LMFDB - Embedded newform 4033.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.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:	$32.2036671352$
Analytic rank:	$1$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.13414 q^{2} -1.44031 q^{3} +2.55454 q^{4} +3.76689 q^{5} +3.07382 q^{6} +1.36855 q^{7} -1.18346 q^{8} -0.925504 q^{9} +O(q^{10})$	\(q-2.13414 q^{2} -1.44031 q^{3} +2.55454 q^{4} +3.76689 q^{5} +3.07382 q^{6} +1.36855 q^{7} -1.18346 q^{8} -0.925504 q^{9} -8.03907 q^{10} -4.23559 q^{11} -3.67933 q^{12} +0.655939 q^{13} -2.92068 q^{14} -5.42550 q^{15} -2.58341 q^{16} +6.15511 q^{17} +1.97515 q^{18} -4.22451 q^{19} +9.62268 q^{20} -1.97114 q^{21} +9.03934 q^{22} -9.48602 q^{23} +1.70456 q^{24} +9.18950 q^{25} -1.39986 q^{26} +5.65395 q^{27} +3.49602 q^{28} +5.22133 q^{29} +11.5788 q^{30} +2.93870 q^{31} +7.88027 q^{32} +6.10057 q^{33} -13.1359 q^{34} +5.15519 q^{35} -2.36424 q^{36} -1.00000 q^{37} +9.01569 q^{38} -0.944756 q^{39} -4.45799 q^{40} -6.27351 q^{41} +4.20668 q^{42} +3.80023 q^{43} -10.8200 q^{44} -3.48628 q^{45} +20.2445 q^{46} -8.83363 q^{47} +3.72091 q^{48} -5.12707 q^{49} -19.6116 q^{50} -8.86528 q^{51} +1.67562 q^{52} +11.2691 q^{53} -12.0663 q^{54} -15.9550 q^{55} -1.61963 q^{56} +6.08461 q^{57} -11.1430 q^{58} -5.74271 q^{59} -13.8597 q^{60} -2.77791 q^{61} -6.27158 q^{62} -1.26660 q^{63} -11.6508 q^{64} +2.47085 q^{65} -13.0195 q^{66} -3.06684 q^{67} +15.7235 q^{68} +13.6628 q^{69} -11.0019 q^{70} +5.09721 q^{71} +1.09530 q^{72} -8.31385 q^{73} +2.13414 q^{74} -13.2357 q^{75} -10.7917 q^{76} -5.79663 q^{77} +2.01624 q^{78} -3.88915 q^{79} -9.73142 q^{80} -5.36693 q^{81} +13.3885 q^{82} -11.8513 q^{83} -5.03536 q^{84} +23.1857 q^{85} -8.11020 q^{86} -7.52033 q^{87} +5.01267 q^{88} -12.2838 q^{89} +7.44019 q^{90} +0.897687 q^{91} -24.2324 q^{92} -4.23264 q^{93} +18.8522 q^{94} -15.9133 q^{95} -11.3500 q^{96} +2.94967 q^{97} +10.9419 q^{98} +3.92006 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) $ 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.13414	−1.50906	−0.754531	−	0.656264i	$-0.772136\pi$
$2$	−2.13414	−1.50906	−0.754531	+	0.656264i	$0.772136\pi$
$3$	−1.44031	−0.831564	−0.415782	−	0.909464i	$-0.636492\pi$
$3$	−1.44031	−0.831564	−0.415782	+	0.909464i	$0.636492\pi$
$4$	2.55454	1.27727
$5$	3.76689	1.68461	0.842303	−	0.539004i	$-0.181199\pi$
$5$	3.76689	1.68461	0.842303	+	0.539004i	$0.181199\pi$
$6$	3.07382	1.25488
$7$	1.36855	0.517264	0.258632	−	0.965976i	$-0.416728\pi$
$7$	1.36855	0.517264	0.258632	+	0.965976i	$0.416728\pi$
$8$	−1.18346	−0.418418
$9$	−0.925504	−0.308501
$10$	−8.03907	−2.54218
$11$	−4.23559	−1.27708	−0.638540	−	0.769589i	$-0.720461\pi$
$11$	−4.23559	−1.27708	−0.638540	+	0.769589i	$0.720461\pi$
$12$	−3.67933	−1.06213
$13$	0.655939	0.181925	0.0909624	−	0.995854i	$-0.471006\pi$
$13$	0.655939	0.181925	0.0909624	+	0.995854i	$0.471006\pi$
$14$	−2.92068	−0.780584
$15$	−5.42550	−1.40086
$16$	−2.58341	−0.645851
$17$	6.15511	1.49283	0.746417	−	0.665478i	$-0.231772\pi$
$17$	6.15511	1.49283	0.746417	+	0.665478i	$0.231772\pi$
$18$	1.97515	0.465548
$19$	−4.22451	−0.969170	−0.484585	−	0.874744i	$-0.661029\pi$
$19$	−4.22451	−0.969170	−0.484585	+	0.874744i	$0.661029\pi$
$20$	9.62268	2.15170
$21$	−1.97114	−0.430138
$22$	9.03934	1.92719
$23$	−9.48602	−1.97797	−0.988986	−	0.148007i	$-0.952714\pi$
$23$	−9.48602	−1.97797	−0.988986	+	0.148007i	$0.952714\pi$
$24$	1.70456	0.347941
$25$	9.18950	1.83790
$26$	−1.39986	−0.274536
$27$	5.65395	1.08810
$28$	3.49602	0.660686
$29$	5.22133	0.969576	0.484788	−	0.874632i	$-0.338897\pi$
$29$	5.22133	0.969576	0.484788	+	0.874632i	$0.338897\pi$
$30$	11.5788	2.11398
$31$	2.93870	0.527805	0.263903	−	0.964549i	$-0.414990\pi$
$31$	2.93870	0.527805	0.263903	+	0.964549i	$0.414990\pi$
$32$	7.88027	1.39305
$33$	6.10057	1.06197
$34$	−13.1359	−2.25278
$35$	5.15519	0.871386
$36$	−2.36424	−0.394040
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	9.01569	1.46254
$39$	−0.944756	−0.151282
$40$	−4.45799	−0.704869
$41$	−6.27351	−0.979758	−0.489879	−	0.871791i	$-0.662959\pi$
$41$	−6.27351	−0.979758	−0.489879	+	0.871791i	$0.662959\pi$
$42$	4.20668	0.649105
$43$	3.80023	0.579529	0.289764	−	0.957098i	$-0.406423\pi$
$43$	3.80023	0.579529	0.289764	+	0.957098i	$0.406423\pi$
$44$	−10.8200	−1.63118
$45$	−3.48628	−0.519704
$46$	20.2445	2.98488
$47$	−8.83363	−1.28852	−0.644258	−	0.764808i	$-0.722834\pi$
$47$	−8.83363	−1.28852	−0.644258	+	0.764808i	$0.722834\pi$
$48$	3.72091	0.537067
$49$	−5.12707	−0.732438
$50$	−19.6116	−2.77351
$51$	−8.86528	−1.24139
$52$	1.67562	0.232367
$53$	11.2691	1.54793	0.773965	−	0.633228i	$-0.218271\pi$
$53$	11.2691	1.54793	0.773965	+	0.633228i	$0.218271\pi$
$54$	−12.0663	−1.64201
$55$	−15.9550	−2.15138
$56$	−1.61963	−0.216432
$57$	6.08461	0.805927
$58$	−11.1430	−1.46315
$59$	−5.74271	−0.747637	−0.373819	−	0.927502i	$-0.621952\pi$
$59$	−5.74271	−0.747637	−0.373819	+	0.927502i	$0.621952\pi$
$60$	−13.8597	−1.78927
$61$	−2.77791	−0.355675	−0.177837	−	0.984060i	$-0.556910\pi$
$61$	−2.77791	−0.355675	−0.177837	+	0.984060i	$0.556910\pi$
$62$	−6.27158	−0.796491
$63$	−1.26660	−0.159577
$64$	−11.6508	−1.45635
$65$	2.47085	0.306472
$66$	−13.0195	−1.60258
$67$	−3.06684	−0.374674	−0.187337	−	0.982296i	$-0.559986\pi$
$67$	−3.06684	−0.374674	−0.187337	+	0.982296i	$0.559986\pi$
$68$	15.7235	1.90675
$69$	13.6628	1.64481
$70$	−11.0019	−1.31498
$71$	5.09721	0.604928	0.302464	−	0.953161i	$-0.402191\pi$
$71$	5.09721	0.604928	0.302464	+	0.953161i	$0.402191\pi$
$72$	1.09530	0.129083
$73$	−8.31385	−0.973063	−0.486531	−	0.873663i	$-0.661738\pi$
$73$	−8.31385	−0.973063	−0.486531	+	0.873663i	$0.661738\pi$
$74$	2.13414	0.248088
$75$	−13.2357	−1.52833
$76$	−10.7917	−1.23789
$77$	−5.79663	−0.660587
$78$	2.01624	0.228294
$79$	−3.88915	−0.437564	−0.218782	−	0.975774i	$-0.570208\pi$
$79$	−3.88915	−0.437564	−0.218782	+	0.975774i	$0.570208\pi$
$80$	−9.73142	−1.08801
$81$	−5.36693	−0.596325
$82$	13.3885	1.47852
$83$	−11.8513	−1.30085	−0.650424	−	0.759571i	$-0.725409\pi$
$83$	−11.8513	−1.30085	−0.650424	+	0.759571i	$0.725409\pi$
$84$	−5.03536	−0.549402
$85$	23.1857	2.51484
$86$	−8.11020	−0.874545
$87$	−7.52033	−0.806264
$88$	5.01267	0.534353
$89$	−12.2838	−1.30208	−0.651041	−	0.759042i	$-0.725667\pi$
$89$	−12.2838	−1.30208	−0.651041	+	0.759042i	$0.725667\pi$
$90$	7.44019	0.784265
$91$	0.897687	0.0941031
$92$	−24.2324	−2.52641
$93$	−4.23264	−0.438904
$94$	18.8522	1.94445
$95$	−15.9133	−1.63267
$96$	−11.3500	−1.15841
$97$	2.94967	0.299493	0.149747	−	0.988724i	$-0.452154\pi$
$97$	2.94967	0.299493	0.149747	+	0.988724i	$0.452154\pi$
$98$	10.9419	1.10529
$99$	3.92006	0.393981
$100$	23.4749	2.34749
$101$	−0.425532	−0.0423420	−0.0211710	−	0.999776i	$-0.506739\pi$
$101$	−0.425532	−0.0423420	−0.0211710	+	0.999776i	$0.506739\pi$
$102$	18.9197	1.87333
$103$	3.34237	0.329334	0.164667	−	0.986349i	$-0.447345\pi$
$103$	3.34237	0.329334	0.164667	+	0.986349i	$0.447345\pi$
$104$	−0.776280	−0.0761206
$105$	−7.42508	−0.724614
$106$	−24.0498	−2.33592
$107$	−5.85588	−0.566109	−0.283055	−	0.959104i	$-0.591348\pi$
$107$	−5.85588	−0.566109	−0.283055	+	0.959104i	$0.591348\pi$
$108$	14.4432	1.38980
$109$	−1.00000	−0.0957826
$109$	−1.00000	−0.0957826
$110$	34.0502	3.24656
$111$	1.44031	0.136708
$112$	−3.53552	−0.334076
$113$	18.8082	1.76933	0.884664	−	0.466229i	$-0.154388\pi$
$113$	18.8082	1.76933	0.884664	+	0.466229i	$0.154388\pi$
$114$	−12.9854	−1.21619
$115$	−35.7329	−3.33211
$116$	13.3381	1.23841
$117$	−0.607074	−0.0561240
$118$	12.2557	1.12823
$119$	8.42359	0.772190
$120$	6.42089	0.586144
$121$	6.94025	0.630932
$122$	5.92844	0.536736
$123$	9.03580	0.814731
$124$	7.50702	0.674150
$125$	15.7814	1.41153
$126$	2.70310	0.240811
$127$	4.72551	0.419321	0.209661	−	0.977774i	$-0.432764\pi$
$127$	4.72551	0.419321	0.209661	+	0.977774i	$0.432764\pi$
$128$	9.10378	0.804668
$129$	−5.47351	−0.481915
$130$	−5.27314	−0.462485
$131$	−2.44067	−0.213242	−0.106621	−	0.994300i	$-0.534003\pi$
$131$	−2.44067	−0.213242	−0.106621	+	0.994300i	$0.534003\pi$
$132$	15.5842	1.35643
$133$	−5.78147	−0.501317
$134$	6.54505	0.565406
$135$	21.2978	1.83302
$136$	−7.28436	−0.624629
$137$	14.5983	1.24721	0.623606	−	0.781738i	$-0.285667\pi$
$137$	14.5983	1.24721	0.623606	+	0.781738i	$0.285667\pi$
$138$	−29.1583	−2.48212
$139$	−9.29174	−0.788115	−0.394057	−	0.919086i	$-0.628929\pi$
$139$	−9.29174	−0.788115	−0.394057	+	0.919086i	$0.628929\pi$
$140$	13.1691	1.11300
$141$	12.7232	1.07148
$142$	−10.8781	−0.912874
$143$	−2.77829	−0.232332
$144$	2.39095	0.199246
$145$	19.6682	1.63335
$146$	17.7429	1.46841
$147$	7.38457	0.609069
$148$	−2.55454	−0.209982
$149$	−6.01718	−0.492947	−0.246473	−	0.969150i	$-0.579272\pi$
$149$	−6.01718	−0.492947	−0.246473	+	0.969150i	$0.579272\pi$
$150$	28.2469	2.30635
$151$	−10.6290	−0.864978	−0.432489	−	0.901639i	$-0.642365\pi$
$151$	−10.6290	−0.864978	−0.432489	+	0.901639i	$0.642365\pi$
$152$	4.99956	0.405518
$153$	−5.69659	−0.460542
$154$	12.3708	0.996867
$155$	11.0698	0.889144
$156$	−2.41342	−0.193228
$157$	−20.1730	−1.60998	−0.804992	−	0.593286i	$-0.797830\pi$
$157$	−20.1730	−1.60998	−0.804992	+	0.593286i	$0.797830\pi$
$158$	8.29998	0.660311
$159$	−16.2310	−1.28720
$160$	29.6841	2.34674
$161$	−12.9821	−1.02313
$162$	11.4538	0.899892
$163$	21.0937	1.65219	0.826094	−	0.563532i	$-0.190558\pi$
$163$	21.0937	1.65219	0.826094	+	0.563532i	$0.190558\pi$
$164$	−16.0259	−1.25141
$165$	22.9802	1.78901
$166$	25.2923	1.96306
$167$	−16.4511	−1.27302	−0.636511	−	0.771268i	$-0.719623\pi$
$167$	−16.4511	−1.27302	−0.636511	+	0.771268i	$0.719623\pi$
$168$	2.33277	0.179977
$169$	−12.5697	−0.966903
$170$	−49.4814	−3.79505
$171$	3.90981	0.298990
$172$	9.70783	0.740215
$173$	−4.92314	−0.374299	−0.187150	−	0.982331i	$-0.559925\pi$
$173$	−4.92314	−0.374299	−0.187150	+	0.982331i	$0.559925\pi$
$174$	16.0494	1.21670
$175$	12.5763	0.950679
$176$	10.9423	0.824803
$177$	8.27129	0.621708
$178$	26.2154	1.96492
$179$	−10.5122	−0.785716	−0.392858	−	0.919599i	$-0.628514\pi$
$179$	−10.5122	−0.785716	−0.392858	+	0.919599i	$0.628514\pi$
$180$	−8.90584	−0.663802
$181$	−3.29512	−0.244924	−0.122462	−	0.992473i	$-0.539079\pi$
$181$	−3.29512	−0.244924	−0.122462	+	0.992473i	$0.539079\pi$
$182$	−1.91579	−0.142008
$183$	4.00105	0.295766
$184$	11.2264	0.827619
$185$	−3.76689	−0.276948
$186$	9.03302	0.662333
$187$	−26.0706	−1.90647
$188$	−22.5659	−1.64578
$189$	7.73772	0.562836
$190$	33.9612	2.46380
$191$	20.8180	1.50634	0.753170	−	0.657826i	$-0.228524\pi$
$191$	20.8180	1.50634	0.753170	+	0.657826i	$0.228524\pi$
$192$	16.7807	1.21104
$193$	6.40909	0.461336	0.230668	−	0.973032i	$-0.425909\pi$
$193$	6.40909	0.461336	0.230668	+	0.973032i	$0.425909\pi$
$194$	−6.29500	−0.451954
$195$	−3.55880	−0.254851
$196$	−13.0973	−0.935521
$197$	−18.9202	−1.34801	−0.674003	−	0.738729i	$-0.735426\pi$
$197$	−18.9202	−1.34801	−0.674003	+	0.738729i	$0.735426\pi$
$198$	−8.36594	−0.594542
$199$	7.33651	0.520071	0.260036	−	0.965599i	$-0.416266\pi$
$199$	7.33651	0.520071	0.260036	+	0.965599i	$0.416266\pi$
$200$	−10.8754	−0.769010
$201$	4.41720	0.311565
$202$	0.908144	0.0638968
$203$	7.14565	0.501527
$204$	−22.6467	−1.58559
$205$	−23.6317	−1.65051
$206$	−7.13308	−0.496985
$207$	8.77936	0.610207
$208$	−1.69456	−0.117496
$209$	17.8933	1.23771
$210$	15.8461	1.09349
$211$	18.6094	1.28113	0.640563	−	0.767906i	$-0.278701\pi$
$211$	18.6094	1.28113	0.640563	+	0.767906i	$0.278701\pi$
$212$	28.7874	1.97712
$213$	−7.34157	−0.503036
$214$	12.4972	0.854294
$215$	14.3150	0.976278
$216$	−6.69124	−0.455282
$217$	4.02176	0.273015
$218$	2.13414	0.144542
$219$	11.9745	0.809164
$220$	−40.7578	−2.74789
$221$	4.03738	0.271584
$222$	−3.07382	−0.206301
$223$	11.8957	0.796593	0.398297	−	0.917257i	$-0.369601\pi$
$223$	11.8957	0.796593	0.398297	+	0.917257i	$0.369601\pi$
$224$	10.7846	0.720574
$225$	−8.50492	−0.566995
$226$	−40.1393	−2.67003
$227$	−9.19316	−0.610172	−0.305086	−	0.952325i	$-0.598685\pi$
$227$	−9.19316	−0.610172	−0.305086	+	0.952325i	$0.598685\pi$
$228$	15.5434	1.02939
$229$	7.32489	0.484042	0.242021	−	0.970271i	$-0.422190\pi$
$229$	7.32489	0.484042	0.242021	+	0.970271i	$0.422190\pi$
$230$	76.2588	5.02836
$231$	8.34895	0.549320
$232$	−6.17925	−0.405688
$233$	−5.87895	−0.385143	−0.192571	−	0.981283i	$-0.561683\pi$
$233$	−5.87895	−0.385143	−0.192571	+	0.981283i	$0.561683\pi$
$234$	1.29558	0.0846947
$235$	−33.2753	−2.17064
$236$	−14.6700	−0.954935
$237$	5.60159	0.363862
$238$	−17.9771	−1.16528
$239$	23.9499	1.54919	0.774595	−	0.632458i	$-0.217954\pi$
$239$	23.9499	1.54919	0.774595	+	0.632458i	$0.217954\pi$
$240$	14.0163	0.904746
$241$	16.4993	1.06281	0.531406	−	0.847117i	$-0.321664\pi$
$241$	16.4993	1.06281	0.531406	+	0.847117i	$0.321664\pi$
$242$	−14.8114	−0.952116
$243$	−9.23180	−0.592220
$244$	−7.09628	−0.454293
$245$	−19.3131	−1.23387
$246$	−19.2836	−1.22948
$247$	−2.77102	−0.176316
$248$	−3.47784	−0.220843
$249$	17.0695	1.08174
$250$	−33.6797	−2.13009
$251$	−21.7809	−1.37480	−0.687400	−	0.726279i	$-0.741248\pi$
$251$	−21.7809	−1.37480	−0.687400	+	0.726279i	$0.741248\pi$
$252$	−3.23558	−0.203823
$253$	40.1789	2.52603
$254$	−10.0849	−0.632782
$255$	−33.3946	−2.09125
$256$	3.87281	0.242050
$257$	−27.4537	−1.71251	−0.856257	−	0.516549i	$-0.827216\pi$
$257$	−27.4537	−1.71251	−0.856257	+	0.516549i	$0.827216\pi$
$258$	11.6812	0.727240
$259$	−1.36855	−0.0850377
$260$	6.31189	0.391447
$261$	−4.83236	−0.299116
$262$	5.20871	0.321795
$263$	−19.0482	−1.17456	−0.587281	−	0.809383i	$-0.699802\pi$
$263$	−19.0482	−1.17456	−0.587281	+	0.809383i	$0.699802\pi$
$264$	−7.21981	−0.444348
$265$	42.4495	2.60765
$266$	12.3384	0.756519
$267$	17.6925	1.08276
$268$	−7.83436	−0.478560
$269$	−28.1125	−1.71405	−0.857026	−	0.515274i	$-0.827690\pi$
$269$	−28.1125	−1.71405	−0.857026	+	0.515274i	$0.827690\pi$
$270$	−45.4525	−2.76615
$271$	7.39562	0.449252	0.224626	−	0.974445i	$-0.427884\pi$
$271$	7.39562	0.449252	0.224626	+	0.974445i	$0.427884\pi$
$272$	−15.9012	−0.964149
$273$	−1.29295	−0.0782528
$274$	−31.1547	−1.88212
$275$	−38.9230	−2.34714
$276$	34.9022	2.10087
$277$	−5.92276	−0.355864	−0.177932	−	0.984043i	$-0.556941\pi$
$277$	−5.92276	−0.355864	−0.177932	+	0.984043i	$0.556941\pi$
$278$	19.8298	1.18931
$279$	−2.71978	−0.162829
$280$	−6.10099	−0.364604
$281$	28.0893	1.67567	0.837834	−	0.545924i	$-0.183821\pi$
$281$	28.0893	1.67567	0.837834	+	0.545924i	$0.183821\pi$
$282$	−27.1530	−1.61694
$283$	21.2649	1.26407	0.632033	−	0.774942i	$-0.282221\pi$
$283$	21.2649	1.26407	0.632033	+	0.774942i	$0.282221\pi$
$284$	13.0210	0.772656
$285$	22.9201	1.35767
$286$	5.92925	0.350604
$287$	−8.58562	−0.506793
$288$	−7.29322	−0.429757
$289$	20.8854	1.22856
$290$	−41.9746	−2.46483
$291$	−4.24844	−0.249048
$292$	−21.2381	−1.24286
$293$	−18.5883	−1.08594	−0.542971	−	0.839751i	$-0.682701\pi$
$293$	−18.5883	−1.08594	−0.542971	+	0.839751i	$0.682701\pi$
$294$	−15.7597	−0.919123
$295$	−21.6322	−1.25947
$296$	1.18346	0.0687875
$297$	−23.9478	−1.38959
$298$	12.8415	0.743888
$299$	−6.22225	−0.359842
$300$	−33.8112	−1.95209
$301$	5.20081	0.299769
$302$	22.6838	1.30531
$303$	0.612899	0.0352101
$304$	10.9136	0.625940
$305$	−10.4641	−0.599172
$306$	12.1573	0.694986
$307$	−15.0461	−0.858725	−0.429363	−	0.903132i	$-0.641262\pi$
$307$	−15.0461	−0.858725	−0.429363	+	0.903132i	$0.641262\pi$
$308$	−14.8077	−0.843748
$309$	−4.81405	−0.273862
$310$	−23.6244	−1.34177
$311$	−23.7016	−1.34399	−0.671996	−	0.740555i	$-0.734563\pi$
$311$	−23.7016	−1.34399	−0.671996	+	0.740555i	$0.734563\pi$
$312$	1.11809	0.0632991
$313$	5.26113	0.297377	0.148688	−	0.988884i	$-0.452495\pi$
$313$	5.26113	0.297377	0.148688	+	0.988884i	$0.452495\pi$
$314$	43.0520	2.42957
$315$	−4.77115	−0.268824
$316$	−9.93500	−0.558887
$317$	6.33348	0.355723	0.177862	−	0.984055i	$-0.443082\pi$
$317$	6.33348	0.355723	0.177862	+	0.984055i	$0.443082\pi$
$318$	34.6392	1.94247
$319$	−22.1154	−1.23823
$320$	−43.8872	−2.45337
$321$	8.43429	0.470756
$322$	27.7056	1.54397
$323$	−26.0024	−1.44681
$324$	−13.7100	−0.761669
$325$	6.02775	0.334359
$326$	−45.0169	−2.49326
$327$	1.44031	0.0796494
$328$	7.42447	0.409948
$329$	−12.0893	−0.666503
$330$	−49.0429	−2.69972
$331$	−7.89057	−0.433705	−0.216853	−	0.976204i	$-0.569579\pi$
$331$	−7.89057	−0.433705	−0.216853	+	0.976204i	$0.569579\pi$
$332$	−30.2746	−1.66153
$333$	0.925504	0.0507173
$334$	35.1088	1.92107
$335$	−11.5525	−0.631178
$336$	5.09225	0.277805
$337$	−26.5677	−1.44724	−0.723618	−	0.690201i	$-0.757522\pi$
$337$	−26.5677	−1.44724	−0.723618	+	0.690201i	$0.757522\pi$
$338$	26.8256	1.45912
$339$	−27.0897	−1.47131
$340$	59.2287	3.21213
$341$	−12.4471	−0.674049
$342$	−8.34406	−0.451195
$343$	−16.5965	−0.896128
$344$	−4.49743	−0.242485
$345$	51.4664	2.77086
$346$	10.5067	0.564841
$347$	−0.918185	−0.0492907	−0.0246454	−	0.999696i	$-0.507846\pi$
$347$	−0.918185	−0.0492907	−0.0246454	+	0.999696i	$0.507846\pi$
$348$	−19.2110	−1.02982
$349$	13.0948	0.700950	0.350475	−	0.936572i	$-0.386020\pi$
$349$	13.0948	0.700950	0.350475	+	0.936572i	$0.386020\pi$
$350$	−26.8396	−1.43463
$351$	3.70864	0.197953
$352$	−33.3776	−1.77903
$353$	9.58472	0.510143	0.255072	−	0.966922i	$-0.417901\pi$
$353$	9.58472	0.510143	0.255072	+	0.966922i	$0.417901\pi$
$354$	−17.6521	−0.938197
$355$	19.2007	1.01907
$356$	−31.3795	−1.66311
$357$	−12.1326	−0.642125
$358$	22.4344	1.18569
$359$	−21.5381	−1.13674	−0.568370	−	0.822773i	$-0.692426\pi$
$359$	−21.5381	−1.13674	−0.568370	+	0.822773i	$0.692426\pi$
$360$	4.12589	0.217453
$361$	−1.15347	−0.0607092
$362$	7.03224	0.369606
$363$	−9.99612	−0.524660
$364$	2.29318	0.120195
$365$	−31.3174	−1.63923
$366$	−8.53880	−0.446330
$367$	−0.944153	−0.0492844	−0.0246422	−	0.999696i	$-0.507845\pi$
$367$	−0.944153	−0.0492844	−0.0246422	+	0.999696i	$0.507845\pi$
$368$	24.5062	1.27748
$369$	5.80616	0.302257
$370$	8.03907	0.417931
$371$	15.4223	0.800689
$372$	−10.8124	−0.560599
$373$	−33.1288	−1.71535	−0.857673	−	0.514196i	$-0.828090\pi$
$373$	−33.1288	−1.71535	−0.857673	+	0.514196i	$0.828090\pi$
$374$	55.6381	2.87698
$375$	−22.7301	−1.17378
$376$	10.4543	0.539138
$377$	3.42487	0.176390
$378$	−16.5134	−0.849355
$379$	14.6053	0.750224	0.375112	−	0.926980i	$-0.377604\pi$
$379$	14.6053	0.750224	0.375112	+	0.926980i	$0.377604\pi$
$380$	−40.6512	−2.08536
$381$	−6.80621	−0.348693
$382$	−44.4285	−2.27316
$383$	−6.41574	−0.327829	−0.163914	−	0.986475i	$-0.552412\pi$
$383$	−6.41574	−0.327829	−0.163914	+	0.986475i	$0.552412\pi$
$384$	−13.1123	−0.669133
$385$	−21.8353	−1.11283
$386$	−13.6779	−0.696185
$387$	−3.51713	−0.178786
$388$	7.53505	0.382534
$389$	13.2814	0.673392	0.336696	−	0.941613i	$-0.390690\pi$
$389$	13.2814	0.673392	0.336696	+	0.941613i	$0.390690\pi$
$390$	7.59496	0.384586
$391$	−58.3876	−2.95279
$392$	6.06770	0.306465
$393$	3.51532	0.177324
$394$	40.3782	2.03422
$395$	−14.6500	−0.737123
$396$	10.0140	0.503220
$397$	−27.3528	−1.37280	−0.686399	−	0.727225i	$-0.740810\pi$
$397$	−27.3528	−1.37280	−0.686399	+	0.727225i	$0.740810\pi$
$398$	−15.6571	−0.784820
$399$	8.32711	0.416877
$400$	−23.7402	−1.18701
$401$	−0.492392	−0.0245889	−0.0122944	−	0.999924i	$-0.503914\pi$
$401$	−0.492392	−0.0245889	−0.0122944	+	0.999924i	$0.503914\pi$
$402$	−9.42691	−0.470172
$403$	1.92760	0.0960208
$404$	−1.08704	−0.0540822
$405$	−20.2167	−1.00457
$406$	−15.2498	−0.756835
$407$	4.23559	0.209951
$408$	10.4917	0.519419
$409$	−27.4873	−1.35916	−0.679581	−	0.733601i	$-0.737838\pi$
$409$	−27.4873	−1.35916	−0.679581	+	0.733601i	$0.737838\pi$
$410$	50.4332	2.49072
$411$	−21.0260	−1.03714
$412$	8.53822	0.420648
$413$	−7.85920	−0.386726
$414$	−18.7363	−0.920841
$415$	−44.6426	−2.19142
$416$	5.16898	0.253430
$417$	13.3830	0.655368
$418$	−38.1868	−1.86778
$419$	−4.38441	−0.214193	−0.107096	−	0.994249i	$-0.534155\pi$
$419$	−4.38441	−0.214193	−0.107096	+	0.994249i	$0.534155\pi$
$420$	−18.9677	−0.925527
$421$	24.2082	1.17984	0.589918	−	0.807463i	$-0.299160\pi$
$421$	24.2082	1.17984	0.589918	+	0.807463i	$0.299160\pi$
$422$	−39.7150	−1.93330
$423$	8.17556	0.397509
$424$	−13.3366	−0.647681
$425$	56.5624	2.74368
$426$	15.6679	0.759113
$427$	−3.80171	−0.183978
$428$	−14.9591	−0.723074
$429$	4.00160	0.193199
$430$	−30.5503	−1.47327
$431$	7.87818	0.379478	0.189739	−	0.981835i	$-0.439236\pi$
$431$	7.87818	0.379478	0.189739	+	0.981835i	$0.439236\pi$
$432$	−14.6064	−0.702753
$433$	−28.2580	−1.35799	−0.678996	−	0.734142i	$-0.737585\pi$
$433$	−28.2580	−1.35799	−0.678996	+	0.734142i	$0.737585\pi$
$434$	−8.58298	−0.411996
$435$	−28.3283	−1.35824
$436$	−2.55454	−0.122340
$437$	40.0738	1.91699
$438$	−25.5553	−1.22108
$439$	32.8960	1.57004	0.785021	−	0.619470i	$-0.212652\pi$
$439$	32.8960	1.57004	0.785021	+	0.619470i	$0.212652\pi$
$440$	18.8822	0.900174
$441$	4.74512	0.225958
$442$	−8.61632	−0.409837
$443$	−14.9879	−0.712095	−0.356047	−	0.934468i	$-0.615876\pi$
$443$	−14.9879	−0.712095	−0.356047	+	0.934468i	$0.615876\pi$
$444$	3.67933	0.174613
$445$	−46.2719	−2.19350
$446$	−25.3870	−1.20211
$447$	8.66662	0.409917
$448$	−15.9447	−0.753315
$449$	−19.8560	−0.937064	−0.468532	−	0.883446i	$-0.655217\pi$
$449$	−19.8560	−0.937064	−0.468532	+	0.883446i	$0.655217\pi$
$450$	18.1507	0.855631
$451$	26.5720	1.25123
$452$	48.0464	2.25991
$453$	15.3091	0.719284
$454$	19.6195	0.920787
$455$	3.38149	0.158527
$456$	−7.20092	−0.337214
$457$	23.3544	1.09247	0.546236	−	0.837631i	$-0.316060\pi$
$457$	23.3544	1.09247	0.546236	+	0.837631i	$0.316060\pi$
$458$	−15.6323	−0.730450
$459$	34.8007	1.62436
$460$	−91.2810	−4.25600
$461$	−13.3668	−0.622555	−0.311278	−	0.950319i	$-0.600757\pi$
$461$	−13.3668	−0.622555	−0.311278	+	0.950319i	$0.600757\pi$
$462$	−17.8178	−0.828959
$463$	9.81123	0.455966	0.227983	−	0.973665i	$-0.426787\pi$
$463$	9.81123	0.455966	0.227983	+	0.973665i	$0.426787\pi$
$464$	−13.4888	−0.626202
$465$	−15.9439	−0.739380
$466$	12.5465	0.581205
$467$	32.5987	1.50849	0.754244	−	0.656594i	$-0.228003\pi$
$467$	32.5987	1.50849	0.754244	+	0.656594i	$0.228003\pi$
$468$	−1.55080	−0.0716856
$469$	−4.19713	−0.193805
$470$	71.0141	3.27564
$471$	29.0554	1.33880
$472$	6.79629	0.312825
$473$	−16.0962	−0.740104
$474$	−11.9546	−0.549091
$475$	−38.8212	−1.78124
$476$	21.5184	0.986295
$477$	−10.4296	−0.477539
$478$	−51.1123	−2.33782
$479$	−18.9961	−0.867952	−0.433976	−	0.900924i	$-0.642890\pi$
$479$	−18.9961	−0.867952	−0.433976	+	0.900924i	$0.642890\pi$
$480$	−42.7544	−1.95146
$481$	−0.655939	−0.0299082
$482$	−35.2117	−1.60385
$483$	18.6983	0.850801
$484$	17.7291	0.805870
$485$	11.1111	0.504529
$486$	19.7019	0.893697
$487$	9.44711	0.428090	0.214045	−	0.976824i	$-0.431336\pi$
$487$	9.44711	0.428090	0.214045	+	0.976824i	$0.431336\pi$
$488$	3.28756	0.148821
$489$	−30.3815	−1.37390
$490$	41.2168	1.86199
$491$	31.4925	1.42124	0.710619	−	0.703577i	$-0.248415\pi$
$491$	31.4925	1.42124	0.710619	+	0.703577i	$0.248415\pi$
$492$	23.0823	1.04063
$493$	32.1379	1.44742
$494$	5.91374	0.266072
$495$	14.7665	0.663703
$496$	−7.59184	−0.340884
$497$	6.97580	0.312907
$498$	−36.4287	−1.63241
$499$	1.61594	0.0723394	0.0361697	−	0.999346i	$-0.488484\pi$
$499$	1.61594	0.0723394	0.0361697	+	0.999346i	$0.488484\pi$
$500$	40.3142	1.80291
$501$	23.6946	1.05860
$502$	46.4835	2.07466
$503$	−26.6470	−1.18813	−0.594066	−	0.804416i	$-0.702478\pi$
$503$	−26.6470	−1.18813	−0.594066	+	0.804416i	$0.702478\pi$
$504$	1.49898	0.0667697
$505$	−1.60294	−0.0713297
$506$	−85.7474	−3.81193
$507$	18.1043	0.804042
$508$	12.0715	0.535587
$509$	−33.1932	−1.47126	−0.735632	−	0.677381i	$-0.763115\pi$
$509$	−33.1932	−1.47126	−0.735632	+	0.677381i	$0.763115\pi$
$510$	71.2686	3.15583
$511$	−11.3779	−0.503330
$512$	−26.4727	−1.16994
$513$	−23.8852	−1.05456
$514$	58.5900	2.58429
$515$	12.5904	0.554798
$516$	−13.9823	−0.615536
$517$	37.4157	1.64554
$518$	2.92068	0.128327
$519$	7.09085	0.311254
$520$	−2.92417	−0.128233
$521$	14.0609	0.616021	0.308010	−	0.951383i	$-0.400337\pi$
$521$	14.0609	0.616021	0.308010	+	0.951383i	$0.400337\pi$
$522$	10.3129	0.451384
$523$	2.53820	0.110988	0.0554940	−	0.998459i	$-0.482327\pi$
$523$	2.53820	0.110988	0.0554940	+	0.998459i	$0.482327\pi$
$524$	−6.23478	−0.272368
$525$	−18.1138	−0.790551
$526$	40.6515	1.77249
$527$	18.0880	0.787926
$528$	−15.7602	−0.685877
$529$	66.9847	2.91238
$530$	−90.5931	−3.93511
$531$	5.31490	0.230647
$532$	−14.7690	−0.640317
$533$	−4.11504	−0.178242
$534$	−37.7583	−1.63396
$535$	−22.0585	−0.953671
$536$	3.62949	0.156770
$537$	15.1408	0.653373
$538$	59.9960	2.58661
$539$	21.7162	0.935381
$540$	54.4061	2.34127
$541$	8.15077	0.350429	0.175214	−	0.984530i	$-0.443938\pi$
$541$	8.15077	0.350429	0.175214	+	0.984530i	$0.443938\pi$
$542$	−15.7833	−0.677950
$543$	4.74600	0.203670
$544$	48.5040	2.07959
$545$	−3.76689	−0.161356
$546$	2.75933	0.118088
$547$	1.65530	0.0707754	0.0353877	−	0.999374i	$-0.488733\pi$
$547$	1.65530	0.0707754	0.0353877	+	0.999374i	$0.488733\pi$
$548$	37.2918	1.59303
$549$	2.57097	0.109726
$550$	83.0670	3.54199
$551$	−22.0576	−0.939684
$552$	−16.1695	−0.688218
$553$	−5.32251	−0.226336
$554$	12.6400	0.537021
$555$	5.42550	0.230300
$556$	−23.7361	−1.00664
$557$	41.4994	1.75839	0.879193	−	0.476466i	$-0.158083\pi$
$557$	41.4994	1.75839	0.879193	+	0.476466i	$0.158083\pi$
$558$	5.80437	0.245719
$559$	2.49272	0.105431
$560$	−13.3179	−0.562786
$561$	37.5497	1.58535
$562$	−59.9465	−2.52869
$563$	1.36805	0.0576565	0.0288283	−	0.999584i	$-0.490822\pi$
$563$	1.36805	0.0576565	0.0288283	+	0.999584i	$0.490822\pi$
$564$	32.5018	1.36857
$565$	70.8486	2.98062
$566$	−45.3821	−1.90755
$567$	−7.34492	−0.308458
$568$	−6.03237	−0.253113
$569$	−42.5324	−1.78305	−0.891525	−	0.452972i	$-0.850364\pi$
$569$	−42.5324	−1.78305	−0.891525	+	0.452972i	$0.850364\pi$
$570$	−48.9146	−2.04881
$571$	20.1118	0.841654	0.420827	−	0.907141i	$-0.361740\pi$
$571$	20.1118	0.841654	0.420827	+	0.907141i	$0.361740\pi$
$572$	−7.09725	−0.296751
$573$	−29.9844	−1.25262
$574$	18.3229	0.764783
$575$	−87.1718	−3.63532
$576$	10.7828	0.449285
$577$	−7.39345	−0.307793	−0.153897	−	0.988087i	$-0.549182\pi$
$577$	−7.39345	−0.307793	−0.153897	+	0.988087i	$0.549182\pi$
$578$	−44.5724	−1.85397
$579$	−9.23108	−0.383631
$580$	50.2432	2.08623
$581$	−16.2191	−0.672882
$582$	9.06675	0.375829
$583$	−47.7313	−1.97683
$584$	9.83915	0.407147
$585$	−2.28679	−0.0945469
$586$	39.6701	1.63876
$587$	−0.977209	−0.0403337	−0.0201669	−	0.999797i	$-0.506420\pi$
$587$	−0.977209	−0.0403337	−0.0201669	+	0.999797i	$0.506420\pi$
$588$	18.8642	0.777945
$589$	−12.4146	−0.511533
$590$	46.1661	1.90063
$591$	27.2509	1.12095
$592$	2.58341	0.106177
$593$	−5.61013	−0.230381	−0.115190	−	0.993343i	$-0.536748\pi$
$593$	−5.61013	−0.230381	−0.115190	+	0.993343i	$0.536748\pi$
$594$	51.1079	2.09698
$595$	31.7308	1.30084
$596$	−15.3711	−0.629626
$597$	−10.5669	−0.432473
$598$	13.2791	0.543024
$599$	0.586628	0.0239690	0.0119845	−	0.999928i	$-0.496185\pi$
$599$	0.586628	0.0239690	0.0119845	+	0.999928i	$0.496185\pi$
$600$	15.6640	0.639481
$601$	−26.7621	−1.09165	−0.545825	−	0.837900i	$-0.683783\pi$
$601$	−26.7621	−1.09165	−0.545825	+	0.837900i	$0.683783\pi$
$602$	−11.0992	−0.452371
$603$	2.83837	0.115587
$604$	−27.1523	−1.10481
$605$	26.1432	1.06287
$606$	−1.30801	−0.0531343
$607$	−28.1114	−1.14101	−0.570504	−	0.821295i	$-0.693252\pi$
$607$	−28.1114	−1.14101	−0.570504	+	0.821295i	$0.693252\pi$
$608$	−33.2903	−1.35010
$609$	−10.2920	−0.417051
$610$	22.3318	0.904189
$611$	−5.79432	−0.234413
$612$	−14.5522	−0.588236
$613$	5.88354	0.237634	0.118817	−	0.992916i	$-0.462090\pi$
$613$	5.88354	0.237634	0.118817	+	0.992916i	$0.462090\pi$
$614$	32.1104	1.29587
$615$	34.0369	1.37250
$616$	6.86010	0.276401
$617$	−43.7079	−1.75961	−0.879807	−	0.475331i	$-0.842328\pi$
$617$	−43.7079	−1.75961	−0.879807	+	0.475331i	$0.842328\pi$
$618$	10.2739	0.413275
$619$	11.2102	0.450577	0.225289	−	0.974292i	$-0.427667\pi$
$619$	11.2102	0.450577	0.225289	+	0.974292i	$0.427667\pi$
$620$	28.2781	1.13568
$621$	−53.6335	−2.15224
$622$	50.5824	2.02817
$623$	−16.8110	−0.673520
$624$	2.44069	0.0977057
$625$	13.4994	0.539975
$626$	−11.2280	−0.448760
$627$	−25.7720	−1.02923
$628$	−51.5328	−2.05638
$629$	−6.15511	−0.245421
$630$	10.1823	0.405672
$631$	34.6028	1.37751	0.688757	−	0.724992i	$-0.258157\pi$
$631$	34.6028	1.37751	0.688757	+	0.724992i	$0.258157\pi$
$632$	4.60267	0.183084
$633$	−26.8033	−1.06534
$634$	−13.5165	−0.536809
$635$	17.8005	0.706392
$636$	−41.4628	−1.64411
$637$	−3.36304	−0.133249
$638$	47.1973	1.86856
$639$	−4.71749	−0.186621
$640$	34.2930	1.35555
$641$	7.71866	0.304869	0.152434	−	0.988314i	$-0.451289\pi$
$641$	7.71866	0.304869	0.152434	+	0.988314i	$0.451289\pi$
$642$	−17.9999	−0.710400
$643$	16.4823	0.650000	0.325000	−	0.945714i	$-0.394636\pi$
$643$	16.4823	0.650000	0.325000	+	0.945714i	$0.394636\pi$
$644$	−33.1633	−1.30682
$645$	−20.6181	−0.811838
$646$	55.4926	2.18333
$647$	7.55485	0.297012	0.148506	−	0.988912i	$-0.452554\pi$
$647$	7.55485	0.297012	0.148506	+	0.988912i	$0.452554\pi$
$648$	6.35157	0.249513
$649$	24.3238	0.954792
$650$	−12.8640	−0.504569
$651$	−5.79258	−0.227029
$652$	53.8848	2.11029
$653$	−9.64330	−0.377371	−0.188686	−	0.982038i	$-0.560423\pi$
$653$	−9.64330	−0.377371	−0.188686	+	0.982038i	$0.560423\pi$
$654$	−3.07382	−0.120196
$655$	−9.19373	−0.359229
$656$	16.2070	0.632778
$657$	7.69451	0.300191
$658$	25.8002	1.00580
$659$	−41.2168	−1.60558	−0.802790	−	0.596262i	$-0.796652\pi$
$659$	−41.2168	−1.60558	−0.802790	+	0.596262i	$0.796652\pi$
$660$	58.7039	2.28504
$661$	40.6401	1.58072	0.790359	−	0.612644i	$-0.209894\pi$
$661$	40.6401	1.58072	0.790359	+	0.612644i	$0.209894\pi$
$662$	16.8396	0.654488
$663$	−5.81508	−0.225839
$664$	14.0256	0.544298
$665$	−21.7782	−0.844522
$666$	−1.97515	−0.0765356
$667$	−49.5296	−1.91779
$668$	−42.0249	−1.62599
$669$	−17.1335	−0.662418
$670$	24.6545	0.952487
$671$	11.7661	0.454225
$672$	−15.5331	−0.599203
$673$	10.4961	0.404594	0.202297	−	0.979324i	$-0.435159\pi$
$673$	10.4961	0.404594	0.202297	+	0.979324i	$0.435159\pi$
$674$	56.6992	2.18397
$675$	51.9569	1.99982
$676$	−32.1099	−1.23500
$677$	−46.9452	−1.80425	−0.902125	−	0.431474i	$-0.857994\pi$
$677$	−46.9452	−1.80425	−0.902125	+	0.431474i	$0.857994\pi$
$678$	57.8131	2.22030
$679$	4.03677	0.154917
$680$	−27.4394	−1.05225
$681$	13.2410	0.507397
$682$	26.5639	1.01718
$683$	−26.5916	−1.01750	−0.508750	−	0.860914i	$-0.669892\pi$
$683$	−26.5916	−1.01750	−0.508750	+	0.860914i	$0.669892\pi$
$684$	9.98776	0.381891
$685$	54.9901	2.10106
$686$	35.4192	1.35231
$687$	−10.5501	−0.402512
$688$	−9.81752	−0.374290
$689$	7.39184	0.281607
$690$	−109.836	−4.18140
$691$	−42.3694	−1.61181	−0.805903	−	0.592047i	$-0.798320\pi$
$691$	−42.3694	−1.61181	−0.805903	+	0.592047i	$0.798320\pi$
$692$	−12.5764	−0.478081
$693$	5.36481	0.203792
$694$	1.95953	0.0743828
$695$	−35.0010	−1.32766
$696$	8.90004	0.337355
$697$	−38.6142	−1.46262
$698$	−27.9462	−1.05778
$699$	8.46752	0.320271
$700$	32.1267	1.21427
$701$	−25.9240	−0.979134	−0.489567	−	0.871966i	$-0.662845\pi$
$701$	−25.9240	−0.979134	−0.489567	+	0.871966i	$0.662845\pi$
$702$	−7.91475	−0.298723
$703$	4.22451	0.159331
$704$	49.3479	1.85987
$705$	47.9268	1.80503
$706$	−20.4551	−0.769838
$707$	−0.582363	−0.0219020
$708$	21.1293	0.794089
$709$	42.6047	1.60005	0.800027	−	0.599964i	$-0.204819\pi$
$709$	42.6047	1.60005	0.800027	+	0.599964i	$0.204819\pi$
$710$	−40.9768	−1.53783
$711$	3.59943	0.134989
$712$	14.5375	0.544814
$713$	−27.8765	−1.04398
$714$	25.8926	0.969007
$715$	−10.4655	−0.391389
$716$	−26.8537	−1.00357
$717$	−34.4953	−1.28825
$718$	45.9653	1.71541
$719$	22.0989	0.824150	0.412075	−	0.911150i	$-0.364804\pi$
$719$	22.0989	0.824150	0.412075	+	0.911150i	$0.364804\pi$
$720$	9.00647	0.335651
$721$	4.57421	0.170352
$722$	2.46167	0.0916140
$723$	−23.7641	−0.883796
$724$	−8.41752	−0.312835
$725$	47.9814	1.78198
$726$	21.3331	0.791745
$727$	−2.79577	−0.103689	−0.0518446	−	0.998655i	$-0.516510\pi$
$727$	−2.79577	−0.103689	−0.0518446	+	0.998655i	$0.516510\pi$
$728$	−1.06238	−0.0393744
$729$	29.3974	1.08879
$730$	66.8356	2.47370
$731$	23.3908	0.865141
$732$	10.2209	0.377774
$733$	21.2125	0.783502	0.391751	−	0.920071i	$-0.371870\pi$
$733$	21.2125	0.783502	0.391751	+	0.920071i	$0.371870\pi$
$734$	2.01495	0.0743732
$735$	27.8169	1.02604
$736$	−74.7524	−2.75541
$737$	12.9899	0.478488
$738$	−12.3911	−0.456124
$739$	3.28407	0.120806	0.0604032	−	0.998174i	$-0.480761\pi$
$739$	3.28407	0.120806	0.0604032	+	0.998174i	$0.480761\pi$
$740$	−9.62268	−0.353737
$741$	3.99114	0.146618
$742$	−32.9134	−1.20829
$743$	−25.3534	−0.930126	−0.465063	−	0.885277i	$-0.653968\pi$
$743$	−25.3534	−0.930126	−0.465063	+	0.885277i	$0.653968\pi$
$744$	5.00917	0.183645
$745$	−22.6661	−0.830422
$746$	70.7015	2.58856
$747$	10.9684	0.401313
$748$	−66.5983	−2.43507
$749$	−8.01407	−0.292828
$750$	48.5092	1.77131
$751$	−15.6180	−0.569907	−0.284954	−	0.958541i	$-0.591978\pi$
$751$	−15.6180	−0.569907	−0.284954	+	0.958541i	$0.591978\pi$
$752$	22.8208	0.832190
$753$	31.3713	1.14323
$754$	−7.30914	−0.266183
$755$	−40.0384	−1.45715
$756$	19.7663	0.718894
$757$	23.6116	0.858180	0.429090	−	0.903262i	$-0.358834\pi$
$757$	23.6116	0.858180	0.429090	+	0.903262i	$0.358834\pi$
$758$	−31.1697	−1.13213
$759$	−57.8702	−2.10055
$760$	18.8328	0.683138
$761$	16.8513	0.610860	0.305430	−	0.952215i	$-0.401200\pi$
$761$	16.8513	0.610860	0.305430	+	0.952215i	$0.401200\pi$
$762$	14.5254	0.526199
$763$	−1.36855	−0.0495449
$764$	53.1805	1.92400
$765$	−21.4584	−0.775832
$766$	13.6921	0.494714
$767$	−3.76687	−0.136014
$768$	−5.57805	−0.201280
$769$	6.15941	0.222114	0.111057	−	0.993814i	$-0.464576\pi$
$769$	6.15941	0.222114	0.111057	+	0.993814i	$0.464576\pi$
$770$	46.5995	1.67933
$771$	39.5419	1.42407
$772$	16.3723	0.589251
$773$	−52.9284	−1.90370	−0.951852	−	0.306559i	$-0.900822\pi$
$773$	−52.9284	−1.90370	−0.951852	+	0.306559i	$0.900822\pi$
$774$	7.50603	0.269799
$775$	27.0051	0.970053
$776$	−3.49083	−0.125313
$777$	1.97114	0.0707143
$778$	−28.3443	−1.01619
$779$	26.5025	0.949552
$780$	−9.09109	−0.325513
$781$	−21.5897	−0.772541
$782$	124.607	4.45594
$783$	29.5211	1.05500
$784$	13.2453	0.473046
$785$	−75.9897	−2.71219
$786$	−7.50217	−0.267594
$787$	11.5430	0.411463	0.205732	−	0.978608i	$-0.434043\pi$
$787$	11.5430	0.411463	0.205732	+	0.978608i	$0.434043\pi$
$788$	−48.3323	−1.72177
$789$	27.4353	0.976723
$790$	31.2652	1.11236
$791$	25.7400	0.915210
$792$	−4.63925	−0.164849
$793$	−1.82214	−0.0647061
$794$	58.3747	2.07164
$795$	−61.1405	−2.16843
$796$	18.7414	0.664272
$797$	−28.5349	−1.01076	−0.505380	−	0.862897i	$-0.668648\pi$
$797$	−28.5349	−1.01076	−0.505380	+	0.862897i	$0.668648\pi$
$798$	−17.7712	−0.629094
$799$	−54.3720	−1.92354
$800$	72.4157	2.56028
$801$	11.3687	0.401694
$802$	1.05083	0.0371062
$803$	35.2141	1.24268
$804$	11.2839	0.397953
$805$	−48.9023	−1.72358
$806$	−4.11377	−0.144901
$807$	40.4908	1.42534
$808$	0.503602	0.0177167
$809$	−2.69962	−0.0949138	−0.0474569	−	0.998873i	$-0.515112\pi$
$809$	−2.69962	−0.0949138	−0.0474569	+	0.998873i	$0.515112\pi$
$810$	43.1451	1.51596
$811$	20.4841	0.719294	0.359647	−	0.933088i	$-0.382897\pi$
$811$	20.4841	0.719294	0.359647	+	0.933088i	$0.382897\pi$
$812$	18.2539	0.640585
$813$	−10.6520	−0.373582
$814$	−9.03934	−0.316829
$815$	79.4579	2.78329
$816$	22.9026	0.801752
$817$	−16.0541	−0.561662
$818$	58.6617	2.05106
$819$	−0.830813	−0.0290310
$820$	−60.3680	−2.10814
$821$	38.9491	1.35933	0.679666	−	0.733521i	$-0.262125\pi$
$821$	38.9491	1.35933	0.679666	+	0.733521i	$0.262125\pi$
$822$	44.8724	1.56510
$823$	−25.4960	−0.888735	−0.444368	−	0.895845i	$-0.646572\pi$
$823$	−25.4960	−0.888735	−0.444368	+	0.895845i	$0.646572\pi$
$824$	−3.95558	−0.137799
$825$	56.0612	1.95180
$826$	16.7726	0.583594
$827$	33.8527	1.17717	0.588586	−	0.808435i	$-0.299685\pi$
$827$	33.8527	1.17717	0.588586	+	0.808435i	$0.299685\pi$
$828$	22.4272	0.779400
$829$	−37.1336	−1.28970	−0.644851	−	0.764308i	$-0.723081\pi$
$829$	−37.1336	−1.28970	−0.644851	+	0.764308i	$0.723081\pi$
$830$	95.2733	3.30699
$831$	8.53061	0.295924
$832$	−7.64219	−0.264945
$833$	−31.5577	−1.09341
$834$	−28.5611	−0.988991
$835$	−61.9694	−2.14454
$836$	45.7092	1.58089
$837$	16.6152	0.574306
$838$	9.35694	0.323230
$839$	−28.9815	−1.00055	−0.500276	−	0.865866i	$-0.666768\pi$
$839$	−28.9815	−1.00055	−0.500276	+	0.865866i	$0.666768\pi$
$840$	8.78732	0.303191
$841$	−1.73776	−0.0599229
$842$	−51.6636	−1.78045
$843$	−40.4574	−1.39343
$844$	47.5385	1.63634
$845$	−47.3489	−1.62885
$846$	−17.4478	−0.599867
$847$	9.49809	0.326358
$848$	−29.1127	−0.999733
$849$	−30.6280	−1.05115
$850$	−120.712	−4.14039
$851$	9.48602	0.325177
$852$	−18.7543	−0.642513
$853$	−52.9216	−1.81200	−0.906000	−	0.423278i	$-0.860879\pi$
$853$	−52.9216	−1.81200	−0.906000	+	0.423278i	$0.860879\pi$
$854$	8.11338	0.277634
$855$	14.7278	0.503681
$856$	6.93022	0.236870
$857$	17.4274	0.595309	0.297655	−	0.954674i	$-0.403796\pi$
$857$	17.4274	0.595309	0.297655	+	0.954674i	$0.403796\pi$
$858$	−8.53997	−0.291550
$859$	2.44307	0.0833565	0.0416783	−	0.999131i	$-0.486730\pi$
$859$	2.44307	0.0833565	0.0416783	+	0.999131i	$0.486730\pi$
$860$	36.5684	1.24697
$861$	12.3660	0.421431
$862$	−16.8131	−0.572657
$863$	−7.88033	−0.268250	−0.134125	−	0.990964i	$-0.542822\pi$
$863$	−7.88033	−0.268250	−0.134125	+	0.990964i	$0.542822\pi$
$864$	44.5546	1.51578
$865$	−18.5449	−0.630547
$866$	60.3064	2.04930
$867$	−30.0815	−1.02162
$868$	10.2737	0.348713
$869$	16.4729	0.558804
$870$	60.4565	2.04967
$871$	−2.01166	−0.0681624
$872$	1.18346	0.0400772
$873$	−2.72993	−0.0923942
$874$	−85.5231	−2.89286
$875$	21.5977	0.730134
$876$	30.5894	1.03352
$877$	−55.7054	−1.88104	−0.940519	−	0.339741i	$-0.889660\pi$
$877$	−55.7054	−1.88104	−0.940519	+	0.339741i	$0.889660\pi$
$878$	−70.2046	−2.36929
$879$	26.7730	0.903031
$880$	41.2183	1.38947
$881$	−30.4788	−1.02686	−0.513429	−	0.858132i	$-0.671625\pi$
$881$	−30.4788	−1.02686	−0.513429	+	0.858132i	$0.671625\pi$
$882$	−10.1267	−0.340985
$883$	22.8460	0.768828	0.384414	−	0.923161i	$-0.374404\pi$
$883$	22.8460	0.768828	0.384414	+	0.923161i	$0.374404\pi$
$884$	10.3136	0.346886
$885$	31.1571	1.04733
$886$	31.9862	1.07460
$887$	6.31334	0.211981	0.105991	−	0.994367i	$-0.466199\pi$
$887$	6.31334	0.211981	0.105991	+	0.994367i	$0.466199\pi$
$888$	−1.70456	−0.0572012
$889$	6.46711	0.216900
$890$	98.7505	3.31012
$891$	22.7321	0.761555
$892$	30.3880	1.01746
$893$	37.3178	1.24879
$894$	−18.4957	−0.618590
$895$	−39.5982	−1.32362
$896$	12.4590	0.416226
$897$	8.96198	0.299232
$898$	42.3755	1.41409
$899$	15.3439	0.511747
$900$	−21.7262	−0.724205
$901$	69.3626	2.31080
$902$	−56.7084	−1.88818
$903$	−7.49078	−0.249277
$904$	−22.2589	−0.740319
$905$	−12.4124	−0.412601
$906$	−32.6717	−1.08545
$907$	−1.87441	−0.0622388	−0.0311194	−	0.999516i	$-0.509907\pi$
$907$	−1.87441	−0.0622388	−0.0311194	+	0.999516i	$0.509907\pi$
$908$	−23.4843	−0.779354
$909$	0.393832	0.0130626
$910$	−7.21656	−0.239227
$911$	−37.7800	−1.25171	−0.625853	−	0.779941i	$-0.715249\pi$
$911$	−37.7800	−1.25171	−0.625853	+	0.779941i	$0.715249\pi$
$912$	−15.7190	−0.520509
$913$	50.1972	1.66129
$914$	−49.8414	−1.64861
$915$	15.0716	0.498250
$916$	18.7117	0.618252
$917$	−3.34018	−0.110302
$918$	−74.2694	−2.45126
$919$	−3.47529	−0.114639	−0.0573196	−	0.998356i	$-0.518255\pi$
$919$	−3.47529	−0.114639	−0.0573196	+	0.998356i	$0.518255\pi$
$920$	42.2886	1.39421
$921$	21.6710	0.714085
$922$	28.5266	0.939475
$923$	3.34346	0.110051
$924$	21.3277	0.701631
$925$	−9.18950	−0.302149
$926$	−20.9385	−0.688082
$927$	−3.09338	−0.101600
$928$	41.1454	1.35067
$929$	−17.0406	−0.559084	−0.279542	−	0.960133i	$-0.590183\pi$
$929$	−17.0406	−0.559084	−0.279542	+	0.960133i	$0.590183\pi$
$930$	34.0264	1.11577
$931$	21.6594	0.709857
$932$	−15.0180	−0.491931
$933$	34.1376	1.11762
$934$	−69.5701	−2.27640
$935$	−98.2051	−3.21165
$936$	0.718451	0.0234833
$937$	−8.35854	−0.273062	−0.136531	−	0.990636i	$-0.543595\pi$
$937$	−8.35854	−0.273062	−0.136531	+	0.990636i	$0.543595\pi$
$938$	8.95724	0.292464
$939$	−7.57766	−0.247288
$940$	−85.0032	−2.77250
$941$	27.9252	0.910334	0.455167	−	0.890406i	$-0.349580\pi$
$941$	27.9252	0.910334	0.455167	+	0.890406i	$0.349580\pi$
$942$	−62.0083	−2.02034
$943$	59.5107	1.93793
$944$	14.8358	0.482863
$945$	29.1472	0.948158
$946$	34.3515	1.11686
$947$	12.0136	0.390388	0.195194	−	0.980765i	$-0.437466\pi$
$947$	12.0136	0.390388	0.195194	+	0.980765i	$0.437466\pi$
$948$	14.3095	0.464750
$949$	−5.45338	−0.177024
$950$	82.8497	2.68800
$951$	−9.12218	−0.295807
$952$	−9.96902	−0.323098
$953$	−33.2861	−1.07824	−0.539122	−	0.842228i	$-0.681244\pi$
$953$	−33.2861	−1.07824	−0.539122	+	0.842228i	$0.681244\pi$
$954$	22.2582	0.720636
$955$	78.4193	2.53759
$956$	61.1809	1.97873
$957$	31.8531	1.02966
$958$	40.5402	1.30979
$959$	19.9785	0.645138
$960$	63.2112	2.04013
$961$	−22.3641	−0.721422
$962$	1.39986	0.0451334
$963$	5.41964	0.174646
$964$	42.1480	1.35750
$965$	24.1424	0.777170
$966$	−39.9047	−1.28391
$967$	−2.75941	−0.0887366	−0.0443683	−	0.999015i	$-0.514128\pi$
$967$	−2.75941	−0.0887366	−0.0443683	+	0.999015i	$0.514128\pi$
$968$	−8.21354	−0.263993
$969$	37.4515	1.20312
$970$	−23.7126	−0.761365
$971$	−7.77037	−0.249363	−0.124681	−	0.992197i	$-0.539791\pi$
$971$	−7.77037	−0.249363	−0.124681	+	0.992197i	$0.539791\pi$
$972$	−23.5830	−0.756425
$973$	−12.7162	−0.407663
$974$	−20.1614	−0.646014
$975$	−8.68183	−0.278041
$976$	7.17647	0.229713
$977$	−43.7443	−1.39950	−0.699751	−	0.714387i	$-0.746706\pi$
$977$	−43.7443	−1.39950	−0.699751	+	0.714387i	$0.746706\pi$
$978$	64.8383	2.07330
$979$	52.0293	1.66286
$980$	−49.3361	−1.57598
$981$	0.925504	0.0295491
$982$	−67.2093	−2.14474
$983$	−12.8214	−0.408939	−0.204469	−	0.978873i	$-0.565547\pi$
$983$	−12.8214	−0.408939	−0.204469	+	0.978873i	$0.565547\pi$
$984$	−10.6936	−0.340898
$985$	−71.2703	−2.27086
$986$	−68.5866	−2.18424
$987$	17.4123	0.554240
$988$	−7.07869	−0.225203
$989$	−36.0490	−1.14629
$990$	−31.5136	−1.00157
$991$	−9.02001	−0.286530	−0.143265	−	0.989684i	$-0.545760\pi$
$991$	−9.02001	−0.286530	−0.143265	+	0.989684i	$0.545760\pi$
$992$	23.1577	0.735258
$993$	11.3649	0.360654
$994$	−14.8873	−0.472197
$995$	27.6359	0.876116
$996$	43.6048	1.38167
$997$	28.3580	0.898106	0.449053	−	0.893505i	$-0.351761\pi$
$997$	28.3580	0.898106	0.449053	+	0.893505i	$0.351761\pi$
$998$	−3.44864	−0.109165
$999$	−5.65395	−0.178883

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.d.1.14	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.d.1.14	✓	79	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.13414 q^{2} -1.44031 q^{3} +2.55454 q^{4} +3.76689 q^{5} +3.07382 q^{6} +1.36855 q^{7} -1.18346 q^{8} -0.925504 q^{9} +O(q^{10})\)	\(q-2.13414 q^{2} -1.44031 q^{3} +2.55454 q^{4} +3.76689 q^{5} +3.07382 q^{6} +1.36855 q^{7} -1.18346 q^{8} -0.925504 q^{9} -8.03907 q^{10} -4.23559 q^{11} -3.67933 q^{12} +0.655939 q^{13} -2.92068 q^{14} -5.42550 q^{15} -2.58341 q^{16} +6.15511 q^{17} +1.97515 q^{18} -4.22451 q^{19} +9.62268 q^{20} -1.97114 q^{21} +9.03934 q^{22} -9.48602 q^{23} +1.70456 q^{24} +9.18950 q^{25} -1.39986 q^{26} +5.65395 q^{27} +3.49602 q^{28} +5.22133 q^{29} +11.5788 q^{30} +2.93870 q^{31} +7.88027 q^{32} +6.10057 q^{33} -13.1359 q^{34} +5.15519 q^{35} -2.36424 q^{36} -1.00000 q^{37} +9.01569 q^{38} -0.944756 q^{39} -4.45799 q^{40} -6.27351 q^{41} +4.20668 q^{42} +3.80023 q^{43} -10.8200 q^{44} -3.48628 q^{45} +20.2445 q^{46} -8.83363 q^{47} +3.72091 q^{48} -5.12707 q^{49} -19.6116 q^{50} -8.86528 q^{51} +1.67562 q^{52} +11.2691 q^{53} -12.0663 q^{54} -15.9550 q^{55} -1.61963 q^{56} +6.08461 q^{57} -11.1430 q^{58} -5.74271 q^{59} -13.8597 q^{60} -2.77791 q^{61} -6.27158 q^{62} -1.26660 q^{63} -11.6508 q^{64} +2.47085 q^{65} -13.0195 q^{66} -3.06684 q^{67} +15.7235 q^{68} +13.6628 q^{69} -11.0019 q^{70} +5.09721 q^{71} +1.09530 q^{72} -8.31385 q^{73} +2.13414 q^{74} -13.2357 q^{75} -10.7917 q^{76} -5.79663 q^{77} +2.01624 q^{78} -3.88915 q^{79} -9.73142 q^{80} -5.36693 q^{81} +13.3885 q^{82} -11.8513 q^{83} -5.03536 q^{84} +23.1857 q^{85} -8.11020 q^{86} -7.52033 q^{87} +5.01267 q^{88} -12.2838 q^{89} +7.44019 q^{90} +0.897687 q^{91} -24.2324 q^{92} -4.23264 q^{93} +18.8522 q^{94} -15.9133 q^{95} -11.3500 q^{96} +2.94967 q^{97} +10.9419 q^{98} +3.92006 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9}+O(q^{10}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9	\( 79 q - 11 q^{2} - 11 q^{3} + 79 q^{4} - 16 q^{5} - 14 q^{6} - 15 q^{7} - 42 q^{8} + 76 q^{9} - 13 q^{10} - 5 q^{11} - 40 q^{12} - 18 q^{13} - 42 q^{14} - 49 q^{15} + 83 q^{16} - 62 q^{17} - 33 q^{18} - 25 q^{19} - 39 q^{20} - 15 q^{21} - 31 q^{22} - 94 q^{23} - 39 q^{24} + 71 q^{25} - 35 q^{26} - 47 q^{27} - 13 q^{28} - 17 q^{29} + 15 q^{30} - 37 q^{31} - 105 q^{32} - 60 q^{33} + 9 q^{34} - 60 q^{35} + 43 q^{36} - 79 q^{37} - 80 q^{38} - 41 q^{39} - 64 q^{40} - 37 q^{41} - 30 q^{42} - 20 q^{43} - 14 q^{44} - 8 q^{45} + 61 q^{46} - 148 q^{47} - 39 q^{48} + 82 q^{49} - 90 q^{50} - 45 q^{51} - 27 q^{52} - 70 q^{53} - 41 q^{54} - 105 q^{55} - 68 q^{56} - 31 q^{57} - 14 q^{58} - 96 q^{59} - 74 q^{60} - 21 q^{61} + 4 q^{62} - 60 q^{63} + 132 q^{64} - 15 q^{65} + 71 q^{66} - 44 q^{67} - 166 q^{68} - 72 q^{69} - 9 q^{70} - 55 q^{71} - 126 q^{72} - 27 q^{73} + 11 q^{74} - 39 q^{75} - 4 q^{76} - 104 q^{77} - 47 q^{78} - 49 q^{79} - 82 q^{80} + 55 q^{81} + 20 q^{82} - 52 q^{83} - 29 q^{84} + 3 q^{85} - 32 q^{86} - 113 q^{87} + 14 q^{88} - 68 q^{89} - 39 q^{90} - 30 q^{91} - 179 q^{92} - 53 q^{93} - 33 q^{94} - 86 q^{95} + 33 q^{96} - 57 q^{97} - 116 q^{98} + q^{99}+O(q^{100}) \) 79 * q - 11 * q^2 - 11 * q^3 + 79 * q^4 - 16 * q^5 - 14 * q^6 - 15 * q^7 - 42 * q^8 + 76 * q^9 - 13 * q^10 - 5 * q^11 - 40 * q^12 - 18 * q^13 - 42 * q^14 - 49 * q^15 + 83 * q^16 - 62 * q^17 - 33 * q^18 - 25 * q^19 - 39 * q^20 - 15 * q^21 - 31 * q^22 - 94 * q^23 - 39 * q^24 + 71 * q^25 - 35 * q^26 - 47 * q^27 - 13 * q^28 - 17 * q^29 + 15 * q^30 - 37 * q^31 - 105 * q^32 - 60 * q^33 + 9 * q^34 - 60 * q^35 + 43 * q^36 - 79 * q^37 - 80 * q^38 - 41 * q^39 - 64 * q^40 - 37 * q^41 - 30 * q^42 - 20 * q^43 - 14 * q^44 - 8 * q^45 + 61 * q^46 - 148 * q^47 - 39 * q^48 + 82 * q^49 - 90 * q^50 - 45 * q^51 - 27 * q^52 - 70 * q^53 - 41 * q^54 - 105 * q^55 - 68 * q^56 - 31 * q^57 - 14 * q^58 - 96 * q^59 - 74 * q^60 - 21 * q^61 + 4 * q^62 - 60 * q^63 + 132 * q^64 - 15 * q^65 + 71 * q^66 - 44 * q^67 - 166 * q^68 - 72 * q^69 - 9 * q^70 - 55 * q^71 - 126 * q^72 - 27 * q^73 + 11 * q^74 - 39 * q^75 - 4 * q^76 - 104 * q^77 - 47 * q^78 - 49 * q^79 - 82 * q^80 + 55 * q^81 + 20 * q^82 - 52 * q^83 - 29 * q^84 + 3 * q^85 - 32 * q^86 - 113 * q^87 + 14 * q^88 - 68 * q^89 - 39 * q^90 - 30 * q^91 - 179 * q^92 - 53 * q^93 - 33 * q^94 - 86 * q^95 + 33 * q^96 - 57 * q^97 - 116 * q^98 + q^99

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