46515 q^{70} -8.73545 q^{71} +4.74811 q^{72} +13.1641 q^{73} -4.75948 q^{74} +0.162649 q^{75} -13.3445 q^{76} -3.65226 q^{77} -2.37655 q^{78} -0.535503 q^{79} +1.99359 q^{80} +8.76261 q^{81} -0.912805 q^{82} +6.93634 q^{83} -1.52568 q^{84} +2.21251 q^{85} +0.227218 q^{86} +1.07741 q^{87} -1.69972 q^{88} +13.3049 q^{89} -6.46970 q^{90} -23.0417 q^{91} -19.9184 q^{92} +0.766642 q^{93} +5.35675 q^{94} +4.88112 q^{95} +1.22493 q^{96} +12.0368 q^{97} -10.3832 q^{98} -3.16524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9}+O(q^{10}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9	\( 127 q - 6 q^{2} - 18 q^{3} + 114 q^{4} - 127 q^{5} - 20 q^{6} + 28 q^{7} - 18 q^{8} + 101 q^{9} + 6 q^{10} - 45 q^{11} - 30 q^{12} - 53 q^{14} + 18 q^{15} + 84 q^{16} - 36 q^{17} - 10 q^{18} - 49 q^{19} - 114 q^{20} - 48 q^{21} + 13 q^{22} - 29 q^{23} - 63 q^{24} + 127 q^{25} - 55 q^{26} - 75 q^{27} + 44 q^{28} - 45 q^{29} + 20 q^{30} - 49 q^{31} - 32 q^{32} - 8 q^{33} - 52 q^{34} - 28 q^{35} + 44 q^{36} + 36 q^{37} - 65 q^{38} - 52 q^{39} + 18 q^{40} - 66 q^{41} - 18 q^{42} - 5 q^{43} - 93 q^{44} - 101 q^{45} - 25 q^{46} - 32 q^{47} - 54 q^{48} + 77 q^{49} - 6 q^{50} - 102 q^{51} - 13 q^{52} - 67 q^{53} - 53 q^{54} + 45 q^{55} - 158 q^{56} + 16 q^{57} + 35 q^{58} - 213 q^{59} + 30 q^{60} - 62 q^{61} - 33 q^{62} + 59 q^{63} + 34 q^{64} - 60 q^{66} + 10 q^{67} - 94 q^{68} - 93 q^{69} + 53 q^{70} - 118 q^{71} - 24 q^{72} + 35 q^{73} - 107 q^{74} - 18 q^{75} - 98 q^{76} - 93 q^{77} + 21 q^{78} - 64 q^{79} - 84 q^{80} + 15 q^{81} + 15 q^{82} - 187 q^{83} - 118 q^{84} + 36 q^{85} - 126 q^{86} - 53 q^{87} + 15 q^{88} - 138 q^{89} + 10 q^{90} - 138 q^{91} - 86 q^{92} + 23 q^{93} - 60 q^{94} + 49 q^{95} - 92 q^{96} + 9 q^{97} - 67 q^{98} - 147 q^{99}+O(q^{100}) \) 127 * q - 6 * q^2 - 18 * q^3 + 114 * q^4 - 127 * q^5 - 20 * q^6 + 28 * q^7 - 18 * q^8 + 101 * q^9 + 6 * q^10 - 45 * q^11 - 30 * q^12 - 53 * q^14 + 18 * q^15 + 84 * q^16 - 36 * q^17 - 10 * q^18 - 49 * q^19 - 114 * q^20 - 48 * q^21 + 13 * q^22 - 29 * q^23 - 63 * q^24 + 127 * q^25 - 55 * q^26 - 75 * q^27 + 44 * q^28 - 45 * q^29 + 20 * q^30 - 49 * q^31 - 32 * q^32 - 8 * q^33 - 52 * q^34 - 28 * q^35 + 44 * q^36 + 36 * q^37 - 65 * q^38 - 52 * q^39 + 18 * q^40 - 66 * q^41 - 18 * q^42 - 5 * q^43 - 93 * q^44 - 101 * q^45 - 25 * q^46 - 32 * q^47 - 54 * q^48 + 77 * q^49 - 6 * q^50 - 102 * q^51 - 13 * q^52 - 67 * q^53 - 53 * q^54 + 45 * q^55 - 158 * q^56 + 16 * q^57 + 35 * q^58 - 213 * q^59 + 30 * q^60 - 62 * q^61 - 33 * q^62 + 59 * q^63 + 34 * q^64 - 60 * q^66 + 10 * q^67 - 94 * q^68 - 93 * q^69 + 53 * q^70 - 118 * q^71 - 24 * q^72 + 35 * q^73 - 107 * q^74 - 18 * q^75 - 98 * q^76 - 93 * q^77 + 21 * q^78 - 64 * q^79 - 84 * q^80 + 15 * q^81 + 15 * q^82 - 187 * q^83 - 118 * q^84 + 36 * q^85 - 126 * q^86 - 53 * q^87 + 15 * q^88 - 138 * q^89 + 10 * q^90 - 138 * q^91 - 86 * q^92 + 23 * q^93 - 60 * q^94 + 49 * q^95 - 92 * q^96 + 9 * q^97 - 67 * q^98 - 147 * q^99

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