LMFDB - Embedded newform 8007.2.a.j.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69904 q^{2} -1.00000 q^{3} +5.28480 q^{4} -1.39519 q^{5} +2.69904 q^{6} -4.02432 q^{7} -8.86580 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.69904 q^{2} -1.00000 q^{3} +5.28480 q^{4} -1.39519 q^{5} +2.69904 q^{6} -4.02432 q^{7} -8.86580 q^{8} +1.00000 q^{9} +3.76567 q^{10} -4.50878 q^{11} -5.28480 q^{12} +6.27088 q^{13} +10.8618 q^{14} +1.39519 q^{15} +13.3595 q^{16} +1.00000 q^{17} -2.69904 q^{18} -0.936912 q^{19} -7.37329 q^{20} +4.02432 q^{21} +12.1694 q^{22} -3.43565 q^{23} +8.86580 q^{24} -3.05345 q^{25} -16.9253 q^{26} -1.00000 q^{27} -21.2677 q^{28} -0.713369 q^{29} -3.76567 q^{30} -4.52582 q^{31} -18.3262 q^{32} +4.50878 q^{33} -2.69904 q^{34} +5.61469 q^{35} +5.28480 q^{36} -4.09969 q^{37} +2.52876 q^{38} -6.27088 q^{39} +12.3695 q^{40} -3.33697 q^{41} -10.8618 q^{42} +0.999978 q^{43} -23.8280 q^{44} -1.39519 q^{45} +9.27296 q^{46} +6.04485 q^{47} -13.3595 q^{48} +9.19517 q^{49} +8.24137 q^{50} -1.00000 q^{51} +33.1404 q^{52} +3.14493 q^{53} +2.69904 q^{54} +6.29059 q^{55} +35.6788 q^{56} +0.936912 q^{57} +1.92541 q^{58} -13.9294 q^{59} +7.37329 q^{60} +14.5661 q^{61} +12.2154 q^{62} -4.02432 q^{63} +22.7442 q^{64} -8.74906 q^{65} -12.1694 q^{66} +7.10967 q^{67} +5.28480 q^{68} +3.43565 q^{69} -15.1543 q^{70} -8.69442 q^{71} -8.86580 q^{72} +3.71040 q^{73} +11.0652 q^{74} +3.05345 q^{75} -4.95139 q^{76} +18.1448 q^{77} +16.9253 q^{78} -11.0868 q^{79} -18.6390 q^{80} +1.00000 q^{81} +9.00660 q^{82} -14.9149 q^{83} +21.2677 q^{84} -1.39519 q^{85} -2.69898 q^{86} +0.713369 q^{87} +39.9739 q^{88} -10.9723 q^{89} +3.76567 q^{90} -25.2360 q^{91} -18.1567 q^{92} +4.52582 q^{93} -16.3153 q^{94} +1.30717 q^{95} +18.3262 q^{96} -15.2770 q^{97} -24.8181 q^{98} -4.50878 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−2.69904	−1.90851	−0.954254	−	0.298998i	$-0.903348\pi$
$2$	−2.69904	−1.90851	−0.954254	+	0.298998i	$0.903348\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.28480	2.64240
$5$	−1.39519	−0.623947	−0.311974	−	0.950091i	$-0.600990\pi$
$5$	−1.39519	−0.623947	−0.311974	+	0.950091i	$0.600990\pi$
$6$	2.69904	1.10188
$7$	−4.02432	−1.52105	−0.760525	−	0.649308i	$-0.775059\pi$
$7$	−4.02432	−1.52105	−0.760525	+	0.649308i	$0.775059\pi$
$8$	−8.86580	−3.13453
$9$	1.00000	0.333333
$10$	3.76567	1.19081
$11$	−4.50878	−1.35945	−0.679723	−	0.733468i	$-0.737900\pi$
$11$	−4.50878	−1.35945	−0.679723	+	0.733468i	$0.737900\pi$
$12$	−5.28480	−1.52559
$13$	6.27088	1.73923	0.869615	−	0.493731i	$-0.164367\pi$
$13$	6.27088	1.73923	0.869615	+	0.493731i	$0.164367\pi$
$14$	10.8618	2.90294
$15$	1.39519	0.360236
$16$	13.3595	3.33988
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.69904	−0.636169
$19$	−0.936912	−0.214942	−0.107471	−	0.994208i	$-0.534275\pi$
$19$	−0.936912	−0.214942	−0.107471	+	0.994208i	$0.534275\pi$
$20$	−7.37329	−1.64872
$21$	4.02432	0.878179
$22$	12.1694	2.59451
$23$	−3.43565	−0.716383	−0.358192	−	0.933648i	$-0.616607\pi$
$23$	−3.43565	−0.716383	−0.358192	+	0.933648i	$0.616607\pi$
$24$	8.86580	1.80972
$25$	−3.05345	−0.610690
$26$	−16.9253	−3.31933
$27$	−1.00000	−0.192450
$28$	−21.2677	−4.01923
$29$	−0.713369	−0.132469	−0.0662346	−	0.997804i	$-0.521099\pi$
$29$	−0.713369	−0.132469	−0.0662346	+	0.997804i	$0.521099\pi$
$30$	−3.76567	−0.687513
$31$	−4.52582	−0.812862	−0.406431	−	0.913682i	$-0.633227\pi$
$31$	−4.52582	−0.812862	−0.406431	+	0.913682i	$0.633227\pi$
$32$	−18.3262	−3.23965
$33$	4.50878	0.784877
$34$	−2.69904	−0.462881
$35$	5.61469	0.949055
$36$	5.28480	0.880800
$37$	−4.09969	−0.673984	−0.336992	−	0.941507i	$-0.609410\pi$
$37$	−4.09969	−0.673984	−0.336992	+	0.941507i	$0.609410\pi$
$38$	2.52876	0.410219
$39$	−6.27088	−1.00414
$40$	12.3695	1.95578
$41$	−3.33697	−0.521147	−0.260573	−	0.965454i	$-0.583912\pi$
$41$	−3.33697	−0.521147	−0.260573	+	0.965454i	$0.583912\pi$
$42$	−10.8618	−1.67601
$43$	0.999978	0.152495	0.0762476	−	0.997089i	$-0.475706\pi$
$43$	0.999978	0.152495	0.0762476	+	0.997089i	$0.475706\pi$
$44$	−23.8280	−3.59220
$45$	−1.39519	−0.207982
$46$	9.27296	1.36722
$47$	6.04485	0.881732	0.440866	−	0.897573i	$-0.354671\pi$
$47$	6.04485	0.881732	0.440866	+	0.897573i	$0.354671\pi$
$48$	−13.3595	−1.92828
$49$	9.19517	1.31360
$50$	8.24137	1.16551
$51$	−1.00000	−0.140028
$52$	33.1404	4.59574
$53$	3.14493	0.431990	0.215995	−	0.976394i	$-0.430701\pi$
$53$	3.14493	0.431990	0.215995	+	0.976394i	$0.430701\pi$
$54$	2.69904	0.367292
$55$	6.29059	0.848223
$56$	35.6788	4.76779
$57$	0.936912	0.124097
$58$	1.92541	0.252819
$59$	−13.9294	−1.81346	−0.906730	−	0.421713i	$-0.861429\pi$
$59$	−13.9294	−1.81346	−0.906730	+	0.421713i	$0.861429\pi$
$60$	7.37329	0.951888
$61$	14.5661	1.86500	0.932499	−	0.361172i	$-0.117623\pi$
$61$	14.5661	1.86500	0.932499	+	0.361172i	$0.117623\pi$
$62$	12.2154	1.55135
$63$	−4.02432	−0.507017
$64$	22.7442	2.84302
$65$	−8.74906	−1.08519
$66$	−12.1694	−1.49794
$67$	7.10967	0.868584	0.434292	−	0.900772i	$-0.356999\pi$
$67$	7.10967	0.868584	0.434292	+	0.900772i	$0.356999\pi$
$68$	5.28480	0.640876
$69$	3.43565	0.413604
$70$	−15.1543	−1.81128
$71$	−8.69442	−1.03184	−0.515919	−	0.856637i	$-0.672549\pi$
$71$	−8.69442	−1.03184	−0.515919	+	0.856637i	$0.672549\pi$
$72$	−8.86580	−1.04484
$73$	3.71040	0.434270	0.217135	−	0.976142i	$-0.430329\pi$
$73$	3.71040	0.434270	0.217135	+	0.976142i	$0.430329\pi$
$74$	11.0652	1.28630
$75$	3.05345	0.352582
$76$	−4.95139	−0.567964
$77$	18.1448	2.06779
$78$	16.9253	1.91642
$79$	−11.0868	−1.24736	−0.623681	−	0.781679i	$-0.714364\pi$
$79$	−11.0868	−1.24736	−0.623681	+	0.781679i	$0.714364\pi$
$80$	−18.6390	−2.08391
$81$	1.00000	0.111111
$82$	9.00660	0.994613
$83$	−14.9149	−1.63713	−0.818564	−	0.574415i	$-0.805229\pi$
$83$	−14.9149	−1.63713	−0.818564	+	0.574415i	$0.805229\pi$
$84$	21.2677	2.32050
$85$	−1.39519	−0.151329
$86$	−2.69898	−0.291038
$87$	0.713369	0.0764812
$88$	39.9739	4.26123
$89$	−10.9723	−1.16306	−0.581530	−	0.813525i	$-0.697546\pi$
$89$	−10.9723	−1.16306	−0.581530	+	0.813525i	$0.697546\pi$
$90$	3.76567	0.396936
$91$	−25.2360	−2.64546
$92$	−18.1567	−1.89297
$93$	4.52582	0.469306
$94$	−16.3153	−1.68279
$95$	1.30717	0.134113
$96$	18.3262	1.87041
$97$	−15.2770	−1.55114	−0.775570	−	0.631261i	$-0.782538\pi$
$97$	−15.2770	−1.55114	−0.775570	+	0.631261i	$0.782538\pi$
$98$	−24.8181	−2.50701
$99$	−4.50878	−0.453149
$100$	−16.1369	−1.61369
$101$	14.2076	1.41371	0.706855	−	0.707358i	$-0.250113\pi$
$101$	14.2076	1.41371	0.706855	+	0.707358i	$0.250113\pi$
$102$	2.69904	0.267244
$103$	11.4058	1.12385	0.561926	−	0.827188i	$-0.310061\pi$
$103$	11.4058	1.12385	0.561926	+	0.827188i	$0.310061\pi$
$104$	−55.5964	−5.45167
$105$	−5.61469	−0.547937
$106$	−8.48830	−0.824456
$107$	1.93080	0.186657	0.0933286	−	0.995635i	$-0.470249\pi$
$107$	1.93080	0.186657	0.0933286	+	0.995635i	$0.470249\pi$
$108$	−5.28480	−0.508530
$109$	−16.3094	−1.56216	−0.781081	−	0.624430i	$-0.785331\pi$
$109$	−16.3094	−1.56216	−0.781081	+	0.624430i	$0.785331\pi$
$110$	−16.9785	−1.61884
$111$	4.09969	0.389125
$112$	−53.7630	−5.08013
$113$	−4.04417	−0.380443	−0.190222	−	0.981741i	$-0.560921\pi$
$113$	−4.04417	−0.380443	−0.190222	+	0.981741i	$0.560921\pi$
$114$	−2.52876	−0.236840
$115$	4.79338	0.446985
$116$	−3.77001	−0.350037
$117$	6.27088	0.579743
$118$	37.5961	3.46100
$119$	−4.02432	−0.368909
$120$	−12.3695	−1.12917
$121$	9.32905	0.848096
$122$	−39.3144	−3.55936
$123$	3.33697	0.300884
$124$	−23.9181	−2.14791
$125$	11.2361	1.00499
$126$	10.8618	0.967646
$127$	−20.7353	−1.83996	−0.919982	−	0.391960i	$-0.871797\pi$
$127$	−20.7353	−1.83996	−0.919982	+	0.391960i	$0.871797\pi$
$128$	−24.7349	−2.18627
$129$	−0.999978	−0.0880431
$130$	23.6140	2.07109
$131$	−3.58003	−0.312789	−0.156395	−	0.987695i	$-0.549987\pi$
$131$	−3.58003	−0.312789	−0.156395	+	0.987695i	$0.549987\pi$
$132$	23.8280	2.07396
$133$	3.77043	0.326938
$134$	−19.1893	−1.65770
$135$	1.39519	0.120079
$136$	−8.86580	−0.760236
$137$	−5.26133	−0.449506	−0.224753	−	0.974416i	$-0.572158\pi$
$137$	−5.26133	−0.449506	−0.224753	+	0.974416i	$0.572158\pi$
$138$	−9.27296	−0.789366
$139$	−1.88082	−0.159529	−0.0797646	−	0.996814i	$-0.525417\pi$
$139$	−1.88082	−0.159529	−0.0797646	+	0.996814i	$0.525417\pi$
$140$	29.6725	2.50778
$141$	−6.04485	−0.509068
$142$	23.4666	1.96927
$143$	−28.2740	−2.36439
$144$	13.3595	1.11329
$145$	0.995284	0.0826538
$146$	−10.0145	−0.828807
$147$	−9.19517	−0.758405
$148$	−21.6660	−1.78094
$149$	−16.2738	−1.33320	−0.666601	−	0.745414i	$-0.732252\pi$
$149$	−16.2738	−1.33320	−0.666601	+	0.745414i	$0.732252\pi$
$150$	−8.24137	−0.672905
$151$	4.31638	0.351262	0.175631	−	0.984456i	$-0.443803\pi$
$151$	4.31638	0.351262	0.175631	+	0.984456i	$0.443803\pi$
$152$	8.30647	0.673744
$153$	1.00000	0.0808452
$154$	−48.9734	−3.94639
$155$	6.31437	0.507183
$156$	−33.1404	−2.65335
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	29.9237	2.38060
$159$	−3.14493	−0.249410
$160$	25.5686	2.02137
$161$	13.8262	1.08966
$162$	−2.69904	−0.212056
$163$	20.7002	1.62136	0.810682	−	0.585487i	$-0.199097\pi$
$163$	20.7002	1.62136	0.810682	+	0.585487i	$0.199097\pi$
$164$	−17.6352	−1.37708
$165$	−6.29059	−0.489722
$166$	40.2560	3.12447
$167$	19.6736	1.52239	0.761193	−	0.648526i	$-0.224614\pi$
$167$	19.6736	1.52239	0.761193	+	0.648526i	$0.224614\pi$
$168$	−35.6788	−2.75268
$169$	26.3239	2.02492
$170$	3.76567	0.288813
$171$	−0.936912	−0.0716474
$172$	5.28468	0.402953
$173$	−5.04254	−0.383377	−0.191689	−	0.981456i	$-0.561396\pi$
$173$	−5.04254	−0.383377	−0.191689	+	0.981456i	$0.561396\pi$
$174$	−1.92541	−0.145965
$175$	12.2881	0.928890
$176$	−60.2351	−4.54039
$177$	13.9294	1.04700
$178$	29.6146	2.21971
$179$	5.27729	0.394443	0.197221	−	0.980359i	$-0.436808\pi$
$179$	5.27729	0.394443	0.197221	+	0.980359i	$0.436808\pi$
$180$	−7.37329	−0.549573
$181$	−21.2415	−1.57887	−0.789435	−	0.613834i	$-0.789626\pi$
$181$	−21.2415	−1.57887	−0.789435	+	0.613834i	$0.789626\pi$
$182$	68.1130	5.04887
$183$	−14.5661	−1.07676
$184$	30.4598	2.24553
$185$	5.71984	0.420531
$186$	−12.2154	−0.895674
$187$	−4.50878	−0.329714
$188$	31.9458	2.32989
$189$	4.02432	0.292726
$190$	−3.52810	−0.255955
$191$	−24.1190	−1.74519	−0.872597	−	0.488442i	$-0.837566\pi$
$191$	−24.1190	−1.74519	−0.872597	+	0.488442i	$0.837566\pi$
$192$	−22.7442	−1.64142
$193$	−12.5692	−0.904754	−0.452377	−	0.891827i	$-0.649424\pi$
$193$	−12.5692	−0.904754	−0.452377	+	0.891827i	$0.649424\pi$
$194$	41.2331	2.96036
$195$	8.74906	0.626533
$196$	48.5946	3.47105
$197$	−11.5162	−0.820494	−0.410247	−	0.911975i	$-0.634557\pi$
$197$	−11.5162	−0.820494	−0.410247	+	0.911975i	$0.634557\pi$
$198$	12.1694	0.864838
$199$	−17.6821	−1.25345	−0.626724	−	0.779241i	$-0.715605\pi$
$199$	−17.6821	−1.25345	−0.626724	+	0.779241i	$0.715605\pi$
$200$	27.0713	1.91423
$201$	−7.10967	−0.501477
$202$	−38.3469	−2.69808
$203$	2.87083	0.201492
$204$	−5.28480	−0.370010
$205$	4.65570	0.325168
$206$	−30.7848	−2.14488
$207$	−3.43565	−0.238794
$208$	83.7760	5.80882
$209$	4.22432	0.292203
$210$	15.1543	1.04574
$211$	12.2510	0.843391	0.421695	−	0.906738i	$-0.361435\pi$
$211$	12.2510	0.843391	0.421695	+	0.906738i	$0.361435\pi$
$212$	16.6204	1.14149
$213$	8.69442	0.595732
$214$	−5.21129	−0.356237
$215$	−1.39516	−0.0951489
$216$	8.86580	0.603241
$217$	18.2134	1.23640
$218$	44.0198	2.98140
$219$	−3.71040	−0.250726
$220$	33.2445	2.24135
$221$	6.27088	0.421825
$222$	−11.0652	−0.742648
$223$	−25.4810	−1.70633	−0.853167	−	0.521638i	$-0.825321\pi$
$223$	−25.4810	−1.70633	−0.853167	+	0.521638i	$0.825321\pi$
$224$	73.7507	4.92768
$225$	−3.05345	−0.203563
$226$	10.9154	0.726079
$227$	−5.35227	−0.355243	−0.177621	−	0.984099i	$-0.556840\pi$
$227$	−5.35227	−0.355243	−0.177621	+	0.984099i	$0.556840\pi$
$228$	4.95139	0.327914
$229$	8.83483	0.583822	0.291911	−	0.956445i	$-0.405709\pi$
$229$	8.83483	0.583822	0.291911	+	0.956445i	$0.405709\pi$
$230$	−12.9375	−0.853075
$231$	−18.1448	−1.19384
$232$	6.32459	0.415229
$233$	−16.2168	−1.06240	−0.531200	−	0.847247i	$-0.678259\pi$
$233$	−16.2168	−1.06240	−0.531200	+	0.847247i	$0.678259\pi$
$234$	−16.9253	−1.10644
$235$	−8.43370	−0.550154
$236$	−73.6143	−4.79189
$237$	11.0868	0.720165
$238$	10.8618	0.704066
$239$	−20.5714	−1.33065	−0.665327	−	0.746552i	$-0.731708\pi$
$239$	−20.5714	−1.33065	−0.665327	+	0.746552i	$0.731708\pi$
$240$	18.6390	1.20315
$241$	0.336297	0.0216628	0.0108314	−	0.999941i	$-0.496552\pi$
$241$	0.336297	0.0216628	0.0108314	+	0.999941i	$0.496552\pi$
$242$	−25.1795	−1.61860
$243$	−1.00000	−0.0641500
$244$	76.9790	4.92807
$245$	−12.8290	−0.819614
$246$	−9.00660	−0.574240
$247$	−5.87526	−0.373834
$248$	40.1250	2.54794
$249$	14.9149	0.945196
$250$	−30.3266	−1.91802
$251$	−8.39917	−0.530151	−0.265075	−	0.964228i	$-0.585397\pi$
$251$	−8.39917	−0.530151	−0.265075	+	0.964228i	$0.585397\pi$
$252$	−21.2677	−1.33974
$253$	15.4906	0.973885
$254$	55.9655	3.51159
$255$	1.39519	0.0873701
$256$	21.2720	1.32950
$257$	21.0428	1.31261	0.656307	−	0.754494i	$-0.272117\pi$
$257$	21.0428	1.31261	0.656307	+	0.754494i	$0.272117\pi$
$258$	2.69898	0.168031
$259$	16.4985	1.02516
$260$	−46.2370	−2.86750
$261$	−0.713369	−0.0441564
$262$	9.66265	0.596960
$263$	30.9109	1.90605	0.953024	−	0.302894i	$-0.0979529\pi$
$263$	30.9109	1.90605	0.953024	+	0.302894i	$0.0979529\pi$
$264$	−39.9739	−2.46022
$265$	−4.38778	−0.269539
$266$	−10.1765	−0.623964
$267$	10.9723	0.671493
$268$	37.5732	2.29515
$269$	−2.47144	−0.150686	−0.0753432	−	0.997158i	$-0.524005\pi$
$269$	−2.47144	−0.150686	−0.0753432	+	0.997158i	$0.524005\pi$
$270$	−3.76567	−0.229171
$271$	−27.2477	−1.65518	−0.827589	−	0.561334i	$-0.810288\pi$
$271$	−27.2477	−1.65518	−0.827589	+	0.561334i	$0.810288\pi$
$272$	13.3595	0.810040
$273$	25.2360	1.52735
$274$	14.2005	0.857886
$275$	13.7673	0.830200
$276$	18.1567	1.09291
$277$	−24.4154	−1.46698	−0.733490	−	0.679700i	$-0.762110\pi$
$277$	−24.4154	−1.46698	−0.733490	+	0.679700i	$0.762110\pi$
$278$	5.07640	0.304463
$279$	−4.52582	−0.270954
$280$	−49.7787	−2.97485
$281$	−6.77651	−0.404252	−0.202126	−	0.979359i	$-0.564785\pi$
$281$	−6.77651	−0.404252	−0.202126	+	0.979359i	$0.564785\pi$
$282$	16.3153	0.971560
$283$	6.54969	0.389338	0.194669	−	0.980869i	$-0.437637\pi$
$283$	6.54969	0.389338	0.194669	+	0.980869i	$0.437637\pi$
$284$	−45.9483	−2.72653
$285$	−1.30717	−0.0774300
$286$	76.3125	4.51246
$287$	13.4290	0.792691
$288$	−18.3262	−1.07988
$289$	1.00000	0.0588235
$290$	−2.68631	−0.157745
$291$	15.2770	0.895551
$292$	19.6087	1.14751
$293$	−10.4943	−0.613081	−0.306541	−	0.951858i	$-0.599172\pi$
$293$	−10.4943	−0.613081	−0.306541	+	0.951858i	$0.599172\pi$
$294$	24.8181	1.44742
$295$	19.4342	1.13150
$296$	36.3470	2.11263
$297$	4.50878	0.261626
$298$	43.9236	2.54443
$299$	−21.5446	−1.24595
$300$	16.1369	0.931663
$301$	−4.02423	−0.231953
$302$	−11.6501	−0.670386
$303$	−14.2076	−0.816206
$304$	−12.5167	−0.717882
$305$	−20.3225	−1.16366
$306$	−2.69904	−0.154294
$307$	−22.9157	−1.30787	−0.653935	−	0.756550i	$-0.726883\pi$
$307$	−22.9157	−1.30787	−0.653935	+	0.756550i	$0.726883\pi$
$308$	95.8915	5.46392
$309$	−11.4058	−0.648856
$310$	−17.0427	−0.967962
$311$	−1.52904	−0.0867040	−0.0433520	−	0.999060i	$-0.513804\pi$
$311$	−1.52904	−0.0867040	−0.0433520	+	0.999060i	$0.513804\pi$
$312$	55.5964	3.14752
$313$	−10.0254	−0.566668	−0.283334	−	0.959021i	$-0.591440\pi$
$313$	−10.0254	−0.566668	−0.283334	+	0.959021i	$0.591440\pi$
$314$	2.69904	0.152315
$315$	5.61469	0.316352
$316$	−58.5915	−3.29603
$317$	18.6589	1.04799	0.523993	−	0.851723i	$-0.324442\pi$
$317$	18.6589	1.04799	0.523993	+	0.851723i	$0.324442\pi$
$318$	8.48830	0.476000
$319$	3.21642	0.180085
$320$	−31.7324	−1.77390
$321$	−1.93080	−0.107767
$322$	−37.3174	−2.07962
$323$	−0.936912	−0.0521312
$324$	5.28480	0.293600
$325$	−19.1478	−1.06213
$326$	−55.8706	−3.09438
$327$	16.3094	0.901914
$328$	29.5849	1.63355
$329$	−24.3264	−1.34116
$330$	16.9785	0.934638
$331$	−2.56682	−0.141085	−0.0705425	−	0.997509i	$-0.522473\pi$
$331$	−2.56682	−0.141085	−0.0705425	+	0.997509i	$0.522473\pi$
$332$	−78.8225	−4.32595
$333$	−4.09969	−0.224661
$334$	−53.0997	−2.90548
$335$	−9.91932	−0.541951
$336$	53.7630	2.93301
$337$	−18.7750	−1.02274	−0.511370	−	0.859361i	$-0.670862\pi$
$337$	−18.7750	−1.02274	−0.511370	+	0.859361i	$0.670862\pi$
$338$	−71.0493	−3.86457
$339$	4.04417	0.219649
$340$	−7.37329	−0.399873
$341$	20.4059	1.10504
$342$	2.52876	0.136740
$343$	−8.83407	−0.476995
$344$	−8.86560	−0.478001
$345$	−4.79338	−0.258067
$346$	13.6100	0.731678
$347$	−16.4101	−0.880940	−0.440470	−	0.897767i	$-0.645188\pi$
$347$	−16.4101	−0.880940	−0.440470	+	0.897767i	$0.645188\pi$
$348$	3.77001	0.202094
$349$	32.2739	1.72758	0.863792	−	0.503848i	$-0.168083\pi$
$349$	32.2739	1.72758	0.863792	+	0.503848i	$0.168083\pi$
$350$	−33.1659	−1.77279
$351$	−6.27088	−0.334715
$352$	82.6289	4.40414
$353$	27.0957	1.44216	0.721079	−	0.692853i	$-0.243647\pi$
$353$	27.0957	1.44216	0.721079	+	0.692853i	$0.243647\pi$
$354$	−37.5961	−1.99821
$355$	12.1304	0.643812
$356$	−57.9864	−3.07327
$357$	4.02432	0.212990
$358$	−14.2436	−0.752797
$359$	4.74384	0.250370	0.125185	−	0.992133i	$-0.460048\pi$
$359$	4.74384	0.250370	0.125185	+	0.992133i	$0.460048\pi$
$360$	12.3695	0.651928
$361$	−18.1222	−0.953800
$362$	57.3317	3.01329
$363$	−9.32905	−0.489648
$364$	−133.367	−6.99035
$365$	−5.17671	−0.270961
$366$	39.3144	2.05500
$367$	22.2165	1.15969	0.579845	−	0.814727i	$-0.303113\pi$
$367$	22.2165	1.15969	0.579845	+	0.814727i	$0.303113\pi$
$368$	−45.8987	−2.39263
$369$	−3.33697	−0.173716
$370$	−15.4381	−0.802586
$371$	−12.6562	−0.657079
$372$	23.9181	1.24009
$373$	28.6253	1.48216	0.741081	−	0.671416i	$-0.234313\pi$
$373$	28.6253	1.48216	0.741081	+	0.671416i	$0.234313\pi$
$374$	12.1694	0.629262
$375$	−11.2361	−0.580229
$376$	−53.5924	−2.76382
$377$	−4.47345	−0.230394
$378$	−10.8618	−0.558670
$379$	−15.4649	−0.794379	−0.397190	−	0.917737i	$-0.630014\pi$
$379$	−15.4649	−0.794379	−0.397190	+	0.917737i	$0.630014\pi$
$380$	6.90813	0.354379
$381$	20.7353	1.06230
$382$	65.0982	3.33071
$383$	−13.8251	−0.706430	−0.353215	−	0.935542i	$-0.614912\pi$
$383$	−13.8251	−0.706430	−0.353215	+	0.935542i	$0.614912\pi$
$384$	24.7349	1.26225
$385$	−25.3154	−1.29019
$386$	33.9248	1.72673
$387$	0.999978	0.0508317
$388$	−80.7357	−4.09873
$389$	1.74249	0.0883477	0.0441739	−	0.999024i	$-0.485934\pi$
$389$	1.74249	0.0883477	0.0441739	+	0.999024i	$0.485934\pi$
$390$	−23.6140	−1.19574
$391$	−3.43565	−0.173748
$392$	−81.5225	−4.11751
$393$	3.58003	0.180589
$394$	31.0826	1.56592
$395$	15.4682	0.778289
$396$	−23.8280	−1.19740
$397$	32.0326	1.60767	0.803836	−	0.594851i	$-0.202789\pi$
$397$	32.0326	1.60767	0.803836	+	0.594851i	$0.202789\pi$
$398$	47.7245	2.39221
$399$	−3.77043	−0.188758
$400$	−40.7926	−2.03963
$401$	−34.0906	−1.70240	−0.851202	−	0.524837i	$-0.824126\pi$
$401$	−34.0906	−1.70240	−0.851202	+	0.524837i	$0.824126\pi$
$402$	19.1893	0.957073
$403$	−28.3809	−1.41375
$404$	75.0844	3.73559
$405$	−1.39519	−0.0693275
$406$	−7.74847	−0.384550
$407$	18.4846	0.916246
$408$	8.86580	0.438923
$409$	23.6999	1.17188	0.585941	−	0.810354i	$-0.300725\pi$
$409$	23.6999	1.17188	0.585941	+	0.810354i	$0.300725\pi$
$410$	−12.5659	−0.620586
$411$	5.26133	0.259522
$412$	60.2776	2.96967
$413$	56.0566	2.75836
$414$	9.27296	0.455741
$415$	20.8092	1.02148
$416$	−114.922	−5.63450
$417$	1.88082	0.0921042
$418$	−11.4016	−0.557671
$419$	−16.0805	−0.785586	−0.392793	−	0.919627i	$-0.628491\pi$
$419$	−16.0805	−0.785586	−0.392793	+	0.919627i	$0.628491\pi$
$420$	−29.6725	−1.44787
$421$	−8.34538	−0.406729	−0.203365	−	0.979103i	$-0.565188\pi$
$421$	−8.34538	−0.406729	−0.203365	+	0.979103i	$0.565188\pi$
$422$	−33.0658	−1.60962
$423$	6.04485	0.293911
$424$	−27.8824	−1.35409
$425$	−3.05345	−0.148114
$426$	−23.4666	−1.13696
$427$	−58.6187	−2.83676
$428$	10.2039	0.493223
$429$	28.2740	1.36508
$430$	3.76558	0.181592
$431$	13.6817	0.659025	0.329513	−	0.944151i	$-0.393116\pi$
$431$	13.6817	0.659025	0.329513	+	0.944151i	$0.393116\pi$
$432$	−13.3595	−0.642760
$433$	−20.4247	−0.981549	−0.490774	−	0.871287i	$-0.663286\pi$
$433$	−20.4247	−0.981549	−0.490774	+	0.871287i	$0.663286\pi$
$434$	−49.1585	−2.35969
$435$	−0.995284	−0.0477202
$436$	−86.1922	−4.12786
$437$	3.21890	0.153981
$438$	10.0145	0.478512
$439$	−6.07071	−0.289739	−0.144870	−	0.989451i	$-0.546276\pi$
$439$	−6.07071	−0.289739	−0.144870	+	0.989451i	$0.546276\pi$
$440$	−55.7711	−2.65878
$441$	9.19517	0.437865
$442$	−16.9253	−0.805056
$443$	11.9603	0.568250	0.284125	−	0.958787i	$-0.408297\pi$
$443$	11.9603	0.568250	0.284125	+	0.958787i	$0.408297\pi$
$444$	21.6660	1.02822
$445$	15.3084	0.725688
$446$	68.7742	3.25655
$447$	16.2738	0.769725
$448$	−91.5299	−4.32438
$449$	16.5254	0.779884	0.389942	−	0.920839i	$-0.372495\pi$
$449$	16.5254	0.779884	0.389942	+	0.920839i	$0.372495\pi$
$450$	8.24137	0.388502
$451$	15.0456	0.708471
$452$	−21.3726	−1.00528
$453$	−4.31638	−0.202801
$454$	14.4460	0.677983
$455$	35.2090	1.65063
$456$	−8.30647	−0.388986
$457$	26.2389	1.22741	0.613703	−	0.789537i	$-0.289679\pi$
$457$	26.2389	1.22741	0.613703	+	0.789537i	$0.289679\pi$
$458$	−23.8455	−1.11423
$459$	−1.00000	−0.0466760
$460$	25.3321	1.18111
$461$	8.72840	0.406522	0.203261	−	0.979125i	$-0.434846\pi$
$461$	8.72840	0.406522	0.203261	+	0.979125i	$0.434846\pi$
$462$	48.9734	2.27845
$463$	−21.2582	−0.987951	−0.493975	−	0.869476i	$-0.664457\pi$
$463$	−21.2582	−0.987951	−0.493975	+	0.869476i	$0.664457\pi$
$464$	−9.53027	−0.442431
$465$	−6.31437	−0.292822
$466$	43.7698	2.02760
$467$	−10.2415	−0.473922	−0.236961	−	0.971519i	$-0.576151\pi$
$467$	−10.2415	−0.473922	−0.236961	+	0.971519i	$0.576151\pi$
$468$	33.1404	1.53191
$469$	−28.6116	−1.32116
$470$	22.7629	1.04997
$471$	1.00000	0.0460776
$472$	123.496	5.68435
$473$	−4.50867	−0.207309
$474$	−29.9237	−1.37444
$475$	2.86081	0.131263
$476$	−21.2677	−0.974805
$477$	3.14493	0.143997
$478$	55.5230	2.53956
$479$	39.8665	1.82155	0.910774	−	0.412905i	$-0.135486\pi$
$479$	39.8665	1.82155	0.910774	+	0.412905i	$0.135486\pi$
$480$	−25.5686	−1.16704
$481$	−25.7086	−1.17221
$482$	−0.907678	−0.0413436
$483$	−13.8262	−0.629113
$484$	49.3022	2.24101
$485$	21.3142	0.967830
$486$	2.69904	0.122431
$487$	10.4861	0.475171	0.237585	−	0.971367i	$-0.423644\pi$
$487$	10.4861	0.475171	0.237585	+	0.971367i	$0.423644\pi$
$488$	−129.140	−5.84590
$489$	−20.7002	−0.936095
$490$	34.6259	1.56424
$491$	−43.2487	−1.95179	−0.975893	−	0.218250i	$-0.929965\pi$
$491$	−43.2487	−1.95179	−0.975893	+	0.218250i	$0.929965\pi$
$492$	17.6352	0.795057
$493$	−0.713369	−0.0321285
$494$	15.8575	0.713465
$495$	6.29059	0.282741
$496$	−60.4628	−2.71486
$497$	34.9892	1.56948
$498$	−40.2560	−1.80391
$499$	21.6555	0.969435	0.484718	−	0.874671i	$-0.338922\pi$
$499$	21.6555	0.969435	0.484718	+	0.874671i	$0.338922\pi$
$500$	59.3804	2.65557
$501$	−19.6736	−0.878950
$502$	22.6697	1.01180
$503$	−2.17687	−0.0970617	−0.0485308	−	0.998822i	$-0.515454\pi$
$503$	−2.17687	−0.0970617	−0.0485308	+	0.998822i	$0.515454\pi$
$504$	35.6788	1.58926
$505$	−19.8223	−0.882081
$506$	−41.8097	−1.85867
$507$	−26.3239	−1.16909
$508$	−109.582	−4.86192
$509$	−12.8570	−0.569876	−0.284938	−	0.958546i	$-0.591973\pi$
$509$	−12.8570	−0.569876	−0.284938	+	0.958546i	$0.591973\pi$
$510$	−3.76567	−0.166746
$511$	−14.9319	−0.660546
$512$	−7.94414	−0.351085
$513$	0.936912	0.0413657
$514$	−56.7953	−2.50514
$515$	−15.9133	−0.701224
$516$	−5.28468	−0.232645
$517$	−27.2549	−1.19867
$518$	−44.5300	−1.95653
$519$	5.04254	0.221343
$520$	77.5674	3.40156
$521$	−3.90165	−0.170934	−0.0854671	−	0.996341i	$-0.527238\pi$
$521$	−3.90165	−0.170934	−0.0854671	+	0.996341i	$0.527238\pi$
$522$	1.92541	0.0842729
$523$	29.9664	1.31034	0.655169	−	0.755483i	$-0.272598\pi$
$523$	29.9664	1.31034	0.655169	+	0.755483i	$0.272598\pi$
$524$	−18.9198	−0.826514
$525$	−12.2881	−0.536295
$526$	−83.4297	−3.63771
$527$	−4.52582	−0.197148
$528$	60.2351	2.62140
$529$	−11.1963	−0.486795
$530$	11.8428	0.514417
$531$	−13.9294	−0.604486
$532$	19.9260	0.863902
$533$	−20.9257	−0.906394
$534$	−29.6146	−1.28155
$535$	−2.69383	−0.116464
$536$	−63.0329	−2.72261
$537$	−5.27729	−0.227732
$538$	6.67051	0.287586
$539$	−41.4590	−1.78576
$540$	7.37329	0.317296
$541$	−10.7641	−0.462784	−0.231392	−	0.972861i	$-0.574328\pi$
$541$	−10.7641	−0.462784	−0.231392	+	0.972861i	$0.574328\pi$
$542$	73.5425	3.15892
$543$	21.2415	0.911561
$544$	−18.3262	−0.785731
$545$	22.7547	0.974706
$546$	−68.1130	−2.91497
$547$	22.8408	0.976602	0.488301	−	0.872675i	$-0.337617\pi$
$547$	22.8408	0.976602	0.488301	+	0.872675i	$0.337617\pi$
$548$	−27.8051	−1.18777
$549$	14.5661	0.621666
$550$	−37.1585	−1.58444
$551$	0.668364	0.0284732
$552$	−30.4598	−1.29646
$553$	44.6169	1.89730
$554$	65.8981	2.79974
$555$	−5.71984	−0.242794
$556$	−9.93976	−0.421540
$557$	31.2493	1.32408	0.662038	−	0.749470i	$-0.269692\pi$
$557$	31.2493	1.32408	0.662038	+	0.749470i	$0.269692\pi$
$558$	12.2154	0.517117
$559$	6.27074	0.265224
$560$	75.0095	3.16973
$561$	4.50878	0.190361
$562$	18.2900	0.771519
$563$	−5.75846	−0.242690	−0.121345	−	0.992610i	$-0.538721\pi$
$563$	−5.75846	−0.242690	−0.121345	+	0.992610i	$0.538721\pi$
$564$	−31.9458	−1.34516
$565$	5.64238	0.237377
$566$	−17.6778	−0.743055
$567$	−4.02432	−0.169006
$568$	77.0830	3.23433
$569$	−25.4846	−1.06837	−0.534184	−	0.845368i	$-0.679381\pi$
$569$	−25.4846	−1.06837	−0.534184	+	0.845368i	$0.679381\pi$
$570$	3.52810	0.147776
$571$	−43.3410	−1.81377	−0.906883	−	0.421383i	$-0.861545\pi$
$571$	−43.3410	−1.81377	−0.906883	+	0.421383i	$0.861545\pi$
$572$	−149.422	−6.24766
$573$	24.1190	1.00759
$574$	−36.2455	−1.51286
$575$	10.4906	0.437488
$576$	22.7442	0.947674
$577$	−25.7345	−1.07134	−0.535671	−	0.844427i	$-0.679941\pi$
$577$	−25.7345	−1.07134	−0.535671	+	0.844427i	$0.679941\pi$
$578$	−2.69904	−0.112265
$579$	12.5692	0.522360
$580$	5.25988	0.218405
$581$	60.0226	2.49016
$582$	−41.2331	−1.70917
$583$	−14.1798	−0.587267
$584$	−32.8957	−1.36123
$585$	−8.74906	−0.361729
$586$	28.3244	1.17007
$587$	−12.1617	−0.501967	−0.250984	−	0.967991i	$-0.580754\pi$
$587$	−12.1617	−0.501967	−0.250984	+	0.967991i	$0.580754\pi$
$588$	−48.5946	−2.00401
$589$	4.24030	0.174718
$590$	−52.4536	−2.15948
$591$	11.5162	0.473712
$592$	−54.7699	−2.25103
$593$	2.22220	0.0912547	0.0456274	−	0.998959i	$-0.485471\pi$
$593$	2.22220	0.0912547	0.0456274	+	0.998959i	$0.485471\pi$
$594$	−12.1694	−0.499315
$595$	5.61469	0.230180
$596$	−86.0039	−3.52286
$597$	17.6821	0.723679
$598$	58.1496	2.37791
$599$	−16.4260	−0.671150	−0.335575	−	0.942013i	$-0.608931\pi$
$599$	−16.4260	−0.671150	−0.335575	+	0.942013i	$0.608931\pi$
$600$	−27.0713	−1.10518
$601$	−15.5393	−0.633863	−0.316932	−	0.948448i	$-0.602653\pi$
$601$	−15.5393	−0.633863	−0.316932	+	0.948448i	$0.602653\pi$
$602$	10.8616	0.442684
$603$	7.10967	0.289528
$604$	22.8112	0.928174
$605$	−13.0158	−0.529167
$606$	38.3469	1.55774
$607$	−1.32603	−0.0538217	−0.0269109	−	0.999638i	$-0.508567\pi$
$607$	−1.32603	−0.0538217	−0.0269109	+	0.999638i	$0.508567\pi$
$608$	17.1701	0.696338
$609$	−2.87083	−0.116332
$610$	54.8511	2.22085
$611$	37.9065	1.53353
$612$	5.28480	0.213625
$613$	−11.4453	−0.462273	−0.231137	−	0.972921i	$-0.574244\pi$
$613$	−11.4453	−0.462273	−0.231137	+	0.972921i	$0.574244\pi$
$614$	61.8504	2.49608
$615$	−4.65570	−0.187736
$616$	−160.868	−6.48155
$617$	−6.20638	−0.249859	−0.124930	−	0.992166i	$-0.539871\pi$
$617$	−6.20638	−0.249859	−0.124930	+	0.992166i	$0.539871\pi$
$618$	30.7848	1.23835
$619$	37.3524	1.50132	0.750660	−	0.660689i	$-0.229736\pi$
$619$	37.3524	1.50132	0.750660	+	0.660689i	$0.229736\pi$
$620$	33.3702	1.34018
$621$	3.43565	0.137868
$622$	4.12694	0.165475
$623$	44.1560	1.76907
$624$	−83.7760	−3.35372
$625$	−0.409202	−0.0163681
$626$	27.0589	1.08149
$627$	−4.22432	−0.168703
$628$	−5.28480	−0.210887
$629$	−4.09969	−0.163465
$630$	−15.1543	−0.603760
$631$	29.3635	1.16894	0.584471	−	0.811415i	$-0.301302\pi$
$631$	29.3635	1.16894	0.584471	+	0.811415i	$0.301302\pi$
$632$	98.2934	3.90990
$633$	−12.2510	−0.486932
$634$	−50.3610	−2.00009
$635$	28.9297	1.14804
$636$	−16.6204	−0.659040
$637$	57.6618	2.28464
$638$	−8.68124	−0.343693
$639$	−8.69442	−0.343946
$640$	34.5098	1.36412
$641$	42.4131	1.67522	0.837608	−	0.546271i	$-0.183953\pi$
$641$	42.4131	1.67522	0.837608	+	0.546271i	$0.183953\pi$
$642$	5.21129	0.205673
$643$	7.99193	0.315171	0.157585	−	0.987505i	$-0.449629\pi$
$643$	7.99193	0.315171	0.157585	+	0.987505i	$0.449629\pi$
$644$	73.0686	2.87931
$645$	1.39516	0.0549343
$646$	2.52876	0.0994927
$647$	−30.2235	−1.18821	−0.594105	−	0.804387i	$-0.702494\pi$
$647$	−30.2235	−1.18821	−0.594105	+	0.804387i	$0.702494\pi$
$648$	−8.86580	−0.348282
$649$	62.8047	2.46530
$650$	51.6807	2.02708
$651$	−18.2134	−0.713838
$652$	109.396	4.28429
$653$	−19.6509	−0.768997	−0.384499	−	0.923126i	$-0.625626\pi$
$653$	−19.6509	−0.768997	−0.384499	+	0.923126i	$0.625626\pi$
$654$	−44.0198	−1.72131
$655$	4.99482	0.195164
$656$	−44.5803	−1.74057
$657$	3.71040	0.144757
$658$	65.6579	2.55961
$659$	23.6072	0.919606	0.459803	−	0.888021i	$-0.347920\pi$
$659$	23.6072	0.919606	0.459803	+	0.888021i	$0.347920\pi$
$660$	−33.2445	−1.29404
$661$	1.05620	0.0410815	0.0205408	−	0.999789i	$-0.493461\pi$
$661$	1.05620	0.0410815	0.0205408	+	0.999789i	$0.493461\pi$
$662$	6.92794	0.269262
$663$	−6.27088	−0.243541
$664$	132.233	5.13163
$665$	−5.26047	−0.203992
$666$	11.0652	0.428768
$667$	2.45089	0.0948988
$668$	103.971	4.02275
$669$	25.4810	0.985153
$670$	26.7726	1.03432
$671$	−65.6753	−2.53537
$672$	−73.7507	−2.84500
$673$	−11.7935	−0.454606	−0.227303	−	0.973824i	$-0.572991\pi$
$673$	−11.7935	−0.454606	−0.227303	+	0.973824i	$0.572991\pi$
$674$	50.6744	1.95191
$675$	3.05345	0.117527
$676$	139.117	5.35065
$677$	31.9014	1.22607	0.613036	−	0.790055i	$-0.289948\pi$
$677$	31.9014	1.22607	0.613036	+	0.790055i	$0.289948\pi$
$678$	−10.9154	−0.419202
$679$	61.4794	2.35936
$680$	12.3695	0.474347
$681$	5.35227	0.205099
$682$	−55.0763	−2.10898
$683$	−21.0274	−0.804591	−0.402296	−	0.915510i	$-0.631788\pi$
$683$	−21.0274	−0.804591	−0.402296	+	0.915510i	$0.631788\pi$
$684$	−4.95139	−0.189321
$685$	7.34055	0.280468
$686$	23.8435	0.910349
$687$	−8.83483	−0.337070
$688$	13.3592	0.509316
$689$	19.7215	0.751330
$690$	12.9375	0.492523
$691$	−17.4800	−0.664970	−0.332485	−	0.943109i	$-0.607887\pi$
$691$	−17.4800	−0.664970	−0.332485	+	0.943109i	$0.607887\pi$
$692$	−26.6488	−1.01304
$693$	18.1448	0.689263
$694$	44.2914	1.68128
$695$	2.62410	0.0995378
$696$	−6.32459	−0.239733
$697$	−3.33697	−0.126397
$698$	−87.1086	−3.29711
$699$	16.2168	0.613376
$700$	64.9400	2.45450
$701$	−1.16361	−0.0439488	−0.0219744	−	0.999759i	$-0.506995\pi$
$701$	−1.16361	−0.0439488	−0.0219744	+	0.999759i	$0.506995\pi$
$702$	16.9253	0.638806
$703$	3.84105	0.144868
$704$	−102.548	−3.86494
$705$	8.43370	0.317632
$706$	−73.1322	−2.75237
$707$	−57.1760	−2.15033
$708$	73.6143	2.76660
$709$	40.1600	1.50824	0.754120	−	0.656737i	$-0.228064\pi$
$709$	40.1600	1.50824	0.754120	+	0.656737i	$0.228064\pi$
$710$	−32.7403	−1.22872
$711$	−11.0868	−0.415788
$712$	97.2781	3.64565
$713$	15.5492	0.582320
$714$	−10.8618	−0.406492
$715$	39.4475	1.47525
$716$	27.8894	1.04228
$717$	20.5714	0.768254
$718$	−12.8038	−0.477833
$719$	32.9365	1.22833	0.614163	−	0.789179i	$-0.289494\pi$
$719$	32.9365	1.22833	0.614163	+	0.789179i	$0.289494\pi$
$720$	−18.6390	−0.694636
$721$	−45.9008	−1.70944
$722$	48.9125	1.82033
$723$	−0.336297	−0.0125070
$724$	−112.257	−4.17201
$725$	2.17824	0.0808976
$726$	25.1795	0.934498
$727$	47.0662	1.74559	0.872795	−	0.488087i	$-0.162305\pi$
$727$	47.0662	1.74559	0.872795	+	0.488087i	$0.162305\pi$
$728$	223.738	8.29227
$729$	1.00000	0.0370370
$730$	13.9721	0.517132
$731$	0.999978	0.0369855
$732$	−76.9790	−2.84522
$733$	12.1862	0.450108	0.225054	−	0.974346i	$-0.427744\pi$
$733$	12.1862	0.450108	0.225054	+	0.974346i	$0.427744\pi$
$734$	−59.9631	−2.21328
$735$	12.8290	0.473205
$736$	62.9626	2.32083
$737$	−32.0559	−1.18079
$738$	9.00660	0.331538
$739$	−28.3800	−1.04397	−0.521987	−	0.852953i	$-0.674809\pi$
$739$	−28.3800	−1.04397	−0.521987	+	0.852953i	$0.674809\pi$
$740$	30.2282	1.11121
$741$	5.87526	0.215833
$742$	34.1596	1.25404
$743$	30.1024	1.10435	0.552174	−	0.833729i	$-0.313798\pi$
$743$	30.1024	1.10435	0.552174	+	0.833729i	$0.313798\pi$
$744$	−40.1250	−1.47106
$745$	22.7050	0.831848
$746$	−77.2608	−2.82872
$747$	−14.9149	−0.545709
$748$	−23.8280	−0.871237
$749$	−7.77015	−0.283915
$750$	30.3266	1.10737
$751$	−45.4570	−1.65875	−0.829375	−	0.558693i	$-0.811303\pi$
$751$	−45.4570	−1.65875	−0.829375	+	0.558693i	$0.811303\pi$
$752$	80.7563	2.94488
$753$	8.39917	0.306083
$754$	12.0740	0.439709
$755$	−6.02216	−0.219169
$756$	21.2677	0.773500
$757$	23.0324	0.837126	0.418563	−	0.908188i	$-0.362534\pi$
$757$	23.0324	0.837126	0.418563	+	0.908188i	$0.362534\pi$
$758$	41.7404	1.51608
$759$	−15.4906	−0.562273
$760$	−11.5891	−0.420381
$761$	−8.12503	−0.294532	−0.147266	−	0.989097i	$-0.547047\pi$
$761$	−8.12503	−0.294532	−0.147266	+	0.989097i	$0.547047\pi$
$762$	−55.9655	−2.02742
$763$	65.6344	2.37613
$764$	−127.464	−4.61150
$765$	−1.39519	−0.0504431
$766$	37.3145	1.34823
$767$	−87.3499	−3.15402
$768$	−21.2720	−0.767586
$769$	6.57902	0.237246	0.118623	−	0.992939i	$-0.462152\pi$
$769$	6.57902	0.237246	0.118623	+	0.992939i	$0.462152\pi$
$770$	68.3271	2.46234
$771$	−21.0428	−0.757839
$772$	−66.4259	−2.39072
$773$	18.3616	0.660420	0.330210	−	0.943907i	$-0.392880\pi$
$773$	18.3616	0.660420	0.330210	+	0.943907i	$0.392880\pi$
$774$	−2.69898	−0.0970127
$775$	13.8194	0.496406
$776$	135.443	4.86210
$777$	−16.4985	−0.591879
$778$	−4.70304	−0.168612
$779$	3.12644	0.112017
$780$	46.2370	1.65555
$781$	39.2012	1.40273
$782$	9.27296	0.331600
$783$	0.713369	0.0254937
$784$	122.843	4.38725
$785$	1.39519	0.0497964
$786$	−9.66265	−0.344655
$787$	37.3127	1.33005	0.665027	−	0.746819i	$-0.268420\pi$
$787$	37.3127	1.33005	0.665027	+	0.746819i	$0.268420\pi$
$788$	−60.8607	−2.16807
$789$	−30.9109	−1.10046
$790$	−41.7492	−1.48537
$791$	16.2750	0.578674
$792$	39.9739	1.42041
$793$	91.3423	3.24366
$794$	−86.4573	−3.06825
$795$	4.38778	0.155618
$796$	−93.4462	−3.31211
$797$	24.9166	0.882591	0.441296	−	0.897362i	$-0.354519\pi$
$797$	24.9166	0.882591	0.441296	+	0.897362i	$0.354519\pi$
$798$	10.1765	0.360246
$799$	6.04485	0.213851
$800$	55.9583	1.97842
$801$	−10.9723	−0.387687
$802$	92.0119	3.24905
$803$	−16.7294	−0.590367
$804$	−37.5732	−1.32510
$805$	−19.2901	−0.679887
$806$	76.6011	2.69816
$807$	2.47144	0.0869988
$808$	−125.962	−4.43132
$809$	−48.7765	−1.71489	−0.857444	−	0.514577i	$-0.827949\pi$
$809$	−48.7765	−1.71489	−0.857444	+	0.514577i	$0.827949\pi$
$810$	3.76567	0.132312
$811$	22.7258	0.798012	0.399006	−	0.916948i	$-0.369355\pi$
$811$	22.7258	0.798012	0.399006	+	0.916948i	$0.369355\pi$
$812$	15.1717	0.532424
$813$	27.2477	0.955618
$814$	−49.8905	−1.74866
$815$	−28.8807	−1.01165
$816$	−13.3595	−0.467677
$817$	−0.936891	−0.0327777
$818$	−63.9668	−2.23655
$819$	−25.2360	−0.881819
$820$	24.6044	0.859225
$821$	−1.65874	−0.0578905	−0.0289452	−	0.999581i	$-0.509215\pi$
$821$	−1.65874	−0.0578905	−0.0289452	+	0.999581i	$0.509215\pi$
$822$	−14.2005	−0.495300
$823$	3.01399	0.105061	0.0525305	−	0.998619i	$-0.483271\pi$
$823$	3.01399	0.105061	0.0525305	+	0.998619i	$0.483271\pi$
$824$	−101.122	−3.52275
$825$	−13.7673	−0.479316
$826$	−151.299	−5.26436
$827$	3.89927	0.135591	0.0677954	−	0.997699i	$-0.478403\pi$
$827$	3.89927	0.135591	0.0677954	+	0.997699i	$0.478403\pi$
$828$	−18.1567	−0.630990
$829$	−10.4469	−0.362837	−0.181419	−	0.983406i	$-0.558069\pi$
$829$	−10.4469	−0.362837	−0.181419	+	0.983406i	$0.558069\pi$
$830$	−56.1647	−1.94951
$831$	24.4154	0.846962
$832$	142.626	4.94466
$833$	9.19517	0.318594
$834$	−5.07640	−0.175782
$835$	−27.4483	−0.949888
$836$	22.3247	0.772116
$837$	4.52582	0.156435
$838$	43.4020	1.49930
$839$	3.61150	0.124683	0.0623413	−	0.998055i	$-0.480143\pi$
$839$	3.61150	0.124683	0.0623413	+	0.998055i	$0.480143\pi$
$840$	49.7787	1.71753
$841$	−28.4911	−0.982452
$842$	22.5245	0.776245
$843$	6.77651	0.233395
$844$	64.7439	2.22858
$845$	−36.7269	−1.26344
$846$	−16.3153	−0.560931
$847$	−37.5431	−1.29000
$848$	42.0148	1.44279
$849$	−6.54969	−0.224785
$850$	8.24137	0.282677
$851$	14.0851	0.482831
$852$	45.9483	1.57416
$853$	−13.4090	−0.459114	−0.229557	−	0.973295i	$-0.573728\pi$
$853$	−13.4090	−0.459114	−0.229557	+	0.973295i	$0.573728\pi$
$854$	158.214	5.41397
$855$	1.30717	0.0447042
$856$	−17.1181	−0.585083
$857$	−1.71381	−0.0585426	−0.0292713	−	0.999572i	$-0.509319\pi$
$857$	−1.71381	−0.0585426	−0.0292713	+	0.999572i	$0.509319\pi$
$858$	−76.3125	−2.60527
$859$	34.3192	1.17096	0.585478	−	0.810688i	$-0.300907\pi$
$859$	34.3192	1.17096	0.585478	+	0.810688i	$0.300907\pi$
$860$	−7.37313	−0.251422
$861$	−13.4290	−0.457660
$862$	−36.9275	−1.25775
$863$	−40.5851	−1.38153	−0.690767	−	0.723077i	$-0.742727\pi$
$863$	−40.5851	−1.38153	−0.690767	+	0.723077i	$0.742727\pi$
$864$	18.3262	0.623471
$865$	7.03530	0.239207
$866$	55.1270	1.87329
$867$	−1.00000	−0.0339618
$868$	96.2540	3.26707
$869$	49.9879	1.69572
$870$	2.68631	0.0910744
$871$	44.5839	1.51067
$872$	144.596	4.89665
$873$	−15.2770	−0.517047
$874$	−8.68794	−0.293874
$875$	−45.2176	−1.52863
$876$	−19.6087	−0.662518
$877$	−27.3672	−0.924125	−0.462063	−	0.886847i	$-0.652890\pi$
$877$	−27.3672	−0.924125	−0.462063	+	0.886847i	$0.652890\pi$
$878$	16.3851	0.552970
$879$	10.4943	0.353963
$880$	84.0393	2.83296
$881$	53.9615	1.81801	0.909005	−	0.416786i	$-0.136844\pi$
$881$	53.9615	1.81801	0.909005	+	0.416786i	$0.136844\pi$
$882$	−24.8181	−0.835669
$883$	−41.4535	−1.39502	−0.697510	−	0.716575i	$-0.745709\pi$
$883$	−41.4535	−1.39502	−0.697510	+	0.716575i	$0.745709\pi$
$884$	33.1404	1.11463
$885$	−19.4342	−0.653273
$886$	−32.2813	−1.08451
$887$	2.87080	0.0963922	0.0481961	−	0.998838i	$-0.484653\pi$
$887$	2.87080	0.0963922	0.0481961	+	0.998838i	$0.484653\pi$
$888$	−36.3470	−1.21973
$889$	83.4457	2.79868
$890$	−41.3180	−1.38498
$891$	−4.50878	−0.151050
$892$	−134.662	−4.50882
$893$	−5.66349	−0.189521
$894$	−43.9236	−1.46903
$895$	−7.36281	−0.246112
$896$	99.5411	3.32543
$897$	21.5446	0.719352
$898$	−44.6028	−1.48841
$899$	3.22858	0.107679
$900$	−16.1369	−0.537896
$901$	3.14493	0.104773
$902$	−40.6087	−1.35212
$903$	4.02423	0.133918
$904$	35.8548	1.19251
$905$	29.6359	0.985132
$906$	11.6501	0.387047
$907$	−10.6288	−0.352924	−0.176462	−	0.984307i	$-0.556465\pi$
$907$	−10.6288	−0.352924	−0.176462	+	0.984307i	$0.556465\pi$
$908$	−28.2857	−0.938693
$909$	14.2076	0.471237
$910$	−95.0305	−3.15023
$911$	32.7399	1.08472	0.542361	−	0.840146i	$-0.317531\pi$
$911$	32.7399	1.08472	0.542361	+	0.840146i	$0.317531\pi$
$912$	12.5167	0.414469
$913$	67.2481	2.22559
$914$	−70.8198	−2.34251
$915$	20.3225	0.671840
$916$	46.6903	1.54269
$917$	14.4072	0.475768
$918$	2.69904	0.0890815
$919$	−31.1715	−1.02825	−0.514127	−	0.857714i	$-0.671884\pi$
$919$	−31.1715	−1.02825	−0.514127	+	0.857714i	$0.671884\pi$
$920$	−42.4972	−1.40109
$921$	22.9157	0.755099
$922$	−23.5583	−0.775850
$923$	−54.5217	−1.79460
$924$	−95.8915	−3.15460
$925$	12.5182	0.411595
$926$	57.3766	1.88551
$927$	11.4058	0.374617
$928$	13.0734	0.429154
$929$	12.1769	0.399511	0.199756	−	0.979846i	$-0.435985\pi$
$929$	12.1769	0.399511	0.199756	+	0.979846i	$0.435985\pi$
$930$	17.0427	0.558853
$931$	−8.61506	−0.282347
$932$	−85.7027	−2.80728
$933$	1.52904	0.0500586
$934$	27.6423	0.904483
$935$	6.29059	0.205724
$936$	−55.5964	−1.81722
$937$	41.0500	1.34105	0.670523	−	0.741889i	$-0.266070\pi$
$937$	41.0500	1.34105	0.670523	+	0.741889i	$0.266070\pi$
$938$	77.2237	2.52144
$939$	10.0254	0.327166
$940$	−44.5704	−1.45373
$941$	11.6761	0.380629	0.190314	−	0.981723i	$-0.439049\pi$
$941$	11.6761	0.380629	0.190314	+	0.981723i	$0.439049\pi$
$942$	−2.69904	−0.0879394
$943$	11.4647	0.373341
$944$	−186.091	−6.05674
$945$	−5.61469	−0.182646
$946$	12.1691	0.395651
$947$	−27.7067	−0.900348	−0.450174	−	0.892941i	$-0.648638\pi$
$947$	−27.7067	−0.900348	−0.450174	+	0.892941i	$0.648638\pi$
$948$	58.5915	1.90296
$949$	23.2675	0.755294
$950$	−7.72144	−0.250517
$951$	−18.6589	−0.605055
$952$	35.6788	1.15636
$953$	17.8327	0.577657	0.288829	−	0.957381i	$-0.406734\pi$
$953$	17.8327	0.577657	0.288829	+	0.957381i	$0.406734\pi$
$954$	−8.48830	−0.274819
$955$	33.6506	1.08891
$956$	−108.716	−3.51612
$957$	−3.21642	−0.103972
$958$	−107.601	−3.47644
$959$	21.1733	0.683721
$960$	31.7324	1.02416
$961$	−10.5169	−0.339256
$962$	69.3886	2.23718
$963$	1.93080	0.0622191
$964$	1.77726	0.0572418
$965$	17.5365	0.564519
$966$	37.3174	1.20067
$967$	−26.1834	−0.842000	−0.421000	−	0.907061i	$-0.638321\pi$
$967$	−26.1834	−0.842000	−0.421000	+	0.907061i	$0.638321\pi$
$968$	−82.7095	−2.65839
$969$	0.936912	0.0300979
$970$	−57.5279	−1.84711
$971$	−24.6119	−0.789833	−0.394916	−	0.918717i	$-0.629226\pi$
$971$	−24.6119	−0.789833	−0.394916	+	0.918717i	$0.629226\pi$
$972$	−5.28480	−0.169510
$973$	7.56903	0.242652
$974$	−28.3024	−0.906867
$975$	19.1478	0.613221
$976$	194.596	6.22887
$977$	58.8177	1.88174	0.940872	−	0.338763i	$-0.110008\pi$
$977$	58.8177	1.88174	0.940872	+	0.338763i	$0.110008\pi$
$978$	55.8706	1.78654
$979$	49.4716	1.58112
$980$	−67.7987	−2.16575
$981$	−16.3094	−0.520720
$982$	116.730	3.72500
$983$	13.7855	0.439689	0.219844	−	0.975535i	$-0.429445\pi$
$983$	13.7855	0.439689	0.219844	+	0.975535i	$0.429445\pi$
$984$	−29.5849	−0.943132
$985$	16.0672	0.511945
$986$	1.92541	0.0613175
$987$	24.3264	0.774318
$988$	−31.0496	−0.987819
$989$	−3.43558	−0.109245
$990$	−16.9785	−0.539613
$991$	−2.98210	−0.0947297	−0.0473648	−	0.998878i	$-0.515082\pi$
$991$	−2.98210	−0.0947297	−0.0473648	+	0.998878i	$0.515082\pi$
$992$	82.9413	2.63339
$993$	2.56682	0.0814555
$994$	−94.4370	−2.99536
$995$	24.6698	0.782085
$996$	78.8225	2.49759
$997$	34.3559	1.08806	0.544030	−	0.839065i	$-0.316898\pi$
$997$	34.3559	1.08806	0.544030	+	0.839065i	$0.316898\pi$
$998$	−58.4491	−1.85017
$999$	4.09969	0.129708

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.3	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.3	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69904 q^{2} -1.00000 q^{3} +5.28480 q^{4} -1.39519 q^{5} +2.69904 q^{6} -4.02432 q^{7} -8.86580 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.69904 q^{2} -1.00000 q^{3} +5.28480 q^{4} -1.39519 q^{5} +2.69904 q^{6} -4.02432 q^{7} -8.86580 q^{8} +1.00000 q^{9} +3.76567 q^{10} -4.50878 q^{11} -5.28480 q^{12} +6.27088 q^{13} +10.8618 q^{14} +1.39519 q^{15} +13.3595 q^{16} +1.00000 q^{17} -2.69904 q^{18} -0.936912 q^{19} -7.37329 q^{20} +4.02432 q^{21} +12.1694 q^{22} -3.43565 q^{23} +8.86580 q^{24} -3.05345 q^{25} -16.9253 q^{26} -1.00000 q^{27} -21.2677 q^{28} -0.713369 q^{29} -3.76567 q^{30} -4.52582 q^{31} -18.3262 q^{32} +4.50878 q^{33} -2.69904 q^{34} +5.61469 q^{35} +5.28480 q^{36} -4.09969 q^{37} +2.52876 q^{38} -6.27088 q^{39} +12.3695 q^{40} -3.33697 q^{41} -10.8618 q^{42} +0.999978 q^{43} -23.8280 q^{44} -1.39519 q^{45} +9.27296 q^{46} +6.04485 q^{47} -13.3595 q^{48} +9.19517 q^{49} +8.24137 q^{50} -1.00000 q^{51} +33.1404 q^{52} +3.14493 q^{53} +2.69904 q^{54} +6.29059 q^{55} +35.6788 q^{56} +0.936912 q^{57} +1.92541 q^{58} -13.9294 q^{59} +7.37329 q^{60} +14.5661 q^{61} +12.2154 q^{62} -4.02432 q^{63} +22.7442 q^{64} -8.74906 q^{65} -12.1694 q^{66} +7.10967 q^{67} +5.28480 q^{68} +3.43565 q^{69} -15.1543 q^{70} -8.69442 q^{71} -8.86580 q^{72} +3.71040 q^{73} +11.0652 q^{74} +3.05345 q^{75} -4.95139 q^{76} +18.1448 q^{77} +16.9253 q^{78} -11.0868 q^{79} -18.6390 q^{80} +1.00000 q^{81} +9.00660 q^{82} -14.9149 q^{83} +21.2677 q^{84} -1.39519 q^{85} -2.69898 q^{86} +0.713369 q^{87} +39.9739 q^{88} -10.9723 q^{89} +3.76567 q^{90} -25.2360 q^{91} -18.1567 q^{92} +4.52582 q^{93} -16.3153 q^{94} +1.30717 q^{95} +18.3262 q^{96} -15.2770 q^{97} -24.8181 q^{98} -4.50878 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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