LMFDB - Embedded newform 8023.2.a.c.1.6

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:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.73131 q^{2} -2.15430 q^{3} +5.46003 q^{4} -2.36711 q^{5} +5.88407 q^{6} -3.03890 q^{7} -9.45041 q^{8} +1.64103 q^{9} +O(q^{10})$	\(q-2.73131 q^{2} -2.15430 q^{3} +5.46003 q^{4} -2.36711 q^{5} +5.88407 q^{6} -3.03890 q^{7} -9.45041 q^{8} +1.64103 q^{9} +6.46530 q^{10} -1.23686 q^{11} -11.7626 q^{12} +0.935944 q^{13} +8.30017 q^{14} +5.09947 q^{15} +14.8919 q^{16} +3.71828 q^{17} -4.48215 q^{18} +6.12994 q^{19} -12.9245 q^{20} +6.54672 q^{21} +3.37824 q^{22} -3.46566 q^{23} +20.3591 q^{24} +0.603200 q^{25} -2.55635 q^{26} +2.92764 q^{27} -16.5925 q^{28} -5.46018 q^{29} -13.9282 q^{30} +4.47779 q^{31} -21.7735 q^{32} +2.66457 q^{33} -10.1558 q^{34} +7.19341 q^{35} +8.96007 q^{36} -1.25753 q^{37} -16.7427 q^{38} -2.01631 q^{39} +22.3701 q^{40} -5.00276 q^{41} -17.8811 q^{42} -8.04498 q^{43} -6.75330 q^{44} -3.88449 q^{45} +9.46578 q^{46} -11.1410 q^{47} -32.0817 q^{48} +2.23492 q^{49} -1.64752 q^{50} -8.01031 q^{51} +5.11029 q^{52} +1.52281 q^{53} -7.99628 q^{54} +2.92778 q^{55} +28.7189 q^{56} -13.2058 q^{57} +14.9134 q^{58} -2.78143 q^{59} +27.8433 q^{60} -10.6917 q^{61} -12.2302 q^{62} -4.98692 q^{63} +29.6864 q^{64} -2.21548 q^{65} -7.27777 q^{66} -5.50665 q^{67} +20.3019 q^{68} +7.46609 q^{69} -19.6474 q^{70} -1.00000 q^{71} -15.5084 q^{72} -7.75902 q^{73} +3.43469 q^{74} -1.29948 q^{75} +33.4697 q^{76} +3.75869 q^{77} +5.50716 q^{78} +12.1551 q^{79} -35.2508 q^{80} -11.2301 q^{81} +13.6641 q^{82} -1.58835 q^{83} +35.7453 q^{84} -8.80157 q^{85} +21.9733 q^{86} +11.7629 q^{87} +11.6888 q^{88} +16.4018 q^{89} +10.6097 q^{90} -2.84424 q^{91} -18.9226 q^{92} -9.64653 q^{93} +30.4296 q^{94} -14.5102 q^{95} +46.9068 q^{96} +8.08872 q^{97} -6.10424 q^{98} -2.02972 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.73131	−1.93133	−0.965663	−	0.259799i	$-0.916344\pi$
$2$	−2.73131	−1.93133	−0.965663	+	0.259799i	$0.916344\pi$
$3$	−2.15430	−1.24379	−0.621894	−	0.783101i	$-0.713637\pi$
$3$	−2.15430	−1.24379	−0.621894	+	0.783101i	$0.713637\pi$
$4$	5.46003	2.73002
$5$	−2.36711	−1.05860	−0.529301	−	0.848434i	$-0.677546\pi$
$5$	−2.36711	−1.05860	−0.529301	+	0.848434i	$0.677546\pi$
$6$	5.88407	2.40216
$7$	−3.03890	−1.14860	−0.574298	−	0.818646i	$-0.694725\pi$
$7$	−3.03890	−1.14860	−0.574298	+	0.818646i	$0.694725\pi$
$8$	−9.45041	−3.34123
$9$	1.64103	0.547010
$10$	6.46530	2.04451
$11$	−1.23686	−0.372927	−0.186464	−	0.982462i	$-0.559703\pi$
$11$	−1.23686	−0.372927	−0.186464	+	0.982462i	$0.559703\pi$
$12$	−11.7626	−3.39556
$13$	0.935944	0.259584	0.129792	−	0.991541i	$-0.458569\pi$
$13$	0.935944	0.259584	0.129792	+	0.991541i	$0.458569\pi$
$14$	8.30017	2.21831
$15$	5.09947	1.31668
$16$	14.8919	3.72298
$17$	3.71828	0.901815	0.450908	−	0.892571i	$-0.351100\pi$
$17$	3.71828	0.901815	0.450908	+	0.892571i	$0.351100\pi$
$18$	−4.48215	−1.05645
$19$	6.12994	1.40631	0.703153	−	0.711039i	$-0.251775\pi$
$19$	6.12994	1.40631	0.703153	+	0.711039i	$0.251775\pi$
$20$	−12.9245	−2.89000
$21$	6.54672	1.42861
$22$	3.37824	0.720244
$23$	−3.46566	−0.722640	−0.361320	−	0.932442i	$-0.617674\pi$
$23$	−3.46566	−0.722640	−0.361320	+	0.932442i	$0.617674\pi$
$24$	20.3591	4.15578
$25$	0.603200	0.120640
$26$	−2.55635	−0.501341
$27$	2.92764	0.563424
$28$	−16.5925	−3.13569
$29$	−5.46018	−1.01393	−0.506965	−	0.861967i	$-0.669233\pi$
$29$	−5.46018	−1.01393	−0.506965	+	0.861967i	$0.669233\pi$
$30$	−13.9282	−2.54293
$31$	4.47779	0.804236	0.402118	−	0.915588i	$-0.368274\pi$
$31$	4.47779	0.804236	0.402118	+	0.915588i	$0.368274\pi$
$32$	−21.7735	−3.84905
$33$	2.66457	0.463843
$34$	−10.1558	−1.74170
$35$	7.19341	1.21591
$36$	8.96007	1.49335
$37$	−1.25753	−0.206736	−0.103368	−	0.994643i	$-0.532962\pi$
$37$	−1.25753	−0.206736	−0.103368	+	0.994643i	$0.532962\pi$
$38$	−16.7427	−2.71603
$39$	−2.01631	−0.322868
$40$	22.3701	3.53703
$41$	−5.00276	−0.781300	−0.390650	−	0.920539i	$-0.627750\pi$
$41$	−5.00276	−0.781300	−0.390650	+	0.920539i	$0.627750\pi$
$42$	−17.8811	−2.75911
$43$	−8.04498	−1.22685	−0.613424	−	0.789754i	$-0.710208\pi$
$43$	−8.04498	−1.22685	−0.613424	+	0.789754i	$0.710208\pi$
$44$	−6.75330	−1.01810
$45$	−3.88449	−0.579066
$46$	9.46578	1.39565
$47$	−11.1410	−1.62509	−0.812544	−	0.582900i	$-0.801918\pi$
$47$	−11.1410	−1.62509	−0.812544	+	0.582900i	$0.801918\pi$
$48$	−32.0817	−4.63060
$49$	2.23492	0.319274
$50$	−1.64752	−0.232995
$51$	−8.01031	−1.12167
$52$	5.11029	0.708669
$53$	1.52281	0.209174	0.104587	−	0.994516i	$-0.466648\pi$
$53$	1.52281	0.209174	0.104587	+	0.994516i	$0.466648\pi$
$54$	−7.99628	−1.08816
$55$	2.92778	0.394782
$56$	28.7189	3.83772
$57$	−13.2058	−1.74915
$58$	14.9134	1.95823
$59$	−2.78143	−0.362111	−0.181056	−	0.983473i	$-0.557951\pi$
$59$	−2.78143	−0.362111	−0.181056	+	0.983473i	$0.557951\pi$
$60$	27.8433	3.59455
$61$	−10.6917	−1.36893	−0.684466	−	0.729044i	$-0.739965\pi$
$61$	−10.6917	−1.36893	−0.684466	+	0.729044i	$0.739965\pi$
$62$	−12.2302	−1.55324
$63$	−4.98692	−0.628293
$64$	29.6864	3.71080
$65$	−2.21548	−0.274797
$66$	−7.27777	−0.895831
$67$	−5.50665	−0.672745	−0.336372	−	0.941729i	$-0.609200\pi$
$67$	−5.50665	−0.672745	−0.336372	+	0.941729i	$0.609200\pi$
$68$	20.3019	2.46197
$69$	7.46609	0.898811
$70$	−19.6474	−2.34831
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−15.5084	−1.82768
$73$	−7.75902	−0.908124	−0.454062	−	0.890970i	$-0.650026\pi$
$73$	−7.75902	−0.908124	−0.454062	+	0.890970i	$0.650026\pi$
$74$	3.43469	0.399274
$75$	−1.29948	−0.150051
$76$	33.4697	3.83924
$77$	3.75869	0.428343
$78$	5.50716	0.623563
$79$	12.1551	1.36755	0.683776	−	0.729692i	$-0.260336\pi$
$79$	12.1551	1.36755	0.683776	+	0.729692i	$0.260336\pi$
$80$	−35.2508	−3.94115
$81$	−11.2301	−1.24779
$82$	13.6641	1.50894
$83$	−1.58835	−0.174344	−0.0871719	−	0.996193i	$-0.527783\pi$
$83$	−1.58835	−0.174344	−0.0871719	+	0.996193i	$0.527783\pi$
$84$	35.7453	3.90013
$85$	−8.80157	−0.954664
$86$	21.9733	2.36944
$87$	11.7629	1.26111
$88$	11.6888	1.24603
$89$	16.4018	1.73859	0.869293	−	0.494296i	$-0.164574\pi$
$89$	16.4018	1.73859	0.869293	+	0.494296i	$0.164574\pi$
$90$	10.6097	1.11836
$91$	−2.84424	−0.298157
$92$	−18.9226	−1.97282
$93$	−9.64653	−1.00030
$94$	30.4296	3.13857
$95$	−14.5102	−1.48872
$96$	46.9068	4.78741
$97$	8.08872	0.821285	0.410643	−	0.911796i	$-0.365304\pi$
$97$	8.08872	0.821285	0.410643	+	0.911796i	$0.365304\pi$
$98$	−6.10424	−0.616622
$99$	−2.02972	−0.203995
$100$	3.29349	0.329349
$101$	7.11014	0.707486	0.353743	−	0.935343i	$-0.384909\pi$
$101$	7.11014	0.707486	0.353743	+	0.935343i	$0.384909\pi$
$102$	21.8786	2.16630
$103$	19.9876	1.96943	0.984716	−	0.174166i	$-0.0557230\pi$
$103$	19.9876	1.96943	0.984716	+	0.174166i	$0.0557230\pi$
$104$	−8.84506	−0.867329
$105$	−15.4968	−1.51233
$106$	−4.15926	−0.403983
$107$	−14.9027	−1.44070	−0.720351	−	0.693610i	$-0.756019\pi$
$107$	−14.9027	−1.44070	−0.720351	+	0.693610i	$0.756019\pi$
$108$	15.9850	1.53816
$109$	15.8787	1.52090	0.760450	−	0.649396i	$-0.224978\pi$
$109$	15.8787	1.52090	0.760450	+	0.649396i	$0.224978\pi$
$110$	−7.99667	−0.762452
$111$	2.70909	0.257136
$112$	−45.2550	−4.27620
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	36.0690	3.37817
$115$	8.20359	0.764989
$116$	−29.8128	−2.76805
$117$	1.53591	0.141995
$118$	7.59694	0.699355
$119$	−11.2995	−1.03582
$120$	−48.1921	−4.39932
$121$	−9.47018	−0.860925
$122$	29.2023	2.64385
$123$	10.7775	0.971772
$124$	24.4489	2.19558
$125$	10.4077	0.930893
$126$	13.6208	1.21344
$127$	19.1330	1.69778	0.848889	−	0.528571i	$-0.177272\pi$
$127$	19.1330	1.69778	0.848889	+	0.528571i	$0.177272\pi$
$128$	−37.5355	−3.31770
$129$	17.3313	1.52594
$130$	6.05116	0.530721
$131$	0.763075	0.0666702	0.0333351	−	0.999444i	$-0.489387\pi$
$131$	0.763075	0.0666702	0.0333351	+	0.999444i	$0.489387\pi$
$132$	14.5487	1.26630
$133$	−18.6283	−1.61528
$134$	15.0404	1.29929
$135$	−6.93004	−0.596443
$136$	−35.1393	−3.01317
$137$	2.64401	0.225893	0.112946	−	0.993601i	$-0.463971\pi$
$137$	2.64401	0.225893	0.112946	+	0.993601i	$0.463971\pi$
$138$	−20.3922	−1.73590
$139$	12.7257	1.07938	0.539690	−	0.841864i	$-0.318541\pi$
$139$	12.7257	1.07938	0.539690	+	0.841864i	$0.318541\pi$
$140$	39.2762	3.31945
$141$	24.0012	2.02127
$142$	2.73131	0.229206
$143$	−1.15763	−0.0968060
$144$	24.4380	2.03650
$145$	12.9248	1.07335
$146$	21.1923	1.75388
$147$	−4.81469	−0.397109
$148$	−6.86613	−0.564392
$149$	9.38599	0.768930	0.384465	−	0.923140i	$-0.374386\pi$
$149$	9.38599	0.768930	0.384465	+	0.923140i	$0.374386\pi$
$150$	3.54927	0.289796
$151$	−19.1757	−1.56050	−0.780249	−	0.625469i	$-0.784908\pi$
$151$	−19.1757	−1.56050	−0.780249	+	0.625469i	$0.784908\pi$
$152$	−57.9305	−4.69878
$153$	6.10180	0.493302
$154$	−10.2661	−0.827270
$155$	−10.5994	−0.851366
$156$	−11.0091	−0.881435
$157$	−12.4573	−0.994201	−0.497101	−	0.867693i	$-0.665602\pi$
$157$	−12.4573	−0.994201	−0.497101	+	0.867693i	$0.665602\pi$
$158$	−33.1992	−2.64119
$159$	−3.28060	−0.260168
$160$	51.5403	4.07462
$161$	10.5318	0.830022
$162$	30.6729	2.40989
$163$	5.12401	0.401343	0.200672	−	0.979659i	$-0.435688\pi$
$163$	5.12401	0.401343	0.200672	+	0.979659i	$0.435688\pi$
$164$	−27.3152	−2.13296
$165$	−6.30733	−0.491025
$166$	4.33826	0.336714
$167$	7.07034	0.547119	0.273560	−	0.961855i	$-0.411799\pi$
$167$	7.07034	0.547119	0.273560	+	0.961855i	$0.411799\pi$
$168$	−61.8692	−4.77331
$169$	−12.1240	−0.932616
$170$	24.0398	1.84377
$171$	10.0594	0.769262
$172$	−43.9259	−3.34932
$173$	17.0444	1.29586	0.647930	−	0.761700i	$-0.275635\pi$
$173$	17.0444	1.29586	0.647930	+	0.761700i	$0.275635\pi$
$174$	−32.1281	−2.43562
$175$	−1.83306	−0.138567
$176$	−18.4192	−1.38840
$177$	5.99205	0.450390
$178$	−44.7983	−3.35778
$179$	12.4273	0.928863	0.464432	−	0.885609i	$-0.346259\pi$
$179$	12.4273	0.928863	0.464432	+	0.885609i	$0.346259\pi$
$180$	−21.2095	−1.58086
$181$	24.8628	1.84803	0.924017	−	0.382351i	$-0.124885\pi$
$181$	24.8628	1.84803	0.924017	+	0.382351i	$0.124885\pi$
$182$	7.76849	0.575839
$183$	23.0332	1.70266
$184$	32.7519	2.41450
$185$	2.97670	0.218851
$186$	26.3476	1.93190
$187$	−4.59899	−0.336312
$188$	−60.8305	−4.43652
$189$	−8.89680	−0.647147
$190$	39.6319	2.87520
$191$	7.44465	0.538676	0.269338	−	0.963046i	$-0.413195\pi$
$191$	7.44465	0.538676	0.269338	+	0.963046i	$0.413195\pi$
$192$	−63.9535	−4.61545
$193$	−16.3689	−1.17826	−0.589128	−	0.808040i	$-0.700529\pi$
$193$	−16.3689	−1.17826	−0.589128	+	0.808040i	$0.700529\pi$
$194$	−22.0928	−1.58617
$195$	4.77282	0.341789
$196$	12.2027	0.871623
$197$	−12.0292	−0.857044	−0.428522	−	0.903531i	$-0.640966\pi$
$197$	−12.0292	−0.857044	−0.428522	+	0.903531i	$0.640966\pi$
$198$	5.54379	0.393980
$199$	−8.12373	−0.575876	−0.287938	−	0.957649i	$-0.592970\pi$
$199$	−8.12373	−0.575876	−0.287938	+	0.957649i	$0.592970\pi$
$200$	−5.70049	−0.403085
$201$	11.8630	0.836752
$202$	−19.4200	−1.36638
$203$	16.5929	1.16460
$204$	−43.7366	−3.06217
$205$	11.8421	0.827086
$206$	−54.5921	−3.80361
$207$	−5.68725	−0.395291
$208$	13.9380	0.966426
$209$	−7.58188	−0.524450
$210$	42.3265	2.92080
$211$	25.7925	1.77563	0.887813	−	0.460204i	$-0.152224\pi$
$211$	25.7925	1.77563	0.887813	+	0.460204i	$0.152224\pi$
$212$	8.31459	0.571049
$213$	2.15430	0.147611
$214$	40.7039	2.78246
$215$	19.0433	1.29875
$216$	−27.6674	−1.88253
$217$	−13.6076	−0.923742
$218$	−43.3695	−2.93735
$219$	16.7153	1.12951
$220$	15.9858	1.07776
$221$	3.48010	0.234097
$222$	−7.39936	−0.496613
$223$	1.06724	0.0714674	0.0357337	−	0.999361i	$-0.488623\pi$
$223$	1.06724	0.0714674	0.0357337	+	0.999361i	$0.488623\pi$
$224$	66.1676	4.42101
$225$	0.989868	0.0659912
$226$	2.73131	0.181684
$227$	−23.0156	−1.52760	−0.763798	−	0.645455i	$-0.776668\pi$
$227$	−23.0156	−1.52760	−0.763798	+	0.645455i	$0.776668\pi$
$228$	−72.1039	−4.77520
$229$	2.63761	0.174298	0.0871492	−	0.996195i	$-0.472224\pi$
$229$	2.63761	0.174298	0.0871492	+	0.996195i	$0.472224\pi$
$230$	−22.4065	−1.47744
$231$	−8.09737	−0.532768
$232$	51.6010	3.38777
$233$	16.4544	1.07796	0.538981	−	0.842318i	$-0.318810\pi$
$233$	16.4544	1.07796	0.538981	+	0.842318i	$0.318810\pi$
$234$	−4.19504	−0.274239
$235$	26.3721	1.72032
$236$	−15.1867	−0.988570
$237$	−26.1857	−1.70095
$238$	30.8624	2.00051
$239$	−22.5202	−1.45671	−0.728356	−	0.685199i	$-0.759715\pi$
$239$	−22.5202	−1.45671	−0.728356	+	0.685199i	$0.759715\pi$
$240$	75.9409	4.90196
$241$	5.06501	0.326266	0.163133	−	0.986604i	$-0.447840\pi$
$241$	5.06501	0.326266	0.163133	+	0.986604i	$0.447840\pi$
$242$	25.8660	1.66273
$243$	15.4102	0.988563
$244$	−58.3771	−3.73721
$245$	−5.29029	−0.337984
$246$	−29.4366	−1.87681
$247$	5.73728	0.365055
$248$	−42.3170	−2.68713
$249$	3.42178	0.216847
$250$	−28.4266	−1.79786
$251$	0.702492	0.0443409	0.0221704	−	0.999754i	$-0.492942\pi$
$251$	0.702492	0.0443409	0.0221704	+	0.999754i	$0.492942\pi$
$252$	−27.2288	−1.71525
$253$	4.28654	0.269492
$254$	−52.2581	−3.27896
$255$	18.9613	1.18740
$256$	43.1483	2.69677
$257$	−8.68978	−0.542054	−0.271027	−	0.962572i	$-0.587363\pi$
$257$	−8.68978	−0.542054	−0.271027	+	0.962572i	$0.587363\pi$
$258$	−47.3372	−2.94709
$259$	3.82149	0.237456
$260$	−12.0966	−0.750199
$261$	−8.96031	−0.554629
$262$	−2.08419	−0.128762
$263$	−17.5100	−1.07972	−0.539858	−	0.841756i	$-0.681522\pi$
$263$	−17.5100	−1.07972	−0.539858	+	0.841756i	$0.681522\pi$
$264$	−25.1813	−1.54980
$265$	−3.60466	−0.221432
$266$	50.8795	3.11963
$267$	−35.3345	−2.16243
$268$	−30.0665	−1.83660
$269$	−17.9562	−1.09481	−0.547406	−	0.836867i	$-0.684385\pi$
$269$	−17.9562	−1.09481	−0.547406	+	0.836867i	$0.684385\pi$
$270$	18.9281	1.15192
$271$	−1.01763	−0.0618164	−0.0309082	−	0.999522i	$-0.509840\pi$
$271$	−1.01763	−0.0618164	−0.0309082	+	0.999522i	$0.509840\pi$
$272$	55.3723	3.35744
$273$	6.12736	0.370845
$274$	−7.22159	−0.436272
$275$	−0.746073	−0.0449899
$276$	40.7651	2.45377
$277$	27.5483	1.65521	0.827607	−	0.561307i	$-0.189701\pi$
$277$	27.5483	1.65521	0.827607	+	0.561307i	$0.189701\pi$
$278$	−34.7578	−2.08464
$279$	7.34819	0.439924
$280$	−67.9807	−4.06262
$281$	14.4506	0.862048	0.431024	−	0.902341i	$-0.358153\pi$
$281$	14.4506	0.862048	0.431024	+	0.902341i	$0.358153\pi$
$282$	−65.5546	−3.90372
$283$	13.2348	0.786730	0.393365	−	0.919382i	$-0.371311\pi$
$283$	13.2348	0.786730	0.393365	+	0.919382i	$0.371311\pi$
$284$	−5.46003	−0.323993
$285$	31.2595	1.85165
$286$	3.16185	0.186964
$287$	15.2029	0.897398
$288$	−35.7310	−2.10547
$289$	−3.17439	−0.186729
$290$	−35.3017	−2.07299
$291$	−17.4256	−1.02151
$292$	−42.3645	−2.47920
$293$	14.9887	0.875648	0.437824	−	0.899061i	$-0.355749\pi$
$293$	14.9887	0.875648	0.437824	+	0.899061i	$0.355749\pi$
$294$	13.1504	0.766947
$295$	6.58395	0.383332
$296$	11.8841	0.690751
$297$	−3.62108	−0.210116
$298$	−25.6360	−1.48505
$299$	−3.24366	−0.187586
$300$	−7.09518	−0.409640
$301$	24.4479	1.40915
$302$	52.3748	3.01383
$303$	−15.3174	−0.879962
$304$	91.2865	5.23564
$305$	25.3084	1.44916
$306$	−16.6659	−0.952726
$307$	21.4218	1.22260	0.611302	−	0.791397i	$-0.290646\pi$
$307$	21.4218	1.22260	0.611302	+	0.791397i	$0.290646\pi$
$308$	20.5226	1.16938
$309$	−43.0593	−2.44956
$310$	28.9503	1.64426
$311$	20.8186	1.18051	0.590257	−	0.807215i	$-0.299026\pi$
$311$	20.8186	1.18051	0.590257	+	0.807215i	$0.299026\pi$
$312$	19.0550	1.07877
$313$	2.42545	0.137094	0.0685472	−	0.997648i	$-0.478164\pi$
$313$	2.42545	0.137094	0.0685472	+	0.997648i	$0.478164\pi$
$314$	34.0247	1.92013
$315$	11.8046	0.665113
$316$	66.3671	3.73344
$317$	−12.9570	−0.727736	−0.363868	−	0.931451i	$-0.618544\pi$
$317$	−12.9570	−0.727736	−0.363868	+	0.931451i	$0.618544\pi$
$318$	8.96031	0.502469
$319$	6.75348	0.378122
$320$	−70.2709	−3.92826
$321$	32.1050	1.79193
$322$	−28.7656	−1.60304
$323$	22.7928	1.26823
$324$	−61.3168	−3.40649
$325$	0.564561	0.0313162
$326$	−13.9952	−0.775124
$327$	−34.2075	−1.89168
$328$	47.2782	2.61050
$329$	33.8565	1.86657
$330$	17.2273	0.948329
$331$	−12.0179	−0.660562	−0.330281	−	0.943883i	$-0.607144\pi$
$331$	−12.0179	−0.660562	−0.330281	+	0.943883i	$0.607144\pi$
$332$	−8.67243	−0.475961
$333$	−2.06363	−0.113086
$334$	−19.3113	−1.05666
$335$	13.0348	0.712169
$336$	97.4931	5.31869
$337$	−15.0255	−0.818492	−0.409246	−	0.912424i	$-0.634208\pi$
$337$	−15.0255	−0.818492	−0.409246	+	0.912424i	$0.634208\pi$
$338$	33.1144	1.80118
$339$	2.15430	0.117006
$340$	−48.0569	−2.60625
$341$	−5.53840	−0.299921
$342$	−27.4753	−1.48570
$343$	14.4806	0.781880
$344$	76.0284	4.09918
$345$	−17.6730	−0.951484
$346$	−46.5534	−2.50273
$347$	−25.1866	−1.35209	−0.676043	−	0.736862i	$-0.736307\pi$
$347$	−25.1866	−1.35209	−0.676043	+	0.736862i	$0.736307\pi$
$348$	64.2258	3.44286
$349$	−24.6754	−1.32084	−0.660422	−	0.750894i	$-0.729623\pi$
$349$	−24.6754	−1.32084	−0.660422	+	0.750894i	$0.729623\pi$
$350$	5.00666	0.267617
$351$	2.74011	0.146256
$352$	26.9308	1.43542
$353$	26.1979	1.39438	0.697188	−	0.716889i	$-0.254434\pi$
$353$	26.1979	1.39438	0.697188	+	0.716889i	$0.254434\pi$
$354$	−16.3661	−0.869850
$355$	2.36711	0.125633
$356$	89.5544	4.74637
$357$	24.3425	1.28834
$358$	−33.9429	−1.79394
$359$	17.8907	0.944236	0.472118	−	0.881535i	$-0.343490\pi$
$359$	17.8907	0.944236	0.472118	+	0.881535i	$0.343490\pi$
$360$	36.7101	1.93479
$361$	18.5762	0.977694
$362$	−67.9078	−3.56916
$363$	20.4016	1.07081
$364$	−15.5297	−0.813975
$365$	18.3664	0.961343
$366$	−62.9107	−3.28840
$367$	20.3121	1.06028	0.530142	−	0.847909i	$-0.322138\pi$
$367$	20.3121	1.06028	0.530142	+	0.847909i	$0.322138\pi$
$368$	−51.6103	−2.69037
$369$	−8.20967	−0.427379
$370$	−8.13027	−0.422673
$371$	−4.62767	−0.240257
$372$	−52.6704	−2.73083
$373$	−22.9192	−1.18671	−0.593356	−	0.804940i	$-0.702197\pi$
$373$	−22.9192	−1.18671	−0.593356	+	0.804940i	$0.702197\pi$
$374$	12.5613	0.649527
$375$	−22.4214	−1.15783
$376$	105.287	5.42979
$377$	−5.11042	−0.263200
$378$	24.2999	1.24985
$379$	4.09003	0.210091	0.105045	−	0.994467i	$-0.466501\pi$
$379$	4.09003	0.210091	0.105045	+	0.994467i	$0.466501\pi$
$380$	−79.2264	−4.06423
$381$	−41.2183	−2.11168
$382$	−20.3336	−1.04036
$383$	9.79989	0.500751	0.250376	−	0.968149i	$-0.419446\pi$
$383$	9.79989	0.500751	0.250376	+	0.968149i	$0.419446\pi$
$384$	80.8629	4.12652
$385$	−8.89724	−0.453445
$386$	44.7084	2.27560
$387$	−13.2020	−0.671098
$388$	44.1647	2.24212
$389$	−31.9861	−1.62176	−0.810881	−	0.585211i	$-0.801012\pi$
$389$	−31.9861	−1.62176	−0.810881	+	0.585211i	$0.801012\pi$
$390$	−13.0360	−0.660105
$391$	−12.8863	−0.651688
$392$	−21.1209	−1.06677
$393$	−1.64390	−0.0829236
$394$	32.8554	1.65523
$395$	−28.7724	−1.44770
$396$	−11.0824	−0.556909
$397$	2.08595	0.104691	0.0523453	−	0.998629i	$-0.483330\pi$
$397$	2.08595	0.104691	0.0523453	+	0.998629i	$0.483330\pi$
$398$	22.1884	1.11220
$399$	40.1310	2.00906
$400$	8.98279	0.449140
$401$	−4.66681	−0.233049	−0.116525	−	0.993188i	$-0.537175\pi$
$401$	−4.66681	−0.233049	−0.116525	+	0.993188i	$0.537175\pi$
$402$	−32.4015	−1.61604
$403$	4.19096	0.208767
$404$	38.8216	1.93145
$405$	26.5829	1.32091
$406$	−45.3204	−2.24921
$407$	1.55538	0.0770974
$408$	75.7007	3.74774
$409$	33.5809	1.66047	0.830234	−	0.557414i	$-0.188207\pi$
$409$	33.5809	1.66047	0.830234	+	0.557414i	$0.188207\pi$
$410$	−32.3443	−1.59737
$411$	−5.69600	−0.280963
$412$	109.133	5.37658
$413$	8.45249	0.415920
$414$	15.5336	0.763435
$415$	3.75979	0.184561
$416$	−20.3788	−0.999153
$417$	−27.4151	−1.34252
$418$	20.7084	1.01288
$419$	37.4391	1.82902	0.914509	−	0.404565i	$-0.132577\pi$
$419$	37.4391	1.82902	0.914509	+	0.404565i	$0.132577\pi$
$420$	−84.6130	−4.12869
$421$	16.7445	0.816075	0.408038	−	0.912965i	$-0.366213\pi$
$421$	16.7445	0.816075	0.408038	+	0.912965i	$0.366213\pi$
$422$	−70.4471	−3.42931
$423$	−18.2828	−0.888939
$424$	−14.3912	−0.698898
$425$	2.24287	0.108795
$426$	−5.88407	−0.285084
$427$	32.4910	1.57235
$428$	−81.3694	−3.93314
$429$	2.49389	0.120406
$430$	−52.0132	−2.50830
$431$	−18.3487	−0.883825	−0.441912	−	0.897058i	$-0.645700\pi$
$431$	−18.3487	−0.883825	−0.441912	+	0.897058i	$0.645700\pi$
$432$	43.5981	2.09762
$433$	3.11096	0.149503	0.0747516	−	0.997202i	$-0.476184\pi$
$433$	3.11096	0.149503	0.0747516	+	0.997202i	$0.476184\pi$
$434$	37.1664	1.78405
$435$	−27.8440	−1.33502
$436$	86.6981	4.15209
$437$	−21.2443	−1.01625
$438$	−45.6546	−2.18146
$439$	−9.54411	−0.455515	−0.227758	−	0.973718i	$-0.573139\pi$
$439$	−9.54411	−0.455515	−0.227758	+	0.973718i	$0.573139\pi$
$440$	−27.6687	−1.31906
$441$	3.66756	0.174646
$442$	−9.50523	−0.452117
$443$	31.0567	1.47555	0.737773	−	0.675048i	$-0.235877\pi$
$443$	31.0567	1.47555	0.737773	+	0.675048i	$0.235877\pi$
$444$	14.7917	0.701985
$445$	−38.8248	−1.84047
$446$	−2.91495	−0.138027
$447$	−20.2203	−0.956386
$448$	−90.2139	−4.26221
$449$	−23.3840	−1.10356	−0.551781	−	0.833989i	$-0.686051\pi$
$449$	−23.3840	−1.10356	−0.551781	+	0.833989i	$0.686051\pi$
$450$	−2.70363	−0.127450
$451$	6.18772	0.291368
$452$	−5.46003	−0.256818
$453$	41.3104	1.94093
$454$	62.8626	2.95029
$455$	6.73262	0.315630
$456$	124.800	5.84429
$457$	−3.43198	−0.160541	−0.0802705	−	0.996773i	$-0.525578\pi$
$457$	−3.43198	−0.160541	−0.0802705	+	0.996773i	$0.525578\pi$
$458$	−7.20413	−0.336627
$459$	10.8858	0.508105
$460$	44.7919	2.08843
$461$	5.27951	0.245891	0.122946	−	0.992413i	$-0.460766\pi$
$461$	5.27951	0.245891	0.122946	+	0.992413i	$0.460766\pi$
$462$	22.1164	1.02895
$463$	−22.0355	−1.02408	−0.512039	−	0.858962i	$-0.671110\pi$
$463$	−22.0355	−1.02408	−0.512039	+	0.858962i	$0.671110\pi$
$464$	−81.3125	−3.77484
$465$	22.8344	1.05892
$466$	−44.9419	−2.08189
$467$	0.867223	0.0401303	0.0200651	−	0.999799i	$-0.493613\pi$
$467$	0.867223	0.0401303	0.0200651	+	0.999799i	$0.493613\pi$
$468$	8.38613	0.387649
$469$	16.7342	0.772712
$470$	−72.0302	−3.32250
$471$	26.8368	1.23658
$472$	26.2857	1.20990
$473$	9.95052	0.457525
$474$	71.5213	3.28508
$475$	3.69758	0.169657
$476$	−61.6956	−2.82781
$477$	2.49897	0.114420
$478$	61.5096	2.81338
$479$	16.1246	0.736751	0.368376	−	0.929677i	$-0.379914\pi$
$479$	16.1246	0.736751	0.368376	+	0.929677i	$0.379914\pi$
$480$	−111.034	−5.06796
$481$	−1.17697	−0.0536654
$482$	−13.8341	−0.630125
$483$	−22.6887	−1.03237
$484$	−51.7075	−2.35034
$485$	−19.1469	−0.869415
$486$	−42.0899	−1.90924
$487$	−0.454083	−0.0205765	−0.0102882	−	0.999947i	$-0.503275\pi$
$487$	−0.454083	−0.0205765	−0.0102882	+	0.999947i	$0.503275\pi$
$488$	101.041	4.57391
$489$	−11.0387	−0.499186
$490$	14.4494	0.652757
$491$	25.4965	1.15064	0.575320	−	0.817928i	$-0.304877\pi$
$491$	25.4965	1.15064	0.575320	+	0.817928i	$0.304877\pi$
$492$	58.8454	2.65295
$493$	−20.3025	−0.914378
$494$	−15.6703	−0.705039
$495$	4.80457	0.215949
$496$	66.6829	2.99415
$497$	3.03890	0.136313
$498$	−9.34594	−0.418802
$499$	22.7943	1.02041	0.510206	−	0.860052i	$-0.329569\pi$
$499$	22.7943	1.02041	0.510206	+	0.860052i	$0.329569\pi$
$500$	56.8264	2.54135
$501$	−15.2317	−0.680500
$502$	−1.91872	−0.0856367
$503$	11.6202	0.518119	0.259060	−	0.965861i	$-0.416587\pi$
$503$	11.6202	0.518119	0.259060	+	0.965861i	$0.416587\pi$
$504$	47.1285	2.09927
$505$	−16.8305	−0.748946
$506$	−11.7078	−0.520477
$507$	26.1188	1.15998
$508$	104.467	4.63496
$509$	−17.7606	−0.787224	−0.393612	−	0.919277i	$-0.628775\pi$
$509$	−17.7606	−0.787224	−0.393612	+	0.919277i	$0.628775\pi$
$510$	−51.7890	−2.29326
$511$	23.5789	1.04307
$512$	−42.7801	−1.89063
$513$	17.9463	0.792346
$514$	23.7345	1.04688
$515$	−47.3127	−2.08485
$516$	94.6297	4.16584
$517$	13.7799	0.606040
$518$	−10.4377	−0.458605
$519$	−36.7188	−1.61178
$520$	20.9372	0.918157
$521$	19.5249	0.855401	0.427700	−	0.903921i	$-0.359324\pi$
$521$	19.5249	0.855401	0.427700	+	0.903921i	$0.359324\pi$
$522$	24.4734	1.07117
$523$	−39.6157	−1.73228	−0.866138	−	0.499806i	$-0.833405\pi$
$523$	−39.6157	−1.73228	−0.866138	+	0.499806i	$0.833405\pi$
$524$	4.16642	0.182011
$525$	3.94898	0.172347
$526$	47.8253	2.08528
$527$	16.6497	0.725272
$528$	39.6806	1.72688
$529$	−10.9892	−0.477791
$530$	9.84542	0.427658
$531$	−4.56441	−0.198078
$532$	−101.711	−4.40973
$533$	−4.68230	−0.202813
$534$	96.5093	4.17636
$535$	35.2764	1.52513
$536$	52.0401	2.24779
$537$	−26.7723	−1.15531
$538$	49.0440	2.11444
$539$	−2.76428	−0.119066
$540$	−37.8382	−1.62830
$541$	−14.9299	−0.641887	−0.320943	−	0.947098i	$-0.604000\pi$
$541$	−14.9299	−0.641887	−0.320943	+	0.947098i	$0.604000\pi$
$542$	2.77945	0.119388
$543$	−53.5620	−2.29856
$544$	−80.9601	−3.47114
$545$	−37.5865	−1.61003
$546$	−16.7357	−0.716222
$547$	27.1105	1.15916	0.579581	−	0.814915i	$-0.303216\pi$
$547$	27.1105	1.15916	0.579581	+	0.814915i	$0.303216\pi$
$548$	14.4364	0.616691
$549$	−17.5454	−0.748819
$550$	2.03775	0.0868902
$551$	−33.4706	−1.42590
$552$	−70.5576	−3.00313
$553$	−36.9381	−1.57077
$554$	−75.2428	−3.19676
$555$	−6.41271	−0.272205
$556$	69.4828	2.94673
$557$	−21.9844	−0.931507	−0.465753	−	0.884915i	$-0.654217\pi$
$557$	−21.9844	−0.931507	−0.465753	+	0.884915i	$0.654217\pi$
$558$	−20.0702	−0.849637
$559$	−7.52965	−0.318470
$560$	107.124	4.52680
$561$	9.90763	0.418300
$562$	−39.4689	−1.66489
$563$	13.6587	0.575646	0.287823	−	0.957684i	$-0.407069\pi$
$563$	13.6587	0.575646	0.287823	+	0.957684i	$0.407069\pi$
$564$	131.047	5.51809
$565$	2.36711	0.0995850
$566$	−36.1484	−1.51943
$567$	34.1272	1.43321
$568$	9.45041	0.396531
$569$	0.482899	0.0202442	0.0101221	−	0.999949i	$-0.496778\pi$
$569$	0.482899	0.0202442	0.0101221	+	0.999949i	$0.496778\pi$
$570$	−85.3792	−3.57614
$571$	−21.6107	−0.904382	−0.452191	−	0.891921i	$-0.649357\pi$
$571$	−21.6107	−0.904382	−0.452191	+	0.891921i	$0.649357\pi$
$572$	−6.32071	−0.264282
$573$	−16.0380	−0.669999
$574$	−41.5238	−1.73317
$575$	−2.09048	−0.0871792
$576$	48.7162	2.02984
$577$	−22.6379	−0.942429	−0.471215	−	0.882019i	$-0.656184\pi$
$577$	−22.6379	−0.942429	−0.471215	+	0.882019i	$0.656184\pi$
$578$	8.67023	0.360634
$579$	35.2635	1.46550
$580$	70.5701	2.93026
$581$	4.82683	0.200251
$582$	47.5946	1.97286
$583$	−1.88350	−0.0780067
$584$	73.3259	3.03425
$585$	−3.63567	−0.150316
$586$	−40.9387	−1.69116
$587$	−19.7275	−0.814239	−0.407120	−	0.913375i	$-0.633467\pi$
$587$	−19.7275	−0.814239	−0.407120	+	0.913375i	$0.633467\pi$
$588$	−26.2884	−1.08411
$589$	27.4486	1.13100
$590$	−17.9828	−0.740339
$591$	25.9145	1.06598
$592$	−18.7269	−0.769673
$593$	−7.00780	−0.287776	−0.143888	−	0.989594i	$-0.545960\pi$
$593$	−7.00780	−0.287776	−0.143888	+	0.989594i	$0.545960\pi$
$594$	9.89028	0.405803
$595$	26.7471	1.09652
$596$	51.2478	2.09919
$597$	17.5010	0.716268
$598$	8.85944	0.362289
$599$	4.92010	0.201030	0.100515	−	0.994936i	$-0.467951\pi$
$599$	4.92010	0.201030	0.100515	+	0.994936i	$0.467951\pi$
$600$	12.2806	0.501353
$601$	−25.5714	−1.04308	−0.521539	−	0.853227i	$-0.674642\pi$
$601$	−25.5714	−1.04308	−0.521539	+	0.853227i	$0.674642\pi$
$602$	−66.7747	−2.72153
$603$	−9.03657	−0.367998
$604$	−104.700	−4.26019
$605$	22.4169	0.911378
$606$	41.8366	1.69949
$607$	36.0934	1.46499	0.732494	−	0.680774i	$-0.238356\pi$
$607$	36.0934	1.46499	0.732494	+	0.680774i	$0.238356\pi$
$608$	−133.470	−5.41294
$609$	−35.7463	−1.44851
$610$	−69.1251	−2.79879
$611$	−10.4274	−0.421847
$612$	33.3161	1.34672
$613$	−24.1949	−0.977225	−0.488612	−	0.872501i	$-0.662497\pi$
$613$	−24.1949	−0.977225	−0.488612	+	0.872501i	$0.662497\pi$
$614$	−58.5094	−2.36125
$615$	−25.5114	−1.02872
$616$	−35.5212	−1.43119
$617$	−28.8112	−1.15990	−0.579948	−	0.814654i	$-0.696927\pi$
$617$	−28.8112	−1.15990	−0.579948	+	0.814654i	$0.696927\pi$
$618$	117.608	4.73089
$619$	−16.4666	−0.661850	−0.330925	−	0.943657i	$-0.607361\pi$
$619$	−16.4666	−0.661850	−0.330925	+	0.943657i	$0.607361\pi$
$620$	−57.8732	−2.32424
$621$	−10.1462	−0.407153
$622$	−56.8620	−2.27996
$623$	−49.8434	−1.99693
$624$	−30.0267	−1.20203
$625$	−27.6521	−1.10609
$626$	−6.62464	−0.264774
$627$	16.3337	0.652304
$628$	−68.0173	−2.71419
$629$	−4.67583	−0.186438
$630$	−32.2419	−1.28455
$631$	−20.6199	−0.820865	−0.410433	−	0.911891i	$-0.634622\pi$
$631$	−20.6199	−0.820865	−0.410433	+	0.911891i	$0.634622\pi$
$632$	−114.870	−4.56930
$633$	−55.5648	−2.20850
$634$	35.3895	1.40549
$635$	−45.2899	−1.79727
$636$	−17.9122	−0.710264
$637$	2.09176	0.0828784
$638$	−18.4458	−0.730277
$639$	−1.64103	−0.0649181
$640$	88.8506	3.51213
$641$	−25.7511	−1.01711	−0.508553	−	0.861031i	$-0.669819\pi$
$641$	−25.7511	−1.01711	−0.508553	+	0.861031i	$0.669819\pi$
$642$	−87.6887	−3.46080
$643$	13.8453	0.546006	0.273003	−	0.962013i	$-0.411983\pi$
$643$	13.8453	0.546006	0.273003	+	0.962013i	$0.411983\pi$
$644$	57.5040	2.26597
$645$	−41.0252	−1.61536
$646$	−62.2542	−2.44936
$647$	−28.6234	−1.12530	−0.562651	−	0.826695i	$-0.690218\pi$
$647$	−28.6234	−1.12530	−0.562651	+	0.826695i	$0.690218\pi$
$648$	106.129	4.16915
$649$	3.44024	0.135041
$650$	−1.54199	−0.0604818
$651$	29.3149	1.14894
$652$	27.9773	1.09567
$653$	20.6703	0.808892	0.404446	−	0.914562i	$-0.367464\pi$
$653$	20.6703	0.808892	0.404446	+	0.914562i	$0.367464\pi$
$654$	93.4312	3.65345
$655$	−1.80628	−0.0705773
$656$	−74.5007	−2.90876
$657$	−12.7328	−0.496753
$658$	−92.4725	−3.60495
$659$	−50.1946	−1.95530	−0.977652	−	0.210230i	$-0.932579\pi$
$659$	−50.1946	−1.95530	−0.977652	+	0.210230i	$0.932579\pi$
$660$	−34.4383	−1.34051
$661$	41.6228	1.61894	0.809469	−	0.587163i	$-0.199755\pi$
$661$	41.6228	1.61894	0.809469	+	0.587163i	$0.199755\pi$
$662$	32.8245	1.27576
$663$	−7.49720	−0.291167
$664$	15.0105	0.582522
$665$	44.0952	1.70994
$666$	5.63642	0.218407
$667$	18.9231	0.732707
$668$	38.6043	1.49364
$669$	−2.29915	−0.0888903
$670$	−35.6021	−1.37543
$671$	13.2241	0.510512
$672$	−142.545	−5.49880
$673$	31.1387	1.20031	0.600155	−	0.799884i	$-0.295106\pi$
$673$	31.1387	1.20031	0.600155	+	0.799884i	$0.295106\pi$
$674$	41.0393	1.58077
$675$	1.76595	0.0679715
$676$	−66.1975	−2.54606
$677$	−3.84088	−0.147617	−0.0738085	−	0.997272i	$-0.523515\pi$
$677$	−3.84088	−0.147617	−0.0738085	+	0.997272i	$0.523515\pi$
$678$	−5.88407	−0.225976
$679$	−24.5808	−0.943325
$680$	83.1785	3.18975
$681$	49.5825	1.90001
$682$	15.1271	0.579246
$683$	40.8975	1.56490	0.782450	−	0.622714i	$-0.213970\pi$
$683$	40.8975	1.56490	0.782450	+	0.622714i	$0.213970\pi$
$684$	54.9247	2.10010
$685$	−6.25865	−0.239131
$686$	−39.5510	−1.51006
$687$	−5.68222	−0.216790
$688$	−119.805	−4.56753
$689$	1.42526	0.0542983
$690$	48.2705	1.83763
$691$	18.0490	0.686615	0.343307	−	0.939223i	$-0.388453\pi$
$691$	18.0490	0.686615	0.343307	+	0.939223i	$0.388453\pi$
$692$	93.0629	3.53772
$693$	6.16813	0.234308
$694$	68.7922	2.61132
$695$	−30.1231	−1.14264
$696$	−111.164	−4.21367
$697$	−18.6017	−0.704588
$698$	67.3961	2.55098
$699$	−35.4477	−1.34076
$700$	−10.0086	−0.378289
$701$	3.32529	0.125595	0.0627973	−	0.998026i	$-0.479998\pi$
$701$	3.32529	0.125595	0.0627973	+	0.998026i	$0.479998\pi$
$702$	−7.48407	−0.282468
$703$	−7.70856	−0.290734
$704$	−36.7179	−1.38386
$705$	−56.8134	−2.13972
$706$	−71.5546	−2.69299
$707$	−21.6070	−0.812616
$708$	32.7168	1.22957
$709$	−40.5549	−1.52307	−0.761535	−	0.648123i	$-0.775554\pi$
$709$	−40.5549	−1.52307	−0.761535	+	0.648123i	$0.775554\pi$
$710$	−6.46530	−0.242638
$711$	19.9468	0.748064
$712$	−155.004	−5.80901
$713$	−15.5185	−0.581173
$714$	−66.4869	−2.48821
$715$	2.74024	0.102479
$716$	67.8537	2.53581
$717$	48.5154	1.81184
$718$	−48.8650	−1.82363
$719$	40.5804	1.51339	0.756696	−	0.653767i	$-0.226812\pi$
$719$	40.5804	1.51339	0.756696	+	0.653767i	$0.226812\pi$
$720$	−57.8475	−2.15585
$721$	−60.7402	−2.26208
$722$	−50.7372	−1.88824
$723$	−10.9116	−0.405805
$724$	135.752	5.04517
$725$	−3.29358	−0.122320
$726$	−55.7231	−2.06808
$727$	25.0655	0.929629	0.464814	−	0.885408i	$-0.346121\pi$
$727$	25.0655	0.929629	0.464814	+	0.885408i	$0.346121\pi$
$728$	26.8793	0.996211
$729$	0.492142	0.0182275
$730$	−50.1644	−1.85667
$731$	−29.9135	−1.10639
$732$	125.762	4.64830
$733$	−2.20054	−0.0812789	−0.0406395	−	0.999174i	$-0.512940\pi$
$733$	−2.20054	−0.0812789	−0.0406395	+	0.999174i	$0.512940\pi$
$734$	−55.4787	−2.04775
$735$	11.3969	0.420381
$736$	75.4597	2.78148
$737$	6.81096	0.250885
$738$	22.4231	0.825407
$739$	−2.52192	−0.0927702	−0.0463851	−	0.998924i	$-0.514770\pi$
$739$	−2.52192	−0.0927702	−0.0463851	+	0.998924i	$0.514770\pi$
$740$	16.2529	0.597467
$741$	−12.3599	−0.454051
$742$	12.6396	0.464014
$743$	−8.75925	−0.321346	−0.160673	−	0.987008i	$-0.551366\pi$
$743$	−8.75925	−0.321346	−0.160673	+	0.987008i	$0.551366\pi$
$744$	91.1637	3.34222
$745$	−22.2176	−0.813992
$746$	62.5994	2.29193
$747$	−2.60652	−0.0953677
$748$	−25.1107	−0.918137
$749$	45.2879	1.65478
$750$	61.2396	2.23615
$751$	2.34396	0.0855324	0.0427662	−	0.999085i	$-0.486383\pi$
$751$	2.34396	0.0855324	0.0427662	+	0.999085i	$0.486383\pi$
$752$	−165.911	−6.05017
$753$	−1.51338	−0.0551507
$754$	13.9581	0.508325
$755$	45.3910	1.65195
$756$	−48.5768	−1.76672
$757$	−28.3654	−1.03096	−0.515478	−	0.856903i	$-0.672386\pi$
$757$	−28.3654	−1.03096	−0.515478	+	0.856903i	$0.672386\pi$
$758$	−11.1711	−0.405754
$759$	−9.23450	−0.335191
$760$	137.128	4.97414
$761$	−36.4088	−1.31982	−0.659909	−	0.751346i	$-0.729405\pi$
$761$	−36.4088	−1.31982	−0.659909	+	0.751346i	$0.729405\pi$
$762$	112.580	4.07834
$763$	−48.2537	−1.74690
$764$	40.6481	1.47060
$765$	−14.4436	−0.522211
$766$	−26.7665	−0.967113
$767$	−2.60326	−0.0939984
$768$	−92.9545	−3.35421
$769$	20.1093	0.725159	0.362579	−	0.931953i	$-0.381896\pi$
$769$	20.1093	0.725159	0.362579	+	0.931953i	$0.381896\pi$
$770$	24.3011	0.875750
$771$	18.7204	0.674200
$772$	−89.3745	−3.21666
$773$	−16.5548	−0.595435	−0.297717	−	0.954654i	$-0.596225\pi$
$773$	−16.5548	−0.595435	−0.297717	+	0.954654i	$0.596225\pi$
$774$	36.0588	1.29611
$775$	2.70100	0.0970229
$776$	−76.4418	−2.74410
$777$	−8.23266	−0.295345
$778$	87.3639	3.13215
$779$	−30.6666	−1.09875
$780$	26.0598	0.933089
$781$	1.23686	0.0442583
$782$	35.1964	1.25862
$783$	−15.9854	−0.571273
$784$	33.2822	1.18865
$785$	29.4878	1.05246
$786$	4.48999	0.160152
$787$	−13.9026	−0.495574	−0.247787	−	0.968815i	$-0.579703\pi$
$787$	−13.9026	−0.495574	−0.247787	+	0.968815i	$0.579703\pi$
$788$	−65.6798	−2.33974
$789$	37.7220	1.34294
$790$	78.5862	2.79597
$791$	3.03890	0.108051
$792$	19.1817	0.681593
$793$	−10.0068	−0.355353
$794$	−5.69736	−0.202192
$795$	7.76553	0.275415
$796$	−44.3558	−1.57215
$797$	−21.7510	−0.770460	−0.385230	−	0.922820i	$-0.625878\pi$
$797$	−21.7510	−0.770460	−0.385230	+	0.922820i	$0.625878\pi$
$798$	−109.610	−3.88015
$799$	−41.4255	−1.46553
$800$	−13.1338	−0.464349
$801$	26.9158	0.951024
$802$	12.7465	0.450094
$803$	9.59682	0.338664
$804$	64.7724	2.28435
$805$	−24.9299	−0.878663
$806$	−11.4468	−0.403197
$807$	38.6832	1.36171
$808$	−67.1938	−2.36387
$809$	22.9969	0.808529	0.404264	−	0.914642i	$-0.367528\pi$
$809$	22.9969	0.808529	0.404264	+	0.914642i	$0.367528\pi$
$810$	−72.6060	−2.55111
$811$	−1.16332	−0.0408496	−0.0204248	−	0.999791i	$-0.506502\pi$
$811$	−1.16332	−0.0408496	−0.0204248	+	0.999791i	$0.506502\pi$
$812$	90.5981	3.17937
$813$	2.19228	0.0768866
$814$	−4.24823	−0.148900
$815$	−12.1291	−0.424863
$816$	−119.289	−4.17594
$817$	−49.3153	−1.72532
$818$	−91.7197	−3.20691
$819$	−4.66748	−0.163095
$820$	64.6581	2.25796
$821$	48.8168	1.70372	0.851859	−	0.523771i	$-0.175475\pi$
$821$	48.8168	1.70372	0.851859	+	0.523771i	$0.175475\pi$
$822$	15.5575	0.542631
$823$	13.0705	0.455609	0.227805	−	0.973707i	$-0.426845\pi$
$823$	13.0705	0.455609	0.227805	+	0.973707i	$0.426845\pi$
$824$	−188.891	−6.58032
$825$	1.60727	0.0559579
$826$	−23.0863	−0.803277
$827$	46.6586	1.62248	0.811240	−	0.584713i	$-0.198793\pi$
$827$	46.6586	1.62248	0.811240	+	0.584713i	$0.198793\pi$
$828$	−31.0526	−1.07915
$829$	29.9062	1.03869	0.519343	−	0.854566i	$-0.326177\pi$
$829$	29.9062	1.03869	0.519343	+	0.854566i	$0.326177\pi$
$830$	−10.2691	−0.356447
$831$	−59.3474	−2.05874
$832$	27.7848	0.963264
$833$	8.31005	0.287926
$834$	74.8789	2.59285
$835$	−16.7362	−0.579182
$836$	−41.3973	−1.43176
$837$	13.1094	0.453126
$838$	−102.258	−3.53243
$839$	18.2890	0.631405	0.315702	−	0.948858i	$-0.397760\pi$
$839$	18.2890	0.631405	0.315702	+	0.948858i	$0.397760\pi$
$840$	146.451	5.05304
$841$	0.813577	0.0280544
$842$	−45.7343	−1.57611
$843$	−31.1309	−1.07220
$844$	140.828	4.84749
$845$	28.6988	0.987270
$846$	49.9358	1.71683
$847$	28.7789	0.988856
$848$	22.6775	0.778750
$849$	−28.5119	−0.978526
$850$	−6.12595	−0.210118
$851$	4.35815	0.149396
$852$	11.7626	0.402979
$853$	19.7229	0.675298	0.337649	−	0.941272i	$-0.390368\pi$
$853$	19.7229	0.675298	0.337649	+	0.941272i	$0.390368\pi$
$854$	−88.7430	−3.03672
$855$	−23.8117	−0.814343
$856$	140.837	4.81371
$857$	10.0471	0.343203	0.171602	−	0.985166i	$-0.445106\pi$
$857$	10.0471	0.343203	0.171602	+	0.985166i	$0.445106\pi$
$858$	−6.81158	−0.232544
$859$	20.1108	0.686173	0.343086	−	0.939304i	$-0.388528\pi$
$859$	20.1108	0.686173	0.343086	+	0.939304i	$0.388528\pi$
$860$	103.977	3.54560
$861$	−32.7517	−1.11617
$862$	50.1159	1.70695
$863$	−6.02748	−0.205178	−0.102589	−	0.994724i	$-0.532713\pi$
$863$	−6.02748	−0.205178	−0.102589	+	0.994724i	$0.532713\pi$
$864$	−63.7450	−2.16865
$865$	−40.3459	−1.37180
$866$	−8.49699	−0.288739
$867$	6.83860	0.232251
$868$	−74.2978	−2.52183
$869$	−15.0341	−0.509998
$870$	76.0506	2.57836
$871$	−5.15392	−0.174634
$872$	−150.060	−5.08167
$873$	13.2738	0.449251
$874$	58.0247	1.96271
$875$	−31.6280	−1.06922
$876$	91.2661	3.08359
$877$	34.2354	1.15605	0.578023	−	0.816020i	$-0.303824\pi$
$877$	34.2354	1.15605	0.578023	+	0.816020i	$0.303824\pi$
$878$	26.0679	0.879748
$879$	−32.2902	−1.08912
$880$	43.6002	1.46976
$881$	15.1195	0.509389	0.254695	−	0.967022i	$-0.418025\pi$
$881$	15.1195	0.509389	0.254695	+	0.967022i	$0.418025\pi$
$882$	−10.0172	−0.337298
$883$	31.2169	1.05053	0.525265	−	0.850938i	$-0.323966\pi$
$883$	31.2169	1.05053	0.525265	+	0.850938i	$0.323966\pi$
$884$	19.0015	0.639089
$885$	−14.1838	−0.476784
$886$	−84.8253	−2.84976
$887$	4.70125	0.157852	0.0789262	−	0.996880i	$-0.474851\pi$
$887$	4.70125	0.157852	0.0789262	+	0.996880i	$0.474851\pi$
$888$	−25.6020	−0.859148
$889$	−58.1433	−1.95006
$890$	106.042	3.55455
$891$	13.8901	0.465335
$892$	5.82714	0.195107
$893$	−68.2939	−2.28537
$894$	55.2278	1.84709
$895$	−29.4169	−0.983297
$896$	114.067	3.81070
$897$	6.98784	0.233317
$898$	63.8690	2.13134
$899$	−24.4496	−0.815439
$900$	5.40471	0.180157
$901$	5.66223	0.188636
$902$	−16.9005	−0.562727
$903$	−52.6682	−1.75269
$904$	9.45041	0.314316
$905$	−58.8528	−1.95633
$906$	−112.831	−3.74857
$907$	−22.0554	−0.732339	−0.366170	−	0.930548i	$-0.619331\pi$
$907$	−22.0554	−0.732339	−0.366170	+	0.930548i	$0.619331\pi$
$908$	−125.666	−4.17036
$909$	11.6679	0.387001
$910$	−18.3889	−0.609585
$911$	35.0388	1.16089	0.580444	−	0.814300i	$-0.302879\pi$
$911$	35.0388	1.16089	0.580444	+	0.814300i	$0.302879\pi$
$912$	−196.659	−6.51203
$913$	1.96456	0.0650175
$914$	9.37378	0.310057
$915$	−54.5221	−1.80244
$916$	14.4015	0.475837
$917$	−2.31891	−0.0765772
$918$	−29.7324	−0.981316
$919$	29.6631	0.978495	0.489247	−	0.872145i	$-0.337272\pi$
$919$	29.6631	0.978495	0.489247	+	0.872145i	$0.337272\pi$
$920$	−77.5273	−2.55600
$921$	−46.1490	−1.52066
$922$	−14.4200	−0.474896
$923$	−0.935944	−0.0308070
$924$	−44.2119	−1.45447
$925$	−0.758539	−0.0249406
$926$	60.1857	1.97783
$927$	32.8002	1.07730
$928$	118.887	3.90267
$929$	3.28682	0.107837	0.0539185	−	0.998545i	$-0.482829\pi$
$929$	3.28682	0.107837	0.0539185	+	0.998545i	$0.482829\pi$
$930$	−62.3677	−2.04512
$931$	13.6999	0.448996
$932$	89.8414	2.94285
$933$	−44.8496	−1.46831
$934$	−2.36865	−0.0775046
$935$	10.8863	0.356020
$936$	−14.5150	−0.474437
$937$	−0.832310	−0.0271904	−0.0135952	−	0.999908i	$-0.504328\pi$
$937$	−0.832310	−0.0271904	−0.0135952	+	0.999908i	$0.504328\pi$
$938$	−45.7061	−1.49236
$939$	−5.22515	−0.170516
$940$	143.992	4.69651
$941$	4.22292	0.137663	0.0688316	−	0.997628i	$-0.478073\pi$
$941$	4.22292	0.137663	0.0688316	+	0.997628i	$0.478073\pi$
$942$	−73.2996	−2.38823
$943$	17.3379	0.564599
$944$	−41.4208	−1.34813
$945$	21.0597	0.685072
$946$	−27.1779	−0.883630
$947$	−0.415723	−0.0135092	−0.00675459	−	0.999977i	$-0.502150\pi$
$947$	−0.415723	−0.0135092	−0.00675459	+	0.999977i	$0.502150\pi$
$948$	−142.975	−4.64361
$949$	−7.26201	−0.235735
$950$	−10.0992	−0.327662
$951$	27.9133	0.905149
$952$	106.785	3.46092
$953$	−20.1205	−0.651768	−0.325884	−	0.945410i	$-0.605662\pi$
$953$	−20.1205	−0.651768	−0.325884	+	0.945410i	$0.605662\pi$
$954$	−6.82547	−0.220983
$955$	−17.6223	−0.570244
$956$	−122.961	−3.97685
$957$	−14.5491	−0.470304
$958$	−44.0412	−1.42291
$959$	−8.03488	−0.259460
$960$	151.385	4.88592
$961$	−10.9494	−0.353205
$962$	3.21467	0.103645
$963$	−24.4558	−0.788078
$964$	27.6551	0.890711
$965$	38.7469	1.24731
$966$	61.9698	1.99385
$967$	−14.3615	−0.461835	−0.230918	−	0.972973i	$-0.574173\pi$
$967$	−14.3615	−0.461835	−0.230918	+	0.972973i	$0.574173\pi$
$968$	89.4971	2.87655
$969$	−49.1027	−1.57741
$970$	52.2960	1.67912
$971$	−6.37382	−0.204545	−0.102273	−	0.994756i	$-0.532611\pi$
$971$	−6.37382	−0.204545	−0.102273	+	0.994756i	$0.532611\pi$
$972$	84.1400	2.69879
$973$	−38.6722	−1.23977
$974$	1.24024	0.0397398
$975$	−1.21624	−0.0389507
$976$	−159.220	−5.09651
$977$	1.79537	0.0574389	0.0287194	−	0.999588i	$-0.490857\pi$
$977$	1.79537	0.0574389	0.0287194	+	0.999588i	$0.490857\pi$
$978$	30.1500	0.964091
$979$	−20.2867	−0.648367
$980$	−28.8852	−0.922703
$981$	26.0574	0.831947
$982$	−69.6387	−2.22226
$983$	−27.1107	−0.864697	−0.432348	−	0.901707i	$-0.642315\pi$
$983$	−27.1107	−0.864697	−0.432348	+	0.901707i	$0.642315\pi$
$984$	−101.852	−3.24691
$985$	28.4744	0.907269
$986$	55.4523	1.76596
$987$	−72.9373	−2.32162
$988$	31.3258	0.996605
$989$	27.8812	0.886570
$990$	−13.1228	−0.417069
$991$	18.1880	0.577762	0.288881	−	0.957365i	$-0.406717\pi$
$991$	18.1880	0.577762	0.288881	+	0.957365i	$0.406717\pi$
$992$	−97.4974	−3.09555
$993$	25.8902	0.821600
$994$	−8.30017	−0.263265
$995$	19.2297	0.609624
$996$	18.6831	0.591995
$997$	49.2180	1.55875	0.779375	−	0.626558i	$-0.215537\pi$
$997$	49.2180	1.55875	0.779375	+	0.626558i	$0.215537\pi$
$998$	−62.2582	−1.97075
$999$	−3.68158	−0.116480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.6	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.6	✓	158	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)

\(f(q)\)	\(=\)	\(q-2.73131 q^{2} -2.15430 q^{3} +5.46003 q^{4} -2.36711 q^{5} +5.88407 q^{6} -3.03890 q^{7} -9.45041 q^{8} +1.64103 q^{9} +O(q^{10})\)	\(q-2.73131 q^{2} -2.15430 q^{3} +5.46003 q^{4} -2.36711 q^{5} +5.88407 q^{6} -3.03890 q^{7} -9.45041 q^{8} +1.64103 q^{9} +6.46530 q^{10} -1.23686 q^{11} -11.7626 q^{12} +0.935944 q^{13} +8.30017 q^{14} +5.09947 q^{15} +14.8919 q^{16} +3.71828 q^{17} -4.48215 q^{18} +6.12994 q^{19} -12.9245 q^{20} +6.54672 q^{21} +3.37824 q^{22} -3.46566 q^{23} +20.3591 q^{24} +0.603200 q^{25} -2.55635 q^{26} +2.92764 q^{27} -16.5925 q^{28} -5.46018 q^{29} -13.9282 q^{30} +4.47779 q^{31} -21.7735 q^{32} +2.66457 q^{33} -10.1558 q^{34} +7.19341 q^{35} +8.96007 q^{36} -1.25753 q^{37} -16.7427 q^{38} -2.01631 q^{39} +22.3701 q^{40} -5.00276 q^{41} -17.8811 q^{42} -8.04498 q^{43} -6.75330 q^{44} -3.88449 q^{45} +9.46578 q^{46} -11.1410 q^{47} -32.0817 q^{48} +2.23492 q^{49} -1.64752 q^{50} -8.01031 q^{51} +5.11029 q^{52} +1.52281 q^{53} -7.99628 q^{54} +2.92778 q^{55} +28.7189 q^{56} -13.2058 q^{57} +14.9134 q^{58} -2.78143 q^{59} +27.8433 q^{60} -10.6917 q^{61} -12.2302 q^{62} -4.98692 q^{63} +29.6864 q^{64} -2.21548 q^{65} -7.27777 q^{66} -5.50665 q^{67} +20.3019 q^{68} +7.46609 q^{69} -19.6474 q^{70} -1.00000 q^{71} -15.5084 q^{72} -7.75902 q^{73} +3.43469 q^{74} -1.29948 q^{75} +33.4697 q^{76} +3.75869 q^{77} +5.50716 q^{78} +12.1551 q^{79} -35.2508 q^{80} -11.2301 q^{81} +13.6641 q^{82} -1.58835 q^{83} +35.7453 q^{84} -8.80157 q^{85} +21.9733 q^{86} +11.7629 q^{87} +11.6888 q^{88} +16.4018 q^{89} +10.6097 q^{90} -2.84424 q^{91} -18.9226 q^{92} -9.64653 q^{93} +30.4296 q^{94} -14.5102 q^{95} +46.9068 q^{96} +8.08872 q^{97} -6.10424 q^{98} -2.02972 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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