LMFDB - Embedded newform 6042.2.a.bd.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 35 x^{9} + 77 x^{8} + 394 x^{7} - 994 x^{6} - 1477 x^{5} + 4683 x^{4} + 563 x^{3} + \cdots + 1534 $ x^11 - 2x^10 - 35x^9 + 77x^8 + 394x^7 - 994x^6 - 1477x^5 + 4683x^4 + 563x^3 - 6194x^2 + 1258x + 1534
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			$-2.56652$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.56652 q^{5} +1.00000 q^{6} -0.973492 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.56652 q^{5} +1.00000 q^{6} -0.973492 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.56652 q^{10} +3.22473 q^{11} -1.00000 q^{12} +5.35788 q^{13} +0.973492 q^{14} +2.56652 q^{15} +1.00000 q^{16} -3.23211 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.56652 q^{20} +0.973492 q^{21} -3.22473 q^{22} -5.36750 q^{23} +1.00000 q^{24} +1.58701 q^{25} -5.35788 q^{26} -1.00000 q^{27} -0.973492 q^{28} -4.32036 q^{29} -2.56652 q^{30} +2.03359 q^{31} -1.00000 q^{32} -3.22473 q^{33} +3.23211 q^{34} +2.49848 q^{35} +1.00000 q^{36} -4.49757 q^{37} -1.00000 q^{38} -5.35788 q^{39} +2.56652 q^{40} +6.31204 q^{41} -0.973492 q^{42} +2.37983 q^{43} +3.22473 q^{44} -2.56652 q^{45} +5.36750 q^{46} -11.6056 q^{47} -1.00000 q^{48} -6.05231 q^{49} -1.58701 q^{50} +3.23211 q^{51} +5.35788 q^{52} +1.00000 q^{53} +1.00000 q^{54} -8.27634 q^{55} +0.973492 q^{56} -1.00000 q^{57} +4.32036 q^{58} -0.929948 q^{59} +2.56652 q^{60} +11.1056 q^{61} -2.03359 q^{62} -0.973492 q^{63} +1.00000 q^{64} -13.7511 q^{65} +3.22473 q^{66} +3.61884 q^{67} -3.23211 q^{68} +5.36750 q^{69} -2.49848 q^{70} +8.80649 q^{71} -1.00000 q^{72} -11.4118 q^{73} +4.49757 q^{74} -1.58701 q^{75} +1.00000 q^{76} -3.13925 q^{77} +5.35788 q^{78} +16.7661 q^{79} -2.56652 q^{80} +1.00000 q^{81} -6.31204 q^{82} +7.05152 q^{83} +0.973492 q^{84} +8.29527 q^{85} -2.37983 q^{86} +4.32036 q^{87} -3.22473 q^{88} +8.87657 q^{89} +2.56652 q^{90} -5.21585 q^{91} -5.36750 q^{92} -2.03359 q^{93} +11.6056 q^{94} -2.56652 q^{95} +1.00000 q^{96} +0.264566 q^{97} +6.05231 q^{98} +3.22473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9} - 2 q^{10} - 6 q^{11} - 11 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{15} + 11 q^{16} - 16 q^{17} - 11 q^{18} + 11 q^{19} + 2 q^{20} + 2 q^{21} + 6 q^{22} - 11 q^{23} + 11 q^{24} + 19 q^{25} + 7 q^{26} - 11 q^{27} - 2 q^{28} - 7 q^{29} + 2 q^{30} + 12 q^{31} - 11 q^{32} + 6 q^{33} + 16 q^{34} - 5 q^{35} + 11 q^{36} + 3 q^{37} - 11 q^{38} + 7 q^{39} - 2 q^{40} + 11 q^{41} - 2 q^{42} + 7 q^{43} - 6 q^{44} + 2 q^{45} + 11 q^{46} - 37 q^{47} - 11 q^{48} + 23 q^{49} - 19 q^{50} + 16 q^{51} - 7 q^{52} + 11 q^{53} + 11 q^{54} - 11 q^{55} + 2 q^{56} - 11 q^{57} + 7 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} - 12 q^{62} - 2 q^{63} + 11 q^{64} - 7 q^{65} - 6 q^{66} - 28 q^{67} - 16 q^{68} + 11 q^{69} + 5 q^{70} + 4 q^{71} - 11 q^{72} - 7 q^{73} - 3 q^{74} - 19 q^{75} + 11 q^{76} - 13 q^{77} - 7 q^{78} + 5 q^{79} + 2 q^{80} + 11 q^{81} - 11 q^{82} - 11 q^{83} + 2 q^{84} - 11 q^{85} - 7 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} - 2 q^{90} - 24 q^{91} - 11 q^{92} - 12 q^{93} + 37 q^{94} + 2 q^{95} + 11 q^{96} - 24 q^{97} - 23 q^{98} - 6 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9 - 2 * q^10 - 6 * q^11 - 11 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^15 + 11 * q^16 - 16 * q^17 - 11 * q^18 + 11 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 - 11 * q^23 + 11 * q^24 + 19 * q^25 + 7 * q^26 - 11 * q^27 - 2 * q^28 - 7 * q^29 + 2 * q^30 + 12 * q^31 - 11 * q^32 + 6 * q^33 + 16 * q^34 - 5 * q^35 + 11 * q^36 + 3 * q^37 - 11 * q^38 + 7 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 + 7 * q^43 - 6 * q^44 + 2 * q^45 + 11 * q^46 - 37 * q^47 - 11 * q^48 + 23 * q^49 - 19 * q^50 + 16 * q^51 - 7 * q^52 + 11 * q^53 + 11 * q^54 - 11 * q^55 + 2 * q^56 - 11 * q^57 + 7 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 - 12 * q^62 - 2 * q^63 + 11 * q^64 - 7 * q^65 - 6 * q^66 - 28 * q^67 - 16 * q^68 + 11 * q^69 + 5 * q^70 + 4 * q^71 - 11 * q^72 - 7 * q^73 - 3 * q^74 - 19 * q^75 + 11 * q^76 - 13 * q^77 - 7 * q^78 + 5 * q^79 + 2 * q^80 + 11 * q^81 - 11 * q^82 - 11 * q^83 + 2 * q^84 - 11 * q^85 - 7 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 - 2 * q^90 - 24 * q^91 - 11 * q^92 - 12 * q^93 + 37 * q^94 + 2 * q^95 + 11 * q^96 - 24 * q^97 - 23 * q^98 - 6 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.56652	−1.14778	−0.573891	−	0.818932i	$-0.694567\pi$
$5$	−2.56652	−1.14778	−0.573891	+	0.818932i	$0.694567\pi$
$6$	1.00000	0.408248
$7$	−0.973492	−0.367945	−0.183973	−	0.982931i	$-0.558896\pi$
$7$	−0.973492	−0.367945	−0.183973	+	0.982931i	$0.558896\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.56652	0.811604
$11$	3.22473	0.972294	0.486147	−	0.873877i	$-0.338402\pi$
$11$	3.22473	0.972294	0.486147	+	0.873877i	$0.338402\pi$
$12$	−1.00000	−0.288675
$13$	5.35788	1.48601	0.743004	−	0.669287i	$-0.233400\pi$
$13$	5.35788	1.48601	0.743004	+	0.669287i	$0.233400\pi$
$14$	0.973492	0.260177
$15$	2.56652	0.662672
$16$	1.00000	0.250000
$17$	−3.23211	−0.783902	−0.391951	−	0.919986i	$-0.628200\pi$
$17$	−3.23211	−0.783902	−0.391951	+	0.919986i	$0.628200\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.56652	−0.573891
$21$	0.973492	0.212433
$22$	−3.22473	−0.687516
$23$	−5.36750	−1.11920	−0.559600	−	0.828763i	$-0.689045\pi$
$23$	−5.36750	−1.11920	−0.559600	+	0.828763i	$0.689045\pi$
$24$	1.00000	0.204124
$25$	1.58701	0.317403
$26$	−5.35788	−1.05077
$27$	−1.00000	−0.192450
$28$	−0.973492	−0.183973
$29$	−4.32036	−0.802271	−0.401135	−	0.916019i	$-0.631384\pi$
$29$	−4.32036	−0.802271	−0.401135	+	0.916019i	$0.631384\pi$
$30$	−2.56652	−0.468580
$31$	2.03359	0.365244	0.182622	−	0.983183i	$-0.441542\pi$
$31$	2.03359	0.365244	0.182622	+	0.983183i	$0.441542\pi$
$32$	−1.00000	−0.176777
$33$	−3.22473	−0.561354
$34$	3.23211	0.554302
$35$	2.49848	0.422321
$36$	1.00000	0.166667
$37$	−4.49757	−0.739396	−0.369698	−	0.929152i	$-0.620539\pi$
$37$	−4.49757	−0.739396	−0.369698	+	0.929152i	$0.620539\pi$
$38$	−1.00000	−0.162221
$39$	−5.35788	−0.857947
$40$	2.56652	0.405802
$41$	6.31204	0.985774	0.492887	−	0.870093i	$-0.335942\pi$
$41$	6.31204	0.985774	0.492887	+	0.870093i	$0.335942\pi$
$42$	−0.973492	−0.150213
$43$	2.37983	0.362920	0.181460	−	0.983398i	$-0.441918\pi$
$43$	2.37983	0.362920	0.181460	+	0.983398i	$0.441918\pi$
$44$	3.22473	0.486147
$45$	−2.56652	−0.382594
$46$	5.36750	0.791394
$47$	−11.6056	−1.69285	−0.846427	−	0.532505i	$-0.821251\pi$
$47$	−11.6056	−1.69285	−0.846427	+	0.532505i	$0.821251\pi$
$48$	−1.00000	−0.144338
$49$	−6.05231	−0.864616
$50$	−1.58701	−0.224438
$51$	3.23211	0.452586
$52$	5.35788	0.743004
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	−8.27634	−1.11598
$56$	0.973492	0.130088
$57$	−1.00000	−0.132453
$58$	4.32036	0.567291
$59$	−0.929948	−0.121069	−0.0605345	−	0.998166i	$-0.519281\pi$
$59$	−0.929948	−0.121069	−0.0605345	+	0.998166i	$0.519281\pi$
$60$	2.56652	0.331336
$61$	11.1056	1.42193	0.710966	−	0.703227i	$-0.248258\pi$
$61$	11.1056	1.42193	0.710966	+	0.703227i	$0.248258\pi$
$62$	−2.03359	−0.258266
$63$	−0.973492	−0.122648
$64$	1.00000	0.125000
$65$	−13.7511	−1.70561
$66$	3.22473	0.396937
$67$	3.61884	0.442112	0.221056	−	0.975261i	$-0.429050\pi$
$67$	3.61884	0.442112	0.221056	+	0.975261i	$0.429050\pi$
$68$	−3.23211	−0.391951
$69$	5.36750	0.646171
$70$	−2.49848	−0.298626
$71$	8.80649	1.04514	0.522569	−	0.852597i	$-0.324974\pi$
$71$	8.80649	1.04514	0.522569	+	0.852597i	$0.324974\pi$
$72$	−1.00000	−0.117851
$73$	−11.4118	−1.33565	−0.667826	−	0.744317i	$-0.732775\pi$
$73$	−11.4118	−1.33565	−0.667826	+	0.744317i	$0.732775\pi$
$74$	4.49757	0.522832
$75$	−1.58701	−0.183253
$76$	1.00000	0.114708
$77$	−3.13925	−0.357751
$78$	5.35788	0.606660
$79$	16.7661	1.88633	0.943165	−	0.332325i	$-0.107833\pi$
$79$	16.7661	1.88633	0.943165	+	0.332325i	$0.107833\pi$
$80$	−2.56652	−0.286945
$81$	1.00000	0.111111
$82$	−6.31204	−0.697048
$83$	7.05152	0.774005	0.387003	−	0.922079i	$-0.373510\pi$
$83$	7.05152	0.774005	0.387003	+	0.922079i	$0.373510\pi$
$84$	0.973492	0.106217
$85$	8.29527	0.899748
$86$	−2.37983	−0.256623
$87$	4.32036	0.463191
$88$	−3.22473	−0.343758
$89$	8.87657	0.940914	0.470457	−	0.882423i	$-0.344089\pi$
$89$	8.87657	0.940914	0.470457	+	0.882423i	$0.344089\pi$
$90$	2.56652	0.270535
$91$	−5.21585	−0.546770
$92$	−5.36750	−0.559600
$93$	−2.03359	−0.210874
$94$	11.6056	1.19703
$95$	−2.56652	−0.263319
$96$	1.00000	0.102062
$97$	0.264566	0.0268626	0.0134313	−	0.999910i	$-0.495725\pi$
$97$	0.264566	0.0268626	0.0134313	+	0.999910i	$0.495725\pi$
$98$	6.05231	0.611376
$99$	3.22473	0.324098
$100$	1.58701	0.158701
$101$	−5.66258	−0.563447	−0.281724	−	0.959496i	$-0.590906\pi$
$101$	−5.66258	−0.563447	−0.281724	+	0.959496i	$0.590906\pi$
$102$	−3.23211	−0.320026
$103$	13.5757	1.33765	0.668825	−	0.743420i	$-0.266797\pi$
$103$	13.5757	1.33765	0.668825	+	0.743420i	$0.266797\pi$
$104$	−5.35788	−0.525383
$105$	−2.49848	−0.243827
$106$	−1.00000	−0.0971286
$107$	−2.97961	−0.288049	−0.144025	−	0.989574i	$-0.546004\pi$
$107$	−2.97961	−0.288049	−0.144025	+	0.989574i	$0.546004\pi$
$108$	−1.00000	−0.0962250
$109$	3.65169	0.349769	0.174884	−	0.984589i	$-0.444045\pi$
$109$	3.65169	0.349769	0.174884	+	0.984589i	$0.444045\pi$
$110$	8.27634	0.789118
$111$	4.49757	0.426891
$112$	−0.973492	−0.0919864
$113$	8.47760	0.797506	0.398753	−	0.917058i	$-0.369443\pi$
$113$	8.47760	0.797506	0.398753	+	0.917058i	$0.369443\pi$
$114$	1.00000	0.0936586
$115$	13.7758	1.28460
$116$	−4.32036	−0.401135
$117$	5.35788	0.495336
$118$	0.929948	0.0856087
$119$	3.14643	0.288433
$120$	−2.56652	−0.234290
$121$	−0.601087	−0.0546443
$122$	−11.1056	−1.00546
$123$	−6.31204	−0.569137
$124$	2.03359	0.182622
$125$	8.75949	0.783473
$126$	0.973492	0.0867256
$127$	−16.7818	−1.48914	−0.744572	−	0.667542i	$-0.767347\pi$
$127$	−16.7818	−1.48914	−0.744572	+	0.667542i	$0.767347\pi$
$128$	−1.00000	−0.0883883
$129$	−2.37983	−0.209532
$130$	13.7511	1.20605
$131$	−13.0626	−1.14128	−0.570641	−	0.821200i	$-0.693305\pi$
$131$	−13.0626	−1.14128	−0.570641	+	0.821200i	$0.693305\pi$
$132$	−3.22473	−0.280677
$133$	−0.973492	−0.0844125
$134$	−3.61884	−0.312620
$135$	2.56652	0.220891
$136$	3.23211	0.277151
$137$	2.53023	0.216172	0.108086	−	0.994142i	$-0.465528\pi$
$137$	2.53023	0.216172	0.108086	+	0.994142i	$0.465528\pi$
$138$	−5.36750	−0.456912
$139$	16.7318	1.41917	0.709584	−	0.704621i	$-0.248883\pi$
$139$	16.7318	1.41917	0.709584	+	0.704621i	$0.248883\pi$
$140$	2.49848	0.211161
$141$	11.6056	0.977369
$142$	−8.80649	−0.739024
$143$	17.2777	1.44484
$144$	1.00000	0.0833333
$145$	11.0883	0.920832
$146$	11.4118	0.944449
$147$	6.05231	0.499186
$148$	−4.49757	−0.369698
$149$	7.71122	0.631728	0.315864	−	0.948804i	$-0.397706\pi$
$149$	7.71122	0.631728	0.315864	+	0.948804i	$0.397706\pi$
$150$	1.58701	0.129579
$151$	−13.3837	−1.08915	−0.544575	−	0.838712i	$-0.683309\pi$
$151$	−13.3837	−1.08915	−0.544575	+	0.838712i	$0.683309\pi$
$152$	−1.00000	−0.0811107
$153$	−3.23211	−0.261301
$154$	3.13925	0.252968
$155$	−5.21925	−0.419220
$156$	−5.35788	−0.428974
$157$	21.0123	1.67697	0.838484	−	0.544926i	$-0.183442\pi$
$157$	21.0123	1.67697	0.838484	+	0.544926i	$0.183442\pi$
$158$	−16.7661	−1.33384
$159$	−1.00000	−0.0793052
$160$	2.56652	0.202901
$161$	5.22521	0.411805
$162$	−1.00000	−0.0785674
$163$	−20.5728	−1.61139	−0.805695	−	0.592331i	$-0.798208\pi$
$163$	−20.5728	−1.61139	−0.805695	+	0.592331i	$0.798208\pi$
$164$	6.31204	0.492887
$165$	8.27634	0.644312
$166$	−7.05152	−0.547304
$167$	−16.9032	−1.30801	−0.654004	−	0.756491i	$-0.726912\pi$
$167$	−16.9032	−1.30801	−0.654004	+	0.756491i	$0.726912\pi$
$168$	−0.973492	−0.0751065
$169$	15.7069	1.20822
$170$	−8.29527	−0.636218
$171$	1.00000	0.0764719
$172$	2.37983	0.181460
$173$	7.44857	0.566304	0.283152	−	0.959075i	$-0.408620\pi$
$173$	7.44857	0.566304	0.283152	+	0.959075i	$0.408620\pi$
$174$	−4.32036	−0.327526
$175$	−1.54495	−0.116787
$176$	3.22473	0.243074
$177$	0.929948	0.0698992
$178$	−8.87657	−0.665327
$179$	−6.93129	−0.518069	−0.259035	−	0.965868i	$-0.583404\pi$
$179$	−6.93129	−0.518069	−0.259035	+	0.965868i	$0.583404\pi$
$180$	−2.56652	−0.191297
$181$	−20.9066	−1.55398	−0.776989	−	0.629514i	$-0.783254\pi$
$181$	−20.9066	−1.55398	−0.776989	+	0.629514i	$0.783254\pi$
$182$	5.21585	0.386625
$183$	−11.1056	−0.820952
$184$	5.36750	0.395697
$185$	11.5431	0.848665
$186$	2.03359	0.149110
$187$	−10.4227	−0.762183
$188$	−11.6056	−0.846427
$189$	0.973492	0.0708111
$190$	2.56652	0.186195
$191$	−25.7047	−1.85992	−0.929962	−	0.367656i	$-0.880160\pi$
$191$	−25.7047	−1.85992	−0.929962	+	0.367656i	$0.880160\pi$
$192$	−1.00000	−0.0721688
$193$	0.749574	0.0539555	0.0269778	−	0.999636i	$-0.491412\pi$
$193$	0.749574	0.0539555	0.0269778	+	0.999636i	$0.491412\pi$
$194$	−0.264566	−0.0189947
$195$	13.7511	0.984736
$196$	−6.05231	−0.432308
$197$	−1.17193	−0.0834963	−0.0417481	−	0.999128i	$-0.513293\pi$
$197$	−1.17193	−0.0834963	−0.0417481	+	0.999128i	$0.513293\pi$
$198$	−3.22473	−0.229172
$199$	14.8806	1.05485	0.527427	−	0.849600i	$-0.323157\pi$
$199$	14.8806	1.05485	0.527427	+	0.849600i	$0.323157\pi$
$200$	−1.58701	−0.112219
$201$	−3.61884	−0.255253
$202$	5.66258	0.398417
$203$	4.20584	0.295192
$204$	3.23211	0.226293
$205$	−16.2000	−1.13145
$206$	−13.5757	−0.945862
$207$	−5.36750	−0.373067
$208$	5.35788	0.371502
$209$	3.22473	0.223060
$210$	2.49848	0.172412
$211$	−8.05579	−0.554583	−0.277292	−	0.960786i	$-0.589437\pi$
$211$	−8.05579	−0.554583	−0.277292	+	0.960786i	$0.589437\pi$
$212$	1.00000	0.0686803
$213$	−8.80649	−0.603411
$214$	2.97961	0.203682
$215$	−6.10787	−0.416553
$216$	1.00000	0.0680414
$217$	−1.97968	−0.134390
$218$	−3.65169	−0.247324
$219$	11.4118	0.771140
$220$	−8.27634	−0.557991
$221$	−17.3172	−1.16488
$222$	−4.49757	−0.301857
$223$	−16.2560	−1.08858	−0.544290	−	0.838897i	$-0.683201\pi$
$223$	−16.2560	−1.08858	−0.544290	+	0.838897i	$0.683201\pi$
$224$	0.973492	0.0650442
$225$	1.58701	0.105801
$226$	−8.47760	−0.563922
$227$	−4.77767	−0.317105	−0.158553	−	0.987351i	$-0.550683\pi$
$227$	−4.77767	−0.317105	−0.158553	+	0.987351i	$0.550683\pi$
$228$	−1.00000	−0.0662266
$229$	−15.1469	−1.00094	−0.500469	−	0.865754i	$-0.666839\pi$
$229$	−15.1469	−1.00094	−0.500469	+	0.865754i	$0.666839\pi$
$230$	−13.7758	−0.908348
$231$	3.13925	0.206548
$232$	4.32036	0.283646
$233$	−27.8508	−1.82457	−0.912284	−	0.409557i	$-0.865683\pi$
$233$	−27.8508	−1.82457	−0.912284	+	0.409557i	$0.865683\pi$
$234$	−5.35788	−0.350255
$235$	29.7860	1.94303
$236$	−0.929948	−0.0605345
$237$	−16.7661	−1.08907
$238$	−3.14643	−0.203953
$239$	−20.1254	−1.30180	−0.650902	−	0.759162i	$-0.725609\pi$
$239$	−20.1254	−1.30180	−0.650902	+	0.759162i	$0.725609\pi$
$240$	2.56652	0.165668
$241$	−20.0355	−1.29060	−0.645301	−	0.763928i	$-0.723268\pi$
$241$	−20.0355	−1.29060	−0.645301	+	0.763928i	$0.723268\pi$
$242$	0.601087	0.0386393
$243$	−1.00000	−0.0641500
$244$	11.1056	0.710966
$245$	15.5334	0.992391
$246$	6.31204	0.402441
$247$	5.35788	0.340914
$248$	−2.03359	−0.129133
$249$	−7.05152	−0.446872
$250$	−8.75949	−0.553999
$251$	−8.27682	−0.522428	−0.261214	−	0.965281i	$-0.584123\pi$
$251$	−8.27682	−0.522428	−0.261214	+	0.965281i	$0.584123\pi$
$252$	−0.973492	−0.0613242
$253$	−17.3087	−1.08819
$254$	16.7818	1.05298
$255$	−8.29527	−0.519470
$256$	1.00000	0.0625000
$257$	−28.7149	−1.79119	−0.895594	−	0.444873i	$-0.853249\pi$
$257$	−28.7149	−1.79119	−0.895594	+	0.444873i	$0.853249\pi$
$258$	2.37983	0.148161
$259$	4.37835	0.272057
$260$	−13.7511	−0.852806
$261$	−4.32036	−0.267424
$262$	13.0626	0.807008
$263$	29.6351	1.82738	0.913691	−	0.406410i	$-0.133220\pi$
$263$	29.6351	1.82738	0.913691	+	0.406410i	$0.133220\pi$
$264$	3.22473	0.198469
$265$	−2.56652	−0.157660
$266$	0.973492	0.0596886
$267$	−8.87657	−0.543237
$268$	3.61884	0.221056
$269$	29.1276	1.77594	0.887970	−	0.459902i	$-0.152115\pi$
$269$	29.1276	1.77594	0.887970	+	0.459902i	$0.152115\pi$
$270$	−2.56652	−0.156193
$271$	19.1693	1.16445	0.582226	−	0.813027i	$-0.302182\pi$
$271$	19.1693	1.16445	0.582226	+	0.813027i	$0.302182\pi$
$272$	−3.23211	−0.195975
$273$	5.21585	0.315678
$274$	−2.53023	−0.152857
$275$	5.11770	0.308609
$276$	5.36750	0.323085
$277$	−6.63206	−0.398482	−0.199241	−	0.979951i	$-0.563848\pi$
$277$	−6.63206	−0.398482	−0.199241	+	0.979951i	$0.563848\pi$
$278$	−16.7318	−1.00350
$279$	2.03359	0.121748
$280$	−2.49848	−0.149313
$281$	−21.1410	−1.26117	−0.630583	−	0.776122i	$-0.717184\pi$
$281$	−21.1410	−1.26117	−0.630583	+	0.776122i	$0.717184\pi$
$282$	−11.6056	−0.691104
$283$	−21.1573	−1.25767	−0.628836	−	0.777538i	$-0.716468\pi$
$283$	−21.1573	−1.25767	−0.628836	+	0.777538i	$0.716468\pi$
$284$	8.80649	0.522569
$285$	2.56652	0.152027
$286$	−17.2777	−1.02165
$287$	−6.14472	−0.362711
$288$	−1.00000	−0.0589256
$289$	−6.55347	−0.385498
$290$	−11.0883	−0.651126
$291$	−0.264566	−0.0155091
$292$	−11.4118	−0.667826
$293$	10.8345	0.632959	0.316480	−	0.948599i	$-0.397499\pi$
$293$	10.8345	0.632959	0.316480	+	0.948599i	$0.397499\pi$
$294$	−6.05231	−0.352978
$295$	2.38673	0.138961
$296$	4.49757	0.261416
$297$	−3.22473	−0.187118
$298$	−7.71122	−0.446699
$299$	−28.7584	−1.66314
$300$	−1.58701	−0.0916263
$301$	−2.31674	−0.133535
$302$	13.3837	0.770146
$303$	5.66258	0.325307
$304$	1.00000	0.0573539
$305$	−28.5028	−1.63207
$306$	3.23211	0.184767
$307$	20.4739	1.16851	0.584254	−	0.811571i	$-0.301387\pi$
$307$	20.4739	1.16851	0.584254	+	0.811571i	$0.301387\pi$
$308$	−3.13925	−0.178876
$309$	−13.5757	−0.772293
$310$	5.21925	0.296433
$311$	−10.4856	−0.594585	−0.297293	−	0.954786i	$-0.596084\pi$
$311$	−10.4856	−0.594585	−0.297293	+	0.954786i	$0.596084\pi$
$312$	5.35788	0.303330
$313$	19.1777	1.08399	0.541995	−	0.840382i	$-0.317669\pi$
$313$	19.1777	1.08399	0.541995	+	0.840382i	$0.317669\pi$
$314$	−21.0123	−1.18580
$315$	2.49848	0.140774
$316$	16.7661	0.943165
$317$	−17.9856	−1.01017	−0.505086	−	0.863069i	$-0.668539\pi$
$317$	−17.9856	−1.01017	−0.505086	+	0.863069i	$0.668539\pi$
$318$	1.00000	0.0560772
$319$	−13.9320	−0.780043
$320$	−2.56652	−0.143473
$321$	2.97961	0.166305
$322$	−5.22521	−0.291190
$323$	−3.23211	−0.179839
$324$	1.00000	0.0555556
$325$	8.50303	0.471663
$326$	20.5728	1.13942
$327$	−3.65169	−0.201939
$328$	−6.31204	−0.348524
$329$	11.2980	0.622878
$330$	−8.27634	−0.455597
$331$	13.4966	0.741841	0.370920	−	0.928665i	$-0.379042\pi$
$331$	13.4966	0.741841	0.370920	+	0.928665i	$0.379042\pi$
$332$	7.05152	0.387003
$333$	−4.49757	−0.246465
$334$	16.9032	0.924901
$335$	−9.28781	−0.507447
$336$	0.973492	0.0531083
$337$	−12.0739	−0.657708	−0.328854	−	0.944381i	$-0.606662\pi$
$337$	−12.0739	−0.657708	−0.328854	+	0.944381i	$0.606662\pi$
$338$	−15.7069	−0.854341
$339$	−8.47760	−0.460440
$340$	8.29527	0.449874
$341$	6.55779	0.355124
$342$	−1.00000	−0.0540738
$343$	12.7063	0.686077
$344$	−2.37983	−0.128312
$345$	−13.7758	−0.741663
$346$	−7.44857	−0.400438
$347$	32.6966	1.75525	0.877624	−	0.479350i	$-0.159128\pi$
$347$	32.6966	1.75525	0.877624	+	0.479350i	$0.159128\pi$
$348$	4.32036	0.231596
$349$	−16.2374	−0.869165	−0.434583	−	0.900632i	$-0.643104\pi$
$349$	−16.2374	−0.869165	−0.434583	+	0.900632i	$0.643104\pi$
$350$	1.54495	0.0825808
$351$	−5.35788	−0.285982
$352$	−3.22473	−0.171879
$353$	−20.2886	−1.07985	−0.539927	−	0.841712i	$-0.681548\pi$
$353$	−20.2886	−1.07985	−0.539927	+	0.841712i	$0.681548\pi$
$354$	−0.929948	−0.0494262
$355$	−22.6020	−1.19959
$356$	8.87657	0.470457
$357$	−3.14643	−0.166527
$358$	6.93129	0.366330
$359$	18.4151	0.971912	0.485956	−	0.873983i	$-0.338471\pi$
$359$	18.4151	0.971912	0.485956	+	0.873983i	$0.338471\pi$
$360$	2.56652	0.135267
$361$	1.00000	0.0526316
$362$	20.9066	1.09883
$363$	0.601087	0.0315489
$364$	−5.21585	−0.273385
$365$	29.2886	1.53304
$366$	11.1056	0.580501
$367$	−11.7896	−0.615411	−0.307705	−	0.951482i	$-0.599561\pi$
$367$	−11.7896	−0.615411	−0.307705	+	0.951482i	$0.599561\pi$
$368$	−5.36750	−0.279800
$369$	6.31204	0.328591
$370$	−11.5431	−0.600097
$371$	−0.973492	−0.0505412
$372$	−2.03359	−0.105437
$373$	19.8470	1.02764	0.513819	−	0.857899i	$-0.328230\pi$
$373$	19.8470	1.02764	0.513819	+	0.857899i	$0.328230\pi$
$374$	10.4227	0.538945
$375$	−8.75949	−0.452338
$376$	11.6056	0.598514
$377$	−23.1480	−1.19218
$378$	−0.973492	−0.0500710
$379$	14.1096	0.724762	0.362381	−	0.932030i	$-0.381964\pi$
$379$	14.1096	0.724762	0.362381	+	0.932030i	$0.381964\pi$
$380$	−2.56652	−0.131660
$381$	16.7818	0.859758
$382$	25.7047	1.31516
$383$	2.72426	0.139203	0.0696017	−	0.997575i	$-0.477827\pi$
$383$	2.72426	0.139203	0.0696017	+	0.997575i	$0.477827\pi$
$384$	1.00000	0.0510310
$385$	8.05695	0.410620
$386$	−0.749574	−0.0381523
$387$	2.37983	0.120973
$388$	0.264566	0.0134313
$389$	16.5900	0.841144	0.420572	−	0.907259i	$-0.361829\pi$
$389$	16.5900	0.841144	0.420572	+	0.907259i	$0.361829\pi$
$390$	−13.7511	−0.696314
$391$	17.3483	0.877343
$392$	6.05231	0.305688
$393$	13.0626	0.658919
$394$	1.17193	0.0590408
$395$	−43.0304	−2.16509
$396$	3.22473	0.162049
$397$	3.46025	0.173665	0.0868325	−	0.996223i	$-0.472326\pi$
$397$	3.46025	0.173665	0.0868325	+	0.996223i	$0.472326\pi$
$398$	−14.8806	−0.745895
$399$	0.973492	0.0487356
$400$	1.58701	0.0793507
$401$	−30.5264	−1.52442	−0.762208	−	0.647332i	$-0.775885\pi$
$401$	−30.5264	−1.52442	−0.762208	+	0.647332i	$0.775885\pi$
$402$	3.61884	0.180491
$403$	10.8957	0.542755
$404$	−5.66258	−0.281724
$405$	−2.56652	−0.127531
$406$	−4.20584	−0.208732
$407$	−14.5035	−0.718911
$408$	−3.23211	−0.160013
$409$	−12.5105	−0.618607	−0.309303	−	0.950963i	$-0.600096\pi$
$409$	−12.5105	−0.618607	−0.309303	+	0.950963i	$0.600096\pi$
$410$	16.2000	0.800059
$411$	−2.53023	−0.124807
$412$	13.5757	0.668825
$413$	0.905297	0.0445468
$414$	5.36750	0.263798
$415$	−18.0979	−0.888389
$416$	−5.35788	−0.262692
$417$	−16.7318	−0.819357
$418$	−3.22473	−0.157727
$419$	−37.1107	−1.81298	−0.906489	−	0.422230i	$-0.861247\pi$
$419$	−37.1107	−1.81298	−0.906489	+	0.422230i	$0.861247\pi$
$420$	−2.49848	−0.121914
$421$	39.1799	1.90951	0.954755	−	0.297394i	$-0.0961175\pi$
$421$	39.1799	1.90951	0.954755	+	0.297394i	$0.0961175\pi$
$422$	8.05579	0.392150
$423$	−11.6056	−0.564284
$424$	−1.00000	−0.0485643
$425$	−5.12940	−0.248813
$426$	8.80649	0.426676
$427$	−10.8113	−0.523193
$428$	−2.97961	−0.144025
$429$	−17.2777	−0.834177
$430$	6.10787	0.294547
$431$	7.11660	0.342794	0.171397	−	0.985202i	$-0.445172\pi$
$431$	7.11660	0.342794	0.171397	+	0.985202i	$0.445172\pi$
$432$	−1.00000	−0.0481125
$433$	4.59399	0.220773	0.110386	−	0.993889i	$-0.464791\pi$
$433$	4.59399	0.220773	0.110386	+	0.993889i	$0.464791\pi$
$434$	1.97968	0.0950279
$435$	−11.0883	−0.531643
$436$	3.65169	0.174884
$437$	−5.36750	−0.256762
$438$	−11.4118	−0.545278
$439$	−26.7776	−1.27802	−0.639011	−	0.769197i	$-0.720656\pi$
$439$	−26.7776	−1.27802	−0.639011	+	0.769197i	$0.720656\pi$
$440$	8.27634	0.394559
$441$	−6.05231	−0.288205
$442$	17.3172	0.823697
$443$	−33.5697	−1.59495	−0.797473	−	0.603355i	$-0.793830\pi$
$443$	−33.5697	−1.59495	−0.797473	+	0.603355i	$0.793830\pi$
$444$	4.49757	0.213445
$445$	−22.7819	−1.07996
$446$	16.2560	0.769742
$447$	−7.71122	−0.364728
$448$	−0.973492	−0.0459932
$449$	31.1233	1.46880	0.734399	−	0.678718i	$-0.237464\pi$
$449$	31.1233	1.46880	0.734399	+	0.678718i	$0.237464\pi$
$450$	−1.58701	−0.0748126
$451$	20.3546	0.958463
$452$	8.47760	0.398753
$453$	13.3837	0.628822
$454$	4.77767	0.224227
$455$	13.3866	0.627572
$456$	1.00000	0.0468293
$457$	39.5179	1.84857	0.924284	−	0.381705i	$-0.124663\pi$
$457$	39.5179	1.84857	0.924284	+	0.381705i	$0.124663\pi$
$458$	15.1469	0.707770
$459$	3.23211	0.150862
$460$	13.7758	0.642299
$461$	−9.63628	−0.448806	−0.224403	−	0.974496i	$-0.572043\pi$
$461$	−9.63628	−0.448806	−0.224403	+	0.974496i	$0.572043\pi$
$462$	−3.13925	−0.146051
$463$	31.1278	1.44663	0.723316	−	0.690517i	$-0.242617\pi$
$463$	31.1278	1.44663	0.723316	+	0.690517i	$0.242617\pi$
$464$	−4.32036	−0.200568
$465$	5.21925	0.242037
$466$	27.8508	1.29016
$467$	−32.7922	−1.51744	−0.758720	−	0.651417i	$-0.774175\pi$
$467$	−32.7922	−1.51744	−0.758720	+	0.651417i	$0.774175\pi$
$468$	5.35788	0.247668
$469$	−3.52291	−0.162673
$470$	−29.7860	−1.37393
$471$	−21.0123	−0.968198
$472$	0.929948	0.0428043
$473$	7.67431	0.352865
$474$	16.7661	0.770091
$475$	1.58701	0.0728172
$476$	3.14643	0.144217
$477$	1.00000	0.0457869
$478$	20.1254	0.920515
$479$	1.99911	0.0913419	0.0456709	−	0.998957i	$-0.485457\pi$
$479$	1.99911	0.0913419	0.0456709	+	0.998957i	$0.485457\pi$
$480$	−2.56652	−0.117145
$481$	−24.0974	−1.09875
$482$	20.0355	0.912594
$483$	−5.22521	−0.237755
$484$	−0.601087	−0.0273221
$485$	−0.679014	−0.0308324
$486$	1.00000	0.0453609
$487$	−22.5327	−1.02105	−0.510527	−	0.859862i	$-0.670550\pi$
$487$	−22.5327	−1.02105	−0.510527	+	0.859862i	$0.670550\pi$
$488$	−11.1056	−0.502729
$489$	20.5728	0.930336
$490$	−15.5334	−0.701726
$491$	19.2950	0.870771	0.435385	−	0.900244i	$-0.356612\pi$
$491$	19.2950	0.870771	0.435385	+	0.900244i	$0.356612\pi$
$492$	−6.31204	−0.284569
$493$	13.9639	0.628901
$494$	−5.35788	−0.241062
$495$	−8.27634	−0.371994
$496$	2.03359	0.0913109
$497$	−8.57305	−0.384554
$498$	7.05152	0.315986
$499$	−23.6082	−1.05685	−0.528425	−	0.848980i	$-0.677217\pi$
$499$	−23.6082	−1.05685	−0.528425	+	0.848980i	$0.677217\pi$
$500$	8.75949	0.391736
$501$	16.9032	0.755178
$502$	8.27682	0.369413
$503$	−1.14102	−0.0508758	−0.0254379	−	0.999676i	$-0.508098\pi$
$503$	−1.14102	−0.0508758	−0.0254379	+	0.999676i	$0.508098\pi$
$504$	0.973492	0.0433628
$505$	14.5331	0.646715
$506$	17.3087	0.769468
$507$	−15.7069	−0.697566
$508$	−16.7818	−0.744572
$509$	−5.79153	−0.256705	−0.128352	−	0.991729i	$-0.540969\pi$
$509$	−5.79153	−0.256705	−0.128352	+	0.991729i	$0.540969\pi$
$510$	8.29527	0.367321
$511$	11.1093	0.491447
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	28.7149	1.26656
$515$	−34.8422	−1.53533
$516$	−2.37983	−0.104766
$517$	−37.4250	−1.64595
$518$	−4.37835	−0.192374
$519$	−7.44857	−0.326956
$520$	13.7511	0.603025
$521$	−31.3130	−1.37185	−0.685923	−	0.727674i	$-0.740601\pi$
$521$	−31.3130	−1.37185	−0.685923	+	0.727674i	$0.740601\pi$
$522$	4.32036	0.189097
$523$	25.3631	1.10905	0.554526	−	0.832166i	$-0.312900\pi$
$523$	25.3631	1.10905	0.554526	+	0.832166i	$0.312900\pi$
$524$	−13.0626	−0.570641
$525$	1.54495	0.0674270
$526$	−29.6351	−1.29215
$527$	−6.57279	−0.286315
$528$	−3.22473	−0.140339
$529$	5.81001	0.252609
$530$	2.56652	0.111482
$531$	−0.929948	−0.0403563
$532$	−0.973492	−0.0422062
$533$	33.8191	1.46487
$534$	8.87657	0.384127
$535$	7.64721	0.330618
$536$	−3.61884	−0.156310
$537$	6.93129	0.299107
$538$	−29.1276	−1.25578
$539$	−19.5171	−0.840661
$540$	2.56652	0.110445
$541$	−32.7359	−1.40743	−0.703714	−	0.710483i	$-0.748476\pi$
$541$	−32.7359	−1.40743	−0.703714	+	0.710483i	$0.748476\pi$
$542$	−19.1693	−0.823391
$543$	20.9066	0.897190
$544$	3.23211	0.138576
$545$	−9.37213	−0.401458
$546$	−5.21585	−0.223218
$547$	−27.5930	−1.17979	−0.589896	−	0.807479i	$-0.700831\pi$
$547$	−27.5930	−1.17979	−0.589896	+	0.807479i	$0.700831\pi$
$548$	2.53023	0.108086
$549$	11.1056	0.473977
$550$	−5.11770	−0.218219
$551$	−4.32036	−0.184054
$552$	−5.36750	−0.228456
$553$	−16.3216	−0.694066
$554$	6.63206	0.281769
$555$	−11.5431	−0.489977
$556$	16.7318	0.709584
$557$	30.2772	1.28289	0.641443	−	0.767171i	$-0.278336\pi$
$557$	30.2772	1.28289	0.641443	+	0.767171i	$0.278336\pi$
$558$	−2.03359	−0.0860887
$559$	12.7508	0.539302
$560$	2.49848	0.105580
$561$	10.4227	0.440046
$562$	21.1410	0.891780
$563$	−38.6573	−1.62921	−0.814605	−	0.580015i	$-0.803047\pi$
$563$	−38.6573	−1.62921	−0.814605	+	0.580015i	$0.803047\pi$
$564$	11.6056	0.488685
$565$	−21.7579	−0.915363
$566$	21.1573	0.889309
$567$	−0.973492	−0.0408828
$568$	−8.80649	−0.369512
$569$	14.0456	0.588821	0.294411	−	0.955679i	$-0.404877\pi$
$569$	14.0456	0.588821	0.294411	+	0.955679i	$0.404877\pi$
$570$	−2.56652	−0.107500
$571$	33.5860	1.40553	0.702765	−	0.711422i	$-0.251948\pi$
$571$	33.5860	1.40553	0.702765	+	0.711422i	$0.251948\pi$
$572$	17.2777	0.722418
$573$	25.7047	1.07383
$574$	6.14472	0.256476
$575$	−8.51829	−0.355237
$576$	1.00000	0.0416667
$577$	−27.5040	−1.14501	−0.572504	−	0.819902i	$-0.694028\pi$
$577$	−27.5040	−1.14501	−0.572504	+	0.819902i	$0.694028\pi$
$578$	6.55347	0.272588
$579$	−0.749574	−0.0311513
$580$	11.0883	0.460416
$581$	−6.86460	−0.284792
$582$	0.264566	0.0109666
$583$	3.22473	0.133555
$584$	11.4118	0.472225
$585$	−13.7511	−0.568538
$586$	−10.8345	−0.447570
$587$	−3.86012	−0.159324	−0.0796622	−	0.996822i	$-0.525384\pi$
$587$	−3.86012	−0.159324	−0.0796622	+	0.996822i	$0.525384\pi$
$588$	6.05231	0.249593
$589$	2.03359	0.0837926
$590$	−2.38673	−0.0982601
$591$	1.17193	0.0482066
$592$	−4.49757	−0.184849
$593$	−46.8498	−1.92389	−0.961946	−	0.273240i	$-0.911905\pi$
$593$	−46.8498	−1.92389	−0.961946	+	0.273240i	$0.911905\pi$
$594$	3.22473	0.132312
$595$	−8.07538	−0.331058
$596$	7.71122	0.315864
$597$	−14.8806	−0.609020
$598$	28.7584	1.17602
$599$	−31.9583	−1.30578	−0.652890	−	0.757453i	$-0.726444\pi$
$599$	−31.9583	−1.30578	−0.652890	+	0.757453i	$0.726444\pi$
$600$	1.58701	0.0647896
$601$	−7.51117	−0.306387	−0.153193	−	0.988196i	$-0.548956\pi$
$601$	−7.51117	−0.306387	−0.153193	+	0.988196i	$0.548956\pi$
$602$	2.31674	0.0944233
$603$	3.61884	0.147371
$604$	−13.3837	−0.544575
$605$	1.54270	0.0627197
$606$	−5.66258	−0.230026
$607$	42.0796	1.70796	0.853980	−	0.520306i	$-0.174182\pi$
$607$	42.0796	1.70796	0.853980	+	0.520306i	$0.174182\pi$
$608$	−1.00000	−0.0405554
$609$	−4.20584	−0.170429
$610$	28.5028	1.15405
$611$	−62.1815	−2.51559
$612$	−3.23211	−0.130650
$613$	−30.8414	−1.24567	−0.622836	−	0.782352i	$-0.714020\pi$
$613$	−30.8414	−1.24567	−0.622836	+	0.782352i	$0.714020\pi$
$614$	−20.4739	−0.826260
$615$	16.2000	0.653245
$616$	3.13925	0.126484
$617$	40.9432	1.64831	0.824155	−	0.566365i	$-0.191651\pi$
$617$	40.9432	1.64831	0.824155	+	0.566365i	$0.191651\pi$
$618$	13.5757	0.546093
$619$	−3.81884	−0.153492	−0.0767461	−	0.997051i	$-0.524453\pi$
$619$	−3.81884	−0.153492	−0.0767461	+	0.997051i	$0.524453\pi$
$620$	−5.21925	−0.209610
$621$	5.36750	0.215390
$622$	10.4856	0.420435
$623$	−8.64127	−0.346205
$624$	−5.35788	−0.214487
$625$	−30.4165	−1.21666
$626$	−19.1777	−0.766496
$627$	−3.22473	−0.128783
$628$	21.0123	0.838484
$629$	14.5366	0.579614
$630$	−2.49848	−0.0995420
$631$	−8.98411	−0.357652	−0.178826	−	0.983881i	$-0.557230\pi$
$631$	−8.98411	−0.357652	−0.178826	+	0.983881i	$0.557230\pi$
$632$	−16.7661	−0.666918
$633$	8.05579	0.320189
$634$	17.9856	0.714299
$635$	43.0708	1.70921
$636$	−1.00000	−0.0396526
$637$	−32.4276	−1.28483
$638$	13.9320	0.551574
$639$	8.80649	0.348379
$640$	2.56652	0.101451
$641$	30.3823	1.20003	0.600015	−	0.799989i	$-0.295161\pi$
$641$	30.3823	1.20003	0.600015	+	0.799989i	$0.295161\pi$
$642$	−2.97961	−0.117596
$643$	−45.0866	−1.77804	−0.889021	−	0.457867i	$-0.848614\pi$
$643$	−45.0866	−1.77804	−0.889021	+	0.457867i	$0.848614\pi$
$644$	5.22521	0.205902
$645$	6.10787	0.240497
$646$	3.23211	0.127166
$647$	20.2777	0.797198	0.398599	−	0.917125i	$-0.369497\pi$
$647$	20.2777	0.797198	0.398599	+	0.917125i	$0.369497\pi$
$648$	−1.00000	−0.0392837
$649$	−2.99884	−0.117715
$650$	−8.50303	−0.333516
$651$	1.97968	0.0775899
$652$	−20.5728	−0.805695
$653$	−13.2841	−0.519848	−0.259924	−	0.965629i	$-0.583697\pi$
$653$	−13.2841	−0.519848	−0.259924	+	0.965629i	$0.583697\pi$
$654$	3.65169	0.142792
$655$	33.5253	1.30994
$656$	6.31204	0.246444
$657$	−11.4118	−0.445218
$658$	−11.2980	−0.440441
$659$	35.1012	1.36735	0.683674	−	0.729787i	$-0.260381\pi$
$659$	35.1012	1.36735	0.683674	+	0.729787i	$0.260381\pi$
$660$	8.27634	0.322156
$661$	−38.7723	−1.50807	−0.754033	−	0.656836i	$-0.771894\pi$
$661$	−38.7723	−1.50807	−0.754033	+	0.656836i	$0.771894\pi$
$662$	−13.4966	−0.524561
$663$	17.3172	0.672546
$664$	−7.05152	−0.273652
$665$	2.49848	0.0968871
$666$	4.49757	0.174277
$667$	23.1895	0.897902
$668$	−16.9032	−0.654004
$669$	16.2560	0.628492
$670$	9.28781	0.358820
$671$	35.8127	1.38254
$672$	−0.973492	−0.0375533
$673$	48.1330	1.85539	0.927696	−	0.373336i	$-0.121786\pi$
$673$	48.1330	1.85539	0.927696	+	0.373336i	$0.121786\pi$
$674$	12.0739	0.465070
$675$	−1.58701	−0.0610842
$676$	15.7069	0.604110
$677$	−27.2073	−1.04566	−0.522831	−	0.852436i	$-0.675124\pi$
$677$	−27.2073	−1.04566	−0.522831	+	0.852436i	$0.675124\pi$
$678$	8.47760	0.325580
$679$	−0.257553	−0.00988398
$680$	−8.29527	−0.318109
$681$	4.77767	0.183081
$682$	−6.55779	−0.251111
$683$	−24.4934	−0.937216	−0.468608	−	0.883406i	$-0.655244\pi$
$683$	−24.4934	−0.937216	−0.468608	+	0.883406i	$0.655244\pi$
$684$	1.00000	0.0382360
$685$	−6.49387	−0.248118
$686$	−12.7063	−0.485130
$687$	15.1469	0.577892
$688$	2.37983	0.0907300
$689$	5.35788	0.204119
$690$	13.7758	0.524435
$691$	−19.9639	−0.759463	−0.379731	−	0.925097i	$-0.623984\pi$
$691$	−19.9639	−0.759463	−0.379731	+	0.925097i	$0.623984\pi$
$692$	7.44857	0.283152
$693$	−3.13925	−0.119250
$694$	−32.6966	−1.24115
$695$	−42.9423	−1.62890
$696$	−4.32036	−0.163763
$697$	−20.4012	−0.772750
$698$	16.2374	0.614593
$699$	27.8508	1.05342
$700$	−1.54495	−0.0583935
$701$	35.2085	1.32981	0.664903	−	0.746930i	$-0.268473\pi$
$701$	35.2085	1.32981	0.664903	+	0.746930i	$0.268473\pi$
$702$	5.35788	0.202220
$703$	−4.49757	−0.169629
$704$	3.22473	0.121537
$705$	−29.7860	−1.12181
$706$	20.2886	0.763573
$707$	5.51247	0.207318
$708$	0.929948	0.0349496
$709$	−22.0885	−0.829553	−0.414776	−	0.909923i	$-0.636140\pi$
$709$	−22.0885	−0.829553	−0.414776	+	0.909923i	$0.636140\pi$
$710$	22.6020	0.848239
$711$	16.7661	0.628777
$712$	−8.87657	−0.332663
$713$	−10.9153	−0.408781
$714$	3.14643	0.117752
$715$	−44.3436	−1.65836
$716$	−6.93129	−0.259035
$717$	20.1254	0.751597
$718$	−18.4151	−0.687246
$719$	−34.8808	−1.30083	−0.650416	−	0.759578i	$-0.725406\pi$
$719$	−34.8808	−1.30083	−0.650416	+	0.759578i	$0.725406\pi$
$720$	−2.56652	−0.0956485
$721$	−13.2158	−0.492182
$722$	−1.00000	−0.0372161
$723$	20.0355	0.745130
$724$	−20.9066	−0.776989
$725$	−6.85647	−0.254643
$726$	−0.601087	−0.0223084
$727$	−49.4667	−1.83462	−0.917310	−	0.398175i	$-0.869644\pi$
$727$	−49.4667	−1.83462	−0.917310	+	0.398175i	$0.869644\pi$
$728$	5.21585	0.193312
$729$	1.00000	0.0370370
$730$	−29.2886	−1.08402
$731$	−7.69186	−0.284494
$732$	−11.1056	−0.410476
$733$	46.1125	1.70320	0.851602	−	0.524188i	$-0.175631\pi$
$733$	46.1125	1.70320	0.851602	+	0.524188i	$0.175631\pi$
$734$	11.7896	0.435161
$735$	−15.5334	−0.572957
$736$	5.36750	0.197849
$737$	11.6698	0.429862
$738$	−6.31204	−0.232349
$739$	−16.5805	−0.609923	−0.304961	−	0.952365i	$-0.598644\pi$
$739$	−16.5805	−0.609923	−0.304961	+	0.952365i	$0.598644\pi$
$740$	11.5431	0.424333
$741$	−5.35788	−0.196827
$742$	0.973492	0.0357380
$743$	−42.7222	−1.56732	−0.783662	−	0.621187i	$-0.786651\pi$
$743$	−42.7222	−1.56732	−0.783662	+	0.621187i	$0.786651\pi$
$744$	2.03359	0.0745550
$745$	−19.7910	−0.725086
$746$	−19.8470	−0.726649
$747$	7.05152	0.258002
$748$	−10.4227	−0.381091
$749$	2.90062	0.105986
$750$	8.75949	0.319851
$751$	−46.1098	−1.68257	−0.841286	−	0.540591i	$-0.818201\pi$
$751$	−46.1098	−1.68257	−0.841286	+	0.540591i	$0.818201\pi$
$752$	−11.6056	−0.423213
$753$	8.27682	0.301624
$754$	23.1480	0.842999
$755$	34.3495	1.25011
$756$	0.973492	0.0354056
$757$	12.9643	0.471195	0.235598	−	0.971851i	$-0.424295\pi$
$757$	12.9643	0.471195	0.235598	+	0.971851i	$0.424295\pi$
$758$	−14.1096	−0.512484
$759$	17.3087	0.628268
$760$	2.56652	0.0930974
$761$	3.25018	0.117819	0.0589094	−	0.998263i	$-0.481238\pi$
$761$	3.25018	0.117819	0.0589094	+	0.998263i	$0.481238\pi$
$762$	−16.7818	−0.607941
$763$	−3.55489	−0.128696
$764$	−25.7047	−0.929962
$765$	8.29527	0.299916
$766$	−2.72426	−0.0984317
$767$	−4.98255	−0.179909
$768$	−1.00000	−0.0360844
$769$	−27.0386	−0.975035	−0.487518	−	0.873113i	$-0.662098\pi$
$769$	−27.0386	−0.975035	−0.487518	+	0.873113i	$0.662098\pi$
$770$	−8.05695	−0.290352
$771$	28.7149	1.03414
$772$	0.749574	0.0269778
$773$	−0.0398090	−0.00143183	−0.000715915	−	1.00000i	$-0.500228\pi$
$773$	−0.0398090	−0.00143183	−0.000715915		1.00000i	$0.500228\pi$
$774$	−2.37983	−0.0855411
$775$	3.22734	0.115929
$776$	−0.264566	−0.00949737
$777$	−4.37835	−0.157072
$778$	−16.5900	−0.594779
$779$	6.31204	0.226152
$780$	13.7511	0.492368
$781$	28.3986	1.01618
$782$	−17.3483	−0.620375
$783$	4.32036	0.154397
$784$	−6.05231	−0.216154
$785$	−53.9286	−1.92479
$786$	−13.0626	−0.465926
$787$	−24.0579	−0.857572	−0.428786	−	0.903406i	$-0.641059\pi$
$787$	−24.0579	−0.857572	−0.428786	+	0.903406i	$0.641059\pi$
$788$	−1.17193	−0.0417481
$789$	−29.6351	−1.05504
$790$	43.0304	1.53095
$791$	−8.25288	−0.293439
$792$	−3.22473	−0.114586
$793$	59.5027	2.11300
$794$	−3.46025	−0.122800
$795$	2.56652	0.0910250
$796$	14.8806	0.527427
$797$	−38.1697	−1.35204	−0.676020	−	0.736884i	$-0.736297\pi$
$797$	−38.1697	−1.35204	−0.676020	+	0.736884i	$0.736297\pi$
$798$	−0.973492	−0.0344612
$799$	37.5106	1.32703
$800$	−1.58701	−0.0561094
$801$	8.87657	0.313638
$802$	30.5264	1.07793
$803$	−36.8001	−1.29865
$804$	−3.61884	−0.127627
$805$	−13.4106	−0.472662
$806$	−10.8957	−0.383786
$807$	−29.1276	−1.02534
$808$	5.66258	0.199209
$809$	23.6126	0.830174	0.415087	−	0.909782i	$-0.363751\pi$
$809$	23.6126	0.830174	0.415087	+	0.909782i	$0.363751\pi$
$810$	2.56652	0.0901782
$811$	−37.2276	−1.30724	−0.653619	−	0.756823i	$-0.726750\pi$
$811$	−37.2276	−1.30724	−0.653619	+	0.756823i	$0.726750\pi$
$812$	4.20584	0.147596
$813$	−19.1693	−0.672296
$814$	14.5035	0.508347
$815$	52.8006	1.84952
$816$	3.23211	0.113146
$817$	2.37983	0.0832596
$818$	12.5105	0.437421
$819$	−5.21585	−0.182257
$820$	−16.2000	−0.565727
$821$	0.223059	0.00778480	0.00389240	−	0.999992i	$-0.498761\pi$
$821$	0.223059	0.00778480	0.00389240	+	0.999992i	$0.498761\pi$
$822$	2.53023	0.0882518
$823$	−16.6561	−0.580597	−0.290298	−	0.956936i	$-0.593755\pi$
$823$	−16.6561	−0.580597	−0.290298	+	0.956936i	$0.593755\pi$
$824$	−13.5757	−0.472931
$825$	−5.11770	−0.178175
$826$	−0.905297	−0.0314993
$827$	−17.4761	−0.607702	−0.303851	−	0.952720i	$-0.598273\pi$
$827$	−17.4761	−0.607702	−0.303851	+	0.952720i	$0.598273\pi$
$828$	−5.36750	−0.186533
$829$	−10.3298	−0.358770	−0.179385	−	0.983779i	$-0.557411\pi$
$829$	−10.3298	−0.358770	−0.179385	+	0.983779i	$0.557411\pi$
$830$	18.0979	0.628186
$831$	6.63206	0.230064
$832$	5.35788	0.185751
$833$	19.5617	0.677774
$834$	16.7318	0.579373
$835$	43.3823	1.50131
$836$	3.22473	0.111530
$837$	−2.03359	−0.0702912
$838$	37.1107	1.28197
$839$	13.0002	0.448816	0.224408	−	0.974495i	$-0.427955\pi$
$839$	13.0002	0.448816	0.224408	+	0.974495i	$0.427955\pi$
$840$	2.49848	0.0862059
$841$	−10.3345	−0.356361
$842$	−39.1799	−1.35023
$843$	21.1410	0.728135
$844$	−8.05579	−0.277292
$845$	−40.3119	−1.38677
$846$	11.6056	0.399009
$847$	0.585153	0.0201061
$848$	1.00000	0.0343401
$849$	21.1573	0.726118
$850$	5.12940	0.175937
$851$	24.1407	0.827532
$852$	−8.80649	−0.301705
$853$	38.9774	1.33456	0.667280	−	0.744807i	$-0.267458\pi$
$853$	38.9774	1.33456	0.667280	+	0.744807i	$0.267458\pi$
$854$	10.8113	0.369953
$855$	−2.56652	−0.0877731
$856$	2.97961	0.101841
$857$	44.0002	1.50302	0.751509	−	0.659723i	$-0.229326\pi$
$857$	44.0002	1.50302	0.751509	+	0.659723i	$0.229326\pi$
$858$	17.2777	0.589852
$859$	−26.0347	−0.888291	−0.444146	−	0.895955i	$-0.646493\pi$
$859$	−26.0347	−0.888291	−0.444146	+	0.895955i	$0.646493\pi$
$860$	−6.10787	−0.208276
$861$	6.14472	0.209411
$862$	−7.11660	−0.242392
$863$	−41.0574	−1.39761	−0.698806	−	0.715312i	$-0.746285\pi$
$863$	−41.0574	−1.39761	−0.698806	+	0.715312i	$0.746285\pi$
$864$	1.00000	0.0340207
$865$	−19.1169	−0.649994
$866$	−4.59399	−0.156110
$867$	6.55347	0.222568
$868$	−1.97968	−0.0671949
$869$	54.0661	1.83407
$870$	11.0883	0.375928
$871$	19.3893	0.656981
$872$	−3.65169	−0.123662
$873$	0.264566	0.00895421
$874$	5.36750	0.181558
$875$	−8.52729	−0.288275
$876$	11.4118	0.385570
$877$	−38.6913	−1.30651	−0.653256	−	0.757137i	$-0.726597\pi$
$877$	−38.6913	−1.30651	−0.653256	+	0.757137i	$0.726597\pi$
$878$	26.7776	0.903699
$879$	−10.8345	−0.365439
$880$	−8.27634	−0.278995
$881$	13.3010	0.448121	0.224060	−	0.974575i	$-0.428069\pi$
$881$	13.3010	0.448121	0.224060	+	0.974575i	$0.428069\pi$
$882$	6.05231	0.203792
$883$	40.8818	1.37578	0.687891	−	0.725814i	$-0.258537\pi$
$883$	40.8818	1.37578	0.687891	+	0.725814i	$0.258537\pi$
$884$	−17.3172	−0.582442
$885$	−2.38673	−0.0802290
$886$	33.5697	1.12780
$887$	−37.5284	−1.26008	−0.630040	−	0.776562i	$-0.716962\pi$
$887$	−37.5284	−1.26008	−0.630040	+	0.776562i	$0.716962\pi$
$888$	−4.49757	−0.150929
$889$	16.3370	0.547924
$890$	22.7819	0.763650
$891$	3.22473	0.108033
$892$	−16.2560	−0.544290
$893$	−11.6056	−0.388367
$894$	7.71122	0.257902
$895$	17.7893	0.594630
$896$	0.973492	0.0325221
$897$	28.7584	0.960215
$898$	−31.1233	−1.03860
$899$	−8.78585	−0.293024
$900$	1.58701	0.0529005
$901$	−3.23211	−0.107677
$902$	−20.3546	−0.677735
$903$	2.31674	0.0770963
$904$	−8.47760	−0.281961
$905$	53.6573	1.78363
$906$	−13.3837	−0.444644
$907$	−27.1026	−0.899926	−0.449963	−	0.893047i	$-0.648563\pi$
$907$	−27.1026	−0.899926	−0.449963	+	0.893047i	$0.648563\pi$
$908$	−4.77767	−0.158553
$909$	−5.66258	−0.187816
$910$	−13.3866	−0.443761
$911$	2.00207	0.0663316	0.0331658	−	0.999450i	$-0.489441\pi$
$911$	2.00207	0.0663316	0.0331658	+	0.999450i	$0.489441\pi$
$912$	−1.00000	−0.0331133
$913$	22.7393	0.752561
$914$	−39.5179	−1.30714
$915$	28.5028	0.942274
$916$	−15.1469	−0.500469
$917$	12.7163	0.419929
$918$	−3.23211	−0.106675
$919$	−20.9104	−0.689769	−0.344885	−	0.938645i	$-0.612082\pi$
$919$	−20.9104	−0.689769	−0.344885	+	0.938645i	$0.612082\pi$
$920$	−13.7758	−0.454174
$921$	−20.4739	−0.674639
$922$	9.63628	0.317354
$923$	47.1841	1.55308
$924$	3.13925	0.103274
$925$	−7.13771	−0.234686
$926$	−31.1278	−1.02292
$927$	13.5757	0.445883
$928$	4.32036	0.141823
$929$	40.9482	1.34347	0.671733	−	0.740793i	$-0.265550\pi$
$929$	40.9482	1.34347	0.671733	+	0.740793i	$0.265550\pi$
$930$	−5.21925	−0.171146
$931$	−6.05231	−0.198357
$932$	−27.8508	−0.912284
$933$	10.4856	0.343284
$934$	32.7922	1.07299
$935$	26.7500	0.874820
$936$	−5.35788	−0.175128
$937$	−1.92718	−0.0629582	−0.0314791	−	0.999504i	$-0.510022\pi$
$937$	−1.92718	−0.0629582	−0.0314791	+	0.999504i	$0.510022\pi$
$938$	3.52291	0.115027
$939$	−19.1777	−0.625841
$940$	29.7860	0.971513
$941$	53.5357	1.74521	0.872606	−	0.488424i	$-0.162428\pi$
$941$	53.5357	1.74521	0.872606	+	0.488424i	$0.162428\pi$
$942$	21.0123	0.684619
$943$	−33.8798	−1.10328
$944$	−0.929948	−0.0302672
$945$	−2.49848	−0.0812757
$946$	−7.67431	−0.249513
$947$	−49.1235	−1.59630	−0.798150	−	0.602459i	$-0.794188\pi$
$947$	−49.1235	−1.59630	−0.798150	+	0.602459i	$0.794188\pi$
$948$	−16.7661	−0.544537
$949$	−61.1432	−1.98479
$950$	−1.58701	−0.0514895
$951$	17.9856	0.583223
$952$	−3.14643	−0.101976
$953$	31.6592	1.02554	0.512771	−	0.858525i	$-0.328619\pi$
$953$	31.6592	1.02554	0.512771	+	0.858525i	$0.328619\pi$
$954$	−1.00000	−0.0323762
$955$	65.9715	2.13479
$956$	−20.1254	−0.650902
$957$	13.9320	0.450358
$958$	−1.99911	−0.0645884
$959$	−2.46315	−0.0795394
$960$	2.56652	0.0828340
$961$	−26.8645	−0.866597
$962$	24.0974	0.776933
$963$	−2.97961	−0.0960164
$964$	−20.0355	−0.645301
$965$	−1.92380	−0.0619292
$966$	5.22521	0.168119
$967$	8.23040	0.264672	0.132336	−	0.991205i	$-0.457752\pi$
$967$	8.23040	0.264672	0.132336	+	0.991205i	$0.457752\pi$
$968$	0.601087	0.0193197
$969$	3.23211	0.103830
$970$	0.679014	0.0218018
$971$	−38.1506	−1.22431	−0.612156	−	0.790737i	$-0.709697\pi$
$971$	−38.1506	−1.22431	−0.612156	+	0.790737i	$0.709697\pi$
$972$	−1.00000	−0.0320750
$973$	−16.2882	−0.522177
$974$	22.5327	0.721994
$975$	−8.50303	−0.272315
$976$	11.1056	0.355483
$977$	15.5774	0.498365	0.249182	−	0.968457i	$-0.419838\pi$
$977$	15.5774	0.498365	0.249182	+	0.968457i	$0.419838\pi$
$978$	−20.5728	−0.657847
$979$	28.6246	0.914845
$980$	15.5334	0.496195
$981$	3.65169	0.116590
$982$	−19.2950	−0.615728
$983$	3.20813	0.102324	0.0511618	−	0.998690i	$-0.483708\pi$
$983$	3.20813	0.102324	0.0511618	+	0.998690i	$0.483708\pi$
$984$	6.31204	0.201220
$985$	3.00777	0.0958355
$986$	−13.9639	−0.444700
$987$	−11.2980	−0.359619
$988$	5.35788	0.170457
$989$	−12.7737	−0.406180
$990$	8.27634	0.263039
$991$	43.2272	1.37316	0.686578	−	0.727056i	$-0.259112\pi$
$991$	43.2272	1.37316	0.686578	+	0.727056i	$0.259112\pi$
$992$	−2.03359	−0.0645666
$993$	−13.4966	−0.428302
$994$	8.57305	0.271921
$995$	−38.1912	−1.21074
$996$	−7.05152	−0.223436
$997$	−20.9674	−0.664045	−0.332023	−	0.943271i	$-0.607731\pi$
$997$	−20.9674	−0.664045	−0.332023	+	0.943271i	$0.607731\pi$
$998$	23.6082	0.747306
$999$	4.49757	0.142297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bd.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bd.1.3	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.56652 q^{5} +1.00000 q^{6} -0.973492 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.56652 q^{5} +1.00000 q^{6} -0.973492 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.56652 q^{10} +3.22473 q^{11} -1.00000 q^{12} +5.35788 q^{13} +0.973492 q^{14} +2.56652 q^{15} +1.00000 q^{16} -3.23211 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.56652 q^{20} +0.973492 q^{21} -3.22473 q^{22} -5.36750 q^{23} +1.00000 q^{24} +1.58701 q^{25} -5.35788 q^{26} -1.00000 q^{27} -0.973492 q^{28} -4.32036 q^{29} -2.56652 q^{30} +2.03359 q^{31} -1.00000 q^{32} -3.22473 q^{33} +3.23211 q^{34} +2.49848 q^{35} +1.00000 q^{36} -4.49757 q^{37} -1.00000 q^{38} -5.35788 q^{39} +2.56652 q^{40} +6.31204 q^{41} -0.973492 q^{42} +2.37983 q^{43} +3.22473 q^{44} -2.56652 q^{45} +5.36750 q^{46} -11.6056 q^{47} -1.00000 q^{48} -6.05231 q^{49} -1.58701 q^{50} +3.23211 q^{51} +5.35788 q^{52} +1.00000 q^{53} +1.00000 q^{54} -8.27634 q^{55} +0.973492 q^{56} -1.00000 q^{57} +4.32036 q^{58} -0.929948 q^{59} +2.56652 q^{60} +11.1056 q^{61} -2.03359 q^{62} -0.973492 q^{63} +1.00000 q^{64} -13.7511 q^{65} +3.22473 q^{66} +3.61884 q^{67} -3.23211 q^{68} +5.36750 q^{69} -2.49848 q^{70} +8.80649 q^{71} -1.00000 q^{72} -11.4118 q^{73} +4.49757 q^{74} -1.58701 q^{75} +1.00000 q^{76} -3.13925 q^{77} +5.35788 q^{78} +16.7661 q^{79} -2.56652 q^{80} +1.00000 q^{81} -6.31204 q^{82} +7.05152 q^{83} +0.973492 q^{84} +8.29527 q^{85} -2.37983 q^{86} +4.32036 q^{87} -3.22473 q^{88} +8.87657 q^{89} +2.56652 q^{90} -5.21585 q^{91} -5.36750 q^{92} -2.03359 q^{93} +11.6056 q^{94} -2.56652 q^{95} +1.00000 q^{96} +0.264566 q^{97} +6.05231 q^{98} +3.22473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9	\( 11 q - 11 q^{2} - 11 q^{3} + 11 q^{4} + 2 q^{5} + 11 q^{6} - 2 q^{7} - 11 q^{8} + 11 q^{9} - 2 q^{10} - 6 q^{11} - 11 q^{12} - 7 q^{13} + 2 q^{14} - 2 q^{15} + 11 q^{16} - 16 q^{17} - 11 q^{18} + 11 q^{19} + 2 q^{20} + 2 q^{21} + 6 q^{22} - 11 q^{23} + 11 q^{24} + 19 q^{25} + 7 q^{26} - 11 q^{27} - 2 q^{28} - 7 q^{29} + 2 q^{30} + 12 q^{31} - 11 q^{32} + 6 q^{33} + 16 q^{34} - 5 q^{35} + 11 q^{36} + 3 q^{37} - 11 q^{38} + 7 q^{39} - 2 q^{40} + 11 q^{41} - 2 q^{42} + 7 q^{43} - 6 q^{44} + 2 q^{45} + 11 q^{46} - 37 q^{47} - 11 q^{48} + 23 q^{49} - 19 q^{50} + 16 q^{51} - 7 q^{52} + 11 q^{53} + 11 q^{54} - 11 q^{55} + 2 q^{56} - 11 q^{57} + 7 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} - 12 q^{62} - 2 q^{63} + 11 q^{64} - 7 q^{65} - 6 q^{66} - 28 q^{67} - 16 q^{68} + 11 q^{69} + 5 q^{70} + 4 q^{71} - 11 q^{72} - 7 q^{73} - 3 q^{74} - 19 q^{75} + 11 q^{76} - 13 q^{77} - 7 q^{78} + 5 q^{79} + 2 q^{80} + 11 q^{81} - 11 q^{82} - 11 q^{83} + 2 q^{84} - 11 q^{85} - 7 q^{86} + 7 q^{87} + 6 q^{88} - 10 q^{89} - 2 q^{90} - 24 q^{91} - 11 q^{92} - 12 q^{93} + 37 q^{94} + 2 q^{95} + 11 q^{96} - 24 q^{97} - 23 q^{98} - 6 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 11 * q^3 + 11 * q^4 + 2 * q^5 + 11 * q^6 - 2 * q^7 - 11 * q^8 + 11 * q^9 - 2 * q^10 - 6 * q^11 - 11 * q^12 - 7 * q^13 + 2 * q^14 - 2 * q^15 + 11 * q^16 - 16 * q^17 - 11 * q^18 + 11 * q^19 + 2 * q^20 + 2 * q^21 + 6 * q^22 - 11 * q^23 + 11 * q^24 + 19 * q^25 + 7 * q^26 - 11 * q^27 - 2 * q^28 - 7 * q^29 + 2 * q^30 + 12 * q^31 - 11 * q^32 + 6 * q^33 + 16 * q^34 - 5 * q^35 + 11 * q^36 + 3 * q^37 - 11 * q^38 + 7 * q^39 - 2 * q^40 + 11 * q^41 - 2 * q^42 + 7 * q^43 - 6 * q^44 + 2 * q^45 + 11 * q^46 - 37 * q^47 - 11 * q^48 + 23 * q^49 - 19 * q^50 + 16 * q^51 - 7 * q^52 + 11 * q^53 + 11 * q^54 - 11 * q^55 + 2 * q^56 - 11 * q^57 + 7 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 - 12 * q^62 - 2 * q^63 + 11 * q^64 - 7 * q^65 - 6 * q^66 - 28 * q^67 - 16 * q^68 + 11 * q^69 + 5 * q^70 + 4 * q^71 - 11 * q^72 - 7 * q^73 - 3 * q^74 - 19 * q^75 + 11 * q^76 - 13 * q^77 - 7 * q^78 + 5 * q^79 + 2 * q^80 + 11 * q^81 - 11 * q^82 - 11 * q^83 + 2 * q^84 - 11 * q^85 - 7 * q^86 + 7 * q^87 + 6 * q^88 - 10 * q^89 - 2 * q^90 - 24 * q^91 - 11 * q^92 - 12 * q^93 + 37 * q^94 + 2 * q^95 + 11 * q^96 - 24 * q^97 - 23 * q^98 - 6 * q^99

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