LMFDB - Embedded newform 8023.2.a.c.1.15

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			1.15
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)

$f(q)$	$=$	$q-2.49733 q^{2} -3.32636 q^{3} +4.23663 q^{4} -4.15753 q^{5} +8.30700 q^{6} -2.74619 q^{7} -5.58560 q^{8} +8.06465 q^{9} +O(q^{10})$	\(q-2.49733 q^{2} -3.32636 q^{3} +4.23663 q^{4} -4.15753 q^{5} +8.30700 q^{6} -2.74619 q^{7} -5.58560 q^{8} +8.06465 q^{9} +10.3827 q^{10} +5.53369 q^{11} -14.0926 q^{12} +4.58517 q^{13} +6.85813 q^{14} +13.8294 q^{15} +5.47580 q^{16} +0.508478 q^{17} -20.1401 q^{18} -0.582777 q^{19} -17.6139 q^{20} +9.13481 q^{21} -13.8194 q^{22} -1.53472 q^{23} +18.5797 q^{24} +12.2851 q^{25} -11.4507 q^{26} -16.8468 q^{27} -11.6346 q^{28} +2.85183 q^{29} -34.5366 q^{30} +6.73575 q^{31} -2.50365 q^{32} -18.4070 q^{33} -1.26984 q^{34} +11.4174 q^{35} +34.1670 q^{36} +3.94226 q^{37} +1.45538 q^{38} -15.2519 q^{39} +23.2223 q^{40} -0.699012 q^{41} -22.8126 q^{42} +9.44515 q^{43} +23.4442 q^{44} -33.5291 q^{45} +3.83269 q^{46} +8.69809 q^{47} -18.2145 q^{48} +0.541563 q^{49} -30.6798 q^{50} -1.69138 q^{51} +19.4257 q^{52} -12.8066 q^{53} +42.0721 q^{54} -23.0065 q^{55} +15.3391 q^{56} +1.93852 q^{57} -7.12195 q^{58} -7.79089 q^{59} +58.5903 q^{60} +7.59599 q^{61} -16.8214 q^{62} -22.1471 q^{63} -4.69917 q^{64} -19.0630 q^{65} +45.9683 q^{66} -12.3897 q^{67} +2.15424 q^{68} +5.10502 q^{69} -28.5129 q^{70} -1.00000 q^{71} -45.0460 q^{72} -12.6786 q^{73} -9.84511 q^{74} -40.8646 q^{75} -2.46901 q^{76} -15.1966 q^{77} +38.0890 q^{78} -2.24538 q^{79} -22.7658 q^{80} +31.8447 q^{81} +1.74566 q^{82} +14.6900 q^{83} +38.7009 q^{84} -2.11401 q^{85} -23.5876 q^{86} -9.48621 q^{87} -30.9090 q^{88} -12.6291 q^{89} +83.7330 q^{90} -12.5917 q^{91} -6.50204 q^{92} -22.4055 q^{93} -21.7220 q^{94} +2.42291 q^{95} +8.32804 q^{96} +4.50089 q^{97} -1.35246 q^{98} +44.6273 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.49733	−1.76588	−0.882938	−	0.469490i	$-0.844438\pi$
$2$	−2.49733	−1.76588	−0.882938	+	0.469490i	$0.844438\pi$
$3$	−3.32636	−1.92047	−0.960237	−	0.279187i	$-0.909935\pi$
$3$	−3.32636	−1.92047	−0.960237	+	0.279187i	$0.909935\pi$
$4$	4.23663	2.11832
$5$	−4.15753	−1.85931	−0.929653	−	0.368437i	$-0.879893\pi$
$5$	−4.15753	−1.85931	−0.929653	+	0.368437i	$0.879893\pi$
$6$	8.30700	3.39132
$7$	−2.74619	−1.03796	−0.518981	−	0.854786i	$-0.673689\pi$
$7$	−2.74619	−1.03796	−0.518981	+	0.854786i	$0.673689\pi$
$8$	−5.58560	−1.97481
$9$	8.06465	2.68822
$10$	10.3827	3.28330
$11$	5.53369	1.66847	0.834235	−	0.551409i	$-0.185910\pi$
$11$	5.53369	1.66847	0.834235	+	0.551409i	$0.185910\pi$
$12$	−14.0926	−4.06817
$13$	4.58517	1.27170	0.635848	−	0.771814i	$-0.280650\pi$
$13$	4.58517	1.27170	0.635848	+	0.771814i	$0.280650\pi$
$14$	6.85813	1.83291
$15$	13.8294	3.57075
$16$	5.47580	1.36895
$17$	0.508478	0.123324	0.0616620	−	0.998097i	$-0.480360\pi$
$17$	0.508478	0.123324	0.0616620	+	0.998097i	$0.480360\pi$
$18$	−20.1401	−4.74706
$19$	−0.582777	−0.133698	−0.0668491	−	0.997763i	$-0.521295\pi$
$19$	−0.582777	−0.133698	−0.0668491	+	0.997763i	$0.521295\pi$
$20$	−17.6139	−3.93860
$21$	9.13481	1.99338
$22$	−13.8194	−2.94631
$23$	−1.53472	−0.320011	−0.160006	−	0.987116i	$-0.551151\pi$
$23$	−1.53472	−0.320011	−0.160006	+	0.987116i	$0.551151\pi$
$24$	18.5797	3.79257
$25$	12.2851	2.45702
$26$	−11.4507	−2.24566
$27$	−16.8468	−3.24218
$28$	−11.6346	−2.19873
$29$	2.85183	0.529572	0.264786	−	0.964307i	$-0.414699\pi$
$29$	2.85183	0.529572	0.264786	+	0.964307i	$0.414699\pi$
$30$	−34.5366	−6.30549
$31$	6.73575	1.20978	0.604889	−	0.796310i	$-0.293218\pi$
$31$	6.73575	1.20978	0.604889	+	0.796310i	$0.293218\pi$
$32$	−2.50365	−0.442588
$33$	−18.4070	−3.20425
$34$	−1.26984	−0.217775
$35$	11.4174	1.92989
$36$	34.1670	5.69450
$37$	3.94226	0.648104	0.324052	−	0.946039i	$-0.394955\pi$
$37$	3.94226	0.648104	0.324052	+	0.946039i	$0.394955\pi$
$38$	1.45538	0.236094
$39$	−15.2519	−2.44226
$40$	23.2223	3.67177
$41$	−0.699012	−0.109167	−0.0545837	−	0.998509i	$-0.517383\pi$
$41$	−0.699012	−0.109167	−0.0545837	+	0.998509i	$0.517383\pi$
$42$	−22.8126	−3.52006
$43$	9.44515	1.44037	0.720186	−	0.693781i	$-0.244057\pi$
$43$	9.44515	1.44037	0.720186	+	0.693781i	$0.244057\pi$
$44$	23.4442	3.53435
$45$	−33.5291	−4.99822
$46$	3.83269	0.565100
$47$	8.69809	1.26875	0.634373	−	0.773027i	$-0.281258\pi$
$47$	8.69809	1.26875	0.634373	+	0.773027i	$0.281258\pi$
$48$	−18.2145	−2.62903
$49$	0.541563	0.0773662
$50$	−30.6798	−4.33878
$51$	−1.69138	−0.236841
$52$	19.4257	2.69386
$53$	−12.8066	−1.75912	−0.879562	−	0.475784i	$-0.842165\pi$
$53$	−12.8066	−1.75912	−0.879562	+	0.475784i	$0.842165\pi$
$54$	42.0721	5.72528
$55$	−23.0065	−3.10220
$56$	15.3391	2.04978
$57$	1.93852	0.256764
$58$	−7.12195	−0.935158
$59$	−7.79089	−1.01429	−0.507144	−	0.861861i	$-0.669299\pi$
$59$	−7.79089	−1.01429	−0.507144	+	0.861861i	$0.669299\pi$
$60$	58.5903	7.56397
$61$	7.59599	0.972566	0.486283	−	0.873801i	$-0.338352\pi$
$61$	7.59599	0.972566	0.486283	+	0.873801i	$0.338352\pi$
$62$	−16.8214	−2.13632
$63$	−22.1471	−2.79027
$64$	−4.69917	−0.587396
$65$	−19.0630	−2.36447
$66$	45.9683	5.65831
$67$	−12.3897	−1.51364	−0.756822	−	0.653621i	$-0.773249\pi$
$67$	−12.3897	−1.51364	−0.756822	+	0.653621i	$0.773249\pi$
$68$	2.15424	0.261239
$69$	5.10502	0.614573
$70$	−28.5129	−3.40794
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−45.0460	−5.30872
$73$	−12.6786	−1.48392	−0.741960	−	0.670444i	$-0.766103\pi$
$73$	−12.6786	−1.48392	−0.741960	+	0.670444i	$0.766103\pi$
$74$	−9.84511	−1.14447
$75$	−40.8646	−4.71863
$76$	−2.46901	−0.283215
$77$	−15.1966	−1.73181
$78$	38.0890	4.31273
$79$	−2.24538	−0.252625	−0.126312	−	0.991991i	$-0.540314\pi$
$79$	−2.24538	−0.252625	−0.126312	+	0.991991i	$0.540314\pi$
$80$	−22.7658	−2.54530
$81$	31.8447	3.53830
$82$	1.74566	0.192776
$83$	14.6900	1.61244	0.806218	−	0.591619i	$-0.201511\pi$
$83$	14.6900	1.61244	0.806218	+	0.591619i	$0.201511\pi$
$84$	38.7009	4.22261
$85$	−2.11401	−0.229297
$86$	−23.5876	−2.54352
$87$	−9.48621	−1.01703
$88$	−30.9090	−3.29491
$89$	−12.6291	−1.33869	−0.669343	−	0.742953i	$-0.733424\pi$
$89$	−12.6291	−1.33869	−0.669343	+	0.742953i	$0.733424\pi$
$90$	83.7330	8.82623
$91$	−12.5917	−1.31997
$92$	−6.50204	−0.677885
$93$	−22.4055	−2.32334
$94$	−21.7220	−2.24045
$95$	2.42291	0.248586
$96$	8.32804	0.849978
$97$	4.50089	0.456996	0.228498	−	0.973544i	$-0.426619\pi$
$97$	4.50089	0.456996	0.228498	+	0.973544i	$0.426619\pi$
$98$	−1.35246	−0.136619
$99$	44.6273	4.48521
$100$	52.0474	5.20474
$101$	−15.1903	−1.51149	−0.755747	−	0.654864i	$-0.772726\pi$
$101$	−15.1903	−1.51149	−0.755747	+	0.654864i	$0.772726\pi$
$102$	4.22393	0.418231
$103$	−13.9046	−1.37006	−0.685029	−	0.728516i	$-0.740210\pi$
$103$	−13.9046	−1.37006	−0.685029	+	0.728516i	$0.740210\pi$
$104$	−25.6109	−2.51136
$105$	−37.9783	−3.70630
$106$	31.9823	3.10640
$107$	−3.40732	−0.329398	−0.164699	−	0.986344i	$-0.552665\pi$
$107$	−3.40732	−0.329398	−0.164699	+	0.986344i	$0.552665\pi$
$108$	−71.3739	−6.86796
$109$	8.66056	0.829531	0.414765	−	0.909928i	$-0.363864\pi$
$109$	8.66056	0.829531	0.414765	+	0.909928i	$0.363864\pi$
$110$	57.4547	5.47809
$111$	−13.1134	−1.24467
$112$	−15.0376	−1.42092
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−4.84112	−0.453413
$115$	6.38064	0.594998
$116$	12.0822	1.12180
$117$	36.9778	3.41860
$118$	19.4564	1.79111
$119$	−1.39638	−0.128006
$120$	−77.2458	−7.05154
$121$	19.6217	1.78379
$122$	−18.9696	−1.71743
$123$	2.32517	0.209653
$124$	28.5369	2.56269
$125$	−30.2880	−2.70904
$126$	55.3085	4.92727
$127$	5.93990	0.527081	0.263541	−	0.964648i	$-0.415110\pi$
$127$	5.93990	0.527081	0.263541	+	0.964648i	$0.415110\pi$
$128$	16.7427	1.47986
$129$	−31.4179	−2.76620
$130$	47.6065	4.17536
$131$	4.82393	0.421468	0.210734	−	0.977543i	$-0.432415\pi$
$131$	4.82393	0.421468	0.210734	+	0.977543i	$0.432415\pi$
$132$	−77.9839	−6.78762
$133$	1.60042	0.138774
$134$	30.9411	2.67291
$135$	70.0413	6.02820
$136$	−2.84016	−0.243541
$137$	7.70416	0.658211	0.329105	−	0.944293i	$-0.393253\pi$
$137$	7.70416	0.658211	0.329105	+	0.944293i	$0.393253\pi$
$138$	−12.7489	−1.08526
$139$	10.0930	0.856079	0.428040	−	0.903760i	$-0.359204\pi$
$139$	10.0930	0.856079	0.428040	+	0.903760i	$0.359204\pi$
$140$	48.3713	4.08812
$141$	−28.9330	−2.43659
$142$	2.49733	0.209571
$143$	25.3729	2.12179
$144$	44.1605	3.68004
$145$	−11.8566	−0.984635
$146$	31.6626	2.62042
$147$	−1.80143	−0.148580
$148$	16.7019	1.37289
$149$	−1.51550	−0.124155	−0.0620773	−	0.998071i	$-0.519773\pi$
$149$	−1.51550	−0.124155	−0.0620773	+	0.998071i	$0.519773\pi$
$150$	102.052	8.33252
$151$	5.78386	0.470684	0.235342	−	0.971913i	$-0.424379\pi$
$151$	5.78386	0.470684	0.235342	+	0.971913i	$0.424379\pi$
$152$	3.25516	0.264028
$153$	4.10070	0.331522
$154$	37.9508	3.05816
$155$	−28.0041	−2.24935
$156$	−64.6167	−5.17348
$157$	−8.46600	−0.675661	−0.337830	−	0.941207i	$-0.609693\pi$
$157$	−8.46600	−0.675661	−0.337830	+	0.941207i	$0.609693\pi$
$158$	5.60744	0.446104
$159$	42.5994	3.37835
$160$	10.4090	0.822905
$161$	4.21463	0.332159
$162$	−79.5265	−6.24819
$163$	−3.59691	−0.281732	−0.140866	−	0.990029i	$-0.544989\pi$
$163$	−3.59691	−0.281732	−0.140866	+	0.990029i	$0.544989\pi$
$164$	−2.96146	−0.231251
$165$	76.5278	5.95768
$166$	−36.6857	−2.84736
$167$	−20.3539	−1.57503	−0.787515	−	0.616296i	$-0.788633\pi$
$167$	−20.3539	−1.57503	−0.787515	+	0.616296i	$0.788633\pi$
$168$	−51.0234	−3.93654
$169$	8.02375	0.617211
$170$	5.27938	0.404910
$171$	−4.69989	−0.359410
$172$	40.0156	3.05116
$173$	−9.73791	−0.740359	−0.370180	−	0.928960i	$-0.620704\pi$
$173$	−9.73791	−0.740359	−0.370180	+	0.928960i	$0.620704\pi$
$174$	23.6901	1.79595
$175$	−33.7372	−2.55029
$176$	30.3014	2.28405
$177$	25.9153	1.94791
$178$	31.5391	2.36395
$179$	−20.2638	−1.51459	−0.757294	−	0.653074i	$-0.773479\pi$
$179$	−20.2638	−1.51459	−0.757294	+	0.653074i	$0.773479\pi$
$180$	−142.050	−10.5878
$181$	23.3241	1.73366	0.866832	−	0.498601i	$-0.166153\pi$
$181$	23.3241	1.73366	0.866832	+	0.498601i	$0.166153\pi$
$182$	31.4457	2.33091
$183$	−25.2670	−1.86779
$184$	8.57233	0.631961
$185$	−16.3901	−1.20502
$186$	55.9539	4.10274
$187$	2.81376	0.205763
$188$	36.8506	2.68761
$189$	46.2647	3.36526
$190$	−6.05080	−0.438971
$191$	4.47219	0.323596	0.161798	−	0.986824i	$-0.448271\pi$
$191$	4.47219	0.323596	0.161798	+	0.986824i	$0.448271\pi$
$192$	15.6311	1.12808
$193$	3.66691	0.263950	0.131975	−	0.991253i	$-0.457868\pi$
$193$	3.66691	0.263950	0.131975	+	0.991253i	$0.457868\pi$
$194$	−11.2402	−0.806998
$195$	63.4103	4.54090
$196$	2.29440	0.163886
$197$	8.93248	0.636413	0.318206	−	0.948021i	$-0.396920\pi$
$197$	8.93248	0.636413	0.318206	+	0.948021i	$0.396920\pi$
$198$	−111.449	−7.92033
$199$	1.47155	0.104315	0.0521576	−	0.998639i	$-0.483390\pi$
$199$	1.47155	0.104315	0.0521576	+	0.998639i	$0.483390\pi$
$200$	−68.6196	−4.85214
$201$	41.2126	2.90691
$202$	37.9352	2.66911
$203$	−7.83167	−0.549675
$204$	−7.16576	−0.501703
$205$	2.90617	0.202976
$206$	34.7242	2.41935
$207$	−12.3770	−0.860259
$208$	25.1075	1.74089
$209$	−3.22491	−0.223071
$210$	94.8441	6.54487
$211$	26.7853	1.84398	0.921989	−	0.387215i	$-0.126563\pi$
$211$	26.7853	1.84398	0.921989	+	0.387215i	$0.126563\pi$
$212$	−54.2570	−3.72638
$213$	3.32636	0.227918
$214$	8.50918	0.581676
$215$	−39.2685	−2.67809
$216$	94.0998	6.40268
$217$	−18.4977	−1.25570
$218$	−21.6282	−1.46485
$219$	42.1736	2.84983
$220$	−97.4701	−6.57143
$221$	2.33146	0.156831
$222$	32.7484	2.19793
$223$	6.06546	0.406173	0.203087	−	0.979161i	$-0.434903\pi$
$223$	6.06546	0.406173	0.203087	+	0.979161i	$0.434903\pi$
$224$	6.87551	0.459389
$225$	99.0749	6.60499
$226$	2.49733	0.166120
$227$	−3.64474	−0.241910	−0.120955	−	0.992658i	$-0.538596\pi$
$227$	−3.64474	−0.241910	−0.120955	+	0.992658i	$0.538596\pi$
$228$	8.21282	0.543907
$229$	−25.4298	−1.68045	−0.840226	−	0.542237i	$-0.817578\pi$
$229$	−25.4298	−1.68045	−0.840226	+	0.542237i	$0.817578\pi$
$230$	−15.9345	−1.05069
$231$	50.5492	3.32589
$232$	−15.9292	−1.04580
$233$	0.660938	0.0432995	0.0216497	−	0.999766i	$-0.493108\pi$
$233$	0.660938	0.0432995	0.0216497	+	0.999766i	$0.493108\pi$
$234$	−92.3455	−6.03682
$235$	−36.1626	−2.35899
$236$	−33.0072	−2.14858
$237$	7.46894	0.485160
$238$	3.48721	0.226042
$239$	−17.9222	−1.15929	−0.579645	−	0.814869i	$-0.696809\pi$
$239$	−17.9222	−1.15929	−0.579645	+	0.814869i	$0.696809\pi$
$240$	75.7273	4.88818
$241$	0.123628	0.00796360	0.00398180	−	0.999992i	$-0.498733\pi$
$241$	0.123628	0.00796360	0.00398180	+	0.999992i	$0.498733\pi$
$242$	−49.0018	−3.14996
$243$	−55.3862	−3.55303
$244$	32.1814	2.06020
$245$	−2.25157	−0.143847
$246$	−5.80669	−0.370221
$247$	−2.67213	−0.170023
$248$	−37.6233	−2.38908
$249$	−48.8641	−3.09664
$250$	75.6389	4.78382
$251$	19.2444	1.21470	0.607349	−	0.794435i	$-0.292233\pi$
$251$	19.2444	1.21470	0.607349	+	0.794435i	$0.292233\pi$
$252$	−93.8291	−5.91068
$253$	−8.49266	−0.533929
$254$	−14.8339	−0.930760
$255$	7.03197	0.440359
$256$	−32.4135	−2.02585
$257$	−18.9575	−1.18254	−0.591269	−	0.806474i	$-0.701373\pi$
$257$	−18.9575	−1.18254	−0.591269	+	0.806474i	$0.701373\pi$
$258$	78.4608	4.88476
$259$	−10.8262	−0.672708
$260$	−80.7629	−5.00870
$261$	22.9990	1.42360
$262$	−12.0469	−0.744261
$263$	27.1592	1.67471	0.837353	−	0.546663i	$-0.184102\pi$
$263$	27.1592	1.67471	0.837353	+	0.546663i	$0.184102\pi$
$264$	102.814	6.32779
$265$	53.2439	3.27075
$266$	−3.99676	−0.245057
$267$	42.0090	2.57091
$268$	−52.4907	−3.20638
$269$	−2.31502	−0.141149	−0.0705747	−	0.997506i	$-0.522483\pi$
$269$	−2.31502	−0.141149	−0.0705747	+	0.997506i	$0.522483\pi$
$270$	−174.916	−10.6450
$271$	16.7506	1.01752	0.508762	−	0.860907i	$-0.330103\pi$
$271$	16.7506	1.01752	0.508762	+	0.860907i	$0.330103\pi$
$272$	2.78433	0.168825
$273$	41.8846	2.53497
$274$	−19.2398	−1.16232
$275$	67.9818	4.09946
$276$	21.6281	1.30186
$277$	−15.3416	−0.921788	−0.460894	−	0.887455i	$-0.652471\pi$
$277$	−15.3416	−0.921788	−0.460894	+	0.887455i	$0.652471\pi$
$278$	−25.2056	−1.51173
$279$	54.3215	3.25214
$280$	−63.7730	−3.81116
$281$	−5.67678	−0.338648	−0.169324	−	0.985560i	$-0.554158\pi$
$281$	−5.67678	−0.338648	−0.169324	+	0.985560i	$0.554158\pi$
$282$	72.2550	4.30272
$283$	−12.6112	−0.749658	−0.374829	−	0.927094i	$-0.622299\pi$
$283$	−12.6112	−0.749658	−0.374829	+	0.927094i	$0.622299\pi$
$284$	−4.23663	−0.251398
$285$	−8.05948	−0.477402
$286$	−63.3644	−3.74681
$287$	1.91962	0.113312
$288$	−20.1911	−1.18977
$289$	−16.7415	−0.984791
$290$	29.6097	1.73874
$291$	−14.9716	−0.877649
$292$	−53.7147	−3.14341
$293$	−21.8904	−1.27885	−0.639426	−	0.768853i	$-0.720828\pi$
$293$	−21.8904	−1.27885	−0.639426	+	0.768853i	$0.720828\pi$
$294$	4.49876	0.262373
$295$	32.3909	1.88587
$296$	−22.0199	−1.27988
$297$	−93.2252	−5.40948
$298$	3.78470	0.219242
$299$	−7.03694	−0.406957
$300$	−173.128	−9.99556
$301$	−25.9382	−1.49505
$302$	−14.4442	−0.831169
$303$	50.5284	2.90278
$304$	−3.19117	−0.183026
$305$	−31.5806	−1.80830
$306$	−10.2408	−0.585427
$307$	14.9123	0.851089	0.425544	−	0.904938i	$-0.360083\pi$
$307$	14.9123	0.851089	0.425544	+	0.904938i	$0.360083\pi$
$308$	−64.3823	−3.66852
$309$	46.2516	2.63116
$310$	69.9354	3.97206
$311$	−5.59134	−0.317056	−0.158528	−	0.987355i	$-0.550675\pi$
$311$	−5.59134	−0.317056	−0.158528	+	0.987355i	$0.550675\pi$
$312$	85.1911	4.82300
$313$	−8.50978	−0.481001	−0.240501	−	0.970649i	$-0.577312\pi$
$313$	−8.50978	−0.481001	−0.240501	+	0.970649i	$0.577312\pi$
$314$	21.1424	1.19313
$315$	92.0772	5.18796
$316$	−9.51285	−0.535140
$317$	−7.64247	−0.429244	−0.214622	−	0.976697i	$-0.568852\pi$
$317$	−7.64247	−0.429244	−0.214622	+	0.976697i	$0.568852\pi$
$318$	−106.385	−5.96575
$319$	15.7811	0.883574
$320$	19.5369	1.09215
$321$	11.3340	0.632600
$322$	−10.5253	−0.586552
$323$	−0.296329	−0.0164882
$324$	134.914	7.49524
$325$	56.3291	3.12458
$326$	8.98267	0.497504
$327$	−28.8081	−1.59309
$328$	3.90441	0.215585
$329$	−23.8866	−1.31691
$330$	−191.115	−10.5205
$331$	−15.7379	−0.865035	−0.432517	−	0.901626i	$-0.642375\pi$
$331$	−15.7379	−0.865035	−0.432517	+	0.901626i	$0.642375\pi$
$332$	62.2361	3.41565
$333$	31.7930	1.74224
$334$	50.8302	2.78131
$335$	51.5106	2.81433
$336$	50.0204	2.72884
$337$	29.4154	1.60236	0.801179	−	0.598425i	$-0.204207\pi$
$337$	29.4154	1.60236	0.801179	+	0.598425i	$0.204207\pi$
$338$	−20.0379	−1.08992
$339$	3.32636	0.180663
$340$	−8.95631	−0.485724
$341$	37.2736	2.01848
$342$	11.7372	0.634673
$343$	17.7361	0.957659
$344$	−52.7569	−2.84446
$345$	−21.2243	−1.14268
$346$	24.3187	1.30738
$347$	−5.33506	−0.286401	−0.143200	−	0.989694i	$-0.545739\pi$
$347$	−5.33506	−0.286401	−0.143200	+	0.989694i	$0.545739\pi$
$348$	−40.1896	−2.15439
$349$	12.5401	0.671256	0.335628	−	0.941995i	$-0.391052\pi$
$349$	12.5401	0.671256	0.335628	+	0.941995i	$0.391052\pi$
$350$	84.2527	4.50350
$351$	−77.2456	−4.12306
$352$	−13.8544	−0.738444
$353$	−35.1401	−1.87032	−0.935158	−	0.354230i	$-0.884743\pi$
$353$	−35.1401	−1.87032	−0.935158	+	0.354230i	$0.884743\pi$
$354$	−64.7189	−3.43977
$355$	4.15753	0.220659
$356$	−53.5051	−2.83576
$357$	4.64485	0.245832
$358$	50.6053	2.67457
$359$	21.6689	1.14364	0.571820	−	0.820379i	$-0.306238\pi$
$359$	21.6689	1.14364	0.571820	+	0.820379i	$0.306238\pi$
$360$	187.280	9.87053
$361$	−18.6604	−0.982125
$362$	−58.2478	−3.06143
$363$	−65.2689	−3.42573
$364$	−53.3466	−2.79612
$365$	52.7118	2.75906
$366$	63.0998	3.29828
$367$	−4.16145	−0.217226	−0.108613	−	0.994084i	$-0.534641\pi$
$367$	−4.16145	−0.217226	−0.108613	+	0.994084i	$0.534641\pi$
$368$	−8.40382	−0.438079
$369$	−5.63729	−0.293466
$370$	40.9314	2.12792
$371$	35.1694	1.82591
$372$	−94.9240	−4.92158
$373$	5.01960	0.259905	0.129953	−	0.991520i	$-0.458517\pi$
$373$	5.01960	0.259905	0.129953	+	0.991520i	$0.458517\pi$
$374$	−7.02687	−0.363351
$375$	100.749	5.20263
$376$	−48.5841	−2.50553
$377$	13.0761	0.673454
$378$	−115.538	−5.94263
$379$	−3.55125	−0.182416	−0.0912078	−	0.995832i	$-0.529073\pi$
$379$	−3.55125	−0.182416	−0.0912078	+	0.995832i	$0.529073\pi$
$380$	10.2650	0.526583
$381$	−19.7582	−1.01225
$382$	−11.1685	−0.571430
$383$	−34.2682	−1.75102	−0.875511	−	0.483198i	$-0.839475\pi$
$383$	−34.2682	−1.75102	−0.875511	+	0.483198i	$0.839475\pi$
$384$	−55.6921	−2.84202
$385$	63.1802	3.21996
$386$	−9.15746	−0.466103
$387$	76.1718	3.87203
$388$	19.0686	0.968063
$389$	18.8182	0.954119	0.477060	−	0.878871i	$-0.341703\pi$
$389$	18.8182	0.954119	0.477060	+	0.878871i	$0.341703\pi$
$390$	−158.356	−8.01867
$391$	−0.780371	−0.0394651
$392$	−3.02496	−0.152783
$393$	−16.0461	−0.809419
$394$	−22.3073	−1.12383
$395$	9.33524	0.469707
$396$	189.070	9.50110
$397$	1.56573	0.0785820	0.0392910	−	0.999228i	$-0.487490\pi$
$397$	1.56573	0.0785820	0.0392910	+	0.999228i	$0.487490\pi$
$398$	−3.67493	−0.184208
$399$	−5.32356	−0.266511
$400$	67.2707	3.36353
$401$	−12.5104	−0.624742	−0.312371	−	0.949960i	$-0.601123\pi$
$401$	−12.5104	−0.624742	−0.312371	+	0.949960i	$0.601123\pi$
$402$	−102.921	−5.13325
$403$	30.8846	1.53847
$404$	−64.3558	−3.20182
$405$	−132.395	−6.57877
$406$	19.5582	0.970658
$407$	21.8153	1.08134
$408$	9.44738	0.467715
$409$	−20.2039	−0.999016	−0.499508	−	0.866309i	$-0.666486\pi$
$409$	−20.2039	−0.999016	−0.499508	+	0.866309i	$0.666486\pi$
$410$	−7.25765	−0.358430
$411$	−25.6268	−1.26408
$412$	−58.9086	−2.90222
$413$	21.3953	1.05279
$414$	30.9093	1.51911
$415$	−61.0741	−2.99801
$416$	−11.4797	−0.562837
$417$	−33.5730	−1.64408
$418$	8.05364	0.393916
$419$	0.780137	0.0381122	0.0190561	−	0.999818i	$-0.493934\pi$
$419$	0.780137	0.0381122	0.0190561	+	0.999818i	$0.493934\pi$
$420$	−160.900	−7.85112
$421$	−1.99035	−0.0970037	−0.0485018	−	0.998823i	$-0.515445\pi$
$421$	−1.99035	−0.0970037	−0.0485018	+	0.998823i	$0.515445\pi$
$422$	−66.8917	−3.25624
$423$	70.1471	3.41067
$424$	71.5327	3.47394
$425$	6.24669	0.303009
$426$	−8.30700	−0.402475
$427$	−20.8600	−1.00949
$428$	−14.4356	−0.697769
$429$	−84.3993	−4.07484
$430$	98.0663	4.72917
$431$	8.69931	0.419031	0.209516	−	0.977805i	$-0.432811\pi$
$431$	8.69931	0.419031	0.209516	+	0.977805i	$0.432811\pi$
$432$	−92.2500	−4.43838
$433$	−30.5003	−1.46575	−0.732875	−	0.680363i	$-0.761822\pi$
$433$	−30.5003	−1.46575	−0.732875	+	0.680363i	$0.761822\pi$
$434$	46.1947	2.21742
$435$	39.4392	1.89097
$436$	36.6916	1.75721
$437$	0.894399	0.0427849
$438$	−105.321	−5.03244
$439$	−11.0461	−0.527203	−0.263601	−	0.964632i	$-0.584910\pi$
$439$	−11.0461	−0.527203	−0.263601	+	0.964632i	$0.584910\pi$
$440$	128.505	6.12624
$441$	4.36752	0.207977
$442$	−5.82241	−0.276944
$443$	−16.3786	−0.778172	−0.389086	−	0.921201i	$-0.627209\pi$
$443$	−16.3786	−0.778172	−0.389086	+	0.921201i	$0.627209\pi$
$444$	−55.5566	−2.63660
$445$	52.5061	2.48903
$446$	−15.1474	−0.717251
$447$	5.04110	0.238436
$448$	12.9048	0.609695
$449$	10.6434	0.502294	0.251147	−	0.967949i	$-0.419192\pi$
$449$	10.6434	0.502294	0.251147	+	0.967949i	$0.419192\pi$
$450$	−247.422	−11.6636
$451$	−3.86812	−0.182143
$452$	−4.23663	−0.199275
$453$	−19.2392	−0.903935
$454$	9.10210	0.427183
$455$	52.3506	2.45423
$456$	−10.8278	−0.507059
$457$	15.4957	0.724860	0.362430	−	0.932011i	$-0.381947\pi$
$457$	15.4957	0.724860	0.362430	+	0.932011i	$0.381947\pi$
$458$	63.5066	2.96747
$459$	−8.56625	−0.399838
$460$	27.0325	1.26039
$461$	−6.19068	−0.288329	−0.144164	−	0.989554i	$-0.546049\pi$
$461$	−6.19068	−0.288329	−0.144164	+	0.989554i	$0.546049\pi$
$462$	−126.238	−5.87312
$463$	−23.7363	−1.10312	−0.551560	−	0.834135i	$-0.685967\pi$
$463$	−23.7363	−1.10312	−0.551560	+	0.834135i	$0.685967\pi$
$464$	15.6161	0.724957
$465$	93.1517	4.31981
$466$	−1.65058	−0.0764615
$467$	−18.5039	−0.856259	−0.428129	−	0.903717i	$-0.640827\pi$
$467$	−18.5039	−0.856259	−0.428129	+	0.903717i	$0.640827\pi$
$468$	156.661	7.24167
$469$	34.0245	1.57111
$470$	90.3098	4.16568
$471$	28.1610	1.29759
$472$	43.5168	2.00303
$473$	52.2665	2.40322
$474$	−18.6524	−0.856731
$475$	−7.15946	−0.328498
$476$	−5.91594	−0.271157
$477$	−103.281	−4.72891
$478$	44.7576	2.04716
$479$	−2.33657	−0.106761	−0.0533803	−	0.998574i	$-0.517000\pi$
$479$	−2.33657	−0.106761	−0.0533803	+	0.998574i	$0.517000\pi$
$480$	−34.6241	−1.58037
$481$	18.0759	0.824191
$482$	−0.308740	−0.0140627
$483$	−14.0194	−0.637903
$484$	83.1301	3.77864
$485$	−18.7126	−0.849695
$486$	138.317	6.27421
$487$	8.72371	0.395309	0.197655	−	0.980272i	$-0.436668\pi$
$487$	8.72371	0.395309	0.197655	+	0.980272i	$0.436668\pi$
$488$	−42.4282	−1.92063
$489$	11.9646	0.541059
$490$	5.62289	0.254016
$491$	−26.6140	−1.20107	−0.600536	−	0.799598i	$-0.705046\pi$
$491$	−26.6140	−1.20107	−0.600536	+	0.799598i	$0.705046\pi$
$492$	9.85087	0.444112
$493$	1.45009	0.0653089
$494$	6.67317	0.300240
$495$	−185.539	−8.33938
$496$	36.8837	1.65613
$497$	2.74619	0.123183
$498$	122.030	5.46828
$499$	34.1636	1.52937	0.764686	−	0.644403i	$-0.222894\pi$
$499$	34.1636	1.52937	0.764686	+	0.644403i	$0.222894\pi$
$500$	−128.319	−5.73860
$501$	67.7042	3.02480
$502$	−48.0596	−2.14500
$503$	−14.0370	−0.625878	−0.312939	−	0.949773i	$-0.601314\pi$
$503$	−14.0370	−0.625878	−0.312939	+	0.949773i	$0.601314\pi$
$504$	123.705	5.51025
$505$	63.1543	2.81033
$506$	21.2089	0.942852
$507$	−26.6899	−1.18534
$508$	25.1652	1.11653
$509$	−15.4094	−0.683009	−0.341505	−	0.939880i	$-0.610937\pi$
$509$	−15.4094	−0.683009	−0.341505	+	0.939880i	$0.610937\pi$
$510$	−17.5611	−0.777619
$511$	34.8179	1.54025
$512$	47.4618	2.09754
$513$	9.81795	0.433473
$514$	47.3431	2.08821
$515$	57.8087	2.54736
$516$	−133.106	−5.85968
$517$	48.1325	2.11687
$518$	27.0366	1.18792
$519$	32.3918	1.42184
$520$	106.478	4.66938
$521$	−34.4747	−1.51036	−0.755181	−	0.655516i	$-0.772451\pi$
$521$	−34.4747	−1.51036	−0.755181	+	0.655516i	$0.772451\pi$
$522$	−57.4360	−2.51391
$523$	−26.2391	−1.14735	−0.573677	−	0.819082i	$-0.694484\pi$
$523$	−26.2391	−1.14735	−0.573677	+	0.819082i	$0.694484\pi$
$524$	20.4372	0.892804
$525$	112.222	4.89776
$526$	−67.8253	−2.95732
$527$	3.42498	0.149195
$528$	−100.793	−4.38646
$529$	−20.6446	−0.897593
$530$	−132.967	−5.77574
$531$	−62.8309	−2.72663
$532$	6.78038	0.293967
$533$	−3.20509	−0.138828
$534$	−104.910	−4.53991
$535$	14.1660	0.612451
$536$	69.2040	2.98916
$537$	67.4046	2.90873
$538$	5.78136	0.249252
$539$	2.99684	0.129083
$540$	296.739	12.7696
$541$	−33.9669	−1.46035	−0.730177	−	0.683258i	$-0.760562\pi$
$541$	−33.9669	−1.46035	−0.730177	+	0.683258i	$0.760562\pi$
$542$	−41.8316	−1.79682
$543$	−77.5841	−3.32945
$544$	−1.27305	−0.0545817
$545$	−36.0065	−1.54235
$546$	−104.600	−4.47645
$547$	40.1183	1.71533	0.857667	−	0.514206i	$-0.171913\pi$
$547$	40.1183	1.71533	0.857667	+	0.514206i	$0.171913\pi$
$548$	32.6397	1.39430
$549$	61.2590	2.61447
$550$	−169.773	−7.23913
$551$	−1.66198	−0.0708027
$552$	−28.5146	−1.21366
$553$	6.16624	0.262215
$554$	38.3130	1.62776
$555$	54.5193	2.31421
$556$	42.7605	1.81345
$557$	7.08731	0.300299	0.150150	−	0.988663i	$-0.452024\pi$
$557$	7.08731	0.300299	0.150150	+	0.988663i	$0.452024\pi$
$558$	−135.659	−5.74288
$559$	43.3076	1.83172
$560$	62.5193	2.64192
$561$	−9.35957	−0.395161
$562$	14.1768	0.598010
$563$	10.4475	0.440310	0.220155	−	0.975465i	$-0.429344\pi$
$563$	10.4475	0.440310	0.220155	+	0.975465i	$0.429344\pi$
$564$	−122.578	−5.16148
$565$	4.15753	0.174909
$566$	31.4943	1.32380
$567$	−87.4515	−3.67262
$568$	5.58560	0.234367
$569$	13.2137	0.553946	0.276973	−	0.960878i	$-0.410669\pi$
$569$	13.2137	0.553946	0.276973	+	0.960878i	$0.410669\pi$
$570$	20.1271	0.843033
$571$	−22.6388	−0.947403	−0.473701	−	0.880686i	$-0.657082\pi$
$571$	−22.6388	−0.947403	−0.473701	+	0.880686i	$0.657082\pi$
$572$	107.496	4.49462
$573$	−14.8761	−0.621458
$574$	−4.79392	−0.200094
$575$	−18.8541	−0.786272
$576$	−37.8972	−1.57905
$577$	−9.06755	−0.377487	−0.188743	−	0.982026i	$-0.560441\pi$
$577$	−9.06755	−0.377487	−0.188743	+	0.982026i	$0.560441\pi$
$578$	41.8088	1.73902
$579$	−12.1974	−0.506909
$580$	−50.2320	−2.08577
$581$	−40.3415	−1.67365
$582$	37.3889	1.54982
$583$	−70.8679	−2.93505
$584$	70.8177	2.93046
$585$	−153.736	−6.35621
$586$	54.6675	2.25829
$587$	21.2743	0.878083	0.439041	−	0.898467i	$-0.355318\pi$
$587$	21.2743	0.878083	0.439041	+	0.898467i	$0.355318\pi$
$588$	−7.63201	−0.314739
$589$	−3.92544	−0.161745
$590$	−80.8906	−3.33021
$591$	−29.7126	−1.22221
$592$	21.5871	0.887222
$593$	−0.00680874	−0.000279601 0	−0.000139801	−	1.00000i	$-0.500044\pi$
$593$	−0.00680874	−0.000279601 0	−0.000139801		1.00000i	$0.500044\pi$
$594$	232.814	9.55246
$595$	5.80549	0.238002
$596$	−6.42062	−0.262999
$597$	−4.89489	−0.200335
$598$	17.5735	0.718635
$599$	−22.1529	−0.905141	−0.452571	−	0.891729i	$-0.649493\pi$
$599$	−22.1529	−0.905141	−0.452571	+	0.891729i	$0.649493\pi$
$600$	228.253	9.31840
$601$	−46.4704	−1.89557	−0.947783	−	0.318915i	$-0.896681\pi$
$601$	−46.4704	−1.89557	−0.947783	+	0.318915i	$0.896681\pi$
$602$	64.7761	2.64008
$603$	−99.9187	−4.06900
$604$	24.5041	0.997057
$605$	−81.5780	−3.31662
$606$	−126.186	−5.12595
$607$	28.2722	1.14753	0.573766	−	0.819019i	$-0.305482\pi$
$607$	28.2722	1.14753	0.573766	+	0.819019i	$0.305482\pi$
$608$	1.45907	0.0591731
$609$	26.0509	1.05564
$610$	78.8669	3.19323
$611$	39.8822	1.61346
$612$	17.3732	0.702269
$613$	−2.86610	−0.115761	−0.0578803	−	0.998324i	$-0.518434\pi$
$613$	−2.86610	−0.115761	−0.0578803	+	0.998324i	$0.518434\pi$
$614$	−37.2408	−1.50292
$615$	−9.66695	−0.389809
$616$	84.8820	3.41999
$617$	−36.8513	−1.48358	−0.741789	−	0.670633i	$-0.766022\pi$
$617$	−36.8513	−1.48358	−0.741789	+	0.670633i	$0.766022\pi$
$618$	−115.505	−4.64630
$619$	−13.3826	−0.537893	−0.268947	−	0.963155i	$-0.586676\pi$
$619$	−13.3826	−0.537893	−0.268947	+	0.963155i	$0.586676\pi$
$620$	−118.643	−4.76483
$621$	25.8552	1.03753
$622$	13.9634	0.559881
$623$	34.6820	1.38951
$624$	−83.5164	−3.34333
$625$	64.4978	2.57991
$626$	21.2517	0.849388
$627$	10.7272	0.428403
$628$	−35.8674	−1.43126
$629$	2.00455	0.0799268
$630$	−229.947	−9.16130
$631$	−42.2000	−1.67996	−0.839978	−	0.542621i	$-0.817432\pi$
$631$	−42.2000	−1.67996	−0.839978	+	0.542621i	$0.817432\pi$
$632$	12.5418	0.498886
$633$	−89.0976	−3.54131
$634$	19.0857	0.757992
$635$	−24.6953	−0.980005
$636$	180.478	7.15642
$637$	2.48316	0.0983863
$638$	−39.4107	−1.56028
$639$	−8.06465	−0.319033
$640$	−69.6082	−2.75150
$641$	23.1027	0.912502	0.456251	−	0.889851i	$-0.349192\pi$
$641$	23.1027	0.912502	0.456251	+	0.889851i	$0.349192\pi$
$642$	−28.3046	−1.11709
$643$	34.9475	1.37819	0.689097	−	0.724670i	$-0.258008\pi$
$643$	34.9475	1.37819	0.689097	+	0.724670i	$0.258008\pi$
$644$	17.8559	0.703619
$645$	130.621	5.14320
$646$	0.740030	0.0291161
$647$	18.4251	0.724364	0.362182	−	0.932107i	$-0.382032\pi$
$647$	18.4251	0.724364	0.362182	+	0.932107i	$0.382032\pi$
$648$	−177.872	−6.98746
$649$	−43.1124	−1.69231
$650$	−140.672	−5.51762
$651$	61.5298	2.41154
$652$	−15.2388	−0.596798
$653$	31.5421	1.23434	0.617168	−	0.786831i	$-0.288280\pi$
$653$	31.5421	1.23434	0.617168	+	0.786831i	$0.288280\pi$
$654$	71.9432	2.81320
$655$	−20.0556	−0.783638
$656$	−3.82765	−0.149445
$657$	−102.249	−3.98910
$658$	59.6526	2.32550
$659$	−15.3148	−0.596578	−0.298289	−	0.954476i	$-0.596416\pi$
$659$	−15.3148	−0.596578	−0.298289	+	0.954476i	$0.596416\pi$
$660$	324.220	12.6203
$661$	−2.33459	−0.0908049	−0.0454025	−	0.998969i	$-0.514457\pi$
$661$	−2.33459	−0.0908049	−0.0454025	+	0.998969i	$0.514457\pi$
$662$	39.3027	1.52754
$663$	−7.75526	−0.301189
$664$	−82.0524	−3.18425
$665$	−6.65378	−0.258023
$666$	−79.3974	−3.07659
$667$	−4.37676	−0.169469
$668$	−86.2319	−3.33641
$669$	−20.1759	−0.780045
$670$	−128.639	−4.96975
$671$	42.0338	1.62270
$672$	−22.8704	−0.882245
$673$	−31.9052	−1.22986	−0.614928	−	0.788583i	$-0.710815\pi$
$673$	−31.9052	−1.22986	−0.614928	+	0.788583i	$0.710815\pi$
$674$	−73.4598	−2.82956
$675$	−206.965	−7.96608
$676$	33.9937	1.30745
$677$	46.1825	1.77494	0.887468	−	0.460869i	$-0.152462\pi$
$677$	46.1825	1.77494	0.887468	+	0.460869i	$0.152462\pi$
$678$	−8.30700	−0.319028
$679$	−12.3603	−0.474345
$680$	11.8080	0.452818
$681$	12.1237	0.464582
$682$	−93.0843	−3.56438
$683$	−19.2195	−0.735413	−0.367706	−	0.929942i	$-0.619857\pi$
$683$	−19.2195	−0.735413	−0.367706	+	0.929942i	$0.619857\pi$
$684$	−19.9117	−0.761344
$685$	−32.0303	−1.22381
$686$	−44.2928	−1.69111
$687$	84.5888	3.22726
$688$	51.7198	1.97180
$689$	−58.7205	−2.23707
$690$	53.0040	2.01783
$691$	−43.1976	−1.64331	−0.821657	−	0.569982i	$-0.806950\pi$
$691$	−43.1976	−1.64331	−0.821657	+	0.569982i	$0.806950\pi$
$692$	−41.2559	−1.56832
$693$	−122.555	−4.65548
$694$	13.3234	0.505748
$695$	−41.9621	−1.59171
$696$	52.9862	2.00844
$697$	−0.355433	−0.0134630
$698$	−31.3167	−1.18535
$699$	−2.19851	−0.0831555
$700$	−142.932	−5.40232
$701$	39.1331	1.47804	0.739018	−	0.673686i	$-0.235290\pi$
$701$	39.1331	1.47804	0.739018	+	0.673686i	$0.235290\pi$
$702$	192.907	7.28082
$703$	−2.29746	−0.0866503
$704$	−26.0037	−0.980053
$705$	120.290	4.53037
$706$	87.7562	3.30275
$707$	41.7155	1.56887
$708$	109.794	4.12630
$709$	−36.3319	−1.36447	−0.682237	−	0.731131i	$-0.738993\pi$
$709$	−36.3319	−1.36447	−0.682237	+	0.731131i	$0.738993\pi$
$710$	−10.3827	−0.389656
$711$	−18.1082	−0.679111
$712$	70.5414	2.64365
$713$	−10.3375	−0.387142
$714$	−11.5997	−0.434108
$715$	−105.489	−3.94505
$716$	−85.8503	−3.20838
$717$	59.6156	2.22639
$718$	−54.1142	−2.01953
$719$	28.4806	1.06215	0.531073	−	0.847326i	$-0.321789\pi$
$719$	28.4806	1.06215	0.531073	+	0.847326i	$0.321789\pi$
$720$	−183.599	−6.84231
$721$	38.1846	1.42207
$722$	46.6010	1.73431
$723$	−0.411232	−0.0152939
$724$	98.8155	3.67245
$725$	35.0350	1.30117
$726$	162.998	6.04941
$727$	7.69073	0.285233	0.142617	−	0.989778i	$-0.454448\pi$
$727$	7.69073	0.285233	0.142617	+	0.989778i	$0.454448\pi$
$728$	70.3325	2.60670
$729$	88.7004	3.28520
$730$	−131.638	−4.87216
$731$	4.80265	0.177632
$732$	−107.047	−3.95657
$733$	43.1288	1.59300	0.796499	−	0.604640i	$-0.206683\pi$
$733$	43.1288	1.59300	0.796499	+	0.604640i	$0.206683\pi$
$734$	10.3925	0.383594
$735$	7.48951	0.276255
$736$	3.84240	0.141633
$737$	−68.5608	−2.52547
$738$	14.0782	0.518224
$739$	13.8586	0.509795	0.254898	−	0.966968i	$-0.417958\pi$
$739$	13.8586	0.509795	0.254898	+	0.966968i	$0.417958\pi$
$740$	−69.4388	−2.55262
$741$	8.88845	0.326526
$742$	−87.8295	−3.22432
$743$	20.1434	0.738990	0.369495	−	0.929233i	$-0.379531\pi$
$743$	20.1434	0.738990	0.369495	+	0.929233i	$0.379531\pi$
$744$	125.148	4.58816
$745$	6.30074	0.230841
$746$	−12.5356	−0.458960
$747$	118.470	4.33458
$748$	11.9209	0.435870
$749$	9.35715	0.341903
$750$	−251.602	−9.18720
$751$	43.1365	1.57407	0.787036	−	0.616907i	$-0.211614\pi$
$751$	43.1365	1.57407	0.787036	+	0.616907i	$0.211614\pi$
$752$	47.6290	1.73685
$753$	−64.0138	−2.33279
$754$	−32.6553	−1.18924
$755$	−24.0466	−0.875144
$756$	196.006	7.12869
$757$	23.5363	0.855442	0.427721	−	0.903911i	$-0.359316\pi$
$757$	23.5363	0.855442	0.427721	+	0.903911i	$0.359316\pi$
$758$	8.86863	0.322123
$759$	28.2496	1.02540
$760$	−13.5334	−0.490909
$761$	−16.0878	−0.583184	−0.291592	−	0.956543i	$-0.594185\pi$
$761$	−16.0878	−0.583184	−0.291592	+	0.956543i	$0.594185\pi$
$762$	49.3428	1.78750
$763$	−23.7835	−0.861022
$764$	18.9470	0.685479
$765$	−17.0488	−0.616400
$766$	85.5788	3.09209
$767$	−35.7225	−1.28987
$768$	107.819	3.89058
$769$	31.5671	1.13834	0.569169	−	0.822220i	$-0.307265\pi$
$769$	31.5671	1.13834	0.569169	+	0.822220i	$0.307265\pi$
$770$	−157.782	−5.68605
$771$	63.0595	2.27103
$772$	15.5353	0.559129
$773$	−19.2836	−0.693583	−0.346791	−	0.937942i	$-0.612729\pi$
$773$	−19.2836	−0.693583	−0.346791	+	0.937942i	$0.612729\pi$
$774$	−190.226	−6.83753
$775$	82.7493	2.97244
$776$	−25.1402	−0.902480
$777$	36.0118	1.29192
$778$	−46.9951	−1.68486
$779$	0.407368	0.0145955
$780$	268.646	9.61908
$781$	−5.53369	−0.198011
$782$	1.94884	0.0696904
$783$	−48.0443	−1.71696
$784$	2.96549	0.105910
$785$	35.1977	1.25626
$786$	40.0723	1.42933
$787$	25.5050	0.909155	0.454577	−	0.890707i	$-0.349790\pi$
$787$	25.5050	0.909155	0.454577	+	0.890707i	$0.349790\pi$
$788$	37.8436	1.34812
$789$	−90.3411	−3.21623
$790$	−23.3131	−0.829444
$791$	2.74619	0.0976433
$792$	−249.270	−8.85744
$793$	34.8289	1.23681
$794$	−3.91015	−0.138766
$795$	−177.108	−6.28139
$796$	6.23441	0.220973
$797$	40.3170	1.42810	0.714050	−	0.700095i	$-0.246859\pi$
$797$	40.3170	1.42810	0.714050	+	0.700095i	$0.246859\pi$
$798$	13.2947	0.470626
$799$	4.42279	0.156467
$800$	−30.7576	−1.08744
$801$	−101.850	−3.59868
$802$	31.2426	1.10322
$803$	−70.1595	−2.47588
$804$	174.603	6.15776
$805$	−17.5225	−0.617586
$806$	−77.1288	−2.71675
$807$	7.70059	0.271074
$808$	84.8471	2.98491
$809$	2.58833	0.0910008	0.0455004	−	0.998964i	$-0.485512\pi$
$809$	2.58833	0.0910008	0.0455004	+	0.998964i	$0.485512\pi$
$810$	330.634	11.6173
$811$	−35.6481	−1.25177	−0.625887	−	0.779914i	$-0.715263\pi$
$811$	−35.6481	−1.25177	−0.625887	+	0.779914i	$0.715263\pi$
$812$	−33.1799	−1.16439
$813$	−55.7184	−1.95413
$814$	−54.4798	−1.90952
$815$	14.9543	0.523826
$816$	−9.26166	−0.324223
$817$	−5.50441	−0.192575
$818$	50.4556	1.76414
$819$	−101.548	−3.54838
$820$	12.3124	0.429967
$821$	−26.2735	−0.916952	−0.458476	−	0.888707i	$-0.651604\pi$
$821$	−26.2735	−0.916952	−0.458476	+	0.888707i	$0.651604\pi$
$822$	63.9984	2.23220
$823$	5.73640	0.199958	0.0999792	−	0.994990i	$-0.468122\pi$
$823$	5.73640	0.199958	0.0999792	+	0.994990i	$0.468122\pi$
$824$	77.6654	2.70560
$825$	−226.132	−7.87290
$826$	−53.4310	−1.85910
$827$	43.3519	1.50749	0.753746	−	0.657165i	$-0.228245\pi$
$827$	43.3519	1.50749	0.753746	+	0.657165i	$0.228245\pi$
$828$	−52.4367	−1.82230
$829$	33.2138	1.15356	0.576781	−	0.816899i	$-0.304309\pi$
$829$	33.2138	1.15356	0.576781	+	0.816899i	$0.304309\pi$
$830$	152.522	5.29411
$831$	51.0317	1.77027
$832$	−21.5465	−0.746989
$833$	0.275373	0.00954111
$834$	83.8427	2.90324
$835$	84.6219	2.92846
$836$	−13.6627	−0.472536
$837$	−113.476	−3.92231
$838$	−1.94826	−0.0673014
$839$	−23.3145	−0.804908	−0.402454	−	0.915440i	$-0.631843\pi$
$839$	−23.3145	−0.804908	−0.402454	+	0.915440i	$0.631843\pi$
$840$	212.132	7.31924
$841$	−20.8671	−0.719554
$842$	4.97055	0.171296
$843$	18.8830	0.650365
$844$	113.480	3.90613
$845$	−33.3590	−1.14758
$846$	−175.180	−6.02281
$847$	−53.8850	−1.85151
$848$	−70.1265	−2.40816
$849$	41.9493	1.43970
$850$	−15.6000	−0.535077
$851$	−6.05027	−0.207400
$852$	14.0926	0.482803
$853$	14.7429	0.504789	0.252394	−	0.967624i	$-0.418782\pi$
$853$	14.7429	0.504789	0.252394	+	0.967624i	$0.418782\pi$
$854$	52.0943	1.78263
$855$	19.5400	0.668252
$856$	19.0319	0.650498
$857$	30.3932	1.03821	0.519106	−	0.854710i	$-0.326265\pi$
$857$	30.3932	1.03821	0.519106	+	0.854710i	$0.326265\pi$
$858$	210.773	7.19565
$859$	−18.6872	−0.637601	−0.318800	−	0.947822i	$-0.603280\pi$
$859$	−18.6872	−0.637601	−0.318800	+	0.947822i	$0.603280\pi$
$860$	−166.366	−5.67304
$861$	−6.38535	−0.217612
$862$	−21.7250	−0.739957
$863$	−1.08737	−0.0370147	−0.0185073	−	0.999829i	$-0.505891\pi$
$863$	−1.08737	−0.0370147	−0.0185073	+	0.999829i	$0.505891\pi$
$864$	42.1787	1.43495
$865$	40.4857	1.37655
$866$	76.1691	2.58833
$867$	55.6880	1.89127
$868$	−78.3679	−2.65998
$869$	−12.4252	−0.421497
$870$	−98.4925	−3.33921
$871$	−56.8089	−1.92490
$872$	−48.3744	−1.63817
$873$	36.2981	1.22851
$874$	−2.23360	−0.0755528
$875$	83.1765	2.81188
$876$	178.674	6.03684
$877$	−14.4087	−0.486546	−0.243273	−	0.969958i	$-0.578221\pi$
$877$	−14.4087	−0.486546	−0.243273	+	0.969958i	$0.578221\pi$
$878$	27.5858	0.930975
$879$	72.8154	2.45600
$880$	−125.979	−4.24675
$881$	18.0172	0.607014	0.303507	−	0.952829i	$-0.401842\pi$
$881$	18.0172	0.607014	0.303507	+	0.952829i	$0.401842\pi$
$882$	−10.9071	−0.367262
$883$	9.93478	0.334332	0.167166	−	0.985929i	$-0.446538\pi$
$883$	9.93478	0.334332	0.167166	+	0.985929i	$0.446538\pi$
$884$	9.87753	0.332217
$885$	−107.744	−3.62176
$886$	40.9028	1.37415
$887$	−6.18386	−0.207634	−0.103817	−	0.994596i	$-0.533106\pi$
$887$	−6.18386	−0.207634	−0.103817	+	0.994596i	$0.533106\pi$
$888$	73.2461	2.45798
$889$	−16.3121	−0.547090
$890$	−131.125	−4.39531
$891$	176.219	5.90354
$892$	25.6971	0.860404
$893$	−5.06904	−0.169629
$894$	−12.5893	−0.421048
$895$	84.2474	2.81608
$896$	−45.9785	−1.53604
$897$	23.4074	0.781550
$898$	−26.5801	−0.886989
$899$	19.2092	0.640664
$900$	419.744	13.9915
$901$	−6.51189	−0.216942
$902$	9.65995	0.321641
$903$	86.2796	2.87121
$904$	5.58560	0.185774
$905$	−96.9705	−3.22341
$906$	48.0465	1.59624
$907$	−39.9220	−1.32559	−0.662793	−	0.748802i	$-0.730629\pi$
$907$	−39.9220	−1.32559	−0.662793	+	0.748802i	$0.730629\pi$
$908$	−15.4414	−0.512442
$909$	−122.505	−4.06322
$910$	−130.736	−4.33387
$911$	−14.9110	−0.494025	−0.247012	−	0.969012i	$-0.579449\pi$
$911$	−14.9110	−0.494025	−0.247012	+	0.969012i	$0.579449\pi$
$912$	10.6150	0.351497
$913$	81.2898	2.69030
$914$	−38.6979	−1.28001
$915$	105.048	3.47279
$916$	−107.737	−3.55973
$917$	−13.2474	−0.437468
$918$	21.3927	0.706065
$919$	−31.0823	−1.02531	−0.512655	−	0.858595i	$-0.671338\pi$
$919$	−31.0823	−1.02531	−0.512655	+	0.858595i	$0.671338\pi$
$920$	−35.6398	−1.17501
$921$	−49.6036	−1.63449
$922$	15.4601	0.509152
$923$	−4.58517	−0.150923
$924$	214.159	7.04530
$925$	48.4310	1.59240
$926$	59.2773	1.94797
$927$	−112.136	−3.68301
$928$	−7.13999	−0.234382
$929$	−41.2500	−1.35337	−0.676684	−	0.736273i	$-0.736584\pi$
$929$	−41.2500	−1.35337	−0.676684	+	0.736273i	$0.736584\pi$
$930$	−232.630	−7.62824
$931$	−0.315610	−0.0103437
$932$	2.80015	0.0917220
$933$	18.5988	0.608897
$934$	46.2103	1.51205
$935$	−11.6983	−0.382575
$936$	−206.543	−6.75108
$937$	−8.76986	−0.286499	−0.143249	−	0.989687i	$-0.545755\pi$
$937$	−8.76986	−0.286499	−0.143249	+	0.989687i	$0.545755\pi$
$938$	−84.9703	−2.77438
$939$	28.3066	0.923750
$940$	−153.208	−4.99708
$941$	−35.8810	−1.16969	−0.584844	−	0.811146i	$-0.698844\pi$
$941$	−35.8810	−1.16969	−0.584844	+	0.811146i	$0.698844\pi$
$942$	−70.3271	−2.29138
$943$	1.07279	0.0349348
$944$	−42.6614	−1.38851
$945$	−192.347	−6.25704
$946$	−130.527	−4.24378
$947$	43.4826	1.41299	0.706497	−	0.707716i	$-0.250274\pi$
$947$	43.4826	1.41299	0.706497	+	0.707716i	$0.250274\pi$
$948$	31.6431	1.02772
$949$	−58.1336	−1.88709
$950$	17.8795	0.580088
$951$	25.4216	0.824352
$952$	7.79961	0.252787
$953$	−30.7698	−0.996730	−0.498365	−	0.866967i	$-0.666066\pi$
$953$	−30.7698	−0.996730	−0.498365	+	0.866967i	$0.666066\pi$
$954$	257.926	8.35067
$955$	−18.5933	−0.601664
$956$	−75.9298	−2.45575
$957$	−52.4937	−1.69688
$958$	5.83517	0.188526
$959$	−21.1571	−0.683198
$960$	−64.9869	−2.09744
$961$	14.3704	0.463561
$962$	−45.1415	−1.45542
$963$	−27.4788	−0.885493
$964$	0.523768	0.0168694
$965$	−15.2453	−0.490763
$966$	35.0109	1.12646
$967$	19.9740	0.642319	0.321159	−	0.947025i	$-0.395927\pi$
$967$	19.9740	0.642319	0.321159	+	0.947025i	$0.395927\pi$
$968$	−109.599	−3.52265
$969$	0.985697	0.0316651
$970$	46.7314	1.50046
$971$	−52.9981	−1.70079	−0.850395	−	0.526145i	$-0.823637\pi$
$971$	−52.9981	−1.70079	−0.850395	+	0.526145i	$0.823637\pi$
$972$	−234.651	−7.52644
$973$	−27.7174	−0.888578
$974$	−21.7859	−0.698067
$975$	−187.371	−6.00067
$976$	41.5941	1.33140
$977$	−60.3597	−1.93108	−0.965539	−	0.260259i	$-0.916192\pi$
$977$	−60.3597	−1.93108	−0.965539	+	0.260259i	$0.916192\pi$
$978$	−29.8796	−0.955443
$979$	−69.8858	−2.23356
$980$	−9.53906	−0.304714
$981$	69.8444	2.22996
$982$	66.4637	2.12094
$983$	38.2268	1.21925	0.609623	−	0.792692i	$-0.291321\pi$
$983$	38.2268	1.21925	0.609623	+	0.792692i	$0.291321\pi$
$984$	−12.9875	−0.414025
$985$	−37.1371	−1.18329
$986$	−3.62135	−0.115327
$987$	79.4554	2.52909
$988$	−11.3208	−0.360164
$989$	−14.4956	−0.460935
$990$	463.352	14.7263
$991$	−0.385132	−0.0122341	−0.00611706	−	0.999981i	$-0.501947\pi$
$991$	−0.385132	−0.0122341	−0.00611706	+	0.999981i	$0.501947\pi$
$992$	−16.8640	−0.535432
$993$	52.3500	1.66128
$994$	−6.85813	−0.217527
$995$	−6.11801	−0.193954
$996$	−207.020	−6.55966
$997$	12.4811	0.395280	0.197640	−	0.980275i	$-0.436672\pi$
$997$	12.4811	0.395280	0.197640	+	0.980275i	$0.436672\pi$
$998$	−85.3176	−2.70068
$999$	−66.4147	−2.10127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.15	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.15	✓	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)

\(f(q)\)	\(=\)	\(q-2.49733 q^{2} -3.32636 q^{3} +4.23663 q^{4} -4.15753 q^{5} +8.30700 q^{6} -2.74619 q^{7} -5.58560 q^{8} +8.06465 q^{9} +O(q^{10})\)	\(q-2.49733 q^{2} -3.32636 q^{3} +4.23663 q^{4} -4.15753 q^{5} +8.30700 q^{6} -2.74619 q^{7} -5.58560 q^{8} +8.06465 q^{9} +10.3827 q^{10} +5.53369 q^{11} -14.0926 q^{12} +4.58517 q^{13} +6.85813 q^{14} +13.8294 q^{15} +5.47580 q^{16} +0.508478 q^{17} -20.1401 q^{18} -0.582777 q^{19} -17.6139 q^{20} +9.13481 q^{21} -13.8194 q^{22} -1.53472 q^{23} +18.5797 q^{24} +12.2851 q^{25} -11.4507 q^{26} -16.8468 q^{27} -11.6346 q^{28} +2.85183 q^{29} -34.5366 q^{30} +6.73575 q^{31} -2.50365 q^{32} -18.4070 q^{33} -1.26984 q^{34} +11.4174 q^{35} +34.1670 q^{36} +3.94226 q^{37} +1.45538 q^{38} -15.2519 q^{39} +23.2223 q^{40} -0.699012 q^{41} -22.8126 q^{42} +9.44515 q^{43} +23.4442 q^{44} -33.5291 q^{45} +3.83269 q^{46} +8.69809 q^{47} -18.2145 q^{48} +0.541563 q^{49} -30.6798 q^{50} -1.69138 q^{51} +19.4257 q^{52} -12.8066 q^{53} +42.0721 q^{54} -23.0065 q^{55} +15.3391 q^{56} +1.93852 q^{57} -7.12195 q^{58} -7.79089 q^{59} +58.5903 q^{60} +7.59599 q^{61} -16.8214 q^{62} -22.1471 q^{63} -4.69917 q^{64} -19.0630 q^{65} +45.9683 q^{66} -12.3897 q^{67} +2.15424 q^{68} +5.10502 q^{69} -28.5129 q^{70} -1.00000 q^{71} -45.0460 q^{72} -12.6786 q^{73} -9.84511 q^{74} -40.8646 q^{75} -2.46901 q^{76} -15.1966 q^{77} +38.0890 q^{78} -2.24538 q^{79} -22.7658 q^{80} +31.8447 q^{81} +1.74566 q^{82} +14.6900 q^{83} +38.7009 q^{84} -2.11401 q^{85} -23.5876 q^{86} -9.48621 q^{87} -30.9090 q^{88} -12.6291 q^{89} +83.7330 q^{90} -12.5917 q^{91} -6.50204 q^{92} -22.4055 q^{93} -21.7220 q^{94} +2.42291 q^{95} +8.32804 q^{96} +4.50089 q^{97} -1.35246 q^{98} +44.6273 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 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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