LMFDB - Embedded newform 4027.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$1$
Dimension:	$159$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59596 q^{2} -2.97309 q^{3} +4.73903 q^{4} -2.99704 q^{5} +7.71803 q^{6} +3.05793 q^{7} -7.11041 q^{8} +5.83925 q^{9} +O(q^{10})$	\(q-2.59596 q^{2} -2.97309 q^{3} +4.73903 q^{4} -2.99704 q^{5} +7.71803 q^{6} +3.05793 q^{7} -7.11041 q^{8} +5.83925 q^{9} +7.78021 q^{10} -1.64872 q^{11} -14.0895 q^{12} +0.354252 q^{13} -7.93826 q^{14} +8.91047 q^{15} +8.98032 q^{16} +4.82411 q^{17} -15.1585 q^{18} -1.52819 q^{19} -14.2031 q^{20} -9.09148 q^{21} +4.28002 q^{22} +1.36801 q^{23} +21.1399 q^{24} +3.98226 q^{25} -0.919624 q^{26} -8.44134 q^{27} +14.4916 q^{28} -4.71673 q^{29} -23.1312 q^{30} +8.38541 q^{31} -9.09176 q^{32} +4.90179 q^{33} -12.5232 q^{34} -9.16473 q^{35} +27.6724 q^{36} +2.49280 q^{37} +3.96712 q^{38} -1.05322 q^{39} +21.3102 q^{40} -2.74085 q^{41} +23.6012 q^{42} -7.59047 q^{43} -7.81333 q^{44} -17.5005 q^{45} -3.55130 q^{46} -9.27098 q^{47} -26.6993 q^{48} +2.35091 q^{49} -10.3378 q^{50} -14.3425 q^{51} +1.67881 q^{52} -11.2786 q^{53} +21.9134 q^{54} +4.94128 q^{55} -21.7431 q^{56} +4.54344 q^{57} +12.2445 q^{58} +1.60082 q^{59} +42.2269 q^{60} +4.23894 q^{61} -21.7682 q^{62} +17.8560 q^{63} +5.64123 q^{64} -1.06171 q^{65} -12.7249 q^{66} -4.93863 q^{67} +22.8616 q^{68} -4.06721 q^{69} +23.7913 q^{70} +10.3646 q^{71} -41.5195 q^{72} -6.10014 q^{73} -6.47121 q^{74} -11.8396 q^{75} -7.24212 q^{76} -5.04166 q^{77} +2.73412 q^{78} +1.64943 q^{79} -26.9144 q^{80} +7.57910 q^{81} +7.11514 q^{82} -8.73178 q^{83} -43.0848 q^{84} -14.4581 q^{85} +19.7046 q^{86} +14.0233 q^{87} +11.7231 q^{88} +13.5604 q^{89} +45.4306 q^{90} +1.08328 q^{91} +6.48303 q^{92} -24.9306 q^{93} +24.0671 q^{94} +4.58004 q^{95} +27.0306 q^{96} -12.2094 q^{97} -6.10288 q^{98} -9.62729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) $ 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * 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 $

$2$	−2.59596	−1.83562	−0.917812	−	0.397016i	$-0.870046\pi$
$2$	−2.59596	−1.83562	−0.917812	+	0.397016i	$0.870046\pi$
$3$	−2.97309	−1.71651	−0.858257	−	0.513221i	$-0.828452\pi$
$3$	−2.97309	−1.71651	−0.858257	+	0.513221i	$0.828452\pi$
$4$	4.73903	2.36951
$5$	−2.99704	−1.34032	−0.670159	−	0.742218i	$-0.733774\pi$
$5$	−2.99704	−1.34032	−0.670159	+	0.742218i	$0.733774\pi$
$6$	7.71803	3.15087
$7$	3.05793	1.15579	0.577894	−	0.816112i	$-0.303875\pi$
$7$	3.05793	1.15579	0.577894	+	0.816112i	$0.303875\pi$
$8$	−7.11041	−2.51391
$9$	5.83925	1.94642
$10$	7.78021	2.46032
$11$	−1.64872	−0.497108	−0.248554	−	0.968618i	$-0.579955\pi$
$11$	−1.64872	−0.497108	−0.248554	+	0.968618i	$0.579955\pi$
$12$	−14.0895	−4.06730
$13$	0.354252	0.0982517	0.0491259	−	0.998793i	$-0.484356\pi$
$13$	0.354252	0.0982517	0.0491259	+	0.998793i	$0.484356\pi$
$14$	−7.93826	−2.12159
$15$	8.91047	2.30067
$16$	8.98032	2.24508
$17$	4.82411	1.17002	0.585009	−	0.811026i	$-0.301091\pi$
$17$	4.82411	1.17002	0.585009	+	0.811026i	$0.301091\pi$
$18$	−15.1585	−3.57289
$19$	−1.52819	−0.350590	−0.175295	−	0.984516i	$-0.556088\pi$
$19$	−1.52819	−0.350590	−0.175295	+	0.984516i	$0.556088\pi$
$20$	−14.2031	−3.17590
$21$	−9.09148	−1.98392
$22$	4.28002	0.912503
$23$	1.36801	0.285249	0.142625	−	0.989777i	$-0.454446\pi$
$23$	1.36801	0.285249	0.142625	+	0.989777i	$0.454446\pi$
$24$	21.1399	4.31516
$25$	3.98226	0.796451
$26$	−0.919624	−0.180353
$27$	−8.44134	−1.62454
$28$	14.4916	2.73865
$29$	−4.71673	−0.875875	−0.437938	−	0.899005i	$-0.644291\pi$
$29$	−4.71673	−0.875875	−0.437938	+	0.899005i	$0.644291\pi$
$30$	−23.1312	−4.22317
$31$	8.38541	1.50606	0.753032	−	0.657984i	$-0.228591\pi$
$31$	8.38541	1.50606	0.753032	+	0.657984i	$0.228591\pi$
$32$	−9.09176	−1.60721
$33$	4.90179	0.853292
$34$	−12.5232	−2.14771
$35$	−9.16473	−1.54912
$36$	27.6724	4.61206
$37$	2.49280	0.409813	0.204907	−	0.978782i	$-0.434311\pi$
$37$	2.49280	0.409813	0.204907	+	0.978782i	$0.434311\pi$
$38$	3.96712	0.643552
$39$	−1.05322	−0.168650
$40$	21.3102	3.36944
$41$	−2.74085	−0.428048	−0.214024	−	0.976828i	$-0.568657\pi$
$41$	−2.74085	−0.428048	−0.214024	+	0.976828i	$0.568657\pi$
$42$	23.6012	3.64174
$43$	−7.59047	−1.15754	−0.578768	−	0.815492i	$-0.696466\pi$
$43$	−7.59047	−1.15754	−0.578768	+	0.815492i	$0.696466\pi$
$44$	−7.81333	−1.17790
$45$	−17.5005	−2.60882
$46$	−3.55130	−0.523611
$47$	−9.27098	−1.35231	−0.676156	−	0.736759i	$-0.736355\pi$
$47$	−9.27098	−1.35231	−0.676156	+	0.736759i	$0.736355\pi$
$48$	−26.6993	−3.85371
$49$	2.35091	0.335844
$50$	−10.3378	−1.46198
$51$	−14.3425	−2.00835
$52$	1.67881	0.232809
$53$	−11.2786	−1.54923	−0.774615	−	0.632434i	$-0.782056\pi$
$53$	−11.2786	−1.54923	−0.774615	+	0.632434i	$0.782056\pi$
$54$	21.9134	2.98204
$55$	4.94128	0.666282
$56$	−21.7431	−2.90555
$57$	4.54344	0.601793
$58$	12.2445	1.60778
$59$	1.60082	0.208409	0.104205	−	0.994556i	$-0.466770\pi$
$59$	1.60082	0.208409	0.104205	+	0.994556i	$0.466770\pi$
$60$	42.2269	5.45147
$61$	4.23894	0.542741	0.271370	−	0.962475i	$-0.412523\pi$
$61$	4.23894	0.542741	0.271370	+	0.962475i	$0.412523\pi$
$62$	−21.7682	−2.76457
$63$	17.8560	2.24964
$64$	5.64123	0.705154
$65$	−1.06171	−0.131689
$66$	−12.7249	−1.56632
$67$	−4.93863	−0.603350	−0.301675	−	0.953411i	$-0.597546\pi$
$67$	−4.93863	−0.603350	−0.301675	+	0.953411i	$0.597546\pi$
$68$	22.8616	2.77238
$69$	−4.06721	−0.489634
$70$	23.7913	2.84360
$71$	10.3646	1.23005	0.615025	−	0.788508i	$-0.289146\pi$
$71$	10.3646	1.23005	0.615025	+	0.788508i	$0.289146\pi$
$72$	−41.5195	−4.89312
$73$	−6.10014	−0.713968	−0.356984	−	0.934111i	$-0.616195\pi$
$73$	−6.10014	−0.713968	−0.356984	+	0.934111i	$0.616195\pi$
$74$	−6.47121	−0.752262
$75$	−11.8396	−1.36712
$76$	−7.24212	−0.830729
$77$	−5.04166	−0.574551
$78$	2.73412	0.309579
$79$	1.64943	0.185575	0.0927877	−	0.995686i	$-0.470422\pi$
$79$	1.64943	0.185575	0.0927877	+	0.995686i	$0.470422\pi$
$80$	−26.9144	−3.00912
$81$	7.57910	0.842122
$82$	7.11514	0.785735
$83$	−8.73178	−0.958438	−0.479219	−	0.877695i	$-0.659080\pi$
$83$	−8.73178	−0.958438	−0.479219	+	0.877695i	$0.659080\pi$
$84$	−43.0848	−4.70093
$85$	−14.4581	−1.56820
$86$	19.7046	2.12480
$87$	14.0233	1.50345
$88$	11.7231	1.24968
$89$	13.5604	1.43740	0.718698	−	0.695322i	$-0.244738\pi$
$89$	13.5604	1.43740	0.718698	+	0.695322i	$0.244738\pi$
$90$	45.4306	4.78881
$91$	1.08328	0.113558
$92$	6.48303	0.675902
$93$	−24.9306	−2.58518
$94$	24.0671	2.48233
$95$	4.58004	0.469902
$96$	27.0306	2.75880
$97$	−12.2094	−1.23967	−0.619836	−	0.784731i	$-0.712801\pi$
$97$	−12.2094	−1.23967	−0.619836	+	0.784731i	$0.712801\pi$
$98$	−6.10288	−0.616484
$99$	−9.62729	−0.967579
$100$	18.8720	1.88720
$101$	10.6462	1.05934	0.529668	−	0.848205i	$-0.322316\pi$
$101$	10.6462	1.05934	0.529668	+	0.848205i	$0.322316\pi$
$102$	37.2326	3.68658
$103$	15.0022	1.47821	0.739104	−	0.673592i	$-0.235249\pi$
$103$	15.0022	1.47821	0.739104	+	0.673592i	$0.235249\pi$
$104$	−2.51888	−0.246996
$105$	27.2475	2.65909
$106$	29.2787	2.84380
$107$	−5.26756	−0.509235	−0.254617	−	0.967042i	$-0.581950\pi$
$107$	−5.26756	−0.509235	−0.254617	+	0.967042i	$0.581950\pi$
$108$	−40.0037	−3.84936
$109$	14.8795	1.42519	0.712596	−	0.701574i	$-0.247519\pi$
$109$	14.8795	1.42519	0.712596	+	0.701574i	$0.247519\pi$
$110$	−12.8274	−1.22304
$111$	−7.41130	−0.703449
$112$	27.4612	2.59484
$113$	0.756616	0.0711764	0.0355882	−	0.999367i	$-0.488670\pi$
$113$	0.756616	0.0711764	0.0355882	+	0.999367i	$0.488670\pi$
$114$	−11.7946	−1.10467
$115$	−4.09998	−0.382325
$116$	−22.3527	−2.07540
$117$	2.06856	0.191239
$118$	−4.15568	−0.382561
$119$	14.7518	1.35229
$120$	−63.3571	−5.78369
$121$	−8.28172	−0.752884
$122$	−11.0041	−0.996268
$123$	8.14878	0.734750
$124$	39.7387	3.56864
$125$	3.05022	0.272820
$126$	−46.3535	−4.12950
$127$	10.3725	0.920408	0.460204	−	0.887813i	$-0.347776\pi$
$127$	10.3725	0.920408	0.460204	+	0.887813i	$0.347776\pi$
$128$	3.53909	0.312814
$129$	22.5671	1.98693
$130$	2.75615	0.241731
$131$	−5.30562	−0.463554	−0.231777	−	0.972769i	$-0.574454\pi$
$131$	−5.30562	−0.463554	−0.231777	+	0.972769i	$0.574454\pi$
$132$	23.2297	2.02189
$133$	−4.67309	−0.405208
$134$	12.8205	1.10752
$135$	25.2991	2.17740
$136$	−34.3014	−2.94132
$137$	−5.13578	−0.438779	−0.219390	−	0.975637i	$-0.570407\pi$
$137$	−5.13578	−0.438779	−0.219390	+	0.975637i	$0.570407\pi$
$138$	10.5583	0.898784
$139$	−12.8816	−1.09260	−0.546301	−	0.837589i	$-0.683964\pi$
$139$	−12.8816	−1.09260	−0.546301	+	0.837589i	$0.683964\pi$
$140$	−43.4319	−3.67067
$141$	27.5634	2.32126
$142$	−26.9061	−2.25791
$143$	−0.584062	−0.0488417
$144$	52.4383	4.36986
$145$	14.1362	1.17395
$146$	15.8357	1.31058
$147$	−6.98946	−0.576481
$148$	11.8134	0.971058
$149$	19.5488	1.60150	0.800749	−	0.599000i	$-0.204435\pi$
$149$	19.5488	1.60150	0.800749	+	0.599000i	$0.204435\pi$
$150$	30.7352	2.50952
$151$	3.25431	0.264832	0.132416	−	0.991194i	$-0.457727\pi$
$151$	3.25431	0.264832	0.132416	+	0.991194i	$0.457727\pi$
$152$	10.8660	0.881353
$153$	28.1692	2.27734
$154$	13.0880	1.05466
$155$	−25.1314	−2.01860
$156$	−4.99124	−0.399619
$157$	11.2887	0.900940	0.450470	−	0.892792i	$-0.351256\pi$
$157$	11.2887	0.900940	0.450470	+	0.892792i	$0.351256\pi$
$158$	−4.28186	−0.340647
$159$	33.5321	2.65927
$160$	27.2484	2.15417
$161$	4.18327	0.329688
$162$	−19.6751	−1.54582
$163$	4.47583	0.350574	0.175287	−	0.984517i	$-0.443915\pi$
$163$	4.47583	0.350574	0.175287	+	0.984517i	$0.443915\pi$
$164$	−12.9889	−1.01427
$165$	−14.6909	−1.14368
$166$	22.6674	1.75933
$167$	3.08569	0.238778	0.119389	−	0.992848i	$-0.461906\pi$
$167$	3.08569	0.238778	0.119389	+	0.992848i	$0.461906\pi$
$168$	64.6442	4.98741
$169$	−12.8745	−0.990347
$170$	37.5326	2.87862
$171$	−8.92347	−0.682395
$172$	−35.9714	−2.74280
$173$	−7.75785	−0.589819	−0.294909	−	0.955525i	$-0.595289\pi$
$173$	−7.75785	−0.589819	−0.294909	+	0.955525i	$0.595289\pi$
$174$	−36.4039	−2.75977
$175$	12.1774	0.920528
$176$	−14.8060	−1.11605
$177$	−4.75939	−0.357738
$178$	−35.2022	−2.63852
$179$	9.66873	0.722675	0.361337	−	0.932435i	$-0.382320\pi$
$179$	9.66873	0.722675	0.361337	+	0.932435i	$0.382320\pi$
$180$	−82.9352	−6.18163
$181$	9.41883	0.700096	0.350048	−	0.936732i	$-0.386165\pi$
$181$	9.41883	0.700096	0.350048	+	0.936732i	$0.386165\pi$
$182$	−2.81214	−0.208450
$183$	−12.6027	−0.931622
$184$	−9.72710	−0.717092
$185$	−7.47101	−0.549280
$186$	64.7188	4.74541
$187$	−7.95361	−0.581626
$188$	−43.9354	−3.20432
$189$	−25.8130	−1.87762
$190$	−11.8896	−0.862564
$191$	10.7025	0.774408	0.387204	−	0.921994i	$-0.373441\pi$
$191$	10.7025	0.774408	0.387204	+	0.921994i	$0.373441\pi$
$192$	−16.7719	−1.21041
$193$	−18.0345	−1.29815	−0.649077	−	0.760723i	$-0.724845\pi$
$193$	−18.0345	−1.29815	−0.649077	+	0.760723i	$0.724845\pi$
$194$	31.6950	2.27557
$195$	3.15655	0.226045
$196$	11.1410	0.795788
$197$	−2.73135	−0.194600	−0.0973002	−	0.995255i	$-0.531021\pi$
$197$	−2.73135	−0.194600	−0.0973002	+	0.995255i	$0.531021\pi$
$198$	24.9921	1.77611
$199$	−17.3579	−1.23047	−0.615234	−	0.788344i	$-0.710939\pi$
$199$	−17.3579	−1.23047	−0.615234	+	0.788344i	$0.710939\pi$
$200$	−28.3155	−2.00221
$201$	14.6830	1.03566
$202$	−27.6371	−1.94454
$203$	−14.4234	−1.01233
$204$	−67.9695	−4.75882
$205$	8.21443	0.573721
$206$	−38.9451	−2.71343
$207$	7.98814	0.555214
$208$	3.18129	0.220583
$209$	2.51955	0.174281
$210$	−70.7336	−4.88108
$211$	25.5188	1.75678	0.878392	−	0.477940i	$-0.158616\pi$
$211$	25.5188	1.75678	0.878392	+	0.477940i	$0.158616\pi$
$212$	−53.4494	−3.67092
$213$	−30.8148	−2.11140
$214$	13.6744	0.934763
$215$	22.7490	1.55147
$216$	60.0214	4.08394
$217$	25.6420	1.74069
$218$	−38.6265	−2.61612
$219$	18.1363	1.22553
$220$	23.4169	1.57876
$221$	1.70895	0.114956
$222$	19.2395	1.29127
$223$	12.3757	0.828739	0.414370	−	0.910109i	$-0.364002\pi$
$223$	12.3757	0.828739	0.414370	+	0.910109i	$0.364002\pi$
$224$	−27.8019	−1.85759
$225$	23.2534	1.55023
$226$	−1.96415	−0.130653
$227$	−16.2860	−1.08094	−0.540470	−	0.841363i	$-0.681754\pi$
$227$	−16.2860	−1.08094	−0.540470	+	0.841363i	$0.681754\pi$
$228$	21.5315	1.42596
$229$	18.7192	1.23700	0.618501	−	0.785784i	$-0.287740\pi$
$229$	18.7192	1.23700	0.618501	+	0.785784i	$0.287740\pi$
$230$	10.6434	0.701805
$231$	14.9893	0.986224
$232$	33.5379	2.20187
$233$	−21.2704	−1.39347	−0.696736	−	0.717328i	$-0.745365\pi$
$233$	−21.2704	−1.39347	−0.696736	+	0.717328i	$0.745365\pi$
$234$	−5.36992	−0.351042
$235$	27.7855	1.81253
$236$	7.58634	0.493829
$237$	−4.90390	−0.318543
$238$	−38.2951	−2.48230
$239$	24.4871	1.58394	0.791968	−	0.610562i	$-0.209057\pi$
$239$	24.4871	1.58394	0.791968	+	0.610562i	$0.209057\pi$
$240$	80.0188	5.16519
$241$	−22.8084	−1.46922	−0.734610	−	0.678490i	$-0.762635\pi$
$241$	−22.8084	−1.46922	−0.734610	+	0.678490i	$0.762635\pi$
$242$	21.4990	1.38201
$243$	2.79070	0.179023
$244$	20.0885	1.28603
$245$	−7.04578	−0.450138
$246$	−21.1539	−1.34873
$247$	−0.541363	−0.0344461
$248$	−59.6237	−3.78611
$249$	25.9604	1.64517
$250$	−7.91826	−0.500795
$251$	18.3408	1.15766	0.578832	−	0.815447i	$-0.303509\pi$
$251$	18.3408	1.15766	0.578832	+	0.815447i	$0.303509\pi$
$252$	84.6200	5.33056
$253$	−2.25546	−0.141800
$254$	−26.9265	−1.68952
$255$	42.9851	2.69183
$256$	−20.4698	−1.27936
$257$	9.50121	0.592669	0.296334	−	0.955084i	$-0.404236\pi$
$257$	9.50121	0.592669	0.296334	+	0.955084i	$0.404236\pi$
$258$	−58.5835	−3.64725
$259$	7.62278	0.473657
$260$	−5.03146	−0.312038
$261$	−27.5422	−1.70482
$262$	13.7732	0.850911
$263$	1.67246	0.103128	0.0515642	−	0.998670i	$-0.483579\pi$
$263$	1.67246	0.103128	0.0515642	+	0.998670i	$0.483579\pi$
$264$	−34.8537	−2.14510
$265$	33.8023	2.07646
$266$	12.1312	0.743809
$267$	−40.3162	−2.46731
$268$	−23.4043	−1.42965
$269$	−14.5380	−0.886399	−0.443199	−	0.896423i	$-0.646157\pi$
$269$	−14.5380	−0.886399	−0.443199	+	0.896423i	$0.646157\pi$
$270$	−65.6754	−3.99688
$271$	−12.2307	−0.742965	−0.371483	−	0.928440i	$-0.621150\pi$
$271$	−12.2307	−0.742965	−0.371483	+	0.928440i	$0.621150\pi$
$272$	43.3221	2.62679
$273$	−3.22067	−0.194924
$274$	13.3323	0.805434
$275$	−6.56563	−0.395922
$276$	−19.2746	−1.16020
$277$	5.54871	0.333390	0.166695	−	0.986009i	$-0.446691\pi$
$277$	5.54871	0.333390	0.166695	+	0.986009i	$0.446691\pi$
$278$	33.4401	2.00560
$279$	48.9645	2.93143
$280$	65.1650	3.89435
$281$	−1.68702	−0.100639	−0.0503197	−	0.998733i	$-0.516024\pi$
$281$	−1.68702	−0.100639	−0.0503197	+	0.998733i	$0.516024\pi$
$282$	−71.5537	−4.26096
$283$	−16.9544	−1.00783	−0.503917	−	0.863752i	$-0.668108\pi$
$283$	−16.9544	−1.00783	−0.503917	+	0.863752i	$0.668108\pi$
$284$	49.1180	2.91462
$285$	−13.6169	−0.806594
$286$	1.51620	0.0896550
$287$	−8.38130	−0.494733
$288$	−53.0891	−3.12830
$289$	6.27205	0.368944
$290$	−36.6972	−2.15493
$291$	36.2995	2.12791
$292$	−28.9087	−1.69176
$293$	0.0257055	0.00150173	0.000750866	−	1.00000i	$-0.499761\pi$
$293$	0.0257055	0.00150173	0.000750866		1.00000i	$0.499761\pi$
$294$	18.1444	1.05820
$295$	−4.79773	−0.279335
$296$	−17.7248	−1.03023
$297$	13.9174	0.807570
$298$	−50.7479	−2.93975
$299$	0.484619	0.0280262
$300$	−56.1082	−3.23941
$301$	−23.2111	−1.33787
$302$	−8.44807	−0.486132
$303$	−31.6521	−1.81836
$304$	−13.7236	−0.787103
$305$	−12.7043	−0.727445
$306$	−73.1262	−4.18035
$307$	−32.5311	−1.85665	−0.928323	−	0.371774i	$-0.878750\pi$
$307$	−32.5311	−1.85665	−0.928323	+	0.371774i	$0.878750\pi$
$308$	−23.8926	−1.36141
$309$	−44.6028	−2.53736
$310$	65.2402	3.70540
$311$	−4.11306	−0.233230	−0.116615	−	0.993177i	$-0.537204\pi$
$311$	−4.11306	−0.233230	−0.116615	+	0.993177i	$0.537204\pi$
$312$	7.48884	0.423972
$313$	5.65581	0.319685	0.159843	−	0.987143i	$-0.448901\pi$
$313$	5.65581	0.319685	0.159843	+	0.987143i	$0.448901\pi$
$314$	−29.3052	−1.65379
$315$	−53.5152	−3.01524
$316$	7.81670	0.439724
$317$	−1.74498	−0.0980078	−0.0490039	−	0.998799i	$-0.515605\pi$
$317$	−1.74498	−0.0980078	−0.0490039	+	0.998799i	$0.515605\pi$
$318$	−87.0482	−4.88142
$319$	7.77657	0.435404
$320$	−16.9070	−0.945130
$321$	15.6609	0.874108
$322$	−10.8596	−0.605183
$323$	−7.37215	−0.410197
$324$	35.9176	1.99542
$325$	1.41072	0.0782527
$326$	−11.6191	−0.643522
$327$	−44.2379	−2.44636
$328$	19.4885	1.07608
$329$	−28.3500	−1.56298
$330$	38.1370	2.09937
$331$	2.53404	0.139284	0.0696418	−	0.997572i	$-0.477814\pi$
$331$	2.53404	0.139284	0.0696418	+	0.997572i	$0.477814\pi$
$332$	−41.3801	−2.27103
$333$	14.5561	0.797667
$334$	−8.01034	−0.438306
$335$	14.8013	0.808680
$336$	−81.6444	−4.45407
$337$	4.61305	0.251289	0.125644	−	0.992075i	$-0.459900\pi$
$337$	4.61305	0.251289	0.125644	+	0.992075i	$0.459900\pi$
$338$	33.4217	1.81790
$339$	−2.24949	−0.122175
$340$	−68.5171	−3.71586
$341$	−13.8252	−0.748676
$342$	23.1650	1.25262
$343$	−14.2166	−0.767623
$344$	53.9714	2.90994
$345$	12.1896	0.656266
$346$	20.1391	1.08268
$347$	23.9397	1.28515	0.642576	−	0.766222i	$-0.277866\pi$
$347$	23.9397	1.28515	0.642576	+	0.766222i	$0.277866\pi$
$348$	66.4566	3.56245
$349$	−5.64226	−0.302023	−0.151012	−	0.988532i	$-0.548253\pi$
$349$	−5.64226	−0.302023	−0.151012	+	0.988532i	$0.548253\pi$
$350$	−31.6122	−1.68974
$351$	−2.99036	−0.159614
$352$	14.9898	0.798957
$353$	4.62983	0.246421	0.123211	−	0.992381i	$-0.460681\pi$
$353$	4.62983	0.246421	0.123211	+	0.992381i	$0.460681\pi$
$354$	12.3552	0.656671
$355$	−31.0631	−1.64866
$356$	64.2630	3.40593
$357$	−43.8583	−2.32123
$358$	−25.0997	−1.32656
$359$	−26.3042	−1.38828	−0.694140	−	0.719840i	$-0.744215\pi$
$359$	−26.3042	−1.38828	−0.694140	+	0.719840i	$0.744215\pi$
$360$	124.436	6.55833
$361$	−16.6646	−0.877086
$362$	−24.4509	−1.28511
$363$	24.6223	1.29233
$364$	5.13367	0.269077
$365$	18.2824	0.956943
$366$	32.7163	1.71011
$367$	20.9796	1.09513	0.547564	−	0.836764i	$-0.315555\pi$
$367$	20.9796	1.09513	0.547564	+	0.836764i	$0.315555\pi$
$368$	12.2852	0.640408
$369$	−16.0045	−0.833160
$370$	19.3945	1.00827
$371$	−34.4890	−1.79058
$372$	−118.147	−6.12561
$373$	8.90638	0.461155	0.230578	−	0.973054i	$-0.425938\pi$
$373$	8.90638	0.461155	0.230578	+	0.973054i	$0.425938\pi$
$374$	20.6473	1.06765
$375$	−9.06857	−0.468299
$376$	65.9205	3.39959
$377$	−1.67091	−0.0860562
$378$	67.0096	3.44660
$379$	18.5544	0.953076	0.476538	−	0.879154i	$-0.341892\pi$
$379$	18.5544	0.953076	0.476538	+	0.879154i	$0.341892\pi$
$380$	21.7049	1.11344
$381$	−30.8383	−1.57989
$382$	−27.7834	−1.42152
$383$	−30.1813	−1.54219	−0.771095	−	0.636720i	$-0.780291\pi$
$383$	−30.1813	−1.54219	−0.771095	+	0.636720i	$0.780291\pi$
$384$	−10.5220	−0.536950
$385$	15.1101	0.770081
$386$	46.8170	2.38292
$387$	−44.3227	−2.25305
$388$	−57.8604	−2.93742
$389$	−5.53967	−0.280872	−0.140436	−	0.990090i	$-0.544850\pi$
$389$	−5.53967	−0.280872	−0.140436	+	0.990090i	$0.544850\pi$
$390$	−8.19428	−0.414934
$391$	6.59943	0.333747
$392$	−16.7159	−0.844283
$393$	15.7741	0.795697
$394$	7.09048	0.357213
$395$	−4.94341	−0.248730
$396$	−45.6240	−2.29269
$397$	−14.3308	−0.719240	−0.359620	−	0.933099i	$-0.617094\pi$
$397$	−14.3308	−0.719240	−0.359620	+	0.933099i	$0.617094\pi$
$398$	45.0605	2.25868
$399$	13.8935	0.695545
$400$	35.7619	1.78810
$401$	−4.79602	−0.239502	−0.119751	−	0.992804i	$-0.538210\pi$
$401$	−4.79602	−0.239502	−0.119751	+	0.992804i	$0.538210\pi$
$402$	−38.1165	−1.90108
$403$	2.97054	0.147973
$404$	50.4526	2.51011
$405$	−22.7149	−1.12871
$406$	37.4427	1.85825
$407$	−4.10992	−0.203721
$408$	101.981	5.04882
$409$	−6.44848	−0.318857	−0.159428	−	0.987209i	$-0.550965\pi$
$409$	−6.44848	−0.318857	−0.159428	+	0.987209i	$0.550965\pi$
$410$	−21.3244	−1.05314
$411$	15.2691	0.753171
$412$	71.0957	3.50263
$413$	4.89520	0.240877
$414$	−20.7369	−1.01916
$415$	26.1695	1.28461
$416$	−3.22077	−0.157911
$417$	38.2981	1.87546
$418$	−6.54067	−0.319915
$419$	−29.2473	−1.42882	−0.714412	−	0.699726i	$-0.753306\pi$
$419$	−29.2473	−1.42882	−0.714412	+	0.699726i	$0.753306\pi$
$420$	129.127	6.30075
$421$	12.7972	0.623696	0.311848	−	0.950132i	$-0.399052\pi$
$421$	12.7972	0.623696	0.311848	+	0.950132i	$0.399052\pi$
$422$	−66.2458	−3.22480
$423$	−54.1356	−2.63216
$424$	80.1952	3.89462
$425$	19.2109	0.931863
$426$	79.9942	3.87573
$427$	12.9624	0.627293
$428$	−24.9631	−1.20664
$429$	1.73647	0.0838374
$430$	−59.0554	−2.84791
$431$	−11.6350	−0.560438	−0.280219	−	0.959936i	$-0.590407\pi$
$431$	−11.6350	−0.560438	−0.280219	+	0.959936i	$0.590407\pi$
$432$	−75.8060	−3.64722
$433$	−24.0539	−1.15596	−0.577979	−	0.816051i	$-0.696159\pi$
$433$	−24.0539	−1.15596	−0.577979	+	0.816051i	$0.696159\pi$
$434$	−66.5656	−3.19525
$435$	−42.0283	−2.01510
$436$	70.5141	3.37701
$437$	−2.09057	−0.100006
$438$	−47.0811	−2.24962
$439$	6.63134	0.316497	0.158248	−	0.987399i	$-0.449415\pi$
$439$	6.63134	0.316497	0.158248	+	0.987399i	$0.449415\pi$
$440$	−35.1346	−1.67497
$441$	13.7276	0.653693
$442$	−4.43637	−0.211017
$443$	19.9567	0.948173	0.474087	−	0.880478i	$-0.342778\pi$
$443$	19.9567	0.948173	0.474087	+	0.880478i	$0.342778\pi$
$444$	−35.1223	−1.66683
$445$	−40.6410	−1.92657
$446$	−32.1269	−1.52125
$447$	−58.1202	−2.74899
$448$	17.2505	0.815008
$449$	18.5978	0.877686	0.438843	−	0.898564i	$-0.355388\pi$
$449$	18.5978	0.877686	0.438843	+	0.898564i	$0.355388\pi$
$450$	−60.3650	−2.84563
$451$	4.51889	0.212786
$452$	3.58562	0.168654
$453$	−9.67535	−0.454587
$454$	42.2779	1.98420
$455$	−3.24662	−0.152204
$456$	−32.3057	−1.51285
$457$	16.9776	0.794177	0.397088	−	0.917780i	$-0.370021\pi$
$457$	16.9776	0.794177	0.397088	+	0.917780i	$0.370021\pi$
$458$	−48.5944	−2.27067
$459$	−40.7220	−1.90074
$460$	−19.4299	−0.905924
$461$	−33.7100	−1.57003	−0.785016	−	0.619476i	$-0.787345\pi$
$461$	−33.7100	−1.57003	−0.785016	+	0.619476i	$0.787345\pi$
$462$	−38.9117	−1.81034
$463$	32.6478	1.51727	0.758636	−	0.651515i	$-0.225866\pi$
$463$	32.6478	1.51727	0.758636	+	0.651515i	$0.225866\pi$
$464$	−42.3578	−1.96641
$465$	74.7179	3.46496
$466$	55.2172	2.55789
$467$	39.3948	1.82297	0.911487	−	0.411329i	$-0.134935\pi$
$467$	39.3948	1.82297	0.911487	+	0.411329i	$0.134935\pi$
$468$	9.80298	0.453143
$469$	−15.1020	−0.697344
$470$	−72.1302	−3.32712
$471$	−33.5624	−1.54648
$472$	−11.3825	−0.523923
$473$	12.5146	0.575420
$474$	12.7304	0.584725
$475$	−6.08564	−0.279228
$476$	69.9091	3.20428
$477$	−65.8583	−3.01545
$478$	−63.5675	−2.90751
$479$	−30.2577	−1.38251	−0.691256	−	0.722610i	$-0.742942\pi$
$479$	−30.2577	−1.38251	−0.691256	+	0.722610i	$0.742942\pi$
$480$	−81.0118	−3.69767
$481$	0.883077	0.0402648
$482$	59.2098	2.69693
$483$	−12.4372	−0.565913
$484$	−39.2473	−1.78397
$485$	36.5919	1.66155
$486$	−7.24456	−0.328620
$487$	19.0346	0.862538	0.431269	−	0.902223i	$-0.358066\pi$
$487$	19.0346	0.862538	0.431269	+	0.902223i	$0.358066\pi$
$488$	−30.1406	−1.36440
$489$	−13.3070	−0.601765
$490$	18.2906	0.826284
$491$	−26.5172	−1.19670	−0.598352	−	0.801233i	$-0.704178\pi$
$491$	−26.5172	−1.19670	−0.598352	+	0.801233i	$0.704178\pi$
$492$	38.6173	1.74100
$493$	−22.7540	−1.02479
$494$	1.40536	0.0632301
$495$	28.8534	1.29686
$496$	75.3036	3.38123
$497$	31.6941	1.42168
$498$	−67.3921	−3.01991
$499$	−0.300093	−0.0134340	−0.00671699	−	0.999977i	$-0.502138\pi$
$499$	−0.300093	−0.0134340	−0.00671699	+	0.999977i	$0.502138\pi$
$500$	14.4551	0.646450
$501$	−9.17403	−0.409865
$502$	−47.6122	−2.12503
$503$	−15.2343	−0.679264	−0.339632	−	0.940558i	$-0.610303\pi$
$503$	−15.2343	−0.679264	−0.339632	+	0.940558i	$0.610303\pi$
$504$	−126.964	−5.65540
$505$	−31.9071	−1.41985
$506$	5.85510	0.260291
$507$	38.2770	1.69994
$508$	49.1554	2.18092
$509$	24.4227	1.08252	0.541258	−	0.840856i	$-0.317948\pi$
$509$	24.4227	1.08252	0.541258	+	0.840856i	$0.317948\pi$
$510$	−111.588	−4.94119
$511$	−18.6538	−0.825195
$512$	46.0607	2.03561
$513$	12.9000	0.569547
$514$	−24.6648	−1.08792
$515$	−44.9621	−1.98127
$516$	106.946	4.70805
$517$	15.2853	0.672245
$518$	−19.7885	−0.869455
$519$	23.0648	1.01243
$520$	7.54917	0.331053
$521$	−35.1401	−1.53951	−0.769757	−	0.638336i	$-0.779623\pi$
$521$	−35.1401	−1.53951	−0.769757	+	0.638336i	$0.779623\pi$
$522$	71.4985	3.12940
$523$	−42.9961	−1.88009	−0.940043	−	0.341055i	$-0.889216\pi$
$523$	−42.9961	−1.88009	−0.940043	+	0.341055i	$0.889216\pi$
$524$	−25.1435	−1.09840
$525$	−36.2046	−1.58010
$526$	−4.34165	−0.189305
$527$	40.4521	1.76212
$528$	44.0196	1.91571
$529$	−21.1286	−0.918633
$530$	−87.7496	−3.81160
$531$	9.34761	0.405652
$532$	−22.1459	−0.960145
$533$	−0.970949	−0.0420565
$534$	104.659	4.52905
$535$	15.7871	0.682536
$536$	35.1157	1.51677
$537$	−28.7460	−1.24048
$538$	37.7402	1.62709
$539$	−3.87599	−0.166951
$540$	119.893	5.15937
$541$	19.0963	0.821015	0.410508	−	0.911857i	$-0.365351\pi$
$541$	19.0963	0.821015	0.410508	+	0.911857i	$0.365351\pi$
$542$	31.7506	1.36380
$543$	−28.0030	−1.20172
$544$	−43.8597	−1.88047
$545$	−44.5943	−1.91021
$546$	8.36075	0.357807
$547$	9.83391	0.420468	0.210234	−	0.977651i	$-0.432577\pi$
$547$	9.83391	0.420468	0.210234	+	0.977651i	$0.432577\pi$
$548$	−24.3386	−1.03969
$549$	24.7522	1.05640
$550$	17.0441	0.726764
$551$	7.20805	0.307073
$552$	28.9195	1.23090
$553$	5.04384	0.214486
$554$	−14.4042	−0.611978
$555$	22.2120	0.942846
$556$	−61.0461	−2.58893
$557$	0.140285	0.00594405	0.00297203	−	0.999996i	$-0.499054\pi$
$557$	0.140285	0.00594405	0.00297203	+	0.999996i	$0.499054\pi$
$558$	−127.110	−5.38100
$559$	−2.68894	−0.113730
$560$	−82.3022	−3.47790
$561$	23.6468	0.998368
$562$	4.37945	0.184736
$563$	19.5387	0.823459	0.411730	−	0.911306i	$-0.364925\pi$
$563$	19.5387	0.823459	0.411730	+	0.911306i	$0.364925\pi$
$564$	130.624	5.50026
$565$	−2.26761	−0.0953990
$566$	44.0130	1.85000
$567$	23.1763	0.973314
$568$	−73.6965	−3.09224
$569$	−30.6481	−1.28483	−0.642417	−	0.766355i	$-0.722068\pi$
$569$	−30.6481	−1.28483	−0.642417	+	0.766355i	$0.722068\pi$
$570$	35.3489	1.48060
$571$	−25.7545	−1.07779	−0.538896	−	0.842372i	$-0.681158\pi$
$571$	−25.7545	−1.07779	−0.538896	+	0.842372i	$0.681158\pi$
$572$	−2.76788	−0.115731
$573$	−31.8196	−1.32928
$574$	21.7576	0.908143
$575$	5.44776	0.227187
$576$	32.9406	1.37252
$577$	−5.32198	−0.221557	−0.110779	−	0.993845i	$-0.535334\pi$
$577$	−5.32198	−0.221557	−0.110779	+	0.993845i	$0.535334\pi$
$578$	−16.2820	−0.677243
$579$	53.6182	2.22830
$580$	66.9920	2.78169
$581$	−26.7011	−1.10775
$582$	−94.2321	−3.90605
$583$	18.5952	0.770134
$584$	43.3745	1.79485
$585$	−6.19957	−0.256321
$586$	−0.0667305	−0.00275661
$587$	7.95035	0.328146	0.164073	−	0.986448i	$-0.447537\pi$
$587$	7.95035	0.328146	0.164073	+	0.986448i	$0.447537\pi$
$588$	−33.1233	−1.36598
$589$	−12.8145	−0.528011
$590$	12.4547	0.512754
$591$	8.12053	0.334034
$592$	22.3861	0.920063
$593$	−8.49060	−0.348667	−0.174334	−	0.984687i	$-0.555777\pi$
$593$	−8.49060	−0.348667	−0.174334	+	0.984687i	$0.555777\pi$
$594$	−36.1291	−1.48239
$595$	−44.2117	−1.81250
$596$	92.6421	3.79477
$597$	51.6065	2.11212
$598$	−1.25805	−0.0514456
$599$	−5.85529	−0.239241	−0.119620	−	0.992820i	$-0.538168\pi$
$599$	−5.85529	−0.239241	−0.119620	+	0.992820i	$0.538168\pi$
$600$	84.1844	3.43682
$601$	42.0287	1.71439	0.857194	−	0.514994i	$-0.172206\pi$
$601$	42.0287	1.71439	0.857194	+	0.514994i	$0.172206\pi$
$602$	60.2552	2.45582
$603$	−28.8379	−1.17437
$604$	15.4223	0.627523
$605$	24.8207	1.00910
$606$	82.1676	3.33783
$607$	22.2217	0.901951	0.450976	−	0.892536i	$-0.351076\pi$
$607$	22.2217	0.901951	0.450976	+	0.892536i	$0.351076\pi$
$608$	13.8939	0.563473
$609$	42.8821	1.73767
$610$	32.9799	1.33532
$611$	−3.28426	−0.132867
$612$	133.495	5.39620
$613$	−30.6304	−1.23715	−0.618575	−	0.785726i	$-0.712290\pi$
$613$	−30.6304	−1.23715	−0.618575	+	0.785726i	$0.712290\pi$
$614$	84.4495	3.40810
$615$	−24.4222	−0.984799
$616$	35.8483	1.44437
$617$	15.2419	0.613616	0.306808	−	0.951772i	$-0.400739\pi$
$617$	15.2419	0.613616	0.306808	+	0.951772i	$0.400739\pi$
$618$	115.787	4.65764
$619$	−0.371020	−0.0149125	−0.00745627	−	0.999972i	$-0.502373\pi$
$619$	−0.371020	−0.0149125	−0.00745627	+	0.999972i	$0.502373\pi$
$620$	−119.098	−4.78311
$621$	−11.5478	−0.463398
$622$	10.6773	0.428123
$623$	41.4666	1.66132
$624$	−9.45826	−0.378634
$625$	−29.0529	−1.16212
$626$	−14.6823	−0.586822
$627$	−7.49086	−0.299156
$628$	53.4977	2.13479
$629$	12.0255	0.479489
$630$	138.923	5.53484
$631$	11.3506	0.451859	0.225929	−	0.974144i	$-0.427458\pi$
$631$	11.3506	0.451859	0.225929	+	0.974144i	$0.427458\pi$
$632$	−11.7281	−0.466520
$633$	−75.8696	−3.01554
$634$	4.52990	0.179905
$635$	−31.0867	−1.23364
$636$	158.910	6.30118
$637$	0.832814	0.0329973
$638$	−20.1877	−0.799238
$639$	60.5214	2.39419
$640$	−10.6068	−0.419270
$641$	−29.0479	−1.14732	−0.573662	−	0.819092i	$-0.694478\pi$
$641$	−29.0479	−1.14732	−0.573662	+	0.819092i	$0.694478\pi$
$642$	−40.6552	−1.60453
$643$	−36.8911	−1.45484	−0.727421	−	0.686191i	$-0.759281\pi$
$643$	−36.8911	−1.45484	−0.727421	+	0.686191i	$0.759281\pi$
$644$	19.8246	0.781199
$645$	−67.6346	−2.66311
$646$	19.1378	0.752968
$647$	0.717532	0.0282091	0.0141045	−	0.999901i	$-0.495510\pi$
$647$	0.717532	0.0282091	0.0141045	+	0.999901i	$0.495510\pi$
$648$	−53.8905	−2.11702
$649$	−2.63931	−0.103602
$650$	−3.66218	−0.143643
$651$	−76.2358	−2.98792
$652$	21.2111	0.830690
$653$	42.4026	1.65934	0.829670	−	0.558254i	$-0.188528\pi$
$653$	42.4026	1.65934	0.829670	+	0.558254i	$0.188528\pi$
$654$	114.840	4.49060
$655$	15.9012	0.621310
$656$	−24.6137	−0.961003
$657$	−35.6203	−1.38968
$658$	73.5955	2.86905
$659$	49.3232	1.92136	0.960680	−	0.277659i	$-0.0895586\pi$
$659$	49.3232	1.92136	0.960680	+	0.277659i	$0.0895586\pi$
$660$	−69.6204	−2.70997
$661$	−1.10529	−0.0429906	−0.0214953	−	0.999769i	$-0.506843\pi$
$661$	−1.10529	−0.0429906	−0.0214953	+	0.999769i	$0.506843\pi$
$662$	−6.57828	−0.255672
$663$	−5.08086	−0.197324
$664$	62.0866	2.40943
$665$	14.0054	0.543107
$666$	−37.7870	−1.46422
$667$	−6.45253	−0.249843
$668$	14.6232	0.565787
$669$	−36.7941	−1.42254
$670$	−38.4236	−1.48443
$671$	−6.98883	−0.269801
$672$	82.6575	3.18858
$673$	−34.9885	−1.34871	−0.674353	−	0.738409i	$-0.735578\pi$
$673$	−34.9885	−1.34871	−0.674353	+	0.738409i	$0.735578\pi$
$674$	−11.9753	−0.461272
$675$	−33.6156	−1.29386
$676$	−61.0126	−2.34664
$677$	45.5252	1.74967	0.874837	−	0.484417i	$-0.160968\pi$
$677$	45.5252	1.74967	0.874837	+	0.484417i	$0.160968\pi$
$678$	5.83958	0.224268
$679$	−37.3353	−1.43280
$680$	102.803	3.94231
$681$	48.4197	1.85545
$682$	35.8897	1.37429
$683$	9.41050	0.360083	0.180041	−	0.983659i	$-0.442377\pi$
$683$	9.41050	0.360083	0.180041	+	0.983659i	$0.442377\pi$
$684$	−42.2886	−1.61694
$685$	15.3922	0.588104
$686$	36.9057	1.40907
$687$	−55.6539	−2.12333
$688$	−68.1648	−2.59876
$689$	−3.99545	−0.152214
$690$	−31.6437	−1.20466
$691$	−13.2314	−0.503345	−0.251673	−	0.967812i	$-0.580981\pi$
$691$	−13.2314	−0.503345	−0.251673	+	0.967812i	$0.580981\pi$
$692$	−36.7647	−1.39758
$693$	−29.4395	−1.11832
$694$	−62.1467	−2.35906
$695$	38.6066	1.46443
$696$	−99.7112	−3.77954
$697$	−13.2221	−0.500825
$698$	14.6471	0.554401
$699$	63.2388	2.39191
$700$	57.7092	2.18120
$701$	18.3424	0.692781	0.346391	−	0.938090i	$-0.387407\pi$
$701$	18.3424	0.692781	0.346391	+	0.938090i	$0.387407\pi$
$702$	7.76286	0.292990
$703$	−3.80946	−0.143677
$704$	−9.30081	−0.350537
$705$	−82.6088	−3.11123
$706$	−12.0189	−0.452336
$707$	32.5553	1.22437
$708$	−22.5549	−0.847664
$709$	−50.8538	−1.90986	−0.954928	−	0.296838i	$-0.904068\pi$
$709$	−50.8538	−1.90986	−0.954928	+	0.296838i	$0.904068\pi$
$710$	80.6386	3.02631
$711$	9.63144	0.361207
$712$	−96.4198	−3.61349
$713$	11.4713	0.429604
$714$	113.855	4.26090
$715$	1.75046	0.0654634
$716$	45.8204	1.71239
$717$	−72.8022	−2.71885
$718$	68.2846	2.54836
$719$	−33.5666	−1.25182	−0.625911	−	0.779895i	$-0.715273\pi$
$719$	−33.5666	−1.25182	−0.625911	+	0.779895i	$0.715273\pi$
$720$	−157.160	−5.85700
$721$	45.8755	1.70849
$722$	43.2608	1.61000
$723$	67.8114	2.52193
$724$	44.6361	1.65889
$725$	−18.7832	−0.697592
$726$	−63.9186	−2.37224
$727$	−46.2990	−1.71714	−0.858568	−	0.512700i	$-0.828645\pi$
$727$	−46.2990	−1.71714	−0.858568	+	0.512700i	$0.828645\pi$
$728$	−7.70253	−0.285475
$729$	−31.0343	−1.14942
$730$	−47.4604	−1.75659
$731$	−36.6173	−1.35434
$732$	−59.7248	−2.20749
$733$	−21.7524	−0.803445	−0.401722	−	0.915762i	$-0.631588\pi$
$733$	−21.7524	−0.803445	−0.401722	+	0.915762i	$0.631588\pi$
$734$	−54.4623	−2.01024
$735$	20.9477	0.772668
$736$	−12.4376	−0.458456
$737$	8.14242	0.299930
$738$	41.5471	1.52937
$739$	50.6564	1.86343	0.931714	−	0.363194i	$-0.118314\pi$
$739$	50.6564	1.86343	0.931714	+	0.363194i	$0.118314\pi$
$740$	−35.4053	−1.30153
$741$	1.60952	0.0591272
$742$	89.5322	3.28683
$743$	−22.1594	−0.812951	−0.406475	−	0.913662i	$-0.633242\pi$
$743$	−22.1594	−0.812951	−0.406475	+	0.913662i	$0.633242\pi$
$744$	177.267	6.49891
$745$	−58.5885	−2.14652
$746$	−23.1206	−0.846507
$747$	−50.9871	−1.86552
$748$	−37.6924	−1.37817
$749$	−16.1078	−0.588567
$750$	23.5417	0.859620
$751$	−45.1757	−1.64848	−0.824242	−	0.566238i	$-0.808398\pi$
$751$	−45.1757	−1.64848	−0.824242	+	0.566238i	$0.808398\pi$
$752$	−83.2564	−3.03605
$753$	−54.5289	−1.98714
$754$	4.33762	0.157967
$755$	−9.75330	−0.354959
$756$	−122.328	−4.44904
$757$	−24.6305	−0.895209	−0.447605	−	0.894232i	$-0.647723\pi$
$757$	−24.6305	−0.895209	−0.447605	+	0.894232i	$0.647723\pi$
$758$	−48.1665	−1.74949
$759$	6.70569	0.243401
$760$	−32.5660	−1.18129
$761$	−34.5777	−1.25344	−0.626721	−	0.779244i	$-0.715603\pi$
$761$	−34.5777	−1.25344	−0.626721	+	0.779244i	$0.715603\pi$
$762$	80.0550	2.90009
$763$	45.5003	1.64722
$764$	50.7196	1.83497
$765$	−84.4243	−3.05237
$766$	78.3495	2.83088
$767$	0.567094	0.0204766
$768$	60.8585	2.19604
$769$	13.1265	0.473354	0.236677	−	0.971588i	$-0.423942\pi$
$769$	13.1265	0.473354	0.236677	+	0.971588i	$0.423942\pi$
$770$	−39.2252	−1.41358
$771$	−28.2479	−1.01732
$772$	−85.4661	−3.07599
$773$	−9.89822	−0.356014	−0.178007	−	0.984029i	$-0.556965\pi$
$773$	−9.89822	−0.356014	−0.178007	+	0.984029i	$0.556965\pi$
$774$	115.060	4.13575
$775$	33.3928	1.19951
$776$	86.8135	3.11642
$777$	−22.6632	−0.813038
$778$	14.3808	0.515576
$779$	4.18853	0.150070
$780$	14.9590	0.535617
$781$	−17.0883	−0.611467
$782$	−17.1319	−0.612634
$783$	39.8155	1.42289
$784$	21.1119	0.753998
$785$	−33.8328	−1.20755
$786$	−40.9489	−1.46060
$787$	−45.6150	−1.62600	−0.812999	−	0.582265i	$-0.802167\pi$
$787$	−45.6150	−1.62600	−0.812999	+	0.582265i	$0.802167\pi$
$788$	−12.9439	−0.461108
$789$	−4.97238	−0.177021
$790$	12.8329	0.456575
$791$	2.31368	0.0822648
$792$	68.4540	2.43241
$793$	1.50165	0.0533252
$794$	37.2021	1.32025
$795$	−100.497	−3.56427
$796$	−82.2595	−2.91561
$797$	−8.22951	−0.291504	−0.145752	−	0.989321i	$-0.546560\pi$
$797$	−8.22951	−0.291504	−0.145752	+	0.989321i	$0.546560\pi$
$798$	−36.0670	−1.27676
$799$	−44.7242	−1.58223
$800$	−36.2057	−1.28007
$801$	79.1824	2.79777
$802$	12.4503	0.439636
$803$	10.0574	0.354919
$804$	69.5830	2.45400
$805$	−12.5374	−0.441886
$806$	−7.71142	−0.271623
$807$	43.2228	1.52152
$808$	−75.6989	−2.66308
$809$	2.30081	0.0808923	0.0404461	−	0.999182i	$-0.487122\pi$
$809$	2.30081	0.0808923	0.0404461	+	0.999182i	$0.487122\pi$
$810$	58.9670	2.07189
$811$	47.9003	1.68201	0.841003	−	0.541030i	$-0.181965\pi$
$811$	47.9003	1.68201	0.841003	+	0.541030i	$0.181965\pi$
$812$	−68.3530	−2.39872
$813$	36.3631	1.27531
$814$	10.6692	0.373956
$815$	−13.4142	−0.469881
$816$	−128.800	−4.50891
$817$	11.5997	0.405821
$818$	16.7400	0.585301
$819$	6.32552	0.221031
$820$	38.9284	1.35944
$821$	40.2069	1.40323	0.701615	−	0.712556i	$-0.252463\pi$
$821$	40.2069	1.40323	0.701615	+	0.712556i	$0.252463\pi$
$822$	−39.6381	−1.38254
$823$	13.1525	0.458466	0.229233	−	0.973372i	$-0.426378\pi$
$823$	13.1525	0.458466	0.229233	+	0.973372i	$0.426378\pi$
$824$	−106.672	−3.71608
$825$	19.5202	0.679606
$826$	−12.7078	−0.442159
$827$	−6.12674	−0.213048	−0.106524	−	0.994310i	$-0.533972\pi$
$827$	−6.12674	−0.213048	−0.106524	+	0.994310i	$0.533972\pi$
$828$	37.8560	1.31559
$829$	−18.8830	−0.655835	−0.327917	−	0.944706i	$-0.606347\pi$
$829$	−18.8830	−0.655835	−0.327917	+	0.944706i	$0.606347\pi$
$830$	−67.9351	−2.35806
$831$	−16.4968	−0.572267
$832$	1.99841	0.0692826
$833$	11.3411	0.392944
$834$	−99.4204	−3.44265
$835$	−9.24794	−0.320038
$836$	11.9402	0.412962
$837$	−70.7841	−2.44666
$838$	75.9249	2.62278
$839$	38.3682	1.32462	0.662309	−	0.749231i	$-0.269577\pi$
$839$	38.3682	1.32462	0.662309	+	0.749231i	$0.269577\pi$
$840$	−193.741	−6.68471
$841$	−6.75244	−0.232843
$842$	−33.2210	−1.14487
$843$	5.01567	0.172749
$844$	120.934	4.16272
$845$	38.5854	1.32738
$846$	140.534	4.83166
$847$	−25.3249	−0.870174
$848$	−101.285	−3.47814
$849$	50.4069	1.72996
$850$	−49.8707	−1.71055
$851$	3.41017	0.116899
$852$	−146.032	−5.00298
$853$	−11.0312	−0.377699	−0.188850	−	0.982006i	$-0.560476\pi$
$853$	−11.0312	−0.377699	−0.188850	+	0.982006i	$0.560476\pi$
$854$	−33.6498	−1.15147
$855$	26.7440	0.914626
$856$	37.4546	1.28017
$857$	40.8381	1.39500	0.697502	−	0.716583i	$-0.254295\pi$
$857$	40.8381	1.39500	0.697502	+	0.716583i	$0.254295\pi$
$858$	−4.50780	−0.153894
$859$	−7.68798	−0.262311	−0.131155	−	0.991362i	$-0.541869\pi$
$859$	−7.68798	−0.262311	−0.131155	+	0.991362i	$0.541869\pi$
$860$	107.808	3.67622
$861$	24.9184	0.849215
$862$	30.2040	1.02875
$863$	29.9726	1.02028	0.510140	−	0.860092i	$-0.329594\pi$
$863$	29.9726	1.02028	0.510140	+	0.860092i	$0.329594\pi$
$864$	76.7466	2.61097
$865$	23.2506	0.790544
$866$	62.4432	2.12191
$867$	−18.6474	−0.633298
$868$	121.518	4.12459
$869$	−2.71945	−0.0922510
$870$	109.104	3.69897
$871$	−1.74952	−0.0592802
$872$	−105.799	−3.58281
$873$	−71.2935	−2.41292
$874$	5.42705	0.183573
$875$	9.32734	0.315322
$876$	85.9482	2.90392
$877$	54.4618	1.83904	0.919521	−	0.393040i	$-0.128577\pi$
$877$	54.4618	1.83904	0.919521	+	0.393040i	$0.128577\pi$
$878$	−17.2147	−0.580969
$879$	−0.0764247	−0.00257774
$880$	44.3743	1.49586
$881$	−3.77769	−0.127274	−0.0636368	−	0.997973i	$-0.520270\pi$
$881$	−3.77769	−0.127274	−0.0636368	+	0.997973i	$0.520270\pi$
$882$	−35.6362	−1.19993
$883$	32.5204	1.09440	0.547199	−	0.837003i	$-0.315694\pi$
$883$	32.5204	1.09440	0.547199	+	0.837003i	$0.315694\pi$
$884$	8.09876	0.272391
$885$	14.2641	0.479482
$886$	−51.8070	−1.74049
$887$	23.3120	0.782741	0.391371	−	0.920233i	$-0.372001\pi$
$887$	23.3120	0.782741	0.391371	+	0.920233i	$0.372001\pi$
$888$	52.6974	1.76841
$889$	31.7182	1.06380
$890$	105.503	3.53645
$891$	−12.4958	−0.418626
$892$	58.6489	1.96371
$893$	14.1678	0.474107
$894$	150.878	5.04611
$895$	−28.9776	−0.968614
$896$	10.8223	0.361547
$897$	−1.44082	−0.0481074
$898$	−48.2793	−1.61110
$899$	−39.5517	−1.31912
$900$	110.198	3.67328
$901$	−54.4090	−1.81263
$902$	−11.7309	−0.390595
$903$	69.0086	2.29646
$904$	−5.37985	−0.178931
$905$	−28.2286	−0.938351
$906$	25.1168	0.834451
$907$	20.8405	0.691999	0.346000	−	0.938235i	$-0.387540\pi$
$907$	20.8405	0.691999	0.346000	+	0.938235i	$0.387540\pi$
$908$	−77.1799	−2.56130
$909$	62.1658	2.06191
$910$	8.42811	0.279389
$911$	−16.8526	−0.558351	−0.279175	−	0.960240i	$-0.590061\pi$
$911$	−16.8526	−0.558351	−0.279175	+	0.960240i	$0.590061\pi$
$912$	40.8015	1.35107
$913$	14.3963	0.476447
$914$	−44.0731	−1.45781
$915$	37.7710	1.24867
$916$	88.7109	2.93109
$917$	−16.2242	−0.535770
$918$	105.713	3.48904
$919$	−3.81387	−0.125808	−0.0629041	−	0.998020i	$-0.520036\pi$
$919$	−3.81387	−0.125808	−0.0629041	+	0.998020i	$0.520036\pi$
$920$	29.1525	0.961131
$921$	96.7177	3.18696
$922$	87.5099	2.88199
$923$	3.67167	0.120855
$924$	71.0347	2.33687
$925$	9.92695	0.326396
$926$	−84.7525	−2.78514
$927$	87.6014	2.87721
$928$	42.8834	1.40772
$929$	−4.96491	−0.162894	−0.0814468	−	0.996678i	$-0.525954\pi$
$929$	−4.96491	−0.162894	−0.0814468	+	0.996678i	$0.525954\pi$
$930$	−193.965	−6.36036
$931$	−3.59263	−0.117744
$932$	−100.801	−3.30185
$933$	12.2285	0.400343
$934$	−102.267	−3.34629
$935$	23.8373	0.779563
$936$	−14.7083	−0.480757
$937$	−15.3533	−0.501571	−0.250785	−	0.968043i	$-0.580689\pi$
$937$	−15.3533	−0.501571	−0.250785	+	0.968043i	$0.580689\pi$
$938$	39.2042	1.28006
$939$	−16.8152	−0.548744
$940$	131.676	4.29481
$941$	12.2317	0.398742	0.199371	−	0.979924i	$-0.436110\pi$
$941$	12.2317	0.398742	0.199371	+	0.979924i	$0.436110\pi$
$942$	87.1268	2.83875
$943$	−3.74950	−0.122101
$944$	14.3759	0.467896
$945$	77.3626	2.51661
$946$	−32.4873	−1.05625
$947$	30.4394	0.989148	0.494574	−	0.869135i	$-0.335324\pi$
$947$	30.4394	0.989148	0.494574	+	0.869135i	$0.335324\pi$
$948$	−23.2397	−0.754791
$949$	−2.16099	−0.0701485
$950$	15.7981	0.512558
$951$	5.18798	0.168232
$952$	−104.891	−3.39954
$953$	−33.4726	−1.08428	−0.542141	−	0.840287i	$-0.682386\pi$
$953$	−33.4726	−1.08428	−0.542141	+	0.840287i	$0.682386\pi$
$954$	170.966	5.53522
$955$	−32.0759	−1.03795
$956$	116.045	3.75316
$957$	−23.1204	−0.747377
$958$	78.5480	2.53777
$959$	−15.7048	−0.507136
$960$	50.2660	1.62233
$961$	39.3151	1.26823
$962$	−2.29244	−0.0739111
$963$	−30.7586	−0.991183
$964$	−108.090	−3.48133
$965$	54.0502	1.73994
$966$	32.2866	1.03880
$967$	15.1892	0.488453	0.244226	−	0.969718i	$-0.421466\pi$
$967$	15.1892	0.488453	0.244226	+	0.969718i	$0.421466\pi$
$968$	58.8865	1.89268
$969$	21.9180	0.704109
$970$	−94.9913	−3.04999
$971$	39.2658	1.26010	0.630049	−	0.776555i	$-0.283035\pi$
$971$	39.2658	1.26010	0.630049	+	0.776555i	$0.283035\pi$
$972$	13.2252	0.424199
$973$	−39.3909	−1.26281
$974$	−49.4130	−1.58330
$975$	−4.19420	−0.134322
$976$	38.0671	1.21850
$977$	−36.9076	−1.18078	−0.590389	−	0.807119i	$-0.701026\pi$
$977$	−36.9076	−1.18078	−0.590389	+	0.807119i	$0.701026\pi$
$978$	34.5446	1.10461
$979$	−22.3573	−0.714541
$980$	−33.3901	−1.06661
$981$	86.8848	2.77402
$982$	68.8377	2.19670
$983$	42.4760	1.35478	0.677388	−	0.735626i	$-0.263112\pi$
$983$	42.4760	1.35478	0.677388	+	0.735626i	$0.263112\pi$
$984$	−57.9412	−1.84710
$985$	8.18596	0.260826
$986$	59.0687	1.88113
$987$	84.2870	2.68288
$988$	−2.56553	−0.0816205
$989$	−10.3838	−0.330186
$990$	−74.9023	−2.38055
$991$	−7.53863	−0.239472	−0.119736	−	0.992806i	$-0.538205\pi$
$991$	−7.53863	−0.239472	−0.119736	+	0.992806i	$0.538205\pi$
$992$	−76.2381	−2.42056
$993$	−7.53393	−0.239082
$994$	−82.2768	−2.60966
$995$	52.0223	1.64922
$996$	123.027	3.89825
$997$	−45.1632	−1.43033	−0.715166	−	0.698954i	$-0.753649\pi$
$997$	−45.1632	−1.43033	−0.715166	+	0.698954i	$0.753649\pi$
$998$	0.779029	0.0246597
$999$	−21.0425	−0.665757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.b.1.10	✓	159

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.b.1.10	✓	159	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59596 q^{2} -2.97309 q^{3} +4.73903 q^{4} -2.99704 q^{5} +7.71803 q^{6} +3.05793 q^{7} -7.11041 q^{8} +5.83925 q^{9} +O(q^{10})\)	\(q-2.59596 q^{2} -2.97309 q^{3} +4.73903 q^{4} -2.99704 q^{5} +7.71803 q^{6} +3.05793 q^{7} -7.11041 q^{8} +5.83925 q^{9} +7.78021 q^{10} -1.64872 q^{11} -14.0895 q^{12} +0.354252 q^{13} -7.93826 q^{14} +8.91047 q^{15} +8.98032 q^{16} +4.82411 q^{17} -15.1585 q^{18} -1.52819 q^{19} -14.2031 q^{20} -9.09148 q^{21} +4.28002 q^{22} +1.36801 q^{23} +21.1399 q^{24} +3.98226 q^{25} -0.919624 q^{26} -8.44134 q^{27} +14.4916 q^{28} -4.71673 q^{29} -23.1312 q^{30} +8.38541 q^{31} -9.09176 q^{32} +4.90179 q^{33} -12.5232 q^{34} -9.16473 q^{35} +27.6724 q^{36} +2.49280 q^{37} +3.96712 q^{38} -1.05322 q^{39} +21.3102 q^{40} -2.74085 q^{41} +23.6012 q^{42} -7.59047 q^{43} -7.81333 q^{44} -17.5005 q^{45} -3.55130 q^{46} -9.27098 q^{47} -26.6993 q^{48} +2.35091 q^{49} -10.3378 q^{50} -14.3425 q^{51} +1.67881 q^{52} -11.2786 q^{53} +21.9134 q^{54} +4.94128 q^{55} -21.7431 q^{56} +4.54344 q^{57} +12.2445 q^{58} +1.60082 q^{59} +42.2269 q^{60} +4.23894 q^{61} -21.7682 q^{62} +17.8560 q^{63} +5.64123 q^{64} -1.06171 q^{65} -12.7249 q^{66} -4.93863 q^{67} +22.8616 q^{68} -4.06721 q^{69} +23.7913 q^{70} +10.3646 q^{71} -41.5195 q^{72} -6.10014 q^{73} -6.47121 q^{74} -11.8396 q^{75} -7.24212 q^{76} -5.04166 q^{77} +2.73412 q^{78} +1.64943 q^{79} -26.9144 q^{80} +7.57910 q^{81} +7.11514 q^{82} -8.73178 q^{83} -43.0848 q^{84} -14.4581 q^{85} +19.7046 q^{86} +14.0233 q^{87} +11.7231 q^{88} +13.5604 q^{89} +45.4306 q^{90} +1.08328 q^{91} +6.48303 q^{92} -24.9306 q^{93} +24.0671 q^{94} +4.58004 q^{95} +27.0306 q^{96} -12.2094 q^{97} -6.10288 q^{98} -9.62729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 159 * q - 22 * q^2 - 19 * q^3 + 148 * q^4 - 70 * q^5 - 23 * q^6 - 19 * q^7 - 66 * q^8 + 126 * q^9 - 23 * q^10 - 33 * q^11 - 57 * q^12 - 90 * q^13 - 28 * q^14 - 22 * q^15 + 130 * q^16 - 145 * q^17 - 50 * q^18 - 28 * q^19 - 121 * q^20 - 69 * q^21 - 26 * q^22 - 79 * q^23 - 62 * q^24 + 123 * q^25 - 40 * q^26 - 70 * q^27 - 43 * q^28 - 109 * q^29 - 43 * q^30 - 21 * q^31 - 139 * q^32 - 83 * q^33 - 93 * q^35 + 75 * q^36 - 65 * q^37 - 122 * q^38 - 18 * q^39 - 43 * q^40 - 71 * q^41 - 88 * q^42 - 72 * q^43 - 79 * q^44 - 181 * q^45 - 11 * q^46 - 114 * q^47 - 118 * q^48 + 118 * q^49 - 77 * q^50 - 29 * q^51 - 169 * q^52 - 220 * q^53 - 80 * q^54 - 37 * q^55 - 72 * q^56 - 90 * q^57 - 8 * q^58 - 60 * q^59 - 42 * q^60 - 108 * q^61 - 152 * q^62 - 65 * q^63 + 114 * q^64 - 81 * q^65 - 40 * q^66 - 50 * q^67 - 319 * q^68 - 103 * q^69 + 4 * q^70 - 7 * q^71 - 129 * q^72 - 94 * q^73 - 79 * q^74 - 59 * q^75 - 46 * q^76 - 329 * q^77 + 8 * q^78 - 18 * q^79 - 190 * q^80 + 59 * q^81 - 56 * q^82 - 201 * q^83 - 71 * q^84 - 26 * q^85 - 52 * q^86 - 126 * q^87 - 66 * q^88 - 114 * q^89 - 33 * q^90 - 30 * q^91 - 204 * q^92 - 125 * q^93 + 9 * q^94 - 84 * q^95 - 88 * q^96 - 56 * q^97 - 110 * q^98 - 46 * q^99

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