LMFDB - Embedded newform 6019.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$108$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.14163 q^{2} -1.26927 q^{3} +2.58656 q^{4} +2.68002 q^{5} +2.71830 q^{6} -0.999709 q^{7} -1.25619 q^{8} -1.38895 q^{9} +O(q^{10})$	\(q-2.14163 q^{2} -1.26927 q^{3} +2.58656 q^{4} +2.68002 q^{5} +2.71830 q^{6} -0.999709 q^{7} -1.25619 q^{8} -1.38895 q^{9} -5.73960 q^{10} +4.98528 q^{11} -3.28304 q^{12} -1.00000 q^{13} +2.14100 q^{14} -3.40167 q^{15} -2.48283 q^{16} -4.20263 q^{17} +2.97462 q^{18} -2.34524 q^{19} +6.93203 q^{20} +1.26890 q^{21} -10.6766 q^{22} +1.15596 q^{23} +1.59444 q^{24} +2.18250 q^{25} +2.14163 q^{26} +5.57077 q^{27} -2.58580 q^{28} +3.60732 q^{29} +7.28510 q^{30} -3.80668 q^{31} +7.82967 q^{32} -6.32767 q^{33} +9.00045 q^{34} -2.67924 q^{35} -3.59261 q^{36} +1.07597 q^{37} +5.02263 q^{38} +1.26927 q^{39} -3.36660 q^{40} +3.96277 q^{41} -2.71751 q^{42} +1.58411 q^{43} +12.8947 q^{44} -3.72242 q^{45} -2.47562 q^{46} +1.95607 q^{47} +3.15139 q^{48} -6.00058 q^{49} -4.67411 q^{50} +5.33427 q^{51} -2.58656 q^{52} +4.00730 q^{53} -11.9305 q^{54} +13.3607 q^{55} +1.25582 q^{56} +2.97674 q^{57} -7.72552 q^{58} -8.29874 q^{59} -8.79861 q^{60} -7.91055 q^{61} +8.15249 q^{62} +1.38855 q^{63} -11.8026 q^{64} -2.68002 q^{65} +13.5515 q^{66} -9.70831 q^{67} -10.8703 q^{68} -1.46722 q^{69} +5.73792 q^{70} +12.3016 q^{71} +1.74479 q^{72} +10.9163 q^{73} -2.30433 q^{74} -2.77019 q^{75} -6.06610 q^{76} -4.98383 q^{77} -2.71830 q^{78} -17.5605 q^{79} -6.65405 q^{80} -2.90395 q^{81} -8.48678 q^{82} +8.28510 q^{83} +3.28208 q^{84} -11.2631 q^{85} -3.39257 q^{86} -4.57866 q^{87} -6.26245 q^{88} +0.581140 q^{89} +7.97204 q^{90} +0.999709 q^{91} +2.98995 q^{92} +4.83171 q^{93} -4.18918 q^{94} -6.28529 q^{95} -9.93797 q^{96} +5.40300 q^{97} +12.8510 q^{98} -6.92433 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) $ 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * 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 $

$2$	−2.14163	−1.51436	−0.757179	−	0.653208i	$-0.773423\pi$
$2$	−2.14163	−1.51436	−0.757179	+	0.653208i	$0.773423\pi$
$3$	−1.26927	−0.732813	−0.366407	−	0.930455i	$-0.619412\pi$
$3$	−1.26927	−0.732813	−0.366407	+	0.930455i	$0.619412\pi$
$4$	2.58656	1.29328
$5$	2.68002	1.19854	0.599271	−	0.800547i	$-0.295457\pi$
$5$	2.68002	1.19854	0.599271	+	0.800547i	$0.295457\pi$
$6$	2.71830	1.10974
$7$	−0.999709	−0.377854	−0.188927	−	0.981991i	$-0.560501\pi$
$7$	−0.999709	−0.377854	−0.188927	+	0.981991i	$0.560501\pi$
$8$	−1.25619	−0.444129
$9$	−1.38895	−0.462985
$10$	−5.73960	−1.81502
$11$	4.98528	1.50312	0.751560	−	0.659665i	$-0.229302\pi$
$11$	4.98528	1.50312	0.751560	+	0.659665i	$0.229302\pi$
$12$	−3.28304	−0.947732
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.14100	0.572207
$15$	−3.40167	−0.878307
$16$	−2.48283	−0.620709
$17$	−4.20263	−1.01929	−0.509643	−	0.860386i	$-0.670223\pi$
$17$	−4.20263	−1.01929	−0.509643	+	0.860386i	$0.670223\pi$
$18$	2.97462	0.701124
$19$	−2.34524	−0.538035	−0.269018	−	0.963135i	$-0.586699\pi$
$19$	−2.34524	−0.538035	−0.269018	+	0.963135i	$0.586699\pi$
$20$	6.93203	1.55005
$21$	1.26890	0.276897
$22$	−10.6766	−2.27626
$23$	1.15596	0.241034	0.120517	−	0.992711i	$-0.461545\pi$
$23$	1.15596	0.241034	0.120517	+	0.992711i	$0.461545\pi$
$24$	1.59444	0.325464
$25$	2.18250	0.436501
$26$	2.14163	0.420007
$27$	5.57077	1.07209
$28$	−2.58580	−0.488671
$29$	3.60732	0.669862	0.334931	−	0.942243i	$-0.391287\pi$
$29$	3.60732	0.669862	0.334931	+	0.942243i	$0.391287\pi$
$30$	7.28510	1.33007
$31$	−3.80668	−0.683701	−0.341850	−	0.939754i	$-0.611054\pi$
$31$	−3.80668	−0.683701	−0.341850	+	0.939754i	$0.611054\pi$
$32$	7.82967	1.38410
$33$	−6.32767	−1.10151
$34$	9.00045	1.54356
$35$	−2.67924	−0.452874
$36$	−3.59261	−0.598768
$37$	1.07597	0.176889	0.0884444	−	0.996081i	$-0.471810\pi$
$37$	1.07597	0.176889	0.0884444	+	0.996081i	$0.471810\pi$
$38$	5.02263	0.814778
$39$	1.26927	0.203246
$40$	−3.36660	−0.532307
$41$	3.96277	0.618881	0.309441	−	0.950919i	$-0.399858\pi$
$41$	3.96277	0.618881	0.309441	+	0.950919i	$0.399858\pi$
$42$	−2.71751	−0.419321
$43$	1.58411	0.241574	0.120787	−	0.992678i	$-0.461458\pi$
$43$	1.58411	0.241574	0.120787	+	0.992678i	$0.461458\pi$
$44$	12.8947	1.94395
$45$	−3.72242	−0.554906
$46$	−2.47562	−0.365011
$47$	1.95607	0.285323	0.142661	−	0.989772i	$-0.454434\pi$
$47$	1.95607	0.285323	0.142661	+	0.989772i	$0.454434\pi$
$48$	3.15139	0.454864
$49$	−6.00058	−0.857226
$50$	−4.67411	−0.661018
$51$	5.33427	0.746947
$52$	−2.58656	−0.358691
$53$	4.00730	0.550445	0.275222	−	0.961381i	$-0.411249\pi$
$53$	4.00730	0.550445	0.275222	+	0.961381i	$0.411249\pi$
$54$	−11.9305	−1.62353
$55$	13.3607	1.80155
$56$	1.25582	0.167816
$57$	2.97674	0.394279
$58$	−7.72552	−1.01441
$59$	−8.29874	−1.08040	−0.540202	−	0.841535i	$-0.681652\pi$
$59$	−8.29874	−1.08040	−0.540202	+	0.841535i	$0.681652\pi$
$60$	−8.79861	−1.13590
$61$	−7.91055	−1.01284	−0.506421	−	0.862286i	$-0.669032\pi$
$61$	−7.91055	−1.01284	−0.506421	+	0.862286i	$0.669032\pi$
$62$	8.15249	1.03537
$63$	1.38855	0.174941
$64$	−11.8026	−1.47532
$65$	−2.68002	−0.332416
$66$	13.5515	1.66807
$67$	−9.70831	−1.18606	−0.593029	−	0.805181i	$-0.702068\pi$
$67$	−9.70831	−1.18606	−0.593029	+	0.805181i	$0.702068\pi$
$68$	−10.8703	−1.31822
$69$	−1.46722	−0.176633
$70$	5.73792	0.685813
$71$	12.3016	1.45993	0.729965	−	0.683485i	$-0.239537\pi$
$71$	12.3016	1.45993	0.729965	+	0.683485i	$0.239537\pi$
$72$	1.74479	0.205625
$73$	10.9163	1.27765	0.638826	−	0.769352i	$-0.279421\pi$
$73$	10.9163	1.27765	0.638826	+	0.769352i	$0.279421\pi$
$74$	−2.30433	−0.267873
$75$	−2.77019	−0.319874
$76$	−6.06610	−0.695830
$77$	−4.98383	−0.567960
$78$	−2.71830	−0.307787
$79$	−17.5605	−1.97571	−0.987856	−	0.155372i	$-0.950342\pi$
$79$	−17.5605	−1.97571	−0.987856	+	0.155372i	$0.950342\pi$
$80$	−6.65405	−0.743945
$81$	−2.90395	−0.322661
$82$	−8.48678	−0.937208
$83$	8.28510	0.909407	0.454704	−	0.890643i	$-0.349745\pi$
$83$	8.28510	0.909407	0.454704	+	0.890643i	$0.349745\pi$
$84$	3.28208	0.358105
$85$	−11.2631	−1.22166
$86$	−3.39257	−0.365830
$87$	−4.57866	−0.490884
$88$	−6.26245	−0.667579
$89$	0.581140	0.0616007	0.0308004	−	0.999526i	$-0.490194\pi$
$89$	0.581140	0.0616007	0.0308004	+	0.999526i	$0.490194\pi$
$90$	7.97204	0.840326
$91$	0.999709	0.104798
$92$	2.98995	0.311724
$93$	4.83171	0.501025
$94$	−4.18918	−0.432081
$95$	−6.28529	−0.644858
$96$	−9.93797	−1.01429
$97$	5.40300	0.548591	0.274296	−	0.961645i	$-0.411555\pi$
$97$	5.40300	0.548591	0.274296	+	0.961645i	$0.411555\pi$
$98$	12.8510	1.29815
$99$	−6.92433	−0.695921
$100$	5.64517	0.564517
$101$	−1.66496	−0.165670	−0.0828348	−	0.996563i	$-0.526397\pi$
$101$	−1.66496	−0.165670	−0.0828348	+	0.996563i	$0.526397\pi$
$102$	−11.4240	−1.13114
$103$	−4.97468	−0.490170	−0.245085	−	0.969502i	$-0.578816\pi$
$103$	−4.97468	−0.490170	−0.245085	+	0.969502i	$0.578816\pi$
$104$	1.25619	0.123179
$105$	3.40068	0.331872
$106$	−8.58213	−0.833570
$107$	−3.44355	−0.332901	−0.166450	−	0.986050i	$-0.553231\pi$
$107$	−3.44355	−0.332901	−0.166450	+	0.986050i	$0.553231\pi$
$108$	14.4091	1.38652
$109$	1.01732	0.0974418	0.0487209	−	0.998812i	$-0.484486\pi$
$109$	1.01732	0.0974418	0.0487209	+	0.998812i	$0.484486\pi$
$110$	−28.6135	−2.72819
$111$	−1.36570	−0.129627
$112$	2.48211	0.234537
$113$	−11.0147	−1.03617	−0.518086	−	0.855328i	$-0.673355\pi$
$113$	−11.0147	−1.03617	−0.518086	+	0.855328i	$0.673355\pi$
$114$	−6.37507	−0.597080
$115$	3.09798	0.288889
$116$	9.33053	0.866318
$117$	1.38895	0.128409
$118$	17.7728	1.63612
$119$	4.20140	0.385142
$120$	4.27313	0.390082
$121$	13.8531	1.25937
$122$	16.9414	1.53381
$123$	−5.02983	−0.453525
$124$	−9.84621	−0.884216
$125$	−7.55094	−0.675377
$126$	−2.97375	−0.264923
$127$	−19.5738	−1.73690	−0.868449	−	0.495778i	$-0.834883\pi$
$127$	−19.5738	−1.73690	−0.868449	+	0.495778i	$0.834883\pi$
$128$	9.61730	0.850057
$129$	−2.01066	−0.177029
$130$	5.73960	0.503396
$131$	−2.15006	−0.187851	−0.0939257	−	0.995579i	$-0.529942\pi$
$131$	−2.15006	−0.187851	−0.0939257	+	0.995579i	$0.529942\pi$
$132$	−16.3669	−1.42455
$133$	2.34456	0.203299
$134$	20.7916	1.79612
$135$	14.9298	1.28495
$136$	5.27928	0.452695
$137$	16.5736	1.41598	0.707991	−	0.706221i	$-0.249602\pi$
$137$	16.5736	1.41598	0.707991	+	0.706221i	$0.249602\pi$
$138$	3.14224	0.267485
$139$	−13.2765	−1.12609	−0.563047	−	0.826425i	$-0.690371\pi$
$139$	−13.2765	−1.12609	−0.563047	+	0.826425i	$0.690371\pi$
$140$	−6.93000	−0.585692
$141$	−2.48279	−0.209088
$142$	−26.3454	−2.21085
$143$	−4.98528	−0.416890
$144$	3.44854	0.287379
$145$	9.66768	0.802857
$146$	−23.3785	−1.93482
$147$	7.61636	0.628187
$148$	2.78307	0.228767
$149$	−19.7151	−1.61512	−0.807562	−	0.589783i	$-0.799213\pi$
$149$	−19.7151	−1.61512	−0.807562	+	0.589783i	$0.799213\pi$
$150$	5.93270	0.484403
$151$	6.87972	0.559864	0.279932	−	0.960020i	$-0.409688\pi$
$151$	6.87972	0.559864	0.279932	+	0.960020i	$0.409688\pi$
$152$	2.94606	0.238957
$153$	5.83725	0.471914
$154$	10.6735	0.860095
$155$	−10.2020	−0.819443
$156$	3.28304	0.262854
$157$	−12.6695	−1.01114	−0.505569	−	0.862786i	$-0.668717\pi$
$157$	−12.6695	−1.01114	−0.505569	+	0.862786i	$0.668717\pi$
$158$	37.6080	2.99193
$159$	−5.08634	−0.403373
$160$	20.9837	1.65891
$161$	−1.15562	−0.0910756
$162$	6.21916	0.488623
$163$	−14.5646	−1.14079	−0.570393	−	0.821372i	$-0.693209\pi$
$163$	−14.5646	−1.14079	−0.570393	+	0.821372i	$0.693209\pi$
$164$	10.2499	0.800386
$165$	−16.9583	−1.32020
$166$	−17.7436	−1.37717
$167$	20.0392	1.55068	0.775340	−	0.631545i	$-0.217579\pi$
$167$	20.0392	1.55068	0.775340	+	0.631545i	$0.217579\pi$
$168$	−1.59398	−0.122978
$169$	1.00000	0.0769231
$170$	24.1214	1.85003
$171$	3.25743	0.249102
$172$	4.09739	0.312423
$173$	−11.6673	−0.887050	−0.443525	−	0.896262i	$-0.646272\pi$
$173$	−11.6673	−0.887050	−0.443525	+	0.896262i	$0.646272\pi$
$174$	9.80577	0.743374
$175$	−2.18187	−0.164934
$176$	−12.3776	−0.932999
$177$	10.5333	0.791734
$178$	−1.24458	−0.0932855
$179$	14.0555	1.05056	0.525279	−	0.850930i	$-0.323961\pi$
$179$	14.0555	1.05056	0.525279	+	0.850930i	$0.323961\pi$
$180$	−9.62826	−0.717648
$181$	8.12199	0.603703	0.301851	−	0.953355i	$-0.402395\pi$
$181$	8.12199	0.603703	0.301851	+	0.953355i	$0.402395\pi$
$182$	−2.14100	−0.158702
$183$	10.0406	0.742224
$184$	−1.45210	−0.107050
$185$	2.88363	0.212009
$186$	−10.3477	−0.758731
$187$	−20.9513	−1.53211
$188$	5.05950	0.369002
$189$	−5.56914	−0.405096
$190$	13.4607	0.976545
$191$	−2.92464	−0.211620	−0.105810	−	0.994386i	$-0.533743\pi$
$191$	−2.92464	−0.211620	−0.105810	+	0.994386i	$0.533743\pi$
$192$	14.9806	1.08113
$193$	23.8904	1.71967	0.859835	−	0.510572i	$-0.170566\pi$
$193$	23.8904	1.71967	0.859835	+	0.510572i	$0.170566\pi$
$194$	−11.5712	−0.830764
$195$	3.40167	0.243599
$196$	−15.5209	−1.10863
$197$	18.6836	1.33115	0.665574	−	0.746332i	$-0.268187\pi$
$197$	18.6836	1.33115	0.665574	+	0.746332i	$0.268187\pi$
$198$	14.8293	1.05387
$199$	−18.0215	−1.27751	−0.638754	−	0.769411i	$-0.720550\pi$
$199$	−18.0215	−1.27751	−0.638754	+	0.769411i	$0.720550\pi$
$200$	−2.74163	−0.193863
$201$	12.3225	0.869159
$202$	3.56572	0.250883
$203$	−3.60627	−0.253110
$204$	13.7974	0.966010
$205$	10.6203	0.741755
$206$	10.6539	0.742293
$207$	−1.60557	−0.111595
$208$	2.48283	0.172154
$209$	−11.6917	−0.808732
$210$	−7.28297	−0.502573
$211$	−18.1423	−1.24897	−0.624483	−	0.781039i	$-0.714690\pi$
$211$	−18.1423	−1.24897	−0.624483	+	0.781039i	$0.714690\pi$
$212$	10.3651	0.711879
$213$	−15.6140	−1.06986
$214$	7.37480	0.504131
$215$	4.24544	0.289537
$216$	−6.99792	−0.476148
$217$	3.80557	0.258339
$218$	−2.17872	−0.147562
$219$	−13.8557	−0.936280
$220$	34.5581	2.32991
$221$	4.20263	0.282699
$222$	2.92482	0.196301
$223$	0.177211	0.0118669	0.00593346	−	0.999982i	$-0.498111\pi$
$223$	0.177211	0.0118669	0.00593346	+	0.999982i	$0.498111\pi$
$224$	−7.82739	−0.522990
$225$	−3.03140	−0.202093
$226$	23.5893	1.56914
$227$	29.1108	1.93215	0.966076	−	0.258257i	$-0.0831483\pi$
$227$	29.1108	1.93215	0.966076	+	0.258257i	$0.0831483\pi$
$228$	7.69952	0.509913
$229$	12.8940	0.852061	0.426031	−	0.904709i	$-0.359912\pi$
$229$	12.8940	0.852061	0.426031	+	0.904709i	$0.359912\pi$
$230$	−6.63472	−0.437481
$231$	6.32583	0.416209
$232$	−4.53146	−0.297505
$233$	−9.52911	−0.624273	−0.312136	−	0.950037i	$-0.601045\pi$
$233$	−9.52911	−0.624273	−0.312136	+	0.950037i	$0.601045\pi$
$234$	−2.97462	−0.194457
$235$	5.24232	0.341971
$236$	−21.4652	−1.39726
$237$	22.2890	1.44783
$238$	−8.99783	−0.583242
$239$	−10.9179	−0.706222	−0.353111	−	0.935581i	$-0.614876\pi$
$239$	−10.9179	−0.706222	−0.353111	+	0.935581i	$0.614876\pi$
$240$	8.44578	0.545173
$241$	−11.9107	−0.767237	−0.383619	−	0.923492i	$-0.625322\pi$
$241$	−11.9107	−0.767237	−0.383619	+	0.923492i	$0.625322\pi$
$242$	−29.6681	−1.90714
$243$	−13.0264	−0.835645
$244$	−20.4611	−1.30989
$245$	−16.0817	−1.02742
$246$	10.7720	0.686798
$247$	2.34524	0.149224
$248$	4.78191	0.303651
$249$	−10.5160	−0.666426
$250$	16.1713	1.02276
$251$	25.1095	1.58490	0.792448	−	0.609939i	$-0.208806\pi$
$251$	25.1095	1.58490	0.792448	+	0.609939i	$0.208806\pi$
$252$	3.59156	0.226247
$253$	5.76277	0.362302
$254$	41.9198	2.63028
$255$	14.2959	0.895246
$256$	3.00846	0.188029
$257$	−18.8644	−1.17673	−0.588364	−	0.808596i	$-0.700228\pi$
$257$	−18.8644	−1.17673	−0.588364	+	0.808596i	$0.700228\pi$
$258$	4.30608	0.268085
$259$	−1.07566	−0.0668382
$260$	−6.93203	−0.429906
$261$	−5.01040	−0.310136
$262$	4.60462	0.284474
$263$	7.41681	0.457340	0.228670	−	0.973504i	$-0.426562\pi$
$263$	7.41681	0.457340	0.228670	+	0.973504i	$0.426562\pi$
$264$	7.94874	0.489211
$265$	10.7396	0.659731
$266$	−5.02116	−0.307867
$267$	−0.737623	−0.0451418
$268$	−25.1111	−1.53390
$269$	−20.5498	−1.25294	−0.626470	−	0.779445i	$-0.715501\pi$
$269$	−20.5498	−1.25294	−0.626470	+	0.779445i	$0.715501\pi$
$270$	−31.9740	−1.94587
$271$	6.58675	0.400116	0.200058	−	0.979784i	$-0.435887\pi$
$271$	6.58675	0.400116	0.200058	+	0.979784i	$0.435887\pi$
$272$	10.4344	0.632680
$273$	−1.26890	−0.0767973
$274$	−35.4945	−2.14430
$275$	10.8804	0.656113
$276$	−3.79505	−0.228435
$277$	13.3562	0.802497	0.401248	−	0.915969i	$-0.368576\pi$
$277$	13.3562	0.802497	0.401248	+	0.915969i	$0.368576\pi$
$278$	28.4332	1.70531
$279$	5.28731	0.316543
$280$	3.36562	0.201134
$281$	−25.0117	−1.49207	−0.746037	−	0.665904i	$-0.768046\pi$
$281$	−25.0117	−1.49207	−0.746037	+	0.665904i	$0.768046\pi$
$282$	5.31720	0.316634
$283$	27.3269	1.62441	0.812207	−	0.583369i	$-0.198266\pi$
$283$	27.3269	1.62441	0.812207	+	0.583369i	$0.198266\pi$
$284$	31.8188	1.88810
$285$	7.97773	0.472560
$286$	10.6766	0.631321
$287$	−3.96162	−0.233847
$288$	−10.8751	−0.640819
$289$	0.662067	0.0389451
$290$	−20.7045	−1.21581
$291$	−6.85786	−0.402015
$292$	28.2355	1.65236
$293$	−26.2963	−1.53625	−0.768125	−	0.640300i	$-0.778810\pi$
$293$	−26.2963	−1.53625	−0.768125	+	0.640300i	$0.778810\pi$
$294$	−16.3114	−0.951299
$295$	−22.2408	−1.29491
$296$	−1.35162	−0.0785615
$297$	27.7719	1.61149
$298$	42.2224	2.44588
$299$	−1.15596	−0.0668507
$300$	−7.16525	−0.413686
$301$	−1.58365	−0.0912799
$302$	−14.7338	−0.847834
$303$	2.11328	0.121405
$304$	5.82285	0.333963
$305$	−21.2004	−1.21393
$306$	−12.5012	−0.714647
$307$	−2.75894	−0.157461	−0.0787306	−	0.996896i	$-0.525087\pi$
$307$	−2.75894	−0.157461	−0.0787306	+	0.996896i	$0.525087\pi$
$308$	−12.8910	−0.734531
$309$	6.31421	0.359203
$310$	21.8488	1.24093
$311$	−2.04105	−0.115738	−0.0578688	−	0.998324i	$-0.518431\pi$
$311$	−2.04105	−0.115738	−0.0578688	+	0.998324i	$0.518431\pi$
$312$	−1.59444	−0.0902674
$313$	3.31670	0.187471	0.0937356	−	0.995597i	$-0.470119\pi$
$313$	3.31670	0.187471	0.0937356	+	0.995597i	$0.470119\pi$
$314$	27.1334	1.53122
$315$	3.72134	0.209674
$316$	−45.4213	−2.55515
$317$	27.1691	1.52597	0.762983	−	0.646418i	$-0.223734\pi$
$317$	27.1691	1.52597	0.762983	+	0.646418i	$0.223734\pi$
$318$	10.8930	0.610851
$319$	17.9835	1.00688
$320$	−31.6311	−1.76823
$321$	4.37080	0.243954
$322$	2.47490	0.137921
$323$	9.85617	0.548412
$324$	−7.51122	−0.417290
$325$	−2.18250	−0.121064
$326$	31.1919	1.72756
$327$	−1.29126	−0.0714066
$328$	−4.97798	−0.274863
$329$	−1.95550	−0.107810
$330$	36.3183	1.99926
$331$	−4.21982	−0.231942	−0.115971	−	0.993253i	$-0.536998\pi$
$331$	−4.21982	−0.231942	−0.115971	+	0.993253i	$0.536998\pi$
$332$	21.4299	1.17612
$333$	−1.49448	−0.0818968
$334$	−42.9164	−2.34828
$335$	−26.0185	−1.42154
$336$	−3.15047	−0.171872
$337$	−4.64781	−0.253182	−0.126591	−	0.991955i	$-0.540404\pi$
$337$	−4.64781	−0.253182	−0.126591	+	0.991955i	$0.540404\pi$
$338$	−2.14163	−0.116489
$339$	13.9806	0.759321
$340$	−29.1327	−1.57994
$341$	−18.9774	−1.02768
$342$	−6.97620	−0.377230
$343$	12.9968	0.701761
$344$	−1.98994	−0.107290
$345$	−3.93218	−0.211701
$346$	24.9870	1.34331
$347$	13.0431	0.700191	0.350095	−	0.936714i	$-0.386149\pi$
$347$	13.0431	0.700191	0.350095	+	0.936714i	$0.386149\pi$
$348$	−11.8430	−0.634850
$349$	19.4208	1.03957	0.519787	−	0.854296i	$-0.326011\pi$
$349$	19.4208	1.03957	0.519787	+	0.854296i	$0.326011\pi$
$350$	4.67274	0.249769
$351$	−5.57077	−0.297346
$352$	39.0332	2.08047
$353$	−33.5958	−1.78812	−0.894061	−	0.447945i	$-0.852156\pi$
$353$	−33.5958	−1.78812	−0.894061	+	0.447945i	$0.852156\pi$
$354$	−22.5585	−1.19897
$355$	32.9685	1.74979
$356$	1.50315	0.0796669
$357$	−5.33271	−0.282237
$358$	−30.1016	−1.59092
$359$	0.295661	0.0156044	0.00780219	−	0.999970i	$-0.497516\pi$
$359$	0.295661	0.0156044	0.00780219	+	0.999970i	$0.497516\pi$
$360$	4.67606	0.246450
$361$	−13.4998	−0.710518
$362$	−17.3943	−0.914222
$363$	−17.5833	−0.922883
$364$	2.58580	0.135533
$365$	29.2558	1.53132
$366$	−21.5033	−1.12399
$367$	−4.54975	−0.237495	−0.118747	−	0.992924i	$-0.537888\pi$
$367$	−4.54975	−0.237495	−0.118747	+	0.992924i	$0.537888\pi$
$368$	−2.87005	−0.149612
$369$	−5.50411	−0.286533
$370$	−6.17565	−0.321057
$371$	−4.00613	−0.207988
$372$	12.4975	0.647965
$373$	−4.79406	−0.248227	−0.124113	−	0.992268i	$-0.539609\pi$
$373$	−4.79406	−0.248227	−0.124113	+	0.992268i	$0.539609\pi$
$374$	44.8698	2.32016
$375$	9.58418	0.494925
$376$	−2.45719	−0.126720
$377$	−3.60732	−0.185786
$378$	11.9270	0.613460
$379$	27.5185	1.41353	0.706765	−	0.707449i	$-0.250154\pi$
$379$	27.5185	1.41353	0.706765	+	0.707449i	$0.250154\pi$
$380$	−16.2573	−0.833981
$381$	24.8445	1.27282
$382$	6.26349	0.320468
$383$	−6.54855	−0.334615	−0.167308	−	0.985905i	$-0.553507\pi$
$383$	−6.54855	−0.334615	−0.167308	+	0.985905i	$0.553507\pi$
$384$	−12.2070	−0.622933
$385$	−13.3568	−0.680724
$386$	−51.1643	−2.60419
$387$	−2.20025	−0.111845
$388$	13.9752	0.709482
$389$	−34.1179	−1.72985	−0.864924	−	0.501903i	$-0.832633\pi$
$389$	−34.1179	−1.72985	−0.864924	+	0.501903i	$0.832633\pi$
$390$	−7.28510	−0.368895
$391$	−4.85805	−0.245682
$392$	7.53785	0.380719
$393$	2.72900	0.137660
$394$	−40.0132	−2.01583
$395$	−47.0625	−2.36797
$396$	−17.9102	−0.900020
$397$	13.7482	0.690003	0.345001	−	0.938602i	$-0.387878\pi$
$397$	13.7482	0.690003	0.345001	+	0.938602i	$0.387878\pi$
$398$	38.5953	1.93461
$399$	−2.97588	−0.148980
$400$	−5.41880	−0.270940
$401$	18.4953	0.923612	0.461806	−	0.886981i	$-0.347202\pi$
$401$	18.4953	0.923612	0.461806	+	0.886981i	$0.347202\pi$
$402$	−26.3901	−1.31622
$403$	3.80668	0.189624
$404$	−4.30651	−0.214257
$405$	−7.78263	−0.386722
$406$	7.72327	0.383299
$407$	5.36403	0.265885
$408$	−6.70083	−0.331741
$409$	−7.68862	−0.380178	−0.190089	−	0.981767i	$-0.560878\pi$
$409$	−7.68862	−0.380178	−0.190089	+	0.981767i	$0.560878\pi$
$410$	−22.7447	−1.12328
$411$	−21.0364	−1.03765
$412$	−12.8673	−0.633926
$413$	8.29632	0.408235
$414$	3.43853	0.168994
$415$	22.2042	1.08996
$416$	−7.82967	−0.383881
$417$	16.8514	0.825217
$418$	25.0392	1.22471
$419$	0.773742	0.0377998	0.0188999	−	0.999821i	$-0.493984\pi$
$419$	0.773742	0.0377998	0.0188999	+	0.999821i	$0.493984\pi$
$420$	8.79605	0.429203
$421$	11.4552	0.558294	0.279147	−	0.960248i	$-0.409948\pi$
$421$	11.4552	0.558294	0.279147	+	0.960248i	$0.409948\pi$
$422$	38.8539	1.89138
$423$	−2.71690	−0.132100
$424$	−5.03392	−0.244469
$425$	−9.17225	−0.444919
$426$	33.4394	1.62014
$427$	7.90825	0.382707
$428$	−8.90694	−0.430533
$429$	6.32767	0.305503
$430$	−9.09215	−0.438462
$431$	20.4471	0.984902	0.492451	−	0.870340i	$-0.336101\pi$
$431$	20.4471	0.984902	0.492451	+	0.870340i	$0.336101\pi$
$432$	−13.8313	−0.665458
$433$	−18.9558	−0.910956	−0.455478	−	0.890247i	$-0.650532\pi$
$433$	−18.9558	−0.910956	−0.455478	+	0.890247i	$0.650532\pi$
$434$	−8.15011	−0.391218
$435$	−12.2709	−0.588344
$436$	2.63136	0.126019
$437$	−2.71100	−0.129685
$438$	29.6737	1.41786
$439$	−12.5710	−0.599983	−0.299991	−	0.953942i	$-0.596984\pi$
$439$	−12.5710	−0.599983	−0.299991	+	0.953942i	$0.596984\pi$
$440$	−16.7835	−0.800121
$441$	8.33453	0.396883
$442$	−9.00045	−0.428108
$443$	22.6978	1.07841	0.539203	−	0.842176i	$-0.318726\pi$
$443$	22.6978	1.07841	0.539203	+	0.842176i	$0.318726\pi$
$444$	−3.53246	−0.167643
$445$	1.55747	0.0738310
$446$	−0.379519	−0.0179708
$447$	25.0238	1.18358
$448$	11.7991	0.557456
$449$	−38.8029	−1.83122	−0.915611	−	0.402064i	$-0.868293\pi$
$449$	−38.8029	−1.83122	−0.915611	+	0.402064i	$0.868293\pi$
$450$	6.49212	0.306041
$451$	19.7556	0.930253
$452$	−28.4901	−1.34006
$453$	−8.73222	−0.410276
$454$	−62.3444	−2.92597
$455$	2.67924	0.125605
$456$	−3.73935	−0.175111
$457$	−31.5600	−1.47631	−0.738157	−	0.674629i	$-0.764304\pi$
$457$	−31.5600	−1.47631	−0.738157	+	0.674629i	$0.764304\pi$
$458$	−27.6142	−1.29033
$459$	−23.4119	−1.09277
$460$	8.01312	0.373613
$461$	−23.7704	−1.10710	−0.553550	−	0.832816i	$-0.686727\pi$
$461$	−23.7704	−1.10710	−0.553550	+	0.832816i	$0.686727\pi$
$462$	−13.5476	−0.630289
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−8.95637	−0.415789
$465$	12.9491	0.600499
$466$	20.4078	0.945372
$467$	18.1742	0.841002	0.420501	−	0.907292i	$-0.361854\pi$
$467$	18.1742	0.841002	0.420501	+	0.907292i	$0.361854\pi$
$468$	3.59261	0.166068
$469$	9.70548	0.448157
$470$	−11.2271	−0.517866
$471$	16.0810	0.740975
$472$	10.4248	0.479839
$473$	7.89723	0.363115
$474$	−47.7347	−2.19253
$475$	−5.11850	−0.234853
$476$	10.8672	0.498096
$477$	−5.56595	−0.254848
$478$	23.3821	1.06947
$479$	−20.2342	−0.924526	−0.462263	−	0.886743i	$-0.652962\pi$
$479$	−20.2342	−0.924526	−0.462263	+	0.886743i	$0.652962\pi$
$480$	−26.6340	−1.21567
$481$	−1.07597	−0.0490602
$482$	25.5083	1.16187
$483$	1.46679	0.0667414
$484$	35.8317	1.62872
$485$	14.4801	0.657509
$486$	27.8977	1.26546
$487$	−37.6508	−1.70612	−0.853061	−	0.521811i	$-0.825257\pi$
$487$	−37.6508	−1.70612	−0.853061	+	0.521811i	$0.825257\pi$
$488$	9.93713	0.449833
$489$	18.4864	0.835984
$490$	34.4409	1.55588
$491$	22.5907	1.01950	0.509752	−	0.860322i	$-0.329737\pi$
$491$	22.5907	1.01950	0.509752	+	0.860322i	$0.329737\pi$
$492$	−13.0099	−0.586534
$493$	−15.1602	−0.682781
$494$	−5.02263	−0.225979
$495$	−18.5573	−0.834090
$496$	9.45137	0.424379
$497$	−12.2980	−0.551641
$498$	22.5214	1.00921
$499$	−24.6952	−1.10551	−0.552755	−	0.833344i	$-0.686423\pi$
$499$	−24.6952	−1.10551	−0.552755	+	0.833344i	$0.686423\pi$
$500$	−19.5309	−0.873451
$501$	−25.4351	−1.13636
$502$	−53.7751	−2.40010
$503$	4.30220	0.191826	0.0959128	−	0.995390i	$-0.469423\pi$
$503$	4.30220	0.191826	0.0959128	+	0.995390i	$0.469423\pi$
$504$	−1.74428	−0.0776963
$505$	−4.46212	−0.198562
$506$	−12.3417	−0.548655
$507$	−1.26927	−0.0563703
$508$	−50.6289	−2.24629
$509$	−7.67043	−0.339986	−0.169993	−	0.985445i	$-0.554374\pi$
$509$	−7.67043	−0.339986	−0.169993	+	0.985445i	$0.554374\pi$
$510$	−30.6165	−1.35572
$511$	−10.9131	−0.482766
$512$	−25.6776	−1.13480
$513$	−13.0648	−0.576825
$514$	40.4004	1.78199
$515$	−13.3322	−0.587489
$516$	−5.20069	−0.228948
$517$	9.75158	0.428874
$518$	2.30366	0.101217
$519$	14.8090	0.650042
$520$	3.36660	0.147635
$521$	5.24240	0.229674	0.114837	−	0.993384i	$-0.463365\pi$
$521$	5.24240	0.229674	0.114837	+	0.993384i	$0.463365\pi$
$522$	10.7304	0.469657
$523$	39.5954	1.73139	0.865693	−	0.500574i	$-0.166878\pi$
$523$	39.5954	1.73139	0.865693	+	0.500574i	$0.166878\pi$
$524$	−5.56125	−0.242944
$525$	2.76938	0.120866
$526$	−15.8840	−0.692577
$527$	15.9981	0.696887
$528$	15.7106	0.683714
$529$	−21.6638	−0.941903
$530$	−23.0003	−0.999068
$531$	11.5266	0.500210
$532$	6.06434	0.262922
$533$	−3.96277	−0.171647
$534$	1.57971	0.0683608
$535$	−9.22879	−0.398995
$536$	12.1954	0.526763
$537$	−17.8402	−0.769862
$538$	44.0099	1.89740
$539$	−29.9146	−1.28851
$540$	38.6167	1.66180
$541$	−20.9979	−0.902769	−0.451385	−	0.892330i	$-0.649070\pi$
$541$	−20.9979	−0.902769	−0.451385	+	0.892330i	$0.649070\pi$
$542$	−14.1063	−0.605919
$543$	−10.3090	−0.442401
$544$	−32.9052	−1.41080
$545$	2.72644	0.116788
$546$	2.71751	0.116299
$547$	−7.75944	−0.331770	−0.165885	−	0.986145i	$-0.553048\pi$
$547$	−7.75944	−0.331770	−0.165885	+	0.986145i	$0.553048\pi$
$548$	42.8687	1.83126
$549$	10.9874	0.468930
$550$	−23.3017	−0.993590
$551$	−8.46003	−0.360409
$552$	1.84310	0.0784477
$553$	17.5554	0.746531
$554$	−28.6040	−1.21527
$555$	−3.66010	−0.155363
$556$	−34.3403	−1.45635
$557$	−7.90723	−0.335040	−0.167520	−	0.985869i	$-0.553576\pi$
$557$	−7.90723	−0.335040	−0.167520	+	0.985869i	$0.553576\pi$
$558$	−11.3234	−0.479359
$559$	−1.58411	−0.0670007
$560$	6.65211	0.281103
$561$	26.5928	1.12275
$562$	53.5657	2.25953
$563$	−10.7445	−0.452826	−0.226413	−	0.974031i	$-0.572700\pi$
$563$	−10.7445	−0.452826	−0.226413	+	0.974031i	$0.572700\pi$
$564$	−6.42187	−0.270409
$565$	−29.5195	−1.24190
$566$	−58.5239	−2.45994
$567$	2.90310	0.121919
$568$	−15.4531	−0.648397
$569$	10.2061	0.427860	0.213930	−	0.976849i	$-0.431374\pi$
$569$	10.2061	0.427860	0.213930	+	0.976849i	$0.431374\pi$
$570$	−17.0853	−0.715625
$571$	−17.3170	−0.724693	−0.362346	−	0.932044i	$-0.618024\pi$
$571$	−17.3170	−0.724693	−0.362346	+	0.932044i	$0.618024\pi$
$572$	−12.8947	−0.539156
$573$	3.71216	0.155078
$574$	8.48430	0.354128
$575$	2.52288	0.105211
$576$	16.3932	0.683050
$577$	−14.0713	−0.585796	−0.292898	−	0.956144i	$-0.594620\pi$
$577$	−14.0713	−0.585796	−0.292898	+	0.956144i	$0.594620\pi$
$578$	−1.41790	−0.0589768
$579$	−30.3234	−1.26020
$580$	25.0060	1.03832
$581$	−8.28268	−0.343624
$582$	14.6870	0.608795
$583$	19.9775	0.827385
$584$	−13.7129	−0.567442
$585$	3.72242	0.153903
$586$	56.3169	2.32643
$587$	3.58274	0.147876	0.0739378	−	0.997263i	$-0.476443\pi$
$587$	3.58274	0.147876	0.0739378	+	0.997263i	$0.476443\pi$
$588$	19.7002	0.812421
$589$	8.92759	0.367855
$590$	47.6314	1.96095
$591$	−23.7145	−0.975483
$592$	−2.67146	−0.109796
$593$	−39.9394	−1.64011	−0.820057	−	0.572282i	$-0.806058\pi$
$593$	−39.9394	−1.64011	−0.820057	+	0.572282i	$0.806058\pi$
$594$	−59.4769	−2.44037
$595$	11.2598	0.461608
$596$	−50.9942	−2.08881
$597$	22.8741	0.936176
$598$	2.47562	0.101236
$599$	−45.3703	−1.85378	−0.926891	−	0.375331i	$-0.877529\pi$
$599$	−45.3703	−1.85378	−0.926891	+	0.375331i	$0.877529\pi$
$600$	3.47987	0.142065
$601$	−36.6776	−1.49611	−0.748055	−	0.663637i	$-0.769012\pi$
$601$	−36.6776	−1.49611	−0.748055	+	0.663637i	$0.769012\pi$
$602$	3.39158	0.138230
$603$	13.4844	0.549127
$604$	17.7948	0.724060
$605$	37.1265	1.50941
$606$	−4.52586	−0.183850
$607$	−4.12365	−0.167374	−0.0836869	−	0.996492i	$-0.526670\pi$
$607$	−4.12365	−0.167374	−0.0836869	+	0.996492i	$0.526670\pi$
$608$	−18.3625	−0.744697
$609$	4.57732	0.185483
$610$	45.4034	1.83833
$611$	−1.95607	−0.0791343
$612$	15.0984	0.610316
$613$	−37.1717	−1.50135	−0.750676	−	0.660671i	$-0.770272\pi$
$613$	−37.1717	−1.50135	−0.750676	+	0.660671i	$0.770272\pi$
$614$	5.90862	0.238453
$615$	−13.4800	−0.543568
$616$	6.26062	0.252248
$617$	−42.8425	−1.72477	−0.862387	−	0.506249i	$-0.831032\pi$
$617$	−42.8425	−1.72477	−0.862387	+	0.506249i	$0.831032\pi$
$618$	−13.5227	−0.543962
$619$	19.3446	0.777526	0.388763	−	0.921338i	$-0.372903\pi$
$619$	19.3446	0.777526	0.388763	+	0.921338i	$0.372903\pi$
$620$	−26.3880	−1.05977
$621$	6.43956	0.258411
$622$	4.37117	0.175268
$623$	−0.580970	−0.0232761
$624$	−3.15139	−0.126156
$625$	−31.1492	−1.24597
$626$	−7.10313	−0.283898
$627$	14.8399	0.592649
$628$	−32.7704	−1.30768
$629$	−4.52191	−0.180300
$630$	−7.96971	−0.317521
$631$	10.4181	0.414740	0.207370	−	0.978263i	$-0.433510\pi$
$631$	10.4181	0.414740	0.207370	+	0.978263i	$0.433510\pi$
$632$	22.0593	0.877471
$633$	23.0274	0.915259
$634$	−58.1860	−2.31086
$635$	−52.4583	−2.08174
$636$	−13.1561	−0.521674
$637$	6.00058	0.237752
$638$	−38.5139	−1.52478
$639$	−17.0863	−0.675925
$640$	25.7746	1.01883
$641$	−45.9029	−1.81306	−0.906528	−	0.422145i	$-0.861277\pi$
$641$	−45.9029	−1.81306	−0.906528	+	0.422145i	$0.861277\pi$
$642$	−9.36061	−0.369434
$643$	15.6251	0.616193	0.308097	−	0.951355i	$-0.400308\pi$
$643$	15.6251	0.616193	0.308097	+	0.951355i	$0.400308\pi$
$644$	−2.98908	−0.117786
$645$	−5.38861	−0.212176
$646$	−21.1082	−0.830492
$647$	−25.3089	−0.994994	−0.497497	−	0.867466i	$-0.665747\pi$
$647$	−25.3089	−0.994994	−0.497497	+	0.867466i	$0.665747\pi$
$648$	3.64790	0.143303
$649$	−41.3716	−1.62398
$650$	4.67411	0.183334
$651$	−4.83030	−0.189314
$652$	−37.6722	−1.47536
$653$	−16.5402	−0.647267	−0.323633	−	0.946183i	$-0.604904\pi$
$653$	−16.5402	−0.647267	−0.323633	+	0.946183i	$0.604904\pi$
$654$	2.76539	0.108135
$655$	−5.76220	−0.225148
$656$	−9.83891	−0.384145
$657$	−15.1622	−0.591533
$658$	4.18796	0.163264
$659$	26.9563	1.05007	0.525034	−	0.851081i	$-0.324053\pi$
$659$	26.9563	1.05007	0.525034	+	0.851081i	$0.324053\pi$
$660$	−43.8636	−1.70739
$661$	−11.6477	−0.453042	−0.226521	−	0.974006i	$-0.572735\pi$
$661$	−11.6477	−0.453042	−0.226521	+	0.974006i	$0.572735\pi$
$662$	9.03728	0.351244
$663$	−5.33427	−0.207166
$664$	−10.4076	−0.403894
$665$	6.28346	0.243662
$666$	3.20061	0.124021
$667$	4.16990	0.161459
$668$	51.8325	2.00546
$669$	−0.224928	−0.00869623
$670$	55.7218	2.15272
$671$	−39.4363	−1.52242
$672$	9.93507	0.383254
$673$	−18.3980	−0.709190	−0.354595	−	0.935020i	$-0.615381\pi$
$673$	−18.3980	−0.709190	−0.354595	+	0.935020i	$0.615381\pi$
$674$	9.95387	0.383409
$675$	12.1582	0.467970
$676$	2.58656	0.0994830
$677$	6.59599	0.253504	0.126752	−	0.991934i	$-0.459545\pi$
$677$	6.59599	0.253504	0.126752	+	0.991934i	$0.459545\pi$
$678$	−29.9412	−1.14988
$679$	−5.40142	−0.207288
$680$	14.1486	0.542573
$681$	−36.9495	−1.41591
$682$	40.6425	1.55628
$683$	−20.7130	−0.792561	−0.396281	−	0.918129i	$-0.629699\pi$
$683$	−20.7130	−0.792561	−0.396281	+	0.918129i	$0.629699\pi$
$684$	8.42554	0.322159
$685$	44.4177	1.69711
$686$	−27.8343	−1.06272
$687$	−16.3660	−0.624402
$688$	−3.93308	−0.149947
$689$	−4.00730	−0.152666
$690$	8.42125	0.320592
$691$	14.3143	0.544541	0.272271	−	0.962221i	$-0.412225\pi$
$691$	14.3143	0.544541	0.272271	+	0.962221i	$0.412225\pi$
$692$	−30.1782	−1.14720
$693$	6.92231	0.262957
$694$	−27.9334	−1.06034
$695$	−35.5812	−1.34967
$696$	5.75165	0.218016
$697$	−16.6541	−0.630818
$698$	−41.5922	−1.57429
$699$	12.0950	0.457475
$700$	−5.64353	−0.213305
$701$	−46.8481	−1.76943	−0.884715	−	0.466133i	$-0.845647\pi$
$701$	−46.8481	−1.76943	−0.884715	+	0.466133i	$0.845647\pi$
$702$	11.9305	0.450287
$703$	−2.52342	−0.0951725
$704$	−58.8391	−2.21758
$705$	−6.65391	−0.250601
$706$	71.9495	2.70786
$707$	1.66447	0.0625990
$708$	27.2451	1.02393
$709$	24.0278	0.902382	0.451191	−	0.892427i	$-0.350999\pi$
$709$	24.0278	0.902382	0.451191	+	0.892427i	$0.350999\pi$
$710$	−70.6061	−2.64980
$711$	24.3907	0.914724
$712$	−0.730020	−0.0273587
$713$	−4.40036	−0.164795
$714$	11.4207	0.427408
$715$	−13.3607	−0.499660
$716$	36.3554	1.35866
$717$	13.8578	0.517529
$718$	−0.633195	−0.0236306
$719$	−10.7621	−0.401357	−0.200678	−	0.979657i	$-0.564315\pi$
$719$	−10.7621	−0.401357	−0.200678	+	0.979657i	$0.564315\pi$
$720$	9.24216	0.344435
$721$	4.97323	0.185213
$722$	28.9116	1.07598
$723$	15.1179	0.562242
$724$	21.0080	0.780756
$725$	7.87299	0.292395
$726$	37.6568	1.39757
$727$	19.1990	0.712052	0.356026	−	0.934476i	$-0.384131\pi$
$727$	19.1990	0.712052	0.356026	+	0.934476i	$0.384131\pi$
$728$	−1.25582	−0.0465438
$729$	25.2459	0.935032
$730$	−62.6549	−2.31896
$731$	−6.65742	−0.246233
$732$	25.9707	0.959903
$733$	30.3036	1.11929	0.559645	−	0.828733i	$-0.310938\pi$
$733$	30.3036	1.11929	0.559645	+	0.828733i	$0.310938\pi$
$734$	9.74385	0.359652
$735$	20.4120	0.752908
$736$	9.05076	0.333615
$737$	−48.3987	−1.78279
$738$	11.7877	0.433913
$739$	−23.5109	−0.864862	−0.432431	−	0.901667i	$-0.642344\pi$
$739$	−23.5109	−0.864862	−0.432431	+	0.901667i	$0.642344\pi$
$740$	7.45867	0.274186
$741$	−2.97674	−0.109353
$742$	8.57963	0.314968
$743$	28.7470	1.05462	0.527312	−	0.849672i	$-0.323200\pi$
$743$	28.7470	1.05462	0.527312	+	0.849672i	$0.323200\pi$
$744$	−6.06953	−0.222520
$745$	−52.8369	−1.93579
$746$	10.2671	0.375904
$747$	−11.5076	−0.421042
$748$	−54.1917	−1.98145
$749$	3.44255	0.125788
$750$	−20.5257	−0.749494
$751$	−8.01252	−0.292381	−0.146190	−	0.989256i	$-0.546701\pi$
$751$	−8.01252	−0.292381	−0.146190	+	0.989256i	$0.546701\pi$
$752$	−4.85661	−0.177102
$753$	−31.8707	−1.16143
$754$	7.72552	0.281347
$755$	18.4378	0.671020
$756$	−14.4049	−0.523902
$757$	−3.73847	−0.135877	−0.0679385	−	0.997690i	$-0.521642\pi$
$757$	−3.73847	−0.135877	−0.0679385	+	0.997690i	$0.521642\pi$
$758$	−58.9343	−2.14059
$759$	−7.31451	−0.265500
$760$	7.89550	0.286400
$761$	30.7600	1.11505	0.557524	−	0.830161i	$-0.311751\pi$
$761$	30.7600	1.11505	0.557524	+	0.830161i	$0.311751\pi$
$762$	−53.2076	−1.92751
$763$	−1.01703	−0.0368188
$764$	−7.56476	−0.273683
$765$	15.6440	0.565608
$766$	14.0245	0.506727
$767$	8.29874	0.299650
$768$	−3.81854	−0.137790
$769$	−38.0363	−1.37162	−0.685811	−	0.727779i	$-0.740553\pi$
$769$	−38.0363	−1.37162	−0.685811	+	0.727779i	$0.740553\pi$
$770$	28.6052	1.03086
$771$	23.9440	0.862322
$772$	61.7939	2.22401
$773$	20.1392	0.724357	0.362179	−	0.932109i	$-0.382033\pi$
$773$	20.1392	0.724357	0.362179	+	0.932109i	$0.382033\pi$
$774$	4.71212	0.169374
$775$	−8.30810	−0.298436
$776$	−6.78717	−0.243645
$777$	1.36530	0.0489799
$778$	73.0678	2.61961
$779$	−9.29367	−0.332980
$780$	8.79861	0.315041
$781$	61.3269	2.19445
$782$	10.4041	0.372051
$783$	20.0955	0.718155
$784$	14.8985	0.532088
$785$	−33.9546	−1.21189
$786$	−5.84450	−0.208467
$787$	27.1517	0.967853	0.483927	−	0.875109i	$-0.339210\pi$
$787$	27.1517	0.967853	0.483927	+	0.875109i	$0.339210\pi$
$788$	48.3261	1.72155
$789$	−9.41394	−0.335145
$790$	100.790	3.58596
$791$	11.0115	0.391522
$792$	8.69825	0.309079
$793$	7.91055	0.280912
$794$	−29.4435	−1.04491
$795$	−13.6315	−0.483459
$796$	−46.6136	−1.65218
$797$	−25.7658	−0.912673	−0.456336	−	0.889807i	$-0.650839\pi$
$797$	−25.7658	−0.912673	−0.456336	+	0.889807i	$0.650839\pi$
$798$	6.37321	0.225609
$799$	−8.22065	−0.290826
$800$	17.0883	0.604163
$801$	−0.807176	−0.0285202
$802$	−39.6100	−1.39868
$803$	54.4206	1.92046
$804$	31.8728	1.12407
$805$	−3.09708	−0.109158
$806$	−8.15249	−0.287159
$807$	26.0832	0.918171
$808$	2.09150	0.0735787
$809$	7.24088	0.254576	0.127288	−	0.991866i	$-0.459373\pi$
$809$	7.24088	0.254576	0.127288	+	0.991866i	$0.459373\pi$
$810$	16.6675	0.585635
$811$	−43.9551	−1.54347	−0.771736	−	0.635943i	$-0.780611\pi$
$811$	−43.9551	−1.54347	−0.771736	+	0.635943i	$0.780611\pi$
$812$	−9.32782	−0.327342
$813$	−8.36036	−0.293211
$814$	−11.4877	−0.402645
$815$	−39.0334	−1.36728
$816$	−13.2441	−0.463636
$817$	−3.71512	−0.129976
$818$	16.4661	0.575725
$819$	−1.38855	−0.0485198
$820$	27.4701	0.959296
$821$	30.2176	1.05460	0.527301	−	0.849679i	$-0.323204\pi$
$821$	30.2176	1.05460	0.527301	+	0.849679i	$0.323204\pi$
$822$	45.0521	1.57137
$823$	−2.32273	−0.0809654	−0.0404827	−	0.999180i	$-0.512890\pi$
$823$	−2.32273	−0.0809654	−0.0404827	+	0.999180i	$0.512890\pi$
$824$	6.24913	0.217699
$825$	−13.8102	−0.480808
$826$	−17.7676	−0.618214
$827$	−36.3428	−1.26376	−0.631881	−	0.775065i	$-0.717717\pi$
$827$	−36.3428	−1.26376	−0.631881	+	0.775065i	$0.717717\pi$
$828$	−4.15290	−0.144323
$829$	49.7278	1.72712	0.863559	−	0.504248i	$-0.168230\pi$
$829$	49.7278	1.72712	0.863559	+	0.504248i	$0.168230\pi$
$830$	−47.5531	−1.65059
$831$	−16.9526	−0.588080
$832$	11.8026	0.409180
$833$	25.2182	0.873759
$834$	−36.0894	−1.24967
$835$	53.7054	1.85855
$836$	−30.2413	−1.04592
$837$	−21.2061	−0.732992
$838$	−1.65706	−0.0572424
$839$	−9.22564	−0.318505	−0.159252	−	0.987238i	$-0.550908\pi$
$839$	−9.22564	−0.318505	−0.159252	+	0.987238i	$0.550908\pi$
$840$	−4.27188	−0.147394
$841$	−15.9873	−0.551285
$842$	−24.5328	−0.845456
$843$	31.7466	1.09341
$844$	−46.9260	−1.61526
$845$	2.68002	0.0921955
$846$	5.81857	0.200047
$847$	−13.8490	−0.475858
$848$	−9.94946	−0.341666
$849$	−34.6852	−1.19039
$850$	19.6435	0.673767
$851$	1.24378	0.0426362
$852$	−40.3866	−1.38362
$853$	−7.90291	−0.270590	−0.135295	−	0.990805i	$-0.543198\pi$
$853$	−7.90291	−0.270590	−0.135295	+	0.990805i	$0.543198\pi$
$854$	−16.9365	−0.579555
$855$	8.72998	0.298559
$856$	4.32574	0.147851
$857$	17.9659	0.613704	0.306852	−	0.951757i	$-0.400724\pi$
$857$	17.9659	0.613704	0.306852	+	0.951757i	$0.400724\pi$
$858$	−13.5515	−0.462641
$859$	19.5492	0.667012	0.333506	−	0.942748i	$-0.391768\pi$
$859$	19.5492	0.667012	0.333506	+	0.942748i	$0.391768\pi$
$860$	10.9811	0.374452
$861$	5.02836	0.171366
$862$	−43.7900	−1.49149
$863$	−46.5262	−1.58377	−0.791885	−	0.610670i	$-0.790900\pi$
$863$	−46.5262	−1.58377	−0.791885	+	0.610670i	$0.790900\pi$
$864$	43.6173	1.48389
$865$	−31.2687	−1.06317
$866$	40.5961	1.37951
$867$	−0.840341	−0.0285395
$868$	9.84334	0.334105
$869$	−87.5442	−2.96973
$870$	26.2797	0.890964
$871$	9.70831	0.328953
$872$	−1.27795	−0.0432767
$873$	−7.50452	−0.253989
$874$	5.80594	0.196389
$875$	7.54874	0.255194
$876$	−35.8385	−1.21087
$877$	−19.4183	−0.655711	−0.327855	−	0.944728i	$-0.606326\pi$
$877$	−19.4183	−0.655711	−0.327855	+	0.944728i	$0.606326\pi$
$878$	26.9224	0.908588
$879$	33.3772	1.12578
$880$	−33.1723	−1.11824
$881$	14.9427	0.503432	0.251716	−	0.967801i	$-0.419005\pi$
$881$	14.9427	0.503432	0.251716	+	0.967801i	$0.419005\pi$
$882$	−17.8494	−0.601022
$883$	4.85666	0.163440	0.0817199	−	0.996655i	$-0.473959\pi$
$883$	4.85666	0.163440	0.0817199	+	0.996655i	$0.473959\pi$
$884$	10.8703	0.365609
$885$	28.2296	0.948926
$886$	−48.6102	−1.63309
$887$	13.8584	0.465321	0.232660	−	0.972558i	$-0.425257\pi$
$887$	13.8584	0.465321	0.232660	+	0.972558i	$0.425257\pi$
$888$	1.71557	0.0575709
$889$	19.5681	0.656294
$890$	−3.33551	−0.111806
$891$	−14.4770	−0.484998
$892$	0.458366	0.0153472
$893$	−4.58747	−0.153514
$894$	−53.5916	−1.79237
$895$	37.6690	1.25914
$896$	−9.61450	−0.321198
$897$	1.46722	0.0489891
$898$	83.1013	2.77313
$899$	−13.7319	−0.457985
$900$	−7.84089	−0.261363
$901$	−16.8412	−0.561061
$902$	−42.3090	−1.40874
$903$	2.01008	0.0668911
$904$	13.8365	0.460194
$905$	21.7671	0.723563
$906$	18.7011	0.621304
$907$	1.34919	0.0447992	0.0223996	−	0.999749i	$-0.492869\pi$
$907$	1.34919	0.0447992	0.0223996	+	0.999749i	$0.492869\pi$
$908$	75.2968	2.49881
$909$	2.31255	0.0767025
$910$	−5.73792	−0.190210
$911$	4.69373	0.155510	0.0777551	−	0.996972i	$-0.475225\pi$
$911$	4.69373	0.155510	0.0777551	+	0.996972i	$0.475225\pi$
$912$	−7.39077	−0.244733
$913$	41.3036	1.36695
$914$	67.5897	2.23567
$915$	26.9091	0.889586
$916$	33.3511	1.10195
$917$	2.14943	0.0709805
$918$	50.1394	1.65485
$919$	−42.8558	−1.41368	−0.706841	−	0.707372i	$-0.749881\pi$
$919$	−42.8558	−1.41368	−0.706841	+	0.707372i	$0.749881\pi$
$920$	−3.89165	−0.128304
$921$	3.50184	0.115390
$922$	50.9074	1.67654
$923$	−12.3016	−0.404912
$924$	16.3621	0.538274
$925$	2.34832	0.0772122
$926$	2.14163	0.0703782
$927$	6.90960	0.226941
$928$	28.2441	0.927159
$929$	−3.71897	−0.122015	−0.0610077	−	0.998137i	$-0.519431\pi$
$929$	−3.71897	−0.122015	−0.0610077	+	0.998137i	$0.519431\pi$
$930$	−27.7321	−0.909370
$931$	14.0728	0.461218
$932$	−24.6476	−0.807359
$933$	2.59065	0.0848141
$934$	−38.9223	−1.27358
$935$	−56.1499	−1.83630
$936$	−1.74479	−0.0570301
$937$	−18.2530	−0.596300	−0.298150	−	0.954519i	$-0.596370\pi$
$937$	−18.2530	−0.596300	−0.298150	+	0.954519i	$0.596370\pi$
$938$	−20.7855	−0.678670
$939$	−4.20979	−0.137381
$940$	13.5596	0.442264
$941$	6.55980	0.213843	0.106922	−	0.994267i	$-0.465901\pi$
$941$	6.55980	0.213843	0.106922	+	0.994267i	$0.465901\pi$
$942$	−34.4396	−1.12210
$943$	4.58079	0.149171
$944$	20.6044	0.670616
$945$	−14.9254	−0.485524
$946$	−16.9129	−0.549886
$947$	−47.2682	−1.53601	−0.768006	−	0.640443i	$-0.778751\pi$
$947$	−47.2682	−1.53601	−0.768006	+	0.640443i	$0.778751\pi$
$948$	57.6519	1.87245
$949$	−10.9163	−0.354357
$950$	10.9619	0.355651
$951$	−34.4849	−1.11825
$952$	−5.27774	−0.171053
$953$	32.0332	1.03766	0.518829	−	0.854878i	$-0.326368\pi$
$953$	32.0332	1.03766	0.518829	+	0.854878i	$0.326368\pi$
$954$	11.9202	0.385930
$955$	−7.83810	−0.253635
$956$	−28.2398	−0.913342
$957$	−22.8259	−0.737857
$958$	43.3342	1.40006
$959$	−16.5688	−0.535035
$960$	40.1484	1.29578
$961$	−16.5092	−0.532554
$962$	2.30433	0.0742946
$963$	4.78293	0.154128
$964$	−30.8078	−0.992252
$965$	64.0268	2.06109
$966$	−3.14132	−0.101070
$967$	31.1878	1.00293	0.501466	−	0.865177i	$-0.332794\pi$
$967$	31.1878	1.00293	0.501466	+	0.865177i	$0.332794\pi$
$968$	−17.4020	−0.559322
$969$	−12.5101	−0.401884
$970$	−31.0110	−0.995704
$971$	−17.4453	−0.559847	−0.279924	−	0.960022i	$-0.590309\pi$
$971$	−17.4453	−0.559847	−0.279924	+	0.960022i	$0.590309\pi$
$972$	−33.6936	−1.08072
$973$	13.2726	0.425500
$974$	80.6340	2.58368
$975$	2.77019	0.0887170
$976$	19.6406	0.628680
$977$	19.5591	0.625750	0.312875	−	0.949794i	$-0.398708\pi$
$977$	19.5591	0.625750	0.312875	+	0.949794i	$0.398708\pi$
$978$	−39.5909	−1.26598
$979$	2.89715	0.0925932
$980$	−41.5962	−1.32874
$981$	−1.41301	−0.0451140
$982$	−48.3808	−1.54389
$983$	34.0565	1.08623	0.543116	−	0.839658i	$-0.317244\pi$
$983$	34.0565	1.08623	0.543116	+	0.839658i	$0.317244\pi$
$984$	6.31841	0.201423
$985$	50.0723	1.59544
$986$	32.4675	1.03398
$987$	2.48206	0.0790049
$988$	6.06610	0.192988
$989$	1.83116	0.0582275
$990$	39.7429	1.26311
$991$	16.6178	0.527881	0.263941	−	0.964539i	$-0.414978\pi$
$991$	16.6178	0.527881	0.263941	+	0.964539i	$0.414978\pi$
$992$	−29.8051	−0.946313
$993$	5.35609	0.169970
$994$	26.3377	0.835381
$995$	−48.2979	−1.53115
$996$	−27.2003	−0.861874
$997$	9.54068	0.302156	0.151078	−	0.988522i	$-0.451725\pi$
$997$	9.54068	0.302156	0.151078	+	0.988522i	$0.451725\pi$
$998$	52.8879	1.67414
$999$	5.99400	0.189642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.c.1.19	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.c.1.19	✓	108	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.14163 q^{2} -1.26927 q^{3} +2.58656 q^{4} +2.68002 q^{5} +2.71830 q^{6} -0.999709 q^{7} -1.25619 q^{8} -1.38895 q^{9} +O(q^{10})\)	\(q-2.14163 q^{2} -1.26927 q^{3} +2.58656 q^{4} +2.68002 q^{5} +2.71830 q^{6} -0.999709 q^{7} -1.25619 q^{8} -1.38895 q^{9} -5.73960 q^{10} +4.98528 q^{11} -3.28304 q^{12} -1.00000 q^{13} +2.14100 q^{14} -3.40167 q^{15} -2.48283 q^{16} -4.20263 q^{17} +2.97462 q^{18} -2.34524 q^{19} +6.93203 q^{20} +1.26890 q^{21} -10.6766 q^{22} +1.15596 q^{23} +1.59444 q^{24} +2.18250 q^{25} +2.14163 q^{26} +5.57077 q^{27} -2.58580 q^{28} +3.60732 q^{29} +7.28510 q^{30} -3.80668 q^{31} +7.82967 q^{32} -6.32767 q^{33} +9.00045 q^{34} -2.67924 q^{35} -3.59261 q^{36} +1.07597 q^{37} +5.02263 q^{38} +1.26927 q^{39} -3.36660 q^{40} +3.96277 q^{41} -2.71751 q^{42} +1.58411 q^{43} +12.8947 q^{44} -3.72242 q^{45} -2.47562 q^{46} +1.95607 q^{47} +3.15139 q^{48} -6.00058 q^{49} -4.67411 q^{50} +5.33427 q^{51} -2.58656 q^{52} +4.00730 q^{53} -11.9305 q^{54} +13.3607 q^{55} +1.25582 q^{56} +2.97674 q^{57} -7.72552 q^{58} -8.29874 q^{59} -8.79861 q^{60} -7.91055 q^{61} +8.15249 q^{62} +1.38855 q^{63} -11.8026 q^{64} -2.68002 q^{65} +13.5515 q^{66} -9.70831 q^{67} -10.8703 q^{68} -1.46722 q^{69} +5.73792 q^{70} +12.3016 q^{71} +1.74479 q^{72} +10.9163 q^{73} -2.30433 q^{74} -2.77019 q^{75} -6.06610 q^{76} -4.98383 q^{77} -2.71830 q^{78} -17.5605 q^{79} -6.65405 q^{80} -2.90395 q^{81} -8.48678 q^{82} +8.28510 q^{83} +3.28208 q^{84} -11.2631 q^{85} -3.39257 q^{86} -4.57866 q^{87} -6.26245 q^{88} +0.581140 q^{89} +7.97204 q^{90} +0.999709 q^{91} +2.98995 q^{92} +4.83171 q^{93} -4.18918 q^{94} -6.28529 q^{95} -9.93797 q^{96} +5.40300 q^{97} +12.8510 q^{98} -6.92433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9}+O(q^{10}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9	\( 108 q - 11 q^{2} + q^{3} + 95 q^{4} - 40 q^{5} - 10 q^{6} - 8 q^{7} - 33 q^{8} + 79 q^{9} - q^{10} - 45 q^{11} - 6 q^{12} - 108 q^{13} - 31 q^{14} - 39 q^{15} + 73 q^{16} + 21 q^{17} - 35 q^{18} - 19 q^{19} - 79 q^{20} - 72 q^{21} - 26 q^{23} - 23 q^{24} + 92 q^{25} + 11 q^{26} + 7 q^{27} - 21 q^{28} - 94 q^{29} - 24 q^{30} - 36 q^{31} - 77 q^{32} - 32 q^{33} - 58 q^{34} - 10 q^{35} + 17 q^{36} - 54 q^{37} - 12 q^{38} - q^{39} - 4 q^{40} - 68 q^{41} - 11 q^{42} - 32 q^{43} - 151 q^{44} - 121 q^{45} - 33 q^{46} - 51 q^{47} - 27 q^{48} + 72 q^{49} - 45 q^{50} - 24 q^{51} - 95 q^{52} - 81 q^{53} - 29 q^{54} + 4 q^{55} - 68 q^{56} - 45 q^{57} - 30 q^{58} - 94 q^{59} - 108 q^{60} - 39 q^{61} - 9 q^{62} - 52 q^{63} + 31 q^{64} + 40 q^{65} - 40 q^{66} - 47 q^{67} + 24 q^{68} - 60 q^{69} - 66 q^{70} - 86 q^{71} - 91 q^{72} - 51 q^{73} - 110 q^{74} - 7 q^{75} - 51 q^{76} - 96 q^{77} + 10 q^{78} - 18 q^{79} - 136 q^{80} - 24 q^{81} - 33 q^{82} - 77 q^{83} - 113 q^{84} - 95 q^{85} - 137 q^{86} + 23 q^{87} + 19 q^{88} - 112 q^{89} - 19 q^{90} + 8 q^{91} - 111 q^{92} - 124 q^{93} - 20 q^{94} - 73 q^{95} - 77 q^{96} - 41 q^{97} - 80 q^{98} - 154 q^{99}+O(q^{100}) \) 108 * q - 11 * q^2 + q^3 + 95 * q^4 - 40 * q^5 - 10 * q^6 - 8 * q^7 - 33 * q^8 + 79 * q^9 - q^10 - 45 * q^11 - 6 * q^12 - 108 * q^13 - 31 * q^14 - 39 * q^15 + 73 * q^16 + 21 * q^17 - 35 * q^18 - 19 * q^19 - 79 * q^20 - 72 * q^21 - 26 * q^23 - 23 * q^24 + 92 * q^25 + 11 * q^26 + 7 * q^27 - 21 * q^28 - 94 * q^29 - 24 * q^30 - 36 * q^31 - 77 * q^32 - 32 * q^33 - 58 * q^34 - 10 * q^35 + 17 * q^36 - 54 * q^37 - 12 * q^38 - q^39 - 4 * q^40 - 68 * q^41 - 11 * q^42 - 32 * q^43 - 151 * q^44 - 121 * q^45 - 33 * q^46 - 51 * q^47 - 27 * q^48 + 72 * q^49 - 45 * q^50 - 24 * q^51 - 95 * q^52 - 81 * q^53 - 29 * q^54 + 4 * q^55 - 68 * q^56 - 45 * q^57 - 30 * q^58 - 94 * q^59 - 108 * q^60 - 39 * q^61 - 9 * q^62 - 52 * q^63 + 31 * q^64 + 40 * q^65 - 40 * q^66 - 47 * q^67 + 24 * q^68 - 60 * q^69 - 66 * q^70 - 86 * q^71 - 91 * q^72 - 51 * q^73 - 110 * q^74 - 7 * q^75 - 51 * q^76 - 96 * q^77 + 10 * q^78 - 18 * q^79 - 136 * q^80 - 24 * q^81 - 33 * q^82 - 77 * q^83 - 113 * q^84 - 95 * q^85 - 137 * q^86 + 23 * q^87 + 19 * q^88 - 112 * q^89 - 19 * q^90 + 8 * q^91 - 111 * q^92 - 124 * q^93 - 20 * q^94 - 73 * q^95 - 77 * q^96 - 41 * q^97 - 80 * q^98 - 154 * q^99

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