LMFDB - Embedded newform 4027.2.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.57109 q^{2} -0.605717 q^{3} +4.61051 q^{4} +3.41025 q^{5} +1.55735 q^{6} -4.02437 q^{7} -6.71185 q^{8} -2.63311 q^{9} +O(q^{10})$	\(q-2.57109 q^{2} -0.605717 q^{3} +4.61051 q^{4} +3.41025 q^{5} +1.55735 q^{6} -4.02437 q^{7} -6.71185 q^{8} -2.63311 q^{9} -8.76807 q^{10} +5.08814 q^{11} -2.79266 q^{12} +2.39550 q^{13} +10.3470 q^{14} -2.06565 q^{15} +8.03577 q^{16} -7.10951 q^{17} +6.76996 q^{18} -3.60365 q^{19} +15.7230 q^{20} +2.43763 q^{21} -13.0821 q^{22} +1.71371 q^{23} +4.06548 q^{24} +6.62983 q^{25} -6.15905 q^{26} +3.41207 q^{27} -18.5544 q^{28} +0.411886 q^{29} +5.31097 q^{30} -4.31345 q^{31} -7.23699 q^{32} -3.08197 q^{33} +18.2792 q^{34} -13.7241 q^{35} -12.1400 q^{36} -0.554814 q^{37} +9.26530 q^{38} -1.45100 q^{39} -22.8891 q^{40} +7.94094 q^{41} -6.26736 q^{42} +1.89412 q^{43} +23.4589 q^{44} -8.97956 q^{45} -4.40610 q^{46} +11.0355 q^{47} -4.86740 q^{48} +9.19555 q^{49} -17.0459 q^{50} +4.30635 q^{51} +11.0445 q^{52} -3.88285 q^{53} -8.77273 q^{54} +17.3518 q^{55} +27.0110 q^{56} +2.18279 q^{57} -1.05900 q^{58} +1.99491 q^{59} -9.52368 q^{60} +0.00532245 q^{61} +11.0903 q^{62} +10.5966 q^{63} +2.53541 q^{64} +8.16927 q^{65} +7.92402 q^{66} -8.20079 q^{67} -32.7785 q^{68} -1.03802 q^{69} +35.2860 q^{70} +8.15620 q^{71} +17.6730 q^{72} -9.26076 q^{73} +1.42648 q^{74} -4.01580 q^{75} -16.6146 q^{76} -20.4765 q^{77} +3.73064 q^{78} -6.15314 q^{79} +27.4040 q^{80} +5.83258 q^{81} -20.4169 q^{82} -13.2778 q^{83} +11.2387 q^{84} -24.2452 q^{85} -4.86995 q^{86} -0.249486 q^{87} -34.1508 q^{88} -8.30029 q^{89} +23.0873 q^{90} -9.64039 q^{91} +7.90107 q^{92} +2.61273 q^{93} -28.3732 q^{94} -12.2893 q^{95} +4.38356 q^{96} +18.2387 q^{97} -23.6426 q^{98} -13.3976 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.57109	−1.81804	−0.909018	−	0.416757i	$-0.863167\pi$
$2$	−2.57109	−1.81804	−0.909018	+	0.416757i	$0.863167\pi$
$3$	−0.605717	−0.349711	−0.174855	−	0.984594i	$-0.555946\pi$
$3$	−0.605717	−0.349711	−0.174855	+	0.984594i	$0.555946\pi$
$4$	4.61051	2.30525
$5$	3.41025	1.52511	0.762556	−	0.646923i	$-0.223944\pi$
$5$	3.41025	1.52511	0.762556	+	0.646923i	$0.223944\pi$
$6$	1.55735	0.635786
$7$	−4.02437	−1.52107	−0.760534	−	0.649298i	$-0.775063\pi$
$7$	−4.02437	−1.52107	−0.760534	+	0.649298i	$0.775063\pi$
$8$	−6.71185	−2.37300
$9$	−2.63311	−0.877702
$10$	−8.76807	−2.77271
$11$	5.08814	1.53413	0.767065	−	0.641569i	$-0.221716\pi$
$11$	5.08814	1.53413	0.767065	+	0.641569i	$0.221716\pi$
$12$	−2.79266	−0.806172
$13$	2.39550	0.664393	0.332196	−	0.943210i	$-0.392210\pi$
$13$	2.39550	0.664393	0.332196	+	0.943210i	$0.392210\pi$
$14$	10.3470	2.76536
$15$	−2.06565	−0.533348
$16$	8.03577	2.00894
$17$	−7.10951	−1.72431	−0.862155	−	0.506645i	$-0.830886\pi$
$17$	−7.10951	−1.72431	−0.862155	+	0.506645i	$0.830886\pi$
$18$	6.76996	1.59569
$19$	−3.60365	−0.826733	−0.413366	−	0.910565i	$-0.635647\pi$
$19$	−3.60365	−0.826733	−0.413366	+	0.910565i	$0.635647\pi$
$20$	15.7230	3.51577
$21$	2.43763	0.531934
$22$	−13.0821	−2.78910
$23$	1.71371	0.357333	0.178667	−	0.983910i	$-0.442822\pi$
$23$	1.71371	0.357333	0.178667	+	0.983910i	$0.442822\pi$
$24$	4.06548	0.829863
$25$	6.62983	1.32597
$26$	−6.15905	−1.20789
$27$	3.41207	0.656653
$28$	−18.5544	−3.50645
$29$	0.411886	0.0764853	0.0382427	−	0.999268i	$-0.487824\pi$
$29$	0.411886	0.0764853	0.0382427	+	0.999268i	$0.487824\pi$
$30$	5.31097	0.969645
$31$	−4.31345	−0.774718	−0.387359	−	0.921929i	$-0.626613\pi$
$31$	−4.31345	−0.774718	−0.387359	+	0.921929i	$0.626613\pi$
$32$	−7.23699	−1.27933
$33$	−3.08197	−0.536502
$34$	18.2792	3.13486
$35$	−13.7241	−2.31980
$36$	−12.1400	−2.02333
$37$	−0.554814	−0.0912109	−0.0456055	−	0.998960i	$-0.514522\pi$
$37$	−0.554814	−0.0912109	−0.0456055	+	0.998960i	$0.514522\pi$
$38$	9.26530	1.50303
$39$	−1.45100	−0.232345
$40$	−22.8891	−3.61909
$41$	7.94094	1.24017	0.620083	−	0.784536i	$-0.287099\pi$
$41$	7.94094	1.24017	0.620083	+	0.784536i	$0.287099\pi$
$42$	−6.26736	−0.967075
$43$	1.89412	0.288850	0.144425	−	0.989516i	$-0.453867\pi$
$43$	1.89412	0.288850	0.144425	+	0.989516i	$0.453867\pi$
$44$	23.4589	3.53656
$45$	−8.97956	−1.33859
$46$	−4.40610	−0.649645
$47$	11.0355	1.60969	0.804844	−	0.593487i	$-0.202249\pi$
$47$	11.0355	1.60969	0.804844	+	0.593487i	$0.202249\pi$
$48$	−4.86740	−0.702549
$49$	9.19555	1.31365
$50$	−17.0459	−2.41065
$51$	4.30635	0.603009
$52$	11.0445	1.53159
$53$	−3.88285	−0.533351	−0.266675	−	0.963786i	$-0.585925\pi$
$53$	−3.88285	−0.533351	−0.266675	+	0.963786i	$0.585925\pi$
$54$	−8.77273	−1.19382
$55$	17.3518	2.33972
$56$	27.0110	3.60949
$57$	2.18279	0.289117
$58$	−1.05900	−0.139053
$59$	1.99491	0.259715	0.129857	−	0.991533i	$-0.458548\pi$
$59$	1.99491	0.259715	0.129857	+	0.991533i	$0.458548\pi$
$60$	−9.52368	−1.22950
$61$	0.00532245	0.000681470 0	0.000340735	−	1.00000i	$-0.499892\pi$
$61$	0.00532245	0.000681470 0	0.000340735		1.00000i	$0.499892\pi$
$62$	11.0903	1.40847
$63$	10.5966	1.33505
$64$	2.53541	0.316926
$65$	8.16927	1.01327
$66$	7.92402	0.975379
$67$	−8.20079	−1.00189	−0.500943	−	0.865480i	$-0.667013\pi$
$67$	−8.20079	−1.00189	−0.500943	+	0.865480i	$0.667013\pi$
$68$	−32.7785	−3.97497
$69$	−1.03802	−0.124963
$70$	35.2860	4.21748
$71$	8.15620	0.967963	0.483981	−	0.875078i	$-0.339190\pi$
$71$	8.15620	0.967963	0.483981	+	0.875078i	$0.339190\pi$
$72$	17.6730	2.08279
$73$	−9.26076	−1.08389	−0.541945	−	0.840414i	$-0.682312\pi$
$73$	−9.26076	−1.08389	−0.541945	+	0.840414i	$0.682312\pi$
$74$	1.42648	0.165825
$75$	−4.01580	−0.463704
$76$	−16.6146	−1.90583
$77$	−20.4765	−2.33352
$78$	3.73064	0.422412
$79$	−6.15314	−0.692282	−0.346141	−	0.938183i	$-0.612508\pi$
$79$	−6.15314	−0.692282	−0.346141	+	0.938183i	$0.612508\pi$
$80$	27.4040	3.06386
$81$	5.83258	0.648064
$82$	−20.4169	−2.25467
$83$	−13.2778	−1.45743	−0.728716	−	0.684816i	$-0.759882\pi$
$83$	−13.2778	−1.45743	−0.728716	+	0.684816i	$0.759882\pi$
$84$	11.2387	1.22624
$85$	−24.2452	−2.62976
$86$	−4.86995	−0.525140
$87$	−0.249486	−0.0267477
$88$	−34.1508	−3.64049
$89$	−8.30029	−0.879829	−0.439914	−	0.898040i	$-0.644991\pi$
$89$	−8.30029	−0.879829	−0.439914	+	0.898040i	$0.644991\pi$
$90$	23.0873	2.43361
$91$	−9.64039	−1.01059
$92$	7.90107	0.823744
$93$	2.61273	0.270927
$94$	−28.3732	−2.92647
$95$	−12.2893	−1.26086
$96$	4.38356	0.447396
$97$	18.2387	1.85186	0.925930	−	0.377694i	$-0.123283\pi$
$97$	18.2387	1.85186	0.925930	+	0.377694i	$0.123283\pi$
$98$	−23.6426	−2.38826
$99$	−13.3976	−1.34651
$100$	30.5669	3.05669
$101$	−5.20715	−0.518131	−0.259065	−	0.965860i	$-0.583415\pi$
$101$	−5.20715	−0.518131	−0.259065	+	0.965860i	$0.583415\pi$
$102$	−11.0720	−1.09629
$103$	−8.62674	−0.850018	−0.425009	−	0.905189i	$-0.639729\pi$
$103$	−8.62674	−0.850018	−0.425009	+	0.905189i	$0.639729\pi$
$104$	−16.0783	−1.57660
$105$	8.31293	0.811259
$106$	9.98316	0.969651
$107$	2.68703	0.259765	0.129883	−	0.991529i	$-0.458540\pi$
$107$	2.68703	0.259765	0.129883	+	0.991529i	$0.458540\pi$
$108$	15.7314	1.51375
$109$	−14.7443	−1.41225	−0.706126	−	0.708087i	$-0.749559\pi$
$109$	−14.7443	−1.41225	−0.706126	+	0.708087i	$0.749559\pi$
$110$	−44.6131	−4.25369
$111$	0.336060	0.0318974
$112$	−32.3389	−3.05574
$113$	−10.3477	−0.973426	−0.486713	−	0.873562i	$-0.661804\pi$
$113$	−10.3477	−0.973426	−0.486713	+	0.873562i	$0.661804\pi$
$114$	−5.61215	−0.525626
$115$	5.84418	0.544973
$116$	1.89900	0.176318
$117$	−6.30761	−0.583139
$118$	−5.12908	−0.472170
$119$	28.6113	2.62279
$120$	13.8643	1.26563
$121$	14.8891	1.35356
$122$	−0.0136845	−0.00123894
$123$	−4.80996	−0.433699
$124$	−19.8872	−1.78592
$125$	5.55812	0.497133
$126$	−27.2448	−2.42716
$127$	−7.49419	−0.665002	−0.332501	−	0.943103i	$-0.607892\pi$
$127$	−7.49419	−0.665002	−0.332501	+	0.943103i	$0.607892\pi$
$128$	7.95520	0.703147
$129$	−1.14730	−0.101014
$130$	−21.0039	−1.84217
$131$	17.6099	1.53859	0.769293	−	0.638896i	$-0.220609\pi$
$131$	17.6099	1.53859	0.769293	+	0.638896i	$0.220609\pi$
$132$	−14.2094	−1.23677
$133$	14.5024	1.25752
$134$	21.0850	1.82147
$135$	11.6360	1.00147
$136$	47.7180	4.09178
$137$	−16.3675	−1.39837	−0.699185	−	0.714941i	$-0.746454\pi$
$137$	−16.3675	−1.39837	−0.699185	+	0.714941i	$0.746454\pi$
$138$	2.66885	0.227188
$139$	17.3477	1.47141	0.735707	−	0.677300i	$-0.236850\pi$
$139$	17.3477	1.47141	0.735707	+	0.677300i	$0.236850\pi$
$140$	−63.2752	−5.34773
$141$	−6.68436	−0.562925
$142$	−20.9703	−1.75979
$143$	12.1886	1.01927
$144$	−21.1590	−1.76325
$145$	1.40464	0.116649
$146$	23.8102	1.97055
$147$	−5.56990	−0.459398
$148$	−2.55798	−0.210264
$149$	−15.5014	−1.26993	−0.634964	−	0.772542i	$-0.718985\pi$
$149$	−15.5014	−1.26993	−0.634964	+	0.772542i	$0.718985\pi$
$150$	10.3250	0.843031
$151$	14.5334	1.18271	0.591354	−	0.806412i	$-0.298594\pi$
$151$	14.5334	1.18271	0.591354	+	0.806412i	$0.298594\pi$
$152$	24.1871	1.96184
$153$	18.7201	1.51343
$154$	52.6470	4.24242
$155$	−14.7100	−1.18153
$156$	−6.68983	−0.535615
$157$	−17.6664	−1.40993	−0.704966	−	0.709241i	$-0.749038\pi$
$157$	−17.6664	−1.40993	−0.704966	+	0.709241i	$0.749038\pi$
$158$	15.8203	1.25859
$159$	2.35191	0.186518
$160$	−24.6800	−1.95112
$161$	−6.89660	−0.543528
$162$	−14.9961	−1.17820
$163$	−7.29349	−0.571270	−0.285635	−	0.958338i	$-0.592205\pi$
$163$	−7.29349	−0.571270	−0.285635	+	0.958338i	$0.592205\pi$
$164$	36.6117	2.85890
$165$	−10.5103	−0.818225
$166$	34.1385	2.64966
$167$	−11.5606	−0.894588	−0.447294	−	0.894387i	$-0.647612\pi$
$167$	−11.5606	−0.894588	−0.447294	+	0.894387i	$0.647612\pi$
$168$	−16.3610	−1.26228
$169$	−7.26157	−0.558582
$170$	62.3367	4.78101
$171$	9.48879	0.725626
$172$	8.73285	0.665873
$173$	0.188083	0.0142997	0.00714984	−	0.999974i	$-0.497724\pi$
$173$	0.188083	0.0142997	0.00714984	+	0.999974i	$0.497724\pi$
$174$	0.641452	0.0486283
$175$	−26.6809	−2.01688
$176$	40.8871	3.08198
$177$	−1.20835	−0.0908249
$178$	21.3408	1.59956
$179$	−18.0355	−1.34804	−0.674020	−	0.738713i	$-0.735434\pi$
$179$	−18.0355	−1.34804	−0.674020	+	0.738713i	$0.735434\pi$
$180$	−41.4003	−3.08580
$181$	2.17088	0.161360	0.0806802	−	0.996740i	$-0.474291\pi$
$181$	2.17088	0.161360	0.0806802	+	0.996740i	$0.474291\pi$
$182$	24.7863	1.83728
$183$	−0.00322390	−0.000238317 0
$184$	−11.5022	−0.847951
$185$	−1.89206	−0.139107
$186$	−6.71756	−0.492555
$187$	−36.1742	−2.64532
$188$	50.8791	3.71074
$189$	−13.7314	−0.998814
$190$	31.5970	2.29229
$191$	13.4174	0.970847	0.485423	−	0.874279i	$-0.338665\pi$
$191$	13.4174	0.970847	0.485423	+	0.874279i	$0.338665\pi$
$192$	−1.53574	−0.110833
$193$	3.93130	0.282981	0.141490	−	0.989940i	$-0.454811\pi$
$193$	3.93130	0.282981	0.141490	+	0.989940i	$0.454811\pi$
$194$	−46.8934	−3.36675
$195$	−4.94826	−0.354352
$196$	42.3962	3.02830
$197$	−21.1093	−1.50398	−0.751988	−	0.659177i	$-0.770905\pi$
$197$	−21.1093	−1.50398	−0.751988	+	0.659177i	$0.770905\pi$
$198$	34.4465	2.44800
$199$	16.6441	1.17987	0.589936	−	0.807450i	$-0.299153\pi$
$199$	16.6441	1.17987	0.589936	+	0.807450i	$0.299153\pi$
$200$	−44.4984	−3.14651
$201$	4.96736	0.350370
$202$	13.3881	0.941980
$203$	−1.65758	−0.116339
$204$	19.8545	1.39009
$205$	27.0806	1.89139
$206$	22.1801	1.54536
$207$	−4.51238	−0.313632
$208$	19.2497	1.33473
$209$	−18.3358	−1.26832
$210$	−21.3733	−1.47490
$211$	−3.64895	−0.251204	−0.125602	−	0.992081i	$-0.540086\pi$
$211$	−3.64895	−0.251204	−0.125602	+	0.992081i	$0.540086\pi$
$212$	−17.9019	−1.22951
$213$	−4.94034	−0.338507
$214$	−6.90860	−0.472262
$215$	6.45942	0.440529
$216$	−22.9013	−1.55824
$217$	17.3589	1.17840
$218$	37.9090	2.56752
$219$	5.60939	0.379048
$220$	80.0008	5.39365
$221$	−17.0308	−1.14562
$222$	−0.864042	−0.0579907
$223$	10.5762	0.708237	0.354118	−	0.935201i	$-0.384781\pi$
$223$	10.5762	0.708237	0.354118	+	0.935201i	$0.384781\pi$
$224$	29.1243	1.94595
$225$	−17.4570	−1.16380
$226$	26.6048	1.76972
$227$	9.02522	0.599025	0.299512	−	0.954092i	$-0.403176\pi$
$227$	9.02522	0.599025	0.299512	+	0.954092i	$0.403176\pi$
$228$	10.0638	0.666489
$229$	9.51269	0.628616	0.314308	−	0.949321i	$-0.398228\pi$
$229$	9.51269	0.628616	0.314308	+	0.949321i	$0.398228\pi$
$230$	−15.0259	−0.990780
$231$	12.4030	0.816056
$232$	−2.76452	−0.181500
$233$	−21.3302	−1.39739	−0.698695	−	0.715419i	$-0.746236\pi$
$233$	−21.3302	−1.39739	−0.698695	+	0.715419i	$0.746236\pi$
$234$	16.2174	1.06017
$235$	37.6337	2.45495
$236$	9.19753	0.598708
$237$	3.72706	0.242098
$238$	−73.5623	−4.76833
$239$	8.85150	0.572556	0.286278	−	0.958147i	$-0.407582\pi$
$239$	8.85150	0.572556	0.286278	+	0.958147i	$0.407582\pi$
$240$	−16.5991	−1.07146
$241$	−14.8884	−0.959044	−0.479522	−	0.877530i	$-0.659190\pi$
$241$	−14.8884	−0.959044	−0.479522	+	0.877530i	$0.659190\pi$
$242$	−38.2813	−2.46081
$243$	−13.7691	−0.883287
$244$	0.0245392	0.00157096
$245$	31.3592	2.00346
$246$	12.3668	0.788481
$247$	−8.63254	−0.549275
$248$	28.9512	1.83841
$249$	8.04260	0.509679
$250$	−14.2904	−0.903806
$251$	18.6551	1.17750	0.588751	−	0.808314i	$-0.299620\pi$
$251$	18.6551	1.17750	0.588751	+	0.808314i	$0.299620\pi$
$252$	48.8557	3.07762
$253$	8.71959	0.548196
$254$	19.2683	1.20900
$255$	14.6857	0.919657
$256$	−25.5244	−1.59527
$257$	18.7419	1.16909	0.584543	−	0.811363i	$-0.301274\pi$
$257$	18.7419	1.16909	0.584543	+	0.811363i	$0.301274\pi$
$258$	2.94981	0.183647
$259$	2.23278	0.138738
$260$	37.6645	2.33585
$261$	−1.08454	−0.0671314
$262$	−45.2767	−2.79720
$263$	−15.0148	−0.925849	−0.462925	−	0.886398i	$-0.653200\pi$
$263$	−15.0148	−0.925849	−0.462925	+	0.886398i	$0.653200\pi$
$264$	20.6857	1.27312
$265$	−13.2415	−0.813419
$266$	−37.2870	−2.28621
$267$	5.02762	0.307685
$268$	−37.8098	−2.30960
$269$	−12.3232	−0.751357	−0.375679	−	0.926750i	$-0.622590\pi$
$269$	−12.3232	−0.751357	−0.375679	+	0.926750i	$0.622590\pi$
$270$	−29.9172	−1.82071
$271$	29.3713	1.78418	0.892089	−	0.451860i	$-0.149239\pi$
$271$	29.3713	1.78418	0.892089	+	0.451860i	$0.149239\pi$
$272$	−57.1304	−3.46404
$273$	5.83934	0.353413
$274$	42.0823	2.54229
$275$	33.7334	2.03420
$276$	−4.78581	−0.288072
$277$	29.0280	1.74412	0.872061	−	0.489397i	$-0.162783\pi$
$277$	29.0280	1.74412	0.872061	+	0.489397i	$0.162783\pi$
$278$	−44.6025	−2.67508
$279$	11.3578	0.679972
$280$	92.1143	5.50488
$281$	−9.19365	−0.548447	−0.274224	−	0.961666i	$-0.588421\pi$
$281$	−9.19365	−0.548447	−0.274224	+	0.961666i	$0.588421\pi$
$282$	17.1861	1.02342
$283$	−29.7072	−1.76591	−0.882955	−	0.469458i	$-0.844449\pi$
$283$	−29.7072	−1.76591	−0.882955	+	0.469458i	$0.844449\pi$
$284$	37.6042	2.23140
$285$	7.44386	0.440936
$286$	−31.3381	−1.85306
$287$	−31.9573	−1.88638
$288$	19.0558	1.12287
$289$	33.5451	1.97324
$290$	−3.61145	−0.212071
$291$	−11.0475	−0.647615
$292$	−42.6968	−2.49864
$293$	−4.41221	−0.257764	−0.128882	−	0.991660i	$-0.541139\pi$
$293$	−4.41221	−0.257764	−0.128882	+	0.991660i	$0.541139\pi$
$294$	14.3207	0.835201
$295$	6.80313	0.396094
$296$	3.72383	0.216443
$297$	17.3611	1.00739
$298$	39.8556	2.30877
$299$	4.10520	0.237410
$300$	−18.5149	−1.06896
$301$	−7.62263	−0.439361
$302$	−37.3666	−2.15021
$303$	3.15406	0.181196
$304$	−28.9581	−1.66086
$305$	0.0181509	0.00103932
$306$	−48.1311	−2.75147
$307$	−25.6025	−1.46121	−0.730607	−	0.682799i	$-0.760763\pi$
$307$	−25.6025	−1.46121	−0.730607	+	0.682799i	$0.760763\pi$
$308$	−94.4073	−5.37935
$309$	5.22536	0.297260
$310$	37.8206	2.14807
$311$	−25.0542	−1.42069	−0.710346	−	0.703852i	$-0.751462\pi$
$311$	−25.0542	−1.42069	−0.710346	+	0.703852i	$0.751462\pi$
$312$	9.73887	0.551355
$313$	20.0674	1.13428	0.567138	−	0.823623i	$-0.308050\pi$
$313$	20.0674	1.13428	0.567138	+	0.823623i	$0.308050\pi$
$314$	45.4219	2.56331
$315$	36.1371	2.03609
$316$	−28.3691	−1.59589
$317$	−27.5568	−1.54774	−0.773871	−	0.633343i	$-0.781682\pi$
$317$	−27.5568	−1.54774	−0.773871	+	0.633343i	$0.781682\pi$
$318$	−6.04697	−0.339097
$319$	2.09573	0.117338
$320$	8.64639	0.483348
$321$	−1.62758	−0.0908426
$322$	17.7318	0.988154
$323$	25.6202	1.42554
$324$	26.8911	1.49395
$325$	15.8818	0.880962
$326$	18.7522	1.03859
$327$	8.93089	0.493879
$328$	−53.2984	−2.94291
$329$	−44.4108	−2.44845
$330$	27.0229	1.48756
$331$	−1.73077	−0.0951319	−0.0475659	−	0.998868i	$-0.515146\pi$
$331$	−1.73077	−0.0951319	−0.0475659	+	0.998868i	$0.515146\pi$
$332$	−61.2176	−3.35975
$333$	1.46089	0.0800561
$334$	29.7234	1.62639
$335$	−27.9668	−1.52799
$336$	19.5882	1.06862
$337$	−29.1699	−1.58899	−0.794493	−	0.607273i	$-0.792264\pi$
$337$	−29.1699	−1.58899	−0.794493	+	0.607273i	$0.792264\pi$
$338$	18.6702	1.01552
$339$	6.26775	0.340417
$340$	−111.783	−6.06228
$341$	−21.9474	−1.18852
$342$	−24.3965	−1.31921
$343$	−8.83572	−0.477084
$344$	−12.7130	−0.685442
$345$	−3.53992	−0.190583
$346$	−0.483578	−0.0259973
$347$	−11.0819	−0.594909	−0.297454	−	0.954736i	$-0.596138\pi$
$347$	−11.0819	−0.594909	−0.297454	+	0.954736i	$0.596138\pi$
$348$	−1.15026	−0.0616603
$349$	−22.7296	−1.21669	−0.608345	−	0.793673i	$-0.708166\pi$
$349$	−22.7296	−1.21669	−0.608345	+	0.793673i	$0.708166\pi$
$350$	68.5989	3.66677
$351$	8.17361	0.436275
$352$	−36.8228	−1.96266
$353$	16.1162	0.857780	0.428890	−	0.903357i	$-0.358905\pi$
$353$	16.1162	0.857780	0.428890	+	0.903357i	$0.358905\pi$
$354$	3.10677	0.165123
$355$	27.8147	1.47625
$356$	−38.2685	−2.02823
$357$	−17.3303	−0.917219
$358$	46.3710	2.45078
$359$	−24.9285	−1.31568	−0.657839	−	0.753158i	$-0.728529\pi$
$359$	−24.9285	−1.31568	−0.657839	+	0.753158i	$0.728529\pi$
$360$	60.2695	3.17648
$361$	−6.01374	−0.316513
$362$	−5.58154	−0.293359
$363$	−9.01859	−0.473353
$364$	−44.4471	−2.32966
$365$	−31.5815	−1.65305
$366$	0.00828893	0.000433269 0
$367$	−5.16415	−0.269566	−0.134783	−	0.990875i	$-0.543034\pi$
$367$	−5.16415	−0.269566	−0.134783	+	0.990875i	$0.543034\pi$
$368$	13.7710	0.717862
$369$	−20.9093	−1.08850
$370$	4.86465	0.252901
$371$	15.6260	0.811263
$372$	12.0460	0.624556
$373$	15.4632	0.800655	0.400327	−	0.916372i	$-0.368896\pi$
$373$	15.4632	0.800655	0.400327	+	0.916372i	$0.368896\pi$
$374$	93.0070	4.80928
$375$	−3.36664	−0.173853
$376$	−74.0684	−3.81979
$377$	0.986674	0.0508163
$378$	35.3047	1.81588
$379$	−12.6492	−0.649748	−0.324874	−	0.945757i	$-0.605322\pi$
$379$	−12.6492	−0.649748	−0.324874	+	0.945757i	$0.605322\pi$
$380$	−56.6601	−2.90660
$381$	4.53936	0.232558
$382$	−34.4973	−1.76503
$383$	−6.33321	−0.323612	−0.161806	−	0.986823i	$-0.551732\pi$
$383$	−6.33321	−0.323612	−0.161806	+	0.986823i	$0.551732\pi$
$384$	−4.81860	−0.245898
$385$	−69.8302	−3.55888
$386$	−10.1077	−0.514469
$387$	−4.98742	−0.253525
$388$	84.0897	4.26901
$389$	0.158750	0.00804893	0.00402446	−	0.999992i	$-0.498719\pi$
$389$	0.158750	0.00804893	0.00402446	+	0.999992i	$0.498719\pi$
$390$	12.7224	0.644225
$391$	−12.1836	−0.616153
$392$	−61.7192	−3.11729
$393$	−10.6666	−0.538060
$394$	54.2739	2.73428
$395$	−20.9838	−1.05581
$396$	−61.7698	−3.10405
$397$	2.50084	0.125513	0.0627567	−	0.998029i	$-0.480011\pi$
$397$	2.50084	0.125513	0.0627567	+	0.998029i	$0.480011\pi$
$398$	−42.7936	−2.14505
$399$	−8.78435	−0.439767
$400$	53.2758	2.66379
$401$	13.0629	0.652329	0.326164	−	0.945313i	$-0.394244\pi$
$401$	13.0629	0.652329	0.326164	+	0.945313i	$0.394244\pi$
$402$	−12.7715	−0.636986
$403$	−10.3329	−0.514717
$404$	−24.0076	−1.19442
$405$	19.8906	0.988370
$406$	4.26179	0.211509
$407$	−2.82297	−0.139929
$408$	−28.9036	−1.43094
$409$	−18.1832	−0.899099	−0.449549	−	0.893255i	$-0.648415\pi$
$409$	−18.1832	−0.899099	−0.449549	+	0.893255i	$0.648415\pi$
$410$	−69.6267	−3.43862
$411$	9.91406	0.489025
$412$	−39.7737	−1.95951
$413$	−8.02824	−0.395044
$414$	11.6017	0.570195
$415$	−45.2808	−2.22275
$416$	−17.3362	−0.849978
$417$	−10.5078	−0.514569
$418$	47.1431	2.30584
$419$	−8.73865	−0.426911	−0.213455	−	0.976953i	$-0.568472\pi$
$419$	−8.73865	−0.426911	−0.213455	+	0.976953i	$0.568472\pi$
$420$	38.3268	1.87016
$421$	7.51295	0.366159	0.183079	−	0.983098i	$-0.441393\pi$
$421$	7.51295	0.366159	0.183079	+	0.983098i	$0.441393\pi$
$422$	9.38179	0.456698
$423$	−29.0576	−1.41283
$424$	26.0611	1.26564
$425$	−47.1348	−2.28637
$426$	12.7021	0.615417
$427$	−0.0214195	−0.00103656
$428$	12.3886	0.598825
$429$	−7.38286	−0.356448
$430$	−16.6078	−0.800897
$431$	−3.16773	−0.152584	−0.0762922	−	0.997086i	$-0.524308\pi$
$431$	−3.16773	−0.152584	−0.0762922	+	0.997086i	$0.524308\pi$
$432$	27.4186	1.31918
$433$	22.8001	1.09570	0.547852	−	0.836575i	$-0.315446\pi$
$433$	22.8001	1.09570	0.547852	+	0.836575i	$0.315446\pi$
$434$	−44.6314	−2.14237
$435$	−0.850811	−0.0407933
$436$	−67.9789	−3.25560
$437$	−6.17560	−0.295419
$438$	−14.4223	−0.689122
$439$	31.0830	1.48351	0.741755	−	0.670671i	$-0.233994\pi$
$439$	31.0830	1.48351	0.741755	+	0.670671i	$0.233994\pi$
$440$	−116.463	−5.55215
$441$	−24.2129	−1.15299
$442$	43.7879	2.08278
$443$	10.2299	0.486036	0.243018	−	0.970022i	$-0.421863\pi$
$443$	10.2299	0.486036	0.243018	+	0.970022i	$0.421863\pi$
$444$	1.54941	0.0735317
$445$	−28.3061	−1.34184
$446$	−27.1925	−1.28760
$447$	9.38948	0.444107
$448$	−10.2034	−0.482067
$449$	8.39349	0.396113	0.198057	−	0.980191i	$-0.436537\pi$
$449$	8.39349	0.396113	0.198057	+	0.980191i	$0.436537\pi$
$450$	44.8836	2.11584
$451$	40.4046	1.90258
$452$	−47.7080	−2.24399
$453$	−8.80310	−0.413606
$454$	−23.2047	−1.08905
$455$	−32.8762	−1.54126
$456$	−14.6506	−0.686075
$457$	−4.66710	−0.218318	−0.109159	−	0.994024i	$-0.534816\pi$
$457$	−4.66710	−0.218318	−0.109159	+	0.994024i	$0.534816\pi$
$458$	−24.4580	−1.14285
$459$	−24.2581	−1.13227
$460$	26.9447	1.25630
$461$	−35.2862	−1.64344	−0.821721	−	0.569891i	$-0.806986\pi$
$461$	−35.2862	−1.64344	−0.821721	+	0.569891i	$0.806986\pi$
$462$	−31.8892	−1.48362
$463$	−0.228141	−0.0106026	−0.00530131	−	0.999986i	$-0.501687\pi$
$463$	−0.228141	−0.0106026	−0.00530131	+	0.999986i	$0.501687\pi$
$464$	3.30982	0.153655
$465$	8.91006	0.413194
$466$	54.8420	2.54051
$467$	−20.0520	−0.927896	−0.463948	−	0.885863i	$-0.653567\pi$
$467$	−20.0520	−0.927896	−0.463948	+	0.885863i	$0.653567\pi$
$468$	−29.0813	−1.34428
$469$	33.0030	1.52394
$470$	−96.7597	−4.46319
$471$	10.7008	0.493068
$472$	−13.3895	−0.616302
$473$	9.63753	0.443134
$474$	−9.58260	−0.440143
$475$	−23.8915	−1.09622
$476$	131.913	6.04621
$477$	10.2240	0.468123
$478$	−22.7580	−1.04093
$479$	25.5892	1.16920	0.584601	−	0.811321i	$-0.301251\pi$
$479$	25.5892	1.16920	0.584601	+	0.811321i	$0.301251\pi$
$480$	14.9491	0.682328
$481$	−1.32906	−0.0605999
$482$	38.2793	1.74358
$483$	4.17739	0.190078
$484$	68.6464	3.12029
$485$	62.1986	2.82429
$486$	35.4016	1.60585
$487$	−12.1406	−0.550141	−0.275071	−	0.961424i	$-0.588701\pi$
$487$	−12.1406	−0.550141	−0.275071	+	0.961424i	$0.588701\pi$
$488$	−0.0357235	−0.00161713
$489$	4.41779	0.199779
$490$	−80.6273	−3.64237
$491$	−16.9032	−0.762833	−0.381416	−	0.924403i	$-0.624564\pi$
$491$	−16.9032	−0.762833	−0.381416	+	0.924403i	$0.624564\pi$
$492$	−22.1763	−0.999787
$493$	−2.92831	−0.131884
$494$	22.1950	0.998602
$495$	−45.6892	−2.05358
$496$	−34.6619	−1.55636
$497$	−32.8236	−1.47234
$498$	−20.6783	−0.926615
$499$	11.4156	0.511031	0.255515	−	0.966805i	$-0.417755\pi$
$499$	11.4156	0.511031	0.255515	+	0.966805i	$0.417755\pi$
$500$	25.6257	1.14602
$501$	7.00246	0.312847
$502$	−47.9641	−2.14074
$503$	−41.2766	−1.84043	−0.920216	−	0.391412i	$-0.871987\pi$
$503$	−41.2766	−1.84043	−0.920216	+	0.391412i	$0.871987\pi$
$504$	−71.1228	−3.16806
$505$	−17.7577	−0.790207
$506$	−22.4189	−0.996640
$507$	4.39845	0.195342
$508$	−34.5520	−1.53300
$509$	−2.94451	−0.130513	−0.0652565	−	0.997869i	$-0.520787\pi$
$509$	−2.94451	−0.130513	−0.0652565	+	0.997869i	$0.520787\pi$
$510$	−37.7584	−1.67197
$511$	37.2687	1.64867
$512$	49.7151	2.19712
$513$	−12.2959	−0.542876
$514$	−48.1870	−2.12544
$515$	−29.4194	−1.29637
$516$	−5.28963	−0.232863
$517$	56.1499	2.46947
$518$	−5.74068	−0.252231
$519$	−0.113925	−0.00500075
$520$	−54.8309	−2.40450
$521$	−4.31616	−0.189094	−0.0945472	−	0.995520i	$-0.530140\pi$
$521$	−4.31616	−0.189094	−0.0945472	+	0.995520i	$0.530140\pi$
$522$	2.78845	0.122047
$523$	25.9776	1.13592	0.567961	−	0.823056i	$-0.307733\pi$
$523$	25.9776	1.13592	0.567961	+	0.823056i	$0.307733\pi$
$524$	81.1907	3.54683
$525$	16.1610	0.705326
$526$	38.6043	1.68323
$527$	30.6665	1.33585
$528$	−24.7660	−1.07780
$529$	−20.0632	−0.872313
$530$	34.0451	1.47883
$531$	−5.25280	−0.227952
$532$	66.8634	2.89890
$533$	19.0225	0.823957
$534$	−12.9265	−0.559383
$535$	9.16346	0.396171
$536$	55.0425	2.37748
$537$	10.9244	0.471424
$538$	31.6840	1.36599
$539$	46.7882	2.01531
$540$	53.6479	2.30864
$541$	−25.9297	−1.11481	−0.557403	−	0.830242i	$-0.688202\pi$
$541$	−25.9297	−1.11481	−0.557403	+	0.830242i	$0.688202\pi$
$542$	−75.5162	−3.24370
$543$	−1.31494	−0.0564295
$544$	51.4514	2.20596
$545$	−50.2819	−2.15384
$546$	−15.0135	−0.642518
$547$	−5.00041	−0.213802	−0.106901	−	0.994270i	$-0.534093\pi$
$547$	−5.00041	−0.213802	−0.106901	+	0.994270i	$0.534093\pi$
$548$	−75.4625	−3.22360
$549$	−0.0140146	−0.000598128 0
$550$	−86.7318	−3.69825
$551$	−1.48429	−0.0632329
$552$	6.96705	0.296538
$553$	24.7625	1.05301
$554$	−74.6336	−3.17088
$555$	1.14605	0.0486471
$556$	79.9818	3.39198
$557$	−45.6356	−1.93364	−0.966822	−	0.255453i	$-0.917775\pi$
$557$	−45.6356	−1.93364	−0.966822	+	0.255453i	$0.917775\pi$
$558$	−29.2019	−1.23621
$559$	4.53736	0.191910
$560$	−110.284	−4.66034
$561$	21.9113	0.925095
$562$	23.6377	0.997096
$563$	−1.50202	−0.0633027	−0.0316514	−	0.999499i	$-0.510077\pi$
$563$	−1.50202	−0.0633027	−0.0316514	+	0.999499i	$0.510077\pi$
$564$	−30.8183	−1.29768
$565$	−35.2881	−1.48458
$566$	76.3799	3.21049
$567$	−23.4724	−0.985750
$568$	−54.7432	−2.29697
$569$	3.75213	0.157297	0.0786487	−	0.996902i	$-0.474939\pi$
$569$	3.75213	0.157297	0.0786487	+	0.996902i	$0.474939\pi$
$570$	−19.1388	−0.801638
$571$	−8.28205	−0.346593	−0.173296	−	0.984870i	$-0.555442\pi$
$571$	−8.28205	−0.346593	−0.173296	+	0.984870i	$0.555442\pi$
$572$	56.1958	2.34967
$573$	−8.12712	−0.339515
$574$	82.1650	3.42950
$575$	11.3616	0.473811
$576$	−6.67601	−0.278167
$577$	−23.0379	−0.959080	−0.479540	−	0.877520i	$-0.659197\pi$
$577$	−23.0379	−0.959080	−0.479540	+	0.877520i	$0.659197\pi$
$578$	−86.2476	−3.58743
$579$	−2.38125	−0.0989614
$580$	6.47608	0.268905
$581$	53.4349	2.21685
$582$	28.4041	1.17739
$583$	−19.7565	−0.818229
$584$	62.1568	2.57207
$585$	−21.5106	−0.889352
$586$	11.3442	0.468624
$587$	−36.9649	−1.52570	−0.762852	−	0.646573i	$-0.776202\pi$
$587$	−36.9649	−1.52570	−0.762852	+	0.646573i	$0.776202\pi$
$588$	−25.6801	−1.05903
$589$	15.5441	0.640485
$590$	−17.4915	−0.720113
$591$	12.7863	0.525956
$592$	−4.45836	−0.183238
$593$	−24.7692	−1.01715	−0.508575	−	0.861018i	$-0.669827\pi$
$593$	−24.7692	−1.01715	−0.508575	+	0.861018i	$0.669827\pi$
$594$	−44.6369	−1.83147
$595$	97.5718	4.00005
$596$	−71.4695	−2.92750
$597$	−10.0816	−0.412613
$598$	−10.5548	−0.431619
$599$	−23.0125	−0.940267	−0.470133	−	0.882595i	$-0.655794\pi$
$599$	−23.0125	−0.940267	−0.470133	+	0.882595i	$0.655794\pi$
$600$	26.9534	1.10037
$601$	−32.6329	−1.33112	−0.665562	−	0.746343i	$-0.731808\pi$
$601$	−32.6329	−1.33112	−0.665562	+	0.746343i	$0.731808\pi$
$602$	19.5985	0.798775
$603$	21.5936	0.879358
$604$	67.0062	2.72644
$605$	50.7757	2.06432
$606$	−8.10937	−0.329421
$607$	4.38938	0.178160	0.0890798	−	0.996024i	$-0.471607\pi$
$607$	4.38938	0.178160	0.0890798	+	0.996024i	$0.471607\pi$
$608$	26.0795	1.05766
$609$	1.00402	0.0406851
$610$	−0.0466676	−0.00188952
$611$	26.4355	1.06946
$612$	86.3092	3.48884
$613$	18.3633	0.741689	0.370844	−	0.928695i	$-0.379068\pi$
$613$	18.3633	0.741689	0.370844	+	0.928695i	$0.379068\pi$
$614$	65.8264	2.65654
$615$	−16.4032	−0.661440
$616$	137.436	5.53744
$617$	47.2579	1.90253	0.951265	−	0.308374i	$-0.0997848\pi$
$617$	47.2579	1.90253	0.951265	+	0.308374i	$0.0997848\pi$
$618$	−13.4349	−0.540430
$619$	−27.4393	−1.10288	−0.551440	−	0.834215i	$-0.685921\pi$
$619$	−27.4393	−1.10288	−0.551440	+	0.834215i	$0.685921\pi$
$620$	−67.8204	−2.72373
$621$	5.84729	0.234644
$622$	64.4166	2.58287
$623$	33.4034	1.33828
$624$	−11.6599	−0.466768
$625$	−14.1945	−0.567782
$626$	−51.5951	−2.06216
$627$	11.1063	0.443544
$628$	−81.4511	−3.25025
$629$	3.94446	0.157276
$630$	−92.9117	−3.70169
$631$	−33.9484	−1.35146	−0.675732	−	0.737148i	$-0.736172\pi$
$631$	−33.9484	−1.35146	−0.675732	+	0.737148i	$0.736172\pi$
$632$	41.2990	1.64278
$633$	2.21023	0.0878488
$634$	70.8509	2.81385
$635$	−25.5571	−1.01420
$636$	10.8435	0.429972
$637$	22.0280	0.872780
$638$	−5.38832	−0.213326
$639$	−21.4761	−0.849583
$640$	27.1292	1.07238
$641$	7.72974	0.305306	0.152653	−	0.988280i	$-0.451218\pi$
$641$	7.72974	0.305306	0.152653	+	0.988280i	$0.451218\pi$
$642$	4.18465	0.165155
$643$	−1.46534	−0.0577875	−0.0288938	−	0.999582i	$-0.509198\pi$
$643$	−1.46534	−0.0577875	−0.0288938	+	0.999582i	$0.509198\pi$
$644$	−31.7968	−1.25297
$645$	−3.91258	−0.154058
$646$	−65.8717	−2.59169
$647$	35.2866	1.38726	0.693630	−	0.720331i	$-0.256010\pi$
$647$	35.2866	1.38726	0.693630	+	0.720331i	$0.256010\pi$
$648$	−39.1474	−1.53786
$649$	10.1503	0.398436
$650$	−40.8334	−1.60162
$651$	−10.5146	−0.412099
$652$	−33.6267	−1.31692
$653$	30.7974	1.20520	0.602598	−	0.798045i	$-0.294132\pi$
$653$	30.7974	1.20520	0.602598	+	0.798045i	$0.294132\pi$
$654$	−22.9621	−0.897890
$655$	60.0543	2.34652
$656$	63.8115	2.49142
$657$	24.3846	0.951332
$658$	114.184	4.45136
$659$	−50.5224	−1.96807	−0.984036	−	0.177969i	$-0.943047\pi$
$659$	−50.5224	−1.96807	−0.984036	+	0.177969i	$0.943047\pi$
$660$	−48.4578	−1.88622
$661$	37.9782	1.47718	0.738590	−	0.674155i	$-0.235492\pi$
$661$	37.9782	1.47718	0.738590	+	0.674155i	$0.235492\pi$
$662$	4.44997	0.172953
$663$	10.3159	0.400635
$664$	89.1189	3.45848
$665$	49.4569	1.91785
$666$	−3.75607	−0.145545
$667$	0.705853	0.0273307
$668$	−53.3004	−2.06225
$669$	−6.40620	−0.247678
$670$	71.9051	2.77794
$671$	0.0270814	0.00104546
$672$	−17.6411	−0.680519
$673$	1.22775	0.0473263	0.0236632	−	0.999720i	$-0.492467\pi$
$673$	1.22775	0.0473263	0.0236632	+	0.999720i	$0.492467\pi$
$674$	74.9985	2.88884
$675$	22.6214	0.870698
$676$	−33.4795	−1.28767
$677$	5.09963	0.195995	0.0979974	−	0.995187i	$-0.468756\pi$
$677$	5.09963	0.195995	0.0979974	+	0.995187i	$0.468756\pi$
$678$	−16.1149	−0.618891
$679$	−73.3993	−2.81681
$680$	162.730	6.24043
$681$	−5.46673	−0.209485
$682$	56.4288	2.16077
$683$	19.4925	0.745859	0.372929	−	0.927860i	$-0.378353\pi$
$683$	19.4925	0.745859	0.372929	+	0.927860i	$0.378353\pi$
$684$	43.7481	1.67275
$685$	−55.8173	−2.13267
$686$	22.7174	0.867356
$687$	−5.76199	−0.219834
$688$	15.2207	0.580284
$689$	−9.30138	−0.354354
$690$	9.10145	0.346486
$691$	−6.81518	−0.259262	−0.129631	−	0.991562i	$-0.541379\pi$
$691$	−6.81518	−0.259262	−0.129631	+	0.991562i	$0.541379\pi$
$692$	0.867157	0.0329644
$693$	53.9169	2.04813
$694$	28.4926	1.08157
$695$	59.1601	2.24407
$696$	1.67452	0.0634723
$697$	−56.4562	−2.13843
$698$	58.4399	2.21198
$699$	12.9201	0.488682
$700$	−123.012	−4.64943
$701$	−8.27264	−0.312453	−0.156227	−	0.987721i	$-0.549933\pi$
$701$	−8.27264	−0.312453	−0.156227	+	0.987721i	$0.549933\pi$
$702$	−21.0151	−0.793164
$703$	1.99935	0.0754071
$704$	12.9005	0.486207
$705$	−22.7954	−0.858523
$706$	−41.4363	−1.55947
$707$	20.9555	0.788113
$708$	−5.57110	−0.209375
$709$	−28.1274	−1.05635	−0.528174	−	0.849136i	$-0.677123\pi$
$709$	−28.1274	−1.05635	−0.528174	+	0.849136i	$0.677123\pi$
$710$	−71.5141	−2.68388
$711$	16.2019	0.607618
$712$	55.7103	2.08783
$713$	−7.39200	−0.276833
$714$	44.5579	1.66754
$715$	41.5663	1.55449
$716$	−83.1530	−3.10757
$717$	−5.36150	−0.200229
$718$	64.0936	2.39195
$719$	−32.2083	−1.20117	−0.600584	−	0.799562i	$-0.705065\pi$
$719$	−32.2083	−1.20117	−0.600584	+	0.799562i	$0.705065\pi$
$720$	−72.1577	−2.68916
$721$	34.7172	1.29294
$722$	15.4619	0.575431
$723$	9.01813	0.335388
$724$	10.0089	0.371977
$725$	2.73073	0.101417
$726$	23.1876	0.860573
$727$	−4.04027	−0.149845	−0.0749226	−	0.997189i	$-0.523871\pi$
$727$	−4.04027	−0.149845	−0.0749226	+	0.997189i	$0.523871\pi$
$728$	64.7049	2.39812
$729$	−9.15757	−0.339169
$730$	81.1990	3.00531
$731$	−13.4663	−0.498067
$732$	−0.0148638	−0.000549382 0
$733$	−16.7012	−0.616874	−0.308437	−	0.951245i	$-0.599806\pi$
$733$	−16.7012	−0.616874	−0.308437	+	0.951245i	$0.599806\pi$
$734$	13.2775	0.490081
$735$	−18.9948	−0.700632
$736$	−12.4021	−0.457147
$737$	−41.7268	−1.53702
$738$	53.7598	1.97893
$739$	5.85394	0.215341	0.107670	−	0.994187i	$-0.465661\pi$
$739$	5.85394	0.215341	0.107670	+	0.994187i	$0.465661\pi$
$740$	−8.72335	−0.320677
$741$	5.22887	0.192087
$742$	−40.1759	−1.47491
$743$	41.1025	1.50790	0.753952	−	0.656929i	$-0.228145\pi$
$743$	41.1025	1.50790	0.753952	+	0.656929i	$0.228145\pi$
$744$	−17.5362	−0.642910
$745$	−52.8638	−1.93678
$746$	−39.7573	−1.45562
$747$	34.9620	1.27919
$748$	−166.781	−6.09813
$749$	−10.8136	−0.395121
$750$	8.65595	0.316070
$751$	24.5738	0.896712	0.448356	−	0.893855i	$-0.352010\pi$
$751$	24.5738	0.896712	0.448356	+	0.893855i	$0.352010\pi$
$752$	88.6784	3.23377
$753$	−11.2997	−0.411785
$754$	−2.53683	−0.0923858
$755$	49.5624	1.80376
$756$	−63.3088	−2.30252
$757$	5.27421	0.191694	0.0958472	−	0.995396i	$-0.469444\pi$
$757$	5.27421	0.191694	0.0958472	+	0.995396i	$0.469444\pi$
$758$	32.5224	1.18127
$759$	−5.28160	−0.191710
$760$	82.4843	2.99202
$761$	2.18960	0.0793730	0.0396865	−	0.999212i	$-0.487364\pi$
$761$	2.18960	0.0793730	0.0396865	+	0.999212i	$0.487364\pi$
$762$	−11.6711	−0.422799
$763$	59.3367	2.14813
$764$	61.8609	2.23805
$765$	63.8403	2.30815
$766$	16.2833	0.588338
$767$	4.77880	0.172552
$768$	15.4605	0.557884
$769$	30.2439	1.09062	0.545311	−	0.838234i	$-0.316411\pi$
$769$	30.2439	1.09062	0.545311	+	0.838234i	$0.316411\pi$
$770$	179.540	6.47016
$771$	−11.3523	−0.408842
$772$	18.1253	0.652343
$773$	6.99007	0.251415	0.125708	−	0.992067i	$-0.459880\pi$
$773$	6.99007	0.251415	0.125708	+	0.992067i	$0.459880\pi$
$774$	12.8231	0.460917
$775$	−28.5974	−1.02725
$776$	−122.416	−4.39446
$777$	−1.35243	−0.0485182
$778$	−0.408160	−0.0146332
$779$	−28.6163	−1.02529
$780$	−22.8140	−0.816872
$781$	41.4998	1.48498
$782$	31.3252	1.12019
$783$	1.40538	0.0502243
$784$	73.8934	2.63905
$785$	−60.2469	−2.15030
$786$	27.4249	0.978212
$787$	8.97724	0.320004	0.160002	−	0.987117i	$-0.448850\pi$
$787$	8.97724	0.320004	0.160002	+	0.987117i	$0.448850\pi$
$788$	−97.3246	−3.46705
$789$	9.09469	0.323779
$790$	53.9511	1.91950
$791$	41.6428	1.48065
$792$	89.9228	3.19527
$793$	0.0127499	0.000452764 0
$794$	−6.42988	−0.228188
$795$	8.02060	0.284461
$796$	76.7379	2.71990
$797$	−4.66120	−0.165108	−0.0825540	−	0.996587i	$-0.526308\pi$
$797$	−4.66120	−0.165108	−0.0825540	+	0.996587i	$0.526308\pi$
$798$	22.5854	0.799513
$799$	−78.4567	−2.77560
$800$	−47.9800	−1.69635
$801$	21.8555	0.772228
$802$	−33.5858	−1.18596
$803$	−47.1200	−1.66283
$804$	22.9020	0.807693
$805$	−23.5192	−0.828941
$806$	26.5668	0.935774
$807$	7.46435	0.262758
$808$	34.9496	1.22952
$809$	16.0328	0.563685	0.281842	−	0.959461i	$-0.409054\pi$
$809$	16.0328	0.563685	0.281842	+	0.959461i	$0.409054\pi$
$810$	−51.1404	−1.79689
$811$	−39.8050	−1.39774	−0.698871	−	0.715248i	$-0.746314\pi$
$811$	−39.8050	−1.39774	−0.698871	+	0.715248i	$0.746314\pi$
$812$	−7.64230	−0.268192
$813$	−17.7907	−0.623946
$814$	7.25812	0.254397
$815$	−24.8726	−0.871251
$816$	34.6048	1.21141
$817$	−6.82573	−0.238802
$818$	46.7505	1.63459
$819$	25.3842	0.886995
$820$	124.855	4.36014
$821$	12.9484	0.451903	0.225952	−	0.974139i	$-0.427451\pi$
$821$	12.9484	0.451903	0.225952	+	0.974139i	$0.427451\pi$
$822$	−25.4900	−0.889065
$823$	48.8583	1.70309	0.851546	−	0.524279i	$-0.175665\pi$
$823$	48.8583	1.70309	0.851546	+	0.524279i	$0.175665\pi$
$824$	57.9014	2.01709
$825$	−20.4329	−0.711383
$826$	20.6413	0.718204
$827$	−12.0882	−0.420348	−0.210174	−	0.977664i	$-0.567403\pi$
$827$	−12.0882	−0.420348	−0.210174	+	0.977664i	$0.567403\pi$
$828$	−20.8044	−0.723002
$829$	48.9359	1.69962	0.849808	−	0.527093i	$-0.176718\pi$
$829$	48.9359	1.69962	0.849808	+	0.527093i	$0.176718\pi$
$830$	116.421	4.04103
$831$	−17.5827	−0.609938
$832$	6.07358	0.210564
$833$	−65.3759	−2.26514
$834$	27.0165	0.935505
$835$	−39.4247	−1.36435
$836$	−84.5375	−2.92379
$837$	−14.7178	−0.508721
$838$	22.4679	0.776139
$839$	−32.7777	−1.13161	−0.565806	−	0.824539i	$-0.691435\pi$
$839$	−32.7777	−1.13161	−0.565806	+	0.824539i	$0.691435\pi$
$840$	−55.7951	−1.92512
$841$	−28.8303	−0.994150
$842$	−19.3165	−0.665690
$843$	5.56874	0.191798
$844$	−16.8235	−0.579090
$845$	−24.7638	−0.851900
$846$	74.7096	2.56857
$847$	−59.9193	−2.05885
$848$	−31.2017	−1.07147
$849$	17.9941	0.617557
$850$	121.188	4.15671
$851$	−0.950791	−0.0325927
$852$	−22.7775	−0.780344
$853$	13.1451	0.450080	0.225040	−	0.974350i	$-0.427749\pi$
$853$	13.1451	0.450080	0.225040	+	0.974350i	$0.427749\pi$
$854$	0.0550715	0.00188451
$855$	32.3592	1.10666
$856$	−18.0350	−0.616422
$857$	−8.98781	−0.307018	−0.153509	−	0.988147i	$-0.549057\pi$
$857$	−8.98781	−0.307018	−0.153509	+	0.988147i	$0.549057\pi$
$858$	18.9820	0.648035
$859$	21.3529	0.728551	0.364275	−	0.931291i	$-0.381317\pi$
$859$	21.3529	0.728551	0.364275	+	0.931291i	$0.381317\pi$
$860$	29.7812	1.01553
$861$	19.3570	0.659686
$862$	8.14453	0.277404
$863$	−41.9097	−1.42662	−0.713312	−	0.700847i	$-0.752806\pi$
$863$	−41.9097	−1.42662	−0.713312	+	0.700847i	$0.752806\pi$
$864$	−24.6931	−0.840076
$865$	0.641410	0.0218086
$866$	−58.6212	−1.99203
$867$	−20.3188	−0.690064
$868$	80.0334	2.71651
$869$	−31.3080	−1.06205
$870$	2.18751	0.0741636
$871$	−19.6450	−0.665646
$872$	98.9618	3.35127
$873$	−48.0245	−1.62538
$874$	15.8780	0.537083
$875$	−22.3679	−0.756174
$876$	25.8622	0.873801
$877$	23.0509	0.778374	0.389187	−	0.921159i	$-0.372756\pi$
$877$	23.0509	0.778374	0.389187	+	0.921159i	$0.372756\pi$
$878$	−79.9172	−2.69707
$879$	2.67255	0.0901428
$880$	139.435	4.70036
$881$	−36.3470	−1.22456	−0.612280	−	0.790641i	$-0.709748\pi$
$881$	−36.3470	−1.22456	−0.612280	+	0.790641i	$0.709748\pi$
$882$	62.2535	2.09618
$883$	20.3924	0.686259	0.343130	−	0.939288i	$-0.388513\pi$
$883$	20.3924	0.686259	0.343130	+	0.939288i	$0.388513\pi$
$884$	−78.5209	−2.64094
$885$	−4.12077	−0.138518
$886$	−26.3019	−0.883631
$887$	4.58309	0.153885	0.0769426	−	0.997036i	$-0.475484\pi$
$887$	4.58309	0.153885	0.0769426	+	0.997036i	$0.475484\pi$
$888$	−2.25559	−0.0756926
$889$	30.1594	1.01151
$890$	72.7775	2.43951
$891$	29.6769	0.994215
$892$	48.7618	1.63267
$893$	−39.7679	−1.33078
$894$	−24.1412	−0.807402
$895$	−61.5058	−2.05591
$896$	−32.0147	−1.06954
$897$	−2.48658	−0.0830246
$898$	−21.5804	−0.720148
$899$	−1.77665	−0.0592546
$900$	−80.4858	−2.68286
$901$	27.6052	0.919662
$902$	−103.884	−3.45895
$903$	4.61716	0.153649
$904$	69.4520	2.30994
$905$	7.40326	0.246093
$906$	22.6336	0.751950
$907$	−7.53004	−0.250031	−0.125016	−	0.992155i	$-0.539898\pi$
$907$	−7.53004	−0.250031	−0.125016	+	0.992155i	$0.539898\pi$
$908$	41.6109	1.38090
$909$	13.7110	0.454765
$910$	84.5276	2.80206
$911$	22.8455	0.756905	0.378453	−	0.925621i	$-0.376456\pi$
$911$	22.8455	0.756905	0.378453	+	0.925621i	$0.376456\pi$
$912$	17.5404	0.580820
$913$	−67.5594	−2.23589
$914$	11.9995	0.396910
$915$	−0.0109943	−0.000363461 0
$916$	43.8583	1.44912
$917$	−70.8689	−2.34030
$918$	62.3698	2.05851
$919$	43.3082	1.42861	0.714303	−	0.699836i	$-0.246744\pi$
$919$	43.3082	1.42861	0.714303	+	0.699836i	$0.246744\pi$
$920$	−39.2253	−1.29322
$921$	15.5079	0.511002
$922$	90.7240	2.98783
$923$	19.5382	0.643107
$924$	57.1840	1.88122
$925$	−3.67832	−0.120943
$926$	0.586572	0.0192760
$927$	22.7151	0.746063
$928$	−2.98081	−0.0978500
$929$	−48.5017	−1.59129	−0.795645	−	0.605763i	$-0.792868\pi$
$929$	−48.5017	−1.59129	−0.795645	+	0.605763i	$0.792868\pi$
$930$	−22.9086	−0.751202
$931$	−33.1375	−1.08604
$932$	−98.3432	−3.22134
$933$	15.1757	0.496831
$934$	51.5555	1.68695
$935$	−123.363	−4.03440
$936$	42.3358	1.38379
$937$	−27.4768	−0.897628	−0.448814	−	0.893625i	$-0.648153\pi$
$937$	−27.4768	−0.897628	−0.448814	+	0.893625i	$0.648153\pi$
$938$	−84.8538	−2.77057
$939$	−12.1552	−0.396669
$940$	173.511	5.65929
$941$	−54.7778	−1.78571	−0.892853	−	0.450348i	$-0.851300\pi$
$941$	−54.7778	−1.78571	−0.892853	+	0.450348i	$0.851300\pi$
$942$	−27.5128	−0.896416
$943$	13.6085	0.443152
$944$	16.0306	0.521752
$945$	−46.8276	−1.52330
$946$	−24.7790	−0.805634
$947$	−32.5814	−1.05875	−0.529377	−	0.848387i	$-0.677574\pi$
$947$	−32.5814	−1.05875	−0.529377	+	0.848387i	$0.677574\pi$
$948$	17.1836	0.558098
$949$	−22.1842	−0.720128
$950$	61.4273	1.99297
$951$	16.6916	0.541262
$952$	−192.035	−6.22389
$953$	−10.1855	−0.329941	−0.164971	−	0.986298i	$-0.552753\pi$
$953$	−10.1855	−0.329941	−0.164971	+	0.986298i	$0.552753\pi$
$954$	−26.2867	−0.851065
$955$	45.7566	1.48065
$956$	40.8099	1.31989
$957$	−1.26942	−0.0410345
$958$	−65.7922	−2.12565
$959$	65.8689	2.12702
$960$	−5.23726	−0.169032
$961$	−12.3941	−0.399811
$962$	3.41713	0.110173
$963$	−7.07524	−0.227996
$964$	−68.6429	−2.21084
$965$	13.4067	0.431577
$966$	−10.7404	−0.345568
$967$	−23.5920	−0.758667	−0.379334	−	0.925260i	$-0.623847\pi$
$967$	−23.5920	−0.758667	−0.379334	+	0.925260i	$0.623847\pi$
$968$	−99.9336	−3.21199
$969$	−15.5186	−0.498528
$970$	−159.918	−5.13467
$971$	57.1034	1.83254	0.916268	−	0.400565i	$-0.131186\pi$
$971$	57.1034	1.83254	0.916268	+	0.400565i	$0.131186\pi$
$972$	−63.4825	−2.03620
$973$	−69.8136	−2.23812
$974$	31.2145	1.00018
$975$	−9.61984	−0.308082
$976$	0.0427700	0.00136903
$977$	24.5934	0.786813	0.393406	−	0.919365i	$-0.371297\pi$
$977$	24.5934	0.786813	0.393406	+	0.919365i	$0.371297\pi$
$978$	−11.3585	−0.363206
$979$	−42.2330	−1.34977
$980$	144.582	4.61849
$981$	38.8234	1.23954
$982$	43.4598	1.38686
$983$	27.4334	0.874988	0.437494	−	0.899221i	$-0.355866\pi$
$983$	27.4334	0.874988	0.437494	+	0.899221i	$0.355866\pi$
$984$	32.2837	1.02917
$985$	−71.9881	−2.29373
$986$	7.52895	0.239771
$987$	26.9003	0.856248
$988$	−39.8004	−1.26622
$989$	3.24597	0.103216
$990$	117.471	3.73348
$991$	33.9504	1.07847	0.539235	−	0.842155i	$-0.318713\pi$
$991$	33.9504	1.07847	0.539235	+	0.842155i	$0.318713\pi$
$992$	31.2164	0.991121
$993$	1.04836	0.0332686
$994$	84.3923	2.67676
$995$	56.7607	1.79944
$996$	37.0805	1.17494
$997$	−28.6261	−0.906597	−0.453298	−	0.891359i	$-0.649753\pi$
$997$	−28.6261	−0.906597	−0.453298	+	0.891359i	$0.649753\pi$
$998$	−29.3504	−0.929072
$999$	−1.89306	−0.0598939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.b.1.13	✓	159

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.57109 q^{2} -0.605717 q^{3} +4.61051 q^{4} +3.41025 q^{5} +1.55735 q^{6} -4.02437 q^{7} -6.71185 q^{8} -2.63311 q^{9} +O(q^{10})\)	\(q-2.57109 q^{2} -0.605717 q^{3} +4.61051 q^{4} +3.41025 q^{5} +1.55735 q^{6} -4.02437 q^{7} -6.71185 q^{8} -2.63311 q^{9} -8.76807 q^{10} +5.08814 q^{11} -2.79266 q^{12} +2.39550 q^{13} +10.3470 q^{14} -2.06565 q^{15} +8.03577 q^{16} -7.10951 q^{17} +6.76996 q^{18} -3.60365 q^{19} +15.7230 q^{20} +2.43763 q^{21} -13.0821 q^{22} +1.71371 q^{23} +4.06548 q^{24} +6.62983 q^{25} -6.15905 q^{26} +3.41207 q^{27} -18.5544 q^{28} +0.411886 q^{29} +5.31097 q^{30} -4.31345 q^{31} -7.23699 q^{32} -3.08197 q^{33} +18.2792 q^{34} -13.7241 q^{35} -12.1400 q^{36} -0.554814 q^{37} +9.26530 q^{38} -1.45100 q^{39} -22.8891 q^{40} +7.94094 q^{41} -6.26736 q^{42} +1.89412 q^{43} +23.4589 q^{44} -8.97956 q^{45} -4.40610 q^{46} +11.0355 q^{47} -4.86740 q^{48} +9.19555 q^{49} -17.0459 q^{50} +4.30635 q^{51} +11.0445 q^{52} -3.88285 q^{53} -8.77273 q^{54} +17.3518 q^{55} +27.0110 q^{56} +2.18279 q^{57} -1.05900 q^{58} +1.99491 q^{59} -9.52368 q^{60} +0.00532245 q^{61} +11.0903 q^{62} +10.5966 q^{63} +2.53541 q^{64} +8.16927 q^{65} +7.92402 q^{66} -8.20079 q^{67} -32.7785 q^{68} -1.03802 q^{69} +35.2860 q^{70} +8.15620 q^{71} +17.6730 q^{72} -9.26076 q^{73} +1.42648 q^{74} -4.01580 q^{75} -16.6146 q^{76} -20.4765 q^{77} +3.73064 q^{78} -6.15314 q^{79} +27.4040 q^{80} +5.83258 q^{81} -20.4169 q^{82} -13.2778 q^{83} +11.2387 q^{84} -24.2452 q^{85} -4.86995 q^{86} -0.249486 q^{87} -34.1508 q^{88} -8.30029 q^{89} +23.0873 q^{90} -9.64039 q^{91} +7.90107 q^{92} +2.61273 q^{93} -28.3732 q^{94} -12.2893 q^{95} +4.38356 q^{96} +18.2387 q^{97} -23.6426 q^{98} -13.3976 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) 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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