LMFDB - Embedded newform 6010.2.a.h.1.18

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			1.18
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.983549 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.983549 q^{6} +0.242326 q^{7} +1.00000 q^{8} -2.03263 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.983549 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.983549 q^{6} +0.242326 q^{7} +1.00000 q^{8} -2.03263 q^{9} -1.00000 q^{10} +1.62343 q^{11} +0.983549 q^{12} +5.09497 q^{13} +0.242326 q^{14} -0.983549 q^{15} +1.00000 q^{16} +3.49127 q^{17} -2.03263 q^{18} -1.69805 q^{19} -1.00000 q^{20} +0.238339 q^{21} +1.62343 q^{22} -1.09900 q^{23} +0.983549 q^{24} +1.00000 q^{25} +5.09497 q^{26} -4.94984 q^{27} +0.242326 q^{28} -1.59214 q^{29} -0.983549 q^{30} +2.05758 q^{31} +1.00000 q^{32} +1.59672 q^{33} +3.49127 q^{34} -0.242326 q^{35} -2.03263 q^{36} -5.24765 q^{37} -1.69805 q^{38} +5.01115 q^{39} -1.00000 q^{40} +11.2879 q^{41} +0.238339 q^{42} +7.08069 q^{43} +1.62343 q^{44} +2.03263 q^{45} -1.09900 q^{46} +3.91355 q^{47} +0.983549 q^{48} -6.94128 q^{49} +1.00000 q^{50} +3.43383 q^{51} +5.09497 q^{52} +3.09802 q^{53} -4.94984 q^{54} -1.62343 q^{55} +0.242326 q^{56} -1.67011 q^{57} -1.59214 q^{58} -5.95468 q^{59} -0.983549 q^{60} +9.17251 q^{61} +2.05758 q^{62} -0.492560 q^{63} +1.00000 q^{64} -5.09497 q^{65} +1.59672 q^{66} -4.42141 q^{67} +3.49127 q^{68} -1.08092 q^{69} -0.242326 q^{70} +5.47502 q^{71} -2.03263 q^{72} +1.43914 q^{73} -5.24765 q^{74} +0.983549 q^{75} -1.69805 q^{76} +0.393399 q^{77} +5.01115 q^{78} +4.74615 q^{79} -1.00000 q^{80} +1.22949 q^{81} +11.2879 q^{82} +1.04464 q^{83} +0.238339 q^{84} -3.49127 q^{85} +7.08069 q^{86} -1.56595 q^{87} +1.62343 q^{88} +8.02018 q^{89} +2.03263 q^{90} +1.23464 q^{91} -1.09900 q^{92} +2.02374 q^{93} +3.91355 q^{94} +1.69805 q^{95} +0.983549 q^{96} +19.3325 q^{97} -6.94128 q^{98} -3.29983 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.983549	0.567852	0.283926	−	0.958846i	$-0.408363\pi$
$3$	0.983549	0.567852	0.283926	+	0.958846i	$0.408363\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.983549	0.401532
$7$	0.242326	0.0915906	0.0457953	−	0.998951i	$-0.485418\pi$
$7$	0.242326	0.0915906	0.0457953	+	0.998951i	$0.485418\pi$
$8$	1.00000	0.353553
$9$	−2.03263	−0.677544
$10$	−1.00000	−0.316228
$11$	1.62343	0.489482	0.244741	−	0.969588i	$-0.421297\pi$
$11$	1.62343	0.489482	0.244741	+	0.969588i	$0.421297\pi$
$12$	0.983549	0.283926
$13$	5.09497	1.41309	0.706545	−	0.707668i	$-0.250253\pi$
$13$	5.09497	1.41309	0.706545	+	0.707668i	$0.250253\pi$
$14$	0.242326	0.0647644
$15$	−0.983549	−0.253951
$16$	1.00000	0.250000
$17$	3.49127	0.846757	0.423378	−	0.905953i	$-0.360844\pi$
$17$	3.49127	0.846757	0.423378	+	0.905953i	$0.360844\pi$
$18$	−2.03263	−0.479096
$19$	−1.69805	−0.389558	−0.194779	−	0.980847i	$-0.562399\pi$
$19$	−1.69805	−0.389558	−0.194779	+	0.980847i	$0.562399\pi$
$20$	−1.00000	−0.223607
$21$	0.238339	0.0520099
$22$	1.62343	0.346116
$23$	−1.09900	−0.229157	−0.114578	−	0.993414i	$-0.536552\pi$
$23$	−1.09900	−0.229157	−0.114578	+	0.993414i	$0.536552\pi$
$24$	0.983549	0.200766
$25$	1.00000	0.200000
$26$	5.09497	0.999206
$27$	−4.94984	−0.952597
$28$	0.242326	0.0457953
$29$	−1.59214	−0.295653	−0.147826	−	0.989013i	$-0.547228\pi$
$29$	−1.59214	−0.295653	−0.147826	+	0.989013i	$0.547228\pi$
$30$	−0.983549	−0.179571
$31$	2.05758	0.369553	0.184777	−	0.982781i	$-0.440844\pi$
$31$	2.05758	0.369553	0.184777	+	0.982781i	$0.440844\pi$
$32$	1.00000	0.176777
$33$	1.59672	0.277954
$34$	3.49127	0.598748
$35$	−0.242326	−0.0409606
$36$	−2.03263	−0.338772
$37$	−5.24765	−0.862709	−0.431354	−	0.902183i	$-0.641964\pi$
$37$	−5.24765	−0.862709	−0.431354	+	0.902183i	$0.641964\pi$
$38$	−1.69805	−0.275459
$39$	5.01115	0.802426
$40$	−1.00000	−0.158114
$41$	11.2879	1.76287	0.881433	−	0.472308i	$-0.156579\pi$
$41$	11.2879	1.76287	0.881433	+	0.472308i	$0.156579\pi$
$42$	0.238339	0.0367766
$43$	7.08069	1.07980	0.539898	−	0.841731i	$-0.318463\pi$
$43$	7.08069	1.07980	0.539898	+	0.841731i	$0.318463\pi$
$44$	1.62343	0.244741
$45$	2.03263	0.303007
$46$	−1.09900	−0.162038
$47$	3.91355	0.570850	0.285425	−	0.958401i	$-0.407865\pi$
$47$	3.91355	0.570850	0.285425	+	0.958401i	$0.407865\pi$
$48$	0.983549	0.141963
$49$	−6.94128	−0.991611
$50$	1.00000	0.141421
$51$	3.43383	0.480833
$52$	5.09497	0.706545
$53$	3.09802	0.425546	0.212773	−	0.977102i	$-0.431750\pi$
$53$	3.09802	0.425546	0.212773	+	0.977102i	$0.431750\pi$
$54$	−4.94984	−0.673588
$55$	−1.62343	−0.218903
$56$	0.242326	0.0323822
$57$	−1.67011	−0.221212
$58$	−1.59214	−0.209058
$59$	−5.95468	−0.775233	−0.387617	−	0.921821i	$-0.626702\pi$
$59$	−5.95468	−0.775233	−0.387617	+	0.921821i	$0.626702\pi$
$60$	−0.983549	−0.126976
$61$	9.17251	1.17442	0.587210	−	0.809435i	$-0.300226\pi$
$61$	9.17251	1.17442	0.587210	+	0.809435i	$0.300226\pi$
$62$	2.05758	0.261314
$63$	−0.492560	−0.0620567
$64$	1.00000	0.125000
$65$	−5.09497	−0.631953
$66$	1.59672	0.196543
$67$	−4.42141	−0.540161	−0.270080	−	0.962838i	$-0.587050\pi$
$67$	−4.42141	−0.540161	−0.270080	+	0.962838i	$0.587050\pi$
$68$	3.49127	0.423378
$69$	−1.08092	−0.130127
$70$	−0.242326	−0.0289635
$71$	5.47502	0.649765	0.324883	−	0.945754i	$-0.394675\pi$
$71$	5.47502	0.649765	0.324883	+	0.945754i	$0.394675\pi$
$72$	−2.03263	−0.239548
$73$	1.43914	0.168438	0.0842192	−	0.996447i	$-0.473160\pi$
$73$	1.43914	0.168438	0.0842192	+	0.996447i	$0.473160\pi$
$74$	−5.24765	−0.610027
$75$	0.983549	0.113570
$76$	−1.69805	−0.194779
$77$	0.393399	0.0448320
$78$	5.01115	0.567401
$79$	4.74615	0.533984	0.266992	−	0.963699i	$-0.413970\pi$
$79$	4.74615	0.533984	0.266992	+	0.963699i	$0.413970\pi$
$80$	−1.00000	−0.111803
$81$	1.22949	0.136610
$82$	11.2879	1.24654
$83$	1.04464	0.114664	0.0573321	−	0.998355i	$-0.481741\pi$
$83$	1.04464	0.114664	0.0573321	+	0.998355i	$0.481741\pi$
$84$	0.238339	0.0260050
$85$	−3.49127	−0.378681
$86$	7.08069	0.763531
$87$	−1.56595	−0.167887
$88$	1.62343	0.173058
$89$	8.02018	0.850138	0.425069	−	0.905161i	$-0.360250\pi$
$89$	8.02018	0.850138	0.425069	+	0.905161i	$0.360250\pi$
$90$	2.03263	0.214258
$91$	1.23464	0.129426
$92$	−1.09900	−0.114578
$93$	2.02374	0.209852
$94$	3.91355	0.403652
$95$	1.69805	0.174216
$96$	0.983549	0.100383
$97$	19.3325	1.96292	0.981461	−	0.191660i	$-0.0613869\pi$
$97$	19.3325	1.96292	0.981461	+	0.191660i	$0.0613869\pi$
$98$	−6.94128	−0.701175
$99$	−3.29983	−0.331646
$100$	1.00000	0.100000
$101$	−9.59858	−0.955095	−0.477547	−	0.878606i	$-0.658474\pi$
$101$	−9.59858	−0.955095	−0.477547	+	0.878606i	$0.658474\pi$
$102$	3.43383	0.340000
$103$	−3.62368	−0.357051	−0.178526	−	0.983935i	$-0.557133\pi$
$103$	−3.62368	−0.357051	−0.178526	+	0.983935i	$0.557133\pi$
$104$	5.09497	0.499603
$105$	−0.238339	−0.0232596
$106$	3.09802	0.300907
$107$	0.308390	0.0298132	0.0149066	−	0.999889i	$-0.495255\pi$
$107$	0.308390	0.0298132	0.0149066	+	0.999889i	$0.495255\pi$
$108$	−4.94984	−0.476298
$109$	10.0201	0.959750	0.479875	−	0.877337i	$-0.340682\pi$
$109$	10.0201	0.959750	0.479875	+	0.877337i	$0.340682\pi$
$110$	−1.62343	−0.154788
$111$	−5.16132	−0.489891
$112$	0.242326	0.0228977
$113$	9.98447	0.939260	0.469630	−	0.882863i	$-0.344387\pi$
$113$	9.98447	0.939260	0.469630	+	0.882863i	$0.344387\pi$
$114$	−1.67011	−0.156420
$115$	1.09900	0.102482
$116$	−1.59214	−0.147826
$117$	−10.3562	−0.957431
$118$	−5.95468	−0.548173
$119$	0.846025	0.0775550
$120$	−0.983549	−0.0897853
$121$	−8.36448	−0.760407
$122$	9.17251	0.830440
$123$	11.1022	1.00105
$124$	2.05758	0.184777
$125$	−1.00000	−0.0894427
$126$	−0.492560	−0.0438807
$127$	−3.88722	−0.344935	−0.172468	−	0.985015i	$-0.555174\pi$
$127$	−3.88722	−0.344935	−0.172468	+	0.985015i	$0.555174\pi$
$128$	1.00000	0.0883883
$129$	6.96421	0.613164
$130$	−5.09497	−0.446858
$131$	−12.8297	−1.12093	−0.560467	−	0.828176i	$-0.689378\pi$
$131$	−12.8297	−1.12093	−0.560467	+	0.828176i	$0.689378\pi$
$132$	1.59672	0.138977
$133$	−0.411481	−0.0356799
$134$	−4.42141	−0.381951
$135$	4.94984	0.426014
$136$	3.49127	0.299374
$137$	−9.08588	−0.776259	−0.388129	−	0.921605i	$-0.626879\pi$
$137$	−9.08588	−0.776259	−0.388129	+	0.921605i	$0.626879\pi$
$138$	−1.08092	−0.0920138
$139$	0.104297	0.00884635	0.00442318	−	0.999990i	$-0.498592\pi$
$139$	0.104297	0.00884635	0.00442318	+	0.999990i	$0.498592\pi$
$140$	−0.242326	−0.0204803
$141$	3.84916	0.324158
$142$	5.47502	0.459453
$143$	8.27132	0.691683
$144$	−2.03263	−0.169386
$145$	1.59214	0.132220
$146$	1.43914	0.119104
$147$	−6.82709	−0.563089
$148$	−5.24765	−0.431354
$149$	10.2068	0.836177	0.418088	−	0.908406i	$-0.362700\pi$
$149$	10.2068	0.836177	0.418088	+	0.908406i	$0.362700\pi$
$150$	0.983549	0.0803064
$151$	16.8466	1.37096	0.685480	−	0.728091i	$-0.259592\pi$
$151$	16.8466	1.37096	0.685480	+	0.728091i	$0.259592\pi$
$152$	−1.69805	−0.137730
$153$	−7.09646	−0.573715
$154$	0.393399	0.0317010
$155$	−2.05758	−0.165269
$156$	5.01115	0.401213
$157$	−17.1840	−1.37143	−0.685716	−	0.727869i	$-0.740511\pi$
$157$	−17.1840	−1.37143	−0.685716	+	0.727869i	$0.740511\pi$
$158$	4.74615	0.377584
$159$	3.04706	0.241647
$160$	−1.00000	−0.0790569
$161$	−0.266316	−0.0209886
$162$	1.22949	0.0965976
$163$	−9.74046	−0.762932	−0.381466	−	0.924383i	$-0.624581\pi$
$163$	−9.74046	−0.762932	−0.381466	+	0.924383i	$0.624581\pi$
$164$	11.2879	0.881433
$165$	−1.59672	−0.124305
$166$	1.04464	0.0810799
$167$	−10.8522	−0.839766	−0.419883	−	0.907578i	$-0.637929\pi$
$167$	−10.8522	−0.839766	−0.419883	+	0.907578i	$0.637929\pi$
$168$	0.238339	0.0183883
$169$	12.9587	0.996825
$170$	−3.49127	−0.267768
$171$	3.45150	0.263943
$172$	7.08069	0.539898
$173$	−19.5592	−1.48706	−0.743530	−	0.668702i	$-0.766850\pi$
$173$	−19.5592	−1.48706	−0.743530	+	0.668702i	$0.766850\pi$
$174$	−1.56595	−0.118714
$175$	0.242326	0.0183181
$176$	1.62343	0.122371
$177$	−5.85672	−0.440218
$178$	8.02018	0.601138
$179$	6.10766	0.456508	0.228254	−	0.973602i	$-0.426698\pi$
$179$	6.10766	0.456508	0.228254	+	0.973602i	$0.426698\pi$
$180$	2.03263	0.151503
$181$	20.7960	1.54575	0.772876	−	0.634557i	$-0.218818\pi$
$181$	20.7960	1.54575	0.772876	+	0.634557i	$0.218818\pi$
$182$	1.23464	0.0915179
$183$	9.02161	0.666897
$184$	−1.09900	−0.0810191
$185$	5.24765	0.385815
$186$	2.02374	0.148387
$187$	5.66783	0.414473
$188$	3.91355	0.285425
$189$	−1.19947	−0.0872490
$190$	1.69805	0.123189
$191$	23.3695	1.69096	0.845479	−	0.534009i	$-0.179315\pi$
$191$	23.3695	1.69096	0.845479	+	0.534009i	$0.179315\pi$
$192$	0.983549	0.0709815
$193$	18.3568	1.32135	0.660677	−	0.750670i	$-0.270269\pi$
$193$	18.3568	1.32135	0.660677	+	0.750670i	$0.270269\pi$
$194$	19.3325	1.38800
$195$	−5.01115	−0.358856
$196$	−6.94128	−0.495806
$197$	23.4142	1.66819	0.834095	−	0.551621i	$-0.185990\pi$
$197$	23.4142	1.66819	0.834095	+	0.551621i	$0.185990\pi$
$198$	−3.29983	−0.234509
$199$	−18.0305	−1.27815	−0.639073	−	0.769146i	$-0.720682\pi$
$199$	−18.0305	−1.27815	−0.639073	+	0.769146i	$0.720682\pi$
$200$	1.00000	0.0707107
$201$	−4.34867	−0.306731
$202$	−9.59858	−0.675354
$203$	−0.385816	−0.0270790
$204$	3.43383	0.240416
$205$	−11.2879	−0.788378
$206$	−3.62368	−0.252473
$207$	2.23386	0.155264
$208$	5.09497	0.353273
$209$	−2.75666	−0.190682
$210$	−0.238339	−0.0164470
$211$	11.2746	0.776178	0.388089	−	0.921622i	$-0.373135\pi$
$211$	11.2746	0.776178	0.388089	+	0.921622i	$0.373135\pi$
$212$	3.09802	0.212773
$213$	5.38495	0.368971
$214$	0.308390	0.0210811
$215$	−7.08069	−0.482899
$216$	−4.94984	−0.336794
$217$	0.498606	0.0338476
$218$	10.0201	0.678646
$219$	1.41546	0.0956481
$220$	−1.62343	−0.109452
$221$	17.7879	1.19654
$222$	−5.16132	−0.346405
$223$	3.08059	0.206292	0.103146	−	0.994666i	$-0.467109\pi$
$223$	3.08059	0.206292	0.103146	+	0.994666i	$0.467109\pi$
$224$	0.242326	0.0161911
$225$	−2.03263	−0.135509
$226$	9.98447	0.664157
$227$	18.6298	1.23651	0.618253	−	0.785979i	$-0.287841\pi$
$227$	18.6298	1.23651	0.618253	+	0.785979i	$0.287841\pi$
$228$	−1.67011	−0.110606
$229$	−2.35428	−0.155575	−0.0777875	−	0.996970i	$-0.524786\pi$
$229$	−2.35428	−0.155575	−0.0777875	+	0.996970i	$0.524786\pi$
$230$	1.09900	0.0724657
$231$	0.386927	0.0254579
$232$	−1.59214	−0.104529
$233$	13.7355	0.899842	0.449921	−	0.893068i	$-0.351452\pi$
$233$	13.7355	0.899842	0.449921	+	0.893068i	$0.351452\pi$
$234$	−10.3562	−0.677006
$235$	−3.91355	−0.255292
$236$	−5.95468	−0.387617
$237$	4.66807	0.303224
$238$	0.846025	0.0548397
$239$	6.34909	0.410688	0.205344	−	0.978690i	$-0.434169\pi$
$239$	6.34909	0.410688	0.205344	+	0.978690i	$0.434169\pi$
$240$	−0.983549	−0.0634878
$241$	4.11858	0.265301	0.132651	−	0.991163i	$-0.457651\pi$
$241$	4.11858	0.265301	0.132651	+	0.991163i	$0.457651\pi$
$242$	−8.36448	−0.537689
$243$	16.0588	1.03017
$244$	9.17251	0.587210
$245$	6.94128	0.443462
$246$	11.1022	0.707848
$247$	−8.65149	−0.550481
$248$	2.05758	0.130657
$249$	1.02746	0.0651124
$250$	−1.00000	−0.0632456
$251$	−0.500646	−0.0316005	−0.0158003	−	0.999875i	$-0.505030\pi$
$251$	−0.500646	−0.0316005	−0.0158003	+	0.999875i	$0.505030\pi$
$252$	−0.492560	−0.0310283
$253$	−1.78414	−0.112168
$254$	−3.88722	−0.243906
$255$	−3.43383	−0.215035
$256$	1.00000	0.0625000
$257$	0.805446	0.0502423	0.0251212	−	0.999684i	$-0.492003\pi$
$257$	0.805446	0.0502423	0.0251212	+	0.999684i	$0.492003\pi$
$258$	6.96421	0.433573
$259$	−1.27164	−0.0790160
$260$	−5.09497	−0.315977
$261$	3.23623	0.200318
$262$	−12.8297	−0.792621
$263$	−28.0289	−1.72834	−0.864168	−	0.503203i	$-0.832155\pi$
$263$	−28.0289	−1.72834	−0.864168	+	0.503203i	$0.832155\pi$
$264$	1.59672	0.0982714
$265$	−3.09802	−0.190310
$266$	−0.411481	−0.0252295
$267$	7.88824	0.482753
$268$	−4.42141	−0.270080
$269$	−8.64589	−0.527149	−0.263575	−	0.964639i	$-0.584901\pi$
$269$	−8.64589	−0.527149	−0.263575	+	0.964639i	$0.584901\pi$
$270$	4.94984	0.301238
$271$	7.22558	0.438923	0.219462	−	0.975621i	$-0.429570\pi$
$271$	7.22558	0.438923	0.219462	+	0.975621i	$0.429570\pi$
$272$	3.49127	0.211689
$273$	1.21433	0.0734947
$274$	−9.08588	−0.548898
$275$	1.62343	0.0978965
$276$	−1.08092	−0.0650636
$277$	1.41764	0.0851779	0.0425889	−	0.999093i	$-0.486439\pi$
$277$	1.41764	0.0851779	0.0425889	+	0.999093i	$0.486439\pi$
$278$	0.104297	0.00625531
$279$	−4.18231	−0.250388
$280$	−0.242326	−0.0144818
$281$	−4.66925	−0.278544	−0.139272	−	0.990254i	$-0.544476\pi$
$281$	−4.66925	−0.278544	−0.139272	+	0.990254i	$0.544476\pi$
$282$	3.84916	0.229214
$283$	−31.1179	−1.84977	−0.924884	−	0.380248i	$-0.875839\pi$
$283$	−31.1179	−1.84977	−0.924884	+	0.380248i	$0.875839\pi$
$284$	5.47502	0.324883
$285$	1.67011	0.0989288
$286$	8.27132	0.489094
$287$	2.73534	0.161462
$288$	−2.03263	−0.119774
$289$	−4.81105	−0.283003
$290$	1.59214	0.0934935
$291$	19.0145	1.11465
$292$	1.43914	0.0842192
$293$	1.66802	0.0974467	0.0487233	−	0.998812i	$-0.484485\pi$
$293$	1.66802	0.0974467	0.0487233	+	0.998812i	$0.484485\pi$
$294$	−6.82709	−0.398164
$295$	5.95468	0.346695
$296$	−5.24765	−0.305014
$297$	−8.03571	−0.466279
$298$	10.2068	0.591266
$299$	−5.59936	−0.323819
$300$	0.983549	0.0567852
$301$	1.71584	0.0988992
$302$	16.8466	0.969415
$303$	−9.44068	−0.542353
$304$	−1.69805	−0.0973896
$305$	−9.17251	−0.525217
$306$	−7.09646	−0.405678
$307$	−23.0883	−1.31772	−0.658860	−	0.752265i	$-0.728961\pi$
$307$	−23.0883	−1.31772	−0.658860	+	0.752265i	$0.728961\pi$
$308$	0.393399	0.0224160
$309$	−3.56406	−0.202752
$310$	−2.05758	−0.116863
$311$	13.6661	0.774931	0.387466	−	0.921884i	$-0.373351\pi$
$311$	13.6661	0.774931	0.387466	+	0.921884i	$0.373351\pi$
$312$	5.01115	0.283701
$313$	20.1587	1.13944	0.569718	−	0.821840i	$-0.307053\pi$
$313$	20.1587	1.13944	0.569718	+	0.821840i	$0.307053\pi$
$314$	−17.1840	−0.969750
$315$	0.492560	0.0277526
$316$	4.74615	0.266992
$317$	−2.62335	−0.147342	−0.0736709	−	0.997283i	$-0.523471\pi$
$317$	−2.62335	−0.147342	−0.0736709	+	0.997283i	$0.523471\pi$
$318$	3.04706	0.170870
$319$	−2.58472	−0.144717
$320$	−1.00000	−0.0559017
$321$	0.303316	0.0169295
$322$	−0.266316	−0.0148412
$323$	−5.92833	−0.329861
$324$	1.22949	0.0683048
$325$	5.09497	0.282618
$326$	−9.74046	−0.539474
$327$	9.85524	0.544996
$328$	11.2879	0.623268
$329$	0.948354	0.0522845
$330$	−1.59672	−0.0878966
$331$	−7.21045	−0.396322	−0.198161	−	0.980169i	$-0.563497\pi$
$331$	−7.21045	−0.396322	−0.198161	+	0.980169i	$0.563497\pi$
$332$	1.04464	0.0573321
$333$	10.6665	0.584523
$334$	−10.8522	−0.593804
$335$	4.42141	0.241567
$336$	0.238339	0.0130025
$337$	−5.87154	−0.319843	−0.159921	−	0.987130i	$-0.551124\pi$
$337$	−5.87154	−0.319843	−0.159921	+	0.987130i	$0.551124\pi$
$338$	12.9587	0.704861
$339$	9.82022	0.533361
$340$	−3.49127	−0.189341
$341$	3.34034	0.180890
$342$	3.45150	0.186636
$343$	−3.37833	−0.182413
$344$	7.08069	0.381765
$345$	1.08092	0.0581946
$346$	−19.5592	−1.05151
$347$	23.4318	1.25789	0.628943	−	0.777452i	$-0.283488\pi$
$347$	23.4318	1.25789	0.628943	+	0.777452i	$0.283488\pi$
$348$	−1.56595	−0.0839435
$349$	−18.8144	−1.00711	−0.503556	−	0.863963i	$-0.667975\pi$
$349$	−18.8144	−1.00711	−0.503556	+	0.863963i	$0.667975\pi$
$350$	0.242326	0.0129529
$351$	−25.2193	−1.34611
$352$	1.62343	0.0865291
$353$	2.37850	0.126595	0.0632973	−	0.997995i	$-0.479838\pi$
$353$	2.37850	0.126595	0.0632973	+	0.997995i	$0.479838\pi$
$354$	−5.85672	−0.311281
$355$	−5.47502	−0.290584
$356$	8.02018	0.425069
$357$	0.832107	0.0440398
$358$	6.10766	0.322800
$359$	19.7315	1.04139	0.520694	−	0.853743i	$-0.325673\pi$
$359$	19.7315	1.04139	0.520694	+	0.853743i	$0.325673\pi$
$360$	2.03263	0.107129
$361$	−16.1166	−0.848244
$362$	20.7960	1.09301
$363$	−8.22687	−0.431799
$364$	1.23464	0.0647129
$365$	−1.43914	−0.0753279
$366$	9.02161	0.471567
$367$	8.80382	0.459556	0.229778	−	0.973243i	$-0.426200\pi$
$367$	8.80382	0.459556	0.229778	+	0.973243i	$0.426200\pi$
$368$	−1.09900	−0.0572892
$369$	−22.9441	−1.19442
$370$	5.24765	0.272812
$371$	0.750731	0.0389760
$372$	2.02374	0.104926
$373$	−3.36224	−0.174090	−0.0870452	−	0.996204i	$-0.527742\pi$
$373$	−3.36224	−0.174090	−0.0870452	+	0.996204i	$0.527742\pi$
$374$	5.66783	0.293076
$375$	−0.983549	−0.0507902
$376$	3.91355	0.201826
$377$	−8.11189	−0.417784
$378$	−1.19947	−0.0616943
$379$	10.6257	0.545805	0.272902	−	0.962042i	$-0.412016\pi$
$379$	10.6257	0.545805	0.272902	+	0.962042i	$0.412016\pi$
$380$	1.69805	0.0871079
$381$	−3.82327	−0.195872
$382$	23.3695	1.19569
$383$	−33.3620	−1.70472	−0.852360	−	0.522955i	$-0.824830\pi$
$383$	−33.3620	−1.70472	−0.852360	+	0.522955i	$0.824830\pi$
$384$	0.983549	0.0501915
$385$	−0.393399	−0.0200495
$386$	18.3568	0.934338
$387$	−14.3924	−0.731609
$388$	19.3325	0.981461
$389$	4.99645	0.253330	0.126665	−	0.991946i	$-0.459573\pi$
$389$	4.99645	0.253330	0.126665	+	0.991946i	$0.459573\pi$
$390$	−5.01115	−0.253750
$391$	−3.83689	−0.194040
$392$	−6.94128	−0.350587
$393$	−12.6186	−0.636525
$394$	23.4142	1.17959
$395$	−4.74615	−0.238805
$396$	−3.29983	−0.165823
$397$	−36.3490	−1.82430	−0.912152	−	0.409852i	$-0.865580\pi$
$397$	−36.3490	−1.82430	−0.912152	+	0.409852i	$0.865580\pi$
$398$	−18.0305	−0.903786
$399$	−0.404711	−0.0202609
$400$	1.00000	0.0500000
$401$	−16.5721	−0.827569	−0.413784	−	0.910375i	$-0.635793\pi$
$401$	−16.5721	−0.827569	−0.413784	+	0.910375i	$0.635793\pi$
$402$	−4.34867	−0.216892
$403$	10.4833	0.522212
$404$	−9.59858	−0.477547
$405$	−1.22949	−0.0610937
$406$	−0.385816	−0.0191477
$407$	−8.51919	−0.422281
$408$	3.43383	0.170000
$409$	−5.63288	−0.278528	−0.139264	−	0.990255i	$-0.544474\pi$
$409$	−5.63288	−0.278528	−0.139264	+	0.990255i	$0.544474\pi$
$410$	−11.2879	−0.557467
$411$	−8.93640	−0.440800
$412$	−3.62368	−0.178526
$413$	−1.44297	−0.0710041
$414$	2.23386	0.109788
$415$	−1.04464	−0.0512794
$416$	5.09497	0.249801
$417$	0.102581	0.00502342
$418$	−2.75666	−0.134833
$419$	18.9557	0.926047	0.463024	−	0.886346i	$-0.346765\pi$
$419$	18.9557	0.926047	0.463024	+	0.886346i	$0.346765\pi$
$420$	−0.238339	−0.0116298
$421$	−20.2566	−0.987248	−0.493624	−	0.869675i	$-0.664328\pi$
$421$	−20.2566	−0.987248	−0.493624	+	0.869675i	$0.664328\pi$
$422$	11.2746	0.548841
$423$	−7.95480	−0.386776
$424$	3.09802	0.150453
$425$	3.49127	0.169351
$426$	5.38495	0.260902
$427$	2.22274	0.107566
$428$	0.308390	0.0149066
$429$	8.13525	0.392774
$430$	−7.08069	−0.341461
$431$	−2.40963	−0.116068	−0.0580340	−	0.998315i	$-0.518483\pi$
$431$	−2.40963	−0.116068	−0.0580340	+	0.998315i	$0.518483\pi$
$432$	−4.94984	−0.238149
$433$	−25.6477	−1.23255	−0.616276	−	0.787530i	$-0.711359\pi$
$433$	−25.6477	−1.23255	−0.616276	+	0.787530i	$0.711359\pi$
$434$	0.498606	0.0239339
$435$	1.56595	0.0750813
$436$	10.0201	0.479875
$437$	1.86615	0.0892699
$438$	1.41546	0.0676334
$439$	23.0494	1.10009	0.550043	−	0.835136i	$-0.314611\pi$
$439$	23.0494	1.10009	0.550043	+	0.835136i	$0.314611\pi$
$440$	−1.62343	−0.0773940
$441$	14.1091	0.671860
$442$	17.7879	0.846085
$443$	10.7549	0.510982	0.255491	−	0.966811i	$-0.417763\pi$
$443$	10.7549	0.510982	0.255491	+	0.966811i	$0.417763\pi$
$444$	−5.16132	−0.244945
$445$	−8.02018	−0.380193
$446$	3.08059	0.145870
$447$	10.0389	0.474825
$448$	0.242326	0.0114488
$449$	13.8605	0.654115	0.327058	−	0.945004i	$-0.393943\pi$
$449$	13.8605	0.654115	0.327058	+	0.945004i	$0.393943\pi$
$450$	−2.03263	−0.0958192
$451$	18.3250	0.862892
$452$	9.98447	0.469630
$453$	16.5695	0.778503
$454$	18.6298	0.874342
$455$	−1.23464	−0.0578810
$456$	−1.67011	−0.0782101
$457$	−21.4038	−1.00123	−0.500615	−	0.865670i	$-0.666893\pi$
$457$	−21.4038	−1.00123	−0.500615	+	0.865670i	$0.666893\pi$
$458$	−2.35428	−0.110008
$459$	−17.2812	−0.806618
$460$	1.09900	0.0512410
$461$	−20.6343	−0.961037	−0.480518	−	0.876985i	$-0.659551\pi$
$461$	−20.6343	−0.961037	−0.480518	+	0.876985i	$0.659551\pi$
$462$	0.386927	0.0180015
$463$	7.90197	0.367235	0.183618	−	0.982998i	$-0.441219\pi$
$463$	7.90197	0.367235	0.183618	+	0.982998i	$0.441219\pi$
$464$	−1.59214	−0.0739131
$465$	−2.02374	−0.0938485
$466$	13.7355	0.636284
$467$	−8.34308	−0.386071	−0.193036	−	0.981192i	$-0.561833\pi$
$467$	−8.34308	−0.386071	−0.193036	+	0.981192i	$0.561833\pi$
$468$	−10.3562	−0.478715
$469$	−1.07142	−0.0494736
$470$	−3.91355	−0.180518
$471$	−16.9013	−0.778771
$472$	−5.95468	−0.274086
$473$	11.4950	0.528541
$474$	4.66807	0.214412
$475$	−1.69805	−0.0779117
$476$	0.846025	0.0387775
$477$	−6.29714	−0.288326
$478$	6.34909	0.290400
$479$	−21.3622	−0.976062	−0.488031	−	0.872826i	$-0.662285\pi$
$479$	−21.3622	−0.976062	−0.488031	+	0.872826i	$0.662285\pi$
$480$	−0.983549	−0.0448927
$481$	−26.7366	−1.21909
$482$	4.11858	0.187596
$483$	−0.261934	−0.0119184
$484$	−8.36448	−0.380204
$485$	−19.3325	−0.877846
$486$	16.0588	0.728441
$487$	−14.0473	−0.636544	−0.318272	−	0.947999i	$-0.603103\pi$
$487$	−14.0473	−0.636544	−0.318272	+	0.947999i	$0.603103\pi$
$488$	9.17251	0.415220
$489$	−9.58022	−0.433232
$490$	6.94128	0.313575
$491$	−33.1698	−1.49693	−0.748466	−	0.663173i	$-0.769210\pi$
$491$	−33.1698	−1.49693	−0.748466	+	0.663173i	$0.769210\pi$
$492$	11.1022	0.500524
$493$	−5.55858	−0.250346
$494$	−8.65149	−0.389249
$495$	3.29983	0.148316
$496$	2.05758	0.0923883
$497$	1.32674	0.0595124
$498$	1.02746	0.0460414
$499$	−25.1270	−1.12484	−0.562421	−	0.826851i	$-0.690130\pi$
$499$	−25.1270	−1.12484	−0.562421	+	0.826851i	$0.690130\pi$
$500$	−1.00000	−0.0447214
$501$	−10.6736	−0.476863
$502$	−0.500646	−0.0223449
$503$	8.76952	0.391013	0.195507	−	0.980702i	$-0.437365\pi$
$503$	8.76952	0.391013	0.195507	+	0.980702i	$0.437365\pi$
$504$	−0.492560	−0.0219403
$505$	9.59858	0.427131
$506$	−1.78414	−0.0793149
$507$	12.7455	0.566049
$508$	−3.88722	−0.172468
$509$	−17.1304	−0.759293	−0.379646	−	0.925132i	$-0.623954\pi$
$509$	−17.1304	−0.759293	−0.379646	+	0.925132i	$0.623954\pi$
$510$	−3.43383	−0.152053
$511$	0.348741	0.0154274
$512$	1.00000	0.0441942
$513$	8.40505	0.371092
$514$	0.805446	0.0355267
$515$	3.62368	0.159678
$516$	6.96421	0.306582
$517$	6.35337	0.279421
$518$	−1.27164	−0.0558728
$519$	−19.2375	−0.844431
$520$	−5.09497	−0.223429
$521$	−32.2576	−1.41323	−0.706615	−	0.707599i	$-0.749778\pi$
$521$	−32.2576	−1.41323	−0.706615	+	0.707599i	$0.749778\pi$
$522$	3.23623	0.141646
$523$	35.4019	1.54802	0.774008	−	0.633176i	$-0.218249\pi$
$523$	35.4019	1.54802	0.774008	+	0.633176i	$0.218249\pi$
$524$	−12.8297	−0.560467
$525$	0.238339	0.0104020
$526$	−28.0289	−1.22212
$527$	7.18358	0.312922
$528$	1.59672	0.0694884
$529$	−21.7922	−0.947487
$530$	−3.09802	−0.134569
$531$	12.1037	0.525255
$532$	−0.411481	−0.0178400
$533$	57.5113	2.49109
$534$	7.88824	0.341358
$535$	−0.308390	−0.0133329
$536$	−4.42141	−0.190976
$537$	6.00718	0.259229
$538$	−8.64589	−0.372751
$539$	−11.2687	−0.485376
$540$	4.94984	0.213007
$541$	−29.0723	−1.24991	−0.624957	−	0.780659i	$-0.714884\pi$
$541$	−29.0723	−1.24991	−0.624957	+	0.780659i	$0.714884\pi$
$542$	7.22558	0.310365
$543$	20.4538	0.877758
$544$	3.49127	0.149687
$545$	−10.0201	−0.429213
$546$	1.21433	0.0519686
$547$	−3.04451	−0.130174	−0.0650870	−	0.997880i	$-0.520732\pi$
$547$	−3.04451	−0.130174	−0.0650870	+	0.997880i	$0.520732\pi$
$548$	−9.08588	−0.388129
$549$	−18.6443	−0.795721
$550$	1.62343	0.0692233
$551$	2.70352	0.115174
$552$	−1.08092	−0.0460069
$553$	1.15012	0.0489079
$554$	1.41764	0.0602299
$555$	5.16132	0.219086
$556$	0.104297	0.00442318
$557$	12.3731	0.524265	0.262133	−	0.965032i	$-0.415574\pi$
$557$	12.3731	0.524265	0.262133	+	0.965032i	$0.415574\pi$
$558$	−4.18231	−0.177051
$559$	36.0759	1.52585
$560$	−0.242326	−0.0102401
$561$	5.57458	0.235359
$562$	−4.66925	−0.196960
$563$	−25.9341	−1.09299	−0.546496	−	0.837461i	$-0.684039\pi$
$563$	−25.9341	−1.09299	−0.546496	+	0.837461i	$0.684039\pi$
$564$	3.84916	0.162079
$565$	−9.98447	−0.420050
$566$	−31.1179	−1.30798
$567$	0.297937	0.0125122
$568$	5.47502	0.229727
$569$	−8.88764	−0.372589	−0.186295	−	0.982494i	$-0.559648\pi$
$569$	−8.88764	−0.372589	−0.186295	+	0.982494i	$0.559648\pi$
$570$	1.67011	0.0699532
$571$	−20.4072	−0.854013	−0.427007	−	0.904249i	$-0.640432\pi$
$571$	−20.4072	−0.854013	−0.427007	+	0.904249i	$0.640432\pi$
$572$	8.27132	0.345841
$573$	22.9850	0.960214
$574$	2.73534	0.114171
$575$	−1.09900	−0.0458313
$576$	−2.03263	−0.0846930
$577$	−18.5732	−0.773211	−0.386606	−	0.922245i	$-0.626353\pi$
$577$	−18.5732	−0.773211	−0.386606	+	0.922245i	$0.626353\pi$
$578$	−4.81105	−0.200113
$579$	18.0548	0.750334
$580$	1.59214	0.0661099
$581$	0.253144	0.0105022
$582$	19.0145	0.788177
$583$	5.02942	0.208297
$584$	1.43914	0.0595519
$585$	10.3562	0.428176
$586$	1.66802	0.0689052
$587$	29.9668	1.23686	0.618431	−	0.785839i	$-0.287769\pi$
$587$	29.9668	1.23686	0.618431	+	0.785839i	$0.287769\pi$
$588$	−6.82709	−0.281544
$589$	−3.49387	−0.143963
$590$	5.95468	0.245150
$591$	23.0290	0.947285
$592$	−5.24765	−0.215677
$593$	−19.3340	−0.793951	−0.396975	−	0.917829i	$-0.629940\pi$
$593$	−19.3340	−0.793951	−0.396975	+	0.917829i	$0.629940\pi$
$594$	−8.03571	−0.329709
$595$	−0.846025	−0.0346837
$596$	10.2068	0.418088
$597$	−17.7339	−0.725798
$598$	−5.59936	−0.228975
$599$	12.0615	0.492819	0.246409	−	0.969166i	$-0.420749\pi$
$599$	12.0615	0.492819	0.246409	+	0.969166i	$0.420749\pi$
$600$	0.983549	0.0401532
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	1.71584	0.0699323
$603$	8.98709	0.365983
$604$	16.8466	0.685480
$605$	8.36448	0.340064
$606$	−9.44068	−0.383501
$607$	−29.5858	−1.20085	−0.600425	−	0.799681i	$-0.705002\pi$
$607$	−29.5858	−1.20085	−0.600425	+	0.799681i	$0.705002\pi$
$608$	−1.69805	−0.0688648
$609$	−0.379469	−0.0153769
$610$	−9.17251	−0.371384
$611$	19.9394	0.806662
$612$	−7.09646	−0.286858
$613$	29.6917	1.19924	0.599619	−	0.800286i	$-0.295319\pi$
$613$	29.6917	1.19924	0.599619	+	0.800286i	$0.295319\pi$
$614$	−23.0883	−0.931769
$615$	−11.1022	−0.447682
$616$	0.393399	0.0158505
$617$	49.2869	1.98422	0.992108	−	0.125387i	$-0.0400172\pi$
$617$	49.2869	1.98422	0.992108	+	0.125387i	$0.0400172\pi$
$618$	−3.56406	−0.143368
$619$	−31.8303	−1.27937	−0.639685	−	0.768637i	$-0.720935\pi$
$619$	−31.8303	−1.27937	−0.639685	+	0.768637i	$0.720935\pi$
$620$	−2.05758	−0.0826346
$621$	5.43986	0.218294
$622$	13.6661	0.547959
$623$	1.94350	0.0778647
$624$	5.01115	0.200607
$625$	1.00000	0.0400000
$626$	20.1587	0.805703
$627$	−2.71131	−0.108279
$628$	−17.1840	−0.685716
$629$	−18.3210	−0.730504
$630$	0.492560	0.0196240
$631$	−18.1985	−0.724472	−0.362236	−	0.932086i	$-0.617986\pi$
$631$	−18.1985	−0.724472	−0.362236	+	0.932086i	$0.617986\pi$
$632$	4.74615	0.188792
$633$	11.0892	0.440755
$634$	−2.62335	−0.104186
$635$	3.88722	0.154260
$636$	3.04706	0.120824
$637$	−35.3656	−1.40124
$638$	−2.58472	−0.102330
$639$	−11.1287	−0.440245
$640$	−1.00000	−0.0395285
$641$	−14.6329	−0.577964	−0.288982	−	0.957334i	$-0.593317\pi$
$641$	−14.6329	−0.577964	−0.288982	+	0.957334i	$0.593317\pi$
$642$	0.303316	0.0119709
$643$	32.8179	1.29421	0.647107	−	0.762399i	$-0.275979\pi$
$643$	32.8179	1.29421	0.647107	+	0.762399i	$0.275979\pi$
$644$	−0.266316	−0.0104943
$645$	−6.96421	−0.274215
$646$	−5.92833	−0.233247
$647$	−4.32732	−0.170125	−0.0850623	−	0.996376i	$-0.527109\pi$
$647$	−4.32732	−0.170125	−0.0850623	+	0.996376i	$0.527109\pi$
$648$	1.22949	0.0482988
$649$	−9.66700	−0.379463
$650$	5.09497	0.199841
$651$	0.490404	0.0192204
$652$	−9.74046	−0.381466
$653$	−41.9269	−1.64073	−0.820364	−	0.571842i	$-0.806229\pi$
$653$	−41.9269	−1.64073	−0.820364	+	0.571842i	$0.806229\pi$
$654$	9.85524	0.385370
$655$	12.8297	0.501297
$656$	11.2879	0.440717
$657$	−2.92524	−0.114124
$658$	0.948354	0.0369707
$659$	−34.1197	−1.32912	−0.664558	−	0.747237i	$-0.731380\pi$
$659$	−34.1197	−1.32912	−0.664558	+	0.747237i	$0.731380\pi$
$660$	−1.59672	−0.0621523
$661$	37.1745	1.44592	0.722960	−	0.690890i	$-0.242781\pi$
$661$	37.1745	1.44592	0.722960	+	0.690890i	$0.242781\pi$
$662$	−7.21045	−0.280242
$663$	17.4953	0.679460
$664$	1.04464	0.0405399
$665$	0.411481	0.0159565
$666$	10.6665	0.413320
$667$	1.74975	0.0677508
$668$	−10.8522	−0.419883
$669$	3.02991	0.117143
$670$	4.42141	0.170814
$671$	14.8909	0.574858
$672$	0.238339	0.00919415
$673$	−28.2666	−1.08960	−0.544798	−	0.838567i	$-0.683394\pi$
$673$	−28.2666	−1.08960	−0.544798	+	0.838567i	$0.683394\pi$
$674$	−5.87154	−0.226163
$675$	−4.94984	−0.190519
$676$	12.9587	0.498412
$677$	−2.42448	−0.0931803	−0.0465901	−	0.998914i	$-0.514835\pi$
$677$	−2.42448	−0.0931803	−0.0465901	+	0.998914i	$0.514835\pi$
$678$	9.82022	0.377143
$679$	4.68478	0.179785
$680$	−3.49127	−0.133884
$681$	18.3234	0.702153
$682$	3.34034	0.127908
$683$	−4.11722	−0.157541	−0.0787705	−	0.996893i	$-0.525099\pi$
$683$	−4.11722	−0.157541	−0.0787705	+	0.996893i	$0.525099\pi$
$684$	3.45150	0.131971
$685$	9.08588	0.347154
$686$	−3.37833	−0.128985
$687$	−2.31555	−0.0883436
$688$	7.08069	0.269949
$689$	15.7843	0.601335
$690$	1.08092	0.0411498
$691$	29.7198	1.13059	0.565297	−	0.824887i	$-0.308761\pi$
$691$	29.7198	1.13059	0.565297	+	0.824887i	$0.308761\pi$
$692$	−19.5592	−0.743530
$693$	−0.799636	−0.0303756
$694$	23.4318	0.889459
$695$	−0.104297	−0.00395621
$696$	−1.56595	−0.0593570
$697$	39.4089	1.49272
$698$	−18.8144	−0.712135
$699$	13.5095	0.510977
$700$	0.242326	0.00915906
$701$	23.7823	0.898244	0.449122	−	0.893470i	$-0.351737\pi$
$701$	23.7823	0.898244	0.449122	+	0.893470i	$0.351737\pi$
$702$	−25.2193	−0.951840
$703$	8.91075	0.336075
$704$	1.62343	0.0611853
$705$	−3.84916	−0.144968
$706$	2.37850	0.0895159
$707$	−2.32599	−0.0874777
$708$	−5.85672	−0.220109
$709$	26.0935	0.979962	0.489981	−	0.871733i	$-0.337004\pi$
$709$	26.0935	0.979962	0.489981	+	0.871733i	$0.337004\pi$
$710$	−5.47502	−0.205474
$711$	−9.64718	−0.361798
$712$	8.02018	0.300569
$713$	−2.26128	−0.0846856
$714$	0.832107	0.0311408
$715$	−8.27132	−0.309330
$716$	6.10766	0.228254
$717$	6.24464	0.233210
$718$	19.7315	0.736373
$719$	27.1019	1.01073	0.505365	−	0.862906i	$-0.331358\pi$
$719$	27.1019	1.01073	0.505365	+	0.862906i	$0.331358\pi$
$720$	2.03263	0.0757517
$721$	−0.878111	−0.0327026
$722$	−16.1166	−0.599799
$723$	4.05083	0.150652
$724$	20.7960	0.772876
$725$	−1.59214	−0.0591305
$726$	−8.22687	−0.305328
$727$	4.54586	0.168596	0.0842982	−	0.996441i	$-0.473135\pi$
$727$	4.54586	0.168596	0.0842982	+	0.996441i	$0.473135\pi$
$728$	1.23464	0.0457589
$729$	12.1061	0.448375
$730$	−1.43914	−0.0532649
$731$	24.7206	0.914325
$732$	9.02161	0.333448
$733$	22.6920	0.838147	0.419074	−	0.907952i	$-0.362355\pi$
$733$	22.6920	0.838147	0.419074	+	0.907952i	$0.362355\pi$
$734$	8.80382	0.324955
$735$	6.82709	0.251821
$736$	−1.09900	−0.0405096
$737$	−7.17784	−0.264399
$738$	−22.9441	−0.844582
$739$	−29.7838	−1.09561	−0.547807	−	0.836605i	$-0.684537\pi$
$739$	−29.7838	−1.09561	−0.547807	+	0.836605i	$0.684537\pi$
$740$	5.24765	0.192907
$741$	−8.50916	−0.312592
$742$	0.750731	0.0275602
$743$	16.6367	0.610342	0.305171	−	0.952298i	$-0.401286\pi$
$743$	16.6367	0.610342	0.305171	+	0.952298i	$0.401286\pi$
$744$	2.02374	0.0741937
$745$	−10.2068	−0.373950
$746$	−3.36224	−0.123100
$747$	−2.12337	−0.0776901
$748$	5.66783	0.207236
$749$	0.0747309	0.00273061
$750$	−0.983549	−0.0359141
$751$	−50.0358	−1.82583	−0.912916	−	0.408148i	$-0.866175\pi$
$751$	−50.0358	−1.82583	−0.912916	+	0.408148i	$0.866175\pi$
$752$	3.91355	0.142712
$753$	−0.492410	−0.0179444
$754$	−8.11189	−0.295418
$755$	−16.8466	−0.613112
$756$	−1.19947	−0.0436245
$757$	−0.740520	−0.0269147	−0.0134573	−	0.999909i	$-0.504284\pi$
$757$	−0.740520	−0.0269147	−0.0134573	+	0.999909i	$0.504284\pi$
$758$	10.6257	0.385942
$759$	−1.75479	−0.0636949
$760$	1.69805	0.0615946
$761$	18.3039	0.663516	0.331758	−	0.943365i	$-0.392358\pi$
$761$	18.3039	0.663516	0.331758	+	0.943365i	$0.392358\pi$
$762$	−3.82327	−0.138503
$763$	2.42813	0.0879041
$764$	23.3695	0.845479
$765$	7.09646	0.256573
$766$	−33.3620	−1.20542
$767$	−30.3389	−1.09547
$768$	0.983549	0.0354908
$769$	−26.6313	−0.960348	−0.480174	−	0.877173i	$-0.659426\pi$
$769$	−26.6313	−0.960348	−0.480174	+	0.877173i	$0.659426\pi$
$770$	−0.393399	−0.0141771
$771$	0.792195	0.0285302
$772$	18.3568	0.660677
$773$	−14.0727	−0.506159	−0.253079	−	0.967446i	$-0.581443\pi$
$773$	−14.0727	−0.506159	−0.253079	+	0.967446i	$0.581443\pi$
$774$	−14.3924	−0.517326
$775$	2.05758	0.0739106
$776$	19.3325	0.693998
$777$	−1.25072	−0.0448694
$778$	4.99645	0.179131
$779$	−19.1673	−0.686740
$780$	−5.01115	−0.179428
$781$	8.88831	0.318049
$782$	−3.83689	−0.137207
$783$	7.88083	0.281638
$784$	−6.94128	−0.247903
$785$	17.1840	0.613323
$786$	−12.6186	−0.450091
$787$	−13.3624	−0.476319	−0.238159	−	0.971226i	$-0.576544\pi$
$787$	−13.3624	−0.476319	−0.238159	+	0.971226i	$0.576544\pi$
$788$	23.4142	0.834095
$789$	−27.5678	−0.981440
$790$	−4.74615	−0.168861
$791$	2.41950	0.0860274
$792$	−3.29983	−0.117254
$793$	46.7337	1.65956
$794$	−36.3490	−1.28998
$795$	−3.04706	−0.108068
$796$	−18.0305	−0.639073
$797$	−40.2287	−1.42497	−0.712486	−	0.701686i	$-0.752431\pi$
$797$	−40.2287	−1.42497	−0.712486	+	0.701686i	$0.752431\pi$
$798$	−0.404711	−0.0143266
$799$	13.6632	0.483371
$800$	1.00000	0.0353553
$801$	−16.3021	−0.576006
$802$	−16.5721	−0.585179
$803$	2.33634	0.0824476
$804$	−4.34867	−0.153366
$805$	0.266316	0.00938639
$806$	10.4833	0.369260
$807$	−8.50365	−0.299343
$808$	−9.59858	−0.337677
$809$	5.02114	0.176534	0.0882670	−	0.996097i	$-0.471867\pi$
$809$	5.02114	0.176534	0.0882670	+	0.996097i	$0.471867\pi$
$810$	−1.22949	−0.0431998
$811$	25.9638	0.911711	0.455856	−	0.890054i	$-0.349333\pi$
$811$	25.9638	0.911711	0.455856	+	0.890054i	$0.349333\pi$
$812$	−0.385816	−0.0135395
$813$	7.10672	0.249243
$814$	−8.51919	−0.298597
$815$	9.74046	0.341193
$816$	3.43383	0.120208
$817$	−12.0233	−0.420644
$818$	−5.63288	−0.196949
$819$	−2.50958	−0.0876917
$820$	−11.2879	−0.394189
$821$	17.1397	0.598179	0.299089	−	0.954225i	$-0.403317\pi$
$821$	17.1397	0.598179	0.299089	+	0.954225i	$0.403317\pi$
$822$	−8.93640	−0.311693
$823$	−29.1289	−1.01537	−0.507684	−	0.861543i	$-0.669498\pi$
$823$	−29.1289	−1.01537	−0.507684	+	0.861543i	$0.669498\pi$
$824$	−3.62368	−0.126237
$825$	1.59672	0.0555907
$826$	−1.44297	−0.0502075
$827$	−48.3880	−1.68262	−0.841308	−	0.540557i	$-0.818214\pi$
$827$	−48.3880	−1.68262	−0.841308	+	0.540557i	$0.818214\pi$
$828$	2.23386	0.0776319
$829$	45.2981	1.57327	0.786634	−	0.617419i	$-0.211822\pi$
$829$	45.2981	1.57327	0.786634	+	0.617419i	$0.211822\pi$
$830$	−1.04464	−0.0362600
$831$	1.39432	0.0483684
$832$	5.09497	0.176636
$833$	−24.2339	−0.839654
$834$	0.102581	0.00355209
$835$	10.8522	0.375555
$836$	−2.75666	−0.0953410
$837$	−10.1847	−0.352035
$838$	18.9557	0.654814
$839$	51.0127	1.76115	0.880577	−	0.473902i	$-0.157155\pi$
$839$	51.0127	1.76115	0.880577	+	0.473902i	$0.157155\pi$
$840$	−0.238339	−0.00822349
$841$	−26.4651	−0.912590
$842$	−20.2566	−0.698090
$843$	−4.59243	−0.158172
$844$	11.2746	0.388089
$845$	−12.9587	−0.445794
$846$	−7.95480	−0.273492
$847$	−2.02693	−0.0696462
$848$	3.09802	0.106387
$849$	−30.6060	−1.05040
$850$	3.49127	0.119750
$851$	5.76715	0.197695
$852$	5.38495	0.184485
$853$	−11.9700	−0.409844	−0.204922	−	0.978778i	$-0.565694\pi$
$853$	−11.9700	−0.409844	−0.204922	+	0.978778i	$0.565694\pi$
$854$	2.22274	0.0760606
$855$	−3.45150	−0.118039
$856$	0.308390	0.0105405
$857$	2.79160	0.0953592	0.0476796	−	0.998863i	$-0.484817\pi$
$857$	2.79160	0.0953592	0.0476796	+	0.998863i	$0.484817\pi$
$858$	8.13525	0.277733
$859$	−44.9930	−1.53514	−0.767571	−	0.640964i	$-0.778535\pi$
$859$	−44.9930	−1.53514	−0.767571	+	0.640964i	$0.778535\pi$
$860$	−7.08069	−0.241450
$861$	2.69034	0.0916866
$862$	−2.40963	−0.0820724
$863$	34.9518	1.18977	0.594886	−	0.803810i	$-0.297197\pi$
$863$	34.9518	1.18977	0.594886	+	0.803810i	$0.297197\pi$
$864$	−4.94984	−0.168397
$865$	19.5592	0.665034
$866$	−25.6477	−0.871546
$867$	−4.73190	−0.160704
$868$	0.498606	0.0169238
$869$	7.70505	0.261376
$870$	1.56595	0.0530905
$871$	−22.5269	−0.763296
$872$	10.0201	0.339323
$873$	−39.2960	−1.32997
$874$	1.86615	0.0631234
$875$	−0.242326	−0.00819212
$876$	1.41546	0.0478240
$877$	−42.3082	−1.42865	−0.714324	−	0.699815i	$-0.753266\pi$
$877$	−42.3082	−1.42865	−0.714324	+	0.699815i	$0.753266\pi$
$878$	23.0494	0.777878
$879$	1.64058	0.0553353
$880$	−1.62343	−0.0547258
$881$	13.1696	0.443697	0.221848	−	0.975081i	$-0.428791\pi$
$881$	13.1696	0.443697	0.221848	+	0.975081i	$0.428791\pi$
$882$	14.1091	0.475077
$883$	−11.2812	−0.379643	−0.189822	−	0.981819i	$-0.560791\pi$
$883$	−11.2812	−0.379643	−0.189822	+	0.981819i	$0.560791\pi$
$884$	17.7879	0.598272
$885$	5.85672	0.196871
$886$	10.7549	0.361319
$887$	−7.86707	−0.264150	−0.132075	−	0.991240i	$-0.542164\pi$
$887$	−7.86707	−0.264150	−0.132075	+	0.991240i	$0.542164\pi$
$888$	−5.16132	−0.173203
$889$	−0.941975	−0.0315928
$890$	−8.02018	−0.268837
$891$	1.99599	0.0668680
$892$	3.08059	0.103146
$893$	−6.64538	−0.222379
$894$	10.0389	0.335752
$895$	−6.10766	−0.204157
$896$	0.242326	0.00809554
$897$	−5.50724	−0.183881
$898$	13.8605	0.462529
$899$	−3.27596	−0.109259
$900$	−2.03263	−0.0677544
$901$	10.8160	0.360334
$902$	18.3250	0.610157
$903$	1.68761	0.0561601
$904$	9.98447	0.332079
$905$	−20.7960	−0.691281
$906$	16.5695	0.550485
$907$	−45.0806	−1.49688	−0.748438	−	0.663205i	$-0.769196\pi$
$907$	−45.0806	−1.49688	−0.748438	+	0.663205i	$0.769196\pi$
$908$	18.6298	0.618253
$909$	19.5104	0.647119
$910$	−1.23464	−0.0409280
$911$	−36.3615	−1.20471	−0.602355	−	0.798228i	$-0.705771\pi$
$911$	−36.3615	−1.20471	−0.602355	+	0.798228i	$0.705771\pi$
$912$	−1.67011	−0.0553029
$913$	1.69590	0.0561261
$914$	−21.4038	−0.707976
$915$	−9.02161	−0.298245
$916$	−2.35428	−0.0777875
$917$	−3.10897	−0.102667
$918$	−17.2812	−0.570365
$919$	−21.4898	−0.708883	−0.354442	−	0.935078i	$-0.615329\pi$
$919$	−21.4898	−0.708883	−0.354442	+	0.935078i	$0.615329\pi$
$920$	1.09900	0.0362329
$921$	−22.7085	−0.748271
$922$	−20.6343	−0.679556
$923$	27.8951	0.918177
$924$	0.386927	0.0127290
$925$	−5.24765	−0.172542
$926$	7.90197	0.259675
$927$	7.36560	0.241918
$928$	−1.59214	−0.0522645
$929$	−9.24071	−0.303178	−0.151589	−	0.988444i	$-0.548439\pi$
$929$	−9.24071	−0.303178	−0.151589	+	0.988444i	$0.548439\pi$
$930$	−2.02374	−0.0663609
$931$	11.7866	0.386290
$932$	13.7355	0.449921
$933$	13.4412	0.440046
$934$	−8.34308	−0.272994
$935$	−5.66783	−0.185358
$936$	−10.3562	−0.338503
$937$	49.7928	1.62666	0.813330	−	0.581803i	$-0.197652\pi$
$937$	49.7928	1.62666	0.813330	+	0.581803i	$0.197652\pi$
$938$	−1.07142	−0.0349832
$939$	19.8270	0.647031
$940$	−3.91355	−0.127646
$941$	−10.5921	−0.345294	−0.172647	−	0.984984i	$-0.555232\pi$
$941$	−10.5921	−0.345294	−0.172647	+	0.984984i	$0.555232\pi$
$942$	−16.9013	−0.550674
$943$	−12.4053	−0.403973
$944$	−5.95468	−0.193808
$945$	1.19947	0.0390189
$946$	11.4950	0.373735
$947$	7.88376	0.256188	0.128094	−	0.991762i	$-0.459114\pi$
$947$	7.88376	0.256188	0.128094	+	0.991762i	$0.459114\pi$
$948$	4.66807	0.151612
$949$	7.33236	0.238019
$950$	−1.69805	−0.0550919
$951$	−2.58019	−0.0836684
$952$	0.846025	0.0274198
$953$	55.0499	1.78324	0.891620	−	0.452784i	$-0.149569\pi$
$953$	55.0499	1.78324	0.891620	+	0.452784i	$0.149569\pi$
$954$	−6.29714	−0.203877
$955$	−23.3695	−0.756219
$956$	6.34909	0.205344
$957$	−2.54220	−0.0821777
$958$	−21.3622	−0.690180
$959$	−2.20174	−0.0710980
$960$	−0.983549	−0.0317439
$961$	−26.7663	−0.863430
$962$	−26.7366	−0.862023
$963$	−0.626843	−0.0201997
$964$	4.11858	0.132651
$965$	−18.3568	−0.590927
$966$	−0.261934	−0.00842760
$967$	25.3541	0.815332	0.407666	−	0.913131i	$-0.366343\pi$
$967$	25.3541	0.815332	0.407666	+	0.913131i	$0.366343\pi$
$968$	−8.36448	−0.268844
$969$	−5.83081	−0.187312
$970$	−19.3325	−0.620731
$971$	14.6496	0.470130	0.235065	−	0.971980i	$-0.424470\pi$
$971$	14.6496	0.470130	0.235065	+	0.971980i	$0.424470\pi$
$972$	16.0588	0.515086
$973$	0.0252739	0.000810243 0
$974$	−14.0473	−0.450104
$975$	5.01115	0.160485
$976$	9.17251	0.293605
$977$	−6.11141	−0.195521	−0.0977607	−	0.995210i	$-0.531168\pi$
$977$	−6.11141	−0.195521	−0.0977607	+	0.995210i	$0.531168\pi$
$978$	−9.58022	−0.306342
$979$	13.0202	0.416127
$980$	6.94128	0.221731
$981$	−20.3671	−0.650273
$982$	−33.1698	−1.05849
$983$	12.2856	0.391851	0.195925	−	0.980619i	$-0.437229\pi$
$983$	12.2856	0.391851	0.195925	+	0.980619i	$0.437229\pi$
$984$	11.1022	0.353924
$985$	−23.4142	−0.746037
$986$	−5.55858	−0.177021
$987$	0.932753	0.0296898
$988$	−8.65149	−0.275241
$989$	−7.78166	−0.247442
$990$	3.29983	0.104876
$991$	−57.3095	−1.82050	−0.910248	−	0.414064i	$-0.864109\pi$
$991$	−57.3095	−1.82050	−0.910248	+	0.414064i	$0.864109\pi$
$992$	2.05758	0.0653284
$993$	−7.09183	−0.225052
$994$	1.32674	0.0420816
$995$	18.0305	0.571604
$996$	1.02746	0.0325562
$997$	−5.09887	−0.161483	−0.0807415	−	0.996735i	$-0.525729\pi$
$997$	−5.09887	−0.161483	−0.0807415	+	0.996735i	$0.525729\pi$
$998$	−25.1270	−0.795383
$999$	25.9750	0.821814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.h.1.18	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.h.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.983549 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.983549 q^{6} +0.242326 q^{7} +1.00000 q^{8} -2.03263 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.983549 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.983549 q^{6} +0.242326 q^{7} +1.00000 q^{8} -2.03263 q^{9} -1.00000 q^{10} +1.62343 q^{11} +0.983549 q^{12} +5.09497 q^{13} +0.242326 q^{14} -0.983549 q^{15} +1.00000 q^{16} +3.49127 q^{17} -2.03263 q^{18} -1.69805 q^{19} -1.00000 q^{20} +0.238339 q^{21} +1.62343 q^{22} -1.09900 q^{23} +0.983549 q^{24} +1.00000 q^{25} +5.09497 q^{26} -4.94984 q^{27} +0.242326 q^{28} -1.59214 q^{29} -0.983549 q^{30} +2.05758 q^{31} +1.00000 q^{32} +1.59672 q^{33} +3.49127 q^{34} -0.242326 q^{35} -2.03263 q^{36} -5.24765 q^{37} -1.69805 q^{38} +5.01115 q^{39} -1.00000 q^{40} +11.2879 q^{41} +0.238339 q^{42} +7.08069 q^{43} +1.62343 q^{44} +2.03263 q^{45} -1.09900 q^{46} +3.91355 q^{47} +0.983549 q^{48} -6.94128 q^{49} +1.00000 q^{50} +3.43383 q^{51} +5.09497 q^{52} +3.09802 q^{53} -4.94984 q^{54} -1.62343 q^{55} +0.242326 q^{56} -1.67011 q^{57} -1.59214 q^{58} -5.95468 q^{59} -0.983549 q^{60} +9.17251 q^{61} +2.05758 q^{62} -0.492560 q^{63} +1.00000 q^{64} -5.09497 q^{65} +1.59672 q^{66} -4.42141 q^{67} +3.49127 q^{68} -1.08092 q^{69} -0.242326 q^{70} +5.47502 q^{71} -2.03263 q^{72} +1.43914 q^{73} -5.24765 q^{74} +0.983549 q^{75} -1.69805 q^{76} +0.393399 q^{77} +5.01115 q^{78} +4.74615 q^{79} -1.00000 q^{80} +1.22949 q^{81} +11.2879 q^{82} +1.04464 q^{83} +0.238339 q^{84} -3.49127 q^{85} +7.08069 q^{86} -1.56595 q^{87} +1.62343 q^{88} +8.02018 q^{89} +2.03263 q^{90} +1.23464 q^{91} -1.09900 q^{92} +2.02374 q^{93} +3.91355 q^{94} +1.69805 q^{95} +0.983549 q^{96} +19.3325 q^{97} -6.94128 q^{98} -3.29983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 4 q^{3} + 28 q^{4} - 28 q^{5} + 4 q^{6} + 10 q^{7} + 28 q^{8} + 40 q^{9}+O(q^{10}) \) 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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