LMFDB - Embedded newform 8034.2.a.ba.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-2.56958$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56958 q^{5} +1.00000 q^{6} +3.96287 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56958 q^{5} +1.00000 q^{6} +3.96287 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56958 q^{10} -3.64940 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.96287 q^{14} -2.56958 q^{15} +1.00000 q^{16} +6.34291 q^{17} -1.00000 q^{18} +6.47887 q^{19} +2.56958 q^{20} -3.96287 q^{21} +3.64940 q^{22} +5.03341 q^{23} +1.00000 q^{24} +1.60272 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.96287 q^{28} +4.90808 q^{29} +2.56958 q^{30} +8.81196 q^{31} -1.00000 q^{32} +3.64940 q^{33} -6.34291 q^{34} +10.1829 q^{35} +1.00000 q^{36} -7.78824 q^{37} -6.47887 q^{38} +1.00000 q^{39} -2.56958 q^{40} +2.82114 q^{41} +3.96287 q^{42} +8.04229 q^{43} -3.64940 q^{44} +2.56958 q^{45} -5.03341 q^{46} -5.14489 q^{47} -1.00000 q^{48} +8.70431 q^{49} -1.60272 q^{50} -6.34291 q^{51} -1.00000 q^{52} +0.106049 q^{53} +1.00000 q^{54} -9.37741 q^{55} -3.96287 q^{56} -6.47887 q^{57} -4.90808 q^{58} -6.22700 q^{59} -2.56958 q^{60} -11.3915 q^{61} -8.81196 q^{62} +3.96287 q^{63} +1.00000 q^{64} -2.56958 q^{65} -3.64940 q^{66} -2.03830 q^{67} +6.34291 q^{68} -5.03341 q^{69} -10.1829 q^{70} +0.802323 q^{71} -1.00000 q^{72} +8.44092 q^{73} +7.78824 q^{74} -1.60272 q^{75} +6.47887 q^{76} -14.4621 q^{77} -1.00000 q^{78} +0.928481 q^{79} +2.56958 q^{80} +1.00000 q^{81} -2.82114 q^{82} -6.12343 q^{83} -3.96287 q^{84} +16.2986 q^{85} -8.04229 q^{86} -4.90808 q^{87} +3.64940 q^{88} +13.7177 q^{89} -2.56958 q^{90} -3.96287 q^{91} +5.03341 q^{92} -8.81196 q^{93} +5.14489 q^{94} +16.6480 q^{95} +1.00000 q^{96} +9.59341 q^{97} -8.70431 q^{98} -3.64940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.56958	1.14915	0.574575	−	0.818452i	$-0.305168\pi$
$5$	2.56958	1.14915	0.574575	+	0.818452i	$0.305168\pi$
$6$	1.00000	0.408248
$7$	3.96287	1.49782	0.748911	−	0.662670i	$-0.230577\pi$
$7$	3.96287	1.49782	0.748911	+	0.662670i	$0.230577\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.56958	−0.812571
$11$	−3.64940	−1.10034	−0.550168	−	0.835054i	$-0.685436\pi$
$11$	−3.64940	−1.10034	−0.550168	+	0.835054i	$0.685436\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.96287	−1.05912
$15$	−2.56958	−0.663462
$16$	1.00000	0.250000
$17$	6.34291	1.53838	0.769190	−	0.639020i	$-0.220660\pi$
$17$	6.34291	1.53838	0.769190	+	0.639020i	$0.220660\pi$
$18$	−1.00000	−0.235702
$19$	6.47887	1.48636	0.743178	−	0.669094i	$-0.233318\pi$
$19$	6.47887	1.48636	0.743178	+	0.669094i	$0.233318\pi$
$20$	2.56958	0.574575
$21$	−3.96287	−0.864768
$22$	3.64940	0.778055
$23$	5.03341	1.04954	0.524769	−	0.851244i	$-0.324152\pi$
$23$	5.03341	1.04954	0.524769	+	0.851244i	$0.324152\pi$
$24$	1.00000	0.204124
$25$	1.60272	0.320544
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	3.96287	0.748911
$29$	4.90808	0.911408	0.455704	−	0.890131i	$-0.349388\pi$
$29$	4.90808	0.911408	0.455704	+	0.890131i	$0.349388\pi$
$30$	2.56958	0.469138
$31$	8.81196	1.58268	0.791338	−	0.611379i	$-0.209385\pi$
$31$	8.81196	1.58268	0.791338	+	0.611379i	$0.209385\pi$
$32$	−1.00000	−0.176777
$33$	3.64940	0.635279
$34$	−6.34291	−1.08780
$35$	10.1829	1.72122
$36$	1.00000	0.166667
$37$	−7.78824	−1.28038	−0.640189	−	0.768217i	$-0.721144\pi$
$37$	−7.78824	−1.28038	−0.640189	+	0.768217i	$0.721144\pi$
$38$	−6.47887	−1.05101
$39$	1.00000	0.160128
$40$	−2.56958	−0.406286
$41$	2.82114	0.440588	0.220294	−	0.975433i	$-0.429298\pi$
$41$	2.82114	0.440588	0.220294	+	0.975433i	$0.429298\pi$
$42$	3.96287	0.611484
$43$	8.04229	1.22644	0.613219	−	0.789913i	$-0.289874\pi$
$43$	8.04229	1.22644	0.613219	+	0.789913i	$0.289874\pi$
$44$	−3.64940	−0.550168
$45$	2.56958	0.383050
$46$	−5.03341	−0.742136
$47$	−5.14489	−0.750459	−0.375230	−	0.926932i	$-0.622436\pi$
$47$	−5.14489	−0.750459	−0.375230	+	0.926932i	$0.622436\pi$
$48$	−1.00000	−0.144338
$49$	8.70431	1.24347
$50$	−1.60272	−0.226659
$51$	−6.34291	−0.888185
$52$	−1.00000	−0.138675
$53$	0.106049	0.0145670	0.00728349	−	0.999973i	$-0.497682\pi$
$53$	0.106049	0.0145670	0.00728349	+	0.999973i	$0.497682\pi$
$54$	1.00000	0.136083
$55$	−9.37741	−1.26445
$56$	−3.96287	−0.529560
$57$	−6.47887	−0.858148
$58$	−4.90808	−0.644463
$59$	−6.22700	−0.810687	−0.405343	−	0.914164i	$-0.632848\pi$
$59$	−6.22700	−0.810687	−0.405343	+	0.914164i	$0.632848\pi$
$60$	−2.56958	−0.331731
$61$	−11.3915	−1.45853	−0.729264	−	0.684232i	$-0.760137\pi$
$61$	−11.3915	−1.45853	−0.729264	+	0.684232i	$0.760137\pi$
$62$	−8.81196	−1.11912
$63$	3.96287	0.499274
$64$	1.00000	0.125000
$65$	−2.56958	−0.318717
$66$	−3.64940	−0.449210
$67$	−2.03830	−0.249017	−0.124509	−	0.992219i	$-0.539735\pi$
$67$	−2.03830	−0.249017	−0.124509	+	0.992219i	$0.539735\pi$
$68$	6.34291	0.769190
$69$	−5.03341	−0.605952
$70$	−10.1829	−1.21709
$71$	0.802323	0.0952182	0.0476091	−	0.998866i	$-0.484840\pi$
$71$	0.802323	0.0952182	0.0476091	+	0.998866i	$0.484840\pi$
$72$	−1.00000	−0.117851
$73$	8.44092	0.987935	0.493967	−	0.869480i	$-0.335546\pi$
$73$	8.44092	0.987935	0.493967	+	0.869480i	$0.335546\pi$
$74$	7.78824	0.905364
$75$	−1.60272	−0.185066
$76$	6.47887	0.743178
$77$	−14.4621	−1.64811
$78$	−1.00000	−0.113228
$79$	0.928481	0.104462	0.0522311	−	0.998635i	$-0.483367\pi$
$79$	0.928481	0.104462	0.0522311	+	0.998635i	$0.483367\pi$
$80$	2.56958	0.287287
$81$	1.00000	0.111111
$82$	−2.82114	−0.311543
$83$	−6.12343	−0.672134	−0.336067	−	0.941838i	$-0.609097\pi$
$83$	−6.12343	−0.672134	−0.336067	+	0.941838i	$0.609097\pi$
$84$	−3.96287	−0.432384
$85$	16.2986	1.76783
$86$	−8.04229	−0.867223
$87$	−4.90808	−0.526202
$88$	3.64940	0.389027
$89$	13.7177	1.45408	0.727038	−	0.686597i	$-0.240896\pi$
$89$	13.7177	1.45408	0.727038	+	0.686597i	$0.240896\pi$
$90$	−2.56958	−0.270857
$91$	−3.96287	−0.415421
$92$	5.03341	0.524769
$93$	−8.81196	−0.913758
$94$	5.14489	0.530655
$95$	16.6480	1.70804
$96$	1.00000	0.102062
$97$	9.59341	0.974063	0.487031	−	0.873384i	$-0.338080\pi$
$97$	9.59341	0.974063	0.487031	+	0.873384i	$0.338080\pi$
$98$	−8.70431	−0.879268
$99$	−3.64940	−0.366779
$100$	1.60272	0.160272
$101$	−2.89765	−0.288327	−0.144163	−	0.989554i	$-0.546049\pi$
$101$	−2.89765	−0.288327	−0.144163	+	0.989554i	$0.546049\pi$
$102$	6.34291	0.628041
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−10.1829	−0.993748
$106$	−0.106049	−0.0103004
$107$	−19.1063	−1.84707	−0.923537	−	0.383509i	$-0.874716\pi$
$107$	−19.1063	−1.84707	−0.923537	+	0.383509i	$0.874716\pi$
$108$	−1.00000	−0.0962250
$109$	18.4619	1.76833	0.884163	−	0.467179i	$-0.154730\pi$
$109$	18.4619	1.76833	0.884163	+	0.467179i	$0.154730\pi$
$110$	9.37741	0.894101
$111$	7.78824	0.739227
$112$	3.96287	0.374456
$113$	−1.45077	−0.136477	−0.0682384	−	0.997669i	$-0.521738\pi$
$113$	−1.45077	−0.136477	−0.0682384	+	0.997669i	$0.521738\pi$
$114$	6.47887	0.606802
$115$	12.9337	1.20608
$116$	4.90808	0.455704
$117$	−1.00000	−0.0924500
$118$	6.22700	0.573242
$119$	25.1361	2.30422
$120$	2.56958	0.234569
$121$	2.31813	0.210739
$122$	11.3915	1.03133
$123$	−2.82114	−0.254374
$124$	8.81196	0.791338
$125$	−8.72957	−0.780796
$126$	−3.96287	−0.353040
$127$	13.3969	1.18878	0.594390	−	0.804177i	$-0.297393\pi$
$127$	13.3969	1.18878	0.594390	+	0.804177i	$0.297393\pi$
$128$	−1.00000	−0.0883883
$129$	−8.04229	−0.708085
$130$	2.56958	0.225367
$131$	−19.3504	−1.69066	−0.845328	−	0.534248i	$-0.820595\pi$
$131$	−19.3504	−1.69066	−0.845328	+	0.534248i	$0.820595\pi$
$132$	3.64940	0.317640
$133$	25.6749	2.22630
$134$	2.03830	0.176082
$135$	−2.56958	−0.221154
$136$	−6.34291	−0.543900
$137$	3.26002	0.278522	0.139261	−	0.990256i	$-0.455527\pi$
$137$	3.26002	0.278522	0.139261	+	0.990256i	$0.455527\pi$
$138$	5.03341	0.428472
$139$	1.29491	0.109833	0.0549164	−	0.998491i	$-0.482511\pi$
$139$	1.29491	0.109833	0.0549164	+	0.998491i	$0.482511\pi$
$140$	10.1829	0.860611
$141$	5.14489	0.433278
$142$	−0.802323	−0.0673294
$143$	3.64940	0.305178
$144$	1.00000	0.0833333
$145$	12.6117	1.04734
$146$	−8.44092	−0.698575
$147$	−8.70431	−0.717919
$148$	−7.78824	−0.640189
$149$	−10.5472	−0.864064	−0.432032	−	0.901858i	$-0.642203\pi$
$149$	−10.5472	−0.864064	−0.432032	+	0.901858i	$0.642203\pi$
$150$	1.60272	0.130862
$151$	−6.01197	−0.489248	−0.244624	−	0.969618i	$-0.578664\pi$
$151$	−6.01197	−0.489248	−0.244624	+	0.969618i	$0.578664\pi$
$152$	−6.47887	−0.525506
$153$	6.34291	0.512794
$154$	14.4621	1.16539
$155$	22.6430	1.81873
$156$	1.00000	0.0800641
$157$	−10.8226	−0.863736	−0.431868	−	0.901937i	$-0.642145\pi$
$157$	−10.8226	−0.863736	−0.431868	+	0.901937i	$0.642145\pi$
$158$	−0.928481	−0.0738660
$159$	−0.106049	−0.00841025
$160$	−2.56958	−0.203143
$161$	19.9467	1.57202
$162$	−1.00000	−0.0785674
$163$	−2.52012	−0.197391	−0.0986957	−	0.995118i	$-0.531467\pi$
$163$	−2.52012	−0.197391	−0.0986957	+	0.995118i	$0.531467\pi$
$164$	2.82114	0.220294
$165$	9.37741	0.730031
$166$	6.12343	0.475271
$167$	−15.1049	−1.16885	−0.584427	−	0.811446i	$-0.698681\pi$
$167$	−15.1049	−1.16885	−0.584427	+	0.811446i	$0.698681\pi$
$168$	3.96287	0.305742
$169$	1.00000	0.0769231
$170$	−16.2986	−1.25004
$171$	6.47887	0.495452
$172$	8.04229	0.613219
$173$	24.7945	1.88509	0.942546	−	0.334075i	$-0.108424\pi$
$173$	24.7945	1.88509	0.942546	+	0.334075i	$0.108424\pi$
$174$	4.90808	0.372081
$175$	6.35137	0.480118
$176$	−3.64940	−0.275084
$177$	6.22700	0.468050
$178$	−13.7177	−1.02819
$179$	6.86824	0.513356	0.256678	−	0.966497i	$-0.417372\pi$
$179$	6.86824	0.513356	0.256678	+	0.966497i	$0.417372\pi$
$180$	2.56958	0.191525
$181$	−10.0027	−0.743496	−0.371748	−	0.928334i	$-0.621241\pi$
$181$	−10.0027	−0.743496	−0.371748	+	0.928334i	$0.621241\pi$
$182$	3.96287	0.293747
$183$	11.3915	0.842081
$184$	−5.03341	−0.371068
$185$	−20.0125	−1.47135
$186$	8.81196	0.646125
$187$	−23.1478	−1.69274
$188$	−5.14489	−0.375230
$189$	−3.96287	−0.288256
$190$	−16.6480	−1.20777
$191$	−13.2993	−0.962300	−0.481150	−	0.876638i	$-0.659781\pi$
$191$	−13.2993	−0.962300	−0.481150	+	0.876638i	$0.659781\pi$
$192$	−1.00000	−0.0721688
$193$	−3.36267	−0.242050	−0.121025	−	0.992649i	$-0.538618\pi$
$193$	−3.36267	−0.242050	−0.121025	+	0.992649i	$0.538618\pi$
$194$	−9.59341	−0.688766
$195$	2.56958	0.184011
$196$	8.70431	0.621736
$197$	−14.3558	−1.02281	−0.511403	−	0.859341i	$-0.670874\pi$
$197$	−14.3558	−1.02281	−0.511403	+	0.859341i	$0.670874\pi$
$198$	3.64940	0.259352
$199$	15.8817	1.12582	0.562911	−	0.826518i	$-0.309682\pi$
$199$	15.8817	1.12582	0.562911	+	0.826518i	$0.309682\pi$
$200$	−1.60272	−0.113329
$201$	2.03830	0.143770
$202$	2.89765	0.203878
$203$	19.4501	1.36513
$204$	−6.34291	−0.444092
$205$	7.24914	0.506302
$206$	−1.00000	−0.0696733
$207$	5.03341	0.349846
$208$	−1.00000	−0.0693375
$209$	−23.6440	−1.63549
$210$	10.1829	0.702686
$211$	−8.19520	−0.564181	−0.282090	−	0.959388i	$-0.591028\pi$
$211$	−8.19520	−0.564181	−0.282090	+	0.959388i	$0.591028\pi$
$212$	0.106049	0.00728349
$213$	−0.802323	−0.0549742
$214$	19.1063	1.30608
$215$	20.6653	1.40936
$216$	1.00000	0.0680414
$217$	34.9206	2.37057
$218$	−18.4619	−1.25039
$219$	−8.44092	−0.570385
$220$	−9.37741	−0.632225
$221$	−6.34291	−0.426670
$222$	−7.78824	−0.522712
$223$	8.14729	0.545583	0.272791	−	0.962073i	$-0.412053\pi$
$223$	8.14729	0.545583	0.272791	+	0.962073i	$0.412053\pi$
$224$	−3.96287	−0.264780
$225$	1.60272	0.106848
$226$	1.45077	0.0965037
$227$	19.9817	1.32623	0.663116	−	0.748517i	$-0.269234\pi$
$227$	19.9817	1.32623	0.663116	+	0.748517i	$0.269234\pi$
$228$	−6.47887	−0.429074
$229$	−14.5611	−0.962228	−0.481114	−	0.876658i	$-0.659768\pi$
$229$	−14.5611	−0.962228	−0.481114	+	0.876658i	$0.659768\pi$
$230$	−12.9337	−0.852825
$231$	14.4621	0.951535
$232$	−4.90808	−0.322231
$233$	−28.6011	−1.87372	−0.936860	−	0.349704i	$-0.886282\pi$
$233$	−28.6011	−1.87372	−0.936860	+	0.349704i	$0.886282\pi$
$234$	1.00000	0.0653720
$235$	−13.2202	−0.862390
$236$	−6.22700	−0.405343
$237$	−0.928481	−0.0603113
$238$	−25.1361	−1.62933
$239$	12.0981	0.782562	0.391281	−	0.920271i	$-0.372032\pi$
$239$	12.0981	0.782562	0.391281	+	0.920271i	$0.372032\pi$
$240$	−2.56958	−0.165865
$241$	−22.0200	−1.41843	−0.709217	−	0.704990i	$-0.750951\pi$
$241$	−22.0200	−1.41843	−0.709217	+	0.704990i	$0.750951\pi$
$242$	−2.31813	−0.149015
$243$	−1.00000	−0.0641500
$244$	−11.3915	−0.729264
$245$	22.3664	1.42894
$246$	2.82114	0.179869
$247$	−6.47887	−0.412241
$248$	−8.81196	−0.559560
$249$	6.12343	0.388057
$250$	8.72957	0.552106
$251$	7.00320	0.442038	0.221019	−	0.975270i	$-0.429062\pi$
$251$	7.00320	0.442038	0.221019	+	0.975270i	$0.429062\pi$
$252$	3.96287	0.249637
$253$	−18.3689	−1.15485
$254$	−13.3969	−0.840595
$255$	−16.2986	−1.02066
$256$	1.00000	0.0625000
$257$	11.6004	0.723615	0.361808	−	0.932253i	$-0.382160\pi$
$257$	11.6004	0.723615	0.361808	+	0.932253i	$0.382160\pi$
$258$	8.04229	0.500691
$259$	−30.8637	−1.91778
$260$	−2.56958	−0.159358
$261$	4.90808	0.303803
$262$	19.3504	1.19547
$263$	6.22816	0.384045	0.192022	−	0.981391i	$-0.438495\pi$
$263$	6.22816	0.384045	0.192022	+	0.981391i	$0.438495\pi$
$264$	−3.64940	−0.224605
$265$	0.272502	0.0167396
$266$	−25.6749	−1.57423
$267$	−13.7177	−0.839512
$268$	−2.03830	−0.124509
$269$	−16.5598	−1.00967	−0.504834	−	0.863216i	$-0.668446\pi$
$269$	−16.5598	−1.00967	−0.504834	+	0.863216i	$0.668446\pi$
$270$	2.56958	0.156379
$271$	15.6676	0.951736	0.475868	−	0.879517i	$-0.342134\pi$
$271$	15.6676	0.951736	0.475868	+	0.879517i	$0.342134\pi$
$272$	6.34291	0.384595
$273$	3.96287	0.239844
$274$	−3.26002	−0.196945
$275$	−5.84897	−0.352706
$276$	−5.03341	−0.302976
$277$	10.8926	0.654473	0.327237	−	0.944942i	$-0.393883\pi$
$277$	10.8926	0.654473	0.327237	+	0.944942i	$0.393883\pi$
$278$	−1.29491	−0.0776636
$279$	8.81196	0.527559
$280$	−10.1829	−0.608544
$281$	4.30113	0.256584	0.128292	−	0.991736i	$-0.459051\pi$
$281$	4.30113	0.256584	0.128292	+	0.991736i	$0.459051\pi$
$282$	−5.14489	−0.306374
$283$	26.2920	1.56290	0.781449	−	0.623970i	$-0.214481\pi$
$283$	26.2920	1.56290	0.781449	+	0.623970i	$0.214481\pi$
$284$	0.802323	0.0476091
$285$	−16.6480	−0.986140
$286$	−3.64940	−0.215794
$287$	11.1798	0.659923
$288$	−1.00000	−0.0589256
$289$	23.2325	1.36662
$290$	−12.6117	−0.740584
$291$	−9.59341	−0.562375
$292$	8.44092	0.493967
$293$	−21.5768	−1.26053	−0.630266	−	0.776380i	$-0.717054\pi$
$293$	−21.5768	−1.26053	−0.630266	+	0.776380i	$0.717054\pi$
$294$	8.70431	0.507646
$295$	−16.0008	−0.931600
$296$	7.78824	0.452682
$297$	3.64940	0.211760
$298$	10.5472	0.610985
$299$	−5.03341	−0.291090
$300$	−1.60272	−0.0925331
$301$	31.8705	1.83699
$302$	6.01197	0.345950
$303$	2.89765	0.166465
$304$	6.47887	0.371589
$305$	−29.2712	−1.67607
$306$	−6.34291	−0.362600
$307$	−7.06343	−0.403132	−0.201566	−	0.979475i	$-0.564603\pi$
$307$	−7.06343	−0.403132	−0.201566	+	0.979475i	$0.564603\pi$
$308$	−14.4621	−0.824054
$309$	−1.00000	−0.0568880
$310$	−22.6430	−1.28604
$311$	−11.6763	−0.662102	−0.331051	−	0.943613i	$-0.607403\pi$
$311$	−11.6763	−0.662102	−0.331051	+	0.943613i	$0.607403\pi$
$312$	−1.00000	−0.0566139
$313$	−13.9503	−0.788520	−0.394260	−	0.918999i	$-0.628999\pi$
$313$	−13.9503	−0.788520	−0.394260	+	0.918999i	$0.628999\pi$
$314$	10.8226	0.610754
$315$	10.1829	0.573741
$316$	0.928481	0.0522311
$317$	10.9418	0.614554	0.307277	−	0.951620i	$-0.400582\pi$
$317$	10.9418	0.614554	0.307277	+	0.951620i	$0.400582\pi$
$318$	0.106049	0.00594695
$319$	−17.9116	−1.00285
$320$	2.56958	0.143644
$321$	19.1063	1.06641
$322$	−19.9467	−1.11159
$323$	41.0949	2.28658
$324$	1.00000	0.0555556
$325$	−1.60272	−0.0889029
$326$	2.52012	0.139577
$327$	−18.4619	−1.02094
$328$	−2.82114	−0.155771
$329$	−20.3885	−1.12405
$330$	−9.37741	−0.516210
$331$	10.9179	0.600100	0.300050	−	0.953923i	$-0.402997\pi$
$331$	10.9179	0.600100	0.300050	+	0.953923i	$0.402997\pi$
$332$	−6.12343	−0.336067
$333$	−7.78824	−0.426793
$334$	15.1049	0.826505
$335$	−5.23755	−0.286158
$336$	−3.96287	−0.216192
$337$	−18.1026	−0.986113	−0.493057	−	0.869997i	$-0.664120\pi$
$337$	−18.1026	−0.986113	−0.493057	+	0.869997i	$0.664120\pi$
$338$	−1.00000	−0.0543928
$339$	1.45077	0.0787949
$340$	16.2986	0.883915
$341$	−32.1584	−1.74147
$342$	−6.47887	−0.350337
$343$	6.75395	0.364679
$344$	−8.04229	−0.433611
$345$	−12.9337	−0.696329
$346$	−24.7945	−1.33296
$347$	−14.4014	−0.773106	−0.386553	−	0.922267i	$-0.626334\pi$
$347$	−14.4014	−0.773106	−0.386553	+	0.922267i	$0.626334\pi$
$348$	−4.90808	−0.263101
$349$	0.791137	0.0423486	0.0211743	−	0.999776i	$-0.493260\pi$
$349$	0.791137	0.0423486	0.0211743	+	0.999776i	$0.493260\pi$
$350$	−6.35137	−0.339495
$351$	1.00000	0.0533761
$352$	3.64940	0.194514
$353$	−13.7134	−0.729891	−0.364945	−	0.931029i	$-0.618912\pi$
$353$	−13.7134	−0.729891	−0.364945	+	0.931029i	$0.618912\pi$
$354$	−6.22700	−0.330962
$355$	2.06163	0.109420
$356$	13.7177	0.727038
$357$	−25.1361	−1.33034
$358$	−6.86824	−0.362998
$359$	−12.0989	−0.638555	−0.319278	−	0.947661i	$-0.603440\pi$
$359$	−12.0989	−0.638555	−0.319278	+	0.947661i	$0.603440\pi$
$360$	−2.56958	−0.135429
$361$	22.9758	1.20925
$362$	10.0027	0.525731
$363$	−2.31813	−0.121670
$364$	−3.96287	−0.207711
$365$	21.6896	1.13528
$366$	−11.3915	−0.595442
$367$	0.484231	0.0252766	0.0126383	−	0.999920i	$-0.495977\pi$
$367$	0.484231	0.0252766	0.0126383	+	0.999920i	$0.495977\pi$
$368$	5.03341	0.262385
$369$	2.82114	0.146863
$370$	20.0125	1.04040
$371$	0.420259	0.0218188
$372$	−8.81196	−0.456879
$373$	−7.50161	−0.388419	−0.194209	−	0.980960i	$-0.562214\pi$
$373$	−7.50161	−0.388419	−0.194209	+	0.980960i	$0.562214\pi$
$374$	23.1478	1.19694
$375$	8.72957	0.450793
$376$	5.14489	0.265327
$377$	−4.90808	−0.252779
$378$	3.96287	0.203828
$379$	6.89886	0.354371	0.177185	−	0.984177i	$-0.443301\pi$
$379$	6.89886	0.354371	0.177185	+	0.984177i	$0.443301\pi$
$380$	16.6480	0.854022
$381$	−13.3969	−0.686343
$382$	13.2993	0.680449
$383$	26.3843	1.34818	0.674088	−	0.738651i	$-0.264537\pi$
$383$	26.3843	1.34818	0.674088	+	0.738651i	$0.264537\pi$
$384$	1.00000	0.0510310
$385$	−37.1614	−1.89392
$386$	3.36267	0.171155
$387$	8.04229	0.408813
$388$	9.59341	0.487031
$389$	−13.2394	−0.671262	−0.335631	−	0.941993i	$-0.608950\pi$
$389$	−13.2394	−0.671262	−0.335631	+	0.941993i	$0.608950\pi$
$390$	−2.56958	−0.130116
$391$	31.9265	1.61459
$392$	−8.70431	−0.439634
$393$	19.3504	0.976100
$394$	14.3558	0.723233
$395$	2.38580	0.120043
$396$	−3.64940	−0.183389
$397$	5.70209	0.286179	0.143090	−	0.989710i	$-0.454296\pi$
$397$	5.70209	0.286179	0.143090	+	0.989710i	$0.454296\pi$
$398$	−15.8817	−0.796076
$399$	−25.6749	−1.28535
$400$	1.60272	0.0801360
$401$	−28.3921	−1.41783	−0.708916	−	0.705293i	$-0.750816\pi$
$401$	−28.3921	−1.41783	−0.708916	+	0.705293i	$0.750816\pi$
$402$	−2.03830	−0.101661
$403$	−8.81196	−0.438955
$404$	−2.89765	−0.144163
$405$	2.56958	0.127683
$406$	−19.4501	−0.965291
$407$	28.4224	1.40885
$408$	6.34291	0.314021
$409$	−35.0655	−1.73388	−0.866938	−	0.498416i	$-0.833915\pi$
$409$	−35.0655	−1.73388	−0.866938	+	0.498416i	$0.833915\pi$
$410$	−7.24914	−0.358009
$411$	−3.26002	−0.160805
$412$	1.00000	0.0492665
$413$	−24.6768	−1.21427
$414$	−5.03341	−0.247379
$415$	−15.7346	−0.772382
$416$	1.00000	0.0490290
$417$	−1.29491	−0.0634120
$418$	23.6440	1.15647
$419$	−31.1781	−1.52315	−0.761575	−	0.648077i	$-0.775574\pi$
$419$	−31.1781	−1.52315	−0.761575	+	0.648077i	$0.775574\pi$
$420$	−10.1829	−0.496874
$421$	−32.6763	−1.59255	−0.796273	−	0.604937i	$-0.793198\pi$
$421$	−32.6763	−1.59255	−0.796273	+	0.604937i	$0.793198\pi$
$422$	8.19520	0.398936
$423$	−5.14489	−0.250153
$424$	−0.106049	−0.00515021
$425$	10.1659	0.493119
$426$	0.802323	0.0388727
$427$	−45.1429	−2.18462
$428$	−19.1063	−0.923537
$429$	−3.64940	−0.176195
$430$	−20.6653	−0.996569
$431$	18.5700	0.894487	0.447244	−	0.894412i	$-0.352406\pi$
$431$	18.5700	0.894487	0.447244	+	0.894412i	$0.352406\pi$
$432$	−1.00000	−0.0481125
$433$	26.0951	1.25405	0.627026	−	0.778998i	$-0.284272\pi$
$433$	26.0951	1.25405	0.627026	+	0.778998i	$0.284272\pi$
$434$	−34.9206	−1.67624
$435$	−12.6117	−0.604684
$436$	18.4619	0.884163
$437$	32.6108	1.55999
$438$	8.44092	0.403323
$439$	17.3656	0.828817	0.414408	−	0.910091i	$-0.363989\pi$
$439$	17.3656	0.828817	0.414408	+	0.910091i	$0.363989\pi$
$440$	9.37741	0.447051
$441$	8.70431	0.414491
$442$	6.34291	0.301701
$443$	1.60727	0.0763635	0.0381818	−	0.999271i	$-0.487843\pi$
$443$	1.60727	0.0763635	0.0381818	+	0.999271i	$0.487843\pi$
$444$	7.78824	0.369613
$445$	35.2488	1.67095
$446$	−8.14729	−0.385785
$447$	10.5472	0.498868
$448$	3.96287	0.187228
$449$	−15.2697	−0.720621	−0.360311	−	0.932832i	$-0.617329\pi$
$449$	−15.2697	−0.720621	−0.360311	+	0.932832i	$0.617329\pi$
$450$	−1.60272	−0.0755530
$451$	−10.2955	−0.484795
$452$	−1.45077	−0.0682384
$453$	6.01197	0.282467
$454$	−19.9817	−0.937788
$455$	−10.1829	−0.477381
$456$	6.47887	0.303401
$457$	−8.07806	−0.377876	−0.188938	−	0.981989i	$-0.560504\pi$
$457$	−8.07806	−0.377876	−0.188938	+	0.981989i	$0.560504\pi$
$458$	14.5611	0.680398
$459$	−6.34291	−0.296062
$460$	12.9337	0.603038
$461$	3.84513	0.179086	0.0895428	−	0.995983i	$-0.471459\pi$
$461$	3.84513	0.179086	0.0895428	+	0.995983i	$0.471459\pi$
$462$	−14.4621	−0.672837
$463$	−11.0796	−0.514913	−0.257457	−	0.966290i	$-0.582884\pi$
$463$	−11.0796	−0.514913	−0.257457	+	0.966290i	$0.582884\pi$
$464$	4.90808	0.227852
$465$	−22.6430	−1.05004
$466$	28.6011	1.32492
$467$	20.7061	0.958165	0.479083	−	0.877770i	$-0.340969\pi$
$467$	20.7061	0.958165	0.479083	+	0.877770i	$0.340969\pi$
$468$	−1.00000	−0.0462250
$469$	−8.07749	−0.372984
$470$	13.2202	0.609802
$471$	10.8226	0.498678
$472$	6.22700	0.286621
$473$	−29.3496	−1.34949
$474$	0.928481	0.0426465
$475$	10.3838	0.476443
$476$	25.1361	1.15211
$477$	0.106049	0.00485566
$478$	−12.0981	−0.553355
$479$	32.4908	1.48454	0.742271	−	0.670100i	$-0.233749\pi$
$479$	32.4908	1.48454	0.742271	+	0.670100i	$0.233749\pi$
$480$	2.56958	0.117285
$481$	7.78824	0.355113
$482$	22.0200	1.00298
$483$	−19.9467	−0.907608
$484$	2.31813	0.105369
$485$	24.6510	1.11934
$486$	1.00000	0.0453609
$487$	6.93601	0.314301	0.157150	−	0.987575i	$-0.449769\pi$
$487$	6.93601	0.314301	0.157150	+	0.987575i	$0.449769\pi$
$488$	11.3915	0.515667
$489$	2.52012	0.113964
$490$	−22.3664	−1.01041
$491$	10.0323	0.452750	0.226375	−	0.974040i	$-0.427313\pi$
$491$	10.0323	0.452750	0.226375	+	0.974040i	$0.427313\pi$
$492$	−2.82114	−0.127187
$493$	31.1315	1.40209
$494$	6.47887	0.291498
$495$	−9.37741	−0.421483
$496$	8.81196	0.395669
$497$	3.17950	0.142620
$498$	−6.12343	−0.274398
$499$	41.3109	1.84933	0.924664	−	0.380783i	$-0.124346\pi$
$499$	41.3109	1.84933	0.924664	+	0.380783i	$0.124346\pi$
$500$	−8.72957	−0.390398
$501$	15.1049	0.674838
$502$	−7.00320	−0.312568
$503$	17.4388	0.777557	0.388778	−	0.921331i	$-0.372897\pi$
$503$	17.4388	0.777557	0.388778	+	0.921331i	$0.372897\pi$
$504$	−3.96287	−0.176520
$505$	−7.44572	−0.331330
$506$	18.3689	0.816599
$507$	−1.00000	−0.0444116
$508$	13.3969	0.594390
$509$	24.1421	1.07008	0.535039	−	0.844827i	$-0.320297\pi$
$509$	24.1421	1.07008	0.535039	+	0.844827i	$0.320297\pi$
$510$	16.2986	0.721713
$511$	33.4502	1.47975
$512$	−1.00000	−0.0441942
$513$	−6.47887	−0.286049
$514$	−11.6004	−0.511673
$515$	2.56958	0.113229
$516$	−8.04229	−0.354042
$517$	18.7758	0.825757
$518$	30.8637	1.35607
$519$	−24.7945	−1.08836
$520$	2.56958	0.112683
$521$	23.0329	1.00909	0.504546	−	0.863385i	$-0.331660\pi$
$521$	23.0329	1.00909	0.504546	+	0.863385i	$0.331660\pi$
$522$	−4.90808	−0.214821
$523$	32.3049	1.41260	0.706298	−	0.707915i	$-0.250364\pi$
$523$	32.3049	1.41260	0.706298	+	0.707915i	$0.250364\pi$
$524$	−19.3504	−0.845328
$525$	−6.35137	−0.277196
$526$	−6.22816	−0.271561
$527$	55.8935	2.43476
$528$	3.64940	0.158820
$529$	2.33523	0.101532
$530$	−0.272502	−0.0118367
$531$	−6.22700	−0.270229
$532$	25.6749	1.11315
$533$	−2.82114	−0.122197
$534$	13.7177	0.593624
$535$	−49.0951	−2.12256
$536$	2.03830	0.0880409
$537$	−6.86824	−0.296386
$538$	16.5598	0.713944
$539$	−31.7655	−1.36824
$540$	−2.56958	−0.110577
$541$	26.0952	1.12192	0.560961	−	0.827842i	$-0.310432\pi$
$541$	26.0952	1.12192	0.560961	+	0.827842i	$0.310432\pi$
$542$	−15.6676	−0.672979
$543$	10.0027	0.429258
$544$	−6.34291	−0.271950
$545$	47.4391	2.03207
$546$	−3.96287	−0.169595
$547$	34.1063	1.45828	0.729141	−	0.684364i	$-0.239920\pi$
$547$	34.1063	1.45828	0.729141	+	0.684364i	$0.239920\pi$
$548$	3.26002	0.139261
$549$	−11.3915	−0.486176
$550$	5.84897	0.249401
$551$	31.7988	1.35468
$552$	5.03341	0.214236
$553$	3.67945	0.156466
$554$	−10.8926	−0.462783
$555$	20.0125	0.849482
$556$	1.29491	0.0549164
$557$	−24.2470	−1.02738	−0.513689	−	0.857977i	$-0.671721\pi$
$557$	−24.2470	−1.02738	−0.513689	+	0.857977i	$0.671721\pi$
$558$	−8.81196	−0.373040
$559$	−8.04229	−0.340153
$560$	10.1829	0.430305
$561$	23.1478	0.977301
$562$	−4.30113	−0.181432
$563$	−12.9740	−0.546787	−0.273393	−	0.961902i	$-0.588146\pi$
$563$	−12.9740	−0.546787	−0.273393	+	0.961902i	$0.588146\pi$
$564$	5.14489	0.216639
$565$	−3.72786	−0.156832
$566$	−26.2920	−1.10514
$567$	3.96287	0.166425
$568$	−0.802323	−0.0336647
$569$	−31.4949	−1.32033	−0.660167	−	0.751119i	$-0.729514\pi$
$569$	−31.4949	−1.32033	−0.660167	+	0.751119i	$0.729514\pi$
$570$	16.6480	0.697306
$571$	−25.1199	−1.05124	−0.525618	−	0.850721i	$-0.676166\pi$
$571$	−25.1199	−1.05124	−0.525618	+	0.850721i	$0.676166\pi$
$572$	3.64940	0.152589
$573$	13.2993	0.555584
$574$	−11.1798	−0.466636
$575$	8.06715	0.336423
$576$	1.00000	0.0416667
$577$	22.2285	0.925383	0.462692	−	0.886519i	$-0.346884\pi$
$577$	22.2285	0.925383	0.462692	+	0.886519i	$0.346884\pi$
$578$	−23.2325	−0.966343
$579$	3.36267	0.139748
$580$	12.6117	0.523672
$581$	−24.2663	−1.00674
$582$	9.59341	0.397659
$583$	−0.387016	−0.0160286
$584$	−8.44092	−0.349288
$585$	−2.56958	−0.106239
$586$	21.5768	0.891330
$587$	−21.1255	−0.871941	−0.435971	−	0.899961i	$-0.643595\pi$
$587$	−21.1255	−0.871941	−0.435971	+	0.899961i	$0.643595\pi$
$588$	−8.70431	−0.358960
$589$	57.0916	2.35242
$590$	16.0008	0.658741
$591$	14.3558	0.590517
$592$	−7.78824	−0.320095
$593$	−39.2122	−1.61025	−0.805126	−	0.593103i	$-0.797903\pi$
$593$	−39.2122	−1.61025	−0.805126	+	0.593103i	$0.797903\pi$
$594$	−3.64940	−0.149737
$595$	64.5891	2.64789
$596$	−10.5472	−0.432032
$597$	−15.8817	−0.649993
$598$	5.03341	0.205831
$599$	44.3292	1.81124	0.905621	−	0.424089i	$-0.139406\pi$
$599$	44.3292	1.81124	0.905621	+	0.424089i	$0.139406\pi$
$600$	1.60272	0.0654308
$601$	11.3666	0.463653	0.231827	−	0.972757i	$-0.425530\pi$
$601$	11.3666	0.463653	0.231827	+	0.972757i	$0.425530\pi$
$602$	−31.8705	−1.29895
$603$	−2.03830	−0.0830058
$604$	−6.01197	−0.244624
$605$	5.95660	0.242170
$606$	−2.89765	−0.117709
$607$	46.4716	1.88622	0.943112	−	0.332477i	$-0.107884\pi$
$607$	46.4716	1.88622	0.943112	+	0.332477i	$0.107884\pi$
$608$	−6.47887	−0.262753
$609$	−19.4501	−0.788157
$610$	29.2712	1.18516
$611$	5.14489	0.208140
$612$	6.34291	0.256397
$613$	−19.0608	−0.769857	−0.384929	−	0.922946i	$-0.625774\pi$
$613$	−19.0608	−0.769857	−0.384929	+	0.922946i	$0.625774\pi$
$614$	7.06343	0.285057
$615$	−7.24914	−0.292313
$616$	14.4621	0.582694
$617$	−41.9363	−1.68829	−0.844147	−	0.536112i	$-0.819892\pi$
$617$	−41.9363	−1.68829	−0.844147	+	0.536112i	$0.819892\pi$
$618$	1.00000	0.0402259
$619$	−9.12921	−0.366934	−0.183467	−	0.983026i	$-0.558732\pi$
$619$	−9.12921	−0.366934	−0.183467	+	0.983026i	$0.558732\pi$
$620$	22.6430	0.909365
$621$	−5.03341	−0.201984
$622$	11.6763	0.468177
$623$	54.3615	2.17795
$624$	1.00000	0.0400320
$625$	−30.4449	−1.21780
$626$	13.9503	0.557568
$627$	23.6440	0.944251
$628$	−10.8226	−0.431868
$629$	−49.4001	−1.96971
$630$	−10.1829	−0.405696
$631$	−7.70347	−0.306670	−0.153335	−	0.988174i	$-0.549001\pi$
$631$	−7.70347	−0.306670	−0.153335	+	0.988174i	$0.549001\pi$
$632$	−0.928481	−0.0369330
$633$	8.19520	0.325730
$634$	−10.9418	−0.434555
$635$	34.4243	1.36609
$636$	−0.106049	−0.00420513
$637$	−8.70431	−0.344877
$638$	17.9116	0.709125
$639$	0.802323	0.0317394
$640$	−2.56958	−0.101571
$641$	−3.59372	−0.141944	−0.0709718	−	0.997478i	$-0.522610\pi$
$641$	−3.59372	−0.141944	−0.0709718	+	0.997478i	$0.522610\pi$
$642$	−19.1063	−0.754065
$643$	−23.6294	−0.931854	−0.465927	−	0.884823i	$-0.654279\pi$
$643$	−23.6294	−0.931854	−0.465927	+	0.884823i	$0.654279\pi$
$644$	19.9467	0.786011
$645$	−20.6653	−0.813695
$646$	−41.0949	−1.61686
$647$	−35.4676	−1.39437	−0.697187	−	0.716889i	$-0.745565\pi$
$647$	−35.4676	−1.39437	−0.697187	+	0.716889i	$0.745565\pi$
$648$	−1.00000	−0.0392837
$649$	22.7248	0.892028
$650$	1.60272	0.0628639
$651$	−34.9206	−1.36865
$652$	−2.52012	−0.0986957
$653$	32.0405	1.25384	0.626921	−	0.779083i	$-0.284315\pi$
$653$	32.0405	1.25384	0.626921	+	0.779083i	$0.284315\pi$
$654$	18.4619	0.721916
$655$	−49.7224	−1.94282
$656$	2.82114	0.110147
$657$	8.44092	0.329312
$658$	20.3885	0.794827
$659$	9.55962	0.372390	0.186195	−	0.982513i	$-0.440384\pi$
$659$	9.55962	0.372390	0.186195	+	0.982513i	$0.440384\pi$
$660$	9.37741	0.365015
$661$	43.2638	1.68277	0.841383	−	0.540439i	$-0.181742\pi$
$661$	43.2638	1.68277	0.841383	+	0.540439i	$0.181742\pi$
$662$	−10.9179	−0.424335
$663$	6.34291	0.246338
$664$	6.12343	0.237635
$665$	65.9736	2.55835
$666$	7.78824	0.301788
$667$	24.7044	0.956558
$668$	−15.1049	−0.584427
$669$	−8.14729	−0.314992
$670$	5.23755	0.202344
$671$	41.5720	1.60487
$672$	3.96287	0.152871
$673$	14.7913	0.570164	0.285082	−	0.958503i	$-0.407979\pi$
$673$	14.7913	0.570164	0.285082	+	0.958503i	$0.407979\pi$
$674$	18.1026	0.697287
$675$	−1.60272	−0.0616887
$676$	1.00000	0.0384615
$677$	−21.5254	−0.827288	−0.413644	−	0.910439i	$-0.635744\pi$
$677$	−21.5254	−0.827288	−0.413644	+	0.910439i	$0.635744\pi$
$678$	−1.45077	−0.0557164
$679$	38.0174	1.45897
$680$	−16.2986	−0.625022
$681$	−19.9817	−0.765700
$682$	32.1584	1.23141
$683$	40.6402	1.55505	0.777527	−	0.628849i	$-0.216474\pi$
$683$	40.6402	1.55505	0.777527	+	0.628849i	$0.216474\pi$
$684$	6.47887	0.247726
$685$	8.37687	0.320064
$686$	−6.75395	−0.257867
$687$	14.5611	0.555542
$688$	8.04229	0.306610
$689$	−0.106049	−0.00404016
$690$	12.9337	0.492379
$691$	30.5525	1.16227	0.581135	−	0.813807i	$-0.302609\pi$
$691$	30.5525	1.16227	0.581135	+	0.813807i	$0.302609\pi$
$692$	24.7945	0.942546
$693$	−14.4621	−0.549369
$694$	14.4014	0.546669
$695$	3.32737	0.126214
$696$	4.90808	0.186040
$697$	17.8942	0.677793
$698$	−0.791137	−0.0299450
$699$	28.6011	1.08179
$700$	6.35137	0.240059
$701$	−6.29600	−0.237797	−0.118898	−	0.992906i	$-0.537936\pi$
$701$	−6.29600	−0.237797	−0.118898	+	0.992906i	$0.537936\pi$
$702$	−1.00000	−0.0377426
$703$	−50.4590	−1.90310
$704$	−3.64940	−0.137542
$705$	13.2202	0.497901
$706$	13.7134	0.516111
$707$	−11.4830	−0.431862
$708$	6.22700	0.234025
$709$	16.7586	0.629382	0.314691	−	0.949194i	$-0.398099\pi$
$709$	16.7586	0.629382	0.314691	+	0.949194i	$0.398099\pi$
$710$	−2.06163	−0.0773715
$711$	0.928481	0.0348208
$712$	−13.7177	−0.514094
$713$	44.3542	1.66108
$714$	25.1361	0.940694
$715$	9.37741	0.350695
$716$	6.86824	0.256678
$717$	−12.0981	−0.451812
$718$	12.0989	0.451527
$719$	−18.3058	−0.682690	−0.341345	−	0.939938i	$-0.610882\pi$
$719$	−18.3058	−0.682690	−0.341345	+	0.939938i	$0.610882\pi$
$720$	2.56958	0.0957624
$721$	3.96287	0.147585
$722$	−22.9758	−0.855071
$723$	22.0200	0.818933
$724$	−10.0027	−0.371748
$725$	7.86628	0.292146
$726$	2.31813	0.0860337
$727$	1.01083	0.0374895	0.0187448	−	0.999824i	$-0.494033\pi$
$727$	1.01083	0.0374895	0.0187448	+	0.999824i	$0.494033\pi$
$728$	3.96287	0.146874
$729$	1.00000	0.0370370
$730$	−21.6896	−0.802768
$731$	51.0115	1.88673
$732$	11.3915	0.421041
$733$	−12.0537	−0.445212	−0.222606	−	0.974909i	$-0.571456\pi$
$733$	−12.0537	−0.445212	−0.222606	+	0.974909i	$0.571456\pi$
$734$	−0.484231	−0.0178733
$735$	−22.3664	−0.824996
$736$	−5.03341	−0.185534
$737$	7.43856	0.274003
$738$	−2.82114	−0.103848
$739$	−34.9428	−1.28539	−0.642696	−	0.766121i	$-0.722184\pi$
$739$	−34.9428	−1.28539	−0.642696	+	0.766121i	$0.722184\pi$
$740$	−20.0125	−0.735673
$741$	6.47887	0.238007
$742$	−0.420259	−0.0154282
$743$	0.0325569	0.00119440	0.000597198	−	1.00000i	$-0.499810\pi$
$743$	0.0325569	0.00119440	0.000597198		1.00000i	$0.499810\pi$
$744$	8.81196	0.323062
$745$	−27.1019	−0.992938
$746$	7.50161	0.274653
$747$	−6.12343	−0.224045
$748$	−23.1478	−0.846368
$749$	−75.7157	−2.76659
$750$	−8.72957	−0.318759
$751$	9.62378	0.351177	0.175588	−	0.984464i	$-0.443817\pi$
$751$	9.62378	0.351177	0.175588	+	0.984464i	$0.443817\pi$
$752$	−5.14489	−0.187615
$753$	−7.00320	−0.255211
$754$	4.90808	0.178742
$755$	−15.4482	−0.562218
$756$	−3.96287	−0.144128
$757$	−29.3975	−1.06847	−0.534235	−	0.845336i	$-0.679400\pi$
$757$	−29.3975	−1.06847	−0.534235	+	0.845336i	$0.679400\pi$
$758$	−6.89886	−0.250578
$759$	18.3689	0.666750
$760$	−16.6480	−0.603885
$761$	−26.4579	−0.959098	−0.479549	−	0.877515i	$-0.659200\pi$
$761$	−26.4579	−0.959098	−0.479549	+	0.877515i	$0.659200\pi$
$762$	13.3969	0.485318
$763$	73.1619	2.64864
$764$	−13.2993	−0.481150
$765$	16.2986	0.589276
$766$	−26.3843	−0.953305
$767$	6.22700	0.224844
$768$	−1.00000	−0.0360844
$769$	14.4811	0.522203	0.261102	−	0.965311i	$-0.415914\pi$
$769$	14.4811	0.522203	0.261102	+	0.965311i	$0.415914\pi$
$770$	37.1614	1.33921
$771$	−11.6004	−0.417779
$772$	−3.36267	−0.121025
$773$	11.6143	0.417736	0.208868	−	0.977944i	$-0.433022\pi$
$773$	11.6143	0.417736	0.208868	+	0.977944i	$0.433022\pi$
$774$	−8.04229	−0.289074
$775$	14.1231	0.507317
$776$	−9.59341	−0.344383
$777$	30.8637	1.10723
$778$	13.2394	0.474654
$779$	18.2778	0.654871
$780$	2.56958	0.0920056
$781$	−2.92800	−0.104772
$782$	−31.9265	−1.14169
$783$	−4.90808	−0.175401
$784$	8.70431	0.310868
$785$	−27.8095	−0.992562
$786$	−19.3504	−0.690207
$787$	20.1342	0.717707	0.358854	−	0.933394i	$-0.383168\pi$
$787$	20.1342	0.717707	0.358854	+	0.933394i	$0.383168\pi$
$788$	−14.3558	−0.511403
$789$	−6.22816	−0.221728
$790$	−2.38580	−0.0848831
$791$	−5.74920	−0.204418
$792$	3.64940	0.129676
$793$	11.3915	0.404523
$794$	−5.70209	−0.202359
$795$	−0.272502	−0.00966464
$796$	15.8817	0.562911
$797$	32.2599	1.14271	0.571353	−	0.820704i	$-0.306419\pi$
$797$	32.2599	1.14271	0.571353	+	0.820704i	$0.306419\pi$
$798$	25.6749	0.908882
$799$	−32.6336	−1.15449
$800$	−1.60272	−0.0566647
$801$	13.7177	0.484692
$802$	28.3921	1.00256
$803$	−30.8043	−1.08706
$804$	2.03830	0.0718851
$805$	51.2547	1.80649
$806$	8.81196	0.310388
$807$	16.5598	0.582932
$808$	2.89765	0.101939
$809$	12.8362	0.451296	0.225648	−	0.974209i	$-0.427550\pi$
$809$	12.8362	0.451296	0.225648	+	0.974209i	$0.427550\pi$
$810$	−2.56958	−0.0902857
$811$	27.6128	0.969618	0.484809	−	0.874620i	$-0.338889\pi$
$811$	27.6128	0.969618	0.484809	+	0.874620i	$0.338889\pi$
$812$	19.4501	0.682564
$813$	−15.6676	−0.549485
$814$	−28.4224	−0.996205
$815$	−6.47565	−0.226832
$816$	−6.34291	−0.222046
$817$	52.1050	1.82292
$818$	35.0655	1.22604
$819$	−3.96287	−0.138474
$820$	7.24914	0.253151
$821$	39.8917	1.39223	0.696115	−	0.717930i	$-0.254910\pi$
$821$	39.8917	1.39223	0.696115	+	0.717930i	$0.254910\pi$
$822$	3.26002	0.113706
$823$	−56.1930	−1.95876	−0.979382	−	0.202018i	$-0.935250\pi$
$823$	−56.1930	−1.95876	−0.979382	+	0.202018i	$0.935250\pi$
$824$	−1.00000	−0.0348367
$825$	5.84897	0.203635
$826$	24.6768	0.858615
$827$	−39.6806	−1.37983	−0.689915	−	0.723890i	$-0.742352\pi$
$827$	−39.6806	−1.37983	−0.689915	+	0.723890i	$0.742352\pi$
$828$	5.03341	0.174923
$829$	−21.0786	−0.732091	−0.366045	−	0.930597i	$-0.619288\pi$
$829$	−21.0786	−0.732091	−0.366045	+	0.930597i	$0.619288\pi$
$830$	15.7346	0.546157
$831$	−10.8926	−0.377860
$832$	−1.00000	−0.0346688
$833$	55.2106	1.91293
$834$	1.29491	0.0448391
$835$	−38.8132	−1.34319
$836$	−23.6440	−0.817745
$837$	−8.81196	−0.304586
$838$	31.1781	1.07703
$839$	40.5913	1.40137	0.700684	−	0.713472i	$-0.252878\pi$
$839$	40.5913	1.40137	0.700684	+	0.713472i	$0.252878\pi$
$840$	10.1829	0.351343
$841$	−4.91074	−0.169336
$842$	32.6763	1.12610
$843$	−4.30113	−0.148139
$844$	−8.19520	−0.282090
$845$	2.56958	0.0883961
$846$	5.14489	0.176885
$847$	9.18643	0.315649
$848$	0.106049	0.00364175
$849$	−26.2920	−0.902339
$850$	−10.1659	−0.348688
$851$	−39.2014	−1.34381
$852$	−0.802323	−0.0274871
$853$	36.4092	1.24663	0.623314	−	0.781971i	$-0.285786\pi$
$853$	36.4092	1.24663	0.623314	+	0.781971i	$0.285786\pi$
$854$	45.1429	1.54476
$855$	16.6480	0.569348
$856$	19.1063	0.653039
$857$	−7.13672	−0.243786	−0.121893	−	0.992543i	$-0.538896\pi$
$857$	−7.13672	−0.243786	−0.121893	+	0.992543i	$0.538896\pi$
$858$	3.64940	0.124588
$859$	17.6543	0.602356	0.301178	−	0.953568i	$-0.402620\pi$
$859$	17.6543	0.602356	0.301178	+	0.953568i	$0.402620\pi$
$860$	20.6653	0.704680
$861$	−11.1798	−0.381007
$862$	−18.5700	−0.632498
$863$	−10.8869	−0.370595	−0.185298	−	0.982682i	$-0.559325\pi$
$863$	−10.8869	−0.370595	−0.185298	+	0.982682i	$0.559325\pi$
$864$	1.00000	0.0340207
$865$	63.7114	2.16625
$866$	−26.0951	−0.886749
$867$	−23.2325	−0.789016
$868$	34.9206	1.18528
$869$	−3.38840	−0.114944
$870$	12.6117	0.427576
$871$	2.03830	0.0690650
$872$	−18.4619	−0.625197
$873$	9.59341	0.324688
$874$	−32.6108	−1.10308
$875$	−34.5941	−1.16949
$876$	−8.44092	−0.285192
$877$	−25.2601	−0.852973	−0.426486	−	0.904494i	$-0.640249\pi$
$877$	−25.2601	−0.852973	−0.426486	+	0.904494i	$0.640249\pi$
$878$	−17.3656	−0.586062
$879$	21.5768	0.727768
$880$	−9.37741	−0.316113
$881$	−52.3880	−1.76500	−0.882498	−	0.470316i	$-0.844140\pi$
$881$	−52.3880	−1.76500	−0.882498	+	0.470316i	$0.844140\pi$
$882$	−8.70431	−0.293089
$883$	40.0791	1.34877	0.674384	−	0.738381i	$-0.264409\pi$
$883$	40.0791	1.34877	0.674384	+	0.738381i	$0.264409\pi$
$884$	−6.34291	−0.213335
$885$	16.0008	0.537860
$886$	−1.60727	−0.0539972
$887$	−48.6269	−1.63273	−0.816367	−	0.577534i	$-0.804015\pi$
$887$	−48.6269	−1.63273	−0.816367	+	0.577534i	$0.804015\pi$
$888$	−7.78824	−0.261356
$889$	53.0900	1.78058
$890$	−35.2488	−1.18154
$891$	−3.64940	−0.122260
$892$	8.14729	0.272791
$893$	−33.3331	−1.11545
$894$	−10.5472	−0.352753
$895$	17.6485	0.589923
$896$	−3.96287	−0.132390
$897$	5.03341	0.168061
$898$	15.2697	0.509556
$899$	43.2498	1.44246
$900$	1.60272	0.0534240
$901$	0.672661	0.0224096
$902$	10.2955	0.342802
$903$	−31.8705	−1.06059
$904$	1.45077	0.0482518
$905$	−25.7027	−0.854388
$906$	−6.01197	−0.199734
$907$	8.81552	0.292715	0.146357	−	0.989232i	$-0.453245\pi$
$907$	8.81552	0.292715	0.146357	+	0.989232i	$0.453245\pi$
$908$	19.9817	0.663116
$909$	−2.89765	−0.0961089
$910$	10.1829	0.337559
$911$	21.1300	0.700068	0.350034	−	0.936737i	$-0.386170\pi$
$911$	21.1300	0.700068	0.350034	+	0.936737i	$0.386170\pi$
$912$	−6.47887	−0.214537
$913$	22.3469	0.739573
$914$	8.07806	0.267198
$915$	29.2712	0.967677
$916$	−14.5611	−0.481114
$917$	−76.6832	−2.53230
$918$	6.34291	0.209347
$919$	−34.7196	−1.14529	−0.572647	−	0.819802i	$-0.694083\pi$
$919$	−34.7196	−1.14529	−0.572647	+	0.819802i	$0.694083\pi$
$920$	−12.9337	−0.426413
$921$	7.06343	0.232748
$922$	−3.84513	−0.126633
$923$	−0.802323	−0.0264088
$924$	14.4621	0.475768
$925$	−12.4824	−0.410418
$926$	11.0796	0.364099
$927$	1.00000	0.0328443
$928$	−4.90808	−0.161116
$929$	26.7065	0.876211	0.438105	−	0.898924i	$-0.355650\pi$
$929$	26.7065	0.876211	0.438105	+	0.898924i	$0.355650\pi$
$930$	22.6430	0.742494
$931$	56.3941	1.84824
$932$	−28.6011	−0.936860
$933$	11.6763	0.382265
$934$	−20.7061	−0.677525
$935$	−59.4800	−1.94521
$936$	1.00000	0.0326860
$937$	−23.9416	−0.782137	−0.391068	−	0.920362i	$-0.627894\pi$
$937$	−23.9416	−0.782137	−0.391068	+	0.920362i	$0.627894\pi$
$938$	8.07749	0.263739
$939$	13.9503	0.455252
$940$	−13.2202	−0.431195
$941$	36.4880	1.18947	0.594737	−	0.803920i	$-0.297256\pi$
$941$	36.4880	1.18947	0.594737	+	0.803920i	$0.297256\pi$
$942$	−10.8226	−0.352619
$943$	14.2000	0.462415
$944$	−6.22700	−0.202672
$945$	−10.1829	−0.331249
$946$	29.3496	0.954236
$947$	−54.2638	−1.76334	−0.881668	−	0.471870i	$-0.843579\pi$
$947$	−54.2638	−1.76334	−0.881668	+	0.471870i	$0.843579\pi$
$948$	−0.928481	−0.0301557
$949$	−8.44092	−0.274004
$950$	−10.3838	−0.336896
$951$	−10.9418	−0.354813
$952$	−25.1361	−0.814665
$953$	5.38962	0.174587	0.0872935	−	0.996183i	$-0.472178\pi$
$953$	5.38962	0.174587	0.0872935	+	0.996183i	$0.472178\pi$
$954$	−0.106049	−0.00343347
$955$	−34.1734	−1.10583
$956$	12.0981	0.391281
$957$	17.9116	0.578998
$958$	−32.4908	−1.04973
$959$	12.9190	0.417177
$960$	−2.56958	−0.0829327
$961$	46.6507	1.50486
$962$	−7.78824	−0.251103
$963$	−19.1063	−0.615691
$964$	−22.0200	−0.709217
$965$	−8.64063	−0.278152
$966$	19.9467	0.641776
$967$	−27.1920	−0.874435	−0.437217	−	0.899356i	$-0.644036\pi$
$967$	−27.1920	−0.874435	−0.437217	+	0.899356i	$0.644036\pi$
$968$	−2.31813	−0.0745074
$969$	−41.0949	−1.32016
$970$	−24.6510	−0.791495
$971$	9.12949	0.292979	0.146490	−	0.989212i	$-0.453202\pi$
$971$	9.12949	0.292979	0.146490	+	0.989212i	$0.453202\pi$
$972$	−1.00000	−0.0320750
$973$	5.13156	0.164510
$974$	−6.93601	−0.222244
$975$	1.60272	0.0513281
$976$	−11.3915	−0.364632
$977$	25.1744	0.805401	0.402701	−	0.915332i	$-0.368072\pi$
$977$	25.1744	0.805401	0.402701	+	0.915332i	$0.368072\pi$
$978$	−2.52012	−0.0805847
$979$	−50.0615	−1.59997
$980$	22.3664	0.714468
$981$	18.4619	0.589442
$982$	−10.0323	−0.320142
$983$	−24.9510	−0.795812	−0.397906	−	0.917426i	$-0.630263\pi$
$983$	−24.9510	−0.795812	−0.397906	+	0.917426i	$0.630263\pi$
$984$	2.82114	0.0899347
$985$	−36.8882	−1.17536
$986$	−31.1315	−0.991429
$987$	20.3885	0.648973
$988$	−6.47887	−0.206120
$989$	40.4802	1.28719
$990$	9.37741	0.298034
$991$	9.90044	0.314498	0.157249	−	0.987559i	$-0.449738\pi$
$991$	9.90044	0.314498	0.157249	+	0.987559i	$0.449738\pi$
$992$	−8.81196	−0.279780
$993$	−10.9179	−0.346468
$994$	−3.17950	−0.100848
$995$	40.8091	1.29374
$996$	6.12343	0.194028
$997$	−44.8987	−1.42196	−0.710978	−	0.703215i	$-0.751747\pi$
$997$	−44.8987	−1.42196	−0.710978	+	0.703215i	$0.751747\pi$
$998$	−41.3109	−1.30767
$999$	7.78824	0.246409

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.12	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.12	✓	14	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56958 q^{5} +1.00000 q^{6} +3.96287 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.56958 q^{5} +1.00000 q^{6} +3.96287 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.56958 q^{10} -3.64940 q^{11} -1.00000 q^{12} -1.00000 q^{13} -3.96287 q^{14} -2.56958 q^{15} +1.00000 q^{16} +6.34291 q^{17} -1.00000 q^{18} +6.47887 q^{19} +2.56958 q^{20} -3.96287 q^{21} +3.64940 q^{22} +5.03341 q^{23} +1.00000 q^{24} +1.60272 q^{25} +1.00000 q^{26} -1.00000 q^{27} +3.96287 q^{28} +4.90808 q^{29} +2.56958 q^{30} +8.81196 q^{31} -1.00000 q^{32} +3.64940 q^{33} -6.34291 q^{34} +10.1829 q^{35} +1.00000 q^{36} -7.78824 q^{37} -6.47887 q^{38} +1.00000 q^{39} -2.56958 q^{40} +2.82114 q^{41} +3.96287 q^{42} +8.04229 q^{43} -3.64940 q^{44} +2.56958 q^{45} -5.03341 q^{46} -5.14489 q^{47} -1.00000 q^{48} +8.70431 q^{49} -1.60272 q^{50} -6.34291 q^{51} -1.00000 q^{52} +0.106049 q^{53} +1.00000 q^{54} -9.37741 q^{55} -3.96287 q^{56} -6.47887 q^{57} -4.90808 q^{58} -6.22700 q^{59} -2.56958 q^{60} -11.3915 q^{61} -8.81196 q^{62} +3.96287 q^{63} +1.00000 q^{64} -2.56958 q^{65} -3.64940 q^{66} -2.03830 q^{67} +6.34291 q^{68} -5.03341 q^{69} -10.1829 q^{70} +0.802323 q^{71} -1.00000 q^{72} +8.44092 q^{73} +7.78824 q^{74} -1.60272 q^{75} +6.47887 q^{76} -14.4621 q^{77} -1.00000 q^{78} +0.928481 q^{79} +2.56958 q^{80} +1.00000 q^{81} -2.82114 q^{82} -6.12343 q^{83} -3.96287 q^{84} +16.2986 q^{85} -8.04229 q^{86} -4.90808 q^{87} +3.64940 q^{88} +13.7177 q^{89} -2.56958 q^{90} -3.96287 q^{91} +5.03341 q^{92} -8.81196 q^{93} +5.14489 q^{94} +16.6480 q^{95} +1.00000 q^{96} +9.59341 q^{97} -8.70431 q^{98} -3.64940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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