LMFDB - Embedded newform 8023.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$165$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.70370 q^{2} -2.31695 q^{3} +5.31001 q^{4} +3.41961 q^{5} +6.26435 q^{6} +0.731020 q^{7} -8.94928 q^{8} +2.36827 q^{9} +O(q^{10})$	\(q-2.70370 q^{2} -2.31695 q^{3} +5.31001 q^{4} +3.41961 q^{5} +6.26435 q^{6} +0.731020 q^{7} -8.94928 q^{8} +2.36827 q^{9} -9.24561 q^{10} -5.32856 q^{11} -12.3030 q^{12} -1.21723 q^{13} -1.97646 q^{14} -7.92307 q^{15} +13.5762 q^{16} +1.27729 q^{17} -6.40308 q^{18} -0.147113 q^{19} +18.1582 q^{20} -1.69374 q^{21} +14.4068 q^{22} -3.24541 q^{23} +20.7350 q^{24} +6.69373 q^{25} +3.29103 q^{26} +1.46370 q^{27} +3.88172 q^{28} +2.40558 q^{29} +21.4216 q^{30} -4.95421 q^{31} -18.8074 q^{32} +12.3460 q^{33} -3.45341 q^{34} +2.49980 q^{35} +12.5755 q^{36} +2.56563 q^{37} +0.397750 q^{38} +2.82026 q^{39} -30.6030 q^{40} +12.2683 q^{41} +4.57936 q^{42} +5.74638 q^{43} -28.2947 q^{44} +8.09854 q^{45} +8.77463 q^{46} +7.66278 q^{47} -31.4553 q^{48} -6.46561 q^{49} -18.0978 q^{50} -2.95942 q^{51} -6.46350 q^{52} +6.50225 q^{53} -3.95741 q^{54} -18.2216 q^{55} -6.54210 q^{56} +0.340854 q^{57} -6.50398 q^{58} -5.56690 q^{59} -42.0716 q^{60} -12.8896 q^{61} +13.3947 q^{62} +1.73125 q^{63} +23.6972 q^{64} -4.16245 q^{65} -33.3799 q^{66} -7.92564 q^{67} +6.78242 q^{68} +7.51946 q^{69} -6.75872 q^{70} +1.00000 q^{71} -21.1943 q^{72} -2.92545 q^{73} -6.93671 q^{74} -15.5090 q^{75} -0.781171 q^{76} -3.89528 q^{77} -7.62516 q^{78} -4.90295 q^{79} +46.4252 q^{80} -10.4961 q^{81} -33.1699 q^{82} -10.0620 q^{83} -8.99376 q^{84} +4.36783 q^{85} -15.5365 q^{86} -5.57362 q^{87} +47.6868 q^{88} +12.6961 q^{89} -21.8960 q^{90} -0.889820 q^{91} -17.2332 q^{92} +11.4787 q^{93} -20.7179 q^{94} -0.503069 q^{95} +43.5758 q^{96} +6.19056 q^{97} +17.4811 q^{98} -12.6194 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) $ 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.70370	−1.91181	−0.955903	−	0.293682i	$-0.905119\pi$
$2$	−2.70370	−1.91181	−0.955903	+	0.293682i	$0.905119\pi$
$3$	−2.31695	−1.33769	−0.668846	−	0.743401i	$-0.733212\pi$
$3$	−2.31695	−1.33769	−0.668846	+	0.743401i	$0.733212\pi$
$4$	5.31001	2.65500
$5$	3.41961	1.52930	0.764648	−	0.644448i	$-0.222913\pi$
$5$	3.41961	1.52930	0.764648	+	0.644448i	$0.222913\pi$
$6$	6.26435	2.55741
$7$	0.731020	0.276300	0.138150	−	0.990411i	$-0.455884\pi$
$7$	0.731020	0.276300	0.138150	+	0.990411i	$0.455884\pi$
$8$	−8.94928	−3.16405
$9$	2.36827	0.789422
$10$	−9.24561	−2.92372
$11$	−5.32856	−1.60662	−0.803310	−	0.595561i	$-0.796930\pi$
$11$	−5.32856	−1.60662	−0.803310	+	0.595561i	$0.796930\pi$
$12$	−12.3030	−3.55158
$13$	−1.21723	−0.337599	−0.168799	−	0.985650i	$-0.553989\pi$
$13$	−1.21723	−0.337599	−0.168799	+	0.985650i	$0.553989\pi$
$14$	−1.97646	−0.528231
$15$	−7.92307	−2.04573
$16$	13.5762	3.39404
$17$	1.27729	0.309788	0.154894	−	0.987931i	$-0.450496\pi$
$17$	1.27729	0.309788	0.154894	+	0.987931i	$0.450496\pi$
$18$	−6.40308	−1.50922
$19$	−0.147113	−0.0337500	−0.0168750	−	0.999858i	$-0.505372\pi$
$19$	−0.147113	−0.0337500	−0.0168750	+	0.999858i	$0.505372\pi$
$20$	18.1582	4.06029
$21$	−1.69374	−0.369604
$22$	14.4068	3.07155
$23$	−3.24541	−0.676715	−0.338358	−	0.941018i	$-0.609871\pi$
$23$	−3.24541	−0.676715	−0.338358	+	0.941018i	$0.609871\pi$
$24$	20.7350	4.23252
$25$	6.69373	1.33875
$26$	3.29103	0.645424
$27$	1.46370	0.281689
$28$	3.88172	0.733577
$29$	2.40558	0.446705	0.223353	−	0.974738i	$-0.428300\pi$
$29$	2.40558	0.446705	0.223353	+	0.974738i	$0.428300\pi$
$30$	21.4216	3.91104
$31$	−4.95421	−0.889803	−0.444901	−	0.895580i	$-0.646761\pi$
$31$	−4.95421	−0.889803	−0.444901	+	0.895580i	$0.646761\pi$
$32$	−18.8074	−3.32471
$33$	12.3460	2.14916
$34$	−3.45341	−0.592255
$35$	2.49980	0.422544
$36$	12.5755	2.09592
$37$	2.56563	0.421788	0.210894	−	0.977509i	$-0.432363\pi$
$37$	2.56563	0.421788	0.210894	+	0.977509i	$0.432363\pi$
$38$	0.397750	0.0645235
$39$	2.82026	0.451604
$40$	−30.6030	−4.83877
$41$	12.2683	1.91599	0.957996	−	0.286783i	$-0.0925859\pi$
$41$	12.2683	1.91599	0.957996	+	0.286783i	$0.0925859\pi$
$42$	4.57936	0.706611
$43$	5.74638	0.876314	0.438157	−	0.898898i	$-0.355631\pi$
$43$	5.74638	0.876314	0.438157	+	0.898898i	$0.355631\pi$
$44$	−28.2947	−4.26558
$45$	8.09854	1.20726
$46$	8.77463	1.29375
$47$	7.66278	1.11773	0.558866	−	0.829258i	$-0.311237\pi$
$47$	7.66278	1.11773	0.558866	+	0.829258i	$0.311237\pi$
$48$	−31.4553	−4.54019
$49$	−6.46561	−0.923659
$50$	−18.0978	−2.55942
$51$	−2.95942	−0.414401
$52$	−6.46350	−0.896327
$53$	6.50225	0.893152	0.446576	−	0.894746i	$-0.352643\pi$
$53$	6.50225	0.893152	0.446576	+	0.894746i	$0.352643\pi$
$54$	−3.95741	−0.538535
$55$	−18.2216	−2.45700
$56$	−6.54210	−0.874225
$57$	0.340854	0.0451472
$58$	−6.50398	−0.854014
$59$	−5.56690	−0.724748	−0.362374	−	0.932033i	$-0.618034\pi$
$59$	−5.56690	−0.724748	−0.362374	+	0.932033i	$0.618034\pi$
$60$	−42.0716	−5.43142
$61$	−12.8896	−1.65035	−0.825173	−	0.564880i	$-0.808922\pi$
$61$	−12.8896	−1.65035	−0.825173	+	0.564880i	$0.808922\pi$
$62$	13.3947	1.70113
$63$	1.73125	0.218117
$64$	23.6972	2.96215
$65$	−4.16245	−0.516289
$66$	−33.3799	−4.10879
$67$	−7.92564	−0.968271	−0.484135	−	0.874993i	$-0.660866\pi$
$67$	−7.92564	−0.968271	−0.484135	+	0.874993i	$0.660866\pi$
$68$	6.78242	0.822489
$69$	7.51946	0.905237
$70$	−6.75872	−0.807822
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−21.1943	−2.49777
$73$	−2.92545	−0.342397	−0.171199	−	0.985237i	$-0.554764\pi$
$73$	−2.92545	−0.342397	−0.171199	+	0.985237i	$0.554764\pi$
$74$	−6.93671	−0.806376
$75$	−15.5090	−1.79083
$76$	−0.781171	−0.0896065
$77$	−3.89528	−0.443909
$78$	−7.62516	−0.863379
$79$	−4.90295	−0.551625	−0.275813	−	0.961211i	$-0.588947\pi$
$79$	−4.90295	−0.551625	−0.275813	+	0.961211i	$0.588947\pi$
$80$	46.4252	5.19050
$81$	−10.4961	−1.16624
$82$	−33.1699	−3.66300
$83$	−10.0620	−1.10445	−0.552226	−	0.833695i	$-0.686221\pi$
$83$	−10.0620	−1.10445	−0.552226	+	0.833695i	$0.686221\pi$
$84$	−8.99376	−0.981300
$85$	4.36783	0.473758
$86$	−15.5365	−1.67534
$87$	−5.57362	−0.597555
$88$	47.6868	5.08343
$89$	12.6961	1.34578	0.672891	−	0.739741i	$-0.265052\pi$
$89$	12.6961	1.34578	0.672891	+	0.739741i	$0.265052\pi$
$90$	−21.8960	−2.30805
$91$	−0.889820	−0.0932785
$92$	−17.2332	−1.79668
$93$	11.4787	1.19028
$94$	−20.7179	−2.13689
$95$	−0.503069	−0.0516138
$96$	43.5758	4.44744
$97$	6.19056	0.628556	0.314278	−	0.949331i	$-0.398238\pi$
$97$	6.19056	0.628556	0.314278	+	0.949331i	$0.398238\pi$
$98$	17.4811	1.76586
$99$	−12.6194	−1.26830
$100$	35.5437	3.55437
$101$	6.92781	0.689343	0.344671	−	0.938723i	$-0.387990\pi$
$101$	6.92781	0.689343	0.344671	+	0.938723i	$0.387990\pi$
$102$	8.00139	0.792255
$103$	1.75542	0.172967	0.0864833	−	0.996253i	$-0.472437\pi$
$103$	1.75542	0.172967	0.0864833	+	0.996253i	$0.472437\pi$
$104$	10.8933	1.06818
$105$	−5.79192	−0.565234
$106$	−17.5801	−1.70753
$107$	−3.47944	−0.336370	−0.168185	−	0.985755i	$-0.553791\pi$
$107$	−3.47944	−0.336370	−0.168185	+	0.985755i	$0.553791\pi$
$108$	7.77226	0.747886
$109$	−2.86939	−0.274838	−0.137419	−	0.990513i	$-0.543881\pi$
$109$	−2.86939	−0.274838	−0.137419	+	0.990513i	$0.543881\pi$
$110$	49.2658	4.69731
$111$	−5.94445	−0.564222
$112$	9.92445	0.937773
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−0.921567	−0.0863126
$115$	−11.0980	−1.03490
$116$	12.7737	1.18600
$117$	−2.88272	−0.266508
$118$	15.0512	1.38558
$119$	0.933724	0.0855944
$120$	70.9058	6.47278
$121$	17.3935	1.58123
$122$	34.8497	3.15514
$123$	−28.4251	−2.56301
$124$	−26.3069	−2.36243
$125$	5.79189	0.518042
$126$	−4.68078	−0.416997
$127$	8.38552	0.744095	0.372047	−	0.928214i	$-0.378656\pi$
$127$	8.38552	0.744095	0.372047	+	0.928214i	$0.378656\pi$
$128$	−26.4555	−2.33836
$129$	−13.3141	−1.17224
$130$	11.2540	0.987044
$131$	3.71796	0.324840	0.162420	−	0.986722i	$-0.448070\pi$
$131$	3.71796	0.324840	0.162420	+	0.986722i	$0.448070\pi$
$132$	65.5574	5.70604
$133$	−0.107543	−0.00932512
$134$	21.4286	1.85115
$135$	5.00528	0.430786
$136$	−11.4308	−0.980185
$137$	16.4225	1.40307	0.701534	−	0.712636i	$-0.252499\pi$
$137$	16.4225	1.40307	0.701534	+	0.712636i	$0.252499\pi$
$138$	−20.3304	−1.73064
$139$	−4.18022	−0.354562	−0.177281	−	0.984160i	$-0.556730\pi$
$139$	−4.18022	−0.354562	−0.177281	+	0.984160i	$0.556730\pi$
$140$	13.2740	1.12186
$141$	−17.7543	−1.49518
$142$	−2.70370	−0.226890
$143$	6.48608	0.542394
$144$	32.1520	2.67933
$145$	8.22615	0.683145
$146$	7.90953	0.654598
$147$	14.9805	1.23557
$148$	13.6235	1.11985
$149$	−2.92212	−0.239389	−0.119695	−	0.992811i	$-0.538192\pi$
$149$	−2.92212	−0.239389	−0.119695	+	0.992811i	$0.538192\pi$
$150$	41.9318	3.42372
$151$	−12.8322	−1.04427	−0.522135	−	0.852863i	$-0.674864\pi$
$151$	−12.8322	−1.04427	−0.522135	+	0.852863i	$0.674864\pi$
$152$	1.31655	0.106787
$153$	3.02496	0.244554
$154$	10.5317	0.848667
$155$	−16.9415	−1.36077
$156$	14.9756	1.19901
$157$	−16.5599	−1.32162	−0.660811	−	0.750552i	$-0.729788\pi$
$157$	−16.5599	−1.32162	−0.660811	+	0.750552i	$0.729788\pi$
$158$	13.2561	1.05460
$159$	−15.0654	−1.19476
$160$	−64.3139	−5.08446
$161$	−2.37246	−0.186976
$162$	28.3784	2.22962
$163$	−5.41129	−0.423845	−0.211922	−	0.977286i	$-0.567972\pi$
$163$	−5.41129	−0.423845	−0.211922	+	0.977286i	$0.567972\pi$
$164$	65.1449	5.08696
$165$	42.2185	3.28671
$166$	27.2047	2.11150
$167$	−3.61668	−0.279867	−0.139934	−	0.990161i	$-0.544689\pi$
$167$	−3.61668	−0.279867	−0.139934	+	0.990161i	$0.544689\pi$
$168$	15.1577	1.16944
$169$	−11.5183	−0.886027
$170$	−11.8093	−0.905733
$171$	−0.348402	−0.0266430
$172$	30.5133	2.32662
$173$	21.2083	1.61244	0.806218	−	0.591619i	$-0.201511\pi$
$173$	21.2083	1.61244	0.806218	+	0.591619i	$0.201511\pi$
$174$	15.0694	1.14241
$175$	4.89325	0.369895
$176$	−72.3414	−5.45294
$177$	12.8982	0.969490
$178$	−34.3265	−2.57288
$179$	−6.40560	−0.478777	−0.239389	−	0.970924i	$-0.576947\pi$
$179$	−6.40560	−0.478777	−0.239389	+	0.970924i	$0.576947\pi$
$180$	43.0033	3.20528
$181$	−20.4491	−1.51997	−0.759984	−	0.649942i	$-0.774793\pi$
$181$	−20.4491	−1.51997	−0.759984	+	0.649942i	$0.774793\pi$
$182$	2.40581	0.178330
$183$	29.8646	2.20766
$184$	29.0441	2.14116
$185$	8.77346	0.645038
$186$	−31.0349	−2.27559
$187$	−6.80611	−0.497712
$188$	40.6894	2.96758
$189$	1.06999	0.0778306
$190$	1.36015	0.0986755
$191$	4.14882	0.300198	0.150099	−	0.988671i	$-0.452041\pi$
$191$	4.14882	0.300198	0.150099	+	0.988671i	$0.452041\pi$
$192$	−54.9053	−3.96245
$193$	15.1720	1.09210	0.546052	−	0.837751i	$-0.316130\pi$
$193$	15.1720	1.09210	0.546052	+	0.837751i	$0.316130\pi$
$194$	−16.7374	−1.20168
$195$	9.64420	0.690636
$196$	−34.3324	−2.45232
$197$	−1.70773	−0.121671	−0.0608353	−	0.998148i	$-0.519376\pi$
$197$	−1.70773	−0.121671	−0.0608353	+	0.998148i	$0.519376\pi$
$198$	34.1192	2.42475
$199$	10.8087	0.766208	0.383104	−	0.923705i	$-0.374855\pi$
$199$	10.8087	0.766208	0.383104	+	0.923705i	$0.374855\pi$
$200$	−59.9040	−4.23586
$201$	18.3633	1.29525
$202$	−18.7307	−1.31789
$203$	1.75853	0.123425
$204$	−15.7145	−1.10024
$205$	41.9529	2.93012
$206$	−4.74613	−0.330679
$207$	−7.68599	−0.534214
$208$	−16.5253	−1.14583
$209$	0.783900	0.0542235
$210$	15.6596	1.08062
$211$	2.72522	0.187612	0.0938060	−	0.995590i	$-0.470097\pi$
$211$	2.72522	0.187612	0.0938060	+	0.995590i	$0.470097\pi$
$212$	34.5270	2.37132
$213$	−2.31695	−0.158755
$214$	9.40737	0.643075
$215$	19.6504	1.34014
$216$	−13.0991	−0.891278
$217$	−3.62163	−0.245852
$218$	7.75798	0.525437
$219$	6.77812	0.458023
$220$	−96.7568	−6.52334
$221$	−1.55476	−0.104584
$222$	16.0720	1.07868
$223$	17.4713	1.16997	0.584983	−	0.811045i	$-0.301101\pi$
$223$	17.4713	1.16997	0.584983	+	0.811045i	$0.301101\pi$
$224$	−13.7486	−0.918615
$225$	15.8525	1.05683
$226$	2.70370	0.179848
$227$	2.68336	0.178101	0.0890503	−	0.996027i	$-0.471617\pi$
$227$	2.68336	0.178101	0.0890503	+	0.996027i	$0.471617\pi$
$228$	1.80994	0.119866
$229$	6.23619	0.412099	0.206050	−	0.978542i	$-0.433939\pi$
$229$	6.23619	0.412099	0.206050	+	0.978542i	$0.433939\pi$
$230$	30.0058	1.97852
$231$	9.02518	0.593813
$232$	−21.5282	−1.41340
$233$	4.59292	0.300892	0.150446	−	0.988618i	$-0.451929\pi$
$233$	4.59292	0.300892	0.150446	+	0.988618i	$0.451929\pi$
$234$	7.79403	0.509512
$235$	26.2037	1.70934
$236$	−29.5603	−1.92421
$237$	11.3599	0.737905
$238$	−2.52451	−0.163640
$239$	1.46564	0.0948042	0.0474021	−	0.998876i	$-0.484906\pi$
$239$	1.46564	0.0948042	0.0474021	+	0.998876i	$0.484906\pi$
$240$	−107.565	−6.94329
$241$	−7.48332	−0.482043	−0.241021	−	0.970520i	$-0.577482\pi$
$241$	−7.48332	−0.482043	−0.241021	+	0.970520i	$0.577482\pi$
$242$	−47.0269	−3.02301
$243$	19.9279	1.27838
$244$	−68.4440	−4.38168
$245$	−22.1099	−1.41255
$246$	76.8531	4.89997
$247$	0.179070	0.0113940
$248$	44.3366	2.81538
$249$	23.3132	1.47742
$250$	−15.6595	−0.990396
$251$	5.94551	0.375277	0.187639	−	0.982238i	$-0.439917\pi$
$251$	5.94551	0.375277	0.187639	+	0.982238i	$0.439917\pi$
$252$	9.19295	0.579101
$253$	17.2934	1.08722
$254$	−22.6720	−1.42257
$255$	−10.1201	−0.633742
$256$	24.1333	1.50833
$257$	18.0602	1.12656	0.563281	−	0.826266i	$-0.309539\pi$
$257$	18.0602	1.12656	0.563281	+	0.826266i	$0.309539\pi$
$258$	35.9973	2.24109
$259$	1.87553	0.116540
$260$	−22.1027	−1.37075
$261$	5.69706	0.352639
$262$	−10.0523	−0.621031
$263$	−14.1553	−0.872854	−0.436427	−	0.899740i	$-0.643756\pi$
$263$	−14.1553	−0.872854	−0.436427	+	0.899740i	$0.643756\pi$
$264$	−110.488	−6.80006
$265$	22.2351	1.36589
$266$	0.290763	0.0178278
$267$	−29.4162	−1.80024
$268$	−42.0852	−2.57076
$269$	−20.2684	−1.23579	−0.617894	−	0.786261i	$-0.712014\pi$
$269$	−20.2684	−1.23579	−0.617894	+	0.786261i	$0.712014\pi$
$270$	−13.5328	−0.823579
$271$	16.1411	0.980505	0.490252	−	0.871581i	$-0.336905\pi$
$271$	16.1411	0.980505	0.490252	+	0.871581i	$0.336905\pi$
$272$	17.3407	1.05143
$273$	2.06167	0.124778
$274$	−44.4015	−2.68239
$275$	−35.6679	−2.15086
$276$	39.9284	2.40341
$277$	17.1224	1.02879	0.514393	−	0.857555i	$-0.328017\pi$
$277$	17.1224	1.02879	0.514393	+	0.857555i	$0.328017\pi$
$278$	11.3021	0.677854
$279$	−11.7329	−0.702430
$280$	−22.3714	−1.33695
$281$	−18.2290	−1.08745	−0.543724	−	0.839264i	$-0.682986\pi$
$281$	−18.2290	−1.08745	−0.543724	+	0.839264i	$0.682986\pi$
$282$	48.0023	2.85850
$283$	−19.3333	−1.14925	−0.574623	−	0.818418i	$-0.694851\pi$
$283$	−19.3333	−1.14925	−0.574623	+	0.818418i	$0.694851\pi$
$284$	5.31001	0.315091
$285$	1.16559	0.0690434
$286$	−17.5364	−1.03695
$287$	8.96839	0.529388
$288$	−44.5409	−2.62460
$289$	−15.3685	−0.904031
$290$	−22.2411	−1.30604
$291$	−14.3432	−0.840814
$292$	−15.5341	−0.909067
$293$	−9.69169	−0.566194	−0.283097	−	0.959091i	$-0.591362\pi$
$293$	−9.69169	−0.566194	−0.283097	+	0.959091i	$0.591362\pi$
$294$	−40.5028	−2.36217
$295$	−19.0366	−1.10835
$296$	−22.9606	−1.33456
$297$	−7.79941	−0.452567
$298$	7.90054	0.457666
$299$	3.95041	0.228458
$300$	−82.3532	−4.75466
$301$	4.20072	0.242125
$302$	34.6945	1.99644
$303$	−16.0514	−0.922129
$304$	−1.99723	−0.114549
$305$	−44.0774	−2.52387
$306$	−8.17859	−0.467539
$307$	26.2328	1.49718	0.748592	−	0.663030i	$-0.230730\pi$
$307$	26.2328	1.49718	0.748592	+	0.663030i	$0.230730\pi$
$308$	−20.6840	−1.17858
$309$	−4.06722	−0.231376
$310$	45.8047	2.60153
$311$	4.40484	0.249775	0.124888	−	0.992171i	$-0.460143\pi$
$311$	4.40484	0.249775	0.124888	+	0.992171i	$0.460143\pi$
$312$	−25.2393	−1.42890
$313$	−11.8728	−0.671090	−0.335545	−	0.942024i	$-0.608921\pi$
$313$	−11.8728	−0.671090	−0.335545	+	0.942024i	$0.608921\pi$
$314$	44.7730	2.52669
$315$	5.92020	0.333565
$316$	−26.0347	−1.46457
$317$	−19.8640	−1.11567	−0.557837	−	0.829950i	$-0.688369\pi$
$317$	−19.8640	−1.11567	−0.557837	+	0.829950i	$0.688369\pi$
$318$	40.7323	2.28416
$319$	−12.8183	−0.717686
$320$	81.0352	4.53001
$321$	8.06169	0.449960
$322$	6.41443	0.357462
$323$	−0.187906	−0.0104554
$324$	−55.7345	−3.09636
$325$	−8.14781	−0.451959
$326$	14.6305	0.810309
$327$	6.64824	0.367649
$328$	−109.793	−6.06229
$329$	5.60165	0.308829
$330$	−114.146	−6.28355
$331$	−15.0114	−0.825102	−0.412551	−	0.910935i	$-0.635362\pi$
$331$	−15.0114	−0.825102	−0.412551	+	0.910935i	$0.635362\pi$
$332$	−53.4295	−2.93232
$333$	6.07610	0.332968
$334$	9.77843	0.535052
$335$	−27.1026	−1.48077
$336$	−22.9945	−1.25445
$337$	29.5340	1.60882	0.804410	−	0.594075i	$-0.202482\pi$
$337$	29.5340	1.60882	0.804410	+	0.594075i	$0.202482\pi$
$338$	31.1422	1.69391
$339$	2.31695	0.125840
$340$	23.1932	1.25783
$341$	26.3988	1.42958
$342$	0.941977	0.0509363
$343$	−9.84363	−0.531506
$344$	−51.4259	−2.77270
$345$	25.7136	1.38437
$346$	−57.3409	−3.08266
$347$	29.9212	1.60625	0.803127	−	0.595807i	$-0.203168\pi$
$347$	29.9212	1.60625	0.803127	+	0.595807i	$0.203168\pi$
$348$	−29.5960	−1.58651
$349$	16.7132	0.894636	0.447318	−	0.894375i	$-0.352379\pi$
$349$	16.7132	0.894636	0.447318	+	0.894375i	$0.352379\pi$
$350$	−13.2299	−0.707167
$351$	−1.78166	−0.0950979
$352$	100.216	5.34154
$353$	−30.5425	−1.62561	−0.812807	−	0.582532i	$-0.802062\pi$
$353$	−30.5425	−1.62561	−0.812807	+	0.582532i	$0.802062\pi$
$354$	−34.8730	−1.85348
$355$	3.41961	0.181494
$356$	67.4163	3.57306
$357$	−2.16339	−0.114499
$358$	17.3188	0.915329
$359$	−9.80134	−0.517295	−0.258648	−	0.965972i	$-0.583277\pi$
$359$	−9.80134	−0.517295	−0.258648	+	0.965972i	$0.583277\pi$
$360$	−72.4761	−3.81983
$361$	−18.9784	−0.998861
$362$	55.2882	2.90588
$363$	−40.3000	−2.11520
$364$	−4.72495	−0.247655
$365$	−10.0039	−0.523627
$366$	−80.7450	−4.22061
$367$	23.3710	1.21996	0.609979	−	0.792418i	$-0.291178\pi$
$367$	23.3710	1.21996	0.609979	+	0.792418i	$0.291178\pi$
$368$	−44.0603	−2.29680
$369$	29.0547	1.51252
$370$	−23.7208	−1.23319
$371$	4.75327	0.246778
$372$	60.9518	3.16021
$373$	−4.82426	−0.249791	−0.124895	−	0.992170i	$-0.539860\pi$
$373$	−4.82426	−0.249791	−0.124895	+	0.992170i	$0.539860\pi$
$374$	18.4017	0.951529
$375$	−13.4195	−0.692981
$376$	−68.5764	−3.53656
$377$	−2.92815	−0.150807
$378$	−2.89294	−0.148797
$379$	22.4708	1.15425	0.577125	−	0.816656i	$-0.304175\pi$
$379$	22.4708	1.15425	0.577125	+	0.816656i	$0.304175\pi$
$380$	−2.67130	−0.137035
$381$	−19.4288	−0.995370
$382$	−11.2172	−0.573921
$383$	−3.54765	−0.181277	−0.0906383	−	0.995884i	$-0.528891\pi$
$383$	−3.54765	−0.181277	−0.0906383	+	0.995884i	$0.528891\pi$
$384$	61.2961	3.12800
$385$	−13.3203	−0.678868
$386$	−41.0206	−2.08789
$387$	13.6089	0.691781
$388$	32.8719	1.66882
$389$	14.7203	0.746348	0.373174	−	0.927761i	$-0.378269\pi$
$389$	14.7203	0.746348	0.373174	+	0.927761i	$0.378269\pi$
$390$	−26.0751	−1.32036
$391$	−4.14533	−0.209638
$392$	57.8625	2.92250
$393$	−8.61434	−0.434536
$394$	4.61719	0.232611
$395$	−16.7662	−0.843598
$396$	−67.0093	−3.36735
$397$	14.9137	0.748498	0.374249	−	0.927328i	$-0.377900\pi$
$397$	14.9137	0.748498	0.374249	+	0.927328i	$0.377900\pi$
$398$	−29.2235	−1.46484
$399$	0.249171	0.0124741
$400$	90.8752	4.54376
$401$	28.0962	1.40306	0.701530	−	0.712640i	$-0.252501\pi$
$401$	28.0962	1.40306	0.701530	+	0.712640i	$0.252501\pi$
$402$	−49.6490	−2.47627
$403$	6.03042	0.300397
$404$	36.7867	1.83021
$405$	−35.8926	−1.78352
$406$	−4.75454	−0.235964
$407$	−13.6711	−0.677653
$408$	26.4847	1.31119
$409$	−28.9968	−1.43380	−0.716900	−	0.697176i	$-0.754440\pi$
$409$	−28.9968	−1.43380	−0.716900	+	0.697176i	$0.754440\pi$
$410$	−113.428	−5.60182
$411$	−38.0501	−1.87687
$412$	9.32129	0.459227
$413$	−4.06951	−0.200248
$414$	20.7806	1.02131
$415$	−34.4082	−1.68903
$416$	22.8929	1.12242
$417$	9.68537	0.474295
$418$	−2.11943	−0.103665
$419$	35.2620	1.72266	0.861332	−	0.508043i	$-0.169631\pi$
$419$	35.2620	1.72266	0.861332	+	0.508043i	$0.169631\pi$
$420$	−30.7552	−1.50070
$421$	−11.8021	−0.575201	−0.287600	−	0.957750i	$-0.592858\pi$
$421$	−11.8021	−0.575201	−0.287600	+	0.957750i	$0.592858\pi$
$422$	−7.36819	−0.358678
$423$	18.1475	0.882362
$424$	−58.1904	−2.82598
$425$	8.54983	0.414728
$426$	6.26435	0.303509
$427$	−9.42256	−0.455990
$428$	−18.4759	−0.893064
$429$	−15.0279	−0.725556
$430$	−53.1287	−2.56210
$431$	10.4358	0.502675	0.251338	−	0.967899i	$-0.419130\pi$
$431$	10.4358	0.502675	0.251338	+	0.967899i	$0.419130\pi$
$432$	19.8714	0.956065
$433$	29.9213	1.43793	0.718964	−	0.695047i	$-0.244617\pi$
$433$	29.9213	1.43793	0.718964	+	0.695047i	$0.244617\pi$
$434$	9.79181	0.470022
$435$	−19.0596	−0.913838
$436$	−15.2365	−0.729696
$437$	0.477442	0.0228392
$438$	−18.3260	−0.875651
$439$	−5.68916	−0.271529	−0.135764	−	0.990741i	$-0.543349\pi$
$439$	−5.68916	−0.271529	−0.135764	+	0.990741i	$0.543349\pi$
$440$	163.070	7.77406
$441$	−15.3123	−0.729156
$442$	4.20360	0.199945
$443$	−9.64273	−0.458140	−0.229070	−	0.973410i	$-0.573568\pi$
$443$	−9.64273	−0.458140	−0.229070	+	0.973410i	$0.573568\pi$
$444$	−31.5651	−1.49801
$445$	43.4157	2.05810
$446$	−47.2373	−2.23675
$447$	6.77041	0.320229
$448$	17.3231	0.818442
$449$	25.6793	1.21188	0.605940	−	0.795510i	$-0.292797\pi$
$449$	25.6793	1.21188	0.605940	+	0.795510i	$0.292797\pi$
$450$	−42.8605	−2.02046
$451$	−65.3725	−3.07827
$452$	−5.31001	−0.249762
$453$	29.7316	1.39691
$454$	−7.25500	−0.340494
$455$	−3.04284	−0.142650
$456$	−3.05039	−0.142848
$457$	28.4058	1.32877	0.664384	−	0.747392i	$-0.268694\pi$
$457$	28.4058	1.32877	0.664384	+	0.747392i	$0.268694\pi$
$458$	−16.8608	−0.787854
$459$	1.86957	0.0872640
$460$	−58.9307	−2.74766
$461$	12.3941	0.577252	0.288626	−	0.957442i	$-0.406802\pi$
$461$	12.3941	0.577252	0.288626	+	0.957442i	$0.406802\pi$
$462$	−24.4014	−1.13526
$463$	−2.94158	−0.136707	−0.0683534	−	0.997661i	$-0.521775\pi$
$463$	−2.94158	−0.136707	−0.0683534	+	0.997661i	$0.521775\pi$
$464$	32.6586	1.51614
$465$	39.2526	1.82029
$466$	−12.4179	−0.575247
$467$	−23.6386	−1.09387	−0.546933	−	0.837177i	$-0.684205\pi$
$467$	−23.6386	−1.09387	−0.546933	+	0.837177i	$0.684205\pi$
$468$	−15.3073	−0.707580
$469$	−5.79380	−0.267533
$470$	−70.8471	−3.26793
$471$	38.3684	1.76792
$472$	49.8197	2.29314
$473$	−30.6199	−1.40790
$474$	−30.7138	−1.41073
$475$	−0.984734	−0.0451827
$476$	4.95808	0.227253
$477$	15.3990	0.705074
$478$	−3.96265	−0.181247
$479$	6.24074	0.285147	0.142573	−	0.989784i	$-0.454462\pi$
$479$	6.24074	0.285147	0.142573	+	0.989784i	$0.454462\pi$
$480$	149.012	6.80144
$481$	−3.12297	−0.142395
$482$	20.2327	0.921573
$483$	5.49688	0.250117
$484$	92.3598	4.19817
$485$	21.1693	0.961248
$486$	−53.8791	−2.44401
$487$	17.3139	0.784568	0.392284	−	0.919844i	$-0.371685\pi$
$487$	17.3139	0.784568	0.392284	+	0.919844i	$0.371685\pi$
$488$	115.353	5.22177
$489$	12.5377	0.566974
$490$	59.7785	2.70052
$491$	34.1610	1.54167	0.770833	−	0.637037i	$-0.219840\pi$
$491$	34.1610	1.54167	0.770833	+	0.637037i	$0.219840\pi$
$492$	−150.938	−6.80480
$493$	3.07263	0.138384
$494$	−0.484153	−0.0217831
$495$	−43.1535	−1.93961
$496$	−67.2592	−3.02003
$497$	0.731020	0.0327907
$498$	−63.0321	−2.82453
$499$	−23.4813	−1.05117	−0.525584	−	0.850741i	$-0.676153\pi$
$499$	−23.4813	−1.05117	−0.525584	+	0.850741i	$0.676153\pi$
$500$	30.7550	1.37540
$501$	8.37968	0.374376
$502$	−16.0749	−0.717458
$503$	−1.73145	−0.0772014	−0.0386007	−	0.999255i	$-0.512290\pi$
$503$	−1.73145	−0.0772014	−0.0386007	+	0.999255i	$0.512290\pi$
$504$	−15.4934	−0.690132
$505$	23.6904	1.05421
$506$	−46.7561	−2.07856
$507$	26.6875	1.18523
$508$	44.5272	1.97557
$509$	16.7091	0.740619	0.370310	−	0.928908i	$-0.379252\pi$
$509$	16.7091	0.740619	0.370310	+	0.928908i	$0.379252\pi$
$510$	27.3616	1.21159
$511$	−2.13856	−0.0946043
$512$	−12.3383	−0.545282
$513$	−0.215329	−0.00950701
$514$	−48.8293	−2.15377
$515$	6.00285	0.264517
$516$	−70.6979	−3.11230
$517$	−40.8316	−1.79577
$518$	−5.07087	−0.222801
$519$	−49.1385	−2.15694
$520$	37.2510	1.63356
$521$	33.0811	1.44931	0.724654	−	0.689113i	$-0.242000\pi$
$521$	33.0811	1.44931	0.724654	+	0.689113i	$0.242000\pi$
$522$	−15.4031	−0.674178
$523$	2.97016	0.129876	0.0649380	−	0.997889i	$-0.479315\pi$
$523$	2.97016	0.129876	0.0649380	+	0.997889i	$0.479315\pi$
$524$	19.7424	0.862451
$525$	−11.3374	−0.494806
$526$	38.2718	1.66873
$527$	−6.32796	−0.275650
$528$	167.612	7.29436
$529$	−12.4673	−0.542057
$530$	−60.1172	−2.61132
$531$	−13.1839	−0.572132
$532$	−0.571052	−0.0247582
$533$	−14.9334	−0.646837
$534$	79.5327	3.44172
$535$	−11.8983	−0.514409
$536$	70.9287	3.06366
$537$	14.8415	0.640457
$538$	54.7998	2.36259
$539$	34.4524	1.48397
$540$	26.5781	1.14374
$541$	−0.642796	−0.0276359	−0.0138180	−	0.999905i	$-0.504399\pi$
$541$	−0.642796	−0.0276359	−0.0138180	+	0.999905i	$0.504399\pi$
$542$	−43.6409	−1.87454
$543$	47.3795	2.03325
$544$	−24.0225	−1.02996
$545$	−9.81220	−0.420308
$546$	−5.57414	−0.238551
$547$	42.6120	1.82196	0.910979	−	0.412452i	$-0.135328\pi$
$547$	42.6120	1.82196	0.910979	+	0.412452i	$0.135328\pi$
$548$	87.2036	3.72515
$549$	−30.5260	−1.30282
$550$	96.4354	4.11202
$551$	−0.353892	−0.0150763
$552$	−67.2938	−2.86421
$553$	−3.58416	−0.152414
$554$	−46.2939	−1.96684
$555$	−20.3277	−0.862862
$556$	−22.1970	−0.941363
$557$	23.2940	0.987000	0.493500	−	0.869746i	$-0.335717\pi$
$557$	23.2940	0.987000	0.493500	+	0.869746i	$0.335717\pi$
$558$	31.7222	1.34291
$559$	−6.99466	−0.295843
$560$	33.9378	1.43413
$561$	15.7694	0.665786
$562$	49.2857	2.07899
$563$	25.1077	1.05816	0.529082	−	0.848571i	$-0.322537\pi$
$563$	25.1077	1.05816	0.529082	+	0.848571i	$0.322537\pi$
$564$	−94.2755	−3.96971
$565$	−3.41961	−0.143864
$566$	52.2715	2.19714
$567$	−7.67287	−0.322230
$568$	−8.94928	−0.375503
$569$	−7.05246	−0.295654	−0.147827	−	0.989013i	$-0.547228\pi$
$569$	−7.05246	−0.295654	−0.147827	+	0.989013i	$0.547228\pi$
$570$	−3.15140	−0.131998
$571$	−27.1927	−1.13798	−0.568990	−	0.822344i	$-0.692666\pi$
$571$	−27.1927	−1.13798	−0.568990	+	0.822344i	$0.692666\pi$
$572$	34.4412	1.44006
$573$	−9.61262	−0.401573
$574$	−24.2479	−1.01209
$575$	−21.7239	−0.905949
$576$	56.1213	2.33839
$577$	−25.2931	−1.05296	−0.526482	−	0.850186i	$-0.676489\pi$
$577$	−25.2931	−1.05296	−0.526482	+	0.850186i	$0.676489\pi$
$578$	41.5519	1.72833
$579$	−35.1528	−1.46090
$580$	43.6809	1.81375
$581$	−7.35555	−0.305159
$582$	38.7798	1.60747
$583$	−34.6476	−1.43496
$584$	26.1806	1.08336
$585$	−9.85779	−0.407570
$586$	26.2034	1.08245
$587$	−13.5891	−0.560884	−0.280442	−	0.959871i	$-0.590481\pi$
$587$	−13.5891	−0.560884	−0.280442	+	0.959871i	$0.590481\pi$
$588$	79.5466	3.28045
$589$	0.728829	0.0300309
$590$	51.4693	2.11896
$591$	3.95672	0.162758
$592$	34.8315	1.43157
$593$	−17.5053	−0.718857	−0.359429	−	0.933173i	$-0.617028\pi$
$593$	−17.5053	−0.718857	−0.359429	+	0.933173i	$0.617028\pi$
$594$	21.0873	0.865221
$595$	3.19297	0.130899
$596$	−15.5165	−0.635580
$597$	−25.0432	−1.02495
$598$	−10.6807	−0.436768
$599$	15.0078	0.613203	0.306601	−	0.951838i	$-0.400808\pi$
$599$	15.0078	0.613203	0.306601	+	0.951838i	$0.400808\pi$
$600$	138.795	5.66627
$601$	23.6963	0.966592	0.483296	−	0.875457i	$-0.339439\pi$
$601$	23.6963	0.966592	0.483296	+	0.875457i	$0.339439\pi$
$602$	−11.3575	−0.462897
$603$	−18.7700	−0.764374
$604$	−68.1391	−2.77254
$605$	59.4791	2.41817
$606$	43.3982	1.76293
$607$	46.8128	1.90007	0.950036	−	0.312139i	$-0.101045\pi$
$607$	46.8128	1.90007	0.950036	+	0.312139i	$0.101045\pi$
$608$	2.76681	0.112209
$609$	−4.07443	−0.165104
$610$	119.172	4.82515
$611$	−9.32737	−0.377345
$612$	16.0626	0.649291
$613$	32.5569	1.31496	0.657480	−	0.753472i	$-0.271622\pi$
$613$	32.5569	1.31496	0.657480	+	0.753472i	$0.271622\pi$
$614$	−70.9257	−2.86233
$615$	−97.2028	−3.91960
$616$	34.8600	1.40455
$617$	17.4587	0.702862	0.351431	−	0.936214i	$-0.385695\pi$
$617$	17.4587	0.702862	0.351431	+	0.936214i	$0.385695\pi$
$618$	10.9966	0.442347
$619$	41.7820	1.67936	0.839680	−	0.543082i	$-0.182743\pi$
$619$	41.7820	1.67936	0.839680	+	0.543082i	$0.182743\pi$
$620$	−89.9593	−3.61285
$621$	−4.75031	−0.190623
$622$	−11.9094	−0.477522
$623$	9.28110	0.371839
$624$	38.2884	1.53276
$625$	−13.6627	−0.546506
$626$	32.1005	1.28299
$627$	−1.81626	−0.0725344
$628$	−87.9331	−3.50891
$629$	3.27706	0.130665
$630$	−16.0064	−0.637712
$631$	−21.4484	−0.853848	−0.426924	−	0.904288i	$-0.640403\pi$
$631$	−21.4484	−0.853848	−0.426924	+	0.904288i	$0.640403\pi$
$632$	43.8779	1.74537
$633$	−6.31421	−0.250967
$634$	53.7064	2.13295
$635$	28.6752	1.13794
$636$	−79.9973	−3.17210
$637$	7.87014	0.311826
$638$	34.6568	1.37208
$639$	2.36827	0.0936871
$640$	−90.4674	−3.57604
$641$	24.3057	0.960018	0.480009	−	0.877263i	$-0.340633\pi$
$641$	24.3057	0.960018	0.480009	+	0.877263i	$0.340633\pi$
$642$	−21.7964	−0.860236
$643$	7.10591	0.280230	0.140115	−	0.990135i	$-0.455253\pi$
$643$	7.10591	0.280230	0.140115	+	0.990135i	$0.455253\pi$
$644$	−12.5978	−0.496422
$645$	−45.5289	−1.79270
$646$	0.508042	0.0199886
$647$	−40.6040	−1.59631	−0.798154	−	0.602454i	$-0.794190\pi$
$647$	−40.6040	−1.59631	−0.798154	+	0.602454i	$0.794190\pi$
$648$	93.9327	3.69002
$649$	29.6635	1.16440
$650$	22.0293	0.864058
$651$	8.39114	0.328875
$652$	−28.7340	−1.12531
$653$	16.1581	0.632313	0.316157	−	0.948707i	$-0.397607\pi$
$653$	16.1581	0.632313	0.316157	+	0.948707i	$0.397607\pi$
$654$	−17.9749	−0.702873
$655$	12.7140	0.496776
$656$	166.557	6.50296
$657$	−6.92823	−0.270296
$658$	−15.1452	−0.590421
$659$	45.8721	1.78692	0.893462	−	0.449139i	$-0.148269\pi$
$659$	45.8721	1.78692	0.893462	+	0.449139i	$0.148269\pi$
$660$	224.181	8.72623
$661$	2.61575	0.101741	0.0508705	−	0.998705i	$-0.483800\pi$
$661$	2.61575	0.101741	0.0508705	+	0.998705i	$0.483800\pi$
$662$	40.5864	1.57743
$663$	3.60229	0.139902
$664$	90.0479	3.49454
$665$	−0.367753	−0.0142609
$666$	−16.4280	−0.636571
$667$	−7.80711	−0.302292
$668$	−19.2046	−0.743049
$669$	−40.4802	−1.56506
$670$	73.2773	2.83095
$671$	68.6830	2.65148
$672$	31.8548	1.22882
$673$	2.99444	0.115427	0.0577136	−	0.998333i	$-0.481619\pi$
$673$	2.99444	0.115427	0.0577136	+	0.998333i	$0.481619\pi$
$674$	−79.8512	−3.07575
$675$	9.79760	0.377110
$676$	−61.1625	−2.35241
$677$	23.0757	0.886869	0.443435	−	0.896307i	$-0.353760\pi$
$677$	23.0757	0.886869	0.443435	+	0.896307i	$0.353760\pi$
$678$	−6.26435	−0.240581
$679$	4.52542	0.173670
$680$	−39.0889	−1.49899
$681$	−6.21721	−0.238244
$682$	−71.3745	−2.73307
$683$	−17.2473	−0.659948	−0.329974	−	0.943990i	$-0.607040\pi$
$683$	−17.2473	−0.659948	−0.329974	+	0.943990i	$0.607040\pi$
$684$	−1.85002	−0.0707373
$685$	56.1585	2.14571
$686$	26.6142	1.01614
$687$	−14.4490	−0.551262
$688$	78.0138	2.97425
$689$	−7.91473	−0.301527
$690$	−69.5220	−2.64666
$691$	−19.4090	−0.738355	−0.369177	−	0.929359i	$-0.620360\pi$
$691$	−19.4090	−0.738355	−0.369177	+	0.929359i	$0.620360\pi$
$692$	112.616	4.28102
$693$	−9.22506	−0.350431
$694$	−80.8981	−3.07085
$695$	−14.2947	−0.542230
$696$	49.8799	1.89069
$697$	15.6702	0.593552
$698$	−45.1875	−1.71037
$699$	−10.6416	−0.402501
$700$	25.9832	0.982072
$701$	−28.6148	−1.08077	−0.540383	−	0.841419i	$-0.681721\pi$
$701$	−28.6148	−1.08077	−0.540383	+	0.841419i	$0.681721\pi$
$702$	4.81708	0.181809
$703$	−0.377438	−0.0142353
$704$	−126.272	−4.75906
$705$	−60.7128	−2.28657
$706$	82.5779	3.10786
$707$	5.06437	0.190465
$708$	68.4897	2.57400
$709$	42.7188	1.60434	0.802169	−	0.597097i	$-0.203679\pi$
$709$	42.7188	1.60434	0.802169	+	0.597097i	$0.203679\pi$
$710$	−9.24561	−0.346981
$711$	−11.6115	−0.435465
$712$	−113.621	−4.25812
$713$	16.0785	0.602143
$714$	5.84917	0.218900
$715$	22.1799	0.829480
$716$	−34.0138	−1.27116
$717$	−3.39581	−0.126819
$718$	26.4999	0.988968
$719$	−37.4090	−1.39512	−0.697561	−	0.716525i	$-0.745731\pi$
$719$	−37.4090	−1.39512	−0.697561	+	0.716525i	$0.745731\pi$
$720$	109.947	4.09749
$721$	1.28325	0.0477906
$722$	51.3118	1.90963
$723$	17.3385	0.644825
$724$	−108.585	−4.03552
$725$	16.1023	0.598025
$726$	108.959	4.04385
$727$	−10.0856	−0.374055	−0.187028	−	0.982355i	$-0.559885\pi$
$727$	−10.0856	−0.374055	−0.187028	+	0.982355i	$0.559885\pi$
$728$	7.96325	0.295138
$729$	−14.6836	−0.543838
$730$	27.0475	1.00107
$731$	7.33979	0.271472
$732$	158.581	5.86133
$733$	10.6583	0.393674	0.196837	−	0.980436i	$-0.436933\pi$
$733$	10.6583	0.393674	0.196837	+	0.980436i	$0.436933\pi$
$734$	−63.1883	−2.33232
$735$	51.2275	1.88955
$736$	61.0377	2.24988
$737$	42.2322	1.55564
$738$	−78.5552	−2.89166
$739$	−32.3735	−1.19088	−0.595439	−	0.803400i	$-0.703022\pi$
$739$	−32.3735	−1.19088	−0.595439	+	0.803400i	$0.703022\pi$
$740$	46.5872	1.71258
$741$	−0.414897	−0.0152416
$742$	−12.8514	−0.471791
$743$	−26.8058	−0.983409	−0.491704	−	0.870762i	$-0.663626\pi$
$743$	−26.8058	−0.983409	−0.491704	+	0.870762i	$0.663626\pi$
$744$	−102.726	−3.76611
$745$	−9.99251	−0.366097
$746$	13.0434	0.477552
$747$	−23.8296	−0.871878
$748$	−36.1405	−1.32143
$749$	−2.54354	−0.0929389
$750$	36.2824	1.32485
$751$	−22.9605	−0.837841	−0.418921	−	0.908023i	$-0.637591\pi$
$751$	−22.9605	−0.837841	−0.418921	+	0.908023i	$0.637591\pi$
$752$	104.031	3.79363
$753$	−13.7755	−0.502006
$754$	7.91684	0.288314
$755$	−43.8811	−1.59700
$756$	5.68167	0.206640
$757$	−16.9695	−0.616766	−0.308383	−	0.951262i	$-0.599788\pi$
$757$	−16.9695	−0.616766	−0.308383	+	0.951262i	$0.599788\pi$
$758$	−60.7545	−2.20670
$759$	−40.0679	−1.45437
$760$	4.50210	0.163308
$761$	38.2921	1.38809	0.694043	−	0.719933i	$-0.255828\pi$
$761$	38.2921	1.38809	0.694043	+	0.719933i	$0.255828\pi$
$762$	52.5298	1.90296
$763$	−2.09758	−0.0759376
$764$	22.0303	0.797028
$765$	10.3442	0.373995
$766$	9.59180	0.346566
$767$	6.77619	0.244674
$768$	−55.9157	−2.01768
$769$	28.3619	1.02276	0.511378	−	0.859356i	$-0.329135\pi$
$769$	28.3619	1.02276	0.511378	+	0.859356i	$0.329135\pi$
$770$	36.0143	1.29786
$771$	−41.8445	−1.50699
$772$	80.5634	2.89954
$773$	−54.8176	−1.97165	−0.985826	−	0.167770i	$-0.946343\pi$
$773$	−54.8176	−1.97165	−0.985826	+	0.167770i	$0.946343\pi$
$774$	−36.7945	−1.32255
$775$	−33.1621	−1.19122
$776$	−55.4010	−1.98878
$777$	−4.34551	−0.155894
$778$	−39.7993	−1.42687
$779$	−1.80483	−0.0646648
$780$	51.2108	1.83364
$781$	−5.32856	−0.190671
$782$	11.2077	0.400788
$783$	3.52105	0.125832
$784$	−87.7782	−3.13494
$785$	−56.6283	−2.02115
$786$	23.2906	0.830749
$787$	53.2775	1.89914	0.949568	−	0.313560i	$-0.101522\pi$
$787$	53.2775	1.89914	0.949568	+	0.313560i	$0.101522\pi$
$788$	−9.06805	−0.323036
$789$	32.7972	1.16761
$790$	45.3308	1.61280
$791$	−0.731020	−0.0259921
$792$	112.935	4.01297
$793$	15.6896	0.557155
$794$	−40.3223	−1.43098
$795$	−51.5177	−1.82715
$796$	57.3943	2.03429
$797$	45.4366	1.60945	0.804724	−	0.593649i	$-0.202313\pi$
$797$	45.4366	1.60945	0.804724	+	0.593649i	$0.202313\pi$
$798$	−0.673684	−0.0238481
$799$	9.78759	0.346260
$800$	−125.891	−4.45094
$801$	30.0677	1.06239
$802$	−75.9639	−2.68238
$803$	15.5884	0.550103
$804$	97.5094	3.43889
$805$	−8.11289	−0.285942
$806$	−16.3045	−0.574300
$807$	46.9610	1.65310
$808$	−61.9989	−2.18111
$809$	−9.55700	−0.336006	−0.168003	−	0.985786i	$-0.553732\pi$
$809$	−9.55700	−0.336006	−0.168003	+	0.985786i	$0.553732\pi$
$810$	97.0430	3.40974
$811$	3.50419	0.123049	0.0615243	−	0.998106i	$-0.480404\pi$
$811$	3.50419	0.123049	0.0615243	+	0.998106i	$0.480404\pi$
$812$	9.33780	0.327693
$813$	−37.3982	−1.31161
$814$	36.9627	1.29554
$815$	−18.5045	−0.648184
$816$	−40.1776	−1.40650
$817$	−0.845366	−0.0295756
$818$	78.3988	2.74115
$819$	−2.10733	−0.0736360
$820$	222.770	7.77947
$821$	−16.6483	−0.581030	−0.290515	−	0.956870i	$-0.593827\pi$
$821$	−16.6483	−0.581030	−0.290515	+	0.956870i	$0.593827\pi$
$822$	102.876	3.58822
$823$	−7.31698	−0.255054	−0.127527	−	0.991835i	$-0.540704\pi$
$823$	−7.31698	−0.255054	−0.127527	+	0.991835i	$0.540704\pi$
$824$	−15.7097	−0.547275
$825$	82.6408	2.87718
$826$	11.0028	0.382835
$827$	−32.1693	−1.11863	−0.559317	−	0.828954i	$-0.688937\pi$
$827$	−32.1693	−1.11863	−0.559317	+	0.828954i	$0.688937\pi$
$828$	−40.8127	−1.41834
$829$	−9.67238	−0.335935	−0.167968	−	0.985792i	$-0.553720\pi$
$829$	−9.67238	−0.335935	−0.167968	+	0.985792i	$0.553720\pi$
$830$	93.0296	3.22910
$831$	−39.6718	−1.37620
$832$	−28.8450	−1.00002
$833$	−8.25846	−0.286139
$834$	−26.1864	−0.906760
$835$	−12.3676	−0.428000
$836$	4.16252	0.143964
$837$	−7.25148	−0.250648
$838$	−95.3381	−3.29340
$839$	−36.9060	−1.27414	−0.637068	−	0.770808i	$-0.719853\pi$
$839$	−36.9060	−1.27414	−0.637068	+	0.770808i	$0.719853\pi$
$840$	51.8335	1.78843
$841$	−23.2132	−0.800454
$842$	31.9095	1.09967
$843$	42.2356	1.45467
$844$	14.4709	0.498111
$845$	−39.3883	−1.35500
$846$	−49.0654	−1.68690
$847$	12.7150	0.436893
$848$	88.2756	3.03140
$849$	44.7943	1.53734
$850$	−23.1162	−0.792879
$851$	−8.32654	−0.285430
$852$	−12.3030	−0.421495
$853$	−41.2142	−1.41115	−0.705574	−	0.708636i	$-0.749311\pi$
$853$	−41.2142	−1.41115	−0.705574	+	0.708636i	$0.749311\pi$
$854$	25.4758	0.871764
$855$	−1.19140	−0.0407450
$856$	31.1385	1.06429
$857$	−25.6632	−0.876637	−0.438318	−	0.898820i	$-0.644426\pi$
$857$	−25.6632	−0.876637	−0.438318	+	0.898820i	$0.644426\pi$
$858$	40.6311	1.38712
$859$	−21.8986	−0.747171	−0.373585	−	0.927596i	$-0.621872\pi$
$859$	−21.8986	−0.747171	−0.373585	+	0.927596i	$0.621872\pi$
$860$	104.344	3.55809
$861$	−20.7793	−0.708158
$862$	−28.2153	−0.961018
$863$	16.7968	0.571771	0.285886	−	0.958264i	$-0.407712\pi$
$863$	16.7968	0.571771	0.285886	+	0.958264i	$0.407712\pi$
$864$	−27.5283	−0.936533
$865$	72.5240	2.46589
$866$	−80.8984	−2.74904
$867$	35.6081	1.20932
$868$	−19.2309	−0.652738
$869$	26.1257	0.886253
$870$	51.5315	1.74708
$871$	9.64733	0.326887
$872$	25.6790	0.869600
$873$	14.6609	0.496196
$874$	−1.29086	−0.0436640
$875$	4.23398	0.143135
$876$	35.9918	1.21605
$877$	−0.419904	−0.0141791	−0.00708957	−	0.999975i	$-0.502257\pi$
$877$	−0.419904	−0.0141791	−0.00708957	+	0.999975i	$0.502257\pi$
$878$	15.3818	0.519110
$879$	22.4552	0.757394
$880$	−247.379	−8.33916
$881$	36.1789	1.21890	0.609449	−	0.792825i	$-0.291391\pi$
$881$	36.1789	1.21890	0.609449	+	0.792825i	$0.291391\pi$
$882$	41.3998	1.39401
$883$	−14.5077	−0.488224	−0.244112	−	0.969747i	$-0.578497\pi$
$883$	−14.5077	−0.488224	−0.244112	+	0.969747i	$0.578497\pi$
$884$	−8.25577	−0.277672
$885$	44.1069	1.48264
$886$	26.0711	0.875874
$887$	−50.9654	−1.71125	−0.855625	−	0.517597i	$-0.826827\pi$
$887$	−50.9654	−1.71125	−0.855625	+	0.517597i	$0.826827\pi$
$888$	53.1985	1.78523
$889$	6.12998	0.205593
$890$	−117.383	−3.93469
$891$	55.9292	1.87370
$892$	92.7729	3.10627
$893$	−1.12729	−0.0377235
$894$	−18.3052	−0.612217
$895$	−21.9047	−0.732192
$896$	−19.3395	−0.646087
$897$	−9.15292	−0.305607
$898$	−69.4292	−2.31688
$899$	−11.9178	−0.397480
$900$	84.1770	2.80590
$901$	8.30525	0.276688
$902$	176.748	5.88506
$903$	−9.73286	−0.323889
$904$	8.94928	0.297649
$905$	−69.9278	−2.32448
$906$	−80.3854	−2.67063
$907$	−10.4013	−0.345371	−0.172685	−	0.984977i	$-0.555244\pi$
$907$	−10.4013	−0.345371	−0.172685	+	0.984977i	$0.555244\pi$
$908$	14.2486	0.472858
$909$	16.4069	0.544182
$910$	8.22692	0.272720
$911$	1.68864	0.0559472	0.0279736	−	0.999609i	$-0.491095\pi$
$911$	1.68864	0.0559472	0.0279736	+	0.999609i	$0.491095\pi$
$912$	4.62749	0.153231
$913$	53.6161	1.77443
$914$	−76.8008	−2.54035
$915$	102.125	3.37616
$916$	33.1142	1.09413
$917$	2.71790	0.0897531
$918$	−5.05476	−0.166832
$919$	−7.39742	−0.244018	−0.122009	−	0.992529i	$-0.538934\pi$
$919$	−7.39742	−0.244018	−0.122009	+	0.992529i	$0.538934\pi$
$920$	99.3195	3.27447
$921$	−60.7801	−2.00277
$922$	−33.5101	−1.10359
$923$	−1.21723	−0.0400656
$924$	47.9238	1.57658
$925$	17.1736	0.564666
$926$	7.95316	0.261357
$927$	4.15730	0.136544
$928$	−45.2427	−1.48516
$929$	−43.5119	−1.42758	−0.713790	−	0.700360i	$-0.753023\pi$
$929$	−43.5119	−1.42758	−0.713790	+	0.700360i	$0.753023\pi$
$930$	−106.127	−3.48005
$931$	0.951175	0.0311735
$932$	24.3884	0.798870
$933$	−10.2058	−0.334123
$934$	63.9118	2.09126
$935$	−23.2742	−0.761149
$936$	25.7983	0.843244
$937$	−38.3222	−1.25193	−0.625965	−	0.779851i	$-0.715295\pi$
$937$	−38.3222	−1.25193	−0.625965	+	0.779851i	$0.715295\pi$
$938$	15.6647	0.511471
$939$	27.5087	0.897713
$940$	139.142	4.53831
$941$	−7.85967	−0.256218	−0.128109	−	0.991760i	$-0.540891\pi$
$941$	−7.85967	−0.256218	−0.128109	+	0.991760i	$0.540891\pi$
$942$	−103.737	−3.37993
$943$	−39.8158	−1.29658
$944$	−75.5771	−2.45983
$945$	3.65896	0.119026
$946$	82.7871	2.69164
$947$	32.6410	1.06069	0.530345	−	0.847782i	$-0.322062\pi$
$947$	32.6410	1.06069	0.530345	+	0.847782i	$0.322062\pi$
$948$	60.3212	1.95914
$949$	3.56094	0.115593
$950$	2.66243	0.0863806
$951$	46.0240	1.49243
$952$	−8.35616	−0.270825
$953$	58.4820	1.89442	0.947209	−	0.320616i	$-0.103890\pi$
$953$	58.4820	1.89442	0.947209	+	0.320616i	$0.103890\pi$
$954$	−41.6344	−1.34796
$955$	14.1874	0.459092
$956$	7.78254	0.251705
$957$	29.6994	0.960044
$958$	−16.8731	−0.545145
$959$	12.0052	0.387667
$960$	−187.755	−6.05976
$961$	−6.45578	−0.208251
$962$	8.44357	0.272232
$963$	−8.24023	−0.265538
$964$	−39.7365	−1.27983
$965$	51.8823	1.67015
$966$	−14.8619	−0.478174
$967$	16.5701	0.532858	0.266429	−	0.963855i	$-0.414156\pi$
$967$	16.5701	0.532858	0.266429	+	0.963855i	$0.414156\pi$
$968$	−155.660	−5.00309
$969$	0.435369	0.0139861
$970$	−57.2355	−1.83772
$971$	9.78119	0.313893	0.156947	−	0.987607i	$-0.449835\pi$
$971$	9.78119	0.313893	0.156947	+	0.987607i	$0.449835\pi$
$972$	105.817	3.39409
$973$	−3.05583	−0.0979653
$974$	−46.8117	−1.49994
$975$	18.8781	0.604582
$976$	−174.992	−5.60135
$977$	3.94721	0.126283	0.0631413	−	0.998005i	$-0.479888\pi$
$977$	3.94721	0.126283	0.0631413	+	0.998005i	$0.479888\pi$
$978$	−33.8982	−1.08394
$979$	−67.6518	−2.16216
$980$	−117.404	−3.75032
$981$	−6.79548	−0.216963
$982$	−92.3613	−2.94737
$983$	35.9880	1.14784	0.573919	−	0.818912i	$-0.305422\pi$
$983$	35.9880	1.14784	0.573919	+	0.818912i	$0.305422\pi$
$984$	254.384	8.10948
$985$	−5.83976	−0.186070
$986$	−8.30747	−0.264564
$987$	−12.9787	−0.413118
$988$	0.950865	0.0302511
$989$	−18.6494	−0.593015
$990$	116.674	3.70815
$991$	30.7254	0.976024	0.488012	−	0.872837i	$-0.337722\pi$
$991$	30.7254	0.976024	0.488012	+	0.872837i	$0.337722\pi$
$992$	93.1758	2.95833
$993$	34.7807	1.10373
$994$	−1.97646	−0.0626895
$995$	36.9615	1.17176
$996$	123.794	3.92255
$997$	−4.12854	−0.130752	−0.0653761	−	0.997861i	$-0.520825\pi$
$997$	−4.12854	−0.130752	−0.0653761	+	0.997861i	$0.520825\pi$
$998$	63.4865	2.00963
$999$	3.75532	0.118813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.3	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.3	✓	165	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70370 q^{2} -2.31695 q^{3} +5.31001 q^{4} +3.41961 q^{5} +6.26435 q^{6} +0.731020 q^{7} -8.94928 q^{8} +2.36827 q^{9} +O(q^{10})\)	\(q-2.70370 q^{2} -2.31695 q^{3} +5.31001 q^{4} +3.41961 q^{5} +6.26435 q^{6} +0.731020 q^{7} -8.94928 q^{8} +2.36827 q^{9} -9.24561 q^{10} -5.32856 q^{11} -12.3030 q^{12} -1.21723 q^{13} -1.97646 q^{14} -7.92307 q^{15} +13.5762 q^{16} +1.27729 q^{17} -6.40308 q^{18} -0.147113 q^{19} +18.1582 q^{20} -1.69374 q^{21} +14.4068 q^{22} -3.24541 q^{23} +20.7350 q^{24} +6.69373 q^{25} +3.29103 q^{26} +1.46370 q^{27} +3.88172 q^{28} +2.40558 q^{29} +21.4216 q^{30} -4.95421 q^{31} -18.8074 q^{32} +12.3460 q^{33} -3.45341 q^{34} +2.49980 q^{35} +12.5755 q^{36} +2.56563 q^{37} +0.397750 q^{38} +2.82026 q^{39} -30.6030 q^{40} +12.2683 q^{41} +4.57936 q^{42} +5.74638 q^{43} -28.2947 q^{44} +8.09854 q^{45} +8.77463 q^{46} +7.66278 q^{47} -31.4553 q^{48} -6.46561 q^{49} -18.0978 q^{50} -2.95942 q^{51} -6.46350 q^{52} +6.50225 q^{53} -3.95741 q^{54} -18.2216 q^{55} -6.54210 q^{56} +0.340854 q^{57} -6.50398 q^{58} -5.56690 q^{59} -42.0716 q^{60} -12.8896 q^{61} +13.3947 q^{62} +1.73125 q^{63} +23.6972 q^{64} -4.16245 q^{65} -33.3799 q^{66} -7.92564 q^{67} +6.78242 q^{68} +7.51946 q^{69} -6.75872 q^{70} +1.00000 q^{71} -21.1943 q^{72} -2.92545 q^{73} -6.93671 q^{74} -15.5090 q^{75} -0.781171 q^{76} -3.89528 q^{77} -7.62516 q^{78} -4.90295 q^{79} +46.4252 q^{80} -10.4961 q^{81} -33.1699 q^{82} -10.0620 q^{83} -8.99376 q^{84} +4.36783 q^{85} -15.5365 q^{86} -5.57362 q^{87} +47.6868 q^{88} +12.6961 q^{89} -21.8960 q^{90} -0.889820 q^{91} -17.2332 q^{92} +11.4787 q^{93} -20.7179 q^{94} -0.503069 q^{95} +43.5758 q^{96} +6.19056 q^{97} +17.4811 q^{98} -12.6194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 165 * q + 22 * q^2 + 18 * q^3 + 166 * q^4 + 28 * q^5 + 16 * q^6 + 24 * q^7 + 66 * q^8 + 177 * q^9 + 14 * q^10 + 18 * q^11 + 54 * q^12 + 44 * q^13 + 26 * q^14 + 24 * q^15 + 168 * q^16 + 143 * q^17 + 57 * q^18 + 20 * q^19 + 49 * q^20 + 39 * q^21 + 25 * q^22 + 52 * q^23 + 27 * q^24 + 175 * q^25 + 48 * q^26 + 69 * q^27 + 28 * q^28 + 58 * q^29 - 11 * q^30 + 28 * q^31 + 114 * q^32 + 110 * q^33 + 55 * q^34 + 67 * q^35 + 202 * q^36 + 44 * q^37 + 35 * q^38 + 27 * q^39 + 53 * q^40 + 141 * q^41 + 40 * q^42 + 29 * q^43 + 52 * q^44 + 54 * q^45 + 29 * q^46 + 87 * q^47 + 53 * q^48 + 143 * q^49 + 16 * q^50 + 37 * q^51 + 105 * q^52 + 101 * q^53 - 36 * q^54 + 72 * q^55 + 57 * q^56 + 82 * q^57 + 4 * q^58 + 103 * q^59 + 53 * q^60 + 16 * q^61 + 54 * q^62 + 126 * q^63 + 136 * q^64 + 159 * q^65 + 53 * q^66 + 60 * q^67 + 220 * q^68 + 81 * q^69 + 16 * q^70 + 165 * q^71 + 176 * q^72 + 124 * q^73 + 29 * q^74 + 44 * q^75 + 18 * q^76 + 127 * q^77 - 91 * q^78 + 14 * q^79 + 158 * q^80 + 213 * q^81 + 20 * q^82 + 116 * q^83 + 67 * q^84 + 59 * q^85 + 30 * q^86 + 28 * q^87 + 79 * q^88 + 195 * q^89 + 16 * q^90 - 26 * q^91 + 173 * q^92 + 116 * q^93 + 53 * q^94 + 26 * q^95 - 36 * q^96 + 88 * q^97 + 150 * q^98 + 12 * q^99

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