LMFDB - Embedded newform 8023.2.a.d.1.20

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			1.20
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)

$f(q)$	$=$	$q-2.14746 q^{2} -2.07357 q^{3} +2.61157 q^{4} +2.08017 q^{5} +4.45290 q^{6} -3.04722 q^{7} -1.31333 q^{8} +1.29970 q^{9} +O(q^{10})$	\(q-2.14746 q^{2} -2.07357 q^{3} +2.61157 q^{4} +2.08017 q^{5} +4.45290 q^{6} -3.04722 q^{7} -1.31333 q^{8} +1.29970 q^{9} -4.46708 q^{10} -5.42448 q^{11} -5.41528 q^{12} +0.463370 q^{13} +6.54377 q^{14} -4.31338 q^{15} -2.40283 q^{16} -4.29729 q^{17} -2.79104 q^{18} -3.96466 q^{19} +5.43252 q^{20} +6.31863 q^{21} +11.6488 q^{22} +2.86102 q^{23} +2.72327 q^{24} -0.672885 q^{25} -0.995067 q^{26} +3.52570 q^{27} -7.95803 q^{28} +4.93723 q^{29} +9.26281 q^{30} +4.95898 q^{31} +7.78663 q^{32} +11.2480 q^{33} +9.22825 q^{34} -6.33874 q^{35} +3.39425 q^{36} -0.718595 q^{37} +8.51393 q^{38} -0.960830 q^{39} -2.73194 q^{40} -6.15874 q^{41} -13.5690 q^{42} -11.4136 q^{43} -14.1664 q^{44} +2.70359 q^{45} -6.14392 q^{46} -7.93999 q^{47} +4.98245 q^{48} +2.28555 q^{49} +1.44499 q^{50} +8.91074 q^{51} +1.21012 q^{52} -9.83817 q^{53} -7.57129 q^{54} -11.2838 q^{55} +4.00199 q^{56} +8.22099 q^{57} -10.6025 q^{58} -13.1985 q^{59} -11.2647 q^{60} -3.49007 q^{61} -10.6492 q^{62} -3.96046 q^{63} -11.9158 q^{64} +0.963889 q^{65} -24.1547 q^{66} +1.91097 q^{67} -11.2227 q^{68} -5.93253 q^{69} +13.6122 q^{70} +1.00000 q^{71} -1.70692 q^{72} +7.91654 q^{73} +1.54315 q^{74} +1.39527 q^{75} -10.3540 q^{76} +16.5296 q^{77} +2.06334 q^{78} -7.47614 q^{79} -4.99831 q^{80} -11.2099 q^{81} +13.2256 q^{82} +0.843662 q^{83} +16.5015 q^{84} -8.93910 q^{85} +24.5103 q^{86} -10.2377 q^{87} +7.12411 q^{88} +7.77557 q^{89} -5.80584 q^{90} -1.41199 q^{91} +7.47177 q^{92} -10.2828 q^{93} +17.0508 q^{94} -8.24716 q^{95} -16.1461 q^{96} -1.30246 q^{97} -4.90811 q^{98} -7.05017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.14746	−1.51848	−0.759241	−	0.650810i	$-0.774430\pi$
$2$	−2.14746	−1.51848	−0.759241	+	0.650810i	$0.774430\pi$
$3$	−2.07357	−1.19718	−0.598588	−	0.801057i	$-0.704271\pi$
$3$	−2.07357	−1.19718	−0.598588	+	0.801057i	$0.704271\pi$
$4$	2.61157	1.30579
$5$	2.08017	0.930281	0.465141	−	0.885237i	$-0.346004\pi$
$5$	2.08017	0.930281	0.465141	+	0.885237i	$0.346004\pi$
$6$	4.45290	1.81789
$7$	−3.04722	−1.15174	−0.575870	−	0.817541i	$-0.695337\pi$
$7$	−3.04722	−1.15174	−0.575870	+	0.817541i	$0.695337\pi$
$8$	−1.31333	−0.464331
$9$	1.29970	0.433232
$10$	−4.46708	−1.41261
$11$	−5.42448	−1.63554	−0.817771	−	0.575544i	$-0.804790\pi$
$11$	−5.42448	−1.63554	−0.817771	+	0.575544i	$0.804790\pi$
$12$	−5.41528	−1.56326
$13$	0.463370	0.128516	0.0642578	−	0.997933i	$-0.479532\pi$
$13$	0.463370	0.128516	0.0642578	+	0.997933i	$0.479532\pi$
$14$	6.54377	1.74890
$15$	−4.31338	−1.11371
$16$	−2.40283	−0.600709
$17$	−4.29729	−1.04225	−0.521123	−	0.853482i	$-0.674487\pi$
$17$	−4.29729	−1.04225	−0.521123	+	0.853482i	$0.674487\pi$
$18$	−2.79104	−0.657854
$19$	−3.96466	−0.909554	−0.454777	−	0.890605i	$-0.650281\pi$
$19$	−3.96466	−0.909554	−0.454777	+	0.890605i	$0.650281\pi$
$20$	5.43252	1.21475
$21$	6.31863	1.37884
$22$	11.6488	2.48354
$23$	2.86102	0.596564	0.298282	−	0.954478i	$-0.403586\pi$
$23$	2.86102	0.596564	0.298282	+	0.954478i	$0.403586\pi$
$24$	2.72327	0.555886
$25$	−0.672885	−0.134577
$26$	−0.995067	−0.195149
$27$	3.52570	0.678522
$28$	−7.95803	−1.50393
$29$	4.93723	0.916821	0.458411	−	0.888741i	$-0.348419\pi$
$29$	4.93723	0.916821	0.458411	+	0.888741i	$0.348419\pi$
$30$	9.26281	1.69115
$31$	4.95898	0.890660	0.445330	−	0.895367i	$-0.353086\pi$
$31$	4.95898	0.890660	0.445330	+	0.895367i	$0.353086\pi$
$32$	7.78663	1.37650
$33$	11.2480	1.95803
$34$	9.22825	1.58263
$35$	−6.33874	−1.07144
$36$	3.39425	0.565708
$37$	−0.718595	−0.118136	−0.0590682	−	0.998254i	$-0.518813\pi$
$37$	−0.718595	−0.118136	−0.0590682	+	0.998254i	$0.518813\pi$
$38$	8.51393	1.38114
$39$	−0.960830	−0.153856
$40$	−2.73194	−0.431958
$41$	−6.15874	−0.961834	−0.480917	−	0.876766i	$-0.659696\pi$
$41$	−6.15874	−0.961834	−0.480917	+	0.876766i	$0.659696\pi$
$42$	−13.5690	−2.09374
$43$	−11.4136	−1.74056	−0.870282	−	0.492554i	$-0.836063\pi$
$43$	−11.4136	−1.74056	−0.870282	+	0.492554i	$0.836063\pi$
$44$	−14.1664	−2.13567
$45$	2.70359	0.403027
$46$	−6.14392	−0.905872
$47$	−7.93999	−1.15817	−0.579083	−	0.815268i	$-0.696589\pi$
$47$	−7.93999	−1.15817	−0.579083	+	0.815268i	$0.696589\pi$
$48$	4.98245	0.719154
$49$	2.28555	0.326507
$50$	1.44499	0.204353
$51$	8.91074	1.24775
$52$	1.21012	0.167814
$53$	−9.83817	−1.35138	−0.675688	−	0.737187i	$-0.736154\pi$
$53$	−9.83817	−1.35138	−0.675688	+	0.737187i	$0.736154\pi$
$54$	−7.57129	−1.03032
$55$	−11.2838	−1.52151
$56$	4.00199	0.534789
$57$	8.22099	1.08890
$58$	−10.6025	−1.39218
$59$	−13.1985	−1.71830	−0.859149	−	0.511726i	$-0.829006\pi$
$59$	−13.1985	−1.71830	−0.859149	+	0.511726i	$0.829006\pi$
$60$	−11.2647	−1.45427
$61$	−3.49007	−0.446858	−0.223429	−	0.974720i	$-0.571725\pi$
$61$	−3.49007	−0.446858	−0.223429	+	0.974720i	$0.571725\pi$
$62$	−10.6492	−1.35245
$63$	−3.96046	−0.498971
$64$	−11.9158	−1.48947
$65$	0.963889	0.119556
$66$	−24.1547	−2.97324
$67$	1.91097	0.233462	0.116731	−	0.993164i	$-0.462759\pi$
$67$	1.91097	0.233462	0.116731	+	0.993164i	$0.462759\pi$
$68$	−11.2227	−1.36095
$69$	−5.93253	−0.714193
$70$	13.6122	1.62697
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−1.70692	−0.201163
$73$	7.91654	0.926561	0.463281	−	0.886212i	$-0.346672\pi$
$73$	7.91654	0.926561	0.463281	+	0.886212i	$0.346672\pi$
$74$	1.54315	0.179388
$75$	1.39527	0.161112
$76$	−10.3540	−1.18768
$77$	16.5296	1.88372
$78$	2.06334	0.233627
$79$	−7.47614	−0.841131	−0.420565	−	0.907262i	$-0.638168\pi$
$79$	−7.47614	−0.841131	−0.420565	+	0.907262i	$0.638168\pi$
$80$	−4.99831	−0.558828
$81$	−11.2099	−1.24554
$82$	13.2256	1.46053
$83$	0.843662	0.0926039	0.0463020	−	0.998927i	$-0.485256\pi$
$83$	0.843662	0.0926039	0.0463020	+	0.998927i	$0.485256\pi$
$84$	16.5015	1.80047
$85$	−8.93910	−0.969582
$86$	24.5103	2.64301
$87$	−10.2377	−1.09760
$88$	7.12411	0.759432
$89$	7.77557	0.824209	0.412104	−	0.911137i	$-0.364794\pi$
$89$	7.77557	0.824209	0.412104	+	0.911137i	$0.364794\pi$
$90$	−5.80584	−0.611989
$91$	−1.41199	−0.148017
$92$	7.47177	0.778986
$93$	−10.2828	−1.06628
$94$	17.0508	1.75865
$95$	−8.24716	−0.846141
$96$	−16.1461	−1.64791
$97$	−1.30246	−0.132244	−0.0661222	−	0.997812i	$-0.521063\pi$
$97$	−1.30246	−0.132244	−0.0661222	+	0.997812i	$0.521063\pi$
$98$	−4.90811	−0.495794
$99$	−7.05017	−0.708569
$100$	−1.75729	−0.175729
$101$	−2.37409	−0.236230	−0.118115	−	0.993000i	$-0.537685\pi$
$101$	−2.37409	−0.236230	−0.118115	+	0.993000i	$0.537685\pi$
$102$	−19.1354	−1.89469
$103$	−3.81149	−0.375557	−0.187778	−	0.982211i	$-0.560129\pi$
$103$	−3.81149	−0.375557	−0.187778	+	0.982211i	$0.560129\pi$
$104$	−0.608556	−0.0596738
$105$	13.1438	1.28271
$106$	21.1271	2.05204
$107$	−15.7277	−1.52046	−0.760229	−	0.649655i	$-0.774913\pi$
$107$	−15.7277	−1.52046	−0.760229	+	0.649655i	$0.774913\pi$
$108$	9.20763	0.886004
$109$	−12.5038	−1.19765	−0.598824	−	0.800881i	$-0.704365\pi$
$109$	−12.5038	−1.19765	−0.598824	+	0.800881i	$0.704365\pi$
$110$	24.2316	2.31039
$111$	1.49006	0.141430
$112$	7.32196	0.691860
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−17.6542	−1.65347
$115$	5.95142	0.554973
$116$	12.8939	1.19717
$117$	0.602240	0.0556771
$118$	28.3432	2.60920
$119$	13.0948	1.20040
$120$	5.66488	0.517130
$121$	18.4250	1.67500
$122$	7.49478	0.678546
$123$	12.7706	1.15149
$124$	12.9507	1.16301
$125$	−11.8006	−1.05548
$126$	8.50491	0.757678
$127$	3.19491	0.283503	0.141751	−	0.989902i	$-0.454727\pi$
$127$	3.19491	0.283503	0.141751	+	0.989902i	$0.454727\pi$
$128$	10.0154	0.885244
$129$	23.6670	2.08376
$130$	−2.06991	−0.181543
$131$	−7.24093	−0.632643	−0.316321	−	0.948652i	$-0.602448\pi$
$131$	−7.24093	−0.632643	−0.316321	+	0.948652i	$0.602448\pi$
$132$	29.3751	2.55677
$133$	12.0812	1.04757
$134$	−4.10372	−0.354507
$135$	7.33407	0.631216
$136$	5.64374	0.483947
$137$	8.42644	0.719919	0.359960	−	0.932968i	$-0.382790\pi$
$137$	8.42644	0.719919	0.359960	+	0.932968i	$0.382790\pi$
$138$	12.7399	1.08449
$139$	10.0173	0.849657	0.424829	−	0.905274i	$-0.360334\pi$
$139$	10.0173	0.849657	0.424829	+	0.905274i	$0.360334\pi$
$140$	−16.5541	−1.39908
$141$	16.4641	1.38653
$142$	−2.14746	−0.180211
$143$	−2.51354	−0.210193
$144$	−3.12295	−0.260246
$145$	10.2703	0.852901
$146$	−17.0004	−1.40697
$147$	−4.73924	−0.390886
$148$	−1.87666	−0.154261
$149$	−3.53824	−0.289864	−0.144932	−	0.989442i	$-0.546296\pi$
$149$	−3.53824	−0.289864	−0.144932	+	0.989442i	$0.546296\pi$
$150$	−2.99629	−0.244646
$151$	−7.70160	−0.626747	−0.313374	−	0.949630i	$-0.601459\pi$
$151$	−7.70160	−0.626747	−0.313374	+	0.949630i	$0.601459\pi$
$152$	5.20688	0.422334
$153$	−5.58517	−0.451534
$154$	−35.4966	−2.86039
$155$	10.3155	0.828564
$156$	−2.50928	−0.200903
$157$	−9.43555	−0.753039	−0.376520	−	0.926409i	$-0.622879\pi$
$157$	−9.43555	−0.753039	−0.376520	+	0.926409i	$0.622879\pi$
$158$	16.0547	1.27724
$159$	20.4001	1.61784
$160$	16.1975	1.28053
$161$	−8.71816	−0.687087
$162$	24.0727	1.89133
$163$	−18.8272	−1.47466	−0.737332	−	0.675531i	$-0.763915\pi$
$163$	−18.8272	−1.47466	−0.737332	+	0.675531i	$0.763915\pi$
$164$	−16.0840	−1.25595
$165$	23.3979	1.82152
$166$	−1.81173	−0.140617
$167$	−7.93312	−0.613883	−0.306942	−	0.951728i	$-0.599306\pi$
$167$	−7.93312	−0.613883	−0.306942	+	0.951728i	$0.599306\pi$
$168$	−8.29841	−0.640236
$169$	−12.7853	−0.983484
$170$	19.1963	1.47229
$171$	−5.15284	−0.394048
$172$	−29.8075	−2.27280
$173$	−10.2064	−0.775975	−0.387988	−	0.921665i	$-0.626830\pi$
$173$	−10.2064	−0.775975	−0.387988	+	0.921665i	$0.626830\pi$
$174$	21.9850	1.66668
$175$	2.05043	0.154998
$176$	13.0341	0.982484
$177$	27.3680	2.05711
$178$	−16.6977	−1.25155
$179$	−6.80678	−0.508763	−0.254381	−	0.967104i	$-0.581872\pi$
$179$	−6.80678	−0.508763	−0.254381	+	0.967104i	$0.581872\pi$
$180$	7.06062	0.526267
$181$	8.34189	0.620048	0.310024	−	0.950729i	$-0.399663\pi$
$181$	8.34189	0.620048	0.310024	+	0.950729i	$0.399663\pi$
$182$	3.03219	0.224761
$183$	7.23692	0.534968
$184$	−3.75745	−0.277003
$185$	−1.49480	−0.109900
$186$	22.0819	1.61912
$187$	23.3106	1.70464
$188$	−20.7359	−1.51232
$189$	−10.7436	−0.781481
$190$	17.7104	1.28485
$191$	−1.86436	−0.134900	−0.0674500	−	0.997723i	$-0.521486\pi$
$191$	−1.86436	−0.134900	−0.0674500	+	0.997723i	$0.521486\pi$
$192$	24.7082	1.78316
$193$	24.1250	1.73656	0.868278	−	0.496078i	$-0.165227\pi$
$193$	24.1250	1.73656	0.868278	+	0.496078i	$0.165227\pi$
$194$	2.79697	0.200811
$195$	−1.99869	−0.143129
$196$	5.96887	0.426348
$197$	−5.37041	−0.382626	−0.191313	−	0.981529i	$-0.561275\pi$
$197$	−5.37041	−0.382626	−0.191313	+	0.981529i	$0.561275\pi$
$198$	15.1399	1.07595
$199$	−18.2081	−1.29074	−0.645369	−	0.763871i	$-0.723296\pi$
$199$	−18.2081	−1.29074	−0.645369	+	0.763871i	$0.723296\pi$
$200$	0.883717	0.0624883
$201$	−3.96252	−0.279495
$202$	5.09825	0.358712
$203$	−15.0448	−1.05594
$204$	23.2710	1.62930
$205$	−12.8112	−0.894776
$206$	8.18500	0.570276
$207$	3.71846	0.258451
$208$	−1.11340	−0.0772005
$209$	21.5062	1.48761
$210$	−28.2258	−1.94777
$211$	−17.0997	−1.17719	−0.588596	−	0.808427i	$-0.700319\pi$
$211$	−17.0997	−1.17719	−0.588596	+	0.808427i	$0.700319\pi$
$212$	−25.6931	−1.76461
$213$	−2.07357	−0.142079
$214$	33.7746	2.30879
$215$	−23.7423	−1.61921
$216$	−4.63040	−0.315059
$217$	−15.1111	−1.02581
$218$	26.8514	1.81861
$219$	−16.4155	−1.10926
$220$	−29.4686	−1.98677
$221$	−1.99124	−0.133945
$222$	−3.19984	−0.214759
$223$	−19.5366	−1.30827	−0.654135	−	0.756378i	$-0.726967\pi$
$223$	−19.5366	−1.30827	−0.654135	+	0.756378i	$0.726967\pi$
$224$	−23.7276	−1.58537
$225$	−0.874545	−0.0583030
$226$	2.14746	0.142847
$227$	1.01773	0.0675490	0.0337745	−	0.999429i	$-0.489247\pi$
$227$	1.01773	0.0675490	0.0337745	+	0.999429i	$0.489247\pi$
$228$	21.4697	1.42187
$229$	−11.0126	−0.727730	−0.363865	−	0.931452i	$-0.618543\pi$
$229$	−11.0126	−0.727730	−0.363865	+	0.931452i	$0.618543\pi$
$230$	−12.7804	−0.842716
$231$	−34.2752	−2.25515
$232$	−6.48419	−0.425708
$233$	18.6084	1.21908	0.609539	−	0.792756i	$-0.291355\pi$
$233$	18.6084	1.21908	0.609539	+	0.792756i	$0.291355\pi$
$234$	−1.29328	−0.0845446
$235$	−16.5165	−1.07742
$236$	−34.4688	−2.24373
$237$	15.5023	1.00698
$238$	−28.1205	−1.82278
$239$	7.00081	0.452845	0.226422	−	0.974029i	$-0.427297\pi$
$239$	7.00081	0.452845	0.226422	+	0.974029i	$0.427297\pi$
$240$	10.3643	0.669016
$241$	−24.2013	−1.55895	−0.779473	−	0.626436i	$-0.784513\pi$
$241$	−24.2013	−1.55895	−0.779473	+	0.626436i	$0.784513\pi$
$242$	−39.5668	−2.54345
$243$	12.6674	0.812612
$244$	−9.11458	−0.583501
$245$	4.75433	0.303743
$246$	−27.4243	−1.74851
$247$	−1.83710	−0.116892
$248$	−6.51276	−0.413561
$249$	−1.74939	−0.110863
$250$	25.3412	1.60272
$251$	1.25693	0.0793370	0.0396685	−	0.999213i	$-0.487370\pi$
$251$	1.25693	0.0793370	0.0396685	+	0.999213i	$0.487370\pi$
$252$	−10.3430	−0.651549
$253$	−15.5196	−0.975706
$254$	−6.86094	−0.430494
$255$	18.5359	1.16076
$256$	2.32396	0.145248
$257$	−3.97181	−0.247755	−0.123877	−	0.992298i	$-0.539533\pi$
$257$	−3.97181	−0.247755	−0.123877	+	0.992298i	$0.539533\pi$
$258$	−50.8238	−3.16415
$259$	2.18972	0.136062
$260$	2.51727	0.156114
$261$	6.41690	0.397196
$262$	15.5496	0.960656
$263$	−3.73814	−0.230504	−0.115252	−	0.993336i	$-0.536767\pi$
$263$	−3.73814	−0.230504	−0.115252	+	0.993336i	$0.536767\pi$
$264$	−14.7723	−0.909175
$265$	−20.4651	−1.25716
$266$	−25.9438	−1.59072
$267$	−16.1232	−0.986723
$268$	4.99063	0.304851
$269$	−1.31880	−0.0804088	−0.0402044	−	0.999191i	$-0.512801\pi$
$269$	−1.31880	−0.0804088	−0.0402044	+	0.999191i	$0.512801\pi$
$270$	−15.7496	−0.958490
$271$	8.43677	0.512497	0.256249	−	0.966611i	$-0.417513\pi$
$271$	8.43677	0.512497	0.256249	+	0.966611i	$0.417513\pi$
$272$	10.3257	0.626086
$273$	2.92786	0.177202
$274$	−18.0954	−1.09318
$275$	3.65005	0.220106
$276$	−15.4932	−0.932583
$277$	2.54190	0.152728	0.0763641	−	0.997080i	$-0.475669\pi$
$277$	2.54190	0.152728	0.0763641	+	0.997080i	$0.475669\pi$
$278$	−21.5118	−1.29019
$279$	6.44517	0.385862
$280$	8.32483	0.497504
$281$	8.96695	0.534923	0.267462	−	0.963569i	$-0.413815\pi$
$281$	8.96695	0.534923	0.267462	+	0.963569i	$0.413815\pi$
$282$	−35.3560	−2.10542
$283$	−3.24517	−0.192906	−0.0964528	−	0.995338i	$-0.530750\pi$
$283$	−3.24517	−0.192906	−0.0964528	+	0.995338i	$0.530750\pi$
$284$	2.61157	0.154968
$285$	17.1011	1.01298
$286$	5.39772	0.319174
$287$	18.7670	1.10778
$288$	10.1203	0.596342
$289$	1.46671	0.0862770
$290$	−22.0550	−1.29511
$291$	2.70073	0.158320
$292$	20.6746	1.20989
$293$	14.5740	0.851422	0.425711	−	0.904859i	$-0.360024\pi$
$293$	14.5740	0.851422	0.425711	+	0.904859i	$0.360024\pi$
$294$	10.1773	0.593554
$295$	−27.4551	−1.59850
$296$	0.943750	0.0548543
$297$	−19.1251	−1.10975
$298$	7.59823	0.440153
$299$	1.32571	0.0766679
$300$	3.64386	0.210378
$301$	34.7799	2.00468
$302$	16.5389	0.951704
$303$	4.92284	0.282810
$304$	9.52641	0.546377
$305$	−7.25995	−0.415704
$306$	11.9939	0.685646
$307$	3.69355	0.210802	0.105401	−	0.994430i	$-0.466387\pi$
$307$	3.69355	0.210802	0.105401	+	0.994430i	$0.466387\pi$
$308$	43.1682	2.45974
$309$	7.90338	0.449608
$310$	−22.1522	−1.25816
$311$	−11.6244	−0.659158	−0.329579	−	0.944128i	$-0.606907\pi$
$311$	−11.6244	−0.659158	−0.329579	+	0.944128i	$0.606907\pi$
$312$	1.26188	0.0714401
$313$	24.2868	1.37277	0.686385	−	0.727238i	$-0.259196\pi$
$313$	24.2868	1.37277	0.686385	+	0.727238i	$0.259196\pi$
$314$	20.2624	1.14348
$315$	−8.23843	−0.464183
$316$	−19.5245	−1.09834
$317$	2.06959	0.116240	0.0581200	−	0.998310i	$-0.481489\pi$
$317$	2.06959	0.116240	0.0581200	+	0.998310i	$0.481489\pi$
$318$	−43.8084	−2.45666
$319$	−26.7819	−1.49950
$320$	−24.7869	−1.38563
$321$	32.6126	1.82026
$322$	18.7219	1.04333
$323$	17.0373	0.947979
$324$	−29.2754	−1.62641
$325$	−0.311795	−0.0172953
$326$	40.4307	2.23925
$327$	25.9275	1.43380
$328$	8.08844	0.446609
$329$	24.1949	1.33391
$330$	−50.2459	−2.76595
$331$	−33.0334	−1.81568	−0.907840	−	0.419317i	$-0.862269\pi$
$331$	−33.0334	−1.81568	−0.907840	+	0.419317i	$0.862269\pi$
$332$	2.20328	0.120921
$333$	−0.933955	−0.0511804
$334$	17.0360	0.932170
$335$	3.97514	0.217185
$336$	−15.1826	−0.828279
$337$	8.73343	0.475740	0.237870	−	0.971297i	$-0.423551\pi$
$337$	8.73343	0.475740	0.237870	+	0.971297i	$0.423551\pi$
$338$	27.4559	1.49340
$339$	2.07357	0.112621
$340$	−23.3451	−1.26607
$341$	−26.8999	−1.45671
$342$	11.0655	0.598354
$343$	14.3660	0.775690
$344$	14.9898	0.808197
$345$	−12.3407	−0.664400
$346$	21.9177	1.17830
$347$	17.0692	0.916324	0.458162	−	0.888869i	$-0.348508\pi$
$347$	17.0692	0.916324	0.458162	+	0.888869i	$0.348508\pi$
$348$	−26.7365	−1.43323
$349$	10.7001	0.572762	0.286381	−	0.958116i	$-0.407548\pi$
$349$	10.7001	0.572762	0.286381	+	0.958116i	$0.407548\pi$
$350$	−4.40321	−0.235361
$351$	1.63370	0.0872007
$352$	−42.2384	−2.25132
$353$	4.34093	0.231044	0.115522	−	0.993305i	$-0.463146\pi$
$353$	4.34093	0.231044	0.115522	+	0.993305i	$0.463146\pi$
$354$	−58.7716	−3.12368
$355$	2.08017	0.110404
$356$	20.3065	1.07624
$357$	−27.1530	−1.43709
$358$	14.6173	0.772547
$359$	−5.19613	−0.274241	−0.137121	−	0.990554i	$-0.543785\pi$
$359$	−5.19613	−0.274241	−0.137121	+	0.990554i	$0.543785\pi$
$360$	−3.55069	−0.187138
$361$	−3.28151	−0.172711
$362$	−17.9138	−0.941531
$363$	−38.2055	−2.00527
$364$	−3.68751	−0.193278
$365$	16.4678	0.861962
$366$	−15.5410	−0.812339
$367$	0.609163	0.0317981	0.0158990	−	0.999874i	$-0.494939\pi$
$367$	0.609163	0.0317981	0.0158990	+	0.999874i	$0.494939\pi$
$368$	−6.87456	−0.358361
$369$	−8.00449	−0.416697
$370$	3.21002	0.166881
$371$	29.9791	1.55644
$372$	−26.8543	−1.39233
$373$	33.2031	1.71919	0.859596	−	0.510974i	$-0.170715\pi$
$373$	33.2031	1.71919	0.859596	+	0.510974i	$0.170715\pi$
$374$	−50.0584	−2.58846
$375$	24.4693	1.26359
$376$	10.4278	0.537772
$377$	2.28777	0.117826
$378$	23.0714	1.18666
$379$	−16.4052	−0.842678	−0.421339	−	0.906903i	$-0.638440\pi$
$379$	−16.4052	−0.842678	−0.421339	+	0.906903i	$0.638440\pi$
$380$	−21.5381	−1.10488
$381$	−6.62488	−0.339403
$382$	4.00362	0.204843
$383$	−31.8758	−1.62878	−0.814389	−	0.580320i	$-0.802928\pi$
$383$	−31.8758	−1.62878	−0.814389	+	0.580320i	$0.802928\pi$
$384$	−20.7676	−1.05979
$385$	34.3844	1.75239
$386$	−51.8074	−2.63693
$387$	−14.8342	−0.754067
$388$	−3.40146	−0.172683
$389$	−30.8890	−1.56614	−0.783068	−	0.621936i	$-0.786346\pi$
$389$	−30.8890	−1.56614	−0.783068	+	0.621936i	$0.786346\pi$
$390$	4.29211	0.217339
$391$	−12.2946	−0.621767
$392$	−3.00167	−0.151607
$393$	15.0146	0.757385
$394$	11.5327	0.581011
$395$	−15.5516	−0.782488
$396$	−18.4120	−0.925239
$397$	−17.8246	−0.894591	−0.447295	−	0.894386i	$-0.647613\pi$
$397$	−17.8246	−0.894591	−0.447295	+	0.894386i	$0.647613\pi$
$398$	39.1011	1.95996
$399$	−25.0512	−1.25413
$400$	1.61683	0.0808416
$401$	17.1480	0.856329	0.428165	−	0.903701i	$-0.359160\pi$
$401$	17.1480	0.856329	0.428165	+	0.903701i	$0.359160\pi$
$402$	8.50935	0.424408
$403$	2.29784	0.114464
$404$	−6.20010	−0.308466
$405$	−23.3185	−1.15870
$406$	32.3081	1.60343
$407$	3.89800	0.193217
$408$	−11.7027	−0.579370
$409$	−27.1759	−1.34376	−0.671881	−	0.740659i	$-0.734514\pi$
$409$	−27.1759	−1.34376	−0.671881	+	0.740659i	$0.734514\pi$
$410$	27.5116	1.35870
$411$	−17.4728	−0.861870
$412$	−9.95397	−0.490397
$413$	40.2187	1.97903
$414$	−7.98523	−0.392452
$415$	1.75496	0.0861477
$416$	3.60809	0.176901
$417$	−20.7716	−1.01719
$418$	−46.1836	−2.25891
$419$	−2.59466	−0.126758	−0.0633788	−	0.997990i	$-0.520188\pi$
$419$	−2.59466	−0.126758	−0.0633788	+	0.997990i	$0.520188\pi$
$420$	34.3261	1.67494
$421$	2.66300	0.129787	0.0648935	−	0.997892i	$-0.479329\pi$
$421$	2.66300	0.129787	0.0648935	+	0.997892i	$0.479329\pi$
$422$	36.7209	1.78754
$423$	−10.3196	−0.501754
$424$	12.9207	0.627486
$425$	2.89158	0.140262
$426$	4.45290	0.215744
$427$	10.6350	0.514665
$428$	−41.0741	−1.98539
$429$	5.21200	0.251638
$430$	50.9856	2.45875
$431$	−24.0627	−1.15906	−0.579531	−	0.814950i	$-0.696764\pi$
$431$	−24.0627	−1.15906	−0.579531	+	0.814950i	$0.696764\pi$
$432$	−8.47168	−0.407594
$433$	−38.6140	−1.85567	−0.927836	−	0.372989i	$-0.878333\pi$
$433$	−38.6140	−1.85567	−0.927836	+	0.372989i	$0.878333\pi$
$434$	32.4505	1.55767
$435$	−21.2962	−1.02107
$436$	−32.6546	−1.56387
$437$	−11.3430	−0.542608
$438$	35.2516	1.68439
$439$	13.7169	0.654670	0.327335	−	0.944908i	$-0.393849\pi$
$439$	13.7169	0.654670	0.327335	+	0.944908i	$0.393849\pi$
$440$	14.8194	0.706486
$441$	2.97051	0.141453
$442$	4.27609	0.203393
$443$	34.0122	1.61597	0.807985	−	0.589203i	$-0.200558\pi$
$443$	34.0122	1.61597	0.807985	+	0.589203i	$0.200558\pi$
$444$	3.89139	0.184677
$445$	16.1745	0.766746
$446$	41.9541	1.98658
$447$	7.33680	0.347019
$448$	36.3101	1.71549
$449$	−27.3173	−1.28918	−0.644592	−	0.764527i	$-0.722973\pi$
$449$	−27.3173	−1.28918	−0.644592	+	0.764527i	$0.722973\pi$
$450$	1.87805	0.0885321
$451$	33.4080	1.57312
$452$	−2.61157	−0.122838
$453$	15.9698	0.750327
$454$	−2.18553	−0.102572
$455$	−2.93718	−0.137697
$456$	−10.7968	−0.505608
$457$	5.83133	0.272778	0.136389	−	0.990655i	$-0.456450\pi$
$457$	5.83133	0.272778	0.136389	+	0.990655i	$0.456450\pi$
$458$	23.6490	1.10504
$459$	−15.1510	−0.707187
$460$	15.5426	0.724676
$461$	−4.17445	−0.194424	−0.0972118	−	0.995264i	$-0.530992\pi$
$461$	−4.17445	−0.194424	−0.0972118	+	0.995264i	$0.530992\pi$
$462$	73.6046	3.42440
$463$	25.4811	1.18421	0.592105	−	0.805861i	$-0.298297\pi$
$463$	25.4811	1.18421	0.592105	+	0.805861i	$0.298297\pi$
$464$	−11.8634	−0.550742
$465$	−21.3900	−0.991937
$466$	−39.9608	−1.85115
$467$	−18.2315	−0.843654	−0.421827	−	0.906676i	$-0.638611\pi$
$467$	−18.2315	−0.843654	−0.421827	+	0.906676i	$0.638611\pi$
$468$	1.57279	0.0727024
$469$	−5.82313	−0.268887
$470$	35.4686	1.63604
$471$	19.5653	0.901521
$472$	17.3339	0.797859
$473$	61.9130	2.84676
$474$	−33.2905	−1.52908
$475$	2.66776	0.122405
$476$	34.1980	1.56746
$477$	−12.7866	−0.585459
$478$	−15.0339	−0.687637
$479$	5.85631	0.267582	0.133791	−	0.991010i	$-0.457285\pi$
$479$	5.85631	0.267582	0.133791	+	0.991010i	$0.457285\pi$
$480$	−33.5867	−1.53302
$481$	−0.332975	−0.0151824
$482$	51.9713	2.36723
$483$	18.0777	0.822565
$484$	48.1181	2.18719
$485$	−2.70933	−0.123024
$486$	−27.2026	−1.23394
$487$	−10.1047	−0.457886	−0.228943	−	0.973440i	$-0.573527\pi$
$487$	−10.1047	−0.457886	−0.228943	+	0.973440i	$0.573527\pi$
$488$	4.58360	0.207490
$489$	39.0396	1.76543
$490$	−10.2097	−0.461228
$491$	8.44545	0.381138	0.190569	−	0.981674i	$-0.438967\pi$
$491$	8.44545	0.381138	0.190569	+	0.981674i	$0.438967\pi$
$492$	33.3513	1.50359
$493$	−21.2167	−0.955553
$494$	3.94510	0.177498
$495$	−14.6656	−0.659168
$496$	−11.9156	−0.535027
$497$	−3.04722	−0.136686
$498$	3.75675	0.168344
$499$	−9.91267	−0.443752	−0.221876	−	0.975075i	$-0.571218\pi$
$499$	−9.91267	−0.443752	−0.221876	+	0.975075i	$0.571218\pi$
$500$	−30.8181	−1.37823
$501$	16.4499	0.734927
$502$	−2.69921	−0.120472
$503$	6.64506	0.296289	0.148144	−	0.988966i	$-0.452670\pi$
$503$	6.64506	0.296289	0.148144	+	0.988966i	$0.452670\pi$
$504$	5.20137	0.231687
$505$	−4.93851	−0.219761
$506$	33.3276	1.48159
$507$	26.5112	1.17740
$508$	8.34375	0.370194
$509$	−21.5535	−0.955341	−0.477671	−	0.878539i	$-0.658519\pi$
$509$	−21.5535	−0.955341	−0.477671	+	0.878539i	$0.658519\pi$
$510$	−39.8050	−1.76259
$511$	−24.1234	−1.06716
$512$	−25.0214	−1.10580
$513$	−13.9782	−0.617152
$514$	8.52929	0.376211
$515$	−7.92854	−0.349373
$516$	61.8080	2.72095
$517$	43.0703	1.89423
$518$	−4.70232	−0.206608
$519$	21.1636	0.928980
$520$	−1.26590	−0.0555134
$521$	−15.1713	−0.664668	−0.332334	−	0.943162i	$-0.607836\pi$
$521$	−15.1713	−0.664668	−0.332334	+	0.943162i	$0.607836\pi$
$522$	−13.7800	−0.603135
$523$	9.12019	0.398798	0.199399	−	0.979918i	$-0.436101\pi$
$523$	9.12019	0.398798	0.199399	+	0.979918i	$0.436101\pi$
$524$	−18.9102	−0.826096
$525$	−4.25171	−0.185560
$526$	8.02750	0.350016
$527$	−21.3102	−0.928287
$528$	−27.0272	−1.17621
$529$	−14.8146	−0.644111
$530$	43.9479	1.90897
$531$	−17.1540	−0.744421
$532$	31.5509	1.36790
$533$	−2.85378	−0.123611
$534$	34.6239	1.49832
$535$	−32.7164	−1.41445
$536$	−2.50972	−0.108403
$537$	14.1143	0.609079
$538$	2.83207	0.122099
$539$	−12.3979	−0.534015
$540$	19.1534	0.824233
$541$	23.5675	1.01325	0.506623	−	0.862168i	$-0.330894\pi$
$541$	23.5675	1.01325	0.506623	+	0.862168i	$0.330894\pi$
$542$	−18.1176	−0.778218
$543$	−17.2975	−0.742306
$544$	−33.4614	−1.43465
$545$	−26.0101	−1.11415
$546$	−6.28746	−0.269078
$547$	−11.8956	−0.508621	−0.254311	−	0.967123i	$-0.581849\pi$
$547$	−11.8956	−0.508621	−0.254311	+	0.967123i	$0.581849\pi$
$548$	22.0063	0.940061
$549$	−4.53603	−0.193593
$550$	−7.83833	−0.334227
$551$	−19.5744	−0.833898
$552$	7.79135	0.331622
$553$	22.7814	0.968765
$554$	−5.45863	−0.231915
$555$	3.09958	0.131570
$556$	26.1609	1.10947
$557$	−10.5593	−0.447411	−0.223705	−	0.974657i	$-0.571815\pi$
$557$	−10.5593	−0.447411	−0.223705	+	0.974657i	$0.571815\pi$
$558$	−13.8407	−0.585924
$559$	−5.28874	−0.223690
$560$	15.2309	0.643625
$561$	−48.3361	−2.04075
$562$	−19.2561	−0.812271
$563$	−12.5448	−0.528699	−0.264349	−	0.964427i	$-0.585157\pi$
$563$	−12.5448	−0.528699	−0.264349	+	0.964427i	$0.585157\pi$
$564$	42.9973	1.81051
$565$	−2.08017	−0.0875135
$566$	6.96887	0.292924
$567$	34.1590	1.43454
$568$	−1.31333	−0.0551059
$569$	12.0975	0.507152	0.253576	−	0.967316i	$-0.418393\pi$
$569$	12.0975	0.507152	0.253576	+	0.967316i	$0.418393\pi$
$570$	−36.7238	−1.53819
$571$	3.05314	0.127770	0.0638849	−	0.997957i	$-0.479651\pi$
$571$	3.05314	0.127770	0.0638849	+	0.997957i	$0.479651\pi$
$572$	−6.56429	−0.274467
$573$	3.86587	0.161499
$574$	−40.3014	−1.68215
$575$	−1.92514	−0.0802839
$576$	−15.4869	−0.645288
$577$	−3.47874	−0.144822	−0.0724109	−	0.997375i	$-0.523069\pi$
$577$	−3.47874	−0.144822	−0.0724109	+	0.997375i	$0.523069\pi$
$578$	−3.14969	−0.131010
$579$	−50.0249	−2.07896
$580$	26.8216	1.11371
$581$	−2.57082	−0.106656
$582$	−5.79971	−0.240406
$583$	53.3670	2.21023
$584$	−10.3970	−0.430231
$585$	1.25276	0.0517953
$586$	−31.2970	−1.29287
$587$	8.45108	0.348814	0.174407	−	0.984674i	$-0.444199\pi$
$587$	8.45108	0.348814	0.174407	+	0.984674i	$0.444199\pi$
$588$	−12.3769	−0.510414
$589$	−19.6607	−0.810103
$590$	58.9587	2.42729
$591$	11.1359	0.458071
$592$	1.72667	0.0709655
$593$	7.83171	0.321610	0.160805	−	0.986986i	$-0.448591\pi$
$593$	7.83171	0.321610	0.160805	+	0.986986i	$0.448591\pi$
$594$	41.0703	1.68514
$595$	27.2394	1.11671
$596$	−9.24038	−0.378501
$597$	37.7558	1.54524
$598$	−2.84691	−0.116419
$599$	−21.6841	−0.885989	−0.442995	−	0.896524i	$-0.646084\pi$
$599$	−21.6841	−0.885989	−0.442995	+	0.896524i	$0.646084\pi$
$600$	−1.83245	−0.0748095
$601$	17.4607	0.712235	0.356118	−	0.934441i	$-0.384100\pi$
$601$	17.4607	0.712235	0.356118	+	0.934441i	$0.384100\pi$
$602$	−74.6883	−3.04407
$603$	2.48367	0.101143
$604$	−20.1133	−0.818398
$605$	38.3271	1.55822
$606$	−10.5716	−0.429441
$607$	27.0315	1.09717	0.548587	−	0.836093i	$-0.315166\pi$
$607$	27.0315	1.09717	0.548587	+	0.836093i	$0.315166\pi$
$608$	−30.8713	−1.25200
$609$	31.1965	1.26415
$610$	15.5904	0.631238
$611$	−3.67915	−0.148843
$612$	−14.5861	−0.589607
$613$	0.292578	0.0118171	0.00590856	−	0.999983i	$-0.498119\pi$
$613$	0.292578	0.0118171	0.00590856	+	0.999983i	$0.498119\pi$
$614$	−7.93173	−0.320099
$615$	26.5650	1.07121
$616$	−21.7087	−0.874669
$617$	31.5844	1.27154	0.635769	−	0.771879i	$-0.280683\pi$
$617$	31.5844	1.27154	0.635769	+	0.771879i	$0.280683\pi$
$618$	−16.9722	−0.682721
$619$	−15.9192	−0.639846	−0.319923	−	0.947444i	$-0.603657\pi$
$619$	−15.9192	−0.639846	−0.319923	+	0.947444i	$0.603657\pi$
$620$	26.9398	1.08193
$621$	10.0871	0.404782
$622$	24.9629	1.00092
$623$	−23.6939	−0.949275
$624$	2.30872	0.0924226
$625$	−21.1828	−0.847312
$626$	−52.1548	−2.08453
$627$	−44.5946	−1.78094
$628$	−24.6416	−0.983308
$629$	3.08801	0.123127
$630$	17.6917	0.704853
$631$	1.96395	0.0781837	0.0390918	−	0.999236i	$-0.487554\pi$
$631$	1.96395	0.0781837	0.0390918	+	0.999236i	$0.487554\pi$
$632$	9.81860	0.390563
$633$	35.4574	1.40931
$634$	−4.44437	−0.176508
$635$	6.64597	0.263737
$636$	53.2765	2.11255
$637$	1.05905	0.0419612
$638$	57.5130	2.27696
$639$	1.29970	0.0514151
$640$	20.8337	0.823526
$641$	−0.513163	−0.0202687	−0.0101344	−	0.999949i	$-0.503226\pi$
$641$	−0.513163	−0.0202687	−0.0101344	+	0.999949i	$0.503226\pi$
$642$	−70.0341	−2.76403
$643$	−32.7255	−1.29057	−0.645284	−	0.763943i	$-0.723261\pi$
$643$	−32.7255	−1.29057	−0.645284	+	0.763943i	$0.723261\pi$
$644$	−22.7681	−0.897189
$645$	49.2314	1.93848
$646$	−36.5868	−1.43949
$647$	1.21671	0.0478339	0.0239170	−	0.999714i	$-0.492386\pi$
$647$	1.21671	0.0478339	0.0239170	+	0.999714i	$0.492386\pi$
$648$	14.7222	0.578343
$649$	71.5950	2.81035
$650$	0.669566	0.0262625
$651$	31.3340	1.22807
$652$	−49.1687	−1.92560
$653$	27.0268	1.05764	0.528819	−	0.848734i	$-0.322635\pi$
$653$	27.0268	1.05764	0.528819	+	0.848734i	$0.322635\pi$
$654$	−55.6783	−2.17719
$655$	−15.0624	−0.588536
$656$	14.7984	0.577782
$657$	10.2891	0.401416
$658$	−51.9575	−2.02551
$659$	2.51825	0.0980970	0.0490485	−	0.998796i	$-0.484381\pi$
$659$	2.51825	0.0980970	0.0490485	+	0.998796i	$0.484381\pi$
$660$	61.1052	2.37852
$661$	−7.18360	−0.279410	−0.139705	−	0.990193i	$-0.544615\pi$
$661$	−7.18360	−0.279410	−0.139705	+	0.990193i	$0.544615\pi$
$662$	70.9378	2.75708
$663$	4.12897	0.160356
$664$	−1.10800	−0.0429989
$665$	25.1309	0.974535
$666$	2.00563	0.0777165
$667$	14.1255	0.546943
$668$	−20.7179	−0.801600
$669$	40.5106	1.56623
$670$	−8.53644	−0.329791
$671$	18.9318	0.730855
$672$	49.2008	1.89796
$673$	−36.8847	−1.42180	−0.710901	−	0.703293i	$-0.751712\pi$
$673$	−36.8847	−1.42180	−0.710901	+	0.703293i	$0.751712\pi$
$674$	−18.7547	−0.722403
$675$	−2.37239	−0.0913134
$676$	−33.3897	−1.28422
$677$	27.1717	1.04430	0.522148	−	0.852855i	$-0.325131\pi$
$677$	27.1717	1.04430	0.522148	+	0.852855i	$0.325131\pi$
$678$	−4.45290	−0.171013
$679$	3.96887	0.152311
$680$	11.7400	0.450207
$681$	−2.11033	−0.0808681
$682$	57.7664	2.21199
$683$	34.9114	1.33585	0.667924	−	0.744230i	$-0.267183\pi$
$683$	34.9114	1.33585	0.667924	+	0.744230i	$0.267183\pi$
$684$	−13.4570	−0.514542
$685$	17.5284	0.669727
$686$	−30.8503	−1.17787
$687$	22.8353	0.871222
$688$	27.4251	1.04557
$689$	−4.55871	−0.173673
$690$	26.5011	1.00888
$691$	34.3179	1.30552	0.652758	−	0.757567i	$-0.273612\pi$
$691$	34.3179	1.30552	0.652758	+	0.757567i	$0.273612\pi$
$692$	−26.6547	−1.01326
$693$	21.4834	0.816087
$694$	−36.6554	−1.39142
$695$	20.8377	0.790420
$696$	13.4454	0.509648
$697$	26.4659	1.00247
$698$	−22.9780	−0.869729
$699$	−38.5859	−1.45945
$700$	5.35484	0.202394
$701$	34.5588	1.30527	0.652635	−	0.757673i	$-0.273664\pi$
$701$	34.5588	1.30527	0.652635	+	0.757673i	$0.273664\pi$
$702$	−3.50831	−0.132413
$703$	2.84898	0.107451
$704$	64.6370	2.43610
$705$	34.2482	1.28986
$706$	−9.32196	−0.350837
$707$	7.23436	0.272076
$708$	71.4735	2.68614
$709$	−38.4211	−1.44293	−0.721467	−	0.692449i	$-0.756532\pi$
$709$	−38.4211	−1.44293	−0.721467	+	0.692449i	$0.756532\pi$
$710$	−4.46708	−0.167647
$711$	−9.71670	−0.364405
$712$	−10.2119	−0.382705
$713$	14.1878	0.531336
$714$	58.3098	2.18219
$715$	−5.22860	−0.195538
$716$	−17.7764	−0.664336
$717$	−14.5167	−0.542135
$718$	11.1585	0.416430
$719$	27.5156	1.02616	0.513079	−	0.858341i	$-0.328505\pi$
$719$	27.5156	1.02616	0.513079	+	0.858341i	$0.328505\pi$
$720$	−6.49628	−0.242102
$721$	11.6144	0.432544
$722$	7.04690	0.262259
$723$	50.1832	1.86633
$724$	21.7854	0.809650
$725$	−3.32219	−0.123383
$726$	82.0446	3.04496
$727$	21.4655	0.796111	0.398056	−	0.917361i	$-0.369685\pi$
$727$	21.4655	0.796111	0.398056	+	0.917361i	$0.369685\pi$
$728$	1.85440	0.0687287
$729$	7.36295	0.272702
$730$	−35.3638	−1.30887
$731$	49.0477	1.81410
$732$	18.8997	0.698554
$733$	32.3306	1.19416	0.597078	−	0.802183i	$-0.296328\pi$
$733$	32.3306	1.19416	0.597078	+	0.802183i	$0.296328\pi$
$734$	−1.30815	−0.0482848
$735$	−9.85844	−0.363634
$736$	22.2777	0.821168
$737$	−10.3660	−0.381836
$738$	17.1893	0.632747
$739$	−14.2269	−0.523344	−0.261672	−	0.965157i	$-0.584274\pi$
$739$	−14.2269	−0.523344	−0.261672	+	0.965157i	$0.584274\pi$
$740$	−3.90378	−0.143506
$741$	3.80936	0.139940
$742$	−64.3788	−2.36342
$743$	45.4452	1.66722	0.833611	−	0.552352i	$-0.186270\pi$
$743$	45.4452	1.66722	0.833611	+	0.552352i	$0.186270\pi$
$744$	13.5047	0.495105
$745$	−7.36016	−0.269655
$746$	−71.3023	−2.61056
$747$	1.09650	0.0401190
$748$	60.8772	2.22589
$749$	47.9259	1.75117
$750$	−52.5468	−1.91874
$751$	15.0927	0.550740	0.275370	−	0.961338i	$-0.411200\pi$
$751$	15.0927	0.550740	0.275370	+	0.961338i	$0.411200\pi$
$752$	19.0785	0.695720
$753$	−2.60634	−0.0949804
$754$	−4.91288	−0.178916
$755$	−16.0207	−0.583051
$756$	−28.0577	−1.02045
$757$	−13.9762	−0.507975	−0.253987	−	0.967208i	$-0.581742\pi$
$757$	−13.9762	−0.507975	−0.253987	+	0.967208i	$0.581742\pi$
$758$	35.2294	1.27959
$759$	32.1809	1.16809
$760$	10.8312	0.392889
$761$	−51.1186	−1.85305	−0.926524	−	0.376236i	$-0.877218\pi$
$761$	−51.1186	−1.85305	−0.926524	+	0.376236i	$0.877218\pi$
$762$	14.2266	0.515377
$763$	38.1019	1.37938
$764$	−4.86890	−0.176151
$765$	−11.6181	−0.420054
$766$	68.4519	2.47327
$767$	−6.11579	−0.220828
$768$	−4.81890	−0.173887
$769$	−6.48223	−0.233755	−0.116878	−	0.993146i	$-0.537289\pi$
$769$	−6.48223	−0.233755	−0.116878	+	0.993146i	$0.537289\pi$
$770$	−73.8389	−2.66097
$771$	8.23583	0.296606
$772$	63.0042	2.26757
$773$	45.5386	1.63791	0.818954	−	0.573859i	$-0.194554\pi$
$773$	45.5386	1.63791	0.818954	+	0.573859i	$0.194554\pi$
$774$	31.8559	1.14504
$775$	−3.33683	−0.119862
$776$	1.71055	0.0614051
$777$	−4.54053	−0.162891
$778$	66.3329	2.37815
$779$	24.4173	0.874841
$780$	−5.21973	−0.186896
$781$	−5.42448	−0.194103
$782$	26.4022	0.944142
$783$	17.4072	0.622083
$784$	−5.49179	−0.196135
$785$	−19.6276	−0.700538
$786$	−32.2432	−1.15008
$787$	−45.6801	−1.62832	−0.814159	−	0.580641i	$-0.802802\pi$
$787$	−45.6801	−1.62832	−0.814159	+	0.580641i	$0.802802\pi$
$788$	−14.0252	−0.499628
$789$	7.75130	0.275954
$790$	33.3965	1.18819
$791$	3.04722	0.108347
$792$	9.25917	0.329010
$793$	−1.61720	−0.0574283
$794$	38.2776	1.35842
$795$	42.4358	1.50504
$796$	−47.5517	−1.68543
$797$	13.9777	0.495114	0.247557	−	0.968873i	$-0.420372\pi$
$797$	13.9777	0.495114	0.247557	+	0.968873i	$0.420372\pi$
$798$	53.7963	1.90437
$799$	34.1204	1.20709
$800$	−5.23951	−0.185245
$801$	10.1059	0.357073
$802$	−36.8246	−1.30032
$803$	−42.9431	−1.51543
$804$	−10.3484	−0.364961
$805$	−18.1353	−0.639185
$806$	−4.93452	−0.173811
$807$	2.73463	0.0962636
$808$	3.11795	0.109689
$809$	−28.3262	−0.995897	−0.497949	−	0.867207i	$-0.665913\pi$
$809$	−28.3262	−0.995897	−0.497949	+	0.867207i	$0.665913\pi$
$810$	50.0754	1.75947
$811$	−19.1078	−0.670967	−0.335484	−	0.942046i	$-0.608900\pi$
$811$	−19.1078	−0.670967	−0.335484	+	0.942046i	$0.608900\pi$
$812$	−39.2907	−1.37883
$813$	−17.4942	−0.613550
$814$	−8.37080	−0.293396
$815$	−39.1639	−1.37185
$816$	−21.4110	−0.749536
$817$	45.2511	1.58314
$818$	58.3591	2.04048
$819$	−1.83516	−0.0641256
$820$	−33.4575	−1.16839
$821$	34.2939	1.19686	0.598432	−	0.801174i	$-0.295791\pi$
$821$	34.2939	1.19686	0.598432	+	0.801174i	$0.295791\pi$
$822$	37.5221	1.30873
$823$	−44.8373	−1.56293	−0.781465	−	0.623949i	$-0.785527\pi$
$823$	−44.8373	−1.56293	−0.781465	+	0.623949i	$0.785527\pi$
$824$	5.00572	0.174383
$825$	−7.56864	−0.263506
$826$	−86.3680	−3.00513
$827$	13.1738	0.458098	0.229049	−	0.973415i	$-0.426438\pi$
$827$	13.1738	0.458098	0.229049	+	0.973415i	$0.426438\pi$
$828$	9.71102	0.337481
$829$	−2.44254	−0.0848330	−0.0424165	−	0.999100i	$-0.513506\pi$
$829$	−2.44254	−0.0848330	−0.0424165	+	0.999100i	$0.513506\pi$
$830$	−3.76871	−0.130814
$831$	−5.27081	−0.182843
$832$	−5.52142	−0.191421
$833$	−9.82166	−0.340300
$834$	44.6061	1.54458
$835$	−16.5023	−0.571084
$836$	56.1650	1.94251
$837$	17.4839	0.604332
$838$	5.57193	0.192479
$839$	32.9524	1.13764	0.568822	−	0.822461i	$-0.307400\pi$
$839$	32.9524	1.13764	0.568822	+	0.822461i	$0.307400\pi$
$840$	−17.2621	−0.595600
$841$	−4.62374	−0.159439
$842$	−5.71869	−0.197079
$843$	−18.5936	−0.640398
$844$	−44.6571	−1.53716
$845$	−26.5956	−0.914916
$846$	22.1608	0.761905
$847$	−56.1449	−1.92916
$848$	23.6395	0.811784
$849$	6.72910	0.230942
$850$	−6.20955	−0.212986
$851$	−2.05592	−0.0704759
$852$	−5.41528	−0.185524
$853$	4.38443	0.150120	0.0750600	−	0.997179i	$-0.476085\pi$
$853$	4.38443	0.150120	0.0750600	+	0.997179i	$0.476085\pi$
$854$	−22.8383	−0.781509
$855$	−10.7188	−0.366575
$856$	20.6556	0.705995
$857$	35.9986	1.22969	0.614844	−	0.788649i	$-0.289219\pi$
$857$	35.9986	1.22969	0.614844	+	0.788649i	$0.289219\pi$
$858$	−11.1926	−0.382107
$859$	−34.0081	−1.16034	−0.580170	−	0.814495i	$-0.697014\pi$
$859$	−34.0081	−1.16034	−0.580170	+	0.814495i	$0.697014\pi$
$860$	−62.0048	−2.11435
$861$	−38.9148	−1.32621
$862$	51.6737	1.76001
$863$	−17.5900	−0.598772	−0.299386	−	0.954132i	$-0.596782\pi$
$863$	−17.5900	−0.598772	−0.299386	+	0.954132i	$0.596782\pi$
$864$	27.4534	0.933982
$865$	−21.2310	−0.721875
$866$	82.9220	2.81780
$867$	−3.04132	−0.103289
$868$	−39.4638	−1.33949
$869$	40.5541	1.37570
$870$	45.7326	1.55048
$871$	0.885484	0.0300035
$872$	16.4216	0.556105
$873$	−1.69280	−0.0572925
$874$	24.3585	0.823940
$875$	35.9589	1.21563
$876$	−42.8703	−1.44845
$877$	−1.47005	−0.0496402	−0.0248201	−	0.999692i	$-0.507901\pi$
$877$	−1.47005	−0.0496402	−0.0248201	+	0.999692i	$0.507901\pi$
$878$	−29.4564	−0.994104
$879$	−30.2202	−1.01930
$880$	27.1132	0.913986
$881$	−10.1507	−0.341987	−0.170994	−	0.985272i	$-0.554698\pi$
$881$	−10.1507	−0.341987	−0.170994	+	0.985272i	$0.554698\pi$
$882$	−6.37905	−0.214794
$883$	17.9304	0.603405	0.301702	−	0.953402i	$-0.402445\pi$
$883$	17.9304	0.603405	0.301702	+	0.953402i	$0.402445\pi$
$884$	−5.20026	−0.174904
$885$	56.9302	1.91369
$886$	−73.0398	−2.45382
$887$	42.8522	1.43884	0.719418	−	0.694577i	$-0.244408\pi$
$887$	42.8522	1.43884	0.719418	+	0.694577i	$0.244408\pi$
$888$	−1.95693	−0.0656703
$889$	−9.73561	−0.326522
$890$	−34.7341	−1.16429
$891$	60.8077	2.03714
$892$	−51.0213	−1.70832
$893$	31.4793	1.05342
$894$	−15.7555	−0.526941
$895$	−14.1593	−0.473293
$896$	−30.5191	−1.01957
$897$	−2.74896	−0.0917850
$898$	58.6627	1.95760
$899$	24.4837	0.816575
$900$	−2.28394	−0.0761313
$901$	42.2775	1.40847
$902$	−71.7422	−2.38875
$903$	−72.1185	−2.39995
$904$	1.31333	0.0436806
$905$	17.3526	0.576819
$906$	−34.2945	−1.13936
$907$	−10.2968	−0.341901	−0.170950	−	0.985280i	$-0.554684\pi$
$907$	−10.2968	−0.341901	−0.170950	+	0.985280i	$0.554684\pi$
$908$	2.65787	0.0882046
$909$	−3.08559	−0.102343
$910$	6.30747	0.209091
$911$	22.7945	0.755216	0.377608	−	0.925966i	$-0.376747\pi$
$911$	22.7945	0.755216	0.377608	+	0.925966i	$0.376747\pi$
$912$	−19.7537	−0.654110
$913$	−4.57643	−0.151458
$914$	−12.5225	−0.414208
$915$	15.0540	0.497671
$916$	−28.7601	−0.950260
$917$	22.0647	0.728640
$918$	32.5361	1.07385
$919$	−18.4666	−0.609156	−0.304578	−	0.952487i	$-0.598515\pi$
$919$	−18.4666	−0.609156	−0.304578	+	0.952487i	$0.598515\pi$
$920$	−7.81615	−0.257691
$921$	−7.65883	−0.252367
$922$	8.96445	0.295229
$923$	0.463370	0.0152520
$924$	−89.5123	−2.94474
$925$	0.483532	0.0158984
$926$	−54.7197	−1.79820
$927$	−4.95377	−0.162703
$928$	38.4444	1.26200
$929$	45.2458	1.48447	0.742234	−	0.670141i	$-0.233766\pi$
$929$	45.2458	1.48447	0.742234	+	0.670141i	$0.233766\pi$
$930$	45.9341	1.50624
$931$	−9.06141	−0.296976
$932$	48.5972	1.59186
$933$	24.1040	0.789128
$934$	39.1514	1.28107
$935$	48.4900	1.58579
$936$	−0.790937	−0.0258526
$937$	15.7831	0.515613	0.257806	−	0.966197i	$-0.417000\pi$
$937$	15.7831	0.515613	0.257806	+	0.966197i	$0.417000\pi$
$938$	12.5049	0.408300
$939$	−50.3604	−1.64345
$940$	−43.1341	−1.40688
$941$	0.257283	0.00838719	0.00419359	−	0.999991i	$-0.498665\pi$
$941$	0.257283	0.00838719	0.00419359	+	0.999991i	$0.498665\pi$
$942$	−42.0156	−1.36894
$943$	−17.6203	−0.573796
$944$	31.7138	1.03220
$945$	−22.3485	−0.726997
$946$	−132.956	−4.32276
$947$	53.6369	1.74297	0.871483	−	0.490426i	$-0.163159\pi$
$947$	53.6369	1.74297	0.871483	+	0.490426i	$0.163159\pi$
$948$	40.4854	1.31490
$949$	3.66829	0.119078
$950$	−5.72889	−0.185870
$951$	−4.29145	−0.139160
$952$	−17.1977	−0.557381
$953$	−54.4001	−1.76219	−0.881096	−	0.472937i	$-0.843194\pi$
$953$	−54.4001	−1.76219	−0.881096	+	0.472937i	$0.843194\pi$
$954$	27.4587	0.889009
$955$	−3.87818	−0.125495
$956$	18.2831	0.591319
$957$	55.5342	1.79517
$958$	−12.5762	−0.406318
$959$	−25.6772	−0.829160
$960$	51.3974	1.65884
$961$	−6.40849	−0.206725
$962$	0.715050	0.0230542
$963$	−20.4413	−0.658710
$964$	−63.2036	−2.03565
$965$	50.1842	1.61549
$966$	−38.8211	−1.24905
$967$	−29.3788	−0.944758	−0.472379	−	0.881396i	$-0.656605\pi$
$967$	−29.3788	−0.944758	−0.472379	+	0.881396i	$0.656605\pi$
$968$	−24.1980	−0.777752
$969$	−35.3280	−1.13490
$970$	5.81818	0.186810
$971$	−14.4318	−0.463138	−0.231569	−	0.972818i	$-0.574386\pi$
$971$	−14.4318	−0.463138	−0.231569	+	0.972818i	$0.574386\pi$
$972$	33.0817	1.06110
$973$	−30.5250	−0.978585
$974$	21.6993	0.695291
$975$	0.646528	0.0207055
$976$	8.38607	0.268432
$977$	−21.8641	−0.699495	−0.349748	−	0.936844i	$-0.613733\pi$
$977$	−21.8641	−0.699495	−0.349748	+	0.936844i	$0.613733\pi$
$978$	−83.8359	−2.68078
$979$	−42.1784	−1.34803
$980$	12.4163	0.396624
$981$	−16.2511	−0.518859
$982$	−18.1362	−0.578751
$983$	23.9205	0.762947	0.381473	−	0.924380i	$-0.375417\pi$
$983$	23.9205	0.762947	0.381473	+	0.924380i	$0.375417\pi$
$984$	−16.7719	−0.534670
$985$	−11.1714	−0.355950
$986$	45.5620	1.45099
$987$	−50.1698	−1.59692
$988$	−4.79772	−0.152636
$989$	−32.6547	−1.03836
$990$	31.4937	1.00093
$991$	35.0569	1.11362	0.556809	−	0.830640i	$-0.312025\pi$
$991$	35.0569	1.11362	0.556809	+	0.830640i	$0.312025\pi$
$992$	38.6138	1.22599
$993$	68.4971	2.17369
$994$	6.54377	0.207556
$995$	−37.8759	−1.20075
$996$	−4.56867	−0.144764
$997$	−34.6474	−1.09729	−0.548647	−	0.836054i	$-0.684857\pi$
$997$	−34.6474	−1.09729	−0.548647	+	0.836054i	$0.684857\pi$
$998$	21.2870	0.673829
$999$	−2.53355	−0.0801581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.d.1.20	✓	165

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.d.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.14746 q^{2} -2.07357 q^{3} +2.61157 q^{4} +2.08017 q^{5} +4.45290 q^{6} -3.04722 q^{7} -1.31333 q^{8} +1.29970 q^{9} +O(q^{10})\)	\(q-2.14746 q^{2} -2.07357 q^{3} +2.61157 q^{4} +2.08017 q^{5} +4.45290 q^{6} -3.04722 q^{7} -1.31333 q^{8} +1.29970 q^{9} -4.46708 q^{10} -5.42448 q^{11} -5.41528 q^{12} +0.463370 q^{13} +6.54377 q^{14} -4.31338 q^{15} -2.40283 q^{16} -4.29729 q^{17} -2.79104 q^{18} -3.96466 q^{19} +5.43252 q^{20} +6.31863 q^{21} +11.6488 q^{22} +2.86102 q^{23} +2.72327 q^{24} -0.672885 q^{25} -0.995067 q^{26} +3.52570 q^{27} -7.95803 q^{28} +4.93723 q^{29} +9.26281 q^{30} +4.95898 q^{31} +7.78663 q^{32} +11.2480 q^{33} +9.22825 q^{34} -6.33874 q^{35} +3.39425 q^{36} -0.718595 q^{37} +8.51393 q^{38} -0.960830 q^{39} -2.73194 q^{40} -6.15874 q^{41} -13.5690 q^{42} -11.4136 q^{43} -14.1664 q^{44} +2.70359 q^{45} -6.14392 q^{46} -7.93999 q^{47} +4.98245 q^{48} +2.28555 q^{49} +1.44499 q^{50} +8.91074 q^{51} +1.21012 q^{52} -9.83817 q^{53} -7.57129 q^{54} -11.2838 q^{55} +4.00199 q^{56} +8.22099 q^{57} -10.6025 q^{58} -13.1985 q^{59} -11.2647 q^{60} -3.49007 q^{61} -10.6492 q^{62} -3.96046 q^{63} -11.9158 q^{64} +0.963889 q^{65} -24.1547 q^{66} +1.91097 q^{67} -11.2227 q^{68} -5.93253 q^{69} +13.6122 q^{70} +1.00000 q^{71} -1.70692 q^{72} +7.91654 q^{73} +1.54315 q^{74} +1.39527 q^{75} -10.3540 q^{76} +16.5296 q^{77} +2.06334 q^{78} -7.47614 q^{79} -4.99831 q^{80} -11.2099 q^{81} +13.2256 q^{82} +0.843662 q^{83} +16.5015 q^{84} -8.93910 q^{85} +24.5103 q^{86} -10.2377 q^{87} +7.12411 q^{88} +7.77557 q^{89} -5.80584 q^{90} -1.41199 q^{91} +7.47177 q^{92} -10.2828 q^{93} +17.0508 q^{94} -8.24716 q^{95} -16.1461 q^{96} -1.30246 q^{97} -4.90811 q^{98} -7.05017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) 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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