LMFDB - Embedded newform 6014.2.a.f.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.813553 q^{3} +1.00000 q^{4} +3.21035 q^{5} -0.813553 q^{6} -2.44817 q^{7} -1.00000 q^{8} -2.33813 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.813553 q^{3} +1.00000 q^{4} +3.21035 q^{5} -0.813553 q^{6} -2.44817 q^{7} -1.00000 q^{8} -2.33813 q^{9} -3.21035 q^{10} -1.33221 q^{11} +0.813553 q^{12} -0.684379 q^{13} +2.44817 q^{14} +2.61179 q^{15} +1.00000 q^{16} +1.98011 q^{17} +2.33813 q^{18} +2.60187 q^{19} +3.21035 q^{20} -1.99172 q^{21} +1.33221 q^{22} -0.735581 q^{23} -0.813553 q^{24} +5.30635 q^{25} +0.684379 q^{26} -4.34285 q^{27} -2.44817 q^{28} -5.70091 q^{29} -2.61179 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.08383 q^{33} -1.98011 q^{34} -7.85949 q^{35} -2.33813 q^{36} -5.79145 q^{37} -2.60187 q^{38} -0.556778 q^{39} -3.21035 q^{40} +3.57243 q^{41} +1.99172 q^{42} +1.06697 q^{43} -1.33221 q^{44} -7.50622 q^{45} +0.735581 q^{46} +6.91340 q^{47} +0.813553 q^{48} -1.00646 q^{49} -5.30635 q^{50} +1.61093 q^{51} -0.684379 q^{52} -1.67436 q^{53} +4.34285 q^{54} -4.27687 q^{55} +2.44817 q^{56} +2.11676 q^{57} +5.70091 q^{58} -4.25925 q^{59} +2.61179 q^{60} -2.08179 q^{61} -1.00000 q^{62} +5.72415 q^{63} +1.00000 q^{64} -2.19710 q^{65} +1.08383 q^{66} +7.38684 q^{67} +1.98011 q^{68} -0.598434 q^{69} +7.85949 q^{70} -2.83781 q^{71} +2.33813 q^{72} -4.96228 q^{73} +5.79145 q^{74} +4.31700 q^{75} +2.60187 q^{76} +3.26149 q^{77} +0.556778 q^{78} -13.7111 q^{79} +3.21035 q^{80} +3.48126 q^{81} -3.57243 q^{82} -1.60052 q^{83} -1.99172 q^{84} +6.35686 q^{85} -1.06697 q^{86} -4.63799 q^{87} +1.33221 q^{88} +9.13438 q^{89} +7.50622 q^{90} +1.67548 q^{91} -0.735581 q^{92} +0.813553 q^{93} -6.91340 q^{94} +8.35291 q^{95} -0.813553 q^{96} +1.00000 q^{97} +1.00646 q^{98} +3.11489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * 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
$3$	0.813553	0.469705	0.234852	−	0.972031i	$-0.424539\pi$
$3$	0.813553	0.469705	0.234852	+	0.972031i	$0.424539\pi$
$4$	1.00000	0.500000
$5$	3.21035	1.43571	0.717856	−	0.696191i	$-0.245123\pi$
$5$	3.21035	1.43571	0.717856	+	0.696191i	$0.245123\pi$
$6$	−0.813553	−0.332132
$7$	−2.44817	−0.925322	−0.462661	−	0.886535i	$-0.653105\pi$
$7$	−2.44817	−0.925322	−0.462661	+	0.886535i	$0.653105\pi$
$8$	−1.00000	−0.353553
$9$	−2.33813	−0.779377
$10$	−3.21035	−1.01520
$11$	−1.33221	−0.401678	−0.200839	−	0.979624i	$-0.564367\pi$
$11$	−1.33221	−0.401678	−0.200839	+	0.979624i	$0.564367\pi$
$12$	0.813553	0.234852
$13$	−0.684379	−0.189813	−0.0949063	−	0.995486i	$-0.530255\pi$
$13$	−0.684379	−0.189813	−0.0949063	+	0.995486i	$0.530255\pi$
$14$	2.44817	0.654301
$15$	2.61179	0.674361
$16$	1.00000	0.250000
$17$	1.98011	0.480248	0.240124	−	0.970742i	$-0.422812\pi$
$17$	1.98011	0.480248	0.240124	+	0.970742i	$0.422812\pi$
$18$	2.33813	0.551103
$19$	2.60187	0.596910	0.298455	−	0.954424i	$-0.403529\pi$
$19$	2.60187	0.596910	0.298455	+	0.954424i	$0.403529\pi$
$20$	3.21035	0.717856
$21$	−1.99172	−0.434628
$22$	1.33221	0.284029
$23$	−0.735581	−0.153379	−0.0766896	−	0.997055i	$-0.524435\pi$
$23$	−0.735581	−0.153379	−0.0766896	+	0.997055i	$0.524435\pi$
$24$	−0.813553	−0.166066
$25$	5.30635	1.06127
$26$	0.684379	0.134218
$27$	−4.34285	−0.835782
$28$	−2.44817	−0.462661
$29$	−5.70091	−1.05863	−0.529316	−	0.848425i	$-0.677552\pi$
$29$	−5.70091	−1.05863	−0.529316	+	0.848425i	$0.677552\pi$
$30$	−2.61179	−0.476845
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−1.08383	−0.188670
$34$	−1.98011	−0.339587
$35$	−7.85949	−1.32850
$36$	−2.33813	−0.389689
$37$	−5.79145	−0.952109	−0.476054	−	0.879416i	$-0.657933\pi$
$37$	−5.79145	−0.952109	−0.476054	+	0.879416i	$0.657933\pi$
$38$	−2.60187	−0.422079
$39$	−0.556778	−0.0891559
$40$	−3.21035	−0.507601
$41$	3.57243	0.557920	0.278960	−	0.960303i	$-0.410010\pi$
$41$	3.57243	0.557920	0.278960	+	0.960303i	$0.410010\pi$
$42$	1.99172	0.307329
$43$	1.06697	0.162711	0.0813557	−	0.996685i	$-0.474075\pi$
$43$	1.06697	0.162711	0.0813557	+	0.996685i	$0.474075\pi$
$44$	−1.33221	−0.200839
$45$	−7.50622	−1.11896
$46$	0.735581	0.108456
$47$	6.91340	1.00842	0.504212	−	0.863580i	$-0.331783\pi$
$47$	6.91340	1.00842	0.504212	+	0.863580i	$0.331783\pi$
$48$	0.813553	0.117426
$49$	−1.00646	−0.143780
$50$	−5.30635	−0.750432
$51$	1.61093	0.225575
$52$	−0.684379	−0.0949063
$53$	−1.67436	−0.229991	−0.114996	−	0.993366i	$-0.536685\pi$
$53$	−1.67436	−0.229991	−0.114996	+	0.993366i	$0.536685\pi$
$54$	4.34285	0.590987
$55$	−4.27687	−0.576694
$56$	2.44817	0.327151
$57$	2.11676	0.280371
$58$	5.70091	0.748566
$59$	−4.25925	−0.554507	−0.277253	−	0.960797i	$-0.589424\pi$
$59$	−4.25925	−0.554507	−0.277253	+	0.960797i	$0.589424\pi$
$60$	2.61179	0.337181
$61$	−2.08179	−0.266547	−0.133273	−	0.991079i	$-0.542549\pi$
$61$	−2.08179	−0.266547	−0.133273	+	0.991079i	$0.542549\pi$
$62$	−1.00000	−0.127000
$63$	5.72415	0.721175
$64$	1.00000	0.125000
$65$	−2.19710	−0.272516
$66$	1.08383	0.133410
$67$	7.38684	0.902446	0.451223	−	0.892411i	$-0.350988\pi$
$67$	7.38684	0.902446	0.451223	+	0.892411i	$0.350988\pi$
$68$	1.98011	0.240124
$69$	−0.598434	−0.0720430
$70$	7.85949	0.939389
$71$	−2.83781	−0.336787	−0.168393	−	0.985720i	$-0.553858\pi$
$71$	−2.83781	−0.336787	−0.168393	+	0.985720i	$0.553858\pi$
$72$	2.33813	0.275551
$73$	−4.96228	−0.580791	−0.290396	−	0.956907i	$-0.593787\pi$
$73$	−4.96228	−0.580791	−0.290396	+	0.956907i	$0.593787\pi$
$74$	5.79145	0.673243
$75$	4.31700	0.498484
$76$	2.60187	0.298455
$77$	3.26149	0.371681
$78$	0.556778	0.0630427
$79$	−13.7111	−1.54262	−0.771309	−	0.636461i	$-0.780398\pi$
$79$	−13.7111	−1.54262	−0.771309	+	0.636461i	$0.780398\pi$
$80$	3.21035	0.358928
$81$	3.48126	0.386806
$82$	−3.57243	−0.394509
$83$	−1.60052	−0.175680	−0.0878399	−	0.996135i	$-0.527996\pi$
$83$	−1.60052	−0.175680	−0.0878399	+	0.996135i	$0.527996\pi$
$84$	−1.99172	−0.217314
$85$	6.35686	0.689499
$86$	−1.06697	−0.115054
$87$	−4.63799	−0.497245
$88$	1.33221	0.142014
$89$	9.13438	0.968243	0.484121	−	0.875001i	$-0.339139\pi$
$89$	9.13438	0.968243	0.484121	+	0.875001i	$0.339139\pi$
$90$	7.50622	0.791226
$91$	1.67548	0.175638
$92$	−0.735581	−0.0766896
$93$	0.813553	0.0843615
$94$	−6.91340	−0.713063
$95$	8.35291	0.856991
$96$	−0.813553	−0.0830329
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	1.00646	0.101668
$99$	3.11489	0.313058
$100$	5.30635	0.530635
$101$	−7.74493	−0.770649	−0.385324	−	0.922781i	$-0.625910\pi$
$101$	−7.74493	−0.770649	−0.385324	+	0.922781i	$0.625910\pi$
$102$	−1.61093	−0.159506
$103$	−4.68746	−0.461869	−0.230934	−	0.972969i	$-0.574178\pi$
$103$	−4.68746	−0.461869	−0.230934	+	0.972969i	$0.574178\pi$
$104$	0.684379	0.0671089
$105$	−6.39411	−0.624001
$106$	1.67436	0.162628
$107$	−3.50802	−0.339133	−0.169567	−	0.985519i	$-0.554237\pi$
$107$	−3.50802	−0.339133	−0.169567	+	0.985519i	$0.554237\pi$
$108$	−4.34285	−0.417891
$109$	4.78229	0.458060	0.229030	−	0.973419i	$-0.426445\pi$
$109$	4.78229	0.458060	0.229030	+	0.973419i	$0.426445\pi$
$110$	4.27687	0.407784
$111$	−4.71165	−0.447210
$112$	−2.44817	−0.231330
$113$	−14.7257	−1.38527	−0.692637	−	0.721287i	$-0.743551\pi$
$113$	−14.7257	−1.38527	−0.692637	+	0.721287i	$0.743551\pi$
$114$	−2.11676	−0.198253
$115$	−2.36147	−0.220209
$116$	−5.70091	−0.529316
$117$	1.60017	0.147936
$118$	4.25925	0.392096
$119$	−4.84766	−0.444384
$120$	−2.61179	−0.238423
$121$	−9.22521	−0.838655
$122$	2.08179	0.188477
$123$	2.90636	0.262058
$124$	1.00000	0.0898027
$125$	0.983507	0.0879675
$126$	−5.72415	−0.509948
$127$	2.85327	0.253187	0.126593	−	0.991955i	$-0.459596\pi$
$127$	2.85327	0.253187	0.126593	+	0.991955i	$0.459596\pi$
$128$	−1.00000	−0.0883883
$129$	0.868037	0.0764264
$130$	2.19710	0.192698
$131$	−21.5537	−1.88316	−0.941580	−	0.336790i	$-0.890659\pi$
$131$	−21.5537	−1.88316	−0.941580	+	0.336790i	$0.890659\pi$
$132$	−1.08383	−0.0943350
$133$	−6.36982	−0.552333
$134$	−7.38684	−0.638126
$135$	−13.9421	−1.19994
$136$	−1.98011	−0.169793
$137$	−23.0432	−1.96872	−0.984358	−	0.176178i	$-0.943627\pi$
$137$	−23.0432	−1.96872	−0.984358	+	0.176178i	$0.943627\pi$
$138$	0.598434	0.0509421
$139$	−0.550659	−0.0467063	−0.0233531	−	0.999727i	$-0.507434\pi$
$139$	−0.550659	−0.0467063	−0.0233531	+	0.999727i	$0.507434\pi$
$140$	−7.85949	−0.664248
$141$	5.62442	0.473661
$142$	2.83781	0.238144
$143$	0.911739	0.0762434
$144$	−2.33813	−0.194844
$145$	−18.3019	−1.51989
$146$	4.96228	0.410681
$147$	−0.818806	−0.0675340
$148$	−5.79145	−0.476054
$149$	23.2275	1.90287	0.951437	−	0.307844i	$-0.0996076\pi$
$149$	23.2275	1.90287	0.951437	+	0.307844i	$0.0996076\pi$
$150$	−4.31700	−0.352482
$151$	23.7558	1.93322	0.966611	−	0.256248i	$-0.0824865\pi$
$151$	23.7558	1.93322	0.966611	+	0.256248i	$0.0824865\pi$
$152$	−2.60187	−0.211039
$153$	−4.62977	−0.374295
$154$	−3.26149	−0.262818
$155$	3.21035	0.257862
$156$	−0.556778	−0.0445779
$157$	−24.1488	−1.92729	−0.963643	−	0.267194i	$-0.913904\pi$
$157$	−24.1488	−1.92729	−0.963643	+	0.267194i	$0.913904\pi$
$158$	13.7111	1.09080
$159$	−1.36218	−0.108028
$160$	−3.21035	−0.253801
$161$	1.80083	0.141925
$162$	−3.48126	−0.273513
$163$	9.28226	0.727043	0.363521	−	0.931586i	$-0.381574\pi$
$163$	9.28226	0.727043	0.363521	+	0.931586i	$0.381574\pi$
$164$	3.57243	0.278960
$165$	−3.47946	−0.270876
$166$	1.60052	0.124224
$167$	−1.75511	−0.135815	−0.0679074	−	0.997692i	$-0.521632\pi$
$167$	−1.75511	−0.135815	−0.0679074	+	0.997692i	$0.521632\pi$
$168$	1.99172	0.153664
$169$	−12.5316	−0.963971
$170$	−6.35686	−0.487549
$171$	−6.08351	−0.465218
$172$	1.06697	0.0813557
$173$	−10.6874	−0.812551	−0.406276	−	0.913751i	$-0.633173\pi$
$173$	−10.6874	−0.812551	−0.406276	+	0.913751i	$0.633173\pi$
$174$	4.63799	0.351605
$175$	−12.9909	−0.982017
$176$	−1.33221	−0.100419
$177$	−3.46512	−0.260455
$178$	−9.13438	−0.684651
$179$	−21.0616	−1.57421	−0.787107	−	0.616816i	$-0.788422\pi$
$179$	−21.0616	−1.57421	−0.787107	+	0.616816i	$0.788422\pi$
$180$	−7.50622	−0.559481
$181$	−10.4945	−0.780049	−0.390024	−	0.920804i	$-0.627533\pi$
$181$	−10.4945	−0.780049	−0.390024	+	0.920804i	$0.627533\pi$
$182$	−1.67548	−0.124195
$183$	−1.69365	−0.125198
$184$	0.735581	0.0542278
$185$	−18.5926	−1.36695
$186$	−0.813553	−0.0596526
$187$	−2.63794	−0.192905
$188$	6.91340	0.504212
$189$	10.6320	0.773368
$190$	−8.35291	−0.605984
$191$	−15.9143	−1.15152	−0.575761	−	0.817618i	$-0.695294\pi$
$191$	−15.9143	−1.15152	−0.575761	+	0.817618i	$0.695294\pi$
$192$	0.813553	0.0587131
$193$	−5.75066	−0.413942	−0.206971	−	0.978347i	$-0.566361\pi$
$193$	−5.75066	−0.413942	−0.206971	+	0.978347i	$0.566361\pi$
$194$	−1.00000	−0.0717958
$195$	−1.78745	−0.128002
$196$	−1.00646	−0.0718898
$197$	5.94855	0.423817	0.211908	−	0.977290i	$-0.432032\pi$
$197$	5.94855	0.423817	0.211908	+	0.977290i	$0.432032\pi$
$198$	−3.11489	−0.221366
$199$	−8.23315	−0.583632	−0.291816	−	0.956474i	$-0.594260\pi$
$199$	−8.23315	−0.583632	−0.291816	+	0.956474i	$0.594260\pi$
$200$	−5.30635	−0.375216
$201$	6.00959	0.423884
$202$	7.74493	0.544931
$203$	13.9568	0.979576
$204$	1.61093	0.112788
$205$	11.4688	0.801013
$206$	4.68746	0.326591
$207$	1.71989	0.119540
$208$	−0.684379	−0.0474531
$209$	−3.46625	−0.239765
$210$	6.39411	0.441235
$211$	−7.24671	−0.498884	−0.249442	−	0.968390i	$-0.580247\pi$
$211$	−7.24671	−0.498884	−0.249442	+	0.968390i	$0.580247\pi$
$212$	−1.67436	−0.114996
$213$	−2.30871	−0.158190
$214$	3.50802	0.239803
$215$	3.42535	0.233607
$216$	4.34285	0.295494
$217$	−2.44817	−0.166193
$218$	−4.78229	−0.323897
$219$	−4.03708	−0.272800
$220$	−4.27687	−0.288347
$221$	−1.35515	−0.0911572
$222$	4.71165	0.316225
$223$	−6.97023	−0.466761	−0.233381	−	0.972385i	$-0.574979\pi$
$223$	−6.97023	−0.466761	−0.233381	+	0.972385i	$0.574979\pi$
$224$	2.44817	0.163575
$225$	−12.4070	−0.827130
$226$	14.7257	0.979536
$227$	−6.13214	−0.407004	−0.203502	−	0.979075i	$-0.565232\pi$
$227$	−6.13214	−0.407004	−0.203502	+	0.979075i	$0.565232\pi$
$228$	2.11676	0.140186
$229$	28.0178	1.85147	0.925735	−	0.378172i	$-0.123447\pi$
$229$	28.0178	1.85147	0.925735	+	0.378172i	$0.123447\pi$
$230$	2.36147	0.155711
$231$	2.65339	0.174580
$232$	5.70091	0.374283
$233$	−14.7016	−0.963132	−0.481566	−	0.876410i	$-0.659932\pi$
$233$	−14.7016	−0.963132	−0.481566	+	0.876410i	$0.659932\pi$
$234$	−1.60017	−0.104606
$235$	22.1944	1.44781
$236$	−4.25925	−0.277253
$237$	−11.1547	−0.724575
$238$	4.84766	0.314227
$239$	9.62179	0.622382	0.311191	−	0.950347i	$-0.399272\pi$
$239$	9.62179	0.622382	0.311191	+	0.950347i	$0.399272\pi$
$240$	2.61179	0.168590
$241$	5.35211	0.344760	0.172380	−	0.985031i	$-0.444854\pi$
$241$	5.35211	0.344760	0.172380	+	0.985031i	$0.444854\pi$
$242$	9.22521	0.593019
$243$	15.8607	1.01747
$244$	−2.08179	−0.133273
$245$	−3.23108	−0.206426
$246$	−2.90636	−0.185303
$247$	−1.78066	−0.113301
$248$	−1.00000	−0.0635001
$249$	−1.30211	−0.0825176
$250$	−0.983507	−0.0622024
$251$	−0.393025	−0.0248075	−0.0124037	−	0.999923i	$-0.503948\pi$
$251$	−0.393025	−0.0248075	−0.0124037	+	0.999923i	$0.503948\pi$
$252$	5.72415	0.360587
$253$	0.979951	0.0616090
$254$	−2.85327	−0.179030
$255$	5.17164	0.323861
$256$	1.00000	0.0625000
$257$	−13.3372	−0.831949	−0.415974	−	0.909376i	$-0.636559\pi$
$257$	−13.3372	−0.831949	−0.415974	+	0.909376i	$0.636559\pi$
$258$	−0.868037	−0.0540416
$259$	14.1785	0.881007
$260$	−2.19710	−0.136258
$261$	13.3295	0.825074
$262$	21.5537	1.33160
$263$	18.4319	1.13656	0.568281	−	0.822835i	$-0.307609\pi$
$263$	18.4319	1.13656	0.568281	+	0.822835i	$0.307609\pi$
$264$	1.08383	0.0667049
$265$	−5.37529	−0.330201
$266$	6.36982	0.390559
$267$	7.43130	0.454788
$268$	7.38684	0.451223
$269$	3.63092	0.221381	0.110691	−	0.993855i	$-0.464694\pi$
$269$	3.63092	0.221381	0.110691	+	0.993855i	$0.464694\pi$
$270$	13.9421	0.848488
$271$	−5.80499	−0.352628	−0.176314	−	0.984334i	$-0.556417\pi$
$271$	−5.80499	−0.352628	−0.176314	+	0.984334i	$0.556417\pi$
$272$	1.98011	0.120062
$273$	1.36309	0.0824979
$274$	23.0432	1.39209
$275$	−7.06920	−0.426289
$276$	−0.598434	−0.0360215
$277$	−11.9685	−0.719119	−0.359559	−	0.933122i	$-0.617073\pi$
$277$	−11.9685	−0.719119	−0.359559	+	0.933122i	$0.617073\pi$
$278$	0.550659	0.0330263
$279$	−2.33813	−0.139980
$280$	7.85949	0.469694
$281$	10.4832	0.625375	0.312687	−	0.949856i	$-0.398771\pi$
$281$	10.4832	0.625375	0.312687	+	0.949856i	$0.398771\pi$
$282$	−5.62442	−0.334929
$283$	−12.9051	−0.767128	−0.383564	−	0.923514i	$-0.625303\pi$
$283$	−12.9051	−0.767128	−0.383564	+	0.923514i	$0.625303\pi$
$284$	−2.83781	−0.168393
$285$	6.79554	0.402533
$286$	−0.911739	−0.0539122
$287$	−8.74592	−0.516255
$288$	2.33813	0.137776
$289$	−13.0791	−0.769361
$290$	18.3019	1.07473
$291$	0.813553	0.0476913
$292$	−4.96228	−0.290396
$293$	15.1548	0.885353	0.442676	−	0.896682i	$-0.354029\pi$
$293$	15.1548	0.885353	0.442676	+	0.896682i	$0.354029\pi$
$294$	0.818806	0.0477538
$295$	−13.6737	−0.796113
$296$	5.79145	0.336621
$297$	5.78561	0.335715
$298$	−23.2275	−1.34553
$299$	0.503416	0.0291133
$300$	4.31700	0.249242
$301$	−2.61213	−0.150560
$302$	−23.7558	−1.36699
$303$	−6.30091	−0.361978
$304$	2.60187	0.149227
$305$	−6.68329	−0.382684
$306$	4.62977	0.264666
$307$	31.8280	1.81652	0.908260	−	0.418407i	$-0.137411\pi$
$307$	31.8280	1.81652	0.908260	+	0.418407i	$0.137411\pi$
$308$	3.26149	0.185841
$309$	−3.81349	−0.216942
$310$	−3.21035	−0.182336
$311$	5.78987	0.328313	0.164157	−	0.986434i	$-0.447510\pi$
$311$	5.78987	0.328313	0.164157	+	0.986434i	$0.447510\pi$
$312$	0.556778	0.0315214
$313$	25.4505	1.43855	0.719274	−	0.694726i	$-0.244474\pi$
$313$	25.4505	1.43855	0.719274	+	0.694726i	$0.244474\pi$
$314$	24.1488	1.36280
$315$	18.3765	1.03540
$316$	−13.7111	−0.771309
$317$	−18.0177	−1.01197	−0.505986	−	0.862542i	$-0.668871\pi$
$317$	−18.0177	−1.01197	−0.505986	+	0.862542i	$0.668871\pi$
$318$	1.36218	0.0763873
$319$	7.59483	0.425229
$320$	3.21035	0.179464
$321$	−2.85396	−0.159293
$322$	−1.80083	−0.100356
$323$	5.15200	0.286665
$324$	3.48126	0.193403
$325$	−3.63156	−0.201443
$326$	−9.28226	−0.514097
$327$	3.89064	0.215153
$328$	−3.57243	−0.197254
$329$	−16.9252	−0.933116
$330$	3.47946	0.191538
$331$	23.7616	1.30606	0.653028	−	0.757334i	$-0.273499\pi$
$331$	23.7616	1.30606	0.653028	+	0.757334i	$0.273499\pi$
$332$	−1.60052	−0.0878399
$333$	13.5412	0.742052
$334$	1.75511	0.0960355
$335$	23.7144	1.29565
$336$	−1.99172	−0.108657
$337$	−3.40518	−0.185492	−0.0927459	−	0.995690i	$-0.529564\pi$
$337$	−3.40518	−0.185492	−0.0927459	+	0.995690i	$0.529564\pi$
$338$	12.5316	0.681631
$339$	−11.9801	−0.650670
$340$	6.35686	0.344749
$341$	−1.33221	−0.0721434
$342$	6.08351	0.328959
$343$	19.6012	1.05836
$344$	−1.06697	−0.0575272
$345$	−1.92118	−0.103433
$346$	10.6874	0.574560
$347$	35.8252	1.92320	0.961598	−	0.274463i	$-0.0885002\pi$
$347$	35.8252	1.92320	0.961598	+	0.274463i	$0.0885002\pi$
$348$	−4.63799	−0.248623
$349$	−29.2191	−1.56406	−0.782030	−	0.623240i	$-0.785816\pi$
$349$	−29.2191	−1.56406	−0.782030	+	0.623240i	$0.785816\pi$
$350$	12.9909	0.694391
$351$	2.97216	0.158642
$352$	1.33221	0.0710072
$353$	8.67082	0.461501	0.230751	−	0.973013i	$-0.425882\pi$
$353$	8.67082	0.461501	0.230751	+	0.973013i	$0.425882\pi$
$354$	3.46512	0.184169
$355$	−9.11038	−0.483529
$356$	9.13438	0.484121
$357$	−3.94383	−0.208730
$358$	21.0616	1.11314
$359$	−6.28877	−0.331908	−0.165954	−	0.986133i	$-0.553070\pi$
$359$	−6.28877	−0.331908	−0.165954	+	0.986133i	$0.553070\pi$
$360$	7.50622	0.395613
$361$	−12.2303	−0.643699
$362$	10.4945	0.551578
$363$	−7.50519	−0.393920
$364$	1.67548	0.0878188
$365$	−15.9307	−0.833849
$366$	1.69365	0.0885285
$367$	8.99218	0.469388	0.234694	−	0.972069i	$-0.424591\pi$
$367$	8.99218	0.469388	0.234694	+	0.972069i	$0.424591\pi$
$368$	−0.735581	−0.0383448
$369$	−8.35281	−0.434830
$370$	18.5926	0.966583
$371$	4.09912	0.212816
$372$	0.813553	0.0421807
$373$	0.850669	0.0440460	0.0220230	−	0.999757i	$-0.492989\pi$
$373$	0.850669	0.0440460	0.0220230	+	0.999757i	$0.492989\pi$
$374$	2.63794	0.136404
$375$	0.800135	0.0413188
$376$	−6.91340	−0.356531
$377$	3.90158	0.200942
$378$	−10.6320	−0.546853
$379$	−23.1234	−1.18777	−0.593886	−	0.804549i	$-0.702407\pi$
$379$	−23.1234	−1.18777	−0.593886	+	0.804549i	$0.702407\pi$
$380$	8.35291	0.428495
$381$	2.32128	0.118923
$382$	15.9143	0.814249
$383$	−2.29931	−0.117489	−0.0587445	−	0.998273i	$-0.518710\pi$
$383$	−2.29931	−0.117489	−0.0587445	+	0.998273i	$0.518710\pi$
$384$	−0.813553	−0.0415164
$385$	10.4705	0.533627
$386$	5.75066	0.292701
$387$	−2.49472	−0.126814
$388$	1.00000	0.0507673
$389$	−9.10438	−0.461610	−0.230805	−	0.973000i	$-0.574136\pi$
$389$	−9.10438	−0.461610	−0.230805	+	0.973000i	$0.574136\pi$
$390$	1.78745	0.0905112
$391$	−1.45654	−0.0736601
$392$	1.00646	0.0508338
$393$	−17.5351	−0.884529
$394$	−5.94855	−0.299684
$395$	−44.0174	−2.21476
$396$	3.11489	0.156529
$397$	28.5240	1.43158	0.715789	−	0.698316i	$-0.246067\pi$
$397$	28.5240	1.43158	0.715789	+	0.698316i	$0.246067\pi$
$398$	8.23315	0.412690
$399$	−5.18219	−0.259434
$400$	5.30635	0.265318
$401$	−13.6996	−0.684127	−0.342064	−	0.939677i	$-0.611126\pi$
$401$	−13.6996	−0.684127	−0.342064	+	0.939677i	$0.611126\pi$
$402$	−6.00959	−0.299731
$403$	−0.684379	−0.0340913
$404$	−7.74493	−0.385324
$405$	11.1761	0.555343
$406$	−13.9568	−0.692665
$407$	7.71545	0.382441
$408$	−1.61093	−0.0797528
$409$	−31.9271	−1.57870	−0.789348	−	0.613946i	$-0.789581\pi$
$409$	−31.9271	−1.57870	−0.789348	+	0.613946i	$0.789581\pi$
$410$	−11.4688	−0.566401
$411$	−18.7469	−0.924716
$412$	−4.68746	−0.230934
$413$	10.4274	0.513097
$414$	−1.71989	−0.0845278
$415$	−5.13823	−0.252226
$416$	0.684379	0.0335544
$417$	−0.447990	−0.0219382
$418$	3.46625	0.169540
$419$	1.76000	0.0859815	0.0429908	−	0.999075i	$-0.486311\pi$
$419$	1.76000	0.0859815	0.0429908	+	0.999075i	$0.486311\pi$
$420$	−6.39411	−0.312001
$421$	5.38600	0.262497	0.131249	−	0.991349i	$-0.458101\pi$
$421$	5.38600	0.262497	0.131249	+	0.991349i	$0.458101\pi$
$422$	7.24671	0.352764
$423$	−16.1644	−0.785942
$424$	1.67436	0.0813142
$425$	10.5072	0.509674
$426$	2.30871	0.111857
$427$	5.09659	0.246641
$428$	−3.50802	−0.169567
$429$	0.741748	0.0358119
$430$	−3.42535	−0.165185
$431$	−36.0744	−1.73764	−0.868821	−	0.495127i	$-0.835122\pi$
$431$	−36.0744	−1.73764	−0.868821	+	0.495127i	$0.835122\pi$
$432$	−4.34285	−0.208946
$433$	−1.92273	−0.0924007	−0.0462003	−	0.998932i	$-0.514711\pi$
$433$	−1.92273	−0.0924007	−0.0462003	+	0.998932i	$0.514711\pi$
$434$	2.44817	0.117516
$435$	−14.8896	−0.713901
$436$	4.78229	0.229030
$437$	−1.91389	−0.0915536
$438$	4.03708	0.192899
$439$	10.1478	0.484328	0.242164	−	0.970235i	$-0.422143\pi$
$439$	10.1478	0.484328	0.242164	+	0.970235i	$0.422143\pi$
$440$	4.27687	0.203892
$441$	2.35323	0.112059
$442$	1.35515	0.0644578
$443$	14.0913	0.669499	0.334749	−	0.942307i	$-0.391348\pi$
$443$	14.0913	0.669499	0.334749	+	0.942307i	$0.391348\pi$
$444$	−4.71165	−0.223605
$445$	29.3246	1.39012
$446$	6.97023	0.330050
$447$	18.8968	0.893789
$448$	−2.44817	−0.115665
$449$	−30.6163	−1.44487	−0.722436	−	0.691438i	$-0.756978\pi$
$449$	−30.6163	−1.44487	−0.722436	+	0.691438i	$0.756978\pi$
$450$	12.4070	0.584870
$451$	−4.75924	−0.224104
$452$	−14.7257	−0.692637
$453$	19.3266	0.908044
$454$	6.13214	0.287795
$455$	5.37887	0.252165
$456$	−2.11676	−0.0991263
$457$	13.0631	0.611064	0.305532	−	0.952182i	$-0.401166\pi$
$457$	13.0631	0.611064	0.305532	+	0.952182i	$0.401166\pi$
$458$	−28.0178	−1.30919
$459$	−8.59935	−0.401383
$460$	−2.36147	−0.110104
$461$	21.5316	1.00282	0.501412	−	0.865209i	$-0.332814\pi$
$461$	21.5316	1.00282	0.501412	+	0.865209i	$0.332814\pi$
$462$	−2.65339	−0.123447
$463$	14.2734	0.663343	0.331671	−	0.943395i	$-0.392387\pi$
$463$	14.2734	0.663343	0.331671	+	0.943395i	$0.392387\pi$
$464$	−5.70091	−0.264658
$465$	2.61179	0.121119
$466$	14.7016	0.681037
$467$	−21.3403	−0.987512	−0.493756	−	0.869600i	$-0.664376\pi$
$467$	−21.3403	−0.987512	−0.493756	+	0.869600i	$0.664376\pi$
$468$	1.60017	0.0739678
$469$	−18.0843	−0.835053
$470$	−22.1944	−1.02375
$471$	−19.6463	−0.905256
$472$	4.25925	0.196048
$473$	−1.42143	−0.0653576
$474$	11.1547	0.512352
$475$	13.8064	0.633483
$476$	−4.84766	−0.222192
$477$	3.91488	0.179250
$478$	−9.62179	−0.440090
$479$	39.3383	1.79741	0.898706	−	0.438552i	$-0.144508\pi$
$479$	39.3383	1.79741	0.898706	+	0.438552i	$0.144508\pi$
$480$	−2.61179	−0.119211
$481$	3.96355	0.180722
$482$	−5.35211	−0.243782
$483$	1.46507	0.0666630
$484$	−9.22521	−0.419328
$485$	3.21035	0.145775
$486$	−15.8607	−0.719458
$487$	−21.6302	−0.980160	−0.490080	−	0.871678i	$-0.663032\pi$
$487$	−21.6302	−0.980160	−0.490080	+	0.871678i	$0.663032\pi$
$488$	2.08179	0.0942384
$489$	7.55161	0.341495
$490$	3.23108	0.145965
$491$	3.42268	0.154463	0.0772317	−	0.997013i	$-0.475392\pi$
$491$	3.42268	0.154463	0.0772317	+	0.997013i	$0.475392\pi$
$492$	2.90636	0.131029
$493$	−11.2885	−0.508407
$494$	1.78066	0.0801159
$495$	9.99990	0.449462
$496$	1.00000	0.0449013
$497$	6.94746	0.311636
$498$	1.30211	0.0583488
$499$	2.48719	0.111342	0.0556710	−	0.998449i	$-0.482270\pi$
$499$	2.48719	0.111342	0.0556710	+	0.998449i	$0.482270\pi$
$500$	0.983507	0.0439838
$501$	−1.42788	−0.0637928
$502$	0.393025	0.0175415
$503$	−28.6820	−1.27887	−0.639433	−	0.768847i	$-0.720831\pi$
$503$	−28.6820	−1.27887	−0.639433	+	0.768847i	$0.720831\pi$
$504$	−5.72415	−0.254974
$505$	−24.8639	−1.10643
$506$	−0.979951	−0.0435642
$507$	−10.1951	−0.452782
$508$	2.85327	0.126593
$509$	−25.2483	−1.11911	−0.559556	−	0.828793i	$-0.689028\pi$
$509$	−25.2483	−1.11911	−0.559556	+	0.828793i	$0.689028\pi$
$510$	−5.17164	−0.229004
$511$	12.1485	0.537419
$512$	−1.00000	−0.0441942
$513$	−11.2995	−0.498887
$514$	13.3372	0.588277
$515$	−15.0484	−0.663111
$516$	0.868037	0.0382132
$517$	−9.21013	−0.405061
$518$	−14.1785	−0.622966
$519$	−8.69480	−0.381659
$520$	2.19710	0.0963490
$521$	33.5784	1.47109	0.735547	−	0.677473i	$-0.236925\pi$
$521$	33.5784	1.47109	0.735547	+	0.677473i	$0.236925\pi$
$522$	−13.3295	−0.583416
$523$	14.1403	0.618311	0.309155	−	0.951012i	$-0.399954\pi$
$523$	14.1403	0.618311	0.309155	+	0.951012i	$0.399954\pi$
$524$	−21.5537	−0.941580
$525$	−10.5688	−0.461258
$526$	−18.4319	−0.803671
$527$	1.98011	0.0862552
$528$	−1.08383	−0.0471675
$529$	−22.4589	−0.976475
$530$	5.37529	0.233488
$531$	9.95869	0.432170
$532$	−6.36982	−0.276167
$533$	−2.44490	−0.105900
$534$	−7.43130	−0.321584
$535$	−11.2620	−0.486898
$536$	−7.38684	−0.319063
$537$	−17.1347	−0.739416
$538$	−3.63092	−0.156540
$539$	1.34082	0.0577531
$540$	−13.9421	−0.599972
$541$	5.04045	0.216706	0.108353	−	0.994112i	$-0.465442\pi$
$541$	5.04045	0.216706	0.108353	+	0.994112i	$0.465442\pi$
$542$	5.80499	0.249346
$543$	−8.53782	−0.366393
$544$	−1.98011	−0.0848967
$545$	15.3528	0.657643
$546$	−1.36309	−0.0583348
$547$	28.2242	1.20678	0.603390	−	0.797446i	$-0.293816\pi$
$547$	28.2242	1.20678	0.603390	+	0.797446i	$0.293816\pi$
$548$	−23.0432	−0.984358
$549$	4.86751	0.207740
$550$	7.06920	0.301432
$551$	−14.8330	−0.631908
$552$	0.598434	0.0254710
$553$	33.5671	1.42742
$554$	11.9685	0.508494
$555$	−15.1261	−0.642065
$556$	−0.550659	−0.0233531
$557$	−23.7028	−1.00432	−0.502160	−	0.864775i	$-0.667461\pi$
$557$	−23.7028	−1.00432	−0.502160	+	0.864775i	$0.667461\pi$
$558$	2.33813	0.0989810
$559$	−0.730212	−0.0308847
$560$	−7.85949	−0.332124
$561$	−2.14610	−0.0906084
$562$	−10.4832	−0.442207
$563$	22.9369	0.966674	0.483337	−	0.875434i	$-0.339425\pi$
$563$	22.9369	0.966674	0.483337	+	0.875434i	$0.339425\pi$
$564$	5.62442	0.236831
$565$	−47.2745	−1.98885
$566$	12.9051	0.542441
$567$	−8.52271	−0.357920
$568$	2.83781	0.119072
$569$	26.7023	1.11942	0.559710	−	0.828689i	$-0.310913\pi$
$569$	26.7023	1.11942	0.559710	+	0.828689i	$0.310913\pi$
$570$	−6.79554	−0.284634
$571$	15.4021	0.644559	0.322279	−	0.946645i	$-0.395551\pi$
$571$	15.4021	0.644559	0.322279	+	0.946645i	$0.395551\pi$
$572$	0.911739	0.0381217
$573$	−12.9472	−0.540875
$574$	8.74592	0.365048
$575$	−3.90325	−0.162777
$576$	−2.33813	−0.0974222
$577$	−28.0719	−1.16865	−0.584324	−	0.811521i	$-0.698640\pi$
$577$	−28.0719	−1.16865	−0.584324	+	0.811521i	$0.698640\pi$
$578$	13.0791	0.544021
$579$	−4.67847	−0.194430
$580$	−18.3019	−0.759946
$581$	3.91834	0.162560
$582$	−0.813553	−0.0337228
$583$	2.23061	0.0923823
$584$	4.96228	0.205341
$585$	5.13710	0.212393
$586$	−15.1548	−0.626039
$587$	24.5066	1.01150	0.505748	−	0.862681i	$-0.331216\pi$
$587$	24.5066	1.01150	0.505748	+	0.862681i	$0.331216\pi$
$588$	−0.818806	−0.0337670
$589$	2.60187	0.107208
$590$	13.6737	0.562937
$591$	4.83946	0.199069
$592$	−5.79145	−0.238027
$593$	10.8250	0.444531	0.222266	−	0.974986i	$-0.428655\pi$
$593$	10.8250	0.444531	0.222266	+	0.974986i	$0.428655\pi$
$594$	−5.78561	−0.237386
$595$	−15.5627	−0.638008
$596$	23.2275	0.951437
$597$	−6.69810	−0.274135
$598$	−0.503416	−0.0205862
$599$	36.5479	1.49331	0.746654	−	0.665213i	$-0.231659\pi$
$599$	36.5479	1.49331	0.746654	+	0.665213i	$0.231659\pi$
$600$	−4.31700	−0.176241
$601$	25.9248	1.05749	0.528747	−	0.848779i	$-0.322662\pi$
$601$	25.9248	1.05749	0.528747	+	0.848779i	$0.322662\pi$
$602$	2.61213	0.106462
$603$	−17.2714	−0.703346
$604$	23.7558	0.966611
$605$	−29.6162	−1.20407
$606$	6.30091	0.255957
$607$	−5.46644	−0.221876	−0.110938	−	0.993827i	$-0.535385\pi$
$607$	−5.46644	−0.221876	−0.110938	+	0.993827i	$0.535385\pi$
$608$	−2.60187	−0.105520
$609$	11.3546	0.460112
$610$	6.68329	0.270599
$611$	−4.73139	−0.191411
$612$	−4.62977	−0.187147
$613$	−30.9312	−1.24930	−0.624649	−	0.780906i	$-0.714758\pi$
$613$	−30.9312	−1.24930	−0.624649	+	0.780906i	$0.714758\pi$
$614$	−31.8280	−1.28447
$615$	9.33044	0.376240
$616$	−3.26149	−0.131409
$617$	−2.46365	−0.0991827	−0.0495914	−	0.998770i	$-0.515792\pi$
$617$	−2.46365	−0.0991827	−0.0495914	+	0.998770i	$0.515792\pi$
$618$	3.81349	0.153401
$619$	−23.8215	−0.957468	−0.478734	−	0.877960i	$-0.658904\pi$
$619$	−23.8215	−0.957468	−0.478734	+	0.877960i	$0.658904\pi$
$620$	3.21035	0.128931
$621$	3.19452	0.128192
$622$	−5.78987	−0.232152
$623$	−22.3625	−0.895936
$624$	−0.556778	−0.0222890
$625$	−23.3744	−0.934975
$626$	−25.4505	−1.01721
$627$	−2.81997	−0.112619
$628$	−24.1488	−0.963643
$629$	−11.4677	−0.457249
$630$	−18.3765	−0.732138
$631$	−17.7501	−0.706619	−0.353309	−	0.935506i	$-0.614944\pi$
$631$	−17.7501	−0.706619	−0.353309	+	0.935506i	$0.614944\pi$
$632$	13.7111	0.545398
$633$	−5.89558	−0.234328
$634$	18.0177	0.715572
$635$	9.15999	0.363503
$636$	−1.36218	−0.0540140
$637$	0.688798	0.0272912
$638$	−7.59483	−0.300682
$639$	6.63518	0.262484
$640$	−3.21035	−0.126900
$641$	7.80701	0.308358	0.154179	−	0.988043i	$-0.450727\pi$
$641$	7.80701	0.308358	0.154179	+	0.988043i	$0.450727\pi$
$642$	2.85396	0.112637
$643$	45.7735	1.80513	0.902565	−	0.430553i	$-0.141681\pi$
$643$	45.7735	1.80513	0.902565	+	0.430553i	$0.141681\pi$
$644$	1.80083	0.0709626
$645$	2.78670	0.109726
$646$	−5.15200	−0.202703
$647$	−2.56556	−0.100863	−0.0504313	−	0.998728i	$-0.516060\pi$
$647$	−2.56556	−0.100863	−0.0504313	+	0.998728i	$0.516060\pi$
$648$	−3.48126	−0.136757
$649$	5.67423	0.222733
$650$	3.63156	0.142441
$651$	−1.99172	−0.0780615
$652$	9.28226	0.363521
$653$	−14.1272	−0.552841	−0.276421	−	0.961037i	$-0.589148\pi$
$653$	−14.1272	−0.552841	−0.276421	+	0.961037i	$0.589148\pi$
$654$	−3.89064	−0.152136
$655$	−69.1951	−2.70368
$656$	3.57243	0.139480
$657$	11.6025	0.452655
$658$	16.9252	0.659813
$659$	−28.5197	−1.11097	−0.555485	−	0.831527i	$-0.687467\pi$
$659$	−28.5197	−1.11097	−0.555485	+	0.831527i	$0.687467\pi$
$660$	−3.47946	−0.135438
$661$	22.0714	0.858477	0.429238	−	0.903191i	$-0.358782\pi$
$661$	22.0714	0.858477	0.429238	+	0.903191i	$0.358782\pi$
$662$	−23.7616	−0.923521
$663$	−1.10248	−0.0428170
$664$	1.60052	0.0621122
$665$	−20.4494	−0.792992
$666$	−13.5412	−0.524710
$667$	4.19348	0.162372
$668$	−1.75511	−0.0679074
$669$	−5.67065	−0.219240
$670$	−23.7144	−0.916166
$671$	2.77340	0.107066
$672$	1.99172	0.0768321
$673$	−35.2889	−1.36029	−0.680144	−	0.733079i	$-0.738083\pi$
$673$	−35.2889	−1.36029	−0.680144	+	0.733079i	$0.738083\pi$
$674$	3.40518	0.131163
$675$	−23.0447	−0.886991
$676$	−12.5316	−0.481986
$677$	35.2869	1.35619	0.678093	−	0.734976i	$-0.262807\pi$
$677$	35.2869	1.35619	0.678093	+	0.734976i	$0.262807\pi$
$678$	11.9801	0.460093
$679$	−2.44817	−0.0939522
$680$	−6.35686	−0.243775
$681$	−4.98882	−0.191172
$682$	1.33221	0.0510131
$683$	19.4192	0.743054	0.371527	−	0.928422i	$-0.378834\pi$
$683$	19.4192	0.743054	0.371527	+	0.928422i	$0.378834\pi$
$684$	−6.08351	−0.232609
$685$	−73.9769	−2.82651
$686$	−19.6012	−0.748376
$687$	22.7940	0.869645
$688$	1.06697	0.0406779
$689$	1.14590	0.0436552
$690$	1.92118	0.0731382
$691$	−20.9143	−0.795619	−0.397809	−	0.917468i	$-0.630229\pi$
$691$	−20.9143	−0.795619	−0.397809	+	0.917468i	$0.630229\pi$
$692$	−10.6874	−0.406276
$693$	−7.62579	−0.289680
$694$	−35.8252	−1.35990
$695$	−1.76781	−0.0670568
$696$	4.63799	0.175803
$697$	7.07382	0.267940
$698$	29.2191	1.10596
$699$	−11.9605	−0.452388
$700$	−12.9909	−0.491009
$701$	5.58711	0.211022	0.105511	−	0.994418i	$-0.466352\pi$
$701$	5.58711	0.211022	0.105511	+	0.994418i	$0.466352\pi$
$702$	−2.97216	−0.112177
$703$	−15.0686	−0.568323
$704$	−1.33221	−0.0502097
$705$	18.0564	0.680042
$706$	−8.67082	−0.326331
$707$	18.9609	0.713098
$708$	−3.46512	−0.130227
$709$	−41.1171	−1.54419	−0.772093	−	0.635510i	$-0.780790\pi$
$709$	−41.1171	−1.54419	−0.772093	+	0.635510i	$0.780790\pi$
$710$	9.11038	0.341906
$711$	32.0583	1.20228
$712$	−9.13438	−0.342325
$713$	−0.735581	−0.0275477
$714$	3.94383	0.147594
$715$	2.92700	0.109464
$716$	−21.0616	−0.787107
$717$	7.82783	0.292336
$718$	6.28877	0.234695
$719$	1.13936	0.0424911	0.0212456	−	0.999774i	$-0.493237\pi$
$719$	1.13936	0.0424911	0.0212456	+	0.999774i	$0.493237\pi$
$720$	−7.50622	−0.279740
$721$	11.4757	0.427377
$722$	12.2303	0.455164
$723$	4.35423	0.161935
$724$	−10.4945	−0.390024
$725$	−30.2511	−1.12350
$726$	7.50519	0.278544
$727$	−37.8502	−1.40378	−0.701892	−	0.712283i	$-0.747661\pi$
$727$	−37.8502	−1.40378	−0.701892	+	0.712283i	$0.747661\pi$
$728$	−1.67548	−0.0620973
$729$	2.45978	0.0911031
$730$	15.9307	0.589620
$731$	2.11272	0.0781419
$732$	−1.69365	−0.0625991
$733$	−49.8648	−1.84180	−0.920899	−	0.389802i	$-0.872543\pi$
$733$	−49.8648	−1.84180	−0.920899	+	0.389802i	$0.872543\pi$
$734$	−8.99218	−0.331907
$735$	−2.62866	−0.0969594
$736$	0.735581	0.0271139
$737$	−9.84085	−0.362493
$738$	8.35281	0.307471
$739$	−6.15382	−0.226372	−0.113186	−	0.993574i	$-0.536106\pi$
$739$	−6.15382	−0.226372	−0.113186	+	0.993574i	$0.536106\pi$
$740$	−18.5926	−0.683477
$741$	−1.44866	−0.0532180
$742$	−4.09912	−0.150484
$743$	34.0794	1.25025	0.625125	−	0.780525i	$-0.285048\pi$
$743$	34.0794	1.25025	0.625125	+	0.780525i	$0.285048\pi$
$744$	−0.813553	−0.0298263
$745$	74.5685	2.73198
$746$	−0.850669	−0.0311452
$747$	3.74222	0.136921
$748$	−2.63794	−0.0964525
$749$	8.58824	0.313807
$750$	−0.800135	−0.0292168
$751$	−8.10496	−0.295754	−0.147877	−	0.989006i	$-0.547244\pi$
$751$	−8.10496	−0.295754	−0.147877	+	0.989006i	$0.547244\pi$
$752$	6.91340	0.252106
$753$	−0.319746	−0.0116522
$754$	−3.90158	−0.142087
$755$	76.2646	2.77555
$756$	10.6320	0.386684
$757$	32.0515	1.16493	0.582466	−	0.812855i	$-0.302088\pi$
$757$	32.0515	1.16493	0.582466	+	0.812855i	$0.302088\pi$
$758$	23.1234	0.839881
$759$	0.797242	0.0289381
$760$	−8.35291	−0.302992
$761$	27.5972	1.00040	0.500198	−	0.865911i	$-0.333260\pi$
$761$	27.5972	1.00040	0.500198	+	0.865911i	$0.333260\pi$
$762$	−2.32128	−0.0840912
$763$	−11.7079	−0.423853
$764$	−15.9143	−0.575761
$765$	−14.8632	−0.537380
$766$	2.29931	0.0830773
$767$	2.91494	0.105252
$768$	0.813553	0.0293566
$769$	−1.98798	−0.0716884	−0.0358442	−	0.999357i	$-0.511412\pi$
$769$	−1.98798	−0.0716884	−0.0358442	+	0.999357i	$0.511412\pi$
$770$	−10.4705	−0.377331
$771$	−10.8505	−0.390770
$772$	−5.75066	−0.206971
$773$	−39.3242	−1.41439	−0.707197	−	0.707017i	$-0.750041\pi$
$773$	−39.3242	−1.41439	−0.707197	+	0.707017i	$0.750041\pi$
$774$	2.49472	0.0896708
$775$	5.30635	0.190610
$776$	−1.00000	−0.0358979
$777$	11.5349	0.413813
$778$	9.10438	0.326408
$779$	9.29499	0.333028
$780$	−1.78745	−0.0640011
$781$	3.78058	0.135280
$782$	1.45654	0.0520856
$783$	24.7582	0.884786
$784$	−1.00646	−0.0359449
$785$	−77.5262	−2.76703
$786$	17.5351	0.625457
$787$	16.6283	0.592735	0.296367	−	0.955074i	$-0.404225\pi$
$787$	16.6283	0.592735	0.296367	+	0.955074i	$0.404225\pi$
$788$	5.94855	0.211908
$789$	14.9954	0.533849
$790$	44.0174	1.56607
$791$	36.0509	1.28182
$792$	−3.11489	−0.110683
$793$	1.42474	0.0505939
$794$	−28.5240	−1.01228
$795$	−4.37308	−0.155097
$796$	−8.23315	−0.291816
$797$	1.31467	0.0465681	0.0232840	−	0.999729i	$-0.492588\pi$
$797$	1.31467	0.0465681	0.0232840	+	0.999729i	$0.492588\pi$
$798$	5.18219	0.183447
$799$	13.6893	0.484294
$800$	−5.30635	−0.187608
$801$	−21.3574	−0.754626
$802$	13.6996	0.483751
$803$	6.61082	0.233291
$804$	6.00959	0.211942
$805$	5.78129	0.203764
$806$	0.684379	0.0241062
$807$	2.95395	0.103984
$808$	7.74493	0.272466
$809$	−3.57330	−0.125631	−0.0628153	−	0.998025i	$-0.520008\pi$
$809$	−3.57330	−0.125631	−0.0628153	+	0.998025i	$0.520008\pi$
$810$	−11.1761	−0.392687
$811$	13.9196	0.488785	0.244392	−	0.969676i	$-0.421412\pi$
$811$	13.9196	0.488785	0.244392	+	0.969676i	$0.421412\pi$
$812$	13.9568	0.489788
$813$	−4.72267	−0.165631
$814$	−7.71545	−0.270426
$815$	29.7993	1.04382
$816$	1.61093	0.0563938
$817$	2.77612	0.0971241
$818$	31.9271	1.11631
$819$	−3.91748	−0.136888
$820$	11.4688	0.400506
$821$	18.3923	0.641894	0.320947	−	0.947097i	$-0.395999\pi$
$821$	18.3923	0.641894	0.320947	+	0.947097i	$0.395999\pi$
$822$	18.7469	0.653873
$823$	−7.08365	−0.246921	−0.123460	−	0.992350i	$-0.539399\pi$
$823$	−7.08365	−0.246921	−0.123460	+	0.992350i	$0.539399\pi$
$824$	4.68746	0.163295
$825$	−5.75117	−0.200230
$826$	−10.4274	−0.362815
$827$	−52.0986	−1.81165	−0.905823	−	0.423657i	$-0.860746\pi$
$827$	−52.0986	−1.81165	−0.905823	+	0.423657i	$0.860746\pi$
$828$	1.71989	0.0597702
$829$	−22.9967	−0.798710	−0.399355	−	0.916796i	$-0.630766\pi$
$829$	−22.9967	−0.798710	−0.399355	+	0.916796i	$0.630766\pi$
$830$	5.13823	0.178350
$831$	−9.73702	−0.337774
$832$	−0.684379	−0.0237266
$833$	−1.99290	−0.0690499
$834$	0.447990	0.0155126
$835$	−5.63453	−0.194991
$836$	−3.46625	−0.119883
$837$	−4.34285	−0.150111
$838$	−1.76000	−0.0607981
$839$	−6.60591	−0.228061	−0.114031	−	0.993477i	$-0.536376\pi$
$839$	−6.60591	−0.228061	−0.114031	+	0.993477i	$0.536376\pi$
$840$	6.39411	0.220618
$841$	3.50039	0.120703
$842$	−5.38600	−0.185614
$843$	8.52863	0.293741
$844$	−7.24671	−0.249442
$845$	−40.2309	−1.38399
$846$	16.1644	0.555745
$847$	22.5849	0.776026
$848$	−1.67436	−0.0574978
$849$	−10.4990	−0.360324
$850$	−10.5072	−0.360394
$851$	4.26008	0.146034
$852$	−2.30871	−0.0790952
$853$	−49.3572	−1.68996	−0.844978	−	0.534800i	$-0.820387\pi$
$853$	−49.3572	−1.68996	−0.844978	+	0.534800i	$0.820387\pi$
$854$	−5.09659	−0.174402
$855$	−19.5302	−0.667919
$856$	3.50802	0.119902
$857$	3.09650	0.105774	0.0528871	−	0.998600i	$-0.483158\pi$
$857$	3.09650	0.105774	0.0528871	+	0.998600i	$0.483158\pi$
$858$	−0.741748	−0.0253228
$859$	−2.23582	−0.0762850	−0.0381425	−	0.999272i	$-0.512144\pi$
$859$	−2.23582	−0.0762850	−0.0381425	+	0.999272i	$0.512144\pi$
$860$	3.42535	0.116803
$861$	−7.11527	−0.242488
$862$	36.0744	1.22870
$863$	31.8410	1.08388	0.541941	−	0.840417i	$-0.317690\pi$
$863$	31.8410	1.08388	0.541941	+	0.840417i	$0.317690\pi$
$864$	4.34285	0.147747
$865$	−34.3104	−1.16659
$866$	1.92273	0.0653372
$867$	−10.6406	−0.361373
$868$	−2.44817	−0.0830963
$869$	18.2661	0.619635
$870$	14.8896	0.504804
$871$	−5.05540	−0.171296
$872$	−4.78229	−0.161949
$873$	−2.33813	−0.0791338
$874$	1.91389	0.0647381
$875$	−2.40779	−0.0813982
$876$	−4.03708	−0.136400
$877$	49.8871	1.68457	0.842285	−	0.539033i	$-0.181210\pi$
$877$	49.8871	1.68457	0.842285	+	0.539033i	$0.181210\pi$
$878$	−10.1478	−0.342472
$879$	12.3292	0.415854
$880$	−4.27687	−0.144173
$881$	2.70739	0.0912144	0.0456072	−	0.998959i	$-0.485478\pi$
$881$	2.70739	0.0912144	0.0456072	+	0.998959i	$0.485478\pi$
$882$	−2.35323	−0.0792374
$883$	36.2872	1.22116	0.610581	−	0.791954i	$-0.290936\pi$
$883$	36.2872	1.22116	0.610581	+	0.791954i	$0.290936\pi$
$884$	−1.35515	−0.0455786
$885$	−11.1243	−0.373938
$886$	−14.0913	−0.473407
$887$	18.6696	0.626864	0.313432	−	0.949611i	$-0.398521\pi$
$887$	18.6696	0.626864	0.313432	+	0.949611i	$0.398521\pi$
$888$	4.71165	0.158113
$889$	−6.98529	−0.234279
$890$	−29.3246	−0.982962
$891$	−4.63778	−0.155371
$892$	−6.97023	−0.233381
$893$	17.9878	0.601938
$894$	−18.8968	−0.632004
$895$	−67.6150	−2.26012
$896$	2.44817	0.0817877
$897$	0.409556	0.0136747
$898$	30.6163	1.02168
$899$	−5.70091	−0.190136
$900$	−12.4070	−0.413565
$901$	−3.31543	−0.110453
$902$	4.75924	0.158465
$903$	−2.12510	−0.0707190
$904$	14.7257	0.489768
$905$	−33.6910	−1.11993
$906$	−19.3266	−0.642084
$907$	26.0131	0.863752	0.431876	−	0.901933i	$-0.357852\pi$
$907$	26.0131	0.863752	0.431876	+	0.901933i	$0.357852\pi$
$908$	−6.13214	−0.203502
$909$	18.1087	0.600626
$910$	−5.37887	−0.178308
$911$	44.1761	1.46362	0.731810	−	0.681509i	$-0.238676\pi$
$911$	44.1761	1.46362	0.731810	+	0.681509i	$0.238676\pi$
$912$	2.11676	0.0700929
$913$	2.13223	0.0705666
$914$	−13.0631	−0.432088
$915$	−5.43721	−0.179749
$916$	28.0178	0.925735
$917$	52.7673	1.74253
$918$	8.59935	0.283821
$919$	−11.2174	−0.370027	−0.185013	−	0.982736i	$-0.559233\pi$
$919$	−11.2174	−0.370027	−0.185013	+	0.982736i	$0.559233\pi$
$920$	2.36147	0.0778555
$921$	25.8938	0.853228
$922$	−21.5316	−0.709104
$923$	1.94214	0.0639263
$924$	2.65339	0.0872902
$925$	−30.7315	−1.01045
$926$	−14.2734	−0.469054
$927$	10.9599	0.359970
$928$	5.70091	0.187142
$929$	33.7793	1.10826	0.554132	−	0.832429i	$-0.313050\pi$
$929$	33.7793	1.10826	0.554132	+	0.832429i	$0.313050\pi$
$930$	−2.61179	−0.0856440
$931$	−2.61867	−0.0858235
$932$	−14.7016	−0.481566
$933$	4.71036	0.154210
$934$	21.3403	0.698277
$935$	−8.46870	−0.276956
$936$	−1.60017	−0.0523031
$937$	−6.15824	−0.201181	−0.100590	−	0.994928i	$-0.532073\pi$
$937$	−6.15824	−0.201181	−0.100590	+	0.994928i	$0.532073\pi$
$938$	18.0843	0.590472
$939$	20.7053	0.675693
$940$	22.1944	0.723903
$941$	−13.2000	−0.430307	−0.215153	−	0.976580i	$-0.569025\pi$
$941$	−13.2000	−0.430307	−0.215153	+	0.976580i	$0.569025\pi$
$942$	19.6463	0.640112
$943$	−2.62781	−0.0855733
$944$	−4.25925	−0.138627
$945$	34.1326	1.11033
$946$	1.42143	0.0462148
$947$	−2.04388	−0.0664173	−0.0332087	−	0.999448i	$-0.510573\pi$
$947$	−2.04388	−0.0664173	−0.0332087	+	0.999448i	$0.510573\pi$
$948$	−11.1547	−0.362288
$949$	3.39608	0.110241
$950$	−13.8064	−0.447940
$951$	−14.6583	−0.475328
$952$	4.84766	0.157114
$953$	11.4075	0.369527	0.184763	−	0.982783i	$-0.440848\pi$
$953$	11.4075	0.369527	0.184763	+	0.982783i	$0.440848\pi$
$954$	−3.91488	−0.126749
$955$	−51.0906	−1.65325
$956$	9.62179	0.311191
$957$	6.17880	0.199732
$958$	−39.3383	−1.27096
$959$	56.4138	1.82170
$960$	2.61179	0.0842952
$961$	1.00000	0.0322581
$962$	−3.96355	−0.127790
$963$	8.20222	0.264313
$964$	5.35211	0.172380
$965$	−18.4616	−0.594301
$966$	−1.46507	−0.0471378
$967$	27.0306	0.869246	0.434623	−	0.900612i	$-0.356882\pi$
$967$	27.0306	0.869246	0.434623	+	0.900612i	$0.356882\pi$
$968$	9.22521	0.296509
$969$	4.19142	0.134648
$970$	−3.21035	−0.103078
$971$	32.6004	1.04620	0.523098	−	0.852273i	$-0.324776\pi$
$971$	32.6004	1.04620	0.523098	+	0.852273i	$0.324776\pi$
$972$	15.8607	0.508734
$973$	1.34811	0.0432183
$974$	21.6302	0.693078
$975$	−2.95446	−0.0946185
$976$	−2.08179	−0.0666366
$977$	−24.6196	−0.787650	−0.393825	−	0.919185i	$-0.628848\pi$
$977$	−24.6196	−0.787650	−0.393825	+	0.919185i	$0.628848\pi$
$978$	−7.55161	−0.241474
$979$	−12.1690	−0.388921
$980$	−3.23108	−0.103213
$981$	−11.1816	−0.357002
$982$	−3.42268	−0.109222
$983$	46.4068	1.48015	0.740073	−	0.672526i	$-0.234791\pi$
$983$	46.4068	1.48015	0.740073	+	0.672526i	$0.234791\pi$
$984$	−2.90636	−0.0926514
$985$	19.0969	0.608479
$986$	11.2885	0.359498
$987$	−13.7695	−0.438289
$988$	−1.78066	−0.0566505
$989$	−0.784843	−0.0249566
$990$	−9.99990	−0.317818
$991$	−5.28236	−0.167800	−0.0838998	−	0.996474i	$-0.526738\pi$
$991$	−5.28236	−0.167800	−0.0838998	+	0.996474i	$0.526738\pi$
$992$	−1.00000	−0.0317500
$993$	19.3313	0.613461
$994$	−6.94746	−0.220360
$995$	−26.4313	−0.837928
$996$	−1.30211	−0.0412588
$997$	19.5862	0.620302	0.310151	−	0.950687i	$-0.399620\pi$
$997$	19.5862	0.620302	0.310151	+	0.950687i	$0.399620\pi$
$998$	−2.48719	−0.0787306
$999$	25.1514	0.795756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.14	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.14	✓	22	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.813553 q^{3} +1.00000 q^{4} +3.21035 q^{5} -0.813553 q^{6} -2.44817 q^{7} -1.00000 q^{8} -2.33813 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.813553 q^{3} +1.00000 q^{4} +3.21035 q^{5} -0.813553 q^{6} -2.44817 q^{7} -1.00000 q^{8} -2.33813 q^{9} -3.21035 q^{10} -1.33221 q^{11} +0.813553 q^{12} -0.684379 q^{13} +2.44817 q^{14} +2.61179 q^{15} +1.00000 q^{16} +1.98011 q^{17} +2.33813 q^{18} +2.60187 q^{19} +3.21035 q^{20} -1.99172 q^{21} +1.33221 q^{22} -0.735581 q^{23} -0.813553 q^{24} +5.30635 q^{25} +0.684379 q^{26} -4.34285 q^{27} -2.44817 q^{28} -5.70091 q^{29} -2.61179 q^{30} +1.00000 q^{31} -1.00000 q^{32} -1.08383 q^{33} -1.98011 q^{34} -7.85949 q^{35} -2.33813 q^{36} -5.79145 q^{37} -2.60187 q^{38} -0.556778 q^{39} -3.21035 q^{40} +3.57243 q^{41} +1.99172 q^{42} +1.06697 q^{43} -1.33221 q^{44} -7.50622 q^{45} +0.735581 q^{46} +6.91340 q^{47} +0.813553 q^{48} -1.00646 q^{49} -5.30635 q^{50} +1.61093 q^{51} -0.684379 q^{52} -1.67436 q^{53} +4.34285 q^{54} -4.27687 q^{55} +2.44817 q^{56} +2.11676 q^{57} +5.70091 q^{58} -4.25925 q^{59} +2.61179 q^{60} -2.08179 q^{61} -1.00000 q^{62} +5.72415 q^{63} +1.00000 q^{64} -2.19710 q^{65} +1.08383 q^{66} +7.38684 q^{67} +1.98011 q^{68} -0.598434 q^{69} +7.85949 q^{70} -2.83781 q^{71} +2.33813 q^{72} -4.96228 q^{73} +5.79145 q^{74} +4.31700 q^{75} +2.60187 q^{76} +3.26149 q^{77} +0.556778 q^{78} -13.7111 q^{79} +3.21035 q^{80} +3.48126 q^{81} -3.57243 q^{82} -1.60052 q^{83} -1.99172 q^{84} +6.35686 q^{85} -1.06697 q^{86} -4.63799 q^{87} +1.33221 q^{88} +9.13438 q^{89} +7.50622 q^{90} +1.67548 q^{91} -0.735581 q^{92} +0.813553 q^{93} -6.91340 q^{94} +8.35291 q^{95} -0.813553 q^{96} +1.00000 q^{97} +1.00646 q^{98} +3.11489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

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