LMFDB - Embedded newform 8007.2.a.d.1.6

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:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.17139 q^{2} +1.00000 q^{3} +2.71494 q^{4} -0.590074 q^{5} -2.17139 q^{6} -3.96431 q^{7} -1.55242 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.17139 q^{2} +1.00000 q^{3} +2.71494 q^{4} -0.590074 q^{5} -2.17139 q^{6} -3.96431 q^{7} -1.55242 q^{8} +1.00000 q^{9} +1.28128 q^{10} +6.46148 q^{11} +2.71494 q^{12} -1.30782 q^{13} +8.60807 q^{14} -0.590074 q^{15} -2.05897 q^{16} +1.00000 q^{17} -2.17139 q^{18} -5.13813 q^{19} -1.60202 q^{20} -3.96431 q^{21} -14.0304 q^{22} +1.75448 q^{23} -1.55242 q^{24} -4.65181 q^{25} +2.83978 q^{26} +1.00000 q^{27} -10.7629 q^{28} -7.00535 q^{29} +1.28128 q^{30} +4.10645 q^{31} +7.57567 q^{32} +6.46148 q^{33} -2.17139 q^{34} +2.33924 q^{35} +2.71494 q^{36} -0.396977 q^{37} +11.1569 q^{38} -1.30782 q^{39} +0.916044 q^{40} +11.0650 q^{41} +8.60807 q^{42} +1.45777 q^{43} +17.5425 q^{44} -0.590074 q^{45} -3.80965 q^{46} -1.88063 q^{47} -2.05897 q^{48} +8.71575 q^{49} +10.1009 q^{50} +1.00000 q^{51} -3.55065 q^{52} +6.90904 q^{53} -2.17139 q^{54} -3.81275 q^{55} +6.15428 q^{56} -5.13813 q^{57} +15.2114 q^{58} -13.0653 q^{59} -1.60202 q^{60} +12.5260 q^{61} -8.91672 q^{62} -3.96431 q^{63} -12.3318 q^{64} +0.771709 q^{65} -14.0304 q^{66} -1.01183 q^{67} +2.71494 q^{68} +1.75448 q^{69} -5.07940 q^{70} +0.00821806 q^{71} -1.55242 q^{72} -5.75478 q^{73} +0.861993 q^{74} -4.65181 q^{75} -13.9497 q^{76} -25.6153 q^{77} +2.83978 q^{78} +6.74411 q^{79} +1.21495 q^{80} +1.00000 q^{81} -24.0264 q^{82} +6.24798 q^{83} -10.7629 q^{84} -0.590074 q^{85} -3.16538 q^{86} -7.00535 q^{87} -10.0309 q^{88} -6.85979 q^{89} +1.28128 q^{90} +5.18459 q^{91} +4.76330 q^{92} +4.10645 q^{93} +4.08358 q^{94} +3.03188 q^{95} +7.57567 q^{96} -2.37523 q^{97} -18.9253 q^{98} +6.46148 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * 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 $

$2$	−2.17139	−1.53541	−0.767703	−	0.640806i	$-0.778600\pi$
$2$	−2.17139	−1.53541	−0.767703	+	0.640806i	$0.778600\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.71494	1.35747
$5$	−0.590074	−0.263889	−0.131945	−	0.991257i	$-0.542122\pi$
$5$	−0.590074	−0.263889	−0.131945	+	0.991257i	$0.542122\pi$
$6$	−2.17139	−0.886467
$7$	−3.96431	−1.49837	−0.749184	−	0.662362i	$-0.769554\pi$
$7$	−3.96431	−1.49837	−0.749184	+	0.662362i	$0.769554\pi$
$8$	−1.55242	−0.548864
$9$	1.00000	0.333333
$10$	1.28128	0.405177
$11$	6.46148	1.94821	0.974104	−	0.226100i	$-0.0725976\pi$
$11$	6.46148	1.94821	0.974104	+	0.226100i	$0.0725976\pi$
$12$	2.71494	0.783737
$13$	−1.30782	−0.362723	−0.181362	−	0.983416i	$-0.558050\pi$
$13$	−1.30782	−0.362723	−0.181362	+	0.983416i	$0.558050\pi$
$14$	8.60807	2.30060
$15$	−0.590074	−0.152356
$16$	−2.05897	−0.514743
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.17139	−0.511802
$19$	−5.13813	−1.17877	−0.589384	−	0.807853i	$-0.700630\pi$
$19$	−5.13813	−1.17877	−0.589384	+	0.807853i	$0.700630\pi$
$20$	−1.60202	−0.358222
$21$	−3.96431	−0.865083
$22$	−14.0304	−2.99129
$23$	1.75448	0.365833	0.182917	−	0.983128i	$-0.441446\pi$
$23$	1.75448	0.365833	0.182917	+	0.983128i	$0.441446\pi$
$24$	−1.55242	−0.316887
$25$	−4.65181	−0.930363
$26$	2.83978	0.556928
$27$	1.00000	0.192450
$28$	−10.7629	−2.03399
$29$	−7.00535	−1.30086	−0.650431	−	0.759566i	$-0.725412\pi$
$29$	−7.00535	−1.30086	−0.650431	+	0.759566i	$0.725412\pi$
$30$	1.28128	0.233929
$31$	4.10645	0.737541	0.368770	−	0.929520i	$-0.379779\pi$
$31$	4.10645	0.737541	0.368770	+	0.929520i	$0.379779\pi$
$32$	7.57567	1.33920
$33$	6.46148	1.12480
$34$	−2.17139	−0.372391
$35$	2.33924	0.395403
$36$	2.71494	0.452491
$37$	−0.396977	−0.0652626	−0.0326313	−	0.999467i	$-0.510389\pi$
$37$	−0.396977	−0.0652626	−0.0326313	+	0.999467i	$0.510389\pi$
$38$	11.1569	1.80989
$39$	−1.30782	−0.209418
$40$	0.916044	0.144839
$41$	11.0650	1.72806	0.864028	−	0.503444i	$-0.167934\pi$
$41$	11.0650	1.72806	0.864028	+	0.503444i	$0.167934\pi$
$42$	8.60807	1.32825
$43$	1.45777	0.222307	0.111154	−	0.993803i	$-0.464545\pi$
$43$	1.45777	0.222307	0.111154	+	0.993803i	$0.464545\pi$
$44$	17.5425	2.64464
$45$	−0.590074	−0.0879631
$46$	−3.80965	−0.561703
$47$	−1.88063	−0.274318	−0.137159	−	0.990549i	$-0.543797\pi$
$47$	−1.88063	−0.274318	−0.137159	+	0.990549i	$0.543797\pi$
$48$	−2.05897	−0.297187
$49$	8.71575	1.24511
$50$	10.1009	1.42848
$51$	1.00000	0.140028
$52$	−3.55065	−0.492387
$53$	6.90904	0.949030	0.474515	−	0.880248i	$-0.342624\pi$
$53$	6.90904	0.949030	0.474515	+	0.880248i	$0.342624\pi$
$54$	−2.17139	−0.295489
$55$	−3.81275	−0.514111
$56$	6.15428	0.822400
$57$	−5.13813	−0.680562
$58$	15.2114	1.99735
$59$	−13.0653	−1.70095	−0.850475	−	0.526015i	$-0.823686\pi$
$59$	−13.0653	−1.70095	−0.850475	+	0.526015i	$0.823686\pi$
$60$	−1.60202	−0.206820
$61$	12.5260	1.60379	0.801893	−	0.597468i	$-0.203827\pi$
$61$	12.5260	1.60379	0.801893	+	0.597468i	$0.203827\pi$
$62$	−8.91672	−1.13242
$63$	−3.96431	−0.499456
$64$	−12.3318	−1.54148
$65$	0.771709	0.0957188
$66$	−14.0304	−1.72702
$67$	−1.01183	−0.123615	−0.0618076	−	0.998088i	$-0.519687\pi$
$67$	−1.01183	−0.123615	−0.0618076	+	0.998088i	$0.519687\pi$
$68$	2.71494	0.329235
$69$	1.75448	0.211214
$70$	−5.07940	−0.607104
$71$	0.00821806	0.000975305 0	0.000487652	−	1.00000i	$-0.499845\pi$
$71$	0.00821806	0.000975305 0	0.000487652		1.00000i	$0.499845\pi$
$72$	−1.55242	−0.182955
$73$	−5.75478	−0.673546	−0.336773	−	0.941586i	$-0.609335\pi$
$73$	−5.75478	−0.673546	−0.336773	+	0.941586i	$0.609335\pi$
$74$	0.861993	0.100205
$75$	−4.65181	−0.537145
$76$	−13.9497	−1.60014
$77$	−25.6153	−2.91913
$78$	2.83978	0.321542
$79$	6.74411	0.758772	0.379386	−	0.925239i	$-0.376135\pi$
$79$	6.74411	0.758772	0.379386	+	0.925239i	$0.376135\pi$
$80$	1.21495	0.135835
$81$	1.00000	0.111111
$82$	−24.0264	−2.65327
$83$	6.24798	0.685805	0.342902	−	0.939371i	$-0.388590\pi$
$83$	6.24798	0.685805	0.342902	+	0.939371i	$0.388590\pi$
$84$	−10.7629	−1.17433
$85$	−0.590074	−0.0640025
$86$	−3.16538	−0.341332
$87$	−7.00535	−0.751053
$88$	−10.0309	−1.06930
$89$	−6.85979	−0.727136	−0.363568	−	0.931568i	$-0.618442\pi$
$89$	−6.85979	−0.727136	−0.363568	+	0.931568i	$0.618442\pi$
$90$	1.28128	0.135059
$91$	5.18459	0.543493
$92$	4.76330	0.496608
$93$	4.10645	0.425819
$94$	4.08358	0.421189
$95$	3.03188	0.311064
$96$	7.57567	0.773189
$97$	−2.37523	−0.241168	−0.120584	−	0.992703i	$-0.538477\pi$
$97$	−2.37523	−0.241168	−0.120584	+	0.992703i	$0.538477\pi$
$98$	−18.9253	−1.91174
$99$	6.46148	0.649403
$100$	−12.6294	−1.26294
$101$	−3.63503	−0.361699	−0.180850	−	0.983511i	$-0.557885\pi$
$101$	−3.63503	−0.361699	−0.180850	+	0.983511i	$0.557885\pi$
$102$	−2.17139	−0.215000
$103$	−12.4551	−1.22724	−0.613618	−	0.789603i	$-0.710287\pi$
$103$	−12.4551	−1.22724	−0.613618	+	0.789603i	$0.710287\pi$
$104$	2.03028	0.199086
$105$	2.33924	0.228286
$106$	−15.0022	−1.45715
$107$	−17.8878	−1.72928	−0.864640	−	0.502391i	$-0.832454\pi$
$107$	−17.8878	−1.72928	−0.864640	+	0.502391i	$0.832454\pi$
$108$	2.71494	0.261246
$109$	−12.0238	−1.15167	−0.575836	−	0.817565i	$-0.695323\pi$
$109$	−12.0238	−1.15167	−0.575836	+	0.817565i	$0.695323\pi$
$110$	8.27897	0.789369
$111$	−0.396977	−0.0376794
$112$	8.16240	0.771274
$113$	−18.7696	−1.76570	−0.882850	−	0.469656i	$-0.844378\pi$
$113$	−18.7696	−1.76570	−0.882850	+	0.469656i	$0.844378\pi$
$114$	11.1569	1.04494
$115$	−1.03527	−0.0965395
$116$	−19.0191	−1.76588
$117$	−1.30782	−0.120908
$118$	28.3698	2.61165
$119$	−3.96431	−0.363408
$120$	0.916044	0.0836230
$121$	30.7507	2.79552
$122$	−27.1988	−2.46246
$123$	11.0650	0.997693
$124$	11.1488	1.00119
$125$	5.69528	0.509402
$126$	8.60807	0.766868
$127$	5.56136	0.493491	0.246745	−	0.969080i	$-0.420639\pi$
$127$	5.56136	0.493491	0.246745	+	0.969080i	$0.420639\pi$
$128$	11.6259	1.02759
$129$	1.45777	0.128349
$130$	−1.67568	−0.146967
$131$	−18.3981	−1.60745	−0.803723	−	0.595004i	$-0.797150\pi$
$131$	−18.3981	−1.60745	−0.803723	+	0.595004i	$0.797150\pi$
$132$	17.5425	1.52688
$133$	20.3692	1.76623
$134$	2.19709	0.189800
$135$	−0.590074	−0.0507855
$136$	−1.55242	−0.133119
$137$	11.2302	0.959459	0.479729	−	0.877416i	$-0.340735\pi$
$137$	11.2302	0.959459	0.479729	+	0.877416i	$0.340735\pi$
$138$	−3.80965	−0.324299
$139$	17.9824	1.52525	0.762624	−	0.646842i	$-0.223911\pi$
$139$	17.9824	1.52525	0.762624	+	0.646842i	$0.223911\pi$
$140$	6.35089	0.536748
$141$	−1.88063	−0.158377
$142$	−0.0178446	−0.00149749
$143$	−8.45043	−0.706661
$144$	−2.05897	−0.171581
$145$	4.13368	0.343283
$146$	12.4959	1.03417
$147$	8.71575	0.718863
$148$	−1.07777	−0.0885922
$149$	−8.05893	−0.660213	−0.330106	−	0.943944i	$-0.607085\pi$
$149$	−8.05893	−0.660213	−0.330106	+	0.943944i	$0.607085\pi$
$150$	10.1009	0.824736
$151$	20.1868	1.64278	0.821389	−	0.570369i	$-0.193200\pi$
$151$	20.1868	1.64278	0.821389	+	0.570369i	$0.193200\pi$
$152$	7.97655	0.646984
$153$	1.00000	0.0808452
$154$	55.6208	4.48205
$155$	−2.42311	−0.194629
$156$	−3.55065	−0.284280
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−14.6441	−1.16502
$159$	6.90904	0.547923
$160$	−4.47021	−0.353401
$161$	−6.95528	−0.548153
$162$	−2.17139	−0.170601
$163$	−12.1468	−0.951412	−0.475706	−	0.879604i	$-0.657807\pi$
$163$	−12.1468	−0.951412	−0.475706	+	0.879604i	$0.657807\pi$
$164$	30.0407	2.34579
$165$	−3.81275	−0.296822
$166$	−13.5668	−1.05299
$167$	17.6646	1.36693	0.683463	−	0.729985i	$-0.260473\pi$
$167$	17.6646	1.36693	0.683463	+	0.729985i	$0.260473\pi$
$168$	6.15428	0.474813
$169$	−11.2896	−0.868432
$170$	1.28128	0.0982699
$171$	−5.13813	−0.392923
$172$	3.95775	0.301776
$173$	12.3749	0.940849	0.470424	−	0.882440i	$-0.344101\pi$
$173$	12.3749	0.940849	0.470424	+	0.882440i	$0.344101\pi$
$174$	15.2114	1.15317
$175$	18.4412	1.39403
$176$	−13.3040	−1.00283
$177$	−13.0653	−0.982044
$178$	14.8953	1.11645
$179$	15.3261	1.14553	0.572763	−	0.819721i	$-0.305872\pi$
$179$	15.3261	1.14553	0.572763	+	0.819721i	$0.305872\pi$
$180$	−1.60202	−0.119407
$181$	−20.4932	−1.52325	−0.761624	−	0.648019i	$-0.775598\pi$
$181$	−20.4932	−1.52325	−0.761624	+	0.648019i	$0.775598\pi$
$182$	−11.2578	−0.834483
$183$	12.5260	0.925946
$184$	−2.72368	−0.200793
$185$	0.234246	0.0172221
$186$	−8.91672	−0.653806
$187$	6.46148	0.472510
$188$	−5.10580	−0.372378
$189$	−3.96431	−0.288361
$190$	−6.58340	−0.477610
$191$	22.7471	1.64593	0.822963	−	0.568096i	$-0.192320\pi$
$191$	22.7471	1.64593	0.822963	+	0.568096i	$0.192320\pi$
$192$	−12.3318	−0.889972
$193$	−23.1999	−1.66996	−0.834982	−	0.550278i	$-0.814522\pi$
$193$	−23.1999	−1.66996	−0.834982	+	0.550278i	$0.814522\pi$
$194$	5.15755	0.370291
$195$	0.771709	0.0552633
$196$	23.6628	1.69020
$197$	5.11502	0.364430	0.182215	−	0.983259i	$-0.441673\pi$
$197$	5.11502	0.364430	0.182215	+	0.983259i	$0.441673\pi$
$198$	−14.0304	−0.997097
$199$	7.90668	0.560490	0.280245	−	0.959929i	$-0.409584\pi$
$199$	7.90668	0.560490	0.280245	+	0.959929i	$0.409584\pi$
$200$	7.22157	0.510642
$201$	−1.01183	−0.0713693
$202$	7.89308	0.555355
$203$	27.7714	1.94917
$204$	2.71494	0.190084
$205$	−6.52914	−0.456015
$206$	27.0449	1.88431
$207$	1.75448	0.121944
$208$	2.69276	0.186709
$209$	−33.1999	−2.29649
$210$	−5.07940	−0.350512
$211$	4.43118	0.305055	0.152528	−	0.988299i	$-0.451259\pi$
$211$	4.43118	0.305055	0.152528	+	0.988299i	$0.451259\pi$
$212$	18.7577	1.28828
$213$	0.00821806	0.000563092 0
$214$	38.8415	2.65515
$215$	−0.860191	−0.0586645
$216$	−1.55242	−0.105629
$217$	−16.2793	−1.10511
$218$	26.1084	1.76828
$219$	−5.75478	−0.388872
$220$	−10.3514	−0.697891
$221$	−1.30782	−0.0879733
$222$	0.861993	0.0578532
$223$	−9.21719	−0.617229	−0.308614	−	0.951187i	$-0.599865\pi$
$223$	−9.21719	−0.617229	−0.308614	+	0.951187i	$0.599865\pi$
$224$	−30.0323	−2.00662
$225$	−4.65181	−0.310121
$226$	40.7562	2.71107
$227$	−6.97144	−0.462711	−0.231355	−	0.972869i	$-0.574316\pi$
$227$	−6.97144	−0.462711	−0.231355	+	0.972869i	$0.574316\pi$
$228$	−13.9497	−0.923844
$229$	22.8134	1.50755	0.753777	−	0.657131i	$-0.228230\pi$
$229$	22.8134	1.50755	0.753777	+	0.657131i	$0.228230\pi$
$230$	2.24798	0.148227
$231$	−25.6153	−1.68536
$232$	10.8753	0.713996
$233$	19.2038	1.25809	0.629043	−	0.777371i	$-0.283447\pi$
$233$	19.2038	1.25809	0.629043	+	0.777371i	$0.283447\pi$
$234$	2.83978	0.185643
$235$	1.10971	0.0723895
$236$	−35.4714	−2.30899
$237$	6.74411	0.438077
$238$	8.60807	0.557978
$239$	−16.3090	−1.05494	−0.527472	−	0.849573i	$-0.676860\pi$
$239$	−16.3090	−1.05494	−0.527472	+	0.849573i	$0.676860\pi$
$240$	1.21495	0.0784244
$241$	−22.3956	−1.44263	−0.721315	−	0.692607i	$-0.756462\pi$
$241$	−22.3956	−1.44263	−0.721315	+	0.692607i	$0.756462\pi$
$242$	−66.7717	−4.29225
$243$	1.00000	0.0641500
$244$	34.0073	2.17709
$245$	−5.14294	−0.328570
$246$	−24.0264	−1.53186
$247$	6.71974	0.427567
$248$	−6.37495	−0.404810
$249$	6.24798	0.395949
$250$	−12.3667	−0.782139
$251$	−17.3712	−1.09646	−0.548230	−	0.836327i	$-0.684698\pi$
$251$	−17.3712	−1.09646	−0.548230	+	0.836327i	$0.684698\pi$
$252$	−10.7629	−0.677997
$253$	11.3365	0.712720
$254$	−12.0759	−0.757709
$255$	−0.590074	−0.0369519
$256$	−0.580666	−0.0362916
$257$	−0.703605	−0.0438897	−0.0219448	−	0.999759i	$-0.506986\pi$
$257$	−0.703605	−0.0438897	−0.0219448	+	0.999759i	$0.506986\pi$
$258$	−3.16538	−0.197068
$259$	1.57374	0.0977875
$260$	2.09515	0.129935
$261$	−7.00535	−0.433621
$262$	39.9494	2.46808
$263$	−19.8442	−1.22364	−0.611822	−	0.790995i	$-0.709563\pi$
$263$	−19.8442	−1.22364	−0.611822	+	0.790995i	$0.709563\pi$
$264$	−10.0309	−0.617361
$265$	−4.07685	−0.250439
$266$	−44.2294	−2.71188
$267$	−6.85979	−0.419812
$268$	−2.74707	−0.167804
$269$	28.1218	1.71462	0.857310	−	0.514801i	$-0.172134\pi$
$269$	28.1218	1.71462	0.857310	+	0.514801i	$0.172134\pi$
$270$	1.28128	0.0779764
$271$	19.7193	1.19786	0.598930	−	0.800801i	$-0.295593\pi$
$271$	19.7193	1.19786	0.598930	+	0.800801i	$0.295593\pi$
$272$	−2.05897	−0.124843
$273$	5.18459	0.313786
$274$	−24.3851	−1.47316
$275$	−30.0576	−1.81254
$276$	4.76330	0.286717
$277$	−9.07317	−0.545154	−0.272577	−	0.962134i	$-0.587876\pi$
$277$	−9.07317	−0.545154	−0.272577	+	0.962134i	$0.587876\pi$
$278$	−39.0469	−2.34188
$279$	4.10645	0.245847
$280$	−3.63148	−0.217022
$281$	−4.79242	−0.285892	−0.142946	−	0.989730i	$-0.545658\pi$
$281$	−4.79242	−0.285892	−0.142946	+	0.989730i	$0.545658\pi$
$282$	4.08358	0.243174
$283$	−18.8554	−1.12084	−0.560419	−	0.828209i	$-0.689360\pi$
$283$	−18.8554	−1.12084	−0.560419	+	0.828209i	$0.689360\pi$
$284$	0.0223116	0.00132395
$285$	3.03188	0.179593
$286$	18.3492	1.08501
$287$	−43.8649	−2.58926
$288$	7.57567	0.446401
$289$	1.00000	0.0588235
$290$	−8.97583	−0.527079
$291$	−2.37523	−0.139238
$292$	−15.6239	−0.914319
$293$	3.03961	0.177576	0.0887880	−	0.996051i	$-0.471701\pi$
$293$	3.03961	0.177576	0.0887880	+	0.996051i	$0.471701\pi$
$294$	−18.9253	−1.10375
$295$	7.70947	0.448862
$296$	0.616276	0.0358203
$297$	6.46148	0.374933
$298$	17.4991	1.01369
$299$	−2.29453	−0.132696
$300$	−12.6294	−0.729159
$301$	−5.77904	−0.333098
$302$	−43.8334	−2.52233
$303$	−3.63503	−0.208827
$304$	10.5793	0.606762
$305$	−7.39125	−0.423222
$306$	−2.17139	−0.124130
$307$	−11.3180	−0.645950	−0.322975	−	0.946407i	$-0.604683\pi$
$307$	−11.3180	−0.645950	−0.322975	+	0.946407i	$0.604683\pi$
$308$	−69.5440	−3.96264
$309$	−12.4551	−0.708545
$310$	5.26153	0.298835
$311$	−25.1335	−1.42519	−0.712595	−	0.701576i	$-0.752480\pi$
$311$	−25.1335	−1.42519	−0.712595	+	0.701576i	$0.752480\pi$
$312$	2.03028	0.114942
$313$	−26.9076	−1.52090	−0.760452	−	0.649394i	$-0.775023\pi$
$313$	−26.9076	−1.52090	−0.760452	+	0.649394i	$0.775023\pi$
$314$	2.17139	0.122539
$315$	2.33924	0.131801
$316$	18.3099	1.03001
$317$	25.6434	1.44028	0.720139	−	0.693830i	$-0.244078\pi$
$317$	25.6434	1.44028	0.720139	+	0.693830i	$0.244078\pi$
$318$	−15.0022	−0.841284
$319$	−45.2649	−2.53435
$320$	7.27669	0.406779
$321$	−17.8878	−0.998401
$322$	15.1026	0.841637
$323$	−5.13813	−0.285893
$324$	2.71494	0.150830
$325$	6.08372	0.337464
$326$	26.3755	1.46080
$327$	−12.0238	−0.664918
$328$	−17.1775	−0.948467
$329$	7.45539	0.411029
$330$	8.27897	0.455742
$331$	17.0344	0.936294	0.468147	−	0.883651i	$-0.344922\pi$
$331$	17.0344	0.936294	0.468147	+	0.883651i	$0.344922\pi$
$332$	16.9629	0.930960
$333$	−0.396977	−0.0217542
$334$	−38.3567	−2.09879
$335$	0.597057	0.0326207
$336$	8.16240	0.445295
$337$	25.7017	1.40006	0.700030	−	0.714114i	$-0.253170\pi$
$337$	25.7017	1.40006	0.700030	+	0.714114i	$0.253170\pi$
$338$	24.5142	1.33340
$339$	−18.7696	−1.01943
$340$	−1.60202	−0.0868816
$341$	26.5338	1.43688
$342$	11.1569	0.603296
$343$	−6.80175	−0.367260
$344$	−2.26307	−0.122016
$345$	−1.03527	−0.0557371
$346$	−26.8708	−1.44458
$347$	−4.01523	−0.215549	−0.107774	−	0.994175i	$-0.534372\pi$
$347$	−4.01523	−0.215549	−0.107774	+	0.994175i	$0.534372\pi$
$348$	−19.0191	−1.01953
$349$	14.1995	0.760084	0.380042	−	0.924969i	$-0.375909\pi$
$349$	14.1995	0.760084	0.380042	+	0.924969i	$0.375909\pi$
$350$	−40.0431	−2.14039
$351$	−1.30782	−0.0698061
$352$	48.9500	2.60905
$353$	−11.6289	−0.618945	−0.309473	−	0.950908i	$-0.600152\pi$
$353$	−11.6289	−0.618945	−0.309473	+	0.950908i	$0.600152\pi$
$354$	28.3698	1.50784
$355$	−0.00484927	−0.000257372 0
$356$	−18.6239	−0.987067
$357$	−3.96431	−0.209813
$358$	−33.2789	−1.75885
$359$	−11.0007	−0.580594	−0.290297	−	0.956937i	$-0.593754\pi$
$359$	−11.0007	−0.580594	−0.290297	+	0.956937i	$0.593754\pi$
$360$	0.916044	0.0482797
$361$	7.40042	0.389496
$362$	44.4988	2.33880
$363$	30.7507	1.61399
$364$	14.0759	0.737776
$365$	3.39574	0.177741
$366$	−27.1988	−1.42170
$367$	−18.3620	−0.958490	−0.479245	−	0.877681i	$-0.659090\pi$
$367$	−18.3620	−0.958490	−0.479245	+	0.877681i	$0.659090\pi$
$368$	−3.61241	−0.188310
$369$	11.0650	0.576018
$370$	−0.508640	−0.0264429
$371$	−27.3896	−1.42200
$372$	11.1488	0.578038
$373$	2.85462	0.147807	0.0739033	−	0.997265i	$-0.476454\pi$
$373$	2.85462	0.147807	0.0739033	+	0.997265i	$0.476454\pi$
$374$	−14.0304	−0.725494
$375$	5.69528	0.294103
$376$	2.91953	0.150563
$377$	9.16173	0.471853
$378$	8.60807	0.442751
$379$	−17.7492	−0.911714	−0.455857	−	0.890053i	$-0.650667\pi$
$379$	−17.7492	−0.911714	−0.455857	+	0.890053i	$0.650667\pi$
$380$	8.23138	0.422261
$381$	5.56136	0.284917
$382$	−49.3930	−2.52716
$383$	3.55062	0.181428	0.0907142	−	0.995877i	$-0.471085\pi$
$383$	3.55062	0.181428	0.0907142	+	0.995877i	$0.471085\pi$
$384$	11.6259	0.593280
$385$	15.1149	0.770328
$386$	50.3760	2.56407
$387$	1.45777	0.0741025
$388$	−6.44861	−0.327379
$389$	−25.7063	−1.30336	−0.651680	−	0.758494i	$-0.725936\pi$
$389$	−25.7063	−1.30336	−0.651680	+	0.758494i	$0.725936\pi$
$390$	−1.67568	−0.0848515
$391$	1.75448	0.0887276
$392$	−13.5305	−0.683394
$393$	−18.3981	−0.928059
$394$	−11.1067	−0.559548
$395$	−3.97953	−0.200232
$396$	17.5425	0.881546
$397$	−4.53480	−0.227595	−0.113798	−	0.993504i	$-0.536302\pi$
$397$	−4.53480	−0.227595	−0.113798	+	0.993504i	$0.536302\pi$
$398$	−17.1685	−0.860579
$399$	20.3692	1.01973
$400$	9.57794	0.478897
$401$	−29.4181	−1.46907	−0.734534	−	0.678572i	$-0.762599\pi$
$401$	−29.4181	−1.46907	−0.734534	+	0.678572i	$0.762599\pi$
$402$	2.19709	0.109581
$403$	−5.37049	−0.267523
$404$	−9.86890	−0.490996
$405$	−0.590074	−0.0293210
$406$	−60.3026	−2.99277
$407$	−2.56506	−0.127145
$408$	−1.55242	−0.0768563
$409$	−29.9625	−1.48155	−0.740775	−	0.671753i	$-0.765542\pi$
$409$	−29.9625	−1.48155	−0.740775	+	0.671753i	$0.765542\pi$
$410$	14.1773	0.700168
$411$	11.2302	0.553944
$412$	−33.8148	−1.66594
$413$	51.7947	2.54865
$414$	−3.80965	−0.187234
$415$	−3.68677	−0.180976
$416$	−9.90760	−0.485760
$417$	17.9824	0.880603
$418$	72.0900	3.52604
$419$	−4.24270	−0.207269	−0.103635	−	0.994615i	$-0.533047\pi$
$419$	−4.24270	−0.207269	−0.103635	+	0.994615i	$0.533047\pi$
$420$	6.35089	0.309892
$421$	19.8952	0.969633	0.484817	−	0.874616i	$-0.338886\pi$
$421$	19.8952	0.969633	0.484817	+	0.874616i	$0.338886\pi$
$422$	−9.62183	−0.468383
$423$	−1.88063	−0.0914392
$424$	−10.7257	−0.520888
$425$	−4.65181	−0.225646
$426$	−0.0178446	−0.000864576 0
$427$	−49.6568	−2.40306
$428$	−48.5644	−2.34745
$429$	−8.45043	−0.407991
$430$	1.86781	0.0900738
$431$	−7.25128	−0.349282	−0.174641	−	0.984632i	$-0.555876\pi$
$431$	−7.25128	−0.349282	−0.174641	+	0.984632i	$0.555876\pi$
$432$	−2.05897	−0.0990623
$433$	8.71383	0.418760	0.209380	−	0.977834i	$-0.432855\pi$
$433$	8.71383	0.418760	0.209380	+	0.977834i	$0.432855\pi$
$434$	35.3486	1.69679
$435$	4.13368	0.198195
$436$	−32.6439	−1.56336
$437$	−9.01473	−0.431233
$438$	12.4959	0.597076
$439$	41.0432	1.95889	0.979443	−	0.201723i	$-0.0646541\pi$
$439$	41.0432	1.95889	0.979443	+	0.201723i	$0.0646541\pi$
$440$	5.91899	0.282177
$441$	8.71575	0.415036
$442$	2.83978	0.135075
$443$	−14.9508	−0.710333	−0.355167	−	0.934803i	$-0.615576\pi$
$443$	−14.9508	−0.710333	−0.355167	+	0.934803i	$0.615576\pi$
$444$	−1.07777	−0.0511487
$445$	4.04778	0.191883
$446$	20.0141	0.947697
$447$	−8.05893	−0.381174
$448$	48.8871	2.30970
$449$	22.7039	1.07147	0.535733	−	0.844388i	$-0.320035\pi$
$449$	22.7039	1.07147	0.535733	+	0.844388i	$0.320035\pi$
$450$	10.1009	0.476161
$451$	71.4959	3.36661
$452$	−50.9585	−2.39689
$453$	20.1868	0.948458
$454$	15.1377	0.710449
$455$	−3.05929	−0.143422
$456$	7.97655	0.373536
$457$	−28.4765	−1.33207	−0.666037	−	0.745919i	$-0.732011\pi$
$457$	−28.4765	−1.33207	−0.666037	+	0.745919i	$0.732011\pi$
$458$	−49.5369	−2.31471
$459$	1.00000	0.0466760
$460$	−2.81070	−0.131050
$461$	16.7453	0.779908	0.389954	−	0.920834i	$-0.372491\pi$
$461$	16.7453	0.779908	0.389954	+	0.920834i	$0.372491\pi$
$462$	55.6208	2.58772
$463$	−10.4543	−0.485854	−0.242927	−	0.970045i	$-0.578107\pi$
$463$	−10.4543	−0.485854	−0.242927	+	0.970045i	$0.578107\pi$
$464$	14.4238	0.669609
$465$	−2.42311	−0.112369
$466$	−41.6991	−1.93167
$467$	−10.8089	−0.500179	−0.250089	−	0.968223i	$-0.580460\pi$
$467$	−10.8089	−0.500179	−0.250089	+	0.968223i	$0.580460\pi$
$468$	−3.55065	−0.164129
$469$	4.01122	0.185221
$470$	−2.40961	−0.111147
$471$	−1.00000	−0.0460776
$472$	20.2828	0.933590
$473$	9.41932	0.433101
$474$	−14.6441	−0.672626
$475$	23.9016	1.09668
$476$	−10.7629	−0.493315
$477$	6.90904	0.316343
$478$	35.4133	1.61977
$479$	−22.2267	−1.01556	−0.507782	−	0.861486i	$-0.669534\pi$
$479$	−22.2267	−1.01556	−0.507782	+	0.861486i	$0.669534\pi$
$480$	−4.47021	−0.204036
$481$	0.519174	0.0236723
$482$	48.6297	2.21502
$483$	−6.95528	−0.316476
$484$	83.4863	3.79483
$485$	1.40156	0.0636416
$486$	−2.17139	−0.0984963
$487$	−22.3139	−1.01114	−0.505570	−	0.862785i	$-0.668718\pi$
$487$	−22.3139	−1.01114	−0.505570	+	0.862785i	$0.668718\pi$
$488$	−19.4456	−0.880260
$489$	−12.1468	−0.549298
$490$	11.1673	0.504489
$491$	9.47979	0.427817	0.213909	−	0.976854i	$-0.431381\pi$
$491$	9.47979	0.427817	0.213909	+	0.976854i	$0.431381\pi$
$492$	30.0407	1.35434
$493$	−7.00535	−0.315505
$494$	−14.5912	−0.656489
$495$	−3.81275	−0.171370
$496$	−8.45507	−0.379644
$497$	−0.0325789	−0.00146137
$498$	−13.5668	−0.607943
$499$	−38.1518	−1.70791	−0.853956	−	0.520346i	$-0.825803\pi$
$499$	−38.1518	−1.70791	−0.853956	+	0.520346i	$0.825803\pi$
$500$	15.4624	0.691498
$501$	17.6646	0.789195
$502$	37.7197	1.68351
$503$	−15.0084	−0.669191	−0.334595	−	0.942362i	$-0.608600\pi$
$503$	−15.0084	−0.669191	−0.334595	+	0.942362i	$0.608600\pi$
$504$	6.15428	0.274133
$505$	2.14494	0.0954485
$506$	−24.6160	−1.09431
$507$	−11.2896	−0.501389
$508$	15.0988	0.669900
$509$	5.38947	0.238884	0.119442	−	0.992841i	$-0.461889\pi$
$509$	5.38947	0.238884	0.119442	+	0.992841i	$0.461889\pi$
$510$	1.28128	0.0567361
$511$	22.8137	1.00922
$512$	−21.9909	−0.971868
$513$	−5.13813	−0.226854
$514$	1.52780	0.0673884
$515$	7.34942	0.323854
$516$	3.95775	0.174230
$517$	−12.1516	−0.534428
$518$	−3.41721	−0.150143
$519$	12.3749	0.543199
$520$	−1.19802	−0.0525366
$521$	4.06694	0.178176	0.0890879	−	0.996024i	$-0.471605\pi$
$521$	4.06694	0.178176	0.0890879	+	0.996024i	$0.471605\pi$
$522$	15.2114	0.665784
$523$	17.1843	0.751416	0.375708	−	0.926738i	$-0.377400\pi$
$523$	17.1843	0.751416	0.375708	+	0.926738i	$0.377400\pi$
$524$	−49.9497	−2.18206
$525$	18.4412	0.804841
$526$	43.0895	1.87879
$527$	4.10645	0.178880
$528$	−13.3040	−0.578982
$529$	−19.9218	−0.866166
$530$	8.85243	0.384525
$531$	−13.0653	−0.566984
$532$	55.3011	2.39761
$533$	−14.4709	−0.626806
$534$	14.8953	0.644582
$535$	10.5551	0.456338
$536$	1.57079	0.0678480
$537$	15.3261	0.661370
$538$	−61.0636	−2.63264
$539$	56.3166	2.42573
$540$	−1.60202	−0.0689399
$541$	33.2155	1.42805	0.714023	−	0.700123i	$-0.246871\pi$
$541$	33.2155	1.42805	0.714023	+	0.700123i	$0.246871\pi$
$542$	−42.8183	−1.83920
$543$	−20.4932	−0.879448
$544$	7.57567	0.324804
$545$	7.09494	0.303914
$546$	−11.2578	−0.481789
$547$	−14.0982	−0.602795	−0.301397	−	0.953499i	$-0.597453\pi$
$547$	−14.0982	−0.602795	−0.301397	+	0.953499i	$0.597453\pi$
$548$	30.4893	1.30244
$549$	12.5260	0.534595
$550$	65.2668	2.78298
$551$	35.9944	1.53341
$552$	−2.72368	−0.115928
$553$	−26.7357	−1.13692
$554$	19.7014	0.837032
$555$	0.234246	0.00994319
$556$	48.8212	2.07048
$557$	−24.0407	−1.01864	−0.509318	−	0.860578i	$-0.670102\pi$
$557$	−24.0407	−1.01864	−0.509318	+	0.860578i	$0.670102\pi$
$558$	−8.91672	−0.377475
$559$	−1.90649	−0.0806361
$560$	−4.81642	−0.203531
$561$	6.46148	0.272804
$562$	10.4062	0.438960
$563$	12.1261	0.511055	0.255527	−	0.966802i	$-0.417751\pi$
$563$	12.1261	0.511055	0.255527	+	0.966802i	$0.417751\pi$
$564$	−5.10580	−0.214993
$565$	11.0755	0.465949
$566$	40.9425	1.72094
$567$	−3.96431	−0.166485
$568$	−0.0127579	−0.000535310 0
$569$	−31.5818	−1.32398	−0.661988	−	0.749514i	$-0.730287\pi$
$569$	−31.5818	−1.32398	−0.661988	+	0.749514i	$0.730287\pi$
$570$	−6.58340	−0.275748
$571$	−33.7049	−1.41051	−0.705254	−	0.708955i	$-0.749167\pi$
$571$	−33.7049	−1.41051	−0.705254	+	0.708955i	$0.749167\pi$
$572$	−22.9424	−0.959272
$573$	22.7471	0.950275
$574$	95.2479	3.97557
$575$	−8.16149	−0.340358
$576$	−12.3318	−0.513826
$577$	−0.903216	−0.0376014	−0.0188007	−	0.999823i	$-0.505985\pi$
$577$	−0.903216	−0.0376014	−0.0188007	+	0.999823i	$0.505985\pi$
$578$	−2.17139	−0.0903180
$579$	−23.1999	−0.964154
$580$	11.2227	0.465997
$581$	−24.7689	−1.02759
$582$	5.15755	0.213787
$583$	44.6426	1.84891
$584$	8.93384	0.369685
$585$	0.771709	0.0319063
$586$	−6.60019	−0.272651
$587$	20.2005	0.833764	0.416882	−	0.908961i	$-0.363123\pi$
$587$	20.2005	0.833764	0.416882	+	0.908961i	$0.363123\pi$
$588$	23.6628	0.975836
$589$	−21.0995	−0.869390
$590$	−16.7403	−0.689186
$591$	5.11502	0.210404
$592$	0.817364	0.0335935
$593$	19.1038	0.784497	0.392249	−	0.919859i	$-0.371697\pi$
$593$	19.1038	0.784497	0.392249	+	0.919859i	$0.371697\pi$
$594$	−14.0304	−0.575674
$595$	2.33924	0.0958993
$596$	−21.8795	−0.896220
$597$	7.90668	0.323599
$598$	4.98233	0.203743
$599$	6.40189	0.261574	0.130787	−	0.991410i	$-0.458250\pi$
$599$	6.40189	0.261574	0.130787	+	0.991410i	$0.458250\pi$
$600$	7.22157	0.294820
$601$	−0.733997	−0.0299404	−0.0149702	−	0.999888i	$-0.504765\pi$
$601$	−0.733997	−0.0299404	−0.0149702	+	0.999888i	$0.504765\pi$
$602$	12.5486	0.511441
$603$	−1.01183	−0.0412051
$604$	54.8060	2.23002
$605$	−18.1452	−0.737706
$606$	7.89308	0.320634
$607$	−28.7646	−1.16752	−0.583760	−	0.811926i	$-0.698419\pi$
$607$	−28.7646	−1.16752	−0.583760	+	0.811926i	$0.698419\pi$
$608$	−38.9248	−1.57861
$609$	27.7714	1.12535
$610$	16.0493	0.649817
$611$	2.45952	0.0995014
$612$	2.71494	0.109745
$613$	−25.7709	−1.04087	−0.520437	−	0.853900i	$-0.674231\pi$
$613$	−25.7709	−1.04087	−0.520437	+	0.853900i	$0.674231\pi$
$614$	24.5757	0.991796
$615$	−6.52914	−0.263280
$616$	39.7657	1.60221
$617$	−47.5476	−1.91419	−0.957097	−	0.289768i	$-0.906422\pi$
$617$	−47.5476	−1.91419	−0.957097	+	0.289768i	$0.906422\pi$
$618$	27.0449	1.08790
$619$	−39.3330	−1.58093	−0.790464	−	0.612509i	$-0.790160\pi$
$619$	−39.3330	−1.58093	−0.790464	+	0.612509i	$0.790160\pi$
$620$	−6.57861	−0.264203
$621$	1.75448	0.0704047
$622$	54.5747	2.18825
$623$	27.1943	1.08952
$624$	2.69276	0.107797
$625$	19.8984	0.795937
$626$	58.4268	2.33521
$627$	−33.1999	−1.32588
$628$	−2.71494	−0.108338
$629$	−0.396977	−0.0158285
$630$	−5.07940	−0.202368
$631$	30.7981	1.22605	0.613026	−	0.790063i	$-0.289952\pi$
$631$	30.7981	1.22605	0.613026	+	0.790063i	$0.289952\pi$
$632$	−10.4697	−0.416462
$633$	4.43118	0.176124
$634$	−55.6819	−2.21141
$635$	−3.28162	−0.130227
$636$	18.7577	0.743789
$637$	−11.3986	−0.451629
$638$	98.2879	3.89125
$639$	0.00821806	0.000325102 0
$640$	−6.86012	−0.271170
$641$	−20.1378	−0.795394	−0.397697	−	0.917517i	$-0.630190\pi$
$641$	−20.1378	−0.795394	−0.397697	+	0.917517i	$0.630190\pi$
$642$	38.8415	1.53295
$643$	−17.7986	−0.701909	−0.350955	−	0.936392i	$-0.614143\pi$
$643$	−17.7986	−0.701909	−0.350955	+	0.936392i	$0.614143\pi$
$644$	−18.8832	−0.744102
$645$	−0.860191	−0.0338700
$646$	11.1569	0.438962
$647$	−37.2669	−1.46511	−0.732556	−	0.680707i	$-0.761673\pi$
$647$	−37.2669	−1.46511	−0.732556	+	0.680707i	$0.761673\pi$
$648$	−1.55242	−0.0609849
$649$	−84.4208	−3.31381
$650$	−13.2101	−0.518145
$651$	−16.2793	−0.638034
$652$	−32.9779	−1.29151
$653$	−25.1114	−0.982685	−0.491342	−	0.870967i	$-0.663494\pi$
$653$	−25.1114	−0.982685	−0.491342	+	0.870967i	$0.663494\pi$
$654$	26.1084	1.02092
$655$	10.8562	0.424187
$656$	−22.7824	−0.889504
$657$	−5.75478	−0.224515
$658$	−16.1886	−0.631096
$659$	−7.86567	−0.306403	−0.153202	−	0.988195i	$-0.548958\pi$
$659$	−7.86567	−0.306403	−0.153202	+	0.988195i	$0.548958\pi$
$660$	−10.3514	−0.402928
$661$	24.5015	0.952998	0.476499	−	0.879175i	$-0.341906\pi$
$661$	24.5015	0.952998	0.476499	+	0.879175i	$0.341906\pi$
$662$	−36.9883	−1.43759
$663$	−1.30782	−0.0507914
$664$	−9.69949	−0.376413
$665$	−12.0193	−0.466089
$666$	0.861993	0.0334015
$667$	−12.2907	−0.475899
$668$	47.9583	1.85556
$669$	−9.21719	−0.356357
$670$	−1.29645	−0.0500861
$671$	80.9362	3.12451
$672$	−30.0323	−1.15852
$673$	−28.9826	−1.11720	−0.558598	−	0.829438i	$-0.688661\pi$
$673$	−28.9826	−1.11720	−0.558598	+	0.829438i	$0.688661\pi$
$674$	−55.8084	−2.14966
$675$	−4.65181	−0.179048
$676$	−30.6507	−1.17887
$677$	−2.02366	−0.0777754	−0.0388877	−	0.999244i	$-0.512381\pi$
$677$	−2.02366	−0.0777754	−0.0388877	+	0.999244i	$0.512381\pi$
$678$	40.7562	1.56523
$679$	9.41614	0.361358
$680$	0.916044	0.0351287
$681$	−6.97144	−0.267146
$682$	−57.6152	−2.20620
$683$	−33.8448	−1.29504	−0.647518	−	0.762051i	$-0.724193\pi$
$683$	−33.8448	−1.29504	−0.647518	+	0.762051i	$0.724193\pi$
$684$	−13.9497	−0.533382
$685$	−6.62664	−0.253191
$686$	14.7693	0.563893
$687$	22.8134	0.870386
$688$	−3.00150	−0.114431
$689$	−9.03576	−0.344235
$690$	2.24798	0.0855791
$691$	45.7095	1.73887	0.869435	−	0.494047i	$-0.164483\pi$
$691$	45.7095	1.73887	0.869435	+	0.494047i	$0.164483\pi$
$692$	33.5972	1.27718
$693$	−25.6153	−0.973044
$694$	8.71863	0.330955
$695$	−10.6110	−0.402497
$696$	10.8753	0.412226
$697$	11.0650	0.419115
$698$	−30.8328	−1.16704
$699$	19.2038	0.726356
$700$	50.0669	1.89235
$701$	11.9106	0.449856	0.224928	−	0.974375i	$-0.427785\pi$
$701$	11.9106	0.449856	0.224928	+	0.974375i	$0.427785\pi$
$702$	2.83978	0.107181
$703$	2.03972	0.0769296
$704$	−79.6817	−3.00312
$705$	1.10971	0.0417941
$706$	25.2509	0.950332
$707$	14.4104	0.541958
$708$	−35.4714	−1.33310
$709$	−2.40322	−0.0902548	−0.0451274	−	0.998981i	$-0.514369\pi$
$709$	−2.40322	−0.0902548	−0.0451274	+	0.998981i	$0.514369\pi$
$710$	0.0105297	0.000395171 0
$711$	6.74411	0.252924
$712$	10.6493	0.399099
$713$	7.20467	0.269817
$714$	8.60807	0.322149
$715$	4.98638	0.186480
$716$	41.6095	1.55502
$717$	−16.3090	−0.609072
$718$	23.8868	0.891448
$719$	2.92059	0.108920	0.0544598	−	0.998516i	$-0.482656\pi$
$719$	2.92059	0.108920	0.0544598	+	0.998516i	$0.482656\pi$
$720$	1.21495	0.0452783
$721$	49.3758	1.83885
$722$	−16.0692	−0.598034
$723$	−22.3956	−0.832903
$724$	−55.6379	−2.06777
$725$	32.5876	1.21027
$726$	−66.7717	−2.47813
$727$	18.5096	0.686482	0.343241	−	0.939247i	$-0.388475\pi$
$727$	18.5096	0.686482	0.343241	+	0.939247i	$0.388475\pi$
$728$	−8.04867	−0.298304
$729$	1.00000	0.0370370
$730$	−7.37349	−0.272905
$731$	1.45777	0.0539175
$732$	34.0073	1.25695
$733$	−12.4054	−0.458203	−0.229102	−	0.973403i	$-0.573579\pi$
$733$	−12.4054	−0.458203	−0.229102	+	0.973403i	$0.573579\pi$
$734$	39.8712	1.47167
$735$	−5.14294	−0.189700
$736$	13.2913	0.489925
$737$	−6.53794	−0.240828
$738$	−24.0264	−0.884422
$739$	−9.77302	−0.359506	−0.179753	−	0.983712i	$-0.557530\pi$
$739$	−9.77302	−0.359506	−0.179753	+	0.983712i	$0.557530\pi$
$740$	0.635964	0.0233785
$741$	6.71974	0.246856
$742$	59.4735	2.18334
$743$	−19.4224	−0.712538	−0.356269	−	0.934383i	$-0.615951\pi$
$743$	−19.4224	−0.712538	−0.356269	+	0.934383i	$0.615951\pi$
$744$	−6.37495	−0.233717
$745$	4.75536	0.174223
$746$	−6.19850	−0.226943
$747$	6.24798	0.228602
$748$	17.5425	0.641419
$749$	70.9128	2.59110
$750$	−12.3667	−0.451568
$751$	−5.91752	−0.215933	−0.107967	−	0.994155i	$-0.534434\pi$
$751$	−5.91752	−0.215933	−0.107967	+	0.994155i	$0.534434\pi$
$752$	3.87216	0.141203
$753$	−17.3712	−0.633042
$754$	−19.8937	−0.724486
$755$	−11.9117	−0.433511
$756$	−10.7629	−0.391442
$757$	−39.9597	−1.45236	−0.726180	−	0.687505i	$-0.758706\pi$
$757$	−39.9597	−1.45236	−0.726180	+	0.687505i	$0.758706\pi$
$758$	38.5404	1.39985
$759$	11.3365	0.411489
$760$	−4.70676	−0.170732
$761$	−6.65333	−0.241183	−0.120591	−	0.992702i	$-0.538479\pi$
$761$	−6.65333	−0.241183	−0.120591	+	0.992702i	$0.538479\pi$
$762$	−12.0759	−0.437463
$763$	47.6661	1.72563
$764$	61.7572	2.23430
$765$	−0.590074	−0.0213342
$766$	−7.70979	−0.278566
$767$	17.0870	0.616975
$768$	−0.580666	−0.0209530
$769$	−18.8416	−0.679447	−0.339723	−	0.940525i	$-0.610333\pi$
$769$	−18.8416	−0.679447	−0.339723	+	0.940525i	$0.610333\pi$
$770$	−32.8204	−1.18277
$771$	−0.703605	−0.0253397
$772$	−62.9863	−2.26693
$773$	−43.0504	−1.54841	−0.774207	−	0.632933i	$-0.781851\pi$
$773$	−43.0504	−1.54841	−0.774207	+	0.632933i	$0.781851\pi$
$774$	−3.16538	−0.113777
$775$	−19.1025	−0.686180
$776$	3.68736	0.132368
$777$	1.57374	0.0564576
$778$	55.8184	2.00119
$779$	−56.8532	−2.03698
$780$	2.09515	0.0750183
$781$	0.0531008	0.00190010
$782$	−3.80965	−0.136233
$783$	−7.00535	−0.250351
$784$	−17.9455	−0.640909
$785$	0.590074	0.0210606
$786$	39.9494	1.42495
$787$	−19.1056	−0.681040	−0.340520	−	0.940237i	$-0.610603\pi$
$787$	−19.1056	−0.681040	−0.340520	+	0.940237i	$0.610603\pi$
$788$	13.8870	0.494704
$789$	−19.8442	−0.706471
$790$	8.64111	0.307437
$791$	74.4087	2.64567
$792$	−10.0309	−0.356434
$793$	−16.3817	−0.581730
$794$	9.84683	0.349451
$795$	−4.07685	−0.144591
$796$	21.4662	0.760849
$797$	−33.1974	−1.17591	−0.587957	−	0.808892i	$-0.700067\pi$
$797$	−33.1974	−1.17591	−0.587957	+	0.808892i	$0.700067\pi$
$798$	−44.2294	−1.56570
$799$	−1.88063	−0.0665318
$800$	−35.2406	−1.24594
$801$	−6.85979	−0.242379
$802$	63.8781	2.25562
$803$	−37.1843	−1.31221
$804$	−2.74707	−0.0968818
$805$	4.10413	0.144652
$806$	11.6614	0.410757
$807$	28.1218	0.989936
$808$	5.64310	0.198524
$809$	−12.4805	−0.438791	−0.219395	−	0.975636i	$-0.570408\pi$
$809$	−12.4805	−0.438791	−0.219395	+	0.975636i	$0.570408\pi$
$810$	1.28128	0.0450197
$811$	−34.5539	−1.21335	−0.606676	−	0.794949i	$-0.707497\pi$
$811$	−34.5539	−1.21335	−0.606676	+	0.794949i	$0.707497\pi$
$812$	75.3977	2.64594
$813$	19.7193	0.691585
$814$	5.56975	0.195220
$815$	7.16752	0.251067
$816$	−2.05897	−0.0720784
$817$	−7.49020	−0.262049
$818$	65.0604	2.27478
$819$	5.18459	0.181164
$820$	−17.7263	−0.619028
$821$	−9.99497	−0.348827	−0.174413	−	0.984673i	$-0.555803\pi$
$821$	−9.99497	−0.348827	−0.174413	+	0.984673i	$0.555803\pi$
$822$	−24.3851	−0.850529
$823$	−30.7052	−1.07032	−0.535159	−	0.844752i	$-0.679748\pi$
$823$	−30.7052	−1.07032	−0.535159	+	0.844752i	$0.679748\pi$
$824$	19.3355	0.673586
$825$	−30.0576	−1.04647
$826$	−112.467	−3.91321
$827$	34.8385	1.21145	0.605726	−	0.795673i	$-0.292883\pi$
$827$	34.8385	1.21145	0.605726	+	0.795673i	$0.292883\pi$
$828$	4.76330	0.165536
$829$	−35.7546	−1.24181	−0.620904	−	0.783887i	$-0.713234\pi$
$829$	−35.7546	−1.24181	−0.620904	+	0.783887i	$0.713234\pi$
$830$	8.00542	0.277872
$831$	−9.07317	−0.314745
$832$	16.1278	0.559130
$833$	8.71575	0.301983
$834$	−39.0469	−1.35208
$835$	−10.4234	−0.360717
$836$	−90.1359	−3.11742
$837$	4.10645	0.141940
$838$	9.21255	0.318242
$839$	23.6459	0.816346	0.408173	−	0.912905i	$-0.366166\pi$
$839$	23.6459	0.816346	0.408173	+	0.912905i	$0.366166\pi$
$840$	−3.63148	−0.125298
$841$	20.0750	0.692241
$842$	−43.2003	−1.48878
$843$	−4.79242	−0.165060
$844$	12.0304	0.414103
$845$	6.66171	0.229170
$846$	4.08358	0.140396
$847$	−121.905	−4.18871
$848$	−14.2255	−0.488506
$849$	−18.8554	−0.647116
$850$	10.1009	0.346458
$851$	−0.696487	−0.0238753
$852$	0.0223116	0.000764382 0
$853$	−12.8822	−0.441077	−0.220538	−	0.975378i	$-0.570781\pi$
$853$	−12.8822	−0.441077	−0.220538	+	0.975378i	$0.570781\pi$
$854$	107.824	3.68967
$855$	3.03188	0.103688
$856$	27.7694	0.949140
$857$	32.1545	1.09838	0.549188	−	0.835699i	$-0.314937\pi$
$857$	32.1545	1.09838	0.549188	+	0.835699i	$0.314937\pi$
$858$	18.3492	0.626431
$859$	8.60864	0.293723	0.146861	−	0.989157i	$-0.453083\pi$
$859$	8.60864	0.293723	0.146861	+	0.989157i	$0.453083\pi$
$860$	−2.33537	−0.0796354
$861$	−43.8649	−1.49491
$862$	15.7454	0.536289
$863$	−55.2073	−1.87928	−0.939639	−	0.342167i	$-0.888839\pi$
$863$	−55.2073	−1.87928	−0.939639	+	0.342167i	$0.888839\pi$
$864$	7.57567	0.257730
$865$	−7.30213	−0.248280
$866$	−18.9211	−0.642967
$867$	1.00000	0.0339618
$868$	−44.1972	−1.50015
$869$	43.5769	1.47825
$870$	−8.97583	−0.304309
$871$	1.32330	0.0448381
$872$	18.6660	0.632111
$873$	−2.37523	−0.0803893
$874$	19.5745	0.662118
$875$	−22.5779	−0.763271
$876$	−15.6239	−0.527882
$877$	24.3253	0.821407	0.410704	−	0.911769i	$-0.365283\pi$
$877$	24.3253	0.821407	0.410704	+	0.911769i	$0.365283\pi$
$878$	−89.1209	−3.00768
$879$	3.03961	0.102524
$880$	7.85034	0.264635
$881$	−3.96475	−0.133576	−0.0667879	−	0.997767i	$-0.521275\pi$
$881$	−3.96475	−0.133576	−0.0667879	+	0.997767i	$0.521275\pi$
$882$	−18.9253	−0.637248
$883$	−39.8834	−1.34218	−0.671092	−	0.741374i	$-0.734175\pi$
$883$	−39.8834	−1.34218	−0.671092	+	0.741374i	$0.734175\pi$
$884$	−3.55065	−0.119421
$885$	7.70947	0.259151
$886$	32.4640	1.09065
$887$	−4.71937	−0.158461	−0.0792305	−	0.996856i	$-0.525246\pi$
$887$	−4.71937	−0.158461	−0.0792305	+	0.996856i	$0.525246\pi$
$888$	0.616276	0.0206809
$889$	−22.0470	−0.739431
$890$	−8.78933	−0.294619
$891$	6.46148	0.216468
$892$	−25.0242	−0.837871
$893$	9.66291	0.323357
$894$	17.4991	0.585257
$895$	−9.04353	−0.302292
$896$	−46.0885	−1.53971
$897$	−2.29453	−0.0766122
$898$	−49.2992	−1.64513
$899$	−28.7672	−0.959439
$900$	−12.6294	−0.420980
$901$	6.90904	0.230174
$902$	−155.246	−5.16912
$903$	−5.77904	−0.192314
$904$	29.1384	0.969129
$905$	12.0925	0.401969
$906$	−43.8334	−1.45627
$907$	4.01359	0.133269	0.0666346	−	0.997777i	$-0.478774\pi$
$907$	4.01359	0.133269	0.0666346	+	0.997777i	$0.478774\pi$
$908$	−18.9271	−0.628116
$909$	−3.63503	−0.120566
$910$	6.64293	0.220211
$911$	−51.2421	−1.69773	−0.848863	−	0.528613i	$-0.822712\pi$
$911$	−51.2421	−1.69773	−0.848863	+	0.528613i	$0.822712\pi$
$912$	10.5793	0.350314
$913$	40.3711	1.33609
$914$	61.8336	2.04527
$915$	−7.39125	−0.244347
$916$	61.9371	2.04646
$917$	72.9356	2.40854
$918$	−2.17139	−0.0716666
$919$	45.9274	1.51501	0.757503	−	0.652831i	$-0.226419\pi$
$919$	45.9274	1.51501	0.757503	+	0.652831i	$0.226419\pi$
$920$	1.60718	0.0529870
$921$	−11.3180	−0.372939
$922$	−36.3607	−1.19748
$923$	−0.0107477	−0.000353766 0
$924$	−69.5440	−2.28783
$925$	1.84666	0.0607179
$926$	22.7004	0.745983
$927$	−12.4551	−0.409079
$928$	−53.0703	−1.74212
$929$	−30.0403	−0.985591	−0.492796	−	0.870145i	$-0.664025\pi$
$929$	−30.0403	−0.985591	−0.492796	+	0.870145i	$0.664025\pi$
$930$	5.26153	0.172532
$931$	−44.7827	−1.46769
$932$	52.1373	1.70782
$933$	−25.1335	−0.822834
$934$	23.4705	0.767977
$935$	−3.81275	−0.124690
$936$	2.03028	0.0663619
$937$	−8.63411	−0.282064	−0.141032	−	0.990005i	$-0.545042\pi$
$937$	−8.63411	−0.282064	−0.141032	+	0.990005i	$0.545042\pi$
$938$	−8.70994	−0.284390
$939$	−26.9076	−0.878095
$940$	3.01280	0.0982666
$941$	48.5566	1.58290	0.791449	−	0.611235i	$-0.209327\pi$
$941$	48.5566	1.58290	0.791449	+	0.611235i	$0.209327\pi$
$942$	2.17139	0.0707478
$943$	19.4132	0.632180
$944$	26.9010	0.875552
$945$	2.33924	0.0760954
$946$	−20.4530	−0.664986
$947$	1.29426	0.0420578	0.0210289	−	0.999779i	$-0.493306\pi$
$947$	1.29426	0.0420578	0.0210289	+	0.999779i	$0.493306\pi$
$948$	18.3099	0.594677
$949$	7.52620	0.244311
$950$	−51.8998	−1.68385
$951$	25.6434	0.831545
$952$	6.15428	0.199461
$953$	−4.92796	−0.159632	−0.0798162	−	0.996810i	$-0.525433\pi$
$953$	−4.92796	−0.159632	−0.0798162	+	0.996810i	$0.525433\pi$
$954$	−15.0022	−0.485715
$955$	−13.4225	−0.434342
$956$	−44.2781	−1.43206
$957$	−45.2649	−1.46321
$958$	48.2629	1.55930
$959$	−44.5199	−1.43762
$960$	7.27669	0.234854
$961$	−14.1370	−0.456033
$962$	−1.12733	−0.0363466
$963$	−17.8878	−0.576427
$964$	−60.8029	−1.95833
$965$	13.6896	0.440685
$966$	15.1026	0.485920
$967$	35.8044	1.15139	0.575696	−	0.817664i	$-0.304731\pi$
$967$	35.8044	1.15139	0.575696	+	0.817664i	$0.304731\pi$
$968$	−47.7380	−1.53436
$969$	−5.13813	−0.165061
$970$	−3.04334	−0.0977157
$971$	4.09774	0.131503	0.0657513	−	0.997836i	$-0.479056\pi$
$971$	4.09774	0.131503	0.0657513	+	0.997836i	$0.479056\pi$
$972$	2.71494	0.0870818
$973$	−71.2878	−2.28538
$974$	48.4523	1.55251
$975$	6.08372	0.194835
$976$	−25.7906	−0.825537
$977$	−17.0903	−0.546767	−0.273383	−	0.961905i	$-0.588143\pi$
$977$	−17.0903	−0.546767	−0.273383	+	0.961905i	$0.588143\pi$
$978$	26.3755	0.843395
$979$	−44.3244	−1.41661
$980$	−13.9628	−0.446025
$981$	−12.0238	−0.383890
$982$	−20.5843	−0.656873
$983$	−43.3420	−1.38240	−0.691198	−	0.722665i	$-0.742917\pi$
$983$	−43.3420	−1.38240	−0.691198	+	0.722665i	$0.742917\pi$
$984$	−17.1775	−0.547598
$985$	−3.01824	−0.0961692
$986$	15.2114	0.484429
$987$	7.45539	0.237308
$988$	18.2437	0.580410
$989$	2.55762	0.0813274
$990$	8.27897	0.263123
$991$	−35.2139	−1.11861	−0.559303	−	0.828964i	$-0.688931\pi$
$991$	−35.2139	−1.11861	−0.559303	+	0.828964i	$0.688931\pi$
$992$	31.1092	0.987717
$993$	17.0344	0.540569
$994$	0.0707417	0.00224379
$995$	−4.66553	−0.147907
$996$	16.9629	0.537490
$997$	−33.7019	−1.06735	−0.533676	−	0.845689i	$-0.679190\pi$
$997$	−33.7019	−1.06735	−0.533676	+	0.845689i	$0.679190\pi$
$998$	82.8426	2.62234
$999$	−0.396977	−0.0125598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.6	✓	40	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)

\(f(q)\)	\(=\)	\(q-2.17139 q^{2} +1.00000 q^{3} +2.71494 q^{4} -0.590074 q^{5} -2.17139 q^{6} -3.96431 q^{7} -1.55242 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.17139 q^{2} +1.00000 q^{3} +2.71494 q^{4} -0.590074 q^{5} -2.17139 q^{6} -3.96431 q^{7} -1.55242 q^{8} +1.00000 q^{9} +1.28128 q^{10} +6.46148 q^{11} +2.71494 q^{12} -1.30782 q^{13} +8.60807 q^{14} -0.590074 q^{15} -2.05897 q^{16} +1.00000 q^{17} -2.17139 q^{18} -5.13813 q^{19} -1.60202 q^{20} -3.96431 q^{21} -14.0304 q^{22} +1.75448 q^{23} -1.55242 q^{24} -4.65181 q^{25} +2.83978 q^{26} +1.00000 q^{27} -10.7629 q^{28} -7.00535 q^{29} +1.28128 q^{30} +4.10645 q^{31} +7.57567 q^{32} +6.46148 q^{33} -2.17139 q^{34} +2.33924 q^{35} +2.71494 q^{36} -0.396977 q^{37} +11.1569 q^{38} -1.30782 q^{39} +0.916044 q^{40} +11.0650 q^{41} +8.60807 q^{42} +1.45777 q^{43} +17.5425 q^{44} -0.590074 q^{45} -3.80965 q^{46} -1.88063 q^{47} -2.05897 q^{48} +8.71575 q^{49} +10.1009 q^{50} +1.00000 q^{51} -3.55065 q^{52} +6.90904 q^{53} -2.17139 q^{54} -3.81275 q^{55} +6.15428 q^{56} -5.13813 q^{57} +15.2114 q^{58} -13.0653 q^{59} -1.60202 q^{60} +12.5260 q^{61} -8.91672 q^{62} -3.96431 q^{63} -12.3318 q^{64} +0.771709 q^{65} -14.0304 q^{66} -1.01183 q^{67} +2.71494 q^{68} +1.75448 q^{69} -5.07940 q^{70} +0.00821806 q^{71} -1.55242 q^{72} -5.75478 q^{73} +0.861993 q^{74} -4.65181 q^{75} -13.9497 q^{76} -25.6153 q^{77} +2.83978 q^{78} +6.74411 q^{79} +1.21495 q^{80} +1.00000 q^{81} -24.0264 q^{82} +6.24798 q^{83} -10.7629 q^{84} -0.590074 q^{85} -3.16538 q^{86} -7.00535 q^{87} -10.0309 q^{88} -6.85979 q^{89} +1.28128 q^{90} +5.18459 q^{91} +4.76330 q^{92} +4.10645 q^{93} +4.08358 q^{94} +3.03188 q^{95} +7.57567 q^{96} -2.37523 q^{97} -18.9253 q^{98} +6.46148 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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