LMFDB - Embedded newform 4019.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$0$
Dimension:	$186$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.34165 q^{2} -0.437788 q^{3} +3.48332 q^{4} +0.358726 q^{5} +1.02515 q^{6} +3.39349 q^{7} -3.47342 q^{8} -2.80834 q^{9} +O(q^{10})$	\(q-2.34165 q^{2} -0.437788 q^{3} +3.48332 q^{4} +0.358726 q^{5} +1.02515 q^{6} +3.39349 q^{7} -3.47342 q^{8} -2.80834 q^{9} -0.840010 q^{10} -1.11610 q^{11} -1.52496 q^{12} -4.45688 q^{13} -7.94637 q^{14} -0.157046 q^{15} +1.16689 q^{16} +6.33668 q^{17} +6.57615 q^{18} -2.34535 q^{19} +1.24956 q^{20} -1.48563 q^{21} +2.61352 q^{22} -0.282972 q^{23} +1.52062 q^{24} -4.87132 q^{25} +10.4365 q^{26} +2.54282 q^{27} +11.8206 q^{28} -9.05378 q^{29} +0.367746 q^{30} -0.329502 q^{31} +4.21439 q^{32} +0.488616 q^{33} -14.8383 q^{34} +1.21733 q^{35} -9.78236 q^{36} +0.0658927 q^{37} +5.49199 q^{38} +1.95117 q^{39} -1.24601 q^{40} -10.2733 q^{41} +3.47882 q^{42} +7.73519 q^{43} -3.88774 q^{44} -1.00742 q^{45} +0.662621 q^{46} -11.0036 q^{47} -0.510852 q^{48} +4.51580 q^{49} +11.4069 q^{50} -2.77412 q^{51} -15.5248 q^{52} +1.11064 q^{53} -5.95439 q^{54} -0.400374 q^{55} -11.7870 q^{56} +1.02676 q^{57} +21.2008 q^{58} +14.2019 q^{59} -0.547041 q^{60} +6.80698 q^{61} +0.771579 q^{62} -9.53009 q^{63} -12.2024 q^{64} -1.59880 q^{65} -1.14417 q^{66} +11.3700 q^{67} +22.0727 q^{68} +0.123882 q^{69} -2.85057 q^{70} +5.88288 q^{71} +9.75456 q^{72} +8.90981 q^{73} -0.154298 q^{74} +2.13260 q^{75} -8.16961 q^{76} -3.78749 q^{77} -4.56895 q^{78} +8.35937 q^{79} +0.418595 q^{80} +7.31181 q^{81} +24.0564 q^{82} +6.63373 q^{83} -5.17493 q^{84} +2.27313 q^{85} -18.1131 q^{86} +3.96363 q^{87} +3.87669 q^{88} -7.80016 q^{89} +2.35904 q^{90} -15.1244 q^{91} -0.985682 q^{92} +0.144252 q^{93} +25.7667 q^{94} -0.841337 q^{95} -1.84501 q^{96} +19.0062 q^{97} -10.5744 q^{98} +3.13440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) $ 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * 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 $

$2$	−2.34165	−1.65580	−0.827898	−	0.560878i	$-0.810464\pi$
$2$	−2.34165	−1.65580	−0.827898	+	0.560878i	$0.810464\pi$
$3$	−0.437788	−0.252757	−0.126378	−	0.991982i	$-0.540335\pi$
$3$	−0.437788	−0.252757	−0.126378	+	0.991982i	$0.540335\pi$
$4$	3.48332	1.74166
$5$	0.358726	0.160427	0.0802135	−	0.996778i	$-0.474440\pi$
$5$	0.358726	0.160427	0.0802135	+	0.996778i	$0.474440\pi$
$6$	1.02515	0.418514
$7$	3.39349	1.28262	0.641310	−	0.767282i	$-0.278391\pi$
$7$	3.39349	1.28262	0.641310	+	0.767282i	$0.278391\pi$
$8$	−3.47342	−1.22804
$9$	−2.80834	−0.936114
$10$	−0.840010	−0.265634
$11$	−1.11610	−0.336517	−0.168259	−	0.985743i	$-0.553814\pi$
$11$	−1.11610	−0.336517	−0.168259	+	0.985743i	$0.553814\pi$
$12$	−1.52496	−0.440217
$13$	−4.45688	−1.23612	−0.618059	−	0.786132i	$-0.712081\pi$
$13$	−4.45688	−1.23612	−0.618059	+	0.786132i	$0.712081\pi$
$14$	−7.94637	−2.12376
$15$	−0.157046	−0.0405490
$16$	1.16689	0.291724
$17$	6.33668	1.53687	0.768435	−	0.639928i	$-0.221036\pi$
$17$	6.33668	1.53687	0.768435	+	0.639928i	$0.221036\pi$
$18$	6.57615	1.55001
$19$	−2.34535	−0.538060	−0.269030	−	0.963132i	$-0.586703\pi$
$19$	−2.34535	−0.538060	−0.269030	+	0.963132i	$0.586703\pi$
$20$	1.24956	0.279410
$21$	−1.48563	−0.324191
$22$	2.61352	0.557204
$23$	−0.282972	−0.0590037	−0.0295019	−	0.999565i	$-0.509392\pi$
$23$	−0.282972	−0.0590037	−0.0295019	+	0.999565i	$0.509392\pi$
$24$	1.52062	0.310396
$25$	−4.87132	−0.974263
$26$	10.4365	2.04676
$27$	2.54282	0.489366
$28$	11.8206	2.23389
$29$	−9.05378	−1.68125	−0.840623	−	0.541621i	$-0.817811\pi$
$29$	−9.05378	−1.68125	−0.840623	+	0.541621i	$0.817811\pi$
$30$	0.367746	0.0671409
$31$	−0.329502	−0.0591804	−0.0295902	−	0.999562i	$-0.509420\pi$
$31$	−0.329502	−0.0591804	−0.0295902	+	0.999562i	$0.509420\pi$
$32$	4.21439	0.745006
$33$	0.488616	0.0850571
$34$	−14.8383	−2.54474
$35$	1.21733	0.205767
$36$	−9.78236	−1.63039
$37$	0.0658927	0.0108327	0.00541634	−	0.999985i	$-0.498276\pi$
$37$	0.0658927	0.0108327	0.00541634	+	0.999985i	$0.498276\pi$
$38$	5.49199	0.890918
$39$	1.95117	0.312437
$40$	−1.24601	−0.197011
$41$	−10.2733	−1.60442	−0.802208	−	0.597045i	$-0.796342\pi$
$41$	−10.2733	−1.60442	−0.802208	+	0.597045i	$0.796342\pi$
$42$	3.47882	0.536794
$43$	7.73519	1.17961	0.589803	−	0.807547i	$-0.299205\pi$
$43$	7.73519	1.17961	0.589803	+	0.807547i	$0.299205\pi$
$44$	−3.88774	−0.586099
$45$	−1.00742	−0.150178
$46$	0.662621	0.0976981
$47$	−11.0036	−1.60505	−0.802524	−	0.596621i	$-0.796510\pi$
$47$	−11.0036	−1.60505	−0.802524	+	0.596621i	$0.796510\pi$
$48$	−0.510852	−0.0737351
$49$	4.51580	0.645114
$50$	11.4069	1.61318
$51$	−2.77412	−0.388454
$52$	−15.5248	−2.15290
$53$	1.11064	0.152558	0.0762788	−	0.997087i	$-0.475696\pi$
$53$	1.11064	0.152558	0.0762788	+	0.997087i	$0.475696\pi$
$54$	−5.95439	−0.810291
$55$	−0.400374	−0.0539865
$56$	−11.7870	−1.57511
$57$	1.02676	0.135998
$58$	21.2008	2.78380
$59$	14.2019	1.84893	0.924466	−	0.381265i	$-0.124511\pi$
$59$	14.2019	1.84893	0.924466	+	0.381265i	$0.124511\pi$
$60$	−0.547041	−0.0706227
$61$	6.80698	0.871545	0.435772	−	0.900057i	$-0.356475\pi$
$61$	6.80698	0.871545	0.435772	+	0.900057i	$0.356475\pi$
$62$	0.771579	0.0979906
$63$	−9.53009	−1.20068
$64$	−12.2024	−1.52530
$65$	−1.59880	−0.198307
$66$	−1.14417	−0.140837
$67$	11.3700	1.38906	0.694530	−	0.719463i	$-0.255612\pi$
$67$	11.3700	1.38906	0.694530	+	0.719463i	$0.255612\pi$
$68$	22.0727	2.67671
$69$	0.123882	0.0149136
$70$	−2.85057	−0.340708
$71$	5.88288	0.698169	0.349085	−	0.937091i	$-0.386493\pi$
$71$	5.88288	0.698169	0.349085	+	0.937091i	$0.386493\pi$
$72$	9.75456	1.14959
$73$	8.90981	1.04281	0.521407	−	0.853308i	$-0.325407\pi$
$73$	8.90981	1.04281	0.521407	+	0.853308i	$0.325407\pi$
$74$	−0.154298	−0.0179367
$75$	2.13260	0.246252
$76$	−8.16961	−0.937118
$77$	−3.78749	−0.431624
$78$	−4.56895	−0.517332
$79$	8.35937	0.940503	0.470252	−	0.882532i	$-0.344163\pi$
$79$	8.35937	0.940503	0.470252	+	0.882532i	$0.344163\pi$
$80$	0.418595	0.0468003
$81$	7.31181	0.812423
$82$	24.0564	2.65659
$83$	6.63373	0.728146	0.364073	−	0.931370i	$-0.381386\pi$
$83$	6.63373	0.728146	0.364073	+	0.931370i	$0.381386\pi$
$84$	−5.17493	−0.564631
$85$	2.27313	0.246555
$86$	−18.1131	−1.95319
$87$	3.96363	0.424946
$88$	3.87669	0.413257
$89$	−7.80016	−0.826816	−0.413408	−	0.910546i	$-0.635662\pi$
$89$	−7.80016	−0.826816	−0.413408	+	0.910546i	$0.635662\pi$
$90$	2.35904	0.248664
$91$	−15.1244	−1.58547
$92$	−0.985682	−0.102764
$93$	0.144252	0.0149582
$94$	25.7667	2.65763
$95$	−0.841337	−0.0863194
$96$	−1.84501	−0.188305
$97$	19.0062	1.92979	0.964895	−	0.262635i	$-0.0845914\pi$
$97$	19.0062	1.92979	0.964895	+	0.262635i	$0.0845914\pi$
$98$	−10.5744	−1.06818
$99$	3.13440	0.315019
$100$	−16.9684	−1.69684
$101$	14.1883	1.41179	0.705894	−	0.708317i	$-0.250545\pi$
$101$	14.1883	1.41179	0.705894	+	0.708317i	$0.250545\pi$
$102$	6.49601	0.643201
$103$	0.329243	0.0324413	0.0162206	−	0.999868i	$-0.494837\pi$
$103$	0.329243	0.0324413	0.0162206	+	0.999868i	$0.494837\pi$
$104$	15.4806	1.51800
$105$	−0.532934	−0.0520090
$106$	−2.60072	−0.252604
$107$	3.18162	0.307579	0.153790	−	0.988104i	$-0.450852\pi$
$107$	3.18162	0.307579	0.153790	+	0.988104i	$0.450852\pi$
$108$	8.85747	0.852310
$109$	0.00227135	0.000217556 0	0.000108778	−	1.00000i	$-0.499965\pi$
$109$	0.00227135	0.000217556 0	0.000108778		1.00000i	$0.499965\pi$
$110$	0.937537	0.0893906
$111$	−0.0288470	−0.00273804
$112$	3.95985	0.374170
$113$	−14.7948	−1.39178	−0.695889	−	0.718149i	$-0.744990\pi$
$113$	−14.7948	−1.39178	−0.695889	+	0.718149i	$0.744990\pi$
$114$	−2.40432	−0.225186
$115$	−0.101509	−0.00946579
$116$	−31.5372	−2.92816
$117$	12.5165	1.15715
$118$	−33.2559	−3.06145
$119$	21.5035	1.97122
$120$	0.545486	0.0497958
$121$	−9.75432	−0.886756
$122$	−15.9396	−1.44310
$123$	4.49751	0.405527
$124$	−1.14776	−0.103072
$125$	−3.54109	−0.316725
$126$	22.3161	1.98808
$127$	8.19744	0.727405	0.363703	−	0.931515i	$-0.381512\pi$
$127$	8.19744	0.727405	0.363703	+	0.931515i	$0.381512\pi$
$128$	20.1450	1.78058
$129$	−3.38637	−0.298153
$130$	3.74383	0.328355
$131$	−16.6557	−1.45522	−0.727609	−	0.685992i	$-0.759368\pi$
$131$	−16.6557	−1.45522	−0.727609	+	0.685992i	$0.759368\pi$
$132$	1.70201	0.148141
$133$	−7.95893	−0.690126
$134$	−26.6244	−2.30000
$135$	0.912175	0.0785075
$136$	−22.0100	−1.88734
$137$	2.44283	0.208705	0.104353	−	0.994540i	$-0.466723\pi$
$137$	2.44283	0.208705	0.104353	+	0.994540i	$0.466723\pi$
$138$	−0.290087	−0.0246939
$139$	−3.01871	−0.256044	−0.128022	−	0.991771i	$-0.540863\pi$
$139$	−3.01871	−0.256044	−0.128022	+	0.991771i	$0.540863\pi$
$140$	4.24037	0.358376
$141$	4.81726	0.405687
$142$	−13.7756	−1.15603
$143$	4.97434	0.415975
$144$	−3.27704	−0.273087
$145$	−3.24782	−0.269717
$146$	−20.8636	−1.72669
$147$	−1.97696	−0.163057
$148$	0.229525	0.0188669
$149$	−17.6155	−1.44312	−0.721558	−	0.692354i	$-0.756574\pi$
$149$	−17.6155	−1.44312	−0.721558	+	0.692354i	$0.756574\pi$
$150$	−4.99381	−0.407743
$151$	6.53463	0.531781	0.265890	−	0.964003i	$-0.414334\pi$
$151$	6.53463	0.531781	0.265890	+	0.964003i	$0.414334\pi$
$152$	8.14639	0.660759
$153$	−17.7956	−1.43869
$154$	8.86896	0.714681
$155$	−0.118201	−0.00949413
$156$	6.79655	0.544160
$157$	21.0609	1.68084	0.840419	−	0.541936i	$-0.182309\pi$
$157$	21.0609	1.68084	0.840419	+	0.541936i	$0.182309\pi$
$158$	−19.5747	−1.55728
$159$	−0.486223	−0.0385600
$160$	1.51181	0.119519
$161$	−0.960263	−0.0756793
$162$	−17.1217	−1.34521
$163$	−8.74516	−0.684974	−0.342487	−	0.939523i	$-0.611269\pi$
$163$	−8.74516	−0.684974	−0.342487	+	0.939523i	$0.611269\pi$
$164$	−35.7851	−2.79435
$165$	0.175279	0.0136455
$166$	−15.5339	−1.20566
$167$	3.65416	0.282767	0.141384	−	0.989955i	$-0.454845\pi$
$167$	3.65416	0.282767	0.141384	+	0.989955i	$0.454845\pi$
$168$	5.16022	0.398120
$169$	6.86382	0.527986
$170$	−5.32287	−0.408246
$171$	6.58654	0.503685
$172$	26.9442	2.05447
$173$	−23.6903	−1.80114	−0.900571	−	0.434709i	$-0.856851\pi$
$173$	−23.6903	−1.80114	−0.900571	+	0.434709i	$0.856851\pi$
$174$	−9.28144	−0.703624
$175$	−16.5308	−1.24961
$176$	−1.30237	−0.0981701
$177$	−6.21742	−0.467330
$178$	18.2653	1.36904
$179$	21.3915	1.59887	0.799436	−	0.600751i	$-0.205132\pi$
$179$	21.3915	1.59887	0.799436	+	0.600751i	$0.205132\pi$
$180$	−3.50919	−0.261559
$181$	12.7464	0.947436	0.473718	−	0.880677i	$-0.342912\pi$
$181$	12.7464	0.947436	0.473718	+	0.880677i	$0.342912\pi$
$182$	35.4161	2.62521
$183$	−2.98001	−0.220289
$184$	0.982881	0.0724589
$185$	0.0236374	0.00173786
$186$	−0.337788	−0.0247678
$187$	−7.07238	−0.517183
$188$	−38.3293	−2.79545
$189$	8.62905	0.627671
$190$	1.97012	0.142927
$191$	−2.71538	−0.196478	−0.0982389	−	0.995163i	$-0.531321\pi$
$191$	−2.71538	−0.196478	−0.0982389	+	0.995163i	$0.531321\pi$
$192$	5.34207	0.385530
$193$	−6.32621	−0.455371	−0.227685	−	0.973735i	$-0.573116\pi$
$193$	−6.32621	−0.455371	−0.227685	+	0.973735i	$0.573116\pi$
$194$	−44.5059	−3.19534
$195$	0.699935	0.0501234
$196$	15.7300	1.12357
$197$	10.2970	0.733632	0.366816	−	0.930294i	$-0.380448\pi$
$197$	10.2970	0.733632	0.366816	+	0.930294i	$0.380448\pi$
$198$	−7.33966	−0.521607
$199$	11.2383	0.796664	0.398332	−	0.917241i	$-0.369589\pi$
$199$	11.2383	0.796664	0.398332	+	0.917241i	$0.369589\pi$
$200$	16.9201	1.19643
$201$	−4.97762	−0.351095
$202$	−33.2240	−2.33763
$203$	−30.7240	−2.15640
$204$	−9.66315	−0.676556
$205$	−3.68529	−0.257392
$206$	−0.770972	−0.0537161
$207$	0.794682	0.0552342
$208$	−5.20071	−0.360605
$209$	2.61765	0.181067
$210$	1.24794	0.0861163
$211$	28.1377	1.93708	0.968541	−	0.248855i	$-0.0800543\pi$
$211$	28.1377	1.93708	0.968541	+	0.248855i	$0.0800543\pi$
$212$	3.86870	0.265704
$213$	−2.57545	−0.176467
$214$	−7.45025	−0.509288
$215$	2.77481	0.189241
$216$	−8.83229	−0.600961
$217$	−1.11816	−0.0759059
$218$	−0.00531870	−0.000360228 0
$219$	−3.90060	−0.263578
$220$	−1.39463	−0.0940262
$221$	−28.2418	−1.89975
$222$	0.0675496	0.00453363
$223$	20.4221	1.36756	0.683782	−	0.729686i	$-0.260334\pi$
$223$	20.4221	1.36756	0.683782	+	0.729686i	$0.260334\pi$
$224$	14.3015	0.955559
$225$	13.6803	0.912021
$226$	34.6443	2.30450
$227$	−14.3892	−0.955043	−0.477522	−	0.878620i	$-0.658465\pi$
$227$	−14.3892	−0.955043	−0.477522	+	0.878620i	$0.658465\pi$
$228$	3.57655	0.236863
$229$	−13.3730	−0.883715	−0.441857	−	0.897085i	$-0.645680\pi$
$229$	−13.3730	−0.883715	−0.441857	+	0.897085i	$0.645680\pi$
$230$	0.237699	0.0156734
$231$	1.65811	0.109096
$232$	31.4476	2.06464
$233$	3.15750	0.206855	0.103427	−	0.994637i	$-0.467019\pi$
$233$	3.15750	0.206855	0.103427	+	0.994637i	$0.467019\pi$
$234$	−29.3092	−1.91600
$235$	−3.94729	−0.257493
$236$	49.4699	3.22021
$237$	−3.65963	−0.237719
$238$	−50.3536	−3.26394
$239$	9.95161	0.643716	0.321858	−	0.946788i	$-0.395693\pi$
$239$	9.95161	0.643716	0.321858	+	0.946788i	$0.395693\pi$
$240$	−0.183256	−0.0118291
$241$	−1.63636	−0.105407	−0.0527036	−	0.998610i	$-0.516784\pi$
$241$	−1.63636	−0.105407	−0.0527036	+	0.998610i	$0.516784\pi$
$242$	22.8412	1.46829
$243$	−10.8295	−0.694712
$244$	23.7109	1.51794
$245$	1.61993	0.103494
$246$	−10.5316	−0.671470
$247$	10.4529	0.665105
$248$	1.14450	0.0726759
$249$	−2.90416	−0.184044
$250$	8.29200	0.524432
$251$	1.02428	0.0646520	0.0323260	−	0.999477i	$-0.489709\pi$
$251$	1.02428	0.0646520	0.0323260	+	0.999477i	$0.489709\pi$
$252$	−33.1964	−2.09118
$253$	0.315825	0.0198558
$254$	−19.1955	−1.20444
$255$	−0.995148	−0.0623186
$256$	−22.7677	−1.42298
$257$	−6.80941	−0.424759	−0.212380	−	0.977187i	$-0.568121\pi$
$257$	−6.80941	−0.424759	−0.212380	+	0.977187i	$0.568121\pi$
$258$	7.92970	0.493681
$259$	0.223606	0.0138942
$260$	−5.56913	−0.345383
$261$	25.4261	1.57384
$262$	39.0019	2.40954
$263$	10.4225	0.642678	0.321339	−	0.946964i	$-0.395867\pi$
$263$	10.4225	0.642678	0.321339	+	0.946964i	$0.395867\pi$
$264$	−1.69717	−0.104454
$265$	0.398414	0.0244744
$266$	18.6370	1.14271
$267$	3.41482	0.208983
$268$	39.6052	2.41927
$269$	−21.5507	−1.31397	−0.656984	−	0.753905i	$-0.728168\pi$
$269$	−21.5507	−1.31397	−0.656984	+	0.753905i	$0.728168\pi$
$270$	−2.13599	−0.129992
$271$	4.26267	0.258939	0.129469	−	0.991583i	$-0.458673\pi$
$271$	4.26267	0.258939	0.129469	+	0.991583i	$0.458673\pi$
$272$	7.39423	0.448341
$273$	6.62128	0.400738
$274$	−5.72026	−0.345573
$275$	5.43689	0.327857
$276$	0.431520	0.0259744
$277$	15.9214	0.956625	0.478313	−	0.878190i	$-0.341249\pi$
$277$	15.9214	0.956625	0.478313	+	0.878190i	$0.341249\pi$
$278$	7.06876	0.423956
$279$	0.925355	0.0553996
$280$	−4.22831	−0.252690
$281$	8.00350	0.477449	0.238724	−	0.971087i	$-0.423271\pi$
$281$	8.00350	0.477449	0.238724	+	0.971087i	$0.423271\pi$
$282$	−11.2803	−0.671734
$283$	2.40190	0.142778	0.0713890	−	0.997449i	$-0.477257\pi$
$283$	2.40190	0.142778	0.0713890	+	0.997449i	$0.477257\pi$
$284$	20.4920	1.21597
$285$	0.368327	0.0218178
$286$	−11.6482	−0.688770
$287$	−34.8623	−2.05786
$288$	−11.8354	−0.697410
$289$	23.1535	1.36197
$290$	7.60527	0.446597
$291$	−8.32069	−0.487768
$292$	31.0357	1.81623
$293$	−19.5879	−1.14433	−0.572167	−	0.820137i	$-0.693897\pi$
$293$	−19.5879	−1.14433	−0.572167	+	0.820137i	$0.693897\pi$
$294$	4.62935	0.269989
$295$	5.09459	0.296619
$296$	−0.228873	−0.0133030
$297$	−2.83805	−0.164680
$298$	41.2493	2.38951
$299$	1.26117	0.0729355
$300$	7.42854	0.428887
$301$	26.2493	1.51299
$302$	−15.3018	−0.880520
$303$	−6.21146	−0.356839
$304$	−2.73677	−0.156965
$305$	2.44184	0.139819
$306$	41.6710	2.38217
$307$	11.7220	0.669009	0.334504	−	0.942394i	$-0.391431\pi$
$307$	11.7220	0.669009	0.334504	+	0.942394i	$0.391431\pi$
$308$	−13.1930	−0.751743
$309$	−0.144138	−0.00819975
$310$	0.276785	0.0157203
$311$	23.6782	1.34267	0.671334	−	0.741155i	$-0.265721\pi$
$311$	23.6782	1.34267	0.671334	+	0.741155i	$0.265721\pi$
$312$	−6.77724	−0.383685
$313$	18.1630	1.02663	0.513316	−	0.858200i	$-0.328417\pi$
$313$	18.1630	1.02663	0.513316	+	0.858200i	$0.328417\pi$
$314$	−49.3171	−2.78313
$315$	−3.41869	−0.192621
$316$	29.1184	1.63804
$317$	19.7993	1.11204	0.556019	−	0.831170i	$-0.312328\pi$
$317$	19.7993	1.11204	0.556019	+	0.831170i	$0.312328\pi$
$318$	1.13856	0.0638475
$319$	10.1049	0.565768
$320$	−4.37732	−0.244700
$321$	−1.39288	−0.0777427
$322$	2.24860	0.125310
$323$	−14.8617	−0.826928
$324$	25.4694	1.41497
$325$	21.7109	1.20430
$326$	20.4781	1.13418
$327$	−0.000994368 0	−5.49887e−5 0
$328$	35.6834	1.97029
$329$	−37.3408	−2.05867
$330$	−0.410442	−0.0225941
$331$	−11.4205	−0.627727	−0.313864	−	0.949468i	$-0.601623\pi$
$331$	−11.4205	−0.627727	−0.313864	+	0.949468i	$0.601623\pi$
$332$	23.1074	1.26818
$333$	−0.185049	−0.0101406
$334$	−8.55676	−0.468205
$335$	4.07869	0.222843
$336$	−1.73357	−0.0945741
$337$	−11.2706	−0.613949	−0.306974	−	0.951718i	$-0.599317\pi$
$337$	−11.2706	−0.613949	−0.306974	+	0.951718i	$0.599317\pi$
$338$	−16.0727	−0.874237
$339$	6.47698	0.351781
$340$	7.91804	0.429416
$341$	0.367758	0.0199152
$342$	−15.4234	−0.834001
$343$	−8.43012	−0.455184
$344$	−26.8676	−1.44860
$345$	0.0444395	0.00239254
$346$	55.4745	2.98232
$347$	−20.1839	−1.08353	−0.541764	−	0.840531i	$-0.682243\pi$
$347$	−20.1839	−1.08353	−0.541764	+	0.840531i	$0.682243\pi$
$348$	13.8066	0.740112
$349$	2.08367	0.111537	0.0557683	−	0.998444i	$-0.482239\pi$
$349$	2.08367	0.111537	0.0557683	+	0.998444i	$0.482239\pi$
$350$	38.7093	2.06910
$351$	−11.3331	−0.604914
$352$	−4.70369	−0.250707
$353$	9.91563	0.527756	0.263878	−	0.964556i	$-0.414998\pi$
$353$	9.91563	0.527756	0.263878	+	0.964556i	$0.414998\pi$
$354$	14.5590	0.773804
$355$	2.11034	0.112005
$356$	−27.1705	−1.44003
$357$	−9.41395	−0.498239
$358$	−50.0913	−2.64741
$359$	26.0532	1.37503	0.687517	−	0.726168i	$-0.258701\pi$
$359$	26.0532	1.37503	0.687517	+	0.726168i	$0.258701\pi$
$360$	3.49921	0.184425
$361$	−13.4993	−0.710491
$362$	−29.8477	−1.56876
$363$	4.27032	0.224134
$364$	−52.6832	−2.76135
$365$	3.19618	0.167296
$366$	6.97814	0.364753
$367$	−6.74178	−0.351918	−0.175959	−	0.984397i	$-0.556303\pi$
$367$	−6.74178	−0.351918	−0.175959	+	0.984397i	$0.556303\pi$
$368$	−0.330198	−0.0172128
$369$	28.8509	1.50192
$370$	−0.0553505	−0.00287754
$371$	3.76894	0.195673
$372$	0.502477	0.0260522
$373$	13.2044	0.683696	0.341848	−	0.939755i	$-0.388947\pi$
$373$	13.2044	0.683696	0.341848	+	0.939755i	$0.388947\pi$
$374$	16.5610	0.856350
$375$	1.55025	0.0800544
$376$	38.2203	1.97106
$377$	40.3517	2.07822
$378$	−20.2062	−1.03929
$379$	−2.26102	−0.116141	−0.0580704	−	0.998312i	$-0.518495\pi$
$379$	−2.26102	−0.116141	−0.0580704	+	0.998312i	$0.518495\pi$
$380$	−2.93065	−0.150339
$381$	−3.58874	−0.183857
$382$	6.35846	0.325327
$383$	−9.86894	−0.504279	−0.252140	−	0.967691i	$-0.581134\pi$
$383$	−9.86894	−0.504279	−0.252140	+	0.967691i	$0.581134\pi$
$384$	−8.81923	−0.450054
$385$	−1.35867	−0.0692441
$386$	14.8138	0.754001
$387$	−21.7231	−1.10425
$388$	66.2049	3.36104
$389$	12.8695	0.652507	0.326254	−	0.945282i	$-0.394214\pi$
$389$	12.8695	0.652507	0.326254	+	0.945282i	$0.394214\pi$
$390$	−1.63900	−0.0829941
$391$	−1.79310	−0.0906810
$392$	−15.6853	−0.792226
$393$	7.29167	0.367816
$394$	−24.1120	−1.21474
$395$	2.99872	0.150882
$396$	10.9181	0.548656
$397$	9.16350	0.459903	0.229951	−	0.973202i	$-0.426143\pi$
$397$	9.16350	0.459903	0.229951	+	0.973202i	$0.426143\pi$
$398$	−26.3162	−1.31911
$399$	3.48432	0.174434
$400$	−5.68431	−0.284216
$401$	−5.55171	−0.277239	−0.138620	−	0.990346i	$-0.544267\pi$
$401$	−5.55171	−0.277239	−0.138620	+	0.990346i	$0.544267\pi$
$402$	11.6559	0.581341
$403$	1.46855	0.0731539
$404$	49.4224	2.45886
$405$	2.62293	0.130335
$406$	71.9447	3.57056
$407$	−0.0735429	−0.00364539
$408$	9.63569	0.477038
$409$	−11.3015	−0.558824	−0.279412	−	0.960171i	$-0.590140\pi$
$409$	−11.3015	−0.558824	−0.279412	+	0.960171i	$0.590140\pi$
$410$	8.62965	0.426188
$411$	−1.06944	−0.0527517
$412$	1.14686	0.0565017
$413$	48.1941	2.37148
$414$	−1.86087	−0.0914566
$415$	2.37969	0.116814
$416$	−18.7830	−0.920915
$417$	1.32155	0.0647168
$418$	−6.12962	−0.299809
$419$	37.8498	1.84908	0.924541	−	0.381083i	$-0.124449\pi$
$419$	37.8498	1.84908	0.924541	+	0.381083i	$0.124449\pi$
$420$	−1.85638	−0.0905821
$421$	6.54301	0.318887	0.159443	−	0.987207i	$-0.449030\pi$
$421$	6.54301	0.318887	0.159443	+	0.987207i	$0.449030\pi$
$422$	−65.8887	−3.20741
$423$	30.9020	1.50251
$424$	−3.85771	−0.187347
$425$	−30.8680	−1.49732
$426$	6.03080	0.292193
$427$	23.0994	1.11786
$428$	11.0826	0.535699
$429$	−2.17770	−0.105141
$430$	−6.49764	−0.313344
$431$	15.1655	0.730496	0.365248	−	0.930910i	$-0.380984\pi$
$431$	15.1655	0.730496	0.365248	+	0.930910i	$0.380984\pi$
$432$	2.96720	0.142760
$433$	−5.51206	−0.264892	−0.132446	−	0.991190i	$-0.542283\pi$
$433$	−5.51206	−0.264892	−0.132446	+	0.991190i	$0.542283\pi$
$434$	2.61835	0.125685
$435$	1.42186	0.0681728
$436$	0.00791184	0.000378908 0
$437$	0.663668	0.0317475
$438$	9.13385	0.436432
$439$	−5.86387	−0.279867	−0.139934	−	0.990161i	$-0.544689\pi$
$439$	−5.86387	−0.279867	−0.139934	+	0.990161i	$0.544689\pi$
$440$	1.39067	0.0662976
$441$	−12.6819	−0.603900
$442$	66.1325	3.14560
$443$	12.0408	0.572078	0.286039	−	0.958218i	$-0.407661\pi$
$443$	12.0408	0.572078	0.286039	+	0.958218i	$0.407661\pi$
$444$	−0.100483	−0.00476873
$445$	−2.79812	−0.132644
$446$	−47.8214	−2.26441
$447$	7.71184	0.364757
$448$	−41.4088	−1.95638
$449$	−28.5061	−1.34529	−0.672643	−	0.739967i	$-0.734841\pi$
$449$	−28.5061	−1.34529	−0.672643	+	0.739967i	$0.734841\pi$
$450$	−32.0345	−1.51012
$451$	11.4660	0.539914
$452$	−51.5351	−2.42401
$453$	−2.86078	−0.134411
$454$	33.6944	1.58136
$455$	−5.42551	−0.254352
$456$	−3.56639	−0.167011
$457$	−0.275369	−0.0128812	−0.00644060	−	0.999979i	$-0.502050\pi$
$457$	−0.275369	−0.0128812	−0.00644060	+	0.999979i	$0.502050\pi$
$458$	31.3150	1.46325
$459$	16.1130	0.752092
$460$	−0.353590	−0.0164862
$461$	27.5656	1.28386	0.641928	−	0.766765i	$-0.278135\pi$
$461$	27.5656	1.28386	0.641928	+	0.766765i	$0.278135\pi$
$462$	−3.88272	−0.180641
$463$	−16.0011	−0.743633	−0.371816	−	0.928306i	$-0.621265\pi$
$463$	−16.0011	−0.743633	−0.371816	+	0.928306i	$0.621265\pi$
$464$	−10.5648	−0.490459
$465$	0.0517469	0.00239971
$466$	−7.39376	−0.342510
$467$	−6.64048	−0.307285	−0.153642	−	0.988127i	$-0.549100\pi$
$467$	−6.64048	−0.307285	−0.153642	+	0.988127i	$0.549100\pi$
$468$	43.5989	2.01536
$469$	38.5839	1.78164
$470$	9.24317	0.426356
$471$	−9.22018	−0.424844
$472$	−49.3293	−2.27056
$473$	−8.63326	−0.396958
$474$	8.56957	0.393614
$475$	11.4249	0.524212
$476$	74.9035	3.43320
$477$	−3.11905	−0.142811
$478$	−23.3032	−1.06586
$479$	5.90173	0.269657	0.134829	−	0.990869i	$-0.456952\pi$
$479$	5.90173	0.269657	0.134829	+	0.990869i	$0.456952\pi$
$480$	−0.661852	−0.0302093
$481$	−0.293676	−0.0133905
$482$	3.83178	0.174533
$483$	0.420391	0.0191285
$484$	−33.9774	−1.54443
$485$	6.81802	0.309591
$486$	25.3589	1.15030
$487$	−13.2061	−0.598427	−0.299214	−	0.954186i	$-0.596724\pi$
$487$	−13.2061	−0.598427	−0.299214	+	0.954186i	$0.596724\pi$
$488$	−23.6435	−1.07029
$489$	3.82852	0.173132
$490$	−3.79332	−0.171365
$491$	15.9325	0.719026	0.359513	−	0.933140i	$-0.382943\pi$
$491$	15.9325	0.719026	0.359513	+	0.933140i	$0.382943\pi$
$492$	15.6663	0.706291
$493$	−57.3709	−2.58385
$494$	−24.4771	−1.10128
$495$	1.12439	0.0505375
$496$	−0.384494	−0.0172643
$497$	19.9635	0.895486
$498$	6.80054	0.304739
$499$	−9.87843	−0.442219	−0.221110	−	0.975249i	$-0.570968\pi$
$499$	−9.87843	−0.442219	−0.221110	+	0.975249i	$0.570968\pi$
$500$	−12.3348	−0.551628
$501$	−1.59975	−0.0714714
$502$	−2.39851	−0.107051
$503$	−22.9873	−1.02495	−0.512477	−	0.858701i	$-0.671272\pi$
$503$	−22.9873	−1.02495	−0.512477	+	0.858701i	$0.671272\pi$
$504$	33.1020	1.47448
$505$	5.08971	0.226489
$506$	−0.739553	−0.0328771
$507$	−3.00490	−0.133452
$508$	28.5543	1.26689
$509$	11.6725	0.517373	0.258687	−	0.965961i	$-0.416710\pi$
$509$	11.6725	0.517373	0.258687	+	0.965961i	$0.416710\pi$
$510$	2.33029	0.103187
$511$	30.2354	1.33753
$512$	13.0240	0.575584
$513$	−5.96380	−0.263308
$514$	15.9453	0.703315
$515$	0.118108	0.00520446
$516$	−11.7958	−0.519282
$517$	12.2812	0.540126
$518$	−0.523608	−0.0230060
$519$	10.3713	0.455251
$520$	5.55331	0.243529
$521$	12.1587	0.532684	0.266342	−	0.963879i	$-0.414185\pi$
$521$	12.1587	0.532684	0.266342	+	0.963879i	$0.414185\pi$
$522$	−59.5391	−2.60595
$523$	10.2136	0.446607	0.223304	−	0.974749i	$-0.428316\pi$
$523$	10.2136	0.446607	0.223304	+	0.974749i	$0.428316\pi$
$524$	−58.0173	−2.53450
$525$	7.23697	0.315847
$526$	−24.4058	−1.06414
$527$	−2.08795	−0.0909525
$528$	0.570163	0.0248132
$529$	−22.9199	−0.996519
$530$	−0.932945	−0.0405245
$531$	−39.8838	−1.73081
$532$	−27.7235	−1.20197
$533$	45.7868	1.98325
$534$	−7.99630	−0.346034
$535$	1.14133	0.0493440
$536$	−39.4927	−1.70582
$537$	−9.36492	−0.404126
$538$	50.4641	2.17566
$539$	−5.04009	−0.217092
$540$	3.17740	0.136734
$541$	12.4937	0.537147	0.268573	−	0.963259i	$-0.413448\pi$
$541$	12.4937	0.537147	0.268573	+	0.963259i	$0.413448\pi$
$542$	−9.98168	−0.428750
$543$	−5.58024	−0.239471
$544$	26.7052	1.14498
$545$	0.000814791 0	3.49018e−5 0
$546$	−15.5047	−0.663541
$547$	−1.80967	−0.0773758	−0.0386879	−	0.999251i	$-0.512318\pi$
$547$	−1.80967	−0.0773758	−0.0386879	+	0.999251i	$0.512318\pi$
$548$	8.50917	0.363494
$549$	−19.1163	−0.815865
$550$	−12.7313	−0.542864
$551$	21.2343	0.904611
$552$	−0.430293	−0.0183145
$553$	28.3675	1.20631
$554$	−37.2824	−1.58398
$555$	−0.0103482	−0.000439255 0
$556$	−10.5151	−0.445942
$557$	11.5872	0.490964	0.245482	−	0.969401i	$-0.421054\pi$
$557$	11.5872	0.490964	0.245482	+	0.969401i	$0.421054\pi$
$558$	−2.16686	−0.0917304
$559$	−34.4749	−1.45813
$560$	1.42050	0.0600271
$561$	3.09620	0.130722
$562$	−18.7414	−0.790558
$563$	−29.6044	−1.24768	−0.623838	−	0.781553i	$-0.714428\pi$
$563$	−29.6044	−1.24768	−0.623838	+	0.781553i	$0.714428\pi$
$564$	16.7801	0.706569
$565$	−5.30728	−0.223279
$566$	−5.62440	−0.236411
$567$	24.8126	1.04203
$568$	−20.4337	−0.857380
$569$	−5.15781	−0.216227	−0.108113	−	0.994139i	$-0.534481\pi$
$569$	−5.15781	−0.216227	−0.108113	+	0.994139i	$0.534481\pi$
$570$	−0.862493	−0.0361258
$571$	−28.9582	−1.21186	−0.605932	−	0.795516i	$-0.707200\pi$
$571$	−28.9582	−1.21186	−0.605932	+	0.795516i	$0.707200\pi$
$572$	17.3272	0.724488
$573$	1.18876	0.0496611
$574$	81.6353	3.40739
$575$	1.37845	0.0574851
$576$	34.2685	1.42786
$577$	37.8112	1.57410	0.787051	−	0.616888i	$-0.211607\pi$
$577$	37.8112	1.57410	0.787051	+	0.616888i	$0.211607\pi$
$578$	−54.2173	−2.25514
$579$	2.76954	0.115098
$580$	−11.3132	−0.469756
$581$	22.5115	0.933935
$582$	19.4842	0.807644
$583$	−1.23958	−0.0513383
$584$	−30.9475	−1.28062
$585$	4.48997	0.185638
$586$	45.8679	1.89478
$587$	−11.0475	−0.455981	−0.227990	−	0.973663i	$-0.573215\pi$
$587$	−11.0475	−0.455981	−0.227990	+	0.973663i	$0.573215\pi$
$588$	−6.88640	−0.283990
$589$	0.772798	0.0318426
$590$	−11.9297	−0.491140
$591$	−4.50791	−0.185430
$592$	0.0768898	0.00316015
$593$	10.6953	0.439202	0.219601	−	0.975590i	$-0.429524\pi$
$593$	10.6953	0.439202	0.219601	+	0.975590i	$0.429524\pi$
$594$	6.64571	0.272677
$595$	7.71385	0.316237
$596$	−61.3604	−2.51342
$597$	−4.92000	−0.201362
$598$	−2.95322	−0.120766
$599$	6.57106	0.268486	0.134243	−	0.990948i	$-0.457140\pi$
$599$	6.57106	0.268486	0.134243	+	0.990948i	$0.457140\pi$
$600$	−7.40743	−0.302407
$601$	41.6967	1.70084	0.850422	−	0.526100i	$-0.176346\pi$
$601$	41.6967	1.70084	0.850422	+	0.526100i	$0.176346\pi$
$602$	−61.4667	−2.50520
$603$	−31.9307	−1.30032
$604$	22.7622	0.926182
$605$	−3.49912	−0.142260
$606$	14.5451	0.590853
$607$	−1.69124	−0.0686454	−0.0343227	−	0.999411i	$-0.510927\pi$
$607$	−1.69124	−0.0686454	−0.0343227	+	0.999411i	$0.510927\pi$
$608$	−9.88421	−0.400858
$609$	13.4506	0.545044
$610$	−5.71793	−0.231512
$611$	49.0420	1.98403
$612$	−61.9877	−2.50570
$613$	−11.0082	−0.444618	−0.222309	−	0.974976i	$-0.571359\pi$
$613$	−11.0082	−0.444618	−0.222309	+	0.974976i	$0.571359\pi$
$614$	−27.4488	−1.10774
$615$	1.61337	0.0650575
$616$	13.1555	0.530052
$617$	21.9853	0.885096	0.442548	−	0.896745i	$-0.354075\pi$
$617$	21.9853	0.885096	0.442548	+	0.896745i	$0.354075\pi$
$618$	0.337522	0.0135771
$619$	24.9238	1.00177	0.500887	−	0.865513i	$-0.333007\pi$
$619$	24.9238	1.00177	0.500887	+	0.865513i	$0.333007\pi$
$620$	−0.411732	−0.0165356
$621$	−0.719547	−0.0288744
$622$	−55.4461	−2.22319
$623$	−26.4698	−1.06049
$624$	2.27681	0.0911453
$625$	23.0863	0.923452
$626$	−42.5313	−1.69989
$627$	−1.14597	−0.0457658
$628$	73.3618	2.92745
$629$	0.417540	0.0166484
$630$	8.00537	0.318942
$631$	−19.8290	−0.789382	−0.394691	−	0.918814i	$-0.629148\pi$
$631$	−19.8290	−0.789382	−0.394691	+	0.918814i	$0.629148\pi$
$632$	−29.0356	−1.15498
$633$	−12.3184	−0.489611
$634$	−46.3629	−1.84131
$635$	2.94063	0.116695
$636$	−1.69367	−0.0671584
$637$	−20.1264	−0.797437
$638$	−23.6622	−0.936797
$639$	−16.5211	−0.653566
$640$	7.22653	0.285654
$641$	−3.79896	−0.150050	−0.0750250	−	0.997182i	$-0.523904\pi$
$641$	−3.79896	−0.150050	−0.0750250	+	0.997182i	$0.523904\pi$
$642$	3.26163	0.128726
$643$	47.1945	1.86117	0.930585	−	0.366075i	$-0.119299\pi$
$643$	47.1945	1.86117	0.930585	+	0.366075i	$0.119299\pi$
$644$	−3.34491	−0.131808
$645$	−1.21478	−0.0478319
$646$	34.8009	1.36922
$647$	6.92533	0.272263	0.136131	−	0.990691i	$-0.456533\pi$
$647$	6.92533	0.272263	0.136131	+	0.990691i	$0.456533\pi$
$648$	−25.3970	−0.997689
$649$	−15.8508	−0.622198
$650$	−50.8393	−1.99408
$651$	0.489518	0.0191857
$652$	−30.4622	−1.19299
$653$	32.2940	1.26376	0.631880	−	0.775066i	$-0.282283\pi$
$653$	32.2940	1.26376	0.631880	+	0.775066i	$0.282283\pi$
$654$	0.00232846	9.10501e−5 0
$655$	−5.97484	−0.233456
$656$	−11.9878	−0.468046
$657$	−25.0218	−0.976193
$658$	87.4391	3.40873
$659$	5.06870	0.197449	0.0987243	−	0.995115i	$-0.468524\pi$
$659$	5.06870	0.197449	0.0987243	+	0.995115i	$0.468524\pi$
$660$	0.610553	0.0237658
$661$	13.0491	0.507550	0.253775	−	0.967263i	$-0.418328\pi$
$661$	13.0491	0.507550	0.253775	+	0.967263i	$0.418328\pi$
$662$	26.7428	1.03939
$663$	12.3639	0.480175
$664$	−23.0418	−0.894193
$665$	−2.85507	−0.110715
$666$	0.433320	0.0167908
$667$	2.56197	0.0991997
$668$	12.7286	0.492485
$669$	−8.94054	−0.345661
$670$	−9.55087	−0.368982
$671$	−7.59728	−0.293290
$672$	−6.26102	−0.241524
$673$	−45.0455	−1.73638	−0.868189	−	0.496234i	$-0.834716\pi$
$673$	−45.0455	−1.73638	−0.868189	+	0.496234i	$0.834716\pi$
$674$	26.3918	1.01657
$675$	−12.3869	−0.476771
$676$	23.9089	0.919573
$677$	32.1256	1.23469	0.617344	−	0.786693i	$-0.288208\pi$
$677$	32.1256	1.23469	0.617344	+	0.786693i	$0.288208\pi$
$678$	−15.1668	−0.582479
$679$	64.4975	2.47519
$680$	−7.89554	−0.302780
$681$	6.29941	0.241394
$682$	−0.861161	−0.0329756
$683$	50.4661	1.93103	0.965515	−	0.260346i	$-0.0838367\pi$
$683$	50.4661	1.93103	0.965515	+	0.260346i	$0.0838367\pi$
$684$	22.9431	0.877250
$685$	0.876306	0.0334819
$686$	19.7404	0.753691
$687$	5.85455	0.223365
$688$	9.02615	0.344119
$689$	−4.94998	−0.188579
$690$	−0.104062	−0.00396156
$691$	48.7678	1.85522	0.927608	−	0.373556i	$-0.121861\pi$
$691$	48.7678	1.85522	0.927608	+	0.373556i	$0.121861\pi$
$692$	−82.5211	−3.13698
$693$	10.6366	0.404049
$694$	47.2636	1.79410
$695$	−1.08289	−0.0410763
$696$	−13.7674	−0.521851
$697$	−65.0984	−2.46578
$698$	−4.87924	−0.184682
$699$	−1.38232	−0.0522840
$700$	−57.5820	−2.17640
$701$	22.0662	0.833428	0.416714	−	0.909038i	$-0.363182\pi$
$701$	22.0662	0.833428	0.416714	+	0.909038i	$0.363182\pi$
$702$	26.5381	1.00161
$703$	−0.154541	−0.00582864
$704$	13.6191	0.513290
$705$	1.72808	0.0650831
$706$	−23.2189	−0.873856
$707$	48.1479	1.81079
$708$	−21.6573	−0.813931
$709$	24.3535	0.914614	0.457307	−	0.889309i	$-0.348814\pi$
$709$	24.3535	0.914614	0.457307	+	0.889309i	$0.348814\pi$
$710$	−4.94168	−0.185458
$711$	−23.4760	−0.880418
$712$	27.0933	1.01536
$713$	0.0932399	0.00349186
$714$	22.0442	0.824983
$715$	1.78442	0.0667336
$716$	74.5134	2.78470
$717$	−4.35669	−0.162704
$718$	−61.0074	−2.27678
$719$	40.9178	1.52598	0.762989	−	0.646412i	$-0.223731\pi$
$719$	40.9178	1.52598	0.762989	+	0.646412i	$0.223731\pi$
$720$	−1.17556	−0.0438105
$721$	1.11728	0.0416098
$722$	31.6107	1.17643
$723$	0.716379	0.0266424
$724$	44.4000	1.65011
$725$	44.1038	1.63798
$726$	−9.99959	−0.371120
$727$	22.8789	0.848531	0.424265	−	0.905538i	$-0.360532\pi$
$727$	22.8789	0.848531	0.424265	+	0.905538i	$0.360532\pi$
$728$	52.5335	1.94702
$729$	−17.1944	−0.636830
$730$	−7.48432	−0.277007
$731$	49.0154	1.81290
$732$	−10.3803	−0.383669
$733$	−37.7703	−1.39508	−0.697538	−	0.716548i	$-0.745721\pi$
$733$	−37.7703	−1.39508	−0.697538	+	0.716548i	$0.745721\pi$
$734$	15.7869	0.582705
$735$	−0.709187	−0.0261588
$736$	−1.19255	−0.0439581
$737$	−12.6900	−0.467443
$738$	−67.5586	−2.48687
$739$	−4.84983	−0.178404	−0.0892019	−	0.996014i	$-0.528432\pi$
$739$	−4.84983	−0.178404	−0.0892019	+	0.996014i	$0.528432\pi$
$740$	0.0823367	0.00302676
$741$	−4.57617	−0.168110
$742$	−8.82553	−0.323995
$743$	−9.93345	−0.364423	−0.182211	−	0.983259i	$-0.558326\pi$
$743$	−9.93345	−0.364423	−0.182211	+	0.983259i	$0.558326\pi$
$744$	−0.501049	−0.0183693
$745$	−6.31912	−0.231515
$746$	−30.9200	−1.13206
$747$	−18.6298	−0.681628
$748$	−24.6354	−0.900759
$749$	10.7968	0.394507
$750$	−3.63014	−0.132554
$751$	4.98144	0.181775	0.0908876	−	0.995861i	$-0.471030\pi$
$751$	4.98144	0.181775	0.0908876	+	0.995861i	$0.471030\pi$
$752$	−12.8401	−0.468230
$753$	−0.448417	−0.0163412
$754$	−94.4894	−3.44110
$755$	2.34414	0.0853120
$756$	30.0578	1.09319
$757$	39.4946	1.43545	0.717727	−	0.696324i	$-0.245182\pi$
$757$	39.4946	1.43545	0.717727	+	0.696324i	$0.245182\pi$
$758$	5.29452	0.192306
$759$	−0.138264	−0.00501868
$760$	2.92232	0.106004
$761$	−16.3169	−0.591488	−0.295744	−	0.955267i	$-0.595568\pi$
$761$	−16.3169	−0.591488	−0.295744	+	0.955267i	$0.595568\pi$
$762$	8.40357	0.304429
$763$	0.00770781	0.000279041 0
$764$	−9.45854	−0.342198
$765$	−6.38372	−0.230804
$766$	23.1096	0.834984
$767$	−63.2963	−2.28550
$768$	9.96742	0.359668
$769$	11.2026	0.403977	0.201989	−	0.979388i	$-0.435260\pi$
$769$	11.2026	0.403977	0.201989	+	0.979388i	$0.435260\pi$
$770$	3.18153	0.114654
$771$	2.98108	0.107361
$772$	−22.0362	−0.793101
$773$	−44.0784	−1.58539	−0.792695	−	0.609618i	$-0.791323\pi$
$773$	−44.0784	−1.58539	−0.792695	+	0.609618i	$0.791323\pi$
$774$	50.8678	1.82841
$775$	1.60511	0.0576573
$776$	−66.0167	−2.36986
$777$	−0.0978921	−0.00351186
$778$	−30.1358	−1.08042
$779$	24.0944	0.863272
$780$	2.43810	0.0872979
$781$	−6.56589	−0.234946
$782$	4.19881	0.150149
$783$	−23.0221	−0.822744
$784$	5.26946	0.188195
$785$	7.55507	0.269652
$786$	−17.0745	−0.609029
$787$	1.98422	0.0707297	0.0353648	−	0.999374i	$-0.488741\pi$
$787$	1.98422	0.0707297	0.0353648	+	0.999374i	$0.488741\pi$
$788$	35.8678	1.27774
$789$	−4.56284	−0.162441
$790$	−7.02196	−0.249830
$791$	−50.2061	−1.78512
$792$	−10.8871	−0.386856
$793$	−30.3379	−1.07733
$794$	−21.4577	−0.761505
$795$	−0.174421	−0.00618606
$796$	39.1467	1.38752
$797$	−28.2809	−1.00176	−0.500880	−	0.865517i	$-0.666990\pi$
$797$	−28.2809	−1.00176	−0.500880	+	0.865517i	$0.666990\pi$
$798$	−8.15906	−0.288827
$799$	−69.7266	−2.46675
$800$	−20.5296	−0.725832
$801$	21.9055	0.773994
$802$	13.0002	0.459052
$803$	−9.94425	−0.350925
$804$	−17.3387	−0.611488
$805$	−0.344471	−0.0121410
$806$	−3.43884	−0.121128
$807$	9.43461	0.332114
$808$	−49.2820	−1.73373
$809$	16.4780	0.579337	0.289668	−	0.957127i	$-0.406455\pi$
$809$	16.4780	0.579337	0.289668	+	0.957127i	$0.406455\pi$
$810$	−6.14199	−0.215808
$811$	−40.5809	−1.42499	−0.712494	−	0.701679i	$-0.752434\pi$
$811$	−40.5809	−1.42499	−0.712494	+	0.701679i	$0.752434\pi$
$812$	−107.021	−3.75572
$813$	−1.86614	−0.0654485
$814$	0.172212	0.00603602
$815$	−3.13711	−0.109888
$816$	−3.23710	−0.113321
$817$	−18.1417	−0.634699
$818$	26.4642	0.925299
$819$	42.4745	1.48418
$820$	−12.8371	−0.448289
$821$	50.5083	1.76275	0.881376	−	0.472416i	$-0.156618\pi$
$821$	50.5083	1.76275	0.881376	+	0.472416i	$0.156618\pi$
$822$	2.50426	0.0873460
$823$	25.7541	0.897731	0.448865	−	0.893599i	$-0.351828\pi$
$823$	25.7541	0.897731	0.448865	+	0.893599i	$0.351828\pi$
$824$	−1.14360	−0.0398392
$825$	−2.38020	−0.0828680
$826$	−112.854	−3.92668
$827$	−10.2641	−0.356917	−0.178459	−	0.983947i	$-0.557111\pi$
$827$	−10.2641	−0.356917	−0.178459	+	0.983947i	$0.557111\pi$
$828$	2.76813	0.0961993
$829$	−25.1531	−0.873605	−0.436802	−	0.899558i	$-0.643889\pi$
$829$	−25.1531	−0.873605	−0.436802	+	0.899558i	$0.643889\pi$
$830$	−5.57240	−0.193421
$831$	−6.97020	−0.241794
$832$	54.3847	1.88545
$833$	28.6152	0.991456
$834$	−3.09462	−0.107158
$835$	1.31084	0.0453635
$836$	9.11812	0.315357
$837$	−0.837865	−0.0289609
$838$	−88.6309	−3.06170
$839$	−14.5706	−0.503034	−0.251517	−	0.967853i	$-0.580929\pi$
$839$	−14.5706	−0.503034	−0.251517	+	0.967853i	$0.580929\pi$
$840$	1.85110	0.0638692
$841$	52.9710	1.82658
$842$	−15.3214	−0.528011
$843$	−3.50383	−0.120678
$844$	98.0128	3.37374
$845$	2.46223	0.0847032
$846$	−72.3617	−2.48785
$847$	−33.1012	−1.13737
$848$	1.29599	0.0445046
$849$	−1.05152	−0.0360881
$850$	72.2819	2.47925
$851$	−0.0186458	−0.000639169 0
$852$	−8.97113	−0.307346
$853$	−48.1849	−1.64982	−0.824910	−	0.565263i	$-0.808774\pi$
$853$	−48.1849	−1.64982	−0.824910	+	0.565263i	$0.808774\pi$
$854$	−54.0908	−1.85095
$855$	2.36276	0.0808048
$856$	−11.0511	−0.377720
$857$	−7.96120	−0.271949	−0.135975	−	0.990712i	$-0.543417\pi$
$857$	−7.96120	−0.271949	−0.135975	+	0.990712i	$0.543417\pi$
$858$	5.09942	0.174091
$859$	−49.9784	−1.70524	−0.852620	−	0.522531i	$-0.824988\pi$
$859$	−49.9784	−1.70524	−0.852620	+	0.522531i	$0.824988\pi$
$860$	9.66557	0.329593
$861$	15.2623	0.520137
$862$	−35.5123	−1.20955
$863$	−20.6894	−0.704274	−0.352137	−	0.935948i	$-0.614545\pi$
$863$	−20.6894	−0.704274	−0.352137	+	0.935948i	$0.614545\pi$
$864$	10.7164	0.364581
$865$	−8.49833	−0.288952
$866$	12.9073	0.438608
$867$	−10.1363	−0.344247
$868$	−3.89493	−0.132202
$869$	−9.32991	−0.316496
$870$	−3.32949	−0.112880
$871$	−50.6746	−1.71704
$872$	−0.00788935	−0.000267167 0
$873$	−53.3760	−1.80650
$874$	−1.55408	−0.0525674
$875$	−12.0167	−0.406238
$876$	−13.5871	−0.459064
$877$	16.7222	0.564668	0.282334	−	0.959316i	$-0.408891\pi$
$877$	16.7222	0.564668	0.282334	+	0.959316i	$0.408891\pi$
$878$	13.7311	0.463403
$879$	8.57532	0.289238
$880$	−0.467195	−0.0157491
$881$	−12.6555	−0.426374	−0.213187	−	0.977011i	$-0.568384\pi$
$881$	−12.6555	−0.426374	−0.213187	+	0.977011i	$0.568384\pi$
$882$	29.6966	0.999936
$883$	24.3092	0.818070	0.409035	−	0.912519i	$-0.365865\pi$
$883$	24.3092	0.818070	0.409035	+	0.912519i	$0.365865\pi$
$884$	−98.3754	−3.30872
$885$	−2.23035	−0.0749724
$886$	−28.1954	−0.947244
$887$	38.9644	1.30830	0.654148	−	0.756367i	$-0.273028\pi$
$887$	38.9644	1.30830	0.654148	+	0.756367i	$0.273028\pi$
$888$	0.100198	0.00336242
$889$	27.8180	0.932985
$890$	6.55222	0.219631
$891$	−8.16073	−0.273395
$892$	71.1368	2.38184
$893$	25.8074	0.863612
$894$	−18.0584	−0.603964
$895$	7.67367	0.256502
$896$	68.3619	2.28381
$897$	−0.552126	−0.0184349
$898$	66.7513	2.22752
$899$	2.98324	0.0994967
$900$	47.6530	1.58843
$901$	7.03774	0.234461
$902$	−26.8494	−0.893988
$903$	−11.4916	−0.382418
$904$	51.3886	1.70916
$905$	4.57248	0.151994
$906$	6.69895	0.222558
$907$	−31.5800	−1.04860	−0.524299	−	0.851534i	$-0.675673\pi$
$907$	−31.5800	−1.04860	−0.524299	+	0.851534i	$0.675673\pi$
$908$	−50.1222	−1.66336
$909$	−39.8456	−1.32159
$910$	12.7047	0.421155
$911$	−50.3164	−1.66706	−0.833528	−	0.552477i	$-0.813683\pi$
$911$	−50.3164	−1.66706	−0.833528	+	0.552477i	$0.813683\pi$
$912$	1.19813	0.0396739
$913$	−7.40392	−0.245034
$914$	0.644817	0.0213287
$915$	−1.06901	−0.0353403
$916$	−46.5826	−1.53913
$917$	−56.5211	−1.86649
$918$	−37.7311	−1.24531
$919$	−10.9756	−0.362051	−0.181026	−	0.983478i	$-0.557942\pi$
$919$	−10.9756	−0.362051	−0.181026	+	0.983478i	$0.557942\pi$
$920$	0.352585	0.0116244
$921$	−5.13174	−0.169097
$922$	−64.5489	−2.12581
$923$	−26.2193	−0.863019
$924$	5.77575	0.190008
$925$	−0.320984	−0.0105539
$926$	37.4689	1.23130
$927$	−0.924627	−0.0303687
$928$	−38.1562	−1.25254
$929$	4.81786	0.158069	0.0790345	−	0.996872i	$-0.474816\pi$
$929$	4.81786	0.158069	0.0790345	+	0.996872i	$0.474816\pi$
$930$	−0.121173	−0.00397342
$931$	−10.5911	−0.347110
$932$	10.9986	0.360271
$933$	−10.3660	−0.339369
$934$	15.5497	0.508801
$935$	−2.53704	−0.0829702
$936$	−43.4749	−1.42102
$937$	−48.8481	−1.59580	−0.797900	−	0.602790i	$-0.794056\pi$
$937$	−48.8481	−1.59580	−0.797900	+	0.602790i	$0.794056\pi$
$938$	−90.3499	−2.95003
$939$	−7.95153	−0.259488
$940$	−13.7497	−0.448466
$941$	−53.4332	−1.74187	−0.870937	−	0.491396i	$-0.836487\pi$
$941$	−53.4332	−1.74187	−0.870937	+	0.491396i	$0.836487\pi$
$942$	21.5904	0.703454
$943$	2.90705	0.0946665
$944$	16.5721	0.539377
$945$	3.09546	0.100695
$946$	20.2161	0.657281
$947$	38.0769	1.23733	0.618666	−	0.785654i	$-0.287673\pi$
$947$	38.0769	1.23733	0.618666	+	0.785654i	$0.287673\pi$
$948$	−12.7477	−0.414025
$949$	−39.7100	−1.28904
$950$	−26.7532	−0.867988
$951$	−8.66787	−0.281075
$952$	−74.6907	−2.42074
$953$	−20.0787	−0.650414	−0.325207	−	0.945643i	$-0.605434\pi$
$953$	−20.0787	−0.650414	−0.325207	+	0.945643i	$0.605434\pi$
$954$	7.30371	0.236466
$955$	−0.974076	−0.0315204
$956$	34.6647	1.12114
$957$	−4.42382	−0.143002
$958$	−13.8198	−0.446497
$959$	8.28973	0.267689
$960$	1.91634	0.0618495
$961$	−30.8914	−0.996498
$962$	0.687686	0.0221719
$963$	−8.93508	−0.287929
$964$	−5.69997	−0.183584
$965$	−2.26937	−0.0730537
$966$	−0.984409	−0.0316729
$967$	13.6347	0.438464	0.219232	−	0.975673i	$-0.429645\pi$
$967$	13.6347	0.438464	0.219232	+	0.975673i	$0.429645\pi$
$968$	33.8809	1.08897
$969$	6.50628	0.209012
$970$	−15.9654	−0.512619
$971$	−30.7116	−0.985581	−0.492790	−	0.870148i	$-0.664023\pi$
$971$	−30.7116	−0.985581	−0.492790	+	0.870148i	$0.664023\pi$
$972$	−37.7226	−1.20995
$973$	−10.2440	−0.328407
$974$	30.9241	0.990873
$975$	−9.50476	−0.304396
$976$	7.94303	0.254250
$977$	−30.2357	−0.967327	−0.483663	−	0.875254i	$-0.660694\pi$
$977$	−30.2357	−0.967327	−0.483663	+	0.875254i	$0.660694\pi$
$978$	−8.96506	−0.286671
$979$	8.70578	0.278238
$980$	5.64275	0.180251
$981$	−0.00637872	−0.000203657 0
$982$	−37.3084	−1.19056
$983$	−12.2019	−0.389181	−0.194591	−	0.980885i	$-0.562338\pi$
$983$	−12.2019	−0.389181	−0.194591	+	0.980885i	$0.562338\pi$
$984$	−15.6218	−0.498004
$985$	3.69380	0.117694
$986$	134.343	4.27834
$987$	16.3473	0.520342
$988$	36.4110	1.15839
$989$	−2.18884	−0.0696011
$990$	−2.63292	−0.0836798
$991$	−32.1730	−1.02201	−0.511005	−	0.859578i	$-0.670726\pi$
$991$	−32.1730	−1.02201	−0.511005	+	0.859578i	$0.670726\pi$
$992$	−1.38865	−0.0440897
$993$	4.99975	0.158662
$994$	−46.7475	−1.48274
$995$	4.03148	0.127806
$996$	−10.1161	−0.320542
$997$	34.1417	1.08128	0.540640	−	0.841254i	$-0.318182\pi$
$997$	34.1417	1.08128	0.540640	+	0.841254i	$0.318182\pi$
$998$	23.1318	0.732225
$999$	0.167553	0.00530115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.20	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.20	✓	186	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.34165 q^{2} -0.437788 q^{3} +3.48332 q^{4} +0.358726 q^{5} +1.02515 q^{6} +3.39349 q^{7} -3.47342 q^{8} -2.80834 q^{9} +O(q^{10})\)	\(q-2.34165 q^{2} -0.437788 q^{3} +3.48332 q^{4} +0.358726 q^{5} +1.02515 q^{6} +3.39349 q^{7} -3.47342 q^{8} -2.80834 q^{9} -0.840010 q^{10} -1.11610 q^{11} -1.52496 q^{12} -4.45688 q^{13} -7.94637 q^{14} -0.157046 q^{15} +1.16689 q^{16} +6.33668 q^{17} +6.57615 q^{18} -2.34535 q^{19} +1.24956 q^{20} -1.48563 q^{21} +2.61352 q^{22} -0.282972 q^{23} +1.52062 q^{24} -4.87132 q^{25} +10.4365 q^{26} +2.54282 q^{27} +11.8206 q^{28} -9.05378 q^{29} +0.367746 q^{30} -0.329502 q^{31} +4.21439 q^{32} +0.488616 q^{33} -14.8383 q^{34} +1.21733 q^{35} -9.78236 q^{36} +0.0658927 q^{37} +5.49199 q^{38} +1.95117 q^{39} -1.24601 q^{40} -10.2733 q^{41} +3.47882 q^{42} +7.73519 q^{43} -3.88774 q^{44} -1.00742 q^{45} +0.662621 q^{46} -11.0036 q^{47} -0.510852 q^{48} +4.51580 q^{49} +11.4069 q^{50} -2.77412 q^{51} -15.5248 q^{52} +1.11064 q^{53} -5.95439 q^{54} -0.400374 q^{55} -11.7870 q^{56} +1.02676 q^{57} +21.2008 q^{58} +14.2019 q^{59} -0.547041 q^{60} +6.80698 q^{61} +0.771579 q^{62} -9.53009 q^{63} -12.2024 q^{64} -1.59880 q^{65} -1.14417 q^{66} +11.3700 q^{67} +22.0727 q^{68} +0.123882 q^{69} -2.85057 q^{70} +5.88288 q^{71} +9.75456 q^{72} +8.90981 q^{73} -0.154298 q^{74} +2.13260 q^{75} -8.16961 q^{76} -3.78749 q^{77} -4.56895 q^{78} +8.35937 q^{79} +0.418595 q^{80} +7.31181 q^{81} +24.0564 q^{82} +6.63373 q^{83} -5.17493 q^{84} +2.27313 q^{85} -18.1131 q^{86} +3.96363 q^{87} +3.87669 q^{88} -7.80016 q^{89} +2.35904 q^{90} -15.1244 q^{91} -0.985682 q^{92} +0.144252 q^{93} +25.7667 q^{94} -0.841337 q^{95} -1.84501 q^{96} +19.0062 q^{97} -10.5744 q^{98} +3.13440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * q^99

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