LMFDB - Embedded newform 6026.2.a.h.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.71989 q^{3} +1.00000 q^{4} -2.14325 q^{5} +1.71989 q^{6} -1.30637 q^{7} -1.00000 q^{8} -0.0419677 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.71989 q^{3} +1.00000 q^{4} -2.14325 q^{5} +1.71989 q^{6} -1.30637 q^{7} -1.00000 q^{8} -0.0419677 q^{9} +2.14325 q^{10} +4.74810 q^{11} -1.71989 q^{12} +1.19392 q^{13} +1.30637 q^{14} +3.68616 q^{15} +1.00000 q^{16} -1.31027 q^{17} +0.0419677 q^{18} +0.113276 q^{19} -2.14325 q^{20} +2.24681 q^{21} -4.74810 q^{22} -1.00000 q^{23} +1.71989 q^{24} -0.406485 q^{25} -1.19392 q^{26} +5.23186 q^{27} -1.30637 q^{28} -8.62398 q^{29} -3.68616 q^{30} -1.19203 q^{31} -1.00000 q^{32} -8.16623 q^{33} +1.31027 q^{34} +2.79987 q^{35} -0.0419677 q^{36} -7.65635 q^{37} -0.113276 q^{38} -2.05342 q^{39} +2.14325 q^{40} +4.88513 q^{41} -2.24681 q^{42} +6.12492 q^{43} +4.74810 q^{44} +0.0899473 q^{45} +1.00000 q^{46} +7.88063 q^{47} -1.71989 q^{48} -5.29341 q^{49} +0.406485 q^{50} +2.25353 q^{51} +1.19392 q^{52} +4.06464 q^{53} -5.23186 q^{54} -10.1764 q^{55} +1.30637 q^{56} -0.194822 q^{57} +8.62398 q^{58} -9.74386 q^{59} +3.68616 q^{60} +0.336312 q^{61} +1.19203 q^{62} +0.0548252 q^{63} +1.00000 q^{64} -2.55887 q^{65} +8.16623 q^{66} +8.95728 q^{67} -1.31027 q^{68} +1.71989 q^{69} -2.79987 q^{70} -1.24515 q^{71} +0.0419677 q^{72} -9.56377 q^{73} +7.65635 q^{74} +0.699111 q^{75} +0.113276 q^{76} -6.20276 q^{77} +2.05342 q^{78} +12.8401 q^{79} -2.14325 q^{80} -8.87234 q^{81} -4.88513 q^{82} +11.4351 q^{83} +2.24681 q^{84} +2.80824 q^{85} -6.12492 q^{86} +14.8323 q^{87} -4.74810 q^{88} +5.53195 q^{89} -0.0899473 q^{90} -1.55970 q^{91} -1.00000 q^{92} +2.05016 q^{93} -7.88063 q^{94} -0.242778 q^{95} +1.71989 q^{96} +8.36663 q^{97} +5.29341 q^{98} -0.199267 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * 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
$3$	−1.71989	−0.992981	−0.496490	−	0.868042i	$-0.665378\pi$
$3$	−1.71989	−0.992981	−0.496490	+	0.868042i	$0.665378\pi$
$4$	1.00000	0.500000
$5$	−2.14325	−0.958490	−0.479245	−	0.877681i	$-0.659089\pi$
$5$	−2.14325	−0.958490	−0.479245	+	0.877681i	$0.659089\pi$
$6$	1.71989	0.702143
$7$	−1.30637	−0.493760	−0.246880	−	0.969046i	$-0.579405\pi$
$7$	−1.30637	−0.493760	−0.246880	+	0.969046i	$0.579405\pi$
$8$	−1.00000	−0.353553
$9$	−0.0419677	−0.0139892
$10$	2.14325	0.677755
$11$	4.74810	1.43161	0.715803	−	0.698302i	$-0.246061\pi$
$11$	4.74810	1.43161	0.715803	+	0.698302i	$0.246061\pi$
$12$	−1.71989	−0.496490
$13$	1.19392	0.331135	0.165567	−	0.986198i	$-0.447054\pi$
$13$	1.19392	0.331135	0.165567	+	0.986198i	$0.447054\pi$
$14$	1.30637	0.349141
$15$	3.68616	0.951762
$16$	1.00000	0.250000
$17$	−1.31027	−0.317788	−0.158894	−	0.987296i	$-0.550793\pi$
$17$	−1.31027	−0.317788	−0.158894	+	0.987296i	$0.550793\pi$
$18$	0.0419677	0.00989189
$19$	0.113276	0.0259873	0.0129936	−	0.999916i	$-0.495864\pi$
$19$	0.113276	0.0259873	0.0129936	+	0.999916i	$0.495864\pi$
$20$	−2.14325	−0.479245
$21$	2.24681	0.490294
$22$	−4.74810	−1.01230
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.71989	0.351072
$25$	−0.406485	−0.0812971
$26$	−1.19392	−0.234148
$27$	5.23186	1.00687
$28$	−1.30637	−0.246880
$29$	−8.62398	−1.60143	−0.800717	−	0.599043i	$-0.795548\pi$
$29$	−8.62398	−1.60143	−0.800717	+	0.599043i	$0.795548\pi$
$30$	−3.68616	−0.672997
$31$	−1.19203	−0.214095	−0.107047	−	0.994254i	$-0.534140\pi$
$31$	−1.19203	−0.214095	−0.107047	+	0.994254i	$0.534140\pi$
$32$	−1.00000	−0.176777
$33$	−8.16623	−1.42156
$34$	1.31027	0.224710
$35$	2.79987	0.473264
$36$	−0.0419677	−0.00699462
$37$	−7.65635	−1.25870	−0.629348	−	0.777123i	$-0.716678\pi$
$37$	−7.65635	−1.25870	−0.629348	+	0.777123i	$0.716678\pi$
$38$	−0.113276	−0.0183758
$39$	−2.05342	−0.328810
$40$	2.14325	0.338877
$41$	4.88513	0.762929	0.381464	−	0.924384i	$-0.375420\pi$
$41$	4.88513	0.762929	0.381464	+	0.924384i	$0.375420\pi$
$42$	−2.24681	−0.346690
$43$	6.12492	0.934042	0.467021	−	0.884246i	$-0.345327\pi$
$43$	6.12492	0.934042	0.467021	+	0.884246i	$0.345327\pi$
$44$	4.74810	0.715803
$45$	0.0899473	0.0134086
$46$	1.00000	0.147442
$47$	7.88063	1.14951	0.574754	−	0.818326i	$-0.305098\pi$
$47$	7.88063	1.14951	0.574754	+	0.818326i	$0.305098\pi$
$48$	−1.71989	−0.248245
$49$	−5.29341	−0.756201
$50$	0.406485	0.0574857
$51$	2.25353	0.315557
$52$	1.19392	0.165567
$53$	4.06464	0.558321	0.279160	−	0.960244i	$-0.409944\pi$
$53$	4.06464	0.558321	0.279160	+	0.960244i	$0.409944\pi$
$54$	−5.23186	−0.711966
$55$	−10.1764	−1.37218
$56$	1.30637	0.174570
$57$	−0.194822	−0.0258049
$58$	8.62398	1.13238
$59$	−9.74386	−1.26854	−0.634271	−	0.773111i	$-0.718700\pi$
$59$	−9.74386	−1.26854	−0.634271	+	0.773111i	$0.718700\pi$
$60$	3.68616	0.475881
$61$	0.336312	0.0430604	0.0215302	−	0.999768i	$-0.493146\pi$
$61$	0.336312	0.0430604	0.0215302	+	0.999768i	$0.493146\pi$
$62$	1.19203	0.151388
$63$	0.0548252	0.00690733
$64$	1.00000	0.125000
$65$	−2.55887	−0.317389
$66$	8.16623	1.00519
$67$	8.95728	1.09431	0.547153	−	0.837033i	$-0.315712\pi$
$67$	8.95728	1.09431	0.547153	+	0.837033i	$0.315712\pi$
$68$	−1.31027	−0.158894
$69$	1.71989	0.207051
$70$	−2.79987	−0.334648
$71$	−1.24515	−0.147772	−0.0738861	−	0.997267i	$-0.523540\pi$
$71$	−1.24515	−0.147772	−0.0738861	+	0.997267i	$0.523540\pi$
$72$	0.0419677	0.00494595
$73$	−9.56377	−1.11935	−0.559677	−	0.828711i	$-0.689075\pi$
$73$	−9.56377	−1.11935	−0.559677	+	0.828711i	$0.689075\pi$
$74$	7.65635	0.890033
$75$	0.699111	0.0807264
$76$	0.113276	0.0129936
$77$	−6.20276	−0.706870
$78$	2.05342	0.232504
$79$	12.8401	1.44462	0.722310	−	0.691569i	$-0.243080\pi$
$79$	12.8401	1.44462	0.722310	+	0.691569i	$0.243080\pi$
$80$	−2.14325	−0.239622
$81$	−8.87234	−0.985815
$82$	−4.88513	−0.539472
$83$	11.4351	1.25517	0.627585	−	0.778548i	$-0.284043\pi$
$83$	11.4351	1.25517	0.627585	+	0.778548i	$0.284043\pi$
$84$	2.24681	0.245147
$85$	2.80824	0.304597
$86$	−6.12492	−0.660467
$87$	14.8323	1.59019
$88$	−4.74810	−0.506149
$89$	5.53195	0.586386	0.293193	−	0.956053i	$-0.405282\pi$
$89$	5.53195	0.586386	0.293193	+	0.956053i	$0.405282\pi$
$90$	−0.0899473	−0.00948128
$91$	−1.55970	−0.163501
$92$	−1.00000	−0.104257
$93$	2.05016	0.212592
$94$	−7.88063	−0.812825
$95$	−0.242778	−0.0249085
$96$	1.71989	0.175536
$97$	8.36663	0.849503	0.424751	−	0.905310i	$-0.360361\pi$
$97$	8.36663	0.849503	0.424751	+	0.905310i	$0.360361\pi$
$98$	5.29341	0.534715
$99$	−0.199267	−0.0200271
$100$	−0.406485	−0.0406485
$101$	2.32659	0.231504	0.115752	−	0.993278i	$-0.463072\pi$
$101$	2.32659	0.231504	0.115752	+	0.993278i	$0.463072\pi$
$102$	−2.25353	−0.223133
$103$	4.35870	0.429475	0.214738	−	0.976672i	$-0.431110\pi$
$103$	4.35870	0.429475	0.214738	+	0.976672i	$0.431110\pi$
$104$	−1.19392	−0.117074
$105$	−4.81547	−0.469942
$106$	−4.06464	−0.394793
$107$	10.8528	1.04918	0.524588	−	0.851356i	$-0.324219\pi$
$107$	10.8528	1.04918	0.524588	+	0.851356i	$0.324219\pi$
$108$	5.23186	0.503436
$109$	17.1537	1.64302	0.821512	−	0.570191i	$-0.193131\pi$
$109$	17.1537	1.64302	0.821512	+	0.570191i	$0.193131\pi$
$110$	10.1764	0.970278
$111$	13.1681	1.24986
$112$	−1.30637	−0.123440
$113$	−4.20293	−0.395378	−0.197689	−	0.980265i	$-0.563344\pi$
$113$	−4.20293	−0.395378	−0.197689	+	0.980265i	$0.563344\pi$
$114$	0.194822	0.0182468
$115$	2.14325	0.199859
$116$	−8.62398	−0.800717
$117$	−0.0501063	−0.00463233
$118$	9.74386	0.896995
$119$	1.71170	0.156911
$120$	−3.68616	−0.336499
$121$	11.5445	1.04950
$122$	−0.336312	−0.0304483
$123$	−8.40190	−0.757573
$124$	−1.19203	−0.107047
$125$	11.5874	1.03641
$126$	−0.0548252	−0.00488422
$127$	13.1941	1.17079	0.585394	−	0.810749i	$-0.300940\pi$
$127$	13.1941	1.17079	0.585394	+	0.810749i	$0.300940\pi$
$128$	−1.00000	−0.0883883
$129$	−10.5342	−0.927485
$130$	2.55887	0.224428
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−8.16623	−0.710779
$133$	−0.147980	−0.0128315
$134$	−8.95728	−0.773791
$135$	−11.2132	−0.965076
$136$	1.31027	0.112355
$137$	15.1515	1.29448	0.647241	−	0.762286i	$-0.275923\pi$
$137$	15.1515	1.29448	0.647241	+	0.762286i	$0.275923\pi$
$138$	−1.71989	−0.146407
$139$	−11.8906	−1.00854	−0.504272	−	0.863545i	$-0.668239\pi$
$139$	−11.8906	−1.00854	−0.504272	+	0.863545i	$0.668239\pi$
$140$	2.79987	0.236632
$141$	−13.5538	−1.14144
$142$	1.24515	0.104491
$143$	5.66887	0.474055
$144$	−0.0419677	−0.00349731
$145$	18.4833	1.53496
$146$	9.56377	0.791503
$147$	9.10410	0.750893
$148$	−7.65635	−0.629348
$149$	6.76725	0.554395	0.277197	−	0.960813i	$-0.410594\pi$
$149$	6.76725	0.554395	0.277197	+	0.960813i	$0.410594\pi$
$150$	−0.699111	−0.0570822
$151$	−14.6117	−1.18908	−0.594541	−	0.804065i	$-0.702666\pi$
$151$	−14.6117	−1.18908	−0.594541	+	0.804065i	$0.702666\pi$
$152$	−0.113276	−0.00918789
$153$	0.0549892	0.00444562
$154$	6.20276	0.499833
$155$	2.55481	0.205208
$156$	−2.05342	−0.164405
$157$	−5.16105	−0.411896	−0.205948	−	0.978563i	$-0.566028\pi$
$157$	−5.16105	−0.411896	−0.205948	+	0.978563i	$0.566028\pi$
$158$	−12.8401	−1.02150
$159$	−6.99074	−0.554402
$160$	2.14325	0.169439
$161$	1.30637	0.102956
$162$	8.87234	0.697077
$163$	−17.9401	−1.40517	−0.702587	−	0.711598i	$-0.747972\pi$
$163$	−17.9401	−1.40517	−0.702587	+	0.711598i	$0.747972\pi$
$164$	4.88513	0.381464
$165$	17.5023	1.36255
$166$	−11.4351	−0.887539
$167$	−15.7089	−1.21559	−0.607795	−	0.794094i	$-0.707946\pi$
$167$	−15.7089	−1.21559	−0.607795	+	0.794094i	$0.707946\pi$
$168$	−2.24681	−0.173345
$169$	−11.5745	−0.890350
$170$	−2.80824	−0.215382
$171$	−0.00475394	−0.000363543 0
$172$	6.12492	0.467021
$173$	−7.13838	−0.542721	−0.271360	−	0.962478i	$-0.587474\pi$
$173$	−7.13838	−0.542721	−0.271360	+	0.962478i	$0.587474\pi$
$174$	−14.8323	−1.12444
$175$	0.531018	0.0401412
$176$	4.74810	0.357902
$177$	16.7584	1.25964
$178$	−5.53195	−0.414637
$179$	−22.6654	−1.69409	−0.847046	−	0.531519i	$-0.821621\pi$
$179$	−22.6654	−1.69409	−0.847046	+	0.531519i	$0.821621\pi$
$180$	0.0899473	0.00670428
$181$	−4.59296	−0.341392	−0.170696	−	0.985324i	$-0.554602\pi$
$181$	−4.59296	−0.341392	−0.170696	+	0.985324i	$0.554602\pi$
$182$	1.55970	0.115613
$183$	−0.578421	−0.0427581
$184$	1.00000	0.0737210
$185$	16.4095	1.20645
$186$	−2.05016	−0.150325
$187$	−6.22131	−0.454948
$188$	7.88063	0.574754
$189$	−6.83472	−0.497153
$190$	0.242778	0.0176130
$191$	−21.9018	−1.58476	−0.792381	−	0.610027i	$-0.791159\pi$
$191$	−21.9018	−1.58476	−0.792381	+	0.610027i	$0.791159\pi$
$192$	−1.71989	−0.124123
$193$	−16.9676	−1.22136	−0.610678	−	0.791879i	$-0.709103\pi$
$193$	−16.9676	−1.22136	−0.610678	+	0.791879i	$0.709103\pi$
$194$	−8.36663	−0.600689
$195$	4.40099	0.315161
$196$	−5.29341	−0.378101
$197$	14.5728	1.03827	0.519133	−	0.854693i	$-0.326255\pi$
$197$	14.5728	1.03827	0.519133	+	0.854693i	$0.326255\pi$
$198$	0.199267	0.0141613
$199$	14.0456	0.995666	0.497833	−	0.867273i	$-0.334129\pi$
$199$	14.0456	0.995666	0.497833	+	0.867273i	$0.334129\pi$
$200$	0.406485	0.0287429
$201$	−15.4056	−1.08662
$202$	−2.32659	−0.163698
$203$	11.2661	0.790724
$204$	2.25353	0.157779
$205$	−10.4700	−0.731259
$206$	−4.35870	−0.303685
$207$	0.0419677	0.00291696
$208$	1.19392	0.0827837
$209$	0.537846	0.0372036
$210$	4.81547	0.332299
$211$	−7.95729	−0.547803	−0.273901	−	0.961758i	$-0.588314\pi$
$211$	−7.95729	−0.547803	−0.273901	+	0.961758i	$0.588314\pi$
$212$	4.06464	0.279160
$213$	2.14153	0.146735
$214$	−10.8528	−0.741880
$215$	−13.1272	−0.895269
$216$	−5.23186	−0.355983
$217$	1.55723	0.105711
$218$	−17.1537	−1.16179
$219$	16.4487	1.11150
$220$	−10.1764	−0.686090
$221$	−1.56437	−0.105231
$222$	−13.1681	−0.883786
$223$	−9.02798	−0.604558	−0.302279	−	0.953219i	$-0.597747\pi$
$223$	−9.02798	−0.604558	−0.302279	+	0.953219i	$0.597747\pi$
$224$	1.30637	0.0872852
$225$	0.0170593	0.00113728
$226$	4.20293	0.279575
$227$	19.7457	1.31057	0.655283	−	0.755383i	$-0.272549\pi$
$227$	19.7457	1.31057	0.655283	+	0.755383i	$0.272549\pi$
$228$	−0.194822	−0.0129024
$229$	−7.72671	−0.510595	−0.255298	−	0.966863i	$-0.582173\pi$
$229$	−7.72671	−0.510595	−0.255298	+	0.966863i	$0.582173\pi$
$230$	−2.14325	−0.141322
$231$	10.6681	0.701908
$232$	8.62398	0.566192
$233$	−5.21127	−0.341402	−0.170701	−	0.985323i	$-0.554603\pi$
$233$	−5.21127	−0.341402	−0.170701	+	0.985323i	$0.554603\pi$
$234$	0.0501063	0.00327555
$235$	−16.8902	−1.10179
$236$	−9.74386	−0.634271
$237$	−22.0835	−1.43448
$238$	−1.71170	−0.110953
$239$	11.9227	0.771213	0.385606	−	0.922663i	$-0.373992\pi$
$239$	11.9227	0.771213	0.385606	+	0.922663i	$0.373992\pi$
$240$	3.68616	0.237941
$241$	0.950549	0.0612303	0.0306151	−	0.999531i	$-0.490253\pi$
$241$	0.950549	0.0612303	0.0306151	+	0.999531i	$0.490253\pi$
$242$	−11.5445	−0.742107
$243$	−0.436109	−0.0279764
$244$	0.336312	0.0215302
$245$	11.3451	0.724811
$246$	8.40190	0.535685
$247$	0.135243	0.00860529
$248$	1.19203	0.0756939
$249$	−19.6672	−1.24636
$250$	−11.5874	−0.732854
$251$	−4.37103	−0.275897	−0.137949	−	0.990439i	$-0.544051\pi$
$251$	−4.37103	−0.275897	−0.137949	+	0.990439i	$0.544051\pi$
$252$	0.0548252	0.00345366
$253$	−4.74810	−0.298511
$254$	−13.1941	−0.827872
$255$	−4.82988	−0.302459
$256$	1.00000	0.0625000
$257$	1.17486	0.0732858	0.0366429	−	0.999328i	$-0.488334\pi$
$257$	1.17486	0.0732858	0.0366429	+	0.999328i	$0.488334\pi$
$258$	10.5342	0.655831
$259$	10.0020	0.621494
$260$	−2.55887	−0.158695
$261$	0.361929	0.0224029
$262$	1.00000	0.0617802
$263$	19.5813	1.20743	0.603717	−	0.797199i	$-0.293686\pi$
$263$	19.5813	1.20743	0.603717	+	0.797199i	$0.293686\pi$
$264$	8.16623	0.502597
$265$	−8.71153	−0.535145
$266$	0.147980	0.00907322
$267$	−9.51437	−0.582270
$268$	8.95728	0.547153
$269$	0.279423	0.0170367	0.00851836	−	0.999964i	$-0.497288\pi$
$269$	0.279423	0.0170367	0.00851836	+	0.999964i	$0.497288\pi$
$270$	11.2132	0.682412
$271$	−26.6202	−1.61706	−0.808531	−	0.588454i	$-0.799737\pi$
$271$	−26.6202	−1.61706	−0.808531	+	0.588454i	$0.799737\pi$
$272$	−1.31027	−0.0794470
$273$	2.68252	0.162353
$274$	−15.1515	−0.915336
$275$	−1.93003	−0.116385
$276$	1.71989	0.103525
$277$	30.0658	1.80648	0.903241	−	0.429134i	$-0.141181\pi$
$277$	30.0658	1.80648	0.903241	+	0.429134i	$0.141181\pi$
$278$	11.8906	0.713148
$279$	0.0500268	0.00299502
$280$	−2.79987	−0.167324
$281$	−20.7955	−1.24055	−0.620277	−	0.784383i	$-0.712980\pi$
$281$	−20.7955	−1.24055	−0.620277	+	0.784383i	$0.712980\pi$
$282$	13.5538	0.807120
$283$	−30.4313	−1.80895	−0.904477	−	0.426522i	$-0.859739\pi$
$283$	−30.4313	−1.80895	−0.904477	+	0.426522i	$0.859739\pi$
$284$	−1.24515	−0.0738861
$285$	0.417553	0.0247337
$286$	−5.66887	−0.335207
$287$	−6.38176	−0.376703
$288$	0.0419677	0.00247297
$289$	−15.2832	−0.899011
$290$	−18.4833	−1.08538
$291$	−14.3897	−0.843540
$292$	−9.56377	−0.559677
$293$	11.6987	0.683444	0.341722	−	0.939801i	$-0.388990\pi$
$293$	11.6987	0.683444	0.341722	+	0.939801i	$0.388990\pi$
$294$	−9.10410	−0.530962
$295$	20.8835	1.21588
$296$	7.65635	0.445016
$297$	24.8414	1.44144
$298$	−6.76725	−0.392016
$299$	−1.19392	−0.0690463
$300$	0.699111	0.0403632
$301$	−8.00138	−0.461192
$302$	14.6117	0.840808
$303$	−4.00148	−0.229879
$304$	0.113276	0.00649682
$305$	−0.720801	−0.0412729
$306$	−0.0549892	−0.00314353
$307$	30.5843	1.74554	0.872769	−	0.488134i	$-0.162322\pi$
$307$	30.5843	1.74554	0.872769	+	0.488134i	$0.162322\pi$
$308$	−6.20276	−0.353435
$309$	−7.49649	−0.426460
$310$	−2.55481	−0.145104
$311$	31.6222	1.79313	0.896566	−	0.442910i	$-0.146054\pi$
$311$	31.6222	1.79313	0.896566	+	0.442910i	$0.146054\pi$
$312$	2.05342	0.116252
$313$	−14.5106	−0.820185	−0.410092	−	0.912044i	$-0.634504\pi$
$313$	−14.5106	−0.820185	−0.410092	+	0.912044i	$0.634504\pi$
$314$	5.16105	0.291255
$315$	−0.117504	−0.00662060
$316$	12.8401	0.722310
$317$	13.2217	0.742604	0.371302	−	0.928512i	$-0.378912\pi$
$317$	13.2217	0.742604	0.371302	+	0.928512i	$0.378912\pi$
$318$	6.99074	0.392021
$319$	−40.9476	−2.29262
$320$	−2.14325	−0.119811
$321$	−18.6656	−1.04181
$322$	−1.30637	−0.0728009
$323$	−0.148422	−0.00825845
$324$	−8.87234	−0.492908
$325$	−0.485312	−0.0269203
$326$	17.9401	0.993608
$327$	−29.5025	−1.63149
$328$	−4.88513	−0.269736
$329$	−10.2950	−0.567581
$330$	−17.5023	−0.963468
$331$	8.20755	0.451128	0.225564	−	0.974228i	$-0.427578\pi$
$331$	8.20755	0.451128	0.225564	+	0.974228i	$0.427578\pi$
$332$	11.4351	0.627585
$333$	0.321320	0.0176082
$334$	15.7089	0.859552
$335$	−19.1977	−1.04888
$336$	2.24681	0.122573
$337$	−16.0731	−0.875557	−0.437779	−	0.899083i	$-0.644235\pi$
$337$	−16.0731	−0.875557	−0.437779	+	0.899083i	$0.644235\pi$
$338$	11.5745	0.629572
$339$	7.22859	0.392603
$340$	2.80824	0.152298
$341$	−5.65987	−0.306499
$342$	0.00475394	0.000257063 0
$343$	16.0597	0.867142
$344$	−6.12492	−0.330234
$345$	−3.68616	−0.198456
$346$	7.13838	0.383762
$347$	−1.50632	−0.0808634	−0.0404317	−	0.999182i	$-0.512873\pi$
$347$	−1.50632	−0.0808634	−0.0404317	+	0.999182i	$0.512873\pi$
$348$	14.8323	0.795096
$349$	32.2290	1.72518	0.862591	−	0.505902i	$-0.168840\pi$
$349$	32.2290	1.72518	0.862591	+	0.505902i	$0.168840\pi$
$350$	−0.531018	−0.0283841
$351$	6.24644	0.333410
$352$	−4.74810	−0.253075
$353$	−18.4442	−0.981688	−0.490844	−	0.871248i	$-0.663311\pi$
$353$	−18.4442	−0.981688	−0.490844	+	0.871248i	$0.663311\pi$
$354$	−16.7584	−0.890699
$355$	2.66867	0.141638
$356$	5.53195	0.293193
$357$	−2.94393	−0.155810
$358$	22.6654	1.19790
$359$	25.0310	1.32108	0.660542	−	0.750789i	$-0.270327\pi$
$359$	25.0310	1.32108	0.660542	+	0.750789i	$0.270327\pi$
$360$	−0.0899473	−0.00474064
$361$	−18.9872	−0.999325
$362$	4.59296	0.241401
$363$	−19.8553	−1.04213
$364$	−1.55970	−0.0817505
$365$	20.4975	1.07289
$366$	0.578421	0.0302346
$367$	0.325219	0.0169763	0.00848814	−	0.999964i	$-0.497298\pi$
$367$	0.325219	0.0169763	0.00848814	+	0.999964i	$0.497298\pi$
$368$	−1.00000	−0.0521286
$369$	−0.205018	−0.0106728
$370$	−16.4095	−0.853088
$371$	−5.30990	−0.275676
$372$	2.05016	0.106296
$373$	−11.1171	−0.575623	−0.287811	−	0.957687i	$-0.592928\pi$
$373$	−11.1171	−0.575623	−0.287811	+	0.957687i	$0.592928\pi$
$374$	6.22131	0.321696
$375$	−19.9292	−1.02914
$376$	−7.88063	−0.406413
$377$	−10.2964	−0.530290
$378$	6.83472	0.351540
$379$	−21.1963	−1.08878	−0.544391	−	0.838832i	$-0.683239\pi$
$379$	−21.1963	−1.08878	−0.544391	+	0.838832i	$0.683239\pi$
$380$	−0.242778	−0.0124543
$381$	−22.6925	−1.16257
$382$	21.9018	1.12060
$383$	−27.9138	−1.42633	−0.713164	−	0.700998i	$-0.752738\pi$
$383$	−27.9138	−1.42633	−0.713164	+	0.700998i	$0.752738\pi$
$384$	1.71989	0.0877679
$385$	13.2941	0.677528
$386$	16.9676	0.863629
$387$	−0.257049	−0.0130665
$388$	8.36663	0.424751
$389$	−16.7983	−0.851708	−0.425854	−	0.904792i	$-0.640026\pi$
$389$	−16.7983	−0.851708	−0.425854	+	0.904792i	$0.640026\pi$
$390$	−4.40099	−0.222853
$391$	1.31027	0.0662634
$392$	5.29341	0.267358
$393$	1.71989	0.0867571
$394$	−14.5728	−0.734166
$395$	−27.5195	−1.38465
$396$	−0.199267	−0.0100136
$397$	7.41739	0.372268	0.186134	−	0.982524i	$-0.440404\pi$
$397$	7.41739	0.372268	0.186134	+	0.982524i	$0.440404\pi$
$398$	−14.0456	−0.704042
$399$	0.254509	0.0127414
$400$	−0.406485	−0.0203243
$401$	8.45159	0.422052	0.211026	−	0.977480i	$-0.432319\pi$
$401$	8.45159	0.422052	0.211026	+	0.977480i	$0.432319\pi$
$402$	15.4056	0.768360
$403$	−1.42319	−0.0708942
$404$	2.32659	0.115752
$405$	19.0156	0.944894
$406$	−11.2661	−0.559126
$407$	−36.3531	−1.80196
$408$	−2.25353	−0.111566
$409$	−19.1937	−0.949065	−0.474533	−	0.880238i	$-0.657383\pi$
$409$	−19.1937	−0.949065	−0.474533	+	0.880238i	$0.657383\pi$
$410$	10.4700	0.517078
$411$	−26.0590	−1.28539
$412$	4.35870	0.214738
$413$	12.7290	0.626355
$414$	−0.0419677	−0.00206260
$415$	−24.5084	−1.20307
$416$	−1.19392	−0.0585369
$417$	20.4505	1.00146
$418$	−0.537846	−0.0263069
$419$	20.3707	0.995172	0.497586	−	0.867415i	$-0.334220\pi$
$419$	20.3707	0.995172	0.497586	+	0.867415i	$0.334220\pi$
$420$	−4.81547	−0.234971
$421$	−37.4866	−1.82699	−0.913493	−	0.406853i	$-0.866626\pi$
$421$	−37.4866	−1.82699	−0.913493	+	0.406853i	$0.866626\pi$
$422$	7.95729	0.387355
$423$	−0.330732	−0.0160808
$424$	−4.06464	−0.197396
$425$	0.532607	0.0258352
$426$	−2.14153	−0.103757
$427$	−0.439347	−0.0212615
$428$	10.8528	0.524588
$429$	−9.74985	−0.470727
$430$	13.1272	0.633051
$431$	−18.6956	−0.900536	−0.450268	−	0.892893i	$-0.648672\pi$
$431$	−18.6956	−0.900536	−0.450268	+	0.892893i	$0.648672\pi$
$432$	5.23186	0.251718
$433$	−7.80537	−0.375102	−0.187551	−	0.982255i	$-0.560055\pi$
$433$	−7.80537	−0.375102	−0.187551	+	0.982255i	$0.560055\pi$
$434$	−1.55723	−0.0747492
$435$	−31.7894	−1.52418
$436$	17.1537	0.821512
$437$	−0.113276	−0.00541872
$438$	−16.4487	−0.785948
$439$	−4.02590	−0.192146	−0.0960729	−	0.995374i	$-0.530628\pi$
$439$	−4.02590	−0.192146	−0.0960729	+	0.995374i	$0.530628\pi$
$440$	10.1764	0.485139
$441$	0.222152	0.0105787
$442$	1.56437	0.0744093
$443$	−11.7695	−0.559187	−0.279593	−	0.960119i	$-0.590200\pi$
$443$	−11.7695	−0.559187	−0.279593	+	0.960119i	$0.590200\pi$
$444$	13.1681	0.624931
$445$	−11.8564	−0.562045
$446$	9.02798	0.427487
$447$	−11.6389	−0.550503
$448$	−1.30637	−0.0617200
$449$	24.8386	1.17220	0.586102	−	0.810237i	$-0.300662\pi$
$449$	24.8386	1.17220	0.586102	+	0.810237i	$0.300662\pi$
$450$	−0.0170593	−0.000804182 0
$451$	23.1951	1.09221
$452$	−4.20293	−0.197689
$453$	25.1305	1.18074
$454$	−19.7457	−0.926711
$455$	3.34282	0.156714
$456$	0.194822	0.00912340
$457$	−8.47035	−0.396226	−0.198113	−	0.980179i	$-0.563481\pi$
$457$	−8.47035	−0.396226	−0.198113	+	0.980179i	$0.563481\pi$
$458$	7.72671	0.361045
$459$	−6.85517	−0.319972
$460$	2.14325	0.0999295
$461$	5.75911	0.268228	0.134114	−	0.990966i	$-0.457181\pi$
$461$	5.75911	0.268228	0.134114	+	0.990966i	$0.457181\pi$
$462$	−10.6681	−0.496324
$463$	−7.74262	−0.359830	−0.179915	−	0.983682i	$-0.557582\pi$
$463$	−7.74262	−0.359830	−0.179915	+	0.983682i	$0.557582\pi$
$464$	−8.62398	−0.400358
$465$	−4.39401	−0.203767
$466$	5.21127	0.241407
$467$	−25.4019	−1.17546	−0.587729	−	0.809058i	$-0.699978\pi$
$467$	−25.4019	−1.17546	−0.587729	+	0.809058i	$0.699978\pi$
$468$	−0.0501063	−0.00231616
$469$	−11.7015	−0.540324
$470$	16.8902	0.779085
$471$	8.87645	0.409005
$472$	9.74386	0.448497
$473$	29.0818	1.33718
$474$	22.0835	1.01433
$475$	−0.0460450	−0.00211269
$476$	1.71170	0.0784555
$477$	−0.170584	−0.00781049
$478$	−11.9227	−0.545330
$479$	−35.9072	−1.64064	−0.820322	−	0.571902i	$-0.806206\pi$
$479$	−35.9072	−1.64064	−0.820322	+	0.571902i	$0.806206\pi$
$480$	−3.68616	−0.168249
$481$	−9.14109	−0.416798
$482$	−0.950549	−0.0432963
$483$	−2.24681	−0.102233
$484$	11.5445	0.524749
$485$	−17.9318	−0.814240
$486$	0.436109	0.0197823
$487$	29.9563	1.35745	0.678725	−	0.734392i	$-0.262533\pi$
$487$	29.9563	1.35745	0.678725	+	0.734392i	$0.262533\pi$
$488$	−0.336312	−0.0152241
$489$	30.8550	1.39531
$490$	−11.3451	−0.512519
$491$	−0.427788	−0.0193058	−0.00965290	−	0.999953i	$-0.503073\pi$
$491$	−0.427788	−0.0193058	−0.00965290	+	0.999953i	$0.503073\pi$
$492$	−8.40190	−0.378787
$493$	11.2998	0.508916
$494$	−0.135243	−0.00608486
$495$	0.427079	0.0191958
$496$	−1.19203	−0.0535237
$497$	1.62662	0.0729640
$498$	19.6672	0.881309
$499$	−32.9391	−1.47456	−0.737279	−	0.675589i	$-0.763890\pi$
$499$	−32.9391	−1.47456	−0.737279	+	0.675589i	$0.763890\pi$
$500$	11.5874	0.518206
$501$	27.0176	1.20706
$502$	4.37103	0.195089
$503$	35.6081	1.58769	0.793844	−	0.608122i	$-0.208077\pi$
$503$	35.6081	1.58769	0.793844	+	0.608122i	$0.208077\pi$
$504$	−0.0548252	−0.00244211
$505$	−4.98646	−0.221894
$506$	4.74810	0.211079
$507$	19.9070	0.884100
$508$	13.1941	0.585394
$509$	−13.4443	−0.595907	−0.297954	−	0.954580i	$-0.596304\pi$
$509$	−13.4443	−0.595907	−0.297954	+	0.954580i	$0.596304\pi$
$510$	4.82988	0.213871
$511$	12.4938	0.552692
$512$	−1.00000	−0.0441942
$513$	0.592644	0.0261659
$514$	−1.17486	−0.0518209
$515$	−9.34177	−0.411648
$516$	−10.5342	−0.463743
$517$	37.4181	1.64564
$518$	−10.0020	−0.439462
$519$	12.2773	0.538911
$520$	2.55887	0.112214
$521$	15.2942	0.670051	0.335025	−	0.942209i	$-0.391255\pi$
$521$	15.2942	0.670051	0.335025	+	0.942209i	$0.391255\pi$
$522$	−0.361929	−0.0158412
$523$	−35.3348	−1.54508	−0.772542	−	0.634963i	$-0.781015\pi$
$523$	−35.3348	−1.54508	−0.772542	+	0.634963i	$0.781015\pi$
$524$	−1.00000	−0.0436852
$525$	−0.913295	−0.0398595
$526$	−19.5813	−0.853784
$527$	1.56188	0.0680367
$528$	−8.16623	−0.355390
$529$	1.00000	0.0434783
$530$	8.71153	0.378405
$531$	0.408928	0.0177460
$532$	−0.147980	−0.00641574
$533$	5.83247	0.252632
$534$	9.51437	0.411727
$535$	−23.2602	−1.00562
$536$	−8.95728	−0.386896
$537$	38.9821	1.68220
$538$	−0.279423	−0.0120468
$539$	−25.1337	−1.08258
$540$	−11.2132	−0.482538
$541$	−2.67913	−0.115185	−0.0575924	−	0.998340i	$-0.518342\pi$
$541$	−2.67913	−0.115185	−0.0575924	+	0.998340i	$0.518342\pi$
$542$	26.6202	1.14343
$543$	7.89940	0.338996
$544$	1.31027	0.0561775
$545$	−36.7646	−1.57482
$546$	−2.68252	−0.114801
$547$	−26.4471	−1.13080	−0.565399	−	0.824818i	$-0.691278\pi$
$547$	−26.4471	−1.13080	−0.565399	+	0.824818i	$0.691278\pi$
$548$	15.1515	0.647241
$549$	−0.0141143	−0.000602382 0
$550$	1.93003	0.0822969
$551$	−0.976890	−0.0416169
$552$	−1.71989	−0.0732035
$553$	−16.7738	−0.713296
$554$	−30.0658	−1.27738
$555$	−28.2225	−1.19798
$556$	−11.8906	−0.504272
$557$	−7.98297	−0.338250	−0.169125	−	0.985595i	$-0.554094\pi$
$557$	−7.98297	−0.338250	−0.169125	+	0.985595i	$0.554094\pi$
$558$	−0.0500268	−0.00211780
$559$	7.31268	0.309294
$560$	2.79987	0.118316
$561$	10.7000	0.451754
$562$	20.7955	0.877204
$563$	−32.5769	−1.37295	−0.686475	−	0.727153i	$-0.740843\pi$
$563$	−32.5769	−1.37295	−0.686475	+	0.727153i	$0.740843\pi$
$564$	−13.5538	−0.570720
$565$	9.00792	0.378966
$566$	30.4313	1.27912
$567$	11.5905	0.486756
$568$	1.24515	0.0522454
$569$	−37.2092	−1.55989	−0.779946	−	0.625847i	$-0.784754\pi$
$569$	−37.2092	−1.55989	−0.779946	+	0.625847i	$0.784754\pi$
$570$	−0.417553	−0.0174894
$571$	−14.1233	−0.591041	−0.295520	−	0.955336i	$-0.595493\pi$
$571$	−14.1233	−0.591041	−0.295520	+	0.955336i	$0.595493\pi$
$572$	5.66887	0.237027
$573$	37.6688	1.57364
$574$	6.38176	0.266370
$575$	0.406485	0.0169516
$576$	−0.0419677	−0.00174866
$577$	27.9249	1.16253	0.581265	−	0.813714i	$-0.302558\pi$
$577$	27.9249	1.16253	0.581265	+	0.813714i	$0.302558\pi$
$578$	15.2832	0.635697
$579$	29.1825	1.21278
$580$	18.4833	0.767479
$581$	−14.9385	−0.619752
$582$	14.3897	0.596473
$583$	19.2993	0.799296
$584$	9.56377	0.395752
$585$	0.107390	0.00444004
$586$	−11.6987	−0.483268
$587$	21.4175	0.883995	0.441998	−	0.897016i	$-0.354270\pi$
$587$	21.4175	0.883995	0.441998	+	0.897016i	$0.354270\pi$
$588$	9.10410	0.375447
$589$	−0.135028	−0.00556374
$590$	−20.8835	−0.859760
$591$	−25.0636	−1.03098
$592$	−7.65635	−0.314674
$593$	5.12394	0.210415	0.105207	−	0.994450i	$-0.466449\pi$
$593$	5.12394	0.210415	0.105207	+	0.994450i	$0.466449\pi$
$594$	−24.8414	−1.01926
$595$	−3.66859	−0.150398
$596$	6.76725	0.277197
$597$	−24.1569	−0.988678
$598$	1.19392	0.0488231
$599$	45.0047	1.83884	0.919422	−	0.393272i	$-0.128657\pi$
$599$	45.0047	1.83884	0.919422	+	0.393272i	$0.128657\pi$
$600$	−0.699111	−0.0285411
$601$	−15.6494	−0.638353	−0.319176	−	0.947695i	$-0.603406\pi$
$601$	−15.6494	−0.638353	−0.319176	+	0.947695i	$0.603406\pi$
$602$	8.00138	0.326112
$603$	−0.375917	−0.0153085
$604$	−14.6117	−0.594541
$605$	−24.7427	−1.00593
$606$	4.00148	0.162549
$607$	8.53550	0.346445	0.173223	−	0.984883i	$-0.444582\pi$
$607$	8.53550	0.346445	0.173223	+	0.984883i	$0.444582\pi$
$608$	−0.113276	−0.00459395
$609$	−19.3764	−0.785173
$610$	0.720801	0.0291844
$611$	9.40887	0.380642
$612$	0.0549892	0.00222281
$613$	24.2113	0.977886	0.488943	−	0.872316i	$-0.337383\pi$
$613$	24.2113	0.977886	0.488943	+	0.872316i	$0.337383\pi$
$614$	−30.5843	−1.23428
$615$	18.0074	0.726127
$616$	6.20276	0.249916
$617$	10.0339	0.403951	0.201975	−	0.979391i	$-0.435264\pi$
$617$	10.0339	0.403951	0.201975	+	0.979391i	$0.435264\pi$
$618$	7.49649	0.301553
$619$	−17.4888	−0.702934	−0.351467	−	0.936200i	$-0.614317\pi$
$619$	−17.4888	−0.702934	−0.351467	+	0.936200i	$0.614317\pi$
$620$	2.55481	0.102604
$621$	−5.23186	−0.209947
$622$	−31.6222	−1.26794
$623$	−7.22675	−0.289534
$624$	−2.05342	−0.0822026
$625$	−22.8023	−0.912094
$626$	14.5106	0.579958
$627$	−0.925037	−0.0369424
$628$	−5.16105	−0.205948
$629$	10.0319	0.399999
$630$	0.117504	0.00468147
$631$	−28.4408	−1.13221	−0.566105	−	0.824333i	$-0.691550\pi$
$631$	−28.4408	−1.13221	−0.566105	+	0.824333i	$0.691550\pi$
$632$	−12.8401	−0.510751
$633$	13.6857	0.543957
$634$	−13.2217	−0.525100
$635$	−28.2783	−1.12219
$636$	−6.99074	−0.277201
$637$	−6.31992	−0.250404
$638$	40.9476	1.62113
$639$	0.0522562	0.00206722
$640$	2.14325	0.0847193
$641$	4.69292	0.185359	0.0926796	−	0.995696i	$-0.470457\pi$
$641$	4.69292	0.185359	0.0926796	+	0.995696i	$0.470457\pi$
$642$	18.6656	0.736672
$643$	25.2909	0.997376	0.498688	−	0.866782i	$-0.333815\pi$
$643$	25.2909	0.997376	0.498688	+	0.866782i	$0.333815\pi$
$644$	1.30637	0.0514780
$645$	22.5774	0.888985
$646$	0.148422	0.00583960
$647$	−38.3839	−1.50903	−0.754514	−	0.656284i	$-0.772127\pi$
$647$	−38.3839	−1.50903	−0.754514	+	0.656284i	$0.772127\pi$
$648$	8.87234	0.348538
$649$	−46.2648	−1.81605
$650$	0.485312	0.0190355
$651$	−2.67826	−0.104969
$652$	−17.9401	−0.702587
$653$	−44.8498	−1.75511	−0.877554	−	0.479478i	$-0.840826\pi$
$653$	−44.8498	−1.75511	−0.877554	+	0.479478i	$0.840826\pi$
$654$	29.5025	1.15364
$655$	2.14325	0.0837437
$656$	4.88513	0.190732
$657$	0.401370	0.0156589
$658$	10.2950	0.401340
$659$	18.6965	0.728311	0.364156	−	0.931338i	$-0.381358\pi$
$659$	18.6965	0.728311	0.364156	+	0.931338i	$0.381358\pi$
$660$	17.5023	0.681275
$661$	21.0524	0.818844	0.409422	−	0.912345i	$-0.365730\pi$
$661$	21.0524	0.818844	0.409422	+	0.912345i	$0.365730\pi$
$662$	−8.20755	−0.318995
$663$	2.69054	0.104492
$664$	−11.4351	−0.443770
$665$	0.317157	0.0122988
$666$	−0.321320	−0.0124509
$667$	8.62398	0.333922
$668$	−15.7089	−0.607795
$669$	15.5272	0.600315
$670$	19.1977	0.741671
$671$	1.59684	0.0616455
$672$	−2.24681	−0.0866725
$673$	−18.4051	−0.709463	−0.354732	−	0.934968i	$-0.615428\pi$
$673$	−18.4051	−0.709463	−0.354732	+	0.934968i	$0.615428\pi$
$674$	16.0731	0.619112
$675$	−2.12667	−0.0818557
$676$	−11.5745	−0.445175
$677$	11.3329	0.435560	0.217780	−	0.975998i	$-0.430118\pi$
$677$	11.3329	0.435560	0.217780	+	0.975998i	$0.430118\pi$
$678$	−7.22859	−0.277612
$679$	−10.9299	−0.419450
$680$	−2.80824	−0.107691
$681$	−33.9605	−1.30137
$682$	5.65987	0.216728
$683$	−36.7981	−1.40804	−0.704021	−	0.710179i	$-0.748614\pi$
$683$	−36.7981	−1.40804	−0.704021	+	0.710179i	$0.748614\pi$
$684$	−0.00475394	−0.000181771 0
$685$	−32.4735	−1.24075
$686$	−16.0597	−0.613162
$687$	13.2891	0.507011
$688$	6.12492	0.233510
$689$	4.85286	0.184879
$690$	3.68616	0.140330
$691$	−34.4811	−1.31172	−0.655862	−	0.754881i	$-0.727695\pi$
$691$	−34.4811	−1.31172	−0.655862	+	0.754881i	$0.727695\pi$
$692$	−7.13838	−0.271360
$693$	0.260316	0.00988858
$694$	1.50632	0.0571790
$695$	25.4844	0.966679
$696$	−14.8323	−0.562218
$697$	−6.40085	−0.242450
$698$	−32.2290	−1.21989
$699$	8.96283	0.339005
$700$	0.531018	0.0200706
$701$	−42.8496	−1.61841	−0.809203	−	0.587529i	$-0.800101\pi$
$701$	−42.8496	−1.61841	−0.809203	+	0.587529i	$0.800101\pi$
$702$	−6.24644	−0.235757
$703$	−0.867280	−0.0327101
$704$	4.74810	0.178951
$705$	29.0493	1.09406
$706$	18.4442	0.694158
$707$	−3.03937	−0.114307
$708$	16.7584	0.629819
$709$	−47.9555	−1.80101	−0.900503	−	0.434850i	$-0.856801\pi$
$709$	−47.9555	−1.80101	−0.900503	+	0.434850i	$0.856801\pi$
$710$	−2.66867	−0.100153
$711$	−0.538869	−0.0202092
$712$	−5.53195	−0.207319
$713$	1.19203	0.0446418
$714$	2.94393	0.110174
$715$	−12.1498	−0.454377
$716$	−22.6654	−0.847046
$717$	−20.5057	−0.765800
$718$	−25.0310	−0.934147
$719$	39.9379	1.48943	0.744716	−	0.667382i	$-0.232585\pi$
$719$	39.9379	1.48943	0.744716	+	0.667382i	$0.232585\pi$
$720$	0.0899473	0.00335214
$721$	−5.69405	−0.212058
$722$	18.9872	0.706629
$723$	−1.63484	−0.0608005
$724$	−4.59296	−0.170696
$725$	3.50552	0.130192
$726$	19.8553	0.736898
$727$	−9.20926	−0.341553	−0.170776	−	0.985310i	$-0.554628\pi$
$727$	−9.20926	−0.341553	−0.170776	+	0.985310i	$0.554628\pi$
$728$	1.55970	0.0578063
$729$	27.3671	1.01360
$730$	−20.4975	−0.758648
$731$	−8.02532	−0.296827
$732$	−0.578421	−0.0213791
$733$	−6.05931	−0.223806	−0.111903	−	0.993719i	$-0.535695\pi$
$733$	−6.05931	−0.223806	−0.111903	+	0.993719i	$0.535695\pi$
$734$	−0.325219	−0.0120040
$735$	−19.5123	−0.719724
$736$	1.00000	0.0368605
$737$	42.5301	1.56662
$738$	0.205018	0.00754681
$739$	−42.3001	−1.55604	−0.778018	−	0.628242i	$-0.783775\pi$
$739$	−42.3001	−1.55604	−0.778018	+	0.628242i	$0.783775\pi$
$740$	16.4095	0.603224
$741$	−0.232603	−0.00854489
$742$	5.30990	0.194933
$743$	−49.9222	−1.83147	−0.915734	−	0.401785i	$-0.868390\pi$
$743$	−49.9222	−1.83147	−0.915734	+	0.401785i	$0.868390\pi$
$744$	−2.05016	−0.0751626
$745$	−14.5039	−0.531382
$746$	11.1171	0.407027
$747$	−0.479907	−0.0175589
$748$	−6.22131	−0.227474
$749$	−14.1777	−0.518041
$750$	19.9292	0.727710
$751$	30.7250	1.12117	0.560586	−	0.828096i	$-0.310576\pi$
$751$	30.7250	1.12117	0.560586	+	0.828096i	$0.310576\pi$
$752$	7.88063	0.287377
$753$	7.51771	0.273961
$754$	10.2964	0.374972
$755$	31.3165	1.13972
$756$	−6.83472	−0.248576
$757$	−48.1973	−1.75176	−0.875881	−	0.482527i	$-0.839719\pi$
$757$	−48.1973	−1.75176	−0.875881	+	0.482527i	$0.839719\pi$
$758$	21.1963	0.769885
$759$	8.16623	0.296415
$760$	0.242778	0.00880650
$761$	−50.9334	−1.84633	−0.923167	−	0.384399i	$-0.874409\pi$
$761$	−50.9334	−1.84633	−0.923167	+	0.384399i	$0.874409\pi$
$762$	22.6925	0.822061
$763$	−22.4090	−0.811260
$764$	−21.9018	−0.792381
$765$	−0.117856	−0.00426108
$766$	27.9138	1.00857
$767$	−11.6334	−0.420058
$768$	−1.71989	−0.0620613
$769$	−30.3248	−1.09354	−0.546771	−	0.837282i	$-0.684143\pi$
$769$	−30.3248	−1.09354	−0.546771	+	0.837282i	$0.684143\pi$
$770$	−13.2941	−0.479084
$771$	−2.02064	−0.0727714
$772$	−16.9676	−0.610678
$773$	40.8243	1.46835	0.734175	−	0.678961i	$-0.237569\pi$
$773$	40.8243	1.46835	0.734175	+	0.678961i	$0.237569\pi$
$774$	0.257049	0.00923944
$775$	0.484542	0.0174053
$776$	−8.36663	−0.300345
$777$	−17.2024	−0.617131
$778$	16.7983	0.602249
$779$	0.553367	0.0198264
$780$	4.40099	0.157581
$781$	−5.91210	−0.211552
$782$	−1.31027	−0.0468553
$783$	−45.1195	−1.61244
$784$	−5.29341	−0.189050
$785$	11.0614	0.394799
$786$	−1.71989	−0.0613466
$787$	33.1044	1.18004	0.590022	−	0.807387i	$-0.299119\pi$
$787$	33.1044	1.18004	0.590022	+	0.807387i	$0.299119\pi$
$788$	14.5728	0.519133
$789$	−33.6777	−1.19896
$790$	27.5195	0.979099
$791$	5.49056	0.195222
$792$	0.199267	0.00708065
$793$	0.401531	0.0142588
$794$	−7.41739	−0.263233
$795$	14.9829	0.531389
$796$	14.0456	0.497833
$797$	17.6413	0.624887	0.312443	−	0.949936i	$-0.398853\pi$
$797$	17.6413	0.624887	0.312443	+	0.949936i	$0.398853\pi$
$798$	−0.254509	−0.00900954
$799$	−10.3258	−0.365300
$800$	0.406485	0.0143714
$801$	−0.232164	−0.00820310
$802$	−8.45159	−0.298436
$803$	−45.4098	−1.60248
$804$	−15.4056	−0.543312
$805$	−2.79987	−0.0986823
$806$	1.42319	0.0501297
$807$	−0.480578	−0.0169171
$808$	−2.32659	−0.0818491
$809$	27.5207	0.967577	0.483788	−	0.875185i	$-0.339260\pi$
$809$	27.5207	0.967577	0.483788	+	0.875185i	$0.339260\pi$
$810$	−19.0156	−0.668141
$811$	34.8704	1.22447	0.612233	−	0.790677i	$-0.290271\pi$
$811$	34.8704	1.22447	0.612233	+	0.790677i	$0.290271\pi$
$812$	11.2661	0.395362
$813$	45.7839	1.60571
$814$	36.3531	1.27418
$815$	38.4500	1.34685
$816$	2.25353	0.0788893
$817$	0.693806	0.0242732
$818$	19.1937	0.671091
$819$	0.0654571	0.00228726
$820$	−10.4700	−0.365630
$821$	15.5996	0.544431	0.272215	−	0.962236i	$-0.412244\pi$
$821$	15.5996	0.544431	0.272215	+	0.962236i	$0.412244\pi$
$822$	26.0590	0.908911
$823$	40.6348	1.41644	0.708219	−	0.705992i	$-0.249499\pi$
$823$	40.6348	1.41644	0.708219	+	0.705992i	$0.249499\pi$
$824$	−4.35870	−0.151842
$825$	3.31945	0.115569
$826$	−12.7290	−0.442900
$827$	16.4536	0.572148	0.286074	−	0.958208i	$-0.407650\pi$
$827$	16.4536	0.572148	0.286074	+	0.958208i	$0.407650\pi$
$828$	0.0419677	0.00145848
$829$	19.2688	0.669233	0.334616	−	0.942354i	$-0.391393\pi$
$829$	19.2688	0.669233	0.334616	+	0.942354i	$0.391393\pi$
$830$	24.5084	0.850697
$831$	−51.7100	−1.79380
$832$	1.19392	0.0413918
$833$	6.93581	0.240312
$834$	−20.4505	−0.708142
$835$	33.6681	1.16513
$836$	0.537846	0.0186018
$837$	−6.23653	−0.215566
$838$	−20.3707	−0.703693
$839$	−17.3927	−0.600462	−0.300231	−	0.953867i	$-0.597064\pi$
$839$	−17.3927	−0.600462	−0.300231	+	0.953867i	$0.597064\pi$
$840$	4.81547	0.166150
$841$	45.3731	1.56459
$842$	37.4866	1.29187
$843$	35.7660	1.23185
$844$	−7.95729	−0.273901
$845$	24.8071	0.853391
$846$	0.330732	0.0113708
$847$	−15.0813	−0.518200
$848$	4.06464	0.139580
$849$	52.3386	1.79626
$850$	−0.532607	−0.0182683
$851$	7.65635	0.262456
$852$	2.14153	0.0733675
$853$	38.0571	1.30305	0.651525	−	0.758627i	$-0.274130\pi$
$853$	38.0571	1.30305	0.651525	+	0.758627i	$0.274130\pi$
$854$	0.439347	0.0150341
$855$	0.0101889	0.000348452 0
$856$	−10.8528	−0.370940
$857$	−55.3565	−1.89094	−0.945470	−	0.325708i	$-0.894397\pi$
$857$	−55.3565	−1.89094	−0.945470	+	0.325708i	$0.894397\pi$
$858$	9.74985	0.332854
$859$	−41.6508	−1.42111	−0.710553	−	0.703643i	$-0.751555\pi$
$859$	−41.6508	−1.42111	−0.710553	+	0.703643i	$0.751555\pi$
$860$	−13.1272	−0.447635
$861$	10.9759	0.374059
$862$	18.6956	0.636775
$863$	−49.3177	−1.67879	−0.839397	−	0.543518i	$-0.817092\pi$
$863$	−49.3177	−1.67879	−0.839397	+	0.543518i	$0.817092\pi$
$864$	−5.23186	−0.177991
$865$	15.2993	0.520193
$866$	7.80537	0.265237
$867$	26.2854	0.892700
$868$	1.55723	0.0528557
$869$	60.9660	2.06813
$870$	31.7894	1.07776
$871$	10.6943	0.362363
$872$	−17.1537	−0.580897
$873$	−0.351129	−0.0118839
$874$	0.113276	0.00383162
$875$	−15.1374	−0.511739
$876$	16.4487	0.555749
$877$	−39.9427	−1.34877	−0.674384	−	0.738381i	$-0.735591\pi$
$877$	−39.9427	−1.34877	−0.674384	+	0.738381i	$0.735591\pi$
$878$	4.02590	0.135868
$879$	−20.1205	−0.678647
$880$	−10.1764	−0.343045
$881$	−45.8060	−1.54324	−0.771622	−	0.636081i	$-0.780554\pi$
$881$	−45.8060	−1.54324	−0.771622	+	0.636081i	$0.780554\pi$
$882$	−0.222152	−0.00748026
$883$	−33.5871	−1.13030	−0.565148	−	0.824990i	$-0.691181\pi$
$883$	−33.5871	−1.13030	−0.565148	+	0.824990i	$0.691181\pi$
$884$	−1.56437	−0.0526153
$885$	−35.9174	−1.20735
$886$	11.7695	0.395405
$887$	50.5726	1.69806	0.849030	−	0.528344i	$-0.177187\pi$
$887$	50.5726	1.69806	0.849030	+	0.528344i	$0.177187\pi$
$888$	−13.1681	−0.441893
$889$	−17.2363	−0.578088
$890$	11.8564	0.397426
$891$	−42.1268	−1.41130
$892$	−9.02798	−0.302279
$893$	0.892686	0.0298726
$894$	11.6389	0.389265
$895$	48.5776	1.62377
$896$	1.30637	0.0436426
$897$	2.05342	0.0685617
$898$	−24.8386	−0.828874
$899$	10.2800	0.342858
$900$	0.0170593	0.000568642 0
$901$	−5.32579	−0.177428
$902$	−23.1951	−0.772312
$903$	13.7615	0.457955
$904$	4.20293	0.139787
$905$	9.84386	0.327221
$906$	−25.1305	−0.834906
$907$	−26.5438	−0.881373	−0.440686	−	0.897661i	$-0.645265\pi$
$907$	−26.5438	−0.881373	−0.440686	+	0.897661i	$0.645265\pi$
$908$	19.7457	0.655283
$909$	−0.0976416	−0.00323857
$910$	−3.34282	−0.110814
$911$	33.1352	1.09782	0.548909	−	0.835882i	$-0.315043\pi$
$911$	33.1352	1.09782	0.548909	+	0.835882i	$0.315043\pi$
$912$	−0.194822	−0.00645122
$913$	54.2952	1.79691
$914$	8.47035	0.280174
$915$	1.23970	0.0409832
$916$	−7.72671	−0.255298
$917$	1.30637	0.0431400
$918$	6.85517	0.226254
$919$	−21.3143	−0.703094	−0.351547	−	0.936170i	$-0.614344\pi$
$919$	−21.3143	−0.703094	−0.351547	+	0.936170i	$0.614344\pi$
$920$	−2.14325	−0.0706608
$921$	−52.6017	−1.73329
$922$	−5.75911	−0.189666
$923$	−1.48661	−0.0489325
$924$	10.6681	0.350954
$925$	3.11220	0.102328
$926$	7.74262	0.254438
$927$	−0.182925	−0.00600803
$928$	8.62398	0.283096
$929$	46.9705	1.54105	0.770526	−	0.637408i	$-0.219993\pi$
$929$	46.9705	1.54105	0.770526	+	0.637408i	$0.219993\pi$
$930$	4.39401	0.144085
$931$	−0.599616	−0.0196516
$932$	−5.21127	−0.170701
$933$	−54.3868	−1.78055
$934$	25.4019	0.831175
$935$	13.3338	0.436063
$936$	0.0501063	0.00163777
$937$	38.7754	1.26674	0.633369	−	0.773850i	$-0.281672\pi$
$937$	38.7754	1.26674	0.633369	+	0.773850i	$0.281672\pi$
$938$	11.7015	0.382067
$939$	24.9566	0.814428
$940$	−16.8902	−0.550896
$941$	−15.6269	−0.509422	−0.254711	−	0.967017i	$-0.581980\pi$
$941$	−15.6269	−0.509422	−0.254711	+	0.967017i	$0.581980\pi$
$942$	−8.87645	−0.289210
$943$	−4.88513	−0.159082
$944$	−9.74386	−0.317136
$945$	14.6485	0.476516
$946$	−29.0818	−0.945529
$947$	−15.6082	−0.507198	−0.253599	−	0.967309i	$-0.581614\pi$
$947$	−15.6082	−0.507198	−0.253599	+	0.967309i	$0.581614\pi$
$948$	−22.0835	−0.717240
$949$	−11.4184	−0.370657
$950$	0.0460450	0.00149390
$951$	−22.7399	−0.737391
$952$	−1.71170	−0.0554764
$953$	46.8772	1.51850	0.759250	−	0.650799i	$-0.225566\pi$
$953$	46.8772	1.51850	0.759250	+	0.650799i	$0.225566\pi$
$954$	0.170584	0.00552285
$955$	46.9411	1.51898
$956$	11.9227	0.385606
$957$	70.4254	2.27653
$958$	35.9072	1.16011
$959$	−19.7934	−0.639163
$960$	3.68616	0.118970
$961$	−29.5791	−0.954163
$962$	9.14109	0.294721
$963$	−0.455466	−0.0146772
$964$	0.950549	0.0306151
$965$	36.3658	1.17066
$966$	2.24681	0.0722899
$967$	21.3384	0.686195	0.343098	−	0.939300i	$-0.388524\pi$
$967$	21.3384	0.686195	0.343098	+	0.939300i	$0.388524\pi$
$968$	−11.5445	−0.371054
$969$	0.255271	0.00820048
$970$	17.9318	0.575755
$971$	−35.3159	−1.13334	−0.566671	−	0.823944i	$-0.691769\pi$
$971$	−35.3159	−1.13334	−0.566671	+	0.823944i	$0.691769\pi$
$972$	−0.436109	−0.0139882
$973$	15.5334	0.497978
$974$	−29.9563	−0.959862
$975$	0.834685	0.0267313
$976$	0.336312	0.0107651
$977$	47.3796	1.51581	0.757903	−	0.652367i	$-0.226224\pi$
$977$	47.3796	1.51581	0.757903	+	0.652367i	$0.226224\pi$
$978$	−30.8550	−0.986634
$979$	26.2663	0.839474
$980$	11.3451	0.362406
$981$	−0.719901	−0.0229847
$982$	0.427788	0.0136513
$983$	−6.18402	−0.197240	−0.0986198	−	0.995125i	$-0.531443\pi$
$983$	−6.18402	−0.197240	−0.0986198	+	0.995125i	$0.531443\pi$
$984$	8.40190	0.267843
$985$	−31.2331	−0.995168
$986$	−11.2998	−0.359858
$987$	17.7063	0.563597
$988$	0.135243	0.00430264
$989$	−6.12492	−0.194761
$990$	−0.427079	−0.0135735
$991$	17.4429	0.554093	0.277046	−	0.960857i	$-0.410644\pi$
$991$	17.4429	0.554093	0.277046	+	0.960857i	$0.410644\pi$
$992$	1.19203	0.0378469
$993$	−14.1161	−0.447961
$994$	−1.62662	−0.0515933
$995$	−30.1032	−0.954336
$996$	−19.6672	−0.623180
$997$	−11.7778	−0.373008	−0.186504	−	0.982454i	$-0.559716\pi$
$997$	−11.7778	−0.373008	−0.186504	+	0.982454i	$0.559716\pi$
$998$	32.9391	1.04267
$999$	−40.0570	−1.26735

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.7	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.7	✓	24	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.71989 q^{3} +1.00000 q^{4} -2.14325 q^{5} +1.71989 q^{6} -1.30637 q^{7} -1.00000 q^{8} -0.0419677 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.71989 q^{3} +1.00000 q^{4} -2.14325 q^{5} +1.71989 q^{6} -1.30637 q^{7} -1.00000 q^{8} -0.0419677 q^{9} +2.14325 q^{10} +4.74810 q^{11} -1.71989 q^{12} +1.19392 q^{13} +1.30637 q^{14} +3.68616 q^{15} +1.00000 q^{16} -1.31027 q^{17} +0.0419677 q^{18} +0.113276 q^{19} -2.14325 q^{20} +2.24681 q^{21} -4.74810 q^{22} -1.00000 q^{23} +1.71989 q^{24} -0.406485 q^{25} -1.19392 q^{26} +5.23186 q^{27} -1.30637 q^{28} -8.62398 q^{29} -3.68616 q^{30} -1.19203 q^{31} -1.00000 q^{32} -8.16623 q^{33} +1.31027 q^{34} +2.79987 q^{35} -0.0419677 q^{36} -7.65635 q^{37} -0.113276 q^{38} -2.05342 q^{39} +2.14325 q^{40} +4.88513 q^{41} -2.24681 q^{42} +6.12492 q^{43} +4.74810 q^{44} +0.0899473 q^{45} +1.00000 q^{46} +7.88063 q^{47} -1.71989 q^{48} -5.29341 q^{49} +0.406485 q^{50} +2.25353 q^{51} +1.19392 q^{52} +4.06464 q^{53} -5.23186 q^{54} -10.1764 q^{55} +1.30637 q^{56} -0.194822 q^{57} +8.62398 q^{58} -9.74386 q^{59} +3.68616 q^{60} +0.336312 q^{61} +1.19203 q^{62} +0.0548252 q^{63} +1.00000 q^{64} -2.55887 q^{65} +8.16623 q^{66} +8.95728 q^{67} -1.31027 q^{68} +1.71989 q^{69} -2.79987 q^{70} -1.24515 q^{71} +0.0419677 q^{72} -9.56377 q^{73} +7.65635 q^{74} +0.699111 q^{75} +0.113276 q^{76} -6.20276 q^{77} +2.05342 q^{78} +12.8401 q^{79} -2.14325 q^{80} -8.87234 q^{81} -4.88513 q^{82} +11.4351 q^{83} +2.24681 q^{84} +2.80824 q^{85} -6.12492 q^{86} +14.8323 q^{87} -4.74810 q^{88} +5.53195 q^{89} -0.0899473 q^{90} -1.55970 q^{91} -1.00000 q^{92} +2.05016 q^{93} -7.88063 q^{94} -0.242778 q^{95} +1.71989 q^{96} +8.36663 q^{97} +5.29341 q^{98} -0.199267 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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