LMFDB - Embedded newform 6034.2.a.q.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.44788 q^{3} +1.00000 q^{4} +2.75672 q^{5} -1.44788 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.903639 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.44788 q^{3} +1.00000 q^{4} +2.75672 q^{5} -1.44788 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.903639 q^{9} +2.75672 q^{10} +4.32657 q^{11} -1.44788 q^{12} -4.62739 q^{13} +1.00000 q^{14} -3.99140 q^{15} +1.00000 q^{16} -3.75104 q^{17} -0.903639 q^{18} +5.86896 q^{19} +2.75672 q^{20} -1.44788 q^{21} +4.32657 q^{22} -5.06004 q^{23} -1.44788 q^{24} +2.59949 q^{25} -4.62739 q^{26} +5.65201 q^{27} +1.00000 q^{28} -3.21888 q^{29} -3.99140 q^{30} +0.439400 q^{31} +1.00000 q^{32} -6.26436 q^{33} -3.75104 q^{34} +2.75672 q^{35} -0.903639 q^{36} +2.74726 q^{37} +5.86896 q^{38} +6.69992 q^{39} +2.75672 q^{40} +7.49621 q^{41} -1.44788 q^{42} +5.66034 q^{43} +4.32657 q^{44} -2.49108 q^{45} -5.06004 q^{46} +4.78053 q^{47} -1.44788 q^{48} +1.00000 q^{49} +2.59949 q^{50} +5.43106 q^{51} -4.62739 q^{52} +11.2470 q^{53} +5.65201 q^{54} +11.9271 q^{55} +1.00000 q^{56} -8.49756 q^{57} -3.21888 q^{58} -0.948157 q^{59} -3.99140 q^{60} -0.397936 q^{61} +0.439400 q^{62} -0.903639 q^{63} +1.00000 q^{64} -12.7564 q^{65} -6.26436 q^{66} -3.89893 q^{67} -3.75104 q^{68} +7.32634 q^{69} +2.75672 q^{70} +13.1851 q^{71} -0.903639 q^{72} +0.148892 q^{73} +2.74726 q^{74} -3.76375 q^{75} +5.86896 q^{76} +4.32657 q^{77} +6.69992 q^{78} +10.9420 q^{79} +2.75672 q^{80} -5.47252 q^{81} +7.49621 q^{82} +8.83012 q^{83} -1.44788 q^{84} -10.3405 q^{85} +5.66034 q^{86} +4.66056 q^{87} +4.32657 q^{88} -7.95707 q^{89} -2.49108 q^{90} -4.62739 q^{91} -5.06004 q^{92} -0.636200 q^{93} +4.78053 q^{94} +16.1791 q^{95} -1.44788 q^{96} -8.34025 q^{97} +1.00000 q^{98} -3.90966 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * 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
$3$	−1.44788	−0.835935	−0.417967	−	0.908462i	$-0.637257\pi$
$3$	−1.44788	−0.835935	−0.417967	+	0.908462i	$0.637257\pi$
$4$	1.00000	0.500000
$5$	2.75672	1.23284	0.616421	−	0.787417i	$-0.288582\pi$
$5$	2.75672	1.23284	0.616421	+	0.787417i	$0.288582\pi$
$6$	−1.44788	−0.591095
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−0.903639	−0.301213
$10$	2.75672	0.871750
$11$	4.32657	1.30451	0.652255	−	0.758000i	$-0.273823\pi$
$11$	4.32657	1.30451	0.652255	+	0.758000i	$0.273823\pi$
$12$	−1.44788	−0.417967
$13$	−4.62739	−1.28341	−0.641704	−	0.766952i	$-0.721772\pi$
$13$	−4.62739	−1.28341	−0.641704	+	0.766952i	$0.721772\pi$
$14$	1.00000	0.267261
$15$	−3.99140	−1.03057
$16$	1.00000	0.250000
$17$	−3.75104	−0.909760	−0.454880	−	0.890553i	$-0.650318\pi$
$17$	−3.75104	−0.909760	−0.454880	+	0.890553i	$0.650318\pi$
$18$	−0.903639	−0.212990
$19$	5.86896	1.34643	0.673216	−	0.739446i	$-0.264912\pi$
$19$	5.86896	1.34643	0.673216	+	0.739446i	$0.264912\pi$
$20$	2.75672	0.616421
$21$	−1.44788	−0.315954
$22$	4.32657	0.922428
$23$	−5.06004	−1.05509	−0.527546	−	0.849526i	$-0.676888\pi$
$23$	−5.06004	−1.05509	−0.527546	+	0.849526i	$0.676888\pi$
$24$	−1.44788	−0.295548
$25$	2.59949	0.519897
$26$	−4.62739	−0.907506
$27$	5.65201	1.08773
$28$	1.00000	0.188982
$29$	−3.21888	−0.597732	−0.298866	−	0.954295i	$-0.596608\pi$
$29$	−3.21888	−0.597732	−0.298866	+	0.954295i	$0.596608\pi$
$30$	−3.99140	−0.728726
$31$	0.439400	0.0789186	0.0394593	−	0.999221i	$-0.487436\pi$
$31$	0.439400	0.0789186	0.0394593	+	0.999221i	$0.487436\pi$
$32$	1.00000	0.176777
$33$	−6.26436	−1.09048
$34$	−3.75104	−0.643297
$35$	2.75672	0.465970
$36$	−0.903639	−0.150607
$37$	2.74726	0.451647	0.225824	−	0.974168i	$-0.427493\pi$
$37$	2.74726	0.451647	0.225824	+	0.974168i	$0.427493\pi$
$38$	5.86896	0.952071
$39$	6.69992	1.07285
$40$	2.75672	0.435875
$41$	7.49621	1.17071	0.585356	−	0.810777i	$-0.300955\pi$
$41$	7.49621	1.17071	0.585356	+	0.810777i	$0.300955\pi$
$42$	−1.44788	−0.223413
$43$	5.66034	0.863194	0.431597	−	0.902066i	$-0.357950\pi$
$43$	5.66034	0.863194	0.431597	+	0.902066i	$0.357950\pi$
$44$	4.32657	0.652255
$45$	−2.49108	−0.371348
$46$	−5.06004	−0.746063
$47$	4.78053	0.697311	0.348656	−	0.937251i	$-0.386638\pi$
$47$	4.78053	0.697311	0.348656	+	0.937251i	$0.386638\pi$
$48$	−1.44788	−0.208984
$49$	1.00000	0.142857
$50$	2.59949	0.367623
$51$	5.43106	0.760500
$52$	−4.62739	−0.641704
$53$	11.2470	1.54490	0.772450	−	0.635076i	$-0.219031\pi$
$53$	11.2470	1.54490	0.772450	+	0.635076i	$0.219031\pi$
$54$	5.65201	0.769141
$55$	11.9271	1.60825
$56$	1.00000	0.133631
$57$	−8.49756	−1.12553
$58$	−3.21888	−0.422660
$59$	−0.948157	−0.123440	−0.0617198	−	0.998094i	$-0.519659\pi$
$59$	−0.948157	−0.123440	−0.0617198	+	0.998094i	$0.519659\pi$
$60$	−3.99140	−0.515287
$61$	−0.397936	−0.0509505	−0.0254753	−	0.999675i	$-0.508110\pi$
$61$	−0.397936	−0.0509505	−0.0254753	+	0.999675i	$0.508110\pi$
$62$	0.439400	0.0558039
$63$	−0.903639	−0.113848
$64$	1.00000	0.125000
$65$	−12.7564	−1.58224
$66$	−6.26436	−0.771089
$67$	−3.89893	−0.476330	−0.238165	−	0.971225i	$-0.576546\pi$
$67$	−3.89893	−0.476330	−0.238165	+	0.971225i	$0.576546\pi$
$68$	−3.75104	−0.454880
$69$	7.32634	0.881988
$70$	2.75672	0.329491
$71$	13.1851	1.56479	0.782394	−	0.622784i	$-0.213999\pi$
$71$	13.1851	1.56479	0.782394	+	0.622784i	$0.213999\pi$
$72$	−0.903639	−0.106495
$73$	0.148892	0.0174265	0.00871323	−	0.999962i	$-0.497226\pi$
$73$	0.148892	0.0174265	0.00871323	+	0.999962i	$0.497226\pi$
$74$	2.74726	0.319363
$75$	−3.76375	−0.434600
$76$	5.86896	0.673216
$77$	4.32657	0.493058
$78$	6.69992	0.758616
$79$	10.9420	1.23107	0.615534	−	0.788110i	$-0.288940\pi$
$79$	10.9420	1.23107	0.615534	+	0.788110i	$0.288940\pi$
$80$	2.75672	0.308210
$81$	−5.47252	−0.608058
$82$	7.49621	0.827818
$83$	8.83012	0.969232	0.484616	−	0.874727i	$-0.338959\pi$
$83$	8.83012	0.969232	0.484616	+	0.874727i	$0.338959\pi$
$84$	−1.44788	−0.157977
$85$	−10.3405	−1.12159
$86$	5.66034	0.610371
$87$	4.66056	0.499665
$88$	4.32657	0.461214
$89$	−7.95707	−0.843448	−0.421724	−	0.906724i	$-0.638575\pi$
$89$	−7.95707	−0.843448	−0.421724	+	0.906724i	$0.638575\pi$
$90$	−2.49108	−0.262583
$91$	−4.62739	−0.485083
$92$	−5.06004	−0.527546
$93$	−0.636200	−0.0659708
$94$	4.78053	0.493074
$95$	16.1791	1.65994
$96$	−1.44788	−0.147774
$97$	−8.34025	−0.846824	−0.423412	−	0.905937i	$-0.639168\pi$
$97$	−8.34025	−0.846824	−0.423412	+	0.905937i	$0.639168\pi$
$98$	1.00000	0.101015
$99$	−3.90966	−0.392935
$100$	2.59949	0.259949
$101$	7.87360	0.783452	0.391726	−	0.920082i	$-0.371878\pi$
$101$	7.87360	0.783452	0.391726	+	0.920082i	$0.371878\pi$
$102$	5.43106	0.537755
$103$	9.60051	0.945966	0.472983	−	0.881072i	$-0.343177\pi$
$103$	9.60051	0.945966	0.472983	+	0.881072i	$0.343177\pi$
$104$	−4.62739	−0.453753
$105$	−3.99140	−0.389521
$106$	11.2470	1.09241
$107$	−14.2067	−1.37342	−0.686709	−	0.726932i	$-0.740945\pi$
$107$	−14.2067	−1.37342	−0.686709	+	0.726932i	$0.740945\pi$
$108$	5.65201	0.543865
$109$	10.9646	1.05022	0.525109	−	0.851035i	$-0.324025\pi$
$109$	10.9646	1.05022	0.525109	+	0.851035i	$0.324025\pi$
$110$	11.9271	1.13721
$111$	−3.97771	−0.377548
$112$	1.00000	0.0944911
$113$	3.05928	0.287793	0.143896	−	0.989593i	$-0.454037\pi$
$113$	3.05928	0.287793	0.143896	+	0.989593i	$0.454037\pi$
$114$	−8.49756	−0.795870
$115$	−13.9491	−1.30076
$116$	−3.21888	−0.298866
$117$	4.18149	0.386579
$118$	−0.948157	−0.0872849
$119$	−3.75104	−0.343857
$120$	−3.99140	−0.364363
$121$	7.71920	0.701745
$122$	−0.397936	−0.0360275
$123$	−10.8536	−0.978638
$124$	0.439400	0.0394593
$125$	−6.61754	−0.591891
$126$	−0.903639	−0.0805026
$127$	0.165133	0.0146532	0.00732661	−	0.999973i	$-0.497668\pi$
$127$	0.165133	0.0146532	0.00732661	+	0.999973i	$0.497668\pi$
$128$	1.00000	0.0883883
$129$	−8.19551	−0.721574
$130$	−12.7564	−1.11881
$131$	−21.7197	−1.89766	−0.948829	−	0.315789i	$-0.897731\pi$
$131$	−21.7197	−1.89766	−0.948829	+	0.315789i	$0.897731\pi$
$132$	−6.26436	−0.545242
$133$	5.86896	0.508904
$134$	−3.89893	−0.336816
$135$	15.5810	1.34100
$136$	−3.75104	−0.321649
$137$	21.3643	1.82527	0.912636	−	0.408773i	$-0.134043\pi$
$137$	21.3643	1.82527	0.912636	+	0.408773i	$0.134043\pi$
$138$	7.32634	0.623660
$139$	−2.43195	−0.206275	−0.103138	−	0.994667i	$-0.532888\pi$
$139$	−2.43195	−0.206275	−0.103138	+	0.994667i	$0.532888\pi$
$140$	2.75672	0.232985
$141$	−6.92163	−0.582907
$142$	13.1851	1.10647
$143$	−20.0207	−1.67422
$144$	−0.903639	−0.0753033
$145$	−8.87355	−0.736908
$146$	0.148892	0.0123224
$147$	−1.44788	−0.119419
$148$	2.74726	0.225824
$149$	14.9991	1.22877	0.614386	−	0.789005i	$-0.289404\pi$
$149$	14.9991	1.22877	0.614386	+	0.789005i	$0.289404\pi$
$150$	−3.76375	−0.307309
$151$	−10.8683	−0.884448	−0.442224	−	0.896905i	$-0.645810\pi$
$151$	−10.8683	−0.884448	−0.442224	+	0.896905i	$0.645810\pi$
$152$	5.86896	0.476036
$153$	3.38958	0.274032
$154$	4.32657	0.348645
$155$	1.21130	0.0972941
$156$	6.69992	0.536423
$157$	−14.7679	−1.17861	−0.589304	−	0.807912i	$-0.700598\pi$
$157$	−14.7679	−1.17861	−0.589304	+	0.807912i	$0.700598\pi$
$158$	10.9420	0.870496
$159$	−16.2844	−1.29144
$160$	2.75672	0.217938
$161$	−5.06004	−0.398787
$162$	−5.47252	−0.429962
$163$	13.6937	1.07257	0.536285	−	0.844037i	$-0.319827\pi$
$163$	13.6937	1.07257	0.536285	+	0.844037i	$0.319827\pi$
$164$	7.49621	0.585356
$165$	−17.2691	−1.34439
$166$	8.83012	0.685350
$167$	8.71801	0.674620	0.337310	−	0.941394i	$-0.390483\pi$
$167$	8.71801	0.674620	0.337310	+	0.941394i	$0.390483\pi$
$168$	−1.44788	−0.111706
$169$	8.41277	0.647136
$170$	−10.3405	−0.793084
$171$	−5.30343	−0.405563
$172$	5.66034	0.431597
$173$	10.3028	0.783304	0.391652	−	0.920113i	$-0.371904\pi$
$173$	10.3028	0.783304	0.391652	+	0.920113i	$0.371904\pi$
$174$	4.66056	0.353316
$175$	2.59949	0.196503
$176$	4.32657	0.326127
$177$	1.37282	0.103187
$178$	−7.95707	−0.596408
$179$	−12.2491	−0.915538	−0.457769	−	0.889071i	$-0.651351\pi$
$179$	−12.2491	−0.915538	−0.457769	+	0.889071i	$0.651351\pi$
$180$	−2.49108	−0.185674
$181$	0.726135	0.0539732	0.0269866	−	0.999636i	$-0.491409\pi$
$181$	0.726135	0.0539732	0.0269866	+	0.999636i	$0.491409\pi$
$182$	−4.62739	−0.343005
$183$	0.576164	0.0425913
$184$	−5.06004	−0.373031
$185$	7.57343	0.556809
$186$	−0.636200	−0.0466484
$187$	−16.2291	−1.18679
$188$	4.78053	0.348656
$189$	5.65201	0.411123
$190$	16.1791	1.17375
$191$	15.3577	1.11124	0.555621	−	0.831435i	$-0.312480\pi$
$191$	15.3577	1.11124	0.555621	+	0.831435i	$0.312480\pi$
$192$	−1.44788	−0.104492
$193$	−3.19869	−0.230247	−0.115124	−	0.993351i	$-0.536726\pi$
$193$	−3.19869	−0.230247	−0.115124	+	0.993351i	$0.536726\pi$
$194$	−8.34025	−0.598795
$195$	18.4698	1.32265
$196$	1.00000	0.0714286
$197$	−0.324783	−0.0231398	−0.0115699	−	0.999933i	$-0.503683\pi$
$197$	−0.324783	−0.0231398	−0.0115699	+	0.999933i	$0.503683\pi$
$198$	−3.90966	−0.277847
$199$	−19.3552	−1.37205	−0.686027	−	0.727576i	$-0.740647\pi$
$199$	−19.3552	−1.37205	−0.686027	+	0.727576i	$0.740647\pi$
$200$	2.59949	0.183811
$201$	5.64519	0.398181
$202$	7.87360	0.553984
$203$	−3.21888	−0.225921
$204$	5.43106	0.380250
$205$	20.6649	1.44330
$206$	9.60051	0.668899
$207$	4.57245	0.317808
$208$	−4.62739	−0.320852
$209$	25.3925	1.75643
$210$	−3.99140	−0.275433
$211$	2.12298	0.146152	0.0730759	−	0.997326i	$-0.476718\pi$
$211$	2.12298	0.146152	0.0730759	+	0.997326i	$0.476718\pi$
$212$	11.2470	0.772450
$213$	−19.0905	−1.30806
$214$	−14.2067	−0.971153
$215$	15.6040	1.06418
$216$	5.65201	0.384570
$217$	0.439400	0.0298284
$218$	10.9646	0.742616
$219$	−0.215578	−0.0145674
$220$	11.9271	0.804127
$221$	17.3575	1.16759
$222$	−3.97771	−0.266967
$223$	16.5456	1.10797	0.553987	−	0.832525i	$-0.313106\pi$
$223$	16.5456	1.10797	0.553987	+	0.832525i	$0.313106\pi$
$224$	1.00000	0.0668153
$225$	−2.34900	−0.156600
$226$	3.05928	0.203500
$227$	−28.8567	−1.91529	−0.957644	−	0.287954i	$-0.907025\pi$
$227$	−28.8567	−1.91529	−0.957644	+	0.287954i	$0.907025\pi$
$228$	−8.49756	−0.562765
$229$	22.4534	1.48376	0.741882	−	0.670531i	$-0.233933\pi$
$229$	22.4534	1.48376	0.741882	+	0.670531i	$0.233933\pi$
$230$	−13.9491	−0.919777
$231$	−6.26436	−0.412165
$232$	−3.21888	−0.211330
$233$	10.7532	0.704466	0.352233	−	0.935912i	$-0.385422\pi$
$233$	10.7532	0.704466	0.352233	+	0.935912i	$0.385422\pi$
$234$	4.18149	0.273353
$235$	13.1786	0.859674
$236$	−0.948157	−0.0617198
$237$	−15.8427	−1.02909
$238$	−3.75104	−0.243144
$239$	−11.9243	−0.771320	−0.385660	−	0.922641i	$-0.626026\pi$
$239$	−11.9243	−0.771320	−0.385660	+	0.922641i	$0.626026\pi$
$240$	−3.99140	−0.257644
$241$	7.32264	0.471692	0.235846	−	0.971790i	$-0.424214\pi$
$241$	7.32264	0.471692	0.235846	+	0.971790i	$0.424214\pi$
$242$	7.71920	0.496209
$243$	−9.03246	−0.579433
$244$	−0.397936	−0.0254753
$245$	2.75672	0.176120
$246$	−10.8536	−0.692002
$247$	−27.1580	−1.72802
$248$	0.439400	0.0279020
$249$	−12.7850	−0.810214
$250$	−6.61754	−0.418530
$251$	17.4159	1.09928	0.549642	−	0.835400i	$-0.314764\pi$
$251$	17.4159	1.09928	0.549642	+	0.835400i	$0.314764\pi$
$252$	−0.903639	−0.0569239
$253$	−21.8926	−1.37638
$254$	0.165133	0.0103614
$255$	14.9719	0.937576
$256$	1.00000	0.0625000
$257$	−21.9368	−1.36838	−0.684190	−	0.729303i	$-0.739844\pi$
$257$	−21.9368	−1.36838	−0.684190	+	0.729303i	$0.739844\pi$
$258$	−8.19551	−0.510230
$259$	2.74726	0.170707
$260$	−12.7564	−0.791119
$261$	2.90871	0.180045
$262$	−21.7197	−1.34185
$263$	−16.6814	−1.02862	−0.514310	−	0.857605i	$-0.671952\pi$
$263$	−16.6814	−1.02862	−0.514310	+	0.857605i	$0.671952\pi$
$264$	−6.26436	−0.385545
$265$	31.0049	1.90462
$266$	5.86896	0.359849
$267$	11.5209	0.705067
$268$	−3.89893	−0.238165
$269$	−9.71605	−0.592398	−0.296199	−	0.955126i	$-0.595719\pi$
$269$	−9.71605	−0.592398	−0.296199	+	0.955126i	$0.595719\pi$
$270$	15.5810	0.948228
$271$	7.53596	0.457777	0.228888	−	0.973453i	$-0.426491\pi$
$271$	7.53596	0.457777	0.228888	+	0.973453i	$0.426491\pi$
$272$	−3.75104	−0.227440
$273$	6.69992	0.405497
$274$	21.3643	1.29066
$275$	11.2469	0.678211
$276$	7.32634	0.440994
$277$	−24.5658	−1.47602	−0.738009	−	0.674791i	$-0.764234\pi$
$277$	−24.5658	−1.47602	−0.738009	+	0.674791i	$0.764234\pi$
$278$	−2.43195	−0.145859
$279$	−0.397059	−0.0237713
$280$	2.75672	0.164745
$281$	4.99545	0.298004	0.149002	−	0.988837i	$-0.452394\pi$
$281$	4.99545	0.298004	0.149002	+	0.988837i	$0.452394\pi$
$282$	−6.92163	−0.412177
$283$	9.50813	0.565200	0.282600	−	0.959238i	$-0.408803\pi$
$283$	9.50813	0.565200	0.282600	+	0.959238i	$0.408803\pi$
$284$	13.1851	0.782394
$285$	−23.4254	−1.38760
$286$	−20.0207	−1.18385
$287$	7.49621	0.442487
$288$	−0.903639	−0.0532475
$289$	−2.92973	−0.172337
$290$	−8.87355	−0.521073
$291$	12.0757	0.707890
$292$	0.148892	0.00871323
$293$	−8.23060	−0.480837	−0.240418	−	0.970669i	$-0.577285\pi$
$293$	−8.23060	−0.480837	−0.240418	+	0.970669i	$0.577285\pi$
$294$	−1.44788	−0.0844422
$295$	−2.61380	−0.152181
$296$	2.74726	0.159681
$297$	24.4538	1.41895
$298$	14.9991	0.868873
$299$	23.4148	1.35411
$300$	−3.76375	−0.217300
$301$	5.66034	0.326257
$302$	−10.8683	−0.625399
$303$	−11.4000	−0.654915
$304$	5.86896	0.336608
$305$	−1.09700	−0.0628139
$306$	3.38958	0.193770
$307$	−17.1144	−0.976770	−0.488385	−	0.872628i	$-0.662414\pi$
$307$	−17.1144	−0.976770	−0.488385	+	0.872628i	$0.662414\pi$
$308$	4.32657	0.246529
$309$	−13.9004	−0.790766
$310$	1.21130	0.0687973
$311$	15.5969	0.884420	0.442210	−	0.896911i	$-0.354195\pi$
$311$	15.5969	0.884420	0.442210	+	0.896911i	$0.354195\pi$
$312$	6.69992	0.379308
$313$	0.233621	0.0132050	0.00660251	−	0.999978i	$-0.497898\pi$
$313$	0.233621	0.0132050	0.00660251	+	0.999978i	$0.497898\pi$
$314$	−14.7679	−0.833401
$315$	−2.49108	−0.140356
$316$	10.9420	0.615534
$317$	−7.89876	−0.443639	−0.221819	−	0.975088i	$-0.571200\pi$
$317$	−7.89876	−0.443639	−0.221819	+	0.975088i	$0.571200\pi$
$318$	−16.2844	−0.913183
$319$	−13.9267	−0.779747
$320$	2.75672	0.154105
$321$	20.5697	1.14809
$322$	−5.06004	−0.281985
$323$	−22.0147	−1.22493
$324$	−5.47252	−0.304029
$325$	−12.0288	−0.667240
$326$	13.6937	0.758422
$327$	−15.8754	−0.877913
$328$	7.49621	0.413909
$329$	4.78053	0.263559
$330$	−17.2691	−0.950631
$331$	25.5828	1.40616	0.703080	−	0.711111i	$-0.251808\pi$
$331$	25.5828	1.40616	0.703080	+	0.711111i	$0.251808\pi$
$332$	8.83012	0.484616
$333$	−2.48254	−0.136042
$334$	8.71801	0.477029
$335$	−10.7482	−0.587239
$336$	−1.44788	−0.0789884
$337$	22.9800	1.25180	0.625900	−	0.779903i	$-0.284732\pi$
$337$	22.9800	1.25180	0.625900	+	0.779903i	$0.284732\pi$
$338$	8.41277	0.457594
$339$	−4.42947	−0.240576
$340$	−10.3405	−0.560795
$341$	1.90110	0.102950
$342$	−5.30343	−0.286776
$343$	1.00000	0.0539949
$344$	5.66034	0.305185
$345$	20.1967	1.08735
$346$	10.3028	0.553880
$347$	−4.11193	−0.220740	−0.110370	−	0.993891i	$-0.535204\pi$
$347$	−4.11193	−0.220740	−0.110370	+	0.993891i	$0.535204\pi$
$348$	4.66056	0.249832
$349$	−23.4625	−1.25592	−0.627960	−	0.778245i	$-0.716110\pi$
$349$	−23.4625	−1.25592	−0.627960	+	0.778245i	$0.716110\pi$
$350$	2.59949	0.138948
$351$	−26.1541	−1.39600
$352$	4.32657	0.230607
$353$	−4.99789	−0.266011	−0.133005	−	0.991115i	$-0.542463\pi$
$353$	−4.99789	−0.266011	−0.133005	+	0.991115i	$0.542463\pi$
$354$	1.37282	0.0729645
$355$	36.3477	1.92913
$356$	−7.95707	−0.421724
$357$	5.43106	0.287442
$358$	−12.2491	−0.647383
$359$	18.6006	0.981704	0.490852	−	0.871243i	$-0.336686\pi$
$359$	18.6006	0.981704	0.490852	+	0.871243i	$0.336686\pi$
$360$	−2.49108	−0.131291
$361$	15.4447	0.812880
$362$	0.726135	0.0381648
$363$	−11.1765	−0.586613
$364$	−4.62739	−0.242541
$365$	0.410452	0.0214841
$366$	0.576164	0.0301166
$367$	−14.1981	−0.741133	−0.370567	−	0.928806i	$-0.620837\pi$
$367$	−14.1981	−0.741133	−0.370567	+	0.928806i	$0.620837\pi$
$368$	−5.06004	−0.263773
$369$	−6.77387	−0.352634
$370$	7.57343	0.393724
$371$	11.2470	0.583917
$372$	−0.636200	−0.0329854
$373$	7.41169	0.383763	0.191881	−	0.981418i	$-0.438541\pi$
$373$	7.41169	0.383763	0.191881	+	0.981418i	$0.438541\pi$
$374$	−16.2291	−0.839188
$375$	9.58141	0.494782
$376$	4.78053	0.246537
$377$	14.8950	0.767134
$378$	5.65201	0.290708
$379$	14.6123	0.750583	0.375291	−	0.926907i	$-0.377543\pi$
$379$	14.6123	0.750583	0.375291	+	0.926907i	$0.377543\pi$
$380$	16.1791	0.829969
$381$	−0.239094	−0.0122491
$382$	15.3577	0.785767
$383$	10.1805	0.520197	0.260099	−	0.965582i	$-0.416245\pi$
$383$	10.1805	0.520197	0.260099	+	0.965582i	$0.416245\pi$
$384$	−1.44788	−0.0738869
$385$	11.9271	0.607863
$386$	−3.19869	−0.162809
$387$	−5.11491	−0.260005
$388$	−8.34025	−0.423412
$389$	28.8509	1.46280	0.731398	−	0.681950i	$-0.238868\pi$
$389$	28.8509	1.46280	0.731398	+	0.681950i	$0.238868\pi$
$390$	18.4698	0.935253
$391$	18.9804	0.959881
$392$	1.00000	0.0505076
$393$	31.4475	1.58632
$394$	−0.324783	−0.0163623
$395$	30.1639	1.51771
$396$	−3.90966	−0.196468
$397$	18.3918	0.923057	0.461529	−	0.887125i	$-0.347301\pi$
$397$	18.3918	0.923057	0.461529	+	0.887125i	$0.347301\pi$
$398$	−19.3552	−0.970189
$399$	−8.49756	−0.425410
$400$	2.59949	0.129974
$401$	4.59899	0.229662	0.114831	−	0.993385i	$-0.463367\pi$
$401$	4.59899	0.229662	0.114831	+	0.993385i	$0.463367\pi$
$402$	5.64519	0.281556
$403$	−2.03328	−0.101285
$404$	7.87360	0.391726
$405$	−15.0862	−0.749638
$406$	−3.21888	−0.159751
$407$	11.8862	0.589178
$408$	5.43106	0.268877
$409$	24.9279	1.23261	0.616303	−	0.787509i	$-0.288630\pi$
$409$	24.9279	1.23261	0.616303	+	0.787509i	$0.288630\pi$
$410$	20.6649	1.02057
$411$	−30.9329	−1.52581
$412$	9.60051	0.472983
$413$	−0.948157	−0.0466557
$414$	4.57245	0.224724
$415$	24.3421	1.19491
$416$	−4.62739	−0.226877
$417$	3.52118	0.172433
$418$	25.3925	1.24199
$419$	−13.1331	−0.641595	−0.320798	−	0.947148i	$-0.603951\pi$
$419$	−13.1331	−0.641595	−0.320798	+	0.947148i	$0.603951\pi$
$420$	−3.99140	−0.194760
$421$	−33.5376	−1.63452	−0.817260	−	0.576269i	$-0.804508\pi$
$421$	−33.5376	−1.63452	−0.817260	+	0.576269i	$0.804508\pi$
$422$	2.12298	0.103345
$423$	−4.31987	−0.210039
$424$	11.2470	0.546205
$425$	−9.75077	−0.472982
$426$	−19.0905	−0.924938
$427$	−0.397936	−0.0192575
$428$	−14.2067	−0.686709
$429$	28.9877	1.39954
$430$	15.6040	0.752490
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	5.65201	0.271932
$433$	25.5889	1.22972	0.614861	−	0.788635i	$-0.289212\pi$
$433$	25.5889	1.22972	0.614861	+	0.788635i	$0.289212\pi$
$434$	0.439400	0.0210919
$435$	12.8479	0.616007
$436$	10.9646	0.525109
$437$	−29.6972	−1.42061
$438$	−0.215578	−0.0103007
$439$	−15.2311	−0.726941	−0.363471	−	0.931606i	$-0.618408\pi$
$439$	−15.2311	−0.726941	−0.363471	+	0.931606i	$0.618408\pi$
$440$	11.9271	0.568603
$441$	−0.903639	−0.0430304
$442$	17.3575	0.825613
$443$	−24.4037	−1.15946	−0.579728	−	0.814810i	$-0.696841\pi$
$443$	−24.4037	−1.15946	−0.579728	+	0.814810i	$0.696841\pi$
$444$	−3.97771	−0.188774
$445$	−21.9354	−1.03984
$446$	16.5456	0.783456
$447$	−21.7169	−1.02717
$448$	1.00000	0.0472456
$449$	−16.3807	−0.773054	−0.386527	−	0.922278i	$-0.626325\pi$
$449$	−16.3807	−0.773054	−0.386527	+	0.922278i	$0.626325\pi$
$450$	−2.34900	−0.110733
$451$	32.4329	1.52720
$452$	3.05928	0.143896
$453$	15.7360	0.739341
$454$	−28.8567	−1.35431
$455$	−12.7564	−0.598030
$456$	−8.49756	−0.397935
$457$	22.8146	1.06722	0.533612	−	0.845730i	$-0.320834\pi$
$457$	22.8146	1.06722	0.533612	+	0.845730i	$0.320834\pi$
$458$	22.4534	1.04918
$459$	−21.2009	−0.989573
$460$	−13.9491	−0.650380
$461$	17.0037	0.791940	0.395970	−	0.918263i	$-0.370408\pi$
$461$	17.0037	0.791940	0.395970	+	0.918263i	$0.370408\pi$
$462$	−6.26436	−0.291444
$463$	39.8590	1.85240	0.926201	−	0.377029i	$-0.123054\pi$
$463$	39.8590	1.85240	0.926201	+	0.377029i	$0.123054\pi$
$464$	−3.21888	−0.149433
$465$	−1.75382	−0.0813315
$466$	10.7532	0.498133
$467$	−39.6053	−1.83272	−0.916358	−	0.400360i	$-0.868885\pi$
$467$	−39.6053	−1.83272	−0.916358	+	0.400360i	$0.868885\pi$
$468$	4.18149	0.193290
$469$	−3.89893	−0.180036
$470$	13.1786	0.607881
$471$	21.3822	0.985239
$472$	−0.948157	−0.0436425
$473$	24.4899	1.12605
$474$	−15.8427	−0.727678
$475$	15.2563	0.700006
$476$	−3.75104	−0.171928
$477$	−10.1633	−0.465344
$478$	−11.9243	−0.545406
$479$	−37.3426	−1.70623	−0.853115	−	0.521724i	$-0.825289\pi$
$479$	−37.3426	−1.70623	−0.853115	+	0.521724i	$0.825289\pi$
$480$	−3.99140	−0.182182
$481$	−12.7127	−0.579648
$482$	7.32264	0.333537
$483$	7.32634	0.333360
$484$	7.71920	0.350873
$485$	−22.9917	−1.04400
$486$	−9.03246	−0.409721
$487$	−6.47668	−0.293487	−0.146743	−	0.989175i	$-0.546879\pi$
$487$	−6.47668	−0.293487	−0.146743	+	0.989175i	$0.546879\pi$
$488$	−0.397936	−0.0180137
$489$	−19.8268	−0.896599
$490$	2.75672	0.124536
$491$	6.64890	0.300061	0.150030	−	0.988681i	$-0.452063\pi$
$491$	6.64890	0.300061	0.150030	+	0.988681i	$0.452063\pi$
$492$	−10.8536	−0.489319
$493$	12.0742	0.543793
$494$	−27.1580	−1.22190
$495$	−10.7778	−0.484427
$496$	0.439400	0.0197297
$497$	13.1851	0.591434
$498$	−12.7850	−0.572908
$499$	21.8030	0.976035	0.488017	−	0.872834i	$-0.337720\pi$
$499$	21.8030	0.976035	0.488017	+	0.872834i	$0.337720\pi$
$500$	−6.61754	−0.295945
$501$	−12.6227	−0.563939
$502$	17.4159	0.777312
$503$	−21.6867	−0.966961	−0.483481	−	0.875355i	$-0.660628\pi$
$503$	−21.6867	−0.966961	−0.483481	+	0.875355i	$0.660628\pi$
$504$	−0.903639	−0.0402513
$505$	21.7053	0.965872
$506$	−21.8926	−0.973246
$507$	−12.1807	−0.540963
$508$	0.165133	0.00732661
$509$	14.0433	0.622458	0.311229	−	0.950335i	$-0.399259\pi$
$509$	14.0433	0.622458	0.311229	+	0.950335i	$0.399259\pi$
$510$	14.9719	0.662966
$511$	0.148892	0.00658658
$512$	1.00000	0.0441942
$513$	33.1714	1.46455
$514$	−21.9368	−0.967591
$515$	26.4659	1.16623
$516$	−8.19551	−0.360787
$517$	20.6833	0.909649
$518$	2.74726	0.120708
$519$	−14.9172	−0.654791
$520$	−12.7564	−0.559406
$521$	6.66792	0.292127	0.146063	−	0.989275i	$-0.453340\pi$
$521$	6.66792	0.292127	0.146063	+	0.989275i	$0.453340\pi$
$522$	2.90871	0.127311
$523$	−11.0117	−0.481506	−0.240753	−	0.970586i	$-0.577394\pi$
$523$	−11.0117	−0.481506	−0.240753	+	0.970586i	$0.577394\pi$
$524$	−21.7197	−0.948829
$525$	−3.76375	−0.164263
$526$	−16.6814	−0.727344
$527$	−1.64821	−0.0717970
$528$	−6.26436	−0.272621
$529$	2.60404	0.113219
$530$	31.0049	1.34677
$531$	0.856792	0.0371816
$532$	5.86896	0.254452
$533$	−34.6879	−1.50250
$534$	11.5209	0.498558
$535$	−39.1640	−1.69321
$536$	−3.89893	−0.168408
$537$	17.7352	0.765330
$538$	−9.71605	−0.418888
$539$	4.32657	0.186359
$540$	15.5810	0.670499
$541$	6.87188	0.295445	0.147723	−	0.989029i	$-0.452806\pi$
$541$	6.87188	0.295445	0.147723	+	0.989029i	$0.452806\pi$
$542$	7.53596	0.323697
$543$	−1.05136	−0.0451181
$544$	−3.75104	−0.160824
$545$	30.2263	1.29475
$546$	6.69992	0.286730
$547$	−40.6903	−1.73979	−0.869896	−	0.493235i	$-0.835814\pi$
$547$	−40.6903	−1.73979	−0.869896	+	0.493235i	$0.835814\pi$
$548$	21.3643	0.912636
$549$	0.359591	0.0153470
$550$	11.2469	0.479567
$551$	−18.8915	−0.804806
$552$	7.32634	0.311830
$553$	10.9420	0.465300
$554$	−24.5658	−1.04370
$555$	−10.9654	−0.465456
$556$	−2.43195	−0.103138
$557$	−31.6513	−1.34111	−0.670553	−	0.741861i	$-0.733943\pi$
$557$	−31.6513	−1.34111	−0.670553	+	0.741861i	$0.733943\pi$
$558$	−0.397059	−0.0168089
$559$	−26.1926	−1.10783
$560$	2.75672	0.116493
$561$	23.4978	0.992080
$562$	4.99545	0.210720
$563$	−24.2615	−1.02250	−0.511251	−	0.859431i	$-0.670818\pi$
$563$	−24.2615	−1.02250	−0.511251	+	0.859431i	$0.670818\pi$
$564$	−6.92163	−0.291453
$565$	8.43356	0.354803
$566$	9.50813	0.399657
$567$	−5.47252	−0.229824
$568$	13.1851	0.553236
$569$	−16.5841	−0.695240	−0.347620	−	0.937635i	$-0.613010\pi$
$569$	−16.5841	−0.695240	−0.347620	+	0.937635i	$0.613010\pi$
$570$	−23.4254	−0.981181
$571$	25.4221	1.06388	0.531941	−	0.846782i	$-0.321463\pi$
$571$	25.4221	1.06388	0.531941	+	0.846782i	$0.321463\pi$
$572$	−20.0207	−0.837109
$573$	−22.2361	−0.928926
$574$	7.49621	0.312886
$575$	−13.1535	−0.548539
$576$	−0.903639	−0.0376516
$577$	−36.8133	−1.53256	−0.766278	−	0.642509i	$-0.777893\pi$
$577$	−36.8133	−1.53256	−0.766278	+	0.642509i	$0.777893\pi$
$578$	−2.92973	−0.121861
$579$	4.63133	0.192472
$580$	−8.87355	−0.368454
$581$	8.83012	0.366335
$582$	12.0757	0.500554
$583$	48.6611	2.01534
$584$	0.148892	0.00616119
$585$	11.5272	0.476591
$586$	−8.23060	−0.340003
$587$	1.68394	0.0695037	0.0347518	−	0.999396i	$-0.488936\pi$
$587$	1.68394	0.0695037	0.0347518	+	0.999396i	$0.488936\pi$
$588$	−1.44788	−0.0597096
$589$	2.57882	0.106259
$590$	−2.61380	−0.107608
$591$	0.470247	0.0193434
$592$	2.74726	0.112912
$593$	40.2062	1.65107	0.825536	−	0.564350i	$-0.190873\pi$
$593$	40.2062	1.65107	0.825536	+	0.564350i	$0.190873\pi$
$594$	24.4538	1.00335
$595$	−10.3405	−0.423921
$596$	14.9991	0.614386
$597$	28.0241	1.14695
$598$	23.4148	0.957503
$599$	22.9947	0.939539	0.469770	−	0.882789i	$-0.344337\pi$
$599$	22.9947	0.939539	0.469770	+	0.882789i	$0.344337\pi$
$600$	−3.76375	−0.153654
$601$	14.6446	0.597365	0.298682	−	0.954353i	$-0.403453\pi$
$601$	14.6446	0.597365	0.298682	+	0.954353i	$0.403453\pi$
$602$	5.66034	0.230698
$603$	3.52323	0.143477
$604$	−10.8683	−0.442224
$605$	21.2796	0.865141
$606$	−11.4000	−0.463095
$607$	−2.49212	−0.101152	−0.0505760	−	0.998720i	$-0.516106\pi$
$607$	−2.49212	−0.101152	−0.0505760	+	0.998720i	$0.516106\pi$
$608$	5.86896	0.238018
$609$	4.66056	0.188856
$610$	−1.09700	−0.0444161
$611$	−22.1214	−0.894935
$612$	3.38958	0.137016
$613$	32.6504	1.31874	0.659368	−	0.751820i	$-0.270824\pi$
$613$	32.6504	1.31874	0.659368	+	0.751820i	$0.270824\pi$
$614$	−17.1144	−0.690681
$615$	−29.9204	−1.20651
$616$	4.32657	0.174322
$617$	−5.00547	−0.201513	−0.100756	−	0.994911i	$-0.532126\pi$
$617$	−5.00547	−0.201513	−0.100756	+	0.994911i	$0.532126\pi$
$618$	−13.9004	−0.559156
$619$	45.7667	1.83952	0.919759	−	0.392484i	$-0.128384\pi$
$619$	45.7667	1.83952	0.919759	+	0.392484i	$0.128384\pi$
$620$	1.21130	0.0486471
$621$	−28.5994	−1.14765
$622$	15.5969	0.625380
$623$	−7.95707	−0.318793
$624$	6.69992	0.268211
$625$	−31.2401	−1.24960
$626$	0.233621	0.00933736
$627$	−36.7653	−1.46826
$628$	−14.7679	−0.589304
$629$	−10.3051	−0.410891
$630$	−2.49108	−0.0992469
$631$	13.4177	0.534151	0.267076	−	0.963676i	$-0.413943\pi$
$631$	13.4177	0.534151	0.267076	+	0.963676i	$0.413943\pi$
$632$	10.9420	0.435248
$633$	−3.07382	−0.122173
$634$	−7.89876	−0.313700
$635$	0.455226	0.0180651
$636$	−16.2844	−0.645718
$637$	−4.62739	−0.183344
$638$	−13.9267	−0.551364
$639$	−11.9146	−0.471334
$640$	2.75672	0.108969
$641$	2.97406	0.117468	0.0587341	−	0.998274i	$-0.481294\pi$
$641$	2.97406	0.117468	0.0587341	+	0.998274i	$0.481294\pi$
$642$	20.5697	0.811821
$643$	−47.0613	−1.85592	−0.927958	−	0.372685i	$-0.878437\pi$
$643$	−47.0613	−1.85592	−0.927958	+	0.372685i	$0.878437\pi$
$644$	−5.06004	−0.199394
$645$	−22.5927	−0.889586
$646$	−22.0147	−0.866157
$647$	−41.6241	−1.63641	−0.818206	−	0.574925i	$-0.805031\pi$
$647$	−41.6241	−1.63641	−0.818206	+	0.574925i	$0.805031\pi$
$648$	−5.47252	−0.214981
$649$	−4.10227	−0.161028
$650$	−12.0288	−0.471810
$651$	−0.636200	−0.0249346
$652$	13.6937	0.536285
$653$	−13.9970	−0.547745	−0.273873	−	0.961766i	$-0.588305\pi$
$653$	−13.9970	−0.547745	−0.273873	+	0.961766i	$0.588305\pi$
$654$	−15.8754	−0.620778
$655$	−59.8750	−2.33951
$656$	7.49621	0.292678
$657$	−0.134544	−0.00524908
$658$	4.78053	0.186364
$659$	−18.7091	−0.728803	−0.364402	−	0.931242i	$-0.618726\pi$
$659$	−18.7091	−0.728803	−0.364402	+	0.931242i	$0.618726\pi$
$660$	−17.2691	−0.672197
$661$	38.1256	1.48292	0.741458	−	0.671000i	$-0.234135\pi$
$661$	38.1256	1.48292	0.741458	+	0.671000i	$0.234135\pi$
$662$	25.5828	0.994305
$663$	−25.1316	−0.976032
$664$	8.83012	0.342675
$665$	16.1791	0.627397
$666$	−2.48254	−0.0961963
$667$	16.2877	0.630662
$668$	8.71801	0.337310
$669$	−23.9560	−0.926194
$670$	−10.7482	−0.415241
$671$	−1.72170	−0.0664654
$672$	−1.44788	−0.0558532
$673$	1.78342	0.0687457	0.0343728	−	0.999409i	$-0.489057\pi$
$673$	1.78342	0.0687457	0.0343728	+	0.999409i	$0.489057\pi$
$674$	22.9800	0.885156
$675$	14.6923	0.565507
$676$	8.41277	0.323568
$677$	−0.0291993	−0.00112222	−0.000561110	−	1.00000i	$-0.500179\pi$
$677$	−0.0291993	−0.00112222	−0.000561110		1.00000i	$0.500179\pi$
$678$	−4.42947	−0.170113
$679$	−8.34025	−0.320069
$680$	−10.3405	−0.396542
$681$	41.7811	1.60106
$682$	1.90110	0.0727967
$683$	8.99621	0.344231	0.172115	−	0.985077i	$-0.444940\pi$
$683$	8.99621	0.344231	0.172115	+	0.985077i	$0.444940\pi$
$684$	−5.30343	−0.202782
$685$	58.8952	2.25027
$686$	1.00000	0.0381802
$687$	−32.5099	−1.24033
$688$	5.66034	0.215799
$689$	−52.0445	−1.98274
$690$	20.1967	0.768873
$691$	−49.2977	−1.87537	−0.937687	−	0.347481i	$-0.887037\pi$
$691$	−49.2977	−1.87537	−0.937687	+	0.347481i	$0.887037\pi$
$692$	10.3028	0.391652
$693$	−3.90966	−0.148516
$694$	−4.11193	−0.156087
$695$	−6.70420	−0.254305
$696$	4.66056	0.176658
$697$	−28.1186	−1.06507
$698$	−23.4625	−0.888070
$699$	−15.5694	−0.588888
$700$	2.59949	0.0982513
$701$	25.8234	0.975337	0.487669	−	0.873029i	$-0.337847\pi$
$701$	25.8234	0.975337	0.487669	+	0.873029i	$0.337847\pi$
$702$	−26.1541	−0.987121
$703$	16.1236	0.608113
$704$	4.32657	0.163064
$705$	−19.0810	−0.718631
$706$	−4.99789	−0.188098
$707$	7.87360	0.296117
$708$	1.37282	0.0515937
$709$	−31.4877	−1.18254	−0.591272	−	0.806472i	$-0.701374\pi$
$709$	−31.4877	−1.18254	−0.591272	+	0.806472i	$0.701374\pi$
$710$	36.3477	1.36410
$711$	−9.88760	−0.370814
$712$	−7.95707	−0.298204
$713$	−2.22339	−0.0832664
$714$	5.43106	0.203252
$715$	−55.1915	−2.06404
$716$	−12.2491	−0.457769
$717$	17.2650	0.644773
$718$	18.6006	0.694169
$719$	−5.43912	−0.202845	−0.101422	−	0.994843i	$-0.532339\pi$
$719$	−5.43912	−0.202845	−0.101422	+	0.994843i	$0.532339\pi$
$720$	−2.49108	−0.0928370
$721$	9.60051	0.357542
$722$	15.4447	0.574793
$723$	−10.6023	−0.394304
$724$	0.726135	0.0269866
$725$	−8.36744	−0.310759
$726$	−11.1765	−0.414798
$727$	−25.2355	−0.935933	−0.467966	−	0.883746i	$-0.655013\pi$
$727$	−25.2355	−0.935933	−0.467966	+	0.883746i	$0.655013\pi$
$728$	−4.62739	−0.171503
$729$	29.4955	1.09243
$730$	0.410452	0.0151915
$731$	−21.2322	−0.785300
$732$	0.576164	0.0212957
$733$	−29.3672	−1.08470	−0.542351	−	0.840152i	$-0.682466\pi$
$733$	−29.3672	−1.08470	−0.542351	+	0.840152i	$0.682466\pi$
$734$	−14.1981	−0.524060
$735$	−3.99140	−0.147225
$736$	−5.06004	−0.186516
$737$	−16.8690	−0.621377
$738$	−6.77387	−0.249350
$739$	40.7509	1.49905	0.749524	−	0.661978i	$-0.230283\pi$
$739$	40.7509	1.49905	0.749524	+	0.661978i	$0.230283\pi$
$740$	7.57343	0.278405
$741$	39.3216	1.44451
$742$	11.2470	0.412892
$743$	21.1845	0.777183	0.388592	−	0.921410i	$-0.372962\pi$
$743$	21.1845	0.777183	0.388592	+	0.921410i	$0.372962\pi$
$744$	−0.636200	−0.0233242
$745$	41.3482	1.51488
$746$	7.41169	0.271361
$747$	−7.97924	−0.291945
$748$	−16.2291	−0.593395
$749$	−14.2067	−0.519103
$750$	9.58141	0.349864
$751$	−27.3673	−0.998647	−0.499323	−	0.866416i	$-0.666418\pi$
$751$	−27.3673	−0.998647	−0.499323	+	0.866416i	$0.666418\pi$
$752$	4.78053	0.174328
$753$	−25.2162	−0.918930
$754$	14.8950	0.542446
$755$	−29.9608	−1.09038
$756$	5.65201	0.205562
$757$	15.0480	0.546930	0.273465	−	0.961882i	$-0.411830\pi$
$757$	15.0480	0.546930	0.273465	+	0.961882i	$0.411830\pi$
$758$	14.6123	0.530742
$759$	31.6979	1.15056
$760$	16.1791	0.586876
$761$	28.9007	1.04765	0.523825	−	0.851826i	$-0.324505\pi$
$761$	28.9007	1.04765	0.523825	+	0.851826i	$0.324505\pi$
$762$	−0.239094	−0.00866145
$763$	10.9646	0.396945
$764$	15.3577	0.555621
$765$	9.34412	0.337837
$766$	10.1805	0.367835
$767$	4.38749	0.158423
$768$	−1.44788	−0.0522459
$769$	−32.8502	−1.18461	−0.592303	−	0.805715i	$-0.701781\pi$
$769$	−32.8502	−1.18461	−0.592303	+	0.805715i	$0.701781\pi$
$770$	11.9271	0.429824
$771$	31.7619	1.14388
$772$	−3.19869	−0.115124
$773$	−40.9489	−1.47283	−0.736414	−	0.676531i	$-0.763482\pi$
$773$	−40.9489	−1.47283	−0.736414	+	0.676531i	$0.763482\pi$
$774$	−5.11491	−0.183852
$775$	1.14221	0.0410296
$776$	−8.34025	−0.299398
$777$	−3.97771	−0.142700
$778$	28.8509	1.03435
$779$	43.9950	1.57628
$780$	18.4698	0.661324
$781$	57.0464	2.04128
$782$	18.9804	0.678738
$783$	−18.1932	−0.650170
$784$	1.00000	0.0357143
$785$	−40.7109	−1.45304
$786$	31.4475	1.12170
$787$	19.5839	0.698090	0.349045	−	0.937106i	$-0.386506\pi$
$787$	19.5839	0.698090	0.349045	+	0.937106i	$0.386506\pi$
$788$	−0.324783	−0.0115699
$789$	24.1527	0.859859
$790$	30.1639	1.07318
$791$	3.05928	0.108775
$792$	−3.90966	−0.138924
$793$	1.84141	0.0653903
$794$	18.3918	0.652700
$795$	−44.8914	−1.59213
$796$	−19.3552	−0.686027
$797$	−15.5736	−0.551645	−0.275822	−	0.961209i	$-0.588950\pi$
$797$	−15.5736	−0.551645	−0.275822	+	0.961209i	$0.588950\pi$
$798$	−8.49756	−0.300810
$799$	−17.9319	−0.634386
$800$	2.59949	0.0919057
$801$	7.19032	0.254057
$802$	4.59899	0.162396
$803$	0.644191	0.0227330
$804$	5.64519	0.199090
$805$	−13.9491	−0.491641
$806$	−2.03328	−0.0716192
$807$	14.0677	0.495206
$808$	7.87360	0.276992
$809$	13.0279	0.458038	0.229019	−	0.973422i	$-0.426448\pi$
$809$	13.0279	0.458038	0.229019	+	0.973422i	$0.426448\pi$
$810$	−15.0862	−0.530074
$811$	10.3332	0.362849	0.181424	−	0.983405i	$-0.441929\pi$
$811$	10.3332	0.362849	0.181424	+	0.983405i	$0.441929\pi$
$812$	−3.21888	−0.112961
$813$	−10.9112	−0.382672
$814$	11.8862	0.416612
$815$	37.7495	1.32231
$816$	5.43106	0.190125
$817$	33.2203	1.16223
$818$	24.9279	0.871584
$819$	4.18149	0.146113
$820$	20.6649	0.721650
$821$	−27.4072	−0.956518	−0.478259	−	0.878219i	$-0.658732\pi$
$821$	−27.4072	−0.956518	−0.478259	+	0.878219i	$0.658732\pi$
$822$	−30.9329	−1.07891
$823$	38.4548	1.34045	0.670224	−	0.742159i	$-0.266198\pi$
$823$	38.4548	1.34045	0.670224	+	0.742159i	$0.266198\pi$
$824$	9.60051	0.334449
$825$	−16.2841	−0.566940
$826$	−0.948157	−0.0329906
$827$	11.1652	0.388251	0.194125	−	0.980977i	$-0.437813\pi$
$827$	11.1652	0.388251	0.194125	+	0.980977i	$0.437813\pi$
$828$	4.57245	0.158904
$829$	−24.4840	−0.850364	−0.425182	−	0.905108i	$-0.639790\pi$
$829$	−24.4840	−0.850364	−0.425182	+	0.905108i	$0.639790\pi$
$830$	24.3421	0.844928
$831$	35.5684	1.23385
$832$	−4.62739	−0.160426
$833$	−3.75104	−0.129966
$834$	3.52118	0.121928
$835$	24.0331	0.831700
$836$	25.3925	0.878217
$837$	2.48349	0.0858421
$838$	−13.1331	−0.453676
$839$	−24.4054	−0.842567	−0.421284	−	0.906929i	$-0.638420\pi$
$839$	−24.4054	−0.842567	−0.421284	+	0.906929i	$0.638420\pi$
$840$	−3.99140	−0.137716
$841$	−18.6388	−0.642717
$842$	−33.5376	−1.15578
$843$	−7.23282	−0.249112
$844$	2.12298	0.0730759
$845$	23.1916	0.797816
$846$	−4.31987	−0.148520
$847$	7.71920	0.265235
$848$	11.2470	0.386225
$849$	−13.7667	−0.472470
$850$	−9.75077	−0.334448
$851$	−13.9013	−0.476530
$852$	−19.0905	−0.654030
$853$	−52.6601	−1.80305	−0.901524	−	0.432730i	$-0.857550\pi$
$853$	−52.6601	−1.80305	−0.901524	+	0.432730i	$0.857550\pi$
$854$	−0.397936	−0.0136171
$855$	−14.6200	−0.499995
$856$	−14.2067	−0.485577
$857$	−14.3098	−0.488813	−0.244407	−	0.969673i	$-0.578593\pi$
$857$	−14.3098	−0.488813	−0.244407	+	0.969673i	$0.578593\pi$
$858$	28.9877	0.989622
$859$	41.2115	1.40612	0.703060	−	0.711131i	$-0.251817\pi$
$859$	41.2115	1.40612	0.703060	+	0.711131i	$0.251817\pi$
$860$	15.6040	0.532091
$861$	−10.8536	−0.369890
$862$	1.00000	0.0340601
$863$	−5.66377	−0.192797	−0.0963985	−	0.995343i	$-0.530732\pi$
$863$	−5.66377	−0.192797	−0.0963985	+	0.995343i	$0.530732\pi$
$864$	5.65201	0.192285
$865$	28.4018	0.965690
$866$	25.5889	0.869545
$867$	4.24190	0.144062
$868$	0.439400	0.0149142
$869$	47.3412	1.60594
$870$	12.8479	0.435583
$871$	18.0419	0.611326
$872$	10.9646	0.371308
$873$	7.53658	0.255075
$874$	−29.6972	−1.00452
$875$	−6.61754	−0.223714
$876$	−0.215578	−0.00728369
$877$	−17.0369	−0.575297	−0.287648	−	0.957736i	$-0.592873\pi$
$877$	−17.0369	−0.575297	−0.287648	+	0.957736i	$0.592873\pi$
$878$	−15.2311	−0.514025
$879$	11.9169	0.401948
$880$	11.9271	0.402063
$881$	−23.6226	−0.795867	−0.397934	−	0.917414i	$-0.630273\pi$
$881$	−23.6226	−0.795867	−0.397934	+	0.917414i	$0.630273\pi$
$882$	−0.903639	−0.0304271
$883$	−38.9673	−1.31135	−0.655676	−	0.755042i	$-0.727616\pi$
$883$	−38.9673	−1.31135	−0.655676	+	0.755042i	$0.727616\pi$
$884$	17.3575	0.583797
$885$	3.78447	0.127214
$886$	−24.4037	−0.819860
$887$	15.6372	0.525046	0.262523	−	0.964926i	$-0.415445\pi$
$887$	15.6372	0.525046	0.262523	+	0.964926i	$0.415445\pi$
$888$	−3.97771	−0.133483
$889$	0.165133	0.00553840
$890$	−21.9354	−0.735276
$891$	−23.6772	−0.793217
$892$	16.5456	0.553987
$893$	28.0567	0.938883
$894$	−21.7169	−0.726321
$895$	−33.7672	−1.12871
$896$	1.00000	0.0334077
$897$	−33.9019	−1.13195
$898$	−16.3807	−0.546632
$899$	−1.41438	−0.0471722
$900$	−2.34900	−0.0782999
$901$	−42.1881	−1.40549
$902$	32.4329	1.07990
$903$	−8.19551	−0.272729
$904$	3.05928	0.101750
$905$	2.00175	0.0665404
$906$	15.7360	0.522793
$907$	−12.2571	−0.406992	−0.203496	−	0.979076i	$-0.565230\pi$
$907$	−12.2571	−0.406992	−0.203496	+	0.979076i	$0.565230\pi$
$908$	−28.8567	−0.957644
$909$	−7.11489	−0.235986
$910$	−12.7564	−0.422871
$911$	−37.6371	−1.24697	−0.623486	−	0.781835i	$-0.714284\pi$
$911$	−37.6371	−1.24697	−0.623486	+	0.781835i	$0.714284\pi$
$912$	−8.49756	−0.281382
$913$	38.2041	1.26437
$914$	22.8146	0.754641
$915$	1.58832	0.0525083
$916$	22.4534	0.741882
$917$	−21.7197	−0.717248
$918$	−21.2009	−0.699733
$919$	23.1580	0.763912	0.381956	−	0.924181i	$-0.375251\pi$
$919$	23.1580	0.763912	0.381956	+	0.924181i	$0.375251\pi$
$920$	−13.9491	−0.459888
$921$	24.7796	0.816516
$922$	17.0037	0.559986
$923$	−61.0128	−2.00826
$924$	−6.26436	−0.206082
$925$	7.14147	0.234810
$926$	39.8590	1.30985
$927$	−8.67539	−0.284937
$928$	−3.21888	−0.105665
$929$	25.0551	0.822031	0.411015	−	0.911628i	$-0.365174\pi$
$929$	25.0551	0.822031	0.411015	+	0.911628i	$0.365174\pi$
$930$	−1.75382	−0.0575101
$931$	5.86896	0.192347
$932$	10.7532	0.352233
$933$	−22.5825	−0.739318
$934$	−39.6053	−1.29593
$935$	−44.7391	−1.46312
$936$	4.18149	0.136676
$937$	−54.3882	−1.77678	−0.888392	−	0.459086i	$-0.848177\pi$
$937$	−54.3882	−1.77678	−0.888392	+	0.459086i	$0.848177\pi$
$938$	−3.89893	−0.127305
$939$	−0.338255	−0.0110385
$940$	13.1786	0.429837
$941$	8.58663	0.279916	0.139958	−	0.990157i	$-0.455303\pi$
$941$	8.58663	0.279916	0.139958	+	0.990157i	$0.455303\pi$
$942$	21.3822	0.696669
$943$	−37.9311	−1.23521
$944$	−0.948157	−0.0308599
$945$	15.5810	0.506849
$946$	24.4899	0.796234
$947$	41.0731	1.33469	0.667347	−	0.744747i	$-0.267430\pi$
$947$	41.0731	1.33469	0.667347	+	0.744747i	$0.267430\pi$
$948$	−15.8427	−0.514546
$949$	−0.688981	−0.0223653
$950$	15.2563	0.494979
$951$	11.4365	0.370853
$952$	−3.75104	−0.121572
$953$	−19.9005	−0.644642	−0.322321	−	0.946630i	$-0.604463\pi$
$953$	−19.9005	−0.644642	−0.322321	+	0.946630i	$0.604463\pi$
$954$	−10.1633	−0.329048
$955$	42.3368	1.36999
$956$	−11.9243	−0.385660
$957$	20.1643	0.651818
$958$	−37.3426	−1.20649
$959$	21.3643	0.689888
$960$	−3.99140	−0.128822
$961$	−30.8069	−0.993772
$962$	−12.7127	−0.409873
$963$	12.8378	0.413692
$964$	7.32264	0.235846
$965$	−8.81789	−0.283858
$966$	7.32634	0.235721
$967$	−40.5073	−1.30263	−0.651314	−	0.758808i	$-0.725782\pi$
$967$	−40.5073	−1.30263	−0.651314	+	0.758808i	$0.725782\pi$
$968$	7.71920	0.248104
$969$	31.8747	1.02396
$970$	−22.9917	−0.738219
$971$	−18.8279	−0.604215	−0.302108	−	0.953274i	$-0.597690\pi$
$971$	−18.8279	−0.604215	−0.302108	+	0.953274i	$0.597690\pi$
$972$	−9.03246	−0.289716
$973$	−2.43195	−0.0779647
$974$	−6.47668	−0.207526
$975$	17.4163	0.557769
$976$	−0.397936	−0.0127376
$977$	47.1838	1.50954	0.754772	−	0.655987i	$-0.227747\pi$
$977$	47.1838	1.50954	0.754772	+	0.655987i	$0.227747\pi$
$978$	−19.8268	−0.633991
$979$	−34.4268	−1.10029
$980$	2.75672	0.0880601
$981$	−9.90804	−0.316339
$982$	6.64890	0.212175
$983$	−38.8399	−1.23880	−0.619400	−	0.785076i	$-0.712624\pi$
$983$	−38.8399	−1.23880	−0.619400	+	0.785076i	$0.712624\pi$
$984$	−10.8536	−0.346001
$985$	−0.895335	−0.0285277
$986$	12.0742	0.384519
$987$	−6.92163	−0.220318
$988$	−27.1580	−0.864011
$989$	−28.6416	−0.910750
$990$	−10.7778	−0.342542
$991$	−48.0981	−1.52789	−0.763943	−	0.645283i	$-0.776739\pi$
$991$	−48.0981	−1.52789	−0.763943	+	0.645283i	$0.776739\pi$
$992$	0.439400	0.0139510
$993$	−37.0409	−1.17546
$994$	13.1851	0.418207
$995$	−53.3568	−1.69153
$996$	−12.7850	−0.405107
$997$	−2.04431	−0.0647441	−0.0323720	−	0.999476i	$-0.510306\pi$
$997$	−2.04431	−0.0647441	−0.0323720	+	0.999476i	$0.510306\pi$
$998$	21.8030	0.690161
$999$	15.5276	0.491270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.q.1.9	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.q.1.9	✓	31	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.44788 q^{3} +1.00000 q^{4} +2.75672 q^{5} -1.44788 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.903639 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.44788 q^{3} +1.00000 q^{4} +2.75672 q^{5} -1.44788 q^{6} +1.00000 q^{7} +1.00000 q^{8} -0.903639 q^{9} +2.75672 q^{10} +4.32657 q^{11} -1.44788 q^{12} -4.62739 q^{13} +1.00000 q^{14} -3.99140 q^{15} +1.00000 q^{16} -3.75104 q^{17} -0.903639 q^{18} +5.86896 q^{19} +2.75672 q^{20} -1.44788 q^{21} +4.32657 q^{22} -5.06004 q^{23} -1.44788 q^{24} +2.59949 q^{25} -4.62739 q^{26} +5.65201 q^{27} +1.00000 q^{28} -3.21888 q^{29} -3.99140 q^{30} +0.439400 q^{31} +1.00000 q^{32} -6.26436 q^{33} -3.75104 q^{34} +2.75672 q^{35} -0.903639 q^{36} +2.74726 q^{37} +5.86896 q^{38} +6.69992 q^{39} +2.75672 q^{40} +7.49621 q^{41} -1.44788 q^{42} +5.66034 q^{43} +4.32657 q^{44} -2.49108 q^{45} -5.06004 q^{46} +4.78053 q^{47} -1.44788 q^{48} +1.00000 q^{49} +2.59949 q^{50} +5.43106 q^{51} -4.62739 q^{52} +11.2470 q^{53} +5.65201 q^{54} +11.9271 q^{55} +1.00000 q^{56} -8.49756 q^{57} -3.21888 q^{58} -0.948157 q^{59} -3.99140 q^{60} -0.397936 q^{61} +0.439400 q^{62} -0.903639 q^{63} +1.00000 q^{64} -12.7564 q^{65} -6.26436 q^{66} -3.89893 q^{67} -3.75104 q^{68} +7.32634 q^{69} +2.75672 q^{70} +13.1851 q^{71} -0.903639 q^{72} +0.148892 q^{73} +2.74726 q^{74} -3.76375 q^{75} +5.86896 q^{76} +4.32657 q^{77} +6.69992 q^{78} +10.9420 q^{79} +2.75672 q^{80} -5.47252 q^{81} +7.49621 q^{82} +8.83012 q^{83} -1.44788 q^{84} -10.3405 q^{85} +5.66034 q^{86} +4.66056 q^{87} +4.32657 q^{88} -7.95707 q^{89} -2.49108 q^{90} -4.62739 q^{91} -5.06004 q^{92} -0.636200 q^{93} +4.78053 q^{94} +16.1791 q^{95} -1.44788 q^{96} -8.34025 q^{97} +1.00000 q^{98} -3.90966 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9	\( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 2 * q^3 + 31 * q^4 + 13 * q^5 + 2 * q^6 + 31 * q^7 + 31 * q^8 + 43 * q^9 + 13 * q^10 + 28 * q^11 + 2 * q^12 + 23 * q^13 + 31 * q^14 + 12 * q^15 + 31 * q^16 + 15 * q^17 + 43 * q^18 + 5 * q^19 + 13 * q^20 + 2 * q^21 + 28 * q^22 + 16 * q^23 + 2 * q^24 + 66 * q^25 + 23 * q^26 + 29 * q^27 + 31 * q^28 + 30 * q^29 + 12 * q^30 + 7 * q^31 + 31 * q^32 - 7 * q^33 + 15 * q^34 + 13 * q^35 + 43 * q^36 + 26 * q^37 + 5 * q^38 + 25 * q^39 + 13 * q^40 + 23 * q^41 + 2 * q^42 + 29 * q^43 + 28 * q^44 + 13 * q^45 + 16 * q^46 + q^47 + 2 * q^48 + 31 * q^49 + 66 * q^50 + 15 * q^51 + 23 * q^52 + 47 * q^53 + 29 * q^54 - 21 * q^55 + 31 * q^56 - 4 * q^57 + 30 * q^58 + 12 * q^59 + 12 * q^60 + q^61 + 7 * q^62 + 43 * q^63 + 31 * q^64 + 42 * q^65 - 7 * q^66 + 40 * q^67 + 15 * q^68 - 25 * q^69 + 13 * q^70 + 32 * q^71 + 43 * q^72 + 9 * q^73 + 26 * q^74 + 13 * q^75 + 5 * q^76 + 28 * q^77 + 25 * q^78 - 9 * q^79 + 13 * q^80 + 63 * q^81 + 23 * q^82 + 7 * q^83 + 2 * q^84 + 32 * q^85 + 29 * q^86 - 53 * q^87 + 28 * q^88 + 61 * q^89 + 13 * q^90 + 23 * q^91 + 16 * q^92 + 3 * q^93 + q^94 + 17 * q^95 + 2 * q^96 + 28 * q^97 + 31 * q^98 + 54 * q^99

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