LMFDB - Embedded newform 289.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.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:	$2.30767661842$
Analytic rank:	$0$
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:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.347296 q^{2} -0.879385 q^{3} -1.87939 q^{4} +2.34730 q^{5} -0.305407 q^{6} +1.87939 q^{7} -1.34730 q^{8} -2.22668 q^{9} +O(q^{10})$	\(q+0.347296 q^{2} -0.879385 q^{3} -1.87939 q^{4} +2.34730 q^{5} -0.305407 q^{6} +1.87939 q^{7} -1.34730 q^{8} -2.22668 q^{9} +0.815207 q^{10} +5.06418 q^{11} +1.65270 q^{12} +4.71688 q^{13} +0.652704 q^{14} -2.06418 q^{15} +3.29086 q^{16} -0.773318 q^{18} +0.347296 q^{19} -4.41147 q^{20} -1.65270 q^{21} +1.75877 q^{22} +1.77332 q^{23} +1.18479 q^{24} +0.509800 q^{25} +1.63816 q^{26} +4.59627 q^{27} -3.53209 q^{28} -2.22668 q^{29} -0.716881 q^{30} -1.94356 q^{31} +3.83750 q^{32} -4.45336 q^{33} +4.41147 q^{35} +4.18479 q^{36} +6.17024 q^{37} +0.120615 q^{38} -4.14796 q^{39} -3.16250 q^{40} -5.17024 q^{41} -0.573978 q^{42} -1.47565 q^{43} -9.51754 q^{44} -5.22668 q^{45} +0.615867 q^{46} -8.53209 q^{47} -2.89393 q^{48} -3.46791 q^{49} +0.177052 q^{50} -8.86484 q^{52} -10.4534 q^{53} +1.59627 q^{54} +11.8871 q^{55} -2.53209 q^{56} -0.305407 q^{57} -0.773318 q^{58} +5.00774 q^{59} +3.87939 q^{60} +0.184793 q^{61} -0.674992 q^{62} -4.18479 q^{63} -5.24897 q^{64} +11.0719 q^{65} -1.54664 q^{66} -2.44831 q^{67} -1.55943 q^{69} +1.53209 q^{70} +9.92127 q^{71} +3.00000 q^{72} -10.9017 q^{73} +2.14290 q^{74} -0.448311 q^{75} -0.652704 q^{76} +9.51754 q^{77} -1.44057 q^{78} -4.43376 q^{79} +7.72462 q^{80} +2.63816 q^{81} -1.79561 q^{82} +13.5817 q^{83} +3.10607 q^{84} -0.512489 q^{86} +1.95811 q^{87} -6.82295 q^{88} -6.32770 q^{89} -1.81521 q^{90} +8.86484 q^{91} -3.33275 q^{92} +1.70914 q^{93} -2.96316 q^{94} +0.815207 q^{95} -3.37464 q^{96} -9.27631 q^{97} -1.20439 q^{98} -11.2763 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 6 q^{10} + 6 q^{11} + 6 q^{12} + 6 q^{13} + 3 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{18} - 3 q^{20} - 6 q^{21} - 6 q^{22} + 12 q^{23} + 3 q^{25} - 12 q^{26} - 6 q^{28} + 6 q^{30} + 9 q^{31} + 9 q^{32} + 3 q^{35} + 9 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 12 q^{40} + 6 q^{41} + 6 q^{42} + 15 q^{43} - 6 q^{44} - 9 q^{45} - 9 q^{46} - 21 q^{47} - 21 q^{48} - 15 q^{49} + 21 q^{50} - 3 q^{52} - 18 q^{53} - 9 q^{54} + 6 q^{55} - 3 q^{56} - 3 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{60} - 3 q^{61} + 3 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{66} - 9 q^{67} + 21 q^{69} + 21 q^{71} + 9 q^{72} - 21 q^{73} + 6 q^{74} - 3 q^{75} - 3 q^{76} + 6 q^{77} - 30 q^{78} + 3 q^{79} - 9 q^{80} - 9 q^{81} - 6 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{86} + 9 q^{87} - 15 q^{89} - 9 q^{90} + 3 q^{91} + 9 q^{92} + 21 q^{93} + 3 q^{94} + 6 q^{95} + 12 q^{96} + 6 q^{97} - 3 q^{98}+O(q^{100}) $ 3 * q + 3 * q^3 + 6 * q^5 - 3 * q^6 - 3 * q^8 + 6 * q^10 + 6 * q^11 + 6 * q^12 + 6 * q^13 + 3 * q^14 + 3 * q^15 - 6 * q^16 - 9 * q^18 - 3 * q^20 - 6 * q^21 - 6 * q^22 + 12 * q^23 + 3 * q^25 - 12 * q^26 - 6 * q^28 + 6 * q^30 + 9 * q^31 + 9 * q^32 + 3 * q^35 + 9 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 12 * q^40 + 6 * q^41 + 6 * q^42 + 15 * q^43 - 6 * q^44 - 9 * q^45 - 9 * q^46 - 21 * q^47 - 21 * q^48 - 15 * q^49 + 21 * q^50 - 3 * q^52 - 18 * q^53 - 9 * q^54 + 6 * q^55 - 3 * q^56 - 3 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^60 - 3 * q^61 + 3 * q^62 - 9 * q^63 - 3 * q^64 - 18 * q^66 - 9 * q^67 + 21 * q^69 + 21 * q^71 + 9 * q^72 - 21 * q^73 + 6 * q^74 - 3 * q^75 - 3 * q^76 + 6 * q^77 - 30 * q^78 + 3 * q^79 - 9 * q^80 - 9 * q^81 - 6 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^86 + 9 * q^87 - 15 * q^89 - 9 * q^90 + 3 * q^91 + 9 * q^92 + 21 * q^93 + 3 * q^94 + 6 * q^95 + 12 * q^96 + 6 * q^97 - 3 * q^98

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	$-0.460817\pi$
$2$	0.347296	0.245576	0.122788	+	0.992433i	$0.460817\pi$
$3$	−0.879385	−0.507713	−0.253857	−	0.967242i	$-0.581699\pi$
$3$	−0.879385	−0.507713	−0.253857	+	0.967242i	$0.581699\pi$
$4$	−1.87939	−0.939693
$5$	2.34730	1.04974	0.524871	−	0.851182i	$-0.324113\pi$
$5$	2.34730	1.04974	0.524871	+	0.851182i	$0.324113\pi$
$6$	−0.305407	−0.124682
$7$	1.87939	0.710341	0.355170	−	0.934802i	$-0.384423\pi$
$7$	1.87939	0.710341	0.355170	+	0.934802i	$0.384423\pi$
$8$	−1.34730	−0.476341
$9$	−2.22668	−0.742227
$10$	0.815207	0.257791
$11$	5.06418	1.52691	0.763454	−	0.645863i	$-0.223502\pi$
$11$	5.06418	1.52691	0.763454	+	0.645863i	$0.223502\pi$
$12$	1.65270	0.477094
$13$	4.71688	1.30823	0.654114	−	0.756396i	$-0.273042\pi$
$13$	4.71688	1.30823	0.654114	+	0.756396i	$0.273042\pi$
$14$	0.652704	0.174442
$15$	−2.06418	−0.532968
$16$	3.29086	0.822715
$17$	0	0
$17$	0	0
$18$	−0.773318	−0.182273
$19$	0.347296	0.0796752	0.0398376	−	0.999206i	$-0.487316\pi$
$19$	0.347296	0.0796752	0.0398376	+	0.999206i	$0.487316\pi$
$20$	−4.41147	−0.986436
$21$	−1.65270	−0.360650
$22$	1.75877	0.374971
$23$	1.77332	0.369762	0.184881	−	0.982761i	$-0.440810\pi$
$23$	1.77332	0.369762	0.184881	+	0.982761i	$0.440810\pi$
$24$	1.18479	0.241845
$25$	0.509800	0.101960
$26$	1.63816	0.321269
$27$	4.59627	0.884552
$28$	−3.53209	−0.667502
$29$	−2.22668	−0.413484	−0.206742	−	0.978395i	$-0.566286\pi$
$29$	−2.22668	−0.413484	−0.206742	+	0.978395i	$0.566286\pi$
$30$	−0.716881	−0.130884
$31$	−1.94356	−0.349074	−0.174537	−	0.984651i	$-0.555843\pi$
$31$	−1.94356	−0.349074	−0.174537	+	0.984651i	$0.555843\pi$
$32$	3.83750	0.678380
$33$	−4.45336	−0.775231
$34$	0	0
$35$	4.41147	0.745675
$36$	4.18479	0.697465
$37$	6.17024	1.01438	0.507191	−	0.861834i	$-0.330684\pi$
$37$	6.17024	1.01438	0.507191	+	0.861834i	$0.330684\pi$
$38$	0.120615	0.0195663
$39$	−4.14796	−0.664205
$40$	−3.16250	−0.500036
$41$	−5.17024	−0.807457	−0.403728	−	0.914879i	$-0.632286\pi$
$41$	−5.17024	−0.807457	−0.403728	+	0.914879i	$0.632286\pi$
$42$	−0.573978	−0.0885667
$43$	−1.47565	−0.225035	−0.112517	−	0.993650i	$-0.535891\pi$
$43$	−1.47565	−0.225035	−0.112517	+	0.993650i	$0.535891\pi$
$44$	−9.51754	−1.43482
$45$	−5.22668	−0.779148
$46$	0.615867	0.0908046
$47$	−8.53209	−1.24453	−0.622267	−	0.782805i	$-0.713788\pi$
$47$	−8.53209	−1.24453	−0.622267	+	0.782805i	$0.713788\pi$
$48$	−2.89393	−0.417703
$49$	−3.46791	−0.495416
$50$	0.177052	0.0250389
$51$	0	0
$52$	−8.86484	−1.22933
$53$	−10.4534	−1.43588	−0.717940	−	0.696105i	$-0.754915\pi$
$53$	−10.4534	−1.43588	−0.717940	+	0.696105i	$0.754915\pi$
$54$	1.59627	0.217224
$55$	11.8871	1.60286
$56$	−2.53209	−0.338365
$57$	−0.305407	−0.0404522
$58$	−0.773318	−0.101542
$59$	5.00774	0.651952	0.325976	−	0.945378i	$-0.394307\pi$
$59$	5.00774	0.651952	0.325976	+	0.945378i	$0.394307\pi$
$60$	3.87939	0.500826
$61$	0.184793	0.0236603	0.0118301	−	0.999930i	$-0.496234\pi$
$61$	0.184793	0.0236603	0.0118301	+	0.999930i	$0.496234\pi$
$62$	−0.674992	−0.0857241
$63$	−4.18479	−0.527234
$64$	−5.24897	−0.656121
$65$	11.0719	1.37330
$66$	−1.54664	−0.190378
$67$	−2.44831	−0.299109	−0.149554	−	0.988754i	$-0.547784\pi$
$67$	−2.44831	−0.299109	−0.149554	+	0.988754i	$0.547784\pi$
$68$	0	0
$69$	−1.55943	−0.187733
$70$	1.53209	0.183120
$71$	9.92127	1.17744	0.588719	−	0.808338i	$-0.299632\pi$
$71$	9.92127	1.17744	0.588719	+	0.808338i	$0.299632\pi$
$72$	3.00000	0.353553
$73$	−10.9017	−1.27594	−0.637972	−	0.770059i	$-0.720227\pi$
$73$	−10.9017	−1.27594	−0.637972	+	0.770059i	$0.720227\pi$
$74$	2.14290	0.249107
$75$	−0.448311	−0.0517665
$76$	−0.652704	−0.0748702
$77$	9.51754	1.08462
$78$	−1.44057	−0.163112
$79$	−4.43376	−0.498837	−0.249419	−	0.968396i	$-0.580240\pi$
$79$	−4.43376	−0.498837	−0.249419	+	0.968396i	$0.580240\pi$
$80$	7.72462	0.863639
$81$	2.63816	0.293128
$82$	−1.79561	−0.198292
$83$	13.5817	1.49079	0.745394	−	0.666625i	$-0.232262\pi$
$83$	13.5817	1.49079	0.745394	+	0.666625i	$0.232262\pi$
$84$	3.10607	0.338900
$85$	0	0
$86$	−0.512489	−0.0552631
$87$	1.95811	0.209932
$88$	−6.82295	−0.727329
$89$	−6.32770	−0.670734	−0.335367	−	0.942087i	$-0.608860\pi$
$89$	−6.32770	−0.670734	−0.335367	+	0.942087i	$0.608860\pi$
$90$	−1.81521	−0.191340
$91$	8.86484	0.929287
$92$	−3.33275	−0.347463
$93$	1.70914	0.177230
$94$	−2.96316	−0.305627
$95$	0.815207	0.0836385
$96$	−3.37464	−0.344422
$97$	−9.27631	−0.941867	−0.470933	−	0.882169i	$-0.656083\pi$
$97$	−9.27631	−0.941867	−0.470933	+	0.882169i	$0.656083\pi$
$98$	−1.20439	−0.121662
$99$	−11.2763	−1.13331
$100$	−0.958111	−0.0958111
$101$	−7.04963	−0.701464	−0.350732	−	0.936476i	$-0.614067\pi$
$101$	−7.04963	−0.701464	−0.350732	+	0.936476i	$0.614067\pi$
$102$	0	0
$103$	5.29860	0.522087	0.261043	−	0.965327i	$-0.415933\pi$
$103$	5.29860	0.522087	0.261043	+	0.965327i	$0.415933\pi$
$104$	−6.35504	−0.623163
$105$	−3.87939	−0.378589
$106$	−3.63041	−0.352617
$107$	15.5963	1.50775	0.753874	−	0.657019i	$-0.228183\pi$
$107$	15.5963	1.50775	0.753874	+	0.657019i	$0.228183\pi$
$108$	−8.63816	−0.831207
$109$	−1.87164	−0.179271	−0.0896355	−	0.995975i	$-0.528570\pi$
$109$	−1.87164	−0.179271	−0.0896355	+	0.995975i	$0.528570\pi$
$110$	4.12836	0.393623
$111$	−5.42602	−0.515015
$112$	6.18479	0.584408
$113$	12.1138	1.13957	0.569786	−	0.821793i	$-0.307026\pi$
$113$	12.1138	1.13957	0.569786	+	0.821793i	$0.307026\pi$
$114$	−0.106067	−0.00993407
$115$	4.16250	0.388155
$116$	4.18479	0.388548
$117$	−10.5030	−0.971002
$118$	1.73917	0.160104
$119$	0	0
$120$	2.78106	0.253875
$121$	14.6459	1.33145
$122$	0.0641778	0.00581038
$123$	4.54664	0.409956
$124$	3.65270	0.328022
$125$	−10.5398	−0.942711
$126$	−1.45336	−0.129476
$127$	−11.5398	−1.02399	−0.511997	−	0.858987i	$-0.671094\pi$
$127$	−11.5398	−1.02399	−0.511997	+	0.858987i	$0.671094\pi$
$128$	−9.49794	−0.839507
$129$	1.29767	0.114253
$130$	3.84524	0.337250
$131$	19.3746	1.69277	0.846385	−	0.532572i	$-0.178774\pi$
$131$	19.3746	1.69277	0.846385	+	0.532572i	$0.178774\pi$
$132$	8.36959	0.728479
$133$	0.652704	0.0565966
$134$	−0.850289	−0.0734538
$135$	10.7888	0.928552
$136$	0	0
$137$	−0.448311	−0.0383018	−0.0191509	−	0.999817i	$-0.506096\pi$
$137$	−0.448311	−0.0383018	−0.0191509	+	0.999817i	$0.506096\pi$
$138$	−0.541584	−0.0461027
$139$	−11.6800	−0.990688	−0.495344	−	0.868697i	$-0.664958\pi$
$139$	−11.6800	−0.990688	−0.495344	+	0.868697i	$0.664958\pi$
$140$	−8.29086	−0.700706
$141$	7.50299	0.631866
$142$	3.44562	0.289150
$143$	23.8871	1.99754
$144$	−7.32770	−0.610641
$145$	−5.22668	−0.434052
$146$	−3.78611	−0.313341
$147$	3.04963	0.251529
$148$	−11.5963	−0.953207
$149$	8.46791	0.693718	0.346859	−	0.937917i	$-0.387248\pi$
$149$	8.46791	0.693718	0.346859	+	0.937917i	$0.387248\pi$
$150$	−0.155697	−0.0127126
$151$	−13.7665	−1.12030	−0.560151	−	0.828390i	$-0.689257\pi$
$151$	−13.7665	−1.12030	−0.560151	+	0.828390i	$0.689257\pi$
$152$	−0.467911	−0.0379526
$153$	0	0
$154$	3.30541	0.266357
$155$	−4.56212	−0.366438
$156$	7.79561	0.624148
$157$	−17.9786	−1.43485	−0.717426	−	0.696635i	$-0.754680\pi$
$157$	−17.9786	−1.43485	−0.717426	+	0.696635i	$0.754680\pi$
$158$	−1.53983	−0.122502
$159$	9.19253	0.729015
$160$	9.00774	0.712124
$161$	3.33275	0.262657
$162$	0.916222	0.0719852
$163$	7.23442	0.566644	0.283322	−	0.959025i	$-0.408564\pi$
$163$	7.23442	0.566644	0.283322	+	0.959025i	$0.408564\pi$
$164$	9.71688	0.758761
$165$	−10.4534	−0.813793
$166$	4.71688	0.366101
$167$	5.10607	0.395119	0.197560	−	0.980291i	$-0.436698\pi$
$167$	5.10607	0.395119	0.197560	+	0.980291i	$0.436698\pi$
$168$	2.22668	0.171792
$169$	9.24897	0.711459
$170$	0	0
$171$	−0.773318	−0.0591371
$172$	2.77332	0.211464
$173$	−12.8256	−0.975115	−0.487558	−	0.873091i	$-0.662112\pi$
$173$	−12.8256	−0.975115	−0.487558	+	0.873091i	$0.662112\pi$
$174$	0.680045	0.0515541
$175$	0.958111	0.0724264
$176$	16.6655	1.25621
$177$	−4.40373	−0.331005
$178$	−2.19759	−0.164716
$179$	4.27126	0.319249	0.159624	−	0.987178i	$-0.448972\pi$
$179$	4.27126	0.319249	0.159624	+	0.987178i	$0.448972\pi$
$180$	9.82295	0.732159
$181$	0.462859	0.0344040	0.0172020	−	0.999852i	$-0.494524\pi$
$181$	0.462859	0.0344040	0.0172020	+	0.999852i	$0.494524\pi$
$182$	3.07873	0.228210
$183$	−0.162504	−0.0120126
$184$	−2.38919	−0.176133
$185$	14.4834	1.06484
$186$	0.593578	0.0435233
$187$	0	0
$188$	16.0351	1.16948
$189$	8.63816	0.628333
$190$	0.283119	0.0205396
$191$	−1.43107	−0.103549	−0.0517745	−	0.998659i	$-0.516488\pi$
$191$	−1.43107	−0.103549	−0.0517745	+	0.998659i	$0.516488\pi$
$192$	4.61587	0.333122
$193$	−24.7246	−1.77972	−0.889859	−	0.456236i	$-0.849197\pi$
$193$	−24.7246	−1.77972	−0.889859	+	0.456236i	$0.849197\pi$
$194$	−3.22163	−0.231299
$195$	−9.73648	−0.697244
$196$	6.51754	0.465539
$197$	−11.7615	−0.837969	−0.418985	−	0.907993i	$-0.637614\pi$
$197$	−11.7615	−0.837969	−0.418985	+	0.907993i	$0.637614\pi$
$198$	−3.91622	−0.278314
$199$	20.5202	1.45464	0.727320	−	0.686298i	$-0.240766\pi$
$199$	20.5202	1.45464	0.727320	+	0.686298i	$0.240766\pi$
$200$	−0.686852	−0.0485678
$201$	2.15301	0.151861
$202$	−2.44831	−0.172263
$203$	−4.18479	−0.293715
$204$	0	0
$205$	−12.1361	−0.847622
$206$	1.84018	0.128212
$207$	−3.94862	−0.274448
$208$	15.5226	1.07630
$209$	1.75877	0.121657
$210$	−1.34730	−0.0929723
$211$	−21.7178	−1.49512	−0.747558	−	0.664197i	$-0.768774\pi$
$211$	−21.7178	−1.49512	−0.747558	+	0.664197i	$0.768774\pi$
$212$	19.6459	1.34929
$213$	−8.72462	−0.597801
$214$	5.41653	0.370266
$215$	−3.46379	−0.236229
$216$	−6.19253	−0.421349
$217$	−3.65270	−0.247962
$218$	−0.650015	−0.0440246
$219$	9.58677	0.647814
$220$	−22.3405	−1.50620
$221$	0	0
$222$	−1.88444	−0.126475
$223$	−19.9513	−1.33604	−0.668019	−	0.744144i	$-0.732858\pi$
$223$	−19.9513	−1.33604	−0.668019	+	0.744144i	$0.732858\pi$
$224$	7.21213	0.481881
$225$	−1.13516	−0.0756775
$226$	4.20708	0.279851
$227$	4.22163	0.280199	0.140100	−	0.990137i	$-0.455258\pi$
$227$	4.22163	0.280199	0.140100	+	0.990137i	$0.455258\pi$
$228$	0.573978	0.0380126
$229$	14.5057	0.958562	0.479281	−	0.877661i	$-0.340897\pi$
$229$	14.5057	0.958562	0.479281	+	0.877661i	$0.340897\pi$
$230$	1.44562	0.0953215
$231$	−8.36959	−0.550678
$232$	3.00000	0.196960
$233$	−5.12742	−0.335909	−0.167954	−	0.985795i	$-0.553716\pi$
$233$	−5.12742	−0.335909	−0.167954	+	0.985795i	$0.553716\pi$
$234$	−3.64765	−0.238454
$235$	−20.0273	−1.30644
$236$	−9.41147	−0.612635
$237$	3.89899	0.253266
$238$	0	0
$239$	−15.8503	−1.02527	−0.512635	−	0.858607i	$-0.671331\pi$
$239$	−15.8503	−1.02527	−0.512635	+	0.858607i	$0.671331\pi$
$240$	−6.79292	−0.438481
$241$	18.1165	1.16699	0.583493	−	0.812118i	$-0.301686\pi$
$241$	18.1165	1.16699	0.583493	+	0.812118i	$0.301686\pi$
$242$	5.08647	0.326970
$243$	−16.1088	−1.03338
$244$	−0.347296	−0.0222334
$245$	−8.14022	−0.520059
$246$	1.57903	0.100675
$247$	1.63816	0.104233
$248$	2.61856	0.166278
$249$	−11.9436	−0.756893
$250$	−3.66044	−0.231507
$251$	−29.6810	−1.87345	−0.936723	−	0.350070i	$-0.886158\pi$
$251$	−29.6810	−1.87345	−0.936723	+	0.350070i	$0.886158\pi$
$252$	7.86484	0.495438
$253$	8.98040	0.564593
$254$	−4.00774	−0.251468
$255$	0	0
$256$	7.19934	0.449959
$257$	7.39693	0.461408	0.230704	−	0.973024i	$-0.425897\pi$
$257$	7.39693	0.461408	0.230704	+	0.973024i	$0.425897\pi$
$258$	0.450675	0.0280578
$259$	11.5963	0.720557
$260$	−20.8084	−1.29048
$261$	4.95811	0.306899
$262$	6.72874	0.415703
$263$	−23.1908	−1.43000	−0.715002	−	0.699122i	$-0.753574\pi$
$263$	−23.1908	−1.43000	−0.715002	+	0.699122i	$0.753574\pi$
$264$	6.00000	0.369274
$265$	−24.5371	−1.50730
$266$	0.226682	0.0138987
$267$	5.56448	0.340541
$268$	4.60132	0.281070
$269$	15.9067	0.969850	0.484925	−	0.874556i	$-0.338847\pi$
$269$	15.9067	0.969850	0.484925	+	0.874556i	$0.338847\pi$
$270$	3.74691	0.228030
$271$	17.0000	1.03268	0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000	1.03268	0.516338	+	0.856385i	$0.327295\pi$
$272$	0	0
$273$	−7.79561	−0.471812
$274$	−0.155697	−0.00940598
$275$	2.58172	0.155683
$276$	2.93077	0.176412
$277$	−16.8057	−1.00976	−0.504879	−	0.863190i	$-0.668463\pi$
$277$	−16.8057	−1.00976	−0.504879	+	0.863190i	$0.668463\pi$
$278$	−4.05644	−0.243289
$279$	4.32770	0.259092
$280$	−5.94356	−0.355196
$281$	28.3209	1.68948	0.844741	−	0.535175i	$-0.179754\pi$
$281$	28.3209	1.68948	0.844741	+	0.535175i	$0.179754\pi$
$282$	2.60576	0.155171
$283$	−32.2344	−1.91614	−0.958069	−	0.286538i	$-0.907495\pi$
$283$	−32.2344	−1.91614	−0.958069	+	0.286538i	$0.907495\pi$
$284$	−18.6459	−1.10643
$285$	−0.716881	−0.0424644
$286$	8.29591	0.490548
$287$	−9.71688	−0.573569
$288$	−8.54488	−0.503512
$289$	0	0
$290$	−1.81521	−0.106593
$291$	8.15745	0.478198
$292$	20.4884	1.19900
$293$	13.9709	0.816189	0.408094	−	0.912940i	$-0.366193\pi$
$293$	13.9709	0.816189	0.408094	+	0.912940i	$0.366193\pi$
$294$	1.05913	0.0617694
$295$	11.7547	0.684382
$296$	−8.31315	−0.483192
$297$	23.2763	1.35063
$298$	2.94087	0.170360
$299$	8.36453	0.483733
$300$	0.842549	0.0486446
$301$	−2.77332	−0.159851
$302$	−4.78106	−0.275119
$303$	6.19934	0.356143
$304$	1.14290	0.0655500
$305$	0.433763	0.0248372
$306$	0	0
$307$	9.04963	0.516490	0.258245	−	0.966080i	$-0.416856\pi$
$307$	9.04963	0.516490	0.258245	+	0.966080i	$0.416856\pi$
$308$	−17.8871	−1.01921
$309$	−4.65951	−0.265070
$310$	−1.58441	−0.0899883
$311$	2.34730	0.133103	0.0665515	−	0.997783i	$-0.478800\pi$
$311$	2.34730	0.133103	0.0665515	+	0.997783i	$0.478800\pi$
$312$	5.58853	0.316388
$313$	15.1284	0.855105	0.427553	−	0.903990i	$-0.359376\pi$
$313$	15.1284	0.855105	0.427553	+	0.903990i	$0.359376\pi$
$314$	−6.24392	−0.352365
$315$	−9.82295	−0.553460
$316$	8.33275	0.468754
$317$	−10.3378	−0.580629	−0.290314	−	0.956931i	$-0.593760\pi$
$317$	−10.3378	−0.580629	−0.290314	+	0.956931i	$0.593760\pi$
$318$	3.19253	0.179028
$319$	−11.2763	−0.631352
$320$	−12.3209	−0.688759
$321$	−13.7151	−0.765504
$322$	1.15745	0.0645022
$323$	0	0
$324$	−4.95811	−0.275451
$325$	2.40467	0.133387
$326$	2.51249	0.139154
$327$	1.64590	0.0910183
$328$	6.96585	0.384625
$329$	−16.0351	−0.884043
$330$	−3.63041	−0.199848
$331$	18.2567	1.00348	0.501740	−	0.865019i	$-0.332693\pi$
$331$	18.2567	1.00348	0.501740	+	0.865019i	$0.332693\pi$
$332$	−25.5253	−1.40088
$333$	−13.7392	−0.752902
$334$	1.77332	0.0970317
$335$	−5.74691	−0.313987
$336$	−5.43882	−0.296712
$337$	−16.4953	−0.898554	−0.449277	−	0.893393i	$-0.648318\pi$
$337$	−16.4953	−0.898554	−0.449277	+	0.893393i	$0.648318\pi$
$338$	3.21213	0.174717
$339$	−10.6527	−0.578575
$340$	0	0
$341$	−9.84255	−0.533004
$342$	−0.268571	−0.0145226
$343$	−19.6732	−1.06225
$344$	1.98814	0.107193
$345$	−3.66044	−0.197072
$346$	−4.45430	−0.239464
$347$	−20.5722	−1.10437	−0.552187	−	0.833720i	$-0.686207\pi$
$347$	−20.5722	−1.10437	−0.552187	+	0.833720i	$0.686207\pi$
$348$	−3.68004	−0.197271
$349$	6.42427	0.343883	0.171942	−	0.985107i	$-0.444996\pi$
$349$	6.42427	0.343883	0.171942	+	0.985107i	$0.444996\pi$
$350$	0.332748	0.0177862
$351$	21.6800	1.15720
$352$	19.4338	1.03582
$353$	27.1685	1.44603	0.723016	−	0.690831i	$-0.242755\pi$
$353$	27.1685	1.44603	0.723016	+	0.690831i	$0.242755\pi$
$354$	−1.52940	−0.0812867
$355$	23.2882	1.23601
$356$	11.8922	0.630284
$357$	0	0
$358$	1.48339	0.0783997
$359$	16.8949	0.891677	0.445838	−	0.895113i	$-0.352906\pi$
$359$	16.8949	0.891677	0.445838	+	0.895113i	$0.352906\pi$
$360$	7.04189	0.371140
$361$	−18.8794	−0.993652
$362$	0.160749	0.00844879
$363$	−12.8794	−0.675992
$364$	−16.6604	−0.873245
$365$	−25.5895	−1.33941
$366$	−0.0564370	−0.00295001
$367$	1.48751	0.0776475	0.0388237	−	0.999246i	$-0.487639\pi$
$367$	1.48751	0.0776475	0.0388237	+	0.999246i	$0.487639\pi$
$368$	5.83574	0.304209
$369$	11.5125	0.599316
$370$	5.03003	0.261499
$371$	−19.6459	−1.01996
$372$	−3.21213	−0.166541
$373$	−24.0496	−1.24524	−0.622621	−	0.782523i	$-0.713932\pi$
$373$	−24.0496	−1.24524	−0.622621	+	0.782523i	$0.713932\pi$
$374$	0	0
$375$	9.26857	0.478627
$376$	11.4953	0.592822
$377$	−10.5030	−0.540932
$378$	3.00000	0.154303
$379$	20.1976	1.03748	0.518740	−	0.854932i	$-0.326401\pi$
$379$	20.1976	1.03748	0.518740	+	0.854932i	$0.326401\pi$
$380$	−1.53209	−0.0785945
$381$	10.1480	0.519896
$382$	−0.497007	−0.0254291
$383$	−8.52528	−0.435622	−0.217811	−	0.975991i	$-0.569892\pi$
$383$	−8.52528	−0.435622	−0.217811	+	0.975991i	$0.569892\pi$
$384$	8.35235	0.426229
$385$	22.3405	1.13858
$386$	−8.58677	−0.437055
$387$	3.28581	0.167027
$388$	17.4338	0.885065
$389$	−12.9162	−0.654878	−0.327439	−	0.944872i	$-0.606186\pi$
$389$	−12.9162	−0.654878	−0.327439	+	0.944872i	$0.606186\pi$
$390$	−3.38144	−0.171226
$391$	0	0
$392$	4.67230	0.235987
$393$	−17.0378	−0.859442
$394$	−4.08471	−0.205785
$395$	−10.4074	−0.523651
$396$	21.1925	1.06496
$397$	24.2249	1.21581	0.607907	−	0.794008i	$-0.292009\pi$
$397$	24.2249	1.21581	0.607907	+	0.794008i	$0.292009\pi$
$398$	7.12660	0.357224
$399$	−0.573978	−0.0287348
$400$	1.67768	0.0838840
$401$	25.5371	1.27526	0.637632	−	0.770341i	$-0.279914\pi$
$401$	25.5371	1.27526	0.637632	+	0.770341i	$0.279914\pi$
$402$	0.747732	0.0372935
$403$	−9.16756	−0.456669
$404$	13.2490	0.659161
$405$	6.19253	0.307709
$406$	−1.45336	−0.0721292
$407$	31.2472	1.54887
$408$	0	0
$409$	10.3523	0.511891	0.255945	−	0.966691i	$-0.417613\pi$
$409$	10.3523	0.511891	0.255945	+	0.966691i	$0.417613\pi$
$410$	−4.21482	−0.208155
$411$	0.394238	0.0194463
$412$	−9.95811	−0.490601
$413$	9.41147	0.463108
$414$	−1.37134	−0.0673977
$415$	31.8803	1.56494
$416$	18.1010	0.887475
$417$	10.2713	0.502986
$418$	0.610815	0.0298759
$419$	1.31315	0.0641515	0.0320757	−	0.999485i	$-0.489788\pi$
$419$	1.31315	0.0641515	0.0320757	+	0.999485i	$0.489788\pi$
$420$	7.29086	0.355758
$421$	8.01548	0.390651	0.195325	−	0.980739i	$-0.437424\pi$
$421$	8.01548	0.390651	0.195325	+	0.980739i	$0.437424\pi$
$422$	−7.54252	−0.367164
$423$	18.9982	0.923726
$424$	14.0838	0.683969
$425$	0	0
$426$	−3.03003	−0.146805
$427$	0.347296	0.0168068
$428$	−29.3114	−1.41682
$429$	−21.0060	−1.01418
$430$	−1.20296	−0.0580120
$431$	14.7270	0.709374	0.354687	−	0.934985i	$-0.384587\pi$
$431$	14.7270	0.709374	0.354687	+	0.934985i	$0.384587\pi$
$432$	15.1257	0.727734
$433$	−8.24123	−0.396048	−0.198024	−	0.980197i	$-0.563452\pi$
$433$	−8.24123	−0.396048	−0.198024	+	0.980197i	$0.563452\pi$
$434$	−1.26857	−0.0608933
$435$	4.59627	0.220374
$436$	3.51754	0.168460
$437$	0.615867	0.0294609
$438$	3.32945	0.159087
$439$	39.9564	1.90701	0.953506	−	0.301373i	$-0.0974448\pi$
$439$	39.9564	1.90701	0.953506	+	0.301373i	$0.0974448\pi$
$440$	−16.0155	−0.763508
$441$	7.72193	0.367711
$442$	0	0
$443$	13.9463	0.662606	0.331303	−	0.943524i	$-0.392512\pi$
$443$	13.9463	0.662606	0.331303	+	0.943524i	$0.392512\pi$
$444$	10.1976	0.483956
$445$	−14.8530	−0.704099
$446$	−6.92902	−0.328098
$447$	−7.44656	−0.352210
$448$	−9.86484	−0.466070
$449$	10.2317	0.482865	0.241433	−	0.970418i	$-0.422383\pi$
$449$	10.2317	0.482865	0.241433	+	0.970418i	$0.422383\pi$
$450$	−0.394238	−0.0185846
$451$	−26.1830	−1.23291
$452$	−22.7665	−1.07085
$453$	12.1061	0.568793
$454$	1.46616	0.0688101
$455$	20.8084	0.975513
$456$	0.411474	0.0192690
$457$	−11.7706	−0.550607	−0.275303	−	0.961357i	$-0.588778\pi$
$457$	−11.7706	−0.550607	−0.275303	+	0.961357i	$0.588778\pi$
$458$	5.03777	0.235400
$459$	0	0
$460$	−7.82295	−0.364747
$461$	19.5003	0.908220	0.454110	−	0.890946i	$-0.349957\pi$
$461$	19.5003	0.908220	0.454110	+	0.890946i	$0.349957\pi$
$462$	−2.90673	−0.135233
$463$	−1.43107	−0.0665077	−0.0332538	−	0.999447i	$-0.510587\pi$
$463$	−1.43107	−0.0665077	−0.0332538	+	0.999447i	$0.510587\pi$
$464$	−7.32770	−0.340180
$465$	4.01186	0.186046
$466$	−1.78073	−0.0824910
$467$	−10.6895	−0.494653	−0.247326	−	0.968932i	$-0.579552\pi$
$467$	−10.6895	−0.494653	−0.247326	+	0.968932i	$0.579552\pi$
$468$	19.7392	0.912443
$469$	−4.60132	−0.212469
$470$	−6.95542	−0.320830
$471$	15.8102	0.728493
$472$	−6.74691	−0.310552
$473$	−7.47296	−0.343607
$474$	1.35410	0.0621960
$475$	0.177052	0.00812369
$476$	0	0
$477$	23.2763	1.06575
$478$	−5.50475	−0.251781
$479$	38.8675	1.77590	0.887951	−	0.459938i	$-0.152128\pi$
$479$	38.8675	1.77590	0.887951	+	0.459938i	$0.152128\pi$
$480$	−7.92127	−0.361555
$481$	29.1043	1.32704
$482$	6.29179	0.286583
$483$	−2.93077	−0.133355
$484$	−27.5253	−1.25115
$485$	−21.7743	−0.988718
$486$	−5.59451	−0.253772
$487$	37.0137	1.67725	0.838626	−	0.544708i	$-0.183359\pi$
$487$	37.0137	1.67725	0.838626	+	0.544708i	$0.183359\pi$
$488$	−0.248970	−0.0112704
$489$	−6.36184	−0.287693
$490$	−2.82707	−0.127714
$491$	−25.4175	−1.14707	−0.573537	−	0.819180i	$-0.694429\pi$
$491$	−25.4175	−1.14707	−0.573537	+	0.819180i	$0.694429\pi$
$492$	−8.54488	−0.385233
$493$	0	0
$494$	0.568926	0.0255972
$495$	−26.4688	−1.18969
$496$	−6.39599	−0.287189
$497$	18.6459	0.836383
$498$	−4.14796	−0.185874
$499$	−21.8239	−0.976971	−0.488486	−	0.872572i	$-0.662451\pi$
$499$	−21.8239	−0.976971	−0.488486	+	0.872572i	$0.662451\pi$
$500$	19.8084	0.885859
$501$	−4.49020	−0.200607
$502$	−10.3081	−0.460073
$503$	33.4371	1.49088	0.745442	−	0.666570i	$-0.232238\pi$
$503$	33.4371	1.49088	0.745442	+	0.666570i	$0.232238\pi$
$504$	5.63816	0.251143
$505$	−16.5476	−0.736357
$506$	3.11886	0.138650
$507$	−8.13341	−0.361217
$508$	21.6878	0.962240
$509$	−19.1530	−0.848942	−0.424471	−	0.905441i	$-0.639540\pi$
$509$	−19.1530	−0.848942	−0.424471	+	0.905441i	$0.639540\pi$
$510$	0	0
$511$	−20.4884	−0.906355
$512$	21.4962	0.950006
$513$	1.59627	0.0704769
$514$	2.56893	0.113310
$515$	12.4374	0.548057
$516$	−2.43882	−0.107363
$517$	−43.2080	−1.90029
$518$	4.02734	0.176951
$519$	11.2787	0.495079
$520$	−14.9172	−0.654161
$521$	−35.5330	−1.55673	−0.778365	−	0.627812i	$-0.783951\pi$
$521$	−35.5330	−1.55673	−0.778365	+	0.627812i	$0.783951\pi$
$522$	1.72193	0.0753670
$523$	−11.8307	−0.517320	−0.258660	−	0.965968i	$-0.583281\pi$
$523$	−11.8307	−0.517320	−0.258660	+	0.965968i	$0.583281\pi$
$524$	−36.4124	−1.59068
$525$	−0.842549	−0.0367718
$526$	−8.05407	−0.351174
$527$	0	0
$528$	−14.6554	−0.637794
$529$	−19.8553	−0.863276
$530$	−8.52166	−0.370157
$531$	−11.1506	−0.483897
$532$	−1.22668	−0.0531834
$533$	−24.3874	−1.05634
$534$	1.93252	0.0836285
$535$	36.6091	1.58275
$536$	3.29860	0.142478
$537$	−3.75608	−0.162087
$538$	5.52435	0.238172
$539$	−17.5621	−0.756454
$540$	−20.2763	−0.872554
$541$	5.55850	0.238978	0.119489	−	0.992835i	$-0.461874\pi$
$541$	5.55850	0.238978	0.119489	+	0.992835i	$0.461874\pi$
$542$	5.90404	0.253600
$543$	−0.407031	−0.0174674
$544$	0	0
$545$	−4.39330	−0.188188
$546$	−2.70739	−0.115865
$547$	5.02465	0.214839	0.107419	−	0.994214i	$-0.465741\pi$
$547$	5.02465	0.214839	0.107419	+	0.994214i	$0.465741\pi$
$548$	0.842549	0.0359919
$549$	−0.411474	−0.0175613
$550$	0.896622	0.0382321
$551$	−0.773318	−0.0329445
$552$	2.10101	0.0894251
$553$	−8.33275	−0.354345
$554$	−5.83656	−0.247972
$555$	−12.7365	−0.540634
$556$	21.9513	0.930943
$557$	3.86659	0.163833	0.0819164	−	0.996639i	$-0.473896\pi$
$557$	3.86659	0.163833	0.0819164	+	0.996639i	$0.473896\pi$
$558$	1.50299	0.0636268
$559$	−6.96048	−0.294397
$560$	14.5175	0.613478
$561$	0	0
$562$	9.83574	0.414896
$563$	28.8411	1.21551	0.607754	−	0.794125i	$-0.292071\pi$
$563$	28.8411	1.21551	0.607754	+	0.794125i	$0.292071\pi$
$564$	−14.1010	−0.593760
$565$	28.4347	1.19626
$566$	−11.1949	−0.470557
$567$	4.95811	0.208221
$568$	−13.3669	−0.560863
$569$	2.16157	0.0906177	0.0453089	−	0.998973i	$-0.485573\pi$
$569$	2.16157	0.0906177	0.0453089	+	0.998973i	$0.485573\pi$
$570$	−0.248970	−0.0104282
$571$	−5.71925	−0.239343	−0.119671	−	0.992814i	$-0.538184\pi$
$571$	−5.71925	−0.239343	−0.119671	+	0.992814i	$0.538184\pi$
$572$	−44.8931	−1.87708
$573$	1.25847	0.0525732
$574$	−3.37464	−0.140855
$575$	0.904038	0.0377010
$576$	11.6878	0.486991
$577$	−10.8007	−0.449637	−0.224819	−	0.974401i	$-0.572179\pi$
$577$	−10.8007	−0.449637	−0.224819	+	0.974401i	$0.572179\pi$
$578$	0	0
$579$	21.7425	0.903586
$580$	9.82295	0.407876
$581$	25.5253	1.05897
$582$	2.83305	0.117434
$583$	−52.9377	−2.19246
$584$	14.6878	0.607785
$585$	−24.6536	−1.01930
$586$	4.85204	0.200436
$587$	20.8188	0.859285	0.429643	−	0.902999i	$-0.358640\pi$
$587$	20.8188	0.859285	0.429643	+	0.902999i	$0.358640\pi$
$588$	−5.73143	−0.236360
$589$	−0.674992	−0.0278126
$590$	4.08235	0.168068
$591$	10.3429	0.425448
$592$	20.3054	0.834547
$593$	20.6313	0.847228	0.423614	−	0.905843i	$-0.360761\pi$
$593$	20.6313	0.847228	0.423614	+	0.905843i	$0.360761\pi$
$594$	8.08378	0.331681
$595$	0	0
$596$	−15.9145	−0.651882
$597$	−18.0452	−0.738540
$598$	2.90497	0.118793
$599$	31.8212	1.30018	0.650089	−	0.759858i	$-0.274731\pi$
$599$	31.8212	1.30018	0.650089	+	0.759858i	$0.274731\pi$
$600$	0.604007	0.0246585
$601$	48.1174	1.96275	0.981375	−	0.192100i	$-0.0615296\pi$
$601$	48.1174	1.96275	0.981375	+	0.192100i	$0.0615296\pi$
$602$	−0.963163	−0.0392556
$603$	5.45161	0.222007
$604$	25.8726	1.05274
$605$	34.3783	1.39768
$606$	2.15301	0.0874600
$607$	−15.4757	−0.628137	−0.314069	−	0.949400i	$-0.601692\pi$
$607$	−15.4757	−0.628137	−0.314069	+	0.949400i	$0.601692\pi$
$608$	1.33275	0.0540501
$609$	3.68004	0.149123
$610$	0.150644	0.00609941
$611$	−40.2449	−1.62813
$612$	0	0
$613$	−5.04963	−0.203953	−0.101976	−	0.994787i	$-0.532517\pi$
$613$	−5.04963	−0.203953	−0.101976	+	0.994787i	$0.532517\pi$
$614$	3.14290	0.126837
$615$	10.6723	0.430349
$616$	−12.8229	−0.516651
$617$	−27.6064	−1.11139	−0.555695	−	0.831386i	$-0.687548\pi$
$617$	−27.6064	−1.11139	−0.555695	+	0.831386i	$0.687548\pi$
$618$	−1.61823	−0.0650948
$619$	14.8331	0.596191	0.298095	−	0.954536i	$-0.403649\pi$
$619$	14.8331	0.596191	0.298095	+	0.954536i	$0.403649\pi$
$620$	8.57398	0.344339
$621$	8.15064	0.327074
$622$	0.815207	0.0326868
$623$	−11.8922	−0.476450
$624$	−13.6503	−0.546451
$625$	−27.2891	−1.09156
$626$	5.25402	0.209993
$627$	−1.54664	−0.0617667
$628$	33.7888	1.34832
$629$	0	0
$630$	−3.41147	−0.135916
$631$	−34.0506	−1.35553	−0.677766	−	0.735278i	$-0.737052\pi$
$631$	−34.0506	−1.35553	−0.677766	+	0.735278i	$0.737052\pi$
$632$	5.97359	0.237617
$633$	19.0983	0.759090
$634$	−3.59028	−0.142588
$635$	−27.0874	−1.07493
$636$	−17.2763	−0.685050
$637$	−16.3577	−0.648117
$638$	−3.91622	−0.155045
$639$	−22.0915	−0.873927
$640$	−22.2945	−0.881267
$641$	−15.0232	−0.593382	−0.296691	−	0.954974i	$-0.595883\pi$
$641$	−15.0232	−0.593382	−0.296691	+	0.954974i	$0.595883\pi$
$642$	−4.76321	−0.187989
$643$	−17.7980	−0.701883	−0.350942	−	0.936397i	$-0.614138\pi$
$643$	−17.7980	−0.701883	−0.350942	+	0.936397i	$0.614138\pi$
$644$	−6.26352	−0.246817
$645$	3.04601	0.119936
$646$	0	0
$647$	−46.4971	−1.82799	−0.913995	−	0.405725i	$-0.867019\pi$
$647$	−46.4971	−1.82799	−0.913995	+	0.405725i	$0.867019\pi$
$648$	−3.55438	−0.139629
$649$	25.3601	0.995471
$650$	0.835132	0.0327566
$651$	3.21213	0.125893
$652$	−13.5963	−0.532471
$653$	30.5303	1.19474	0.597372	−	0.801964i	$-0.296212\pi$
$653$	30.5303	1.19474	0.597372	+	0.801964i	$0.296212\pi$
$654$	0.571614	0.0223519
$655$	45.4780	1.77697
$656$	−17.0145	−0.664306
$657$	24.2746	0.947041
$658$	−5.56893	−0.217099
$659$	−9.83481	−0.383110	−0.191555	−	0.981482i	$-0.561353\pi$
$659$	−9.83481	−0.383110	−0.191555	+	0.981482i	$0.561353\pi$
$660$	19.6459	0.764715
$661$	12.4361	0.483709	0.241855	−	0.970312i	$-0.422244\pi$
$661$	12.4361	0.483709	0.241855	+	0.970312i	$0.422244\pi$
$662$	6.34049	0.246430
$663$	0	0
$664$	−18.2986	−0.710123
$665$	1.53209	0.0594119
$666$	−4.77156	−0.184894
$667$	−3.94862	−0.152891
$668$	−9.59627	−0.371291
$669$	17.5449	0.678324
$670$	−1.99588	−0.0771076
$671$	0.935822	0.0361270
$672$	−6.34224	−0.244657
$673$	−12.6117	−0.486147	−0.243074	−	0.970008i	$-0.578156\pi$
$673$	−12.6117	−0.486147	−0.243074	+	0.970008i	$0.578156\pi$
$674$	−5.72874	−0.220663
$675$	2.34318	0.0901889
$676$	−17.3824	−0.668553
$677$	−4.54900	−0.174832	−0.0874162	−	0.996172i	$-0.527861\pi$
$677$	−4.54900	−0.174832	−0.0874162	+	0.996172i	$0.527861\pi$
$678$	−3.69965	−0.142084
$679$	−17.4338	−0.669046
$680$	0	0
$681$	−3.71244	−0.142261
$682$	−3.41828	−0.130893
$683$	4.86753	0.186251	0.0931253	−	0.995654i	$-0.470314\pi$
$683$	4.86753	0.186251	0.0931253	+	0.995654i	$0.470314\pi$
$684$	1.45336	0.0555707
$685$	−1.05232	−0.0402070
$686$	−6.83244	−0.260864
$687$	−12.7561	−0.486675
$688$	−4.85616	−0.185139
$689$	−49.3073	−1.87846
$690$	−1.27126	−0.0483960
$691$	5.51661	0.209862	0.104931	−	0.994480i	$-0.466538\pi$
$691$	5.51661	0.209862	0.104931	+	0.994480i	$0.466538\pi$
$692$	24.1043	0.916308
$693$	−21.1925	−0.805038
$694$	−7.14466	−0.271208
$695$	−27.4165	−1.03997
$696$	−2.63816	−0.0999990
$697$	0	0
$698$	2.23112	0.0844493
$699$	4.50898	0.170545
$700$	−1.80066	−0.0680585
$701$	22.3233	0.843138	0.421569	−	0.906796i	$-0.361480\pi$
$701$	22.3233	0.843138	0.421569	+	0.906796i	$0.361480\pi$
$702$	7.52940	0.284179
$703$	2.14290	0.0808211
$704$	−26.5817	−1.00184
$705$	17.6117	0.663297
$706$	9.43552	0.355110
$707$	−13.2490	−0.498279
$708$	8.27631	0.311043
$709$	34.7766	1.30606	0.653032	−	0.757331i	$-0.273497\pi$
$709$	34.7766	1.30606	0.653032	+	0.757331i	$0.273497\pi$
$710$	8.08790	0.303533
$711$	9.87258	0.370251
$712$	8.52528	0.319498
$713$	−3.44656	−0.129075
$714$	0	0
$715$	56.0702	2.09691
$716$	−8.02734	−0.299996
$717$	13.9385	0.520543
$718$	5.86753	0.218974
$719$	−4.24990	−0.158495	−0.0792473	−	0.996855i	$-0.525252\pi$
$719$	−4.24990	−0.158495	−0.0792473	+	0.996855i	$0.525252\pi$
$720$	−17.2003	−0.641016
$721$	9.95811	0.370859
$722$	−6.55674	−0.244017
$723$	−15.9314	−0.592494
$724$	−0.869890	−0.0323292
$725$	−1.13516	−0.0421589
$726$	−4.47296	−0.166007
$727$	29.1644	1.08165	0.540823	−	0.841136i	$-0.318113\pi$
$727$	29.1644	1.08165	0.540823	+	0.841136i	$0.318113\pi$
$728$	−11.9436	−0.442658
$729$	6.25133	0.231531
$730$	−8.88713	−0.328927
$731$	0	0
$732$	0.305407	0.0112882
$733$	−0.502993	−0.0185785	−0.00928924	−	0.999957i	$-0.502957\pi$
$733$	−0.502993	−0.0185785	−0.00928924	+	0.999957i	$0.502957\pi$
$734$	0.516607	0.0190683
$735$	7.15839	0.264041
$736$	6.80510	0.250839
$737$	−12.3987	−0.456711
$738$	3.99825	0.147177
$739$	14.9581	0.550243	0.275122	−	0.961409i	$-0.411282\pi$
$739$	14.9581	0.550243	0.275122	+	0.961409i	$0.411282\pi$
$740$	−27.2199	−1.00062
$741$	−1.44057	−0.0529207
$742$	−6.82295	−0.250478
$743$	−23.3756	−0.857567	−0.428783	−	0.903407i	$-0.641058\pi$
$743$	−23.3756	−0.857567	−0.428783	+	0.903407i	$0.641058\pi$
$744$	−2.30272	−0.0844218
$745$	19.8767	0.728226
$746$	−8.35235	−0.305801
$747$	−30.2422	−1.10650
$748$	0	0
$749$	29.3114	1.07102
$750$	3.21894	0.117539
$751$	−17.0291	−0.621401	−0.310700	−	0.950508i	$-0.600564\pi$
$751$	−17.0291	−0.621401	−0.310700	+	0.950508i	$0.600564\pi$
$752$	−28.0779	−1.02390
$753$	26.1010	0.951174
$754$	−3.64765	−0.132840
$755$	−32.3141	−1.17603
$756$	−16.2344	−0.590440
$757$	16.3746	0.595146	0.297573	−	0.954699i	$-0.403823\pi$
$757$	16.3746	0.595146	0.297573	+	0.954699i	$0.403823\pi$
$758$	7.01455	0.254780
$759$	−7.89723	−0.286651
$760$	−1.09833	−0.0398405
$761$	−18.8803	−0.684411	−0.342206	−	0.939625i	$-0.611174\pi$
$761$	−18.8803	−0.684411	−0.342206	+	0.939625i	$0.611174\pi$
$762$	3.52435	0.127674
$763$	−3.51754	−0.127344
$764$	2.68954	0.0973042
$765$	0	0
$766$	−2.96080	−0.106978
$767$	23.6209	0.852902
$768$	−6.33099	−0.228450
$769$	−27.4766	−0.990831	−0.495416	−	0.868656i	$-0.664984\pi$
$769$	−27.4766	−0.990831	−0.495416	+	0.868656i	$0.664984\pi$
$770$	7.75877	0.279607
$771$	−6.50475	−0.234263
$772$	46.4671	1.67239
$773$	9.90436	0.356235	0.178118	−	0.984009i	$-0.442999\pi$
$773$	9.90436	0.356235	0.178118	+	0.984009i	$0.442999\pi$
$774$	1.14115	0.0410177
$775$	−0.990829	−0.0355916
$776$	12.4979	0.448650
$777$	−10.1976	−0.365836
$778$	−4.48576	−0.160822
$779$	−1.79561	−0.0643343
$780$	18.2986	0.655195
$781$	50.2431	1.79784
$782$	0	0
$783$	−10.2344	−0.365748
$784$	−11.4124	−0.407586
$785$	−42.2012	−1.50623
$786$	−5.91716	−0.211058
$787$	50.8444	1.81241	0.906204	−	0.422841i	$-0.138967\pi$
$787$	50.8444	1.81241	0.906204	+	0.422841i	$0.138967\pi$
$788$	22.1043	0.787434
$789$	20.3936	0.726032
$790$	−3.61444	−0.128596
$791$	22.7665	0.809484
$792$	15.1925	0.539843
$793$	0.871644	0.0309530
$794$	8.41323	0.298574
$795$	21.5776	0.765279
$796$	−38.5654	−1.36691
$797$	5.38650	0.190800	0.0953998	−	0.995439i	$-0.469587\pi$
$797$	5.38650	0.190800	0.0953998	+	0.995439i	$0.469587\pi$
$798$	−0.199340	−0.00705658
$799$	0	0
$800$	1.95636	0.0691676
$801$	14.0898	0.497837
$802$	8.86896	0.313174
$803$	−55.2080	−1.94825
$804$	−4.04633	−0.142703
$805$	7.82295	0.275723
$806$	−3.18386	−0.112147
$807$	−13.9881	−0.492406
$808$	9.49794	0.334136
$809$	48.6819	1.71156	0.855782	−	0.517336i	$-0.173076\pi$
$809$	48.6819	1.71156	0.855782	+	0.517336i	$0.173076\pi$
$810$	2.15064	0.0755659
$811$	−15.9281	−0.559311	−0.279655	−	0.960100i	$-0.590220\pi$
$811$	−15.9281	−0.559311	−0.279655	+	0.960100i	$0.590220\pi$
$812$	7.86484	0.276002
$813$	−14.9495	−0.524304
$814$	10.8520	0.380364
$815$	16.9813	0.594830
$816$	0	0
$817$	−0.512489	−0.0179297
$818$	3.59533	0.125708
$819$	−19.7392	−0.689742
$820$	22.8084	0.796504
$821$	−17.1010	−0.596830	−0.298415	−	0.954436i	$-0.596458\pi$
$821$	−17.1010	−0.596830	−0.298415	+	0.954436i	$0.596458\pi$
$822$	0.136917	0.00477554
$823$	−5.62267	−0.195994	−0.0979971	−	0.995187i	$-0.531244\pi$
$823$	−5.62267	−0.195994	−0.0979971	+	0.995187i	$0.531244\pi$
$824$	−7.13878	−0.248691
$825$	−2.27033	−0.0790426
$826$	3.26857	0.113728
$827$	17.8607	0.621078	0.310539	−	0.950561i	$-0.399490\pi$
$827$	17.8607	0.621078	0.310539	+	0.950561i	$0.399490\pi$
$828$	7.42097	0.257897
$829$	35.8161	1.24395	0.621973	−	0.783039i	$-0.286331\pi$
$829$	35.8161	1.24395	0.621973	+	0.783039i	$0.286331\pi$
$830$	11.0719	0.384312
$831$	14.7787	0.512667
$832$	−24.7588	−0.858356
$833$	0	0
$834$	3.56717	0.123521
$835$	11.9855	0.414774
$836$	−3.30541	−0.114320
$837$	−8.93313	−0.308774
$838$	0.456052	0.0157540
$839$	35.7733	1.23503	0.617516	−	0.786558i	$-0.288139\pi$
$839$	35.7733	1.23503	0.617516	+	0.786558i	$0.288139\pi$
$840$	5.22668	0.180338
$841$	−24.0419	−0.829031
$842$	2.78375	0.0959343
$843$	−24.9050	−0.857773
$844$	40.8161	1.40495
$845$	21.7101	0.746849
$846$	6.59802	0.226845
$847$	27.5253	0.945780
$848$	−34.4005	−1.18132
$849$	28.3465	0.972849
$850$	0	0
$851$	10.9418	0.375080
$852$	16.3969	0.561749
$853$	11.0669	0.378922	0.189461	−	0.981888i	$-0.439326\pi$
$853$	11.0669	0.378922	0.189461	+	0.981888i	$0.439326\pi$
$854$	0.120615	0.00412735
$855$	−1.81521	−0.0620788
$856$	−21.0128	−0.718202
$857$	27.0746	0.924851	0.462425	−	0.886658i	$-0.346979\pi$
$857$	27.0746	0.924851	0.462425	+	0.886658i	$0.346979\pi$
$858$	−7.29530	−0.249058
$859$	−51.7279	−1.76493	−0.882467	−	0.470374i	$-0.844119\pi$
$859$	−51.7279	−1.76493	−0.882467	+	0.470374i	$0.844119\pi$
$860$	6.50980	0.221982
$861$	8.54488	0.291209
$862$	5.11463	0.174205
$863$	45.4712	1.54786	0.773929	−	0.633272i	$-0.218289\pi$
$863$	45.4712	1.54786	0.773929	+	0.633272i	$0.218289\pi$
$864$	17.6382	0.600062
$865$	−30.1056	−1.02362
$866$	−2.86215	−0.0972598
$867$	0	0
$868$	6.86484	0.233008
$869$	−22.4534	−0.761678
$870$	1.59627	0.0541185
$871$	−11.5484	−0.391302
$872$	2.52166	0.0853942
$873$	20.6554	0.699079
$874$	0.213888	0.00723488
$875$	−19.8084	−0.669646
$876$	−18.0172	−0.608746
$877$	37.4834	1.26572	0.632862	−	0.774265i	$-0.281880\pi$
$877$	37.4834	1.26572	0.632862	+	0.774265i	$0.281880\pi$
$878$	13.8767	0.468316
$879$	−12.2858	−0.414390
$880$	39.1189	1.31870
$881$	−18.1958	−0.613033	−0.306517	−	0.951865i	$-0.599163\pi$
$881$	−18.1958	−0.613033	−0.306517	+	0.951865i	$0.599163\pi$
$882$	2.68180	0.0903009
$883$	0.397860	0.0133891	0.00669453	−	0.999978i	$-0.497869\pi$
$883$	0.397860	0.0133891	0.00669453	+	0.999978i	$0.497869\pi$
$884$	0	0
$885$	−10.3369	−0.347470
$886$	4.84348	0.162720
$887$	−23.7834	−0.798569	−0.399285	−	0.916827i	$-0.630741\pi$
$887$	−23.7834	−0.798569	−0.399285	+	0.916827i	$0.630741\pi$
$888$	7.31046	0.245323
$889$	−21.6878	−0.727385
$890$	−5.15839	−0.172909
$891$	13.3601	0.447580
$892$	37.4962	1.25547
$893$	−2.96316	−0.0991585
$894$	−2.58616	−0.0864942
$895$	10.0259	0.335129
$896$	−17.8503	−0.596336
$897$	−7.35565	−0.245598
$898$	3.55344	0.118580
$899$	4.32770	0.144337
$900$	2.13341	0.0711136
$901$	0	0
$902$	−9.09327	−0.302773
$903$	2.43882	0.0811587
$904$	−16.3209	−0.542825
$905$	1.08647	0.0361154
$906$	4.20439	0.139682
$907$	−37.5212	−1.24587	−0.622935	−	0.782274i	$-0.714060\pi$
$907$	−37.5212	−1.24587	−0.622935	+	0.782274i	$0.714060\pi$
$908$	−7.93407	−0.263301
$909$	15.6973	0.520646
$910$	7.22668	0.239562
$911$	−14.7648	−0.489178	−0.244589	−	0.969627i	$-0.578653\pi$
$911$	−14.7648	−0.489178	−0.244589	+	0.969627i	$0.578653\pi$
$912$	−1.00505	−0.0332806
$913$	68.7802	2.27629
$914$	−4.08790	−0.135216
$915$	−0.381445	−0.0126102
$916$	−27.2618	−0.900754
$917$	36.4124	1.20244
$918$	0	0
$919$	−48.5476	−1.60144	−0.800718	−	0.599041i	$-0.795549\pi$
$919$	−48.5476	−1.60144	−0.800718	+	0.599041i	$0.795549\pi$
$920$	−5.60813	−0.184894
$921$	−7.95811	−0.262229
$922$	6.77238	0.223037
$923$	46.7975	1.54036
$924$	15.7297	0.517468
$925$	3.14559	0.103426
$926$	−0.497007	−0.0163327
$927$	−11.7983	−0.387507
$928$	−8.54488	−0.280499
$929$	11.2635	0.369544	0.184772	−	0.982781i	$-0.440845\pi$
$929$	11.2635	0.369544	0.184772	+	0.982781i	$0.440845\pi$
$930$	1.39330	0.0456882
$931$	−1.20439	−0.0394724
$932$	9.63640	0.315651
$933$	−2.06418	−0.0675781
$934$	−3.71244	−0.121475
$935$	0	0
$936$	14.1506	0.462528
$937$	2.39775	0.0783310	0.0391655	−	0.999233i	$-0.487530\pi$
$937$	2.39775	0.0783310	0.0391655	+	0.999233i	$0.487530\pi$
$938$	−1.59802	−0.0521772
$939$	−13.3037	−0.434148
$940$	37.6391	1.22765
$941$	−34.3797	−1.12075	−0.560373	−	0.828240i	$-0.689342\pi$
$941$	−34.3797	−1.12075	−0.560373	+	0.828240i	$0.689342\pi$
$942$	5.49081	0.178900
$943$	−9.16849	−0.298567
$944$	16.4798	0.536371
$945$	20.2763	0.659588
$946$	−2.59533	−0.0843816
$947$	−20.5294	−0.667116	−0.333558	−	0.942730i	$-0.608249\pi$
$947$	−20.5294	−0.667116	−0.333558	+	0.942730i	$0.608249\pi$
$948$	−7.32770	−0.237993
$949$	−51.4219	−1.66923
$950$	0.0614894	0.00199498
$951$	9.09091	0.294793
$952$	0	0
$953$	16.5517	0.536162	0.268081	−	0.963396i	$-0.413611\pi$
$953$	16.5517	0.536162	0.268081	+	0.963396i	$0.413611\pi$
$954$	8.08378	0.261722
$955$	−3.35916	−0.108700
$956$	29.7888	0.963439
$957$	9.91622	0.320546
$958$	13.4986	0.436118
$959$	−0.842549	−0.0272073
$960$	10.8348	0.349692
$961$	−27.2226	−0.878147
$962$	10.1078	0.325889
$963$	−34.7279	−1.11909
$964$	−34.0479	−1.09661
$965$	−58.0360	−1.86825
$966$	−1.01785	−0.0327486
$967$	3.92665	0.126273	0.0631363	−	0.998005i	$-0.479890\pi$
$967$	3.92665	0.126273	0.0631363	+	0.998005i	$0.479890\pi$
$968$	−19.7324	−0.634222
$969$	0	0
$970$	−7.56212	−0.242805
$971$	−4.25402	−0.136518	−0.0682590	−	0.997668i	$-0.521744\pi$
$971$	−4.25402	−0.136518	−0.0682590	+	0.997668i	$0.521744\pi$
$972$	30.2746	0.971057
$973$	−21.9513	−0.703726
$974$	12.8547	0.411892
$975$	−2.11463	−0.0677223
$976$	0.608126	0.0194656
$977$	−48.5431	−1.55303	−0.776516	−	0.630097i	$-0.783015\pi$
$977$	−48.5431	−1.55303	−0.776516	+	0.630097i	$0.783015\pi$
$978$	−2.20945	−0.0706503
$979$	−32.0446	−1.02415
$980$	15.2986	0.488696
$981$	4.16756	0.133060
$982$	−8.82739	−0.281693
$983$	35.0597	1.11823	0.559116	−	0.829089i	$-0.311141\pi$
$983$	35.0597	1.11823	0.559116	+	0.829089i	$0.311141\pi$
$984$	−6.12567	−0.195279
$985$	−27.6076	−0.879652
$986$	0	0
$987$	14.1010	0.448840
$988$	−3.07873	−0.0979473
$989$	−2.61680	−0.0832094
$990$	−9.19253	−0.292158
$991$	−53.1995	−1.68994	−0.844968	−	0.534817i	$-0.820381\pi$
$991$	−53.1995	−1.68994	−0.844968	+	0.534817i	$0.820381\pi$
$992$	−7.45842	−0.236805
$993$	−16.0547	−0.509480
$994$	6.47565	0.205395
$995$	48.1671	1.52700
$996$	22.4466	0.711246
$997$	−22.5794	−0.715095	−0.357548	−	0.933895i	$-0.616387\pi$
$997$	−22.5794	−0.715095	−0.357548	+	0.933895i	$0.616387\pi$
$998$	−7.57935	−0.239920
$999$	28.3601	0.897274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.a.e.1.2	yes	3
3.2	odd	2		2601.2.a.w.1.2		3
4.3	odd	2		4624.2.a.bd.1.3		3
5.4	even	2		7225.2.a.s.1.2		3
17.2	even	8		289.2.c.d.38.3		12
17.3	odd	16		289.2.d.f.179.3		24
17.4	even	4		289.2.b.d.288.4		6
17.5	odd	16		289.2.d.f.110.4		24
17.6	odd	16		289.2.d.f.155.3		24
17.7	odd	16		289.2.d.f.134.4		24
17.8	even	8		289.2.c.d.251.4		12
17.9	even	8		289.2.c.d.251.3		12
17.10	odd	16		289.2.d.f.134.3		24
17.11	odd	16		289.2.d.f.155.4		24
17.12	odd	16		289.2.d.f.110.3		24
17.13	even	4		289.2.b.d.288.3		6
17.14	odd	16		289.2.d.f.179.4		24
17.15	even	8		289.2.c.d.38.4		12
17.16	even	2		289.2.a.d.1.2	✓	3
51.50	odd	2		2601.2.a.x.1.2		3
68.67	odd	2		4624.2.a.bg.1.1		3
85.84	even	2		7225.2.a.t.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.a.d.1.2	✓	3	17.16	even	2
289.2.a.e.1.2	yes	3	1.1	even	1	trivial
289.2.b.d.288.3		6	17.13	even	4
289.2.b.d.288.4		6	17.4	even	4
289.2.c.d.38.3		12	17.2	even	8
289.2.c.d.38.4		12	17.15	even	8
289.2.c.d.251.3		12	17.9	even	8
289.2.c.d.251.4		12	17.8	even	8
289.2.d.f.110.3		24	17.12	odd	16
289.2.d.f.110.4		24	17.5	odd	16
289.2.d.f.134.3		24	17.10	odd	16
289.2.d.f.134.4		24	17.7	odd	16
289.2.d.f.155.3		24	17.6	odd	16
289.2.d.f.155.4		24	17.11	odd	16
289.2.d.f.179.3		24	17.3	odd	16
289.2.d.f.179.4		24	17.14	odd	16
2601.2.a.w.1.2		3	3.2	odd	2
2601.2.a.x.1.2		3	51.50	odd	2
4624.2.a.bd.1.3		3	4.3	odd	2
4624.2.a.bg.1.1		3	68.67	odd	2
7225.2.a.s.1.2		3	5.4	even	2
7225.2.a.t.1.2		3	85.84	even	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+0.347296 q^{2} -0.879385 q^{3} -1.87939 q^{4} +2.34730 q^{5} -0.305407 q^{6} +1.87939 q^{7} -1.34730 q^{8} -2.22668 q^{9} +O(q^{10})\)	\(q+0.347296 q^{2} -0.879385 q^{3} -1.87939 q^{4} +2.34730 q^{5} -0.305407 q^{6} +1.87939 q^{7} -1.34730 q^{8} -2.22668 q^{9} +0.815207 q^{10} +5.06418 q^{11} +1.65270 q^{12} +4.71688 q^{13} +0.652704 q^{14} -2.06418 q^{15} +3.29086 q^{16} -0.773318 q^{18} +0.347296 q^{19} -4.41147 q^{20} -1.65270 q^{21} +1.75877 q^{22} +1.77332 q^{23} +1.18479 q^{24} +0.509800 q^{25} +1.63816 q^{26} +4.59627 q^{27} -3.53209 q^{28} -2.22668 q^{29} -0.716881 q^{30} -1.94356 q^{31} +3.83750 q^{32} -4.45336 q^{33} +4.41147 q^{35} +4.18479 q^{36} +6.17024 q^{37} +0.120615 q^{38} -4.14796 q^{39} -3.16250 q^{40} -5.17024 q^{41} -0.573978 q^{42} -1.47565 q^{43} -9.51754 q^{44} -5.22668 q^{45} +0.615867 q^{46} -8.53209 q^{47} -2.89393 q^{48} -3.46791 q^{49} +0.177052 q^{50} -8.86484 q^{52} -10.4534 q^{53} +1.59627 q^{54} +11.8871 q^{55} -2.53209 q^{56} -0.305407 q^{57} -0.773318 q^{58} +5.00774 q^{59} +3.87939 q^{60} +0.184793 q^{61} -0.674992 q^{62} -4.18479 q^{63} -5.24897 q^{64} +11.0719 q^{65} -1.54664 q^{66} -2.44831 q^{67} -1.55943 q^{69} +1.53209 q^{70} +9.92127 q^{71} +3.00000 q^{72} -10.9017 q^{73} +2.14290 q^{74} -0.448311 q^{75} -0.652704 q^{76} +9.51754 q^{77} -1.44057 q^{78} -4.43376 q^{79} +7.72462 q^{80} +2.63816 q^{81} -1.79561 q^{82} +13.5817 q^{83} +3.10607 q^{84} -0.512489 q^{86} +1.95811 q^{87} -6.82295 q^{88} -6.32770 q^{89} -1.81521 q^{90} +8.86484 q^{91} -3.33275 q^{92} +1.70914 q^{93} -2.96316 q^{94} +0.815207 q^{95} -3.37464 q^{96} -9.27631 q^{97} -1.20439 q^{98} -11.2763 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 6 q^{5} - 3 q^{6} - 3 q^{8}+O(q^{10}) \) 3 * q + 3 * q^3 + 6 * q^5 - 3 * q^6 - 3 * q^8	\( 3 q + 3 q^{3} + 6 q^{5} - 3 q^{6} - 3 q^{8} + 6 q^{10} + 6 q^{11} + 6 q^{12} + 6 q^{13} + 3 q^{14} + 3 q^{15} - 6 q^{16} - 9 q^{18} - 3 q^{20} - 6 q^{21} - 6 q^{22} + 12 q^{23} + 3 q^{25} - 12 q^{26} - 6 q^{28} + 6 q^{30} + 9 q^{31} + 9 q^{32} + 3 q^{35} + 9 q^{36} - 3 q^{37} + 6 q^{38} + 3 q^{39} - 12 q^{40} + 6 q^{41} + 6 q^{42} + 15 q^{43} - 6 q^{44} - 9 q^{45} - 9 q^{46} - 21 q^{47} - 21 q^{48} - 15 q^{49} + 21 q^{50} - 3 q^{52} - 18 q^{53} - 9 q^{54} + 6 q^{55} - 3 q^{56} - 3 q^{57} - 9 q^{58} - 9 q^{59} + 6 q^{60} - 3 q^{61} + 3 q^{62} - 9 q^{63} - 3 q^{64} - 18 q^{66} - 9 q^{67} + 21 q^{69} + 21 q^{71} + 9 q^{72} - 21 q^{73} + 6 q^{74} - 3 q^{75} - 3 q^{76} + 6 q^{77} - 30 q^{78} + 3 q^{79} - 9 q^{80} - 9 q^{81} - 6 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{86} + 9 q^{87} - 15 q^{89} - 9 q^{90} + 3 q^{91} + 9 q^{92} + 21 q^{93} + 3 q^{94} + 6 q^{95} + 12 q^{96} + 6 q^{97} - 3 q^{98}+O(q^{100}) \) 3 * q + 3 * q^3 + 6 * q^5 - 3 * q^6 - 3 * q^8 + 6 * q^10 + 6 * q^11 + 6 * q^12 + 6 * q^13 + 3 * q^14 + 3 * q^15 - 6 * q^16 - 9 * q^18 - 3 * q^20 - 6 * q^21 - 6 * q^22 + 12 * q^23 + 3 * q^25 - 12 * q^26 - 6 * q^28 + 6 * q^30 + 9 * q^31 + 9 * q^32 + 3 * q^35 + 9 * q^36 - 3 * q^37 + 6 * q^38 + 3 * q^39 - 12 * q^40 + 6 * q^41 + 6 * q^42 + 15 * q^43 - 6 * q^44 - 9 * q^45 - 9 * q^46 - 21 * q^47 - 21 * q^48 - 15 * q^49 + 21 * q^50 - 3 * q^52 - 18 * q^53 - 9 * q^54 + 6 * q^55 - 3 * q^56 - 3 * q^57 - 9 * q^58 - 9 * q^59 + 6 * q^60 - 3 * q^61 + 3 * q^62 - 9 * q^63 - 3 * q^64 - 18 * q^66 - 9 * q^67 + 21 * q^69 + 21 * q^71 + 9 * q^72 - 21 * q^73 + 6 * q^74 - 3 * q^75 - 3 * q^76 + 6 * q^77 - 30 * q^78 + 3 * q^79 - 9 * q^80 - 9 * q^81 - 6 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^86 + 9 * q^87 - 15 * q^89 - 9 * q^90 + 3 * q^91 + 9 * q^92 + 21 * q^93 + 3 * q^94 + 6 * q^95 + 12 * q^96 + 6 * q^97 - 3 * q^98

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