LMFDB - Embedded newform 8018.2.a.g.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.234828 q^{3} +1.00000 q^{4} -3.98534 q^{5} -0.234828 q^{6} +1.98646 q^{7} -1.00000 q^{8} -2.94486 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.234828 q^{3} +1.00000 q^{4} -3.98534 q^{5} -0.234828 q^{6} +1.98646 q^{7} -1.00000 q^{8} -2.94486 q^{9} +3.98534 q^{10} -0.00620422 q^{11} +0.234828 q^{12} -1.24463 q^{13} -1.98646 q^{14} -0.935868 q^{15} +1.00000 q^{16} -1.24710 q^{17} +2.94486 q^{18} +1.00000 q^{19} -3.98534 q^{20} +0.466477 q^{21} +0.00620422 q^{22} +3.24348 q^{23} -0.234828 q^{24} +10.8829 q^{25} +1.24463 q^{26} -1.39602 q^{27} +1.98646 q^{28} +9.98393 q^{29} +0.935868 q^{30} -8.91705 q^{31} -1.00000 q^{32} -0.00145692 q^{33} +1.24710 q^{34} -7.91673 q^{35} -2.94486 q^{36} -1.10153 q^{37} -1.00000 q^{38} -0.292274 q^{39} +3.98534 q^{40} -0.105317 q^{41} -0.466477 q^{42} -12.1551 q^{43} -0.00620422 q^{44} +11.7362 q^{45} -3.24348 q^{46} +9.56923 q^{47} +0.234828 q^{48} -3.05396 q^{49} -10.8829 q^{50} -0.292854 q^{51} -1.24463 q^{52} -0.871837 q^{53} +1.39602 q^{54} +0.0247259 q^{55} -1.98646 q^{56} +0.234828 q^{57} -9.98393 q^{58} -1.55869 q^{59} -0.935868 q^{60} +13.1715 q^{61} +8.91705 q^{62} -5.84985 q^{63} +1.00000 q^{64} +4.96028 q^{65} +0.00145692 q^{66} -1.29883 q^{67} -1.24710 q^{68} +0.761659 q^{69} +7.91673 q^{70} +11.5041 q^{71} +2.94486 q^{72} -9.06206 q^{73} +1.10153 q^{74} +2.55561 q^{75} +1.00000 q^{76} -0.0123245 q^{77} +0.292274 q^{78} -9.98203 q^{79} -3.98534 q^{80} +8.50674 q^{81} +0.105317 q^{82} +11.7885 q^{83} +0.466477 q^{84} +4.97012 q^{85} +12.1551 q^{86} +2.34450 q^{87} +0.00620422 q^{88} +11.2792 q^{89} -11.7362 q^{90} -2.47242 q^{91} +3.24348 q^{92} -2.09397 q^{93} -9.56923 q^{94} -3.98534 q^{95} -0.234828 q^{96} -1.04561 q^{97} +3.05396 q^{98} +0.0182705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * 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
$3$	0.234828	0.135578	0.0677889	−	0.997700i	$-0.478406\pi$
$3$	0.234828	0.135578	0.0677889	+	0.997700i	$0.478406\pi$
$4$	1.00000	0.500000
$5$	−3.98534	−1.78230	−0.891149	−	0.453711i	$-0.850100\pi$
$5$	−3.98534	−1.78230	−0.891149	+	0.453711i	$0.850100\pi$
$6$	−0.234828	−0.0958680
$7$	1.98646	0.750813	0.375407	−	0.926860i	$-0.377503\pi$
$7$	1.98646	0.750813	0.375407	+	0.926860i	$0.377503\pi$
$8$	−1.00000	−0.353553
$9$	−2.94486	−0.981619
$10$	3.98534	1.26027
$11$	−0.00620422	−0.00187064	−0.000935322	−	1.00000i	$-0.500298\pi$
$11$	−0.00620422	−0.00187064	−0.000935322		1.00000i	$0.500298\pi$
$12$	0.234828	0.0677889
$13$	−1.24463	−0.345199	−0.172599	−	0.984992i	$-0.555217\pi$
$13$	−1.24463	−0.345199	−0.172599	+	0.984992i	$0.555217\pi$
$14$	−1.98646	−0.530905
$15$	−0.935868	−0.241640
$16$	1.00000	0.250000
$17$	−1.24710	−0.302467	−0.151233	−	0.988498i	$-0.548324\pi$
$17$	−1.24710	−0.302467	−0.151233	+	0.988498i	$0.548324\pi$
$18$	2.94486	0.694109
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.98534	−0.891149
$21$	0.466477	0.101794
$22$	0.00620422	0.00132274
$23$	3.24348	0.676312	0.338156	−	0.941090i	$-0.390197\pi$
$23$	3.24348	0.676312	0.338156	+	0.941090i	$0.390197\pi$
$24$	−0.234828	−0.0479340
$25$	10.8829	2.17658
$26$	1.24463	0.244093
$27$	−1.39602	−0.268664
$28$	1.98646	0.375407
$29$	9.98393	1.85397	0.926984	−	0.375100i	$-0.122392\pi$
$29$	9.98393	1.85397	0.926984	+	0.375100i	$0.122392\pi$
$30$	0.935868	0.170865
$31$	−8.91705	−1.60155	−0.800774	−	0.598966i	$-0.795578\pi$
$31$	−8.91705	−1.60155	−0.800774	+	0.598966i	$0.795578\pi$
$32$	−1.00000	−0.176777
$33$	−0.00145692	−0.000253618 0
$34$	1.24710	0.213876
$35$	−7.91673	−1.33817
$36$	−2.94486	−0.490809
$37$	−1.10153	−0.181090	−0.0905450	−	0.995892i	$-0.528861\pi$
$37$	−1.10153	−0.181090	−0.0905450	+	0.995892i	$0.528861\pi$
$38$	−1.00000	−0.162221
$39$	−0.292274	−0.0468013
$40$	3.98534	0.630137
$41$	−0.105317	−0.0164478	−0.00822390	−	0.999966i	$-0.502618\pi$
$41$	−0.105317	−0.0164478	−0.00822390	+	0.999966i	$0.502618\pi$
$42$	−0.466477	−0.0719790
$43$	−12.1551	−1.85363	−0.926816	−	0.375515i	$-0.877466\pi$
$43$	−12.1551	−1.85363	−0.926816	+	0.375515i	$0.877466\pi$
$44$	−0.00620422	−0.000935322 0
$45$	11.7362	1.74954
$46$	−3.24348	−0.478225
$47$	9.56923	1.39582	0.697908	−	0.716188i	$-0.254115\pi$
$47$	9.56923	1.39582	0.697908	+	0.716188i	$0.254115\pi$
$48$	0.234828	0.0338945
$49$	−3.05396	−0.436280
$50$	−10.8829	−1.53908
$51$	−0.292854	−0.0410078
$52$	−1.24463	−0.172599
$53$	−0.871837	−0.119756	−0.0598780	−	0.998206i	$-0.519071\pi$
$53$	−0.871837	−0.119756	−0.0598780	+	0.998206i	$0.519071\pi$
$54$	1.39602	0.189974
$55$	0.0247259	0.00333404
$56$	−1.98646	−0.265453
$57$	0.234828	0.0311037
$58$	−9.98393	−1.31095
$59$	−1.55869	−0.202924	−0.101462	−	0.994839i	$-0.532352\pi$
$59$	−1.55869	−0.202924	−0.101462	+	0.994839i	$0.532352\pi$
$60$	−0.935868	−0.120820
$61$	13.1715	1.68644	0.843218	−	0.537571i	$-0.180658\pi$
$61$	13.1715	1.68644	0.843218	+	0.537571i	$0.180658\pi$
$62$	8.91705	1.13247
$63$	−5.84985	−0.737012
$64$	1.00000	0.125000
$65$	4.96028	0.615247
$66$	0.00145692	0.000179335 0
$67$	−1.29883	−0.158678	−0.0793388	−	0.996848i	$-0.525281\pi$
$67$	−1.29883	−0.158678	−0.0793388	+	0.996848i	$0.525281\pi$
$68$	−1.24710	−0.151233
$69$	0.761659	0.0916929
$70$	7.91673	0.946231
$71$	11.5041	1.36529	0.682643	−	0.730752i	$-0.260830\pi$
$71$	11.5041	1.36529	0.682643	+	0.730752i	$0.260830\pi$
$72$	2.94486	0.347055
$73$	−9.06206	−1.06063	−0.530317	−	0.847799i	$-0.677927\pi$
$73$	−9.06206	−1.06063	−0.530317	+	0.847799i	$0.677927\pi$
$74$	1.10153	0.128050
$75$	2.55561	0.295097
$76$	1.00000	0.114708
$77$	−0.0123245	−0.00140450
$78$	0.292274	0.0330935
$79$	−9.98203	−1.12307	−0.561533	−	0.827454i	$-0.689788\pi$
$79$	−9.98203	−1.12307	−0.561533	+	0.827454i	$0.689788\pi$
$80$	−3.98534	−0.445574
$81$	8.50674	0.945194
$82$	0.105317	0.0116304
$83$	11.7885	1.29395	0.646975	−	0.762511i	$-0.276034\pi$
$83$	11.7885	1.29395	0.646975	+	0.762511i	$0.276034\pi$
$84$	0.466477	0.0508968
$85$	4.97012	0.539086
$86$	12.1551	1.31072
$87$	2.34450	0.251357
$88$	0.00620422	0.000661372 0
$89$	11.2792	1.19559	0.597797	−	0.801647i	$-0.296043\pi$
$89$	11.2792	1.19559	0.597797	+	0.801647i	$0.296043\pi$
$90$	−11.7362	−1.23711
$91$	−2.47242	−0.259180
$92$	3.24348	0.338156
$93$	−2.09397	−0.217135
$94$	−9.56923	−0.986991
$95$	−3.98534	−0.408887
$96$	−0.234828	−0.0239670
$97$	−1.04561	−0.106165	−0.0530826	−	0.998590i	$-0.516905\pi$
$97$	−1.04561	−0.106165	−0.0530826	+	0.998590i	$0.516905\pi$
$98$	3.05396	0.308496
$99$	0.0182705	0.00183626
$100$	10.8829	1.08829
$101$	7.70446	0.766622	0.383311	−	0.923619i	$-0.374784\pi$
$101$	7.70446	0.766622	0.383311	+	0.923619i	$0.374784\pi$
$102$	0.292854	0.0289969
$103$	17.9213	1.76584	0.882918	−	0.469527i	$-0.155576\pi$
$103$	17.9213	1.76584	0.882918	+	0.469527i	$0.155576\pi$
$104$	1.24463	0.122046
$105$	−1.85907	−0.181427
$106$	0.871837	0.0846803
$107$	−9.24043	−0.893306	−0.446653	−	0.894707i	$-0.647384\pi$
$107$	−9.24043	−0.893306	−0.446653	+	0.894707i	$0.647384\pi$
$108$	−1.39602	−0.134332
$109$	12.6031	1.20715	0.603577	−	0.797305i	$-0.293742\pi$
$109$	12.6031	1.20715	0.603577	+	0.797305i	$0.293742\pi$
$110$	−0.0247259	−0.00235753
$111$	−0.258669	−0.0245518
$112$	1.98646	0.187703
$113$	7.45006	0.700842	0.350421	−	0.936592i	$-0.386038\pi$
$113$	7.45006	0.700842	0.350421	+	0.936592i	$0.386038\pi$
$114$	−0.234828	−0.0219936
$115$	−12.9264	−1.20539
$116$	9.98393	0.926984
$117$	3.66526	0.338854
$118$	1.55869	0.143489
$119$	−2.47732	−0.227096
$120$	0.935868	0.0854327
$121$	−11.0000	−0.999997
$122$	−13.1715	−1.19249
$123$	−0.0247314	−0.00222996
$124$	−8.91705	−0.800774
$125$	−23.4454	−2.09702
$126$	5.84985	0.521146
$127$	−7.21524	−0.640249	−0.320124	−	0.947376i	$-0.603725\pi$
$127$	−7.21524	−0.640249	−0.320124	+	0.947376i	$0.603725\pi$
$128$	−1.00000	−0.0883883
$129$	−2.85435	−0.251312
$130$	−4.96028	−0.435045
$131$	−8.17605	−0.714345	−0.357172	−	0.934038i	$-0.616259\pi$
$131$	−8.17605	−0.714345	−0.357172	+	0.934038i	$0.616259\pi$
$132$	−0.00145692	−0.000126809 0
$133$	1.98646	0.172248
$134$	1.29883	0.112202
$135$	5.56360	0.478838
$136$	1.24710	0.106938
$137$	−4.14463	−0.354099	−0.177050	−	0.984202i	$-0.556655\pi$
$137$	−4.14463	−0.354099	−0.177050	+	0.984202i	$0.556655\pi$
$138$	−0.761659	−0.0648367
$139$	2.00340	0.169926	0.0849631	−	0.996384i	$-0.472923\pi$
$139$	2.00340	0.169926	0.0849631	+	0.996384i	$0.472923\pi$
$140$	−7.91673	−0.669086
$141$	2.24712	0.189242
$142$	−11.5041	−0.965403
$143$	0.00772198	0.000645744 0
$144$	−2.94486	−0.245405
$145$	−39.7893	−3.30432
$146$	9.06206	0.749982
$147$	−0.717154	−0.0591499
$148$	−1.10153	−0.0905450
$149$	10.1313	0.829990	0.414995	−	0.909824i	$-0.363783\pi$
$149$	10.1313	0.829990	0.414995	+	0.909824i	$0.363783\pi$
$150$	−2.55561	−0.208665
$151$	12.0303	0.979009	0.489504	−	0.872001i	$-0.337178\pi$
$151$	12.0303	0.979009	0.489504	+	0.872001i	$0.337178\pi$
$152$	−1.00000	−0.0811107
$153$	3.67254	0.296907
$154$	0.0123245	0.000993134 0
$155$	35.5374	2.85444
$156$	−0.292274	−0.0234007
$157$	−4.21227	−0.336176	−0.168088	−	0.985772i	$-0.553759\pi$
$157$	−4.21227	−0.336176	−0.168088	+	0.985772i	$0.553759\pi$
$158$	9.98203	0.794128
$159$	−0.204731	−0.0162363
$160$	3.98534	0.315069
$161$	6.44306	0.507784
$162$	−8.50674	−0.668353
$163$	−21.3952	−1.67580	−0.837899	−	0.545825i	$-0.816216\pi$
$163$	−21.3952	−1.67580	−0.837899	+	0.545825i	$0.816216\pi$
$164$	−0.105317	−0.00822390
$165$	0.00580633	0.000452023 0
$166$	−11.7885	−0.914961
$167$	−17.7724	−1.37527	−0.687636	−	0.726056i	$-0.741352\pi$
$167$	−17.7724	−1.37527	−0.687636	+	0.726056i	$0.741352\pi$
$168$	−0.466477	−0.0359895
$169$	−11.4509	−0.880838
$170$	−4.97012	−0.381191
$171$	−2.94486	−0.225199
$172$	−12.1551	−0.926816
$173$	−6.56770	−0.499333	−0.249667	−	0.968332i	$-0.580321\pi$
$173$	−6.56770	−0.499333	−0.249667	+	0.968332i	$0.580321\pi$
$174$	−2.34450	−0.177736
$175$	21.6185	1.63421
$176$	−0.00620422	−0.000467661 0
$177$	−0.366023	−0.0275119
$178$	−11.2792	−0.845413
$179$	10.2982	0.769724	0.384862	−	0.922974i	$-0.374249\pi$
$179$	10.2982	0.769724	0.384862	+	0.922974i	$0.374249\pi$
$180$	11.7362	0.874768
$181$	−19.9049	−1.47952	−0.739759	−	0.672872i	$-0.765060\pi$
$181$	−19.9049	−1.47952	−0.739759	+	0.672872i	$0.765060\pi$
$182$	2.47242	0.183268
$183$	3.09303	0.228643
$184$	−3.24348	−0.239112
$185$	4.38996	0.322756
$186$	2.09397	0.153537
$187$	0.00773730	0.000565808 0
$188$	9.56923	0.697908
$189$	−2.77314	−0.201716
$190$	3.98534	0.289127
$191$	−21.5224	−1.55731	−0.778653	−	0.627455i	$-0.784097\pi$
$191$	−21.5224	−1.55731	−0.778653	+	0.627455i	$0.784097\pi$
$192$	0.234828	0.0169472
$193$	−0.201542	−0.0145073	−0.00725367	−	0.999974i	$-0.502309\pi$
$193$	−0.201542	−0.0145073	−0.00725367	+	0.999974i	$0.502309\pi$
$194$	1.04561	0.0750702
$195$	1.16481	0.0834139
$196$	−3.05396	−0.218140
$197$	20.2943	1.44591	0.722953	−	0.690897i	$-0.242784\pi$
$197$	20.2943	1.44591	0.722953	+	0.690897i	$0.242784\pi$
$198$	−0.0182705	−0.00129843
$199$	5.82216	0.412722	0.206361	−	0.978476i	$-0.433838\pi$
$199$	5.82216	0.412722	0.206361	+	0.978476i	$0.433838\pi$
$200$	−10.8829	−0.769539
$201$	−0.305002	−0.0215132
$202$	−7.70446	−0.542084
$203$	19.8327	1.39198
$204$	−0.292854	−0.0205039
$205$	0.419725	0.0293149
$206$	−17.9213	−1.24863
$207$	−9.55158	−0.663880
$208$	−1.24463	−0.0862997
$209$	−0.00620422	−0.000429155 0
$210$	1.85907	0.128288
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−0.871837	−0.0598780
$213$	2.70148	0.185103
$214$	9.24043	0.631663
$215$	48.4421	3.30372
$216$	1.39602	0.0949869
$217$	−17.7134	−1.20246
$218$	−12.6031	−0.853587
$219$	−2.12802	−0.143799
$220$	0.0247259	0.00166702
$221$	1.55218	0.104411
$222$	0.258669	0.0173607
$223$	−5.62182	−0.376465	−0.188232	−	0.982124i	$-0.560276\pi$
$223$	−5.62182	−0.376465	−0.188232	+	0.982124i	$0.560276\pi$
$224$	−1.98646	−0.132726
$225$	−32.0486	−2.13658
$226$	−7.45006	−0.495570
$227$	−17.1686	−1.13952	−0.569760	−	0.821811i	$-0.692964\pi$
$227$	−17.1686	−1.13952	−0.569760	+	0.821811i	$0.692964\pi$
$228$	0.234828	0.0155518
$229$	3.37279	0.222880	0.111440	−	0.993771i	$-0.464454\pi$
$229$	3.37279	0.222880	0.111440	+	0.993771i	$0.464454\pi$
$230$	12.9264	0.852339
$231$	−0.00289413	−0.000190420 0
$232$	−9.98393	−0.655477
$233$	5.74656	0.376470	0.188235	−	0.982124i	$-0.439723\pi$
$233$	5.74656	0.376470	0.188235	+	0.982124i	$0.439723\pi$
$234$	−3.66526	−0.239606
$235$	−38.1366	−2.48776
$236$	−1.55869	−0.101462
$237$	−2.34406	−0.152263
$238$	2.47732	0.160581
$239$	−25.5311	−1.65147	−0.825736	−	0.564057i	$-0.809240\pi$
$239$	−25.5311	−1.65147	−0.825736	+	0.564057i	$0.809240\pi$
$240$	−0.935868	−0.0604100
$241$	−0.374843	−0.0241457	−0.0120729	−	0.999927i	$-0.503843\pi$
$241$	−0.374843	−0.0241457	−0.0120729	+	0.999927i	$0.503843\pi$
$242$	11.0000	0.707104
$243$	6.18567	0.396811
$244$	13.1715	0.843218
$245$	12.1711	0.777580
$246$	0.0247314	0.00157682
$247$	−1.24463	−0.0791941
$248$	8.91705	0.566233
$249$	2.76826	0.175431
$250$	23.4454	1.48282
$251$	−5.36609	−0.338705	−0.169352	−	0.985556i	$-0.554168\pi$
$251$	−5.36609	−0.338705	−0.169352	+	0.985556i	$0.554168\pi$
$252$	−5.84985	−0.368506
$253$	−0.0201233	−0.00126514
$254$	7.21524	0.452724
$255$	1.16712	0.0730881
$256$	1.00000	0.0625000
$257$	0.195904	0.0122201	0.00611007	−	0.999981i	$-0.498055\pi$
$257$	0.195904	0.0122201	0.00611007	+	0.999981i	$0.498055\pi$
$258$	2.85435	0.177704
$259$	−2.18815	−0.135965
$260$	4.96028	0.307624
$261$	−29.4012	−1.81989
$262$	8.17605	0.505118
$263$	14.4592	0.891591	0.445796	−	0.895135i	$-0.352921\pi$
$263$	14.4592	0.891591	0.445796	+	0.895135i	$0.352921\pi$
$264$	0.00145692	8.96675e−5 0
$265$	3.47456	0.213441
$266$	−1.98646	−0.121798
$267$	2.64867	0.162096
$268$	−1.29883	−0.0793388
$269$	−16.8661	−1.02834	−0.514171	−	0.857688i	$-0.671900\pi$
$269$	−16.8661	−1.02834	−0.514171	+	0.857688i	$0.671900\pi$
$270$	−5.56360	−0.338590
$271$	10.0143	0.608328	0.304164	−	0.952620i	$-0.401623\pi$
$271$	10.0143	0.608328	0.304164	+	0.952620i	$0.401623\pi$
$272$	−1.24710	−0.0756167
$273$	−0.580592	−0.0351391
$274$	4.14463	0.250386
$275$	−0.0675201	−0.00407161
$276$	0.761659	0.0458465
$277$	−7.66757	−0.460700	−0.230350	−	0.973108i	$-0.573987\pi$
$277$	−7.66757	−0.460700	−0.230350	+	0.973108i	$0.573987\pi$
$278$	−2.00340	−0.120156
$279$	26.2594	1.57211
$280$	7.91673	0.473115
$281$	−16.8843	−1.00723	−0.503616	−	0.863928i	$-0.667997\pi$
$281$	−16.8843	−1.00723	−0.503616	+	0.863928i	$0.667997\pi$
$282$	−2.24712	−0.133814
$283$	31.6302	1.88022	0.940111	−	0.340868i	$-0.110721\pi$
$283$	31.6302	1.88022	0.940111	+	0.340868i	$0.110721\pi$
$284$	11.5041	0.682643
$285$	−0.935868	−0.0554360
$286$	−0.00772198	−0.000456610 0
$287$	−0.209209	−0.0123492
$288$	2.94486	0.173527
$289$	−15.4447	−0.908514
$290$	39.7893	2.33651
$291$	−0.245537	−0.0143937
$292$	−9.06206	−0.530317
$293$	23.9345	1.39827	0.699134	−	0.714991i	$-0.253569\pi$
$293$	23.9345	1.39827	0.699134	+	0.714991i	$0.253569\pi$
$294$	0.717154	0.0418253
$295$	6.21189	0.361670
$296$	1.10153	0.0640250
$297$	0.00866120	0.000502574 0
$298$	−10.1313	−0.586891
$299$	−4.03694	−0.233462
$300$	2.55561	0.147548
$301$	−24.1456	−1.39173
$302$	−12.0303	−0.692264
$303$	1.80922	0.103937
$304$	1.00000	0.0573539
$305$	−52.4928	−3.00573
$306$	−3.67254	−0.209945
$307$	12.3024	0.702137	0.351068	−	0.936350i	$-0.385818\pi$
$307$	12.3024	0.702137	0.351068	+	0.936350i	$0.385818\pi$
$308$	−0.0123245	−0.000702252 0
$309$	4.20841	0.239408
$310$	−35.5374	−2.01839
$311$	3.83480	0.217451	0.108726	−	0.994072i	$-0.465323\pi$
$311$	3.83480	0.217451	0.108726	+	0.994072i	$0.465323\pi$
$312$	0.292274	0.0165468
$313$	−2.12774	−0.120267	−0.0601335	−	0.998190i	$-0.519153\pi$
$313$	−2.12774	−0.120267	−0.0601335	+	0.998190i	$0.519153\pi$
$314$	4.21227	0.237712
$315$	23.3136	1.31357
$316$	−9.98203	−0.561533
$317$	−25.3278	−1.42255	−0.711275	−	0.702914i	$-0.751882\pi$
$317$	−25.3278	−1.42255	−0.711275	+	0.702914i	$0.751882\pi$
$318$	0.204731	0.0114808
$319$	−0.0619425	−0.00346812
$320$	−3.98534	−0.222787
$321$	−2.16991	−0.121113
$322$	−6.44306	−0.359057
$323$	−1.24710	−0.0693906
$324$	8.50674	0.472597
$325$	−13.5452	−0.751355
$326$	21.3952	1.18497
$327$	2.95955	0.163663
$328$	0.105317	0.00581518
$329$	19.0089	1.04800
$330$	−0.00580633	−0.000319628 0
$331$	19.1453	1.05232	0.526162	−	0.850385i	$-0.323631\pi$
$331$	19.1453	1.05232	0.526162	+	0.850385i	$0.323631\pi$
$332$	11.7885	0.646975
$333$	3.24384	0.177761
$334$	17.7724	0.972464
$335$	5.17629	0.282811
$336$	0.466477	0.0254484
$337$	13.5073	0.735789	0.367895	−	0.929867i	$-0.380079\pi$
$337$	13.5073	0.735789	0.367895	+	0.929867i	$0.380079\pi$
$338$	11.4509	0.622846
$339$	1.74948	0.0950187
$340$	4.97012	0.269543
$341$	0.0553234	0.00299593
$342$	2.94486	0.159240
$343$	−19.9718	−1.07838
$344$	12.1551	0.655358
$345$	−3.03547	−0.163424
$346$	6.56770	0.353082
$347$	32.0805	1.72217	0.861086	−	0.508460i	$-0.169785\pi$
$347$	32.0805	1.72217	0.861086	+	0.508460i	$0.169785\pi$
$348$	2.34450	0.125679
$349$	−31.1960	−1.66988	−0.834942	−	0.550338i	$-0.814499\pi$
$349$	−31.1960	−1.66988	−0.834942	+	0.550338i	$0.814499\pi$
$350$	−21.6185	−1.15556
$351$	1.73753	0.0927424
$352$	0.00620422	0.000330686 0
$353$	9.52089	0.506746	0.253373	−	0.967369i	$-0.418460\pi$
$353$	9.52089	0.506746	0.253373	+	0.967369i	$0.418460\pi$
$354$	0.366023	0.0194539
$355$	−45.8477	−2.43335
$356$	11.2792	0.597797
$357$	−0.581744	−0.0307892
$358$	−10.2982	−0.544277
$359$	−24.3633	−1.28584	−0.642922	−	0.765932i	$-0.722278\pi$
$359$	−24.3633	−1.28584	−0.642922	+	0.765932i	$0.722278\pi$
$360$	−11.7362	−0.618555
$361$	1.00000	0.0526316
$362$	19.9049	1.04618
$363$	−2.58310	−0.135577
$364$	−2.47242	−0.129590
$365$	36.1154	1.89037
$366$	−3.09303	−0.161675
$367$	−12.9240	−0.674628	−0.337314	−	0.941392i	$-0.609518\pi$
$367$	−12.9240	−0.674628	−0.337314	+	0.941392i	$0.609518\pi$
$368$	3.24348	0.169078
$369$	0.310144	0.0161455
$370$	−4.38996	−0.228223
$371$	−1.73187	−0.0899143
$372$	−2.09397	−0.108567
$373$	−37.4597	−1.93959	−0.969795	−	0.243923i	$-0.921566\pi$
$373$	−37.4597	−1.93959	−0.969795	+	0.243923i	$0.921566\pi$
$374$	−0.00773730	−0.000400086 0
$375$	−5.50564	−0.284310
$376$	−9.56923	−0.493495
$377$	−12.4263	−0.639988
$378$	2.77314	0.142635
$379$	−27.0018	−1.38699	−0.693493	−	0.720463i	$-0.743929\pi$
$379$	−27.0018	−1.38699	−0.693493	+	0.720463i	$0.743929\pi$
$380$	−3.98534	−0.204444
$381$	−1.69434	−0.0868035
$382$	21.5224	1.10118
$383$	−17.8365	−0.911401	−0.455700	−	0.890133i	$-0.650611\pi$
$383$	−17.8365	−0.911401	−0.455700	+	0.890133i	$0.650611\pi$
$384$	−0.234828	−0.0119835
$385$	0.0491172	0.00250324
$386$	0.201542	0.0102582
$387$	35.7950	1.81956
$388$	−1.04561	−0.0530826
$389$	0.429589	0.0217810	0.0108905	−	0.999941i	$-0.496533\pi$
$389$	0.429589	0.0217810	0.0108905	+	0.999941i	$0.496533\pi$
$390$	−1.16481	−0.0589825
$391$	−4.04495	−0.204562
$392$	3.05396	0.154248
$393$	−1.91996	−0.0968493
$394$	−20.2943	−1.02241
$395$	39.7818	2.00164
$396$	0.0182705	0.000918129 0
$397$	−39.3498	−1.97491	−0.987455	−	0.157899i	$-0.949528\pi$
$397$	−39.3498	−1.97491	−0.987455	+	0.157899i	$0.949528\pi$
$398$	−5.82216	−0.291839
$399$	0.466477	0.0233531
$400$	10.8829	0.544146
$401$	−5.14778	−0.257068	−0.128534	−	0.991705i	$-0.541027\pi$
$401$	−5.14778	−0.257068	−0.128534	+	0.991705i	$0.541027\pi$
$402$	0.305002	0.0152121
$403$	11.0984	0.552853
$404$	7.70446	0.383311
$405$	−33.9023	−1.68462
$406$	−19.8327	−0.984281
$407$	0.00683412	0.000338755 0
$408$	0.292854	0.0144984
$409$	−17.8814	−0.884178	−0.442089	−	0.896971i	$-0.645762\pi$
$409$	−17.8814	−0.884178	−0.442089	+	0.896971i	$0.645762\pi$
$410$	−0.419725	−0.0207288
$411$	−0.973273	−0.0480080
$412$	17.9213	0.882918
$413$	−3.09627	−0.152358
$414$	9.55158	0.469434
$415$	−46.9810	−2.30621
$416$	1.24463	0.0610231
$417$	0.470454	0.0230382
$418$	0.00620422	0.000303459 0
$419$	6.30074	0.307811	0.153906	−	0.988086i	$-0.450815\pi$
$419$	6.30074	0.307811	0.153906	+	0.988086i	$0.450815\pi$
$420$	−1.85907	−0.0907133
$421$	13.0216	0.634632	0.317316	−	0.948320i	$-0.397218\pi$
$421$	13.0216	0.634632	0.317316	+	0.948320i	$0.397218\pi$
$422$	−1.00000	−0.0486792
$423$	−28.1800	−1.37016
$424$	0.871837	0.0423401
$425$	−13.5721	−0.658344
$426$	−2.70148	−0.130887
$427$	26.1647	1.26620
$428$	−9.24043	−0.446653
$429$	0.00181333	8.75486e−5 0
$430$	−48.4421	−2.33609
$431$	−20.8185	−1.00279	−0.501395	−	0.865219i	$-0.667180\pi$
$431$	−20.8185	−1.00279	−0.501395	+	0.865219i	$0.667180\pi$
$432$	−1.39602	−0.0671659
$433$	−10.8532	−0.521572	−0.260786	−	0.965397i	$-0.583982\pi$
$433$	−10.8532	−0.521572	−0.260786	+	0.965397i	$0.583982\pi$
$434$	17.7134	0.850270
$435$	−9.34364	−0.447993
$436$	12.6031	0.603577
$437$	3.24348	0.155157
$438$	2.12802	0.101681
$439$	−5.47447	−0.261282	−0.130641	−	0.991430i	$-0.541704\pi$
$439$	−5.47447	−0.261282	−0.130641	+	0.991430i	$0.541704\pi$
$440$	−0.0247259	−0.00117876
$441$	8.99347	0.428260
$442$	−1.55218	−0.0738299
$443$	−19.3254	−0.918178	−0.459089	−	0.888390i	$-0.651824\pi$
$443$	−19.3254	−0.918178	−0.459089	+	0.888390i	$0.651824\pi$
$444$	−0.258669	−0.0122759
$445$	−44.9515	−2.13091
$446$	5.62182	0.266201
$447$	2.37911	0.112528
$448$	1.98646	0.0938516
$449$	−17.4401	−0.823049	−0.411524	−	0.911399i	$-0.635004\pi$
$449$	−17.4401	−0.823049	−0.411524	+	0.911399i	$0.635004\pi$
$450$	32.0486	1.51079
$451$	0.000653412 0	3.07680e−5 0
$452$	7.45006	0.350421
$453$	2.82504	0.132732
$454$	17.1686	0.805762
$455$	9.85342	0.461936
$456$	−0.234828	−0.0109968
$457$	7.36595	0.344564	0.172282	−	0.985048i	$-0.444886\pi$
$457$	7.36595	0.344564	0.172282	+	0.985048i	$0.444886\pi$
$458$	−3.37279	−0.157600
$459$	1.74098	0.0812618
$460$	−12.9264	−0.602695
$461$	13.3927	0.623760	0.311880	−	0.950121i	$-0.399041\pi$
$461$	13.3927	0.623760	0.311880	+	0.950121i	$0.399041\pi$
$462$	0.00289413	0.000134647 0
$463$	8.69432	0.404060	0.202030	−	0.979379i	$-0.435246\pi$
$463$	8.69432	0.404060	0.202030	+	0.979379i	$0.435246\pi$
$464$	9.98393	0.463492
$465$	8.34518	0.386998
$466$	−5.74656	−0.266204
$467$	−2.31913	−0.107316	−0.0536582	−	0.998559i	$-0.517088\pi$
$467$	−2.31913	−0.107316	−0.0536582	+	0.998559i	$0.517088\pi$
$468$	3.66526	0.169427
$469$	−2.58009	−0.119137
$470$	38.1366	1.75911
$471$	−0.989157	−0.0455780
$472$	1.55869	0.0717443
$473$	0.0754128	0.00346749
$474$	2.34406	0.107666
$475$	10.8829	0.499343
$476$	−2.47732	−0.113548
$477$	2.56743	0.117555
$478$	25.5311	1.16777
$479$	14.5184	0.663361	0.331680	−	0.943392i	$-0.392384\pi$
$479$	14.5184	0.663361	0.331680	+	0.943392i	$0.392384\pi$
$480$	0.935868	0.0427163
$481$	1.37100	0.0625121
$482$	0.374843	0.0170736
$483$	1.51301	0.0688443
$484$	−11.0000	−0.499998
$485$	4.16710	0.189218
$486$	−6.18567	−0.280588
$487$	8.06203	0.365326	0.182663	−	0.983176i	$-0.441528\pi$
$487$	8.06203	0.365326	0.182663	+	0.983176i	$0.441528\pi$
$488$	−13.1715	−0.596245
$489$	−5.02418	−0.227201
$490$	−12.1711	−0.549832
$491$	−15.0839	−0.680728	−0.340364	−	0.940294i	$-0.610550\pi$
$491$	−15.0839	−0.680728	−0.340364	+	0.940294i	$0.610550\pi$
$492$	−0.0247314	−0.00111498
$493$	−12.4510	−0.560764
$494$	1.24463	0.0559987
$495$	−0.0728143	−0.00327276
$496$	−8.91705	−0.400387
$497$	22.8525	1.02507
$498$	−2.76826	−0.124048
$499$	12.5738	0.562881	0.281440	−	0.959579i	$-0.409188\pi$
$499$	12.5738	0.562881	0.281440	+	0.959579i	$0.409188\pi$
$500$	−23.4454	−1.04851
$501$	−4.17346	−0.186456
$502$	5.36609	0.239500
$503$	−15.2500	−0.679963	−0.339982	−	0.940432i	$-0.610421\pi$
$503$	−15.2500	−0.679963	−0.339982	+	0.940432i	$0.610421\pi$
$504$	5.84985	0.260573
$505$	−30.7049	−1.36635
$506$	0.0201233	0.000894588 0
$507$	−2.68899	−0.119422
$508$	−7.21524	−0.320124
$509$	25.6679	1.13771	0.568854	−	0.822439i	$-0.307387\pi$
$509$	25.6679	1.13771	0.568854	+	0.822439i	$0.307387\pi$
$510$	−1.16712	−0.0516811
$511$	−18.0015	−0.796338
$512$	−1.00000	−0.0441942
$513$	−1.39602	−0.0616357
$514$	−0.195904	−0.00864094
$515$	−71.4224	−3.14724
$516$	−2.85435	−0.125656
$517$	−0.0593696	−0.00261107
$518$	2.18815	0.0961416
$519$	−1.54228	−0.0676985
$520$	−4.96028	−0.217523
$521$	−43.3766	−1.90036	−0.950182	−	0.311695i	$-0.899103\pi$
$521$	−43.3766	−1.90036	−0.950182	+	0.311695i	$0.899103\pi$
$522$	29.4012	1.28686
$523$	−4.02932	−0.176190	−0.0880948	−	0.996112i	$-0.528078\pi$
$523$	−4.02932	−0.176190	−0.0880948	+	0.996112i	$0.528078\pi$
$524$	−8.17605	−0.357172
$525$	5.07663	0.221562
$526$	−14.4592	−0.630450
$527$	11.1205	0.484415
$528$	−0.00145692	−6.34045e−5 0
$529$	−12.4798	−0.542602
$530$	−3.47456	−0.150925
$531$	4.59010	0.199194
$532$	1.98646	0.0861242
$533$	0.131081	0.00567777
$534$	−2.64867	−0.114619
$535$	36.8262	1.59214
$536$	1.29883	0.0561010
$537$	2.41830	0.104358
$538$	16.8661	0.727147
$539$	0.0189474	0.000816124 0
$540$	5.56360	0.239419
$541$	−1.72617	−0.0742139	−0.0371070	−	0.999311i	$-0.511814\pi$
$541$	−1.72617	−0.0742139	−0.0371070	+	0.999311i	$0.511814\pi$
$542$	−10.0143	−0.430153
$543$	−4.67422	−0.200590
$544$	1.24710	0.0534691
$545$	−50.2275	−2.15151
$546$	0.580592	0.0248471
$547$	−6.22593	−0.266202	−0.133101	−	0.991103i	$-0.542493\pi$
$547$	−6.22593	−0.266202	−0.133101	+	0.991103i	$0.542493\pi$
$548$	−4.14463	−0.177050
$549$	−38.7881	−1.65544
$550$	0.0675201	0.00287907
$551$	9.98393	0.425330
$552$	−0.761659	−0.0324183
$553$	−19.8290	−0.843213
$554$	7.66757	0.325764
$555$	1.03088	0.0437586
$556$	2.00340	0.0849631
$557$	−26.2287	−1.11135	−0.555674	−	0.831401i	$-0.687540\pi$
$557$	−26.2287	−1.11135	−0.555674	+	0.831401i	$0.687540\pi$
$558$	−26.2594	−1.11165
$559$	15.1286	0.639872
$560$	−7.91673	−0.334543
$561$	0.00181693	7.67110e−5 0
$562$	16.8843	0.712220
$563$	−16.5941	−0.699356	−0.349678	−	0.936870i	$-0.613709\pi$
$563$	−16.5941	−0.699356	−0.349678	+	0.936870i	$0.613709\pi$
$564$	2.24712	0.0946208
$565$	−29.6910	−1.24911
$566$	−31.6302	−1.32952
$567$	16.8983	0.709664
$568$	−11.5041	−0.482702
$569$	−9.37844	−0.393165	−0.196582	−	0.980487i	$-0.562984\pi$
$569$	−9.37844	−0.393165	−0.196582	+	0.980487i	$0.562984\pi$
$570$	0.935868	0.0391992
$571$	−5.36159	−0.224375	−0.112188	−	0.993687i	$-0.535786\pi$
$571$	−5.36159	−0.224375	−0.112188	+	0.993687i	$0.535786\pi$
$572$	0.00772198	0.000322872 0
$573$	−5.05406	−0.211136
$574$	0.209209	0.00873222
$575$	35.2985	1.47205
$576$	−2.94486	−0.122702
$577$	−16.0014	−0.666147	−0.333073	−	0.942901i	$-0.608086\pi$
$577$	−16.0014	−0.666147	−0.333073	+	0.942901i	$0.608086\pi$
$578$	15.4447	0.642416
$579$	−0.0473278	−0.00196687
$580$	−39.7893	−1.65216
$581$	23.4173	0.971515
$582$	0.245537	0.0101779
$583$	0.00540907	0.000224021 0
$584$	9.06206	0.374991
$585$	−14.6073	−0.603938
$586$	−23.9345	−0.988724
$587$	−8.89264	−0.367038	−0.183519	−	0.983016i	$-0.558749\pi$
$587$	−8.89264	−0.367038	−0.183519	+	0.983016i	$0.558749\pi$
$588$	−0.717154	−0.0295749
$589$	−8.91705	−0.367421
$590$	−6.21189	−0.255739
$591$	4.76565	0.196033
$592$	−1.10153	−0.0452725
$593$	20.2668	0.832258	0.416129	−	0.909306i	$-0.363386\pi$
$593$	20.2668	0.832258	0.416129	+	0.909306i	$0.363386\pi$
$594$	−0.00866120	−0.000355373 0
$595$	9.87298	0.404753
$596$	10.1313	0.414995
$597$	1.36720	0.0559560
$598$	4.03694	0.165083
$599$	19.5908	0.800459	0.400230	−	0.916415i	$-0.368930\pi$
$599$	19.5908	0.800459	0.400230	+	0.916415i	$0.368930\pi$
$600$	−2.55561	−0.104332
$601$	−12.4855	−0.509293	−0.254647	−	0.967034i	$-0.581959\pi$
$601$	−12.4855	−0.509293	−0.254647	+	0.967034i	$0.581959\pi$
$602$	24.1456	0.984103
$603$	3.82488	0.155761
$604$	12.0303	0.489504
$605$	43.8386	1.78229
$606$	−1.80922	−0.0734946
$607$	16.9067	0.686220	0.343110	−	0.939295i	$-0.388520\pi$
$607$	16.9067	0.686220	0.343110	+	0.939295i	$0.388520\pi$
$608$	−1.00000	−0.0405554
$609$	4.65727	0.188722
$610$	52.4928	2.12537
$611$	−11.9102	−0.481834
$612$	3.67254	0.148453
$613$	−3.56057	−0.143810	−0.0719051	−	0.997411i	$-0.522908\pi$
$613$	−3.56057	−0.143810	−0.0719051	+	0.997411i	$0.522908\pi$
$614$	−12.3024	−0.496486
$615$	0.0985631	0.00397445
$616$	0.0123245	0.000496567 0
$617$	−23.3349	−0.939426	−0.469713	−	0.882819i	$-0.655643\pi$
$617$	−23.3349	−0.939426	−0.469713	+	0.882819i	$0.655643\pi$
$618$	−4.20841	−0.169287
$619$	47.5901	1.91281	0.956403	−	0.292051i	$-0.0943376\pi$
$619$	47.5901	1.91281	0.956403	+	0.292051i	$0.0943376\pi$
$620$	35.5374	1.42722
$621$	−4.52795	−0.181700
$622$	−3.83480	−0.153761
$623$	22.4058	0.897668
$624$	−0.292274	−0.0117003
$625$	39.0234	1.56093
$626$	2.12774	0.0850416
$627$	−0.00145692	−5.81839e−5 0
$628$	−4.21227	−0.168088
$629$	1.37372	0.0547737
$630$	−23.3136	−0.928838
$631$	−7.47891	−0.297731	−0.148865	−	0.988857i	$-0.547562\pi$
$631$	−7.47891	−0.297731	−0.148865	+	0.988857i	$0.547562\pi$
$632$	9.98203	0.397064
$633$	0.234828	0.00933356
$634$	25.3278	1.00590
$635$	28.7552	1.14111
$636$	−0.204731	−0.00811813
$637$	3.80106	0.150603
$638$	0.0619425	0.00245233
$639$	−33.8779	−1.34019
$640$	3.98534	0.157534
$641$	−20.8494	−0.823502	−0.411751	−	0.911296i	$-0.635083\pi$
$641$	−20.8494	−0.823502	−0.411751	+	0.911296i	$0.635083\pi$
$642$	2.16991	0.0856395
$643$	18.1971	0.717622	0.358811	−	0.933410i	$-0.383182\pi$
$643$	18.1971	0.717622	0.358811	+	0.933410i	$0.383182\pi$
$644$	6.44306	0.253892
$645$	11.3756	0.447912
$646$	1.24710	0.0490666
$647$	16.0021	0.629108	0.314554	−	0.949240i	$-0.398145\pi$
$647$	16.0021	0.629108	0.314554	+	0.949240i	$0.398145\pi$
$648$	−8.50674	−0.334176
$649$	0.00967043	0.000379598 0
$650$	13.5452	0.531288
$651$	−4.15960	−0.163027
$652$	−21.3952	−0.837899
$653$	−36.7809	−1.43935	−0.719674	−	0.694312i	$-0.755709\pi$
$653$	−36.7809	−1.43935	−0.719674	+	0.694312i	$0.755709\pi$
$654$	−2.95955	−0.115727
$655$	32.5843	1.27317
$656$	−0.105317	−0.00411195
$657$	26.6865	1.04114
$658$	−19.0089	−0.741046
$659$	−3.16568	−0.123317	−0.0616587	−	0.998097i	$-0.519639\pi$
$659$	−3.16568	−0.123317	−0.0616587	+	0.998097i	$0.519639\pi$
$660$	0.00580633	0.000226011 0
$661$	41.5440	1.61587	0.807937	−	0.589268i	$-0.200584\pi$
$661$	41.5440	1.61587	0.807937	+	0.589268i	$0.200584\pi$
$662$	−19.1453	−0.744105
$663$	0.364496	0.0141558
$664$	−11.7885	−0.457481
$665$	−7.91673	−0.306998
$666$	−3.24384	−0.125696
$667$	32.3827	1.25386
$668$	−17.7724	−0.687636
$669$	−1.32016	−0.0510403
$670$	−5.17629	−0.199977
$671$	−0.0817189	−0.00315472
$672$	−0.466477	−0.0179947
$673$	33.1562	1.27808	0.639038	−	0.769175i	$-0.279333\pi$
$673$	33.1562	1.27808	0.639038	+	0.769175i	$0.279333\pi$
$674$	−13.5073	−0.520282
$675$	−15.1927	−0.584769
$676$	−11.4509	−0.440419
$677$	−9.84381	−0.378328	−0.189164	−	0.981945i	$-0.560578\pi$
$677$	−9.84381	−0.378328	−0.189164	+	0.981945i	$0.560578\pi$
$678$	−1.74948	−0.0671884
$679$	−2.07706	−0.0797103
$680$	−4.97012	−0.190596
$681$	−4.03166	−0.154494
$682$	−0.0553234	−0.00211844
$683$	23.7953	0.910501	0.455250	−	0.890363i	$-0.349550\pi$
$683$	23.7953	0.910501	0.455250	+	0.890363i	$0.349550\pi$
$684$	−2.94486	−0.112599
$685$	16.5177	0.631110
$686$	19.9718	0.762528
$687$	0.792024	0.0302176
$688$	−12.1551	−0.463408
$689$	1.08512	0.0413396
$690$	3.03547	0.115558
$691$	22.0168	0.837557	0.418779	−	0.908088i	$-0.362458\pi$
$691$	22.0168	0.837557	0.418779	+	0.908088i	$0.362458\pi$
$692$	−6.56770	−0.249667
$693$	0.0362938	0.00137869
$694$	−32.0805	−1.21776
$695$	−7.98423	−0.302859
$696$	−2.34450	−0.0888682
$697$	0.131342	0.00497491
$698$	31.1960	1.18079
$699$	1.34945	0.0510410
$700$	21.6185	0.817104
$701$	33.8195	1.27735	0.638673	−	0.769478i	$-0.279484\pi$
$701$	33.8195	1.27735	0.638673	+	0.769478i	$0.279484\pi$
$702$	−1.73753	−0.0655788
$703$	−1.10153	−0.0415449
$704$	−0.00620422	−0.000233830 0
$705$	−8.95554	−0.337285
$706$	−9.52089	−0.358323
$707$	15.3046	0.575590
$708$	−0.366023	−0.0137560
$709$	13.4582	0.505432	0.252716	−	0.967541i	$-0.418676\pi$
$709$	13.4582	0.505432	0.252716	+	0.967541i	$0.418676\pi$
$710$	45.8477	1.72064
$711$	29.3957	1.10242
$712$	−11.2792	−0.422707
$713$	−28.9222	−1.08315
$714$	0.581744	0.0217712
$715$	−0.0307747	−0.00115091
$716$	10.2982	0.384862
$717$	−5.99542	−0.223903
$718$	24.3633	0.909229
$719$	−21.1137	−0.787407	−0.393703	−	0.919238i	$-0.628806\pi$
$719$	−21.1137	−0.787407	−0.393703	+	0.919238i	$0.628806\pi$
$720$	11.7362	0.437384
$721$	35.6000	1.32581
$722$	−1.00000	−0.0372161
$723$	−0.0880234	−0.00327363
$724$	−19.9049	−0.739759
$725$	108.654	4.03532
$726$	2.58310	0.0958677
$727$	−13.2120	−0.490006	−0.245003	−	0.969522i	$-0.578789\pi$
$727$	−13.2120	−0.490006	−0.245003	+	0.969522i	$0.578789\pi$
$728$	2.47242	0.0916339
$729$	−24.0677	−0.891395
$730$	−36.1154	−1.33669
$731$	15.1586	0.560662
$732$	3.09303	0.114322
$733$	−12.5862	−0.464882	−0.232441	−	0.972611i	$-0.574671\pi$
$733$	−12.5862	−0.464882	−0.232441	+	0.972611i	$0.574671\pi$
$734$	12.9240	0.477034
$735$	2.85810	0.105423
$736$	−3.24348	−0.119556
$737$	0.00805825	0.000296829 0
$738$	−0.310144	−0.0114166
$739$	13.4862	0.496099	0.248049	−	0.968747i	$-0.420210\pi$
$739$	13.4862	0.496099	0.248049	+	0.968747i	$0.420210\pi$
$740$	4.38996	0.161378
$741$	−0.292274	−0.0107370
$742$	1.73187	0.0635790
$743$	−43.8054	−1.60706	−0.803531	−	0.595262i	$-0.797048\pi$
$743$	−43.8054	−1.60706	−0.803531	+	0.595262i	$0.797048\pi$
$744$	2.09397	0.0767687
$745$	−40.3767	−1.47929
$746$	37.4597	1.37150
$747$	−34.7153	−1.27017
$748$	0.00773730	0.000282904 0
$749$	−18.3558	−0.670706
$750$	5.50564	0.201037
$751$	−5.50413	−0.200848	−0.100424	−	0.994945i	$-0.532020\pi$
$751$	−5.50413	−0.200848	−0.100424	+	0.994945i	$0.532020\pi$
$752$	9.56923	0.348954
$753$	−1.26011	−0.0459209
$754$	12.4263	0.452540
$755$	−47.9447	−1.74488
$756$	−2.77314	−0.100858
$757$	16.1313	0.586303	0.293152	−	0.956066i	$-0.405296\pi$
$757$	16.1313	0.586303	0.293152	+	0.956066i	$0.405296\pi$
$758$	27.0018	0.980748
$759$	−0.00472550	−0.000171525 0
$760$	3.98534	0.144563
$761$	26.7322	0.969042	0.484521	−	0.874779i	$-0.338994\pi$
$761$	26.7322	0.969042	0.484521	+	0.874779i	$0.338994\pi$
$762$	1.69434	0.0613794
$763$	25.0355	0.906347
$764$	−21.5224	−0.778653
$765$	−14.6363	−0.529177
$766$	17.8365	0.644458
$767$	1.93999	0.0700490
$768$	0.234828	0.00847362
$769$	−19.6651	−0.709142	−0.354571	−	0.935029i	$-0.615373\pi$
$769$	−19.6651	−0.709142	−0.354571	+	0.935029i	$0.615373\pi$
$770$	−0.0491172	−0.00177006
$771$	0.0460036	0.00165678
$772$	−0.201542	−0.00725367
$773$	−9.23659	−0.332217	−0.166108	−	0.986107i	$-0.553120\pi$
$773$	−9.23659	−0.332217	−0.166108	+	0.986107i	$0.553120\pi$
$774$	−35.7950	−1.28662
$775$	−97.0435	−3.48591
$776$	1.04561	0.0375351
$777$	−0.513837	−0.0184338
$778$	−0.429589	−0.0154015
$779$	−0.105317	−0.00377339
$780$	1.16481	0.0417069
$781$	−0.0713740	−0.00255396
$782$	4.04495	0.144647
$783$	−13.9377	−0.498094
$784$	−3.05396	−0.109070
$785$	16.7873	0.599165
$786$	1.91996	0.0684828
$787$	17.1134	0.610025	0.305013	−	0.952348i	$-0.401339\pi$
$787$	17.1134	0.610025	0.305013	+	0.952348i	$0.401339\pi$
$788$	20.2943	0.722953
$789$	3.39542	0.120880
$790$	−39.7818	−1.41537
$791$	14.7993	0.526202
$792$	−0.0182705	−0.000649216 0
$793$	−16.3937	−0.582156
$794$	39.3498	1.39647
$795$	0.815924	0.0289378
$796$	5.82216	0.206361
$797$	−22.7041	−0.804221	−0.402111	−	0.915591i	$-0.631723\pi$
$797$	−22.7041	−0.804221	−0.402111	+	0.915591i	$0.631723\pi$
$798$	−0.466477	−0.0165131
$799$	−11.9338	−0.422188
$800$	−10.8829	−0.384769
$801$	−33.2157	−1.17362
$802$	5.14778	0.181774
$803$	0.0562231	0.00198407
$804$	−0.305002	−0.0107566
$805$	−25.6778	−0.905022
$806$	−11.0984	−0.390926
$807$	−3.96062	−0.139420
$808$	−7.70446	−0.271042
$809$	22.0928	0.776742	0.388371	−	0.921503i	$-0.373038\pi$
$809$	22.0928	0.776742	0.388371	+	0.921503i	$0.373038\pi$
$810$	33.9023	1.19120
$811$	−25.0161	−0.878434	−0.439217	−	0.898381i	$-0.644744\pi$
$811$	−25.0161	−0.878434	−0.439217	+	0.898381i	$0.644744\pi$
$812$	19.8327	0.695992
$813$	2.35165	0.0824759
$814$	−0.00683412	−0.000239536 0
$815$	85.2670	2.98677
$816$	−0.292854	−0.0102519
$817$	−12.1551	−0.425252
$818$	17.8814	0.625208
$819$	7.28092	0.254416
$820$	0.419725	0.0146574
$821$	−21.9075	−0.764576	−0.382288	−	0.924043i	$-0.624864\pi$
$821$	−21.9075	−0.764576	−0.382288	+	0.924043i	$0.624864\pi$
$822$	0.973273	0.0339468
$823$	−13.0970	−0.456532	−0.228266	−	0.973599i	$-0.573306\pi$
$823$	−13.0970	−0.456532	−0.228266	+	0.973599i	$0.573306\pi$
$824$	−17.9213	−0.624317
$825$	−0.0158556	−0.000552021 0
$826$	3.09627	0.107733
$827$	−21.6282	−0.752086	−0.376043	−	0.926602i	$-0.622716\pi$
$827$	−21.6282	−0.752086	−0.376043	+	0.926602i	$0.622716\pi$
$828$	−9.55158	−0.331940
$829$	24.0251	0.834426	0.417213	−	0.908809i	$-0.363007\pi$
$829$	24.0251	0.834426	0.417213	+	0.908809i	$0.363007\pi$
$830$	46.9810	1.63073
$831$	−1.80056	−0.0624607
$832$	−1.24463	−0.0431499
$833$	3.80860	0.131960
$834$	−0.470454	−0.0162905
$835$	70.8292	2.45114
$836$	−0.00620422	−0.000214578 0
$837$	12.4483	0.430278
$838$	−6.30074	−0.217655
$839$	−26.6535	−0.920180	−0.460090	−	0.887872i	$-0.652183\pi$
$839$	−26.6535	−0.920180	−0.460090	+	0.887872i	$0.652183\pi$
$840$	1.85907	0.0641440
$841$	70.6788	2.43720
$842$	−13.0216	−0.448752
$843$	−3.96490	−0.136558
$844$	1.00000	0.0344214
$845$	45.6357	1.56991
$846$	28.1800	0.968848
$847$	−21.8510	−0.750810
$848$	−0.871837	−0.0299390
$849$	7.42766	0.254917
$850$	13.5721	0.465520
$851$	−3.57278	−0.122473
$852$	2.70148	0.0925513
$853$	−14.9342	−0.511337	−0.255668	−	0.966765i	$-0.582295\pi$
$853$	−14.9342	−0.511337	−0.255668	+	0.966765i	$0.582295\pi$
$854$	−26.1647	−0.895338
$855$	11.7362	0.401371
$856$	9.24043	0.315831
$857$	−33.4984	−1.14429	−0.572143	−	0.820154i	$-0.693888\pi$
$857$	−33.4984	−1.14429	−0.572143	+	0.820154i	$0.693888\pi$
$858$	−0.00181333	−6.19062e−5 0
$859$	−46.0772	−1.57213	−0.786066	−	0.618142i	$-0.787886\pi$
$859$	−46.0772	−1.57213	−0.786066	+	0.618142i	$0.787886\pi$
$860$	48.4421	1.65186
$861$	−0.0491281	−0.00167428
$862$	20.8185	0.709080
$863$	−35.7323	−1.21634	−0.608171	−	0.793806i	$-0.708097\pi$
$863$	−35.7323	−1.21634	−0.608171	+	0.793806i	$0.708097\pi$
$864$	1.39602	0.0474935
$865$	26.1745	0.889960
$866$	10.8532	0.368807
$867$	−3.62685	−0.123174
$868$	−17.7134	−0.601232
$869$	0.0619308	0.00210086
$870$	9.34364	0.316779
$871$	1.61657	0.0547754
$872$	−12.6031	−0.426793
$873$	3.07916	0.104214
$874$	−3.24348	−0.109712
$875$	−46.5735	−1.57447
$876$	−2.12802	−0.0718993
$877$	−58.6473	−1.98038	−0.990189	−	0.139732i	$-0.955376\pi$
$877$	−58.6473	−1.98038	−0.990189	+	0.139732i	$0.955376\pi$
$878$	5.47447	0.184754
$879$	5.62048	0.189574
$880$	0.0247259	0.000833511 0
$881$	22.3681	0.753600	0.376800	−	0.926295i	$-0.377024\pi$
$881$	22.3681	0.753600	0.376800	+	0.926295i	$0.377024\pi$
$882$	−8.99347	−0.302826
$883$	−39.1696	−1.31816	−0.659081	−	0.752072i	$-0.729055\pi$
$883$	−39.1696	−1.31816	−0.659081	+	0.752072i	$0.729055\pi$
$884$	1.55218	0.0522056
$885$	1.45872	0.0490345
$886$	19.3254	0.649250
$887$	−8.78914	−0.295110	−0.147555	−	0.989054i	$-0.547140\pi$
$887$	−8.78914	−0.295110	−0.147555	+	0.989054i	$0.547140\pi$
$888$	0.258669	0.00868037
$889$	−14.3328	−0.480707
$890$	44.9515	1.50678
$891$	−0.0527777	−0.00176812
$892$	−5.62182	−0.188232
$893$	9.56923	0.320222
$894$	−2.37911	−0.0795695
$895$	−41.0418	−1.37188
$896$	−1.98646	−0.0663631
$897$	−0.947985	−0.0316523
$898$	17.4401	0.581984
$899$	−89.0271	−2.96922
$900$	−32.0486	−1.06829
$901$	1.08727	0.0362222
$902$	−0.000653412 0	−2.17563e−5 0
$903$	−5.67007	−0.188688
$904$	−7.45006	−0.247785
$905$	79.3276	2.63694
$906$	−2.82504	−0.0938556
$907$	15.5391	0.515966	0.257983	−	0.966149i	$-0.416942\pi$
$907$	15.5391	0.515966	0.257983	+	0.966149i	$0.416942\pi$
$908$	−17.1686	−0.569760
$909$	−22.6885	−0.752531
$910$	−9.85342	−0.326638
$911$	−42.7020	−1.41478	−0.707390	−	0.706823i	$-0.750128\pi$
$911$	−42.7020	−1.41478	−0.707390	+	0.706823i	$0.750128\pi$
$912$	0.234828	0.00777592
$913$	−0.0731382	−0.00242052
$914$	−7.36595	−0.243644
$915$	−12.3268	−0.407511
$916$	3.37279	0.111440
$917$	−16.2414	−0.536339
$918$	−1.74098	−0.0574608
$919$	−49.4393	−1.63085	−0.815425	−	0.578862i	$-0.803497\pi$
$919$	−49.4393	−1.63085	−0.815425	+	0.578862i	$0.803497\pi$
$920$	12.9264	0.426169
$921$	2.88895	0.0951942
$922$	−13.3927	−0.441065
$923$	−14.3184	−0.471295
$924$	−0.00289413	−9.52098e−5 0
$925$	−11.9878	−0.394158
$926$	−8.69432	−0.285713
$927$	−52.7756	−1.73338
$928$	−9.98393	−0.327738
$929$	28.4539	0.933542	0.466771	−	0.884378i	$-0.345417\pi$
$929$	28.4539	0.933542	0.466771	+	0.884378i	$0.345417\pi$
$930$	−8.34518	−0.273649
$931$	−3.05396	−0.100089
$932$	5.74656	0.188235
$933$	0.900516	0.0294816
$934$	2.31913	0.0758842
$935$	−0.0308358	−0.00100844
$936$	−3.66526	−0.119803
$937$	27.6942	0.904731	0.452365	−	0.891833i	$-0.350580\pi$
$937$	27.6942	0.904731	0.452365	+	0.891833i	$0.350580\pi$
$938$	2.58009	0.0842428
$939$	−0.499653	−0.0163055
$940$	−38.1366	−1.24388
$941$	−13.7594	−0.448544	−0.224272	−	0.974527i	$-0.572000\pi$
$941$	−13.7594	−0.448544	−0.224272	+	0.974527i	$0.572000\pi$
$942$	0.989157	0.0322285
$943$	−0.341595	−0.0111239
$944$	−1.55869	−0.0507309
$945$	11.0519	0.359518
$946$	−0.0754128	−0.00245188
$947$	44.8866	1.45862	0.729309	−	0.684185i	$-0.239842\pi$
$947$	44.8866	1.45862	0.729309	+	0.684185i	$0.239842\pi$
$948$	−2.34406	−0.0761315
$949$	11.2789	0.366130
$950$	−10.8829	−0.353089
$951$	−5.94767	−0.192866
$952$	2.47732	0.0802905
$953$	−20.2021	−0.654411	−0.327205	−	0.944953i	$-0.606107\pi$
$953$	−20.2021	−0.654411	−0.327205	+	0.944953i	$0.606107\pi$
$954$	−2.56743	−0.0831237
$955$	85.7741	2.77558
$956$	−25.5311	−0.825736
$957$	−0.0145458	−0.000470200 0
$958$	−14.5184	−0.469067
$959$	−8.23315	−0.265862
$960$	−0.935868	−0.0302050
$961$	48.5137	1.56496
$962$	−1.37100	−0.0442027
$963$	27.2117	0.876886
$964$	−0.374843	−0.0120729
$965$	0.803215	0.0258564
$966$	−1.51301	−0.0486802
$967$	−27.1595	−0.873390	−0.436695	−	0.899610i	$-0.643851\pi$
$967$	−27.1595	−0.873390	−0.436695	+	0.899610i	$0.643851\pi$
$968$	11.0000	0.353552
$969$	−0.292854	−0.00940783
$970$	−4.16710	−0.133797
$971$	−60.5076	−1.94178	−0.970891	−	0.239523i	$-0.923009\pi$
$971$	−60.5076	−1.94178	−0.970891	+	0.239523i	$0.923009\pi$
$972$	6.18567	0.198405
$973$	3.97968	0.127583
$974$	−8.06203	−0.258324
$975$	−3.18080	−0.101867
$976$	13.1715	0.421609
$977$	51.7410	1.65534	0.827670	−	0.561215i	$-0.189666\pi$
$977$	51.7410	1.65534	0.827670	+	0.561215i	$0.189666\pi$
$978$	5.02418	0.160656
$979$	−0.0699788	−0.00223653
$980$	12.1711	0.388790
$981$	−37.1142	−1.18497
$982$	15.0839	0.481347
$983$	57.4184	1.83136	0.915682	−	0.401904i	$-0.131652\pi$
$983$	57.4184	1.83136	0.915682	+	0.401904i	$0.131652\pi$
$984$	0.0247314	0.000788409 0
$985$	−80.8795	−2.57703
$986$	12.4510	0.396520
$987$	4.46383	0.142085
$988$	−1.24463	−0.0395970
$989$	−39.4247	−1.25363
$990$	0.0728143	0.00231419
$991$	2.96323	0.0941302	0.0470651	−	0.998892i	$-0.485013\pi$
$991$	2.96323	0.0941302	0.0470651	+	0.998892i	$0.485013\pi$
$992$	8.91705	0.283117
$993$	4.49586	0.142672
$994$	−22.8525	−0.724837
$995$	−23.2033	−0.735593
$996$	2.76826	0.0877155
$997$	−10.2109	−0.323381	−0.161691	−	0.986842i	$-0.551695\pi$
$997$	−10.2109	−0.323381	−0.161691	+	0.986842i	$0.551695\pi$
$998$	−12.5738	−0.398017
$999$	1.53775	0.0486523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.g.1.20	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.g.1.20	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.234828 q^{3} +1.00000 q^{4} -3.98534 q^{5} -0.234828 q^{6} +1.98646 q^{7} -1.00000 q^{8} -2.94486 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.234828 q^{3} +1.00000 q^{4} -3.98534 q^{5} -0.234828 q^{6} +1.98646 q^{7} -1.00000 q^{8} -2.94486 q^{9} +3.98534 q^{10} -0.00620422 q^{11} +0.234828 q^{12} -1.24463 q^{13} -1.98646 q^{14} -0.935868 q^{15} +1.00000 q^{16} -1.24710 q^{17} +2.94486 q^{18} +1.00000 q^{19} -3.98534 q^{20} +0.466477 q^{21} +0.00620422 q^{22} +3.24348 q^{23} -0.234828 q^{24} +10.8829 q^{25} +1.24463 q^{26} -1.39602 q^{27} +1.98646 q^{28} +9.98393 q^{29} +0.935868 q^{30} -8.91705 q^{31} -1.00000 q^{32} -0.00145692 q^{33} +1.24710 q^{34} -7.91673 q^{35} -2.94486 q^{36} -1.10153 q^{37} -1.00000 q^{38} -0.292274 q^{39} +3.98534 q^{40} -0.105317 q^{41} -0.466477 q^{42} -12.1551 q^{43} -0.00620422 q^{44} +11.7362 q^{45} -3.24348 q^{46} +9.56923 q^{47} +0.234828 q^{48} -3.05396 q^{49} -10.8829 q^{50} -0.292854 q^{51} -1.24463 q^{52} -0.871837 q^{53} +1.39602 q^{54} +0.0247259 q^{55} -1.98646 q^{56} +0.234828 q^{57} -9.98393 q^{58} -1.55869 q^{59} -0.935868 q^{60} +13.1715 q^{61} +8.91705 q^{62} -5.84985 q^{63} +1.00000 q^{64} +4.96028 q^{65} +0.00145692 q^{66} -1.29883 q^{67} -1.24710 q^{68} +0.761659 q^{69} +7.91673 q^{70} +11.5041 q^{71} +2.94486 q^{72} -9.06206 q^{73} +1.10153 q^{74} +2.55561 q^{75} +1.00000 q^{76} -0.0123245 q^{77} +0.292274 q^{78} -9.98203 q^{79} -3.98534 q^{80} +8.50674 q^{81} +0.105317 q^{82} +11.7885 q^{83} +0.466477 q^{84} +4.97012 q^{85} +12.1551 q^{86} +2.34450 q^{87} +0.00620422 q^{88} +11.2792 q^{89} -11.7362 q^{90} -2.47242 q^{91} +3.24348 q^{92} -2.09397 q^{93} -9.56923 q^{94} -3.98534 q^{95} -0.234828 q^{96} -1.04561 q^{97} +3.05396 q^{98} +0.0182705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9	\( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 6 * q^3 + 34 * q^4 + q^5 + 6 * q^6 - 22 * q^7 - 34 * q^8 + 30 * q^9 - q^10 + 7 * q^11 - 6 * q^12 - 11 * q^13 + 22 * q^14 - 18 * q^15 + 34 * q^16 - 10 * q^17 - 30 * q^18 + 34 * q^19 + q^20 + 14 * q^21 - 7 * q^22 - 30 * q^23 + 6 * q^24 + 11 * q^25 + 11 * q^26 - 21 * q^27 - 22 * q^28 + 12 * q^29 + 18 * q^30 - 13 * q^31 - 34 * q^32 - 4 * q^33 + 10 * q^34 - 16 * q^35 + 30 * q^36 - 46 * q^37 - 34 * q^38 - 36 * q^39 - q^40 + 25 * q^41 - 14 * q^42 - 51 * q^43 + 7 * q^44 - 17 * q^45 + 30 * q^46 - 20 * q^47 - 6 * q^48 - 2 * q^49 - 11 * q^50 + 4 * q^51 - 11 * q^52 - 7 * q^53 + 21 * q^54 - 39 * q^55 + 22 * q^56 - 6 * q^57 - 12 * q^58 + 19 * q^59 - 18 * q^60 - 26 * q^61 + 13 * q^62 - 57 * q^63 + 34 * q^64 + 20 * q^65 + 4 * q^66 - 54 * q^67 - 10 * q^68 + 16 * q^70 + 9 * q^71 - 30 * q^72 - 57 * q^73 + 46 * q^74 + 26 * q^75 + 34 * q^76 + 2 * q^77 + 36 * q^78 - 7 * q^79 + q^80 + 22 * q^81 - 25 * q^82 - 15 * q^83 + 14 * q^84 - 30 * q^85 + 51 * q^86 - 37 * q^87 - 7 * q^88 + 78 * q^89 + 17 * q^90 - 31 * q^91 - 30 * q^92 - 43 * q^93 + 20 * q^94 + q^95 + 6 * q^96 - 38 * q^97 + 2 * q^98 + 2 * q^99

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