LMFDB - Embedded newform 4034.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.59634 q^{3} +1.00000 q^{4} -2.79905 q^{5} -2.59634 q^{6} +1.81461 q^{7} +1.00000 q^{8} +3.74100 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.59634 q^{3} +1.00000 q^{4} -2.79905 q^{5} -2.59634 q^{6} +1.81461 q^{7} +1.00000 q^{8} +3.74100 q^{9} -2.79905 q^{10} +3.73633 q^{11} -2.59634 q^{12} -2.30742 q^{13} +1.81461 q^{14} +7.26729 q^{15} +1.00000 q^{16} +5.01126 q^{17} +3.74100 q^{18} +8.09803 q^{19} -2.79905 q^{20} -4.71134 q^{21} +3.73633 q^{22} -7.38910 q^{23} -2.59634 q^{24} +2.83467 q^{25} -2.30742 q^{26} -1.92388 q^{27} +1.81461 q^{28} -6.39213 q^{29} +7.26729 q^{30} -7.51818 q^{31} +1.00000 q^{32} -9.70078 q^{33} +5.01126 q^{34} -5.07917 q^{35} +3.74100 q^{36} +0.201937 q^{37} +8.09803 q^{38} +5.99084 q^{39} -2.79905 q^{40} +4.54257 q^{41} -4.71134 q^{42} +5.72003 q^{43} +3.73633 q^{44} -10.4712 q^{45} -7.38910 q^{46} -6.67146 q^{47} -2.59634 q^{48} -3.70721 q^{49} +2.83467 q^{50} -13.0109 q^{51} -2.30742 q^{52} -8.13695 q^{53} -1.92388 q^{54} -10.4582 q^{55} +1.81461 q^{56} -21.0253 q^{57} -6.39213 q^{58} +12.9865 q^{59} +7.26729 q^{60} +5.99606 q^{61} -7.51818 q^{62} +6.78843 q^{63} +1.00000 q^{64} +6.45857 q^{65} -9.70078 q^{66} -11.1756 q^{67} +5.01126 q^{68} +19.1846 q^{69} -5.07917 q^{70} +10.8218 q^{71} +3.74100 q^{72} +2.14894 q^{73} +0.201937 q^{74} -7.35978 q^{75} +8.09803 q^{76} +6.77995 q^{77} +5.99084 q^{78} +12.4748 q^{79} -2.79905 q^{80} -6.22794 q^{81} +4.54257 q^{82} +8.15019 q^{83} -4.71134 q^{84} -14.0268 q^{85} +5.72003 q^{86} +16.5962 q^{87} +3.73633 q^{88} +1.40180 q^{89} -10.4712 q^{90} -4.18705 q^{91} -7.38910 q^{92} +19.5198 q^{93} -6.67146 q^{94} -22.6668 q^{95} -2.59634 q^{96} -0.714395 q^{97} -3.70721 q^{98} +13.9776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * 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
$3$	−2.59634	−1.49900	−0.749500	−	0.662005i	$-0.769706\pi$
$3$	−2.59634	−1.49900	−0.749500	+	0.662005i	$0.769706\pi$
$4$	1.00000	0.500000
$5$	−2.79905	−1.25177	−0.625886	−	0.779914i	$-0.715263\pi$
$5$	−2.79905	−1.25177	−0.625886	+	0.779914i	$0.715263\pi$
$6$	−2.59634	−1.05995
$7$	1.81461	0.685856	0.342928	−	0.939362i	$-0.388581\pi$
$7$	1.81461	0.685856	0.342928	+	0.939362i	$0.388581\pi$
$8$	1.00000	0.353553
$9$	3.74100	1.24700
$10$	−2.79905	−0.885137
$11$	3.73633	1.12654	0.563272	−	0.826271i	$-0.309542\pi$
$11$	3.73633	1.12654	0.563272	+	0.826271i	$0.309542\pi$
$12$	−2.59634	−0.749500
$13$	−2.30742	−0.639962	−0.319981	−	0.947424i	$-0.603676\pi$
$13$	−2.30742	−0.639962	−0.319981	+	0.947424i	$0.603676\pi$
$14$	1.81461	0.484974
$15$	7.26729	1.87641
$16$	1.00000	0.250000
$17$	5.01126	1.21541	0.607704	−	0.794163i	$-0.292091\pi$
$17$	5.01126	1.21541	0.607704	+	0.794163i	$0.292091\pi$
$18$	3.74100	0.881761
$19$	8.09803	1.85781	0.928907	−	0.370312i	$-0.120749\pi$
$19$	8.09803	1.85781	0.928907	+	0.370312i	$0.120749\pi$
$20$	−2.79905	−0.625886
$21$	−4.71134	−1.02810
$22$	3.73633	0.796587
$23$	−7.38910	−1.54073	−0.770367	−	0.637601i	$-0.779927\pi$
$23$	−7.38910	−1.54073	−0.770367	+	0.637601i	$0.779927\pi$
$24$	−2.59634	−0.529976
$25$	2.83467	0.566935
$26$	−2.30742	−0.452521
$27$	−1.92388	−0.370251
$28$	1.81461	0.342928
$29$	−6.39213	−1.18699	−0.593494	−	0.804838i	$-0.702252\pi$
$29$	−6.39213	−1.18699	−0.593494	+	0.804838i	$0.702252\pi$
$30$	7.26729	1.32682
$31$	−7.51818	−1.35030	−0.675152	−	0.737678i	$-0.735922\pi$
$31$	−7.51818	−1.35030	−0.675152	+	0.737678i	$0.735922\pi$
$32$	1.00000	0.176777
$33$	−9.70078	−1.68869
$34$	5.01126	0.859424
$35$	−5.07917	−0.858536
$36$	3.74100	0.623499
$37$	0.201937	0.0331982	0.0165991	−	0.999862i	$-0.494716\pi$
$37$	0.201937	0.0331982	0.0165991	+	0.999862i	$0.494716\pi$
$38$	8.09803	1.31367
$39$	5.99084	0.959302
$40$	−2.79905	−0.442568
$41$	4.54257	0.709431	0.354715	−	0.934974i	$-0.384578\pi$
$41$	4.54257	0.709431	0.354715	+	0.934974i	$0.384578\pi$
$42$	−4.71134	−0.726975
$43$	5.72003	0.872297	0.436148	−	0.899875i	$-0.356342\pi$
$43$	5.72003	0.872297	0.436148	+	0.899875i	$0.356342\pi$
$44$	3.73633	0.563272
$45$	−10.4712	−1.56096
$46$	−7.38910	−1.08946
$47$	−6.67146	−0.973132	−0.486566	−	0.873644i	$-0.661751\pi$
$47$	−6.67146	−0.973132	−0.486566	+	0.873644i	$0.661751\pi$
$48$	−2.59634	−0.374750
$49$	−3.70721	−0.529601
$50$	2.83467	0.400883
$51$	−13.0109	−1.82190
$52$	−2.30742	−0.319981
$53$	−8.13695	−1.11770	−0.558848	−	0.829270i	$-0.688756\pi$
$53$	−8.13695	−1.11770	−0.558848	+	0.829270i	$0.688756\pi$
$54$	−1.92388	−0.261807
$55$	−10.4582	−1.41018
$56$	1.81461	0.242487
$57$	−21.0253	−2.78486
$58$	−6.39213	−0.839328
$59$	12.9865	1.69070	0.845351	−	0.534211i	$-0.179391\pi$
$59$	12.9865	1.69070	0.845351	+	0.534211i	$0.179391\pi$
$60$	7.26729	0.938203
$61$	5.99606	0.767717	0.383858	−	0.923392i	$-0.374595\pi$
$61$	5.99606	0.767717	0.383858	+	0.923392i	$0.374595\pi$
$62$	−7.51818	−0.954809
$63$	6.78843	0.855262
$64$	1.00000	0.125000
$65$	6.45857	0.801087
$66$	−9.70078	−1.19408
$67$	−11.1756	−1.36532	−0.682659	−	0.730737i	$-0.739177\pi$
$67$	−11.1756	−1.36532	−0.682659	+	0.730737i	$0.739177\pi$
$68$	5.01126	0.607704
$69$	19.1846	2.30956
$70$	−5.07917	−0.607077
$71$	10.8218	1.28431	0.642153	−	0.766576i	$-0.278041\pi$
$71$	10.8218	1.28431	0.642153	+	0.766576i	$0.278041\pi$
$72$	3.74100	0.440881
$73$	2.14894	0.251514	0.125757	−	0.992061i	$-0.459864\pi$
$73$	2.14894	0.251514	0.125757	+	0.992061i	$0.459864\pi$
$74$	0.201937	0.0234747
$75$	−7.35978	−0.849835
$76$	8.09803	0.928907
$77$	6.77995	0.772648
$78$	5.99084	0.678329
$79$	12.4748	1.40353	0.701765	−	0.712409i	$-0.252396\pi$
$79$	12.4748	1.40353	0.701765	+	0.712409i	$0.252396\pi$
$80$	−2.79905	−0.312943
$81$	−6.22794	−0.691993
$82$	4.54257	0.501643
$83$	8.15019	0.894599	0.447300	−	0.894384i	$-0.352386\pi$
$83$	8.15019	0.894599	0.447300	+	0.894384i	$0.352386\pi$
$84$	−4.71134	−0.514049
$85$	−14.0268	−1.52142
$86$	5.72003	0.616807
$87$	16.5962	1.77930
$88$	3.73633	0.398294
$89$	1.40180	0.148591	0.0742955	−	0.997236i	$-0.476329\pi$
$89$	1.40180	0.148591	0.0742955	+	0.997236i	$0.476329\pi$
$90$	−10.4712	−1.10376
$91$	−4.18705	−0.438922
$92$	−7.38910	−0.770367
$93$	19.5198	2.02411
$94$	−6.67146	−0.688108
$95$	−22.6668	−2.32556
$96$	−2.59634	−0.264988
$97$	−0.714395	−0.0725358	−0.0362679	−	0.999342i	$-0.511547\pi$
$97$	−0.714395	−0.0725358	−0.0362679	+	0.999342i	$0.511547\pi$
$98$	−3.70721	−0.374485
$99$	13.9776	1.40480
$100$	2.83467	0.283467
$101$	−5.60599	−0.557817	−0.278908	−	0.960318i	$-0.589973\pi$
$101$	−5.60599	−0.557817	−0.278908	+	0.960318i	$0.589973\pi$
$102$	−13.0109	−1.28828
$103$	18.3479	1.80787	0.903936	−	0.427668i	$-0.140665\pi$
$103$	18.3479	1.80787	0.903936	+	0.427668i	$0.140665\pi$
$104$	−2.30742	−0.226261
$105$	13.1873	1.28694
$106$	−8.13695	−0.790330
$107$	−8.61101	−0.832457	−0.416229	−	0.909260i	$-0.636648\pi$
$107$	−8.61101	−0.832457	−0.416229	+	0.909260i	$0.636648\pi$
$108$	−1.92388	−0.185125
$109$	16.1371	1.54565	0.772827	−	0.634617i	$-0.218842\pi$
$109$	16.1371	1.54565	0.772827	+	0.634617i	$0.218842\pi$
$110$	−10.4582	−0.997146
$111$	−0.524297	−0.0497640
$112$	1.81461	0.171464
$113$	−3.25029	−0.305762	−0.152881	−	0.988245i	$-0.548855\pi$
$113$	−3.25029	−0.305762	−0.152881	+	0.988245i	$0.548855\pi$
$114$	−21.0253	−1.96920
$115$	20.6825	1.92865
$116$	−6.39213	−0.593494
$117$	−8.63203	−0.798032
$118$	12.9865	1.19551
$119$	9.09345	0.833596
$120$	7.26729	0.663410
$121$	2.96012	0.269102
$122$	5.99606	0.542858
$123$	−11.7941	−1.06344
$124$	−7.51818	−0.675152
$125$	6.06085	0.542099
$126$	6.78843	0.604761
$127$	3.05914	0.271455	0.135728	−	0.990746i	$-0.456663\pi$
$127$	3.05914	0.271455	0.135728	+	0.990746i	$0.456663\pi$
$128$	1.00000	0.0883883
$129$	−14.8512	−1.30757
$130$	6.45857	0.566454
$131$	10.0018	0.873861	0.436931	−	0.899495i	$-0.356066\pi$
$131$	10.0018	0.873861	0.436931	+	0.899495i	$0.356066\pi$
$132$	−9.70078	−0.844345
$133$	14.6947	1.27419
$134$	−11.1756	−0.965426
$135$	5.38503	0.463470
$136$	5.01126	0.429712
$137$	8.84414	0.755606	0.377803	−	0.925886i	$-0.376680\pi$
$137$	8.84414	0.755606	0.377803	+	0.925886i	$0.376680\pi$
$138$	19.1846	1.63310
$139$	2.97770	0.252566	0.126283	−	0.991994i	$-0.459695\pi$
$139$	2.97770	0.252566	0.126283	+	0.991994i	$0.459695\pi$
$140$	−5.07917	−0.429268
$141$	17.3214	1.45872
$142$	10.8218	0.908142
$143$	−8.62125	−0.720945
$144$	3.74100	0.311750
$145$	17.8919	1.48584
$146$	2.14894	0.177847
$147$	9.62518	0.793872
$148$	0.201937	0.0165991
$149$	−18.6279	−1.52606	−0.763029	−	0.646365i	$-0.776289\pi$
$149$	−18.6279	−1.52606	−0.763029	+	0.646365i	$0.776289\pi$
$150$	−7.35978	−0.600924
$151$	−9.68586	−0.788224	−0.394112	−	0.919062i	$-0.628948\pi$
$151$	−9.68586	−0.788224	−0.394112	+	0.919062i	$0.628948\pi$
$152$	8.09803	0.656837
$153$	18.7471	1.51561
$154$	6.77995	0.546344
$155$	21.0437	1.69027
$156$	5.99084	0.479651
$157$	11.0835	0.884558	0.442279	−	0.896877i	$-0.354170\pi$
$157$	11.0835	0.884558	0.442279	+	0.896877i	$0.354170\pi$
$158$	12.4748	0.992445
$159$	21.1263	1.67542
$160$	−2.79905	−0.221284
$161$	−13.4083	−1.05672
$162$	−6.22794	−0.489313
$163$	17.7999	1.39420	0.697099	−	0.716975i	$-0.254474\pi$
$163$	17.7999	1.39420	0.697099	+	0.716975i	$0.254474\pi$
$164$	4.54257	0.354715
$165$	27.1530	2.11385
$166$	8.15019	0.632577
$167$	−15.4874	−1.19845	−0.599227	−	0.800579i	$-0.704525\pi$
$167$	−15.4874	−1.19845	−0.599227	+	0.800579i	$0.704525\pi$
$168$	−4.71134	−0.363488
$169$	−7.67584	−0.590449
$170$	−14.0268	−1.07580
$171$	30.2947	2.31669
$172$	5.72003	0.436148
$173$	11.8491	0.900873	0.450436	−	0.892809i	$-0.351268\pi$
$173$	11.8491	0.900873	0.450436	+	0.892809i	$0.351268\pi$
$174$	16.5962	1.25815
$175$	5.14381	0.388836
$176$	3.73633	0.281636
$177$	−33.7175	−2.53436
$178$	1.40180	0.105070
$179$	18.8961	1.41236	0.706181	−	0.708031i	$-0.250416\pi$
$179$	18.8961	1.41236	0.706181	+	0.708031i	$0.250416\pi$
$180$	−10.4712	−0.780479
$181$	19.7139	1.46532	0.732661	−	0.680593i	$-0.238278\pi$
$181$	19.7139	1.46532	0.732661	+	0.680593i	$0.238278\pi$
$182$	−4.18705	−0.310365
$183$	−15.5678	−1.15081
$184$	−7.38910	−0.544732
$185$	−0.565230	−0.0415566
$186$	19.5198	1.43126
$187$	18.7237	1.36921
$188$	−6.67146	−0.486566
$189$	−3.49108	−0.253939
$190$	−22.6668	−1.64442
$191$	2.81685	0.203820	0.101910	−	0.994794i	$-0.467505\pi$
$191$	2.81685	0.203820	0.101910	+	0.994794i	$0.467505\pi$
$192$	−2.59634	−0.187375
$193$	2.38607	0.171753	0.0858767	−	0.996306i	$-0.472631\pi$
$193$	2.38607	0.171753	0.0858767	+	0.996306i	$0.472631\pi$
$194$	−0.714395	−0.0512906
$195$	−16.7687	−1.20083
$196$	−3.70721	−0.264801
$197$	2.28133	0.162538	0.0812689	−	0.996692i	$-0.474103\pi$
$197$	2.28133	0.162538	0.0812689	+	0.996692i	$0.474103\pi$
$198$	13.9776	0.993343
$199$	5.50846	0.390484	0.195242	−	0.980755i	$-0.437451\pi$
$199$	5.50846	0.390484	0.195242	+	0.980755i	$0.437451\pi$
$200$	2.83467	0.200442
$201$	29.0157	2.04661
$202$	−5.60599	−0.394436
$203$	−11.5992	−0.814104
$204$	−13.0109	−0.910948
$205$	−12.7149	−0.888046
$206$	18.3479	1.27836
$207$	−27.6426	−1.92129
$208$	−2.30742	−0.159990
$209$	30.2569	2.09291
$210$	13.1873	0.910008
$211$	−11.7839	−0.811240	−0.405620	−	0.914042i	$-0.632944\pi$
$211$	−11.7839	−0.811240	−0.405620	+	0.914042i	$0.632944\pi$
$212$	−8.13695	−0.558848
$213$	−28.0970	−1.92517
$214$	−8.61101	−0.588636
$215$	−16.0107	−1.09192
$216$	−1.92388	−0.130903
$217$	−13.6425	−0.926115
$218$	16.1371	1.09294
$219$	−5.57937	−0.377019
$220$	−10.4582	−0.705089
$221$	−11.5631	−0.777815
$222$	−0.524297	−0.0351885
$223$	−25.7948	−1.72735	−0.863673	−	0.504052i	$-0.831842\pi$
$223$	−25.7948	−1.72735	−0.863673	+	0.504052i	$0.831842\pi$
$224$	1.81461	0.121243
$225$	10.6045	0.706967
$226$	−3.25029	−0.216206
$227$	−5.89354	−0.391168	−0.195584	−	0.980687i	$-0.562660\pi$
$227$	−5.89354	−0.391168	−0.195584	+	0.980687i	$0.562660\pi$
$228$	−21.0253	−1.39243
$229$	9.92639	0.655955	0.327977	−	0.944686i	$-0.393633\pi$
$229$	9.92639	0.655955	0.327977	+	0.944686i	$0.393633\pi$
$230$	20.6825	1.36376
$231$	−17.6031	−1.15820
$232$	−6.39213	−0.419664
$233$	4.76540	0.312192	0.156096	−	0.987742i	$-0.450109\pi$
$233$	4.76540	0.312192	0.156096	+	0.987742i	$0.450109\pi$
$234$	−8.63203	−0.564293
$235$	18.6737	1.21814
$236$	12.9865	0.845351
$237$	−32.3890	−2.10389
$238$	9.09345	0.589441
$239$	−20.1082	−1.30069	−0.650347	−	0.759637i	$-0.725376\pi$
$239$	−20.1082	−1.30069	−0.650347	+	0.759637i	$0.725376\pi$
$240$	7.26729	0.469102
$241$	26.0099	1.67545	0.837723	−	0.546095i	$-0.183886\pi$
$241$	26.0099	1.67545	0.837723	+	0.546095i	$0.183886\pi$
$242$	2.96012	0.190284
$243$	21.9415	1.40755
$244$	5.99606	0.383858
$245$	10.3767	0.662940
$246$	−11.7941	−0.751963
$247$	−18.6855	−1.18893
$248$	−7.51818	−0.477405
$249$	−21.1607	−1.34100
$250$	6.06085	0.383322
$251$	−0.843188	−0.0532216	−0.0266108	−	0.999646i	$-0.508471\pi$
$251$	−0.843188	−0.0532216	−0.0266108	+	0.999646i	$0.508471\pi$
$252$	6.78843	0.427631
$253$	−27.6081	−1.73571
$254$	3.05914	0.191948
$255$	36.4183	2.28060
$256$	1.00000	0.0625000
$257$	−6.69460	−0.417598	−0.208799	−	0.977959i	$-0.566955\pi$
$257$	−6.69460	−0.417598	−0.208799	+	0.977959i	$0.566955\pi$
$258$	−14.8512	−0.924593
$259$	0.366435	0.0227692
$260$	6.45857	0.400543
$261$	−23.9129	−1.48017
$262$	10.0018	0.617913
$263$	1.56168	0.0962971	0.0481486	−	0.998840i	$-0.484668\pi$
$263$	1.56168	0.0962971	0.0481486	+	0.998840i	$0.484668\pi$
$264$	−9.70078	−0.597042
$265$	22.7757	1.39910
$266$	14.6947	0.900991
$267$	−3.63956	−0.222738
$268$	−11.1756	−0.682659
$269$	20.3991	1.24376	0.621878	−	0.783114i	$-0.286370\pi$
$269$	20.3991	1.24376	0.621878	+	0.783114i	$0.286370\pi$
$270$	5.38503	0.327723
$271$	−8.75555	−0.531862	−0.265931	−	0.963992i	$-0.585679\pi$
$271$	−8.75555	−0.531862	−0.265931	+	0.963992i	$0.585679\pi$
$272$	5.01126	0.303852
$273$	10.8710	0.657943
$274$	8.84414	0.534294
$275$	10.5913	0.638677
$276$	19.1846	1.15478
$277$	−4.81514	−0.289314	−0.144657	−	0.989482i	$-0.546208\pi$
$277$	−4.81514	−0.289314	−0.144657	+	0.989482i	$0.546208\pi$
$278$	2.97770	0.178591
$279$	−28.1255	−1.68383
$280$	−5.07917	−0.303538
$281$	−9.86698	−0.588614	−0.294307	−	0.955711i	$-0.595089\pi$
$281$	−9.86698	−0.588614	−0.294307	+	0.955711i	$0.595089\pi$
$282$	17.3214	1.03147
$283$	15.5724	0.925683	0.462842	−	0.886441i	$-0.346830\pi$
$283$	15.5724	0.925683	0.462842	+	0.886441i	$0.346830\pi$
$284$	10.8218	0.642153
$285$	58.8507	3.48602
$286$	−8.62125	−0.509785
$287$	8.24298	0.486567
$288$	3.74100	0.220440
$289$	8.11270	0.477218
$290$	17.8919	1.05065
$291$	1.85481	0.108731
$292$	2.14894	0.125757
$293$	6.10995	0.356947	0.178474	−	0.983945i	$-0.442884\pi$
$293$	6.10995	0.356947	0.178474	+	0.983945i	$0.442884\pi$
$294$	9.62518	0.561352
$295$	−36.3499	−2.11638
$296$	0.201937	0.0117373
$297$	−7.18824	−0.417104
$298$	−18.6279	−1.07909
$299$	17.0497	0.986011
$300$	−7.35978	−0.424917
$301$	10.3796	0.598270
$302$	−9.68586	−0.557358
$303$	14.5551	0.836167
$304$	8.09803	0.464454
$305$	−16.7833	−0.961007
$306$	18.7471	1.07170
$307$	3.61652	0.206406	0.103203	−	0.994660i	$-0.467091\pi$
$307$	3.61652	0.206406	0.103203	+	0.994660i	$0.467091\pi$
$308$	6.77995	0.386324
$309$	−47.6374	−2.71000
$310$	21.0437	1.19520
$311$	30.0397	1.70340	0.851698	−	0.524033i	$-0.175573\pi$
$311$	30.0397	1.70340	0.851698	+	0.524033i	$0.175573\pi$
$312$	5.99084	0.339165
$313$	−4.83636	−0.273367	−0.136684	−	0.990615i	$-0.543644\pi$
$313$	−4.83636	−0.273367	−0.136684	+	0.990615i	$0.543644\pi$
$314$	11.0835	0.625477
$315$	−19.0011	−1.07059
$316$	12.4748	0.701765
$317$	5.25987	0.295424	0.147712	−	0.989030i	$-0.452809\pi$
$317$	5.25987	0.295424	0.147712	+	0.989030i	$0.452809\pi$
$318$	21.1263	1.18470
$319$	−23.8831	−1.33720
$320$	−2.79905	−0.156472
$321$	22.3571	1.24785
$322$	−13.4083	−0.747215
$323$	40.5813	2.25800
$324$	−6.22794	−0.345996
$325$	−6.54077	−0.362817
$326$	17.7999	0.985847
$327$	−41.8975	−2.31693
$328$	4.54257	0.250822
$329$	−12.1061	−0.667429
$330$	27.1530	1.49472
$331$	7.85381	0.431685	0.215842	−	0.976428i	$-0.430750\pi$
$331$	7.85381	0.431685	0.215842	+	0.976428i	$0.430750\pi$
$332$	8.15019	0.447300
$333$	0.755444	0.0413981
$334$	−15.4874	−0.847435
$335$	31.2811	1.70907
$336$	−4.71134	−0.257025
$337$	35.5945	1.93896	0.969478	−	0.245179i	$-0.0788468\pi$
$337$	35.5945	1.93896	0.969478	+	0.245179i	$0.0788468\pi$
$338$	−7.67584	−0.417510
$339$	8.43888	0.458337
$340$	−14.0268	−0.760708
$341$	−28.0904	−1.52118
$342$	30.2947	1.63815
$343$	−19.4294	−1.04909
$344$	5.72003	0.308404
$345$	−53.6987	−2.89104
$346$	11.8491	0.637013
$347$	−3.55494	−0.190839	−0.0954195	−	0.995437i	$-0.530419\pi$
$347$	−3.55494	−0.190839	−0.0954195	+	0.995437i	$0.530419\pi$
$348$	16.5962	0.889648
$349$	−14.5467	−0.778669	−0.389334	−	0.921096i	$-0.627295\pi$
$349$	−14.5467	−0.778669	−0.389334	+	0.921096i	$0.627295\pi$
$350$	5.14381	0.274948
$351$	4.43919	0.236946
$352$	3.73633	0.199147
$353$	15.8453	0.843360	0.421680	−	0.906745i	$-0.361441\pi$
$353$	15.8453	0.843360	0.421680	+	0.906745i	$0.361441\pi$
$354$	−33.7175	−1.79206
$355$	−30.2906	−1.60766
$356$	1.40180	0.0742955
$357$	−23.6097	−1.24956
$358$	18.8961	0.998691
$359$	−10.6745	−0.563380	−0.281690	−	0.959505i	$-0.590895\pi$
$359$	−10.6745	−0.563380	−0.281690	+	0.959505i	$0.590895\pi$
$360$	−10.4712	−0.551882
$361$	46.5780	2.45148
$362$	19.7139	1.03614
$363$	−7.68550	−0.403384
$364$	−4.18705	−0.219461
$365$	−6.01498	−0.314838
$366$	−15.5678	−0.813743
$367$	18.2218	0.951169	0.475584	−	0.879670i	$-0.342237\pi$
$367$	18.2218	0.951169	0.475584	+	0.879670i	$0.342237\pi$
$368$	−7.38910	−0.385183
$369$	16.9937	0.884659
$370$	−0.565230	−0.0293849
$371$	−14.7653	−0.766578
$372$	19.5198	1.01205
$373$	10.5185	0.544625	0.272312	−	0.962209i	$-0.412212\pi$
$373$	10.5185	0.544625	0.272312	+	0.962209i	$0.412212\pi$
$374$	18.7237	0.968179
$375$	−15.7361	−0.812606
$376$	−6.67146	−0.344054
$377$	14.7493	0.759627
$378$	−3.49108	−0.179562
$379$	21.7891	1.11923	0.559614	−	0.828753i	$-0.310949\pi$
$379$	21.7891	1.11923	0.559614	+	0.828753i	$0.310949\pi$
$380$	−22.6668	−1.16278
$381$	−7.94258	−0.406911
$382$	2.81685	0.144123
$383$	−20.7204	−1.05876	−0.529381	−	0.848384i	$-0.677576\pi$
$383$	−20.7204	−1.05876	−0.529381	+	0.848384i	$0.677576\pi$
$384$	−2.59634	−0.132494
$385$	−18.9774	−0.967179
$386$	2.38607	0.121448
$387$	21.3986	1.08775
$388$	−0.714395	−0.0362679
$389$	11.3569	0.575816	0.287908	−	0.957658i	$-0.407040\pi$
$389$	11.3569	0.575816	0.287908	+	0.957658i	$0.407040\pi$
$390$	−16.7687	−0.849114
$391$	−37.0287	−1.87262
$392$	−3.70721	−0.187242
$393$	−25.9681	−1.30992
$394$	2.28133	0.114932
$395$	−34.9177	−1.75690
$396$	13.9776	0.702400
$397$	−11.6878	−0.586593	−0.293296	−	0.956022i	$-0.594752\pi$
$397$	−11.6878	−0.586593	−0.293296	+	0.956022i	$0.594752\pi$
$398$	5.50846	0.276114
$399$	−38.1525	−1.91002
$400$	2.83467	0.141734
$401$	30.2649	1.51135	0.755677	−	0.654944i	$-0.227308\pi$
$401$	30.2649	1.51135	0.755677	+	0.654944i	$0.227308\pi$
$402$	29.0157	1.44717
$403$	17.3476	0.864143
$404$	−5.60599	−0.278908
$405$	17.4323	0.866218
$406$	−11.5992	−0.575658
$407$	0.754501	0.0373992
$408$	−13.0109	−0.644138
$409$	−19.3460	−0.956597	−0.478299	−	0.878197i	$-0.658746\pi$
$409$	−19.3460	−0.956597	−0.478299	+	0.878197i	$0.658746\pi$
$410$	−12.7149	−0.627943
$411$	−22.9624	−1.13265
$412$	18.3479	0.903936
$413$	23.5654	1.15958
$414$	−27.6426	−1.35856
$415$	−22.8128	−1.11983
$416$	−2.30742	−0.113130
$417$	−7.73114	−0.378596
$418$	30.2569	1.47991
$419$	−0.160620	−0.00784679	−0.00392339	−	0.999992i	$-0.501249\pi$
$419$	−0.160620	−0.00784679	−0.00392339	+	0.999992i	$0.501249\pi$
$420$	13.1873	0.643472
$421$	23.3447	1.13775	0.568876	−	0.822423i	$-0.307378\pi$
$421$	23.3447	1.13775	0.568876	+	0.822423i	$0.307378\pi$
$422$	−11.7839	−0.573633
$423$	−24.9579	−1.21349
$424$	−8.13695	−0.395165
$425$	14.2053	0.689057
$426$	−28.0970	−1.36130
$427$	10.8805	0.526543
$428$	−8.61101	−0.416229
$429$	22.3837	1.08070
$430$	−16.0107	−0.772102
$431$	−18.3971	−0.886157	−0.443079	−	0.896483i	$-0.646114\pi$
$431$	−18.3971	−0.886157	−0.443079	+	0.896483i	$0.646114\pi$
$432$	−1.92388	−0.0925627
$433$	35.9253	1.72646	0.863229	−	0.504813i	$-0.168438\pi$
$433$	35.9253	1.72646	0.863229	+	0.504813i	$0.168438\pi$
$434$	−13.6425	−0.654862
$435$	−46.4535	−2.22727
$436$	16.1371	0.772827
$437$	−59.8371	−2.86240
$438$	−5.57937	−0.266593
$439$	6.02526	0.287570	0.143785	−	0.989609i	$-0.454073\pi$
$439$	6.02526	0.287570	0.143785	+	0.989609i	$0.454073\pi$
$440$	−10.4582	−0.498573
$441$	−13.8687	−0.660412
$442$	−11.5631	−0.549998
$443$	−25.0509	−1.19020	−0.595101	−	0.803651i	$-0.702888\pi$
$443$	−25.0509	−1.19020	−0.595101	+	0.803651i	$0.702888\pi$
$444$	−0.524297	−0.0248820
$445$	−3.92372	−0.186002
$446$	−25.7948	−1.22142
$447$	48.3644	2.28756
$448$	1.81461	0.0857320
$449$	17.5393	0.827731	0.413866	−	0.910338i	$-0.364178\pi$
$449$	17.5393	0.827731	0.413866	+	0.910338i	$0.364178\pi$
$450$	10.6045	0.499901
$451$	16.9725	0.799205
$452$	−3.25029	−0.152881
$453$	25.1478	1.18155
$454$	−5.89354	−0.276598
$455$	11.7197	0.549430
$456$	−21.0253	−0.984598
$457$	7.55158	0.353248	0.176624	−	0.984278i	$-0.443482\pi$
$457$	7.55158	0.353248	0.176624	+	0.984278i	$0.443482\pi$
$458$	9.92639	0.463830
$459$	−9.64106	−0.450006
$460$	20.6825	0.964324
$461$	23.5472	1.09670	0.548351	−	0.836248i	$-0.315256\pi$
$461$	23.5472	1.09670	0.548351	+	0.836248i	$0.315256\pi$
$462$	−17.6031	−0.818970
$463$	22.0830	1.02628	0.513142	−	0.858303i	$-0.328481\pi$
$463$	22.0830	1.02628	0.513142	+	0.858303i	$0.328481\pi$
$464$	−6.39213	−0.296747
$465$	−54.6368	−2.53372
$466$	4.76540	0.220753
$467$	−17.9243	−0.829437	−0.414719	−	0.909950i	$-0.636120\pi$
$467$	−17.9243	−0.829437	−0.414719	+	0.909950i	$0.636120\pi$
$468$	−8.63203	−0.399016
$469$	−20.2793	−0.936412
$470$	18.6737	0.861355
$471$	−28.7765	−1.32595
$472$	12.9865	0.597754
$473$	21.3719	0.982681
$474$	−32.3890	−1.48767
$475$	22.9553	1.05326
$476$	9.09345	0.416798
$477$	−30.4403	−1.39376
$478$	−20.1082	−0.919730
$479$	1.78123	0.0813865	0.0406933	−	0.999172i	$-0.487043\pi$
$479$	1.78123	0.0813865	0.0406933	+	0.999172i	$0.487043\pi$
$480$	7.26729	0.331705
$481$	−0.465952	−0.0212456
$482$	26.0099	1.18472
$483$	34.8125	1.58403
$484$	2.96012	0.134551
$485$	1.99963	0.0907984
$486$	21.9415	0.995287
$487$	−7.91140	−0.358500	−0.179250	−	0.983804i	$-0.557367\pi$
$487$	−7.91140	−0.358500	−0.179250	+	0.983804i	$0.557367\pi$
$488$	5.99606	0.271429
$489$	−46.2147	−2.08990
$490$	10.3767	0.468770
$491$	−16.6083	−0.749520	−0.374760	−	0.927122i	$-0.622275\pi$
$491$	−16.6083	−0.749520	−0.374760	+	0.927122i	$0.622275\pi$
$492$	−11.7941	−0.531718
$493$	−32.0326	−1.44268
$494$	−18.6855	−0.840701
$495$	−39.1239	−1.75849
$496$	−7.51818	−0.337576
$497$	19.6372	0.880850
$498$	−21.1607	−0.948233
$499$	−15.9285	−0.713056	−0.356528	−	0.934285i	$-0.616040\pi$
$499$	−15.9285	−0.713056	−0.356528	+	0.934285i	$0.616040\pi$
$500$	6.06085	0.271050
$501$	40.2107	1.79648
$502$	−0.843188	−0.0376333
$503$	10.2612	0.457522	0.228761	−	0.973483i	$-0.426533\pi$
$503$	10.2612	0.457522	0.228761	+	0.973483i	$0.426533\pi$
$504$	6.78843	0.302381
$505$	15.6914	0.698260
$506$	−27.6081	−1.22733
$507$	19.9291	0.885082
$508$	3.05914	0.135728
$509$	2.45716	0.108912	0.0544559	−	0.998516i	$-0.482658\pi$
$509$	2.45716	0.108912	0.0544559	+	0.998516i	$0.482658\pi$
$510$	36.4183	1.61263
$511$	3.89947	0.172502
$512$	1.00000	0.0441942
$513$	−15.5796	−0.687858
$514$	−6.69460	−0.295286
$515$	−51.3567	−2.26304
$516$	−14.8512	−0.653786
$517$	−24.9267	−1.09628
$518$	0.366435	0.0161002
$519$	−30.7644	−1.35041
$520$	6.45857	0.283227
$521$	−3.29420	−0.144322	−0.0721608	−	0.997393i	$-0.522989\pi$
$521$	−3.29420	−0.144322	−0.0721608	+	0.997393i	$0.522989\pi$
$522$	−23.9129	−1.04664
$523$	−3.01703	−0.131926	−0.0659628	−	0.997822i	$-0.521012\pi$
$523$	−3.01703	−0.131926	−0.0659628	+	0.997822i	$0.521012\pi$
$524$	10.0018	0.436931
$525$	−13.3551	−0.582864
$526$	1.56168	0.0680924
$527$	−37.6755	−1.64117
$528$	−9.70078	−0.422172
$529$	31.5988	1.37386
$530$	22.7757	0.989313
$531$	48.5826	2.10830
$532$	14.6947	0.637097
$533$	−10.4816	−0.454008
$534$	−3.63956	−0.157499
$535$	24.1026	1.04205
$536$	−11.1756	−0.482713
$537$	−49.0608	−2.11713
$538$	20.3991	0.879469
$539$	−13.8513	−0.596619
$540$	5.38503	0.231735
$541$	31.2687	1.34434	0.672172	−	0.740395i	$-0.265361\pi$
$541$	31.2687	1.34434	0.672172	+	0.740395i	$0.265361\pi$
$542$	−8.75555	−0.376083
$543$	−51.1841	−2.19652
$544$	5.01126	0.214856
$545$	−45.1685	−1.93481
$546$	10.8710	0.465236
$547$	13.6270	0.582650	0.291325	−	0.956624i	$-0.405904\pi$
$547$	13.6270	0.582650	0.291325	+	0.956624i	$0.405904\pi$
$548$	8.84414	0.377803
$549$	22.4312	0.957342
$550$	10.5913	0.451613
$551$	−51.7636	−2.20521
$552$	19.1846	0.816552
$553$	22.6369	0.962620
$554$	−4.81514	−0.204576
$555$	1.46753	0.0622933
$556$	2.97770	0.126283
$557$	22.0573	0.934599	0.467299	−	0.884099i	$-0.345227\pi$
$557$	22.0573	0.934599	0.467299	+	0.884099i	$0.345227\pi$
$558$	−28.1255	−1.19065
$559$	−13.1985	−0.558237
$560$	−5.07917	−0.214634
$561$	−48.6131	−2.05245
$562$	−9.86698	−0.416213
$563$	10.3023	0.434191	0.217095	−	0.976150i	$-0.430342\pi$
$563$	10.3023	0.434191	0.217095	+	0.976150i	$0.430342\pi$
$564$	17.3214	0.729362
$565$	9.09773	0.382744
$566$	15.5724	0.654557
$567$	−11.3012	−0.474608
$568$	10.8218	0.454071
$569$	32.0750	1.34465	0.672326	−	0.740255i	$-0.265295\pi$
$569$	32.0750	1.34465	0.672326	+	0.740255i	$0.265295\pi$
$570$	58.8507	2.46499
$571$	−33.4574	−1.40015	−0.700075	−	0.714070i	$-0.746850\pi$
$571$	−33.4574	−1.40015	−0.700075	+	0.714070i	$0.746850\pi$
$572$	−8.62125	−0.360473
$573$	−7.31350	−0.305526
$574$	8.24298	0.344055
$575$	−20.9457	−0.873495
$576$	3.74100	0.155875
$577$	−28.4013	−1.18236	−0.591182	−	0.806538i	$-0.701338\pi$
$577$	−28.4013	−1.18236	−0.591182	+	0.806538i	$0.701338\pi$
$578$	8.11270	0.337444
$579$	−6.19507	−0.257458
$580$	17.8919	0.742920
$581$	14.7894	0.613567
$582$	1.85481	0.0768845
$583$	−30.4023	−1.25913
$584$	2.14894	0.0889236
$585$	24.1615	0.998954
$586$	6.10995	0.252400
$587$	−17.2172	−0.710628	−0.355314	−	0.934747i	$-0.615626\pi$
$587$	−17.2172	−0.710628	−0.355314	+	0.934747i	$0.615626\pi$
$588$	9.62518	0.396936
$589$	−60.8824	−2.50862
$590$	−36.3499	−1.49650
$591$	−5.92310	−0.243644
$592$	0.201937	0.00829955
$593$	−17.8587	−0.733370	−0.366685	−	0.930345i	$-0.619507\pi$
$593$	−17.8587	−0.733370	−0.366685	+	0.930345i	$0.619507\pi$
$594$	−7.18824	−0.294937
$595$	−25.4530	−1.04347
$596$	−18.6279	−0.763029
$597$	−14.3018	−0.585335
$598$	17.0497	0.697215
$599$	−18.4898	−0.755471	−0.377736	−	0.925913i	$-0.623297\pi$
$599$	−18.4898	−0.755471	−0.377736	+	0.925913i	$0.623297\pi$
$600$	−7.35978	−0.300462
$601$	−42.8072	−1.74614	−0.873071	−	0.487593i	$-0.837875\pi$
$601$	−42.8072	−1.74614	−0.873071	+	0.487593i	$0.837875\pi$
$602$	10.3796	0.423041
$603$	−41.8079	−1.70255
$604$	−9.68586	−0.394112
$605$	−8.28553	−0.336855
$606$	14.5551	0.591259
$607$	−1.14822	−0.0466050	−0.0233025	−	0.999728i	$-0.507418\pi$
$607$	−1.14822	−0.0466050	−0.0233025	+	0.999728i	$0.507418\pi$
$608$	8.09803	0.328418
$609$	30.1155	1.22034
$610$	−16.7833	−0.679534
$611$	15.3938	0.622767
$612$	18.7471	0.757806
$613$	2.43867	0.0984968	0.0492484	−	0.998787i	$-0.484317\pi$
$613$	2.43867	0.0984968	0.0492484	+	0.998787i	$0.484317\pi$
$614$	3.61652	0.145951
$615$	33.0122	1.33118
$616$	6.77995	0.273172
$617$	−46.9897	−1.89173	−0.945867	−	0.324555i	$-0.894785\pi$
$617$	−46.9897	−1.89173	−0.945867	+	0.324555i	$0.894785\pi$
$618$	−47.6374	−1.91626
$619$	41.2650	1.65858	0.829291	−	0.558817i	$-0.188745\pi$
$619$	41.2650	1.65858	0.829291	+	0.558817i	$0.188745\pi$
$620$	21.0437	0.845137
$621$	14.2157	0.570458
$622$	30.0397	1.20448
$623$	2.54372	0.101912
$624$	5.99084	0.239826
$625$	−31.1380	−1.24552
$626$	−4.83636	−0.193300
$627$	−78.5572	−3.13727
$628$	11.0835	0.442279
$629$	1.01196	0.0403494
$630$	−19.0011	−0.757024
$631$	−34.1921	−1.36116	−0.680582	−	0.732671i	$-0.738273\pi$
$631$	−34.1921	−1.36116	−0.680582	+	0.732671i	$0.738273\pi$
$632$	12.4748	0.496223
$633$	30.5952	1.21605
$634$	5.25987	0.208896
$635$	−8.56269	−0.339800
$636$	21.1263	0.837712
$637$	8.55407	0.338925
$638$	−23.8831	−0.945540
$639$	40.4842	1.60153
$640$	−2.79905	−0.110642
$641$	−48.9695	−1.93418	−0.967090	−	0.254436i	$-0.918110\pi$
$641$	−48.9695	−1.93418	−0.967090	+	0.254436i	$0.918110\pi$
$642$	22.3571	0.882365
$643$	6.23411	0.245849	0.122925	−	0.992416i	$-0.460773\pi$
$643$	6.23411	0.245849	0.122925	+	0.992416i	$0.460773\pi$
$644$	−13.4083	−0.528361
$645$	41.5691	1.63678
$646$	40.5813	1.59665
$647$	−41.3964	−1.62746	−0.813731	−	0.581242i	$-0.802567\pi$
$647$	−41.3964	−1.62746	−0.813731	+	0.581242i	$0.802567\pi$
$648$	−6.22794	−0.244656
$649$	48.5219	1.90465
$650$	−6.54077	−0.256550
$651$	35.4207	1.38825
$652$	17.7999	0.697099
$653$	41.3329	1.61748	0.808741	−	0.588166i	$-0.200150\pi$
$653$	41.3329	1.61748	0.808741	+	0.588166i	$0.200150\pi$
$654$	−41.8975	−1.63832
$655$	−27.9955	−1.09388
$656$	4.54257	0.177358
$657$	8.03916	0.313637
$658$	−12.1061	−0.471943
$659$	−17.8082	−0.693707	−0.346854	−	0.937919i	$-0.612750\pi$
$659$	−17.8082	−0.693707	−0.346854	+	0.937919i	$0.612750\pi$
$660$	27.1530	1.05693
$661$	36.8165	1.43200	0.715999	−	0.698101i	$-0.245972\pi$
$661$	36.8165	1.43200	0.715999	+	0.698101i	$0.245972\pi$
$662$	7.85381	0.305247
$663$	30.0216	1.16594
$664$	8.15019	0.316289
$665$	−41.1312	−1.59500
$666$	0.755444	0.0292729
$667$	47.2321	1.82883
$668$	−15.4874	−0.599227
$669$	66.9721	2.58929
$670$	31.2811	1.20849
$671$	22.4032	0.864867
$672$	−4.71134	−0.181744
$673$	25.2726	0.974188	0.487094	−	0.873350i	$-0.338057\pi$
$673$	25.2726	0.974188	0.487094	+	0.873350i	$0.338057\pi$
$674$	35.5945	1.37105
$675$	−5.45357	−0.209908
$676$	−7.67584	−0.295224
$677$	−28.0981	−1.07990	−0.539949	−	0.841698i	$-0.681556\pi$
$677$	−28.0981	−1.07990	−0.539949	+	0.841698i	$0.681556\pi$
$678$	8.43888	0.324093
$679$	−1.29634	−0.0497491
$680$	−14.0268	−0.537901
$681$	15.3016	0.586360
$682$	−28.0904	−1.07564
$683$	17.1968	0.658017	0.329008	−	0.944327i	$-0.393286\pi$
$683$	17.1968	0.658017	0.329008	+	0.944327i	$0.393286\pi$
$684$	30.2947	1.15835
$685$	−24.7552	−0.945846
$686$	−19.4294	−0.741816
$687$	−25.7723	−0.983275
$688$	5.72003	0.218074
$689$	18.7753	0.715282
$690$	−53.6987	−2.04428
$691$	−8.36409	−0.318185	−0.159092	−	0.987264i	$-0.550857\pi$
$691$	−8.36409	−0.318185	−0.159092	+	0.987264i	$0.550857\pi$
$692$	11.8491	0.450436
$693$	25.3638	0.963490
$694$	−3.55494	−0.134944
$695$	−8.33474	−0.316155
$696$	16.5962	0.629076
$697$	22.7640	0.862248
$698$	−14.5467	−0.550602
$699$	−12.3726	−0.467976
$700$	5.14381	0.194418
$701$	−37.4475	−1.41437	−0.707187	−	0.707027i	$-0.750036\pi$
$701$	−37.4475	−1.41437	−0.707187	+	0.707027i	$0.750036\pi$
$702$	4.43919	0.167546
$703$	1.63529	0.0616761
$704$	3.73633	0.140818
$705$	−48.4834	−1.82599
$706$	15.8453	0.596345
$707$	−10.1727	−0.382582
$708$	−33.7175	−1.26718
$709$	40.2774	1.51265	0.756324	−	0.654197i	$-0.226993\pi$
$709$	40.2774	1.51265	0.756324	+	0.654197i	$0.226993\pi$
$710$	−30.2906	−1.13679
$711$	46.6683	1.75020
$712$	1.40180	0.0525348
$713$	55.5526	2.08046
$714$	−23.6097	−0.883572
$715$	24.1313	0.902460
$716$	18.8961	0.706181
$717$	52.2079	1.94974
$718$	−10.6745	−0.398370
$719$	−12.2314	−0.456155	−0.228077	−	0.973643i	$-0.573244\pi$
$719$	−12.2314	−0.456155	−0.228077	+	0.973643i	$0.573244\pi$
$720$	−10.4712	−0.390240
$721$	33.2942	1.23994
$722$	46.5780	1.73346
$723$	−67.5307	−2.51149
$724$	19.7139	0.732661
$725$	−18.1196	−0.672945
$726$	−7.68550	−0.285236
$727$	19.4032	0.719624	0.359812	−	0.933025i	$-0.382841\pi$
$727$	19.4032	0.719624	0.359812	+	0.933025i	$0.382841\pi$
$728$	−4.18705	−0.155182
$729$	−38.2838	−1.41792
$730$	−6.01498	−0.222624
$731$	28.6646	1.06020
$732$	−15.5678	−0.575403
$733$	−3.14593	−0.116198	−0.0580988	−	0.998311i	$-0.518504\pi$
$733$	−3.14593	−0.116198	−0.0580988	+	0.998311i	$0.518504\pi$
$734$	18.2218	0.672578
$735$	−26.9414	−0.993747
$736$	−7.38910	−0.272366
$737$	−41.7557	−1.53809
$738$	16.9937	0.625548
$739$	−6.45304	−0.237379	−0.118690	−	0.992931i	$-0.537869\pi$
$739$	−6.45304	−0.237379	−0.118690	+	0.992931i	$0.537869\pi$
$740$	−0.565230	−0.0207783
$741$	48.5140	1.78221
$742$	−14.7653	−0.542053
$743$	37.2173	1.36537	0.682685	−	0.730713i	$-0.260812\pi$
$743$	37.2173	1.36537	0.682685	+	0.730713i	$0.260812\pi$
$744$	19.5198	0.715629
$745$	52.1404	1.91028
$746$	10.5185	0.385108
$747$	30.4898	1.11556
$748$	18.7237	0.684606
$749$	−15.6256	−0.570946
$750$	−15.7361	−0.574600
$751$	−28.7137	−1.04778	−0.523888	−	0.851787i	$-0.675519\pi$
$751$	−28.7137	−1.04778	−0.523888	+	0.851787i	$0.675519\pi$
$752$	−6.67146	−0.243283
$753$	2.18921	0.0797791
$754$	14.7493	0.537138
$755$	27.1112	0.986677
$756$	−3.49108	−0.126969
$757$	5.54213	0.201432	0.100716	−	0.994915i	$-0.467887\pi$
$757$	5.54213	0.201432	0.100716	+	0.994915i	$0.467887\pi$
$758$	21.7891	0.791414
$759$	71.6800	2.60182
$760$	−22.6668	−0.822210
$761$	42.3560	1.53540	0.767702	−	0.640807i	$-0.221400\pi$
$761$	42.3560	1.53540	0.767702	+	0.640807i	$0.221400\pi$
$762$	−7.94258	−0.287729
$763$	29.2825	1.06010
$764$	2.81685	0.101910
$765$	−52.4740	−1.89720
$766$	−20.7204	−0.748658
$767$	−29.9653	−1.08199
$768$	−2.59634	−0.0936875
$769$	15.1038	0.544657	0.272328	−	0.962204i	$-0.412206\pi$
$769$	15.1038	0.544657	0.272328	+	0.962204i	$0.412206\pi$
$770$	−18.9774	−0.683899
$771$	17.3815	0.625979
$772$	2.38607	0.0858767
$773$	0.217543	0.00782449	0.00391225	−	0.999992i	$-0.498755\pi$
$773$	0.217543	0.00782449	0.00391225	+	0.999992i	$0.498755\pi$
$774$	21.3986	0.769158
$775$	−21.3116	−0.765534
$776$	−0.714395	−0.0256453
$777$	−0.951392	−0.0341310
$778$	11.3569	0.407163
$779$	36.7859	1.31799
$780$	−16.7687	−0.600414
$781$	40.4336	1.44683
$782$	−37.0287	−1.32414
$783$	12.2977	0.439484
$784$	−3.70721	−0.132400
$785$	−31.0232	−1.10727
$786$	−25.9681	−0.926251
$787$	−46.9844	−1.67481	−0.837407	−	0.546580i	$-0.815930\pi$
$787$	−46.9844	−1.67481	−0.837407	+	0.546580i	$0.815930\pi$
$788$	2.28133	0.0812689
$789$	−4.05465	−0.144349
$790$	−34.9177	−1.24232
$791$	−5.89800	−0.209709
$792$	13.9776	0.496672
$793$	−13.8354	−0.491309
$794$	−11.6878	−0.414784
$795$	−59.1335	−2.09725
$796$	5.50846	0.195242
$797$	32.9004	1.16539	0.582696	−	0.812690i	$-0.301998\pi$
$797$	32.9004	1.16539	0.582696	+	0.812690i	$0.301998\pi$
$798$	−38.1525	−1.35059
$799$	−33.4324	−1.18275
$800$	2.83467	0.100221
$801$	5.24414	0.185293
$802$	30.2649	1.06869
$803$	8.02912	0.283342
$804$	29.0157	1.02331
$805$	37.5305	1.32278
$806$	17.3476	0.611042
$807$	−52.9631	−1.86439
$808$	−5.60599	−0.197218
$809$	36.9609	1.29948	0.649738	−	0.760158i	$-0.274878\pi$
$809$	36.9609	1.29948	0.649738	+	0.760158i	$0.274878\pi$
$810$	17.4323	0.612509
$811$	19.8919	0.698499	0.349249	−	0.937030i	$-0.386437\pi$
$811$	19.8919	0.698499	0.349249	+	0.937030i	$0.386437\pi$
$812$	−11.5992	−0.407052
$813$	22.7324	0.797260
$814$	0.754501	0.0264452
$815$	−49.8229	−1.74522
$816$	−13.0109	−0.455474
$817$	46.3210	1.62057
$818$	−19.3460	−0.676416
$819$	−15.6637	−0.547335
$820$	−12.7149	−0.444023
$821$	22.9557	0.801160	0.400580	−	0.916262i	$-0.368809\pi$
$821$	22.9557	0.801160	0.400580	+	0.916262i	$0.368809\pi$
$822$	−22.9624	−0.800906
$823$	−5.46848	−0.190619	−0.0953095	−	0.995448i	$-0.530384\pi$
$823$	−5.46848	−0.190619	−0.0953095	+	0.995448i	$0.530384\pi$
$824$	18.3479	0.639179
$825$	−27.4985	−0.957376
$826$	23.5654	0.819946
$827$	−46.7998	−1.62739	−0.813695	−	0.581292i	$-0.802547\pi$
$827$	−46.7998	−1.62739	−0.813695	+	0.581292i	$0.802547\pi$
$828$	−27.6426	−0.960647
$829$	−25.0318	−0.869389	−0.434695	−	0.900578i	$-0.643144\pi$
$829$	−25.0318	−0.869389	−0.434695	+	0.900578i	$0.643144\pi$
$830$	−22.8128	−0.791843
$831$	12.5018	0.433681
$832$	−2.30742	−0.0799952
$833$	−18.5778	−0.643682
$834$	−7.73114	−0.267707
$835$	43.3501	1.50019
$836$	30.2569	1.04646
$837$	14.4641	0.499951
$838$	−0.160620	−0.00554852
$839$	4.01981	0.138779	0.0693897	−	0.997590i	$-0.477895\pi$
$839$	4.01981	0.138779	0.0693897	+	0.997590i	$0.477895\pi$
$840$	13.1873	0.455004
$841$	11.8593	0.408942
$842$	23.3447	0.804512
$843$	25.6181	0.882333
$844$	−11.7839	−0.405620
$845$	21.4850	0.739108
$846$	−24.9579	−0.858070
$847$	5.37146	0.184565
$848$	−8.13695	−0.279424
$849$	−40.4313	−1.38760
$850$	14.2053	0.487237
$851$	−1.49213	−0.0511496
$852$	−28.0970	−0.962587
$853$	2.39122	0.0818739	0.0409370	−	0.999162i	$-0.486966\pi$
$853$	2.39122	0.0818739	0.0409370	+	0.999162i	$0.486966\pi$
$854$	10.8805	0.372322
$855$	−84.7963	−2.89997
$856$	−8.61101	−0.294318
$857$	−36.6836	−1.25309	−0.626545	−	0.779386i	$-0.715531\pi$
$857$	−36.6836	−1.25309	−0.626545	+	0.779386i	$0.715531\pi$
$858$	22.3837	0.764168
$859$	31.0239	1.05852	0.529261	−	0.848459i	$-0.322469\pi$
$859$	31.0239	1.05852	0.529261	+	0.848459i	$0.322469\pi$
$860$	−16.0107	−0.545959
$861$	−21.4016	−0.729364
$862$	−18.3971	−0.626608
$863$	14.1474	0.481582	0.240791	−	0.970577i	$-0.422593\pi$
$863$	14.1474	0.481582	0.240791	+	0.970577i	$0.422593\pi$
$864$	−1.92388	−0.0654517
$865$	−33.1663	−1.12769
$866$	35.9253	1.22079
$867$	−21.0634	−0.715349
$868$	−13.6425	−0.463057
$869$	46.6101	1.58114
$870$	−46.4535	−1.57492
$871$	25.7868	0.873751
$872$	16.1371	0.546471
$873$	−2.67255	−0.0904521
$874$	−59.8371	−2.02402
$875$	10.9981	0.371802
$876$	−5.57937	−0.188510
$877$	23.2864	0.786326	0.393163	−	0.919469i	$-0.371381\pi$
$877$	23.2864	0.786326	0.393163	+	0.919469i	$0.371381\pi$
$878$	6.02526	0.203343
$879$	−15.8635	−0.535064
$880$	−10.4582	−0.352544
$881$	−40.3612	−1.35980	−0.679902	−	0.733303i	$-0.737978\pi$
$881$	−40.3612	−1.35980	−0.679902	+	0.733303i	$0.737978\pi$
$882$	−13.8687	−0.466982
$883$	−33.0022	−1.11061	−0.555307	−	0.831645i	$-0.687399\pi$
$883$	−33.0022	−1.11061	−0.555307	+	0.831645i	$0.687399\pi$
$884$	−11.5631	−0.388908
$885$	94.3769	3.17245
$886$	−25.0509	−0.841600
$887$	−30.9691	−1.03984	−0.519921	−	0.854215i	$-0.674039\pi$
$887$	−30.9691	−1.03984	−0.519921	+	0.854215i	$0.674039\pi$
$888$	−0.524297	−0.0175942
$889$	5.55114	0.186179
$890$	−3.92372	−0.131523
$891$	−23.2696	−0.779561
$892$	−25.7948	−0.863673
$893$	−54.0257	−1.80790
$894$	48.3644	1.61755
$895$	−52.8912	−1.76796
$896$	1.81461	0.0606217
$897$	−44.2669	−1.47803
$898$	17.5393	0.585295
$899$	48.0572	1.60280
$900$	10.6045	0.353483
$901$	−40.7763	−1.35846
$902$	16.9725	0.565123
$903$	−26.9490	−0.896807
$904$	−3.25029	−0.108103
$905$	−55.1802	−1.83425
$906$	25.1478	0.835480
$907$	20.5672	0.682922	0.341461	−	0.939896i	$-0.389078\pi$
$907$	20.5672	0.682922	0.341461	+	0.939896i	$0.389078\pi$
$908$	−5.89354	−0.195584
$909$	−20.9720	−0.695597
$910$	11.7197	0.388506
$911$	38.0326	1.26008	0.630039	−	0.776564i	$-0.283039\pi$
$911$	38.0326	1.26008	0.630039	+	0.776564i	$0.283039\pi$
$912$	−21.0253	−0.696216
$913$	30.4518	1.00781
$914$	7.55158	0.249784
$915$	43.5751	1.44055
$916$	9.92639	0.327977
$917$	18.1493	0.599343
$918$	−9.64106	−0.318202
$919$	49.7426	1.64086	0.820428	−	0.571749i	$-0.193735\pi$
$919$	49.7426	1.64086	0.820428	+	0.571749i	$0.193735\pi$
$920$	20.6825	0.681880
$921$	−9.38972	−0.309402
$922$	23.5472	0.775485
$923$	−24.9703	−0.821907
$924$	−17.6031	−0.579099
$925$	0.572424	0.0188212
$926$	22.0830	0.725693
$927$	68.6394	2.25441
$928$	−6.39213	−0.209832
$929$	−20.5080	−0.672847	−0.336424	−	0.941711i	$-0.609217\pi$
$929$	−20.5080	−0.672847	−0.336424	+	0.941711i	$0.609217\pi$
$930$	−54.6368	−1.79161
$931$	−30.0211	−0.983901
$932$	4.76540	0.156096
$933$	−77.9934	−2.55339
$934$	−17.9243	−0.586501
$935$	−52.4085	−1.71394
$936$	−8.63203	−0.282147
$937$	−40.5348	−1.32421	−0.662107	−	0.749409i	$-0.730338\pi$
$937$	−40.5348	−1.32421	−0.662107	+	0.749409i	$0.730338\pi$
$938$	−20.2793	−0.662143
$939$	12.5568	0.409777
$940$	18.6737	0.609070
$941$	−40.1789	−1.30980	−0.654898	−	0.755718i	$-0.727288\pi$
$941$	−40.1789	−1.30980	−0.654898	+	0.755718i	$0.727288\pi$
$942$	−28.7765	−0.937590
$943$	−33.5655	−1.09304
$944$	12.9865	0.422676
$945$	9.77171	0.317874
$946$	21.3719	0.694861
$947$	48.5772	1.57855	0.789273	−	0.614042i	$-0.210458\pi$
$947$	48.5772	1.57855	0.789273	+	0.614042i	$0.210458\pi$
$948$	−32.3890	−1.05194
$949$	−4.95849	−0.160959
$950$	22.9553	0.744767
$951$	−13.6564	−0.442840
$952$	9.09345	0.294721
$953$	−21.1309	−0.684498	−0.342249	−	0.939609i	$-0.611189\pi$
$953$	−21.1309	−0.684498	−0.342249	+	0.939609i	$0.611189\pi$
$954$	−30.4403	−0.985540
$955$	−7.88450	−0.255136
$956$	−20.1082	−0.650347
$957$	62.0086	2.00445
$958$	1.78123	0.0575490
$959$	16.0486	0.518237
$960$	7.26729	0.234551
$961$	25.5230	0.823322
$962$	−0.465952	−0.0150229
$963$	−32.2137	−1.03807
$964$	26.0099	0.837723
$965$	−6.67874	−0.214996
$966$	34.8125	1.12008
$967$	−23.8068	−0.765574	−0.382787	−	0.923837i	$-0.625036\pi$
$967$	−23.8068	−0.765574	−0.382787	+	0.923837i	$0.625036\pi$
$968$	2.96012	0.0951420
$969$	−105.363	−3.38475
$970$	1.99963	0.0642041
$971$	−31.5328	−1.01194	−0.505968	−	0.862553i	$-0.668864\pi$
$971$	−31.5328	−1.01194	−0.505968	+	0.862553i	$0.668864\pi$
$972$	21.9415	0.703774
$973$	5.40336	0.173224
$974$	−7.91140	−0.253498
$975$	16.9821	0.543862
$976$	5.99606	0.191929
$977$	−61.2465	−1.95945	−0.979725	−	0.200348i	$-0.935793\pi$
$977$	−61.2465	−1.95945	−0.979725	+	0.200348i	$0.935793\pi$
$978$	−46.2147	−1.47778
$979$	5.23760	0.167394
$980$	10.3767	0.331470
$981$	60.3688	1.92743
$982$	−16.6083	−0.529991
$983$	27.9383	0.891094	0.445547	−	0.895259i	$-0.353009\pi$
$983$	27.9383	0.891094	0.445547	+	0.895259i	$0.353009\pi$
$984$	−11.7941	−0.375981
$985$	−6.38554	−0.203460
$986$	−32.0326	−1.02013
$987$	31.4315	1.00048
$988$	−18.6855	−0.594465
$989$	−42.2659	−1.34398
$990$	−39.1239	−1.24344
$991$	16.1529	0.513114	0.256557	−	0.966529i	$-0.417412\pi$
$991$	16.1529	0.513114	0.256557	+	0.966529i	$0.417412\pi$
$992$	−7.51818	−0.238702
$993$	−20.3912	−0.647095
$994$	19.6372	0.622855
$995$	−15.4184	−0.488797
$996$	−21.1607	−0.670502
$997$	61.0563	1.93367	0.966837	−	0.255395i	$-0.0822054\pi$
$997$	61.0563	1.93367	0.966837	+	0.255395i	$0.0822054\pi$
$998$	−15.9285	−0.504207
$999$	−0.388502	−0.0122917

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.5	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.5	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.59634 q^{3} +1.00000 q^{4} -2.79905 q^{5} -2.59634 q^{6} +1.81461 q^{7} +1.00000 q^{8} +3.74100 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.59634 q^{3} +1.00000 q^{4} -2.79905 q^{5} -2.59634 q^{6} +1.81461 q^{7} +1.00000 q^{8} +3.74100 q^{9} -2.79905 q^{10} +3.73633 q^{11} -2.59634 q^{12} -2.30742 q^{13} +1.81461 q^{14} +7.26729 q^{15} +1.00000 q^{16} +5.01126 q^{17} +3.74100 q^{18} +8.09803 q^{19} -2.79905 q^{20} -4.71134 q^{21} +3.73633 q^{22} -7.38910 q^{23} -2.59634 q^{24} +2.83467 q^{25} -2.30742 q^{26} -1.92388 q^{27} +1.81461 q^{28} -6.39213 q^{29} +7.26729 q^{30} -7.51818 q^{31} +1.00000 q^{32} -9.70078 q^{33} +5.01126 q^{34} -5.07917 q^{35} +3.74100 q^{36} +0.201937 q^{37} +8.09803 q^{38} +5.99084 q^{39} -2.79905 q^{40} +4.54257 q^{41} -4.71134 q^{42} +5.72003 q^{43} +3.73633 q^{44} -10.4712 q^{45} -7.38910 q^{46} -6.67146 q^{47} -2.59634 q^{48} -3.70721 q^{49} +2.83467 q^{50} -13.0109 q^{51} -2.30742 q^{52} -8.13695 q^{53} -1.92388 q^{54} -10.4582 q^{55} +1.81461 q^{56} -21.0253 q^{57} -6.39213 q^{58} +12.9865 q^{59} +7.26729 q^{60} +5.99606 q^{61} -7.51818 q^{62} +6.78843 q^{63} +1.00000 q^{64} +6.45857 q^{65} -9.70078 q^{66} -11.1756 q^{67} +5.01126 q^{68} +19.1846 q^{69} -5.07917 q^{70} +10.8218 q^{71} +3.74100 q^{72} +2.14894 q^{73} +0.201937 q^{74} -7.35978 q^{75} +8.09803 q^{76} +6.77995 q^{77} +5.99084 q^{78} +12.4748 q^{79} -2.79905 q^{80} -6.22794 q^{81} +4.54257 q^{82} +8.15019 q^{83} -4.71134 q^{84} -14.0268 q^{85} +5.72003 q^{86} +16.5962 q^{87} +3.73633 q^{88} +1.40180 q^{89} -10.4712 q^{90} -4.18705 q^{91} -7.38910 q^{92} +19.5198 q^{93} -6.67146 q^{94} -22.6668 q^{95} -2.59634 q^{96} -0.714395 q^{97} -3.70721 q^{98} +13.9776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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