LMFDB - Embedded newform 8021.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, 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("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41415 q^{2} +1.51661 q^{3} +3.82811 q^{4} -1.37172 q^{5} -3.66132 q^{6} -4.25980 q^{7} -4.41333 q^{8} -0.699894 q^{9} +O(q^{10})$	\(q-2.41415 q^{2} +1.51661 q^{3} +3.82811 q^{4} -1.37172 q^{5} -3.66132 q^{6} -4.25980 q^{7} -4.41333 q^{8} -0.699894 q^{9} +3.31154 q^{10} -0.120447 q^{11} +5.80575 q^{12} +1.00000 q^{13} +10.2838 q^{14} -2.08037 q^{15} +2.99821 q^{16} +7.08689 q^{17} +1.68965 q^{18} -3.24930 q^{19} -5.25110 q^{20} -6.46045 q^{21} +0.290777 q^{22} +7.25383 q^{23} -6.69330 q^{24} -3.11838 q^{25} -2.41415 q^{26} -5.61130 q^{27} -16.3070 q^{28} +9.31990 q^{29} +5.02231 q^{30} -5.08312 q^{31} +1.58853 q^{32} -0.182671 q^{33} -17.1088 q^{34} +5.84326 q^{35} -2.67927 q^{36} +0.851436 q^{37} +7.84428 q^{38} +1.51661 q^{39} +6.05386 q^{40} -7.90111 q^{41} +15.5965 q^{42} +8.93148 q^{43} -0.461084 q^{44} +0.960059 q^{45} -17.5118 q^{46} -10.4025 q^{47} +4.54712 q^{48} +11.1459 q^{49} +7.52824 q^{50} +10.7480 q^{51} +3.82811 q^{52} -9.41266 q^{53} +13.5465 q^{54} +0.165220 q^{55} +18.7999 q^{56} -4.92792 q^{57} -22.4996 q^{58} -11.1430 q^{59} -7.96387 q^{60} -9.69409 q^{61} +12.2714 q^{62} +2.98141 q^{63} -9.83138 q^{64} -1.37172 q^{65} +0.440995 q^{66} +11.6941 q^{67} +27.1294 q^{68} +11.0012 q^{69} -14.1065 q^{70} -5.11862 q^{71} +3.08886 q^{72} +7.97343 q^{73} -2.05549 q^{74} -4.72937 q^{75} -12.4387 q^{76} +0.513080 q^{77} -3.66132 q^{78} -3.28493 q^{79} -4.11271 q^{80} -6.41047 q^{81} +19.0745 q^{82} +13.9819 q^{83} -24.7313 q^{84} -9.72123 q^{85} -21.5619 q^{86} +14.1347 q^{87} +0.531572 q^{88} +14.1334 q^{89} -2.31773 q^{90} -4.25980 q^{91} +27.7685 q^{92} -7.70911 q^{93} +25.1131 q^{94} +4.45713 q^{95} +2.40918 q^{96} +5.25629 q^{97} -26.9078 q^{98} +0.0843001 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) $ 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * 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 $

$2$	−2.41415	−1.70706	−0.853530	−	0.521043i	$-0.825543\pi$
$2$	−2.41415	−1.70706	−0.853530	+	0.521043i	$0.825543\pi$
$3$	1.51661	0.875615	0.437808	−	0.899069i	$-0.355755\pi$
$3$	1.51661	0.875615	0.437808	+	0.899069i	$0.355755\pi$
$4$	3.82811	1.91406
$5$	−1.37172	−0.613452	−0.306726	−	0.951798i	$-0.599234\pi$
$5$	−1.37172	−0.613452	−0.306726	+	0.951798i	$0.599234\pi$
$6$	−3.66132	−1.49473
$7$	−4.25980	−1.61005	−0.805026	−	0.593239i	$-0.797849\pi$
$7$	−4.25980	−1.61005	−0.805026	+	0.593239i	$0.797849\pi$
$8$	−4.41333	−1.56035
$9$	−0.699894	−0.233298
$10$	3.31154	1.04720
$11$	−0.120447	−0.0363161	−0.0181581	−	0.999835i	$-0.505780\pi$
$11$	−0.120447	−0.0363161	−0.0181581	+	0.999835i	$0.505780\pi$
$12$	5.80575	1.67598
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	10.2838	2.74846
$15$	−2.08037	−0.537148
$16$	2.99821	0.749554
$17$	7.08689	1.71882	0.859411	−	0.511285i	$-0.170830\pi$
$17$	7.08689	1.71882	0.859411	+	0.511285i	$0.170830\pi$
$18$	1.68965	0.398254
$19$	−3.24930	−0.745440	−0.372720	−	0.927944i	$-0.621575\pi$
$19$	−3.24930	−0.745440	−0.372720	+	0.927944i	$0.621575\pi$
$20$	−5.25110	−1.17418
$21$	−6.46045	−1.40979
$22$	0.290777	0.0619938
$23$	7.25383	1.51253	0.756264	−	0.654266i	$-0.227022\pi$
$23$	7.25383	1.51253	0.756264	+	0.654266i	$0.227022\pi$
$24$	−6.69330	−1.36626
$25$	−3.11838	−0.623676
$26$	−2.41415	−0.473453
$27$	−5.61130	−1.07989
$28$	−16.3070	−3.08173
$29$	9.31990	1.73066	0.865331	−	0.501201i	$-0.167108\pi$
$29$	9.31990	1.73066	0.865331	+	0.501201i	$0.167108\pi$
$30$	5.02231	0.916944
$31$	−5.08312	−0.912956	−0.456478	−	0.889735i	$-0.650889\pi$
$31$	−5.08312	−0.912956	−0.456478	+	0.889735i	$0.650889\pi$
$32$	1.58853	0.280815
$33$	−0.182671	−0.0317989
$34$	−17.1088	−2.93413
$35$	5.84326	0.987691
$36$	−2.67927	−0.446545
$37$	0.851436	0.139975	0.0699876	−	0.997548i	$-0.477704\pi$
$37$	0.851436	0.139975	0.0699876	+	0.997548i	$0.477704\pi$
$38$	7.84428	1.27251
$39$	1.51661	0.242852
$40$	6.05386	0.957199
$41$	−7.90111	−1.23395	−0.616973	−	0.786984i	$-0.711641\pi$
$41$	−7.90111	−1.23395	−0.616973	+	0.786984i	$0.711641\pi$
$42$	15.5965	2.40659
$43$	8.93148	1.36204	0.681019	−	0.732266i	$-0.261537\pi$
$43$	8.93148	1.36204	0.681019	+	0.732266i	$0.261537\pi$
$44$	−0.461084	−0.0695111
$45$	0.960059	0.143117
$46$	−17.5118	−2.58198
$47$	−10.4025	−1.51736	−0.758679	−	0.651465i	$-0.774155\pi$
$47$	−10.4025	−1.51736	−0.758679	+	0.651465i	$0.774155\pi$
$48$	4.54712	0.656321
$49$	11.1459	1.59227
$50$	7.52824	1.06465
$51$	10.7480	1.50503
$52$	3.82811	0.530864
$53$	−9.41266	−1.29293	−0.646464	−	0.762944i	$-0.723753\pi$
$53$	−9.41266	−1.29293	−0.646464	+	0.762944i	$0.723753\pi$
$54$	13.5465	1.84345
$55$	0.165220	0.0222782
$56$	18.7999	2.51224
$57$	−4.92792	−0.652718
$58$	−22.4996	−2.95434
$59$	−11.1430	−1.45069	−0.725345	−	0.688385i	$-0.758320\pi$
$59$	−11.1430	−1.45069	−0.725345	+	0.688385i	$0.758320\pi$
$60$	−7.96387	−1.02813
$61$	−9.69409	−1.24120	−0.620601	−	0.784127i	$-0.713111\pi$
$61$	−9.69409	−1.24120	−0.620601	+	0.784127i	$0.713111\pi$
$62$	12.2714	1.55847
$63$	2.98141	0.375622
$64$	−9.83138	−1.22892
$65$	−1.37172	−0.170141
$66$	0.440995	0.0542827
$67$	11.6941	1.42866	0.714328	−	0.699811i	$-0.246732\pi$
$67$	11.6941	1.42866	0.714328	+	0.699811i	$0.246732\pi$
$68$	27.1294	3.28992
$69$	11.0012	1.32439
$70$	−14.1065	−1.68605
$71$	−5.11862	−0.607468	−0.303734	−	0.952757i	$-0.598233\pi$
$71$	−5.11862	−0.607468	−0.303734	+	0.952757i	$0.598233\pi$
$72$	3.08886	0.364026
$73$	7.97343	0.933220	0.466610	−	0.884463i	$-0.345475\pi$
$73$	7.97343	0.933220	0.466610	+	0.884463i	$0.345475\pi$
$74$	−2.05549	−0.238946
$75$	−4.72937	−0.546100
$76$	−12.4387	−1.42681
$77$	0.513080	0.0584709
$78$	−3.66132	−0.414563
$79$	−3.28493	−0.369583	−0.184791	−	0.982778i	$-0.559161\pi$
$79$	−3.28493	−0.369583	−0.184791	+	0.982778i	$0.559161\pi$
$80$	−4.11271	−0.459815
$81$	−6.41047	−0.712274
$82$	19.0745	2.10642
$83$	13.9819	1.53471	0.767356	−	0.641221i	$-0.221572\pi$
$83$	13.9819	1.53471	0.767356	+	0.641221i	$0.221572\pi$
$84$	−24.7313	−2.69841
$85$	−9.72123	−1.05442
$86$	−21.5619	−2.32508
$87$	14.1347	1.51539
$88$	0.531572	0.0566658
$89$	14.1334	1.49814	0.749068	−	0.662493i	$-0.230502\pi$
$89$	14.1334	1.49814	0.749068	+	0.662493i	$0.230502\pi$
$90$	−2.31773	−0.244310
$91$	−4.25980	−0.446548
$92$	27.7685	2.89506
$93$	−7.70911	−0.799398
$94$	25.1131	2.59022
$95$	4.45713	0.457292
$96$	2.40918	0.245886
$97$	5.25629	0.533695	0.266848	−	0.963739i	$-0.414018\pi$
$97$	5.25629	0.533695	0.266848	+	0.963739i	$0.414018\pi$
$98$	−26.9078	−2.71810
$99$	0.0843001	0.00847248
$100$	−11.9375	−1.19375
$101$	−9.28845	−0.924235	−0.462118	−	0.886819i	$-0.652910\pi$
$101$	−9.28845	−0.924235	−0.462118	+	0.886819i	$0.652910\pi$
$102$	−25.9474	−2.56917
$103$	1.28294	0.126412	0.0632060	−	0.998001i	$-0.479867\pi$
$103$	1.28294	0.126412	0.0632060	+	0.998001i	$0.479867\pi$
$104$	−4.41333	−0.432763
$105$	8.86194	0.864837
$106$	22.7236	2.20711
$107$	2.32187	0.224463	0.112232	−	0.993682i	$-0.464200\pi$
$107$	2.32187	0.224463	0.112232	+	0.993682i	$0.464200\pi$
$108$	−21.4807	−2.06698
$109$	−11.3089	−1.08320	−0.541599	−	0.840637i	$-0.682181\pi$
$109$	−11.3089	−1.08320	−0.541599	+	0.840637i	$0.682181\pi$
$110$	−0.398865	−0.0380302
$111$	1.29130	0.122564
$112$	−12.7718	−1.20682
$113$	−16.0345	−1.50840	−0.754201	−	0.656644i	$-0.771976\pi$
$113$	−16.0345	−1.50840	−0.754201	+	0.656644i	$0.771976\pi$
$114$	11.8967	1.11423
$115$	−9.95023	−0.927864
$116$	35.6776	3.31258
$117$	−0.699894	−0.0647052
$118$	26.9008	2.47642
$119$	−30.1887	−2.76739
$120$	9.18134	0.838138
$121$	−10.9855	−0.998681
$122$	23.4030	2.11881
$123$	−11.9829	−1.08046
$124$	−19.4588	−1.74745
$125$	11.1362	0.996048
$126$	−7.19756	−0.641210
$127$	−15.8039	−1.40237	−0.701185	−	0.712980i	$-0.747345\pi$
$127$	−15.8039	−1.40237	−0.701185	+	0.712980i	$0.747345\pi$
$128$	20.5573	1.81703
$129$	13.5456	1.19262
$130$	3.31154	0.290441
$131$	−14.9134	−1.30299	−0.651495	−	0.758653i	$-0.725858\pi$
$131$	−14.9134	−1.30299	−0.651495	+	0.758653i	$0.725858\pi$
$132$	−0.699285	−0.0608650
$133$	13.8414	1.20020
$134$	−28.2312	−2.43880
$135$	7.69713	0.662464
$136$	−31.2768	−2.68196
$137$	−12.1418	−1.03734	−0.518672	−	0.854973i	$-0.673573\pi$
$137$	−12.1418	−1.03734	−0.518672	+	0.854973i	$0.673573\pi$
$138$	−26.5586	−2.26082
$139$	−9.79923	−0.831160	−0.415580	−	0.909557i	$-0.636421\pi$
$139$	−9.79923	−0.831160	−0.415580	+	0.909557i	$0.636421\pi$
$140$	22.3686	1.89049
$141$	−15.7765	−1.32862
$142$	12.3571	1.03699
$143$	−0.120447	−0.0100723
$144$	−2.09843	−0.174869
$145$	−12.7843	−1.06168
$146$	−19.2490	−1.59306
$147$	16.9040	1.39422
$148$	3.25939	0.267920
$149$	17.8470	1.46209	0.731043	−	0.682331i	$-0.239034\pi$
$149$	17.8470	1.46209	0.731043	+	0.682331i	$0.239034\pi$
$150$	11.4174	0.932227
$151$	−2.02821	−0.165053	−0.0825267	−	0.996589i	$-0.526299\pi$
$151$	−2.02821	−0.165053	−0.0825267	+	0.996589i	$0.526299\pi$
$152$	14.3402	1.16315
$153$	−4.96007	−0.400998
$154$	−1.23865	−0.0998133
$155$	6.97262	0.560055
$156$	5.80575	0.464832
$157$	−11.7213	−0.935458	−0.467729	−	0.883872i	$-0.654928\pi$
$157$	−11.7213	−0.935458	−0.467729	+	0.883872i	$0.654928\pi$
$158$	7.93030	0.630900
$159$	−14.2753	−1.13211
$160$	−2.17902	−0.172267
$161$	−30.8999	−2.43525
$162$	15.4758	1.21589
$163$	−6.79545	−0.532261	−0.266130	−	0.963937i	$-0.585745\pi$
$163$	−6.79545	−0.532261	−0.266130	+	0.963937i	$0.585745\pi$
$164$	−30.2463	−2.36184
$165$	0.250574	0.0195071
$166$	−33.7544	−2.61985
$167$	2.14595	0.166059	0.0830293	−	0.996547i	$-0.473541\pi$
$167$	2.14595	0.166059	0.0830293	+	0.996547i	$0.473541\pi$
$168$	28.5121	2.19976
$169$	1.00000	0.0769231
$170$	23.4685	1.79995
$171$	2.27416	0.173910
$172$	34.1907	2.60702
$173$	−13.4666	−1.02384	−0.511922	−	0.859032i	$-0.671066\pi$
$173$	−13.4666	−1.02384	−0.511922	+	0.859032i	$0.671066\pi$
$174$	−34.1231	−2.58687
$175$	13.2837	1.00415
$176$	−0.361126	−0.0272209
$177$	−16.8995	−1.27025
$178$	−34.1201	−2.55741
$179$	18.0623	1.35004	0.675021	−	0.737798i	$-0.264134\pi$
$179$	18.0623	1.35004	0.675021	+	0.737798i	$0.264134\pi$
$180$	3.67521	0.273934
$181$	21.0842	1.56717	0.783587	−	0.621282i	$-0.213388\pi$
$181$	21.0842	1.56717	0.783587	+	0.621282i	$0.213388\pi$
$182$	10.2838	0.762285
$183$	−14.7022	−1.08681
$184$	−32.0136	−2.36007
$185$	−1.16793	−0.0858681
$186$	18.6109	1.36462
$187$	−0.853594	−0.0624210
$188$	−39.8218	−2.90431
$189$	23.9030	1.73869
$190$	−10.7602	−0.780625
$191$	11.9459	0.864376	0.432188	−	0.901784i	$-0.357742\pi$
$191$	11.9459	0.864376	0.432188	+	0.901784i	$0.357742\pi$
$192$	−14.9104	−1.07606
$193$	19.1843	1.38092	0.690458	−	0.723373i	$-0.257409\pi$
$193$	19.1843	1.38092	0.690458	+	0.723373i	$0.257409\pi$
$194$	−12.6895	−0.911050
$195$	−2.08037	−0.148978
$196$	42.6677	3.04769
$197$	2.18778	0.155873	0.0779365	−	0.996958i	$-0.475167\pi$
$197$	2.18778	0.155873	0.0779365	+	0.996958i	$0.475167\pi$
$198$	−0.203513	−0.0144630
$199$	24.5533	1.74054	0.870270	−	0.492576i	$-0.163945\pi$
$199$	24.5533	1.74054	0.870270	+	0.492576i	$0.163945\pi$
$200$	13.7625	0.973152
$201$	17.7353	1.25095
$202$	22.4237	1.57773
$203$	−39.7009	−2.78646
$204$	41.1447	2.88071
$205$	10.8381	0.756967
$206$	−3.09721	−0.215793
$207$	−5.07691	−0.352870
$208$	2.99821	0.207889
$209$	0.391368	0.0270715
$210$	−21.3940	−1.47633
$211$	−5.24723	−0.361234	−0.180617	−	0.983553i	$-0.557809\pi$
$211$	−5.24723	−0.361234	−0.180617	+	0.983553i	$0.557809\pi$
$212$	−36.0327	−2.47474
$213$	−7.76295	−0.531909
$214$	−5.60533	−0.383173
$215$	−12.2515	−0.835545
$216$	24.7645	1.68501
$217$	21.6531	1.46991
$218$	27.3014	1.84909
$219$	12.0926	0.817141
$220$	0.632479	0.0426417
$221$	7.08689	0.476716
$222$	−3.11738	−0.209225
$223$	19.9378	1.33513	0.667565	−	0.744551i	$-0.267336\pi$
$223$	19.9378	1.33513	0.667565	+	0.744551i	$0.267336\pi$
$224$	−6.76682	−0.452127
$225$	2.18254	0.145502
$226$	38.7097	2.57493
$227$	−14.6865	−0.974775	−0.487387	−	0.873186i	$-0.662050\pi$
$227$	−14.6865	−0.974775	−0.487387	+	0.873186i	$0.662050\pi$
$228$	−18.8646	−1.24934
$229$	14.7912	0.977433	0.488716	−	0.872443i	$-0.337465\pi$
$229$	14.7912	0.977433	0.488716	+	0.872443i	$0.337465\pi$
$230$	24.0213	1.58392
$231$	0.778142	0.0511980
$232$	−41.1318	−2.70044
$233$	−0.0358893	−0.00235119	−0.00117559	−	0.999999i	$-0.500374\pi$
$233$	−0.0358893	−0.00235119	−0.00117559	+	0.999999i	$0.500374\pi$
$234$	1.68965	0.110456
$235$	14.2693	0.930826
$236$	−42.6565	−2.77670
$237$	−4.98195	−0.323612
$238$	72.8800	4.72411
$239$	11.5721	0.748534	0.374267	−	0.927321i	$-0.377894\pi$
$239$	11.5721	0.748534	0.374267	+	0.927321i	$0.377894\pi$
$240$	−6.23738	−0.402621
$241$	9.68993	0.624183	0.312092	−	0.950052i	$-0.398970\pi$
$241$	9.68993	0.624183	0.312092	+	0.950052i	$0.398970\pi$
$242$	26.5206	1.70481
$243$	7.11171	0.456216
$244$	−37.1101	−2.37573
$245$	−15.2890	−0.976782
$246$	28.9285	1.84441
$247$	−3.24930	−0.206748
$248$	22.4335	1.42453
$249$	21.2051	1.34382
$250$	−26.8843	−1.70031
$251$	23.5508	1.48651	0.743256	−	0.669007i	$-0.233280\pi$
$251$	23.5508	1.48651	0.743256	+	0.669007i	$0.233280\pi$
$252$	11.4132	0.718962
$253$	−0.873702	−0.0549292
$254$	38.1530	2.39393
$255$	−14.7433	−0.923262
$256$	−29.9657	−1.87286
$257$	−28.0941	−1.75246	−0.876232	−	0.481890i	$-0.839950\pi$
$257$	−28.0941	−1.75246	−0.876232	+	0.481890i	$0.839950\pi$
$258$	−32.7010	−2.03588
$259$	−3.62695	−0.225367
$260$	−5.25110	−0.325659
$261$	−6.52294	−0.403760
$262$	36.0031	2.22428
$263$	10.1815	0.627815	0.313908	−	0.949454i	$-0.398362\pi$
$263$	10.1815	0.627815	0.313908	+	0.949454i	$0.398362\pi$
$264$	0.806188	0.0496174
$265$	12.9115	0.793150
$266$	−33.4151	−2.04881
$267$	21.4348	1.31179
$268$	44.7662	2.73453
$269$	2.41952	0.147521	0.0737605	−	0.997276i	$-0.476500\pi$
$269$	2.41952	0.147521	0.0737605	+	0.997276i	$0.476500\pi$
$270$	−18.5820	−1.13087
$271$	13.3023	0.808057	0.404028	−	0.914746i	$-0.367610\pi$
$271$	13.3023	0.808057	0.404028	+	0.914746i	$0.367610\pi$
$272$	21.2480	1.28835
$273$	−6.46045	−0.391004
$274$	29.3121	1.77081
$275$	0.375599	0.0226495
$276$	42.1139	2.53496
$277$	25.3937	1.52576	0.762881	−	0.646539i	$-0.223784\pi$
$277$	25.3937	1.52576	0.762881	+	0.646539i	$0.223784\pi$
$278$	23.6568	1.41884
$279$	3.55765	0.212991
$280$	−25.7882	−1.54114
$281$	14.7838	0.881930	0.440965	−	0.897524i	$-0.354636\pi$
$281$	14.7838	0.881930	0.440965	+	0.897524i	$0.354636\pi$
$282$	38.0868	2.26804
$283$	8.86248	0.526819	0.263410	−	0.964684i	$-0.415153\pi$
$283$	8.86248	0.526819	0.263410	+	0.964684i	$0.415153\pi$
$284$	−19.5946	−1.16273
$285$	6.75973	0.400412
$286$	0.290777	0.0171940
$287$	33.6571	1.98672
$288$	−1.11180	−0.0655136
$289$	33.2240	1.95435
$290$	30.8632	1.81235
$291$	7.97174	0.467312
$292$	30.5232	1.78623
$293$	−3.37167	−0.196975	−0.0984874	−	0.995138i	$-0.531400\pi$
$293$	−3.37167	−0.196975	−0.0984874	+	0.995138i	$0.531400\pi$
$294$	−40.8087	−2.38001
$295$	15.2850	0.889930
$296$	−3.75767	−0.218410
$297$	0.675863	0.0392176
$298$	−43.0854	−2.49587
$299$	7.25383	0.419500
$300$	−18.1046	−1.04527
$301$	−38.0463	−2.19295
$302$	4.89640	0.281756
$303$	−14.0870	−0.809274
$304$	−9.74209	−0.558747
$305$	13.2976	0.761418
$306$	11.9743	0.684528
$307$	30.6109	1.74706	0.873529	−	0.486772i	$-0.161826\pi$
$307$	30.6109	1.74706	0.873529	+	0.486772i	$0.161826\pi$
$308$	1.96413	0.111916
$309$	1.94572	0.110688
$310$	−16.8329	−0.956047
$311$	1.38828	0.0787223	0.0393612	−	0.999225i	$-0.487468\pi$
$311$	1.38828	0.0787223	0.0393612	+	0.999225i	$0.487468\pi$
$312$	−6.69330	−0.378934
$313$	−12.3326	−0.697080	−0.348540	−	0.937294i	$-0.613323\pi$
$313$	−12.3326	−0.697080	−0.348540	+	0.937294i	$0.613323\pi$
$314$	28.2968	1.59688
$315$	−4.08966	−0.230426
$316$	−12.5751	−0.707402
$317$	−22.2298	−1.24855	−0.624274	−	0.781205i	$-0.714605\pi$
$317$	−22.2298	−1.24855	−0.624274	+	0.781205i	$0.714605\pi$
$318$	34.4628	1.93258
$319$	−1.12255	−0.0628509
$320$	13.4859	0.753885
$321$	3.52137	0.196544
$322$	74.5969	4.15712
$323$	−23.0274	−1.28128
$324$	−24.5400	−1.36333
$325$	−3.11838	−0.172977
$326$	16.4052	0.908602
$327$	−17.1512	−0.948465
$328$	34.8702	1.92539
$329$	44.3125	2.44303
$330$	−0.604922	−0.0332999
$331$	22.2439	1.22264	0.611318	−	0.791385i	$-0.290640\pi$
$331$	22.2439	1.22264	0.611318	+	0.791385i	$0.290640\pi$
$332$	53.5242	2.93752
$333$	−0.595915	−0.0326559
$334$	−5.18064	−0.283472
$335$	−16.0410	−0.876413
$336$	−19.3698	−1.05671
$337$	−20.9299	−1.14012	−0.570062	−	0.821602i	$-0.693081\pi$
$337$	−20.9299	−1.14012	−0.570062	+	0.821602i	$0.693081\pi$
$338$	−2.41415	−0.131312
$339$	−24.3181	−1.32078
$340$	−37.2140	−2.01821
$341$	0.612246	0.0331550
$342$	−5.49017	−0.296874
$343$	−17.6607	−0.953586
$344$	−39.4176	−2.12525
$345$	−15.0906	−0.812452
$346$	32.5103	1.74776
$347$	18.9926	1.01958	0.509789	−	0.860300i	$-0.329724\pi$
$347$	18.9926	1.01958	0.509789	+	0.860300i	$0.329724\pi$
$348$	54.1090	2.90055
$349$	−15.6168	−0.835946	−0.417973	−	0.908459i	$-0.637259\pi$
$349$	−15.6168	−0.835946	−0.417973	+	0.908459i	$0.637259\pi$
$350$	−32.0688	−1.71415
$351$	−5.61130	−0.299509
$352$	−0.191334	−0.0101981
$353$	23.3723	1.24398	0.621991	−	0.783024i	$-0.286324\pi$
$353$	23.3723	1.24398	0.621991	+	0.783024i	$0.286324\pi$
$354$	40.7980	2.16839
$355$	7.02132	0.372653
$356$	54.1042	2.86752
$357$	−45.7845	−2.42317
$358$	−43.6052	−2.30460
$359$	22.2293	1.17322	0.586610	−	0.809870i	$-0.300462\pi$
$359$	22.2293	1.17322	0.586610	+	0.809870i	$0.300462\pi$
$360$	−4.23706	−0.223313
$361$	−8.44207	−0.444319
$362$	−50.9003	−2.67526
$363$	−16.6607	−0.874460
$364$	−16.3070	−0.854718
$365$	−10.9373	−0.572486
$366$	35.4932	1.85526
$367$	3.22752	0.168475	0.0842375	−	0.996446i	$-0.473155\pi$
$367$	3.22752	0.168475	0.0842375	+	0.996446i	$0.473155\pi$
$368$	21.7485	1.13372
$369$	5.52994	0.287877
$370$	2.81956	0.146582
$371$	40.0960	2.08168
$372$	−29.5113	−1.53009
$373$	−32.7555	−1.69602	−0.848008	−	0.529983i	$-0.822198\pi$
$373$	−32.7555	−1.69602	−0.848008	+	0.529983i	$0.822198\pi$
$374$	2.06070	0.106556
$375$	16.8892	0.872155
$376$	45.9096	2.36761
$377$	9.31990	0.479999
$378$	−57.7054	−2.96804
$379$	32.6702	1.67816	0.839078	−	0.544011i	$-0.183095\pi$
$379$	32.6702	1.67816	0.839078	+	0.544011i	$0.183095\pi$
$380$	17.0624	0.875282
$381$	−23.9684	−1.22794
$382$	−28.8392	−1.47554
$383$	−8.58685	−0.438768	−0.219384	−	0.975639i	$-0.570405\pi$
$383$	−8.58685	−0.438768	−0.219384	+	0.975639i	$0.570405\pi$
$384$	31.1775	1.59102
$385$	−0.703802	−0.0358691
$386$	−46.3137	−2.35731
$387$	−6.25109	−0.317761
$388$	20.1217	1.02152
$389$	−11.1461	−0.565128	−0.282564	−	0.959249i	$-0.591185\pi$
$389$	−11.1461	−0.565128	−0.282564	+	0.959249i	$0.591185\pi$
$390$	5.02231	0.254315
$391$	51.4071	2.59977
$392$	−49.1905	−2.48450
$393$	−22.6178	−1.14092
$394$	−5.28163	−0.266085
$395$	4.50600	0.226722
$396$	0.322710	0.0162168
$397$	−4.86532	−0.244184	−0.122092	−	0.992519i	$-0.538960\pi$
$397$	−4.86532	−0.244184	−0.122092	+	0.992519i	$0.538960\pi$
$398$	−59.2754	−2.97121
$399$	20.9919	1.05091
$400$	−9.34958	−0.467479
$401$	−6.78329	−0.338741	−0.169371	−	0.985552i	$-0.554173\pi$
$401$	−6.78329	−0.338741	−0.169371	+	0.985552i	$0.554173\pi$
$402$	−42.8157	−2.13545
$403$	−5.08312	−0.253208
$404$	−35.5572	−1.76904
$405$	8.79337	0.436946
$406$	95.8439	4.75665
$407$	−0.102553	−0.00508336
$408$	−47.4347	−2.34837
$409$	−28.3580	−1.40221	−0.701107	−	0.713056i	$-0.747310\pi$
$409$	−28.3580	−1.40221	−0.701107	+	0.713056i	$0.747310\pi$
$410$	−26.1648	−1.29219
$411$	−18.4144	−0.908314
$412$	4.91124	0.241960
$413$	47.4668	2.33569
$414$	12.2564	0.602370
$415$	−19.1793	−0.941473
$416$	1.58853	0.0778841
$417$	−14.8616	−0.727776
$418$	−0.944820	−0.0462127
$419$	13.2785	0.648697	0.324349	−	0.945938i	$-0.394855\pi$
$419$	13.2785	0.648697	0.324349	+	0.945938i	$0.394855\pi$
$420$	33.9245	1.65535
$421$	11.9134	0.580622	0.290311	−	0.956932i	$-0.406241\pi$
$421$	11.9134	0.580622	0.290311	+	0.956932i	$0.406241\pi$
$422$	12.6676	0.616649
$423$	7.28063	0.353996
$424$	41.5412	2.01742
$425$	−22.0996	−1.07199
$426$	18.7409	0.908000
$427$	41.2949	1.99840
$428$	8.88837	0.429636
$429$	−0.182671	−0.00881944
$430$	29.5769	1.42633
$431$	−2.84791	−0.137179	−0.0685895	−	0.997645i	$-0.521850\pi$
$431$	−2.84791	−0.137179	−0.0685895	+	0.997645i	$0.521850\pi$
$432$	−16.8239	−0.809439
$433$	34.2714	1.64698	0.823489	−	0.567333i	$-0.192025\pi$
$433$	34.2714	1.64698	0.823489	+	0.567333i	$0.192025\pi$
$434$	−52.2737	−2.50922
$435$	−19.3888	−0.929622
$436$	−43.2918	−2.07330
$437$	−23.5699	−1.12750
$438$	−29.1933	−1.39491
$439$	17.8634	0.852573	0.426287	−	0.904588i	$-0.359821\pi$
$439$	17.8634	0.852573	0.426287	+	0.904588i	$0.359821\pi$
$440$	−0.729169	−0.0347618
$441$	−7.80094	−0.371473
$442$	−17.1088	−0.813782
$443$	−30.3919	−1.44396	−0.721982	−	0.691912i	$-0.756769\pi$
$443$	−30.3919	−1.44396	−0.721982	+	0.691912i	$0.756769\pi$
$444$	4.94323	0.234595
$445$	−19.3871	−0.919035
$446$	−48.1327	−2.27915
$447$	27.0670	1.28023
$448$	41.8797	1.97863
$449$	−30.2097	−1.42568	−0.712841	−	0.701326i	$-0.752592\pi$
$449$	−30.2097	−1.42568	−0.712841	+	0.701326i	$0.752592\pi$
$450$	−5.26897	−0.248381
$451$	0.951665	0.0448121
$452$	−61.3820	−2.88717
$453$	−3.07600	−0.144523
$454$	35.4553	1.66400
$455$	5.84326	0.273936
$456$	21.7485	1.01847
$457$	18.8896	0.883616	0.441808	−	0.897110i	$-0.354337\pi$
$457$	18.8896	0.883616	0.441808	+	0.897110i	$0.354337\pi$
$458$	−35.7082	−1.66854
$459$	−39.7666	−1.85615
$460$	−38.0906	−1.77598
$461$	−13.7455	−0.640189	−0.320095	−	0.947386i	$-0.603715\pi$
$461$	−13.7455	−0.640189	−0.320095	+	0.947386i	$0.603715\pi$
$462$	−1.87855	−0.0873981
$463$	8.19459	0.380835	0.190417	−	0.981703i	$-0.439016\pi$
$463$	8.19459	0.380835	0.190417	+	0.981703i	$0.439016\pi$
$464$	27.9431	1.29722
$465$	10.5748	0.490392
$466$	0.0866421	0.00401362
$467$	−18.1415	−0.839490	−0.419745	−	0.907642i	$-0.637880\pi$
$467$	−18.1415	−0.839490	−0.419745	+	0.907642i	$0.637880\pi$
$468$	−2.67927	−0.123849
$469$	−49.8143	−2.30021
$470$	−34.4482	−1.58898
$471$	−17.7766	−0.819101
$472$	49.1776	2.26358
$473$	−1.07577	−0.0494639
$474$	12.0272	0.552426
$475$	10.1325	0.464913
$476$	−115.566	−5.29695
$477$	6.58786	0.301638
$478$	−27.9366	−1.27779
$479$	4.75377	0.217205	0.108603	−	0.994085i	$-0.465362\pi$
$479$	4.75377	0.217205	0.108603	+	0.994085i	$0.465362\pi$
$480$	−3.30472	−0.150839
$481$	0.851436	0.0388221
$482$	−23.3929	−1.06552
$483$	−46.8630	−2.13234
$484$	−42.0537	−1.91153
$485$	−7.21016	−0.327397
$486$	−17.1687	−0.778789
$487$	17.6996	0.802045	0.401023	−	0.916068i	$-0.368655\pi$
$487$	17.6996	0.802045	0.401023	+	0.916068i	$0.368655\pi$
$488$	42.7832	1.93671
$489$	−10.3061	−0.466056
$490$	36.9100	1.66743
$491$	16.9337	0.764207	0.382104	−	0.924119i	$-0.375200\pi$
$491$	16.9337	0.764207	0.382104	+	0.924119i	$0.375200\pi$
$492$	−45.8719	−2.06806
$493$	66.0491	2.97470
$494$	7.84428	0.352931
$495$	−0.115636	−0.00519746
$496$	−15.2403	−0.684309
$497$	21.8043	0.978056
$498$	−51.1922	−2.29398
$499$	9.57907	0.428818	0.214409	−	0.976744i	$-0.431217\pi$
$499$	9.57907	0.428818	0.214409	+	0.976744i	$0.431217\pi$
$500$	42.6304	1.90649
$501$	3.25457	0.145403
$502$	−56.8551	−2.53757
$503$	20.7549	0.925414	0.462707	−	0.886511i	$-0.346878\pi$
$503$	20.7549	0.925414	0.462707	+	0.886511i	$0.346878\pi$
$504$	−13.1579	−0.586101
$505$	12.7412	0.566974
$506$	2.10925	0.0937674
$507$	1.51661	0.0673550
$508$	−60.4991	−2.68421
$509$	16.3137	0.723092	0.361546	−	0.932354i	$-0.382249\pi$
$509$	16.3137	0.723092	0.361546	+	0.932354i	$0.382249\pi$
$510$	35.5925	1.57606
$511$	−33.9652	−1.50253
$512$	31.2270	1.38005
$513$	18.2328	0.804996
$514$	67.8234	2.99156
$515$	−1.75984	−0.0775477
$516$	51.8540	2.28274
$517$	1.25295	0.0551045
$518$	8.75599	0.384716
$519$	−20.4235	−0.896493
$520$	6.05386	0.265479
$521$	28.6771	1.25637	0.628183	−	0.778066i	$-0.283799\pi$
$521$	28.6771	1.25637	0.628183	+	0.778066i	$0.283799\pi$
$522$	15.7473	0.689243
$523$	−4.49617	−0.196604	−0.0983020	−	0.995157i	$-0.531341\pi$
$523$	−4.49617	−0.196604	−0.0983020	+	0.995157i	$0.531341\pi$
$524$	−57.0901	−2.49399
$525$	20.1462	0.879251
$526$	−24.5795	−1.07172
$527$	−36.0235	−1.56921
$528$	−0.547687	−0.0238350
$529$	29.6181	1.28774
$530$	−31.1704	−1.35395
$531$	7.79890	0.338443
$532$	52.9862	2.29724
$533$	−7.90111	−0.342235
$534$	−51.7469	−2.23931
$535$	−3.18495	−0.137698
$536$	−51.6098	−2.22920
$537$	27.3935	1.18212
$538$	−5.84109	−0.251827
$539$	−1.34249	−0.0578251
$540$	29.4655	1.26799
$541$	10.2869	0.442267	0.221133	−	0.975244i	$-0.429024\pi$
$541$	10.2869	0.442267	0.221133	+	0.975244i	$0.429024\pi$
$542$	−32.1137	−1.37940
$543$	31.9765	1.37224
$544$	11.2577	0.482671
$545$	15.5127	0.664491
$546$	15.5965	0.667468
$547$	−18.4575	−0.789185	−0.394592	−	0.918856i	$-0.629114\pi$
$547$	−18.4575	−0.789185	−0.394592	+	0.918856i	$0.629114\pi$
$548$	−46.4802	−1.98553
$549$	6.78484	0.289570
$550$	−0.906753	−0.0386641
$551$	−30.2831	−1.29010
$552$	−48.5521	−2.06651
$553$	13.9931	0.595048
$554$	−61.3042	−2.60457
$555$	−1.77130	−0.0751874
$556$	−37.5126	−1.59089
$557$	16.5963	0.703207	0.351604	−	0.936149i	$-0.385637\pi$
$557$	16.5963	0.703207	0.351604	+	0.936149i	$0.385637\pi$
$558$	−8.58868	−0.363588
$559$	8.93148	0.377761
$560$	17.5193	0.740327
$561$	−1.29457	−0.0546567
$562$	−35.6904	−1.50551
$563$	3.99184	0.168236	0.0841180	−	0.996456i	$-0.473193\pi$
$563$	3.99184	0.168236	0.0841180	+	0.996456i	$0.473193\pi$
$564$	−60.3942	−2.54305
$565$	21.9949	0.925333
$566$	−21.3953	−0.899313
$567$	27.3073	1.14680
$568$	22.5902	0.947863
$569$	29.5934	1.24062	0.620310	−	0.784357i	$-0.287007\pi$
$569$	29.5934	1.24062	0.620310	+	0.784357i	$0.287007\pi$
$570$	−16.3190	−0.683527
$571$	7.79199	0.326085	0.163042	−	0.986619i	$-0.447869\pi$
$571$	7.79199	0.326085	0.163042	+	0.986619i	$0.447869\pi$
$572$	−0.461084	−0.0192789
$573$	18.1173	0.756861
$574$	−81.2533	−3.39145
$575$	−22.6202	−0.943328
$576$	6.88092	0.286705
$577$	23.1909	0.965452	0.482726	−	0.875771i	$-0.339647\pi$
$577$	23.1909	0.965452	0.482726	+	0.875771i	$0.339647\pi$
$578$	−80.2075	−3.33619
$579$	29.0951	1.20915
$580$	−48.9397	−2.03211
$581$	−59.5601	−2.47097
$582$	−19.2450	−0.797729
$583$	1.13373	0.0469541
$584$	−35.1894	−1.45615
$585$	0.960059	0.0396936
$586$	8.13970	0.336248
$587$	−12.2548	−0.505812	−0.252906	−	0.967491i	$-0.581386\pi$
$587$	−12.2548	−0.505812	−0.252906	+	0.967491i	$0.581386\pi$
$588$	64.7103	2.66861
$589$	16.5166	0.680553
$590$	−36.9004	−1.51916
$591$	3.31801	0.136485
$592$	2.55279	0.104919
$593$	−25.1941	−1.03460	−0.517298	−	0.855805i	$-0.673062\pi$
$593$	−25.1941	−1.03460	−0.517298	+	0.855805i	$0.673062\pi$
$594$	−1.63163	−0.0669468
$595$	41.4105	1.69766
$596$	68.3205	2.79852
$597$	37.2378	1.52404
$598$	−17.5118	−0.716112
$599$	5.66604	0.231508	0.115754	−	0.993278i	$-0.463072\pi$
$599$	5.66604	0.231508	0.115754	+	0.993278i	$0.463072\pi$
$600$	20.8723	0.852107
$601$	14.9721	0.610724	0.305362	−	0.952236i	$-0.401223\pi$
$601$	14.9721	0.610724	0.305362	+	0.952236i	$0.401223\pi$
$602$	91.8495	3.74350
$603$	−8.18460	−0.333303
$604$	−7.76421	−0.315921
$605$	15.0690	0.612643
$606$	34.0080	1.38148
$607$	16.7069	0.678113	0.339056	−	0.940766i	$-0.389892\pi$
$607$	16.7069	0.678113	0.339056	+	0.940766i	$0.389892\pi$
$608$	−5.16161	−0.209331
$609$	−60.2108	−2.43986
$610$	−32.1024	−1.29979
$611$	−10.4025	−0.420839
$612$	−18.9877	−0.767532
$613$	10.5524	0.426208	0.213104	−	0.977030i	$-0.431643\pi$
$613$	10.5524	0.426208	0.213104	+	0.977030i	$0.431643\pi$
$614$	−73.8993	−2.98233
$615$	16.4372	0.662812
$616$	−2.26439	−0.0912349
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−4.69726	−0.188952
$619$	42.3852	1.70361	0.851803	−	0.523862i	$-0.175509\pi$
$619$	42.3852	1.70361	0.851803	+	0.523862i	$0.175509\pi$
$620$	26.6920	1.07198
$621$	−40.7034	−1.63337
$622$	−3.35152	−0.134384
$623$	−60.2054	−2.41208
$624$	4.54712	0.182031
$625$	0.316211	0.0126484
$626$	29.7727	1.18996
$627$	0.593552	0.0237042
$628$	−44.8703	−1.79052
$629$	6.03403	0.240593
$630$	9.87304	0.393351
$631$	12.1103	0.482105	0.241053	−	0.970512i	$-0.422507\pi$
$631$	12.1103	0.482105	0.241053	+	0.970512i	$0.422507\pi$
$632$	14.4975	0.576678
$633$	−7.95800	−0.316302
$634$	53.6660	2.13135
$635$	21.6785	0.860287
$636$	−54.6476	−2.16692
$637$	11.1459	0.441616
$638$	2.71001	0.107290
$639$	3.58249	0.141721
$640$	−28.1989	−1.11466
$641$	30.8460	1.21834	0.609172	−	0.793038i	$-0.291502\pi$
$641$	30.8460	1.21834	0.609172	+	0.793038i	$0.291502\pi$
$642$	−8.50110	−0.335512
$643$	28.2457	1.11390	0.556951	−	0.830545i	$-0.311971\pi$
$643$	28.2457	1.11390	0.556951	+	0.830545i	$0.311971\pi$
$644$	−118.288	−4.66121
$645$	−18.5807	−0.731616
$646$	55.5916	2.18722
$647$	−38.5451	−1.51536	−0.757682	−	0.652624i	$-0.773668\pi$
$647$	−38.5451	−1.51536	−0.757682	+	0.652624i	$0.773668\pi$
$648$	28.2915	1.11140
$649$	1.34214	0.0526835
$650$	7.52824	0.295282
$651$	32.8393	1.28707
$652$	−26.0137	−1.01878
$653$	12.1043	0.473677	0.236839	−	0.971549i	$-0.423889\pi$
$653$	12.1043	0.473677	0.236839	+	0.971549i	$0.423889\pi$
$654$	41.4056	1.61909
$655$	20.4570	0.799322
$656$	−23.6892	−0.924909
$657$	−5.58056	−0.217718
$658$	−106.977	−4.17039
$659$	2.63736	0.102737	0.0513685	−	0.998680i	$-0.483642\pi$
$659$	2.63736	0.102737	0.0513685	+	0.998680i	$0.483642\pi$
$660$	0.959224	0.0373377
$661$	−44.3094	−1.72344	−0.861718	−	0.507387i	$-0.830611\pi$
$661$	−44.3094	−1.72344	−0.861718	+	0.507387i	$0.830611\pi$
$662$	−53.7001	−2.08711
$663$	10.7480	0.417419
$664$	−61.7067	−2.39469
$665$	−18.9865	−0.736264
$666$	1.43863	0.0557457
$667$	67.6050	2.61768
$668$	8.21493	0.317845
$669$	30.2378	1.16906
$670$	38.7253	1.49609
$671$	1.16762	0.0450756
$672$	−10.2626	−0.395889
$673$	−26.7621	−1.03160	−0.515801	−	0.856708i	$-0.672506\pi$
$673$	−26.7621	−1.03160	−0.515801	+	0.856708i	$0.672506\pi$
$674$	50.5278	1.94626
$675$	17.4982	0.673505
$676$	3.82811	0.147235
$677$	−2.43751	−0.0936812	−0.0468406	−	0.998902i	$-0.514915\pi$
$677$	−2.43751	−0.0936812	−0.0468406	+	0.998902i	$0.514915\pi$
$678$	58.7076	2.25465
$679$	−22.3907	−0.859278
$680$	42.9030	1.64526
$681$	−22.2736	−0.853527
$682$	−1.47805	−0.0565976
$683$	−5.23213	−0.200202	−0.100101	−	0.994977i	$-0.531917\pi$
$683$	−5.23213	−0.200202	−0.100101	+	0.994977i	$0.531917\pi$
$684$	8.70575	0.332873
$685$	16.6552	0.636361
$686$	42.6354	1.62783
$687$	22.4325	0.855855
$688$	26.7785	1.02092
$689$	−9.41266	−0.358594
$690$	36.4310	1.38690
$691$	−5.87948	−0.223666	−0.111833	−	0.993727i	$-0.535672\pi$
$691$	−5.87948	−0.223666	−0.111833	+	0.993727i	$0.535672\pi$
$692$	−51.5515	−1.95969
$693$	−0.359101	−0.0136411
$694$	−45.8510	−1.74048
$695$	13.4418	0.509877
$696$	−62.3809	−2.36454
$697$	−55.9943	−2.12093
$698$	37.7012	1.42701
$699$	−0.0544301	−0.00205873
$700$	50.8514	1.92200
$701$	−12.1277	−0.458055	−0.229028	−	0.973420i	$-0.573555\pi$
$701$	−12.1277	−0.458055	−0.229028	+	0.973420i	$0.573555\pi$
$702$	13.5465	0.511280
$703$	−2.76657	−0.104343
$704$	1.18416	0.0446297
$705$	21.6410	0.815046
$706$	−56.4242	−2.12355
$707$	39.5669	1.48807
$708$	−64.6933	−2.43132
$709$	35.7969	1.34438	0.672190	−	0.740379i	$-0.265354\pi$
$709$	35.7969	1.34438	0.672190	+	0.740379i	$0.265354\pi$
$710$	−16.9505	−0.636141
$711$	2.29910	0.0862230
$712$	−62.3753	−2.33761
$713$	−36.8721	−1.38087
$714$	110.531	4.13650
$715$	0.165220	0.00617886
$716$	69.1447	2.58406
$717$	17.5503	0.655428
$718$	−53.6649	−2.00276
$719$	11.2013	0.417738	0.208869	−	0.977944i	$-0.433022\pi$
$719$	11.2013	0.417738	0.208869	+	0.977944i	$0.433022\pi$
$720$	2.87846	0.107274
$721$	−5.46507	−0.203530
$722$	20.3804	0.758480
$723$	14.6958	0.546544
$724$	80.7125	2.99966
$725$	−29.0630	−1.07937
$726$	40.2214	1.49276
$727$	−50.4164	−1.86984	−0.934920	−	0.354858i	$-0.884529\pi$
$727$	−50.4164	−1.86984	−0.934920	+	0.354858i	$0.884529\pi$
$728$	18.7999	0.696771
$729$	30.0171	1.11174
$730$	26.4043	0.977268
$731$	63.2964	2.34110
$732$	−56.2815	−2.08022
$733$	−10.1552	−0.375090	−0.187545	−	0.982256i	$-0.560053\pi$
$733$	−10.1552	−0.375090	−0.187545	+	0.982256i	$0.560053\pi$
$734$	−7.79171	−0.287597
$735$	−23.1875	−0.855285
$736$	11.5229	0.424741
$737$	−1.40851	−0.0518833
$738$	−13.3501	−0.491424
$739$	0.923412	0.0339683	0.0169841	−	0.999856i	$-0.494594\pi$
$739$	0.923412	0.0339683	0.0169841	+	0.999856i	$0.494594\pi$
$740$	−4.47098	−0.164356
$741$	−4.92792	−0.181032
$742$	−96.7978	−3.55356
$743$	−1.39886	−0.0513192	−0.0256596	−	0.999671i	$-0.508169\pi$
$743$	−1.39886	−0.0513192	−0.0256596	+	0.999671i	$0.508169\pi$
$744$	34.0229	1.24734
$745$	−24.4812	−0.896920
$746$	79.0767	2.89520
$747$	−9.78584	−0.358045
$748$	−3.26765	−0.119477
$749$	−9.89069	−0.361398
$750$	−40.7730	−1.48882
$751$	−46.2602	−1.68806	−0.844030	−	0.536296i	$-0.819823\pi$
$751$	−46.2602	−1.68806	−0.844030	+	0.536296i	$0.819823\pi$
$752$	−31.1889	−1.13734
$753$	35.7174	1.30161
$754$	−22.4996	−0.819388
$755$	2.78214	0.101252
$756$	91.5033	3.32794
$757$	22.3316	0.811657	0.405828	−	0.913949i	$-0.366983\pi$
$757$	22.3316	0.811657	0.405828	+	0.913949i	$0.366983\pi$
$758$	−78.8707	−2.86471
$759$	−1.32506	−0.0480968
$760$	−19.6708	−0.713535
$761$	−50.0690	−1.81500	−0.907500	−	0.420051i	$-0.862012\pi$
$761$	−50.0690	−1.81500	−0.907500	+	0.420051i	$0.862012\pi$
$762$	57.8632	2.09616
$763$	48.1738	1.74401
$764$	45.7303	1.65446
$765$	6.80383	0.245993
$766$	20.7299	0.749003
$767$	−11.1430	−0.402349
$768$	−45.4463	−1.63990
$769$	−38.3938	−1.38452	−0.692258	−	0.721650i	$-0.743384\pi$
$769$	−38.3938	−1.38452	−0.692258	+	0.721650i	$0.743384\pi$
$770$	1.69908	0.0612307
$771$	−42.6078	−1.53448
$772$	73.4396	2.64315
$773$	−2.52714	−0.0908948	−0.0454474	−	0.998967i	$-0.514471\pi$
$773$	−2.52714	−0.0908948	−0.0454474	+	0.998967i	$0.514471\pi$
$774$	15.0911	0.542437
$775$	15.8511	0.569389
$776$	−23.1977	−0.832751
$777$	−5.50066	−0.197335
$778$	26.9082	0.964707
$779$	25.6731	0.919833
$780$	−7.96387	−0.285152
$781$	0.616522	0.0220609
$782$	−124.104	−4.43796
$783$	−52.2967	−1.86893
$784$	33.4178	1.19349
$785$	16.0783	0.573859
$786$	54.6027	1.94762
$787$	40.4494	1.44187	0.720933	−	0.693004i	$-0.243713\pi$
$787$	40.4494	1.44187	0.720933	+	0.693004i	$0.243713\pi$
$788$	8.37507	0.298350
$789$	15.4413	0.549724
$790$	−10.8782	−0.387027
$791$	68.3039	2.42861
$792$	−0.372044	−0.0132200
$793$	−9.69409	−0.344247
$794$	11.7456	0.416836
$795$	19.5818	0.694494
$796$	93.9929	3.33149
$797$	−4.82544	−0.170926	−0.0854629	−	0.996341i	$-0.527237\pi$
$797$	−4.82544	−0.170926	−0.0854629	+	0.996341i	$0.527237\pi$
$798$	−50.6776	−1.79397
$799$	−73.7212	−2.60807
$800$	−4.95364	−0.175138
$801$	−9.89187	−0.349512
$802$	16.3759	0.578252
$803$	−0.960375	−0.0338909
$804$	67.8928	2.39439
$805$	42.3860	1.49391
$806$	12.2714	0.432242
$807$	3.66948	0.129172
$808$	40.9930	1.44213
$809$	−15.4356	−0.542688	−0.271344	−	0.962482i	$-0.587468\pi$
$809$	−15.4356	−0.542688	−0.271344	+	0.962482i	$0.587468\pi$
$810$	−21.2285	−0.745894
$811$	−2.12480	−0.0746119	−0.0373060	−	0.999304i	$-0.511878\pi$
$811$	−2.12480	−0.0746119	−0.0373060	+	0.999304i	$0.511878\pi$
$812$	−151.979	−5.33343
$813$	20.1744	0.707547
$814$	0.247578	0.00867760
$815$	9.32146	0.326517
$816$	32.2249	1.12810
$817$	−29.0210	−1.01532
$818$	68.4605	2.39366
$819$	2.98141	0.104179
$820$	41.4895	1.44888
$821$	−44.1372	−1.54040	−0.770200	−	0.637802i	$-0.779844\pi$
$821$	−44.1372	−1.54040	−0.770200	+	0.637802i	$0.779844\pi$
$822$	44.4550	1.55055
$823$	30.7906	1.07329	0.536646	−	0.843808i	$-0.319691\pi$
$823$	30.7906	1.07329	0.536646	+	0.843808i	$0.319691\pi$
$824$	−5.66205	−0.197247
$825$	0.569638	0.0198322
$826$	−114.592	−3.98716
$827$	25.8691	0.899558	0.449779	−	0.893140i	$-0.351503\pi$
$827$	25.8691	0.899558	0.449779	+	0.893140i	$0.351503\pi$
$828$	−19.4350	−0.675413
$829$	−27.9888	−0.972091	−0.486045	−	0.873934i	$-0.661561\pi$
$829$	−27.9888	−0.972091	−0.486045	+	0.873934i	$0.661561\pi$
$830$	46.3016	1.60715
$831$	38.5124	1.33598
$832$	−9.83138	−0.340842
$833$	78.9896	2.73683
$834$	35.8781	1.24236
$835$	−2.94364	−0.101869
$836$	1.49820	0.0518163
$837$	28.5229	0.985896
$838$	−32.0563	−1.10737
$839$	−19.0626	−0.658115	−0.329058	−	0.944310i	$-0.606731\pi$
$839$	−19.0626	−0.658115	−0.329058	+	0.944310i	$0.606731\pi$
$840$	−39.1107	−1.34945
$841$	57.8605	1.99519
$842$	−28.7606	−0.991157
$843$	22.4213	0.772231
$844$	−20.0870	−0.691422
$845$	−1.37172	−0.0471886
$846$	−17.5765	−0.604293
$847$	46.7960	1.60793
$848$	−28.2212	−0.969119
$849$	13.4409	0.461291
$850$	53.3517	1.82995
$851$	6.17617	0.211717
$852$	−29.7174	−1.01810
$853$	−37.8796	−1.29697	−0.648486	−	0.761227i	$-0.724598\pi$
$853$	−37.8796	−1.29697	−0.648486	+	0.761227i	$0.724598\pi$
$854$	−99.6920	−3.41139
$855$	−3.11952	−0.106685
$856$	−10.2472	−0.350241
$857$	8.90302	0.304121	0.152061	−	0.988371i	$-0.451409\pi$
$857$	8.90302	0.304121	0.152061	+	0.988371i	$0.451409\pi$
$858$	0.440995	0.0150553
$859$	18.9460	0.646428	0.323214	−	0.946326i	$-0.395237\pi$
$859$	18.9460	0.646428	0.323214	+	0.946326i	$0.395237\pi$
$860$	−46.9001	−1.59928
$861$	51.0448	1.73960
$862$	6.87528	0.234173
$863$	−30.9031	−1.05195	−0.525976	−	0.850499i	$-0.676300\pi$
$863$	−30.9031	−1.05195	−0.525976	+	0.850499i	$0.676300\pi$
$864$	−8.91371	−0.303251
$865$	18.4724	0.628079
$866$	−82.7362	−2.81149
$867$	50.3878	1.71126
$868$	82.8904	2.81348
$869$	0.395659	0.0134218
$870$	46.8074	1.58692
$871$	11.6941	0.396238
$872$	49.9100	1.69017
$873$	−3.67884	−0.124510
$874$	56.9011	1.92471
$875$	−47.4378	−1.60369
$876$	46.2918	1.56405
$877$	−23.1694	−0.782374	−0.391187	−	0.920311i	$-0.627935\pi$
$877$	−23.1694	−0.782374	−0.391187	+	0.920311i	$0.627935\pi$
$878$	−43.1249	−1.45539
$879$	−5.11350	−0.172474
$880$	0.495364	0.0166987
$881$	43.2531	1.45723	0.728617	−	0.684921i	$-0.240163\pi$
$881$	43.2531	1.45723	0.728617	+	0.684921i	$0.240163\pi$
$882$	18.8326	0.634128
$883$	−1.96185	−0.0660217	−0.0330108	−	0.999455i	$-0.510510\pi$
$883$	−1.96185	−0.0660217	−0.0330108	+	0.999455i	$0.510510\pi$
$884$	27.1294	0.912460
$885$	23.1814	0.779236
$886$	73.3706	2.46493
$887$	30.4610	1.02278	0.511389	−	0.859349i	$-0.329131\pi$
$887$	30.4610	1.02278	0.511389	+	0.859349i	$0.329131\pi$
$888$	−5.69892	−0.191243
$889$	67.3214	2.25789
$890$	46.8032	1.56885
$891$	0.772121	0.0258670
$892$	76.3240	2.55552
$893$	33.8007	1.13110
$894$	−65.3438	−2.18542
$895$	−24.7765	−0.828187
$896$	−87.5701	−2.92551
$897$	11.0012	0.367321
$898$	72.9306	2.43372
$899$	−47.3742	−1.58002
$900$	8.35499	0.278500
$901$	−66.7064	−2.22231
$902$	−2.29746	−0.0764970
$903$	−57.7014	−1.92018
$904$	70.7657	2.35363
$905$	−28.9216	−0.961386
$906$	7.42593	0.246710
$907$	−5.14653	−0.170888	−0.0854439	−	0.996343i	$-0.527231\pi$
$907$	−5.14653	−0.170888	−0.0854439	+	0.996343i	$0.527231\pi$
$908$	−56.2214	−1.86577
$909$	6.50093	0.215622
$910$	−14.1065	−0.467625
$911$	3.69022	0.122262	0.0611312	−	0.998130i	$-0.480529\pi$
$911$	3.69022	0.122262	0.0611312	+	0.998130i	$0.480529\pi$
$912$	−14.7750	−0.489247
$913$	−1.68408	−0.0557348
$914$	−45.6022	−1.50839
$915$	20.1673	0.666709
$916$	56.6225	1.87086
$917$	63.5281	2.09788
$918$	96.0025	3.16855
$919$	40.1647	1.32491	0.662455	−	0.749102i	$-0.269515\pi$
$919$	40.1647	1.32491	0.662455	+	0.749102i	$0.269515\pi$
$920$	43.9137	1.44779
$921$	46.4248	1.52975
$922$	33.1836	1.09284
$923$	−5.11862	−0.168481
$924$	2.97881	0.0979958
$925$	−2.65510	−0.0872992
$926$	−19.7830	−0.650108
$927$	−0.897923	−0.0294917
$928$	14.8049	0.485996
$929$	60.7694	1.99378	0.996889	−	0.0788128i	$-0.0251129\pi$
$929$	60.7694	1.99378	0.996889	+	0.0788128i	$0.0251129\pi$
$930$	−25.5290	−0.837130
$931$	−36.2163	−1.18694
$932$	−0.137388	−0.00450030
$933$	2.10548	0.0689304
$934$	43.7963	1.43306
$935$	1.17089	0.0382923
$936$	3.08886	0.100963
$937$	52.6147	1.71885	0.859423	−	0.511265i	$-0.170823\pi$
$937$	52.6147	1.71885	0.859423	+	0.511265i	$0.170823\pi$
$938$	120.259	3.92660
$939$	−18.7038	−0.610374
$940$	54.6245	1.78165
$941$	−12.7321	−0.415055	−0.207527	−	0.978229i	$-0.566542\pi$
$941$	−12.7321	−0.415055	−0.207527	+	0.978229i	$0.566542\pi$
$942$	42.9153	1.39826
$943$	−57.3133	−1.86638
$944$	−33.4090	−1.08737
$945$	−32.7882	−1.06660
$946$	2.59707	0.0844379
$947$	−9.94923	−0.323306	−0.161653	−	0.986848i	$-0.551683\pi$
$947$	−9.94923	−0.323306	−0.161653	+	0.986848i	$0.551683\pi$
$948$	−19.0715	−0.619412
$949$	7.97343	0.258829
$950$	−24.4615	−0.793635
$951$	−33.7139	−1.09325
$952$	133.233	4.31810
$953$	12.1140	0.392411	0.196206	−	0.980563i	$-0.437138\pi$
$953$	12.1140	0.392411	0.196206	+	0.980563i	$0.437138\pi$
$954$	−15.9041	−0.514914
$955$	−16.3865	−0.530253
$956$	44.2991	1.43274
$957$	−1.70248	−0.0550332
$958$	−11.4763	−0.370783
$959$	51.7216	1.67018
$960$	20.4529	0.660113
$961$	−5.16188	−0.166512
$962$	−2.05549	−0.0662717
$963$	−1.62506	−0.0523669
$964$	37.0941	1.19472
$965$	−26.3155	−0.847126
$966$	113.134	3.64004
$967$	5.26636	0.169355	0.0846774	−	0.996408i	$-0.473014\pi$
$967$	5.26636	0.169355	0.0846774	+	0.996408i	$0.473014\pi$
$968$	48.4826	1.55829
$969$	−34.9236	−1.12191
$970$	17.4064	0.558886
$971$	33.1848	1.06495	0.532475	−	0.846446i	$-0.321262\pi$
$971$	33.1848	1.06495	0.532475	+	0.846446i	$0.321262\pi$
$972$	27.2244	0.873224
$973$	41.7428	1.33821
$974$	−42.7295	−1.36914
$975$	−4.72937	−0.151461
$976$	−29.0650	−0.930347
$977$	−3.69121	−0.118092	−0.0590461	−	0.998255i	$-0.518806\pi$
$977$	−3.69121	−0.118092	−0.0590461	+	0.998255i	$0.518806\pi$
$978$	24.8803	0.795585
$979$	−1.70232	−0.0544065
$980$	−58.5282	−1.86961
$981$	7.91505	0.252708
$982$	−40.8805	−1.30455
$983$	47.9115	1.52814	0.764070	−	0.645134i	$-0.223198\pi$
$983$	47.9115	1.52814	0.764070	+	0.645134i	$0.223198\pi$
$984$	52.8845	1.68590
$985$	−3.00103	−0.0956206
$986$	−159.452	−5.07799
$987$	67.2047	2.13915
$988$	−12.4387	−0.395727
$989$	64.7875	2.06012
$990$	0.279163	0.00887238
$991$	−7.38352	−0.234545	−0.117273	−	0.993100i	$-0.537415\pi$
$991$	−7.38352	−0.234545	−0.117273	+	0.993100i	$0.537415\pi$
$992$	−8.07469	−0.256372
$993$	33.7353	1.07056
$994$	−52.6388	−1.66960
$995$	−33.6803	−1.06774
$996$	81.1754	2.57214
$997$	−49.2276	−1.55905	−0.779527	−	0.626368i	$-0.784541\pi$
$997$	−49.2276	−1.55905	−0.779527	+	0.626368i	$0.784541\pi$
$998$	−23.1253	−0.732018
$999$	−4.77766	−0.151158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.18	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.18	✓	174	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41415 q^{2} +1.51661 q^{3} +3.82811 q^{4} -1.37172 q^{5} -3.66132 q^{6} -4.25980 q^{7} -4.41333 q^{8} -0.699894 q^{9} +O(q^{10})\)	\(q-2.41415 q^{2} +1.51661 q^{3} +3.82811 q^{4} -1.37172 q^{5} -3.66132 q^{6} -4.25980 q^{7} -4.41333 q^{8} -0.699894 q^{9} +3.31154 q^{10} -0.120447 q^{11} +5.80575 q^{12} +1.00000 q^{13} +10.2838 q^{14} -2.08037 q^{15} +2.99821 q^{16} +7.08689 q^{17} +1.68965 q^{18} -3.24930 q^{19} -5.25110 q^{20} -6.46045 q^{21} +0.290777 q^{22} +7.25383 q^{23} -6.69330 q^{24} -3.11838 q^{25} -2.41415 q^{26} -5.61130 q^{27} -16.3070 q^{28} +9.31990 q^{29} +5.02231 q^{30} -5.08312 q^{31} +1.58853 q^{32} -0.182671 q^{33} -17.1088 q^{34} +5.84326 q^{35} -2.67927 q^{36} +0.851436 q^{37} +7.84428 q^{38} +1.51661 q^{39} +6.05386 q^{40} -7.90111 q^{41} +15.5965 q^{42} +8.93148 q^{43} -0.461084 q^{44} +0.960059 q^{45} -17.5118 q^{46} -10.4025 q^{47} +4.54712 q^{48} +11.1459 q^{49} +7.52824 q^{50} +10.7480 q^{51} +3.82811 q^{52} -9.41266 q^{53} +13.5465 q^{54} +0.165220 q^{55} +18.7999 q^{56} -4.92792 q^{57} -22.4996 q^{58} -11.1430 q^{59} -7.96387 q^{60} -9.69409 q^{61} +12.2714 q^{62} +2.98141 q^{63} -9.83138 q^{64} -1.37172 q^{65} +0.440995 q^{66} +11.6941 q^{67} +27.1294 q^{68} +11.0012 q^{69} -14.1065 q^{70} -5.11862 q^{71} +3.08886 q^{72} +7.97343 q^{73} -2.05549 q^{74} -4.72937 q^{75} -12.4387 q^{76} +0.513080 q^{77} -3.66132 q^{78} -3.28493 q^{79} -4.11271 q^{80} -6.41047 q^{81} +19.0745 q^{82} +13.9819 q^{83} -24.7313 q^{84} -9.72123 q^{85} -21.5619 q^{86} +14.1347 q^{87} +0.531572 q^{88} +14.1334 q^{89} -2.31773 q^{90} -4.25980 q^{91} +27.7685 q^{92} -7.70911 q^{93} +25.1131 q^{94} +4.45713 q^{95} +2.40918 q^{96} +5.25629 q^{97} -26.9078 q^{98} +0.0843001 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * q^99

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