LMFDB - Embedded newform 6022.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.88590 q^{3} +1.00000 q^{4} -3.47728 q^{5} +2.88590 q^{6} -4.98917 q^{7} -1.00000 q^{8} +5.32845 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.88590 q^{3} +1.00000 q^{4} -3.47728 q^{5} +2.88590 q^{6} -4.98917 q^{7} -1.00000 q^{8} +5.32845 q^{9} +3.47728 q^{10} +1.43274 q^{11} -2.88590 q^{12} +4.14007 q^{13} +4.98917 q^{14} +10.0351 q^{15} +1.00000 q^{16} +4.42706 q^{17} -5.32845 q^{18} -1.97827 q^{19} -3.47728 q^{20} +14.3983 q^{21} -1.43274 q^{22} -0.320330 q^{23} +2.88590 q^{24} +7.09148 q^{25} -4.14007 q^{26} -6.71967 q^{27} -4.98917 q^{28} -6.26162 q^{29} -10.0351 q^{30} -1.23259 q^{31} -1.00000 q^{32} -4.13476 q^{33} -4.42706 q^{34} +17.3487 q^{35} +5.32845 q^{36} +4.52106 q^{37} +1.97827 q^{38} -11.9478 q^{39} +3.47728 q^{40} +2.83258 q^{41} -14.3983 q^{42} -0.342637 q^{43} +1.43274 q^{44} -18.5285 q^{45} +0.320330 q^{46} +10.9324 q^{47} -2.88590 q^{48} +17.8918 q^{49} -7.09148 q^{50} -12.7761 q^{51} +4.14007 q^{52} +11.9140 q^{53} +6.71967 q^{54} -4.98205 q^{55} +4.98917 q^{56} +5.70909 q^{57} +6.26162 q^{58} -11.5012 q^{59} +10.0351 q^{60} -4.00801 q^{61} +1.23259 q^{62} -26.5845 q^{63} +1.00000 q^{64} -14.3962 q^{65} +4.13476 q^{66} +4.76192 q^{67} +4.42706 q^{68} +0.924441 q^{69} -17.3487 q^{70} -7.19504 q^{71} -5.32845 q^{72} -0.0870054 q^{73} -4.52106 q^{74} -20.4653 q^{75} -1.97827 q^{76} -7.14819 q^{77} +11.9478 q^{78} -14.5627 q^{79} -3.47728 q^{80} +3.40699 q^{81} -2.83258 q^{82} +11.2361 q^{83} +14.3983 q^{84} -15.3941 q^{85} +0.342637 q^{86} +18.0704 q^{87} -1.43274 q^{88} -17.9940 q^{89} +18.5285 q^{90} -20.6555 q^{91} -0.320330 q^{92} +3.55713 q^{93} -10.9324 q^{94} +6.87899 q^{95} +2.88590 q^{96} -10.2862 q^{97} -17.8918 q^{98} +7.63429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * 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
$3$	−2.88590	−1.66618	−0.833089	−	0.553139i	$-0.813430\pi$
$3$	−2.88590	−1.66618	−0.833089	+	0.553139i	$0.813430\pi$
$4$	1.00000	0.500000
$5$	−3.47728	−1.55509	−0.777544	−	0.628829i	$-0.783535\pi$
$5$	−3.47728	−1.55509	−0.777544	+	0.628829i	$0.783535\pi$
$6$	2.88590	1.17817
$7$	−4.98917	−1.88573	−0.942864	−	0.333178i	$-0.891879\pi$
$7$	−4.98917	−1.88573	−0.942864	+	0.333178i	$0.891879\pi$
$8$	−1.00000	−0.353553
$9$	5.32845	1.77615
$10$	3.47728	1.09961
$11$	1.43274	0.431988	0.215994	−	0.976395i	$-0.430701\pi$
$11$	1.43274	0.431988	0.215994	+	0.976395i	$0.430701\pi$
$12$	−2.88590	−0.833089
$13$	4.14007	1.14825	0.574124	−	0.818768i	$-0.305343\pi$
$13$	4.14007	1.14825	0.574124	+	0.818768i	$0.305343\pi$
$14$	4.98917	1.33341
$15$	10.0351	2.59105
$16$	1.00000	0.250000
$17$	4.42706	1.07372	0.536860	−	0.843671i	$-0.319610\pi$
$17$	4.42706	1.07372	0.536860	+	0.843671i	$0.319610\pi$
$18$	−5.32845	−1.25593
$19$	−1.97827	−0.453845	−0.226923	−	0.973913i	$-0.572866\pi$
$19$	−1.97827	−0.453845	−0.226923	+	0.973913i	$0.572866\pi$
$20$	−3.47728	−0.777544
$21$	14.3983	3.14196
$22$	−1.43274	−0.305462
$23$	−0.320330	−0.0667934	−0.0333967	−	0.999442i	$-0.510632\pi$
$23$	−0.320330	−0.0667934	−0.0333967	+	0.999442i	$0.510632\pi$
$24$	2.88590	0.589083
$25$	7.09148	1.41830
$26$	−4.14007	−0.811934
$27$	−6.71967	−1.29320
$28$	−4.98917	−0.942864
$29$	−6.26162	−1.16275	−0.581377	−	0.813634i	$-0.697486\pi$
$29$	−6.26162	−1.16275	−0.581377	+	0.813634i	$0.697486\pi$
$30$	−10.0351	−1.83215
$31$	−1.23259	−0.221380	−0.110690	−	0.993855i	$-0.535306\pi$
$31$	−1.23259	−0.221380	−0.110690	+	0.993855i	$0.535306\pi$
$32$	−1.00000	−0.176777
$33$	−4.13476	−0.719769
$34$	−4.42706	−0.759235
$35$	17.3487	2.93247
$36$	5.32845	0.888074
$37$	4.52106	0.743258	0.371629	−	0.928381i	$-0.378799\pi$
$37$	4.52106	0.743258	0.371629	+	0.928381i	$0.378799\pi$
$38$	1.97827	0.320917
$39$	−11.9478	−1.91319
$40$	3.47728	0.549806
$41$	2.83258	0.442375	0.221188	−	0.975231i	$-0.429007\pi$
$41$	2.83258	0.442375	0.221188	+	0.975231i	$0.429007\pi$
$42$	−14.3983	−2.22170
$43$	−0.342637	−0.0522517	−0.0261259	−	0.999659i	$-0.508317\pi$
$43$	−0.342637	−0.0522517	−0.0261259	+	0.999659i	$0.508317\pi$
$44$	1.43274	0.215994
$45$	−18.5285	−2.76207
$46$	0.320330	0.0472301
$47$	10.9324	1.59466	0.797328	−	0.603546i	$-0.206246\pi$
$47$	10.9324	1.59466	0.797328	+	0.603546i	$0.206246\pi$
$48$	−2.88590	−0.416544
$49$	17.8918	2.55597
$50$	−7.09148	−1.00289
$51$	−12.7761	−1.78901
$52$	4.14007	0.574124
$53$	11.9140	1.63651	0.818257	−	0.574853i	$-0.194941\pi$
$53$	11.9140	1.63651	0.818257	+	0.574853i	$0.194941\pi$
$54$	6.71967	0.914431
$55$	−4.98205	−0.671779
$56$	4.98917	0.666705
$57$	5.70909	0.756187
$58$	6.26162	0.822191
$59$	−11.5012	−1.49733	−0.748666	−	0.662948i	$-0.769305\pi$
$59$	−11.5012	−1.49733	−0.748666	+	0.662948i	$0.769305\pi$
$60$	10.0351	1.29553
$61$	−4.00801	−0.513173	−0.256587	−	0.966521i	$-0.582598\pi$
$61$	−4.00801	−0.513173	−0.256587	+	0.966521i	$0.582598\pi$
$62$	1.23259	0.156539
$63$	−26.5845	−3.34933
$64$	1.00000	0.125000
$65$	−14.3962	−1.78563
$66$	4.13476	0.508953
$67$	4.76192	0.581761	0.290880	−	0.956759i	$-0.406052\pi$
$67$	4.76192	0.581761	0.290880	+	0.956759i	$0.406052\pi$
$68$	4.42706	0.536860
$69$	0.924441	0.111290
$70$	−17.3487	−2.07357
$71$	−7.19504	−0.853894	−0.426947	−	0.904277i	$-0.640411\pi$
$71$	−7.19504	−0.853894	−0.426947	+	0.904277i	$0.640411\pi$
$72$	−5.32845	−0.627963
$73$	−0.0870054	−0.0101832	−0.00509161	−	0.999987i	$-0.501621\pi$
$73$	−0.0870054	−0.0101832	−0.00509161	+	0.999987i	$0.501621\pi$
$74$	−4.52106	−0.525563
$75$	−20.4653	−2.36313
$76$	−1.97827	−0.226923
$77$	−7.14819	−0.814612
$78$	11.9478	1.35283
$79$	−14.5627	−1.63844	−0.819219	−	0.573481i	$-0.805592\pi$
$79$	−14.5627	−1.63844	−0.819219	+	0.573481i	$0.805592\pi$
$80$	−3.47728	−0.388772
$81$	3.40699	0.378555
$82$	−2.83258	−0.312807
$83$	11.2361	1.23333	0.616663	−	0.787227i	$-0.288484\pi$
$83$	11.2361	1.23333	0.616663	+	0.787227i	$0.288484\pi$
$84$	14.3983	1.57098
$85$	−15.3941	−1.66973
$86$	0.342637	0.0369475
$87$	18.0704	1.93735
$88$	−1.43274	−0.152731
$89$	−17.9940	−1.90736	−0.953681	−	0.300820i	$-0.902740\pi$
$89$	−17.9940	−1.90736	−0.953681	+	0.300820i	$0.902740\pi$
$90$	18.5285	1.95308
$91$	−20.6555	−2.16528
$92$	−0.320330	−0.0333967
$93$	3.55713	0.368858
$94$	−10.9324	−1.12759
$95$	6.87899	0.705769
$96$	2.88590	0.294541
$97$	−10.2862	−1.04440	−0.522202	−	0.852822i	$-0.674889\pi$
$97$	−10.2862	−1.04440	−0.522202	+	0.852822i	$0.674889\pi$
$98$	−17.8918	−1.80734
$99$	7.63429	0.767275
$100$	7.09148	0.709148
$101$	1.32692	0.132033	0.0660166	−	0.997819i	$-0.478971\pi$
$101$	1.32692	0.132033	0.0660166	+	0.997819i	$0.478971\pi$
$102$	12.7761	1.26502
$103$	−1.34209	−0.132240	−0.0661198	−	0.997812i	$-0.521062\pi$
$103$	−1.34209	−0.132240	−0.0661198	+	0.997812i	$0.521062\pi$
$104$	−4.14007	−0.405967
$105$	−50.0668	−4.88602
$106$	−11.9140	−1.15719
$107$	−16.7808	−1.62226	−0.811131	−	0.584865i	$-0.801147\pi$
$107$	−16.7808	−1.62226	−0.811131	+	0.584865i	$0.801147\pi$
$108$	−6.71967	−0.646601
$109$	6.06486	0.580908	0.290454	−	0.956889i	$-0.406194\pi$
$109$	6.06486	0.580908	0.290454	+	0.956889i	$0.406194\pi$
$110$	4.98205	0.475020
$111$	−13.0474	−1.23840
$112$	−4.98917	−0.471432
$113$	−0.185978	−0.0174954	−0.00874769	−	0.999962i	$-0.502785\pi$
$113$	−0.185978	−0.0174954	−0.00874769	+	0.999962i	$0.502785\pi$
$114$	−5.70909	−0.534705
$115$	1.11388	0.103870
$116$	−6.26162	−0.581377
$117$	22.0601	2.03946
$118$	11.5012	1.05877
$119$	−22.0874	−2.02475
$120$	−10.0351	−0.916075
$121$	−8.94725	−0.813386
$122$	4.00801	0.362868
$123$	−8.17457	−0.737076
$124$	−1.23259	−0.110690
$125$	−7.27268	−0.650488
$126$	26.5845	2.36834
$127$	−21.5175	−1.90937	−0.954684	−	0.297621i	$-0.903807\pi$
$127$	−21.5175	−1.90937	−0.954684	+	0.297621i	$0.903807\pi$
$128$	−1.00000	−0.0883883
$129$	0.988819	0.0870606
$130$	14.3962	1.26263
$131$	15.0441	1.31441	0.657206	−	0.753711i	$-0.271738\pi$
$131$	15.0441	1.31441	0.657206	+	0.753711i	$0.271738\pi$
$132$	−4.13476	−0.359884
$133$	9.86990	0.855829
$134$	−4.76192	−0.411367
$135$	23.3662	2.01104
$136$	−4.42706	−0.379618
$137$	10.4250	0.890664	0.445332	−	0.895366i	$-0.353086\pi$
$137$	10.4250	0.890664	0.445332	+	0.895366i	$0.353086\pi$
$138$	−0.924441	−0.0786937
$139$	6.52484	0.553430	0.276715	−	0.960952i	$-0.410754\pi$
$139$	6.52484	0.553430	0.276715	+	0.960952i	$0.410754\pi$
$140$	17.3487	1.46624
$141$	−31.5499	−2.65698
$142$	7.19504	0.603794
$143$	5.93165	0.496030
$144$	5.32845	0.444037
$145$	21.7734	1.80818
$146$	0.0870054	0.00720062
$147$	−51.6340	−4.25870
$148$	4.52106	0.371629
$149$	−0.662956	−0.0543115	−0.0271557	−	0.999631i	$-0.508645\pi$
$149$	−0.662956	−0.0543115	−0.0271557	+	0.999631i	$0.508645\pi$
$150$	20.4653	1.67099
$151$	3.58173	0.291477	0.145739	−	0.989323i	$-0.453444\pi$
$151$	3.58173	0.291477	0.145739	+	0.989323i	$0.453444\pi$
$152$	1.97827	0.160459
$153$	23.5894	1.90709
$154$	7.14819	0.576018
$155$	4.28606	0.344264
$156$	−11.9478	−0.956593
$157$	17.5009	1.39673	0.698363	−	0.715744i	$-0.253912\pi$
$157$	17.5009	1.39673	0.698363	+	0.715744i	$0.253912\pi$
$158$	14.5627	1.15855
$159$	−34.3827	−2.72672
$160$	3.47728	0.274903
$161$	1.59818	0.125954
$162$	−3.40699	−0.267679
$163$	−17.7837	−1.39292	−0.696462	−	0.717593i	$-0.745244\pi$
$163$	−17.7837	−1.39292	−0.696462	+	0.717593i	$0.745244\pi$
$164$	2.83258	0.221188
$165$	14.3777	1.11930
$166$	−11.2361	−0.872093
$167$	5.39088	0.417159	0.208579	−	0.978005i	$-0.433116\pi$
$167$	5.39088	0.417159	0.208579	+	0.978005i	$0.433116\pi$
$168$	−14.3983	−1.11085
$169$	4.14018	0.318475
$170$	15.3941	1.18068
$171$	−10.5411	−0.806097
$172$	−0.342637	−0.0261259
$173$	3.71380	0.282355	0.141177	−	0.989984i	$-0.454911\pi$
$173$	3.71380	0.282355	0.141177	+	0.989984i	$0.454911\pi$
$174$	−18.0704	−1.36992
$175$	−35.3806	−2.67452
$176$	1.43274	0.107997
$177$	33.1914	2.49482
$178$	17.9940	1.34871
$179$	−6.54452	−0.489160	−0.244580	−	0.969629i	$-0.578650\pi$
$179$	−6.54452	−0.489160	−0.244580	+	0.969629i	$0.578650\pi$
$180$	−18.5285	−1.38103
$181$	15.1923	1.12923	0.564617	−	0.825353i	$-0.309024\pi$
$181$	15.1923	1.12923	0.564617	+	0.825353i	$0.309024\pi$
$182$	20.6555	1.53109
$183$	11.5667	0.855038
$184$	0.320330	0.0236150
$185$	−15.7210	−1.15583
$186$	−3.55713	−0.260822
$187$	6.34284	0.463835
$188$	10.9324	0.797328
$189$	33.5256	2.43863
$190$	−6.87899	−0.499054
$191$	15.4803	1.12012	0.560058	−	0.828454i	$-0.310779\pi$
$191$	15.4803	1.12012	0.560058	+	0.828454i	$0.310779\pi$
$192$	−2.88590	−0.208272
$193$	−12.7138	−0.915157	−0.457579	−	0.889169i	$-0.651283\pi$
$193$	−12.7138	−0.915157	−0.457579	+	0.889169i	$0.651283\pi$
$194$	10.2862	0.738505
$195$	41.5460	2.97517
$196$	17.8918	1.27798
$197$	−5.97128	−0.425436	−0.212718	−	0.977114i	$-0.568232\pi$
$197$	−5.97128	−0.425436	−0.212718	+	0.977114i	$0.568232\pi$
$198$	−7.63429	−0.542545
$199$	13.8541	0.982093	0.491047	−	0.871133i	$-0.336614\pi$
$199$	13.8541	0.982093	0.491047	+	0.871133i	$0.336614\pi$
$200$	−7.09148	−0.501444
$201$	−13.7424	−0.969316
$202$	−1.32692	−0.0933616
$203$	31.2403	2.19264
$204$	−12.7761	−0.894505
$205$	−9.84969	−0.687932
$206$	1.34209	0.0935076
$207$	−1.70686	−0.118635
$208$	4.14007	0.287062
$209$	−2.83435	−0.196056
$210$	50.0668	3.45494
$211$	16.1078	1.10891	0.554454	−	0.832214i	$-0.312927\pi$
$211$	16.1078	1.10891	0.554454	+	0.832214i	$0.312927\pi$
$212$	11.9140	0.818257
$213$	20.7642	1.42274
$214$	16.7808	1.14711
$215$	1.19145	0.0812560
$216$	6.71967	0.457216
$217$	6.14959	0.417462
$218$	−6.06486	−0.410764
$219$	0.251089	0.0169670
$220$	−4.98205	−0.335890
$221$	18.3284	1.23290
$222$	13.0474	0.875681
$223$	1.07495	0.0719838	0.0359919	−	0.999352i	$-0.488541\pi$
$223$	1.07495	0.0719838	0.0359919	+	0.999352i	$0.488541\pi$
$224$	4.98917	0.333353
$225$	37.7866	2.51911
$226$	0.185978	0.0123711
$227$	−11.6088	−0.770502	−0.385251	−	0.922812i	$-0.625885\pi$
$227$	−11.6088	−0.770502	−0.385251	+	0.922812i	$0.625885\pi$
$228$	5.70909	0.378093
$229$	−1.95136	−0.128950	−0.0644748	−	0.997919i	$-0.520537\pi$
$229$	−1.95136	−0.128950	−0.0644748	+	0.997919i	$0.520537\pi$
$230$	−1.11388	−0.0734469
$231$	20.6290	1.35729
$232$	6.26162	0.411096
$233$	2.84696	0.186510	0.0932551	−	0.995642i	$-0.470273\pi$
$233$	2.84696	0.186510	0.0932551	+	0.995642i	$0.470273\pi$
$234$	−22.0601	−1.44212
$235$	−38.0151	−2.47983
$236$	−11.5012	−0.748666
$237$	42.0267	2.72993
$238$	22.0874	1.43171
$239$	−11.1355	−0.720294	−0.360147	−	0.932896i	$-0.617274\pi$
$239$	−11.1355	−0.720294	−0.360147	+	0.932896i	$0.617274\pi$
$240$	10.0351	0.647763
$241$	−28.5967	−1.84208	−0.921038	−	0.389473i	$-0.872657\pi$
$241$	−28.5967	−1.84208	−0.921038	+	0.389473i	$0.872657\pi$
$242$	8.94725	0.575151
$243$	10.3268	0.662462
$244$	−4.00801	−0.256587
$245$	−62.2148	−3.97476
$246$	8.17457	0.521191
$247$	−8.19016	−0.521127
$248$	1.23259	0.0782695
$249$	−32.4264	−2.05494
$250$	7.27268	0.459964
$251$	−17.7477	−1.12022	−0.560112	−	0.828417i	$-0.689242\pi$
$251$	−17.7477	−1.12022	−0.560112	+	0.828417i	$0.689242\pi$
$252$	−26.5845	−1.67467
$253$	−0.458950	−0.0288539
$254$	21.5175	1.35013
$255$	44.4260	2.78207
$256$	1.00000	0.0625000
$257$	−12.2708	−0.765430	−0.382715	−	0.923866i	$-0.625011\pi$
$257$	−12.2708	−0.765430	−0.382715	+	0.923866i	$0.625011\pi$
$258$	−0.988819	−0.0615612
$259$	−22.5563	−1.40158
$260$	−14.3962	−0.892814
$261$	−33.3647	−2.06522
$262$	−15.0441	−0.929430
$263$	23.2186	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$263$	23.2186	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$264$	4.13476	0.254477
$265$	−41.4283	−2.54492
$266$	−9.86990	−0.605162
$267$	51.9290	3.17800
$268$	4.76192	0.290880
$269$	−4.03789	−0.246194	−0.123097	−	0.992395i	$-0.539283\pi$
$269$	−4.03789	−0.246194	−0.123097	+	0.992395i	$0.539283\pi$
$270$	−23.3662	−1.42202
$271$	5.43254	0.330003	0.165002	−	0.986293i	$-0.447237\pi$
$271$	5.43254	0.330003	0.165002	+	0.986293i	$0.447237\pi$
$272$	4.42706	0.268430
$273$	59.6098	3.60775
$274$	−10.4250	−0.629794
$275$	10.1603	0.612687
$276$	0.924441	0.0556448
$277$	−1.42900	−0.0858604	−0.0429302	−	0.999078i	$-0.513669\pi$
$277$	−1.42900	−0.0858604	−0.0429302	+	0.999078i	$0.513669\pi$
$278$	−6.52484	−0.391334
$279$	−6.56778	−0.393203
$280$	−17.3487	−1.03679
$281$	25.9790	1.54978	0.774890	−	0.632096i	$-0.217805\pi$
$281$	25.9790	1.54978	0.774890	+	0.632096i	$0.217805\pi$
$282$	31.5499	1.87877
$283$	−32.0987	−1.90807	−0.954034	−	0.299698i	$-0.903114\pi$
$283$	−32.0987	−1.90807	−0.954034	+	0.299698i	$0.903114\pi$
$284$	−7.19504	−0.426947
$285$	−19.8521	−1.17594
$286$	−5.93165	−0.350746
$287$	−14.1322	−0.834200
$288$	−5.32845	−0.313982
$289$	2.59890	0.152876
$290$	−21.7734	−1.27858
$291$	29.6849	1.74016
$292$	−0.0870054	−0.00509161
$293$	9.89567	0.578111	0.289055	−	0.957312i	$-0.406659\pi$
$293$	9.89567	0.578111	0.289055	+	0.957312i	$0.406659\pi$
$294$	51.6340	3.01136
$295$	39.9930	2.32848
$296$	−4.52106	−0.262781
$297$	−9.62755	−0.558647
$298$	0.662956	0.0384040
$299$	−1.32619	−0.0766954
$300$	−20.4653	−1.18157
$301$	1.70947	0.0985325
$302$	−3.58173	−0.206106
$303$	−3.82936	−0.219991
$304$	−1.97827	−0.113461
$305$	13.9370	0.798029
$306$	−23.5894	−1.34851
$307$	−23.3382	−1.33198	−0.665991	−	0.745960i	$-0.731991\pi$
$307$	−23.3382	−1.33198	−0.665991	+	0.745960i	$0.731991\pi$
$308$	−7.14819	−0.407306
$309$	3.87313	0.220335
$310$	−4.28606	−0.243432
$311$	10.9755	0.622366	0.311183	−	0.950350i	$-0.399275\pi$
$311$	10.9755	0.622366	0.311183	+	0.950350i	$0.399275\pi$
$312$	11.9478	0.676414
$313$	27.8040	1.57157	0.785787	−	0.618497i	$-0.212258\pi$
$313$	27.8040	1.57157	0.785787	+	0.618497i	$0.212258\pi$
$314$	−17.5009	−0.987634
$315$	92.4418	5.20850
$316$	−14.5627	−0.819219
$317$	21.7608	1.22221	0.611105	−	0.791550i	$-0.290725\pi$
$317$	21.7608	1.22221	0.611105	+	0.791550i	$0.290725\pi$
$318$	34.3827	1.92808
$319$	−8.97129	−0.502296
$320$	−3.47728	−0.194386
$321$	48.4278	2.70298
$322$	−1.59818	−0.0890630
$323$	−8.75791	−0.487303
$324$	3.40699	0.189277
$325$	29.3592	1.62856
$326$	17.7837	0.984946
$327$	−17.5026	−0.967896
$328$	−2.83258	−0.156403
$329$	−54.5436	−3.00709
$330$	−14.3777	−0.791467
$331$	−12.7252	−0.699438	−0.349719	−	0.936855i	$-0.613723\pi$
$331$	−12.7252	−0.699438	−0.349719	+	0.936855i	$0.613723\pi$
$332$	11.2361	0.616663
$333$	24.0902	1.32014
$334$	−5.39088	−0.294976
$335$	−16.5585	−0.904688
$336$	14.3983	0.785489
$337$	−3.03003	−0.165056	−0.0825282	−	0.996589i	$-0.526299\pi$
$337$	−3.03003	−0.165056	−0.0825282	+	0.996589i	$0.526299\pi$
$338$	−4.14018	−0.225196
$339$	0.536716	0.0291504
$340$	−15.3941	−0.834865
$341$	−1.76598	−0.0956333
$342$	10.5411	0.569996
$343$	−54.3409	−2.93413
$344$	0.342637	0.0184738
$345$	−3.21454	−0.173065
$346$	−3.71380	−0.199655
$347$	34.3637	1.84474	0.922370	−	0.386309i	$-0.126250\pi$
$347$	34.3637	1.84474	0.922370	+	0.386309i	$0.126250\pi$
$348$	18.0704	0.968677
$349$	9.06231	0.485094	0.242547	−	0.970140i	$-0.422017\pi$
$349$	9.06231	0.485094	0.242547	+	0.970140i	$0.422017\pi$
$350$	35.3806	1.89117
$351$	−27.8199	−1.48492
$352$	−1.43274	−0.0763654
$353$	3.28223	0.174695	0.0873476	−	0.996178i	$-0.472161\pi$
$353$	3.28223	0.174695	0.0873476	+	0.996178i	$0.472161\pi$
$354$	−33.1914	−1.76410
$355$	25.0192	1.32788
$356$	−17.9940	−0.953681
$357$	63.7420	3.37359
$358$	6.54452	0.345889
$359$	26.0884	1.37690	0.688448	−	0.725286i	$-0.258293\pi$
$359$	26.0884	1.37690	0.688448	+	0.725286i	$0.258293\pi$
$360$	18.5285	0.976538
$361$	−15.0865	−0.794024
$362$	−15.1923	−0.798490
$363$	25.8209	1.35525
$364$	−20.6555	−1.08264
$365$	0.302542	0.0158358
$366$	−11.5667	−0.604603
$367$	32.5982	1.70161	0.850806	−	0.525480i	$-0.176114\pi$
$367$	32.5982	1.70161	0.850806	+	0.525480i	$0.176114\pi$
$368$	−0.320330	−0.0166983
$369$	15.0933	0.785724
$370$	15.7210	0.817296
$371$	−59.4409	−3.08602
$372$	3.55713	0.184429
$373$	−6.54154	−0.338708	−0.169354	−	0.985555i	$-0.554168\pi$
$373$	−6.54154	−0.338708	−0.169354	+	0.985555i	$0.554168\pi$
$374$	−6.34284	−0.327981
$375$	20.9882	1.08383
$376$	−10.9324	−0.563796
$377$	−25.9236	−1.33513
$378$	−33.5256	−1.72437
$379$	−12.3051	−0.632069	−0.316034	−	0.948748i	$-0.602351\pi$
$379$	−12.3051	−0.632069	−0.316034	+	0.948748i	$0.602351\pi$
$380$	6.87899	0.352885
$381$	62.0974	3.18135
$382$	−15.4803	−0.792041
$383$	−14.4291	−0.737291	−0.368646	−	0.929570i	$-0.620178\pi$
$383$	−14.4291	−0.737291	−0.368646	+	0.929570i	$0.620178\pi$
$384$	2.88590	0.147271
$385$	24.8563	1.26679
$386$	12.7138	0.647114
$387$	−1.82572	−0.0928068
$388$	−10.2862	−0.522202
$389$	−0.596064	−0.0302216	−0.0151108	−	0.999886i	$-0.504810\pi$
$389$	−0.596064	−0.0302216	−0.0151108	+	0.999886i	$0.504810\pi$
$390$	−41.5460	−2.10376
$391$	−1.41812	−0.0717175
$392$	−17.8918	−0.903672
$393$	−43.4160	−2.19005
$394$	5.97128	0.300829
$395$	50.6388	2.54791
$396$	7.63429	0.383637
$397$	29.9992	1.50562	0.752809	−	0.658239i	$-0.228698\pi$
$397$	29.9992	1.50562	0.752809	+	0.658239i	$0.228698\pi$
$398$	−13.8541	−0.694445
$399$	−28.4836	−1.42596
$400$	7.09148	0.354574
$401$	−21.3253	−1.06493	−0.532467	−	0.846451i	$-0.678735\pi$
$401$	−21.3253	−1.06493	−0.532467	+	0.846451i	$0.678735\pi$
$402$	13.7424	0.685410
$403$	−5.10300	−0.254199
$404$	1.32692	0.0660166
$405$	−11.8471	−0.588685
$406$	−31.2403	−1.55043
$407$	6.47752	0.321079
$408$	12.7761	0.632510
$409$	−1.02973	−0.0509171	−0.0254586	−	0.999676i	$-0.508105\pi$
$409$	−1.02973	−0.0509171	−0.0254586	+	0.999676i	$0.508105\pi$
$410$	9.84969	0.486442
$411$	−30.0854	−1.48400
$412$	−1.34209	−0.0661198
$413$	57.3815	2.82356
$414$	1.70686	0.0838876
$415$	−39.0712	−1.91793
$416$	−4.14007	−0.202984
$417$	−18.8301	−0.922113
$418$	2.83435	0.138632
$419$	−32.1400	−1.57014	−0.785070	−	0.619407i	$-0.787373\pi$
$419$	−32.1400	−1.57014	−0.785070	+	0.619407i	$0.787373\pi$
$420$	−50.0668	−2.44301
$421$	2.81336	0.137115	0.0685573	−	0.997647i	$-0.478160\pi$
$421$	2.81336	0.137115	0.0685573	+	0.997647i	$0.478160\pi$
$422$	−16.1078	−0.784116
$423$	58.2528	2.83235
$424$	−11.9140	−0.578595
$425$	31.3945	1.52285
$426$	−20.7642	−1.00603
$427$	19.9966	0.967705
$428$	−16.7808	−0.811131
$429$	−17.1182	−0.826474
$430$	−1.19145	−0.0574566
$431$	3.08396	0.148549	0.0742746	−	0.997238i	$-0.476336\pi$
$431$	3.08396	0.148549	0.0742746	+	0.997238i	$0.476336\pi$
$432$	−6.71967	−0.323300
$433$	−37.6843	−1.81099	−0.905496	−	0.424356i	$-0.860501\pi$
$433$	−37.6843	−1.81099	−0.905496	+	0.424356i	$0.860501\pi$
$434$	−6.14959	−0.295190
$435$	−62.8360	−3.01276
$436$	6.06486	0.290454
$437$	0.633698	0.0303139
$438$	−0.251089	−0.0119975
$439$	36.5805	1.74589	0.872945	−	0.487819i	$-0.162207\pi$
$439$	36.5805	1.74589	0.872945	+	0.487819i	$0.162207\pi$
$440$	4.98205	0.237510
$441$	95.3354	4.53978
$442$	−18.3284	−0.871791
$443$	19.5991	0.931180	0.465590	−	0.885000i	$-0.345842\pi$
$443$	19.5991	0.931180	0.465590	+	0.885000i	$0.345842\pi$
$444$	−13.0474	−0.619200
$445$	62.5703	2.96611
$446$	−1.07495	−0.0509003
$447$	1.91323	0.0904925
$448$	−4.98917	−0.235716
$449$	−28.7956	−1.35895	−0.679475	−	0.733698i	$-0.737793\pi$
$449$	−28.7956	−1.35895	−0.679475	+	0.733698i	$0.737793\pi$
$450$	−37.7866	−1.78128
$451$	4.05836	0.191101
$452$	−0.185978	−0.00874769
$453$	−10.3365	−0.485653
$454$	11.6088	0.544828
$455$	71.8250	3.36721
$456$	−5.70909	−0.267352
$457$	28.9992	1.35653	0.678264	−	0.734819i	$-0.262733\pi$
$457$	28.9992	1.35653	0.678264	+	0.734819i	$0.262733\pi$
$458$	1.95136	0.0911811
$459$	−29.7484	−1.38854
$460$	1.11388	0.0519348
$461$	23.8213	1.10947	0.554735	−	0.832027i	$-0.312820\pi$
$461$	23.8213	1.10947	0.554735	+	0.832027i	$0.312820\pi$
$462$	−20.6290	−0.959748
$463$	−0.274049	−0.0127361	−0.00636806	−	0.999980i	$-0.502027\pi$
$463$	−0.274049	−0.0127361	−0.00636806	+	0.999980i	$0.502027\pi$
$464$	−6.26162	−0.290689
$465$	−12.3692	−0.573606
$466$	−2.84696	−0.131883
$467$	8.64001	0.399812	0.199906	−	0.979815i	$-0.435936\pi$
$467$	8.64001	0.399812	0.199906	+	0.979815i	$0.435936\pi$
$468$	22.0601	1.01973
$469$	−23.7580	−1.09704
$470$	38.0151	1.75350
$471$	−50.5060	−2.32719
$472$	11.5012	0.529386
$473$	−0.490911	−0.0225721
$474$	−42.0267	−1.93035
$475$	−14.0288	−0.643687
$476$	−22.0874	−1.01237
$477$	63.4831	2.90669
$478$	11.1355	0.509325
$479$	−4.66706	−0.213243	−0.106622	−	0.994300i	$-0.534003\pi$
$479$	−4.66706	−0.213243	−0.106622	+	0.994300i	$0.534003\pi$
$480$	−10.0351	−0.458038
$481$	18.7175	0.853445
$482$	28.5967	1.30254
$483$	−4.61219	−0.209862
$484$	−8.94725	−0.406693
$485$	35.7680	1.62414
$486$	−10.3268	−0.468431
$487$	−38.5257	−1.74577	−0.872883	−	0.487929i	$-0.837752\pi$
$487$	−38.5257	−1.74577	−0.872883	+	0.487929i	$0.837752\pi$
$488$	4.00801	0.181434
$489$	51.3220	2.32086
$490$	62.2148	2.81058
$491$	4.81399	0.217252	0.108626	−	0.994083i	$-0.465355\pi$
$491$	4.81399	0.217252	0.108626	+	0.994083i	$0.465355\pi$
$492$	−8.17457	−0.368538
$493$	−27.7206	−1.24847
$494$	8.19016	0.368493
$495$	−26.5466	−1.19318
$496$	−1.23259	−0.0553449
$497$	35.8972	1.61021
$498$	32.4264	1.45306
$499$	3.27009	0.146389	0.0731947	−	0.997318i	$-0.476681\pi$
$499$	3.27009	0.146389	0.0731947	+	0.997318i	$0.476681\pi$
$500$	−7.27268	−0.325244
$501$	−15.5576	−0.695060
$502$	17.7477	0.792118
$503$	13.0445	0.581627	0.290813	−	0.956780i	$-0.406074\pi$
$503$	13.0445	0.581627	0.290813	+	0.956780i	$0.406074\pi$
$504$	26.5845	1.18417
$505$	−4.61406	−0.205323
$506$	0.458950	0.0204028
$507$	−11.9482	−0.530636
$508$	−21.5175	−0.954684
$509$	4.66993	0.206991	0.103496	−	0.994630i	$-0.466997\pi$
$509$	4.66993	0.206991	0.103496	+	0.994630i	$0.466997\pi$
$510$	−44.4260	−1.96722
$511$	0.434084	0.0192028
$512$	−1.00000	−0.0441942
$513$	13.2933	0.586913
$514$	12.2708	0.541241
$515$	4.66681	0.205644
$516$	0.988819	0.0435303
$517$	15.6633	0.688872
$518$	22.5563	0.991068
$519$	−10.7177	−0.470453
$520$	14.3962	0.631314
$521$	−3.90356	−0.171018	−0.0855090	−	0.996337i	$-0.527252\pi$
$521$	−3.90356	−0.171018	−0.0855090	+	0.996337i	$0.527252\pi$
$522$	33.3647	1.46033
$523$	−4.20862	−0.184030	−0.0920151	−	0.995758i	$-0.529331\pi$
$523$	−4.20862	−0.184030	−0.0920151	+	0.995758i	$0.529331\pi$
$524$	15.0441	0.657206
$525$	102.105	4.45623
$526$	−23.2186	−1.01238
$527$	−5.45675	−0.237700
$528$	−4.13476	−0.179942
$529$	−22.8974	−0.995539
$530$	41.4283	1.79953
$531$	−61.2836	−2.65948
$532$	9.86990	0.427914
$533$	11.7271	0.507957
$534$	−51.9290	−2.24719
$535$	58.3516	2.52276
$536$	−4.76192	−0.205683
$537$	18.8869	0.815028
$538$	4.03789	0.174086
$539$	25.6343	1.10415
$540$	23.3662	1.00552
$541$	−22.8957	−0.984363	−0.492182	−	0.870493i	$-0.663800\pi$
$541$	−22.8957	−0.984363	−0.492182	+	0.870493i	$0.663800\pi$
$542$	−5.43254	−0.233347
$543$	−43.8435	−1.88151
$544$	−4.42706	−0.189809
$545$	−21.0892	−0.903363
$546$	−59.6098	−2.55106
$547$	−15.6744	−0.670188	−0.335094	−	0.942185i	$-0.608768\pi$
$547$	−15.6744	−0.670188	−0.335094	+	0.942185i	$0.608768\pi$
$548$	10.4250	0.445332
$549$	−21.3565	−0.911472
$550$	−10.1603	−0.433235
$551$	12.3872	0.527710
$552$	−0.924441	−0.0393468
$553$	72.6560	3.08965
$554$	1.42900	0.0607125
$555$	45.3693	1.92582
$556$	6.52484	0.276715
$557$	−34.2556	−1.45146	−0.725728	−	0.687982i	$-0.758497\pi$
$557$	−34.2556	−1.45146	−0.725728	+	0.687982i	$0.758497\pi$
$558$	6.56778	0.278036
$559$	−1.41854	−0.0599979
$560$	17.3487	0.733118
$561$	−18.3048	−0.772831
$562$	−25.9790	−1.09586
$563$	−12.2543	−0.516457	−0.258229	−	0.966084i	$-0.583139\pi$
$563$	−12.2543	−0.516457	−0.258229	+	0.966084i	$0.583139\pi$
$564$	−31.5499	−1.32849
$565$	0.646699	0.0272068
$566$	32.0987	1.34921
$567$	−16.9980	−0.713851
$568$	7.19504	0.301897
$569$	−24.5568	−1.02948	−0.514738	−	0.857348i	$-0.672111\pi$
$569$	−24.5568	−1.02948	−0.514738	+	0.857348i	$0.672111\pi$
$570$	19.8521	0.831513
$571$	37.4768	1.56835	0.784177	−	0.620538i	$-0.213086\pi$
$571$	37.4768	1.56835	0.784177	+	0.620538i	$0.213086\pi$
$572$	5.93165	0.248015
$573$	−44.6747	−1.86631
$574$	14.1322	0.589868
$575$	−2.27161	−0.0947328
$576$	5.32845	0.222019
$577$	1.16820	0.0486326	0.0243163	−	0.999704i	$-0.492259\pi$
$577$	1.16820	0.0486326	0.0243163	+	0.999704i	$0.492259\pi$
$578$	−2.59890	−0.108100
$579$	36.6907	1.52482
$580$	21.7734	0.904092
$581$	−56.0590	−2.32572
$582$	−29.6849	−1.23048
$583$	17.0697	0.706954
$584$	0.0870054	0.00360031
$585$	−76.7093	−3.17154
$586$	−9.89567	−0.408786
$587$	19.2800	0.795772	0.397886	−	0.917435i	$-0.369744\pi$
$587$	19.2800	0.795772	0.397886	+	0.917435i	$0.369744\pi$
$588$	−51.6340	−2.12935
$589$	2.43839	0.100472
$590$	−39.9930	−1.64648
$591$	17.2325	0.708852
$592$	4.52106	0.185815
$593$	27.2019	1.11705	0.558525	−	0.829488i	$-0.311367\pi$
$593$	27.2019	1.11705	0.558525	+	0.829488i	$0.311367\pi$
$594$	9.62755	0.395023
$595$	76.8040	3.14866
$596$	−0.662956	−0.0271557
$597$	−39.9817	−1.63634
$598$	1.32619	0.0542319
$599$	−18.2948	−0.747507	−0.373753	−	0.927528i	$-0.621929\pi$
$599$	−18.2948	−0.747507	−0.373753	+	0.927528i	$0.621929\pi$
$600$	20.4653	0.835494
$601$	6.25745	0.255247	0.127623	−	0.991823i	$-0.459265\pi$
$601$	6.25745	0.255247	0.127623	+	0.991823i	$0.459265\pi$
$602$	−1.70947	−0.0696730
$603$	25.3736	1.03329
$604$	3.58173	0.145739
$605$	31.1121	1.26489
$606$	3.82936	0.155557
$607$	−28.1381	−1.14209	−0.571045	−	0.820919i	$-0.693462\pi$
$607$	−28.1381	−1.14209	−0.571045	+	0.820919i	$0.693462\pi$
$608$	1.97827	0.0802293
$609$	−90.1565	−3.65332
$610$	−13.9370	−0.564292
$611$	45.2609	1.83106
$612$	23.5894	0.953544
$613$	−43.9463	−1.77497	−0.887487	−	0.460833i	$-0.847551\pi$
$613$	−43.9463	−1.77497	−0.887487	+	0.460833i	$0.847551\pi$
$614$	23.3382	0.941854
$615$	28.4253	1.14622
$616$	7.14819	0.288009
$617$	−5.85256	−0.235615	−0.117808	−	0.993036i	$-0.537587\pi$
$617$	−5.85256	−0.235615	−0.117808	+	0.993036i	$0.537587\pi$
$618$	−3.87313	−0.155800
$619$	−18.4875	−0.743074	−0.371537	−	0.928418i	$-0.621169\pi$
$619$	−18.4875	−0.743074	−0.371537	+	0.928418i	$0.621169\pi$
$620$	4.28606	0.172132
$621$	2.15251	0.0863773
$622$	−10.9755	−0.440079
$623$	89.7751	3.59677
$624$	−11.9478	−0.478297
$625$	−10.1683	−0.406731
$626$	−27.8040	−1.11127
$627$	8.17965	0.326664
$628$	17.5009	0.698363
$629$	20.0150	0.798052
$630$	−92.4418	−3.68297
$631$	−45.0381	−1.79294	−0.896470	−	0.443105i	$-0.853877\pi$
$631$	−45.0381	−1.79294	−0.896470	+	0.443105i	$0.853877\pi$
$632$	14.5627	0.579275
$633$	−46.4856	−1.84764
$634$	−21.7608	−0.864233
$635$	74.8224	2.96923
$636$	−34.3827	−1.36336
$637$	74.0732	2.93489
$638$	8.97129	0.355177
$639$	−38.3384	−1.51664
$640$	3.47728	0.137452
$641$	18.1578	0.717191	0.358596	−	0.933493i	$-0.383256\pi$
$641$	18.1578	0.717191	0.358596	+	0.933493i	$0.383256\pi$
$642$	−48.4278	−1.91129
$643$	−31.6000	−1.24618	−0.623092	−	0.782148i	$-0.714124\pi$
$643$	−31.6000	−1.24618	−0.623092	+	0.782148i	$0.714124\pi$
$644$	1.59818	0.0629771
$645$	−3.43840	−0.135387
$646$	8.75791	0.344575
$647$	24.0473	0.945396	0.472698	−	0.881225i	$-0.343280\pi$
$647$	24.0473	0.945396	0.472698	+	0.881225i	$0.343280\pi$
$648$	−3.40699	−0.133839
$649$	−16.4783	−0.646829
$650$	−29.3592	−1.15156
$651$	−17.7471	−0.695565
$652$	−17.7837	−0.696462
$653$	−40.0866	−1.56871	−0.784355	−	0.620312i	$-0.787006\pi$
$653$	−40.0866	−1.56871	−0.784355	+	0.620312i	$0.787006\pi$
$654$	17.5026	0.684406
$655$	−52.3127	−2.04403
$656$	2.83258	0.110594
$657$	−0.463603	−0.0180869
$658$	54.5436	2.12633
$659$	−9.12876	−0.355606	−0.177803	−	0.984066i	$-0.556899\pi$
$659$	−9.12876	−0.355606	−0.177803	+	0.984066i	$0.556899\pi$
$660$	14.3777	0.559652
$661$	−2.92728	−0.113858	−0.0569290	−	0.998378i	$-0.518131\pi$
$661$	−2.92728	−0.113858	−0.0569290	+	0.998378i	$0.518131\pi$
$662$	12.7252	0.494577
$663$	−52.8939	−2.05423
$664$	−11.2361	−0.436047
$665$	−34.3204	−1.33089
$666$	−24.0902	−0.933477
$667$	2.00578	0.0776643
$668$	5.39088	0.208579
$669$	−3.10220	−0.119938
$670$	16.5585	0.639711
$671$	−5.74245	−0.221685
$672$	−14.3983	−0.555425
$673$	−15.3680	−0.592392	−0.296196	−	0.955127i	$-0.595718\pi$
$673$	−15.3680	−0.592392	−0.296196	+	0.955127i	$0.595718\pi$
$674$	3.03003	0.116712
$675$	−47.6524	−1.83414
$676$	4.14018	0.159238
$677$	10.0766	0.387275	0.193638	−	0.981073i	$-0.437971\pi$
$677$	10.0766	0.387275	0.193638	+	0.981073i	$0.437971\pi$
$678$	−0.536716	−0.0206124
$679$	51.3195	1.96946
$680$	15.3941	0.590339
$681$	33.5019	1.28379
$682$	1.76598	0.0676230
$683$	14.8322	0.567540	0.283770	−	0.958892i	$-0.408415\pi$
$683$	14.8322	0.567540	0.283770	+	0.958892i	$0.408415\pi$
$684$	−10.5411	−0.403048
$685$	−36.2505	−1.38506
$686$	54.3409	2.07475
$687$	5.63144	0.214853
$688$	−0.342637	−0.0130629
$689$	49.3248	1.87912
$690$	3.21454	0.122376
$691$	4.42273	0.168249	0.0841243	−	0.996455i	$-0.473191\pi$
$691$	4.42273	0.168249	0.0841243	+	0.996455i	$0.473191\pi$
$692$	3.71380	0.141177
$693$	−38.0887	−1.44687
$694$	−34.3637	−1.30443
$695$	−22.6887	−0.860632
$696$	−18.0704	−0.684958
$697$	12.5400	0.474988
$698$	−9.06231	−0.343013
$699$	−8.21604	−0.310759
$700$	−35.3806	−1.33726
$701$	32.1081	1.21271	0.606353	−	0.795196i	$-0.292632\pi$
$701$	32.1081	1.21271	0.606353	+	0.795196i	$0.292632\pi$
$702$	27.8199	1.04999
$703$	−8.94386	−0.337324
$704$	1.43274	0.0539985
$705$	109.708	4.13184
$706$	−3.28223	−0.123528
$707$	−6.62021	−0.248979
$708$	33.1914	1.24741
$709$	4.16543	0.156436	0.0782181	−	0.996936i	$-0.475077\pi$
$709$	4.16543	0.156436	0.0782181	+	0.996936i	$0.475077\pi$
$710$	−25.0192	−0.938952
$711$	−77.5968	−2.91011
$712$	17.9940	0.674354
$713$	0.394835	0.0147867
$714$	−63.7420	−2.38549
$715$	−20.6260	−0.771370
$716$	−6.54452	−0.244580
$717$	32.1359	1.20014
$718$	−26.0884	−0.973612
$719$	22.9416	0.855578	0.427789	−	0.903879i	$-0.359293\pi$
$719$	22.9416	0.855578	0.427789	+	0.903879i	$0.359293\pi$
$720$	−18.5285	−0.690516
$721$	6.69589	0.249368
$722$	15.0865	0.561460
$723$	82.5274	3.06923
$724$	15.1923	0.564617
$725$	−44.4042	−1.64913
$726$	−25.8209	−0.958304
$727$	−39.6194	−1.46940	−0.734701	−	0.678391i	$-0.762677\pi$
$727$	−39.6194	−1.46940	−0.734701	+	0.678391i	$0.762677\pi$
$728$	20.6555	0.765544
$729$	−40.0230	−1.48233
$730$	−0.302542	−0.0111976
$731$	−1.51688	−0.0561037
$732$	11.5667	0.427519
$733$	5.24599	0.193765	0.0968826	−	0.995296i	$-0.469113\pi$
$733$	5.24599	0.193765	0.0968826	+	0.995296i	$0.469113\pi$
$734$	−32.5982	−1.20322
$735$	179.546	6.62265
$736$	0.320330	0.0118075
$737$	6.82260	0.251314
$738$	−15.0933	−0.555591
$739$	26.0182	0.957096	0.478548	−	0.878061i	$-0.341163\pi$
$739$	26.0182	0.957096	0.478548	+	0.878061i	$0.341163\pi$
$740$	−15.7210	−0.577916
$741$	23.6360	0.868291
$742$	59.4409	2.18215
$743$	−15.4426	−0.566535	−0.283268	−	0.959041i	$-0.591419\pi$
$743$	−15.4426	−0.566535	−0.283268	+	0.959041i	$0.591419\pi$
$744$	−3.55713	−0.130411
$745$	2.30528	0.0844591
$746$	6.54154	0.239503
$747$	59.8711	2.19057
$748$	6.34284	0.231917
$749$	83.7222	3.05914
$750$	−20.9882	−0.766383
$751$	−53.1640	−1.93998	−0.969992	−	0.243139i	$-0.921823\pi$
$751$	−53.1640	−1.93998	−0.969992	+	0.243139i	$0.921823\pi$
$752$	10.9324	0.398664
$753$	51.2181	1.86649
$754$	25.9236	0.944080
$755$	−12.4547	−0.453273
$756$	33.5256	1.21931
$757$	42.7560	1.55399	0.776997	−	0.629504i	$-0.216742\pi$
$757$	42.7560	1.55399	0.776997	+	0.629504i	$0.216742\pi$
$758$	12.3051	0.446940
$759$	1.32449	0.0480758
$760$	−6.87899	−0.249527
$761$	−11.3230	−0.410458	−0.205229	−	0.978714i	$-0.565794\pi$
$761$	−11.3230	−0.410458	−0.205229	+	0.978714i	$0.565794\pi$
$762$	−62.0974	−2.24955
$763$	−30.2586	−1.09543
$764$	15.4803	0.560058
$765$	−82.0269	−2.96569
$766$	14.4291	0.521344
$767$	−47.6158	−1.71931
$768$	−2.88590	−0.104136
$769$	−36.8125	−1.32749	−0.663747	−	0.747957i	$-0.731035\pi$
$769$	−36.8125	−1.32749	−0.663747	+	0.747957i	$0.731035\pi$
$770$	−24.8563	−0.895758
$771$	35.4123	1.27534
$772$	−12.7138	−0.457579
$773$	10.8293	0.389502	0.194751	−	0.980853i	$-0.437610\pi$
$773$	10.8293	0.389502	0.194751	+	0.980853i	$0.437610\pi$
$774$	1.82572	0.0656243
$775$	−8.74088	−0.313982
$776$	10.2862	0.369252
$777$	65.0954	2.33529
$778$	0.596064	0.0213699
$779$	−5.60361	−0.200770
$780$	41.5460	1.48759
$781$	−10.3086	−0.368872
$782$	1.41812	0.0507119
$783$	42.0760	1.50367
$784$	17.8918	0.638992
$785$	−60.8556	−2.17203
$786$	43.4160	1.54860
$787$	1.11239	0.0396524	0.0198262	−	0.999803i	$-0.493689\pi$
$787$	1.11239	0.0396524	0.0198262	+	0.999803i	$0.493689\pi$
$788$	−5.97128	−0.212718
$789$	−67.0067	−2.38550
$790$	−50.6388	−1.80165
$791$	0.927877	0.0329915
$792$	−7.63429	−0.271273
$793$	−16.5934	−0.589251
$794$	−29.9992	−1.06463
$795$	119.558	4.24029
$796$	13.8541	0.491047
$797$	−13.4796	−0.477471	−0.238736	−	0.971085i	$-0.576733\pi$
$797$	−13.4796	−0.477471	−0.238736	+	0.971085i	$0.576733\pi$
$798$	28.4836	1.00831
$799$	48.3985	1.71222
$800$	−7.09148	−0.250722
$801$	−95.8801	−3.38776
$802$	21.3253	0.753022
$803$	−0.124656	−0.00439902
$804$	−13.7424	−0.484658
$805$	−5.55732	−0.195870
$806$	5.10300	0.179746
$807$	11.6530	0.410203
$808$	−1.32692	−0.0466808
$809$	30.8522	1.08471	0.542353	−	0.840151i	$-0.317534\pi$
$809$	30.8522	1.08471	0.542353	+	0.840151i	$0.317534\pi$
$810$	11.8471	0.416263
$811$	−9.80911	−0.344445	−0.172222	−	0.985058i	$-0.555095\pi$
$811$	−9.80911	−0.344445	−0.172222	+	0.985058i	$0.555095\pi$
$812$	31.2403	1.09632
$813$	−15.6778	−0.549844
$814$	−6.47752	−0.227037
$815$	61.8388	2.16612
$816$	−12.7761	−0.447252
$817$	0.677828	0.0237142
$818$	1.02973	0.0360038
$819$	−110.062	−3.84587
$820$	−9.84969	−0.343966
$821$	4.03985	0.140992	0.0704959	−	0.997512i	$-0.477542\pi$
$821$	4.03985	0.140992	0.0704959	+	0.997512i	$0.477542\pi$
$822$	30.0854	1.04935
$823$	2.50086	0.0871744	0.0435872	−	0.999050i	$-0.486121\pi$
$823$	2.50086	0.0871744	0.0435872	+	0.999050i	$0.486121\pi$
$824$	1.34209	0.0467538
$825$	−29.3216	−1.02085
$826$	−57.3815	−1.99656
$827$	−13.1579	−0.457546	−0.228773	−	0.973480i	$-0.573471\pi$
$827$	−13.1579	−0.457546	−0.228773	+	0.973480i	$0.573471\pi$
$828$	−1.70686	−0.0593175
$829$	28.2954	0.982740	0.491370	−	0.870951i	$-0.336496\pi$
$829$	28.2954	0.982740	0.491370	+	0.870951i	$0.336496\pi$
$830$	39.0712	1.35618
$831$	4.12396	0.143059
$832$	4.14007	0.143531
$833$	79.2081	2.74440
$834$	18.8301	0.652032
$835$	−18.7456	−0.648718
$836$	−2.83435	−0.0980279
$837$	8.28259	0.286288
$838$	32.1400	1.11026
$839$	−53.3612	−1.84223	−0.921116	−	0.389287i	$-0.872721\pi$
$839$	−53.3612	−1.84223	−0.921116	+	0.389287i	$0.872721\pi$
$840$	50.0668	1.72747
$841$	10.2079	0.351997
$842$	−2.81336	−0.0969547
$843$	−74.9730	−2.58221
$844$	16.1078	0.554454
$845$	−14.3966	−0.495257
$846$	−58.2528	−2.00277
$847$	44.6393	1.53383
$848$	11.9140	0.409128
$849$	92.6337	3.17918
$850$	−31.3945	−1.07682
$851$	−1.44823	−0.0496447
$852$	20.7642	0.711369
$853$	19.6531	0.672909	0.336454	−	0.941700i	$-0.390772\pi$
$853$	19.6531	0.672909	0.336454	+	0.941700i	$0.390772\pi$
$854$	−19.9966	−0.684271
$855$	36.6543	1.25355
$856$	16.7808	0.573556
$857$	9.09007	0.310511	0.155256	−	0.987874i	$-0.450380\pi$
$857$	9.09007	0.310511	0.155256	+	0.987874i	$0.450380\pi$
$858$	17.1182	0.584405
$859$	34.5991	1.18051	0.590253	−	0.807218i	$-0.299028\pi$
$859$	34.5991	1.18051	0.590253	+	0.807218i	$0.299028\pi$
$860$	1.19145	0.0406280
$861$	40.7843	1.38992
$862$	−3.08396	−0.105040
$863$	7.45551	0.253788	0.126894	−	0.991916i	$-0.459499\pi$
$863$	7.45551	0.253788	0.126894	+	0.991916i	$0.459499\pi$
$864$	6.71967	0.228608
$865$	−12.9139	−0.439086
$866$	37.6843	1.28056
$867$	−7.50017	−0.254719
$868$	6.14959	0.208731
$869$	−20.8647	−0.707785
$870$	62.8360	2.13034
$871$	19.7147	0.668006
$872$	−6.06486	−0.205382
$873$	−54.8094	−1.85502
$874$	−0.633698	−0.0214351
$875$	36.2846	1.22664
$876$	0.251089	0.00848352
$877$	−39.1258	−1.32118	−0.660592	−	0.750745i	$-0.729695\pi$
$877$	−39.1258	−1.32118	−0.660592	+	0.750745i	$0.729695\pi$
$878$	−36.5805	−1.23453
$879$	−28.5579	−0.963236
$880$	−4.98205	−0.167945
$881$	14.4448	0.486659	0.243329	−	0.969944i	$-0.421760\pi$
$881$	14.4448	0.486659	0.243329	+	0.969944i	$0.421760\pi$
$882$	−95.3354	−3.21011
$883$	−0.512057	−0.0172321	−0.00861604	−	0.999963i	$-0.502743\pi$
$883$	−0.512057	−0.0172321	−0.00861604	+	0.999963i	$0.502743\pi$
$884$	18.3284	0.616449
$885$	−115.416	−3.87966
$886$	−19.5991	−0.658444
$887$	55.3485	1.85842	0.929211	−	0.369550i	$-0.120488\pi$
$887$	55.3485	1.85842	0.929211	+	0.369550i	$0.120488\pi$
$888$	13.0474	0.437841
$889$	107.354	3.60055
$890$	−62.5703	−2.09736
$891$	4.88134	0.163531
$892$	1.07495	0.0359919
$893$	−21.6272	−0.723727
$894$	−1.91323	−0.0639879
$895$	22.7571	0.760687
$896$	4.98917	0.166676
$897$	3.82725	0.127788
$898$	28.7956	0.960923
$899$	7.71801	0.257410
$900$	37.7866	1.25955
$901$	52.7440	1.75716
$902$	−4.05836	−0.135129
$903$	−4.93338	−0.164173
$904$	0.185978	0.00618555
$905$	−52.8279	−1.75606
$906$	10.3365	0.343408
$907$	45.8559	1.52262	0.761310	−	0.648388i	$-0.224557\pi$
$907$	45.8559	1.52262	0.761310	+	0.648388i	$0.224557\pi$
$908$	−11.6088	−0.385251
$909$	7.07041	0.234511
$910$	−71.8250	−2.38097
$911$	2.89386	0.0958780	0.0479390	−	0.998850i	$-0.484735\pi$
$911$	2.89386	0.0958780	0.0479390	+	0.998850i	$0.484735\pi$
$912$	5.70909	0.189047
$913$	16.0985	0.532782
$914$	−28.9992	−0.959210
$915$	−40.2208	−1.32966
$916$	−1.95136	−0.0644748
$917$	−75.0577	−2.47862
$918$	29.7484	0.981844
$919$	46.0930	1.52047	0.760234	−	0.649649i	$-0.225084\pi$
$919$	46.0930	1.52047	0.760234	+	0.649649i	$0.225084\pi$
$920$	−1.11388	−0.0367234
$921$	67.3519	2.21932
$922$	−23.8213	−0.784513
$923$	−29.7879	−0.980482
$924$	20.6290	0.678644
$925$	32.0610	1.05416
$926$	0.274049	0.00900580
$927$	−7.15123	−0.234877
$928$	6.26162	0.205548
$929$	28.0738	0.921072	0.460536	−	0.887641i	$-0.347657\pi$
$929$	28.0738	0.921072	0.460536	+	0.887641i	$0.347657\pi$
$930$	12.3692	0.405601
$931$	−35.3947	−1.16001
$932$	2.84696	0.0932551
$933$	−31.6744	−1.03697
$934$	−8.64001	−0.282710
$935$	−22.0558	−0.721303
$936$	−22.0601	−0.721058
$937$	−28.1283	−0.918912	−0.459456	−	0.888200i	$-0.651956\pi$
$937$	−28.1283	−0.918912	−0.459456	+	0.888200i	$0.651956\pi$
$938$	23.7580	0.775726
$939$	−80.2397	−2.61852
$940$	−38.0151	−1.23991
$941$	−2.42192	−0.0789524	−0.0394762	−	0.999221i	$-0.512569\pi$
$941$	−2.42192	−0.0789524	−0.0394762	+	0.999221i	$0.512569\pi$
$942$	50.5060	1.64557
$943$	−0.907361	−0.0295478
$944$	−11.5012	−0.374333
$945$	−116.578	−3.79228
$946$	0.490911	0.0159609
$947$	−17.6364	−0.573107	−0.286554	−	0.958064i	$-0.592510\pi$
$947$	−17.6364	−0.573107	−0.286554	+	0.958064i	$0.592510\pi$
$948$	42.0267	1.36496
$949$	−0.360208	−0.0116929
$950$	14.0288	0.455156
$951$	−62.7997	−2.03642
$952$	22.0874	0.715855
$953$	−39.1454	−1.26804	−0.634022	−	0.773315i	$-0.718597\pi$
$953$	−39.1454	−1.26804	−0.634022	+	0.773315i	$0.718597\pi$
$954$	−63.4831	−2.05534
$955$	−53.8294	−1.74188
$956$	−11.1355	−0.360147
$957$	25.8903	0.836914
$958$	4.66706	0.150786
$959$	−52.0118	−1.67955
$960$	10.0351	0.323881
$961$	−29.4807	−0.950991
$962$	−18.7175	−0.603477
$963$	−89.4156	−2.88138
$964$	−28.5967	−0.921038
$965$	44.2094	1.42315
$966$	4.61219	0.148395
$967$	14.0554	0.451992	0.225996	−	0.974128i	$-0.427436\pi$
$967$	14.0554	0.451992	0.225996	+	0.974128i	$0.427436\pi$
$968$	8.94725	0.287575
$969$	25.2745	0.811934
$970$	−35.7680	−1.14844
$971$	51.2662	1.64521	0.822606	−	0.568612i	$-0.192520\pi$
$971$	51.2662	1.64521	0.822606	+	0.568612i	$0.192520\pi$
$972$	10.3268	0.331231
$973$	−32.5535	−1.04362
$974$	38.5257	1.23444
$975$	−84.7279	−2.71347
$976$	−4.00801	−0.128293
$977$	−18.8259	−0.602294	−0.301147	−	0.953578i	$-0.597370\pi$
$977$	−18.8259	−0.602294	−0.301147	+	0.953578i	$0.597370\pi$
$978$	−51.3220	−1.64110
$979$	−25.7808	−0.823958
$980$	−62.2148	−1.98738
$981$	32.3163	1.03178
$982$	−4.81399	−0.153621
$983$	25.4218	0.810828	0.405414	−	0.914133i	$-0.367127\pi$
$983$	25.4218	0.810828	0.405414	+	0.914133i	$0.367127\pi$
$984$	8.17457	0.260596
$985$	20.7638	0.661590
$986$	27.7206	0.882804
$987$	157.408	5.01034
$988$	−8.19016	−0.260564
$989$	0.109757	0.00349007
$990$	26.5466	0.843705
$991$	−51.2840	−1.62909	−0.814545	−	0.580100i	$-0.803014\pi$
$991$	−51.2840	−1.62909	−0.814545	+	0.580100i	$0.803014\pi$
$992$	1.23259	0.0391347
$993$	36.7236	1.16539
$994$	−35.8972	−1.13859
$995$	−48.1747	−1.52724
$996$	−32.4264	−1.02747
$997$	0.364197	0.0115342	0.00576712	−	0.999983i	$-0.498164\pi$
$997$	0.364197	0.0115342	0.00576712	+	0.999983i	$0.498164\pi$
$998$	−3.27009	−0.103513
$999$	−30.3800	−0.961182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.3	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.3	✓	61	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.88590 q^{3} +1.00000 q^{4} -3.47728 q^{5} +2.88590 q^{6} -4.98917 q^{7} -1.00000 q^{8} +5.32845 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.88590 q^{3} +1.00000 q^{4} -3.47728 q^{5} +2.88590 q^{6} -4.98917 q^{7} -1.00000 q^{8} +5.32845 q^{9} +3.47728 q^{10} +1.43274 q^{11} -2.88590 q^{12} +4.14007 q^{13} +4.98917 q^{14} +10.0351 q^{15} +1.00000 q^{16} +4.42706 q^{17} -5.32845 q^{18} -1.97827 q^{19} -3.47728 q^{20} +14.3983 q^{21} -1.43274 q^{22} -0.320330 q^{23} +2.88590 q^{24} +7.09148 q^{25} -4.14007 q^{26} -6.71967 q^{27} -4.98917 q^{28} -6.26162 q^{29} -10.0351 q^{30} -1.23259 q^{31} -1.00000 q^{32} -4.13476 q^{33} -4.42706 q^{34} +17.3487 q^{35} +5.32845 q^{36} +4.52106 q^{37} +1.97827 q^{38} -11.9478 q^{39} +3.47728 q^{40} +2.83258 q^{41} -14.3983 q^{42} -0.342637 q^{43} +1.43274 q^{44} -18.5285 q^{45} +0.320330 q^{46} +10.9324 q^{47} -2.88590 q^{48} +17.8918 q^{49} -7.09148 q^{50} -12.7761 q^{51} +4.14007 q^{52} +11.9140 q^{53} +6.71967 q^{54} -4.98205 q^{55} +4.98917 q^{56} +5.70909 q^{57} +6.26162 q^{58} -11.5012 q^{59} +10.0351 q^{60} -4.00801 q^{61} +1.23259 q^{62} -26.5845 q^{63} +1.00000 q^{64} -14.3962 q^{65} +4.13476 q^{66} +4.76192 q^{67} +4.42706 q^{68} +0.924441 q^{69} -17.3487 q^{70} -7.19504 q^{71} -5.32845 q^{72} -0.0870054 q^{73} -4.52106 q^{74} -20.4653 q^{75} -1.97827 q^{76} -7.14819 q^{77} +11.9478 q^{78} -14.5627 q^{79} -3.47728 q^{80} +3.40699 q^{81} -2.83258 q^{82} +11.2361 q^{83} +14.3983 q^{84} -15.3941 q^{85} +0.342637 q^{86} +18.0704 q^{87} -1.43274 q^{88} -17.9940 q^{89} +18.5285 q^{90} -20.6555 q^{91} -0.320330 q^{92} +3.55713 q^{93} -10.9324 q^{94} +6.87899 q^{95} +2.88590 q^{96} -10.2862 q^{97} -17.8918 q^{98} +7.63429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

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