LMFDB - Embedded newform 289.2.a.d.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:	$1$
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:	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	$-0.418301\pi$
$3$	0.879385	0.507713	0.253857	+	0.967242i	$0.418301\pi$
$4$	−1.87939	−0.939693
$5$	−2.34730	−1.04974	−0.524871	−	0.851182i	$-0.675887\pi$
$5$	−2.34730	−1.04974	−0.524871	+	0.851182i	$0.675887\pi$
$6$	0.305407	0.124682
$7$	−1.87939	−0.710341	−0.355170	−	0.934802i	$-0.615577\pi$
$7$	−1.87939	−0.710341	−0.355170	+	0.934802i	$0.615577\pi$
$8$	−1.34730	−0.476341
$9$	−2.22668	−0.742227
$10$	−0.815207	−0.257791
$11$	−5.06418	−1.52691	−0.763454	−	0.645863i	$-0.776498\pi$
$11$	−5.06418	−1.52691	−0.763454	+	0.645863i	$0.776498\pi$
$12$	−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	$-0.559190\pi$
$23$	−1.77332	−0.369762	−0.184881	+	0.982761i	$0.559190\pi$
$24$	−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	$-0.433714\pi$
$29$	2.22668	0.413484	0.206742	+	0.978395i	$0.433714\pi$
$30$	−0.716881	−0.130884
$31$	1.94356	0.349074	0.174537	−	0.984651i	$-0.444157\pi$
$31$	1.94356	0.349074	0.174537	+	0.984651i	$0.444157\pi$
$32$	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	$-0.669316\pi$
$37$	−6.17024	−1.01438	−0.507191	+	0.861834i	$0.669316\pi$
$38$	0.120615	0.0195663
$39$	4.14796	0.664205
$40$	3.16250	0.500036
$41$	5.17024	0.807457	0.403728	−	0.914879i	$-0.367714\pi$
$41$	5.17024	0.807457	0.403728	+	0.914879i	$0.367714\pi$
$42$	−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	$-0.503766\pi$
$61$	−0.184793	−0.0236603	−0.0118301	+	0.999930i	$0.503766\pi$
$62$	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	$-0.700368\pi$
$71$	−9.92127	−1.17744	−0.588719	+	0.808338i	$0.700368\pi$
$72$	3.00000	0.353553
$73$	10.9017	1.27594	0.637972	−	0.770059i	$-0.279773\pi$
$73$	10.9017	1.27594	0.637972	+	0.770059i	$0.279773\pi$
$74$	−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	$-0.419760\pi$
$79$	4.43376	0.498837	0.249419	+	0.968396i	$0.419760\pi$
$80$	−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	$-0.343917\pi$
$97$	9.27631	0.941867	0.470933	+	0.882169i	$0.343917\pi$
$98$	−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	$-0.771817\pi$
$107$	−15.5963	−1.50775	−0.753874	+	0.657019i	$0.771817\pi$
$108$	8.63816	0.831207
$109$	1.87164	0.179271	0.0896355	−	0.995975i	$-0.471430\pi$
$109$	1.87164	0.179271	0.0896355	+	0.995975i	$0.471430\pi$
$110$	4.12836	0.393623
$111$	−5.42602	−0.515015
$112$	−6.18479	−0.584408
$113$	−12.1138	−1.13957	−0.569786	−	0.821793i	$-0.692974\pi$
$113$	−12.1138	−1.13957	−0.569786	+	0.821793i	$0.692974\pi$
$114$	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	$-0.821226\pi$
$131$	−19.3746	−1.69277	−0.846385	+	0.532572i	$0.821226\pi$
$132$	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	$-0.335042\pi$
$139$	11.6800	0.990688	0.495344	+	0.868697i	$0.335042\pi$
$140$	−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	$-0.591436\pi$
$163$	−7.23442	−0.566644	−0.283322	+	0.959025i	$0.591436\pi$
$164$	−9.71688	−0.758761
$165$	10.4534	0.813793
$166$	4.71688	0.366101
$167$	−5.10607	−0.395119	−0.197560	−	0.980291i	$-0.563302\pi$
$167$	−5.10607	−0.395119	−0.197560	+	0.980291i	$0.563302\pi$
$168$	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	$-0.337888\pi$
$173$	12.8256	0.975115	0.487558	+	0.873091i	$0.337888\pi$
$174$	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	$-0.505476\pi$
$181$	−0.462859	−0.0344040	−0.0172020	+	0.999852i	$0.505476\pi$
$182$	−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	$-0.150803\pi$
$193$	24.7246	1.77972	0.889859	+	0.456236i	$0.150803\pi$
$194$	3.22163	0.231299
$195$	−9.73648	−0.697244
$196$	6.51754	0.465539
$197$	11.7615	0.837969	0.418985	−	0.907993i	$-0.362386\pi$
$197$	11.7615	0.837969	0.418985	+	0.907993i	$0.362386\pi$
$198$	3.91622	0.278314
$199$	−20.5202	−1.45464	−0.727320	−	0.686298i	$-0.759234\pi$
$199$	−20.5202	−1.45464	−0.727320	+	0.686298i	$0.759234\pi$
$200$	−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	$-0.231226\pi$
$211$	21.7178	1.49512	0.747558	+	0.664197i	$0.231226\pi$
$212$	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	$-0.544742\pi$
$227$	−4.22163	−0.280199	−0.140100	+	0.990137i	$0.544742\pi$
$228$	−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	$-0.446284\pi$
$233$	5.12742	0.335909	0.167954	+	0.985795i	$0.446284\pi$
$234$	−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	$-0.698314\pi$
$241$	−18.1165	−1.16699	−0.583493	+	0.812118i	$0.698314\pi$
$242$	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	$-0.661153\pi$
$269$	−15.9067	−0.969850	−0.484925	+	0.874556i	$0.661153\pi$
$270$	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	$-0.331537\pi$
$277$	16.8057	1.00976	0.504879	+	0.863190i	$0.331537\pi$
$278$	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	$-0.0925046\pi$
$283$	32.2344	1.91614	0.958069	+	0.286538i	$0.0925046\pi$
$284$	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	$-0.521200\pi$
$311$	−2.34730	−0.133103	−0.0665515	+	0.997783i	$0.521200\pi$
$312$	−5.58853	−0.316388
$313$	−15.1284	−0.855105	−0.427553	−	0.903990i	$-0.640624\pi$
$313$	−15.1284	−0.855105	−0.427553	+	0.903990i	$0.640624\pi$
$314$	−6.24392	−0.352365
$315$	−9.82295	−0.553460
$316$	−8.33275	−0.468754
$317$	10.3378	0.580629	0.290314	−	0.956931i	$-0.406240\pi$
$317$	10.3378	0.580629	0.290314	+	0.956931i	$0.406240\pi$
$318$	−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	$-0.351682\pi$
$337$	16.4953	0.898554	0.449277	+	0.893393i	$0.351682\pi$
$338$	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	$-0.313793\pi$
$347$	20.5722	1.10437	0.552187	+	0.833720i	$0.313793\pi$
$348$	−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	$-0.512361\pi$
$367$	−1.48751	−0.0776475	−0.0388237	+	0.999246i	$0.512361\pi$
$368$	−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	$-0.673599\pi$
$379$	−20.1976	−1.03748	−0.518740	+	0.854932i	$0.673599\pi$
$380$	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	$-0.707991\pi$
$397$	−24.2249	−1.21581	−0.607907	+	0.794008i	$0.707991\pi$
$398$	−7.12660	−0.357224
$399$	−0.573978	−0.0287348
$400$	1.67768	0.0838840
$401$	−25.5371	−1.27526	−0.637632	−	0.770341i	$-0.720086\pi$
$401$	−25.5371	−1.27526	−0.637632	+	0.770341i	$0.720086\pi$
$402$	−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	$-0.510212\pi$
$419$	−1.31315	−0.0641515	−0.0320757	+	0.999485i	$0.510212\pi$
$420$	−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	$-0.615413\pi$
$431$	−14.7270	−0.709374	−0.354687	+	0.934985i	$0.615413\pi$
$432$	−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	$-0.902555\pi$
$439$	−39.9564	−1.90701	−0.953506	+	0.301373i	$0.902555\pi$
$440$	−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	$-0.577617\pi$
$449$	−10.2317	−0.482865	−0.241433	+	0.970418i	$0.577617\pi$
$450$	−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	$-0.847872\pi$
$479$	−38.8675	−1.77590	−0.887951	+	0.459938i	$0.847872\pi$
$480$	−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	$-0.816641\pi$
$487$	−37.0137	−1.67725	−0.838626	+	0.544708i	$0.816641\pi$
$488$	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	$-0.337549\pi$
$499$	21.8239	0.976971	0.488486	+	0.872572i	$0.337549\pi$
$500$	−19.8084	−0.885859
$501$	−4.49020	−0.200607
$502$	−10.3081	−0.460073
$503$	−33.4371	−1.49088	−0.745442	−	0.666570i	$-0.767762\pi$
$503$	−33.4371	−1.49088	−0.745442	+	0.666570i	$0.767762\pi$
$504$	−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	$-0.216049\pi$
$521$	35.5330	1.55673	0.778365	+	0.627812i	$0.216049\pi$
$522$	−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	$-0.538126\pi$
$541$	−5.55850	−0.238978	−0.119489	+	0.992835i	$0.538126\pi$
$542$	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	$-0.534259\pi$
$547$	−5.02465	−0.214839	−0.107419	+	0.994214i	$0.534259\pi$
$548$	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	$-0.461816\pi$
$571$	5.71925	0.239343	0.119671	+	0.992814i	$0.461816\pi$
$572$	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	$-0.938470\pi$
$601$	−48.1174	−1.96275	−0.981375	+	0.192100i	$0.938470\pi$
$602$	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	$-0.398308\pi$
$607$	15.4757	0.628137	0.314069	+	0.949400i	$0.398308\pi$
$608$	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	$-0.312452\pi$
$617$	27.6064	1.11139	0.555695	+	0.831386i	$0.312452\pi$
$618$	1.61823	0.0650948
$619$	−14.8331	−0.596191	−0.298095	−	0.954536i	$-0.596351\pi$
$619$	−14.8331	−0.596191	−0.298095	+	0.954536i	$0.596351\pi$
$620$	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	$-0.404117\pi$
$641$	15.0232	0.593382	0.296691	+	0.954974i	$0.404117\pi$
$642$	−4.76321	−0.187989
$643$	17.7980	0.701883	0.350942	−	0.936397i	$-0.385862\pi$
$643$	17.7980	0.701883	0.350942	+	0.936397i	$0.385862\pi$
$644$	−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	$-0.703788\pi$
$653$	−30.5303	−1.19474	−0.597372	+	0.801964i	$0.703788\pi$
$654$	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	$-0.421844\pi$
$673$	12.6117	0.486147	0.243074	+	0.970008i	$0.421844\pi$
$674$	5.72874	0.220663
$675$	−2.34318	−0.0901889
$676$	−17.3824	−0.668553
$677$	4.54900	0.174832	0.0874162	−	0.996172i	$-0.472139\pi$
$677$	4.54900	0.174832	0.0874162	+	0.996172i	$0.472139\pi$
$678$	−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	$-0.529686\pi$
$683$	−4.86753	−0.186251	−0.0931253	+	0.995654i	$0.529686\pi$
$684$	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	$-0.533462\pi$
$691$	−5.51661	−0.209862	−0.104931	+	0.994480i	$0.533462\pi$
$692$	−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	$-0.726503\pi$
$709$	−34.7766	−1.30606	−0.653032	+	0.757331i	$0.726503\pi$
$710$	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	$-0.474748\pi$
$719$	4.24990	0.158495	0.0792473	+	0.996855i	$0.474748\pi$
$720$	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	$-0.358942\pi$
$743$	23.3756	0.857567	0.428783	+	0.903407i	$0.358942\pi$
$744$	−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	$-0.399436\pi$
$751$	17.0291	0.621401	0.310700	+	0.950508i	$0.399436\pi$
$752$	−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	$-0.861033\pi$
$787$	−50.8444	−1.81241	−0.906204	+	0.422841i	$0.861033\pi$
$788$	−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	$-0.826924\pi$
$809$	−48.6819	−1.71156	−0.855782	+	0.517336i	$0.826924\pi$
$810$	−2.15064	−0.0755659
$811$	15.9281	0.559311	0.279655	−	0.960100i	$-0.409780\pi$
$811$	15.9281	0.559311	0.279655	+	0.960100i	$0.409780\pi$
$812$	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	$-0.403542\pi$
$821$	17.1010	0.596830	0.298415	+	0.954436i	$0.403542\pi$
$822$	−0.136917	−0.00477554
$823$	5.62267	0.195994	0.0979971	−	0.995187i	$-0.468756\pi$
$823$	5.62267	0.195994	0.0979971	+	0.995187i	$0.468756\pi$
$824$	−7.13878	−0.248691
$825$	−2.27033	−0.0790426
$826$	−3.26857	−0.113728
$827$	−17.8607	−0.621078	−0.310539	−	0.950561i	$-0.600510\pi$
$827$	−17.8607	−0.621078	−0.310539	+	0.950561i	$0.600510\pi$
$828$	−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	$-0.711861\pi$
$839$	−35.7733	−1.23503	−0.617516	+	0.786558i	$0.711861\pi$
$840$	−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	$-0.560674\pi$
$853$	−11.0669	−0.378922	−0.189461	+	0.981888i	$0.560674\pi$
$854$	0.120615	0.00412735
$855$	1.81521	0.0620788
$856$	21.0128	0.718202
$857$	−27.0746	−0.924851	−0.462425	−	0.886658i	$-0.653021\pi$
$857$	−27.0746	−0.924851	−0.462425	+	0.886658i	$0.653021\pi$
$858$	−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	$-0.718120\pi$
$877$	−37.4834	−1.26572	−0.632862	+	0.774265i	$0.718120\pi$
$878$	−13.8767	−0.468316
$879$	12.2858	0.414390
$880$	39.1189	1.31870
$881$	18.1958	0.613033	0.306517	−	0.951865i	$-0.400837\pi$
$881$	18.1958	0.613033	0.306517	+	0.951865i	$0.400837\pi$
$882$	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	$-0.369259\pi$
$887$	23.7834	0.798569	0.399285	+	0.916827i	$0.369259\pi$
$888$	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	$-0.285940\pi$
$907$	37.5212	1.24587	0.622935	+	0.782274i	$0.285940\pi$
$908$	7.93407	0.263301
$909$	15.6973	0.520646
$910$	7.22668	0.239562
$911$	14.7648	0.489178	0.244589	−	0.969627i	$-0.421347\pi$
$911$	14.7648	0.489178	0.244589	+	0.969627i	$0.421347\pi$
$912$	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	$-0.559155\pi$
$929$	−11.2635	−0.369544	−0.184772	+	0.982781i	$0.559155\pi$
$930$	−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	$-0.310658\pi$
$941$	34.3797	1.12075	0.560373	+	0.828240i	$0.310658\pi$
$942$	−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	$-0.391751\pi$
$947$	20.5294	0.667116	0.333558	+	0.942730i	$0.391751\pi$
$948$	−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	$-0.688859\pi$
$983$	−35.0597	−1.11823	−0.559116	+	0.829089i	$0.688859\pi$
$984$	−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	$-0.179619\pi$
$991$	53.1995	1.68994	0.844968	+	0.534817i	$0.179619\pi$
$992$	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	$-0.383613\pi$
$997$	22.5794	0.715095	0.357548	+	0.933895i	$0.383613\pi$
$998$	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.d.1.2	✓	3
3.2	odd	2		2601.2.a.x.1.2		3
4.3	odd	2		4624.2.a.bg.1.1		3
5.4	even	2		7225.2.a.t.1.2		3
17.2	even	8		289.2.c.d.38.4		12
17.3	odd	16		289.2.d.f.179.4		24
17.4	even	4		289.2.b.d.288.3		6
17.5	odd	16		289.2.d.f.110.3		24
17.6	odd	16		289.2.d.f.155.4		24
17.7	odd	16		289.2.d.f.134.3		24
17.8	even	8		289.2.c.d.251.3		12
17.9	even	8		289.2.c.d.251.4		12
17.10	odd	16		289.2.d.f.134.4		24
17.11	odd	16		289.2.d.f.155.3		24
17.12	odd	16		289.2.d.f.110.4		24
17.13	even	4		289.2.b.d.288.4		6
17.14	odd	16		289.2.d.f.179.3		24
17.15	even	8		289.2.c.d.38.3		12
17.16	even	2		289.2.a.e.1.2	yes	3
51.50	odd	2		2601.2.a.w.1.2		3
68.67	odd	2		4624.2.a.bd.1.3		3
85.84	even	2		7225.2.a.s.1.2		3

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