LMFDB - Embedded newform 539.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(1,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, 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("539.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.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:	$4.30393666895$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	539.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.347296 q^{2} +0.532089 q^{3} -1.87939 q^{4} -0.120615 q^{5} -0.184793 q^{6} +1.34730 q^{8} -2.71688 q^{9} +O(q^{10})$	\(q-0.347296 q^{2} +0.532089 q^{3} -1.87939 q^{4} -0.120615 q^{5} -0.184793 q^{6} +1.34730 q^{8} -2.71688 q^{9} +0.0418891 q^{10} +1.00000 q^{11} -1.00000 q^{12} +1.22668 q^{13} -0.0641778 q^{15} +3.29086 q^{16} -6.17024 q^{17} +0.943563 q^{18} -6.41147 q^{19} +0.226682 q^{20} -0.347296 q^{22} -2.02229 q^{23} +0.716881 q^{24} -4.98545 q^{25} -0.426022 q^{26} -3.04189 q^{27} +3.24897 q^{29} +0.0222887 q^{30} -4.87939 q^{31} -3.83750 q^{32} +0.532089 q^{33} +2.14290 q^{34} +5.10607 q^{36} +2.36959 q^{37} +2.22668 q^{38} +0.652704 q^{39} -0.162504 q^{40} -8.29086 q^{41} +2.22668 q^{43} -1.87939 q^{44} +0.327696 q^{45} +0.702333 q^{46} -9.23442 q^{47} +1.75103 q^{48} +1.73143 q^{50} -3.28312 q^{51} -2.30541 q^{52} +9.68004 q^{53} +1.05644 q^{54} -0.120615 q^{55} -3.41147 q^{57} -1.12836 q^{58} +9.74422 q^{59} +0.120615 q^{60} +1.43376 q^{61} +1.69459 q^{62} -5.24897 q^{64} -0.147956 q^{65} -0.184793 q^{66} -3.06418 q^{67} +11.5963 q^{68} -1.07604 q^{69} -8.49525 q^{71} -3.66044 q^{72} -3.53209 q^{73} -0.822948 q^{74} -2.65270 q^{75} +12.0496 q^{76} -0.226682 q^{78} +9.09152 q^{79} -0.396926 q^{80} +6.53209 q^{81} +2.87939 q^{82} +7.02229 q^{83} +0.744223 q^{85} -0.773318 q^{86} +1.72874 q^{87} +1.34730 q^{88} +6.87939 q^{89} -0.113808 q^{90} +3.80066 q^{92} -2.59627 q^{93} +3.20708 q^{94} +0.773318 q^{95} -2.04189 q^{96} -16.5321 q^{97} -2.71688 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} + 3 q^{8}+O(q^{10}) $ 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 + 3 * q^8	$ 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} + 3 q^{8} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{13} + 9 q^{15} - 6 q^{16} + 3 q^{17} - 12 q^{18} - 9 q^{19} - 6 q^{20} - 6 q^{24} + 3 q^{25} - 9 q^{26} - 6 q^{27} - 3 q^{29} - 6 q^{30} - 9 q^{31} - 9 q^{32} - 3 q^{33} + 6 q^{34} + 3 q^{36} + 3 q^{39} - 3 q^{40} - 9 q^{41} - 3 q^{45} - 24 q^{46} + 3 q^{47} + 18 q^{48} + 15 q^{50} - 18 q^{51} - 9 q^{52} + 9 q^{53} + 18 q^{54} - 6 q^{55} + 15 q^{58} + 6 q^{60} - 12 q^{61} + 3 q^{62} - 3 q^{64} + 15 q^{65} + 3 q^{66} + 21 q^{68} - 21 q^{69} - 9 q^{71} + 12 q^{72} - 6 q^{73} + 18 q^{74} - 9 q^{75} + 9 q^{76} + 6 q^{78} - 3 q^{79} + 27 q^{80} + 15 q^{81} + 3 q^{82} + 15 q^{83} - 27 q^{85} - 9 q^{86} + 24 q^{87} + 3 q^{88} + 15 q^{89} + 36 q^{90} - 3 q^{92} + 6 q^{93} + 9 q^{95} - 3 q^{96} - 45 q^{97}+O(q^{100}) $ 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 + 3 * q^8 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^13 + 9 * q^15 - 6 * q^16 + 3 * q^17 - 12 * q^18 - 9 * q^19 - 6 * q^20 - 6 * q^24 + 3 * q^25 - 9 * q^26 - 6 * q^27 - 3 * q^29 - 6 * q^30 - 9 * q^31 - 9 * q^32 - 3 * q^33 + 6 * q^34 + 3 * q^36 + 3 * q^39 - 3 * q^40 - 9 * q^41 - 3 * q^45 - 24 * q^46 + 3 * q^47 + 18 * q^48 + 15 * q^50 - 18 * q^51 - 9 * q^52 + 9 * q^53 + 18 * q^54 - 6 * q^55 + 15 * q^58 + 6 * q^60 - 12 * q^61 + 3 * q^62 - 3 * q^64 + 15 * q^65 + 3 * q^66 + 21 * q^68 - 21 * q^69 - 9 * q^71 + 12 * q^72 - 6 * q^73 + 18 * q^74 - 9 * q^75 + 9 * q^76 + 6 * q^78 - 3 * q^79 + 27 * q^80 + 15 * q^81 + 3 * q^82 + 15 * q^83 - 27 * q^85 - 9 * q^86 + 24 * q^87 + 3 * q^88 + 15 * q^89 + 36 * q^90 - 3 * q^92 + 6 * q^93 + 9 * q^95 - 3 * q^96 - 45 * q^97

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 $

$2$	−0.347296	−0.245576	−0.122788	−	0.992433i	$-0.539183\pi$
$2$	−0.347296	−0.245576	−0.122788	+	0.992433i	$0.539183\pi$
$3$	0.532089	0.307202	0.153601	−	0.988133i	$-0.450913\pi$
$3$	0.532089	0.307202	0.153601	+	0.988133i	$0.450913\pi$
$4$	−1.87939	−0.939693
$5$	−0.120615	−0.0539406	−0.0269703	−	0.999636i	$-0.508586\pi$
$5$	−0.120615	−0.0539406	−0.0269703	+	0.999636i	$0.508586\pi$
$6$	−0.184793	−0.0754412
$7$	0	0
$7$	0	0
$8$	1.34730	0.476341
$9$	−2.71688	−0.905627
$10$	0.0418891	0.0132465
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	1.22668	0.340220	0.170110	−	0.985425i	$-0.445588\pi$
$13$	1.22668	0.340220	0.170110	+	0.985425i	$0.445588\pi$
$14$	0	0
$15$	−0.0641778	−0.0165706
$16$	3.29086	0.822715
$17$	−6.17024	−1.49650	−0.748252	−	0.663415i	$-0.769107\pi$
$17$	−6.17024	−1.49650	−0.748252	+	0.663415i	$0.769107\pi$
$18$	0.943563	0.222400
$19$	−6.41147	−1.47089	−0.735447	−	0.677583i	$-0.763028\pi$
$19$	−6.41147	−1.47089	−0.735447	+	0.677583i	$0.763028\pi$
$20$	0.226682	0.0506875
$21$	0	0
$22$	−0.347296	−0.0740438
$23$	−2.02229	−0.421676	−0.210838	−	0.977521i	$-0.567619\pi$
$23$	−2.02229	−0.421676	−0.210838	+	0.977521i	$0.567619\pi$
$24$	0.716881	0.146333
$25$	−4.98545	−0.997090
$26$	−0.426022	−0.0835498
$27$	−3.04189	−0.585412
$28$	0	0
$29$	3.24897	0.603319	0.301659	−	0.953416i	$-0.402459\pi$
$29$	3.24897	0.603319	0.301659	+	0.953416i	$0.402459\pi$
$30$	0.0222887	0.00406934
$31$	−4.87939	−0.876363	−0.438182	−	0.898886i	$-0.644377\pi$
$31$	−4.87939	−0.876363	−0.438182	+	0.898886i	$0.644377\pi$
$32$	−3.83750	−0.678380
$33$	0.532089	0.0926248
$34$	2.14290	0.367505
$35$	0	0
$36$	5.10607	0.851011
$37$	2.36959	0.389557	0.194779	−	0.980847i	$-0.437601\pi$
$37$	2.36959	0.389557	0.194779	+	0.980847i	$0.437601\pi$
$38$	2.22668	0.361215
$39$	0.652704	0.104516
$40$	−0.162504	−0.0256941
$41$	−8.29086	−1.29481	−0.647407	−	0.762144i	$-0.724147\pi$
$41$	−8.29086	−1.29481	−0.647407	+	0.762144i	$0.724147\pi$
$42$	0	0
$43$	2.22668	0.339566	0.169783	−	0.985481i	$-0.445693\pi$
$43$	2.22668	0.339566	0.169783	+	0.985481i	$0.445693\pi$
$44$	−1.87939	−0.283328
$45$	0.327696	0.0488500
$46$	0.702333	0.103553
$47$	−9.23442	−1.34698	−0.673489	−	0.739197i	$-0.735205\pi$
$47$	−9.23442	−1.34698	−0.673489	+	0.739197i	$0.735205\pi$
$48$	1.75103	0.252739
$49$	0	0
$50$	1.73143	0.244861
$51$	−3.28312	−0.459729
$52$	−2.30541	−0.319702
$53$	9.68004	1.32966	0.664828	−	0.746996i	$-0.268505\pi$
$53$	9.68004	1.32966	0.664828	+	0.746996i	$0.268505\pi$
$54$	1.05644	0.143763
$55$	−0.120615	−0.0162637
$56$	0	0
$57$	−3.41147	−0.451861
$58$	−1.12836	−0.148160
$59$	9.74422	1.26859	0.634295	−	0.773091i	$-0.281291\pi$
$59$	9.74422	1.26859	0.634295	+	0.773091i	$0.281291\pi$
$60$	0.120615	0.0155713
$61$	1.43376	0.183575	0.0917873	−	0.995779i	$-0.470742\pi$
$61$	1.43376	0.183575	0.0917873	+	0.995779i	$0.470742\pi$
$62$	1.69459	0.215213
$63$	0	0
$64$	−5.24897	−0.656121
$65$	−0.147956	−0.0183517
$66$	−0.184793	−0.0227464
$67$	−3.06418	−0.374349	−0.187174	−	0.982327i	$-0.559933\pi$
$67$	−3.06418	−0.374349	−0.187174	+	0.982327i	$0.559933\pi$
$68$	11.5963	1.40625
$69$	−1.07604	−0.129540
$70$	0	0
$71$	−8.49525	−1.00820	−0.504100	−	0.863645i	$-0.668176\pi$
$71$	−8.49525	−1.00820	−0.504100	+	0.863645i	$0.668176\pi$
$72$	−3.66044	−0.431388
$73$	−3.53209	−0.413400	−0.206700	−	0.978404i	$-0.566272\pi$
$73$	−3.53209	−0.413400	−0.206700	+	0.978404i	$0.566272\pi$
$74$	−0.822948	−0.0956658
$75$	−2.65270	−0.306308
$76$	12.0496	1.38219
$77$	0	0
$78$	−0.226682	−0.0256666
$79$	9.09152	1.02288	0.511438	−	0.859320i	$-0.329113\pi$
$79$	9.09152	1.02288	0.511438	+	0.859320i	$0.329113\pi$
$80$	−0.396926	−0.0443777
$81$	6.53209	0.725788
$82$	2.87939	0.317975
$83$	7.02229	0.770796	0.385398	−	0.922750i	$-0.374064\pi$
$83$	7.02229	0.770796	0.385398	+	0.922750i	$0.374064\pi$
$84$	0	0
$85$	0.744223	0.0807223
$86$	−0.773318	−0.0833891
$87$	1.72874	0.185340
$88$	1.34730	0.143622
$89$	6.87939	0.729213	0.364607	−	0.931162i	$-0.381203\pi$
$89$	6.87939	0.729213	0.364607	+	0.931162i	$0.381203\pi$
$90$	−0.113808	−0.0119964
$91$	0	0
$92$	3.80066	0.396246
$93$	−2.59627	−0.269220
$94$	3.20708	0.330785
$95$	0.773318	0.0793408
$96$	−2.04189	−0.208399
$97$	−16.5321	−1.67858	−0.839290	−	0.543685i	$-0.817029\pi$
$97$	−16.5321	−1.67858	−0.839290	+	0.543685i	$0.817029\pi$
$98$	0	0
$99$	−2.71688	−0.273057
$100$	9.36959	0.936959
$101$	6.80066	0.676691	0.338345	−	0.941022i	$-0.390133\pi$
$101$	6.80066	0.676691	0.338345	+	0.941022i	$0.390133\pi$
$102$	1.14022	0.112898
$103$	9.17024	0.903571	0.451786	−	0.892127i	$-0.350787\pi$
$103$	9.17024	0.903571	0.451786	+	0.892127i	$0.350787\pi$
$104$	1.65270	0.162061
$105$	0	0
$106$	−3.36184	−0.326531
$107$	−8.12061	−0.785049	−0.392525	−	0.919741i	$-0.628398\pi$
$107$	−8.12061	−0.785049	−0.392525	+	0.919741i	$0.628398\pi$
$108$	5.71688	0.550107
$109$	−6.49020	−0.621648	−0.310824	−	0.950467i	$-0.600605\pi$
$109$	−6.49020	−0.621648	−0.310824	+	0.950467i	$0.600605\pi$
$110$	0.0418891	0.00399397
$111$	1.26083	0.119673
$112$	0	0
$113$	−10.8648	−1.02208	−0.511039	−	0.859558i	$-0.670739\pi$
$113$	−10.8648	−1.02208	−0.511039	+	0.859558i	$0.670739\pi$
$114$	1.18479	0.110966
$115$	0.243918	0.0227455
$116$	−6.10607	−0.566934
$117$	−3.33275	−0.308113
$118$	−3.38413	−0.311535
$119$	0	0
$120$	−0.0864665	−0.00789327
$121$	1.00000	0.0909091
$122$	−0.497941	−0.0450814
$123$	−4.41147	−0.397769
$124$	9.17024	0.823512
$125$	1.20439	0.107724
$126$	0	0
$127$	2.68004	0.237816	0.118908	−	0.992905i	$-0.462061\pi$
$127$	2.68004	0.237816	0.118908	+	0.992905i	$0.462061\pi$
$128$	9.49794	0.839507
$129$	1.18479	0.104315
$130$	0.0513845	0.00450672
$131$	14.0273	1.22557	0.612787	−	0.790248i	$-0.290048\pi$
$131$	14.0273	1.22557	0.612787	+	0.790248i	$0.290048\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	1.06418	0.0919310
$135$	0.366897	0.0315774
$136$	−8.31315	−0.712847
$137$	14.6408	1.25085	0.625426	−	0.780284i	$-0.284925\pi$
$137$	14.6408	1.25085	0.625426	+	0.780284i	$0.284925\pi$
$138$	0.373704	0.0318118
$139$	−11.0155	−0.934321	−0.467160	−	0.884173i	$-0.654723\pi$
$139$	−11.0155	−0.934321	−0.467160	+	0.884173i	$0.654723\pi$
$140$	0	0
$141$	−4.91353	−0.413794
$142$	2.95037	0.247590
$143$	1.22668	0.102580
$144$	−8.94087	−0.745073
$145$	−0.391874	−0.0325433
$146$	1.22668	0.101521
$147$	0	0
$148$	−4.45336	−0.366064
$149$	14.7297	1.20670	0.603351	−	0.797476i	$-0.293832\pi$
$149$	14.7297	1.20670	0.603351	+	0.797476i	$0.293832\pi$
$150$	0.921274	0.0752217
$151$	23.2422	1.89142	0.945710	−	0.325011i	$-0.105368\pi$
$151$	23.2422	1.89142	0.945710	+	0.325011i	$0.105368\pi$
$152$	−8.63816	−0.700647
$153$	16.7638	1.35527
$154$	0	0
$155$	0.588526	0.0472715
$156$	−1.22668	−0.0982131
$157$	−16.0642	−1.28206	−0.641030	−	0.767515i	$-0.721493\pi$
$157$	−16.0642	−1.28206	−0.641030	+	0.767515i	$0.721493\pi$
$158$	−3.15745	−0.251193
$159$	5.15064	0.408473
$160$	0.462859	0.0365922
$161$	0	0
$162$	−2.26857	−0.178236
$163$	−10.6013	−0.830359	−0.415180	−	0.909739i	$-0.636281\pi$
$163$	−10.6013	−0.830359	−0.415180	+	0.909739i	$0.636281\pi$
$164$	15.5817	1.21673
$165$	−0.0641778	−0.00499623
$166$	−2.43882	−0.189289
$167$	21.1361	1.63556	0.817780	−	0.575531i	$-0.195205\pi$
$167$	21.1361	1.63556	0.817780	+	0.575531i	$0.195205\pi$
$168$	0	0
$169$	−11.4953	−0.884250
$170$	−0.258466	−0.0198234
$171$	17.4192	1.33208
$172$	−4.18479	−0.319087
$173$	−2.31996	−0.176383	−0.0881915	−	0.996104i	$-0.528109\pi$
$173$	−2.31996	−0.176383	−0.0881915	+	0.996104i	$0.528109\pi$
$174$	−0.600385	−0.0455151
$175$	0	0
$176$	3.29086	0.248058
$177$	5.18479	0.389713
$178$	−2.38919	−0.179077
$179$	11.4192	0.853512	0.426756	−	0.904367i	$-0.359656\pi$
$179$	11.4192	0.853512	0.426756	+	0.904367i	$0.359656\pi$
$180$	−0.615867	−0.0459040
$181$	−16.4679	−1.22405	−0.612025	−	0.790838i	$-0.709645\pi$
$181$	−16.4679	−1.22405	−0.612025	+	0.790838i	$0.709645\pi$
$182$	0	0
$183$	0.762889	0.0563944
$184$	−2.72462	−0.200862
$185$	−0.285807	−0.0210129
$186$	0.901674	0.0661139
$187$	−6.17024	−0.451213
$188$	17.3550	1.26575
$189$	0	0
$190$	−0.268571	−0.0194842
$191$	−11.1676	−0.808056	−0.404028	−	0.914747i	$-0.632390\pi$
$191$	−11.1676	−0.808056	−0.404028	+	0.914747i	$0.632390\pi$
$192$	−2.79292	−0.201562
$193$	−20.0496	−1.44320	−0.721602	−	0.692308i	$-0.756594\pi$
$193$	−20.0496	−1.44320	−0.721602	+	0.692308i	$0.756594\pi$
$194$	5.74153	0.412218
$195$	−0.0787257	−0.00563766
$196$	0	0
$197$	15.9932	1.13947	0.569734	−	0.821829i	$-0.307046\pi$
$197$	15.9932	1.13947	0.569734	+	0.821829i	$0.307046\pi$
$198$	0.943563	0.0670561
$199$	−6.26857	−0.444367	−0.222184	−	0.975005i	$-0.571318\pi$
$199$	−6.26857	−0.444367	−0.222184	+	0.975005i	$0.571318\pi$
$200$	−6.71688	−0.474955
$201$	−1.63041	−0.115001
$202$	−2.36184	−0.166179
$203$	0	0
$204$	6.17024	0.432004
$205$	1.00000	0.0698430
$206$	−3.18479	−0.221895
$207$	5.49432	0.381882
$208$	4.03684	0.279904
$209$	−6.41147	−0.443491
$210$	0	0
$211$	11.0642	0.761689	0.380845	−	0.924639i	$-0.375633\pi$
$211$	11.0642	0.761689	0.380845	+	0.924639i	$0.375633\pi$
$212$	−18.1925	−1.24947
$213$	−4.52023	−0.309721
$214$	2.82026	0.192789
$215$	−0.268571	−0.0183164
$216$	−4.09833	−0.278856
$217$	0	0
$218$	2.25402	0.152662
$219$	−1.87939	−0.126997
$220$	0.226682	0.0152829
$221$	−7.56893	−0.509141
$222$	−0.437882	−0.0293887
$223$	−9.25671	−0.619875	−0.309938	−	0.950757i	$-0.600308\pi$
$223$	−9.25671	−0.619875	−0.309938	+	0.950757i	$0.600308\pi$
$224$	0	0
$225$	13.5449	0.902992
$226$	3.77332	0.250997
$227$	20.5057	1.36101	0.680505	−	0.732743i	$-0.261760\pi$
$227$	20.5057	1.36101	0.680505	+	0.732743i	$0.261760\pi$
$228$	6.41147	0.424610
$229$	−26.0642	−1.72237	−0.861185	−	0.508292i	$-0.830277\pi$
$229$	−26.0642	−1.72237	−0.861185	+	0.508292i	$0.830277\pi$
$230$	−0.0847118	−0.00558573
$231$	0	0
$232$	4.37733	0.287386
$233$	2.78787	0.182639	0.0913196	−	0.995822i	$-0.470892\pi$
$233$	2.78787	0.182639	0.0913196	+	0.995822i	$0.470892\pi$
$234$	1.15745	0.0756650
$235$	1.11381	0.0726568
$236$	−18.3131	−1.19208
$237$	4.83750	0.314229
$238$	0	0
$239$	−11.2199	−0.725753	−0.362877	−	0.931837i	$-0.618205\pi$
$239$	−11.2199	−0.725753	−0.362877	+	0.931837i	$0.618205\pi$
$240$	−0.211200	−0.0136329
$241$	−10.2558	−0.660633	−0.330316	−	0.943870i	$-0.607155\pi$
$241$	−10.2558	−0.660633	−0.330316	+	0.943870i	$0.607155\pi$
$242$	−0.347296	−0.0223251
$243$	12.6013	0.808375
$244$	−2.69459	−0.172504
$245$	0	0
$246$	1.53209	0.0976824
$247$	−7.86484	−0.500428
$248$	−6.57398	−0.417448
$249$	3.73648	0.236790
$250$	−0.418281	−0.0264544
$251$	−29.1215	−1.83814	−0.919068	−	0.394099i	$-0.871057\pi$
$251$	−29.1215	−1.83814	−0.919068	+	0.394099i	$0.871057\pi$
$252$	0	0
$253$	−2.02229	−0.127140
$254$	−0.930770	−0.0584017
$255$	0.395993	0.0247980
$256$	7.19934	0.449959
$257$	−8.39693	−0.523786	−0.261893	−	0.965097i	$-0.584347\pi$
$257$	−8.39693	−0.523786	−0.261893	+	0.965097i	$0.584347\pi$
$258$	−0.411474	−0.0256173
$259$	0	0
$260$	0.278066	0.0172449
$261$	−8.82707	−0.546382
$262$	−4.87164	−0.300971
$263$	−24.3628	−1.50227	−0.751137	−	0.660147i	$-0.770494\pi$
$263$	−24.3628	−1.50227	−0.751137	+	0.660147i	$0.770494\pi$
$264$	0.716881	0.0441210
$265$	−1.16756	−0.0717224
$266$	0	0
$267$	3.66044	0.224016
$268$	5.75877	0.351773
$269$	−29.1908	−1.77979	−0.889897	−	0.456162i	$-0.849224\pi$
$269$	−29.1908	−1.77979	−0.889897	+	0.456162i	$0.849224\pi$
$270$	−0.127422	−0.00775465
$271$	−9.56624	−0.581108	−0.290554	−	0.956859i	$-0.593840\pi$
$271$	−9.56624	−0.581108	−0.290554	+	0.956859i	$0.593840\pi$
$272$	−20.3054	−1.23120
$273$	0	0
$274$	−5.08471	−0.307179
$275$	−4.98545	−0.300634
$276$	2.02229	0.121727
$277$	−20.2814	−1.21859	−0.609295	−	0.792944i	$-0.708547\pi$
$277$	−20.2814	−1.21859	−0.609295	+	0.792944i	$0.708547\pi$
$278$	3.82564	0.229446
$279$	13.2567	0.793659
$280$	0	0
$281$	−5.52528	−0.329611	−0.164805	−	0.986326i	$-0.552700\pi$
$281$	−5.52528	−0.329611	−0.164805	+	0.986326i	$0.552700\pi$
$282$	1.70645	0.101618
$283$	−4.06687	−0.241750	−0.120875	−	0.992668i	$-0.538570\pi$
$283$	−4.06687	−0.241750	−0.120875	+	0.992668i	$0.538570\pi$
$284$	15.9659	0.947399
$285$	0.411474	0.0243736
$286$	−0.426022	−0.0251912
$287$	0	0
$288$	10.4260	0.614359
$289$	21.0719	1.23952
$290$	0.136096	0.00799185
$291$	−8.79654	−0.515662
$292$	6.63816	0.388469
$293$	23.2567	1.35867	0.679336	−	0.733828i	$-0.262268\pi$
$293$	23.2567	1.35867	0.679336	+	0.733828i	$0.262268\pi$
$294$	0	0
$295$	−1.17530	−0.0684284
$296$	3.19253	0.185562
$297$	−3.04189	−0.176508
$298$	−5.11556	−0.296337
$299$	−2.48070	−0.143463
$300$	4.98545	0.287835
$301$	0	0
$302$	−8.07192	−0.464487
$303$	3.61856	0.207881
$304$	−21.0993	−1.21013
$305$	−0.172933	−0.00990211
$306$	−5.82201	−0.332822
$307$	15.3131	0.873968	0.436984	−	0.899469i	$-0.356047\pi$
$307$	15.3131	0.873968	0.436984	+	0.899469i	$0.356047\pi$
$308$	0	0
$309$	4.87939	0.277579
$310$	−0.204393	−0.0116087
$311$	7.07192	0.401012	0.200506	−	0.979693i	$-0.435741\pi$
$311$	7.07192	0.401012	0.200506	+	0.979693i	$0.435741\pi$
$312$	0.879385	0.0497854
$313$	−26.3979	−1.49210	−0.746048	−	0.665893i	$-0.768051\pi$
$313$	−26.3979	−1.49210	−0.746048	+	0.665893i	$0.768051\pi$
$314$	5.57903	0.314843
$315$	0	0
$316$	−17.0865	−0.961189
$317$	−0.171999	−0.00966044	−0.00483022	−	0.999988i	$-0.501538\pi$
$317$	−0.171999	−0.00966044	−0.00483022	+	0.999988i	$0.501538\pi$
$318$	−1.78880	−0.100311
$319$	3.24897	0.181907
$320$	0.633103	0.0353915
$321$	−4.32089	−0.241168
$322$	0	0
$323$	39.5604	2.20120
$324$	−12.2763	−0.682017
$325$	−6.11556	−0.339230
$326$	3.68180	0.203916
$327$	−3.45336	−0.190971
$328$	−11.1702	−0.616774
$329$	0	0
$330$	0.0222887	0.00122695
$331$	−0.108755	−0.00597773	−0.00298886	−	0.999996i	$-0.500951\pi$
$331$	−0.108755	−0.00597773	−0.00298886	+	0.999996i	$0.500951\pi$
$332$	−13.1976	−0.724312
$333$	−6.43788	−0.352794
$334$	−7.34049	−0.401654
$335$	0.369585	0.0201926
$336$	0	0
$337$	−4.69728	−0.255877	−0.127939	−	0.991782i	$-0.540836\pi$
$337$	−4.69728	−0.255877	−0.127939	+	0.991782i	$0.540836\pi$
$338$	3.99226	0.217150
$339$	−5.78106	−0.313984
$340$	−1.39868	−0.0758541
$341$	−4.87939	−0.264234
$342$	−6.04963	−0.327127
$343$	0	0
$344$	3.00000	0.161749
$345$	0.129786	0.00698744
$346$	0.805712	0.0433153
$347$	4.15570	0.223089	0.111545	−	0.993759i	$-0.464420\pi$
$347$	4.15570	0.223089	0.111545	+	0.993759i	$0.464420\pi$
$348$	−3.24897	−0.174163
$349$	−16.4730	−0.881778	−0.440889	−	0.897562i	$-0.645337\pi$
$349$	−16.4730	−0.881778	−0.440889	+	0.897562i	$0.645337\pi$
$350$	0	0
$351$	−3.73143	−0.199169
$352$	−3.83750	−0.204539
$353$	22.6023	1.20300	0.601498	−	0.798874i	$-0.294571\pi$
$353$	22.6023	1.20300	0.601498	+	0.798874i	$0.294571\pi$
$354$	−1.80066	−0.0957040
$355$	1.02465	0.0543829
$356$	−12.9290	−0.685236
$357$	0	0
$358$	−3.96585	−0.209602
$359$	−35.0729	−1.85107	−0.925537	−	0.378657i	$-0.876386\pi$
$359$	−35.0729	−1.85107	−0.925537	+	0.378657i	$0.876386\pi$
$360$	0.441504	0.0232693
$361$	22.1070	1.16353
$362$	5.71925	0.300597
$363$	0.532089	0.0279274
$364$	0	0
$365$	0.426022	0.0222990
$366$	−0.264949	−0.0138491
$367$	11.8598	0.619076	0.309538	−	0.950887i	$-0.399826\pi$
$367$	11.8598	0.619076	0.309538	+	0.950887i	$0.399826\pi$
$368$	−6.65507	−0.346919
$369$	22.5253	1.17262
$370$	0.0992597	0.00516027
$371$	0	0
$372$	4.87939	0.252984
$373$	29.0155	1.50236	0.751182	−	0.660095i	$-0.229484\pi$
$373$	29.0155	1.50236	0.751182	+	0.660095i	$0.229484\pi$
$374$	2.14290	0.110807
$375$	0.640844	0.0330930
$376$	−12.4415	−0.641622
$377$	3.98545	0.205261
$378$	0	0
$379$	18.2695	0.938441	0.469221	−	0.883081i	$-0.344535\pi$
$379$	18.2695	0.938441	0.469221	+	0.883081i	$0.344535\pi$
$380$	−1.45336	−0.0745560
$381$	1.42602	0.0730573
$382$	3.87845	0.198439
$383$	15.4388	0.788887	0.394443	−	0.918920i	$-0.370937\pi$
$383$	15.4388	0.788887	0.394443	+	0.918920i	$0.370937\pi$
$384$	5.05375	0.257898
$385$	0	0
$386$	6.96316	0.354416
$387$	−6.04963	−0.307520
$388$	31.0702	1.57735
$389$	−24.0428	−1.21902	−0.609510	−	0.792779i	$-0.708634\pi$
$389$	−24.0428	−1.21902	−0.609510	+	0.792779i	$0.708634\pi$
$390$	0.0273411	0.00138447
$391$	12.4780	0.631040
$392$	0	0
$393$	7.46379	0.376499
$394$	−5.55438	−0.279826
$395$	−1.09657	−0.0551745
$396$	5.10607	0.256590
$397$	9.14796	0.459123	0.229561	−	0.973294i	$-0.426271\pi$
$397$	9.14796	0.459123	0.229561	+	0.973294i	$0.426271\pi$
$398$	2.17705	0.109126
$399$	0	0
$400$	−16.4064	−0.820321
$401$	8.03003	0.401001	0.200500	−	0.979694i	$-0.435743\pi$
$401$	8.03003	0.401001	0.200500	+	0.979694i	$0.435743\pi$
$402$	0.566237	0.0282413
$403$	−5.98545	−0.298157
$404$	−12.7811	−0.635881
$405$	−0.787866	−0.0391494
$406$	0	0
$407$	2.36959	0.117456
$408$	−4.42333	−0.218988
$409$	−1.81521	−0.0897562	−0.0448781	−	0.998992i	$-0.514290\pi$
$409$	−1.81521	−0.0897562	−0.0448781	+	0.998992i	$0.514290\pi$
$410$	−0.347296	−0.0171517
$411$	7.79023	0.384264
$412$	−17.2344	−0.849079
$413$	0	0
$414$	−1.90816	−0.0937808
$415$	−0.846992	−0.0415772
$416$	−4.70739	−0.230799
$417$	−5.86122	−0.287025
$418$	2.22668	0.108911
$419$	36.3756	1.77706	0.888531	−	0.458816i	$-0.151726\pi$
$419$	36.3756	1.77706	0.888531	+	0.458816i	$0.151726\pi$
$420$	0	0
$421$	−13.3432	−0.650307	−0.325153	−	0.945661i	$-0.605416\pi$
$421$	−13.3432	−0.650307	−0.325153	+	0.945661i	$0.605416\pi$
$422$	−3.84255	−0.187052
$423$	25.0888	1.21986
$424$	13.0419	0.633370
$425$	30.7615	1.49215
$426$	1.56986	0.0760599
$427$	0	0
$428$	15.2618	0.737705
$429$	0.652704	0.0315128
$430$	0.0932736	0.00449805
$431$	10.7980	0.520120	0.260060	−	0.965592i	$-0.416258\pi$
$431$	10.7980	0.520120	0.260060	+	0.965592i	$0.416258\pi$
$432$	−10.0104	−0.481627
$433$	17.8425	0.857458	0.428729	−	0.903433i	$-0.358961\pi$
$433$	17.8425	0.857458	0.428729	+	0.903433i	$0.358961\pi$
$434$	0	0
$435$	−0.208512	−0.00999737
$436$	12.1976	0.584158
$437$	12.9659	0.620241
$438$	0.652704	0.0311874
$439$	9.28850	0.443316	0.221658	−	0.975125i	$-0.428853\pi$
$439$	9.28850	0.443316	0.221658	+	0.975125i	$0.428853\pi$
$440$	−0.162504	−0.00774707
$441$	0	0
$442$	2.62866	0.125033
$443$	16.4219	0.780228	0.390114	−	0.920767i	$-0.372436\pi$
$443$	16.4219	0.780228	0.390114	+	0.920767i	$0.372436\pi$
$444$	−2.36959	−0.112456
$445$	−0.829755	−0.0393342
$446$	3.21482	0.152226
$447$	7.83750	0.370701
$448$	0	0
$449$	−36.5621	−1.72547	−0.862737	−	0.505654i	$-0.831251\pi$
$449$	−36.5621	−1.72547	−0.862737	+	0.505654i	$0.831251\pi$
$450$	−4.70409	−0.221753
$451$	−8.29086	−0.390401
$452$	20.4192	0.960439
$453$	12.3669	0.581047
$454$	−7.12155	−0.334231
$455$	0	0
$456$	−4.59627	−0.215240
$457$	−8.99319	−0.420684	−0.210342	−	0.977628i	$-0.567458\pi$
$457$	−8.99319	−0.420684	−0.210342	+	0.977628i	$0.567458\pi$
$458$	9.05199	0.422972
$459$	18.7692	0.876071
$460$	−0.458416	−0.0213737
$461$	−13.8844	−0.646663	−0.323331	−	0.946286i	$-0.604803\pi$
$461$	−13.8844	−0.646663	−0.323331	+	0.946286i	$0.604803\pi$
$462$	0	0
$463$	−11.0624	−0.514114	−0.257057	−	0.966396i	$-0.582753\pi$
$463$	−11.0624	−0.514114	−0.257057	+	0.966396i	$0.582753\pi$
$464$	10.6919	0.496359
$465$	0.313148	0.0145219
$466$	−0.968216	−0.0448517
$467$	−5.09657	−0.235841	−0.117921	−	0.993023i	$-0.537623\pi$
$467$	−5.09657	−0.235841	−0.117921	+	0.993023i	$0.537623\pi$
$468$	6.26352	0.289531
$469$	0	0
$470$	−0.386821	−0.0178427
$471$	−8.54757	−0.393851
$472$	13.1284	0.604282
$473$	2.22668	0.102383
$474$	−1.68004	−0.0771670
$475$	31.9641	1.46661
$476$	0	0
$477$	−26.2995	−1.20417
$478$	3.89662	0.178227
$479$	−18.9941	−0.867864	−0.433932	−	0.900946i	$-0.642874\pi$
$479$	−18.9941	−0.867864	−0.433932	+	0.900946i	$0.642874\pi$
$480$	0.246282	0.0112412
$481$	2.90673	0.132535
$482$	3.56179	0.162235
$483$	0	0
$484$	−1.87939	−0.0854266
$485$	1.99401	0.0905435
$486$	−4.37639	−0.198517
$487$	−18.7246	−0.848494	−0.424247	−	0.905547i	$-0.639461\pi$
$487$	−18.7246	−0.848494	−0.424247	+	0.905547i	$0.639461\pi$
$488$	1.93170	0.0874441
$489$	−5.64084	−0.255088
$490$	0	0
$491$	3.08378	0.139169	0.0695845	−	0.997576i	$-0.477833\pi$
$491$	3.08378	0.139169	0.0695845	+	0.997576i	$0.477833\pi$
$492$	8.29086	0.373781
$493$	−20.0469	−0.902869
$494$	2.73143	0.122893
$495$	0.327696	0.0147288
$496$	−16.0574	−0.720997
$497$	0	0
$498$	−1.29767	−0.0581498
$499$	9.62866	0.431038	0.215519	−	0.976500i	$-0.430856\pi$
$499$	9.62866	0.431038	0.215519	+	0.976500i	$0.430856\pi$
$500$	−2.26352	−0.101228
$501$	11.2463	0.502447
$502$	10.1138	0.451401
$503$	0.802414	0.0357779	0.0178889	−	0.999840i	$-0.494305\pi$
$503$	0.802414	0.0357779	0.0178889	+	0.999840i	$0.494305\pi$
$504$	0	0
$505$	−0.820260	−0.0365011
$506$	0.702333	0.0312225
$507$	−6.11650	−0.271643
$508$	−5.03684	−0.223473
$509$	14.6486	0.649287	0.324644	−	0.945836i	$-0.394756\pi$
$509$	14.6486	0.649287	0.324644	+	0.945836i	$0.394756\pi$
$510$	−0.137527	−0.00608979
$511$	0	0
$512$	−21.4962	−0.950006
$513$	19.5030	0.861078
$514$	2.91622	0.128629
$515$	−1.10607	−0.0487391
$516$	−2.22668	−0.0980242
$517$	−9.23442	−0.406129
$518$	0	0
$519$	−1.23442	−0.0541851
$520$	−0.199340	−0.00874166
$521$	−12.0324	−0.527149	−0.263574	−	0.964639i	$-0.584901\pi$
$521$	−12.0324	−0.527149	−0.263574	+	0.964639i	$0.584901\pi$
$522$	3.06561	0.134178
$523$	15.3027	0.669141	0.334571	−	0.942371i	$-0.391409\pi$
$523$	15.3027	0.669141	0.334571	+	0.942371i	$0.391409\pi$
$524$	−26.3628	−1.15166
$525$	0	0
$526$	8.46110	0.368922
$527$	30.1070	1.31148
$528$	1.75103	0.0762038
$529$	−18.9103	−0.822189
$530$	0.405488	0.0176133
$531$	−26.4739	−1.14887
$532$	0	0
$533$	−10.1702	−0.440522
$534$	−1.27126	−0.0550128
$535$	0.979466	0.0423460
$536$	−4.12836	−0.178318
$537$	6.07604	0.262200
$538$	10.1379	0.437074
$539$	0	0
$540$	−0.689540	−0.0296731
$541$	−16.4861	−0.708792	−0.354396	−	0.935095i	$-0.615314\pi$
$541$	−16.4861	−0.708792	−0.354396	+	0.935095i	$0.615314\pi$
$542$	3.32232	0.142706
$543$	−8.76239	−0.376030
$544$	23.6783	1.01520
$545$	0.782814	0.0335321
$546$	0	0
$547$	−16.0060	−0.684367	−0.342183	−	0.939633i	$-0.611166\pi$
$547$	−16.0060	−0.684367	−0.342183	+	0.939633i	$0.611166\pi$
$548$	−27.5158	−1.17542
$549$	−3.89536	−0.166250
$550$	1.73143	0.0738284
$551$	−20.8307	−0.887417
$552$	−1.44974	−0.0617051
$553$	0	0
$554$	7.04364	0.299256
$555$	−0.152075	−0.00645521
$556$	20.7023	0.877975
$557$	19.3286	0.818980	0.409490	−	0.912315i	$-0.365707\pi$
$557$	19.3286	0.818980	0.409490	+	0.912315i	$0.365707\pi$
$558$	−4.60401	−0.194903
$559$	2.73143	0.115527
$560$	0	0
$561$	−3.28312	−0.138613
$562$	1.91891	0.0809443
$563$	32.4611	1.36807	0.684036	−	0.729448i	$-0.260223\pi$
$563$	32.4611	1.36807	0.684036	+	0.729448i	$0.260223\pi$
$564$	9.23442	0.388839
$565$	1.31046	0.0551315
$566$	1.41241	0.0593679
$567$	0	0
$568$	−11.4456	−0.480248
$569$	−4.44656	−0.186409	−0.0932047	−	0.995647i	$-0.529711\pi$
$569$	−4.44656	−0.186409	−0.0932047	+	0.995647i	$0.529711\pi$
$570$	−0.142903	−0.00598557
$571$	7.76146	0.324807	0.162403	−	0.986724i	$-0.448075\pi$
$571$	7.76146	0.324807	0.162403	+	0.986724i	$0.448075\pi$
$572$	−2.30541	−0.0963939
$573$	−5.94213	−0.248236
$574$	0	0
$575$	10.0820	0.420449
$576$	14.2608	0.594201
$577$	21.5303	0.896320	0.448160	−	0.893953i	$-0.352080\pi$
$577$	21.5303	0.896320	0.448160	+	0.893953i	$0.352080\pi$
$578$	−7.31820	−0.304397
$579$	−10.6682	−0.443355
$580$	0.736482	0.0305807
$581$	0	0
$582$	3.05501	0.126634
$583$	9.68004	0.400906
$584$	−4.75877	−0.196919
$585$	0.401979	0.0166198
$586$	−8.07697	−0.333657
$587$	−24.2523	−1.00100	−0.500499	−	0.865737i	$-0.666850\pi$
$587$	−24.2523	−1.00100	−0.500499	+	0.865737i	$0.666850\pi$
$588$	0	0
$589$	31.2841	1.28904
$590$	0.408176	0.0168044
$591$	8.50980	0.350046
$592$	7.79797	0.320495
$593$	8.25847	0.339135	0.169567	−	0.985519i	$-0.445763\pi$
$593$	8.25847	0.339135	0.169567	+	0.985519i	$0.445763\pi$
$594$	1.05644	0.0433461
$595$	0	0
$596$	−27.6827	−1.13393
$597$	−3.33544	−0.136510
$598$	0.861540	0.0352310
$599$	14.4834	0.591775	0.295888	−	0.955223i	$-0.404385\pi$
$599$	14.4834	0.591775	0.295888	+	0.955223i	$0.404385\pi$
$600$	−3.57398	−0.145907
$601$	9.81109	0.400203	0.200101	−	0.979775i	$-0.435873\pi$
$601$	9.81109	0.400203	0.200101	+	0.979775i	$0.435873\pi$
$602$	0	0
$603$	8.32501	0.339021
$604$	−43.6810	−1.77735
$605$	−0.120615	−0.00490369
$606$	−1.25671	−0.0510504
$607$	35.0711	1.42349	0.711746	−	0.702437i	$-0.247905\pi$
$607$	35.0711	1.42349	0.711746	+	0.702437i	$0.247905\pi$
$608$	24.6040	0.997824
$609$	0	0
$610$	0.0600590	0.00243172
$611$	−11.3277	−0.458270
$612$	−31.5057	−1.27354
$613$	−35.8188	−1.44671	−0.723354	−	0.690477i	$-0.757401\pi$
$613$	−35.8188	−1.44671	−0.723354	+	0.690477i	$0.757401\pi$
$614$	−5.31820	−0.214625
$615$	0.532089	0.0214559
$616$	0	0
$617$	0.650015	0.0261686	0.0130843	−	0.999914i	$-0.495835\pi$
$617$	0.650015	0.0261686	0.0130843	+	0.999914i	$0.495835\pi$
$618$	−1.69459	−0.0681665
$619$	−16.1575	−0.649423	−0.324711	−	0.945813i	$-0.605267\pi$
$619$	−16.1575	−0.649423	−0.324711	+	0.945813i	$0.605267\pi$
$620$	−1.10607	−0.0444207
$621$	6.15158	0.246854
$622$	−2.45605	−0.0984787
$623$	0	0
$624$	2.14796	0.0859871
$625$	24.7820	0.991280
$626$	9.16788	0.366422
$627$	−3.41147	−0.136241
$628$	30.1908	1.20474
$629$	−14.6209	−0.582974
$630$	0	0
$631$	4.31584	0.171811	0.0859054	−	0.996303i	$-0.472622\pi$
$631$	4.31584	0.171811	0.0859054	+	0.996303i	$0.472622\pi$
$632$	12.2490	0.487238
$633$	5.88713	0.233992
$634$	0.0597347	0.00237237
$635$	−0.323253	−0.0128279
$636$	−9.68004	−0.383839
$637$	0	0
$638$	−1.12836	−0.0446720
$639$	23.0806	0.913054
$640$	−1.14559	−0.0452835
$641$	12.9186	0.510253	0.255127	−	0.966908i	$-0.417883\pi$
$641$	12.9186	0.510253	0.255127	+	0.966908i	$0.417883\pi$
$642$	1.50063	0.0592251
$643$	42.4296	1.67326	0.836631	−	0.547767i	$-0.184522\pi$
$643$	42.4296	1.67326	0.836631	+	0.547767i	$0.184522\pi$
$644$	0	0
$645$	−0.142903	−0.00562682
$646$	−13.7392	−0.540560
$647$	30.2431	1.18898	0.594489	−	0.804103i	$-0.297354\pi$
$647$	30.2431	1.18898	0.594489	+	0.804103i	$0.297354\pi$
$648$	8.80066	0.345723
$649$	9.74422	0.382494
$650$	2.12391	0.0833067
$651$	0	0
$652$	19.9240	0.780283
$653$	−10.2071	−0.399434	−0.199717	−	0.979854i	$-0.564002\pi$
$653$	−10.2071	−0.399434	−0.199717	+	0.979854i	$0.564002\pi$
$654$	1.19934	0.0468979
$655$	−1.69190	−0.0661082
$656$	−27.2841	−1.06526
$657$	9.59627	0.374386
$658$	0	0
$659$	−27.9777	−1.08986	−0.544928	−	0.838483i	$-0.683443\pi$
$659$	−27.9777	−1.08986	−0.544928	+	0.838483i	$0.683443\pi$
$660$	0.120615	0.00469492
$661$	−8.16519	−0.317589	−0.158795	−	0.987312i	$-0.550761\pi$
$661$	−8.16519	−0.317589	−0.158795	+	0.987312i	$0.550761\pi$
$662$	0.0377703	0.00146798
$663$	−4.02734	−0.156409
$664$	9.46110	0.367162
$665$	0	0
$666$	2.23585	0.0866375
$667$	−6.57036	−0.254405
$668$	−39.7229	−1.53692
$669$	−4.92539	−0.190427
$670$	−0.128356	−0.00495881
$671$	1.43376	0.0553498
$672$	0	0
$673$	17.6905	0.681918	0.340959	−	0.940078i	$-0.389248\pi$
$673$	17.6905	0.681918	0.340959	+	0.940078i	$0.389248\pi$
$674$	1.63135	0.0628372
$675$	15.1652	0.583709
$676$	21.6040	0.830923
$677$	−45.1061	−1.73357	−0.866783	−	0.498685i	$-0.833817\pi$
$677$	−45.1061	−1.73357	−0.866783	+	0.498685i	$0.833817\pi$
$678$	2.00774	0.0771068
$679$	0	0
$680$	1.00269	0.0384513
$681$	10.9108	0.418104
$682$	1.69459	0.0648893
$683$	−10.6004	−0.405612	−0.202806	−	0.979219i	$-0.565006\pi$
$683$	−10.6004	−0.405612	−0.202806	+	0.979219i	$0.565006\pi$
$684$	−32.7374	−1.25175
$685$	−1.76590	−0.0674716
$686$	0	0
$687$	−13.8685	−0.529115
$688$	7.32770	0.279366
$689$	11.8743	0.452376
$690$	−0.0450742	−0.00171595
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	4.36009	0.165746
$693$	0	0
$694$	−1.44326	−0.0547853
$695$	1.32863	0.0503978
$696$	2.32913	0.0882853
$697$	51.1566	1.93770
$698$	5.72100	0.216543
$699$	1.48339	0.0561071
$700$	0	0
$701$	41.0533	1.55056	0.775280	−	0.631618i	$-0.217609\pi$
$701$	41.0533	1.55056	0.775280	+	0.631618i	$0.217609\pi$
$702$	1.29591	0.0489110
$703$	−15.1925	−0.572997
$704$	−5.24897	−0.197828
$705$	0.592645	0.0223203
$706$	−7.84968	−0.295427
$707$	0	0
$708$	−9.74422	−0.366210
$709$	−33.1070	−1.24336	−0.621680	−	0.783272i	$-0.713549\pi$
$709$	−33.1070	−1.24336	−0.621680	+	0.783272i	$0.713549\pi$
$710$	−0.355858	−0.0133551
$711$	−24.7006	−0.926344
$712$	9.26857	0.347354
$713$	9.86753	0.369542
$714$	0	0
$715$	−0.147956	−0.00553324
$716$	−21.4611	−0.802039
$717$	−5.96997	−0.222953
$718$	12.1807	0.454579
$719$	−27.5152	−1.02614	−0.513071	−	0.858346i	$-0.671492\pi$
$719$	−27.5152	−1.02614	−0.513071	+	0.858346i	$0.671492\pi$
$720$	1.07840	0.0401896
$721$	0	0
$722$	−7.67768	−0.285734
$723$	−5.45699	−0.202947
$724$	30.9495	1.15023
$725$	−16.1976	−0.601563
$726$	−0.184793	−0.00685829
$727$	−10.1111	−0.375001	−0.187500	−	0.982265i	$-0.560039\pi$
$727$	−10.1111	−0.375001	−0.187500	+	0.982265i	$0.560039\pi$
$728$	0	0
$729$	−12.8912	−0.477454
$730$	−0.147956	−0.00547609
$731$	−13.7392	−0.508162
$732$	−1.43376	−0.0529934
$733$	−37.8708	−1.39879	−0.699395	−	0.714735i	$-0.746547\pi$
$733$	−37.8708	−1.39879	−0.699395	+	0.714735i	$0.746547\pi$
$734$	−4.11886	−0.152030
$735$	0	0
$736$	7.76053	0.286057
$737$	−3.06418	−0.112870
$738$	−7.82295	−0.287967
$739$	0.882074	0.0324476	0.0162238	−	0.999868i	$-0.494836\pi$
$739$	0.882074	0.0324476	0.0162238	+	0.999868i	$0.494836\pi$
$740$	0.537141	0.0197457
$741$	−4.18479	−0.153732
$742$	0	0
$743$	22.5800	0.828379	0.414189	−	0.910191i	$-0.364065\pi$
$743$	22.5800	0.828379	0.414189	+	0.910191i	$0.364065\pi$
$744$	−3.49794	−0.128241
$745$	−1.77662	−0.0650902
$746$	−10.0770	−0.368944
$747$	−19.0787	−0.698054
$748$	11.5963	0.424002
$749$	0	0
$750$	−0.222563	−0.00812684
$751$	−39.5954	−1.44486	−0.722429	−	0.691445i	$-0.756974\pi$
$751$	−39.5954	−1.44486	−0.722429	+	0.691445i	$0.756974\pi$
$752$	−30.3892	−1.10818
$753$	−15.4953	−0.564678
$754$	−1.38413	−0.0504072
$755$	−2.80335	−0.102024
$756$	0	0
$757$	19.5253	0.709658	0.354829	−	0.934931i	$-0.384539\pi$
$757$	19.5253	0.709658	0.354829	+	0.934931i	$0.384539\pi$
$758$	−6.34493	−0.230458
$759$	−1.07604	−0.0390577
$760$	1.04189	0.0377933
$761$	23.2094	0.841342	0.420671	−	0.907213i	$-0.361795\pi$
$761$	23.2094	0.841342	0.420671	+	0.907213i	$0.361795\pi$
$762$	−0.495252	−0.0179411
$763$	0	0
$764$	20.9881	0.759324
$765$	−2.02196	−0.0731043
$766$	−5.36184	−0.193731
$767$	11.9531	0.431600
$768$	3.83069	0.138228
$769$	−37.2222	−1.34227	−0.671134	−	0.741336i	$-0.734193\pi$
$769$	−37.2222	−1.34227	−0.671134	+	0.741336i	$0.734193\pi$
$770$	0	0
$771$	−4.46791	−0.160908
$772$	37.6810	1.35617
$773$	−41.2891	−1.48507	−0.742533	−	0.669810i	$-0.766376\pi$
$773$	−41.2891	−1.48507	−0.742533	+	0.669810i	$0.766376\pi$
$774$	2.10101	0.0755194
$775$	24.3259	0.873814
$776$	−22.2736	−0.799576
$777$	0	0
$778$	8.34998	0.299361
$779$	53.1566	1.90453
$780$	0.147956	0.00529767
$781$	−8.49525	−0.303984
$782$	−4.33357	−0.154968
$783$	−9.88301	−0.353190
$784$	0	0
$785$	1.93758	0.0691551
$786$	−2.59215	−0.0924589
$787$	22.5321	0.803182	0.401591	−	0.915819i	$-0.368457\pi$
$787$	22.5321	0.803182	0.401591	+	0.915819i	$0.368457\pi$
$788$	−30.0574	−1.07075
$789$	−12.9632	−0.461501
$790$	0.380835	0.0135495
$791$	0	0
$792$	−3.66044	−0.130068
$793$	1.75877	0.0624558
$794$	−3.17705	−0.112749
$795$	−0.621244	−0.0220332
$796$	11.7811	0.417569
$797$	4.79528	0.169858	0.0849288	−	0.996387i	$-0.472934\pi$
$797$	4.79528	0.169858	0.0849288	+	0.996387i	$0.472934\pi$
$798$	0	0
$799$	56.9786	2.01576
$800$	19.1317	0.676406
$801$	−18.6905	−0.660395
$802$	−2.78880	−0.0984760
$803$	−3.53209	−0.124645
$804$	3.06418	0.108065
$805$	0	0
$806$	2.07873	0.0732200
$807$	−15.5321	−0.546755
$808$	9.16250	0.322336
$809$	−40.9181	−1.43860	−0.719302	−	0.694698i	$-0.755538\pi$
$809$	−40.9181	−1.43860	−0.719302	+	0.694698i	$0.755538\pi$
$810$	0.273623	0.00961414
$811$	30.8408	1.08297	0.541483	−	0.840711i	$-0.317863\pi$
$811$	30.8408	1.08297	0.541483	+	0.840711i	$0.317863\pi$
$812$	0	0
$813$	−5.09009	−0.178517
$814$	−0.822948	−0.0288443
$815$	1.27868	0.0447901
$816$	−10.8043	−0.378226
$817$	−14.2763	−0.499465
$818$	0.630415	0.0220419
$819$	0	0
$820$	−1.87939	−0.0656310
$821$	−12.1652	−0.424568	−0.212284	−	0.977208i	$-0.568090\pi$
$821$	−12.1652	−0.424568	−0.212284	+	0.977208i	$0.568090\pi$
$822$	−2.70552	−0.0943658
$823$	−25.7760	−0.898495	−0.449248	−	0.893407i	$-0.648308\pi$
$823$	−25.7760	−0.898495	−0.449248	+	0.893407i	$0.648308\pi$
$824$	12.3550	0.430408
$825$	−2.65270	−0.0923553
$826$	0	0
$827$	−23.6355	−0.821886	−0.410943	−	0.911661i	$-0.634800\pi$
$827$	−23.6355	−0.821886	−0.410943	+	0.911661i	$0.634800\pi$
$828$	−10.3259	−0.358851
$829$	10.1922	0.353990	0.176995	−	0.984212i	$-0.443362\pi$
$829$	10.1922	0.353990	0.176995	+	0.984212i	$0.443362\pi$
$830$	0.294157	0.0102103
$831$	−10.7915	−0.374353
$832$	−6.43882	−0.223226
$833$	0	0
$834$	2.03558	0.0704863
$835$	−2.54933	−0.0882230
$836$	12.0496	0.416745
$837$	14.8425	0.513034
$838$	−12.6331	−0.436403
$839$	−12.5193	−0.432214	−0.216107	−	0.976370i	$-0.569336\pi$
$839$	−12.5193	−0.432214	−0.216107	+	0.976370i	$0.569336\pi$
$840$	0	0
$841$	−18.4442	−0.636007
$842$	4.63404	0.159699
$843$	−2.93994	−0.101257
$844$	−20.7939	−0.715754
$845$	1.38650	0.0476969
$846$	−8.71326	−0.299568
$847$	0	0
$848$	31.8557	1.09393
$849$	−2.16393	−0.0742660
$850$	−10.6833	−0.366436
$851$	−4.79199	−0.164267
$852$	8.49525	0.291043
$853$	−0.427777	−0.0146468	−0.00732340	−	0.999973i	$-0.502331\pi$
$853$	−0.427777	−0.0146468	−0.00732340	+	0.999973i	$0.502331\pi$
$854$	0	0
$855$	−2.10101	−0.0718532
$856$	−10.9409	−0.373951
$857$	−45.6991	−1.56105	−0.780527	−	0.625123i	$-0.785049\pi$
$857$	−45.6991	−1.56105	−0.780527	+	0.625123i	$0.785049\pi$
$858$	−0.226682	−0.00773878
$859$	−47.9023	−1.63440	−0.817202	−	0.576351i	$-0.804476\pi$
$859$	−47.9023	−1.63440	−0.817202	+	0.576351i	$0.804476\pi$
$860$	0.504748	0.0172118
$861$	0	0
$862$	−3.75010	−0.127729
$863$	12.1753	0.414452	0.207226	−	0.978293i	$-0.433556\pi$
$863$	12.1753	0.414452	0.207226	+	0.978293i	$0.433556\pi$
$864$	11.6732	0.397132
$865$	0.279821	0.00951419
$866$	−6.19665	−0.210571
$867$	11.2121	0.380784
$868$	0	0
$869$	9.09152	0.308409
$870$	0.0724153	0.00245511
$871$	−3.75877	−0.127361
$872$	−8.74422	−0.296117
$873$	44.9157	1.52017
$874$	−4.50299	−0.152316
$875$	0	0
$876$	3.53209	0.119338
$877$	−13.1179	−0.442961	−0.221480	−	0.975165i	$-0.571089\pi$
$877$	−13.1179	−0.442961	−0.221480	+	0.975165i	$0.571089\pi$
$878$	−3.22586	−0.108868
$879$	12.3746	0.417386
$880$	−0.396926	−0.0133804
$881$	−16.8571	−0.567930	−0.283965	−	0.958835i	$-0.591650\pi$
$881$	−16.8571	−0.567930	−0.283965	+	0.958835i	$0.591650\pi$
$882$	0	0
$883$	9.24030	0.310961	0.155480	−	0.987839i	$-0.450307\pi$
$883$	9.24030	0.310961	0.155480	+	0.987839i	$0.450307\pi$
$884$	14.2249	0.478436
$885$	−0.625362	−0.0210213
$886$	−5.70327	−0.191605
$887$	24.0182	0.806451	0.403226	−	0.915101i	$-0.367889\pi$
$887$	24.0182	0.806451	0.403226	+	0.915101i	$0.367889\pi$
$888$	1.69871	0.0570050
$889$	0	0
$890$	0.288171	0.00965951
$891$	6.53209	0.218833
$892$	17.3969	0.582492
$893$	59.2063	1.98126
$894$	−2.72193	−0.0910351
$895$	−1.37733	−0.0460389
$896$	0	0
$897$	−1.31996	−0.0440720
$898$	12.6979	0.423734
$899$	−15.8530	−0.528726
$900$	−25.4561	−0.848535
$901$	−59.7282	−1.98984
$902$	2.87939	0.0958730
$903$	0	0
$904$	−14.6382	−0.486858
$905$	1.98627	0.0660260
$906$	−4.29498	−0.142691
$907$	5.79385	0.192382	0.0961909	−	0.995363i	$-0.469334\pi$
$907$	5.79385	0.192382	0.0961909	+	0.995363i	$0.469334\pi$
$908$	−38.5381	−1.27893
$909$	−18.4766	−0.612830
$910$	0	0
$911$	0.421903	0.0139783	0.00698914	−	0.999976i	$-0.497775\pi$
$911$	0.421903	0.0139783	0.00698914	+	0.999976i	$0.497775\pi$
$912$	−11.2267	−0.371753
$913$	7.02229	0.232404
$914$	3.12330	0.103310
$915$	−0.0920157	−0.00304195
$916$	48.9846	1.61850
$917$	0	0
$918$	−6.51847	−0.215142
$919$	−0.472964	−0.0156016	−0.00780081	−	0.999970i	$-0.502483\pi$
$919$	−0.472964	−0.0156016	−0.00780081	+	0.999970i	$0.502483\pi$
$920$	0.328630	0.0108346
$921$	8.14796	0.268484
$922$	4.82201	0.158805
$923$	−10.4210	−0.343010
$924$	0	0
$925$	−11.8135	−0.388424
$926$	3.84194	0.126254
$927$	−24.9145	−0.818298
$928$	−12.4679	−0.409279
$929$	6.99825	0.229605	0.114802	−	0.993388i	$-0.463376\pi$
$929$	6.99825	0.229605	0.114802	+	0.993388i	$0.463376\pi$
$930$	−0.108755	−0.00356622
$931$	0	0
$932$	−5.23947	−0.171625
$933$	3.76289	0.123191
$934$	1.77002	0.0579168
$935$	0.744223	0.0243387
$936$	−4.49020	−0.146767
$937$	−8.19017	−0.267561	−0.133781	−	0.991011i	$-0.542712\pi$
$937$	−8.19017	−0.267561	−0.133781	+	0.991011i	$0.542712\pi$
$938$	0	0
$939$	−14.0460	−0.458374
$940$	−2.09327	−0.0682751
$941$	−40.3705	−1.31604	−0.658021	−	0.753000i	$-0.728606\pi$
$941$	−40.3705	−1.31604	−0.658021	+	0.753000i	$0.728606\pi$
$942$	2.96854	0.0967203
$943$	16.7665	0.545993
$944$	32.0669	1.04369
$945$	0	0
$946$	−0.773318	−0.0251428
$947$	−41.9240	−1.36235	−0.681173	−	0.732123i	$-0.738530\pi$
$947$	−41.9240	−1.36235	−0.681173	+	0.732123i	$0.738530\pi$
$948$	−9.09152	−0.295279
$949$	−4.33275	−0.140647
$950$	−11.1010	−0.360164
$951$	−0.0915189	−0.00296770
$952$	0	0
$953$	−38.6040	−1.25051	−0.625253	−	0.780422i	$-0.715004\pi$
$953$	−38.6040	−1.25051	−0.625253	+	0.780422i	$0.715004\pi$
$954$	9.13373	0.295715
$955$	1.34697	0.0435870
$956$	21.0865	0.681985
$957$	1.72874	0.0558823
$958$	6.59659	0.213126
$959$	0	0
$960$	0.336867	0.0108723
$961$	−7.19160	−0.231987
$962$	−1.00950	−0.0325474
$963$	22.0627	0.710962
$964$	19.2746	0.620792
$965$	2.41828	0.0778472
$966$	0	0
$967$	−2.04364	−0.0657192	−0.0328596	−	0.999460i	$-0.510461\pi$
$967$	−2.04364	−0.0657192	−0.0328596	+	0.999460i	$0.510461\pi$
$968$	1.34730	0.0433037
$969$	21.0496	0.676212
$970$	−0.692514	−0.0222353
$971$	9.55531	0.306645	0.153322	−	0.988176i	$-0.451003\pi$
$971$	9.55531	0.306645	0.153322	+	0.988176i	$0.451003\pi$
$972$	−23.6827	−0.759624
$973$	0	0
$974$	6.50299	0.208369
$975$	−3.25402	−0.104212
$976$	4.71831	0.151029
$977$	−47.1958	−1.50993	−0.754964	−	0.655766i	$-0.772346\pi$
$977$	−47.1958	−1.50993	−0.754964	+	0.655766i	$0.772346\pi$
$978$	1.95904	0.0626433
$979$	6.87939	0.219866
$980$	0	0
$981$	17.6331	0.562982
$982$	−1.07098	−0.0341765
$983$	−2.05375	−0.0655044	−0.0327522	−	0.999464i	$-0.510427\pi$
$983$	−2.05375	−0.0655044	−0.0327522	+	0.999464i	$0.510427\pi$
$984$	−5.94356	−0.189474
$985$	−1.92902	−0.0614635
$986$	6.96223	0.221723
$987$	0	0
$988$	14.7811	0.470248
$989$	−4.50299	−0.143187
$990$	−0.113808	−0.00361704
$991$	47.6979	1.51517	0.757587	−	0.652735i	$-0.226378\pi$
$991$	47.6979	1.51517	0.757587	+	0.652735i	$0.226378\pi$
$992$	18.7246	0.594507
$993$	−0.0578674	−0.00183637
$994$	0	0
$995$	0.756082	0.0239694
$996$	−7.02229	−0.222510
$997$	46.7205	1.47965	0.739827	−	0.672798i	$-0.234908\pi$
$997$	46.7205	1.47965	0.739827	+	0.672798i	$0.234908\pi$
$998$	−3.34400	−0.105852
$999$	−7.20801	−0.228051

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.a.g.1.2		3
3.2	odd	2		4851.2.a.bk.1.2		3
4.3	odd	2		8624.2.a.co.1.1		3
7.2	even	3		539.2.e.m.67.2		6
7.3	odd	6		77.2.e.a.23.2	✓	6
7.4	even	3		539.2.e.m.177.2		6
7.5	odd	6		77.2.e.a.67.2	yes	6
7.6	odd	2		539.2.a.j.1.2		3
11.10	odd	2		5929.2.a.u.1.2		3
21.5	even	6		693.2.i.h.298.2		6
21.17	even	6		693.2.i.h.100.2		6
21.20	even	2		4851.2.a.bj.1.2		3
28.3	even	6		1232.2.q.m.177.1		6
28.19	even	6		1232.2.q.m.529.1		6
28.27	even	2		8624.2.a.ch.1.3		3
77.3	odd	30		847.2.n.g.9.2		24
77.5	odd	30		847.2.n.g.487.2		24
77.10	even	6		847.2.e.c.485.2		6
77.17	even	30		847.2.n.f.366.2		24
77.19	even	30		847.2.n.f.130.2		24
77.24	even	30		847.2.n.f.807.2		24
77.26	odd	30		847.2.n.g.753.2		24
77.31	odd	30		847.2.n.g.807.2		24
77.38	odd	30		847.2.n.g.366.2		24
77.40	even	30		847.2.n.f.753.2		24
77.47	odd	30		847.2.n.g.130.2		24
77.52	even	30		847.2.n.f.9.2		24
77.54	even	6		847.2.e.c.606.2		6
77.59	odd	30		847.2.n.g.632.2		24
77.61	even	30		847.2.n.f.487.2		24
77.68	even	30		847.2.n.f.81.2		24
77.73	even	30		847.2.n.f.632.2		24
77.75	odd	30		847.2.n.g.81.2		24
77.76	even	2		5929.2.a.x.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.2	✓	6	7.3	odd	6
77.2.e.a.67.2	yes	6	7.5	odd	6
539.2.a.g.1.2		3	1.1	even	1	trivial
539.2.a.j.1.2		3	7.6	odd	2
539.2.e.m.67.2		6	7.2	even	3
539.2.e.m.177.2		6	7.4	even	3
693.2.i.h.100.2		6	21.17	even	6
693.2.i.h.298.2		6	21.5	even	6
847.2.e.c.485.2		6	77.10	even	6
847.2.e.c.606.2		6	77.54	even	6
847.2.n.f.9.2		24	77.52	even	30
847.2.n.f.81.2		24	77.68	even	30
847.2.n.f.130.2		24	77.19	even	30
847.2.n.f.366.2		24	77.17	even	30
847.2.n.f.487.2		24	77.61	even	30
847.2.n.f.632.2		24	77.73	even	30
847.2.n.f.753.2		24	77.40	even	30
847.2.n.f.807.2		24	77.24	even	30
847.2.n.g.9.2		24	77.3	odd	30
847.2.n.g.81.2		24	77.75	odd	30
847.2.n.g.130.2		24	77.47	odd	30
847.2.n.g.366.2		24	77.38	odd	30
847.2.n.g.487.2		24	77.5	odd	30
847.2.n.g.632.2		24	77.59	odd	30
847.2.n.g.753.2		24	77.26	odd	30
847.2.n.g.807.2		24	77.31	odd	30
1232.2.q.m.177.1		6	28.3	even	6
1232.2.q.m.529.1		6	28.19	even	6
4851.2.a.bj.1.2		3	21.20	even	2
4851.2.a.bk.1.2		3	3.2	odd	2
5929.2.a.u.1.2		3	11.10	odd	2
5929.2.a.x.1.2		3	77.76	even	2
8624.2.a.ch.1.3		3	28.27	even	2
8624.2.a.co.1.1		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.a (trivial)

\(f(q)\)	\(=\)	\(q-0.347296 q^{2} +0.532089 q^{3} -1.87939 q^{4} -0.120615 q^{5} -0.184793 q^{6} +1.34730 q^{8} -2.71688 q^{9} +O(q^{10})\)	\(q-0.347296 q^{2} +0.532089 q^{3} -1.87939 q^{4} -0.120615 q^{5} -0.184793 q^{6} +1.34730 q^{8} -2.71688 q^{9} +0.0418891 q^{10} +1.00000 q^{11} -1.00000 q^{12} +1.22668 q^{13} -0.0641778 q^{15} +3.29086 q^{16} -6.17024 q^{17} +0.943563 q^{18} -6.41147 q^{19} +0.226682 q^{20} -0.347296 q^{22} -2.02229 q^{23} +0.716881 q^{24} -4.98545 q^{25} -0.426022 q^{26} -3.04189 q^{27} +3.24897 q^{29} +0.0222887 q^{30} -4.87939 q^{31} -3.83750 q^{32} +0.532089 q^{33} +2.14290 q^{34} +5.10607 q^{36} +2.36959 q^{37} +2.22668 q^{38} +0.652704 q^{39} -0.162504 q^{40} -8.29086 q^{41} +2.22668 q^{43} -1.87939 q^{44} +0.327696 q^{45} +0.702333 q^{46} -9.23442 q^{47} +1.75103 q^{48} +1.73143 q^{50} -3.28312 q^{51} -2.30541 q^{52} +9.68004 q^{53} +1.05644 q^{54} -0.120615 q^{55} -3.41147 q^{57} -1.12836 q^{58} +9.74422 q^{59} +0.120615 q^{60} +1.43376 q^{61} +1.69459 q^{62} -5.24897 q^{64} -0.147956 q^{65} -0.184793 q^{66} -3.06418 q^{67} +11.5963 q^{68} -1.07604 q^{69} -8.49525 q^{71} -3.66044 q^{72} -3.53209 q^{73} -0.822948 q^{74} -2.65270 q^{75} +12.0496 q^{76} -0.226682 q^{78} +9.09152 q^{79} -0.396926 q^{80} +6.53209 q^{81} +2.87939 q^{82} +7.02229 q^{83} +0.744223 q^{85} -0.773318 q^{86} +1.72874 q^{87} +1.34730 q^{88} +6.87939 q^{89} -0.113808 q^{90} +3.80066 q^{92} -2.59627 q^{93} +3.20708 q^{94} +0.773318 q^{95} -2.04189 q^{96} -16.5321 q^{97} -2.71688 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} + 3 q^{8}+O(q^{10}) \) 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 + 3 * q^8	\( 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} + 3 q^{8} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{13} + 9 q^{15} - 6 q^{16} + 3 q^{17} - 12 q^{18} - 9 q^{19} - 6 q^{20} - 6 q^{24} + 3 q^{25} - 9 q^{26} - 6 q^{27} - 3 q^{29} - 6 q^{30} - 9 q^{31} - 9 q^{32} - 3 q^{33} + 6 q^{34} + 3 q^{36} + 3 q^{39} - 3 q^{40} - 9 q^{41} - 3 q^{45} - 24 q^{46} + 3 q^{47} + 18 q^{48} + 15 q^{50} - 18 q^{51} - 9 q^{52} + 9 q^{53} + 18 q^{54} - 6 q^{55} + 15 q^{58} + 6 q^{60} - 12 q^{61} + 3 q^{62} - 3 q^{64} + 15 q^{65} + 3 q^{66} + 21 q^{68} - 21 q^{69} - 9 q^{71} + 12 q^{72} - 6 q^{73} + 18 q^{74} - 9 q^{75} + 9 q^{76} + 6 q^{78} - 3 q^{79} + 27 q^{80} + 15 q^{81} + 3 q^{82} + 15 q^{83} - 27 q^{85} - 9 q^{86} + 24 q^{87} + 3 q^{88} + 15 q^{89} + 36 q^{90} - 3 q^{92} + 6 q^{93} + 9 q^{95} - 3 q^{96} - 45 q^{97}+O(q^{100}) \) 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 + 3 * q^8 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^13 + 9 * q^15 - 6 * q^16 + 3 * q^17 - 12 * q^18 - 9 * q^19 - 6 * q^20 - 6 * q^24 + 3 * q^25 - 9 * q^26 - 6 * q^27 - 3 * q^29 - 6 * q^30 - 9 * q^31 - 9 * q^32 - 3 * q^33 + 6 * q^34 + 3 * q^36 + 3 * q^39 - 3 * q^40 - 9 * q^41 - 3 * q^45 - 24 * q^46 + 3 * q^47 + 18 * q^48 + 15 * q^50 - 18 * q^51 - 9 * q^52 + 9 * q^53 + 18 * q^54 - 6 * q^55 + 15 * q^58 + 6 * q^60 - 12 * q^61 + 3 * q^62 - 3 * q^64 + 15 * q^65 + 3 * q^66 + 21 * q^68 - 21 * q^69 - 9 * q^71 + 12 * q^72 - 6 * q^73 + 18 * q^74 - 9 * q^75 + 9 * q^76 + 6 * q^78 - 3 * q^79 + 27 * q^80 + 15 * q^81 + 3 * q^82 + 15 * q^83 - 27 * q^85 - 9 * q^86 + 24 * q^87 + 3 * q^88 + 15 * q^89 + 36 * q^90 - 3 * q^92 + 6 * q^93 + 9 * q^95 - 3 * q^96 - 45 * q^97

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