LMFDB - Embedded newform 482.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [482,2,Mod(1,482)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(482, 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("482.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 482 = 2 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	482.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:	$3.84878937743$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.131357120.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 10x^{4} + 16x^{3} + 26x^{2} - 30x - 13 $ x^6 - 2x^5 - 10x^4 + 16x^3 + 26x^2 - 30*x - 13
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.353400$ of defining polynomial
Character	$\chi$	$=$	482.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.353400 q^{3} +1.00000 q^{4} -2.12850 q^{5} +0.353400 q^{6} -2.50020 q^{7} -1.00000 q^{8} -2.87511 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.353400 q^{3} +1.00000 q^{4} -2.12850 q^{5} +0.353400 q^{6} -2.50020 q^{7} -1.00000 q^{8} -2.87511 q^{9} +2.12850 q^{10} +2.52171 q^{11} -0.353400 q^{12} +5.05984 q^{13} +2.50020 q^{14} +0.752214 q^{15} +1.00000 q^{16} +4.65021 q^{17} +2.87511 q^{18} +5.59797 q^{19} -2.12850 q^{20} +0.883571 q^{21} -2.52171 q^{22} -0.393203 q^{23} +0.353400 q^{24} -0.469468 q^{25} -5.05984 q^{26} +2.07627 q^{27} -2.50020 q^{28} -3.27392 q^{29} -0.752214 q^{30} +3.41645 q^{31} -1.00000 q^{32} -0.891172 q^{33} -4.65021 q^{34} +5.32169 q^{35} -2.87511 q^{36} +11.9026 q^{37} -5.59797 q^{38} -1.78815 q^{39} +2.12850 q^{40} -6.50158 q^{41} -0.883571 q^{42} +0.0565882 q^{43} +2.52171 q^{44} +6.11968 q^{45} +0.393203 q^{46} +11.9265 q^{47} -0.353400 q^{48} -0.749001 q^{49} +0.469468 q^{50} -1.64339 q^{51} +5.05984 q^{52} +0.324051 q^{53} -2.07627 q^{54} -5.36747 q^{55} +2.50020 q^{56} -1.97833 q^{57} +3.27392 q^{58} -9.42767 q^{59} +0.752214 q^{60} +10.8153 q^{61} -3.41645 q^{62} +7.18834 q^{63} +1.00000 q^{64} -10.7699 q^{65} +0.891172 q^{66} +2.67034 q^{67} +4.65021 q^{68} +0.138958 q^{69} -5.32169 q^{70} +6.56464 q^{71} +2.87511 q^{72} -3.79563 q^{73} -11.9026 q^{74} +0.165910 q^{75} +5.59797 q^{76} -6.30477 q^{77} +1.78815 q^{78} +4.39560 q^{79} -2.12850 q^{80} +7.89157 q^{81} +6.50158 q^{82} -9.14257 q^{83} +0.883571 q^{84} -9.89800 q^{85} -0.0565882 q^{86} +1.15701 q^{87} -2.52171 q^{88} -5.81491 q^{89} -6.11968 q^{90} -12.6506 q^{91} -0.393203 q^{92} -1.20738 q^{93} -11.9265 q^{94} -11.9153 q^{95} +0.353400 q^{96} +8.52085 q^{97} +0.749001 q^{98} -7.25018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 6 q^{9} + 5 q^{10} - 4 q^{11} + 2 q^{12} + 9 q^{13} - 10 q^{14} + 5 q^{15} + 6 q^{16} + q^{17} - 6 q^{18} + 10 q^{19} - 5 q^{20} + 8 q^{21} + 4 q^{22} + 9 q^{23} - 2 q^{24} + 13 q^{25} - 9 q^{26} + 8 q^{27} + 10 q^{28} - q^{29} - 5 q^{30} + 14 q^{31} - 6 q^{32} + 10 q^{33} - q^{34} - 3 q^{35} + 6 q^{36} + 20 q^{37} - 10 q^{38} + 13 q^{39} + 5 q^{40} - 4 q^{41} - 8 q^{42} + 19 q^{43} - 4 q^{44} - 6 q^{45} - 9 q^{46} + q^{47} + 2 q^{48} + 14 q^{49} - 13 q^{50} + 5 q^{51} + 9 q^{52} - 3 q^{53} - 8 q^{54} + 11 q^{55} - 10 q^{56} + 12 q^{57} + q^{58} - q^{59} + 5 q^{60} + 4 q^{61} - 14 q^{62} + 14 q^{63} + 6 q^{64} + 5 q^{65} - 10 q^{66} + 5 q^{67} + q^{68} - 15 q^{69} + 3 q^{70} + 2 q^{71} - 6 q^{72} + 15 q^{73} - 20 q^{74} - 11 q^{75} + 10 q^{76} - 6 q^{77} - 13 q^{78} + 12 q^{79} - 5 q^{80} - 18 q^{81} + 4 q^{82} - 8 q^{83} + 8 q^{84} - 32 q^{85} - 19 q^{86} + 11 q^{87} + 4 q^{88} - 24 q^{89} + 6 q^{90} + q^{91} + 9 q^{92} - 18 q^{93} - q^{94} + 9 q^{95} - 2 q^{96} - 12 q^{97} - 14 q^{98} - 40 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 6 * q^9 + 5 * q^10 - 4 * q^11 + 2 * q^12 + 9 * q^13 - 10 * q^14 + 5 * q^15 + 6 * q^16 + q^17 - 6 * q^18 + 10 * q^19 - 5 * q^20 + 8 * q^21 + 4 * q^22 + 9 * q^23 - 2 * q^24 + 13 * q^25 - 9 * q^26 + 8 * q^27 + 10 * q^28 - q^29 - 5 * q^30 + 14 * q^31 - 6 * q^32 + 10 * q^33 - q^34 - 3 * q^35 + 6 * q^36 + 20 * q^37 - 10 * q^38 + 13 * q^39 + 5 * q^40 - 4 * q^41 - 8 * q^42 + 19 * q^43 - 4 * q^44 - 6 * q^45 - 9 * q^46 + q^47 + 2 * q^48 + 14 * q^49 - 13 * q^50 + 5 * q^51 + 9 * q^52 - 3 * q^53 - 8 * q^54 + 11 * q^55 - 10 * q^56 + 12 * q^57 + q^58 - q^59 + 5 * q^60 + 4 * q^61 - 14 * q^62 + 14 * q^63 + 6 * q^64 + 5 * q^65 - 10 * q^66 + 5 * q^67 + q^68 - 15 * q^69 + 3 * q^70 + 2 * q^71 - 6 * q^72 + 15 * q^73 - 20 * q^74 - 11 * q^75 + 10 * q^76 - 6 * q^77 - 13 * q^78 + 12 * q^79 - 5 * q^80 - 18 * q^81 + 4 * q^82 - 8 * q^83 + 8 * q^84 - 32 * q^85 - 19 * q^86 + 11 * q^87 + 4 * q^88 - 24 * q^89 + 6 * q^90 + q^91 + 9 * q^92 - 18 * q^93 - q^94 + 9 * q^95 - 2 * q^96 - 12 * q^97 - 14 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.353400	−0.204036	−0.102018	−	0.994783i	$-0.532530\pi$
$3$	−0.353400	−0.204036	−0.102018	+	0.994783i	$0.532530\pi$
$4$	1.00000	0.500000
$5$	−2.12850	−0.951896	−0.475948	−	0.879473i	$-0.657895\pi$
$5$	−2.12850	−0.951896	−0.475948	+	0.879473i	$0.657895\pi$
$6$	0.353400	0.144275
$7$	−2.50020	−0.944987	−0.472493	−	0.881334i	$-0.656646\pi$
$7$	−2.50020	−0.944987	−0.472493	+	0.881334i	$0.656646\pi$
$8$	−1.00000	−0.353553
$9$	−2.87511	−0.958369
$10$	2.12850	0.673092
$11$	2.52171	0.760324	0.380162	−	0.924920i	$-0.375868\pi$
$11$	2.52171	0.760324	0.380162	+	0.924920i	$0.375868\pi$
$12$	−0.353400	−0.102018
$13$	5.05984	1.40335	0.701674	−	0.712499i	$-0.252436\pi$
$13$	5.05984	1.40335	0.701674	+	0.712499i	$0.252436\pi$
$14$	2.50020	0.668207
$15$	0.752214	0.194221
$16$	1.00000	0.250000
$17$	4.65021	1.12784	0.563921	−	0.825829i	$-0.309292\pi$
$17$	4.65021	1.12784	0.563921	+	0.825829i	$0.309292\pi$
$18$	2.87511	0.677670
$19$	5.59797	1.28426	0.642132	−	0.766594i	$-0.278050\pi$
$19$	5.59797	1.28426	0.642132	+	0.766594i	$0.278050\pi$
$20$	−2.12850	−0.475948
$21$	0.883571	0.192811
$22$	−2.52171	−0.537630
$23$	−0.393203	−0.0819886	−0.0409943	−	0.999159i	$-0.513053\pi$
$23$	−0.393203	−0.0819886	−0.0409943	+	0.999159i	$0.513053\pi$
$24$	0.353400	0.0721375
$25$	−0.469468	−0.0938937
$26$	−5.05984	−0.992316
$27$	2.07627	0.399577
$28$	−2.50020	−0.472493
$29$	−3.27392	−0.607952	−0.303976	−	0.952680i	$-0.598314\pi$
$29$	−3.27392	−0.607952	−0.303976	+	0.952680i	$0.598314\pi$
$30$	−0.752214	−0.137335
$31$	3.41645	0.613613	0.306807	−	0.951772i	$-0.400740\pi$
$31$	3.41645	0.613613	0.306807	+	0.951772i	$0.400740\pi$
$32$	−1.00000	−0.176777
$33$	−0.891172	−0.155133
$34$	−4.65021	−0.797505
$35$	5.32169	0.899529
$36$	−2.87511	−0.479185
$37$	11.9026	1.95678	0.978390	−	0.206769i	$-0.0662947\pi$
$37$	11.9026	1.95678	0.978390	+	0.206769i	$0.0662947\pi$
$38$	−5.59797	−0.908111
$39$	−1.78815	−0.286333
$40$	2.12850	0.336546
$41$	−6.50158	−1.01538	−0.507688	−	0.861541i	$-0.669500\pi$
$41$	−6.50158	−1.01538	−0.507688	+	0.861541i	$0.669500\pi$
$42$	−0.883571	−0.136338
$43$	0.0565882	0.00862962	0.00431481	−	0.999991i	$-0.498627\pi$
$43$	0.0565882	0.00862962	0.00431481	+	0.999991i	$0.498627\pi$
$44$	2.52171	0.380162
$45$	6.11968	0.912268
$46$	0.393203	0.0579747
$47$	11.9265	1.73966	0.869828	−	0.493354i	$-0.164229\pi$
$47$	11.9265	1.73966	0.869828	+	0.493354i	$0.164229\pi$
$48$	−0.353400	−0.0510089
$49$	−0.749001	−0.107000
$50$	0.469468	0.0663929
$51$	−1.64339	−0.230120
$52$	5.05984	0.701674
$53$	0.324051	0.0445118	0.0222559	−	0.999752i	$-0.492915\pi$
$53$	0.324051	0.0445118	0.0222559	+	0.999752i	$0.492915\pi$
$54$	−2.07627	−0.282544
$55$	−5.36747	−0.723749
$56$	2.50020	0.334103
$57$	−1.97833	−0.262036
$58$	3.27392	0.429887
$59$	−9.42767	−1.22738	−0.613689	−	0.789548i	$-0.710315\pi$
$59$	−9.42767	−1.22738	−0.613689	+	0.789548i	$0.710315\pi$
$60$	0.752214	0.0971104
$61$	10.8153	1.38476	0.692379	−	0.721534i	$-0.256563\pi$
$61$	10.8153	1.38476	0.692379	+	0.721534i	$0.256563\pi$
$62$	−3.41645	−0.433890
$63$	7.18834	0.905646
$64$	1.00000	0.125000
$65$	−10.7699	−1.33584
$66$	0.891172	0.109696
$67$	2.67034	0.326234	0.163117	−	0.986607i	$-0.447845\pi$
$67$	2.67034	0.326234	0.163117	+	0.986607i	$0.447845\pi$
$68$	4.65021	0.563921
$69$	0.138958	0.0167286
$70$	−5.32169	−0.636063
$71$	6.56464	0.779079	0.389539	−	0.921010i	$-0.372634\pi$
$71$	6.56464	0.779079	0.389539	+	0.921010i	$0.372634\pi$
$72$	2.87511	0.338835
$73$	−3.79563	−0.444245	−0.222122	−	0.975019i	$-0.571298\pi$
$73$	−3.79563	−0.444245	−0.222122	+	0.975019i	$0.571298\pi$
$74$	−11.9026	−1.38365
$75$	0.165910	0.0191577
$76$	5.59797	0.642132
$77$	−6.30477	−0.718496
$78$	1.78815	0.202468
$79$	4.39560	0.494544	0.247272	−	0.968946i	$-0.420466\pi$
$79$	4.39560	0.494544	0.247272	+	0.968946i	$0.420466\pi$
$80$	−2.12850	−0.237974
$81$	7.89157	0.876841
$82$	6.50158	0.717980
$83$	−9.14257	−1.00353	−0.501764	−	0.865005i	$-0.667315\pi$
$83$	−9.14257	−1.00353	−0.501764	+	0.865005i	$0.667315\pi$
$84$	0.883571	0.0964055
$85$	−9.89800	−1.07359
$86$	−0.0565882	−0.00610206
$87$	1.15701	0.124044
$88$	−2.52171	−0.268815
$89$	−5.81491	−0.616379	−0.308189	−	0.951325i	$-0.599723\pi$
$89$	−5.81491	−0.616379	−0.308189	+	0.951325i	$0.599723\pi$
$90$	−6.11968	−0.645071
$91$	−12.6506	−1.32614
$92$	−0.393203	−0.0409943
$93$	−1.20738	−0.125199
$94$	−11.9265	−1.23012
$95$	−11.9153	−1.22249
$96$	0.353400	0.0360688
$97$	8.52085	0.865161	0.432580	−	0.901595i	$-0.357603\pi$
$97$	8.52085	0.865161	0.432580	+	0.901595i	$0.357603\pi$
$98$	0.749001	0.0756605
$99$	−7.25018	−0.728671
$100$	−0.469468	−0.0469468
$101$	−7.87373	−0.783465	−0.391733	−	0.920079i	$-0.628124\pi$
$101$	−7.87373	−0.783465	−0.391733	+	0.920079i	$0.628124\pi$
$102$	1.64339	0.162720
$103$	18.5767	1.83042	0.915208	−	0.402981i	$-0.132026\pi$
$103$	18.5767	1.83042	0.915208	+	0.402981i	$0.132026\pi$
$104$	−5.05984	−0.496158
$105$	−1.88069	−0.183536
$106$	−0.324051	−0.0314746
$107$	14.4257	1.39459	0.697293	−	0.716786i	$-0.254388\pi$
$107$	14.4257	1.39459	0.697293	+	0.716786i	$0.254388\pi$
$108$	2.07627	0.199789
$109$	−12.1790	−1.16654	−0.583270	−	0.812278i	$-0.698227\pi$
$109$	−12.1790	−1.16654	−0.583270	+	0.812278i	$0.698227\pi$
$110$	5.36747	0.511768
$111$	−4.20639	−0.399253
$112$	−2.50020	−0.236247
$113$	−17.0290	−1.60196	−0.800978	−	0.598694i	$-0.795687\pi$
$113$	−17.0290	−1.60196	−0.800978	+	0.598694i	$0.795687\pi$
$114$	1.97833	0.185287
$115$	0.836935	0.0780446
$116$	−3.27392	−0.303976
$117$	−14.5476	−1.34493
$118$	9.42767	0.867887
$119$	−11.6265	−1.06580
$120$	−0.752214	−0.0686674
$121$	−4.64099	−0.421908
$122$	−10.8153	−0.979172
$123$	2.29766	0.207173
$124$	3.41645	0.306807
$125$	11.6418	1.04127
$126$	−7.18834	−0.640389
$127$	10.5721	0.938124	0.469062	−	0.883165i	$-0.344592\pi$
$127$	10.5721	0.938124	0.469062	+	0.883165i	$0.344592\pi$
$128$	−1.00000	−0.0883883
$129$	−0.0199983	−0.00176075
$130$	10.7699	0.944582
$131$	16.1642	1.41227	0.706137	−	0.708075i	$-0.250436\pi$
$131$	16.1642	1.41227	0.706137	+	0.708075i	$0.250436\pi$
$132$	−0.891172	−0.0775666
$133$	−13.9961	−1.21361
$134$	−2.67034	−0.230682
$135$	−4.41934	−0.380356
$136$	−4.65021	−0.398752
$137$	−3.56378	−0.304474	−0.152237	−	0.988344i	$-0.548648\pi$
$137$	−3.56378	−0.304474	−0.152237	+	0.988344i	$0.548648\pi$
$138$	−0.138958	−0.0118289
$139$	−4.63976	−0.393539	−0.196770	−	0.980450i	$-0.563045\pi$
$139$	−4.63976	−0.393539	−0.196770	+	0.980450i	$0.563045\pi$
$140$	5.32169	0.449765
$141$	−4.21482	−0.354952
$142$	−6.56464	−0.550892
$143$	12.7594	1.06700
$144$	−2.87511	−0.239592
$145$	6.96856	0.578707
$146$	3.79563	0.314129
$147$	0.264697	0.0218319
$148$	11.9026	0.978390
$149$	7.11248	0.582677	0.291339	−	0.956620i	$-0.405899\pi$
$149$	7.11248	0.582677	0.291339	+	0.956620i	$0.405899\pi$
$150$	−0.165910	−0.0135465
$151$	−10.2961	−0.837883	−0.418941	−	0.908013i	$-0.637599\pi$
$151$	−10.2961	−0.837883	−0.418941	+	0.908013i	$0.637599\pi$
$152$	−5.59797	−0.454056
$153$	−13.3699	−1.08089
$154$	6.30477	0.508053
$155$	−7.27194	−0.584096
$156$	−1.78815	−0.143167
$157$	−13.1714	−1.05119	−0.525597	−	0.850734i	$-0.676158\pi$
$157$	−13.1714	−1.05119	−0.525597	+	0.850734i	$0.676158\pi$
$158$	−4.39560	−0.349695
$159$	−0.114520	−0.00908200
$160$	2.12850	0.168273
$161$	0.983087	0.0774781
$162$	−7.89157	−0.620020
$163$	2.96133	0.231949	0.115975	−	0.993252i	$-0.463001\pi$
$163$	2.96133	0.231949	0.115975	+	0.993252i	$0.463001\pi$
$164$	−6.50158	−0.507688
$165$	1.89686	0.147671
$166$	9.14257	0.709601
$167$	−10.2365	−0.792125	−0.396062	−	0.918224i	$-0.629624\pi$
$167$	−10.2365	−0.792125	−0.396062	+	0.918224i	$0.629624\pi$
$168$	−0.883571	−0.0681690
$169$	12.6020	0.969383
$170$	9.89800	0.759142
$171$	−16.0948	−1.23080
$172$	0.0565882	0.00431481
$173$	−6.09578	−0.463453	−0.231727	−	0.972781i	$-0.574437\pi$
$173$	−6.09578	−0.463453	−0.231727	+	0.972781i	$0.574437\pi$
$174$	−1.15701	−0.0877123
$175$	1.17376	0.0887283
$176$	2.52171	0.190081
$177$	3.33174	0.250429
$178$	5.81491	0.435846
$179$	13.7361	1.02668	0.513342	−	0.858184i	$-0.328407\pi$
$179$	13.7361	1.02668	0.513342	+	0.858184i	$0.328407\pi$
$180$	6.11968	0.456134
$181$	4.38316	0.325798	0.162899	−	0.986643i	$-0.447916\pi$
$181$	4.38316	0.325798	0.162899	+	0.986643i	$0.447916\pi$
$182$	12.6506	0.937726
$183$	−3.82213	−0.282540
$184$	0.393203	0.0289873
$185$	−25.3348	−1.86265
$186$	1.20738	0.0885291
$187$	11.7265	0.857525
$188$	11.9265	0.869828
$189$	−5.19108	−0.377595
$190$	11.9153	0.864428
$191$	11.0285	0.797994	0.398997	−	0.916952i	$-0.369358\pi$
$191$	11.0285	0.797994	0.398997	+	0.916952i	$0.369358\pi$
$192$	−0.353400	−0.0255045
$193$	10.9494	0.788153	0.394077	−	0.919078i	$-0.371064\pi$
$193$	10.9494	0.788153	0.394077	+	0.919078i	$0.371064\pi$
$194$	−8.52085	−0.611761
$195$	3.80608	0.272559
$196$	−0.749001	−0.0535001
$197$	−3.19880	−0.227905	−0.113952	−	0.993486i	$-0.536351\pi$
$197$	−3.19880	−0.227905	−0.113952	+	0.993486i	$0.536351\pi$
$198$	7.25018	0.515248
$199$	17.6047	1.24796	0.623981	−	0.781440i	$-0.285514\pi$
$199$	17.6047	1.24796	0.623981	+	0.781440i	$0.285514\pi$
$200$	0.469468	0.0331964
$201$	−0.943698	−0.0665634
$202$	7.87373	0.553993
$203$	8.18546	0.574507
$204$	−1.64339	−0.115060
$205$	13.8386	0.966533
$206$	−18.5767	−1.29430
$207$	1.13050	0.0785753
$208$	5.05984	0.350837
$209$	14.1165	0.976455
$210$	1.88069	0.129780
$211$	−19.6602	−1.35346	−0.676732	−	0.736229i	$-0.736604\pi$
$211$	−19.6602	−1.35346	−0.676732	+	0.736229i	$0.736604\pi$
$212$	0.324051	0.0222559
$213$	−2.31994	−0.158960
$214$	−14.4257	−0.986122
$215$	−0.120448	−0.00821450
$216$	−2.07627	−0.141272
$217$	−8.54182	−0.579856
$218$	12.1790	0.824868
$219$	1.34138	0.0906418
$220$	−5.36747	−0.361875
$221$	23.5293	1.58275
$222$	4.20639	0.282315
$223$	24.8591	1.66469	0.832345	−	0.554258i	$-0.186998\pi$
$223$	24.8591	1.66469	0.832345	+	0.554258i	$0.186998\pi$
$224$	2.50020	0.167052
$225$	1.34977	0.0899848
$226$	17.0290	1.13275
$227$	18.8885	1.25367	0.626836	−	0.779151i	$-0.284349\pi$
$227$	18.8885	1.25367	0.626836	+	0.779151i	$0.284349\pi$
$228$	−1.97833	−0.131018
$229$	−16.6787	−1.10216	−0.551080	−	0.834453i	$-0.685784\pi$
$229$	−16.6787	−1.10216	−0.551080	+	0.834453i	$0.685784\pi$
$230$	−0.836935	−0.0551859
$231$	2.22811	0.146599
$232$	3.27392	0.214944
$233$	2.79678	0.183223	0.0916115	−	0.995795i	$-0.470798\pi$
$233$	2.79678	0.183223	0.0916115	+	0.995795i	$0.470798\pi$
$234$	14.5476	0.951006
$235$	−25.3856	−1.65597
$236$	−9.42767	−0.613689
$237$	−1.55341	−0.100905
$238$	11.6265	0.753631
$239$	−13.7309	−0.888181	−0.444090	−	0.895982i	$-0.646473\pi$
$239$	−13.7309	−0.888181	−0.444090	+	0.895982i	$0.646473\pi$
$240$	0.752214	0.0485552
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	4.64099	0.298334
$243$	−9.01768	−0.578484
$244$	10.8153	0.692379
$245$	1.59425	0.101853
$246$	−2.29766	−0.146494
$247$	28.3249	1.80227
$248$	−3.41645	−0.216945
$249$	3.23099	0.204756
$250$	−11.6418	−0.736291
$251$	−1.18757	−0.0749589	−0.0374794	−	0.999297i	$-0.511933\pi$
$251$	−1.18757	−0.0749589	−0.0374794	+	0.999297i	$0.511933\pi$
$252$	7.18834	0.452823
$253$	−0.991544	−0.0623378
$254$	−10.5721	−0.663354
$255$	3.49796	0.219050
$256$	1.00000	0.0625000
$257$	19.7847	1.23413	0.617067	−	0.786910i	$-0.288321\pi$
$257$	19.7847	1.23413	0.617067	+	0.786910i	$0.288321\pi$
$258$	0.0199983	0.00124504
$259$	−29.7589	−1.84913
$260$	−10.7699	−0.667920
$261$	9.41288	0.582643
$262$	−16.1642	−0.998629
$263$	14.6704	0.904614	0.452307	−	0.891862i	$-0.350601\pi$
$263$	14.6704	0.904614	0.452307	+	0.891862i	$0.350601\pi$
$264$	0.891172	0.0548479
$265$	−0.689744	−0.0423706
$266$	13.9961	0.858153
$267$	2.05499	0.125763
$268$	2.67034	0.163117
$269$	−16.8314	−1.02623	−0.513113	−	0.858321i	$-0.671508\pi$
$269$	−16.8314	−1.02623	−0.513113	+	0.858321i	$0.671508\pi$
$270$	4.41934	0.268952
$271$	−8.63365	−0.524457	−0.262229	−	0.965006i	$-0.584457\pi$
$271$	−8.63365	−0.524457	−0.262229	+	0.965006i	$0.584457\pi$
$272$	4.65021	0.281961
$273$	4.47073	0.270581
$274$	3.56378	0.215296
$275$	−1.18386	−0.0713896
$276$	0.138958	0.00836430
$277$	25.9188	1.55731	0.778655	−	0.627453i	$-0.215902\pi$
$277$	25.9188	1.55731	0.778655	+	0.627453i	$0.215902\pi$
$278$	4.63976	0.278274
$279$	−9.82267	−0.588068
$280$	−5.32169	−0.318032
$281$	0.273027	0.0162874	0.00814371	−	0.999967i	$-0.497408\pi$
$281$	0.273027	0.0162874	0.00814371	+	0.999967i	$0.497408\pi$
$282$	4.21482	0.250989
$283$	0.514995	0.0306133	0.0153066	−	0.999883i	$-0.495128\pi$
$283$	0.514995	0.0306133	0.0153066	+	0.999883i	$0.495128\pi$
$284$	6.56464	0.389539
$285$	4.21087	0.249431
$286$	−12.7594	−0.754481
$287$	16.2553	0.959517
$288$	2.87511	0.169417
$289$	4.62448	0.272028
$290$	−6.96856	−0.409208
$291$	−3.01127	−0.176524
$292$	−3.79563	−0.222122
$293$	−26.9687	−1.57553	−0.787765	−	0.615976i	$-0.788762\pi$
$293$	−26.9687	−1.57553	−0.787765	+	0.615976i	$0.788762\pi$
$294$	−0.264697	−0.0154375
$295$	20.0668	1.16834
$296$	−11.9026	−0.691826
$297$	5.23573	0.303808
$298$	−7.11248	−0.412015
$299$	−1.98955	−0.115058
$300$	0.165910	0.00957884
$301$	−0.141482	−0.00815487
$302$	10.2961	0.592473
$303$	2.78258	0.159855
$304$	5.59797	0.321066
$305$	−23.0204	−1.31815
$306$	13.3699	0.764304
$307$	−29.6437	−1.69186	−0.845928	−	0.533297i	$-0.820953\pi$
$307$	−29.6437	−1.69186	−0.845928	+	0.533297i	$0.820953\pi$
$308$	−6.30477	−0.359248
$309$	−6.56501	−0.373470
$310$	7.27194	0.413018
$311$	24.3411	1.38026	0.690128	−	0.723688i	$-0.257554\pi$
$311$	24.3411	1.38026	0.690128	+	0.723688i	$0.257554\pi$
$312$	1.78815	0.101234
$313$	−16.8506	−0.952451	−0.476226	−	0.879323i	$-0.657995\pi$
$313$	−16.8506	−0.952451	−0.476226	+	0.879323i	$0.657995\pi$
$314$	13.1714	0.743306
$315$	−15.3004	−0.862081
$316$	4.39560	0.247272
$317$	−29.9346	−1.68130	−0.840648	−	0.541582i	$-0.817826\pi$
$317$	−29.9346	−1.68130	−0.840648	+	0.541582i	$0.817826\pi$
$318$	0.114520	0.00642195
$319$	−8.25588	−0.462240
$320$	−2.12850	−0.118987
$321$	−5.09805	−0.284546
$322$	−0.983087	−0.0547853
$323$	26.0318	1.44845
$324$	7.89157	0.438421
$325$	−2.37544	−0.131765
$326$	−2.96133	−0.164013
$327$	4.30407	0.238016
$328$	6.50158	0.358990
$329$	−29.8186	−1.64395
$330$	−1.89686	−0.104419
$331$	−24.1991	−1.33010	−0.665052	−	0.746797i	$-0.731591\pi$
$331$	−24.1991	−1.33010	−0.665052	+	0.746797i	$0.731591\pi$
$332$	−9.14257	−0.501764
$333$	−34.2213	−1.87532
$334$	10.2365	0.560117
$335$	−5.68383	−0.310541
$336$	0.883571	0.0482028
$337$	24.0554	1.31038	0.655190	−	0.755464i	$-0.272588\pi$
$337$	24.0554	1.31038	0.655190	+	0.755464i	$0.272588\pi$
$338$	−12.6020	−0.685458
$339$	6.01806	0.326856
$340$	−9.89800	−0.536794
$341$	8.61530	0.466545
$342$	16.0948	0.870306
$343$	19.3741	1.04610
$344$	−0.0565882	−0.00305103
$345$	−0.295773	−0.0159239
$346$	6.09578	0.327711
$347$	24.2366	1.30109	0.650543	−	0.759469i	$-0.274541\pi$
$347$	24.2366	1.30109	0.650543	+	0.759469i	$0.274541\pi$
$348$	1.15701	0.0620220
$349$	20.8748	1.11740	0.558700	−	0.829370i	$-0.311300\pi$
$349$	20.8748	1.11740	0.558700	+	0.829370i	$0.311300\pi$
$350$	−1.17376	−0.0627404
$351$	10.5056	0.560746
$352$	−2.52171	−0.134407
$353$	16.8655	0.897663	0.448831	−	0.893617i	$-0.351840\pi$
$353$	16.8655	0.897663	0.448831	+	0.893617i	$0.351840\pi$
$354$	−3.33174	−0.177080
$355$	−13.9729	−0.741602
$356$	−5.81491	−0.308189
$357$	4.10879	0.217460
$358$	−13.7361	−0.725975
$359$	24.4996	1.29304	0.646519	−	0.762898i	$-0.276224\pi$
$359$	24.4996	1.29304	0.646519	+	0.762898i	$0.276224\pi$
$360$	−6.11968	−0.322536
$361$	12.3373	0.649332
$362$	−4.38316	−0.230374
$363$	1.64013	0.0860843
$364$	−12.6506	−0.663072
$365$	8.07902	0.422875
$366$	3.82213	0.199786
$367$	−17.6489	−0.921267	−0.460633	−	0.887590i	$-0.652378\pi$
$367$	−17.6489	−0.921267	−0.460633	+	0.887590i	$0.652378\pi$
$368$	−0.393203	−0.0204971
$369$	18.6928	0.973106
$370$	25.3348	1.31709
$371$	−0.810192	−0.0420631
$372$	−1.20738	−0.0625995
$373$	27.6104	1.42961	0.714807	−	0.699321i	$-0.246514\pi$
$373$	27.6104	1.42961	0.714807	+	0.699321i	$0.246514\pi$
$374$	−11.7265	−0.606362
$375$	−4.11421	−0.212457
$376$	−11.9265	−0.615062
$377$	−16.5655	−0.853168
$378$	5.19108	0.267000
$379$	−11.5761	−0.594622	−0.297311	−	0.954781i	$-0.596090\pi$
$379$	−11.5761	−0.594622	−0.297311	+	0.954781i	$0.596090\pi$
$380$	−11.9153	−0.611243
$381$	−3.73619	−0.191411
$382$	−11.0285	−0.564267
$383$	−34.8424	−1.78037	−0.890183	−	0.455604i	$-0.849423\pi$
$383$	−34.8424	−1.78037	−0.890183	+	0.455604i	$0.849423\pi$
$384$	0.353400	0.0180344
$385$	13.4197	0.683933
$386$	−10.9494	−0.557309
$387$	−0.162697	−0.00827036
$388$	8.52085	0.432580
$389$	27.5774	1.39823	0.699115	−	0.715009i	$-0.253577\pi$
$389$	27.5774	1.39823	0.699115	+	0.715009i	$0.253577\pi$
$390$	−3.80608	−0.192729
$391$	−1.82848	−0.0924702
$392$	0.749001	0.0378303
$393$	−5.71244	−0.288154
$394$	3.19880	0.161153
$395$	−9.35606	−0.470754
$396$	−7.25018	−0.364335
$397$	−34.7402	−1.74356	−0.871780	−	0.489897i	$-0.837034\pi$
$397$	−34.7402	−1.74356	−0.871780	+	0.489897i	$0.837034\pi$
$398$	−17.6047	−0.882442
$399$	4.94621	0.247620
$400$	−0.469468	−0.0234734
$401$	9.34627	0.466731	0.233365	−	0.972389i	$-0.425026\pi$
$401$	9.34627	0.466731	0.233365	+	0.972389i	$0.425026\pi$
$402$	0.943698	0.0470674
$403$	17.2867	0.861112
$404$	−7.87373	−0.391733
$405$	−16.7972	−0.834662
$406$	−8.18546	−0.406238
$407$	30.0149	1.48779
$408$	1.64339	0.0813598
$409$	−18.6410	−0.921737	−0.460868	−	0.887468i	$-0.652462\pi$
$409$	−18.6410	−0.921737	−0.460868	+	0.887468i	$0.652462\pi$
$410$	−13.8386	−0.683442
$411$	1.25944	0.0621236
$412$	18.5767	0.915208
$413$	23.5711	1.15986
$414$	−1.13050	−0.0555612
$415$	19.4600	0.955254
$416$	−5.05984	−0.248079
$417$	1.63969	0.0802961
$418$	−14.1165	−0.690458
$419$	−23.8188	−1.16362	−0.581812	−	0.813323i	$-0.697656\pi$
$419$	−23.8188	−1.16362	−0.581812	+	0.813323i	$0.697656\pi$
$420$	−1.88069	−0.0917681
$421$	−17.3129	−0.843780	−0.421890	−	0.906647i	$-0.638633\pi$
$421$	−17.3129	−0.843780	−0.421890	+	0.906647i	$0.638633\pi$
$422$	19.6602	0.957044
$423$	−34.2899	−1.66723
$424$	−0.324051	−0.0157373
$425$	−2.18313	−0.105897
$426$	2.31994	0.112402
$427$	−27.0404	−1.30858
$428$	14.4257	0.697293
$429$	−4.50919	−0.217706
$430$	0.120448	0.00580853
$431$	12.1208	0.583840	0.291920	−	0.956443i	$-0.405706\pi$
$431$	12.1208	0.583840	0.291920	+	0.956443i	$0.405706\pi$
$432$	2.07627	0.0998943
$433$	−3.98023	−0.191278	−0.0956388	−	0.995416i	$-0.530489\pi$
$433$	−3.98023	−0.191278	−0.0956388	+	0.995416i	$0.530489\pi$
$434$	8.54182	0.410020
$435$	−2.46269	−0.118077
$436$	−12.1790	−0.583270
$437$	−2.20114	−0.105295
$438$	−1.34138	−0.0640935
$439$	−11.4715	−0.547504	−0.273752	−	0.961800i	$-0.588265\pi$
$439$	−11.4715	−0.547504	−0.273752	+	0.961800i	$0.588265\pi$
$440$	5.36747	0.255884
$441$	2.15346	0.102546
$442$	−23.5293	−1.11918
$443$	−8.06760	−0.383303	−0.191652	−	0.981463i	$-0.561384\pi$
$443$	−8.06760	−0.383303	−0.191652	+	0.981463i	$0.561384\pi$
$444$	−4.20639	−0.199627
$445$	12.3771	0.586729
$446$	−24.8591	−1.17711
$447$	−2.51355	−0.118887
$448$	−2.50020	−0.118123
$449$	−2.77955	−0.131175	−0.0655875	−	0.997847i	$-0.520892\pi$
$449$	−2.77955	−0.131175	−0.0655875	+	0.997847i	$0.520892\pi$
$450$	−1.34977	−0.0636289
$451$	−16.3951	−0.772015
$452$	−17.0290	−0.800978
$453$	3.63864	0.170958
$454$	−18.8885	−0.886481
$455$	26.9269	1.26235
$456$	1.97833	0.0926436
$457$	−25.5469	−1.19503	−0.597516	−	0.801857i	$-0.703846\pi$
$457$	−25.5469	−1.19503	−0.597516	+	0.801857i	$0.703846\pi$
$458$	16.6787	0.779344
$459$	9.65507	0.450660
$460$	0.836935	0.0390223
$461$	−3.40760	−0.158708	−0.0793539	−	0.996847i	$-0.525286\pi$
$461$	−3.40760	−0.158708	−0.0793539	+	0.996847i	$0.525286\pi$
$462$	−2.22811	−0.103661
$463$	11.5667	0.537551	0.268775	−	0.963203i	$-0.413381\pi$
$463$	11.5667	0.537551	0.268775	+	0.963203i	$0.413381\pi$
$464$	−3.27392	−0.151988
$465$	2.56991	0.119176
$466$	−2.79678	−0.129558
$467$	10.0267	0.463979	0.231990	−	0.972718i	$-0.425476\pi$
$467$	10.0267	0.463979	0.231990	+	0.972718i	$0.425476\pi$
$468$	−14.5476	−0.672463
$469$	−6.67638	−0.308287
$470$	25.3856	1.17095
$471$	4.65478	0.214481
$472$	9.42767	0.433944
$473$	0.142699	0.00656130
$474$	1.55341	0.0713503
$475$	−2.62807	−0.120584
$476$	−11.6265	−0.532898
$477$	−0.931681	−0.0426588
$478$	13.7309	0.628039
$479$	−16.1601	−0.738375	−0.369187	−	0.929355i	$-0.620364\pi$
$479$	−16.1601	−0.738375	−0.369187	+	0.929355i	$0.620364\pi$
$480$	−0.752214	−0.0343337
$481$	60.2254	2.74604
$482$	−1.00000	−0.0455488
$483$	−0.347423	−0.0158083
$484$	−4.64099	−0.210954
$485$	−18.1367	−0.823543
$486$	9.01768	0.409050
$487$	−36.0715	−1.63456	−0.817279	−	0.576243i	$-0.804518\pi$
$487$	−36.0715	−1.63456	−0.817279	+	0.576243i	$0.804518\pi$
$488$	−10.8153	−0.489586
$489$	−1.04654	−0.0473260
$490$	−1.59425	−0.0720210
$491$	−18.3779	−0.829381	−0.414691	−	0.909963i	$-0.636110\pi$
$491$	−18.3779	−0.829381	−0.414691	+	0.909963i	$0.636110\pi$
$492$	2.29766	0.103587
$493$	−15.2244	−0.685674
$494$	−28.3249	−1.27440
$495$	15.4320	0.693619
$496$	3.41645	0.153403
$497$	−16.4129	−0.736219
$498$	−3.23099	−0.144784
$499$	26.1542	1.17082	0.585412	−	0.810736i	$-0.300933\pi$
$499$	26.1542	1.17082	0.585412	+	0.810736i	$0.300933\pi$
$500$	11.6418	0.520637
$501$	3.61759	0.161622
$502$	1.18757	0.0530039
$503$	19.7899	0.882389	0.441194	−	0.897412i	$-0.354555\pi$
$503$	19.7899	0.882389	0.441194	+	0.897412i	$0.354555\pi$
$504$	−7.18834	−0.320194
$505$	16.7593	0.745777
$506$	0.991544	0.0440795
$507$	−4.45355	−0.197789
$508$	10.5721	0.469062
$509$	−34.4634	−1.52756	−0.763781	−	0.645475i	$-0.776659\pi$
$509$	−34.4634	−1.52756	−0.763781	+	0.645475i	$0.776659\pi$
$510$	−3.49796	−0.154892
$511$	9.48983	0.419806
$512$	−1.00000	−0.0441942
$513$	11.6229	0.513162
$514$	−19.7847	−0.872665
$515$	−39.5406	−1.74237
$516$	−0.0199983	−0.000880375 0
$517$	30.0751	1.32270
$518$	29.7589	1.30753
$519$	2.15425	0.0945610
$520$	10.7699	0.472291
$521$	16.2715	0.712868	0.356434	−	0.934321i	$-0.383992\pi$
$521$	16.2715	0.712868	0.356434	+	0.934321i	$0.383992\pi$
$522$	−9.41288	−0.411991
$523$	−4.59657	−0.200994	−0.100497	−	0.994937i	$-0.532043\pi$
$523$	−4.59657	−0.200994	−0.100497	+	0.994937i	$0.532043\pi$
$524$	16.1642	0.706137
$525$	−0.414809	−0.0181037
$526$	−14.6704	−0.639659
$527$	15.8872	0.692059
$528$	−0.891172	−0.0387833
$529$	−22.8454	−0.993278
$530$	0.689744	0.0299606
$531$	27.1056	1.17628
$532$	−13.9961	−0.606806
$533$	−32.8970	−1.42493
$534$	−2.05499	−0.0889281
$535$	−30.7052	−1.32750
$536$	−2.67034	−0.115341
$537$	−4.85434	−0.209480
$538$	16.8314	0.725651
$539$	−1.88876	−0.0813547
$540$	−4.41934	−0.190178
$541$	44.1029	1.89613	0.948065	−	0.318077i	$-0.103037\pi$
$541$	44.1029	1.89613	0.948065	+	0.318077i	$0.103037\pi$
$542$	8.63365	0.370847
$543$	−1.54901	−0.0664744
$544$	−4.65021	−0.199376
$545$	25.9231	1.11042
$546$	−4.47073	−0.191330
$547$	−22.5046	−0.962226	−0.481113	−	0.876659i	$-0.659767\pi$
$547$	−22.5046	−0.962226	−0.481113	+	0.876659i	$0.659767\pi$
$548$	−3.56378	−0.152237
$549$	−31.0952	−1.32711
$550$	1.18386	0.0504801
$551$	−18.3273	−0.780770
$552$	−0.138958	−0.00591445
$553$	−10.9899	−0.467337
$554$	−25.9188	−1.10118
$555$	8.95332	0.380047
$556$	−4.63976	−0.196770
$557$	24.0445	1.01880	0.509399	−	0.860531i	$-0.329868\pi$
$557$	24.0445	1.01880	0.509399	+	0.860531i	$0.329868\pi$
$558$	9.82267	0.415827
$559$	0.286327	0.0121103
$560$	5.32169	0.224882
$561$	−4.14414	−0.174966
$562$	−0.273027	−0.0115169
$563$	−0.851224	−0.0358748	−0.0179374	−	0.999839i	$-0.505710\pi$
$563$	−0.851224	−0.0358748	−0.0179374	+	0.999839i	$0.505710\pi$
$564$	−4.21482	−0.177476
$565$	36.2464	1.52490
$566$	−0.514995	−0.0216469
$567$	−19.7305	−0.828603
$568$	−6.56464	−0.275446
$569$	1.04696	0.0438909	0.0219455	−	0.999759i	$-0.493014\pi$
$569$	1.04696	0.0438909	0.0219455	+	0.999759i	$0.493014\pi$
$570$	−4.21087	−0.176374
$571$	18.5352	0.775675	0.387838	−	0.921728i	$-0.373222\pi$
$571$	18.5352	0.775675	0.387838	+	0.921728i	$0.373222\pi$
$572$	12.7594	0.533499
$573$	−3.89748	−0.162819
$574$	−16.2553	−0.678481
$575$	0.184597	0.00769821
$576$	−2.87511	−0.119796
$577$	37.4999	1.56114	0.780570	−	0.625068i	$-0.214929\pi$
$577$	37.4999	1.56114	0.780570	+	0.625068i	$0.214929\pi$
$578$	−4.62448	−0.192353
$579$	−3.86951	−0.160811
$580$	6.96856	0.289354
$581$	22.8583	0.948320
$582$	3.01127	0.124821
$583$	0.817162	0.0338434
$584$	3.79563	0.157064
$585$	30.9646	1.28023
$586$	26.9687	1.11407
$587$	−19.1994	−0.792446	−0.396223	−	0.918154i	$-0.629679\pi$
$587$	−19.1994	−0.792446	−0.396223	+	0.918154i	$0.629679\pi$
$588$	0.264697	0.0109159
$589$	19.1252	0.788041
$590$	−20.0668	−0.826138
$591$	1.13046	0.0465008
$592$	11.9026	0.489195
$593$	−29.7156	−1.22027	−0.610137	−	0.792296i	$-0.708886\pi$
$593$	−29.7156	−1.22027	−0.610137	+	0.792296i	$0.708886\pi$
$594$	−5.23573	−0.214825
$595$	24.7470	1.01453
$596$	7.11248	0.291339
$597$	−6.22149	−0.254629
$598$	1.98955	0.0813586
$599$	−15.1679	−0.619743	−0.309871	−	0.950778i	$-0.600286\pi$
$599$	−15.1679	−0.619743	−0.309871	+	0.950778i	$0.600286\pi$
$600$	−0.165910	−0.00677326
$601$	21.4884	0.876531	0.438265	−	0.898846i	$-0.355593\pi$
$601$	21.4884	0.876531	0.438265	+	0.898846i	$0.355593\pi$
$602$	0.141482	0.00576637
$603$	−7.67751	−0.312652
$604$	−10.2961	−0.418941
$605$	9.87837	0.401613
$606$	−2.78258	−0.113034
$607$	8.41526	0.341565	0.170782	−	0.985309i	$-0.445370\pi$
$607$	8.41526	0.341565	0.170782	+	0.985309i	$0.445370\pi$
$608$	−5.59797	−0.227028
$609$	−2.89274	−0.117220
$610$	23.0204	0.932070
$611$	60.3461	2.44134
$612$	−13.3699	−0.540445
$613$	20.7262	0.837122	0.418561	−	0.908189i	$-0.362535\pi$
$613$	20.7262	0.837122	0.418561	+	0.908189i	$0.362535\pi$
$614$	29.6437	1.19632
$615$	−4.89058	−0.197207
$616$	6.30477	0.254027
$617$	17.7218	0.713455	0.356727	−	0.934209i	$-0.383893\pi$
$617$	17.7218	0.713455	0.356727	+	0.934209i	$0.383893\pi$
$618$	6.56501	0.264083
$619$	−25.2795	−1.01607	−0.508034	−	0.861337i	$-0.669628\pi$
$619$	−25.2795	−1.01607	−0.508034	+	0.861337i	$0.669628\pi$
$620$	−7.27194	−0.292048
$621$	−0.816394	−0.0327608
$622$	−24.3411	−0.975988
$623$	14.5384	0.582470
$624$	−1.78815	−0.0715833
$625$	−22.4323	−0.897290
$626$	16.8506	0.673485
$627$	−4.98876	−0.199232
$628$	−13.1714	−0.525597
$629$	55.3497	2.20694
$630$	15.3004	0.609584
$631$	−1.21500	−0.0483685	−0.0241843	−	0.999708i	$-0.507699\pi$
$631$	−1.21500	−0.0483685	−0.0241843	+	0.999708i	$0.507699\pi$
$632$	−4.39560	−0.174848
$633$	6.94792	0.276155
$634$	29.9346	1.18886
$635$	−22.5028	−0.892996
$636$	−0.114520	−0.00454100
$637$	−3.78983	−0.150158
$638$	8.25588	0.326853
$639$	−18.8740	−0.746645
$640$	2.12850	0.0841365
$641$	43.7799	1.72920	0.864600	−	0.502461i	$-0.167572\pi$
$641$	43.7799	1.72920	0.864600	+	0.502461i	$0.167572\pi$
$642$	5.09805	0.201204
$643$	7.85863	0.309914	0.154957	−	0.987921i	$-0.450476\pi$
$643$	7.85863	0.309914	0.154957	+	0.987921i	$0.450476\pi$
$644$	0.983087	0.0387391
$645$	0.0425664	0.00167605
$646$	−26.0318	−1.02421
$647$	−37.9648	−1.49255	−0.746275	−	0.665638i	$-0.768160\pi$
$647$	−37.9648	−1.49255	−0.746275	+	0.665638i	$0.768160\pi$
$648$	−7.89157	−0.310010
$649$	−23.7738	−0.933204
$650$	2.37544	0.0931722
$651$	3.01868	0.118311
$652$	2.96133	0.115975
$653$	40.6310	1.59001	0.795006	−	0.606601i	$-0.207467\pi$
$653$	40.6310	1.59001	0.795006	+	0.606601i	$0.207467\pi$
$654$	−4.30407	−0.168303
$655$	−34.4056	−1.34434
$656$	−6.50158	−0.253844
$657$	10.9128	0.425751
$658$	29.8186	1.16245
$659$	−5.99805	−0.233651	−0.116825	−	0.993152i	$-0.537272\pi$
$659$	−5.99805	−0.233651	−0.116825	+	0.993152i	$0.537272\pi$
$660$	1.89686	0.0738353
$661$	−30.0600	−1.16920	−0.584600	−	0.811322i	$-0.698748\pi$
$661$	−30.0600	−1.16920	−0.584600	+	0.811322i	$0.698748\pi$
$662$	24.1991	0.940526
$663$	−8.31527	−0.322938
$664$	9.14257	0.354801
$665$	29.7907	1.15523
$666$	34.2213	1.32605
$667$	1.28732	0.0498451
$668$	−10.2365	−0.396062
$669$	−8.78522	−0.339656
$670$	5.68383	0.219585
$671$	27.2730	1.05286
$672$	−0.883571	−0.0340845
$673$	−25.9606	−1.00071	−0.500354	−	0.865821i	$-0.666797\pi$
$673$	−25.9606	−1.00071	−0.500354	+	0.865821i	$0.666797\pi$
$674$	−24.0554	−0.926579
$675$	−0.974741	−0.0375178
$676$	12.6020	0.484692
$677$	−7.21350	−0.277237	−0.138619	−	0.990346i	$-0.544266\pi$
$677$	−7.21350	−0.277237	−0.138619	+	0.990346i	$0.544266\pi$
$678$	−6.01806	−0.231122
$679$	−21.3038	−0.817565
$680$	9.89800	0.379571
$681$	−6.67520	−0.255794
$682$	−8.61530	−0.329897
$683$	30.7701	1.17739	0.588693	−	0.808357i	$-0.299643\pi$
$683$	30.7701	1.17739	0.588693	+	0.808357i	$0.299643\pi$
$684$	−16.0948	−0.615399
$685$	7.58552	0.289828
$686$	−19.3741	−0.739705
$687$	5.89426	0.224880
$688$	0.0565882	0.00215740
$689$	1.63965	0.0624655
$690$	0.295773	0.0112599
$691$	15.6465	0.595221	0.297610	−	0.954687i	$-0.403810\pi$
$691$	15.6465	0.595221	0.297610	+	0.954687i	$0.403810\pi$
$692$	−6.09578	−0.231727
$693$	18.1269	0.688584
$694$	−24.2366	−0.920007
$695$	9.87575	0.374608
$696$	−1.15701	−0.0438562
$697$	−30.2337	−1.14518
$698$	−20.8748	−0.790121
$699$	−0.988383	−0.0373841
$700$	1.17376	0.0443641
$701$	−46.2103	−1.74534	−0.872670	−	0.488311i	$-0.837613\pi$
$701$	−46.2103	−1.74534	−0.872670	+	0.488311i	$0.837613\pi$
$702$	−10.5056	−0.396507
$703$	66.6306	2.51302
$704$	2.52171	0.0950404
$705$	8.97127	0.337878
$706$	−16.8655	−0.634743
$707$	19.6859	0.740364
$708$	3.33174	0.125214
$709$	−5.22166	−0.196104	−0.0980518	−	0.995181i	$-0.531261\pi$
$709$	−5.22166	−0.196104	−0.0980518	+	0.995181i	$0.531261\pi$
$710$	13.9729	0.524392
$711$	−12.6378	−0.473956
$712$	5.81491	0.217923
$713$	−1.34336	−0.0503093
$714$	−4.10879	−0.153768
$715$	−27.1585	−1.01567
$716$	13.7361	0.513342
$717$	4.85252	0.181221
$718$	−24.4996	−0.914316
$719$	−31.5509	−1.17665	−0.588326	−	0.808624i	$-0.700213\pi$
$719$	−31.5509	−1.17665	−0.588326	+	0.808624i	$0.700213\pi$
$720$	6.11968	0.228067
$721$	−46.4455	−1.72972
$722$	−12.3373	−0.459147
$723$	−0.353400	−0.0131431
$724$	4.38316	0.162899
$725$	1.53700	0.0570829
$726$	−1.64013	−0.0608708
$727$	10.5409	0.390941	0.195470	−	0.980710i	$-0.437377\pi$
$727$	10.5409	0.390941	0.195470	+	0.980710i	$0.437377\pi$
$728$	12.6506	0.468863
$729$	−20.4879	−0.758810
$730$	−8.07902	−0.299018
$731$	0.263147	0.00973284
$732$	−3.82213	−0.141270
$733$	−35.2735	−1.30286	−0.651429	−	0.758710i	$-0.725830\pi$
$733$	−35.2735	−1.30286	−0.651429	+	0.758710i	$0.725830\pi$
$734$	17.6489	0.651434
$735$	−0.563409	−0.0207817
$736$	0.393203	0.0144937
$737$	6.73381	0.248043
$738$	−18.6928	−0.688090
$739$	6.52067	0.239867	0.119933	−	0.992782i	$-0.461732\pi$
$739$	6.52067	0.239867	0.119933	+	0.992782i	$0.461732\pi$
$740$	−25.3348	−0.931326
$741$	−10.0100	−0.367727
$742$	0.810192	0.0297431
$743$	0.908293	0.0333220	0.0166610	−	0.999861i	$-0.494696\pi$
$743$	0.908293	0.0333220	0.0166610	+	0.999861i	$0.494696\pi$
$744$	1.20738	0.0442645
$745$	−15.1389	−0.554648
$746$	−27.6104	−1.01089
$747$	26.2859	0.961750
$748$	11.7265	0.428762
$749$	−36.0672	−1.31787
$750$	4.11421	0.150230
$751$	−25.4559	−0.928900	−0.464450	−	0.885599i	$-0.653748\pi$
$751$	−25.4559	−0.928900	−0.464450	+	0.885599i	$0.653748\pi$
$752$	11.9265	0.434914
$753$	0.419688	0.0152943
$754$	16.5655	0.603281
$755$	21.9152	0.797577
$756$	−5.19108	−0.188798
$757$	−8.83081	−0.320961	−0.160481	−	0.987039i	$-0.551304\pi$
$757$	−8.83081	−0.320961	−0.160481	+	0.987039i	$0.551304\pi$
$758$	11.5761	0.420461
$759$	0.350412	0.0127191
$760$	11.9153	0.432214
$761$	−35.1999	−1.27600	−0.637998	−	0.770038i	$-0.720237\pi$
$761$	−35.1999	−1.27600	−0.637998	+	0.770038i	$0.720237\pi$
$762$	3.73619	0.135348
$763$	30.4500	1.10236
$764$	11.0285	0.398997
$765$	28.4578	1.02889
$766$	34.8424	1.25891
$767$	−47.7025	−1.72244
$768$	−0.353400	−0.0127522
$769$	−24.8776	−0.897108	−0.448554	−	0.893756i	$-0.648061\pi$
$769$	−24.8776	−0.897108	−0.448554	+	0.893756i	$0.648061\pi$
$770$	−13.4197	−0.483614
$771$	−6.99191	−0.251808
$772$	10.9494	0.394077
$773$	−7.64940	−0.275130	−0.137565	−	0.990493i	$-0.543928\pi$
$773$	−7.64940	−0.275130	−0.137565	+	0.990493i	$0.543928\pi$
$774$	0.162697	0.00584803
$775$	−1.60392	−0.0576144
$776$	−8.52085	−0.305881
$777$	10.5168	0.377289
$778$	−27.5774	−0.988698
$779$	−36.3957	−1.30401
$780$	3.80608	0.136280
$781$	16.5541	0.592352
$782$	1.82848	0.0653863
$783$	−6.79753	−0.242924
$784$	−0.749001	−0.0267500
$785$	28.0354	1.00063
$786$	5.71244	0.203756
$787$	−34.1467	−1.21720	−0.608599	−	0.793478i	$-0.708268\pi$
$787$	−34.1467	−1.21720	−0.608599	+	0.793478i	$0.708268\pi$
$788$	−3.19880	−0.113952
$789$	−5.18452	−0.184574
$790$	9.35606	0.332874
$791$	42.5760	1.51383
$792$	7.25018	0.257624
$793$	54.7237	1.94330
$794$	34.7402	1.23288
$795$	0.243756	0.00864512
$796$	17.6047	0.623981
$797$	30.7836	1.09041	0.545206	−	0.838302i	$-0.316452\pi$
$797$	30.7836	1.09041	0.545206	+	0.838302i	$0.316452\pi$
$798$	−4.94621	−0.175094
$799$	55.4607	1.96206
$800$	0.469468	0.0165982
$801$	16.7185	0.590719
$802$	−9.34627	−0.330028
$803$	−9.57147	−0.337770
$804$	−0.943698	−0.0332817
$805$	−2.09251	−0.0737511
$806$	−17.2867	−0.608898
$807$	5.94821	0.209387
$808$	7.87373	0.276997
$809$	35.8170	1.25926	0.629629	−	0.776896i	$-0.283207\pi$
$809$	35.8170	1.25926	0.629629	+	0.776896i	$0.283207\pi$
$810$	16.7972	0.590195
$811$	−5.94610	−0.208796	−0.104398	−	0.994536i	$-0.533292\pi$
$811$	−5.94610	−0.208796	−0.104398	+	0.994536i	$0.533292\pi$
$812$	8.18546	0.287253
$813$	3.05114	0.107008
$814$	−30.0149	−1.05202
$815$	−6.30321	−0.220792
$816$	−1.64339	−0.0575300
$817$	0.316779	0.0110827
$818$	18.6410	0.651766
$819$	36.3719	1.27094
$820$	13.8386	0.483266
$821$	28.6429	0.999643	0.499821	−	0.866129i	$-0.333399\pi$
$821$	28.6429	0.999643	0.499821	+	0.866129i	$0.333399\pi$
$822$	−1.25944	−0.0439281
$823$	−19.9544	−0.695568	−0.347784	−	0.937575i	$-0.613066\pi$
$823$	−19.9544	−0.695568	−0.347784	+	0.937575i	$0.613066\pi$
$824$	−18.5767	−0.647150
$825$	0.418377	0.0145660
$826$	−23.5711	−0.820142
$827$	18.0517	0.627721	0.313860	−	0.949469i	$-0.398378\pi$
$827$	18.0517	0.627721	0.313860	+	0.949469i	$0.398378\pi$
$828$	1.13050	0.0392877
$829$	−16.9709	−0.589423	−0.294711	−	0.955586i	$-0.595224\pi$
$829$	−16.9709	−0.589423	−0.294711	+	0.955586i	$0.595224\pi$
$830$	−19.4600	−0.675467
$831$	−9.15971	−0.317747
$832$	5.05984	0.175418
$833$	−3.48301	−0.120679
$834$	−1.63969	−0.0567779
$835$	21.7885	0.754021
$836$	14.1165	0.488228
$837$	7.09346	0.245186
$838$	23.8188	0.822806
$839$	16.9523	0.585257	0.292629	−	0.956226i	$-0.405470\pi$
$839$	16.9523	0.585257	0.292629	+	0.956226i	$0.405470\pi$
$840$	1.88069	0.0648898
$841$	−18.2814	−0.630394
$842$	17.3129	0.596642
$843$	−0.0964878	−0.00332322
$844$	−19.6602	−0.676732
$845$	−26.8234	−0.922752
$846$	34.2899	1.17891
$847$	11.6034	0.398698
$848$	0.324051	0.0111280
$849$	−0.181999	−0.00624620
$850$	2.18313	0.0748807
$851$	−4.68015	−0.160434
$852$	−2.31994	−0.0794800
$853$	−39.2726	−1.34467	−0.672335	−	0.740247i	$-0.734708\pi$
$853$	−39.2726	−1.34467	−0.672335	+	0.740247i	$0.734708\pi$
$854$	27.0404	0.925304
$855$	34.2578	1.17159
$856$	−14.4257	−0.493061
$857$	−18.3927	−0.628282	−0.314141	−	0.949376i	$-0.601717\pi$
$857$	−18.3927	−0.628282	−0.314141	+	0.949376i	$0.601717\pi$
$858$	4.50919	0.153941
$859$	−17.8753	−0.609896	−0.304948	−	0.952369i	$-0.598639\pi$
$859$	−17.8753	−0.609896	−0.304948	+	0.952369i	$0.598639\pi$
$860$	−0.120448	−0.00410725
$861$	−5.74461	−0.195776
$862$	−12.1208	−0.412837
$863$	27.3927	0.932458	0.466229	−	0.884664i	$-0.345612\pi$
$863$	27.3927	0.932458	0.466229	+	0.884664i	$0.345612\pi$
$864$	−2.07627	−0.0706360
$865$	12.9749	0.441159
$866$	3.98023	0.135254
$867$	−1.63429	−0.0555034
$868$	−8.54182	−0.289928
$869$	11.0844	0.376013
$870$	2.46269	0.0834930
$871$	13.5115	0.457819
$872$	12.1790	0.412434
$873$	−24.4984	−0.829144
$874$	2.20114	0.0744547
$875$	−29.1068	−0.983989
$876$	1.34138	0.0453209
$877$	−18.6533	−0.629876	−0.314938	−	0.949112i	$-0.601984\pi$
$877$	−18.6533	−0.629876	−0.314938	+	0.949112i	$0.601984\pi$
$878$	11.4715	0.387144
$879$	9.53075	0.321464
$880$	−5.36747	−0.180937
$881$	21.6705	0.730097	0.365049	−	0.930988i	$-0.381052\pi$
$881$	21.6705	0.730097	0.365049	+	0.930988i	$0.381052\pi$
$882$	−2.15346	−0.0725107
$883$	−44.9288	−1.51198	−0.755988	−	0.654586i	$-0.772843\pi$
$883$	−44.9288	−1.51198	−0.755988	+	0.654586i	$0.772843\pi$
$884$	23.5293	0.791377
$885$	−7.09163	−0.238382
$886$	8.06760	0.271036
$887$	51.5840	1.73202	0.866011	−	0.500025i	$-0.166676\pi$
$887$	51.5840	1.73202	0.866011	+	0.500025i	$0.166676\pi$
$888$	4.20639	0.141157
$889$	−26.4324	−0.886514
$890$	−12.3771	−0.414880
$891$	19.9002	0.666683
$892$	24.8591	0.832345
$893$	66.7641	2.23418
$894$	2.51355	0.0840658
$895$	−29.2374	−0.977297
$896$	2.50020	0.0835258
$897$	0.703106	0.0234760
$898$	2.77955	0.0927547
$899$	−11.1852	−0.373047
$900$	1.34977	0.0449924
$901$	1.50691	0.0502023
$902$	16.3951	0.545897
$903$	0.0499997	0.00166389
$904$	17.0290	0.566377
$905$	−9.32958	−0.310126
$906$	−3.63864	−0.120886
$907$	−20.8619	−0.692709	−0.346355	−	0.938104i	$-0.612581\pi$
$907$	−20.8619	−0.692709	−0.346355	+	0.938104i	$0.612581\pi$
$908$	18.8885	0.626836
$909$	22.6378	0.750849
$910$	−26.9269	−0.892618
$911$	−40.8440	−1.35322	−0.676611	−	0.736341i	$-0.736552\pi$
$911$	−40.8440	−1.35322	−0.676611	+	0.736341i	$0.736552\pi$
$912$	−1.97833	−0.0655089
$913$	−23.0549	−0.763006
$914$	25.5469	0.845016
$915$	8.13543	0.268949
$916$	−16.6787	−0.551080
$917$	−40.4138	−1.33458
$918$	−9.65507	−0.318665
$919$	16.3664	0.539878	0.269939	−	0.962877i	$-0.412996\pi$
$919$	16.3664	0.539878	0.269939	+	0.962877i	$0.412996\pi$
$920$	−0.836935	−0.0275929
$921$	10.4761	0.345199
$922$	3.40760	0.112223
$923$	33.2160	1.09332
$924$	2.22811	0.0732994
$925$	−5.58791	−0.183729
$926$	−11.5667	−0.380106
$927$	−53.4100	−1.75422
$928$	3.27392	0.107472
$929$	−30.7584	−1.00915	−0.504576	−	0.863367i	$-0.668351\pi$
$929$	−30.7584	−1.00915	−0.504576	+	0.863367i	$0.668351\pi$
$930$	−2.56991	−0.0842705
$931$	−4.19289	−0.137416
$932$	2.79678	0.0916115
$933$	−8.60214	−0.281621
$934$	−10.0267	−0.328083
$935$	−24.9599	−0.816275
$936$	14.5476	0.475503
$937$	−1.18830	−0.0388202	−0.0194101	−	0.999812i	$-0.506179\pi$
$937$	−1.18830	−0.0388202	−0.0194101	+	0.999812i	$0.506179\pi$
$938$	6.67638	0.217992
$939$	5.95500	0.194334
$940$	−25.3856	−0.827986
$941$	35.2371	1.14870	0.574348	−	0.818611i	$-0.305256\pi$
$941$	35.2371	1.14870	0.574348	+	0.818611i	$0.305256\pi$
$942$	−4.65478	−0.151661
$943$	2.55644	0.0832493
$944$	−9.42767	−0.306844
$945$	11.0492	0.359432
$946$	−0.142699	−0.00463954
$947$	−17.8807	−0.581045	−0.290522	−	0.956868i	$-0.593829\pi$
$947$	−17.8807	−0.581045	−0.290522	+	0.956868i	$0.593829\pi$
$948$	−1.55341	−0.0504523
$949$	−19.2053	−0.623430
$950$	2.62807	0.0852659
$951$	10.5789	0.343045
$952$	11.6265	0.376816
$953$	35.4110	1.14708	0.573538	−	0.819179i	$-0.305571\pi$
$953$	35.4110	1.14708	0.573538	+	0.819179i	$0.305571\pi$
$954$	0.931681	0.0301643
$955$	−23.4742	−0.759608
$956$	−13.7309	−0.444090
$957$	2.91763	0.0943135
$958$	16.1601	0.522110
$959$	8.91016	0.287724
$960$	0.752214	0.0242776
$961$	−19.3278	−0.623479
$962$	−60.2254	−1.94174
$963$	−41.4755	−1.33653
$964$	1.00000	0.0322078
$965$	−23.3058	−0.750240
$966$	0.347423	0.0111782
$967$	−2.90006	−0.0932598	−0.0466299	−	0.998912i	$-0.514848\pi$
$967$	−2.90006	−0.0932598	−0.0466299	+	0.998912i	$0.514848\pi$
$968$	4.64099	0.149167
$969$	−9.19963	−0.295535
$970$	18.1367	0.582333
$971$	−19.3462	−0.620850	−0.310425	−	0.950598i	$-0.600471\pi$
$971$	−19.3462	−0.620850	−0.310425	+	0.950598i	$0.600471\pi$
$972$	−9.01768	−0.289242
$973$	11.6003	0.371889
$974$	36.0715	1.15581
$975$	0.839480	0.0268849
$976$	10.8153	0.346190
$977$	−3.76131	−0.120335	−0.0601675	−	0.998188i	$-0.519163\pi$
$977$	−3.76131	−0.120335	−0.0601675	+	0.998188i	$0.519163\pi$
$978$	1.04654	0.0334645
$979$	−14.6635	−0.468647
$980$	1.59425	0.0509265
$981$	35.0160	1.11798
$982$	18.3779	0.586461
$983$	−49.3781	−1.57492	−0.787459	−	0.616367i	$-0.788604\pi$
$983$	−49.3781	−1.57492	−0.787459	+	0.616367i	$0.788604\pi$
$984$	−2.29766	−0.0732468
$985$	6.80866	0.216942
$986$	15.2244	0.484845
$987$	10.5379	0.335425
$988$	28.3249	0.901134
$989$	−0.0222507	−0.000707530 0
$990$	−15.4320	−0.490463
$991$	−20.3997	−0.648018	−0.324009	−	0.946054i	$-0.605031\pi$
$991$	−20.3997	−0.648018	−0.324009	+	0.946054i	$0.605031\pi$
$992$	−3.41645	−0.108473
$993$	8.55198	0.271389
$994$	16.4129	0.520586
$995$	−37.4716	−1.18793
$996$	3.23099	0.102378
$997$	8.50276	0.269285	0.134643	−	0.990894i	$-0.457011\pi$
$997$	8.50276	0.269285	0.134643	+	0.990894i	$0.457011\pi$
$998$	−26.1542	−0.827897
$999$	24.7130	0.781885

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	482.2.a.d.1.3	✓	6
3.2	odd	2		4338.2.a.u.1.4		6
4.3	odd	2		3856.2.a.h.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
482.2.a.d.1.3	✓	6	1.1	even	1	trivial
3856.2.a.h.1.4		6	4.3	odd	2
4338.2.a.u.1.4		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 482 = 2 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	482.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.353400 q^{3} +1.00000 q^{4} -2.12850 q^{5} +0.353400 q^{6} -2.50020 q^{7} -1.00000 q^{8} -2.87511 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.353400 q^{3} +1.00000 q^{4} -2.12850 q^{5} +0.353400 q^{6} -2.50020 q^{7} -1.00000 q^{8} -2.87511 q^{9} +2.12850 q^{10} +2.52171 q^{11} -0.353400 q^{12} +5.05984 q^{13} +2.50020 q^{14} +0.752214 q^{15} +1.00000 q^{16} +4.65021 q^{17} +2.87511 q^{18} +5.59797 q^{19} -2.12850 q^{20} +0.883571 q^{21} -2.52171 q^{22} -0.393203 q^{23} +0.353400 q^{24} -0.469468 q^{25} -5.05984 q^{26} +2.07627 q^{27} -2.50020 q^{28} -3.27392 q^{29} -0.752214 q^{30} +3.41645 q^{31} -1.00000 q^{32} -0.891172 q^{33} -4.65021 q^{34} +5.32169 q^{35} -2.87511 q^{36} +11.9026 q^{37} -5.59797 q^{38} -1.78815 q^{39} +2.12850 q^{40} -6.50158 q^{41} -0.883571 q^{42} +0.0565882 q^{43} +2.52171 q^{44} +6.11968 q^{45} +0.393203 q^{46} +11.9265 q^{47} -0.353400 q^{48} -0.749001 q^{49} +0.469468 q^{50} -1.64339 q^{51} +5.05984 q^{52} +0.324051 q^{53} -2.07627 q^{54} -5.36747 q^{55} +2.50020 q^{56} -1.97833 q^{57} +3.27392 q^{58} -9.42767 q^{59} +0.752214 q^{60} +10.8153 q^{61} -3.41645 q^{62} +7.18834 q^{63} +1.00000 q^{64} -10.7699 q^{65} +0.891172 q^{66} +2.67034 q^{67} +4.65021 q^{68} +0.138958 q^{69} -5.32169 q^{70} +6.56464 q^{71} +2.87511 q^{72} -3.79563 q^{73} -11.9026 q^{74} +0.165910 q^{75} +5.59797 q^{76} -6.30477 q^{77} +1.78815 q^{78} +4.39560 q^{79} -2.12850 q^{80} +7.89157 q^{81} +6.50158 q^{82} -9.14257 q^{83} +0.883571 q^{84} -9.89800 q^{85} -0.0565882 q^{86} +1.15701 q^{87} -2.52171 q^{88} -5.81491 q^{89} -6.11968 q^{90} -12.6506 q^{91} -0.393203 q^{92} -1.20738 q^{93} -11.9265 q^{94} -11.9153 q^{95} +0.353400 q^{96} +8.52085 q^{97} +0.749001 q^{98} -7.25018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} + 2 q^{3} + 6 q^{4} - 5 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 6 q^{9} + 5 q^{10} - 4 q^{11} + 2 q^{12} + 9 q^{13} - 10 q^{14} + 5 q^{15} + 6 q^{16} + q^{17} - 6 q^{18} + 10 q^{19} - 5 q^{20} + 8 q^{21} + 4 q^{22} + 9 q^{23} - 2 q^{24} + 13 q^{25} - 9 q^{26} + 8 q^{27} + 10 q^{28} - q^{29} - 5 q^{30} + 14 q^{31} - 6 q^{32} + 10 q^{33} - q^{34} - 3 q^{35} + 6 q^{36} + 20 q^{37} - 10 q^{38} + 13 q^{39} + 5 q^{40} - 4 q^{41} - 8 q^{42} + 19 q^{43} - 4 q^{44} - 6 q^{45} - 9 q^{46} + q^{47} + 2 q^{48} + 14 q^{49} - 13 q^{50} + 5 q^{51} + 9 q^{52} - 3 q^{53} - 8 q^{54} + 11 q^{55} - 10 q^{56} + 12 q^{57} + q^{58} - q^{59} + 5 q^{60} + 4 q^{61} - 14 q^{62} + 14 q^{63} + 6 q^{64} + 5 q^{65} - 10 q^{66} + 5 q^{67} + q^{68} - 15 q^{69} + 3 q^{70} + 2 q^{71} - 6 q^{72} + 15 q^{73} - 20 q^{74} - 11 q^{75} + 10 q^{76} - 6 q^{77} - 13 q^{78} + 12 q^{79} - 5 q^{80} - 18 q^{81} + 4 q^{82} - 8 q^{83} + 8 q^{84} - 32 q^{85} - 19 q^{86} + 11 q^{87} + 4 q^{88} - 24 q^{89} + 6 q^{90} + q^{91} + 9 q^{92} - 18 q^{93} - q^{94} + 9 q^{95} - 2 q^{96} - 12 q^{97} - 14 q^{98} - 40 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 2 * q^3 + 6 * q^4 - 5 * q^5 - 2 * q^6 + 10 * q^7 - 6 * q^8 + 6 * q^9 + 5 * q^10 - 4 * q^11 + 2 * q^12 + 9 * q^13 - 10 * q^14 + 5 * q^15 + 6 * q^16 + q^17 - 6 * q^18 + 10 * q^19 - 5 * q^20 + 8 * q^21 + 4 * q^22 + 9 * q^23 - 2 * q^24 + 13 * q^25 - 9 * q^26 + 8 * q^27 + 10 * q^28 - q^29 - 5 * q^30 + 14 * q^31 - 6 * q^32 + 10 * q^33 - q^34 - 3 * q^35 + 6 * q^36 + 20 * q^37 - 10 * q^38 + 13 * q^39 + 5 * q^40 - 4 * q^41 - 8 * q^42 + 19 * q^43 - 4 * q^44 - 6 * q^45 - 9 * q^46 + q^47 + 2 * q^48 + 14 * q^49 - 13 * q^50 + 5 * q^51 + 9 * q^52 - 3 * q^53 - 8 * q^54 + 11 * q^55 - 10 * q^56 + 12 * q^57 + q^58 - q^59 + 5 * q^60 + 4 * q^61 - 14 * q^62 + 14 * q^63 + 6 * q^64 + 5 * q^65 - 10 * q^66 + 5 * q^67 + q^68 - 15 * q^69 + 3 * q^70 + 2 * q^71 - 6 * q^72 + 15 * q^73 - 20 * q^74 - 11 * q^75 + 10 * q^76 - 6 * q^77 - 13 * q^78 + 12 * q^79 - 5 * q^80 - 18 * q^81 + 4 * q^82 - 8 * q^83 + 8 * q^84 - 32 * q^85 - 19 * q^86 + 11 * q^87 + 4 * q^88 - 24 * q^89 + 6 * q^90 + q^91 + 9 * q^92 - 18 * q^93 - q^94 + 9 * q^95 - 2 * q^96 - 12 * q^97 - 14 * q^98 - 40 * q^99

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