LMFDB - Embedded newform 4019.2.a.a.1.9

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:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.51991 q^{2} -1.75801 q^{3} +4.34994 q^{4} +3.61499 q^{5} +4.43004 q^{6} +3.76242 q^{7} -5.92164 q^{8} +0.0906134 q^{9} +O(q^{10})$	\(q-2.51991 q^{2} -1.75801 q^{3} +4.34994 q^{4} +3.61499 q^{5} +4.43004 q^{6} +3.76242 q^{7} -5.92164 q^{8} +0.0906134 q^{9} -9.10944 q^{10} -2.65435 q^{11} -7.64726 q^{12} -1.06645 q^{13} -9.48095 q^{14} -6.35520 q^{15} +6.22210 q^{16} +1.98365 q^{17} -0.228337 q^{18} -5.79589 q^{19} +15.7250 q^{20} -6.61438 q^{21} +6.68873 q^{22} -5.71239 q^{23} +10.4103 q^{24} +8.06815 q^{25} +2.68735 q^{26} +5.11474 q^{27} +16.3663 q^{28} +5.03229 q^{29} +16.0145 q^{30} +5.95576 q^{31} -3.83585 q^{32} +4.66639 q^{33} -4.99862 q^{34} +13.6011 q^{35} +0.394163 q^{36} -8.11290 q^{37} +14.6051 q^{38} +1.87483 q^{39} -21.4066 q^{40} -1.81819 q^{41} +16.6676 q^{42} -10.3126 q^{43} -11.5463 q^{44} +0.327566 q^{45} +14.3947 q^{46} +5.14571 q^{47} -10.9385 q^{48} +7.15578 q^{49} -20.3310 q^{50} -3.48729 q^{51} -4.63898 q^{52} -10.6408 q^{53} -12.8887 q^{54} -9.59546 q^{55} -22.2797 q^{56} +10.1893 q^{57} -12.6809 q^{58} +6.03247 q^{59} -27.6447 q^{60} -15.1839 q^{61} -15.0080 q^{62} +0.340925 q^{63} -2.77820 q^{64} -3.85520 q^{65} -11.7589 q^{66} -6.50744 q^{67} +8.62877 q^{68} +10.0425 q^{69} -34.2735 q^{70} +6.70982 q^{71} -0.536579 q^{72} -8.15108 q^{73} +20.4438 q^{74} -14.1839 q^{75} -25.2118 q^{76} -9.98678 q^{77} -4.72440 q^{78} +10.6938 q^{79} +22.4928 q^{80} -9.26363 q^{81} +4.58168 q^{82} +15.8767 q^{83} -28.7722 q^{84} +7.17088 q^{85} +25.9868 q^{86} -8.84683 q^{87} +15.7181 q^{88} -10.7186 q^{89} -0.825437 q^{90} -4.01242 q^{91} -24.8485 q^{92} -10.4703 q^{93} -12.9667 q^{94} -20.9521 q^{95} +6.74348 q^{96} -13.2012 q^{97} -18.0319 q^{98} -0.240520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * 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 $

$2$	−2.51991	−1.78184	−0.890922	−	0.454156i	$-0.849941\pi$
$2$	−2.51991	−1.78184	−0.890922	+	0.454156i	$0.849941\pi$
$3$	−1.75801	−1.01499	−0.507495	−	0.861655i	$-0.669428\pi$
$3$	−1.75801	−1.01499	−0.507495	+	0.861655i	$0.669428\pi$
$4$	4.34994	2.17497
$5$	3.61499	1.61667	0.808336	−	0.588721i	$-0.200368\pi$
$5$	3.61499	1.61667	0.808336	+	0.588721i	$0.200368\pi$
$6$	4.43004	1.80855
$7$	3.76242	1.42206	0.711030	−	0.703162i	$-0.248229\pi$
$7$	3.76242	1.42206	0.711030	+	0.703162i	$0.248229\pi$
$8$	−5.92164	−2.09361
$9$	0.0906134	0.0302045
$10$	−9.10944	−2.88066
$11$	−2.65435	−0.800317	−0.400159	−	0.916446i	$-0.631045\pi$
$11$	−2.65435	−0.800317	−0.400159	+	0.916446i	$0.631045\pi$
$12$	−7.64726	−2.20757
$13$	−1.06645	−0.295779	−0.147890	−	0.989004i	$-0.547248\pi$
$13$	−1.06645	−0.295779	−0.147890	+	0.989004i	$0.547248\pi$
$14$	−9.48095	−2.53389
$15$	−6.35520	−1.64091
$16$	6.22210	1.55552
$17$	1.98365	0.481106	0.240553	−	0.970636i	$-0.422671\pi$
$17$	1.98365	0.481106	0.240553	+	0.970636i	$0.422671\pi$
$18$	−0.228337	−0.0538197
$19$	−5.79589	−1.32967	−0.664835	−	0.746991i	$-0.731498\pi$
$19$	−5.79589	−1.32967	−0.664835	+	0.746991i	$0.731498\pi$
$20$	15.7250	3.51621
$21$	−6.61438	−1.44338
$22$	6.68873	1.42604
$23$	−5.71239	−1.19112	−0.595558	−	0.803313i	$-0.703069\pi$
$23$	−5.71239	−1.19112	−0.595558	+	0.803313i	$0.703069\pi$
$24$	10.4103	2.12500
$25$	8.06815	1.61363
$26$	2.68735	0.527033
$27$	5.11474	0.984333
$28$	16.3663	3.09294
$29$	5.03229	0.934472	0.467236	−	0.884133i	$-0.345250\pi$
$29$	5.03229	0.934472	0.467236	+	0.884133i	$0.345250\pi$
$30$	16.0145	2.92384
$31$	5.95576	1.06969	0.534843	−	0.844951i	$-0.320371\pi$
$31$	5.95576	1.06969	0.534843	+	0.844951i	$0.320371\pi$
$32$	−3.83585	−0.678090
$33$	4.66639	0.812314
$34$	−4.99862	−0.857257
$35$	13.6011	2.29900
$36$	0.394163	0.0656938
$37$	−8.11290	−1.33375	−0.666877	−	0.745168i	$-0.732369\pi$
$37$	−8.11290	−1.33375	−0.666877	+	0.745168i	$0.732369\pi$
$38$	14.6051	2.36926
$39$	1.87483	0.300213
$40$	−21.4066	−3.38469
$41$	−1.81819	−0.283954	−0.141977	−	0.989870i	$-0.545346\pi$
$41$	−1.81819	−0.283954	−0.141977	+	0.989870i	$0.545346\pi$
$42$	16.6676	2.57187
$43$	−10.3126	−1.57266	−0.786329	−	0.617808i	$-0.788021\pi$
$43$	−10.3126	−1.57266	−0.786329	+	0.617808i	$0.788021\pi$
$44$	−11.5463	−1.74067
$45$	0.327566	0.0488307
$46$	14.3947	2.12238
$47$	5.14571	0.750579	0.375289	−	0.926908i	$-0.377543\pi$
$47$	5.14571	0.750579	0.375289	+	0.926908i	$0.377543\pi$
$48$	−10.9385	−1.57884
$49$	7.15578	1.02225
$50$	−20.3310	−2.87524
$51$	−3.48729	−0.488318
$52$	−4.63898	−0.643311
$53$	−10.6408	−1.46163	−0.730813	−	0.682578i	$-0.760859\pi$
$53$	−10.6408	−1.46163	−0.730813	+	0.682578i	$0.760859\pi$
$54$	−12.8887	−1.75393
$55$	−9.59546	−1.29385
$56$	−22.2797	−2.97724
$57$	10.1893	1.34960
$58$	−12.6809	−1.66508
$59$	6.03247	0.785361	0.392680	−	0.919675i	$-0.371548\pi$
$59$	6.03247	0.785361	0.392680	+	0.919675i	$0.371548\pi$
$60$	−27.6447	−3.56892
$61$	−15.1839	−1.94410	−0.972051	−	0.234769i	$-0.924567\pi$
$61$	−15.1839	−1.94410	−0.972051	+	0.234769i	$0.924567\pi$
$62$	−15.0080	−1.90601
$63$	0.340925	0.0429525
$64$	−2.77820	−0.347275
$65$	−3.85520	−0.478178
$66$	−11.7589	−1.44742
$67$	−6.50744	−0.795010	−0.397505	−	0.917600i	$-0.630124\pi$
$67$	−6.50744	−0.795010	−0.397505	+	0.917600i	$0.630124\pi$
$68$	8.62877	1.04639
$69$	10.0425	1.20897
$70$	−34.2735	−4.09647
$71$	6.70982	0.796309	0.398155	−	0.917318i	$-0.369651\pi$
$71$	6.70982	0.796309	0.398155	+	0.917318i	$0.369651\pi$
$72$	−0.536579	−0.0632365
$73$	−8.15108	−0.954011	−0.477006	−	0.878900i	$-0.658278\pi$
$73$	−8.15108	−0.954011	−0.477006	+	0.878900i	$0.658278\pi$
$74$	20.4438	2.37654
$75$	−14.1839	−1.63782
$76$	−25.2118	−2.89199
$77$	−9.98678	−1.13810
$78$	−4.72440	−0.534933
$79$	10.6938	1.20314	0.601572	−	0.798819i	$-0.294541\pi$
$79$	10.6938	1.20314	0.601572	+	0.798819i	$0.294541\pi$
$80$	22.4928	2.51477
$81$	−9.26363	−1.02929
$82$	4.58168	0.505962
$83$	15.8767	1.74269	0.871346	−	0.490669i	$-0.163248\pi$
$83$	15.8767	1.74269	0.871346	+	0.490669i	$0.163248\pi$
$84$	−28.7722	−3.13930
$85$	7.17088	0.777791
$86$	25.9868	2.80223
$87$	−8.84683	−0.948480
$88$	15.7181	1.67556
$89$	−10.7186	−1.13617	−0.568085	−	0.822970i	$-0.692315\pi$
$89$	−10.7186	−1.13617	−0.568085	+	0.822970i	$0.692315\pi$
$90$	−0.825437	−0.0870087
$91$	−4.01242	−0.420616
$92$	−24.8485	−2.59064
$93$	−10.4703	−1.08572
$94$	−12.9667	−1.33741
$95$	−20.9521	−2.14964
$96$	6.74348	0.688254
$97$	−13.2012	−1.34038	−0.670191	−	0.742188i	$-0.733788\pi$
$97$	−13.2012	−1.34038	−0.670191	+	0.742188i	$0.733788\pi$
$98$	−18.0319	−1.82150
$99$	−0.240520	−0.0241732
$100$	35.0960	3.50960
$101$	−10.2347	−1.01839	−0.509193	−	0.860652i	$-0.670056\pi$
$101$	−10.2347	−1.01839	−0.509193	+	0.860652i	$0.670056\pi$
$102$	8.78765	0.870107
$103$	13.2264	1.30323	0.651616	−	0.758549i	$-0.274091\pi$
$103$	13.2264	1.30323	0.651616	+	0.758549i	$0.274091\pi$
$104$	6.31511	0.619248
$105$	−23.9109	−2.33347
$106$	26.8138	2.60439
$107$	−8.41067	−0.813090	−0.406545	−	0.913631i	$-0.633267\pi$
$107$	−8.41067	−0.813090	−0.406545	+	0.913631i	$0.633267\pi$
$108$	22.2488	2.14089
$109$	−5.22256	−0.500230	−0.250115	−	0.968216i	$-0.580468\pi$
$109$	−5.22256	−0.500230	−0.250115	+	0.968216i	$0.580468\pi$
$110$	24.1797	2.30544
$111$	14.2626	1.35375
$112$	23.4101	2.21205
$113$	14.5033	1.36435	0.682176	−	0.731188i	$-0.261034\pi$
$113$	14.5033	1.36435	0.682176	+	0.731188i	$0.261034\pi$
$114$	−25.6760	−2.40478
$115$	−20.6502	−1.92564
$116$	21.8901	2.03245
$117$	−0.0966344	−0.00893385
$118$	−15.2013	−1.39939
$119$	7.46333	0.684162
$120$	37.6332	3.43542
$121$	−3.95441	−0.359492
$122$	38.2621	3.46409
$123$	3.19641	0.288211
$124$	25.9072	2.32654
$125$	11.0913	0.992037
$126$	−0.859101	−0.0765348
$127$	16.4431	1.45909	0.729545	−	0.683933i	$-0.239732\pi$
$127$	16.4431	1.45909	0.729545	+	0.683933i	$0.239732\pi$
$128$	14.6725	1.29688
$129$	18.1297	1.59623
$130$	9.71474	0.852039
$131$	−3.81990	−0.333746	−0.166873	−	0.985978i	$-0.553367\pi$
$131$	−3.81990	−0.333746	−0.166873	+	0.985978i	$0.553367\pi$
$132$	20.2985	1.76676
$133$	−21.8066	−1.89087
$134$	16.3982	1.41659
$135$	18.4897	1.59134
$136$	−11.7465	−1.00725
$137$	−7.44842	−0.636362	−0.318181	−	0.948030i	$-0.603072\pi$
$137$	−7.44842	−0.636362	−0.318181	+	0.948030i	$0.603072\pi$
$138$	−25.3061	−2.15420
$139$	−17.0724	−1.44806	−0.724032	−	0.689766i	$-0.757713\pi$
$139$	−17.0724	−1.44806	−0.724032	+	0.689766i	$0.757713\pi$
$140$	59.1639	5.00027
$141$	−9.04623	−0.761830
$142$	−16.9081	−1.41890
$143$	2.83073	0.236717
$144$	0.563806	0.0469838
$145$	18.1917	1.51074
$146$	20.5400	1.69990
$147$	−12.5800	−1.03758
$148$	−35.2906	−2.90087
$149$	−9.28734	−0.760848	−0.380424	−	0.924812i	$-0.624222\pi$
$149$	−9.28734	−0.760848	−0.380424	+	0.924812i	$0.624222\pi$
$150$	35.7422	2.91834
$151$	−17.5588	−1.42892	−0.714459	−	0.699677i	$-0.753327\pi$
$151$	−17.5588	−1.42892	−0.714459	+	0.699677i	$0.753327\pi$
$152$	34.3212	2.78381
$153$	0.179745	0.0145316
$154$	25.1658	2.02792
$155$	21.5300	1.72933
$156$	8.15540	0.652954
$157$	−7.08032	−0.565071	−0.282536	−	0.959257i	$-0.591176\pi$
$157$	−7.08032	−0.565071	−0.282536	+	0.959257i	$0.591176\pi$
$158$	−26.9473	−2.14382
$159$	18.7067	1.48354
$160$	−13.8666	−1.09625
$161$	−21.4924	−1.69384
$162$	23.3435	1.83404
$163$	10.8189	0.847398	0.423699	−	0.905803i	$-0.360731\pi$
$163$	10.8189	0.847398	0.423699	+	0.905803i	$0.360731\pi$
$164$	−7.90904	−0.617592
$165$	16.8689	1.31325
$166$	−40.0078	−3.10521
$167$	−12.5701	−0.972702	−0.486351	−	0.873764i	$-0.661672\pi$
$167$	−12.5701	−0.972702	−0.486351	+	0.873764i	$0.661672\pi$
$168$	39.1679	3.02187
$169$	−11.8627	−0.912515
$170$	−18.0700	−1.38590
$171$	−0.525186	−0.0401619
$172$	−44.8592	−3.42049
$173$	−1.97257	−0.149972	−0.0749859	−	0.997185i	$-0.523891\pi$
$173$	−1.97257	−0.149972	−0.0749859	+	0.997185i	$0.523891\pi$
$174$	22.2932	1.69004
$175$	30.3557	2.29468
$176$	−16.5156	−1.24491
$177$	−10.6052	−0.797133
$178$	27.0099	2.02448
$179$	0.271577	0.0202986	0.0101493	−	0.999948i	$-0.496769\pi$
$179$	0.271577	0.0202986	0.0101493	+	0.999948i	$0.496769\pi$
$180$	1.42489	0.106205
$181$	−7.03812	−0.523139	−0.261570	−	0.965185i	$-0.584240\pi$
$181$	−7.03812	−0.523139	−0.261570	+	0.965185i	$0.584240\pi$
$182$	10.1109	0.749472
$183$	26.6936	1.97324
$184$	33.8267	2.49374
$185$	−29.3281	−2.15624
$186$	26.3842	1.93459
$187$	−5.26531	−0.385038
$188$	22.3835	1.63249
$189$	19.2438	1.39978
$190$	52.7974	3.83032
$191$	−26.1842	−1.89462	−0.947310	−	0.320318i	$-0.896210\pi$
$191$	−26.1842	−1.89462	−0.947310	+	0.320318i	$0.896210\pi$
$192$	4.88411	0.352480
$193$	13.6287	0.981014	0.490507	−	0.871437i	$-0.336812\pi$
$193$	13.6287	0.981014	0.490507	+	0.871437i	$0.336812\pi$
$194$	33.2659	2.38835
$195$	6.77749	0.485346
$196$	31.1272	2.22337
$197$	0.989413	0.0704928	0.0352464	−	0.999379i	$-0.488778\pi$
$197$	0.989413	0.0704928	0.0352464	+	0.999379i	$0.488778\pi$
$198$	0.606088	0.0430728
$199$	−8.00337	−0.567344	−0.283672	−	0.958921i	$-0.591553\pi$
$199$	−8.00337	−0.567344	−0.283672	+	0.958921i	$0.591553\pi$
$200$	−47.7766	−3.37832
$201$	11.4402	0.806928
$202$	25.7904	1.81461
$203$	18.9336	1.32888
$204$	−15.1695	−1.06208
$205$	−6.57275	−0.459061
$206$	−33.3292	−2.32216
$207$	−0.517619	−0.0359770
$208$	−6.63554	−0.460092
$209$	15.3843	1.06416
$210$	60.2533	4.15787
$211$	−10.0684	−0.693137	−0.346569	−	0.938025i	$-0.612653\pi$
$211$	−10.0684	−0.693137	−0.346569	+	0.938025i	$0.612653\pi$
$212$	−46.2868	−3.17899
$213$	−11.7960	−0.808246
$214$	21.1941	1.44880
$215$	−37.2800	−2.54247
$216$	−30.2876	−2.06081
$217$	22.4080	1.52116
$218$	13.1604	0.891333
$219$	14.3297	0.968312
$220$	−41.7397	−2.81409
$221$	−2.11546	−0.142301
$222$	−35.9404	−2.41216
$223$	27.9783	1.87356	0.936782	−	0.349915i	$-0.113789\pi$
$223$	27.9783	1.87356	0.936782	+	0.349915i	$0.113789\pi$
$224$	−14.4321	−0.964284
$225$	0.731082	0.0487388
$226$	−36.5469	−2.43106
$227$	26.8537	1.78234	0.891172	−	0.453666i	$-0.149884\pi$
$227$	26.8537	1.78234	0.891172	+	0.453666i	$0.149884\pi$
$228$	44.3227	2.93534
$229$	−11.7697	−0.777763	−0.388881	−	0.921288i	$-0.627138\pi$
$229$	−11.7697	−0.777763	−0.388881	+	0.921288i	$0.627138\pi$
$230$	52.0367	3.43120
$231$	17.5569	1.15516
$232$	−29.7994	−1.95642
$233$	21.8954	1.43441	0.717207	−	0.696861i	$-0.245420\pi$
$233$	21.8954	1.43441	0.717207	+	0.696861i	$0.245420\pi$
$234$	0.243510	0.0159187
$235$	18.6017	1.21344
$236$	26.2409	1.70814
$237$	−18.7998	−1.22118
$238$	−18.8069	−1.21907
$239$	−4.47702	−0.289594	−0.144797	−	0.989461i	$-0.546253\pi$
$239$	−4.47702	−0.289594	−0.144797	+	0.989461i	$0.546253\pi$
$240$	−39.5427	−2.55247
$241$	23.4519	1.51067	0.755335	−	0.655339i	$-0.227474\pi$
$241$	23.4519	1.51067	0.755335	+	0.655339i	$0.227474\pi$
$242$	9.96476	0.640559
$243$	0.941363	0.0603885
$244$	−66.0492	−4.22836
$245$	25.8681	1.65265
$246$	−8.05467	−0.513547
$247$	6.18101	0.393289
$248$	−35.2678	−2.23951
$249$	−27.9114	−1.76881
$250$	−27.9491	−1.76766
$251$	11.6087	0.732732	0.366366	−	0.930471i	$-0.380602\pi$
$251$	11.6087	0.732732	0.366366	+	0.930471i	$0.380602\pi$
$252$	1.48300	0.0934205
$253$	15.1627	0.953270
$254$	−41.4351	−2.59987
$255$	−12.6065	−0.789450
$256$	−31.4170	−1.96356
$257$	6.31616	0.393991	0.196996	−	0.980404i	$-0.436882\pi$
$257$	6.31616	0.393991	0.196996	+	0.980404i	$0.436882\pi$
$258$	−45.6852	−2.84424
$259$	−30.5241	−1.89668
$260$	−16.7699	−1.04002
$261$	0.455993	0.0282252
$262$	9.62579	0.594683
$263$	−1.83645	−0.113240	−0.0566201	−	0.998396i	$-0.518032\pi$
$263$	−1.83645	−0.113240	−0.0566201	+	0.998396i	$0.518032\pi$
$264$	−27.6327	−1.70067
$265$	−38.4664	−2.36297
$266$	54.9506	3.36923
$267$	18.8435	1.15320
$268$	−28.3070	−1.72912
$269$	6.19551	0.377747	0.188873	−	0.982001i	$-0.439516\pi$
$269$	6.19551	0.377747	0.188873	+	0.982001i	$0.439516\pi$
$270$	−46.5925	−2.83553
$271$	−6.39358	−0.388382	−0.194191	−	0.980964i	$-0.562208\pi$
$271$	−6.39358	−0.388382	−0.194191	+	0.980964i	$0.562208\pi$
$272$	12.3425	0.748373
$273$	7.05389	0.426921
$274$	18.7693	1.13390
$275$	−21.4157	−1.29142
$276$	43.6841	2.62947
$277$	−25.7288	−1.54589	−0.772946	−	0.634471i	$-0.781218\pi$
$277$	−25.7288	−1.54589	−0.772946	+	0.634471i	$0.781218\pi$
$278$	43.0210	2.58023
$279$	0.539672	0.0323093
$280$	−80.5407	−4.81323
$281$	29.9691	1.78781	0.893904	−	0.448258i	$-0.147955\pi$
$281$	29.9691	1.78781	0.893904	+	0.448258i	$0.147955\pi$
$282$	22.7957	1.35746
$283$	15.1263	0.899167	0.449583	−	0.893238i	$-0.351572\pi$
$283$	15.1263	0.899167	0.449583	+	0.893238i	$0.351572\pi$
$284$	29.1873	1.73195
$285$	36.8341	2.18186
$286$	−7.13317	−0.421793
$287$	−6.84081	−0.403800
$288$	−0.347580	−0.0204813
$289$	−13.0651	−0.768537
$290$	−45.8413	−2.69190
$291$	23.2080	1.36047
$292$	−35.4567	−2.07495
$293$	−9.02238	−0.527093	−0.263547	−	0.964647i	$-0.584892\pi$
$293$	−9.02238	−0.527093	−0.263547	+	0.964647i	$0.584892\pi$
$294$	31.7003	1.84880
$295$	21.8073	1.26967
$296$	48.0417	2.79236
$297$	−13.5763	−0.787779
$298$	23.4032	1.35571
$299$	6.09196	0.352307
$300$	−61.6992	−3.56220
$301$	−38.8003	−2.23641
$302$	44.2467	2.54611
$303$	17.9927	1.03365
$304$	−36.0626	−2.06833
$305$	−54.8897	−3.14298
$306$	−0.452942	−0.0258930
$307$	−27.0108	−1.54159	−0.770794	−	0.637084i	$-0.780140\pi$
$307$	−27.0108	−1.54159	−0.770794	+	0.637084i	$0.780140\pi$
$308$	−43.4419	−2.47533
$309$	−23.2521	−1.32277
$310$	−54.2536	−3.08140
$311$	12.6343	0.716423	0.358211	−	0.933640i	$-0.383387\pi$
$311$	12.6343	0.716423	0.358211	+	0.933640i	$0.383387\pi$
$312$	−11.1021	−0.628530
$313$	23.1721	1.30977	0.654883	−	0.755730i	$-0.272718\pi$
$313$	23.1721	1.30977	0.654883	+	0.755730i	$0.272718\pi$
$314$	17.8418	1.00687
$315$	1.23244	0.0694402
$316$	46.5173	2.61680
$317$	−16.4840	−0.925834	−0.462917	−	0.886402i	$-0.653197\pi$
$317$	−16.4840	−0.925834	−0.462917	+	0.886402i	$0.653197\pi$
$318$	−47.1391	−2.64343
$319$	−13.3575	−0.747874
$320$	−10.0432	−0.561430
$321$	14.7861	0.825278
$322$	54.1588	3.01815
$323$	−11.4970	−0.639712
$324$	−40.2962	−2.23868
$325$	−8.60425	−0.477278
$326$	−27.2625	−1.50993
$327$	9.18133	0.507729
$328$	10.7667	0.594491
$329$	19.3603	1.06737
$330$	−42.5082	−2.34000
$331$	8.29874	0.456140	0.228070	−	0.973645i	$-0.426759\pi$
$331$	8.29874	0.456140	0.228070	+	0.973645i	$0.426759\pi$
$332$	69.0626	3.79030
$333$	−0.735138	−0.0402853
$334$	31.6755	1.73320
$335$	−23.5243	−1.28527
$336$	−41.1553	−2.24521
$337$	−11.7556	−0.640367	−0.320184	−	0.947356i	$-0.603745\pi$
$337$	−11.7556	−0.640367	−0.320184	+	0.947356i	$0.603745\pi$
$338$	29.8929	1.62596
$339$	−25.4969	−1.38480
$340$	31.1929	1.69167
$341$	−15.8087	−0.856088
$342$	1.32342	0.0715623
$343$	0.586098	0.0316463
$344$	61.0675	3.29254
$345$	36.3034	1.95451
$346$	4.97070	0.267226
$347$	−9.24769	−0.496442	−0.248221	−	0.968703i	$-0.579846\pi$
$347$	−9.24769	−0.496442	−0.248221	+	0.968703i	$0.579846\pi$
$348$	−38.4832	−2.06292
$349$	2.54396	0.136175	0.0680874	−	0.997679i	$-0.478310\pi$
$349$	2.54396	0.136175	0.0680874	+	0.997679i	$0.478310\pi$
$350$	−76.4937	−4.08876
$351$	−5.45460	−0.291145
$352$	10.1817	0.542687
$353$	30.7916	1.63887	0.819434	−	0.573173i	$-0.194288\pi$
$353$	30.7916	1.63887	0.819434	+	0.573173i	$0.194288\pi$
$354$	26.7240	1.42037
$355$	24.2559	1.28737
$356$	−46.6253	−2.47114
$357$	−13.1206	−0.694418
$358$	−0.684349	−0.0361690
$359$	−15.2789	−0.806388	−0.403194	−	0.915114i	$-0.632100\pi$
$359$	−15.2789	−0.806388	−0.403194	+	0.915114i	$0.632100\pi$
$360$	−1.93973	−0.102233
$361$	14.5924	0.768020
$362$	17.7354	0.932153
$363$	6.95191	0.364881
$364$	−17.4538	−0.914827
$365$	−29.4661	−1.54232
$366$	−67.2653	−3.51601
$367$	−33.5665	−1.75216	−0.876078	−	0.482169i	$-0.839849\pi$
$367$	−33.5665	−1.75216	−0.876078	+	0.482169i	$0.839849\pi$
$368$	−35.5431	−1.85281
$369$	−0.164753	−0.00857669
$370$	73.9040	3.84209
$371$	−40.0351	−2.07852
$372$	−45.5452	−2.36141
$373$	−20.4315	−1.05790	−0.528951	−	0.848652i	$-0.677414\pi$
$373$	−20.4315	−1.05790	−0.528951	+	0.848652i	$0.677414\pi$
$374$	13.2681	0.686078
$375$	−19.4987	−1.00691
$376$	−30.4710	−1.57142
$377$	−5.36667	−0.276397
$378$	−48.4926	−2.49419
$379$	30.2350	1.55307	0.776535	−	0.630074i	$-0.216976\pi$
$379$	30.2350	1.55307	0.776535	+	0.630074i	$0.216976\pi$
$380$	−91.1404	−4.67540
$381$	−28.9072	−1.48096
$382$	65.9817	3.37592
$383$	−27.9920	−1.43032	−0.715161	−	0.698960i	$-0.753647\pi$
$383$	−27.9920	−1.43032	−0.715161	+	0.698960i	$0.753647\pi$
$384$	−25.7945	−1.31632
$385$	−36.1021	−1.83993
$386$	−34.3430	−1.74801
$387$	−0.934461	−0.0475013
$388$	−57.4246	−2.91529
$389$	−0.219917	−0.0111502	−0.00557512	−	0.999984i	$-0.501775\pi$
$389$	−0.219917	−0.0111502	−0.00557512	+	0.999984i	$0.501775\pi$
$390$	−17.0786	−0.864811
$391$	−11.3314	−0.573053
$392$	−42.3739	−2.14021
$393$	6.71543	0.338749
$394$	−2.49323	−0.125607
$395$	38.6579	1.94509
$396$	−1.04625	−0.0525759
$397$	9.34542	0.469033	0.234517	−	0.972112i	$-0.424649\pi$
$397$	9.34542	0.469033	0.234517	+	0.972112i	$0.424649\pi$
$398$	20.1678	1.01092
$399$	38.3362	1.91921
$400$	50.2008	2.51004
$401$	−28.6021	−1.42832	−0.714161	−	0.699982i	$-0.753191\pi$
$401$	−28.6021	−1.42832	−0.714161	+	0.699982i	$0.753191\pi$
$402$	−28.8282	−1.43782
$403$	−6.35150	−0.316391
$404$	−44.5201	−2.21496
$405$	−33.4879	−1.66403
$406$	−47.7108	−2.36785
$407$	21.5345	1.06743
$408$	20.6505	1.02235
$409$	−29.0580	−1.43682	−0.718412	−	0.695617i	$-0.755131\pi$
$409$	−29.0580	−1.43682	−0.718412	+	0.695617i	$0.755131\pi$
$410$	16.5627	0.817975
$411$	13.0944	0.645901
$412$	57.5339	2.83449
$413$	22.6967	1.11683
$414$	1.30435	0.0641054
$415$	57.3940	2.81736
$416$	4.09074	0.200565
$417$	30.0136	1.46977
$418$	−38.7671	−1.89616
$419$	1.65822	0.0810093	0.0405047	−	0.999179i	$-0.487103\pi$
$419$	1.65822	0.0810093	0.0405047	+	0.999179i	$0.487103\pi$
$420$	−104.011	−5.07522
$421$	−10.0784	−0.491193	−0.245596	−	0.969372i	$-0.578984\pi$
$421$	−10.0784	−0.491193	−0.245596	+	0.969372i	$0.578984\pi$
$422$	25.3714	1.23506
$423$	0.466270	0.0226708
$424$	63.0109	3.06008
$425$	16.0044	0.776327
$426$	29.7247	1.44017
$427$	−57.1283	−2.76463
$428$	−36.5859	−1.76845
$429$	−4.97646	−0.240266
$430$	93.9421	4.53029
$431$	−13.5958	−0.654888	−0.327444	−	0.944871i	$-0.606187\pi$
$431$	−13.5958	−0.654888	−0.327444	+	0.944871i	$0.606187\pi$
$432$	31.8244	1.53115
$433$	36.0928	1.73451	0.867255	−	0.497865i	$-0.165882\pi$
$433$	36.0928	1.73451	0.867255	+	0.497865i	$0.165882\pi$
$434$	−56.4662	−2.71047
$435$	−31.9812	−1.53338
$436$	−22.7178	−1.08799
$437$	33.1084	1.58379
$438$	−36.1096	−1.72538
$439$	9.72235	0.464022	0.232011	−	0.972713i	$-0.425469\pi$
$439$	9.72235	0.464022	0.232011	+	0.972713i	$0.425469\pi$
$440$	56.8208	2.70882
$441$	0.648409	0.0308766
$442$	5.33077	0.253559
$443$	−12.0312	−0.571620	−0.285810	−	0.958286i	$-0.592263\pi$
$443$	−12.0312	−0.571620	−0.285810	+	0.958286i	$0.592263\pi$
$444$	62.0415	2.94436
$445$	−38.7476	−1.83681
$446$	−70.5027	−3.33840
$447$	16.3273	0.772253
$448$	−10.4527	−0.493845
$449$	0.345502	0.0163052	0.00815262	−	0.999967i	$-0.497405\pi$
$449$	0.345502	0.0163052	0.00815262	+	0.999967i	$0.497405\pi$
$450$	−1.84226	−0.0868450
$451$	4.82613	0.227254
$452$	63.0883	2.96742
$453$	30.8687	1.45034
$454$	−67.6689	−3.17586
$455$	−14.5048	−0.679998
$456$	−60.3371	−2.82554
$457$	2.68464	0.125582	0.0627911	−	0.998027i	$-0.480000\pi$
$457$	2.68464	0.125582	0.0627911	+	0.998027i	$0.480000\pi$
$458$	29.6585	1.38585
$459$	10.1459	0.473569
$460$	−89.8272	−4.18822
$461$	−9.16814	−0.427003	−0.213501	−	0.976943i	$-0.568487\pi$
$461$	−9.16814	−0.427003	−0.213501	+	0.976943i	$0.568487\pi$
$462$	−44.2418	−2.05831
$463$	−7.65934	−0.355960	−0.177980	−	0.984034i	$-0.556956\pi$
$463$	−7.65934	−0.355960	−0.177980	+	0.984034i	$0.556956\pi$
$464$	31.3114	1.45359
$465$	−37.8501	−1.75525
$466$	−55.1743	−2.55590
$467$	12.0380	0.557051	0.278525	−	0.960429i	$-0.410154\pi$
$467$	12.0380	0.557051	0.278525	+	0.960429i	$0.410154\pi$
$468$	−0.420354	−0.0194309
$469$	−24.4837	−1.13055
$470$	−46.8745	−2.16216
$471$	12.4473	0.573541
$472$	−35.7221	−1.64424
$473$	27.3733	1.25863
$474$	47.3738	2.17595
$475$	−46.7621	−2.14559
$476$	32.4650	1.48803
$477$	−0.964199	−0.0441476
$478$	11.2817	0.516012
$479$	7.31953	0.334438	0.167219	−	0.985920i	$-0.446521\pi$
$479$	7.31953	0.334438	0.167219	+	0.985920i	$0.446521\pi$
$480$	24.3776	1.11268
$481$	8.65198	0.394496
$482$	−59.0967	−2.69178
$483$	37.7839	1.71923
$484$	−17.2015	−0.781884
$485$	−47.7223	−2.16696
$486$	−2.37215	−0.107603
$487$	−7.16613	−0.324728	−0.162364	−	0.986731i	$-0.551912\pi$
$487$	−7.16613	−0.324728	−0.162364	+	0.986731i	$0.551912\pi$
$488$	89.9137	4.07020
$489$	−19.0197	−0.860101
$490$	−65.1851	−2.94476
$491$	−35.0979	−1.58394	−0.791972	−	0.610557i	$-0.790946\pi$
$491$	−35.0979	−1.58394	−0.791972	+	0.610557i	$0.790946\pi$
$492$	13.9042	0.626850
$493$	9.98231	0.449581
$494$	−15.5756	−0.700779
$495$	−0.869477	−0.0390801
$496$	37.0573	1.66392
$497$	25.2451	1.13240
$498$	70.3342	3.15175
$499$	16.7820	0.751266	0.375633	−	0.926769i	$-0.377425\pi$
$499$	16.7820	0.751266	0.375633	+	0.926769i	$0.377425\pi$
$500$	48.2466	2.15765
$501$	22.0984	0.987283
$502$	−29.2528	−1.30561
$503$	25.9901	1.15884	0.579421	−	0.815029i	$-0.303279\pi$
$503$	25.9901	1.15884	0.579421	+	0.815029i	$0.303279\pi$
$504$	−2.01884	−0.0899261
$505$	−36.9981	−1.64640
$506$	−38.2086	−1.69858
$507$	20.8548	0.926193
$508$	71.5265	3.17348
$509$	−9.84835	−0.436521	−0.218260	−	0.975891i	$-0.570038\pi$
$509$	−9.84835	−0.436521	−0.218260	+	0.975891i	$0.570038\pi$
$510$	31.7673	1.40668
$511$	−30.6677	−1.35666
$512$	49.8229	2.20188
$513$	−29.6445	−1.30884
$514$	−15.9161	−0.702031
$515$	47.8132	2.10690
$516$	78.8632	3.47176
$517$	−13.6585	−0.600701
$518$	76.9180	3.37958
$519$	3.46781	0.152220
$520$	22.8291	1.00112
$521$	24.4008	1.06902	0.534510	−	0.845162i	$-0.320496\pi$
$521$	24.4008	1.06902	0.534510	+	0.845162i	$0.320496\pi$
$522$	−1.14906	−0.0502930
$523$	12.1948	0.533241	0.266620	−	0.963802i	$-0.414093\pi$
$523$	12.1948	0.533241	0.266620	+	0.963802i	$0.414093\pi$
$524$	−16.6163	−0.725887
$525$	−53.3658	−2.32907
$526$	4.62768	0.201776
$527$	11.8142	0.514633
$528$	29.0347	1.26357
$529$	9.63138	0.418756
$530$	96.9317	4.21045
$531$	0.546622	0.0237214
$532$	−94.8573	−4.11258
$533$	1.93901	0.0839878
$534$	−47.4838	−2.05482
$535$	−30.4045	−1.31450
$536$	38.5347	1.66445
$537$	−0.477436	−0.0206029
$538$	−15.6121	−0.673086
$539$	−18.9940	−0.818128
$540$	80.4293	3.46112
$541$	4.02487	0.173043	0.0865213	−	0.996250i	$-0.472425\pi$
$541$	4.02487	0.173043	0.0865213	+	0.996250i	$0.472425\pi$
$542$	16.1112	0.692037
$543$	12.3731	0.530981
$544$	−7.60900	−0.326233
$545$	−18.8795	−0.808708
$546$	−17.7752	−0.760706
$547$	−14.4863	−0.619389	−0.309695	−	0.950836i	$-0.600227\pi$
$547$	−14.4863	−0.619389	−0.309695	+	0.950836i	$0.600227\pi$
$548$	−32.4002	−1.38407
$549$	−1.37587	−0.0587206
$550$	53.9656	2.30110
$551$	−29.1666	−1.24254
$552$	−59.4678	−2.53112
$553$	40.2345	1.71094
$554$	64.8342	2.75454
$555$	51.5591	2.18856
$556$	−74.2640	−3.14950
$557$	−1.72953	−0.0732826	−0.0366413	−	0.999328i	$-0.511666\pi$
$557$	−1.72953	−0.0732826	−0.0366413	+	0.999328i	$0.511666\pi$
$558$	−1.35992	−0.0575701
$559$	10.9979	0.465160
$560$	84.6274	3.57616
$561$	9.25650	0.390810
$562$	−75.5195	−3.18560
$563$	44.7539	1.88615	0.943076	−	0.332578i	$-0.107918\pi$
$563$	44.7539	1.88615	0.943076	+	0.332578i	$0.107918\pi$
$564$	−39.3505	−1.65696
$565$	52.4291	2.20571
$566$	−38.1170	−1.60218
$567$	−34.8536	−1.46371
$568$	−39.7331	−1.66716
$569$	7.40625	0.310486	0.155243	−	0.987876i	$-0.450384\pi$
$569$	7.40625	0.310486	0.155243	+	0.987876i	$0.450384\pi$
$570$	−92.8185	−3.88774
$571$	25.3196	1.05959	0.529796	−	0.848125i	$-0.322268\pi$
$571$	25.3196	1.05959	0.529796	+	0.848125i	$0.322268\pi$
$572$	12.3135	0.514853
$573$	46.0321	1.92302
$574$	17.2382	0.719509
$575$	−46.0884	−1.92202
$576$	−0.251742	−0.0104892
$577$	30.1390	1.25470	0.627351	−	0.778737i	$-0.284139\pi$
$577$	30.1390	1.25470	0.627351	+	0.778737i	$0.284139\pi$
$578$	32.9229	1.36941
$579$	−23.9594	−0.995719
$580$	79.1326	3.28580
$581$	59.7347	2.47821
$582$	−58.4820	−2.42415
$583$	28.2444	1.16976
$584$	48.2677	1.99733
$585$	−0.349332	−0.0144431
$586$	22.7356	0.939198
$587$	9.27583	0.382855	0.191427	−	0.981507i	$-0.438688\pi$
$587$	9.27583	0.382855	0.191427	+	0.981507i	$0.438688\pi$
$588$	−54.7221	−2.25670
$589$	−34.5189	−1.42233
$590$	−54.9524	−2.26236
$591$	−1.73940	−0.0715494
$592$	−50.4793	−2.07469
$593$	34.4843	1.41610	0.708050	−	0.706162i	$-0.249575\pi$
$593$	34.4843	1.41610	0.708050	+	0.706162i	$0.249575\pi$
$594$	34.2111	1.40370
$595$	26.9798	1.10607
$596$	−40.3994	−1.65482
$597$	14.0700	0.575848
$598$	−15.3512	−0.627757
$599$	−30.9818	−1.26588	−0.632941	−	0.774200i	$-0.718153\pi$
$599$	−30.9818	−1.26588	−0.632941	+	0.774200i	$0.718153\pi$
$600$	83.9920	3.42896
$601$	−30.8853	−1.25984	−0.629920	−	0.776660i	$-0.716912\pi$
$601$	−30.8853	−1.25984	−0.629920	+	0.776660i	$0.716912\pi$
$602$	97.7733	3.98494
$603$	−0.589661	−0.0240129
$604$	−76.3799	−3.10785
$605$	−14.2952	−0.581181
$606$	−45.3399	−1.84181
$607$	−3.79971	−0.154225	−0.0771127	−	0.997022i	$-0.524570\pi$
$607$	−3.79971	−0.154225	−0.0771127	+	0.997022i	$0.524570\pi$
$608$	22.2322	0.901635
$609$	−33.2855	−1.34880
$610$	138.317	5.60030
$611$	−5.48763	−0.222006
$612$	0.781882	0.0316057
$613$	−26.1129	−1.05469	−0.527346	−	0.849651i	$-0.676813\pi$
$613$	−26.1129	−1.05469	−0.527346	+	0.849651i	$0.676813\pi$
$614$	68.0648	2.74687
$615$	11.5550	0.465942
$616$	59.1381	2.38274
$617$	−15.6107	−0.628462	−0.314231	−	0.949347i	$-0.601747\pi$
$617$	−15.6107	−0.628462	−0.314231	+	0.949347i	$0.601747\pi$
$618$	58.5933	2.35697
$619$	22.3203	0.897130	0.448565	−	0.893750i	$-0.351935\pi$
$619$	22.3203	0.897130	0.448565	+	0.893750i	$0.351935\pi$
$620$	93.6542	3.76124
$621$	−29.2174	−1.17245
$622$	−31.8372	−1.27655
$623$	−40.3279	−1.61570
$624$	11.6654	0.466989
$625$	−0.245751	−0.00983002
$626$	−58.3916	−2.33380
$627$	−27.0459	−1.08011
$628$	−30.7990	−1.22901
$629$	−16.0932	−0.641677
$630$	−3.10564	−0.123732
$631$	−9.65728	−0.384450	−0.192225	−	0.981351i	$-0.561570\pi$
$631$	−9.65728	−0.384450	−0.192225	+	0.981351i	$0.561570\pi$
$632$	−63.3247	−2.51892
$633$	17.7004	0.703527
$634$	41.5382	1.64969
$635$	59.4416	2.35887
$636$	81.3729	3.22665
$637$	−7.63126	−0.302361
$638$	33.6596	1.33260
$639$	0.608000	0.0240521
$640$	53.0410	2.09663
$641$	−30.5757	−1.20767	−0.603833	−	0.797111i	$-0.706361\pi$
$641$	−30.5757	−1.20767	−0.603833	+	0.797111i	$0.706361\pi$
$642$	−37.2595	−1.47052
$643$	−5.58433	−0.220225	−0.110112	−	0.993919i	$-0.535121\pi$
$643$	−5.58433	−0.220225	−0.110112	+	0.993919i	$0.535121\pi$
$644$	−93.4906	−3.68405
$645$	65.5387	2.58058
$646$	28.9715	1.13987
$647$	−19.7511	−0.776497	−0.388248	−	0.921555i	$-0.626920\pi$
$647$	−19.7511	−0.776497	−0.388248	+	0.921555i	$0.626920\pi$
$648$	54.8558	2.15494
$649$	−16.0123	−0.628538
$650$	21.6819	0.850435
$651$	−39.3937	−1.54396
$652$	47.0614	1.84307
$653$	−42.6845	−1.67037	−0.835187	−	0.549966i	$-0.814641\pi$
$653$	−42.6845	−1.67037	−0.835187	+	0.549966i	$0.814641\pi$
$654$	−23.1361	−0.904694
$655$	−13.8089	−0.539558
$656$	−11.3130	−0.441698
$657$	−0.738597	−0.0288154
$658$	−48.7862	−1.90188
$659$	31.5419	1.22870	0.614348	−	0.789035i	$-0.289419\pi$
$659$	31.5419	1.22870	0.614348	+	0.789035i	$0.289419\pi$
$660$	73.3789	2.85627
$661$	18.3398	0.713337	0.356669	−	0.934231i	$-0.383913\pi$
$661$	18.3398	0.713337	0.356669	+	0.934231i	$0.383913\pi$
$662$	−20.9121	−0.812770
$663$	3.71901	0.144434
$664$	−94.0159	−3.64852
$665$	−78.8305	−3.05692
$666$	1.85248	0.0717821
$667$	−28.7464	−1.11306
$668$	−54.6791	−2.11560
$669$	−49.1862	−1.90165
$670$	59.2792	2.29015
$671$	40.3035	1.55590
$672$	25.3718	0.978738
$673$	−29.7331	−1.14613	−0.573064	−	0.819510i	$-0.694245\pi$
$673$	−29.7331	−1.14613	−0.573064	+	0.819510i	$0.694245\pi$
$674$	29.6230	1.14103
$675$	41.2665	1.58835
$676$	−51.6020	−1.98469
$677$	45.2545	1.73927	0.869636	−	0.493694i	$-0.164354\pi$
$677$	45.2545	1.73927	0.869636	+	0.493694i	$0.164354\pi$
$678$	64.2500	2.46750
$679$	−49.6686	−1.90610
$680$	−42.4634	−1.62840
$681$	−47.2092	−1.80906
$682$	39.8364	1.52542
$683$	16.3356	0.625063	0.312531	−	0.949907i	$-0.398823\pi$
$683$	16.3356	0.625063	0.312531	+	0.949907i	$0.398823\pi$
$684$	−2.28453	−0.0873510
$685$	−26.9260	−1.02879
$686$	−1.47691	−0.0563888
$687$	20.6913	0.789421
$688$	−64.1661	−2.44631
$689$	11.3478	0.432319
$690$	−91.4812	−3.48263
$691$	3.49917	0.133115	0.0665573	−	0.997783i	$-0.478798\pi$
$691$	3.49917	0.133115	0.0665573	+	0.997783i	$0.478798\pi$
$692$	−8.58056	−0.326184
$693$	−0.904936	−0.0343757
$694$	23.3033	0.884582
$695$	−61.7166	−2.34105
$696$	52.3877	1.98575
$697$	−3.60667	−0.136612
$698$	−6.41054	−0.242642
$699$	−38.4924	−1.45592
$700$	132.046	4.99085
$701$	41.5029	1.56754	0.783772	−	0.621049i	$-0.213293\pi$
$701$	41.5029	1.56754	0.783772	+	0.621049i	$0.213293\pi$
$702$	13.7451	0.518775
$703$	47.0215	1.77345
$704$	7.37432	0.277930
$705$	−32.7020	−1.23163
$706$	−77.5919	−2.92021
$707$	−38.5070	−1.44821
$708$	−46.1318	−1.73374
$709$	14.3085	0.537366	0.268683	−	0.963229i	$-0.413412\pi$
$709$	14.3085	0.537366	0.268683	+	0.963229i	$0.413412\pi$
$710$	−61.1227	−2.29389
$711$	0.969000	0.0363403
$712$	63.4717	2.37870
$713$	−34.0216	−1.27412
$714$	33.0628	1.23734
$715$	10.2330	0.382694
$716$	1.18134	0.0441489
$717$	7.87066	0.293935
$718$	38.5014	1.43686
$719$	36.6709	1.36759	0.683797	−	0.729672i	$-0.260327\pi$
$719$	36.6709	1.36759	0.683797	+	0.729672i	$0.260327\pi$
$720$	2.03815	0.0759574
$721$	49.7631	1.85328
$722$	−36.7715	−1.36849
$723$	−41.2288	−1.53332
$724$	−30.6154	−1.13781
$725$	40.6012	1.50789
$726$	−17.5182	−0.650161
$727$	0.281826	0.0104524	0.00522618	−	0.999986i	$-0.498336\pi$
$727$	0.281826	0.0104524	0.00522618	+	0.999986i	$0.498336\pi$
$728$	23.7601	0.880607
$729$	26.1360	0.967998
$730$	74.2518	2.74818
$731$	−20.4566	−0.756616
$732$	116.115	4.29175
$733$	−15.1708	−0.560347	−0.280173	−	0.959949i	$-0.590392\pi$
$733$	−15.1708	−0.560347	−0.280173	+	0.959949i	$0.590392\pi$
$734$	84.5845	3.12207
$735$	−45.4764	−1.67742
$736$	21.9119	0.807683
$737$	17.2730	0.636261
$738$	0.415162	0.0152823
$739$	−5.52677	−0.203305	−0.101653	−	0.994820i	$-0.532413\pi$
$739$	−5.52677	−0.203305	−0.101653	+	0.994820i	$0.532413\pi$
$740$	−127.575	−4.68976
$741$	−10.8663	−0.399184
$742$	100.885	3.70360
$743$	−23.7042	−0.869624	−0.434812	−	0.900521i	$-0.643185\pi$
$743$	−23.7042	−0.869624	−0.434812	+	0.900521i	$0.643185\pi$
$744$	62.0013	2.27308
$745$	−33.5736	−1.23004
$746$	51.4855	1.88502
$747$	1.43864	0.0526371
$748$	−22.9038	−0.837446
$749$	−31.6444	−1.15626
$750$	49.1349	1.79415
$751$	−27.4396	−1.00128	−0.500642	−	0.865654i	$-0.666903\pi$
$751$	−27.4396	−1.00128	−0.500642	+	0.865654i	$0.666903\pi$
$752$	32.0171	1.16754
$753$	−20.4082	−0.743715
$754$	13.5235	0.492497
$755$	−63.4750	−2.31009
$756$	83.7093	3.04448
$757$	23.0663	0.838357	0.419179	−	0.907904i	$-0.362318\pi$
$757$	23.0663	0.838357	0.419179	+	0.907904i	$0.362318\pi$
$758$	−76.1895	−2.76733
$759$	−26.6562	−0.967560
$760$	124.071	4.50052
$761$	−9.91102	−0.359274	−0.179637	−	0.983733i	$-0.557492\pi$
$761$	−9.91102	−0.359274	−0.179637	+	0.983733i	$0.557492\pi$
$762$	72.8435	2.63884
$763$	−19.6494	−0.711357
$764$	−113.900	−4.12074
$765$	0.649778	0.0234928
$766$	70.5372	2.54861
$767$	−6.43331	−0.232293
$768$	55.2315	1.99300
$769$	−54.0335	−1.94850	−0.974249	−	0.225475i	$-0.927607\pi$
$769$	−54.0335	−1.94850	−0.974249	+	0.225475i	$0.927607\pi$
$770$	90.9740	3.27848
$771$	−11.1039	−0.399897
$772$	59.2839	2.13368
$773$	−37.2758	−1.34072	−0.670358	−	0.742037i	$-0.733860\pi$
$773$	−37.2758	−1.34072	−0.670358	+	0.742037i	$0.733860\pi$
$774$	2.35476	0.0846399
$775$	48.0519	1.72608
$776$	78.1729	2.80624
$777$	53.6618	1.92511
$778$	0.554171	0.0198680
$779$	10.5381	0.377565
$780$	29.4817	1.05561
$781$	−17.8102	−0.637300
$782$	28.5541	1.02109
$783$	25.7389	0.919832
$784$	44.5240	1.59014
$785$	−25.5953	−0.913535
$786$	−16.9223	−0.603598
$787$	−11.1333	−0.396861	−0.198430	−	0.980115i	$-0.563584\pi$
$787$	−11.1333	−0.396861	−0.198430	+	0.980115i	$0.563584\pi$
$788$	4.30389	0.153320
$789$	3.22850	0.114938
$790$	−97.4144	−3.46585
$791$	54.5673	1.94019
$792$	1.42427	0.0506093
$793$	16.1929	0.575025
$794$	−23.5496	−0.835744
$795$	67.6244	2.39839
$796$	−34.8142	−1.23396
$797$	47.7109	1.69001	0.845004	−	0.534760i	$-0.179598\pi$
$797$	47.7109	1.69001	0.845004	+	0.534760i	$0.179598\pi$
$798$	−96.6039	−3.41974
$799$	10.2073	0.361108
$800$	−30.9482	−1.09419
$801$	−0.971249	−0.0343174
$802$	72.0747	2.54505
$803$	21.6358	0.763512
$804$	49.7641	1.75504
$805$	−77.6947	−2.73838
$806$	16.0052	0.563759
$807$	−10.8918	−0.383409
$808$	60.6059	2.13211
$809$	−30.2212	−1.06252	−0.531261	−	0.847208i	$-0.678282\pi$
$809$	−30.2212	−1.06252	−0.531261	+	0.847208i	$0.678282\pi$
$810$	84.3865	2.96504
$811$	−50.2424	−1.76425	−0.882124	−	0.471018i	$-0.843887\pi$
$811$	−50.2424	−1.76425	−0.882124	+	0.471018i	$0.843887\pi$
$812$	82.3599	2.89026
$813$	11.2400	0.394204
$814$	−54.2650	−1.90199
$815$	39.1100	1.36997
$816$	−21.6983	−0.759591
$817$	59.7708	2.09112
$818$	73.2235	2.56020
$819$	−0.363579	−0.0127045
$820$	−28.5911	−0.998444
$821$	3.06912	0.107113	0.0535565	−	0.998565i	$-0.482944\pi$
$821$	3.06912	0.107113	0.0535565	+	0.998565i	$0.482944\pi$
$822$	−32.9968	−1.15089
$823$	20.3906	0.710773	0.355386	−	0.934720i	$-0.384349\pi$
$823$	20.3906	0.710773	0.355386	+	0.934720i	$0.384349\pi$
$824$	−78.3217	−2.72847
$825$	37.6491	1.31077
$826$	−57.1935	−1.99002
$827$	−25.8499	−0.898888	−0.449444	−	0.893309i	$-0.648378\pi$
$827$	−25.8499	−0.898888	−0.449444	+	0.893309i	$0.648378\pi$
$828$	−2.25161	−0.0782489
$829$	−0.282666	−0.00981740	−0.00490870	−	0.999988i	$-0.501562\pi$
$829$	−0.282666	−0.00981740	−0.00490870	+	0.999988i	$0.501562\pi$
$830$	−144.628	−5.02010
$831$	45.2316	1.56907
$832$	2.96280	0.102717
$833$	14.1946	0.491813
$834$	−75.6314	−2.61890
$835$	−45.4407	−1.57254
$836$	66.9210	2.31451
$837$	30.4622	1.05293
$838$	−4.17856	−0.144346
$839$	−18.1127	−0.625319	−0.312659	−	0.949865i	$-0.601220\pi$
$839$	−18.1127	−0.625319	−0.312659	+	0.949865i	$0.601220\pi$
$840$	141.592	4.88538
$841$	−3.67609	−0.126762
$842$	25.3967	0.875229
$843$	−52.6862	−1.81461
$844$	−43.7969	−1.50755
$845$	−42.8835	−1.47524
$846$	−1.17496	−0.0403959
$847$	−14.8781	−0.511219
$848$	−66.2081	−2.27360
$849$	−26.5923	−0.912645
$850$	−40.3296	−1.38329
$851$	46.3441	1.58865
$852$	−51.3117	−1.75791
$853$	−3.39871	−0.116369	−0.0581847	−	0.998306i	$-0.518531\pi$
$853$	−3.39871	−0.116369	−0.0581847	+	0.998306i	$0.518531\pi$
$854$	143.958	4.92614
$855$	−1.89854	−0.0649287
$856$	49.8049	1.70230
$857$	16.2823	0.556192	0.278096	−	0.960553i	$-0.410297\pi$
$857$	16.2823	0.556192	0.278096	+	0.960553i	$0.410297\pi$
$858$	12.5402	0.428116
$859$	−22.3854	−0.763779	−0.381889	−	0.924208i	$-0.624726\pi$
$859$	−22.3854	−0.763779	−0.381889	+	0.924208i	$0.624726\pi$
$860$	−162.166	−5.52980
$861$	12.0262	0.409853
$862$	34.2602	1.16691
$863$	16.9565	0.577206	0.288603	−	0.957449i	$-0.406809\pi$
$863$	16.9565	0.577206	0.288603	+	0.957449i	$0.406809\pi$
$864$	−19.6194	−0.667466
$865$	−7.13082	−0.242455
$866$	−90.9506	−3.09063
$867$	22.9687	0.780057
$868$	97.4737	3.30847
$869$	−28.3851	−0.962897
$870$	80.5897	2.73225
$871$	6.93984	0.235148
$872$	30.9261	1.04729
$873$	−1.19621	−0.0404855
$874$	−83.4301	−2.82207
$875$	41.7301	1.41074
$876$	62.3334	2.10605
$877$	−55.1611	−1.86266	−0.931329	−	0.364178i	$-0.881350\pi$
$877$	−55.1611	−1.86266	−0.931329	+	0.364178i	$0.881350\pi$
$878$	−24.4994	−0.826816
$879$	15.8615	0.534994
$880$	−59.7039	−2.01262
$881$	−39.6379	−1.33544	−0.667718	−	0.744414i	$-0.732729\pi$
$881$	−39.6379	−1.33544	−0.667718	+	0.744414i	$0.732729\pi$
$882$	−1.63393	−0.0550174
$883$	−37.6542	−1.26716	−0.633582	−	0.773676i	$-0.718416\pi$
$883$	−37.6542	−1.26716	−0.633582	+	0.773676i	$0.718416\pi$
$884$	−9.20213	−0.309501
$885$	−38.3376	−1.28870
$886$	30.3176	1.01854
$887$	−29.5686	−0.992816	−0.496408	−	0.868089i	$-0.665348\pi$
$887$	−29.5686	−0.992816	−0.496408	+	0.868089i	$0.665348\pi$
$888$	−84.4579	−2.83422
$889$	61.8658	2.07491
$890$	97.6405	3.27292
$891$	24.5889	0.823760
$892$	121.704	4.07494
$893$	−29.8240	−0.998021
$894$	−41.1432	−1.37604
$895$	0.981748	0.0328162
$896$	55.2041	1.84424
$897$	−10.7098	−0.357588
$898$	−0.870633	−0.0290534
$899$	29.9711	0.999592
$900$	3.18016	0.106005
$901$	−21.1076	−0.703198
$902$	−12.1614	−0.404931
$903$	68.2115	2.26994
$904$	−85.8830	−2.85643
$905$	−25.4427	−0.845745
$906$	−77.7863	−2.58428
$907$	−40.6141	−1.34857	−0.674284	−	0.738472i	$-0.735548\pi$
$907$	−40.6141	−1.34857	−0.674284	+	0.738472i	$0.735548\pi$
$908$	116.812	3.87654
$909$	−0.927396	−0.0307598
$910$	36.5509	1.21165
$911$	9.41530	0.311943	0.155971	−	0.987762i	$-0.450149\pi$
$911$	9.41530	0.311943	0.155971	+	0.987762i	$0.450149\pi$
$912$	63.3986	2.09934
$913$	−42.1423	−1.39471
$914$	−6.76505	−0.223768
$915$	96.4969	3.19009
$916$	−51.1974	−1.69161
$917$	−14.3720	−0.474607
$918$	−25.5667	−0.843826
$919$	−2.11495	−0.0697657	−0.0348828	−	0.999391i	$-0.511106\pi$
$919$	−2.11495	−0.0697657	−0.0348828	+	0.999391i	$0.511106\pi$
$920$	122.283	4.03155
$921$	47.4854	1.56470
$922$	23.1029	0.760853
$923$	−7.15567	−0.235532
$924$	76.3715	2.51244
$925$	−65.4561	−2.15218
$926$	19.3008	0.634265
$927$	1.19849	0.0393634
$928$	−19.3031	−0.633656
$929$	14.9786	0.491430	0.245715	−	0.969342i	$-0.420977\pi$
$929$	14.9786	0.491430	0.245715	+	0.969342i	$0.420977\pi$
$930$	95.3787	3.12759
$931$	−41.4741	−1.35926
$932$	95.2435	3.11981
$933$	−22.2112	−0.727162
$934$	−30.3346	−0.992578
$935$	−19.0341	−0.622480
$936$	0.572234	0.0187040
$937$	−10.7360	−0.350728	−0.175364	−	0.984504i	$-0.556110\pi$
$937$	−10.7360	−0.350728	−0.175364	+	0.984504i	$0.556110\pi$
$938$	61.6967	2.01447
$939$	−40.7369	−1.32940
$940$	80.9162	2.63919
$941$	−1.07314	−0.0349835	−0.0174918	−	0.999847i	$-0.505568\pi$
$941$	−1.07314	−0.0349835	−0.0174918	+	0.999847i	$0.505568\pi$
$942$	−31.3661	−1.02196
$943$	10.3862	0.338222
$944$	37.5346	1.22165
$945$	69.5661	2.26299
$946$	−68.9782	−2.24268
$947$	−5.76876	−0.187460	−0.0937298	−	0.995598i	$-0.529879\pi$
$947$	−5.76876	−0.187460	−0.0937298	+	0.995598i	$0.529879\pi$
$948$	−81.7781	−2.65603
$949$	8.69269	0.282177
$950$	117.836	3.82311
$951$	28.9791	0.939712
$952$	−44.1951	−1.43237
$953$	33.9668	1.10029	0.550147	−	0.835068i	$-0.314572\pi$
$953$	33.9668	1.10029	0.550147	+	0.835068i	$0.314572\pi$
$954$	2.42969	0.0786642
$955$	−94.6555	−3.06298
$956$	−19.4748	−0.629859
$957$	23.4826	0.759085
$958$	−18.4446	−0.595917
$959$	−28.0241	−0.904944
$960$	17.6560	0.569845
$961$	4.47107	0.144228
$962$	−21.8022	−0.702931
$963$	−0.762119	−0.0245589
$964$	102.014	3.28566
$965$	49.2675	1.58598
$966$	−95.2120	−3.06340
$967$	14.8668	0.478083	0.239041	−	0.971009i	$-0.423167\pi$
$967$	14.8668	0.478083	0.239041	+	0.971009i	$0.423167\pi$
$968$	23.4166	0.752638
$969$	20.2120	0.649302
$970$	120.256	3.86119
$971$	2.10258	0.0674749	0.0337375	−	0.999431i	$-0.489259\pi$
$971$	2.10258	0.0674749	0.0337375	+	0.999431i	$0.489259\pi$
$972$	4.09487	0.131343
$973$	−64.2336	−2.05923
$974$	18.0580	0.578615
$975$	15.1264	0.484432
$976$	−94.4759	−3.02410
$977$	26.6057	0.851193	0.425597	−	0.904913i	$-0.360064\pi$
$977$	26.6057	0.851193	0.425597	+	0.904913i	$0.360064\pi$
$978$	47.9279	1.53257
$979$	28.4510	0.909296
$980$	112.524	3.59446
$981$	−0.473234	−0.0151092
$982$	88.4434	2.82234
$983$	−27.4944	−0.876935	−0.438468	−	0.898747i	$-0.644479\pi$
$983$	−27.4944	−0.876935	−0.438468	+	0.898747i	$0.644479\pi$
$984$	−18.9280	−0.603402
$985$	3.57672	0.113964
$986$	−25.1545	−0.801083
$987$	−34.0357	−1.08337
$988$	26.8870	0.855391
$989$	58.9096	1.87322
$990$	2.19100	0.0696346
$991$	28.0495	0.891021	0.445510	−	0.895277i	$-0.353022\pi$
$991$	28.0495	0.891021	0.445510	+	0.895277i	$0.353022\pi$
$992$	−22.8454	−0.725343
$993$	−14.5893	−0.462977
$994$	−63.6154	−2.01776
$995$	−28.9321	−0.917209
$996$	−121.413	−3.84712
$997$	45.0139	1.42560	0.712802	−	0.701365i	$-0.247426\pi$
$997$	45.0139	1.42560	0.712802	+	0.701365i	$0.247426\pi$
$998$	−42.2891	−1.33864
$999$	−41.4954	−1.31286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.9	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.9	✓	149	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)

\(f(q)\)	\(=\)	\(q-2.51991 q^{2} -1.75801 q^{3} +4.34994 q^{4} +3.61499 q^{5} +4.43004 q^{6} +3.76242 q^{7} -5.92164 q^{8} +0.0906134 q^{9} +O(q^{10})\)	\(q-2.51991 q^{2} -1.75801 q^{3} +4.34994 q^{4} +3.61499 q^{5} +4.43004 q^{6} +3.76242 q^{7} -5.92164 q^{8} +0.0906134 q^{9} -9.10944 q^{10} -2.65435 q^{11} -7.64726 q^{12} -1.06645 q^{13} -9.48095 q^{14} -6.35520 q^{15} +6.22210 q^{16} +1.98365 q^{17} -0.228337 q^{18} -5.79589 q^{19} +15.7250 q^{20} -6.61438 q^{21} +6.68873 q^{22} -5.71239 q^{23} +10.4103 q^{24} +8.06815 q^{25} +2.68735 q^{26} +5.11474 q^{27} +16.3663 q^{28} +5.03229 q^{29} +16.0145 q^{30} +5.95576 q^{31} -3.83585 q^{32} +4.66639 q^{33} -4.99862 q^{34} +13.6011 q^{35} +0.394163 q^{36} -8.11290 q^{37} +14.6051 q^{38} +1.87483 q^{39} -21.4066 q^{40} -1.81819 q^{41} +16.6676 q^{42} -10.3126 q^{43} -11.5463 q^{44} +0.327566 q^{45} +14.3947 q^{46} +5.14571 q^{47} -10.9385 q^{48} +7.15578 q^{49} -20.3310 q^{50} -3.48729 q^{51} -4.63898 q^{52} -10.6408 q^{53} -12.8887 q^{54} -9.59546 q^{55} -22.2797 q^{56} +10.1893 q^{57} -12.6809 q^{58} +6.03247 q^{59} -27.6447 q^{60} -15.1839 q^{61} -15.0080 q^{62} +0.340925 q^{63} -2.77820 q^{64} -3.85520 q^{65} -11.7589 q^{66} -6.50744 q^{67} +8.62877 q^{68} +10.0425 q^{69} -34.2735 q^{70} +6.70982 q^{71} -0.536579 q^{72} -8.15108 q^{73} +20.4438 q^{74} -14.1839 q^{75} -25.2118 q^{76} -9.98678 q^{77} -4.72440 q^{78} +10.6938 q^{79} +22.4928 q^{80} -9.26363 q^{81} +4.58168 q^{82} +15.8767 q^{83} -28.7722 q^{84} +7.17088 q^{85} +25.9868 q^{86} -8.84683 q^{87} +15.7181 q^{88} -10.7186 q^{89} -0.825437 q^{90} -4.01242 q^{91} -24.8485 q^{92} -10.4703 q^{93} -12.9667 q^{94} -20.9521 q^{95} +6.74348 q^{96} -13.2012 q^{97} -18.0319 q^{98} -0.240520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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