LMFDB - Embedded newform 8023.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.47898 q^{2} -2.90151 q^{3} +4.14536 q^{4} +3.57893 q^{5} +7.19280 q^{6} -1.12807 q^{7} -5.31832 q^{8} +5.41877 q^{9} +O(q^{10})$	\(q-2.47898 q^{2} -2.90151 q^{3} +4.14536 q^{4} +3.57893 q^{5} +7.19280 q^{6} -1.12807 q^{7} -5.31832 q^{8} +5.41877 q^{9} -8.87212 q^{10} +0.204988 q^{11} -12.0278 q^{12} +1.55947 q^{13} +2.79647 q^{14} -10.3843 q^{15} +4.89331 q^{16} +7.24763 q^{17} -13.4330 q^{18} -5.70230 q^{19} +14.8360 q^{20} +3.27311 q^{21} -0.508163 q^{22} -0.771205 q^{23} +15.4312 q^{24} +7.80877 q^{25} -3.86590 q^{26} -7.01808 q^{27} -4.67627 q^{28} -0.395684 q^{29} +25.7426 q^{30} +5.52002 q^{31} -1.49379 q^{32} -0.594776 q^{33} -17.9668 q^{34} -4.03730 q^{35} +22.4628 q^{36} +8.17853 q^{37} +14.1359 q^{38} -4.52481 q^{39} -19.0339 q^{40} -7.30912 q^{41} -8.11400 q^{42} -2.91328 q^{43} +0.849752 q^{44} +19.3934 q^{45} +1.91181 q^{46} -4.45058 q^{47} -14.1980 q^{48} -5.72745 q^{49} -19.3578 q^{50} -21.0291 q^{51} +6.46456 q^{52} -8.40259 q^{53} +17.3977 q^{54} +0.733640 q^{55} +5.99945 q^{56} +16.5453 q^{57} +0.980894 q^{58} +1.06870 q^{59} -43.0468 q^{60} +7.75435 q^{61} -13.6840 q^{62} -6.11276 q^{63} -6.08353 q^{64} +5.58123 q^{65} +1.47444 q^{66} +14.5015 q^{67} +30.0441 q^{68} +2.23766 q^{69} +10.0084 q^{70} -1.00000 q^{71} -28.8187 q^{72} -6.67040 q^{73} -20.2745 q^{74} -22.6572 q^{75} -23.6381 q^{76} -0.231242 q^{77} +11.2169 q^{78} +2.86324 q^{79} +17.5128 q^{80} +4.10675 q^{81} +18.1192 q^{82} -7.60282 q^{83} +13.5682 q^{84} +25.9388 q^{85} +7.22197 q^{86} +1.14808 q^{87} -1.09019 q^{88} +5.95285 q^{89} -48.0760 q^{90} -1.75919 q^{91} -3.19693 q^{92} -16.0164 q^{93} +11.0329 q^{94} -20.4081 q^{95} +4.33425 q^{96} +2.19926 q^{97} +14.1983 q^{98} +1.11079 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	−2.47898	−1.75291	−0.876453	−	0.481487i	$-0.840097\pi$
$2$	−2.47898	−1.75291	−0.876453	+	0.481487i	$0.840097\pi$
$3$	−2.90151	−1.67519	−0.837594	−	0.546293i	$-0.816039\pi$
$3$	−2.90151	−1.67519	−0.837594	+	0.546293i	$0.816039\pi$
$4$	4.14536	2.07268
$5$	3.57893	1.60055	0.800274	−	0.599635i	$-0.204687\pi$
$5$	3.57893	1.60055	0.800274	+	0.599635i	$0.204687\pi$
$6$	7.19280	2.93645
$7$	−1.12807	−0.426371	−0.213186	−	0.977012i	$-0.568384\pi$
$7$	−1.12807	−0.426371	−0.213186	+	0.977012i	$0.568384\pi$
$8$	−5.31832	−1.88031
$9$	5.41877	1.80626
$10$	−8.87212	−2.80561
$11$	0.204988	0.0618064	0.0309032	−	0.999522i	$-0.490162\pi$
$11$	0.204988	0.0618064	0.0309032	+	0.999522i	$0.490162\pi$
$12$	−12.0278	−3.47213
$13$	1.55947	0.432519	0.216259	−	0.976336i	$-0.430614\pi$
$13$	1.55947	0.432519	0.216259	+	0.976336i	$0.430614\pi$
$14$	2.79647	0.747389
$15$	−10.3843	−2.68122
$16$	4.89331	1.22333
$17$	7.24763	1.75781	0.878904	−	0.476998i	$-0.158275\pi$
$17$	7.24763	1.75781	0.878904	+	0.476998i	$0.158275\pi$
$18$	−13.4330	−3.16620
$19$	−5.70230	−1.30820	−0.654098	−	0.756409i	$-0.726952\pi$
$19$	−5.70230	−1.30820	−0.654098	+	0.756409i	$0.726952\pi$
$20$	14.8360	3.31743
$21$	3.27311	0.714252
$22$	−0.508163	−0.108341
$23$	−0.771205	−0.160807	−0.0804037	−	0.996762i	$-0.525621\pi$
$23$	−0.771205	−0.160807	−0.0804037	+	0.996762i	$0.525621\pi$
$24$	15.4312	3.14987
$25$	7.80877	1.56175
$26$	−3.86590	−0.758165
$27$	−7.01808	−1.35063
$28$	−4.67627	−0.883732
$29$	−0.395684	−0.0734767	−0.0367383	−	0.999325i	$-0.511697\pi$
$29$	−0.395684	−0.0734767	−0.0367383	+	0.999325i	$0.511697\pi$
$30$	25.7426	4.69993
$31$	5.52002	0.991425	0.495713	−	0.868487i	$-0.334907\pi$
$31$	5.52002	0.991425	0.495713	+	0.868487i	$0.334907\pi$
$32$	−1.49379	−0.264067
$33$	−0.594776	−0.103537
$34$	−17.9668	−3.08127
$35$	−4.03730	−0.682428
$36$	22.4628	3.74379
$37$	8.17853	1.34454	0.672271	−	0.740305i	$-0.265319\pi$
$37$	8.17853	1.34454	0.672271	+	0.740305i	$0.265319\pi$
$38$	14.1359	2.29315
$39$	−4.52481	−0.724550
$40$	−19.0339	−3.00953
$41$	−7.30912	−1.14149	−0.570746	−	0.821127i	$-0.693346\pi$
$41$	−7.30912	−1.14149	−0.570746	+	0.821127i	$0.693346\pi$
$42$	−8.11400	−1.25202
$43$	−2.91328	−0.444271	−0.222135	−	0.975016i	$-0.571303\pi$
$43$	−2.91328	−0.444271	−0.222135	+	0.975016i	$0.571303\pi$
$44$	0.849752	0.128105
$45$	19.3934	2.89100
$46$	1.91181	0.281880
$47$	−4.45058	−0.649184	−0.324592	−	0.945854i	$-0.605227\pi$
$47$	−4.45058	−0.649184	−0.324592	+	0.945854i	$0.605227\pi$
$48$	−14.1980	−2.04930
$49$	−5.72745	−0.818208
$50$	−19.3578	−2.73761
$51$	−21.0291	−2.94466
$52$	6.46456	0.896473
$53$	−8.40259	−1.15418	−0.577092	−	0.816679i	$-0.695813\pi$
$53$	−8.40259	−1.15418	−0.577092	+	0.816679i	$0.695813\pi$
$54$	17.3977	2.36753
$55$	0.733640	0.0989240
$56$	5.99945	0.801710
$57$	16.5453	2.19148
$58$	0.980894	0.128798
$59$	1.06870	0.139133	0.0695667	−	0.997577i	$-0.477838\pi$
$59$	1.06870	0.139133	0.0695667	+	0.997577i	$0.477838\pi$
$60$	−43.0468	−5.55731
$61$	7.75435	0.992843	0.496422	−	0.868082i	$-0.334647\pi$
$61$	7.75435	0.992843	0.496422	+	0.868082i	$0.334647\pi$
$62$	−13.6840	−1.73788
$63$	−6.11276	−0.770136
$64$	−6.08353	−0.760442
$65$	5.58123	0.692267
$66$	1.47444	0.181491
$67$	14.5015	1.77165	0.885823	−	0.464024i	$-0.153595\pi$
$67$	14.5015	1.77165	0.885823	+	0.464024i	$0.153595\pi$
$68$	30.0441	3.64338
$69$	2.23766	0.269383
$70$	10.0084	1.19623
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−28.8187	−3.39632
$73$	−6.67040	−0.780712	−0.390356	−	0.920664i	$-0.627648\pi$
$73$	−6.67040	−0.780712	−0.390356	+	0.920664i	$0.627648\pi$
$74$	−20.2745	−2.35686
$75$	−22.6572	−2.61623
$76$	−23.6381	−2.71147
$77$	−0.231242	−0.0263524
$78$	11.2169	1.27007
$79$	2.86324	0.322140	0.161070	−	0.986943i	$-0.448506\pi$
$79$	2.86324	0.322140	0.161070	+	0.986943i	$0.448506\pi$
$80$	17.5128	1.95799
$81$	4.10675	0.456305
$82$	18.1192	2.00093
$83$	−7.60282	−0.834518	−0.417259	−	0.908788i	$-0.637009\pi$
$83$	−7.60282	−0.834518	−0.417259	+	0.908788i	$0.637009\pi$
$84$	13.5682	1.48042
$85$	25.9388	2.81346
$86$	7.22197	0.778765
$87$	1.14808	0.123087
$88$	−1.09019	−0.116215
$89$	5.95285	0.631001	0.315500	−	0.948925i	$-0.397828\pi$
$89$	5.95285	0.631001	0.315500	+	0.948925i	$0.397828\pi$
$90$	−48.0760	−5.06765
$91$	−1.75919	−0.184413
$92$	−3.19693	−0.333303
$93$	−16.0164	−1.66082
$94$	11.0329	1.13796
$95$	−20.4081	−2.09383
$96$	4.33425	0.442362
$97$	2.19926	0.223301	0.111651	−	0.993748i	$-0.464386\pi$
$97$	2.19926	0.223301	0.111651	+	0.993748i	$0.464386\pi$
$98$	14.1983	1.43424
$99$	1.11079	0.111638
$100$	32.3702	3.23702
$101$	−2.47526	−0.246298	−0.123149	−	0.992388i	$-0.539299\pi$
$101$	−2.47526	−0.246298	−0.123149	+	0.992388i	$0.539299\pi$
$102$	52.1308	5.16171
$103$	−3.53296	−0.348113	−0.174056	−	0.984736i	$-0.555687\pi$
$103$	−3.53296	−0.348113	−0.174056	+	0.984736i	$0.555687\pi$
$104$	−8.29375	−0.813269
$105$	11.7143	1.14319
$106$	20.8299	2.02318
$107$	13.8473	1.33867	0.669336	−	0.742960i	$-0.266579\pi$
$107$	13.8473	1.33867	0.669336	+	0.742960i	$0.266579\pi$
$108$	−29.0925	−2.79943
$109$	12.4444	1.19196	0.595979	−	0.803000i	$-0.296764\pi$
$109$	12.4444	1.19196	0.595979	+	0.803000i	$0.296764\pi$
$110$	−1.81868	−0.173405
$111$	−23.7301	−2.25236
$112$	−5.52000	−0.521591
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−41.0155	−3.84145
$115$	−2.76009	−0.257380
$116$	−1.64025	−0.152294
$117$	8.45040	0.781239
$118$	−2.64930	−0.243888
$119$	−8.17585	−0.749479
$120$	55.2271	5.04152
$121$	−10.9580	−0.996180
$122$	−19.2229	−1.74036
$123$	21.2075	1.91221
$124$	22.8825	2.05491
$125$	10.0524	0.899114
$126$	15.1534	1.34998
$127$	16.2523	1.44216	0.721078	−	0.692854i	$-0.243647\pi$
$127$	16.2523	1.44216	0.721078	+	0.692854i	$0.243647\pi$
$128$	18.0686	1.59705
$129$	8.45291	0.744237
$130$	−13.8358	−1.21348
$131$	3.44792	0.301246	0.150623	−	0.988591i	$-0.451872\pi$
$131$	3.44792	0.301246	0.150623	+	0.988591i	$0.451872\pi$
$132$	−2.46556	−0.214600
$133$	6.43260	0.557777
$134$	−35.9491	−3.10553
$135$	−25.1173	−2.16175
$136$	−38.5452	−3.30523
$137$	5.93433	0.507004	0.253502	−	0.967335i	$-0.418418\pi$
$137$	5.93433	0.507004	0.253502	+	0.967335i	$0.418418\pi$
$138$	−5.54713	−0.472203
$139$	10.3786	0.880300	0.440150	−	0.897924i	$-0.354925\pi$
$139$	10.3786	0.880300	0.440150	+	0.897924i	$0.354925\pi$
$140$	−16.7361	−1.41445
$141$	12.9134	1.08751
$142$	2.47898	0.208032
$143$	0.319673	0.0267324
$144$	26.5157	2.20964
$145$	−1.41613	−0.117603
$146$	16.5358	1.36851
$147$	16.6183	1.37065
$148$	33.9030	2.78681
$149$	5.89093	0.482604	0.241302	−	0.970450i	$-0.422426\pi$
$149$	5.89093	0.482604	0.241302	+	0.970450i	$0.422426\pi$
$150$	56.1669	4.58601
$151$	−0.169937	−0.0138293	−0.00691464	−	0.999976i	$-0.502201\pi$
$151$	−0.169937	−0.0138293	−0.00691464	+	0.999976i	$0.502201\pi$
$152$	30.3266	2.45982
$153$	39.2732	3.17505
$154$	0.573245	0.0461934
$155$	19.7558	1.58682
$156$	−18.7570	−1.50176
$157$	13.5559	1.08188	0.540938	−	0.841062i	$-0.318069\pi$
$157$	13.5559	1.08188	0.540938	+	0.841062i	$0.318069\pi$
$158$	−7.09793	−0.564681
$159$	24.3802	1.93348
$160$	−5.34617	−0.422652
$161$	0.869975	0.0685637
$162$	−10.1806	−0.799860
$163$	2.49238	0.195219	0.0976093	−	0.995225i	$-0.468880\pi$
$163$	2.49238	0.195219	0.0976093	+	0.995225i	$0.468880\pi$
$164$	−30.2989	−2.36595
$165$	−2.12867	−0.165716
$166$	18.8473	1.46283
$167$	17.0022	1.31567	0.657835	−	0.753162i	$-0.271472\pi$
$167$	17.0022	1.31567	0.657835	+	0.753162i	$0.271472\pi$
$168$	−17.4075	−1.34302
$169$	−10.5681	−0.812928
$170$	−64.3019	−4.93173
$171$	−30.8994	−2.36294
$172$	−12.0766	−0.920831
$173$	20.7277	1.57590	0.787948	−	0.615741i	$-0.211143\pi$
$173$	20.7277	1.57590	0.787948	+	0.615741i	$0.211143\pi$
$174$	−2.84608	−0.215760
$175$	−8.80885	−0.665887
$176$	1.00307	0.0756094
$177$	−3.10086	−0.233075
$178$	−14.7570	−1.10609
$179$	−1.31084	−0.0979771	−0.0489885	−	0.998799i	$-0.515600\pi$
$179$	−1.31084	−0.0979771	−0.0489885	+	0.998799i	$0.515600\pi$
$180$	80.3927	5.99212
$181$	−11.9803	−0.890490	−0.445245	−	0.895409i	$-0.646883\pi$
$181$	−11.9803	−0.890490	−0.445245	+	0.895409i	$0.646883\pi$
$182$	4.36101	0.323260
$183$	−22.4993	−1.66320
$184$	4.10152	0.302368
$185$	29.2704	2.15200
$186$	39.7044	2.91127
$187$	1.48568	0.108644
$188$	−18.4493	−1.34555
$189$	7.91691	0.575870
$190$	50.5915	3.67029
$191$	−23.9220	−1.73093	−0.865466	−	0.500967i	$-0.832978\pi$
$191$	−23.9220	−1.73093	−0.865466	+	0.500967i	$0.832978\pi$
$192$	17.6514	1.27388
$193$	17.3203	1.24674	0.623371	−	0.781927i	$-0.285763\pi$
$193$	17.3203	1.24674	0.623371	+	0.781927i	$0.285763\pi$
$194$	−5.45194	−0.391426
$195$	−16.1940	−1.15968
$196$	−23.7424	−1.69588
$197$	22.7460	1.62058	0.810292	−	0.586026i	$-0.199308\pi$
$197$	22.7460	1.62058	0.810292	+	0.586026i	$0.199308\pi$
$198$	−2.75362	−0.195691
$199$	−6.20382	−0.439777	−0.219888	−	0.975525i	$-0.570569\pi$
$199$	−6.20382	−0.439777	−0.219888	+	0.975525i	$0.570569\pi$
$200$	−41.5295	−2.93658
$201$	−42.0764	−2.96784
$202$	6.13614	0.431737
$203$	0.446360	0.0313283
$204$	−87.1732	−6.10334
$205$	−26.1588	−1.82701
$206$	8.75814	0.610209
$207$	−4.17898	−0.290459
$208$	7.63096	0.529112
$209$	−1.16891	−0.0808549
$210$	−29.0395	−2.00391
$211$	−13.6010	−0.936332	−0.468166	−	0.883641i	$-0.655085\pi$
$211$	−13.6010	−0.936332	−0.468166	+	0.883641i	$0.655085\pi$
$212$	−34.8318	−2.39226
$213$	2.90151	0.198808
$214$	−34.3273	−2.34657
$215$	−10.4264	−0.711076
$216$	37.3244	2.53961
$217$	−6.22698	−0.422715
$218$	−30.8495	−2.08939
$219$	19.3543	1.30784
$220$	3.04120	0.205038
$221$	11.3024	0.760285
$222$	58.8266	3.94818
$223$	−6.21746	−0.416352	−0.208176	−	0.978091i	$-0.566753\pi$
$223$	−6.21746	−0.416352	−0.208176	+	0.978091i	$0.566753\pi$
$224$	1.68510	0.112591
$225$	42.3139	2.82093
$226$	−2.47898	−0.164900
$227$	−7.32299	−0.486044	−0.243022	−	0.970021i	$-0.578139\pi$
$227$	−7.32299	−0.486044	−0.243022	+	0.970021i	$0.578139\pi$
$228$	68.5862	4.54223
$229$	0.376556	0.0248835	0.0124418	−	0.999923i	$-0.496040\pi$
$229$	0.376556	0.0248835	0.0124418	+	0.999923i	$0.496040\pi$
$230$	6.84223	0.451163
$231$	0.670951	0.0441453
$232$	2.10437	0.138159
$233$	−19.1099	−1.25193	−0.625966	−	0.779850i	$-0.715295\pi$
$233$	−19.1099	−1.25193	−0.625966	+	0.779850i	$0.715295\pi$
$234$	−20.9484	−1.36944
$235$	−15.9283	−1.03905
$236$	4.43017	0.288379
$237$	−8.30773	−0.539645
$238$	20.2678	1.31377
$239$	2.17505	0.140692	0.0703461	−	0.997523i	$-0.477590\pi$
$239$	2.17505	0.140692	0.0703461	+	0.997523i	$0.477590\pi$
$240$	−50.8136	−3.28001
$241$	22.5984	1.45569	0.727847	−	0.685740i	$-0.240521\pi$
$241$	22.5984	1.45569	0.727847	+	0.685740i	$0.240521\pi$
$242$	27.1647	1.74621
$243$	9.13848	0.586234
$244$	32.1446	2.05785
$245$	−20.4982	−1.30958
$246$	−52.5730	−3.35193
$247$	−8.89255	−0.565819
$248$	−29.3572	−1.86419
$249$	22.0597	1.39798
$250$	−24.9197	−1.57606
$251$	−10.1738	−0.642162	−0.321081	−	0.947052i	$-0.604046\pi$
$251$	−10.1738	−0.642162	−0.321081	+	0.947052i	$0.604046\pi$
$252$	−25.3396	−1.59625
$253$	−0.158088	−0.00993892
$254$	−40.2891	−2.52796
$255$	−75.2617	−4.71307
$256$	−32.6246	−2.03904
$257$	26.5320	1.65502	0.827511	−	0.561449i	$-0.189756\pi$
$257$	26.5320	1.65502	0.827511	+	0.561449i	$0.189756\pi$
$258$	−20.9546	−1.30458
$259$	−9.22598	−0.573274
$260$	23.1362	1.43485
$261$	−2.14412	−0.132718
$262$	−8.54733	−0.528056
$263$	26.9804	1.66368	0.831841	−	0.555014i	$-0.187287\pi$
$263$	26.9804	1.66368	0.831841	+	0.555014i	$0.187287\pi$
$264$	3.16321	0.194682
$265$	−30.0723	−1.84733
$266$	−15.9463	−0.977732
$267$	−17.2723	−1.05705
$268$	60.1142	3.67206
$269$	16.8492	1.02732	0.513658	−	0.857995i	$-0.328290\pi$
$269$	16.8492	1.02732	0.513658	+	0.857995i	$0.328290\pi$
$270$	62.2653	3.78935
$271$	−29.0276	−1.76330	−0.881649	−	0.471905i	$-0.843566\pi$
$271$	−29.0276	−1.76330	−0.881649	+	0.471905i	$0.843566\pi$
$272$	35.4649	2.15037
$273$	5.10432	0.308927
$274$	−14.7111	−0.888730
$275$	1.60071	0.0965263
$276$	9.27592	0.558345
$277$	−23.4916	−1.41147	−0.705737	−	0.708474i	$-0.749384\pi$
$277$	−23.4916	−1.41147	−0.705737	+	0.708474i	$0.749384\pi$
$278$	−25.7283	−1.54308
$279$	29.9117	1.79077
$280$	21.4716	1.28318
$281$	−18.2967	−1.09149	−0.545746	−	0.837951i	$-0.683754\pi$
$281$	−18.2967	−1.09149	−0.545746	+	0.837951i	$0.683754\pi$
$282$	−32.0122	−1.90630
$283$	−15.6932	−0.932863	−0.466432	−	0.884557i	$-0.654461\pi$
$283$	−15.6932	−0.932863	−0.466432	+	0.884557i	$0.654461\pi$
$284$	−4.14536	−0.245982
$285$	59.2145	3.50756
$286$	−0.792464	−0.0468594
$287$	8.24521	0.486699
$288$	−8.09450	−0.476973
$289$	35.5282	2.08989
$290$	3.51056	0.206147
$291$	−6.38119	−0.374072
$292$	−27.6512	−1.61817
$293$	−3.86403	−0.225739	−0.112869	−	0.993610i	$-0.536004\pi$
$293$	−3.86403	−0.225739	−0.112869	+	0.993610i	$0.536004\pi$
$294$	−41.1964	−2.40262
$295$	3.82482	0.222690
$296$	−43.4961	−2.52816
$297$	−1.43863	−0.0834776
$298$	−14.6035	−0.845960
$299$	−1.20267	−0.0695522
$300$	−93.9224	−5.42261
$301$	3.28639	0.189424
$302$	0.421271	0.0242414
$303$	7.18201	0.412595
$304$	−27.9031	−1.60035
$305$	27.7523	1.58909
$306$	−97.3577	−5.56557
$307$	−3.41772	−0.195060	−0.0975298	−	0.995233i	$-0.531094\pi$
$307$	−3.41772	−0.195060	−0.0975298	+	0.995233i	$0.531094\pi$
$308$	−0.958581	−0.0546202
$309$	10.2509	0.583154
$310$	−48.9743	−2.78155
$311$	27.6084	1.56553	0.782766	−	0.622317i	$-0.213808\pi$
$311$	27.6084	1.56553	0.782766	+	0.622317i	$0.213808\pi$
$312$	24.0644	1.36238
$313$	−20.8178	−1.17669	−0.588345	−	0.808610i	$-0.700220\pi$
$313$	−20.8178	−1.17669	−0.588345	+	0.808610i	$0.700220\pi$
$314$	−33.6048	−1.89643
$315$	−21.8772	−1.23264
$316$	11.8692	0.667693
$317$	−8.27996	−0.465049	−0.232524	−	0.972591i	$-0.574699\pi$
$317$	−8.27996	−0.465049	−0.232524	+	0.972591i	$0.574699\pi$
$318$	−60.4381	−3.38920
$319$	−0.0811106	−0.00454132
$320$	−21.7726	−1.21712
$321$	−40.1782	−2.24253
$322$	−2.15666	−0.120186
$323$	−41.3281	−2.29956
$324$	17.0240	0.945775
$325$	12.1775	0.675488
$326$	−6.17858	−0.342200
$327$	−36.1076	−1.99676
$328$	38.8722	2.14636
$329$	5.02058	0.276793
$330$	5.27693	0.290485
$331$	−10.5143	−0.577919	−0.288960	−	0.957341i	$-0.593309\pi$
$331$	−10.5143	−0.577919	−0.288960	+	0.957341i	$0.593309\pi$
$332$	−31.5165	−1.72969
$333$	44.3176	2.42859
$334$	−42.1482	−2.30625
$335$	51.9001	2.83560
$336$	16.0164	0.873764
$337$	−0.489205	−0.0266487	−0.0133243	−	0.999911i	$-0.504241\pi$
$337$	−0.489205	−0.0266487	−0.0133243	+	0.999911i	$0.504241\pi$
$338$	26.1981	1.42499
$339$	−2.90151	−0.157588
$340$	107.526	5.83140
$341$	1.13154	0.0612764
$342$	76.5992	4.14201
$343$	14.3575	0.775231
$344$	15.4937	0.835366
$345$	8.00844	0.431160
$346$	−51.3836	−2.76240
$347$	−9.83271	−0.527848	−0.263924	−	0.964544i	$-0.585017\pi$
$347$	−9.83271	−0.527848	−0.263924	+	0.964544i	$0.585017\pi$
$348$	4.75921	0.255121
$349$	1.06699	0.0571146	0.0285573	−	0.999592i	$-0.490909\pi$
$349$	1.06699	0.0571146	0.0285573	+	0.999592i	$0.490909\pi$
$350$	21.8370	1.16724
$351$	−10.9445	−0.584173
$352$	−0.306210	−0.0163210
$353$	10.1302	0.539178	0.269589	−	0.962975i	$-0.413112\pi$
$353$	10.1302	0.539178	0.269589	+	0.962975i	$0.413112\pi$
$354$	7.68698	0.408558
$355$	−3.57893	−0.189950
$356$	24.6767	1.30786
$357$	23.7223	1.25552
$358$	3.24956	0.171745
$359$	−19.7918	−1.04457	−0.522285	−	0.852771i	$-0.674920\pi$
$359$	−19.7918	−1.04457	−0.522285	+	0.852771i	$0.674920\pi$
$360$	−103.140	−5.43598
$361$	13.5162	0.711379
$362$	29.6990	1.56095
$363$	31.7947	1.66879
$364$	−7.29249	−0.382230
$365$	−23.8729	−1.24957
$366$	55.7755	2.91543
$367$	−19.3877	−1.01203	−0.506016	−	0.862524i	$-0.668882\pi$
$367$	−19.3877	−1.01203	−0.506016	+	0.862524i	$0.668882\pi$
$368$	−3.77374	−0.196720
$369$	−39.6064	−2.06183
$370$	−72.5609	−3.77226
$371$	9.47873	0.492111
$372$	−66.3938	−3.44236
$373$	−15.0471	−0.779110	−0.389555	−	0.921003i	$-0.627371\pi$
$373$	−15.0471	−0.779110	−0.389555	+	0.921003i	$0.627371\pi$
$374$	−3.68298	−0.190442
$375$	−29.1671	−1.50618
$376$	23.6696	1.22067
$377$	−0.617056	−0.0317800
$378$	−19.6259	−1.00945
$379$	−29.1894	−1.49936	−0.749679	−	0.661802i	$-0.769792\pi$
$379$	−29.1894	−1.49936	−0.749679	+	0.661802i	$0.769792\pi$
$380$	−84.5992	−4.33985
$381$	−47.1561	−2.41588
$382$	59.3022	3.03416
$383$	24.1340	1.23319	0.616596	−	0.787280i	$-0.288511\pi$
$383$	24.1340	1.23319	0.616596	+	0.787280i	$0.288511\pi$
$384$	−52.4261	−2.67536
$385$	−0.827599	−0.0421784
$386$	−42.9367	−2.18542
$387$	−15.7864	−0.802466
$388$	9.11674	0.462833
$389$	28.5060	1.44531	0.722657	−	0.691207i	$-0.242921\pi$
$389$	28.5060	1.44531	0.722657	+	0.691207i	$0.242921\pi$
$390$	40.1447	2.03281
$391$	−5.58941	−0.282669
$392$	30.4604	1.53848
$393$	−10.0042	−0.504643
$394$	−56.3870	−2.84073
$395$	10.2473	0.515600
$396$	4.60461	0.231390
$397$	−17.6822	−0.887446	−0.443723	−	0.896164i	$-0.646343\pi$
$397$	−17.6822	−0.887446	−0.443723	+	0.896164i	$0.646343\pi$
$398$	15.3792	0.770888
$399$	−18.6643	−0.934382
$400$	38.2107	1.91053
$401$	−21.3262	−1.06498	−0.532489	−	0.846437i	$-0.678743\pi$
$401$	−21.3262	−1.06498	−0.532489	+	0.846437i	$0.678743\pi$
$402$	104.307	5.20235
$403$	8.60830	0.428810
$404$	−10.2609	−0.510497
$405$	14.6978	0.730338
$406$	−1.10652	−0.0549156
$407$	1.67651	0.0831013
$408$	111.839	5.53688
$409$	15.8761	0.785021	0.392510	−	0.919748i	$-0.371607\pi$
$409$	15.8761	0.785021	0.392510	+	0.919748i	$0.371607\pi$
$410$	64.8474	3.20258
$411$	−17.2185	−0.849327
$412$	−14.6454	−0.721526
$413$	−1.20558	−0.0593225
$414$	10.3596	0.509148
$415$	−27.2100	−1.33569
$416$	−2.32952	−0.114214
$417$	−30.1136	−1.47467
$418$	2.89770	0.141731
$419$	29.1336	1.42327	0.711634	−	0.702551i	$-0.247956\pi$
$419$	29.1336	1.42327	0.711634	+	0.702551i	$0.247956\pi$
$420$	48.5599	2.36948
$421$	4.03312	0.196562	0.0982811	−	0.995159i	$-0.468666\pi$
$421$	4.03312	0.196562	0.0982811	+	0.995159i	$0.468666\pi$
$422$	33.7167	1.64130
$423$	−24.1167	−1.17259
$424$	44.6877	2.17022
$425$	56.5951	2.74526
$426$	−7.19280	−0.348492
$427$	−8.74747	−0.423320
$428$	57.4022	2.77464
$429$	−0.927535	−0.0447818
$430$	25.8469	1.24645
$431$	−10.0478	−0.483983	−0.241992	−	0.970278i	$-0.577801\pi$
$431$	−10.0478	−0.483983	−0.241992	+	0.970278i	$0.577801\pi$
$432$	−34.3416	−1.65226
$433$	19.2049	0.922930	0.461465	−	0.887158i	$-0.347324\pi$
$433$	19.2049	0.922930	0.461465	+	0.887158i	$0.347324\pi$
$434$	15.4366	0.740980
$435$	4.10891	0.197007
$436$	51.5866	2.47055
$437$	4.39764	0.210368
$438$	−47.9789	−2.29252
$439$	18.6438	0.889822	0.444911	−	0.895575i	$-0.353235\pi$
$439$	18.6438	0.889822	0.444911	+	0.895575i	$0.353235\pi$
$440$	−3.90173	−0.186008
$441$	−31.0357	−1.47789
$442$	−28.0186	−1.33271
$443$	−4.95727	−0.235527	−0.117764	−	0.993042i	$-0.537572\pi$
$443$	−4.95727	−0.235527	−0.117764	+	0.993042i	$0.537572\pi$
$444$	−98.3699	−4.66843
$445$	21.3049	1.00995
$446$	15.4130	0.729826
$447$	−17.0926	−0.808452
$448$	6.86266	0.324230
$449$	−3.50154	−0.165248	−0.0826240	−	0.996581i	$-0.526330\pi$
$449$	−3.50154	−0.165248	−0.0826240	+	0.996581i	$0.526330\pi$
$450$	−104.896	−4.94482
$451$	−1.49828	−0.0705515
$452$	4.14536	0.194981
$453$	0.493074	0.0231667
$454$	18.1536	0.851990
$455$	−6.29603	−0.295163
$456$	−87.9931	−4.12065
$457$	6.84695	0.320287	0.160143	−	0.987094i	$-0.448804\pi$
$457$	6.84695	0.320287	0.160143	+	0.987094i	$0.448804\pi$
$458$	−0.933476	−0.0436185
$459$	−50.8645	−2.37415
$460$	−11.4416	−0.533467
$461$	0.129925	0.00605120	0.00302560	−	0.999995i	$-0.499037\pi$
$461$	0.129925	0.00605120	0.00302560	+	0.999995i	$0.499037\pi$
$462$	−1.66328	−0.0773826
$463$	−30.6600	−1.42489	−0.712446	−	0.701727i	$-0.752413\pi$
$463$	−30.6600	−1.42489	−0.712446	+	0.701727i	$0.752413\pi$
$464$	−1.93620	−0.0898860
$465$	−57.3217	−2.65823
$466$	47.3732	2.19452
$467$	30.5692	1.41457	0.707287	−	0.706927i	$-0.249919\pi$
$467$	30.5692	1.41457	0.707287	+	0.706927i	$0.249919\pi$
$468$	35.0300	1.61926
$469$	−16.3588	−0.755379
$470$	39.4861	1.82136
$471$	−39.3325	−1.81235
$472$	−5.68371	−0.261614
$473$	−0.597188	−0.0274587
$474$	20.5947	0.945947
$475$	−44.5279	−2.04308
$476$	−33.8919	−1.55343
$477$	−45.5317	−2.08475
$478$	−5.39191	−0.246620
$479$	25.6368	1.17138	0.585688	−	0.810536i	$-0.300824\pi$
$479$	25.6368	1.17138	0.585688	+	0.810536i	$0.300824\pi$
$480$	15.5120	0.708022
$481$	12.7542	0.581540
$482$	−56.0212	−2.55170
$483$	−2.52424	−0.114857
$484$	−45.4248	−2.06476
$485$	7.87102	0.357405
$486$	−22.6542	−1.02761
$487$	2.02854	0.0919219	0.0459609	−	0.998943i	$-0.485365\pi$
$487$	2.02854	0.0919219	0.0459609	+	0.998943i	$0.485365\pi$
$488$	−41.2401	−1.86685
$489$	−7.23168	−0.327028
$490$	50.8147	2.29557
$491$	−6.81383	−0.307504	−0.153752	−	0.988109i	$-0.549136\pi$
$491$	−6.81383	−0.307504	−0.153752	+	0.988109i	$0.549136\pi$
$492$	87.9127	3.96341
$493$	−2.86777	−0.129158
$494$	22.0445	0.991829
$495$	3.97543	0.178682
$496$	27.0112	1.21284
$497$	1.12807	0.0506010
$498$	−54.6856	−2.45052
$499$	11.6664	0.522260	0.261130	−	0.965304i	$-0.415905\pi$
$499$	11.6664	0.522260	0.261130	+	0.965304i	$0.415905\pi$
$500$	41.6708	1.86358
$501$	−49.3321	−2.20399
$502$	25.2206	1.12565
$503$	28.6419	1.27708	0.638540	−	0.769588i	$-0.279539\pi$
$503$	28.6419	1.27708	0.638540	+	0.769588i	$0.279539\pi$
$504$	32.5096	1.44809
$505$	−8.85881	−0.394212
$506$	0.391898	0.0174220
$507$	30.6633	1.36181
$508$	67.3715	2.98913
$509$	−23.1231	−1.02491	−0.512456	−	0.858713i	$-0.671264\pi$
$509$	−23.1231	−1.02491	−0.512456	+	0.858713i	$0.671264\pi$
$510$	186.573	8.26157
$511$	7.52470	0.332873
$512$	44.7388	1.97719
$513$	40.0192	1.76689
$514$	−65.7725	−2.90110
$515$	−12.6442	−0.557171
$516$	35.0404	1.54257
$517$	−0.912318	−0.0401237
$518$	22.8710	1.00490
$519$	−60.1416	−2.63992
$520$	−29.6828	−1.30168
$521$	24.5083	1.07373	0.536864	−	0.843669i	$-0.319609\pi$
$521$	24.5083	1.07373	0.536864	+	0.843669i	$0.319609\pi$
$522$	5.31524	0.232642
$523$	−17.4157	−0.761535	−0.380767	−	0.924671i	$-0.624340\pi$
$523$	−17.4157	−0.761535	−0.380767	+	0.924671i	$0.624340\pi$
$524$	14.2929	0.624387
$525$	25.5590	1.11549
$526$	−66.8840	−2.91628
$527$	40.0071	1.74274
$528$	−2.91042	−0.126660
$529$	−22.4052	−0.974141
$530$	74.5488	3.23819
$531$	5.79106	0.251311
$532$	26.6655	1.15609
$533$	−11.3983	−0.493717
$534$	42.8177	1.85290
$535$	49.5587	2.14261
$536$	−77.1238	−3.33124
$537$	3.80343	0.164130
$538$	−41.7690	−1.80079
$539$	−1.17406	−0.0505704
$540$	−104.120	−4.48062
$541$	7.33235	0.315242	0.157621	−	0.987500i	$-0.449618\pi$
$541$	7.33235	0.315242	0.157621	+	0.987500i	$0.449618\pi$
$542$	71.9588	3.09090
$543$	34.7610	1.49174
$544$	−10.8264	−0.464179
$545$	44.5377	1.90779
$546$	−12.6535	−0.541521
$547$	0.0435608	0.00186252	0.000931262	−	1.00000i	$-0.499704\pi$
$547$	0.0435608	0.00186252	0.000931262		1.00000i	$0.499704\pi$
$548$	24.5999	1.05086
$549$	42.0190	1.79333
$550$	−3.96813	−0.169202
$551$	2.25631	0.0961219
$552$	−11.9006	−0.506523
$553$	−3.22994	−0.137351
$554$	58.2354	2.47418
$555$	−84.9285	−3.60501
$556$	43.0230	1.82458
$557$	8.87179	0.375910	0.187955	−	0.982178i	$-0.439814\pi$
$557$	8.87179	0.375910	0.187955	+	0.982178i	$0.439814\pi$
$558$	−74.1507	−3.13905
$559$	−4.54316	−0.192155
$560$	−19.7557	−0.834832
$561$	−4.31072	−0.181999
$562$	45.3573	1.91328
$563$	−8.80640	−0.371146	−0.185573	−	0.982631i	$-0.559414\pi$
$563$	−8.80640	−0.371146	−0.185573	+	0.982631i	$0.559414\pi$
$564$	53.5308	2.25405
$565$	3.57893	0.150567
$566$	38.9032	1.63522
$567$	−4.63271	−0.194555
$568$	5.31832	0.223152
$569$	−10.0166	−0.419919	−0.209960	−	0.977710i	$-0.567333\pi$
$569$	−10.0166	−0.419919	−0.209960	+	0.977710i	$0.567333\pi$
$570$	−146.792	−6.14843
$571$	32.0942	1.34310	0.671550	−	0.740960i	$-0.265629\pi$
$571$	32.0942	1.34310	0.671550	+	0.740960i	$0.265629\pi$
$572$	1.32516	0.0554077
$573$	69.4098	2.89964
$574$	−20.4397	−0.853139
$575$	−6.02216	−0.251142
$576$	−32.9653	−1.37355
$577$	2.53406	0.105494	0.0527470	−	0.998608i	$-0.483202\pi$
$577$	2.53406	0.105494	0.0527470	+	0.998608i	$0.483202\pi$
$578$	−88.0737	−3.66338
$579$	−50.2550	−2.08853
$580$	−5.87036	−0.243753
$581$	8.57653	0.355815
$582$	15.8189	0.655713
$583$	−1.72243	−0.0713359
$584$	35.4753	1.46798
$585$	30.2434	1.25041
$586$	9.57886	0.395699
$587$	−45.1654	−1.86417	−0.932087	−	0.362235i	$-0.882014\pi$
$587$	−45.1654	−1.86417	−0.932087	+	0.362235i	$0.882014\pi$
$588$	68.8888	2.84092
$589$	−31.4768	−1.29698
$590$	−9.48167	−0.390354
$591$	−65.9978	−2.71479
$592$	40.0201	1.64481
$593$	−30.4196	−1.24918	−0.624591	−	0.780952i	$-0.714734\pi$
$593$	−30.4196	−1.24918	−0.624591	+	0.780952i	$0.714734\pi$
$594$	3.56633	0.146328
$595$	−29.2608	−1.19958
$596$	24.4200	1.00028
$597$	18.0004	0.736709
$598$	2.98140	0.121919
$599$	13.4347	0.548925	0.274463	−	0.961598i	$-0.411500\pi$
$599$	13.4347	0.548925	0.274463	+	0.961598i	$0.411500\pi$
$600$	120.498	4.91933
$601$	4.55627	0.185854	0.0929270	−	0.995673i	$-0.470378\pi$
$601$	4.55627	0.185854	0.0929270	+	0.995673i	$0.470378\pi$
$602$	−8.14690	−0.332043
$603$	78.5805	3.20005
$604$	−0.704451	−0.0286637
$605$	−39.2179	−1.59443
$606$	−17.8041	−0.723241
$607$	6.64830	0.269846	0.134923	−	0.990856i	$-0.456921\pi$
$607$	6.64830	0.269846	0.134923	+	0.990856i	$0.456921\pi$
$608$	8.51803	0.345452
$609$	−1.29512	−0.0524809
$610$	−68.7976	−2.78553
$611$	−6.94054	−0.280784
$612$	162.802	6.58087
$613$	−31.7864	−1.28384	−0.641921	−	0.766771i	$-0.721862\pi$
$613$	−31.7864	−1.28384	−0.641921	+	0.766771i	$0.721862\pi$
$614$	8.47248	0.341921
$615$	75.9002	3.06059
$616$	1.22982	0.0495508
$617$	2.45449	0.0988141	0.0494071	−	0.998779i	$-0.484267\pi$
$617$	2.45449	0.0988141	0.0494071	+	0.998779i	$0.484267\pi$
$618$	−25.4119	−1.02221
$619$	−22.9664	−0.923096	−0.461548	−	0.887115i	$-0.652706\pi$
$619$	−22.9664	−0.923096	−0.461548	+	0.887115i	$0.652706\pi$
$620$	81.8949	3.28898
$621$	5.41238	0.217192
$622$	−68.4409	−2.74423
$623$	−6.71524	−0.269041
$624$	−22.1413	−0.886362
$625$	−3.06698	−0.122679
$626$	51.6069	2.06263
$627$	3.39159	0.135447
$628$	56.1940	2.24238
$629$	59.2750	2.36345
$630$	54.2332	2.16070
$631$	44.1694	1.75836	0.879179	−	0.476492i	$-0.158092\pi$
$631$	44.1694	1.75836	0.879179	+	0.476492i	$0.158092\pi$
$632$	−15.2276	−0.605723
$633$	39.4635	1.56853
$634$	20.5259	0.815187
$635$	58.1658	2.30824
$636$	101.065	4.00748
$637$	−8.93178	−0.353890
$638$	0.201072	0.00796052
$639$	−5.41877	−0.214363
$640$	64.6662	2.55616
$641$	−12.2138	−0.482417	−0.241209	−	0.970473i	$-0.577544\pi$
$641$	−12.2138	−0.482417	−0.241209	+	0.970473i	$0.577544\pi$
$642$	99.6011	3.93094
$643$	5.09063	0.200755	0.100377	−	0.994949i	$-0.467995\pi$
$643$	5.09063	0.200755	0.100377	+	0.994949i	$0.467995\pi$
$644$	3.60636	0.142111
$645$	30.2524	1.19119
$646$	102.452	4.03091
$647$	−36.6949	−1.44263	−0.721314	−	0.692609i	$-0.756461\pi$
$647$	−36.6949	−1.44263	−0.721314	+	0.692609i	$0.756461\pi$
$648$	−21.8410	−0.857995
$649$	0.219072	0.00859933
$650$	−30.1879	−1.18407
$651$	18.0677	0.708127
$652$	10.3318	0.404626
$653$	31.3755	1.22782	0.613910	−	0.789376i	$-0.289596\pi$
$653$	31.3755	1.22782	0.613910	+	0.789376i	$0.289596\pi$
$654$	89.5102	3.50013
$655$	12.3399	0.482158
$656$	−35.7657	−1.39642
$657$	−36.1454	−1.41017
$658$	−12.4459	−0.485193
$659$	10.0358	0.390938	0.195469	−	0.980710i	$-0.437377\pi$
$659$	10.0358	0.390938	0.195469	+	0.980710i	$0.437377\pi$
$660$	−8.82409	−0.343477
$661$	4.13355	0.160776	0.0803881	−	0.996764i	$-0.474384\pi$
$661$	4.13355	0.160776	0.0803881	+	0.996764i	$0.474384\pi$
$662$	26.0648	1.01304
$663$	−32.7942	−1.27362
$664$	40.4342	1.56915
$665$	23.0219	0.892749
$666$	−109.863	−4.25709
$667$	0.305154	0.0118156
$668$	70.4803	2.72696
$669$	18.0400	0.697468
$670$	−128.659	−4.97055
$671$	1.58955	0.0613640
$672$	−4.88934	−0.188610
$673$	28.1551	1.08530	0.542650	−	0.839959i	$-0.317421\pi$
$673$	28.1551	1.08530	0.542650	+	0.839959i	$0.317421\pi$
$674$	1.21273	0.0467127
$675$	−54.8026	−2.10935
$676$	−43.8084	−1.68494
$677$	27.3670	1.05180	0.525900	−	0.850546i	$-0.323729\pi$
$677$	27.3670	1.05180	0.525900	+	0.850546i	$0.323729\pi$
$678$	7.19280	0.276238
$679$	−2.48093	−0.0952093
$680$	−137.951	−5.29017
$681$	21.2477	0.814215
$682$	−2.80507	−0.107412
$683$	−28.3023	−1.08296	−0.541480	−	0.840714i	$-0.682136\pi$
$683$	−28.3023	−1.08296	−0.541480	+	0.840714i	$0.682136\pi$
$684$	−128.089	−4.89762
$685$	21.2386	0.811484
$686$	−35.5920	−1.35891
$687$	−1.09258	−0.0416846
$688$	−14.2556	−0.543488
$689$	−13.1036	−0.499206
$690$	−19.8528	−0.755783
$691$	17.1051	0.650709	0.325354	−	0.945592i	$-0.394516\pi$
$691$	17.1051	0.650709	0.325354	+	0.945592i	$0.394516\pi$
$692$	85.9238	3.26633
$693$	−1.25305	−0.0475993
$694$	24.3751	0.925267
$695$	37.1443	1.40896
$696$	−6.10586	−0.231442
$697$	−52.9738	−2.00652
$698$	−2.64505	−0.100117
$699$	55.4476	2.09722
$700$	−36.5159	−1.38017
$701$	14.3426	0.541713	0.270856	−	0.962620i	$-0.412693\pi$
$701$	14.3426	0.541713	0.270856	+	0.962620i	$0.412693\pi$
$702$	27.1312	1.02400
$703$	−46.6364	−1.75893
$704$	−1.24705	−0.0470001
$705$	46.2163	1.74061
$706$	−25.1127	−0.945129
$707$	2.79228	0.105014
$708$	−12.8542	−0.483090
$709$	13.5043	0.507166	0.253583	−	0.967314i	$-0.418391\pi$
$709$	13.5043	0.507166	0.253583	+	0.967314i	$0.418391\pi$
$710$	8.87212	0.332965
$711$	15.5152	0.581867
$712$	−31.6592	−1.18648
$713$	−4.25707	−0.159429
$714$	−58.8073	−2.20081
$715$	1.14409	0.0427865
$716$	−5.43392	−0.203075
$717$	−6.31093	−0.235686
$718$	49.0635	1.83103
$719$	−13.1076	−0.488831	−0.244415	−	0.969671i	$-0.578596\pi$
$719$	−13.1076	−0.488831	−0.244415	+	0.969671i	$0.578596\pi$
$720$	94.8979	3.53664
$721$	3.98543	0.148425
$722$	−33.5064	−1.24698
$723$	−65.5696	−2.43856
$724$	−49.6628	−1.84570
$725$	−3.08980	−0.114752
$726$	−78.8186	−2.92523
$727$	5.30787	0.196858	0.0984290	−	0.995144i	$-0.468618\pi$
$727$	5.30787	0.196858	0.0984290	+	0.995144i	$0.468618\pi$
$728$	9.35595	0.346755
$729$	−38.8356	−1.43836
$730$	59.1806	2.19037
$731$	−21.1144	−0.780943
$732$	−93.2679	−3.44728
$733$	18.7748	0.693463	0.346732	−	0.937964i	$-0.387291\pi$
$733$	18.7748	0.693463	0.346732	+	0.937964i	$0.387291\pi$
$734$	48.0619	1.77400
$735$	59.4757	2.19379
$736$	1.15202	0.0424639
$737$	2.97265	0.109499
$738$	98.1837	3.61419
$739$	24.3833	0.896954	0.448477	−	0.893794i	$-0.351967\pi$
$739$	24.3833	0.896954	0.448477	+	0.893794i	$0.351967\pi$
$740$	121.337	4.46042
$741$	25.8018	0.947854
$742$	−23.4976	−0.862624
$743$	47.4862	1.74210	0.871049	−	0.491195i	$-0.163440\pi$
$743$	47.4862	1.74210	0.871049	+	0.491195i	$0.163440\pi$
$744$	85.1804	3.12286
$745$	21.0833	0.772431
$746$	37.3016	1.36571
$747$	−41.1979	−1.50735
$748$	6.15869	0.225184
$749$	−15.6208	−0.570771
$750$	72.3049	2.64020
$751$	48.7757	1.77985	0.889925	−	0.456106i	$-0.150756\pi$
$751$	48.7757	1.77985	0.889925	+	0.456106i	$0.150756\pi$
$752$	−21.7781	−0.794164
$753$	29.5193	1.07574
$754$	1.52967	0.0557074
$755$	−0.608194	−0.0221344
$756$	32.8184	1.19360
$757$	43.4647	1.57975	0.789875	−	0.613268i	$-0.210145\pi$
$757$	43.4647	1.57975	0.789875	+	0.613268i	$0.210145\pi$
$758$	72.3600	2.62823
$759$	0.458695	0.0166496
$760$	108.537	3.93705
$761$	−20.3965	−0.739374	−0.369687	−	0.929156i	$-0.620535\pi$
$761$	−20.3965	−0.739374	−0.369687	+	0.929156i	$0.620535\pi$
$762$	116.899	4.23481
$763$	−14.0382	−0.508217
$764$	−99.1652	−3.58767
$765$	140.556	5.08182
$766$	−59.8279	−2.16167
$767$	1.66661	0.0601778
$768$	94.6607	3.41577
$769$	48.6895	1.75579	0.877893	−	0.478856i	$-0.158948\pi$
$769$	48.6895	1.75579	0.877893	+	0.478856i	$0.158948\pi$
$770$	2.05161	0.0739347
$771$	−76.9830	−2.77248
$772$	71.7988	2.58410
$773$	−36.9528	−1.32910	−0.664551	−	0.747243i	$-0.731377\pi$
$773$	−36.9528	−1.32910	−0.664551	+	0.747243i	$0.731377\pi$
$774$	39.1342	1.40665
$775$	43.1046	1.54836
$776$	−11.6964	−0.419876
$777$	26.7693	0.960342
$778$	−70.6660	−2.53350
$779$	41.6788	1.49330
$780$	−67.1301	−2.40364
$781$	−0.204988	−0.00733506
$782$	13.8561	0.495492
$783$	2.77694	0.0992399
$784$	−28.0262	−1.00094
$785$	48.5156	1.73159
$786$	24.8002	0.884593
$787$	19.3020	0.688043	0.344021	−	0.938962i	$-0.388211\pi$
$787$	19.3020	0.688043	0.344021	+	0.938962i	$0.388211\pi$
$788$	94.2904	3.35896
$789$	−78.2839	−2.78698
$790$	−25.4030	−0.903799
$791$	−1.12807	−0.0401096
$792$	−5.90751	−0.209914
$793$	12.0927	0.429423
$794$	43.8340	1.55561
$795$	87.2551	3.09462
$796$	−25.7171	−0.911517
$797$	15.2447	0.539996	0.269998	−	0.962861i	$-0.412977\pi$
$797$	15.2447	0.539996	0.269998	+	0.962861i	$0.412977\pi$
$798$	46.2684	1.63788
$799$	−32.2562	−1.14114
$800$	−11.6647	−0.412408
$801$	32.2571	1.13975
$802$	52.8672	1.86681
$803$	−1.36736	−0.0482529
$804$	−174.422	−6.15139
$805$	3.11358	0.109739
$806$	−21.3398	−0.751664
$807$	−48.8883	−1.72095
$808$	13.1642	0.463117
$809$	−14.2202	−0.499956	−0.249978	−	0.968251i	$-0.580423\pi$
$809$	−14.2202	−0.499956	−0.249978	+	0.968251i	$0.580423\pi$
$810$	−36.4356	−1.28021
$811$	−5.48191	−0.192496	−0.0962480	−	0.995357i	$-0.530684\pi$
$811$	−5.48191	−0.192496	−0.0962480	+	0.995357i	$0.530684\pi$
$812$	1.85032	0.0649336
$813$	84.2238	2.95386
$814$	−4.15603	−0.145669
$815$	8.92008	0.312457
$816$	−102.902	−3.60228
$817$	16.6124	0.581193
$818$	−39.3565	−1.37607
$819$	−9.53266	−0.333098
$820$	−108.438	−3.78682
$821$	11.2994	0.394351	0.197175	−	0.980368i	$-0.436823\pi$
$821$	11.2994	0.394351	0.197175	+	0.980368i	$0.436823\pi$
$822$	42.6844	1.48879
$823$	−40.1218	−1.39856	−0.699279	−	0.714849i	$-0.746495\pi$
$823$	−40.1218	−1.39856	−0.699279	+	0.714849i	$0.746495\pi$
$824$	18.7894	0.654560
$825$	−4.64447	−0.161700
$826$	2.98860	0.103987
$827$	−55.6372	−1.93470	−0.967348	−	0.253453i	$-0.918434\pi$
$827$	−55.6372	−1.93470	−0.967348	+	0.253453i	$0.918434\pi$
$828$	−17.3234	−0.602030
$829$	−31.9970	−1.11130	−0.555652	−	0.831415i	$-0.687531\pi$
$829$	−31.9970	−1.11130	−0.555652	+	0.831415i	$0.687531\pi$
$830$	67.4532	2.34133
$831$	68.1612	2.36449
$832$	−9.48708	−0.328905
$833$	−41.5105	−1.43825
$834$	74.6511	2.58496
$835$	60.8498	2.10579
$836$	−4.84554	−0.167586
$837$	−38.7400	−1.33905
$838$	−72.2216	−2.49485
$839$	−8.87475	−0.306391	−0.153195	−	0.988196i	$-0.548956\pi$
$839$	−8.87475	−0.306391	−0.153195	+	0.988196i	$0.548956\pi$
$840$	−62.3002	−2.14956
$841$	−28.8434	−0.994601
$842$	−9.99804	−0.344555
$843$	53.0882	1.82846
$844$	−56.3811	−1.94072
$845$	−37.8224	−1.30113
$846$	59.7849	2.05545
$847$	12.3614	0.424742
$848$	−41.1164	−1.41194
$849$	45.5340	1.56272
$850$	−140.298	−4.81219
$851$	−6.30733	−0.216212
$852$	12.0278	0.412066
$853$	−18.4825	−0.632828	−0.316414	−	0.948621i	$-0.602479\pi$
$853$	−18.4825	−0.632828	−0.316414	+	0.948621i	$0.602479\pi$
$854$	21.6848	0.742040
$855$	−110.587	−3.78200
$856$	−73.6445	−2.51712
$857$	13.2219	0.451652	0.225826	−	0.974168i	$-0.427492\pi$
$857$	13.2219	0.451652	0.225826	+	0.974168i	$0.427492\pi$
$858$	2.29934	0.0784983
$859$	−47.4168	−1.61784	−0.808921	−	0.587918i	$-0.799948\pi$
$859$	−47.4168	−1.61784	−0.808921	+	0.587918i	$0.799948\pi$
$860$	−43.2213	−1.47383
$861$	−23.9236	−0.815313
$862$	24.9082	0.848377
$863$	22.7594	0.774738	0.387369	−	0.921925i	$-0.373384\pi$
$863$	22.7594	0.774738	0.387369	+	0.921925i	$0.373384\pi$
$864$	10.4835	0.356657
$865$	74.1830	2.52230
$866$	−47.6087	−1.61781
$867$	−103.085	−3.50096
$868$	−25.8131	−0.876154
$869$	0.586931	0.0199103
$870$	−10.1859	−0.345335
$871$	22.6147	0.766270
$872$	−66.1834	−2.24125
$873$	11.9173	0.403339
$874$	−10.9017	−0.368755
$875$	−11.3398	−0.383356
$876$	80.2304	2.71073
$877$	−37.6250	−1.27051	−0.635254	−	0.772304i	$-0.719104\pi$
$877$	−37.6250	−1.27051	−0.635254	+	0.772304i	$0.719104\pi$
$878$	−46.2178	−1.55978
$879$	11.2115	0.378155
$880$	3.58993	0.121016
$881$	8.84337	0.297941	0.148970	−	0.988842i	$-0.452404\pi$
$881$	8.84337	0.297941	0.148970	+	0.988842i	$0.452404\pi$
$882$	76.9371	2.59061
$883$	−40.3670	−1.35846	−0.679230	−	0.733926i	$-0.737686\pi$
$883$	−40.3670	−1.35846	−0.679230	+	0.733926i	$0.737686\pi$
$884$	46.8528	1.57583
$885$	−11.0978	−0.373047
$886$	12.2890	0.412857
$887$	38.3497	1.28766	0.643828	−	0.765170i	$-0.277345\pi$
$887$	38.3497	1.28766	0.643828	+	0.765170i	$0.277345\pi$
$888$	126.204	4.23514
$889$	−18.3337	−0.614893
$890$	−52.8144	−1.77034
$891$	0.841836	0.0282026
$892$	−25.7736	−0.862964
$893$	25.3785	0.849261
$894$	42.3723	1.41714
$895$	−4.69142	−0.156817
$896$	−20.3826	−0.680936
$897$	3.48956	0.116513
$898$	8.68027	0.289664
$899$	−2.18418	−0.0728466
$900$	175.406	5.84688
$901$	−60.8989	−2.02883
$902$	3.71422	0.123670
$903$	−9.53549	−0.317321
$904$	−5.31832	−0.176885
$905$	−42.8768	−1.42527
$906$	−1.22232	−0.0406090
$907$	12.9572	0.430238	0.215119	−	0.976588i	$-0.430986\pi$
$907$	12.9572	0.430238	0.215119	+	0.976588i	$0.430986\pi$
$908$	−30.3564	−1.00741
$909$	−13.4129	−0.444877
$910$	15.6078	0.517393
$911$	20.1551	0.667770	0.333885	−	0.942614i	$-0.391640\pi$
$911$	20.1551	0.667770	0.333885	+	0.942614i	$0.391640\pi$
$912$	80.9611	2.68089
$913$	−1.55849	−0.0515785
$914$	−16.9735	−0.561433
$915$	−80.5237	−2.66203
$916$	1.56096	0.0515756
$917$	−3.88950	−0.128443
$918$	126.092	4.16166
$919$	29.0964	0.959801	0.479900	−	0.877323i	$-0.340673\pi$
$919$	29.0964	0.959801	0.479900	+	0.877323i	$0.340673\pi$
$920$	14.6791	0.483954
$921$	9.91656	0.326762
$922$	−0.322081	−0.0106072
$923$	−1.55947	−0.0513305
$924$	2.78133	0.0914992
$925$	63.8643	2.09984
$926$	76.0057	2.49770
$927$	−19.1443	−0.628780
$928$	0.591068	0.0194028
$929$	5.09323	0.167103	0.0835517	−	0.996503i	$-0.473374\pi$
$929$	5.09323	0.167103	0.0835517	+	0.996503i	$0.473374\pi$
$930$	142.099	4.65963
$931$	32.6596	1.07038
$932$	−79.2175	−2.59486
$933$	−80.1062	−2.62256
$934$	−75.7805	−2.47961
$935$	5.31715	0.173890
$936$	−44.9419	−1.46897
$937$	21.0401	0.687350	0.343675	−	0.939089i	$-0.388328\pi$
$937$	21.0401	0.687350	0.343675	+	0.939089i	$0.388328\pi$
$938$	40.5532	1.32411
$939$	60.4030	1.97118
$940$	−66.0288	−2.15362
$941$	9.82818	0.320390	0.160195	−	0.987085i	$-0.448788\pi$
$941$	9.82818	0.320390	0.160195	+	0.987085i	$0.448788\pi$
$942$	97.5047	3.17687
$943$	5.63683	0.183560
$944$	5.22950	0.170206
$945$	28.3341	0.921708
$946$	1.48042	0.0481326
$947$	30.9950	1.00720	0.503601	−	0.863936i	$-0.332008\pi$
$947$	30.9950	1.00720	0.503601	+	0.863936i	$0.332008\pi$
$948$	−34.4385	−1.11851
$949$	−10.4023	−0.337672
$950$	110.384	3.58133
$951$	24.0244	0.779044
$952$	43.4818	1.40925
$953$	11.1722	0.361902	0.180951	−	0.983492i	$-0.442082\pi$
$953$	11.1722	0.361902	0.180951	+	0.983492i	$0.442082\pi$
$954$	112.872	3.65438
$955$	−85.6151	−2.77044
$956$	9.01636	0.291610
$957$	0.235343	0.00760757
$958$	−63.5533	−2.05331
$959$	−6.69435	−0.216172
$960$	63.1733	2.03891
$961$	−0.529363	−0.0170762
$962$	−31.6174	−1.01938
$963$	75.0355	2.41798
$964$	93.6787	3.01719
$965$	61.9881	1.99547
$966$	6.25756	0.201334
$967$	50.8964	1.63672	0.818360	−	0.574707i	$-0.194884\pi$
$967$	50.8964	1.63672	0.818360	+	0.574707i	$0.194884\pi$
$968$	58.2780	1.87313
$969$	119.914	3.85220
$970$	−19.5121	−0.626497
$971$	−5.63028	−0.180684	−0.0903422	−	0.995911i	$-0.528796\pi$
$971$	−5.63028	−0.180684	−0.0903422	+	0.995911i	$0.528796\pi$
$972$	37.8823	1.21508
$973$	−11.7078	−0.375335
$974$	−5.02872	−0.161130
$975$	−35.3332	−1.13157
$976$	37.9444	1.21457
$977$	−19.1329	−0.612116	−0.306058	−	0.952013i	$-0.599010\pi$
$977$	−19.1329	−0.612116	−0.306058	+	0.952013i	$0.599010\pi$
$978$	17.9272	0.573249
$979$	1.22027	0.0389999
$980$	−84.9724	−2.71434
$981$	67.4334	2.15298
$982$	16.8914	0.539025
$983$	0.721672	0.0230177	0.0115089	−	0.999934i	$-0.496337\pi$
$983$	0.721672	0.0230177	0.0115089	+	0.999934i	$0.496337\pi$
$984$	−112.788	−3.59556
$985$	81.4064	2.59382
$986$	7.10916	0.226402
$987$	−14.5673	−0.463681
$988$	−36.8629	−1.17276
$989$	2.24673	0.0714420
$990$	−9.85502	−0.313213
$991$	23.2274	0.737843	0.368922	−	0.929461i	$-0.379727\pi$
$991$	23.2274	0.737843	0.368922	+	0.929461i	$0.379727\pi$
$992$	−8.24575	−0.261803
$993$	30.5074	0.968124
$994$	−2.79647	−0.0886987
$995$	−22.2030	−0.703884
$996$	91.4454	2.89756
$997$	20.3738	0.645245	0.322622	−	0.946528i	$-0.395436\pi$
$997$	20.3738	0.645245	0.322622	+	0.946528i	$0.395436\pi$
$998$	−28.9208	−0.915473
$999$	−57.3976	−1.81598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.10	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.10	✓	172	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)

\(f(q)\)	\(=\)	\(q-2.47898 q^{2} -2.90151 q^{3} +4.14536 q^{4} +3.57893 q^{5} +7.19280 q^{6} -1.12807 q^{7} -5.31832 q^{8} +5.41877 q^{9} +O(q^{10})\)	\(q-2.47898 q^{2} -2.90151 q^{3} +4.14536 q^{4} +3.57893 q^{5} +7.19280 q^{6} -1.12807 q^{7} -5.31832 q^{8} +5.41877 q^{9} -8.87212 q^{10} +0.204988 q^{11} -12.0278 q^{12} +1.55947 q^{13} +2.79647 q^{14} -10.3843 q^{15} +4.89331 q^{16} +7.24763 q^{17} -13.4330 q^{18} -5.70230 q^{19} +14.8360 q^{20} +3.27311 q^{21} -0.508163 q^{22} -0.771205 q^{23} +15.4312 q^{24} +7.80877 q^{25} -3.86590 q^{26} -7.01808 q^{27} -4.67627 q^{28} -0.395684 q^{29} +25.7426 q^{30} +5.52002 q^{31} -1.49379 q^{32} -0.594776 q^{33} -17.9668 q^{34} -4.03730 q^{35} +22.4628 q^{36} +8.17853 q^{37} +14.1359 q^{38} -4.52481 q^{39} -19.0339 q^{40} -7.30912 q^{41} -8.11400 q^{42} -2.91328 q^{43} +0.849752 q^{44} +19.3934 q^{45} +1.91181 q^{46} -4.45058 q^{47} -14.1980 q^{48} -5.72745 q^{49} -19.3578 q^{50} -21.0291 q^{51} +6.46456 q^{52} -8.40259 q^{53} +17.3977 q^{54} +0.733640 q^{55} +5.99945 q^{56} +16.5453 q^{57} +0.980894 q^{58} +1.06870 q^{59} -43.0468 q^{60} +7.75435 q^{61} -13.6840 q^{62} -6.11276 q^{63} -6.08353 q^{64} +5.58123 q^{65} +1.47444 q^{66} +14.5015 q^{67} +30.0441 q^{68} +2.23766 q^{69} +10.0084 q^{70} -1.00000 q^{71} -28.8187 q^{72} -6.67040 q^{73} -20.2745 q^{74} -22.6572 q^{75} -23.6381 q^{76} -0.231242 q^{77} +11.2169 q^{78} +2.86324 q^{79} +17.5128 q^{80} +4.10675 q^{81} +18.1192 q^{82} -7.60282 q^{83} +13.5682 q^{84} +25.9388 q^{85} +7.22197 q^{86} +1.14808 q^{87} -1.09019 q^{88} +5.95285 q^{89} -48.0760 q^{90} -1.75919 q^{91} -3.19693 q^{92} -16.0164 q^{93} +11.0329 q^{94} -20.4081 q^{95} +4.33425 q^{96} +2.19926 q^{97} +14.1983 q^{98} +1.11079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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