LMFDB - Embedded newform 7942.2.a.bz.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 27 x^{13} + 83 x^{12} + 264 x^{11} - 828 x^{10} - 1171 x^{9} + 3624 x^{8} + 2634 x^{7} + \cdots - 8 $ x^15 - 3x^14 - 27x^13 + 83x^12 + 264x^11 - 828x^10 - 1171x^9 + 3624x^8 + 2634x^7 - 6798x^6 - 3621x^5 + 3936x^4 + 3195x^3 + 618x^2 - 12x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.0975736$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.0975736 q^{3} +1.00000 q^{4} +1.88847 q^{5} +0.0975736 q^{6} -3.81151 q^{7} -1.00000 q^{8} -2.99048 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.0975736 q^{3} +1.00000 q^{4} +1.88847 q^{5} +0.0975736 q^{6} -3.81151 q^{7} -1.00000 q^{8} -2.99048 q^{9} -1.88847 q^{10} +1.00000 q^{11} -0.0975736 q^{12} -6.37439 q^{13} +3.81151 q^{14} -0.184265 q^{15} +1.00000 q^{16} +2.53921 q^{17} +2.99048 q^{18} +1.88847 q^{20} +0.371903 q^{21} -1.00000 q^{22} -4.56852 q^{23} +0.0975736 q^{24} -1.43368 q^{25} +6.37439 q^{26} +0.584512 q^{27} -3.81151 q^{28} +1.96697 q^{29} +0.184265 q^{30} -10.1025 q^{31} -1.00000 q^{32} -0.0975736 q^{33} -2.53921 q^{34} -7.19793 q^{35} -2.99048 q^{36} +6.50021 q^{37} +0.621972 q^{39} -1.88847 q^{40} -1.18698 q^{41} -0.371903 q^{42} +9.70779 q^{43} +1.00000 q^{44} -5.64743 q^{45} +4.56852 q^{46} +0.143539 q^{47} -0.0975736 q^{48} +7.52760 q^{49} +1.43368 q^{50} -0.247760 q^{51} -6.37439 q^{52} +3.50282 q^{53} -0.584512 q^{54} +1.88847 q^{55} +3.81151 q^{56} -1.96697 q^{58} -9.30356 q^{59} -0.184265 q^{60} -6.68403 q^{61} +10.1025 q^{62} +11.3982 q^{63} +1.00000 q^{64} -12.0379 q^{65} +0.0975736 q^{66} -9.40066 q^{67} +2.53921 q^{68} +0.445767 q^{69} +7.19793 q^{70} -9.48963 q^{71} +2.99048 q^{72} +3.62336 q^{73} -6.50021 q^{74} +0.139889 q^{75} -3.81151 q^{77} -0.621972 q^{78} -0.848108 q^{79} +1.88847 q^{80} +8.91441 q^{81} +1.18698 q^{82} -2.01595 q^{83} +0.371903 q^{84} +4.79523 q^{85} -9.70779 q^{86} -0.191924 q^{87} -1.00000 q^{88} -2.48263 q^{89} +5.64743 q^{90} +24.2961 q^{91} -4.56852 q^{92} +0.985734 q^{93} -0.143539 q^{94} +0.0975736 q^{96} -14.7837 q^{97} -7.52760 q^{98} -2.99048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 12 q^{7} - 15 q^{8} + 18 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 12 * q^7 - 15 * q^8 + 18 * q^9	\( 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 12 q^{7} - 15 q^{8} + 18 q^{9} - 9 q^{10} + 15 q^{11} - 3 q^{12} - 12 q^{14} + 9 q^{15} + 15 q^{16} + 21 q^{17} - 18 q^{18} + 9 q^{20} + 27 q^{21} - 15 q^{22} + 21 q^{23} + 3 q^{24} + 36 q^{25} - 3 q^{27} + 12 q^{28} + 15 q^{29} - 9 q^{30} - 30 q^{31} - 15 q^{32} - 3 q^{33} - 21 q^{34} + 30 q^{35} + 18 q^{36} + 9 q^{37} - 9 q^{40} - 9 q^{41} - 27 q^{42} + 33 q^{43} + 15 q^{44} + 18 q^{45} - 21 q^{46} + 39 q^{47} - 3 q^{48} + 33 q^{49} - 36 q^{50} - 6 q^{51} + 6 q^{53} + 3 q^{54} + 9 q^{55} - 12 q^{56} - 15 q^{58} + 6 q^{59} + 9 q^{60} + 36 q^{61} + 30 q^{62} + 30 q^{63} + 15 q^{64} - 18 q^{65} + 3 q^{66} - 15 q^{67} + 21 q^{68} - 48 q^{69} - 30 q^{70} + 3 q^{71} - 18 q^{72} + 60 q^{73} - 9 q^{74} - 21 q^{75} + 12 q^{77} - 18 q^{79} + 9 q^{80} + 27 q^{81} + 9 q^{82} + 36 q^{83} + 27 q^{84} + 15 q^{85} - 33 q^{86} + 21 q^{87} - 15 q^{88} - 6 q^{89} - 18 q^{90} + 18 q^{91} + 21 q^{92} - 54 q^{93} - 39 q^{94} + 3 q^{96} - 33 q^{98} + 18 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 12 * q^7 - 15 * q^8 + 18 * q^9 - 9 * q^10 + 15 * q^11 - 3 * q^12 - 12 * q^14 + 9 * q^15 + 15 * q^16 + 21 * q^17 - 18 * q^18 + 9 * q^20 + 27 * q^21 - 15 * q^22 + 21 * q^23 + 3 * q^24 + 36 * q^25 - 3 * q^27 + 12 * q^28 + 15 * q^29 - 9 * q^30 - 30 * q^31 - 15 * q^32 - 3 * q^33 - 21 * q^34 + 30 * q^35 + 18 * q^36 + 9 * q^37 - 9 * q^40 - 9 * q^41 - 27 * q^42 + 33 * q^43 + 15 * q^44 + 18 * q^45 - 21 * q^46 + 39 * q^47 - 3 * q^48 + 33 * q^49 - 36 * q^50 - 6 * q^51 + 6 * q^53 + 3 * q^54 + 9 * q^55 - 12 * q^56 - 15 * q^58 + 6 * q^59 + 9 * q^60 + 36 * q^61 + 30 * q^62 + 30 * q^63 + 15 * q^64 - 18 * q^65 + 3 * q^66 - 15 * q^67 + 21 * q^68 - 48 * q^69 - 30 * q^70 + 3 * q^71 - 18 * q^72 + 60 * q^73 - 9 * q^74 - 21 * q^75 + 12 * q^77 - 18 * q^79 + 9 * q^80 + 27 * q^81 + 9 * q^82 + 36 * q^83 + 27 * q^84 + 15 * q^85 - 33 * q^86 + 21 * q^87 - 15 * q^88 - 6 * q^89 - 18 * q^90 + 18 * q^91 + 21 * q^92 - 54 * q^93 - 39 * q^94 + 3 * q^96 - 33 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.0975736	−0.0563341	−0.0281671	−	0.999603i	$-0.508967\pi$
$3$	−0.0975736	−0.0563341	−0.0281671	+	0.999603i	$0.508967\pi$
$4$	1.00000	0.500000
$5$	1.88847	0.844550	0.422275	−	0.906468i	$-0.361232\pi$
$5$	1.88847	0.844550	0.422275	+	0.906468i	$0.361232\pi$
$6$	0.0975736	0.0398342
$7$	−3.81151	−1.44062	−0.720308	−	0.693655i	$-0.755999\pi$
$7$	−3.81151	−1.44062	−0.720308	+	0.693655i	$0.755999\pi$
$8$	−1.00000	−0.353553
$9$	−2.99048	−0.996826
$10$	−1.88847	−0.597187
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.0975736	−0.0281671
$13$	−6.37439	−1.76794	−0.883969	−	0.467545i	$-0.845139\pi$
$13$	−6.37439	−1.76794	−0.883969	+	0.467545i	$0.845139\pi$
$14$	3.81151	1.01867
$15$	−0.184265	−0.0475770
$16$	1.00000	0.250000
$17$	2.53921	0.615850	0.307925	−	0.951411i	$-0.400365\pi$
$17$	2.53921	0.615850	0.307925	+	0.951411i	$0.400365\pi$
$18$	2.99048	0.704863
$19$	0	0
$19$	0	0
$20$	1.88847	0.422275
$21$	0.371903	0.0811558
$22$	−1.00000	−0.213201
$23$	−4.56852	−0.952602	−0.476301	−	0.879282i	$-0.658023\pi$
$23$	−4.56852	−0.952602	−0.476301	+	0.879282i	$0.658023\pi$
$24$	0.0975736	0.0199171
$25$	−1.43368	−0.286735
$26$	6.37439	1.25012
$27$	0.584512	0.112489
$28$	−3.81151	−0.720308
$29$	1.96697	0.365256	0.182628	−	0.983182i	$-0.441540\pi$
$29$	1.96697	0.365256	0.182628	+	0.983182i	$0.441540\pi$
$30$	0.184265	0.0336420
$31$	−10.1025	−1.81446	−0.907228	−	0.420639i	$-0.861806\pi$
$31$	−10.1025	−1.81446	−0.907228	+	0.420639i	$0.861806\pi$
$32$	−1.00000	−0.176777
$33$	−0.0975736	−0.0169854
$34$	−2.53921	−0.435471
$35$	−7.19793	−1.21667
$36$	−2.99048	−0.498413
$37$	6.50021	1.06863	0.534314	−	0.845286i	$-0.320570\pi$
$37$	6.50021	1.06863	0.534314	+	0.845286i	$0.320570\pi$
$38$	0	0
$39$	0.621972	0.0995953
$40$	−1.88847	−0.298594
$41$	−1.18698	−0.185375	−0.0926873	−	0.995695i	$-0.529546\pi$
$41$	−1.18698	−0.185375	−0.0926873	+	0.995695i	$0.529546\pi$
$42$	−0.371903	−0.0573858
$43$	9.70779	1.48042	0.740212	−	0.672373i	$-0.234725\pi$
$43$	9.70779	1.48042	0.740212	+	0.672373i	$0.234725\pi$
$44$	1.00000	0.150756
$45$	−5.64743	−0.841870
$46$	4.56852	0.673592
$47$	0.143539	0.0209374	0.0104687	−	0.999945i	$-0.496668\pi$
$47$	0.143539	0.0209374	0.0104687	+	0.999945i	$0.496668\pi$
$48$	−0.0975736	−0.0140835
$49$	7.52760	1.07537
$50$	1.43368	0.202752
$51$	−0.247760	−0.0346934
$52$	−6.37439	−0.883969
$53$	3.50282	0.481149	0.240575	−	0.970631i	$-0.422664\pi$
$53$	3.50282	0.481149	0.240575	+	0.970631i	$0.422664\pi$
$54$	−0.584512	−0.0795421
$55$	1.88847	0.254641
$56$	3.81151	0.509334
$57$	0	0
$58$	−1.96697	−0.258275
$59$	−9.30356	−1.21122	−0.605610	−	0.795761i	$-0.707071\pi$
$59$	−9.30356	−1.21122	−0.605610	+	0.795761i	$0.707071\pi$
$60$	−0.184265	−0.0237885
$61$	−6.68403	−0.855803	−0.427901	−	0.903825i	$-0.640747\pi$
$61$	−6.68403	−0.855803	−0.427901	+	0.903825i	$0.640747\pi$
$62$	10.1025	1.28301
$63$	11.3982	1.43604
$64$	1.00000	0.125000
$65$	−12.0379	−1.49311
$66$	0.0975736	0.0120105
$67$	−9.40066	−1.14847	−0.574237	−	0.818689i	$-0.694701\pi$
$67$	−9.40066	−1.14847	−0.574237	+	0.818689i	$0.694701\pi$
$68$	2.53921	0.307925
$69$	0.445767	0.0536640
$70$	7.19793	0.860317
$71$	−9.48963	−1.12621	−0.563106	−	0.826385i	$-0.690394\pi$
$71$	−9.48963	−1.12621	−0.563106	+	0.826385i	$0.690394\pi$
$72$	2.99048	0.352431
$73$	3.62336	0.424082	0.212041	−	0.977261i	$-0.431989\pi$
$73$	3.62336	0.424082	0.212041	+	0.977261i	$0.431989\pi$
$74$	−6.50021	−0.755635
$75$	0.139889	0.0161530
$76$	0	0
$77$	−3.81151	−0.434362
$78$	−0.621972	−0.0704245
$79$	−0.848108	−0.0954196	−0.0477098	−	0.998861i	$-0.515192\pi$
$79$	−0.848108	−0.0954196	−0.0477098	+	0.998861i	$0.515192\pi$
$80$	1.88847	0.211138
$81$	8.91441	0.990489
$82$	1.18698	0.131080
$83$	−2.01595	−0.221279	−0.110639	−	0.993861i	$-0.535290\pi$
$83$	−2.01595	−0.221279	−0.110639	+	0.993861i	$0.535290\pi$
$84$	0.371903	0.0405779
$85$	4.79523	0.520116
$86$	−9.70779	−1.04682
$87$	−0.191924	−0.0205764
$88$	−1.00000	−0.106600
$89$	−2.48263	−0.263158	−0.131579	−	0.991306i	$-0.542005\pi$
$89$	−2.48263	−0.263158	−0.131579	+	0.991306i	$0.542005\pi$
$90$	5.64743	0.595292
$91$	24.2961	2.54692
$92$	−4.56852	−0.476301
$93$	0.985734	0.102216
$94$	−0.143539	−0.0148050
$95$	0	0
$96$	0.0975736	0.00995856
$97$	−14.7837	−1.50106	−0.750531	−	0.660836i	$-0.770202\pi$
$97$	−14.7837	−1.50106	−0.750531	+	0.660836i	$0.770202\pi$
$98$	−7.52760	−0.760403
$99$	−2.99048	−0.300554
$100$	−1.43368	−0.143368
$101$	4.47356	0.445136	0.222568	−	0.974917i	$-0.428556\pi$
$101$	4.47356	0.445136	0.222568	+	0.974917i	$0.428556\pi$
$102$	0.247760	0.0245319
$103$	13.6015	1.34020	0.670099	−	0.742271i	$-0.266251\pi$
$103$	13.6015	1.34020	0.670099	+	0.742271i	$0.266251\pi$
$104$	6.37439	0.625061
$105$	0.702327	0.0685401
$106$	−3.50282	−0.340224
$107$	−4.27832	−0.413601	−0.206800	−	0.978383i	$-0.566305\pi$
$107$	−4.27832	−0.413601	−0.206800	+	0.978383i	$0.566305\pi$
$108$	0.584512	0.0562447
$109$	12.8440	1.23023	0.615115	−	0.788438i	$-0.289110\pi$
$109$	12.8440	1.23023	0.615115	+	0.788438i	$0.289110\pi$
$110$	−1.88847	−0.180059
$111$	−0.634249	−0.0602003
$112$	−3.81151	−0.360154
$113$	−14.6855	−1.38150	−0.690748	−	0.723096i	$-0.742719\pi$
$113$	−14.6855	−1.38150	−0.690748	+	0.723096i	$0.742719\pi$
$114$	0	0
$115$	−8.62752	−0.804520
$116$	1.96697	0.182628
$117$	19.0625	1.76233
$118$	9.30356	0.856463
$119$	−9.67823	−0.887202
$120$	0.184265	0.0168210
$121$	1.00000	0.0909091
$122$	6.68403	0.605144
$123$	0.115818	0.0104429
$124$	−10.1025	−0.907228
$125$	−12.1498	−1.08671
$126$	−11.3982	−1.01544
$127$	11.6672	1.03529	0.517647	−	0.855594i	$-0.326808\pi$
$127$	11.6672	1.03529	0.517647	+	0.855594i	$0.326808\pi$
$128$	−1.00000	−0.0883883
$129$	−0.947224	−0.0833984
$130$	12.0379	1.05579
$131$	2.55270	0.223031	0.111515	−	0.993763i	$-0.464430\pi$
$131$	2.55270	0.223031	0.111515	+	0.993763i	$0.464430\pi$
$132$	−0.0975736	−0.00849269
$133$	0	0
$134$	9.40066	0.812094
$135$	1.10384	0.0950030
$136$	−2.53921	−0.217736
$137$	14.2058	1.21369	0.606843	−	0.794822i	$-0.292436\pi$
$137$	14.2058	1.21369	0.606843	+	0.794822i	$0.292436\pi$
$138$	−0.445767	−0.0379462
$139$	12.9499	1.09839	0.549197	−	0.835693i	$-0.314934\pi$
$139$	12.9499	1.09839	0.549197	+	0.835693i	$0.314934\pi$
$140$	−7.19793	−0.608336
$141$	−0.0140057	−0.00117949
$142$	9.48963	0.796352
$143$	−6.37439	−0.533053
$144$	−2.99048	−0.249207
$145$	3.71456	0.308477
$146$	−3.62336	−0.299871
$147$	−0.734495	−0.0605801
$148$	6.50021	0.534314
$149$	−17.3979	−1.42530	−0.712648	−	0.701522i	$-0.752504\pi$
$149$	−17.3979	−1.42530	−0.712648	+	0.701522i	$0.752504\pi$
$150$	−0.139889	−0.0114219
$151$	0.263312	0.0214280	0.0107140	−	0.999943i	$-0.496590\pi$
$151$	0.263312	0.0214280	0.0107140	+	0.999943i	$0.496590\pi$
$152$	0	0
$153$	−7.59346	−0.613895
$154$	3.81151	0.307140
$155$	−19.0782	−1.53240
$156$	0.621972	0.0497976
$157$	8.03667	0.641396	0.320698	−	0.947181i	$-0.396083\pi$
$157$	8.03667	0.641396	0.320698	+	0.947181i	$0.396083\pi$
$158$	0.848108	0.0674719
$159$	−0.341783	−0.0271051
$160$	−1.88847	−0.149297
$161$	17.4130	1.37233
$162$	−8.91441	−0.700382
$163$	−0.895824	−0.0701664	−0.0350832	−	0.999384i	$-0.511170\pi$
$163$	−0.895824	−0.0701664	−0.0350832	+	0.999384i	$0.511170\pi$
$164$	−1.18698	−0.0926873
$165$	−0.184265	−0.0143450
$166$	2.01595	0.156468
$167$	−18.6912	−1.44637	−0.723185	−	0.690654i	$-0.757323\pi$
$167$	−18.6912	−1.44637	−0.723185	+	0.690654i	$0.757323\pi$
$168$	−0.371903	−0.0286929
$169$	27.6329	2.12561
$170$	−4.79523	−0.367777
$171$	0	0
$172$	9.70779	0.740212
$173$	15.7737	1.19926	0.599628	−	0.800279i	$-0.295315\pi$
$173$	15.7737	1.19926	0.599628	+	0.800279i	$0.295315\pi$
$174$	0.191924	0.0145497
$175$	5.46447	0.413075
$176$	1.00000	0.0753778
$177$	0.907782	0.0682331
$178$	2.48263	0.186081
$179$	−11.9803	−0.895450	−0.447725	−	0.894171i	$-0.647766\pi$
$179$	−11.9803	−0.895450	−0.447725	+	0.894171i	$0.647766\pi$
$180$	−5.64743	−0.420935
$181$	7.39779	0.549874	0.274937	−	0.961462i	$-0.411343\pi$
$181$	7.39779	0.549874	0.274937	+	0.961462i	$0.411343\pi$
$182$	−24.2961	−1.80094
$183$	0.652185	0.0482109
$184$	4.56852	0.336796
$185$	12.2755	0.902510
$186$	−0.985734	−0.0722775
$187$	2.53921	0.185686
$188$	0.143539	0.0104687
$189$	−2.22787	−0.162054
$190$	0	0
$191$	1.64578	0.119084	0.0595421	−	0.998226i	$-0.481036\pi$
$191$	1.64578	0.119084	0.0595421	+	0.998226i	$0.481036\pi$
$192$	−0.0975736	−0.00704177
$193$	4.81056	0.346271	0.173136	−	0.984898i	$-0.444610\pi$
$193$	4.81056	0.346271	0.173136	+	0.984898i	$0.444610\pi$
$194$	14.7837	1.06141
$195$	1.17458	0.0841132
$196$	7.52760	0.537686
$197$	24.7360	1.76237	0.881184	−	0.472773i	$-0.156747\pi$
$197$	24.7360	1.76237	0.881184	+	0.472773i	$0.156747\pi$
$198$	2.99048	0.212524
$199$	18.0107	1.27675	0.638373	−	0.769727i	$-0.279608\pi$
$199$	18.0107	1.27675	0.638373	+	0.769727i	$0.279608\pi$
$200$	1.43368	0.101376
$201$	0.917256	0.0646983
$202$	−4.47356	−0.314759
$203$	−7.49711	−0.526194
$204$	−0.247760	−0.0173467
$205$	−2.24157	−0.156558
$206$	−13.6015	−0.947664
$207$	13.6621	0.949579
$208$	−6.37439	−0.441985
$209$	0	0
$210$	−0.702327	−0.0484652
$211$	16.7130	1.15057	0.575287	−	0.817952i	$-0.304891\pi$
$211$	16.7130	1.15057	0.575287	+	0.817952i	$0.304891\pi$
$212$	3.50282	0.240575
$213$	0.925937	0.0634442
$214$	4.27832	0.292460
$215$	18.3329	1.25029
$216$	−0.584512	−0.0397710
$217$	38.5056	2.61393
$218$	−12.8440	−0.869904
$219$	−0.353544	−0.0238903
$220$	1.88847	0.127321
$221$	−16.1859	−1.08878
$222$	0.634249	0.0425680
$223$	−5.21375	−0.349138	−0.174569	−	0.984645i	$-0.555853\pi$
$223$	−5.21375	−0.349138	−0.174569	+	0.984645i	$0.555853\pi$
$224$	3.81151	0.254667
$225$	4.28738	0.285825
$226$	14.6855	0.976865
$227$	1.37964	0.0915703	0.0457851	−	0.998951i	$-0.485421\pi$
$227$	1.37964	0.0915703	0.0457851	+	0.998951i	$0.485421\pi$
$228$	0	0
$229$	−17.1491	−1.13325	−0.566624	−	0.823977i	$-0.691751\pi$
$229$	−17.1491	−1.13325	−0.566624	+	0.823977i	$0.691751\pi$
$230$	8.62752	0.568882
$231$	0.371903	0.0244694
$232$	−1.96697	−0.129138
$233$	22.4644	1.47169	0.735845	−	0.677150i	$-0.236785\pi$
$233$	22.4644	1.47169	0.735845	+	0.677150i	$0.236785\pi$
$234$	−19.0625	−1.24615
$235$	0.271070	0.0176827
$236$	−9.30356	−0.605610
$237$	0.0827530	0.00537538
$238$	9.67823	0.627347
$239$	1.89757	0.122744	0.0613718	−	0.998115i	$-0.480452\pi$
$239$	1.89757	0.122744	0.0613718	+	0.998115i	$0.480452\pi$
$240$	−0.184265	−0.0118942
$241$	−19.6348	−1.26479	−0.632394	−	0.774647i	$-0.717928\pi$
$241$	−19.6348	−1.26479	−0.632394	+	0.774647i	$0.717928\pi$
$242$	−1.00000	−0.0642824
$243$	−2.62335	−0.168288
$244$	−6.68403	−0.427901
$245$	14.2157	0.908206
$246$	−0.115818	−0.00738426
$247$	0	0
$248$	10.1025	0.641507
$249$	0.196703	0.0124656
$250$	12.1498	0.768422
$251$	22.9858	1.45085	0.725424	−	0.688302i	$-0.241644\pi$
$251$	22.9858	1.45085	0.725424	+	0.688302i	$0.241644\pi$
$252$	11.3982	0.718022
$253$	−4.56852	−0.287220
$254$	−11.6672	−0.732064
$255$	−0.467888	−0.0293003
$256$	1.00000	0.0625000
$257$	26.2860	1.63967	0.819837	−	0.572596i	$-0.194064\pi$
$257$	26.2860	1.63967	0.819837	+	0.572596i	$0.194064\pi$
$258$	0.947224	0.0589716
$259$	−24.7756	−1.53948
$260$	−12.0379	−0.746556
$261$	−5.88217	−0.364097
$262$	−2.55270	−0.157707
$263$	21.4172	1.32064	0.660320	−	0.750984i	$-0.270421\pi$
$263$	21.4172	1.32064	0.660320	+	0.750984i	$0.270421\pi$
$264$	0.0975736	0.00600524
$265$	6.61498	0.406355
$266$	0	0
$267$	0.242239	0.0148248
$268$	−9.40066	−0.574237
$269$	26.7497	1.63096	0.815480	−	0.578785i	$-0.196473\pi$
$269$	26.7497	1.63096	0.815480	+	0.578785i	$0.196473\pi$
$270$	−1.10384	−0.0671773
$271$	20.0312	1.21681	0.608405	−	0.793627i	$-0.291810\pi$
$271$	20.0312	1.21681	0.608405	+	0.793627i	$0.291810\pi$
$272$	2.53921	0.153962
$273$	−2.37065	−0.143478
$274$	−14.2058	−0.858206
$275$	−1.43368	−0.0864539
$276$	0.445767	0.0268320
$277$	1.50565	0.0904660	0.0452330	−	0.998976i	$-0.485597\pi$
$277$	1.50565	0.0904660	0.0452330	+	0.998976i	$0.485597\pi$
$278$	−12.9499	−0.776681
$279$	30.2112	1.80870
$280$	7.19793	0.430158
$281$	2.63706	0.157314	0.0786569	−	0.996902i	$-0.474937\pi$
$281$	2.63706	0.157314	0.0786569	+	0.996902i	$0.474937\pi$
$282$	0.0140057	0.000834025 0
$283$	0.404517	0.0240460	0.0120230	−	0.999928i	$-0.496173\pi$
$283$	0.404517	0.0240460	0.0120230	+	0.999928i	$0.496173\pi$
$284$	−9.48963	−0.563106
$285$	0	0
$286$	6.37439	0.376926
$287$	4.52417	0.267054
$288$	2.99048	0.176216
$289$	−10.5524	−0.620729
$290$	−3.71456	−0.218126
$291$	1.44250	0.0845610
$292$	3.62336	0.212041
$293$	13.5742	0.793016	0.396508	−	0.918031i	$-0.370222\pi$
$293$	13.5742	0.793016	0.396508	+	0.918031i	$0.370222\pi$
$294$	0.734495	0.0428366
$295$	−17.5695	−1.02294
$296$	−6.50021	−0.377817
$297$	0.584512	0.0339169
$298$	17.3979	1.00784
$299$	29.1215	1.68414
$300$	0.139889	0.00807649
$301$	−37.0013	−2.13272
$302$	−0.263312	−0.0151519
$303$	−0.436501	−0.0250763
$304$	0	0
$305$	−12.6226	−0.722768
$306$	7.59346	0.434089
$307$	−29.2441	−1.66905	−0.834524	−	0.550972i	$-0.814257\pi$
$307$	−29.2441	−1.66905	−0.834524	+	0.550972i	$0.814257\pi$
$308$	−3.81151	−0.217181
$309$	−1.32715	−0.0754989
$310$	19.0782	1.08357
$311$	31.8078	1.80366	0.901828	−	0.432095i	$-0.142226\pi$
$311$	31.8078	1.80366	0.901828	+	0.432095i	$0.142226\pi$
$312$	−0.621972	−0.0352122
$313$	−19.7579	−1.11678	−0.558391	−	0.829578i	$-0.688581\pi$
$313$	−19.7579	−1.11678	−0.558391	+	0.829578i	$0.688581\pi$
$314$	−8.03667	−0.453536
$315$	21.5253	1.21281
$316$	−0.848108	−0.0477098
$317$	−23.8676	−1.34054	−0.670268	−	0.742119i	$-0.733821\pi$
$317$	−23.8676	−1.34054	−0.670268	+	0.742119i	$0.733821\pi$
$318$	0.341783	0.0191662
$319$	1.96697	0.110129
$320$	1.88847	0.105569
$321$	0.417451	0.0232998
$322$	−17.4130	−0.970386
$323$	0	0
$324$	8.91441	0.495245
$325$	9.13881	0.506930
$326$	0.895824	0.0496151
$327$	−1.25323	−0.0693039
$328$	1.18698	0.0655398
$329$	−0.547102	−0.0301627
$330$	0.184265	0.0101434
$331$	−12.3676	−0.679784	−0.339892	−	0.940465i	$-0.610390\pi$
$331$	−12.3676	−0.679784	−0.339892	+	0.940465i	$0.610390\pi$
$332$	−2.01595	−0.110639
$333$	−19.4388	−1.06524
$334$	18.6912	1.02274
$335$	−17.7529	−0.969944
$336$	0.371903	0.0202890
$337$	15.4826	0.843390	0.421695	−	0.906738i	$-0.361435\pi$
$337$	15.4826	0.843390	0.421695	+	0.906738i	$0.361435\pi$
$338$	−27.6329	−1.50303
$339$	1.43292	0.0778254
$340$	4.79523	0.260058
$341$	−10.1025	−0.547079
$342$	0	0
$343$	−2.01097	−0.108582
$344$	−9.70779	−0.523409
$345$	0.841818	0.0453220
$346$	−15.7737	−0.848002
$347$	−25.5023	−1.36903	−0.684517	−	0.728997i	$-0.739987\pi$
$347$	−25.5023	−1.36903	−0.684517	+	0.728997i	$0.739987\pi$
$348$	−0.191924	−0.0102882
$349$	15.8090	0.846238	0.423119	−	0.906074i	$-0.360935\pi$
$349$	15.8090	0.846238	0.423119	+	0.906074i	$0.360935\pi$
$350$	−5.46447	−0.292088
$351$	−3.72591	−0.198874
$352$	−1.00000	−0.0533002
$353$	−34.1849	−1.81948	−0.909739	−	0.415180i	$-0.863718\pi$
$353$	−34.1849	−1.81948	−0.909739	+	0.415180i	$0.863718\pi$
$354$	−0.907782	−0.0482481
$355$	−17.9209	−0.951142
$356$	−2.48263	−0.131579
$357$	0.944340	0.0499798
$358$	11.9803	0.633179
$359$	−26.3024	−1.38819	−0.694093	−	0.719886i	$-0.744194\pi$
$359$	−26.3024	−1.38819	−0.694093	+	0.719886i	$0.744194\pi$
$360$	5.64743	0.297646
$361$	0	0
$362$	−7.39779	−0.388819
$363$	−0.0975736	−0.00512128
$364$	24.2961	1.27346
$365$	6.84261	0.358159
$366$	−0.652185	−0.0340903
$367$	17.9861	0.938869	0.469434	−	0.882967i	$-0.344458\pi$
$367$	17.9861	0.938869	0.469434	+	0.882967i	$0.344458\pi$
$368$	−4.56852	−0.238151
$369$	3.54963	0.184786
$370$	−12.2755	−0.638171
$371$	−13.3510	−0.693151
$372$	0.985734	0.0511079
$373$	−4.06237	−0.210342	−0.105171	−	0.994454i	$-0.533539\pi$
$373$	−4.06237	−0.210342	−0.105171	+	0.994454i	$0.533539\pi$
$374$	−2.53921	−0.131300
$375$	1.18550	0.0612190
$376$	−0.143539	−0.00740248
$377$	−12.5382	−0.645751
$378$	2.22787	0.114590
$379$	−16.9146	−0.868844	−0.434422	−	0.900709i	$-0.643047\pi$
$379$	−16.9146	−0.868844	−0.434422	+	0.900709i	$0.643047\pi$
$380$	0	0
$381$	−1.13841	−0.0583224
$382$	−1.64578	−0.0842053
$383$	24.2822	1.24076	0.620382	−	0.784300i	$-0.286978\pi$
$383$	24.2822	1.24076	0.620382	+	0.784300i	$0.286978\pi$
$384$	0.0975736	0.00497928
$385$	−7.19793	−0.366840
$386$	−4.81056	−0.244851
$387$	−29.0310	−1.47573
$388$	−14.7837	−0.750531
$389$	−35.6362	−1.80683	−0.903414	−	0.428770i	$-0.858947\pi$
$389$	−35.6362	−1.80683	−0.903414	+	0.428770i	$0.858947\pi$
$390$	−1.17458	−0.0594770
$391$	−11.6004	−0.586660
$392$	−7.52760	−0.380201
$393$	−0.249077	−0.0125642
$394$	−24.7360	−1.24618
$395$	−1.60163	−0.0805867
$396$	−2.99048	−0.150277
$397$	14.7536	0.740462	0.370231	−	0.928940i	$-0.379278\pi$
$397$	14.7536	0.740462	0.370231	+	0.928940i	$0.379278\pi$
$398$	−18.0107	−0.902796
$399$	0	0
$400$	−1.43368	−0.0716838
$401$	−9.70497	−0.484643	−0.242322	−	0.970196i	$-0.577909\pi$
$401$	−9.70497	−0.484643	−0.242322	+	0.970196i	$0.577909\pi$
$402$	−0.917256	−0.0457486
$403$	64.3971	3.20785
$404$	4.47356	0.222568
$405$	16.8346	0.836518
$406$	7.49711	0.372075
$407$	6.50021	0.322204
$408$	0.247760	0.0122660
$409$	4.29458	0.212353	0.106177	−	0.994347i	$-0.466139\pi$
$409$	4.29458	0.212353	0.106177	+	0.994347i	$0.466139\pi$
$410$	2.24157	0.110703
$411$	−1.38611	−0.0683720
$412$	13.6015	0.670099
$413$	35.4606	1.74490
$414$	−13.6621	−0.671454
$415$	−3.80706	−0.186881
$416$	6.37439	0.312530
$417$	−1.26356	−0.0618770
$418$	0	0
$419$	−12.0304	−0.587726	−0.293863	−	0.955848i	$-0.594941\pi$
$419$	−12.0304	−0.587726	−0.293863	+	0.955848i	$0.594941\pi$
$420$	0.702327	0.0342701
$421$	−5.13912	−0.250465	−0.125233	−	0.992127i	$-0.539968\pi$
$421$	−5.13912	−0.250465	−0.125233	+	0.992127i	$0.539968\pi$
$422$	−16.7130	−0.813578
$423$	−0.429252	−0.0208709
$424$	−3.50282	−0.170112
$425$	−3.64041	−0.176586
$426$	−0.925937	−0.0448618
$427$	25.4763	1.23288
$428$	−4.27832	−0.206800
$429$	0.621972	0.0300291
$430$	−18.3329	−0.884090
$431$	−38.3437	−1.84695	−0.923475	−	0.383659i	$-0.874664\pi$
$431$	−38.3437	−1.84695	−0.923475	+	0.383659i	$0.874664\pi$
$432$	0.584512	0.0281224
$433$	−8.17645	−0.392935	−0.196468	−	0.980510i	$-0.562947\pi$
$433$	−8.17645	−0.392935	−0.196468	+	0.980510i	$0.562947\pi$
$434$	−38.5056	−1.84833
$435$	−0.362443	−0.0173778
$436$	12.8440	0.615115
$437$	0	0
$438$	0.353544	0.0168930
$439$	10.9266	0.521497	0.260748	−	0.965407i	$-0.416031\pi$
$439$	10.9266	0.521497	0.260748	+	0.965407i	$0.416031\pi$
$440$	−1.88847	−0.0900293
$441$	−22.5111	−1.07196
$442$	16.1859	0.769887
$443$	39.8645	1.89402	0.947009	−	0.321206i	$-0.104088\pi$
$443$	39.8645	1.89402	0.947009	+	0.321206i	$0.104088\pi$
$444$	−0.634249	−0.0301001
$445$	−4.68837	−0.222250
$446$	5.21375	0.246878
$447$	1.69758	0.0802928
$448$	−3.81151	−0.180077
$449$	0.825534	0.0389593	0.0194797	−	0.999810i	$-0.493799\pi$
$449$	0.825534	0.0389593	0.0194797	+	0.999810i	$0.493799\pi$
$450$	−4.28738	−0.202109
$451$	−1.18698	−0.0558926
$452$	−14.6855	−0.690748
$453$	−0.0256923	−0.00120713
$454$	−1.37964	−0.0647499
$455$	45.8824	2.15100
$456$	0	0
$457$	−10.2987	−0.481755	−0.240878	−	0.970556i	$-0.577435\pi$
$457$	−10.2987	−0.481755	−0.240878	+	0.970556i	$0.577435\pi$
$458$	17.1491	0.801327
$459$	1.48420	0.0692766
$460$	−8.62752	−0.402260
$461$	4.42459	0.206074	0.103037	−	0.994678i	$-0.467144\pi$
$461$	4.42459	0.206074	0.103037	+	0.994678i	$0.467144\pi$
$462$	−0.371903	−0.0173025
$463$	6.13904	0.285305	0.142653	−	0.989773i	$-0.454437\pi$
$463$	6.13904	0.285305	0.142653	+	0.989773i	$0.454437\pi$
$464$	1.96697	0.0913141
$465$	1.86153	0.0863264
$466$	−22.4644	−1.04064
$467$	−38.8206	−1.79640	−0.898202	−	0.439583i	$-0.855126\pi$
$467$	−38.8206	−1.79640	−0.898202	+	0.439583i	$0.855126\pi$
$468$	19.0625	0.881164
$469$	35.8307	1.65451
$470$	−0.271070	−0.0125035
$471$	−0.784167	−0.0361325
$472$	9.30356	0.428231
$473$	9.70779	0.446365
$474$	−0.0827530	−0.00380097
$475$	0	0
$476$	−9.67823	−0.443601
$477$	−10.4751	−0.479623
$478$	−1.89757	−0.0867928
$479$	−6.84310	−0.312669	−0.156335	−	0.987704i	$-0.549968\pi$
$479$	−6.84310	−0.312669	−0.156335	+	0.987704i	$0.549968\pi$
$480$	0.184265	0.00841050
$481$	−41.4349	−1.88927
$482$	19.6348	0.894340
$483$	−1.69904	−0.0773092
$484$	1.00000	0.0454545
$485$	−27.9187	−1.26772
$486$	2.62335	0.118997
$487$	37.0683	1.67973	0.839863	−	0.542798i	$-0.182635\pi$
$487$	37.0683	1.67973	0.839863	+	0.542798i	$0.182635\pi$
$488$	6.68403	0.302572
$489$	0.0874088	0.00395276
$490$	−14.2157	−0.642198
$491$	−15.9454	−0.719606	−0.359803	−	0.933028i	$-0.617156\pi$
$491$	−15.9454	−0.719606	−0.359803	+	0.933028i	$0.617156\pi$
$492$	0.115818	0.00522146
$493$	4.99454	0.224943
$494$	0	0
$495$	−5.64743	−0.253833
$496$	−10.1025	−0.453614
$497$	36.1698	1.62244
$498$	−0.196703	−0.00881448
$499$	−17.6403	−0.789687	−0.394844	−	0.918748i	$-0.629201\pi$
$499$	−17.6403	−0.789687	−0.394844	+	0.918748i	$0.629201\pi$
$500$	−12.1498	−0.543356
$501$	1.82377	0.0814800
$502$	−22.9858	−1.02590
$503$	1.84748	0.0823752	0.0411876	−	0.999151i	$-0.486886\pi$
$503$	1.84748	0.0823752	0.0411876	+	0.999151i	$0.486886\pi$
$504$	−11.3982	−0.507718
$505$	8.44819	0.375940
$506$	4.56852	0.203095
$507$	−2.69624	−0.119744
$508$	11.6672	0.517647
$509$	41.5807	1.84303	0.921517	−	0.388339i	$-0.126951\pi$
$509$	41.5807	1.84303	0.921517	+	0.388339i	$0.126951\pi$
$510$	0.467888	0.0207184
$511$	−13.8105	−0.610939
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−26.2860	−1.15943
$515$	25.6861	1.13187
$516$	−0.947224	−0.0416992
$517$	0.143539	0.00631286
$518$	24.7756	1.08858
$519$	−1.53910	−0.0675590
$520$	12.0379	0.527895
$521$	18.2155	0.798035	0.399018	−	0.916943i	$-0.369351\pi$
$521$	18.2155	0.798035	0.399018	+	0.916943i	$0.369351\pi$
$522$	5.88217	0.257456
$523$	−3.73807	−0.163454	−0.0817271	−	0.996655i	$-0.526044\pi$
$523$	−3.73807	−0.163454	−0.0817271	+	0.996655i	$0.526044\pi$
$524$	2.55270	0.111515
$525$	−0.533188	−0.0232702
$526$	−21.4172	−0.933834
$527$	−25.6523	−1.11743
$528$	−0.0975736	−0.00424634
$529$	−2.12862	−0.0925488
$530$	−6.61498	−0.287336
$531$	27.8221	1.20738
$532$	0	0
$533$	7.56626	0.327731
$534$	−0.242239	−0.0104827
$535$	−8.07949	−0.349307
$536$	9.40066	0.406047
$537$	1.16896	0.0504444
$538$	−26.7497	−1.15326
$539$	7.52760	0.324237
$540$	1.10384	0.0475015
$541$	32.8418	1.41198	0.705989	−	0.708222i	$-0.250503\pi$
$541$	32.8418	1.41198	0.705989	+	0.708222i	$0.250503\pi$
$542$	−20.0312	−0.860414
$543$	−0.721829	−0.0309766
$544$	−2.53921	−0.108868
$545$	24.2555	1.03899
$546$	2.37065	0.101455
$547$	29.3830	1.25632	0.628162	−	0.778082i	$-0.283807\pi$
$547$	29.3830	1.25632	0.628162	+	0.778082i	$0.283807\pi$
$548$	14.2058	0.606843
$549$	19.9885	0.853087
$550$	1.43368	0.0611321
$551$	0	0
$552$	−0.445767	−0.0189731
$553$	3.23257	0.137463
$554$	−1.50565	−0.0639691
$555$	−1.19776	−0.0508421
$556$	12.9499	0.549197
$557$	30.0129	1.27169	0.635843	−	0.771818i	$-0.280652\pi$
$557$	30.0129	1.27169	0.635843	+	0.771818i	$0.280652\pi$
$558$	−30.2112	−1.27894
$559$	−61.8813	−2.61730
$560$	−7.19793	−0.304168
$561$	−0.247760	−0.0104604
$562$	−2.63706	−0.111238
$563$	−3.57082	−0.150492	−0.0752461	−	0.997165i	$-0.523974\pi$
$563$	−3.57082	−0.150492	−0.0752461	+	0.997165i	$0.523974\pi$
$564$	−0.0140057	−0.000589745 0
$565$	−27.7332	−1.16674
$566$	−0.404517	−0.0170031
$567$	−33.9773	−1.42691
$568$	9.48963	0.398176
$569$	29.0243	1.21676	0.608382	−	0.793645i	$-0.291819\pi$
$569$	29.0243	1.21676	0.608382	+	0.793645i	$0.291819\pi$
$570$	0	0
$571$	−20.7613	−0.868835	−0.434418	−	0.900712i	$-0.643046\pi$
$571$	−20.7613	−0.868835	−0.434418	+	0.900712i	$0.643046\pi$
$572$	−6.37439	−0.266527
$573$	−0.160584	−0.00670851
$574$	−4.52417	−0.188835
$575$	6.54978	0.273145
$576$	−2.99048	−0.124603
$577$	−3.81943	−0.159005	−0.0795026	−	0.996835i	$-0.525333\pi$
$577$	−3.81943	−0.159005	−0.0795026	+	0.996835i	$0.525333\pi$
$578$	10.5524	0.438922
$579$	−0.469383	−0.0195069
$580$	3.71456	0.154239
$581$	7.68380	0.318778
$582$	−1.44250	−0.0597937
$583$	3.50282	0.145072
$584$	−3.62336	−0.149936
$585$	35.9990	1.48837
$586$	−13.5742	−0.560747
$587$	−0.221967	−0.00916155	−0.00458077	−	0.999990i	$-0.501458\pi$
$587$	−0.221967	−0.00916155	−0.00458077	+	0.999990i	$0.501458\pi$
$588$	−0.734495	−0.0302901
$589$	0	0
$590$	17.5695	0.723326
$591$	−2.41358	−0.0992815
$592$	6.50021	0.267157
$593$	29.3719	1.20616	0.603080	−	0.797681i	$-0.293940\pi$
$593$	29.3719	1.20616	0.603080	+	0.797681i	$0.293940\pi$
$594$	−0.584512	−0.0239828
$595$	−18.2771	−0.749287
$596$	−17.3979	−0.712648
$597$	−1.75737	−0.0719244
$598$	−29.1215	−1.19087
$599$	−6.64897	−0.271669	−0.135835	−	0.990732i	$-0.543372\pi$
$599$	−6.64897	−0.271669	−0.135835	+	0.990732i	$0.543372\pi$
$600$	−0.139889	−0.00571094
$601$	17.7898	0.725661	0.362830	−	0.931855i	$-0.381810\pi$
$601$	17.7898	0.725661	0.362830	+	0.931855i	$0.381810\pi$
$602$	37.0013	1.50806
$603$	28.1125	1.14483
$604$	0.263312	0.0107140
$605$	1.88847	0.0767773
$606$	0.436501	0.0177317
$607$	31.0441	1.26004	0.630021	−	0.776578i	$-0.283046\pi$
$607$	31.0441	1.26004	0.630021	+	0.776578i	$0.283046\pi$
$608$	0	0
$609$	0.731520	0.0296427
$610$	12.6226	0.511074
$611$	−0.914977	−0.0370160
$612$	−7.59346	−0.306948
$613$	28.8005	1.16324	0.581621	−	0.813460i	$-0.302419\pi$
$613$	28.8005	1.16324	0.581621	+	0.813460i	$0.302419\pi$
$614$	29.2441	1.18019
$615$	0.218718	0.00881957
$616$	3.81151	0.153570
$617$	−18.1108	−0.729112	−0.364556	−	0.931182i	$-0.618779\pi$
$617$	−18.1108	−0.729112	−0.364556	+	0.931182i	$0.618779\pi$
$618$	1.32715	0.0533858
$619$	−28.4550	−1.14370	−0.571851	−	0.820357i	$-0.693774\pi$
$619$	−28.4550	−1.14370	−0.571851	+	0.820357i	$0.693774\pi$
$620$	−19.0782	−0.766200
$621$	−2.67036	−0.107158
$622$	−31.8078	−1.27538
$623$	9.46256	0.379109
$624$	0.621972	0.0248988
$625$	−15.7762	−0.631048
$626$	19.7579	0.789684
$627$	0	0
$628$	8.03667	0.320698
$629$	16.5054	0.658115
$630$	−21.5253	−0.857587
$631$	28.4306	1.13180	0.565902	−	0.824473i	$-0.308528\pi$
$631$	28.4306	1.13180	0.565902	+	0.824473i	$0.308528\pi$
$632$	0.848108	0.0337359
$633$	−1.63075	−0.0648165
$634$	23.8676	0.947903
$635$	22.0331	0.874358
$636$	−0.341783	−0.0135526
$637$	−47.9839	−1.90119
$638$	−1.96697	−0.0778729
$639$	28.3785	1.12264
$640$	−1.88847	−0.0746484
$641$	−37.9649	−1.49953	−0.749763	−	0.661707i	$-0.769832\pi$
$641$	−37.9649	−1.49953	−0.749763	+	0.661707i	$0.769832\pi$
$642$	−0.417451	−0.0164755
$643$	−33.2110	−1.30972	−0.654858	−	0.755752i	$-0.727271\pi$
$643$	−33.2110	−1.30972	−0.654858	+	0.755752i	$0.727271\pi$
$644$	17.4130	0.686167
$645$	−1.78881	−0.0704341
$646$	0	0
$647$	11.7952	0.463717	0.231859	−	0.972750i	$-0.425519\pi$
$647$	11.7952	0.463717	0.231859	+	0.972750i	$0.425519\pi$
$648$	−8.91441	−0.350191
$649$	−9.30356	−0.365197
$650$	−9.13881	−0.358454
$651$	−3.75713	−0.147254
$652$	−0.895824	−0.0350832
$653$	4.56389	0.178599	0.0892995	−	0.996005i	$-0.471537\pi$
$653$	4.56389	0.178599	0.0892995	+	0.996005i	$0.471537\pi$
$654$	1.25323	0.0490053
$655$	4.82071	0.188361
$656$	−1.18698	−0.0463437
$657$	−10.8356	−0.422736
$658$	0.547102	0.0213283
$659$	−5.25702	−0.204785	−0.102392	−	0.994744i	$-0.532650\pi$
$659$	−5.25702	−0.204785	−0.102392	+	0.994744i	$0.532650\pi$
$660$	−0.184265	−0.00717250
$661$	41.0223	1.59558	0.797791	−	0.602935i	$-0.206002\pi$
$661$	41.0223	1.59558	0.797791	+	0.602935i	$0.206002\pi$
$662$	12.3676	0.480680
$663$	1.57932	0.0613357
$664$	2.01595	0.0782339
$665$	0	0
$666$	19.4388	0.753236
$667$	−8.98612	−0.347944
$668$	−18.6912	−0.723185
$669$	0.508724	0.0196684
$670$	17.7529	0.685854
$671$	−6.68403	−0.258034
$672$	−0.371903	−0.0143465
$673$	−28.6206	−1.10324	−0.551622	−	0.834094i	$-0.685991\pi$
$673$	−28.6206	−1.10324	−0.551622	+	0.834094i	$0.685991\pi$
$674$	−15.4826	−0.596367
$675$	−0.838001	−0.0322547
$676$	27.6329	1.06280
$677$	16.6490	0.639874	0.319937	−	0.947439i	$-0.396338\pi$
$677$	16.6490	0.639874	0.319937	+	0.947439i	$0.396338\pi$
$678$	−1.43292	−0.0550309
$679$	56.3484	2.16245
$680$	−4.79523	−0.183889
$681$	−0.134617	−0.00515853
$682$	10.1025	0.386843
$683$	−2.67552	−0.102376	−0.0511879	−	0.998689i	$-0.516301\pi$
$683$	−2.67552	−0.102376	−0.0511879	+	0.998689i	$0.516301\pi$
$684$	0	0
$685$	26.8273	1.02502
$686$	2.01097	0.0767791
$687$	1.67330	0.0638405
$688$	9.70779	0.370106
$689$	−22.3284	−0.850643
$690$	−0.841818	−0.0320475
$691$	−8.40458	−0.319725	−0.159863	−	0.987139i	$-0.551105\pi$
$691$	−8.40458	−0.319725	−0.159863	+	0.987139i	$0.551105\pi$
$692$	15.7737	0.599628
$693$	11.3982	0.432983
$694$	25.5023	0.968054
$695$	24.4554	0.927648
$696$	0.191924	0.00727486
$697$	−3.01399	−0.114163
$698$	−15.8090	−0.598381
$699$	−2.19193	−0.0829063
$700$	5.46447	0.206537
$701$	−14.5407	−0.549195	−0.274597	−	0.961559i	$-0.588545\pi$
$701$	−14.5407	−0.549195	−0.274597	+	0.961559i	$0.588545\pi$
$702$	3.72591	0.140625
$703$	0	0
$704$	1.00000	0.0376889
$705$	−0.0264493	−0.000996138 0
$706$	34.1849	1.28657
$707$	−17.0510	−0.641270
$708$	0.907782	0.0341165
$709$	−15.7113	−0.590052	−0.295026	−	0.955489i	$-0.595328\pi$
$709$	−15.7113	−0.590052	−0.295026	+	0.955489i	$0.595328\pi$
$710$	17.9209	0.672559
$711$	2.53625	0.0951168
$712$	2.48263	0.0930404
$713$	46.1533	1.72846
$714$	−0.944340	−0.0353410
$715$	−12.0379	−0.450190
$716$	−11.9803	−0.447725
$717$	−0.185153	−0.00691465
$718$	26.3024	0.981595
$719$	−16.3193	−0.608606	−0.304303	−	0.952575i	$-0.598424\pi$
$719$	−16.3193	−0.608606	−0.304303	+	0.952575i	$0.598424\pi$
$720$	−5.64743	−0.210467
$721$	−51.8424	−1.93071
$722$	0	0
$723$	1.91584	0.0712507
$724$	7.39779	0.274937
$725$	−2.81999	−0.104732
$726$	0.0975736	0.00362130
$727$	−39.3143	−1.45809	−0.729043	−	0.684468i	$-0.760035\pi$
$727$	−39.3143	−1.45809	−0.729043	+	0.684468i	$0.760035\pi$
$728$	−24.2961	−0.900472
$729$	−26.4872	−0.981009
$730$	−6.84261	−0.253256
$731$	24.6502	0.911719
$732$	0.652185	0.0241055
$733$	21.8648	0.807594	0.403797	−	0.914849i	$-0.367690\pi$
$733$	21.8648	0.807594	0.403797	+	0.914849i	$0.367690\pi$
$734$	−17.9861	−0.663881
$735$	−1.38707	−0.0511630
$736$	4.56852	0.168398
$737$	−9.40066	−0.346278
$738$	−3.54963	−0.130664
$739$	−41.2272	−1.51657	−0.758283	−	0.651926i	$-0.773961\pi$
$739$	−41.2272	−1.51657	−0.758283	+	0.651926i	$0.773961\pi$
$740$	12.2755	0.451255
$741$	0	0
$742$	13.3510	0.490132
$743$	−6.15387	−0.225763	−0.112882	−	0.993608i	$-0.536008\pi$
$743$	−6.15387	−0.225763	−0.112882	+	0.993608i	$0.536008\pi$
$744$	−0.985734	−0.0361388
$745$	−32.8555	−1.20373
$746$	4.06237	0.148734
$747$	6.02865	0.220577
$748$	2.53921	0.0928428
$749$	16.3069	0.595840
$750$	−1.18550	−0.0432884
$751$	−2.69962	−0.0985105	−0.0492553	−	0.998786i	$-0.515685\pi$
$751$	−2.69962	−0.0985105	−0.0492553	+	0.998786i	$0.515685\pi$
$752$	0.143539	0.00523435
$753$	−2.24280	−0.0817323
$754$	12.5382	0.456615
$755$	0.497257	0.0180970
$756$	−2.22787	−0.0810270
$757$	19.1424	0.695744	0.347872	−	0.937542i	$-0.386904\pi$
$757$	19.1424	0.695744	0.347872	+	0.937542i	$0.386904\pi$
$758$	16.9146	0.614365
$759$	0.445767	0.0161803
$760$	0	0
$761$	−26.3003	−0.953384	−0.476692	−	0.879070i	$-0.658164\pi$
$761$	−26.3003	−0.953384	−0.476692	+	0.879070i	$0.658164\pi$
$762$	1.13841	0.0412402
$763$	−48.9549	−1.77229
$764$	1.64578	0.0595421
$765$	−14.3400	−0.518465
$766$	−24.2822	−0.877353
$767$	59.3046	2.14136
$768$	−0.0975736	−0.00352088
$769$	28.7172	1.03557	0.517785	−	0.855511i	$-0.326757\pi$
$769$	28.7172	1.03557	0.517785	+	0.855511i	$0.326757\pi$
$770$	7.19793	0.259395
$771$	−2.56482	−0.0923697
$772$	4.81056	0.173136
$773$	6.99825	0.251710	0.125855	−	0.992049i	$-0.459833\pi$
$773$	6.99825	0.251710	0.125855	+	0.992049i	$0.459833\pi$
$774$	29.0310	1.04350
$775$	14.4837	0.520268
$776$	14.7837	0.530705
$777$	2.41745	0.0867254
$778$	35.6362	1.27762
$779$	0	0
$780$	1.17458	0.0420566
$781$	−9.48963	−0.339566
$782$	11.6004	0.414831
$783$	1.14972	0.0410875
$784$	7.52760	0.268843
$785$	15.1770	0.541691
$786$	0.249077	0.00888427
$787$	41.0676	1.46390	0.731950	−	0.681358i	$-0.238610\pi$
$787$	41.0676	1.46390	0.731950	+	0.681358i	$0.238610\pi$
$788$	24.7360	0.881184
$789$	−2.08975	−0.0743971
$790$	1.60163	0.0569834
$791$	55.9739	1.99020
$792$	2.99048	0.106262
$793$	42.6067	1.51301
$794$	−14.7536	−0.523586
$795$	−0.645447	−0.0228916
$796$	18.0107	0.638373
$797$	24.4910	0.867514	0.433757	−	0.901030i	$-0.357188\pi$
$797$	24.4910	0.867514	0.433757	+	0.901030i	$0.357188\pi$
$798$	0	0
$799$	0.364477	0.0128943
$800$	1.43368	0.0506881
$801$	7.42424	0.262323
$802$	9.70497	0.342694
$803$	3.62336	0.127866
$804$	0.917256	0.0323491
$805$	32.8839	1.15900
$806$	−64.3971	−2.26829
$807$	−2.61007	−0.0918787
$808$	−4.47356	−0.157379
$809$	36.9664	1.29967	0.649835	−	0.760075i	$-0.274838\pi$
$809$	36.9664	1.29967	0.649835	+	0.760075i	$0.274838\pi$
$810$	−16.8346	−0.591508
$811$	−49.0643	−1.72288	−0.861440	−	0.507859i	$-0.830437\pi$
$811$	−49.0643	−1.72288	−0.861440	+	0.507859i	$0.830437\pi$
$812$	−7.49711	−0.263097
$813$	−1.95452	−0.0685479
$814$	−6.50021	−0.227832
$815$	−1.69174	−0.0592590
$816$	−0.247760	−0.00867334
$817$	0	0
$818$	−4.29458	−0.150157
$819$	−72.6569	−2.53884
$820$	−2.24157	−0.0782791
$821$	0.169547	0.00591725	0.00295862	−	0.999996i	$-0.499058\pi$
$821$	0.169547	0.00591725	0.00295862	+	0.999996i	$0.499058\pi$
$822$	1.38611	0.0483463
$823$	−9.74733	−0.339771	−0.169885	−	0.985464i	$-0.554340\pi$
$823$	−9.74733	−0.339771	−0.169885	+	0.985464i	$0.554340\pi$
$824$	−13.6015	−0.473832
$825$	0.139889	0.00487031
$826$	−35.4606	−1.23383
$827$	6.58489	0.228979	0.114490	−	0.993424i	$-0.463477\pi$
$827$	6.58489	0.228979	0.114490	+	0.993424i	$0.463477\pi$
$828$	13.6621	0.474790
$829$	−0.366921	−0.0127437	−0.00637185	−	0.999980i	$-0.502028\pi$
$829$	−0.366921	−0.0127437	−0.00637185	+	0.999980i	$0.502028\pi$
$830$	3.80706	0.132145
$831$	−0.146912	−0.00509632
$832$	−6.37439	−0.220992
$833$	19.1142	0.662267
$834$	1.26356	0.0437537
$835$	−35.2978	−1.22153
$836$	0	0
$837$	−5.90502	−0.204107
$838$	12.0304	0.415585
$839$	24.2622	0.837625	0.418812	−	0.908073i	$-0.362446\pi$
$839$	24.2622	0.837625	0.418812	+	0.908073i	$0.362446\pi$
$840$	−0.702327	−0.0242326
$841$	−25.1310	−0.866588
$842$	5.13912	0.177106
$843$	−0.257307	−0.00886214
$844$	16.7130	0.575287
$845$	52.1839	1.79518
$846$	0.429252	0.0147580
$847$	−3.81151	−0.130965
$848$	3.50282	0.120287
$849$	−0.0394702	−0.00135461
$850$	3.64041	0.124865
$851$	−29.6964	−1.01798
$852$	0.925937	0.0317221
$853$	47.8814	1.63943	0.819714	−	0.572773i	$-0.194132\pi$
$853$	47.8814	1.63943	0.819714	+	0.572773i	$0.194132\pi$
$854$	−25.4763	−0.871780
$855$	0	0
$856$	4.27832	0.146230
$857$	23.0400	0.787031	0.393515	−	0.919318i	$-0.371259\pi$
$857$	23.0400	0.787031	0.393515	+	0.919318i	$0.371259\pi$
$858$	−0.621972	−0.0212338
$859$	25.6409	0.874856	0.437428	−	0.899253i	$-0.355889\pi$
$859$	25.6409	0.874856	0.437428	+	0.899253i	$0.355889\pi$
$860$	18.3329	0.625146
$861$	−0.441440	−0.0150442
$862$	38.3437	1.30599
$863$	2.70664	0.0921349	0.0460675	−	0.998938i	$-0.485331\pi$
$863$	2.70664	0.0921349	0.0460675	+	0.998938i	$0.485331\pi$
$864$	−0.584512	−0.0198855
$865$	29.7883	1.01283
$866$	8.17645	0.277847
$867$	1.02964	0.0349682
$868$	38.5056	1.30697
$869$	−0.848108	−0.0287701
$870$	0.362443	0.0122880
$871$	59.9235	2.03043
$872$	−12.8440	−0.434952
$873$	44.2105	1.49630
$874$	0	0
$875$	46.3091	1.56553
$876$	−0.353544	−0.0119451
$877$	10.7534	0.363117	0.181558	−	0.983380i	$-0.441886\pi$
$877$	10.7534	0.363117	0.181558	+	0.983380i	$0.441886\pi$
$878$	−10.9266	−0.368754
$879$	−1.32449	−0.0446739
$880$	1.88847	0.0636604
$881$	−4.12321	−0.138914	−0.0694572	−	0.997585i	$-0.522127\pi$
$881$	−4.12321	−0.138914	−0.0694572	+	0.997585i	$0.522127\pi$
$882$	22.5111	0.757990
$883$	11.3989	0.383604	0.191802	−	0.981434i	$-0.438567\pi$
$883$	11.3989	0.383604	0.191802	+	0.981434i	$0.438567\pi$
$884$	−16.1859	−0.544392
$885$	1.71432	0.0576263
$886$	−39.8645	−1.33927
$887$	4.17841	0.140297	0.0701487	−	0.997537i	$-0.477653\pi$
$887$	4.17841	0.140297	0.0701487	+	0.997537i	$0.477653\pi$
$888$	0.634249	0.0212840
$889$	−44.4696	−1.49146
$890$	4.68837	0.157155
$891$	8.91441	0.298644
$892$	−5.21375	−0.174569
$893$	0	0
$894$	−1.69758	−0.0567756
$895$	−22.6245	−0.756252
$896$	3.81151	0.127334
$897$	−2.84149	−0.0948747
$898$	−0.825534	−0.0275484
$899$	−19.8712	−0.662742
$900$	4.28738	0.142913
$901$	8.89441	0.296316
$902$	1.18698	0.0395220
$903$	3.61035	0.120145
$904$	14.6855	0.488433
$905$	13.9705	0.464396
$906$	0.0256923	0.000853568 0
$907$	−28.6488	−0.951268	−0.475634	−	0.879643i	$-0.657781\pi$
$907$	−28.6488	−0.951268	−0.475634	+	0.879643i	$0.657781\pi$
$908$	1.37964	0.0457851
$909$	−13.3781	−0.443723
$910$	−45.8824	−1.52099
$911$	−16.2010	−0.536762	−0.268381	−	0.963313i	$-0.586489\pi$
$911$	−16.2010	−0.536762	−0.268381	+	0.963313i	$0.586489\pi$
$912$	0	0
$913$	−2.01595	−0.0667181
$914$	10.2987	0.340652
$915$	1.23163	0.0407165
$916$	−17.1491	−0.566624
$917$	−9.72966	−0.321302
$918$	−1.48420	−0.0489860
$919$	−58.9439	−1.94438	−0.972190	−	0.234192i	$-0.924756\pi$
$919$	−58.9439	−1.94438	−0.972190	+	0.234192i	$0.924756\pi$
$920$	8.62752	0.284441
$921$	2.85345	0.0940243
$922$	−4.42459	−0.145716
$923$	60.4906	1.99107
$924$	0.371903	0.0122347
$925$	−9.31920	−0.306413
$926$	−6.13904	−0.201741
$927$	−40.6751	−1.33595
$928$	−1.96697	−0.0645688
$929$	12.4981	0.410049	0.205024	−	0.978757i	$-0.434273\pi$
$929$	12.4981	0.410049	0.205024	+	0.978757i	$0.434273\pi$
$930$	−1.86153	−0.0610420
$931$	0	0
$932$	22.4644	0.735845
$933$	−3.10360	−0.101607
$934$	38.8206	1.27025
$935$	4.79523	0.156821
$936$	−19.0625	−0.623077
$937$	20.1842	0.659388	0.329694	−	0.944088i	$-0.393054\pi$
$937$	20.1842	0.659388	0.329694	+	0.944088i	$0.393054\pi$
$938$	−35.8307	−1.16991
$939$	1.92785	0.0629130
$940$	0.271070	0.00884133
$941$	1.64453	0.0536100	0.0268050	−	0.999641i	$-0.491467\pi$
$941$	1.64453	0.0536100	0.0268050	+	0.999641i	$0.491467\pi$
$942$	0.784167	0.0255495
$943$	5.42273	0.176588
$944$	−9.30356	−0.302805
$945$	−4.20728	−0.136863
$946$	−9.70779	−0.315628
$947$	1.25387	0.0407453	0.0203726	−	0.999792i	$-0.493515\pi$
$947$	1.25387	0.0407453	0.0203726	+	0.999792i	$0.493515\pi$
$948$	0.0827530	0.00268769
$949$	−23.0967	−0.749751
$950$	0	0
$951$	2.32884	0.0755180
$952$	9.67823	0.313673
$953$	47.9823	1.55430	0.777149	−	0.629317i	$-0.216665\pi$
$953$	47.9823	1.55430	0.777149	+	0.629317i	$0.216665\pi$
$954$	10.4751	0.339144
$955$	3.10800	0.100573
$956$	1.89757	0.0613718
$957$	−0.191924	−0.00620402
$958$	6.84310	0.221091
$959$	−54.1457	−1.74846
$960$	−0.184265	−0.00594712
$961$	71.0598	2.29225
$962$	41.4349	1.33592
$963$	12.7942	0.412288
$964$	−19.6348	−0.632394
$965$	9.08460	0.292444
$966$	1.69904	0.0546659
$967$	10.8293	0.348246	0.174123	−	0.984724i	$-0.444291\pi$
$967$	10.8293	0.348246	0.174123	+	0.984724i	$0.444291\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	27.9187	0.896415
$971$	−37.0314	−1.18839	−0.594196	−	0.804320i	$-0.702530\pi$
$971$	−37.0314	−1.18839	−0.594196	+	0.804320i	$0.702530\pi$
$972$	−2.62335	−0.0841439
$973$	−49.3585	−1.58236
$974$	−37.0683	−1.18775
$975$	−0.891707	−0.0285575
$976$	−6.68403	−0.213951
$977$	24.2772	0.776696	0.388348	−	0.921513i	$-0.373046\pi$
$977$	24.2772	0.776696	0.388348	+	0.921513i	$0.373046\pi$
$978$	−0.0874088	−0.00279502
$979$	−2.48263	−0.0793451
$980$	14.2157	0.454103
$981$	−38.4096	−1.22633
$982$	15.9454	0.508838
$983$	31.8714	1.01654	0.508270	−	0.861198i	$-0.330285\pi$
$983$	31.8714	1.01654	0.508270	+	0.861198i	$0.330285\pi$
$984$	−0.115818	−0.00369213
$985$	46.7133	1.48841
$986$	−4.99454	−0.159059
$987$	0.0533827	0.00169919
$988$	0	0
$989$	−44.3502	−1.41026
$990$	5.64743	0.179487
$991$	19.8993	0.632121	0.316060	−	0.948739i	$-0.397640\pi$
$991$	19.8993	0.632121	0.316060	+	0.948739i	$0.397640\pi$
$992$	10.1025	0.320754
$993$	1.20675	0.0382950
$994$	−36.1698	−1.14724
$995$	34.0127	1.07828
$996$	0.196703	0.00623278
$997$	1.38008	0.0437076	0.0218538	−	0.999761i	$-0.493043\pi$
$997$	1.38008	0.0437076	0.0218538	+	0.999761i	$0.493043\pi$
$998$	17.6403	0.558393
$999$	3.79946	0.120209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bz.1.7		15
19.4	even	9		418.2.j.c.111.3	✓	30
19.5	even	9		418.2.j.c.177.3	yes	30
19.18	odd	2		7942.2.a.cb.1.9		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.c.111.3	✓	30	19.4	even	9
418.2.j.c.177.3	yes	30	19.5	even	9
7942.2.a.bz.1.7		15	1.1	even	1	trivial
7942.2.a.cb.1.9		15	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.0975736 q^{3} +1.00000 q^{4} +1.88847 q^{5} +0.0975736 q^{6} -3.81151 q^{7} -1.00000 q^{8} -2.99048 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.0975736 q^{3} +1.00000 q^{4} +1.88847 q^{5} +0.0975736 q^{6} -3.81151 q^{7} -1.00000 q^{8} -2.99048 q^{9} -1.88847 q^{10} +1.00000 q^{11} -0.0975736 q^{12} -6.37439 q^{13} +3.81151 q^{14} -0.184265 q^{15} +1.00000 q^{16} +2.53921 q^{17} +2.99048 q^{18} +1.88847 q^{20} +0.371903 q^{21} -1.00000 q^{22} -4.56852 q^{23} +0.0975736 q^{24} -1.43368 q^{25} +6.37439 q^{26} +0.584512 q^{27} -3.81151 q^{28} +1.96697 q^{29} +0.184265 q^{30} -10.1025 q^{31} -1.00000 q^{32} -0.0975736 q^{33} -2.53921 q^{34} -7.19793 q^{35} -2.99048 q^{36} +6.50021 q^{37} +0.621972 q^{39} -1.88847 q^{40} -1.18698 q^{41} -0.371903 q^{42} +9.70779 q^{43} +1.00000 q^{44} -5.64743 q^{45} +4.56852 q^{46} +0.143539 q^{47} -0.0975736 q^{48} +7.52760 q^{49} +1.43368 q^{50} -0.247760 q^{51} -6.37439 q^{52} +3.50282 q^{53} -0.584512 q^{54} +1.88847 q^{55} +3.81151 q^{56} -1.96697 q^{58} -9.30356 q^{59} -0.184265 q^{60} -6.68403 q^{61} +10.1025 q^{62} +11.3982 q^{63} +1.00000 q^{64} -12.0379 q^{65} +0.0975736 q^{66} -9.40066 q^{67} +2.53921 q^{68} +0.445767 q^{69} +7.19793 q^{70} -9.48963 q^{71} +2.99048 q^{72} +3.62336 q^{73} -6.50021 q^{74} +0.139889 q^{75} -3.81151 q^{77} -0.621972 q^{78} -0.848108 q^{79} +1.88847 q^{80} +8.91441 q^{81} +1.18698 q^{82} -2.01595 q^{83} +0.371903 q^{84} +4.79523 q^{85} -9.70779 q^{86} -0.191924 q^{87} -1.00000 q^{88} -2.48263 q^{89} +5.64743 q^{90} +24.2961 q^{91} -4.56852 q^{92} +0.985734 q^{93} -0.143539 q^{94} +0.0975736 q^{96} -14.7837 q^{97} -7.52760 q^{98} -2.99048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 12 q^{7} - 15 q^{8} + 18 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 12 * q^7 - 15 * q^8 + 18 * q^9	\( 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 12 q^{7} - 15 q^{8} + 18 q^{9} - 9 q^{10} + 15 q^{11} - 3 q^{12} - 12 q^{14} + 9 q^{15} + 15 q^{16} + 21 q^{17} - 18 q^{18} + 9 q^{20} + 27 q^{21} - 15 q^{22} + 21 q^{23} + 3 q^{24} + 36 q^{25} - 3 q^{27} + 12 q^{28} + 15 q^{29} - 9 q^{30} - 30 q^{31} - 15 q^{32} - 3 q^{33} - 21 q^{34} + 30 q^{35} + 18 q^{36} + 9 q^{37} - 9 q^{40} - 9 q^{41} - 27 q^{42} + 33 q^{43} + 15 q^{44} + 18 q^{45} - 21 q^{46} + 39 q^{47} - 3 q^{48} + 33 q^{49} - 36 q^{50} - 6 q^{51} + 6 q^{53} + 3 q^{54} + 9 q^{55} - 12 q^{56} - 15 q^{58} + 6 q^{59} + 9 q^{60} + 36 q^{61} + 30 q^{62} + 30 q^{63} + 15 q^{64} - 18 q^{65} + 3 q^{66} - 15 q^{67} + 21 q^{68} - 48 q^{69} - 30 q^{70} + 3 q^{71} - 18 q^{72} + 60 q^{73} - 9 q^{74} - 21 q^{75} + 12 q^{77} - 18 q^{79} + 9 q^{80} + 27 q^{81} + 9 q^{82} + 36 q^{83} + 27 q^{84} + 15 q^{85} - 33 q^{86} + 21 q^{87} - 15 q^{88} - 6 q^{89} - 18 q^{90} + 18 q^{91} + 21 q^{92} - 54 q^{93} - 39 q^{94} + 3 q^{96} - 33 q^{98} + 18 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 12 * q^7 - 15 * q^8 + 18 * q^9 - 9 * q^10 + 15 * q^11 - 3 * q^12 - 12 * q^14 + 9 * q^15 + 15 * q^16 + 21 * q^17 - 18 * q^18 + 9 * q^20 + 27 * q^21 - 15 * q^22 + 21 * q^23 + 3 * q^24 + 36 * q^25 - 3 * q^27 + 12 * q^28 + 15 * q^29 - 9 * q^30 - 30 * q^31 - 15 * q^32 - 3 * q^33 - 21 * q^34 + 30 * q^35 + 18 * q^36 + 9 * q^37 - 9 * q^40 - 9 * q^41 - 27 * q^42 + 33 * q^43 + 15 * q^44 + 18 * q^45 - 21 * q^46 + 39 * q^47 - 3 * q^48 + 33 * q^49 - 36 * q^50 - 6 * q^51 + 6 * q^53 + 3 * q^54 + 9 * q^55 - 12 * q^56 - 15 * q^58 + 6 * q^59 + 9 * q^60 + 36 * q^61 + 30 * q^62 + 30 * q^63 + 15 * q^64 - 18 * q^65 + 3 * q^66 - 15 * q^67 + 21 * q^68 - 48 * q^69 - 30 * q^70 + 3 * q^71 - 18 * q^72 + 60 * q^73 - 9 * q^74 - 21 * q^75 + 12 * q^77 - 18 * q^79 + 9 * q^80 + 27 * q^81 + 9 * q^82 + 36 * q^83 + 27 * q^84 + 15 * q^85 - 33 * q^86 + 21 * q^87 - 15 * q^88 - 6 * q^89 - 18 * q^90 + 18 * q^91 + 21 * q^92 - 54 * q^93 - 39 * q^94 + 3 * q^96 - 33 * q^98 + 18 * q^99

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