LMFDB - Embedded newform 6010.2.a.h.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.503837 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.503837 q^{6} -4.37336 q^{7} +1.00000 q^{8} -2.74615 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.503837 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.503837 q^{6} -4.37336 q^{7} +1.00000 q^{8} -2.74615 q^{9} -1.00000 q^{10} -4.14877 q^{11} -0.503837 q^{12} +4.25115 q^{13} -4.37336 q^{14} +0.503837 q^{15} +1.00000 q^{16} -1.89488 q^{17} -2.74615 q^{18} -3.65123 q^{19} -1.00000 q^{20} +2.20346 q^{21} -4.14877 q^{22} -3.31519 q^{23} -0.503837 q^{24} +1.00000 q^{25} +4.25115 q^{26} +2.89512 q^{27} -4.37336 q^{28} -3.21629 q^{29} +0.503837 q^{30} -0.405515 q^{31} +1.00000 q^{32} +2.09030 q^{33} -1.89488 q^{34} +4.37336 q^{35} -2.74615 q^{36} -3.77489 q^{37} -3.65123 q^{38} -2.14188 q^{39} -1.00000 q^{40} +3.67235 q^{41} +2.20346 q^{42} -1.67508 q^{43} -4.14877 q^{44} +2.74615 q^{45} -3.31519 q^{46} -2.95950 q^{47} -0.503837 q^{48} +12.1263 q^{49} +1.00000 q^{50} +0.954708 q^{51} +4.25115 q^{52} +2.50135 q^{53} +2.89512 q^{54} +4.14877 q^{55} -4.37336 q^{56} +1.83962 q^{57} -3.21629 q^{58} +4.43851 q^{59} +0.503837 q^{60} +12.4966 q^{61} -0.405515 q^{62} +12.0099 q^{63} +1.00000 q^{64} -4.25115 q^{65} +2.09030 q^{66} +2.79669 q^{67} -1.89488 q^{68} +1.67031 q^{69} +4.37336 q^{70} +13.9850 q^{71} -2.74615 q^{72} +9.53108 q^{73} -3.77489 q^{74} -0.503837 q^{75} -3.65123 q^{76} +18.1440 q^{77} -2.14188 q^{78} -15.9642 q^{79} -1.00000 q^{80} +6.77978 q^{81} +3.67235 q^{82} -13.8499 q^{83} +2.20346 q^{84} +1.89488 q^{85} -1.67508 q^{86} +1.62049 q^{87} -4.14877 q^{88} -14.1083 q^{89} +2.74615 q^{90} -18.5918 q^{91} -3.31519 q^{92} +0.204313 q^{93} -2.95950 q^{94} +3.65123 q^{95} -0.503837 q^{96} -14.0299 q^{97} +12.1263 q^{98} +11.3931 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.503837	−0.290890	−0.145445	−	0.989366i	$-0.546461\pi$
$3$	−0.503837	−0.290890	−0.145445	+	0.989366i	$0.546461\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.503837	−0.205691
$7$	−4.37336	−1.65297	−0.826487	−	0.562956i	$-0.809664\pi$
$7$	−4.37336	−1.65297	−0.826487	+	0.562956i	$0.809664\pi$
$8$	1.00000	0.353553
$9$	−2.74615	−0.915383
$10$	−1.00000	−0.316228
$11$	−4.14877	−1.25090	−0.625450	−	0.780264i	$-0.715085\pi$
$11$	−4.14877	−1.25090	−0.625450	+	0.780264i	$0.715085\pi$
$12$	−0.503837	−0.145445
$13$	4.25115	1.17906	0.589528	−	0.807748i	$-0.299314\pi$
$13$	4.25115	1.17906	0.589528	+	0.807748i	$0.299314\pi$
$14$	−4.37336	−1.16883
$15$	0.503837	0.130090
$16$	1.00000	0.250000
$17$	−1.89488	−0.459575	−0.229787	−	0.973241i	$-0.573803\pi$
$17$	−1.89488	−0.459575	−0.229787	+	0.973241i	$0.573803\pi$
$18$	−2.74615	−0.647273
$19$	−3.65123	−0.837650	−0.418825	−	0.908067i	$-0.637558\pi$
$19$	−3.65123	−0.837650	−0.418825	+	0.908067i	$0.637558\pi$
$20$	−1.00000	−0.223607
$21$	2.20346	0.480834
$22$	−4.14877	−0.884520
$23$	−3.31519	−0.691264	−0.345632	−	0.938370i	$-0.612335\pi$
$23$	−3.31519	−0.691264	−0.345632	+	0.938370i	$0.612335\pi$
$24$	−0.503837	−0.102845
$25$	1.00000	0.200000
$26$	4.25115	0.833719
$27$	2.89512	0.557166
$28$	−4.37336	−0.826487
$29$	−3.21629	−0.597250	−0.298625	−	0.954371i	$-0.596528\pi$
$29$	−3.21629	−0.597250	−0.298625	+	0.954371i	$0.596528\pi$
$30$	0.503837	0.0919876
$31$	−0.405515	−0.0728326	−0.0364163	−	0.999337i	$-0.511594\pi$
$31$	−0.405515	−0.0728326	−0.0364163	+	0.999337i	$0.511594\pi$
$32$	1.00000	0.176777
$33$	2.09030	0.363875
$34$	−1.89488	−0.324969
$35$	4.37336	0.739232
$36$	−2.74615	−0.457691
$37$	−3.77489	−0.620588	−0.310294	−	0.950641i	$-0.600428\pi$
$37$	−3.77489	−0.620588	−0.310294	+	0.950641i	$0.600428\pi$
$38$	−3.65123	−0.592308
$39$	−2.14188	−0.342976
$40$	−1.00000	−0.158114
$41$	3.67235	0.573525	0.286762	−	0.958002i	$-0.407421\pi$
$41$	3.67235	0.573525	0.286762	+	0.958002i	$0.407421\pi$
$42$	2.20346	0.340001
$43$	−1.67508	−0.255448	−0.127724	−	0.991810i	$-0.540767\pi$
$43$	−1.67508	−0.255448	−0.127724	+	0.991810i	$0.540767\pi$
$44$	−4.14877	−0.625450
$45$	2.74615	0.409372
$46$	−3.31519	−0.488798
$47$	−2.95950	−0.431688	−0.215844	−	0.976428i	$-0.569250\pi$
$47$	−2.95950	−0.431688	−0.215844	+	0.976428i	$0.569250\pi$
$48$	−0.503837	−0.0727226
$49$	12.1263	1.73232
$50$	1.00000	0.141421
$51$	0.954708	0.133686
$52$	4.25115	0.589528
$53$	2.50135	0.343587	0.171794	−	0.985133i	$-0.445044\pi$
$53$	2.50135	0.343587	0.171794	+	0.985133i	$0.445044\pi$
$54$	2.89512	0.393976
$55$	4.14877	0.559420
$56$	−4.37336	−0.584415
$57$	1.83962	0.243664
$58$	−3.21629	−0.422320
$59$	4.43851	0.577845	0.288922	−	0.957353i	$-0.406703\pi$
$59$	4.43851	0.577845	0.288922	+	0.957353i	$0.406703\pi$
$60$	0.503837	0.0650451
$61$	12.4966	1.60003	0.800015	−	0.599979i	$-0.204825\pi$
$61$	12.4966	1.60003	0.800015	+	0.599979i	$0.204825\pi$
$62$	−0.405515	−0.0515005
$63$	12.0099	1.51310
$64$	1.00000	0.125000
$65$	−4.25115	−0.527290
$66$	2.09030	0.257298
$67$	2.79669	0.341670	0.170835	−	0.985300i	$-0.445354\pi$
$67$	2.79669	0.341670	0.170835	+	0.985300i	$0.445354\pi$
$68$	−1.89488	−0.229787
$69$	1.67031	0.201082
$70$	4.37336	0.522716
$71$	13.9850	1.65971	0.829856	−	0.557977i	$-0.188422\pi$
$71$	13.9850	1.65971	0.829856	+	0.557977i	$0.188422\pi$
$72$	−2.74615	−0.323637
$73$	9.53108	1.11553	0.557765	−	0.829999i	$-0.311659\pi$
$73$	9.53108	1.11553	0.557765	+	0.829999i	$0.311659\pi$
$74$	−3.77489	−0.438822
$75$	−0.503837	−0.0581781
$76$	−3.65123	−0.418825
$77$	18.1440	2.06771
$78$	−2.14188	−0.242521
$79$	−15.9642	−1.79611	−0.898054	−	0.439886i	$-0.855019\pi$
$79$	−15.9642	−1.79611	−0.898054	+	0.439886i	$0.855019\pi$
$80$	−1.00000	−0.111803
$81$	6.77978	0.753309
$82$	3.67235	0.405543
$83$	−13.8499	−1.52022	−0.760112	−	0.649792i	$-0.774856\pi$
$83$	−13.8499	−1.52022	−0.760112	+	0.649792i	$0.774856\pi$
$84$	2.20346	0.240417
$85$	1.89488	0.205528
$86$	−1.67508	−0.180629
$87$	1.62049	0.173734
$88$	−4.14877	−0.442260
$89$	−14.1083	−1.49548	−0.747740	−	0.663991i	$-0.768861\pi$
$89$	−14.1083	−1.49548	−0.747740	+	0.663991i	$0.768861\pi$
$90$	2.74615	0.289469
$91$	−18.5918	−1.94895
$92$	−3.31519	−0.345632
$93$	0.204313	0.0211863
$94$	−2.95950	−0.305250
$95$	3.65123	0.374608
$96$	−0.503837	−0.0514226
$97$	−14.0299	−1.42452	−0.712259	−	0.701917i	$-0.752328\pi$
$97$	−14.0299	−1.42452	−0.712259	+	0.701917i	$0.752328\pi$
$98$	12.1263	1.22494
$99$	11.3931	1.14505
$100$	1.00000	0.100000
$101$	6.27612	0.624497	0.312249	−	0.950000i	$-0.398918\pi$
$101$	6.27612	0.624497	0.312249	+	0.950000i	$0.398918\pi$
$102$	0.954708	0.0945302
$103$	−7.32578	−0.721831	−0.360915	−	0.932599i	$-0.617536\pi$
$103$	−7.32578	−0.721831	−0.360915	+	0.932599i	$0.617536\pi$
$104$	4.25115	0.416859
$105$	−2.20346	−0.215036
$106$	2.50135	0.242953
$107$	7.52799	0.727758	0.363879	−	0.931446i	$-0.381452\pi$
$107$	7.52799	0.727758	0.363879	+	0.931446i	$0.381452\pi$
$108$	2.89512	0.278583
$109$	−8.82232	−0.845025	−0.422512	−	0.906357i	$-0.638852\pi$
$109$	−8.82232	−0.845025	−0.422512	+	0.906357i	$0.638852\pi$
$110$	4.14877	0.395569
$111$	1.90193	0.180523
$112$	−4.37336	−0.413243
$113$	14.2400	1.33959	0.669794	−	0.742547i	$-0.266382\pi$
$113$	14.2400	1.33959	0.669794	+	0.742547i	$0.266382\pi$
$114$	1.83962	0.172297
$115$	3.31519	0.309143
$116$	−3.21629	−0.298625
$117$	−11.6743	−1.07929
$118$	4.43851	0.408598
$119$	8.28697	0.759665
$120$	0.503837	0.0459938
$121$	6.21227	0.564752
$122$	12.4966	1.13139
$123$	−1.85027	−0.166833
$124$	−0.405515	−0.0364163
$125$	−1.00000	−0.0894427
$126$	12.0099	1.06993
$127$	6.48023	0.575028	0.287514	−	0.957777i	$-0.407171\pi$
$127$	6.48023	0.575028	0.287514	+	0.957777i	$0.407171\pi$
$128$	1.00000	0.0883883
$129$	0.843969	0.0743073
$130$	−4.25115	−0.372850
$131$	6.63187	0.579429	0.289715	−	0.957113i	$-0.406440\pi$
$131$	6.63187	0.579429	0.289715	+	0.957113i	$0.406440\pi$
$132$	2.09030	0.181937
$133$	15.9681	1.38461
$134$	2.79669	0.241597
$135$	−2.89512	−0.249172
$136$	−1.89488	−0.162484
$137$	18.7830	1.60474	0.802371	−	0.596825i	$-0.203572\pi$
$137$	18.7830	1.60474	0.802371	+	0.596825i	$0.203572\pi$
$138$	1.67031	0.142186
$139$	0.726317	0.0616054	0.0308027	−	0.999525i	$-0.490194\pi$
$139$	0.726317	0.0616054	0.0308027	+	0.999525i	$0.490194\pi$
$140$	4.37336	0.369616
$141$	1.49111	0.125574
$142$	13.9850	1.17359
$143$	−17.6370	−1.47488
$144$	−2.74615	−0.228846
$145$	3.21629	0.267098
$146$	9.53108	0.788798
$147$	−6.10966	−0.503916
$148$	−3.77489	−0.310294
$149$	15.6847	1.28494	0.642471	−	0.766310i	$-0.277909\pi$
$149$	15.6847	1.28494	0.642471	+	0.766310i	$0.277909\pi$
$150$	−0.503837	−0.0411381
$151$	21.5623	1.75471	0.877357	−	0.479838i	$-0.159304\pi$
$151$	21.5623	1.75471	0.877357	+	0.479838i	$0.159304\pi$
$152$	−3.65123	−0.296154
$153$	5.20361	0.420687
$154$	18.1440	1.46209
$155$	0.405515	0.0325717
$156$	−2.14188	−0.171488
$157$	0.631254	0.0503795	0.0251898	−	0.999683i	$-0.491981\pi$
$157$	0.631254	0.0503795	0.0251898	+	0.999683i	$0.491981\pi$
$158$	−15.9642	−1.27004
$159$	−1.26027	−0.0999462
$160$	−1.00000	−0.0790569
$161$	14.4985	1.14264
$162$	6.77978	0.532670
$163$	1.14720	0.0898559	0.0449279	−	0.998990i	$-0.485694\pi$
$163$	1.14720	0.0898559	0.0449279	+	0.998990i	$0.485694\pi$
$164$	3.67235	0.286762
$165$	−2.09030	−0.162730
$166$	−13.8499	−1.07496
$167$	16.8809	1.30628	0.653140	−	0.757237i	$-0.273451\pi$
$167$	16.8809	1.30628	0.653140	+	0.757237i	$0.273451\pi$
$168$	2.20346	0.170001
$169$	5.07225	0.390173
$170$	1.89488	0.145330
$171$	10.0268	0.766770
$172$	−1.67508	−0.127724
$173$	−20.0131	−1.52157	−0.760784	−	0.649006i	$-0.775185\pi$
$173$	−20.0131	−1.52157	−0.760784	+	0.649006i	$0.775185\pi$
$174$	1.62049	0.122849
$175$	−4.37336	−0.330595
$176$	−4.14877	−0.312725
$177$	−2.23628	−0.168089
$178$	−14.1083	−1.05746
$179$	17.6539	1.31951	0.659757	−	0.751479i	$-0.270659\pi$
$179$	17.6539	1.31951	0.659757	+	0.751479i	$0.270659\pi$
$180$	2.74615	0.204686
$181$	17.3446	1.28922	0.644609	−	0.764513i	$-0.277020\pi$
$181$	17.3446	1.28922	0.644609	+	0.764513i	$0.277020\pi$
$182$	−18.5918	−1.37812
$183$	−6.29627	−0.465433
$184$	−3.31519	−0.244399
$185$	3.77489	0.277536
$186$	0.204313	0.0149810
$187$	7.86140	0.574883
$188$	−2.95950	−0.215844
$189$	−12.6614	−0.920981
$190$	3.65123	0.264888
$191$	−2.33808	−0.169178	−0.0845888	−	0.996416i	$-0.526958\pi$
$191$	−2.33808	−0.169178	−0.0845888	+	0.996416i	$0.526958\pi$
$192$	−0.503837	−0.0363613
$193$	4.31559	0.310643	0.155322	−	0.987864i	$-0.450359\pi$
$193$	4.31559	0.310643	0.155322	+	0.987864i	$0.450359\pi$
$194$	−14.0299	−1.00729
$195$	2.14188	0.153384
$196$	12.1263	0.866162
$197$	−3.01182	−0.214583	−0.107292	−	0.994228i	$-0.534218\pi$
$197$	−3.01182	−0.214583	−0.107292	+	0.994228i	$0.534218\pi$
$198$	11.3931	0.809675
$199$	−24.9085	−1.76572	−0.882860	−	0.469637i	$-0.844385\pi$
$199$	−24.9085	−1.76572	−0.882860	+	0.469637i	$0.844385\pi$
$200$	1.00000	0.0707107
$201$	−1.40907	−0.0993884
$202$	6.27612	0.441586
$203$	14.0660	0.987239
$204$	0.954708	0.0668429
$205$	−3.67235	−0.256488
$206$	−7.32578	−0.510411
$207$	9.10399	0.632771
$208$	4.25115	0.294764
$209$	15.1481	1.04782
$210$	−2.20346	−0.152053
$211$	−10.1226	−0.696871	−0.348436	−	0.937333i	$-0.613287\pi$
$211$	−10.1226	−0.696871	−0.348436	+	0.937333i	$0.613287\pi$
$212$	2.50135	0.171794
$213$	−7.04615	−0.482794
$214$	7.52799	0.514602
$215$	1.67508	0.114240
$216$	2.89512	0.196988
$217$	1.77346	0.120390
$218$	−8.82232	−0.597523
$219$	−4.80211	−0.324497
$220$	4.14877	0.279710
$221$	−8.05540	−0.541865
$222$	1.90193	0.127649
$223$	1.37115	0.0918190	0.0459095	−	0.998946i	$-0.485381\pi$
$223$	1.37115	0.0918190	0.0459095	+	0.998946i	$0.485381\pi$
$224$	−4.37336	−0.292207
$225$	−2.74615	−0.183077
$226$	14.2400	0.947232
$227$	−16.5849	−1.10078	−0.550388	−	0.834909i	$-0.685520\pi$
$227$	−16.5849	−1.10078	−0.550388	+	0.834909i	$0.685520\pi$
$228$	1.83962	0.121832
$229$	−3.68235	−0.243337	−0.121668	−	0.992571i	$-0.538824\pi$
$229$	−3.68235	−0.243337	−0.121668	+	0.992571i	$0.538824\pi$
$230$	3.31519	0.218597
$231$	−9.14164	−0.601476
$232$	−3.21629	−0.211160
$233$	21.0206	1.37711	0.688553	−	0.725186i	$-0.258246\pi$
$233$	21.0206	1.37711	0.688553	+	0.725186i	$0.258246\pi$
$234$	−11.6743	−0.763172
$235$	2.95950	0.193057
$236$	4.43851	0.288922
$237$	8.04333	0.522470
$238$	8.28697	0.537165
$239$	−5.41936	−0.350550	−0.175275	−	0.984520i	$-0.556081\pi$
$239$	−5.41936	−0.350550	−0.175275	+	0.984520i	$0.556081\pi$
$240$	0.503837	0.0325225
$241$	0.112705	0.00725997	0.00362998	−	0.999993i	$-0.498845\pi$
$241$	0.112705	0.00725997	0.00362998	+	0.999993i	$0.498845\pi$
$242$	6.21227	0.399340
$243$	−12.1013	−0.776296
$244$	12.4966	0.800015
$245$	−12.1263	−0.774718
$246$	−1.85027	−0.117969
$247$	−15.5219	−0.987636
$248$	−0.405515	−0.0257502
$249$	6.97809	0.442218
$250$	−1.00000	−0.0632456
$251$	6.23182	0.393349	0.196675	−	0.980469i	$-0.436986\pi$
$251$	6.23182	0.393349	0.196675	+	0.980469i	$0.436986\pi$
$252$	12.0099	0.756552
$253$	13.7539	0.864703
$254$	6.48023	0.406606
$255$	−0.954708	−0.0597862
$256$	1.00000	0.0625000
$257$	6.83681	0.426468	0.213234	−	0.977001i	$-0.431600\pi$
$257$	6.83681	0.426468	0.213234	+	0.977001i	$0.431600\pi$
$258$	0.843969	0.0525432
$259$	16.5090	1.02582
$260$	−4.25115	−0.263645
$261$	8.83241	0.546712
$262$	6.63187	0.409718
$263$	−2.40801	−0.148484	−0.0742422	−	0.997240i	$-0.523654\pi$
$263$	−2.40801	−0.148484	−0.0742422	+	0.997240i	$0.523654\pi$
$264$	2.09030	0.128649
$265$	−2.50135	−0.153657
$266$	15.9681	0.979069
$267$	7.10830	0.435021
$268$	2.79669	0.170835
$269$	13.9967	0.853392	0.426696	−	0.904395i	$-0.359677\pi$
$269$	13.9967	0.853392	0.426696	+	0.904395i	$0.359677\pi$
$270$	−2.89512	−0.176191
$271$	−21.5536	−1.30929	−0.654644	−	0.755937i	$-0.727182\pi$
$271$	−21.5536	−1.30929	−0.654644	+	0.755937i	$0.727182\pi$
$272$	−1.89488	−0.114894
$273$	9.36723	0.566930
$274$	18.7830	1.13472
$275$	−4.14877	−0.250180
$276$	1.67031	0.100541
$277$	3.65354	0.219520	0.109760	−	0.993958i	$-0.464992\pi$
$277$	3.65354	0.219520	0.109760	+	0.993958i	$0.464992\pi$
$278$	0.726317	0.0435616
$279$	1.11360	0.0666697
$280$	4.37336	0.261358
$281$	−14.3691	−0.857187	−0.428594	−	0.903497i	$-0.640991\pi$
$281$	−14.3691	−0.857187	−0.428594	+	0.903497i	$0.640991\pi$
$282$	1.49111	0.0887941
$283$	16.8309	1.00049	0.500246	−	0.865883i	$-0.333243\pi$
$283$	16.8309	1.00049	0.500246	+	0.865883i	$0.333243\pi$
$284$	13.9850	0.829856
$285$	−1.83962	−0.108970
$286$	−17.6370	−1.04290
$287$	−16.0605	−0.948022
$288$	−2.74615	−0.161818
$289$	−13.4094	−0.788791
$290$	3.21629	0.188867
$291$	7.06877	0.414379
$292$	9.53108	0.557765
$293$	−12.0696	−0.705111	−0.352556	−	0.935791i	$-0.614687\pi$
$293$	−12.0696	−0.705111	−0.352556	+	0.935791i	$0.614687\pi$
$294$	−6.10966	−0.356322
$295$	−4.43851	−0.258420
$296$	−3.77489	−0.219411
$297$	−12.0112	−0.696960
$298$	15.6847	0.908591
$299$	−14.0933	−0.815039
$300$	−0.503837	−0.0290890
$301$	7.32574	0.422249
$302$	21.5623	1.24077
$303$	−3.16214	−0.181660
$304$	−3.65123	−0.209412
$305$	−12.4966	−0.715556
$306$	5.20361	0.297471
$307$	18.7051	1.06756	0.533779	−	0.845624i	$-0.320771\pi$
$307$	18.7051	1.06756	0.533779	+	0.845624i	$0.320771\pi$
$308$	18.1440	1.03385
$309$	3.69100	0.209974
$310$	0.405515	0.0230317
$311$	−24.7855	−1.40546	−0.702728	−	0.711459i	$-0.748035\pi$
$311$	−24.7855	−1.40546	−0.702728	+	0.711459i	$0.748035\pi$
$312$	−2.14188	−0.121260
$313$	−5.10921	−0.288790	−0.144395	−	0.989520i	$-0.546124\pi$
$313$	−5.10921	−0.288790	−0.144395	+	0.989520i	$0.546124\pi$
$314$	0.631254	0.0356237
$315$	−12.0099	−0.676681
$316$	−15.9642	−0.898054
$317$	22.1950	1.24659	0.623297	−	0.781985i	$-0.285793\pi$
$317$	22.1950	1.24659	0.623297	+	0.781985i	$0.285793\pi$
$318$	−1.26027	−0.0706726
$319$	13.3436	0.747100
$320$	−1.00000	−0.0559017
$321$	−3.79288	−0.211698
$322$	14.4985	0.807970
$323$	6.91863	0.384963
$324$	6.77978	0.376654
$325$	4.25115	0.235811
$326$	1.14720	0.0635377
$327$	4.44501	0.245810
$328$	3.67235	0.202772
$329$	12.9430	0.713569
$330$	−2.09030	−0.115067
$331$	−10.9297	−0.600749	−0.300374	−	0.953821i	$-0.597112\pi$
$331$	−10.9297	−0.600749	−0.300374	+	0.953821i	$0.597112\pi$
$332$	−13.8499	−0.760112
$333$	10.3664	0.568076
$334$	16.8809	0.923680
$335$	−2.79669	−0.152799
$336$	2.20346	0.120209
$337$	−9.34428	−0.509016	−0.254508	−	0.967071i	$-0.581913\pi$
$337$	−9.34428	−0.509016	−0.254508	+	0.967071i	$0.581913\pi$
$338$	5.07225	0.275894
$339$	−7.17465	−0.389673
$340$	1.89488	0.102764
$341$	1.68239	0.0911064
$342$	10.0268	0.542188
$343$	−22.4190	−1.21051
$344$	−1.67508	−0.0903144
$345$	−1.67031	−0.0899266
$346$	−20.0131	−1.07591
$347$	4.90501	0.263315	0.131657	−	0.991295i	$-0.457970\pi$
$347$	4.90501	0.263315	0.131657	+	0.991295i	$0.457970\pi$
$348$	1.62049	0.0868671
$349$	−9.27756	−0.496616	−0.248308	−	0.968681i	$-0.579875\pi$
$349$	−9.27756	−0.496616	−0.248308	+	0.968681i	$0.579875\pi$
$350$	−4.37336	−0.233766
$351$	12.3076	0.656930
$352$	−4.14877	−0.221130
$353$	−16.0568	−0.854616	−0.427308	−	0.904106i	$-0.640538\pi$
$353$	−16.0568	−0.854616	−0.427308	+	0.904106i	$0.640538\pi$
$354$	−2.23628	−0.118857
$355$	−13.9850	−0.742246
$356$	−14.1083	−0.747740
$357$	−4.17528	−0.220979
$358$	17.6539	0.933037
$359$	−0.358253	−0.0189079	−0.00945393	−	0.999955i	$-0.503009\pi$
$359$	−0.358253	−0.0189079	−0.00945393	+	0.999955i	$0.503009\pi$
$360$	2.74615	0.144735
$361$	−5.66852	−0.298343
$362$	17.3446	0.911614
$363$	−3.12997	−0.164281
$364$	−18.5918	−0.974474
$365$	−9.53108	−0.498880
$366$	−6.29627	−0.329111
$367$	−23.0938	−1.20548	−0.602742	−	0.797936i	$-0.705925\pi$
$367$	−23.0938	−1.20548	−0.602742	+	0.797936i	$0.705925\pi$
$368$	−3.31519	−0.172816
$369$	−10.0848	−0.524995
$370$	3.77489	0.196247
$371$	−10.9393	−0.567941
$372$	0.204313	0.0105932
$373$	12.5738	0.651044	0.325522	−	0.945534i	$-0.394460\pi$
$373$	12.5738	0.651044	0.325522	+	0.945534i	$0.394460\pi$
$374$	7.86140	0.406503
$375$	0.503837	0.0260180
$376$	−2.95950	−0.152625
$377$	−13.6729	−0.704191
$378$	−12.6614	−0.651232
$379$	−26.7618	−1.37466	−0.687332	−	0.726344i	$-0.741218\pi$
$379$	−26.7618	−1.37466	−0.687332	+	0.726344i	$0.741218\pi$
$380$	3.65123	0.187304
$381$	−3.26498	−0.167270
$382$	−2.33808	−0.119627
$383$	20.3127	1.03793	0.518964	−	0.854796i	$-0.326318\pi$
$383$	20.3127	1.03793	0.518964	+	0.854796i	$0.326318\pi$
$384$	−0.503837	−0.0257113
$385$	−18.1440	−0.924706
$386$	4.31559	0.219658
$387$	4.60003	0.233833
$388$	−14.0299	−0.712259
$389$	23.3088	1.18180	0.590901	−	0.806744i	$-0.298772\pi$
$389$	23.3088	1.18180	0.590901	+	0.806744i	$0.298772\pi$
$390$	2.14188	0.108459
$391$	6.28187	0.317688
$392$	12.1263	0.612469
$393$	−3.34138	−0.168550
$394$	−3.01182	−0.151733
$395$	15.9642	0.803244
$396$	11.3931	0.572526
$397$	28.7637	1.44361	0.721805	−	0.692097i	$-0.243313\pi$
$397$	28.7637	1.44361	0.721805	+	0.692097i	$0.243313\pi$
$398$	−24.9085	−1.24855
$399$	−8.04533	−0.402770
$400$	1.00000	0.0500000
$401$	23.4982	1.17345	0.586723	−	0.809788i	$-0.300418\pi$
$401$	23.4982	1.17345	0.586723	+	0.809788i	$0.300418\pi$
$402$	−1.40907	−0.0702782
$403$	−1.72390	−0.0858738
$404$	6.27612	0.312249
$405$	−6.77978	−0.336890
$406$	14.0660	0.698083
$407$	15.6611	0.776294
$408$	0.954708	0.0472651
$409$	20.7403	1.02554	0.512771	−	0.858525i	$-0.328619\pi$
$409$	20.7403	1.02554	0.512771	+	0.858525i	$0.328619\pi$
$410$	−3.67235	−0.181365
$411$	−9.46358	−0.466804
$412$	−7.32578	−0.360915
$413$	−19.4112	−0.955162
$414$	9.10399	0.447437
$415$	13.8499	0.679865
$416$	4.25115	0.208430
$417$	−0.365945	−0.0179204
$418$	15.1481	0.740918
$419$	−15.4722	−0.755866	−0.377933	−	0.925833i	$-0.623365\pi$
$419$	−15.4722	−0.755866	−0.377933	+	0.925833i	$0.623365\pi$
$420$	−2.20346	−0.107518
$421$	15.3252	0.746904	0.373452	−	0.927650i	$-0.378174\pi$
$421$	15.3252	0.746904	0.373452	+	0.927650i	$0.378174\pi$
$422$	−10.1226	−0.492762
$423$	8.12724	0.395160
$424$	2.50135	0.121476
$425$	−1.89488	−0.0919150
$426$	−7.04615	−0.341387
$427$	−54.6523	−2.64481
$428$	7.52799	0.363879
$429$	8.88618	0.429029
$430$	1.67508	0.0807797
$431$	4.15642	0.200208	0.100104	−	0.994977i	$-0.468082\pi$
$431$	4.15642	0.200208	0.100104	+	0.994977i	$0.468082\pi$
$432$	2.89512	0.139292
$433$	37.7483	1.81407	0.907035	−	0.421056i	$-0.138340\pi$
$433$	37.7483	1.81407	0.907035	+	0.421056i	$0.138340\pi$
$434$	1.77346	0.0851289
$435$	−1.62049	−0.0776963
$436$	−8.82232	−0.422512
$437$	12.1045	0.579037
$438$	−4.80211	−0.229454
$439$	−33.5515	−1.60133	−0.800663	−	0.599115i	$-0.795519\pi$
$439$	−33.5515	−1.60133	−0.800663	+	0.599115i	$0.795519\pi$
$440$	4.14877	0.197785
$441$	−33.3005	−1.58574
$442$	−8.05540	−0.383156
$443$	−15.2829	−0.726115	−0.363057	−	0.931767i	$-0.618267\pi$
$443$	−15.2829	−0.726115	−0.363057	+	0.931767i	$0.618267\pi$
$444$	1.90193	0.0902616
$445$	14.1083	0.668799
$446$	1.37115	0.0649258
$447$	−7.90254	−0.373777
$448$	−4.37336	−0.206622
$449$	−11.0152	−0.519838	−0.259919	−	0.965630i	$-0.583696\pi$
$449$	−11.0152	−0.519838	−0.259919	+	0.965630i	$0.583696\pi$
$450$	−2.74615	−0.129455
$451$	−15.2357	−0.717423
$452$	14.2400	0.669794
$453$	−10.8639	−0.510429
$454$	−16.5849	−0.778366
$455$	18.5918	0.871596
$456$	1.83962	0.0861483
$457$	−33.5641	−1.57006	−0.785031	−	0.619457i	$-0.787353\pi$
$457$	−33.5641	−1.57006	−0.785031	+	0.619457i	$0.787353\pi$
$458$	−3.68235	−0.172065
$459$	−5.48590	−0.256060
$460$	3.31519	0.154571
$461$	−39.4186	−1.83591	−0.917955	−	0.396686i	$-0.870160\pi$
$461$	−39.4186	−1.83591	−0.917955	+	0.396686i	$0.870160\pi$
$462$	−9.14164	−0.425307
$463$	−2.10909	−0.0980179	−0.0490089	−	0.998798i	$-0.515606\pi$
$463$	−2.10909	−0.0980179	−0.0490089	+	0.998798i	$0.515606\pi$
$464$	−3.21629	−0.149313
$465$	−0.204313	−0.00947481
$466$	21.0206	0.973761
$467$	9.62070	0.445193	0.222597	−	0.974911i	$-0.428547\pi$
$467$	9.62070	0.445193	0.222597	+	0.974911i	$0.428547\pi$
$468$	−11.6743	−0.539644
$469$	−12.2309	−0.564771
$470$	2.95950	0.136512
$471$	−0.318049	−0.0146549
$472$	4.43851	0.204299
$473$	6.94953	0.319540
$474$	8.04333	0.369442
$475$	−3.65123	−0.167530
$476$	8.28697	0.379833
$477$	−6.86908	−0.314514
$478$	−5.41936	−0.247876
$479$	32.6483	1.49174	0.745869	−	0.666093i	$-0.232035\pi$
$479$	32.6483	1.49174	0.745869	+	0.666093i	$0.232035\pi$
$480$	0.503837	0.0229969
$481$	−16.0476	−0.731709
$482$	0.112705	0.00513357
$483$	−7.30488	−0.332383
$484$	6.21227	0.282376
$485$	14.0299	0.637064
$486$	−12.1013	−0.548924
$487$	5.04969	0.228823	0.114412	−	0.993433i	$-0.463502\pi$
$487$	5.04969	0.228823	0.114412	+	0.993433i	$0.463502\pi$
$488$	12.4966	0.565696
$489$	−0.578003	−0.0261382
$490$	−12.1263	−0.547809
$491$	21.5224	0.971294	0.485647	−	0.874155i	$-0.338584\pi$
$491$	21.5224	0.971294	0.485647	+	0.874155i	$0.338584\pi$
$492$	−1.85027	−0.0834164
$493$	6.09447	0.274481
$494$	−15.5219	−0.698364
$495$	−11.3931	−0.512083
$496$	−0.405515	−0.0182082
$497$	−61.1614	−2.74346
$498$	6.97809	0.312696
$499$	−9.98510	−0.446995	−0.223497	−	0.974705i	$-0.571747\pi$
$499$	−9.98510	−0.446995	−0.223497	+	0.974705i	$0.571747\pi$
$500$	−1.00000	−0.0447214
$501$	−8.50520	−0.379984
$502$	6.23182	0.278140
$503$	22.8384	1.01831	0.509157	−	0.860674i	$-0.329957\pi$
$503$	22.8384	1.01831	0.509157	+	0.860674i	$0.329957\pi$
$504$	12.0099	0.534963
$505$	−6.27612	−0.279284
$506$	13.7539	0.611437
$507$	−2.55559	−0.113498
$508$	6.48023	0.287514
$509$	2.47393	0.109655	0.0548276	−	0.998496i	$-0.482539\pi$
$509$	2.47393	0.109655	0.0548276	+	0.998496i	$0.482539\pi$
$510$	−0.954708	−0.0422752
$511$	−41.6828	−1.84394
$512$	1.00000	0.0441942
$513$	−10.5708	−0.466710
$514$	6.83681	0.301559
$515$	7.32578	0.322812
$516$	0.843969	0.0371536
$517$	12.2783	0.539999
$518$	16.5090	0.725362
$519$	10.0833	0.442609
$520$	−4.25115	−0.186425
$521$	−13.6187	−0.596648	−0.298324	−	0.954465i	$-0.596428\pi$
$521$	−13.6187	−0.596648	−0.298324	+	0.954465i	$0.596428\pi$
$522$	8.83241	0.386584
$523$	28.0135	1.22495	0.612473	−	0.790491i	$-0.290175\pi$
$523$	28.0135	1.22495	0.612473	+	0.790491i	$0.290175\pi$
$524$	6.63187	0.289715
$525$	2.20346	0.0961668
$526$	−2.40801	−0.104994
$527$	0.768401	0.0334721
$528$	2.09030	0.0909687
$529$	−12.0095	−0.522154
$530$	−2.50135	−0.108652
$531$	−12.1888	−0.528949
$532$	15.9681	0.692306
$533$	15.6117	0.676218
$534$	7.10830	0.307606
$535$	−7.52799	−0.325463
$536$	2.79669	0.120799
$537$	−8.89468	−0.383834
$538$	13.9967	0.603440
$539$	−50.3090	−2.16696
$540$	−2.89512	−0.124586
$541$	−25.8178	−1.10999	−0.554997	−	0.831853i	$-0.687280\pi$
$541$	−25.8178	−1.10999	−0.554997	+	0.831853i	$0.687280\pi$
$542$	−21.5536	−0.925807
$543$	−8.73887	−0.375021
$544$	−1.89488	−0.0812421
$545$	8.82232	0.377907
$546$	9.36723	0.400880
$547$	−22.8184	−0.975646	−0.487823	−	0.872943i	$-0.662209\pi$
$547$	−22.8184	−0.975646	−0.487823	+	0.872943i	$0.662209\pi$
$548$	18.7830	0.802371
$549$	−34.3176	−1.46464
$550$	−4.14877	−0.176904
$551$	11.7434	0.500286
$552$	1.67031	0.0710932
$553$	69.8169	2.96892
$554$	3.65354	0.155224
$555$	−1.90193	−0.0807324
$556$	0.726317	0.0308027
$557$	−19.7436	−0.836565	−0.418283	−	0.908317i	$-0.637368\pi$
$557$	−19.7436	−0.836565	−0.418283	+	0.908317i	$0.637368\pi$
$558$	1.11360	0.0471426
$559$	−7.12103	−0.301187
$560$	4.37336	0.184808
$561$	−3.96086	−0.167228
$562$	−14.3691	−0.606123
$563$	39.8723	1.68042	0.840208	−	0.542264i	$-0.182433\pi$
$563$	39.8723	1.68042	0.840208	+	0.542264i	$0.182433\pi$
$564$	1.49111	0.0627869
$565$	−14.2400	−0.599082
$566$	16.8309	0.707455
$567$	−29.6504	−1.24520
$568$	13.9850	0.586797
$569$	2.94628	0.123515	0.0617573	−	0.998091i	$-0.480330\pi$
$569$	2.94628	0.123515	0.0617573	+	0.998091i	$0.480330\pi$
$570$	−1.83962	−0.0770534
$571$	−4.97527	−0.208208	−0.104104	−	0.994566i	$-0.533198\pi$
$571$	−4.97527	−0.208208	−0.104104	+	0.994566i	$0.533198\pi$
$572$	−17.6370	−0.737441
$573$	1.17801	0.0492121
$574$	−16.0605	−0.670353
$575$	−3.31519	−0.138253
$576$	−2.74615	−0.114423
$577$	33.2125	1.38265	0.691326	−	0.722543i	$-0.257027\pi$
$577$	33.2125	1.38265	0.691326	+	0.722543i	$0.257027\pi$
$578$	−13.4094	−0.557759
$579$	−2.17435	−0.0903631
$580$	3.21629	0.133549
$581$	60.5706	2.51289
$582$	7.06877	0.293010
$583$	−10.3775	−0.429793
$584$	9.53108	0.394399
$585$	11.6743	0.482672
$586$	−12.0696	−0.498589
$587$	13.3895	0.552643	0.276321	−	0.961065i	$-0.410885\pi$
$587$	13.3895	0.552643	0.276321	+	0.961065i	$0.410885\pi$
$588$	−6.10966	−0.251958
$589$	1.48063	0.0610082
$590$	−4.43851	−0.182731
$591$	1.51747	0.0624202
$592$	−3.77489	−0.155147
$593$	41.6939	1.71216	0.856081	−	0.516841i	$-0.172892\pi$
$593$	41.6939	1.71216	0.856081	+	0.516841i	$0.172892\pi$
$594$	−12.0112	−0.492825
$595$	−8.28697	−0.339733
$596$	15.6847	0.642471
$597$	12.5498	0.513631
$598$	−14.0933	−0.576320
$599$	−15.2470	−0.622976	−0.311488	−	0.950250i	$-0.600827\pi$
$599$	−15.2470	−0.622976	−0.311488	+	0.950250i	$0.600827\pi$
$600$	−0.503837	−0.0205691
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	7.32574	0.298575
$603$	−7.68012	−0.312759
$604$	21.5623	0.877357
$605$	−6.21227	−0.252565
$606$	−3.16214	−0.128453
$607$	2.78677	0.113111	0.0565557	−	0.998399i	$-0.481988\pi$
$607$	2.78677	0.113111	0.0565557	+	0.998399i	$0.481988\pi$
$608$	−3.65123	−0.148077
$609$	−7.08696	−0.287178
$610$	−12.4966	−0.505974
$611$	−12.5813	−0.508984
$612$	5.20361	0.210344
$613$	30.8104	1.24442	0.622210	−	0.782850i	$-0.286235\pi$
$613$	30.8104	1.24442	0.622210	+	0.782850i	$0.286235\pi$
$614$	18.7051	0.754878
$615$	1.85027	0.0746099
$616$	18.1440	0.731044
$617$	−15.6075	−0.628333	−0.314166	−	0.949368i	$-0.601725\pi$
$617$	−15.6075	−0.628333	−0.314166	+	0.949368i	$0.601725\pi$
$618$	3.69100	0.148474
$619$	9.67538	0.388886	0.194443	−	0.980914i	$-0.437710\pi$
$619$	9.67538	0.388886	0.194443	+	0.980914i	$0.437710\pi$
$620$	0.405515	0.0162859
$621$	−9.59787	−0.385149
$622$	−24.7855	−0.993807
$623$	61.7008	2.47199
$624$	−2.14188	−0.0857440
$625$	1.00000	0.0400000
$626$	−5.10921	−0.204205
$627$	−7.63217	−0.304800
$628$	0.631254	0.0251898
$629$	7.15295	0.285207
$630$	−12.0099	−0.478485
$631$	11.7790	0.468916	0.234458	−	0.972126i	$-0.424669\pi$
$631$	11.7790	0.468916	0.234458	+	0.972126i	$0.424669\pi$
$632$	−15.9642	−0.635020
$633$	5.10016	0.202713
$634$	22.1950	0.881476
$635$	−6.48023	−0.257160
$636$	−1.26027	−0.0499731
$637$	51.5505	2.04251
$638$	13.3436	0.528280
$639$	−38.4049	−1.51927
$640$	−1.00000	−0.0395285
$641$	−25.7466	−1.01693	−0.508464	−	0.861083i	$-0.669787\pi$
$641$	−25.7466	−1.01693	−0.508464	+	0.861083i	$0.669787\pi$
$642$	−3.79288	−0.149693
$643$	7.09738	0.279893	0.139947	−	0.990159i	$-0.455307\pi$
$643$	7.09738	0.279893	0.139947	+	0.990159i	$0.455307\pi$
$644$	14.4985	0.571321
$645$	−0.843969	−0.0332312
$646$	6.91863	0.272210
$647$	40.1554	1.57867	0.789336	−	0.613962i	$-0.210425\pi$
$647$	40.1554	1.57867	0.789336	+	0.613962i	$0.210425\pi$
$648$	6.77978	0.266335
$649$	−18.4143	−0.722826
$650$	4.25115	0.166744
$651$	−0.893535	−0.0350204
$652$	1.14720	0.0449279
$653$	4.20977	0.164741	0.0823706	−	0.996602i	$-0.473751\pi$
$653$	4.20977	0.164741	0.0823706	+	0.996602i	$0.473751\pi$
$654$	4.44501	0.173814
$655$	−6.63187	−0.259129
$656$	3.67235	0.143381
$657$	−26.1738	−1.02114
$658$	12.9430	0.504570
$659$	4.32805	0.168597	0.0842985	−	0.996441i	$-0.473135\pi$
$659$	4.32805	0.168597	0.0842985	+	0.996441i	$0.473135\pi$
$660$	−2.09030	−0.0813649
$661$	6.05588	0.235546	0.117773	−	0.993041i	$-0.462424\pi$
$661$	6.05588	0.235546	0.117773	+	0.993041i	$0.462424\pi$
$662$	−10.9297	−0.424794
$663$	4.05861	0.157623
$664$	−13.8499	−0.537480
$665$	−15.9681	−0.619218
$666$	10.3664	0.401690
$667$	10.6626	0.412858
$668$	16.8809	0.653140
$669$	−0.690836	−0.0267092
$670$	−2.79669	−0.108045
$671$	−51.8457	−2.00148
$672$	2.20346	0.0850003
$673$	24.6256	0.949246	0.474623	−	0.880189i	$-0.342584\pi$
$673$	24.6256	0.949246	0.474623	+	0.880189i	$0.342584\pi$
$674$	−9.34428	−0.359928
$675$	2.89512	0.111433
$676$	5.07225	0.195087
$677$	−44.5257	−1.71126	−0.855631	−	0.517586i	$-0.826831\pi$
$677$	−44.5257	−1.71126	−0.855631	+	0.517586i	$0.826831\pi$
$678$	−7.17465	−0.275541
$679$	61.3577	2.35469
$680$	1.89488	0.0726652
$681$	8.35606	0.320205
$682$	1.68239	0.0644219
$683$	2.56574	0.0981754	0.0490877	−	0.998794i	$-0.484369\pi$
$683$	2.56574	0.0981754	0.0490877	+	0.998794i	$0.484369\pi$
$684$	10.0268	0.383385
$685$	−18.7830	−0.717662
$686$	−22.4190	−0.855960
$687$	1.85530	0.0707842
$688$	−1.67508	−0.0638620
$689$	10.6336	0.405109
$690$	−1.67031	−0.0635877
$691$	48.0191	1.82673	0.913366	−	0.407139i	$-0.133474\pi$
$691$	48.0191	1.82673	0.913366	+	0.407139i	$0.133474\pi$
$692$	−20.0131	−0.760784
$693$	−49.8262	−1.89274
$694$	4.90501	0.186192
$695$	−0.726317	−0.0275508
$696$	1.62049	0.0614243
$697$	−6.95865	−0.263578
$698$	−9.27756	−0.351161
$699$	−10.5910	−0.400587
$700$	−4.37336	−0.165297
$701$	14.5044	0.547823	0.273912	−	0.961755i	$-0.411682\pi$
$701$	14.5044	0.547823	0.273912	+	0.961755i	$0.411682\pi$
$702$	12.3076	0.464520
$703$	13.7830	0.519836
$704$	−4.14877	−0.156363
$705$	−1.49111	−0.0561583
$706$	−16.0568	−0.604305
$707$	−27.4477	−1.03228
$708$	−2.23628	−0.0840447
$709$	−38.5369	−1.44728	−0.723642	−	0.690175i	$-0.757533\pi$
$709$	−38.5369	−1.44728	−0.723642	+	0.690175i	$0.757533\pi$
$710$	−13.9850	−0.524847
$711$	43.8399	1.64413
$712$	−14.1083	−0.528732
$713$	1.34436	0.0503466
$714$	−4.17528	−0.156256
$715$	17.6370	0.659587
$716$	17.6539	0.659757
$717$	2.73048	0.101971
$718$	−0.358253	−0.0133699
$719$	−24.8479	−0.926670	−0.463335	−	0.886183i	$-0.653347\pi$
$719$	−24.8479	−0.926670	−0.463335	+	0.886183i	$0.653347\pi$
$720$	2.74615	0.102343
$721$	32.0383	1.19317
$722$	−5.66852	−0.210961
$723$	−0.0567849	−0.00211185
$724$	17.3446	0.644609
$725$	−3.21629	−0.119450
$726$	−3.12997	−0.116164
$727$	−13.7128	−0.508578	−0.254289	−	0.967128i	$-0.581841\pi$
$727$	−13.7128	−0.508578	−0.254289	+	0.967128i	$0.581841\pi$
$728$	−18.5918	−0.689058
$729$	−14.2423	−0.527491
$730$	−9.53108	−0.352761
$731$	3.17408	0.117397
$732$	−6.29627	−0.232717
$733$	−14.5726	−0.538251	−0.269126	−	0.963105i	$-0.586735\pi$
$733$	−14.5726	−0.538251	−0.269126	+	0.963105i	$0.586735\pi$
$734$	−23.0938	−0.852406
$735$	6.10966	0.225358
$736$	−3.31519	−0.122199
$737$	−11.6028	−0.427395
$738$	−10.0848	−0.371227
$739$	−7.84808	−0.288696	−0.144348	−	0.989527i	$-0.546109\pi$
$739$	−7.84808	−0.288696	−0.144348	+	0.989527i	$0.546109\pi$
$740$	3.77489	0.138768
$741$	7.82051	0.287294
$742$	−10.9393	−0.401595
$743$	28.5621	1.04784	0.523921	−	0.851767i	$-0.324469\pi$
$743$	28.5621	1.04784	0.523921	+	0.851767i	$0.324469\pi$
$744$	0.204313	0.00749049
$745$	−15.6847	−0.574643
$746$	12.5738	0.460358
$747$	38.0339	1.39159
$748$	7.86140	0.287441
$749$	−32.9226	−1.20296
$750$	0.503837	0.0183975
$751$	32.6233	1.19044	0.595221	−	0.803562i	$-0.297064\pi$
$751$	32.6233	1.19044	0.595221	+	0.803562i	$0.297064\pi$
$752$	−2.95950	−0.107922
$753$	−3.13982	−0.114421
$754$	−13.6729	−0.497938
$755$	−21.5623	−0.784732
$756$	−12.6614	−0.460491
$757$	17.0840	0.620928	0.310464	−	0.950585i	$-0.399516\pi$
$757$	17.0840	0.620928	0.310464	+	0.950585i	$0.399516\pi$
$758$	−26.7618	−0.972034
$759$	−6.92974	−0.251534
$760$	3.65123	0.132444
$761$	5.95689	0.215937	0.107968	−	0.994154i	$-0.465565\pi$
$761$	5.95689	0.215937	0.107968	+	0.994154i	$0.465565\pi$
$762$	−3.26498	−0.118278
$763$	38.5832	1.39680
$764$	−2.33808	−0.0845888
$765$	−5.20361	−0.188137
$766$	20.3127	0.733926
$767$	18.8688	0.681311
$768$	−0.503837	−0.0181806
$769$	−34.5075	−1.24437	−0.622187	−	0.782869i	$-0.713756\pi$
$769$	−34.5075	−1.24437	−0.622187	+	0.782869i	$0.713756\pi$
$770$	−18.1440	−0.653866
$771$	−3.44463	−0.124055
$772$	4.31559	0.155322
$773$	17.6150	0.633568	0.316784	−	0.948498i	$-0.397397\pi$
$773$	17.6150	0.633568	0.316784	+	0.948498i	$0.397397\pi$
$774$	4.60003	0.165345
$775$	−0.405515	−0.0145665
$776$	−14.0299	−0.503643
$777$	−8.31782	−0.298400
$778$	23.3088	0.835660
$779$	−13.4086	−0.480413
$780$	2.14188	0.0766918
$781$	−58.0205	−2.07614
$782$	6.28187	0.224639
$783$	−9.31155	−0.332768
$784$	12.1263	0.433081
$785$	−0.631254	−0.0225304
$786$	−3.34138	−0.119183
$787$	23.3892	0.833734	0.416867	−	0.908967i	$-0.363128\pi$
$787$	23.3892	0.833734	0.416867	+	0.908967i	$0.363128\pi$
$788$	−3.01182	−0.107292
$789$	1.21325	0.0431927
$790$	15.9642	0.567979
$791$	−62.2767	−2.21430
$792$	11.3931	0.404837
$793$	53.1251	1.88653
$794$	28.7637	1.02079
$795$	1.26027	0.0446973
$796$	−24.9085	−0.882860
$797$	6.89464	0.244221	0.122110	−	0.992517i	$-0.461034\pi$
$797$	6.89464	0.244221	0.122110	+	0.992517i	$0.461034\pi$
$798$	−8.04533	−0.284802
$799$	5.60789	0.198393
$800$	1.00000	0.0353553
$801$	38.7436	1.36894
$802$	23.4982	0.829751
$803$	−39.5423	−1.39542
$804$	−1.40907	−0.0496942
$805$	−14.4985	−0.511005
$806$	−1.72390	−0.0607219
$807$	−7.05204	−0.248244
$808$	6.27612	0.220793
$809$	−2.77737	−0.0976472	−0.0488236	−	0.998807i	$-0.515547\pi$
$809$	−2.77737	−0.0976472	−0.0488236	+	0.998807i	$0.515547\pi$
$810$	−6.77978	−0.238217
$811$	−15.2572	−0.535752	−0.267876	−	0.963453i	$-0.586322\pi$
$811$	−15.2572	−0.535752	−0.267876	+	0.963453i	$0.586322\pi$
$812$	14.0660	0.493619
$813$	10.8595	0.380859
$814$	15.6611	0.548923
$815$	−1.14720	−0.0401848
$816$	0.954708	0.0334215
$817$	6.11611	0.213976
$818$	20.7403	0.725168
$819$	51.0558	1.78403
$820$	−3.67235	−0.128244
$821$	−10.1547	−0.354401	−0.177201	−	0.984175i	$-0.556704\pi$
$821$	−10.1547	−0.354401	−0.177201	+	0.984175i	$0.556704\pi$
$822$	−9.46358	−0.330080
$823$	−21.8300	−0.760946	−0.380473	−	0.924792i	$-0.624239\pi$
$823$	−21.8300	−0.760946	−0.380473	+	0.924792i	$0.624239\pi$
$824$	−7.32578	−0.255206
$825$	2.09030	0.0727750
$826$	−19.4112	−0.675402
$827$	−12.9744	−0.451163	−0.225582	−	0.974224i	$-0.572428\pi$
$827$	−12.9744	−0.451163	−0.225582	+	0.974224i	$0.572428\pi$
$828$	9.10399	0.316386
$829$	0.341908	0.0118749	0.00593747	−	0.999982i	$-0.498110\pi$
$829$	0.341908	0.0118749	0.00593747	+	0.999982i	$0.498110\pi$
$830$	13.8499	0.480737
$831$	−1.84079	−0.0638563
$832$	4.25115	0.147382
$833$	−22.9778	−0.796132
$834$	−0.365945	−0.0126716
$835$	−16.8809	−0.584186
$836$	15.1481	0.523908
$837$	−1.17401	−0.0405799
$838$	−15.4722	−0.534478
$839$	−39.9922	−1.38068	−0.690342	−	0.723483i	$-0.742540\pi$
$839$	−39.9922	−1.38068	−0.690342	+	0.723483i	$0.742540\pi$
$840$	−2.20346	−0.0760265
$841$	−18.6555	−0.643292
$842$	15.3252	0.528141
$843$	7.23967	0.249348
$844$	−10.1226	−0.348436
$845$	−5.07225	−0.174491
$846$	8.12724	0.279420
$847$	−27.1685	−0.933520
$848$	2.50135	0.0858968
$849$	−8.48002	−0.291033
$850$	−1.89488	−0.0649937
$851$	12.5145	0.428990
$852$	−7.04615	−0.241397
$853$	23.8144	0.815391	0.407695	−	0.913118i	$-0.366332\pi$
$853$	23.8144	0.815391	0.407695	+	0.913118i	$0.366332\pi$
$854$	−54.6523	−1.87016
$855$	−10.0268	−0.342910
$856$	7.52799	0.257301
$857$	56.2875	1.92275	0.961373	−	0.275250i	$-0.0887606\pi$
$857$	56.2875	1.92275	0.961373	+	0.275250i	$0.0887606\pi$
$858$	8.88618	0.303369
$859$	40.9367	1.39674	0.698371	−	0.715736i	$-0.253909\pi$
$859$	40.9367	1.39674	0.698371	+	0.715736i	$0.253909\pi$
$860$	1.67508	0.0571199
$861$	8.09188	0.275770
$862$	4.15642	0.141568
$863$	−52.7029	−1.79403	−0.897013	−	0.442003i	$-0.854268\pi$
$863$	−52.7029	−1.79403	−0.897013	+	0.442003i	$0.854268\pi$
$864$	2.89512	0.0984940
$865$	20.0131	0.680465
$866$	37.7483	1.28274
$867$	6.75617	0.229452
$868$	1.77346	0.0601952
$869$	66.2316	2.24675
$870$	−1.62049	−0.0549396
$871$	11.8891	0.402848
$872$	−8.82232	−0.298761
$873$	38.5281	1.30398
$874$	12.1045	0.409441
$875$	4.37336	0.147846
$876$	−4.80211	−0.162248
$877$	1.36584	0.0461210	0.0230605	−	0.999734i	$-0.492659\pi$
$877$	1.36584	0.0461210	0.0230605	+	0.999734i	$0.492659\pi$
$878$	−33.5515	−1.13231
$879$	6.08109	0.205110
$880$	4.14877	0.139855
$881$	−59.0186	−1.98839	−0.994194	−	0.107603i	$-0.965682\pi$
$881$	−59.0186	−1.98839	−0.994194	+	0.107603i	$0.965682\pi$
$882$	−33.3005	−1.12129
$883$	4.03982	0.135951	0.0679754	−	0.997687i	$-0.478346\pi$
$883$	4.03982	0.135951	0.0679754	+	0.997687i	$0.478346\pi$
$884$	−8.05540	−0.270932
$885$	2.23628	0.0751719
$886$	−15.2829	−0.513440
$887$	−6.24812	−0.209791	−0.104896	−	0.994483i	$-0.533451\pi$
$887$	−6.24812	−0.209791	−0.104896	+	0.994483i	$0.533451\pi$
$888$	1.90193	0.0638246
$889$	−28.3404	−0.950506
$890$	14.1083	0.472913
$891$	−28.1277	−0.942314
$892$	1.37115	0.0459095
$893$	10.8058	0.361603
$894$	−7.90254	−0.264300
$895$	−17.6539	−0.590105
$896$	−4.37336	−0.146104
$897$	7.10075	0.237087
$898$	−11.0152	−0.367581
$899$	1.30425	0.0434993
$900$	−2.74615	−0.0915383
$901$	−4.73975	−0.157904
$902$	−15.2357	−0.507294
$903$	−3.69098	−0.122828
$904$	14.2400	0.473616
$905$	−17.3446	−0.576556
$906$	−10.8639	−0.360928
$907$	−13.0379	−0.432917	−0.216459	−	0.976292i	$-0.569451\pi$
$907$	−13.0379	−0.432917	−0.216459	+	0.976292i	$0.569451\pi$
$908$	−16.5849	−0.550388
$909$	−17.2352	−0.571654
$910$	18.5918	0.616312
$911$	30.8367	1.02166	0.510832	−	0.859680i	$-0.329337\pi$
$911$	30.8367	1.02166	0.510832	+	0.859680i	$0.329337\pi$
$912$	1.83962	0.0609160
$913$	57.4600	1.90165
$914$	−33.5641	−1.11020
$915$	6.29627	0.208148
$916$	−3.68235	−0.121668
$917$	−29.0036	−0.957782
$918$	−5.48590	−0.181062
$919$	−9.68078	−0.319340	−0.159670	−	0.987170i	$-0.551043\pi$
$919$	−9.68078	−0.319340	−0.159670	+	0.987170i	$0.551043\pi$
$920$	3.31519	0.109298
$921$	−9.42434	−0.310543
$922$	−39.4186	−1.29818
$923$	59.4522	1.95689
$924$	−9.14164	−0.300738
$925$	−3.77489	−0.124118
$926$	−2.10909	−0.0693091
$927$	20.1177	0.660751
$928$	−3.21629	−0.105580
$929$	−35.5913	−1.16771	−0.583856	−	0.811857i	$-0.698457\pi$
$929$	−35.5913	−1.16771	−0.583856	+	0.811857i	$0.698457\pi$
$930$	−0.204313	−0.00669970
$931$	−44.2758	−1.45108
$932$	21.0206	0.688553
$933$	12.4878	0.408833
$934$	9.62070	0.314799
$935$	−7.86140	−0.257095
$936$	−11.6743	−0.381586
$937$	26.4776	0.864987	0.432493	−	0.901637i	$-0.357634\pi$
$937$	26.4776	0.864987	0.432493	+	0.901637i	$0.357634\pi$
$938$	−12.2309	−0.399354
$939$	2.57421	0.0840061
$940$	2.95950	0.0965284
$941$	−57.5358	−1.87561	−0.937807	−	0.347158i	$-0.887147\pi$
$941$	−57.5358	−1.87561	−0.937807	+	0.347158i	$0.887147\pi$
$942$	−0.318049	−0.0103626
$943$	−12.1745	−0.396457
$944$	4.43851	0.144461
$945$	12.6614	0.411875
$946$	6.94953	0.225949
$947$	1.18654	0.0385573	0.0192786	−	0.999814i	$-0.493863\pi$
$947$	1.18654	0.0385573	0.0192786	+	0.999814i	$0.493863\pi$
$948$	8.04333	0.261235
$949$	40.5180	1.31527
$950$	−3.65123	−0.118462
$951$	−11.1827	−0.362622
$952$	8.28697	0.268582
$953$	−51.0447	−1.65350	−0.826750	−	0.562570i	$-0.809813\pi$
$953$	−51.0447	−1.65350	−0.826750	+	0.562570i	$0.809813\pi$
$954$	−6.86908	−0.222395
$955$	2.33808	0.0756585
$956$	−5.41936	−0.175275
$957$	−6.72302	−0.217324
$958$	32.6483	1.05482
$959$	−82.1449	−2.65260
$960$	0.503837	0.0162613
$961$	−30.8356	−0.994695
$962$	−16.0476	−0.517396
$963$	−20.6730	−0.666177
$964$	0.112705	0.00362998
$965$	−4.31559	−0.138924
$966$	−7.30488	−0.235031
$967$	−7.93534	−0.255183	−0.127592	−	0.991827i	$-0.540725\pi$
$967$	−7.93534	−0.255183	−0.127592	+	0.991827i	$0.540725\pi$
$968$	6.21227	0.199670
$969$	−3.48586	−0.111982
$970$	14.0299	0.450472
$971$	37.3817	1.19963	0.599817	−	0.800137i	$-0.295240\pi$
$971$	37.3817	1.19963	0.599817	+	0.800137i	$0.295240\pi$
$972$	−12.1013	−0.388148
$973$	−3.17644	−0.101832
$974$	5.04969	0.161802
$975$	−2.14188	−0.0685952
$976$	12.4966	0.400008
$977$	25.1735	0.805370	0.402685	−	0.915339i	$-0.368077\pi$
$977$	25.1735	0.805370	0.402685	+	0.915339i	$0.368077\pi$
$978$	−0.578003	−0.0184825
$979$	58.5322	1.87070
$980$	−12.1263	−0.387359
$981$	24.2274	0.773521
$982$	21.5224	0.686808
$983$	−42.0003	−1.33960	−0.669801	−	0.742541i	$-0.733621\pi$
$983$	−42.0003	−1.33960	−0.669801	+	0.742541i	$0.733621\pi$
$984$	−1.85027	−0.0589843
$985$	3.01182	0.0959645
$986$	6.09447	0.194088
$987$	−6.52115	−0.207570
$988$	−15.5219	−0.493818
$989$	5.55321	0.176582
$990$	−11.3931	−0.362097
$991$	−23.7817	−0.755452	−0.377726	−	0.925918i	$-0.623294\pi$
$991$	−23.7817	−0.755452	−0.377726	+	0.925918i	$0.623294\pi$
$992$	−0.405515	−0.0128751
$993$	5.50677	0.174752
$994$	−61.1614	−1.93992
$995$	24.9085	0.789654
$996$	6.97809	0.221109
$997$	−12.3835	−0.392188	−0.196094	−	0.980585i	$-0.562826\pi$
$997$	−12.3835	−0.392188	−0.196094	+	0.980585i	$0.562826\pi$
$998$	−9.98510	−0.316073
$999$	−10.9288	−0.345771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.12	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.12	✓	28	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.503837 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.503837 q^{6} -4.37336 q^{7} +1.00000 q^{8} -2.74615 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.503837 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.503837 q^{6} -4.37336 q^{7} +1.00000 q^{8} -2.74615 q^{9} -1.00000 q^{10} -4.14877 q^{11} -0.503837 q^{12} +4.25115 q^{13} -4.37336 q^{14} +0.503837 q^{15} +1.00000 q^{16} -1.89488 q^{17} -2.74615 q^{18} -3.65123 q^{19} -1.00000 q^{20} +2.20346 q^{21} -4.14877 q^{22} -3.31519 q^{23} -0.503837 q^{24} +1.00000 q^{25} +4.25115 q^{26} +2.89512 q^{27} -4.37336 q^{28} -3.21629 q^{29} +0.503837 q^{30} -0.405515 q^{31} +1.00000 q^{32} +2.09030 q^{33} -1.89488 q^{34} +4.37336 q^{35} -2.74615 q^{36} -3.77489 q^{37} -3.65123 q^{38} -2.14188 q^{39} -1.00000 q^{40} +3.67235 q^{41} +2.20346 q^{42} -1.67508 q^{43} -4.14877 q^{44} +2.74615 q^{45} -3.31519 q^{46} -2.95950 q^{47} -0.503837 q^{48} +12.1263 q^{49} +1.00000 q^{50} +0.954708 q^{51} +4.25115 q^{52} +2.50135 q^{53} +2.89512 q^{54} +4.14877 q^{55} -4.37336 q^{56} +1.83962 q^{57} -3.21629 q^{58} +4.43851 q^{59} +0.503837 q^{60} +12.4966 q^{61} -0.405515 q^{62} +12.0099 q^{63} +1.00000 q^{64} -4.25115 q^{65} +2.09030 q^{66} +2.79669 q^{67} -1.89488 q^{68} +1.67031 q^{69} +4.37336 q^{70} +13.9850 q^{71} -2.74615 q^{72} +9.53108 q^{73} -3.77489 q^{74} -0.503837 q^{75} -3.65123 q^{76} +18.1440 q^{77} -2.14188 q^{78} -15.9642 q^{79} -1.00000 q^{80} +6.77978 q^{81} +3.67235 q^{82} -13.8499 q^{83} +2.20346 q^{84} +1.89488 q^{85} -1.67508 q^{86} +1.62049 q^{87} -4.14877 q^{88} -14.1083 q^{89} +2.74615 q^{90} -18.5918 q^{91} -3.31519 q^{92} +0.204313 q^{93} -2.95950 q^{94} +3.65123 q^{95} -0.503837 q^{96} -14.0299 q^{97} +12.1263 q^{98} +11.3931 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9} - 28 q^{10} + 4 q^{11} + 4 q^{12} + 22 q^{13} + 10 q^{14} - 4 q^{15} + 28 q^{16} + 15 q^{17} + 40 q^{18} - 11 q^{19} - 28 q^{20} + 18 q^{21} + 4 q^{22} + 23 q^{23} + 4 q^{24} + 28 q^{25} + 22 q^{26} + 19 q^{27} + 10 q^{28} + 19 q^{29} - 4 q^{30} + 7 q^{31} + 28 q^{32} + 33 q^{33} + 15 q^{34} - 10 q^{35} + 40 q^{36} + 22 q^{37} - 11 q^{38} + 8 q^{39} - 28 q^{40} + 41 q^{41} + 18 q^{42} + 7 q^{43} + 4 q^{44} - 40 q^{45} + 23 q^{46} + 51 q^{47} + 4 q^{48} + 60 q^{49} + 28 q^{50} - 5 q^{51} + 22 q^{52} + 25 q^{53} + 19 q^{54} - 4 q^{55} + 10 q^{56} + 8 q^{57} + 19 q^{58} + 32 q^{59} - 4 q^{60} + 24 q^{61} + 7 q^{62} + 33 q^{63} + 28 q^{64} - 22 q^{65} + 33 q^{66} + 3 q^{67} + 15 q^{68} + 43 q^{69} - 10 q^{70} + 8 q^{71} + 40 q^{72} + 47 q^{73} + 22 q^{74} + 4 q^{75} - 11 q^{76} + 46 q^{77} + 8 q^{78} - 22 q^{79} - 28 q^{80} + 76 q^{81} + 41 q^{82} + 36 q^{83} + 18 q^{84} - 15 q^{85} + 7 q^{86} + 72 q^{87} + 4 q^{88} + 70 q^{89} - 40 q^{90} - 21 q^{91} + 23 q^{92} + 24 q^{93} + 51 q^{94} + 11 q^{95} + 4 q^{96} + 43 q^{97} + 60 q^{98} - 9 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 4 * q^3 + 28 * q^4 - 28 * q^5 + 4 * q^6 + 10 * q^7 + 28 * q^8 + 40 * q^9 - 28 * q^10 + 4 * q^11 + 4 * q^12 + 22 * q^13 + 10 * q^14 - 4 * q^15 + 28 * q^16 + 15 * q^17 + 40 * q^18 - 11 * q^19 - 28 * q^20 + 18 * q^21 + 4 * q^22 + 23 * q^23 + 4 * q^24 + 28 * q^25 + 22 * q^26 + 19 * q^27 + 10 * q^28 + 19 * q^29 - 4 * q^30 + 7 * q^31 + 28 * q^32 + 33 * q^33 + 15 * q^34 - 10 * q^35 + 40 * q^36 + 22 * q^37 - 11 * q^38 + 8 * q^39 - 28 * q^40 + 41 * q^41 + 18 * q^42 + 7 * q^43 + 4 * q^44 - 40 * q^45 + 23 * q^46 + 51 * q^47 + 4 * q^48 + 60 * q^49 + 28 * q^50 - 5 * q^51 + 22 * q^52 + 25 * q^53 + 19 * q^54 - 4 * q^55 + 10 * q^56 + 8 * q^57 + 19 * q^58 + 32 * q^59 - 4 * q^60 + 24 * q^61 + 7 * q^62 + 33 * q^63 + 28 * q^64 - 22 * q^65 + 33 * q^66 + 3 * q^67 + 15 * q^68 + 43 * q^69 - 10 * q^70 + 8 * q^71 + 40 * q^72 + 47 * q^73 + 22 * q^74 + 4 * q^75 - 11 * q^76 + 46 * q^77 + 8 * q^78 - 22 * q^79 - 28 * q^80 + 76 * q^81 + 41 * q^82 + 36 * q^83 + 18 * q^84 - 15 * q^85 + 7 * q^86 + 72 * q^87 + 4 * q^88 + 70 * q^89 - 40 * q^90 - 21 * q^91 + 23 * q^92 + 24 * q^93 + 51 * q^94 + 11 * q^95 + 4 * q^96 + 43 * q^97 + 60 * q^98 - 9 * q^99

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