LMFDB - Embedded newform 4730.2.a.w.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 7x^{5} + 41x^{4} - 6x^{3} - 28x^{2} + 2x + 4 $ x^8 - x^7 - 12x^6 + 7x^5 + 41x^4 - 6x^3 - 28x^2 + 2x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.70201$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.70201 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.70201 q^{6} +0.961819 q^{7} -1.00000 q^{8} -0.103166 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.70201 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.70201 q^{6} +0.961819 q^{7} -1.00000 q^{8} -0.103166 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.70201 q^{12} -2.37582 q^{13} -0.961819 q^{14} +1.70201 q^{15} +1.00000 q^{16} +0.206466 q^{17} +0.103166 q^{18} -0.413677 q^{19} +1.00000 q^{20} +1.63702 q^{21} -1.00000 q^{22} -4.37582 q^{23} -1.70201 q^{24} +1.00000 q^{25} +2.37582 q^{26} -5.28162 q^{27} +0.961819 q^{28} -5.05157 q^{29} -1.70201 q^{30} -6.59571 q^{31} -1.00000 q^{32} +1.70201 q^{33} -0.206466 q^{34} +0.961819 q^{35} -0.103166 q^{36} -9.05446 q^{37} +0.413677 q^{38} -4.04367 q^{39} -1.00000 q^{40} -7.15062 q^{41} -1.63702 q^{42} -1.00000 q^{43} +1.00000 q^{44} -0.103166 q^{45} +4.37582 q^{46} -10.4220 q^{47} +1.70201 q^{48} -6.07490 q^{49} -1.00000 q^{50} +0.351408 q^{51} -2.37582 q^{52} +9.81295 q^{53} +5.28162 q^{54} +1.00000 q^{55} -0.961819 q^{56} -0.704082 q^{57} +5.05157 q^{58} +5.21881 q^{59} +1.70201 q^{60} +7.54665 q^{61} +6.59571 q^{62} -0.0992265 q^{63} +1.00000 q^{64} -2.37582 q^{65} -1.70201 q^{66} +7.11705 q^{67} +0.206466 q^{68} -7.44769 q^{69} -0.961819 q^{70} +1.63446 q^{71} +0.103166 q^{72} -9.11062 q^{73} +9.05446 q^{74} +1.70201 q^{75} -0.413677 q^{76} +0.961819 q^{77} +4.04367 q^{78} +2.19376 q^{79} +1.00000 q^{80} -8.67986 q^{81} +7.15062 q^{82} -5.54961 q^{83} +1.63702 q^{84} +0.206466 q^{85} +1.00000 q^{86} -8.59782 q^{87} -1.00000 q^{88} -16.7071 q^{89} +0.103166 q^{90} -2.28511 q^{91} -4.37582 q^{92} -11.2260 q^{93} +10.4220 q^{94} -0.413677 q^{95} -1.70201 q^{96} +2.79975 q^{97} +6.07490 q^{98} -0.103166 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9} - 8 q^{10} + 8 q^{11} - 7 q^{12} - 2 q^{13} + 6 q^{14} - 7 q^{15} + 8 q^{16} - 8 q^{17} - 7 q^{18} + 8 q^{20} + 14 q^{21} - 8 q^{22} - 18 q^{23} + 7 q^{24} + 8 q^{25} + 2 q^{26} - 22 q^{27} - 6 q^{28} + 8 q^{29} + 7 q^{30} - 11 q^{31} - 8 q^{32} - 7 q^{33} + 8 q^{34} - 6 q^{35} + 7 q^{36} - 17 q^{37} - 6 q^{39} - 8 q^{40} + 12 q^{41} - 14 q^{42} - 8 q^{43} + 8 q^{44} + 7 q^{45} + 18 q^{46} - 19 q^{47} - 7 q^{48} - 2 q^{49} - 8 q^{50} - q^{51} - 2 q^{52} - 7 q^{53} + 22 q^{54} + 8 q^{55} + 6 q^{56} - 3 q^{57} - 8 q^{58} + q^{59} - 7 q^{60} + 6 q^{61} + 11 q^{62} - 15 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} - 22 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - 14 q^{71} - 7 q^{72} - 13 q^{73} + 17 q^{74} - 7 q^{75} - 6 q^{77} + 6 q^{78} - 8 q^{79} + 8 q^{80} + 28 q^{81} - 12 q^{82} - 4 q^{83} + 14 q^{84} - 8 q^{85} + 8 q^{86} - 30 q^{87} - 8 q^{88} + 5 q^{89} - 7 q^{90} - 8 q^{91} - 18 q^{92} + q^{93} + 19 q^{94} + 7 q^{96} - 23 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9 - 8 * q^10 + 8 * q^11 - 7 * q^12 - 2 * q^13 + 6 * q^14 - 7 * q^15 + 8 * q^16 - 8 * q^17 - 7 * q^18 + 8 * q^20 + 14 * q^21 - 8 * q^22 - 18 * q^23 + 7 * q^24 + 8 * q^25 + 2 * q^26 - 22 * q^27 - 6 * q^28 + 8 * q^29 + 7 * q^30 - 11 * q^31 - 8 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^35 + 7 * q^36 - 17 * q^37 - 6 * q^39 - 8 * q^40 + 12 * q^41 - 14 * q^42 - 8 * q^43 + 8 * q^44 + 7 * q^45 + 18 * q^46 - 19 * q^47 - 7 * q^48 - 2 * q^49 - 8 * q^50 - q^51 - 2 * q^52 - 7 * q^53 + 22 * q^54 + 8 * q^55 + 6 * q^56 - 3 * q^57 - 8 * q^58 + q^59 - 7 * q^60 + 6 * q^61 + 11 * q^62 - 15 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 - 22 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - 14 * q^71 - 7 * q^72 - 13 * q^73 + 17 * q^74 - 7 * q^75 - 6 * q^77 + 6 * q^78 - 8 * q^79 + 8 * q^80 + 28 * q^81 - 12 * q^82 - 4 * q^83 + 14 * q^84 - 8 * q^85 + 8 * q^86 - 30 * q^87 - 8 * q^88 + 5 * q^89 - 7 * q^90 - 8 * q^91 - 18 * q^92 + q^93 + 19 * q^94 + 7 * q^96 - 23 * q^97 + 2 * q^98 + 7 * 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
$3$	1.70201	0.982655	0.491328	−	0.870975i	$-0.336512\pi$
$3$	1.70201	0.982655	0.491328	+	0.870975i	$0.336512\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.70201	−0.694842
$7$	0.961819	0.363533	0.181767	−	0.983342i	$-0.441818\pi$
$7$	0.961819	0.363533	0.181767	+	0.983342i	$0.441818\pi$
$8$	−1.00000	−0.353553
$9$	−0.103166	−0.0343885
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.70201	0.491328
$13$	−2.37582	−0.658935	−0.329468	−	0.944167i	$-0.606869\pi$
$13$	−2.37582	−0.658935	−0.329468	+	0.944167i	$0.606869\pi$
$14$	−0.961819	−0.257057
$15$	1.70201	0.439457
$16$	1.00000	0.250000
$17$	0.206466	0.0500755	0.0250377	−	0.999687i	$-0.492029\pi$
$17$	0.206466	0.0500755	0.0250377	+	0.999687i	$0.492029\pi$
$18$	0.103166	0.0243163
$19$	−0.413677	−0.0949041	−0.0474520	−	0.998874i	$-0.515110\pi$
$19$	−0.413677	−0.0949041	−0.0474520	+	0.998874i	$0.515110\pi$
$20$	1.00000	0.223607
$21$	1.63702	0.357228
$22$	−1.00000	−0.213201
$23$	−4.37582	−0.912422	−0.456211	−	0.889872i	$-0.650794\pi$
$23$	−4.37582	−0.912422	−0.456211	+	0.889872i	$0.650794\pi$
$24$	−1.70201	−0.347421
$25$	1.00000	0.200000
$26$	2.37582	0.465937
$27$	−5.28162	−1.01645
$28$	0.961819	0.181767
$29$	−5.05157	−0.938053	−0.469026	−	0.883184i	$-0.655395\pi$
$29$	−5.05157	−0.938053	−0.469026	+	0.883184i	$0.655395\pi$
$30$	−1.70201	−0.310743
$31$	−6.59571	−1.18462	−0.592312	−	0.805709i	$-0.701785\pi$
$31$	−6.59571	−1.18462	−0.592312	+	0.805709i	$0.701785\pi$
$32$	−1.00000	−0.176777
$33$	1.70201	0.296282
$34$	−0.206466	−0.0354087
$35$	0.961819	0.162577
$36$	−0.103166	−0.0171943
$37$	−9.05446	−1.48854	−0.744272	−	0.667877i	$-0.767203\pi$
$37$	−9.05446	−1.48854	−0.744272	+	0.667877i	$0.767203\pi$
$38$	0.413677	0.0671073
$39$	−4.04367	−0.647506
$40$	−1.00000	−0.158114
$41$	−7.15062	−1.11674	−0.558370	−	0.829592i	$-0.688573\pi$
$41$	−7.15062	−1.11674	−0.558370	+	0.829592i	$0.688573\pi$
$42$	−1.63702	−0.252598
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−0.103166	−0.0153790
$46$	4.37582	0.645180
$47$	−10.4220	−1.52020	−0.760102	−	0.649804i	$-0.774851\pi$
$47$	−10.4220	−1.52020	−0.760102	+	0.649804i	$0.774851\pi$
$48$	1.70201	0.245664
$49$	−6.07490	−0.867843
$50$	−1.00000	−0.141421
$51$	0.351408	0.0492069
$52$	−2.37582	−0.329468
$53$	9.81295	1.34791	0.673956	−	0.738771i	$-0.264594\pi$
$53$	9.81295	1.34791	0.673956	+	0.738771i	$0.264594\pi$
$54$	5.28162	0.718737
$55$	1.00000	0.134840
$56$	−0.961819	−0.128528
$57$	−0.704082	−0.0932580
$58$	5.05157	0.663303
$59$	5.21881	0.679431	0.339716	−	0.940528i	$-0.389669\pi$
$59$	5.21881	0.679431	0.339716	+	0.940528i	$0.389669\pi$
$60$	1.70201	0.219728
$61$	7.54665	0.966249	0.483124	−	0.875552i	$-0.339502\pi$
$61$	7.54665	0.966249	0.483124	+	0.875552i	$0.339502\pi$
$62$	6.59571	0.837656
$63$	−0.0992265	−0.0125014
$64$	1.00000	0.125000
$65$	−2.37582	−0.294685
$66$	−1.70201	−0.209503
$67$	7.11705	0.869486	0.434743	−	0.900555i	$-0.356839\pi$
$67$	7.11705	0.869486	0.434743	+	0.900555i	$0.356839\pi$
$68$	0.206466	0.0250377
$69$	−7.44769	−0.896597
$70$	−0.961819	−0.114959
$71$	1.63446	0.193974	0.0969872	−	0.995286i	$-0.469079\pi$
$71$	1.63446	0.193974	0.0969872	+	0.995286i	$0.469079\pi$
$72$	0.103166	0.0121582
$73$	−9.11062	−1.06632	−0.533159	−	0.846015i	$-0.678995\pi$
$73$	−9.11062	−1.06632	−0.533159	+	0.846015i	$0.678995\pi$
$74$	9.05446	1.05256
$75$	1.70201	0.196531
$76$	−0.413677	−0.0474520
$77$	0.961819	0.109609
$78$	4.04367	0.457856
$79$	2.19376	0.246818	0.123409	−	0.992356i	$-0.460617\pi$
$79$	2.19376	0.246818	0.123409	+	0.992356i	$0.460617\pi$
$80$	1.00000	0.111803
$81$	−8.67986	−0.964429
$82$	7.15062	0.789654
$83$	−5.54961	−0.609148	−0.304574	−	0.952489i	$-0.598514\pi$
$83$	−5.54961	−0.609148	−0.304574	+	0.952489i	$0.598514\pi$
$84$	1.63702	0.178614
$85$	0.206466	0.0223944
$86$	1.00000	0.107833
$87$	−8.59782	−0.921783
$88$	−1.00000	−0.106600
$89$	−16.7071	−1.77095	−0.885474	−	0.464689i	$-0.846166\pi$
$89$	−16.7071	−1.77095	−0.885474	+	0.464689i	$0.846166\pi$
$90$	0.103166	0.0108746
$91$	−2.28511	−0.239545
$92$	−4.37582	−0.456211
$93$	−11.2260	−1.16408
$94$	10.4220	1.07495
$95$	−0.413677	−0.0424424
$96$	−1.70201	−0.173711
$97$	2.79975	0.284271	0.142136	−	0.989847i	$-0.454603\pi$
$97$	2.79975	0.284271	0.142136	+	0.989847i	$0.454603\pi$
$98$	6.07490	0.613658
$99$	−0.103166	−0.0103685
$100$	1.00000	0.100000
$101$	18.4724	1.83807	0.919036	−	0.394174i	$-0.128969\pi$
$101$	18.4724	1.83807	0.919036	+	0.394174i	$0.128969\pi$
$102$	−0.351408	−0.0347945
$103$	−14.9220	−1.47031	−0.735153	−	0.677901i	$-0.762890\pi$
$103$	−14.9220	−1.47031	−0.735153	+	0.677901i	$0.762890\pi$
$104$	2.37582	0.232969
$105$	1.63702	0.159757
$106$	−9.81295	−0.953118
$107$	17.2230	1.66501	0.832503	−	0.554020i	$-0.186907\pi$
$107$	17.2230	1.66501	0.832503	+	0.554020i	$0.186907\pi$
$108$	−5.28162	−0.508224
$109$	4.94258	0.473413	0.236706	−	0.971581i	$-0.423932\pi$
$109$	4.94258	0.473413	0.236706	+	0.971581i	$0.423932\pi$
$110$	−1.00000	−0.0953463
$111$	−15.4108	−1.46273
$112$	0.961819	0.0908833
$113$	−1.33914	−0.125976	−0.0629880	−	0.998014i	$-0.520063\pi$
$113$	−1.33914	−0.125976	−0.0629880	+	0.998014i	$0.520063\pi$
$114$	0.704082	0.0659434
$115$	−4.37582	−0.408048
$116$	−5.05157	−0.469026
$117$	0.245103	0.0226598
$118$	−5.21881	−0.480431
$119$	0.198583	0.0182041
$120$	−1.70201	−0.155371
$121$	1.00000	0.0909091
$122$	−7.54665	−0.683241
$123$	−12.1704	−1.09737
$124$	−6.59571	−0.592312
$125$	1.00000	0.0894427
$126$	0.0992265	0.00883980
$127$	−2.61565	−0.232101	−0.116051	−	0.993243i	$-0.537024\pi$
$127$	−2.61565	−0.232101	−0.116051	+	0.993243i	$0.537024\pi$
$128$	−1.00000	−0.0883883
$129$	−1.70201	−0.149854
$130$	2.37582	0.208374
$131$	−9.98567	−0.872452	−0.436226	−	0.899837i	$-0.643685\pi$
$131$	−9.98567	−0.872452	−0.436226	+	0.899837i	$0.643685\pi$
$132$	1.70201	0.148141
$133$	−0.397883	−0.0345008
$134$	−7.11705	−0.614820
$135$	−5.28162	−0.454569
$136$	−0.206466	−0.0177043
$137$	−15.5593	−1.32932	−0.664661	−	0.747145i	$-0.731424\pi$
$137$	−15.5593	−1.32932	−0.664661	+	0.747145i	$0.731424\pi$
$138$	7.44769	0.633990
$139$	9.87107	0.837253	0.418627	−	0.908158i	$-0.362512\pi$
$139$	9.87107	0.837253	0.418627	+	0.908158i	$0.362512\pi$
$140$	0.961819	0.0812885
$141$	−17.7383	−1.49384
$142$	−1.63446	−0.137161
$143$	−2.37582	−0.198676
$144$	−0.103166	−0.00859713
$145$	−5.05157	−0.419510
$146$	9.11062	0.754000
$147$	−10.3395	−0.852791
$148$	−9.05446	−0.744272
$149$	19.6052	1.60612	0.803060	−	0.595898i	$-0.203204\pi$
$149$	19.6052	1.60612	0.803060	+	0.595898i	$0.203204\pi$
$150$	−1.70201	−0.138968
$151$	−8.91621	−0.725591	−0.362795	−	0.931869i	$-0.618178\pi$
$151$	−8.91621	−0.725591	−0.362795	+	0.931869i	$0.618178\pi$
$152$	0.413677	0.0335537
$153$	−0.0213002	−0.00172202
$154$	−0.961819	−0.0775056
$155$	−6.59571	−0.529780
$156$	−4.04367	−0.323753
$157$	13.1048	1.04588	0.522940	−	0.852369i	$-0.324835\pi$
$157$	13.1048	1.04588	0.522940	+	0.852369i	$0.324835\pi$
$158$	−2.19376	−0.174527
$159$	16.7017	1.32453
$160$	−1.00000	−0.0790569
$161$	−4.20875	−0.331696
$162$	8.67986	0.681954
$163$	9.93240	0.777965	0.388983	−	0.921245i	$-0.372827\pi$
$163$	9.93240	0.777965	0.388983	+	0.921245i	$0.372827\pi$
$164$	−7.15062	−0.558370
$165$	1.70201	0.132501
$166$	5.54961	0.430733
$167$	5.82283	0.450584	0.225292	−	0.974291i	$-0.427666\pi$
$167$	5.82283	0.450584	0.225292	+	0.974291i	$0.427666\pi$
$168$	−1.63702	−0.126299
$169$	−7.35546	−0.565805
$170$	−0.206466	−0.0158353
$171$	0.0426772	0.00326361
$172$	−1.00000	−0.0762493
$173$	21.4892	1.63379	0.816897	−	0.576784i	$-0.195693\pi$
$173$	21.4892	1.63379	0.816897	+	0.576784i	$0.195693\pi$
$174$	8.59782	0.651799
$175$	0.961819	0.0727067
$176$	1.00000	0.0753778
$177$	8.88246	0.667647
$178$	16.7071	1.25225
$179$	−5.87243	−0.438926	−0.219463	−	0.975621i	$-0.570431\pi$
$179$	−5.87243	−0.438926	−0.219463	+	0.975621i	$0.570431\pi$
$180$	−0.103166	−0.00768950
$181$	2.70569	0.201113	0.100556	−	0.994931i	$-0.467938\pi$
$181$	2.70569	0.201113	0.100556	+	0.994931i	$0.467938\pi$
$182$	2.28511	0.169384
$183$	12.8445	0.949490
$184$	4.37582	0.322590
$185$	−9.05446	−0.665697
$186$	11.2260	0.823127
$187$	0.206466	0.0150983
$188$	−10.4220	−0.760102
$189$	−5.07996	−0.369513
$190$	0.413677	0.0300113
$191$	17.2199	1.24599	0.622994	−	0.782227i	$-0.285916\pi$
$191$	17.2199	1.24599	0.622994	+	0.782227i	$0.285916\pi$
$192$	1.70201	0.122832
$193$	−9.74778	−0.701660	−0.350830	−	0.936439i	$-0.614101\pi$
$193$	−9.74778	−0.701660	−0.350830	+	0.936439i	$0.614101\pi$
$194$	−2.79975	−0.201010
$195$	−4.04367	−0.289574
$196$	−6.07490	−0.433922
$197$	−20.1939	−1.43875	−0.719377	−	0.694619i	$-0.755573\pi$
$197$	−20.1939	−1.43875	−0.719377	+	0.694619i	$0.755573\pi$
$198$	0.103166	0.00733165
$199$	−11.4718	−0.813216	−0.406608	−	0.913603i	$-0.633289\pi$
$199$	−11.4718	−0.813216	−0.406608	+	0.913603i	$0.633289\pi$
$200$	−1.00000	−0.0707107
$201$	12.1133	0.854405
$202$	−18.4724	−1.29971
$203$	−4.85869	−0.341013
$204$	0.351408	0.0246035
$205$	−7.15062	−0.499421
$206$	14.9220	1.03966
$207$	0.451434	0.0313768
$208$	−2.37582	−0.164734
$209$	−0.413677	−0.0286147
$210$	−1.63702	−0.112965
$211$	−4.90180	−0.337454	−0.168727	−	0.985663i	$-0.553966\pi$
$211$	−4.90180	−0.337454	−0.168727	+	0.985663i	$0.553966\pi$
$212$	9.81295	0.673956
$213$	2.78186	0.190610
$214$	−17.2230	−1.17734
$215$	−1.00000	−0.0681994
$216$	5.28162	0.359368
$217$	−6.34388	−0.430650
$218$	−4.94258	−0.334753
$219$	−15.5064	−1.04782
$220$	1.00000	0.0674200
$221$	−0.490528	−0.0329965
$222$	15.4108	1.03430
$223$	23.1695	1.55155	0.775773	−	0.631012i	$-0.217360\pi$
$223$	23.1695	1.55155	0.775773	+	0.631012i	$0.217360\pi$
$224$	−0.961819	−0.0642642
$225$	−0.103166	−0.00687770
$226$	1.33914	0.0890785
$227$	1.95283	0.129614	0.0648068	−	0.997898i	$-0.479357\pi$
$227$	1.95283	0.129614	0.0648068	+	0.997898i	$0.479357\pi$
$228$	−0.704082	−0.0466290
$229$	−27.9257	−1.84538	−0.922692	−	0.385537i	$-0.874016\pi$
$229$	−27.9257	−1.84538	−0.922692	+	0.385537i	$0.874016\pi$
$230$	4.37582	0.288533
$231$	1.63702	0.107708
$232$	5.05157	0.331652
$233$	−17.6982	−1.15945	−0.579724	−	0.814813i	$-0.696840\pi$
$233$	−17.6982	−1.15945	−0.579724	+	0.814813i	$0.696840\pi$
$234$	−0.245103	−0.0160229
$235$	−10.4220	−0.679856
$236$	5.21881	0.339716
$237$	3.73381	0.242537
$238$	−0.198583	−0.0128722
$239$	1.11014	0.0718088	0.0359044	−	0.999355i	$-0.488569\pi$
$239$	1.11014	0.0718088	0.0359044	+	0.999355i	$0.488569\pi$
$240$	1.70201	0.109864
$241$	7.88619	0.507994	0.253997	−	0.967205i	$-0.418255\pi$
$241$	7.88619	0.507994	0.253997	+	0.967205i	$0.418255\pi$
$242$	−1.00000	−0.0642824
$243$	1.07165	0.0687461
$244$	7.54665	0.483124
$245$	−6.07490	−0.388111
$246$	12.1704	0.775958
$247$	0.982824	0.0625356
$248$	6.59571	0.418828
$249$	−9.44548	−0.598583
$250$	−1.00000	−0.0632456
$251$	15.9387	1.00604	0.503020	−	0.864275i	$-0.332222\pi$
$251$	15.9387	1.00604	0.503020	+	0.864275i	$0.332222\pi$
$252$	−0.0992265	−0.00625068
$253$	−4.37582	−0.275106
$254$	2.61565	0.164121
$255$	0.351408	0.0220060
$256$	1.00000	0.0625000
$257$	1.73607	0.108293	0.0541465	−	0.998533i	$-0.482756\pi$
$257$	1.73607	0.108293	0.0541465	+	0.998533i	$0.482756\pi$
$258$	1.70201	0.105962
$259$	−8.70875	−0.541135
$260$	−2.37582	−0.147342
$261$	0.521148	0.0322582
$262$	9.98567	0.616917
$263$	3.85858	0.237931	0.118965	−	0.992898i	$-0.462042\pi$
$263$	3.85858	0.237931	0.118965	+	0.992898i	$0.462042\pi$
$264$	−1.70201	−0.104751
$265$	9.81295	0.602805
$266$	0.397883	0.0243957
$267$	−28.4356	−1.74023
$268$	7.11705	0.434743
$269$	−0.849440	−0.0517913	−0.0258957	−	0.999665i	$-0.508244\pi$
$269$	−0.849440	−0.0517913	−0.0258957	+	0.999665i	$0.508244\pi$
$270$	5.28162	0.321429
$271$	8.59360	0.522024	0.261012	−	0.965336i	$-0.415944\pi$
$271$	8.59360	0.522024	0.261012	+	0.965336i	$0.415944\pi$
$272$	0.206466	0.0125189
$273$	−3.88928	−0.235390
$274$	15.5593	0.939972
$275$	1.00000	0.0603023
$276$	−7.44769	−0.448298
$277$	9.73658	0.585015	0.292507	−	0.956263i	$-0.405510\pi$
$277$	9.73658	0.585015	0.292507	+	0.956263i	$0.405510\pi$
$278$	−9.87107	−0.592028
$279$	0.680450	0.0407374
$280$	−0.961819	−0.0574797
$281$	−8.69294	−0.518578	−0.259289	−	0.965800i	$-0.583488\pi$
$281$	−8.69294	−0.518578	−0.259289	+	0.965800i	$0.583488\pi$
$282$	17.7383	1.05630
$283$	−8.80745	−0.523548	−0.261774	−	0.965129i	$-0.584308\pi$
$283$	−8.80745	−0.523548	−0.261774	+	0.965129i	$0.584308\pi$
$284$	1.63446	0.0969872
$285$	−0.704082	−0.0417062
$286$	2.37582	0.140485
$287$	−6.87760	−0.405972
$288$	0.103166	0.00607909
$289$	−16.9574	−0.997492
$290$	5.05157	0.296638
$291$	4.76520	0.279341
$292$	−9.11062	−0.533159
$293$	9.46882	0.553174	0.276587	−	0.960989i	$-0.410797\pi$
$293$	9.46882	0.553174	0.276587	+	0.960989i	$0.410797\pi$
$294$	10.3395	0.603014
$295$	5.21881	0.303851
$296$	9.05446	0.526280
$297$	−5.28162	−0.306470
$298$	−19.6052	−1.13570
$299$	10.3962	0.601227
$300$	1.70201	0.0982655
$301$	−0.961819	−0.0554383
$302$	8.91621	0.513070
$303$	31.4402	1.80619
$304$	−0.413677	−0.0237260
$305$	7.54665	0.432120
$306$	0.0213002	0.00121765
$307$	−8.96899	−0.511887	−0.255944	−	0.966692i	$-0.582386\pi$
$307$	−8.96899	−0.511887	−0.255944	+	0.966692i	$0.582386\pi$
$308$	0.961819	0.0548047
$309$	−25.3973	−1.44480
$310$	6.59571	0.374611
$311$	18.6547	1.05781	0.528905	−	0.848681i	$-0.322603\pi$
$311$	18.6547	1.05781	0.528905	+	0.848681i	$0.322603\pi$
$312$	4.04367	0.228928
$313$	25.3697	1.43398	0.716990	−	0.697084i	$-0.245519\pi$
$313$	25.3697	1.43398	0.716990	+	0.697084i	$0.245519\pi$
$314$	−13.1048	−0.739549
$315$	−0.0992265	−0.00559078
$316$	2.19376	0.123409
$317$	−28.8646	−1.62120	−0.810600	−	0.585600i	$-0.800859\pi$
$317$	−28.8646	−1.62120	−0.810600	+	0.585600i	$0.800859\pi$
$318$	−16.7017	−0.936586
$319$	−5.05157	−0.282834
$320$	1.00000	0.0559017
$321$	29.3136	1.63613
$322$	4.20875	0.234545
$323$	−0.0854105	−0.00475236
$324$	−8.67986	−0.482214
$325$	−2.37582	−0.131787
$326$	−9.93240	−0.550105
$327$	8.41231	0.465202
$328$	7.15062	0.394827
$329$	−10.0241	−0.552645
$330$	−1.70201	−0.0936925
$331$	32.7920	1.80241	0.901205	−	0.433394i	$-0.142684\pi$
$331$	32.7920	1.80241	0.901205	+	0.433394i	$0.142684\pi$
$332$	−5.54961	−0.304574
$333$	0.934108	0.0511888
$334$	−5.82283	−0.318611
$335$	7.11705	0.388846
$336$	1.63702	0.0893070
$337$	−26.1589	−1.42497	−0.712483	−	0.701689i	$-0.752430\pi$
$337$	−26.1589	−1.42497	−0.712483	+	0.701689i	$0.752430\pi$
$338$	7.35546	0.400084
$339$	−2.27923	−0.123791
$340$	0.206466	0.0111972
$341$	−6.59571	−0.357178
$342$	−0.0426772	−0.00230772
$343$	−12.5757	−0.679023
$344$	1.00000	0.0539164
$345$	−7.44769	−0.400970
$346$	−21.4892	−1.15527
$347$	17.0650	0.916099	0.458049	−	0.888927i	$-0.348548\pi$
$347$	17.0650	0.916099	0.458049	+	0.888927i	$0.348548\pi$
$348$	−8.59782	−0.460891
$349$	22.3693	1.19740	0.598701	−	0.800973i	$-0.295684\pi$
$349$	22.3693	1.19740	0.598701	+	0.800973i	$0.295684\pi$
$350$	−0.961819	−0.0514114
$351$	12.5482	0.669773
$352$	−1.00000	−0.0533002
$353$	31.2738	1.66454	0.832269	−	0.554372i	$-0.187042\pi$
$353$	31.2738	1.66454	0.832269	+	0.554372i	$0.187042\pi$
$354$	−8.88246	−0.472098
$355$	1.63446	0.0867480
$356$	−16.7071	−0.885474
$357$	0.337991	0.0178884
$358$	5.87243	0.310368
$359$	24.3617	1.28576	0.642881	−	0.765966i	$-0.277739\pi$
$359$	24.3617	1.28576	0.642881	+	0.765966i	$0.277739\pi$
$360$	0.103166	0.00543730
$361$	−18.8289	−0.990993
$362$	−2.70569	−0.142208
$363$	1.70201	0.0893323
$364$	−2.28511	−0.119772
$365$	−9.11062	−0.476872
$366$	−12.8445	−0.671391
$367$	−30.0924	−1.57081	−0.785404	−	0.618983i	$-0.787545\pi$
$367$	−30.0924	−1.57081	−0.785404	+	0.618983i	$0.787545\pi$
$368$	−4.37582	−0.228106
$369$	0.737698	0.0384030
$370$	9.05446	0.470719
$371$	9.43828	0.490011
$372$	−11.2260	−0.582039
$373$	7.87615	0.407811	0.203906	−	0.978991i	$-0.434636\pi$
$373$	7.87615	0.407811	0.203906	+	0.978991i	$0.434636\pi$
$374$	−0.206466	−0.0106761
$375$	1.70201	0.0878914
$376$	10.4220	0.537473
$377$	12.0016	0.618116
$378$	5.07996	0.261285
$379$	−33.5862	−1.72521	−0.862603	−	0.505882i	$-0.831167\pi$
$379$	−33.5862	−1.72521	−0.862603	+	0.505882i	$0.831167\pi$
$380$	−0.413677	−0.0212212
$381$	−4.45186	−0.228076
$382$	−17.2199	−0.881046
$383$	−35.5745	−1.81777	−0.908886	−	0.417044i	$-0.863066\pi$
$383$	−35.5745	−1.81777	−0.908886	+	0.417044i	$0.863066\pi$
$384$	−1.70201	−0.0868553
$385$	0.961819	0.0490188
$386$	9.74778	0.496149
$387$	0.103166	0.00524420
$388$	2.79975	0.142136
$389$	−9.06568	−0.459648	−0.229824	−	0.973232i	$-0.573815\pi$
$389$	−9.06568	−0.459648	−0.229824	+	0.973232i	$0.573815\pi$
$390$	4.04367	0.204759
$391$	−0.903461	−0.0456900
$392$	6.07490	0.306829
$393$	−16.9957	−0.857319
$394$	20.1939	1.01735
$395$	2.19376	0.110380
$396$	−0.103166	−0.00518426
$397$	−13.6754	−0.686350	−0.343175	−	0.939272i	$-0.611502\pi$
$397$	−13.6754	−0.686350	−0.343175	+	0.939272i	$0.611502\pi$
$398$	11.4718	0.575031
$399$	−0.677200	−0.0339024
$400$	1.00000	0.0500000
$401$	21.7514	1.08622	0.543108	−	0.839663i	$-0.317247\pi$
$401$	21.7514	1.08622	0.543108	+	0.839663i	$0.317247\pi$
$402$	−12.1133	−0.604156
$403$	15.6702	0.780590
$404$	18.4724	0.919036
$405$	−8.67986	−0.431306
$406$	4.85869	0.241133
$407$	−9.05446	−0.448813
$408$	−0.351408	−0.0173973
$409$	19.7331	0.975737	0.487869	−	0.872917i	$-0.337775\pi$
$409$	19.7331	0.975737	0.487869	+	0.872917i	$0.337775\pi$
$410$	7.15062	0.353144
$411$	−26.4821	−1.30626
$412$	−14.9220	−0.735153
$413$	5.01955	0.246996
$414$	−0.451434	−0.0221868
$415$	−5.54961	−0.272419
$416$	2.37582	0.116484
$417$	16.8007	0.822731
$418$	0.413677	0.0202336
$419$	−33.4352	−1.63342	−0.816708	−	0.577052i	$-0.804203\pi$
$419$	−33.4352	−1.63342	−0.816708	+	0.577052i	$0.804203\pi$
$420$	1.63702	0.0798786
$421$	16.1852	0.788820	0.394410	−	0.918935i	$-0.370949\pi$
$421$	16.1852	0.788820	0.394410	+	0.918935i	$0.370949\pi$
$422$	4.90180	0.238616
$423$	1.07519	0.0522775
$424$	−9.81295	−0.476559
$425$	0.206466	0.0100151
$426$	−2.78186	−0.134782
$427$	7.25851	0.351264
$428$	17.2230	0.832503
$429$	−4.04367	−0.195230
$430$	1.00000	0.0482243
$431$	23.9093	1.15167	0.575834	−	0.817566i	$-0.304677\pi$
$431$	23.9093	1.15167	0.575834	+	0.817566i	$0.304677\pi$
$432$	−5.28162	−0.254112
$433$	−26.9709	−1.29614	−0.648069	−	0.761581i	$-0.724423\pi$
$433$	−26.9709	−1.29614	−0.648069	+	0.761581i	$0.724423\pi$
$434$	6.34388	0.304516
$435$	−8.59782	−0.412234
$436$	4.94258	0.236706
$437$	1.81018	0.0865926
$438$	15.5064	0.740923
$439$	−34.1093	−1.62795	−0.813974	−	0.580901i	$-0.802700\pi$
$439$	−34.1093	−1.62795	−0.813974	+	0.580901i	$0.802700\pi$
$440$	−1.00000	−0.0476731
$441$	0.626721	0.0298438
$442$	0.490528	0.0233320
$443$	−16.1902	−0.769220	−0.384610	−	0.923079i	$-0.625664\pi$
$443$	−16.1902	−0.769220	−0.384610	+	0.923079i	$0.625664\pi$
$444$	−15.4108	−0.731363
$445$	−16.7071	−0.791992
$446$	−23.1695	−1.09711
$447$	33.3682	1.57826
$448$	0.961819	0.0454417
$449$	15.2420	0.719315	0.359657	−	0.933084i	$-0.382894\pi$
$449$	15.2420	0.719315	0.359657	+	0.933084i	$0.382894\pi$
$450$	0.103166	0.00486327
$451$	−7.15062	−0.336710
$452$	−1.33914	−0.0629880
$453$	−15.1755	−0.713006
$454$	−1.95283	−0.0916507
$455$	−2.28511	−0.107128
$456$	0.704082	0.0329717
$457$	−12.3146	−0.576054	−0.288027	−	0.957622i	$-0.592999\pi$
$457$	−12.3146	−0.576054	−0.288027	+	0.957622i	$0.592999\pi$
$458$	27.9257	1.30488
$459$	−1.09048	−0.0508991
$460$	−4.37582	−0.204024
$461$	−7.78904	−0.362772	−0.181386	−	0.983412i	$-0.558058\pi$
$461$	−7.78904	−0.362772	−0.181386	+	0.983412i	$0.558058\pi$
$462$	−1.63702	−0.0761613
$463$	−32.6817	−1.51885	−0.759424	−	0.650596i	$-0.774519\pi$
$463$	−32.6817	−1.51885	−0.759424	+	0.650596i	$0.774519\pi$
$464$	−5.05157	−0.234513
$465$	−11.2260	−0.520591
$466$	17.6982	0.819853
$467$	4.73048	0.218900	0.109450	−	0.993992i	$-0.465091\pi$
$467$	4.73048	0.218900	0.109450	+	0.993992i	$0.465091\pi$
$468$	0.245103	0.0113299
$469$	6.84531	0.316087
$470$	10.4220	0.480731
$471$	22.3046	1.02774
$472$	−5.21881	−0.240215
$473$	−1.00000	−0.0459800
$474$	−3.73381	−0.171499
$475$	−0.413677	−0.0189808
$476$	0.198583	0.00910205
$477$	−1.01236	−0.0463527
$478$	−1.11014	−0.0507765
$479$	4.04389	0.184770	0.0923851	−	0.995723i	$-0.470551\pi$
$479$	4.04389	0.184770	0.0923851	+	0.995723i	$0.470551\pi$
$480$	−1.70201	−0.0776857
$481$	21.5118	0.980854
$482$	−7.88619	−0.359206
$483$	−7.16333	−0.325943
$484$	1.00000	0.0454545
$485$	2.79975	0.127130
$486$	−1.07165	−0.0486109
$487$	−3.81325	−0.172795	−0.0863975	−	0.996261i	$-0.527536\pi$
$487$	−3.81325	−0.172795	−0.0863975	+	0.996261i	$0.527536\pi$
$488$	−7.54665	−0.341621
$489$	16.9050	0.764472
$490$	6.07490	0.274436
$491$	−34.9008	−1.57505	−0.787526	−	0.616281i	$-0.788639\pi$
$491$	−34.9008	−1.57505	−0.787526	+	0.616281i	$0.788639\pi$
$492$	−12.1704	−0.548685
$493$	−1.04298	−0.0469734
$494$	−0.982824	−0.0442194
$495$	−0.103166	−0.00463694
$496$	−6.59571	−0.296156
$497$	1.57205	0.0705162
$498$	9.44548	0.423262
$499$	−14.5870	−0.653005	−0.326502	−	0.945196i	$-0.605870\pi$
$499$	−14.5870	−0.653005	−0.326502	+	0.945196i	$0.605870\pi$
$500$	1.00000	0.0447214
$501$	9.91050	0.442769
$502$	−15.9387	−0.711378
$503$	−12.2195	−0.544840	−0.272420	−	0.962179i	$-0.587824\pi$
$503$	−12.2195	−0.544840	−0.272420	+	0.962179i	$0.587824\pi$
$504$	0.0992265	0.00441990
$505$	18.4724	0.822011
$506$	4.37582	0.194529
$507$	−12.5191	−0.555991
$508$	−2.61565	−0.116051
$509$	11.9850	0.531226	0.265613	−	0.964080i	$-0.414426\pi$
$509$	11.9850	0.531226	0.265613	+	0.964080i	$0.414426\pi$
$510$	−0.351408	−0.0155606
$511$	−8.76277	−0.387642
$512$	−1.00000	−0.0441942
$513$	2.18488	0.0964650
$514$	−1.73607	−0.0765747
$515$	−14.9220	−0.657541
$516$	−1.70201	−0.0749268
$517$	−10.4220	−0.458359
$518$	8.70875	0.382641
$519$	36.5748	1.60546
$520$	2.37582	0.104187
$521$	12.3064	0.539151	0.269576	−	0.962979i	$-0.413117\pi$
$521$	12.3064	0.539151	0.269576	+	0.962979i	$0.413117\pi$
$522$	−0.521148	−0.0228100
$523$	24.2620	1.06090	0.530451	−	0.847715i	$-0.322022\pi$
$523$	24.2620	1.06090	0.530451	+	0.847715i	$0.322022\pi$
$524$	−9.98567	−0.436226
$525$	1.63702	0.0714456
$526$	−3.85858	−0.168242
$527$	−1.36179	−0.0593206
$528$	1.70201	0.0740704
$529$	−3.85216	−0.167485
$530$	−9.81295	−0.426247
$531$	−0.538401	−0.0233646
$532$	−0.397883	−0.0172504
$533$	16.9886	0.735859
$534$	28.4356	1.23053
$535$	17.2230	0.744614
$536$	−7.11705	−0.307410
$537$	−9.99493	−0.431313
$538$	0.849440	0.0366220
$539$	−6.07490	−0.261665
$540$	−5.28162	−0.227285
$541$	3.56831	0.153414	0.0767068	−	0.997054i	$-0.475559\pi$
$541$	3.56831	0.153414	0.0767068	+	0.997054i	$0.475559\pi$
$542$	−8.59360	−0.369127
$543$	4.60511	0.197624
$544$	−0.206466	−0.00885217
$545$	4.94258	0.211717
$546$	3.88928	0.166446
$547$	15.1247	0.646684	0.323342	−	0.946282i	$-0.395194\pi$
$547$	15.1247	0.646684	0.323342	+	0.946282i	$0.395194\pi$
$548$	−15.5593	−0.664661
$549$	−0.778553	−0.0332279
$550$	−1.00000	−0.0426401
$551$	2.08972	0.0890250
$552$	7.44769	0.316995
$553$	2.11000	0.0897265
$554$	−9.73658	−0.413668
$555$	−15.4108	−0.654151
$556$	9.87107	0.418627
$557$	−0.572118	−0.0242414	−0.0121207	−	0.999927i	$-0.503858\pi$
$557$	−0.572118	−0.0242414	−0.0121207	+	0.999927i	$0.503858\pi$
$558$	−0.680450	−0.0288057
$559$	2.37582	0.100487
$560$	0.961819	0.0406443
$561$	0.351408	0.0148364
$562$	8.69294	0.366690
$563$	37.1756	1.56676	0.783382	−	0.621540i	$-0.213493\pi$
$563$	37.1756	1.56676	0.783382	+	0.621540i	$0.213493\pi$
$564$	−17.7383	−0.746918
$565$	−1.33914	−0.0563382
$566$	8.80745	0.370205
$567$	−8.34845	−0.350602
$568$	−1.63446	−0.0685803
$569$	14.7054	0.616482	0.308241	−	0.951308i	$-0.400260\pi$
$569$	14.7054	0.616482	0.308241	+	0.951308i	$0.400260\pi$
$570$	0.704082	0.0294908
$571$	22.3192	0.934029	0.467014	−	0.884250i	$-0.345330\pi$
$571$	22.3192	0.934029	0.467014	+	0.884250i	$0.345330\pi$
$572$	−2.37582	−0.0993382
$573$	29.3084	1.22438
$574$	6.87760	0.287066
$575$	−4.37582	−0.182484
$576$	−0.103166	−0.00429856
$577$	−29.7288	−1.23763	−0.618814	−	0.785538i	$-0.712387\pi$
$577$	−29.7288	−1.23763	−0.618814	+	0.785538i	$0.712387\pi$
$578$	16.9574	0.705334
$579$	−16.5908	−0.689490
$580$	−5.05157	−0.209755
$581$	−5.33772	−0.221446
$582$	−4.76520	−0.197524
$583$	9.81295	0.406411
$584$	9.11062	0.377000
$585$	0.245103	0.0101338
$586$	−9.46882	−0.391153
$587$	−27.2434	−1.12445	−0.562227	−	0.826983i	$-0.690055\pi$
$587$	−27.2434	−1.12445	−0.562227	+	0.826983i	$0.690055\pi$
$588$	−10.3395	−0.426396
$589$	2.72849	0.112426
$590$	−5.21881	−0.214855
$591$	−34.3702	−1.41380
$592$	−9.05446	−0.372136
$593$	−10.1627	−0.417333	−0.208666	−	0.977987i	$-0.566912\pi$
$593$	−10.1627	−0.417333	−0.208666	+	0.977987i	$0.566912\pi$
$594$	5.28162	0.216707
$595$	0.198583	0.00814112
$596$	19.6052	0.803060
$597$	−19.5251	−0.799111
$598$	−10.3962	−0.425132
$599$	8.32534	0.340164	0.170082	−	0.985430i	$-0.445597\pi$
$599$	8.32534	0.340164	0.170082	+	0.985430i	$0.445597\pi$
$600$	−1.70201	−0.0694842
$601$	−15.7094	−0.640799	−0.320400	−	0.947282i	$-0.603817\pi$
$601$	−15.7094	−0.640799	−0.320400	+	0.947282i	$0.603817\pi$
$602$	0.961819	0.0392008
$603$	−0.734234	−0.0299003
$604$	−8.91621	−0.362795
$605$	1.00000	0.0406558
$606$	−31.4402	−1.27717
$607$	−32.9503	−1.33741	−0.668706	−	0.743527i	$-0.733151\pi$
$607$	−32.9503	−1.33741	−0.668706	+	0.743527i	$0.733151\pi$
$608$	0.413677	0.0167768
$609$	−8.26954	−0.335099
$610$	−7.54665	−0.305555
$611$	24.7608	1.00172
$612$	−0.0213002	−0.000861010 0
$613$	−28.9790	−1.17045	−0.585226	−	0.810870i	$-0.698994\pi$
$613$	−28.9790	−1.17045	−0.585226	+	0.810870i	$0.698994\pi$
$614$	8.96899	0.361959
$615$	−12.1704	−0.490759
$616$	−0.961819	−0.0387528
$617$	−17.1103	−0.688833	−0.344416	−	0.938817i	$-0.611923\pi$
$617$	−17.1103	−0.688833	−0.344416	+	0.938817i	$0.611923\pi$
$618$	25.3973	1.02163
$619$	7.74766	0.311405	0.155702	−	0.987804i	$-0.450236\pi$
$619$	7.74766	0.311405	0.155702	+	0.987804i	$0.450236\pi$
$620$	−6.59571	−0.264890
$621$	23.1114	0.927429
$622$	−18.6547	−0.747985
$623$	−16.0692	−0.643799
$624$	−4.04367	−0.161877
$625$	1.00000	0.0400000
$626$	−25.3697	−1.01398
$627$	−0.704082	−0.0281183
$628$	13.1048	0.522940
$629$	−1.86944	−0.0745395
$630$	0.0992265	0.00395328
$631$	−11.5964	−0.461646	−0.230823	−	0.972996i	$-0.574142\pi$
$631$	−11.5964	−0.461646	−0.230823	+	0.972996i	$0.574142\pi$
$632$	−2.19376	−0.0872633
$633$	−8.34291	−0.331601
$634$	28.8646	1.14636
$635$	−2.61565	−0.103799
$636$	16.7017	0.662267
$637$	14.4329	0.571853
$638$	5.05157	0.199994
$639$	−0.168620	−0.00667049
$640$	−1.00000	−0.0395285
$641$	3.15569	0.124642	0.0623211	−	0.998056i	$-0.480150\pi$
$641$	3.15569	0.124642	0.0623211	+	0.998056i	$0.480150\pi$
$642$	−29.3136	−1.15692
$643$	−23.6766	−0.933715	−0.466858	−	0.884332i	$-0.654614\pi$
$643$	−23.6766	−0.933715	−0.466858	+	0.884332i	$0.654614\pi$
$644$	−4.20875	−0.165848
$645$	−1.70201	−0.0670165
$646$	0.0854105	0.00336043
$647$	33.0208	1.29818	0.649091	−	0.760710i	$-0.275149\pi$
$647$	33.0208	1.29818	0.649091	+	0.760710i	$0.275149\pi$
$648$	8.67986	0.340977
$649$	5.21881	0.204856
$650$	2.37582	0.0931875
$651$	−10.7973	−0.423181
$652$	9.93240	0.388983
$653$	−39.1416	−1.53173	−0.765865	−	0.643001i	$-0.777689\pi$
$653$	−39.1416	−1.53173	−0.765865	+	0.643001i	$0.777689\pi$
$654$	−8.41231	−0.328947
$655$	−9.98567	−0.390172
$656$	−7.15062	−0.279185
$657$	0.939902	0.0366691
$658$	10.0241	0.390779
$659$	−33.6319	−1.31011	−0.655056	−	0.755580i	$-0.727355\pi$
$659$	−33.6319	−1.31011	−0.655056	+	0.755580i	$0.727355\pi$
$660$	1.70201	0.0662506
$661$	43.8811	1.70678	0.853389	−	0.521275i	$-0.174543\pi$
$661$	43.8811	1.70678	0.853389	+	0.521275i	$0.174543\pi$
$662$	−32.7920	−1.27450
$663$	−0.834883	−0.0324242
$664$	5.54961	0.215366
$665$	−0.397883	−0.0154292
$666$	−0.934108	−0.0361959
$667$	22.1048	0.855900
$668$	5.82283	0.225292
$669$	39.4347	1.52463
$670$	−7.11705	−0.274956
$671$	7.54665	0.291335
$672$	−1.63702	−0.0631496
$673$	−14.1334	−0.544802	−0.272401	−	0.962184i	$-0.587818\pi$
$673$	−14.1334	−0.544802	−0.272401	+	0.962184i	$0.587818\pi$
$674$	26.1589	1.00760
$675$	−5.28162	−0.203289
$676$	−7.35546	−0.282902
$677$	−20.3729	−0.782995	−0.391498	−	0.920179i	$-0.628043\pi$
$677$	−20.3729	−0.782995	−0.391498	+	0.920179i	$0.628043\pi$
$678$	2.27923	0.0875334
$679$	2.69285	0.103342
$680$	−0.206466	−0.00791763
$681$	3.32373	0.127366
$682$	6.59571	0.252563
$683$	16.1894	0.619471	0.309736	−	0.950823i	$-0.399759\pi$
$683$	16.1894	0.619471	0.309736	+	0.950823i	$0.399759\pi$
$684$	0.0426772	0.00163180
$685$	−15.5593	−0.594491
$686$	12.5757	0.480142
$687$	−47.5299	−1.81338
$688$	−1.00000	−0.0381246
$689$	−23.3138	−0.888187
$690$	7.44769	0.283529
$691$	10.5271	0.400470	0.200235	−	0.979748i	$-0.435829\pi$
$691$	10.5271	0.400470	0.200235	+	0.979748i	$0.435829\pi$
$692$	21.4892	0.816897
$693$	−0.0992265	−0.00376930
$694$	−17.0650	−0.647779
$695$	9.87107	0.374431
$696$	8.59782	0.325899
$697$	−1.47636	−0.0559212
$698$	−22.3693	−0.846690
$699$	−30.1225	−1.13934
$700$	0.961819	0.0363533
$701$	37.6120	1.42059	0.710293	−	0.703906i	$-0.248562\pi$
$701$	37.6120	1.42059	0.710293	+	0.703906i	$0.248562\pi$
$702$	−12.5482	−0.473601
$703$	3.74562	0.141269
$704$	1.00000	0.0376889
$705$	−17.7383	−0.668064
$706$	−31.2738	−1.17701
$707$	17.7671	0.668200
$708$	8.88246	0.333823
$709$	−5.33959	−0.200532	−0.100266	−	0.994961i	$-0.531969\pi$
$709$	−5.33959	−0.200532	−0.100266	+	0.994961i	$0.531969\pi$
$710$	−1.63446	−0.0613401
$711$	−0.226321	−0.00848769
$712$	16.7071	0.626125
$713$	28.8617	1.08088
$714$	−0.337991	−0.0126490
$715$	−2.37582	−0.0888508
$716$	−5.87243	−0.219463
$717$	1.88946	0.0705633
$718$	−24.3617	−0.909171
$719$	28.7331	1.07156	0.535782	−	0.844356i	$-0.320017\pi$
$719$	28.7331	1.07156	0.535782	+	0.844356i	$0.320017\pi$
$720$	−0.103166	−0.00384475
$721$	−14.3522	−0.534505
$722$	18.8289	0.700738
$723$	13.4224	0.499183
$724$	2.70569	0.100556
$725$	−5.05157	−0.187611
$726$	−1.70201	−0.0631675
$727$	−40.7811	−1.51249	−0.756244	−	0.654289i	$-0.772968\pi$
$727$	−40.7811	−1.51249	−0.756244	+	0.654289i	$0.772968\pi$
$728$	2.28511	0.0846919
$729$	27.8635	1.03198
$730$	9.11062	0.337199
$731$	−0.206466	−0.00763644
$732$	12.8445	0.474745
$733$	−0.227142	−0.00838967	−0.00419484	−	0.999991i	$-0.501335\pi$
$733$	−0.227142	−0.00838967	−0.00419484	+	0.999991i	$0.501335\pi$
$734$	30.0924	1.11073
$735$	−10.3395	−0.381380
$736$	4.37582	0.161295
$737$	7.11705	0.262160
$738$	−0.737698	−0.0271550
$739$	−20.3171	−0.747375	−0.373688	−	0.927555i	$-0.621907\pi$
$739$	−20.3171	−0.747375	−0.373688	+	0.927555i	$0.621907\pi$
$740$	−9.05446	−0.332849
$741$	1.67278	0.0614510
$742$	−9.43828	−0.346490
$743$	34.4385	1.26343	0.631713	−	0.775202i	$-0.282352\pi$
$743$	34.4385	1.26343	0.631713	+	0.775202i	$0.282352\pi$
$744$	11.2260	0.411563
$745$	19.6052	0.718279
$746$	−7.87615	−0.288366
$747$	0.572528	0.0209477
$748$	0.206466	0.00754916
$749$	16.5654	0.605286
$750$	−1.70201	−0.0621486
$751$	17.0082	0.620638	0.310319	−	0.950632i	$-0.399564\pi$
$751$	17.0082	0.620638	0.310319	+	0.950632i	$0.399564\pi$
$752$	−10.4220	−0.380051
$753$	27.1278	0.988591
$754$	−12.0016	−0.437074
$755$	−8.91621	−0.324494
$756$	−5.07996	−0.184756
$757$	−14.1239	−0.513342	−0.256671	−	0.966499i	$-0.582626\pi$
$757$	−14.1239	−0.513342	−0.256671	+	0.966499i	$0.582626\pi$
$758$	33.5862	1.21990
$759$	−7.44769	−0.270334
$760$	0.413677	0.0150057
$761$	−44.1831	−1.60163	−0.800817	−	0.598909i	$-0.795601\pi$
$761$	−44.1831	−1.60163	−0.800817	+	0.598909i	$0.795601\pi$
$762$	4.45186	0.161274
$763$	4.75386	0.172101
$764$	17.2199	0.622994
$765$	−0.0213002	−0.000770111 0
$766$	35.5745	1.28536
$767$	−12.3990	−0.447701
$768$	1.70201	0.0614160
$769$	−4.06495	−0.146586	−0.0732929	−	0.997310i	$-0.523351\pi$
$769$	−4.06495	−0.146586	−0.0732929	+	0.997310i	$0.523351\pi$
$770$	−0.961819	−0.0346615
$771$	2.95480	0.106415
$772$	−9.74778	−0.350830
$773$	13.8922	0.499669	0.249834	−	0.968289i	$-0.419624\pi$
$773$	13.8922	0.499669	0.249834	+	0.968289i	$0.419624\pi$
$774$	−0.103166	−0.00370821
$775$	−6.59571	−0.236925
$776$	−2.79975	−0.100505
$777$	−14.8224	−0.531750
$778$	9.06568	0.325020
$779$	2.95805	0.105983
$780$	−4.04367	−0.144787
$781$	1.63446	0.0584855
$782$	0.903461	0.0323077
$783$	26.6804	0.953481
$784$	−6.07490	−0.216961
$785$	13.1048	0.467732
$786$	16.9957	0.606216
$787$	−16.0702	−0.572840	−0.286420	−	0.958104i	$-0.592465\pi$
$787$	−16.0702	−0.572840	−0.286420	+	0.958104i	$0.592465\pi$
$788$	−20.1939	−0.719377
$789$	6.56735	0.233804
$790$	−2.19376	−0.0780506
$791$	−1.28801	−0.0457965
$792$	0.103166	0.00366583
$793$	−17.9295	−0.636695
$794$	13.6754	0.485323
$795$	16.7017	0.592349
$796$	−11.4718	−0.406608
$797$	−24.5095	−0.868172	−0.434086	−	0.900872i	$-0.642929\pi$
$797$	−24.5095	−0.868172	−0.434086	+	0.900872i	$0.642929\pi$
$798$	0.677200	0.0239726
$799$	−2.15179	−0.0761249
$800$	−1.00000	−0.0353553
$801$	1.72360	0.0609002
$802$	−21.7514	−0.768070
$803$	−9.11062	−0.321507
$804$	12.1133	0.427203
$805$	−4.20875	−0.148339
$806$	−15.6702	−0.551961
$807$	−1.44576	−0.0508930
$808$	−18.4724	−0.649856
$809$	−22.7326	−0.799237	−0.399618	−	0.916682i	$-0.630857\pi$
$809$	−22.7326	−0.799237	−0.399618	+	0.916682i	$0.630857\pi$
$810$	8.67986	0.304979
$811$	8.81751	0.309625	0.154812	−	0.987944i	$-0.450523\pi$
$811$	8.81751	0.309625	0.154812	+	0.987944i	$0.450523\pi$
$812$	−4.85869	−0.170507
$813$	14.6264	0.512970
$814$	9.05446	0.317359
$815$	9.93240	0.347917
$816$	0.351408	0.0123017
$817$	0.413677	0.0144727
$818$	−19.7331	−0.689950
$819$	0.235745	0.00823759
$820$	−7.15062	−0.249711
$821$	39.0023	1.36119	0.680595	−	0.732660i	$-0.261721\pi$
$821$	39.0023	1.36119	0.680595	+	0.732660i	$0.261721\pi$
$822$	26.4821	0.923669
$823$	−31.2002	−1.08757	−0.543786	−	0.839224i	$-0.683010\pi$
$823$	−31.2002	−1.08757	−0.543786	+	0.839224i	$0.683010\pi$
$824$	14.9220	0.519832
$825$	1.70201	0.0592563
$826$	−5.01955	−0.174653
$827$	−55.4006	−1.92647	−0.963234	−	0.268664i	$-0.913418\pi$
$827$	−55.4006	−1.92647	−0.963234	+	0.268664i	$0.913418\pi$
$828$	0.451434	0.0156884
$829$	1.43127	0.0497101	0.0248551	−	0.999691i	$-0.492088\pi$
$829$	1.43127	0.0497101	0.0248551	+	0.999691i	$0.492088\pi$
$830$	5.54961	0.192630
$831$	16.5718	0.574868
$832$	−2.37582	−0.0823669
$833$	−1.25426	−0.0434577
$834$	−16.8007	−0.581759
$835$	5.82283	0.201507
$836$	−0.413677	−0.0143073
$837$	34.8360	1.20411
$838$	33.4352	1.15500
$839$	2.47077	0.0853005	0.0426503	−	0.999090i	$-0.486420\pi$
$839$	2.47077	0.0853005	0.0426503	+	0.999090i	$0.486420\pi$
$840$	−1.63702	−0.0564827
$841$	−3.48165	−0.120057
$842$	−16.1852	−0.557780
$843$	−14.7955	−0.509583
$844$	−4.90180	−0.168727
$845$	−7.35546	−0.253035
$846$	−1.07519	−0.0369658
$847$	0.961819	0.0330485
$848$	9.81295	0.336978
$849$	−14.9904	−0.514468
$850$	−0.206466	−0.00708174
$851$	39.6207	1.35818
$852$	2.78186	0.0953050
$853$	−49.5735	−1.69736	−0.848682	−	0.528903i	$-0.822604\pi$
$853$	−49.5735	−1.69736	−0.848682	+	0.528903i	$0.822604\pi$
$854$	−7.25851	−0.248381
$855$	0.0426772	0.00145953
$856$	−17.2230	−0.588669
$857$	−32.4395	−1.10811	−0.554056	−	0.832479i	$-0.686921\pi$
$857$	−32.4395	−1.10811	−0.554056	+	0.832479i	$0.686921\pi$
$858$	4.04367	0.138049
$859$	−2.78379	−0.0949816	−0.0474908	−	0.998872i	$-0.515122\pi$
$859$	−2.78379	−0.0949816	−0.0474908	+	0.998872i	$0.515122\pi$
$860$	−1.00000	−0.0340997
$861$	−11.7057	−0.398931
$862$	−23.9093	−0.814353
$863$	−37.1206	−1.26360	−0.631801	−	0.775131i	$-0.717684\pi$
$863$	−37.1206	−1.26360	−0.631801	+	0.775131i	$0.717684\pi$
$864$	5.28162	0.179684
$865$	21.4892	0.730655
$866$	26.9709	0.916508
$867$	−28.8616	−0.980191
$868$	−6.34388	−0.215325
$869$	2.19376	0.0744184
$870$	8.59782	0.291493
$871$	−16.9089	−0.572935
$872$	−4.94258	−0.167377
$873$	−0.288838	−0.00977567
$874$	−1.81018	−0.0612302
$875$	0.961819	0.0325154
$876$	−15.5064	−0.523911
$877$	−41.3812	−1.39734	−0.698672	−	0.715442i	$-0.746225\pi$
$877$	−41.3812	−1.39734	−0.698672	+	0.715442i	$0.746225\pi$
$878$	34.1093	1.15113
$879$	16.1160	0.543580
$880$	1.00000	0.0337100
$881$	50.3228	1.69542	0.847709	−	0.530462i	$-0.177982\pi$
$881$	50.3228	1.69542	0.847709	+	0.530462i	$0.177982\pi$
$882$	−0.626721	−0.0211028
$883$	9.51376	0.320163	0.160082	−	0.987104i	$-0.448824\pi$
$883$	9.51376	0.320163	0.160082	+	0.987104i	$0.448824\pi$
$884$	−0.490528	−0.0164982
$885$	8.88246	0.298581
$886$	16.1902	0.543920
$887$	49.4737	1.66116	0.830582	−	0.556896i	$-0.188008\pi$
$887$	49.4737	1.66116	0.830582	+	0.556896i	$0.188008\pi$
$888$	15.4108	0.517152
$889$	−2.51578	−0.0843766
$890$	16.7071	0.560023
$891$	−8.67986	−0.290786
$892$	23.1695	0.775773
$893$	4.31134	0.144273
$894$	−33.3682	−1.11600
$895$	−5.87243	−0.196294
$896$	−0.961819	−0.0321321
$897$	17.6944	0.590799
$898$	−15.2420	−0.508632
$899$	33.3187	1.11124
$900$	−0.103166	−0.00343885
$901$	2.02604	0.0674973
$902$	7.15062	0.238090
$903$	−1.63702	−0.0544768
$904$	1.33914	0.0445392
$905$	2.70569	0.0899403
$906$	15.1755	0.504171
$907$	36.9144	1.22572	0.612862	−	0.790190i	$-0.290018\pi$
$907$	36.9144	1.22572	0.612862	+	0.790190i	$0.290018\pi$
$908$	1.95283	0.0648068
$909$	−1.90571	−0.0632085
$910$	2.28511	0.0757508
$911$	−20.1105	−0.666291	−0.333146	−	0.942875i	$-0.608110\pi$
$911$	−20.1105	−0.666291	−0.333146	+	0.942875i	$0.608110\pi$
$912$	−0.704082	−0.0233145
$913$	−5.54961	−0.183665
$914$	12.3146	0.407331
$915$	12.8445	0.424625
$916$	−27.9257	−0.922692
$917$	−9.60440	−0.317165
$918$	1.09048	0.0359911
$919$	−3.83727	−0.126580	−0.0632899	−	0.997995i	$-0.520159\pi$
$919$	−3.83727	−0.126580	−0.0632899	+	0.997995i	$0.520159\pi$
$920$	4.37582	0.144267
$921$	−15.2653	−0.503009
$922$	7.78904	0.256518
$923$	−3.88318	−0.127817
$924$	1.63702	0.0538542
$925$	−9.05446	−0.297709
$926$	32.6817	1.07399
$927$	1.53943	0.0505616
$928$	5.05157	0.165826
$929$	57.2835	1.87941	0.939705	−	0.341985i	$-0.111099\pi$
$929$	57.2835	1.87941	0.939705	+	0.341985i	$0.111099\pi$
$930$	11.2260	0.368114
$931$	2.51305	0.0823619
$932$	−17.6982	−0.579724
$933$	31.7505	1.03946
$934$	−4.73048	−0.154786
$935$	0.206466	0.00675217
$936$	−0.245103	−0.00801145
$937$	17.9301	0.585751	0.292876	−	0.956151i	$-0.405388\pi$
$937$	17.9301	0.585751	0.292876	+	0.956151i	$0.405388\pi$
$938$	−6.84531	−0.223507
$939$	43.1794	1.40911
$940$	−10.4220	−0.339928
$941$	42.8854	1.39802	0.699012	−	0.715110i	$-0.253623\pi$
$941$	42.8854	1.39802	0.699012	+	0.715110i	$0.253623\pi$
$942$	−22.3046	−0.726722
$943$	31.2899	1.01894
$944$	5.21881	0.169858
$945$	−5.07996	−0.165251
$946$	1.00000	0.0325128
$947$	−16.2404	−0.527742	−0.263871	−	0.964558i	$-0.584999\pi$
$947$	−16.2404	−0.527742	−0.263871	+	0.964558i	$0.584999\pi$
$948$	3.73381	0.121268
$949$	21.6452	0.702634
$950$	0.413677	0.0134215
$951$	−49.1279	−1.59308
$952$	−0.198583	−0.00643612
$953$	42.8358	1.38759	0.693794	−	0.720173i	$-0.255938\pi$
$953$	42.8358	1.38759	0.693794	+	0.720173i	$0.255938\pi$
$954$	1.01236	0.0327763
$955$	17.2199	0.557223
$956$	1.11014	0.0359044
$957$	−8.59782	−0.277928
$958$	−4.04389	−0.130652
$959$	−14.9652	−0.483253
$960$	1.70201	0.0549321
$961$	12.5034	0.403334
$962$	−21.5118	−0.693568
$963$	−1.77682	−0.0572571
$964$	7.88619	0.253997
$965$	−9.74778	−0.313792
$966$	7.16333	0.230476
$967$	47.4970	1.52740	0.763700	−	0.645572i	$-0.223381\pi$
$967$	47.4970	1.52740	0.763700	+	0.645572i	$0.223381\pi$
$968$	−1.00000	−0.0321412
$969$	−0.145369	−0.00466994
$970$	−2.79975	−0.0898945
$971$	1.33889	0.0429669	0.0214835	−	0.999769i	$-0.493161\pi$
$971$	1.33889	0.0429669	0.0214835	+	0.999769i	$0.493161\pi$
$972$	1.07165	0.0343731
$973$	9.49418	0.304370
$974$	3.81325	0.122185
$975$	−4.04367	−0.129501
$976$	7.54665	0.241562
$977$	21.7838	0.696926	0.348463	−	0.937323i	$-0.386704\pi$
$977$	21.7838	0.696926	0.348463	+	0.937323i	$0.386704\pi$
$978$	−16.9050	−0.540563
$979$	−16.7071	−0.533961
$980$	−6.07490	−0.194056
$981$	−0.509903	−0.0162800
$982$	34.9008	1.11373
$983$	12.9448	0.412873	0.206437	−	0.978460i	$-0.433813\pi$
$983$	12.9448	0.412873	0.206437	+	0.978460i	$0.433813\pi$
$984$	12.1704	0.387979
$985$	−20.1939	−0.643431
$986$	1.04298	0.0332152
$987$	−17.0611	−0.543059
$988$	0.982824	0.0312678
$989$	4.37582	0.139143
$990$	0.103166	0.00327881
$991$	−47.3675	−1.50468	−0.752340	−	0.658775i	$-0.771075\pi$
$991$	−47.3675	−1.50468	−0.752340	+	0.658775i	$0.771075\pi$
$992$	6.59571	0.209414
$993$	55.8122	1.77115
$994$	−1.57205	−0.0498625
$995$	−11.4718	−0.363681
$996$	−9.44548	−0.299291
$997$	13.6998	0.433877	0.216939	−	0.976185i	$-0.430393\pi$
$997$	13.6998	0.433877	0.216939	+	0.976185i	$0.430393\pi$
$998$	14.5870	0.461744
$999$	47.8222	1.51303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.w.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.w.1.8	✓	8	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.70201 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.70201 q^{6} +0.961819 q^{7} -1.00000 q^{8} -0.103166 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.70201 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.70201 q^{6} +0.961819 q^{7} -1.00000 q^{8} -0.103166 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.70201 q^{12} -2.37582 q^{13} -0.961819 q^{14} +1.70201 q^{15} +1.00000 q^{16} +0.206466 q^{17} +0.103166 q^{18} -0.413677 q^{19} +1.00000 q^{20} +1.63702 q^{21} -1.00000 q^{22} -4.37582 q^{23} -1.70201 q^{24} +1.00000 q^{25} +2.37582 q^{26} -5.28162 q^{27} +0.961819 q^{28} -5.05157 q^{29} -1.70201 q^{30} -6.59571 q^{31} -1.00000 q^{32} +1.70201 q^{33} -0.206466 q^{34} +0.961819 q^{35} -0.103166 q^{36} -9.05446 q^{37} +0.413677 q^{38} -4.04367 q^{39} -1.00000 q^{40} -7.15062 q^{41} -1.63702 q^{42} -1.00000 q^{43} +1.00000 q^{44} -0.103166 q^{45} +4.37582 q^{46} -10.4220 q^{47} +1.70201 q^{48} -6.07490 q^{49} -1.00000 q^{50} +0.351408 q^{51} -2.37582 q^{52} +9.81295 q^{53} +5.28162 q^{54} +1.00000 q^{55} -0.961819 q^{56} -0.704082 q^{57} +5.05157 q^{58} +5.21881 q^{59} +1.70201 q^{60} +7.54665 q^{61} +6.59571 q^{62} -0.0992265 q^{63} +1.00000 q^{64} -2.37582 q^{65} -1.70201 q^{66} +7.11705 q^{67} +0.206466 q^{68} -7.44769 q^{69} -0.961819 q^{70} +1.63446 q^{71} +0.103166 q^{72} -9.11062 q^{73} +9.05446 q^{74} +1.70201 q^{75} -0.413677 q^{76} +0.961819 q^{77} +4.04367 q^{78} +2.19376 q^{79} +1.00000 q^{80} -8.67986 q^{81} +7.15062 q^{82} -5.54961 q^{83} +1.63702 q^{84} +0.206466 q^{85} +1.00000 q^{86} -8.59782 q^{87} -1.00000 q^{88} -16.7071 q^{89} +0.103166 q^{90} -2.28511 q^{91} -4.37582 q^{92} -11.2260 q^{93} +10.4220 q^{94} -0.413677 q^{95} -1.70201 q^{96} +2.79975 q^{97} +6.07490 q^{98} -0.103166 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9} - 8 q^{10} + 8 q^{11} - 7 q^{12} - 2 q^{13} + 6 q^{14} - 7 q^{15} + 8 q^{16} - 8 q^{17} - 7 q^{18} + 8 q^{20} + 14 q^{21} - 8 q^{22} - 18 q^{23} + 7 q^{24} + 8 q^{25} + 2 q^{26} - 22 q^{27} - 6 q^{28} + 8 q^{29} + 7 q^{30} - 11 q^{31} - 8 q^{32} - 7 q^{33} + 8 q^{34} - 6 q^{35} + 7 q^{36} - 17 q^{37} - 6 q^{39} - 8 q^{40} + 12 q^{41} - 14 q^{42} - 8 q^{43} + 8 q^{44} + 7 q^{45} + 18 q^{46} - 19 q^{47} - 7 q^{48} - 2 q^{49} - 8 q^{50} - q^{51} - 2 q^{52} - 7 q^{53} + 22 q^{54} + 8 q^{55} + 6 q^{56} - 3 q^{57} - 8 q^{58} + q^{59} - 7 q^{60} + 6 q^{61} + 11 q^{62} - 15 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} - 22 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - 14 q^{71} - 7 q^{72} - 13 q^{73} + 17 q^{74} - 7 q^{75} - 6 q^{77} + 6 q^{78} - 8 q^{79} + 8 q^{80} + 28 q^{81} - 12 q^{82} - 4 q^{83} + 14 q^{84} - 8 q^{85} + 8 q^{86} - 30 q^{87} - 8 q^{88} + 5 q^{89} - 7 q^{90} - 8 q^{91} - 18 q^{92} + q^{93} + 19 q^{94} + 7 q^{96} - 23 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9 - 8 * q^10 + 8 * q^11 - 7 * q^12 - 2 * q^13 + 6 * q^14 - 7 * q^15 + 8 * q^16 - 8 * q^17 - 7 * q^18 + 8 * q^20 + 14 * q^21 - 8 * q^22 - 18 * q^23 + 7 * q^24 + 8 * q^25 + 2 * q^26 - 22 * q^27 - 6 * q^28 + 8 * q^29 + 7 * q^30 - 11 * q^31 - 8 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^35 + 7 * q^36 - 17 * q^37 - 6 * q^39 - 8 * q^40 + 12 * q^41 - 14 * q^42 - 8 * q^43 + 8 * q^44 + 7 * q^45 + 18 * q^46 - 19 * q^47 - 7 * q^48 - 2 * q^49 - 8 * q^50 - q^51 - 2 * q^52 - 7 * q^53 + 22 * q^54 + 8 * q^55 + 6 * q^56 - 3 * q^57 - 8 * q^58 + q^59 - 7 * q^60 + 6 * q^61 + 11 * q^62 - 15 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 - 22 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - 14 * q^71 - 7 * q^72 - 13 * q^73 + 17 * q^74 - 7 * q^75 - 6 * q^77 + 6 * q^78 - 8 * q^79 + 8 * q^80 + 28 * q^81 - 12 * q^82 - 4 * q^83 + 14 * q^84 - 8 * q^85 + 8 * q^86 - 30 * q^87 - 8 * q^88 + 5 * q^89 - 7 * q^90 - 8 * q^91 - 18 * q^92 + q^93 + 19 * q^94 + 7 * q^96 - 23 * q^97 + 2 * q^98 + 7 * q^99

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