LMFDB - Embedded newform 8003.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76521 q^{2} +1.30852 q^{3} +5.64636 q^{4} -2.58270 q^{5} -3.61833 q^{6} -0.870652 q^{7} -10.0829 q^{8} -1.28777 q^{9} +O(q^{10})$	\(q-2.76521 q^{2} +1.30852 q^{3} +5.64636 q^{4} -2.58270 q^{5} -3.61833 q^{6} -0.870652 q^{7} -10.0829 q^{8} -1.28777 q^{9} +7.14170 q^{10} -1.36817 q^{11} +7.38839 q^{12} -1.36903 q^{13} +2.40753 q^{14} -3.37952 q^{15} +16.5887 q^{16} +6.73794 q^{17} +3.56095 q^{18} +0.887237 q^{19} -14.5829 q^{20} -1.13927 q^{21} +3.78328 q^{22} -8.40069 q^{23} -13.1938 q^{24} +1.67034 q^{25} +3.78564 q^{26} -5.61064 q^{27} -4.91602 q^{28} -5.53716 q^{29} +9.34506 q^{30} +9.82817 q^{31} -25.7053 q^{32} -1.79029 q^{33} -18.6318 q^{34} +2.24863 q^{35} -7.27122 q^{36} -1.35972 q^{37} -2.45339 q^{38} -1.79140 q^{39} +26.0412 q^{40} -9.71324 q^{41} +3.15031 q^{42} -2.00043 q^{43} -7.72521 q^{44} +3.32593 q^{45} +23.2296 q^{46} +4.14628 q^{47} +21.7067 q^{48} -6.24197 q^{49} -4.61883 q^{50} +8.81674 q^{51} -7.73002 q^{52} -1.00000 q^{53} +15.5146 q^{54} +3.53358 q^{55} +8.77873 q^{56} +1.16097 q^{57} +15.3114 q^{58} -9.95832 q^{59} -19.0820 q^{60} -11.1445 q^{61} -27.1769 q^{62} +1.12120 q^{63} +37.9029 q^{64} +3.53578 q^{65} +4.95051 q^{66} +3.20481 q^{67} +38.0449 q^{68} -10.9925 q^{69} -6.21793 q^{70} +13.5027 q^{71} +12.9845 q^{72} +4.99035 q^{73} +3.75991 q^{74} +2.18567 q^{75} +5.00966 q^{76} +1.19120 q^{77} +4.95359 q^{78} +10.3250 q^{79} -42.8436 q^{80} -3.47833 q^{81} +26.8591 q^{82} +13.0696 q^{83} -6.43271 q^{84} -17.4021 q^{85} +5.53161 q^{86} -7.24550 q^{87} +13.7952 q^{88} +0.764070 q^{89} -9.19687 q^{90} +1.19195 q^{91} -47.4334 q^{92} +12.8604 q^{93} -11.4653 q^{94} -2.29147 q^{95} -33.6359 q^{96} -7.44042 q^{97} +17.2603 q^{98} +1.76190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) $ 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * 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 $

$2$	−2.76521	−1.95530	−0.977648	−	0.210249i	$-0.932573\pi$
$2$	−2.76521	−1.95530	−0.977648	+	0.210249i	$0.932573\pi$
$3$	1.30852	0.755475	0.377738	−	0.925913i	$-0.376702\pi$
$3$	1.30852	0.755475	0.377738	+	0.925913i	$0.376702\pi$
$4$	5.64636	2.82318
$5$	−2.58270	−1.15502	−0.577509	−	0.816384i	$-0.695975\pi$
$5$	−2.58270	−1.15502	−0.577509	+	0.816384i	$0.695975\pi$
$6$	−3.61833	−1.47718
$7$	−0.870652	−0.329075	−0.164538	−	0.986371i	$-0.552613\pi$
$7$	−0.870652	−0.329075	−0.164538	+	0.986371i	$0.552613\pi$
$8$	−10.0829	−3.56486
$9$	−1.28777	−0.429257
$10$	7.14170	2.25840
$11$	−1.36817	−0.412520	−0.206260	−	0.978497i	$-0.566129\pi$
$11$	−1.36817	−0.412520	−0.206260	+	0.978497i	$0.566129\pi$
$12$	7.38839	2.13284
$13$	−1.36903	−0.379700	−0.189850	−	0.981813i	$-0.560800\pi$
$13$	−1.36903	−0.379700	−0.189850	+	0.981813i	$0.560800\pi$
$14$	2.40753	0.643440
$15$	−3.37952	−0.872588
$16$	16.5887	4.14717
$17$	6.73794	1.63419	0.817095	−	0.576503i	$-0.195583\pi$
$17$	6.73794	1.63419	0.817095	+	0.576503i	$0.195583\pi$
$18$	3.56095	0.839324
$19$	0.887237	0.203546	0.101773	−	0.994808i	$-0.467548\pi$
$19$	0.887237	0.203546	0.101773	+	0.994808i	$0.467548\pi$
$20$	−14.5829	−3.26083
$21$	−1.13927	−0.248608
$22$	3.78328	0.806599
$23$	−8.40069	−1.75167	−0.875833	−	0.482615i	$-0.839687\pi$
$23$	−8.40069	−1.75167	−0.875833	+	0.482615i	$0.839687\pi$
$24$	−13.1938	−2.69316
$25$	1.67034	0.334067
$26$	3.78564	0.742425
$27$	−5.61064	−1.07977
$28$	−4.91602	−0.929040
$29$	−5.53716	−1.02823	−0.514113	−	0.857723i	$-0.671879\pi$
$29$	−5.53716	−1.02823	−0.514113	+	0.857723i	$0.671879\pi$
$30$	9.34506	1.70617
$31$	9.82817	1.76519	0.882596	−	0.470132i	$-0.155794\pi$
$31$	9.82817	1.76519	0.882596	+	0.470132i	$0.155794\pi$
$32$	−25.7053	−4.54409
$33$	−1.79029	−0.311649
$34$	−18.6318	−3.19533
$35$	2.24863	0.380088
$36$	−7.27122	−1.21187
$37$	−1.35972	−0.223537	−0.111768	−	0.993734i	$-0.535651\pi$
$37$	−1.35972	−0.223537	−0.111768	+	0.993734i	$0.535651\pi$
$38$	−2.45339	−0.397993
$39$	−1.79140	−0.286854
$40$	26.0412	4.11748
$41$	−9.71324	−1.51695	−0.758476	−	0.651701i	$-0.774056\pi$
$41$	−9.71324	−1.51695	−0.758476	+	0.651701i	$0.774056\pi$
$42$	3.15031	0.486103
$43$	−2.00043	−0.305063	−0.152532	−	0.988299i	$-0.548743\pi$
$43$	−2.00043	−0.305063	−0.152532	+	0.988299i	$0.548743\pi$
$44$	−7.72521	−1.16462
$45$	3.32593	0.495800
$46$	23.2296	3.42502
$47$	4.14628	0.604797	0.302398	−	0.953182i	$-0.402213\pi$
$47$	4.14628	0.604797	0.302398	+	0.953182i	$0.402213\pi$
$48$	21.7067	3.13309
$49$	−6.24197	−0.891709
$50$	−4.61883	−0.653201
$51$	8.81674	1.23459
$52$	−7.73002	−1.07196
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	15.5146	2.11127
$55$	3.53358	0.476468
$56$	8.77873	1.17311
$57$	1.16097	0.153774
$58$	15.3114	2.01048
$59$	−9.95832	−1.29646	−0.648232	−	0.761443i	$-0.724491\pi$
$59$	−9.95832	−1.29646	−0.648232	+	0.761443i	$0.724491\pi$
$60$	−19.0820	−2.46347
$61$	−11.1445	−1.42690	−0.713452	−	0.700704i	$-0.752869\pi$
$61$	−11.1445	−1.42690	−0.713452	+	0.700704i	$0.752869\pi$
$62$	−27.1769	−3.45147
$63$	1.12120	0.141258
$64$	37.9029	4.73787
$65$	3.53578	0.438560
$66$	4.95051	0.609366
$67$	3.20481	0.391530	0.195765	−	0.980651i	$-0.437281\pi$
$67$	3.20481	0.391530	0.195765	+	0.980651i	$0.437281\pi$
$68$	38.0449	4.61362
$69$	−10.9925	−1.32334
$70$	−6.21793	−0.743185
$71$	13.5027	1.60248	0.801238	−	0.598346i	$-0.204175\pi$
$71$	13.5027	1.60248	0.801238	+	0.598346i	$0.204175\pi$
$72$	12.9845	1.53024
$73$	4.99035	0.584076	0.292038	−	0.956407i	$-0.405667\pi$
$73$	4.99035	0.584076	0.292038	+	0.956407i	$0.405667\pi$
$74$	3.75991	0.437080
$75$	2.18567	0.252380
$76$	5.00966	0.574648
$77$	1.19120	0.135750
$78$	4.95359	0.560884
$79$	10.3250	1.16165	0.580827	−	0.814027i	$-0.302729\pi$
$79$	10.3250	1.16165	0.580827	+	0.814027i	$0.302729\pi$
$80$	−42.8436	−4.79006
$81$	−3.47833	−0.386482
$82$	26.8591	2.96609
$83$	13.0696	1.43457	0.717285	−	0.696780i	$-0.245385\pi$
$83$	13.0696	1.43457	0.717285	+	0.696780i	$0.245385\pi$
$84$	−6.43271	−0.701867
$85$	−17.4021	−1.88752
$86$	5.53161	0.596489
$87$	−7.24550	−0.776799
$88$	13.7952	1.47058
$89$	0.764070	0.0809913	0.0404957	−	0.999180i	$-0.487106\pi$
$89$	0.764070	0.0809913	0.0404957	+	0.999180i	$0.487106\pi$
$90$	−9.19687	−0.969435
$91$	1.19195	0.124950
$92$	−47.4334	−4.94527
$93$	12.8604	1.33356
$94$	−11.4653	−1.18256
$95$	−2.29147	−0.235099
$96$	−33.6359	−3.43295
$97$	−7.44042	−0.755460	−0.377730	−	0.925916i	$-0.623295\pi$
$97$	−7.44042	−0.755460	−0.377730	+	0.925916i	$0.623295\pi$
$98$	17.2603	1.74356
$99$	1.76190	0.177077
$100$	9.43133	0.943133
$101$	−15.0436	−1.49689	−0.748446	−	0.663196i	$-0.769199\pi$
$101$	−15.0436	−1.49689	−0.748446	+	0.663196i	$0.769199\pi$
$102$	−24.3801	−2.41399
$103$	9.12994	0.899600	0.449800	−	0.893129i	$-0.351495\pi$
$103$	9.12994	0.899600	0.449800	+	0.893129i	$0.351495\pi$
$104$	13.8038	1.35358
$105$	2.94238	0.287147
$106$	2.76521	0.268581
$107$	0.948839	0.0917277	0.0458639	−	0.998948i	$-0.485396\pi$
$107$	0.948839	0.0917277	0.0458639	+	0.998948i	$0.485396\pi$
$108$	−31.6797	−3.04838
$109$	−17.8479	−1.70952	−0.854760	−	0.519023i	$-0.826296\pi$
$109$	−17.8479	−1.70952	−0.854760	+	0.519023i	$0.826296\pi$
$110$	−9.77109	−0.931637
$111$	−1.77922	−0.168876
$112$	−14.4430	−1.36473
$113$	−13.8273	−1.30077	−0.650383	−	0.759606i	$-0.725392\pi$
$113$	−13.8273	−1.30077	−0.650383	+	0.759606i	$0.725392\pi$
$114$	−3.21032	−0.300674
$115$	21.6965	2.02321
$116$	−31.2648	−2.90287
$117$	1.76299	0.162989
$118$	27.5368	2.53497
$119$	−5.86640	−0.537772
$120$	34.0755	3.11065
$121$	−9.12810	−0.829827
$122$	30.8168	2.79002
$123$	−12.7100	−1.14602
$124$	55.4934	4.98346
$125$	8.59952	0.769164
$126$	−3.10035	−0.276201
$127$	−12.4913	−1.10842	−0.554212	−	0.832376i	$-0.686980\pi$
$127$	−12.4913	−1.10842	−0.554212	+	0.832376i	$0.686980\pi$
$128$	−53.3989	−4.71984
$129$	−2.61761	−0.230468
$130$	−9.77717	−0.857514
$131$	−13.4412	−1.17436	−0.587180	−	0.809456i	$-0.699762\pi$
$131$	−13.4412	−1.17436	−0.587180	+	0.809456i	$0.699762\pi$
$132$	−10.1086	−0.879841
$133$	−0.772474	−0.0669820
$134$	−8.86196	−0.765556
$135$	14.4906	1.24715
$136$	−67.9383	−5.82566
$137$	−14.4835	−1.23741	−0.618703	−	0.785625i	$-0.712342\pi$
$137$	−14.4835	−1.23741	−0.618703	+	0.785625i	$0.712342\pi$
$138$	30.3965	2.58752
$139$	14.0154	1.18877	0.594386	−	0.804180i	$-0.297395\pi$
$139$	14.0154	1.18877	0.594386	+	0.804180i	$0.297395\pi$
$140$	12.6966	1.07306
$141$	5.42550	0.456909
$142$	−37.3377	−3.13331
$143$	1.87307	0.156634
$144$	−21.3624	−1.78020
$145$	14.3008	1.18762
$146$	−13.7993	−1.14204
$147$	−8.16775	−0.673664
$148$	−7.67747	−0.631084
$149$	19.5312	1.60006	0.800029	−	0.599962i	$-0.204818\pi$
$149$	19.5312	1.60006	0.800029	+	0.599962i	$0.204818\pi$
$150$	−6.04383	−0.493477
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−8.94596	−0.725613
$153$	−8.67692	−0.701488
$154$	−3.29392	−0.265432
$155$	−25.3832	−2.03883
$156$	−10.1149	−0.809840
$157$	12.5422	1.00098	0.500488	−	0.865743i	$-0.333154\pi$
$157$	12.5422	1.00098	0.500488	+	0.865743i	$0.333154\pi$
$158$	−28.5508	−2.27138
$159$	−1.30852	−0.103773
$160$	66.3889	5.24851
$161$	7.31408	0.576430
$162$	9.61831	0.755686
$163$	2.55442	0.200077	0.100039	−	0.994984i	$-0.468103\pi$
$163$	2.55442	0.200077	0.100039	+	0.994984i	$0.468103\pi$
$164$	−54.8445	−4.28263
$165$	4.62377	0.359960
$166$	−36.1400	−2.80501
$167$	0.587083	0.0454298	0.0227149	−	0.999742i	$-0.492769\pi$
$167$	0.587083	0.0454298	0.0227149	+	0.999742i	$0.492769\pi$
$168$	11.4872	0.886254
$169$	−11.1258	−0.855828
$170$	48.1203	3.69066
$171$	−1.14256	−0.0873736
$172$	−11.2952	−0.861250
$173$	6.03433	0.458781	0.229391	−	0.973334i	$-0.426327\pi$
$173$	6.03433	0.458781	0.229391	+	0.973334i	$0.426327\pi$
$174$	20.0353	1.51887
$175$	−1.45428	−0.109933
$176$	−22.6962	−1.71079
$177$	−13.0307	−0.979446
$178$	−2.11281	−0.158362
$179$	4.56945	0.341537	0.170769	−	0.985311i	$-0.445375\pi$
$179$	4.56945	0.341537	0.170769	+	0.985311i	$0.445375\pi$
$180$	18.7794	1.39973
$181$	15.6096	1.16025	0.580125	−	0.814527i	$-0.303004\pi$
$181$	15.6096	1.16025	0.580125	+	0.814527i	$0.303004\pi$
$182$	−3.29597	−0.244314
$183$	−14.5828	−1.07799
$184$	84.7037	6.24444
$185$	3.51175	0.258189
$186$	−35.5616	−2.60750
$187$	−9.21868	−0.674137
$188$	23.4114	1.70745
$189$	4.88492	0.355325
$190$	6.33638	0.459689
$191$	−14.7198	−1.06509	−0.532544	−	0.846402i	$-0.678764\pi$
$191$	−14.7198	−1.06509	−0.532544	+	0.846402i	$0.678764\pi$
$192$	49.5968	3.57934
$193$	10.1684	0.731938	0.365969	−	0.930627i	$-0.380738\pi$
$193$	10.1684	0.731938	0.365969	+	0.930627i	$0.380738\pi$
$194$	20.5743	1.47715
$195$	4.62665	0.331321
$196$	−35.2444	−2.51746
$197$	−16.2865	−1.16037	−0.580183	−	0.814486i	$-0.697019\pi$
$197$	−16.2865	−1.16037	−0.580183	+	0.814486i	$0.697019\pi$
$198$	−4.87200	−0.346238
$199$	−1.90904	−0.135328	−0.0676640	−	0.997708i	$-0.521555\pi$
$199$	−1.90904	−0.135328	−0.0676640	+	0.997708i	$0.521555\pi$
$200$	−16.8419	−1.19090
$201$	4.19356	0.295791
$202$	41.5986	2.92686
$203$	4.82094	0.338364
$204$	49.7825	3.48547
$205$	25.0864	1.75211
$206$	−25.2462	−1.75898
$207$	10.8182	0.751914
$208$	−22.7104	−1.57468
$209$	−1.21390	−0.0839669
$210$	−8.13630	−0.561458
$211$	2.76745	0.190519	0.0952597	−	0.995452i	$-0.469632\pi$
$211$	2.76745	0.190519	0.0952597	+	0.995452i	$0.469632\pi$
$212$	−5.64636	−0.387794
$213$	17.6686	1.21063
$214$	−2.62373	−0.179355
$215$	5.16652	0.352354
$216$	56.5718	3.84922
$217$	−8.55692	−0.580881
$218$	49.3532	3.34262
$219$	6.52998	0.441255
$220$	19.9519	1.34516
$221$	−9.22442	−0.620501
$222$	4.91992	0.330203
$223$	6.70188	0.448791	0.224396	−	0.974498i	$-0.427959\pi$
$223$	6.70188	0.448791	0.224396	+	0.974498i	$0.427959\pi$
$224$	22.3803	1.49535
$225$	−2.15101	−0.143401
$226$	38.2354	2.54338
$227$	3.85759	0.256037	0.128019	−	0.991772i	$-0.459138\pi$
$227$	3.85759	0.256037	0.128019	+	0.991772i	$0.459138\pi$
$228$	6.55525	0.434132
$229$	−27.9711	−1.84838	−0.924192	−	0.381929i	$-0.875260\pi$
$229$	−27.9711	−1.84838	−0.924192	+	0.381929i	$0.875260\pi$
$230$	−59.9952	−3.95597
$231$	1.55872	0.102556
$232$	55.8309	3.66548
$233$	4.11746	0.269744	0.134872	−	0.990863i	$-0.456938\pi$
$233$	4.11746	0.269744	0.134872	+	0.990863i	$0.456938\pi$
$234$	−4.87504	−0.318691
$235$	−10.7086	−0.698551
$236$	−56.2283	−3.66015
$237$	13.5105	0.877601
$238$	16.2218	1.05150
$239$	15.5130	1.00346	0.501728	−	0.865026i	$-0.332698\pi$
$239$	15.5130	1.00346	0.501728	+	0.865026i	$0.332698\pi$
$240$	−56.0618	−3.61877
$241$	−13.8534	−0.892373	−0.446186	−	0.894940i	$-0.647218\pi$
$241$	−13.8534	−0.892373	−0.446186	+	0.894940i	$0.647218\pi$
$242$	25.2411	1.62256
$243$	12.2804	0.787791
$244$	−62.9258	−4.02841
$245$	16.1211	1.02994
$246$	35.1457	2.24081
$247$	−1.21465	−0.0772864
$248$	−99.0969	−6.29266
$249$	17.1018	1.08378
$250$	−23.7794	−1.50394
$251$	9.19677	0.580495	0.290248	−	0.956952i	$-0.406262\pi$
$251$	9.19677	0.580495	0.290248	+	0.956952i	$0.406262\pi$
$252$	6.33070	0.398797
$253$	11.4936	0.722597
$254$	34.5410	2.16730
$255$	−22.7710	−1.42597
$256$	71.8531	4.49082
$257$	−4.59812	−0.286823	−0.143411	−	0.989663i	$-0.545807\pi$
$257$	−4.59812	−0.286823	−0.143411	+	0.989663i	$0.545807\pi$
$258$	7.23824	0.450633
$259$	1.18384	0.0735604
$260$	19.9643	1.23813
$261$	7.13060	0.441373
$262$	37.1676	2.29622
$263$	−20.1315	−1.24136	−0.620679	−	0.784065i	$-0.713143\pi$
$263$	−20.1315	−1.24136	−0.620679	+	0.784065i	$0.713143\pi$
$264$	18.0514	1.11098
$265$	2.58270	0.158654
$266$	2.13605	0.130970
$267$	0.999803	0.0611869
$268$	18.0955	1.10536
$269$	−23.2392	−1.41692	−0.708458	−	0.705753i	$-0.750609\pi$
$269$	−23.2392	−1.41692	−0.708458	+	0.705753i	$0.750609\pi$
$270$	−40.0695	−2.43855
$271$	5.21526	0.316805	0.158402	−	0.987375i	$-0.449366\pi$
$271$	5.21526	0.316805	0.158402	+	0.987375i	$0.449366\pi$
$272$	111.774	6.77727
$273$	1.55969	0.0943965
$274$	40.0498	2.41950
$275$	−2.28531	−0.137810
$276$	−62.0676	−3.73603
$277$	−15.5892	−0.936663	−0.468331	−	0.883553i	$-0.655145\pi$
$277$	−15.5892	−0.936663	−0.468331	+	0.883553i	$0.655145\pi$
$278$	−38.7555	−2.32440
$279$	−12.6564	−0.757721
$280$	−22.6728	−1.35496
$281$	17.7271	1.05751	0.528754	−	0.848775i	$-0.322660\pi$
$281$	17.7271	1.05751	0.528754	+	0.848775i	$0.322660\pi$
$282$	−15.0026	−0.893393
$283$	24.9313	1.48201	0.741006	−	0.671499i	$-0.234349\pi$
$283$	24.9313	1.48201	0.741006	+	0.671499i	$0.234349\pi$
$284$	76.2411	4.52408
$285$	−2.99843	−0.177612
$286$	−5.17942	−0.306265
$287$	8.45685	0.499192
$288$	33.1025	1.95058
$289$	28.3998	1.67058
$290$	−39.5447	−2.32215
$291$	−9.73595	−0.570731
$292$	28.1773	1.64895
$293$	16.0157	0.935650	0.467825	−	0.883821i	$-0.345038\pi$
$293$	16.0157	0.935650	0.467825	+	0.883821i	$0.345038\pi$
$294$	22.5855	1.31721
$295$	25.7194	1.49744
$296$	13.7100	0.796877
$297$	7.67634	0.445426
$298$	−54.0077	−3.12858
$299$	11.5008	0.665107
$300$	12.3411	0.712514
$301$	1.74168	0.100389
$302$	−2.76521	−0.159120
$303$	−19.6848	−1.13086
$304$	14.7181	0.844141
$305$	28.7828	1.64810
$306$	23.9935	1.37162
$307$	−7.35235	−0.419621	−0.209810	−	0.977742i	$-0.567285\pi$
$307$	−7.35235	−0.419621	−0.209810	+	0.977742i	$0.567285\pi$
$308$	6.72597	0.383248
$309$	11.9467	0.679625
$310$	70.1898	3.98651
$311$	5.84369	0.331365	0.165683	−	0.986179i	$-0.447017\pi$
$311$	5.84369	0.331365	0.165683	+	0.986179i	$0.447017\pi$
$312$	18.0626	1.02259
$313$	−11.6986	−0.661244	−0.330622	−	0.943763i	$-0.607258\pi$
$313$	−11.6986	−0.661244	−0.330622	+	0.943763i	$0.607258\pi$
$314$	−34.6818	−1.95721
$315$	−2.89572	−0.163155
$316$	58.2988	3.27956
$317$	13.4761	0.756892	0.378446	−	0.925623i	$-0.376459\pi$
$317$	13.4761	0.756892	0.378446	+	0.925623i	$0.376459\pi$
$318$	3.61833	0.202906
$319$	7.57581	0.424164
$320$	−97.8919	−5.47232
$321$	1.24158	0.0692980
$322$	−20.2249	−1.12709
$323$	5.97815	0.332633
$324$	−19.6399	−1.09111
$325$	−2.28674	−0.126845
$326$	−7.06349	−0.391211
$327$	−23.3544	−1.29150
$328$	97.9380	5.40772
$329$	−3.60996	−0.199024
$330$	−12.7857	−0.703829
$331$	12.6596	0.695837	0.347919	−	0.937525i	$-0.386889\pi$
$331$	12.6596	0.695837	0.347919	+	0.937525i	$0.386889\pi$
$332$	73.7954	4.05005
$333$	1.75101	0.0959546
$334$	−1.62340	−0.0888288
$335$	−8.27706	−0.452224
$336$	−18.8989	−1.03102
$337$	−2.57834	−0.140451	−0.0702255	−	0.997531i	$-0.522372\pi$
$337$	−2.57834	−0.140451	−0.0702255	+	0.997531i	$0.522372\pi$
$338$	30.7650	1.67340
$339$	−18.0934	−0.982697
$340$	−98.2584	−5.32881
$341$	−13.4467	−0.728177
$342$	3.15941	0.170841
$343$	11.5291	0.622515
$344$	20.1703	1.08751
$345$	28.3903	1.52848
$346$	−16.6862	−0.897053
$347$	19.8839	1.06742	0.533712	−	0.845666i	$-0.320797\pi$
$347$	19.8839	1.06742	0.533712	+	0.845666i	$0.320797\pi$
$348$	−40.9107	−2.19304
$349$	9.17365	0.491054	0.245527	−	0.969390i	$-0.421039\pi$
$349$	9.17365	0.491054	0.245527	+	0.969390i	$0.421039\pi$
$350$	4.02139	0.214952
$351$	7.68111	0.409988
$352$	35.1693	1.87453
$353$	9.53825	0.507670	0.253835	−	0.967248i	$-0.418308\pi$
$353$	9.53825	0.507670	0.253835	+	0.967248i	$0.418308\pi$
$354$	36.0325	1.91511
$355$	−34.8734	−1.85089
$356$	4.31422	0.228653
$357$	−7.67631	−0.406273
$358$	−12.6355	−0.667806
$359$	21.4229	1.13066	0.565330	−	0.824865i	$-0.308749\pi$
$359$	21.4229	1.13066	0.565330	+	0.824865i	$0.308749\pi$
$360$	−33.5351	−1.76746
$361$	−18.2128	−0.958569
$362$	−43.1637	−2.26863
$363$	−11.9443	−0.626914
$364$	6.73015	0.352756
$365$	−12.8886	−0.674618
$366$	40.3244	2.10779
$367$	27.3120	1.42568	0.712838	−	0.701329i	$-0.247410\pi$
$367$	27.3120	1.42568	0.712838	+	0.701329i	$0.247410\pi$
$368$	−139.356	−7.26446
$369$	12.5084	0.651162
$370$	−9.71071	−0.504836
$371$	0.870652	0.0452020
$372$	72.6144	3.76488
$373$	33.2452	1.72137	0.860686	−	0.509136i	$-0.170035\pi$
$373$	33.2452	1.72137	0.860686	+	0.509136i	$0.170035\pi$
$374$	25.4915	1.31814
$375$	11.2527	0.581085
$376$	−41.8067	−2.15602
$377$	7.58052	0.390417
$378$	−13.5078	−0.694766
$379$	−17.6342	−0.905809	−0.452904	−	0.891559i	$-0.649612\pi$
$379$	−17.6342	−0.905809	−0.452904	+	0.891559i	$0.649612\pi$
$380$	−12.9385	−0.663729
$381$	−16.3451	−0.837387
$382$	40.7033	2.08256
$383$	−22.6558	−1.15766	−0.578829	−	0.815449i	$-0.696490\pi$
$383$	−22.6558	−1.15766	−0.578829	+	0.815449i	$0.696490\pi$
$384$	−69.8736	−3.56572
$385$	−3.07652	−0.156794
$386$	−28.1178	−1.43116
$387$	2.57610	0.130951
$388$	−42.0113	−2.13280
$389$	22.0901	1.12001	0.560006	−	0.828489i	$-0.310799\pi$
$389$	22.0901	1.12001	0.560006	+	0.828489i	$0.310799\pi$
$390$	−12.7936	−0.647831
$391$	−56.6034	−2.86255
$392$	62.9374	3.17882
$393$	−17.5881	−0.887200
$394$	45.0355	2.26886
$395$	−26.6664	−1.34173
$396$	9.94830	0.499921
$397$	30.3661	1.52403	0.762016	−	0.647558i	$-0.224210\pi$
$397$	30.3661	1.52403	0.762016	+	0.647558i	$0.224210\pi$
$398$	5.27888	0.264606
$399$	−1.01080	−0.0506033
$400$	27.7087	1.38544
$401$	26.3611	1.31641	0.658206	−	0.752838i	$-0.271316\pi$
$401$	26.3611	1.31641	0.658206	+	0.752838i	$0.271316\pi$
$402$	−11.5961	−0.578359
$403$	−13.4550	−0.670243
$404$	−84.9415	−4.22600
$405$	8.98349	0.446393
$406$	−13.3309	−0.661601
$407$	1.86033	0.0922134
$408$	−88.8987	−4.40114
$409$	5.34941	0.264511	0.132256	−	0.991216i	$-0.457778\pi$
$409$	5.34941	0.264511	0.132256	+	0.991216i	$0.457778\pi$
$410$	−69.3690	−3.42589
$411$	−18.9519	−0.934830
$412$	51.5510	2.53973
$413$	8.67023	0.426634
$414$	−29.9145	−1.47022
$415$	−33.7547	−1.65695
$416$	35.1912	1.72539
$417$	18.3395	0.898088
$418$	3.35667	0.164180
$419$	5.73842	0.280340	0.140170	−	0.990127i	$-0.455235\pi$
$419$	5.73842	0.280340	0.140170	+	0.990127i	$0.455235\pi$
$420$	16.6138	0.810669
$421$	6.94429	0.338444	0.169222	−	0.985578i	$-0.445874\pi$
$421$	6.94429	0.338444	0.169222	+	0.985578i	$0.445874\pi$
$422$	−7.65258	−0.372522
$423$	−5.33946	−0.259613
$424$	10.0829	0.489671
$425$	11.2546	0.545930
$426$	−48.8572	−2.36714
$427$	9.70296	0.469559
$428$	5.35749	0.258964
$429$	2.45095	0.118333
$430$	−14.2865	−0.688956
$431$	−35.1784	−1.69448	−0.847241	−	0.531209i	$-0.821738\pi$
$431$	−35.1784	−1.69448	−0.847241	+	0.531209i	$0.821738\pi$
$432$	−93.0732	−4.47799
$433$	−1.91625	−0.0920890	−0.0460445	−	0.998939i	$-0.514662\pi$
$433$	−1.91625	−0.0920890	−0.0460445	+	0.998939i	$0.514662\pi$
$434$	23.6616	1.13580
$435$	18.7129	0.897217
$436$	−100.776	−4.82629
$437$	−7.45340	−0.356545
$438$	−18.0567	−0.862784
$439$	−26.8615	−1.28203	−0.641014	−	0.767529i	$-0.721486\pi$
$439$	−26.8615	−1.28203	−0.641014	+	0.767529i	$0.721486\pi$
$440$	−35.6289	−1.69854
$441$	8.03822	0.382772
$442$	25.5074	1.21326
$443$	25.6380	1.21810	0.609048	−	0.793133i	$-0.291552\pi$
$443$	25.6380	1.21810	0.609048	+	0.793133i	$0.291552\pi$
$444$	−10.0461	−0.476769
$445$	−1.97336	−0.0935464
$446$	−18.5321	−0.877519
$447$	25.5570	1.20880
$448$	−33.0003	−1.55912
$449$	−28.3608	−1.33843	−0.669214	−	0.743070i	$-0.733369\pi$
$449$	−28.3608	−1.33843	−0.669214	+	0.743070i	$0.733369\pi$
$450$	5.94799	0.280391
$451$	13.2894	0.625774
$452$	−78.0741	−3.67230
$453$	1.30852	0.0614797
$454$	−10.6670	−0.500628
$455$	−3.07844	−0.144319
$456$	−11.7060	−0.548183
$457$	−9.26310	−0.433309	−0.216655	−	0.976248i	$-0.569515\pi$
$457$	−9.26310	−0.433309	−0.216655	+	0.976248i	$0.569515\pi$
$458$	77.3459	3.61414
$459$	−37.8042	−1.76455
$460$	122.506	5.71188
$461$	2.52915	0.117794	0.0588972	−	0.998264i	$-0.481242\pi$
$461$	2.52915	0.117794	0.0588972	+	0.998264i	$0.481242\pi$
$462$	−4.31017	−0.200527
$463$	13.4133	0.623368	0.311684	−	0.950186i	$-0.399107\pi$
$463$	13.4133	0.623368	0.311684	+	0.950186i	$0.399107\pi$
$464$	−91.8543	−4.26423
$465$	−33.2145	−1.54029
$466$	−11.3856	−0.527429
$467$	8.95977	0.414609	0.207304	−	0.978276i	$-0.433531\pi$
$467$	8.95977	0.414609	0.207304	+	0.978276i	$0.433531\pi$
$468$	9.95449	0.460147
$469$	−2.79027	−0.128843
$470$	29.6115	1.36587
$471$	16.4117	0.756213
$472$	100.409	4.62171
$473$	2.73694	0.125845
$474$	−37.3593	−1.71597
$475$	1.48198	0.0679981
$476$	−33.1238	−1.51823
$477$	1.28777	0.0589630
$478$	−42.8968	−1.96205
$479$	−26.3714	−1.20494	−0.602471	−	0.798141i	$-0.705817\pi$
$479$	−26.3714	−1.20494	−0.602471	+	0.798141i	$0.705817\pi$
$480$	86.8714	3.96512
$481$	1.86149	0.0848767
$482$	38.3074	1.74485
$483$	9.57063	0.435479
$484$	−51.5406	−2.34275
$485$	19.2164	0.872570
$486$	−33.9580	−1.54036
$487$	21.7392	0.985095	0.492548	−	0.870285i	$-0.336066\pi$
$487$	21.7392	0.985095	0.492548	+	0.870285i	$0.336066\pi$
$488$	112.369	5.08671
$489$	3.34251	0.151154
$490$	−44.5782	−2.01384
$491$	−23.5346	−1.06210	−0.531051	−	0.847340i	$-0.678203\pi$
$491$	−23.5346	−1.06210	−0.531051	+	0.847340i	$0.678203\pi$
$492$	−71.7652	−3.23542
$493$	−37.3091	−1.68032
$494$	3.35876	0.151118
$495$	−4.55045	−0.204527
$496$	163.037	7.32056
$497$	−11.7561	−0.527335
$498$	−47.2900	−2.11911
$499$	−8.52970	−0.381842	−0.190921	−	0.981605i	$-0.561147\pi$
$499$	−8.52970	−0.381842	−0.190921	+	0.981605i	$0.561147\pi$
$500$	48.5560	2.17149
$501$	0.768211	0.0343211
$502$	−25.4310	−1.13504
$503$	17.3956	0.775629	0.387815	−	0.921737i	$-0.373230\pi$
$503$	17.3956	0.775629	0.387815	+	0.921737i	$0.373230\pi$
$504$	−11.3050	−0.503565
$505$	38.8530	1.72894
$506$	−31.7822	−1.41289
$507$	−14.5583	−0.646557
$508$	−70.5304	−3.12928
$509$	42.4568	1.88186	0.940931	−	0.338598i	$-0.109953\pi$
$509$	42.4568	1.88186	0.940931	+	0.338598i	$0.109953\pi$
$510$	62.9665	2.78820
$511$	−4.34485	−0.192205
$512$	−91.8908	−4.06104
$513$	−4.97797	−0.219783
$514$	12.7147	0.560823
$515$	−23.5799	−1.03905
$516$	−14.7800	−0.650653
$517$	−5.67283	−0.249491
$518$	−3.27357	−0.143832
$519$	7.89605	0.346598
$520$	−35.6511	−1.56340
$521$	−17.4569	−0.764802	−0.382401	−	0.923997i	$-0.624903\pi$
$521$	−17.4569	−0.764802	−0.382401	+	0.923997i	$0.624903\pi$
$522$	−19.7176	−0.863014
$523$	26.8010	1.17193	0.585964	−	0.810337i	$-0.300716\pi$
$523$	26.8010	1.17193	0.585964	+	0.810337i	$0.300716\pi$
$524$	−75.8937	−3.31543
$525$	−1.90296	−0.0830520
$526$	55.6676	2.42722
$527$	66.2216	2.88466
$528$	−29.6985	−1.29246
$529$	47.5716	2.06833
$530$	−7.14170	−0.310215
$531$	12.8240	0.556516
$532$	−4.36167	−0.189102
$533$	13.2977	0.575986
$534$	−2.76466	−0.119639
$535$	−2.45057	−0.105947
$536$	−32.3139	−1.39575
$537$	5.97923	0.258023
$538$	64.2610	2.77049
$539$	8.54010	0.367848
$540$	81.8192	3.52094
$541$	−7.92219	−0.340602	−0.170301	−	0.985392i	$-0.554474\pi$
$541$	−7.92219	−0.340602	−0.170301	+	0.985392i	$0.554474\pi$
$542$	−14.4213	−0.619447
$543$	20.4255	0.876540
$544$	−173.200	−7.42591
$545$	46.0958	1.97453
$546$	−4.31285	−0.184573
$547$	12.9126	0.552103	0.276051	−	0.961143i	$-0.410974\pi$
$547$	12.9126	0.552103	0.276051	+	0.961143i	$0.410974\pi$
$548$	−81.7789	−3.49342
$549$	14.3515	0.612508
$550$	6.31936	0.269458
$551$	−4.91278	−0.209291
$552$	110.837	4.71752
$553$	−8.98949	−0.382272
$554$	43.1073	1.83145
$555$	4.59520	0.195055
$556$	79.1361	3.35612
$557$	40.2565	1.70572	0.852861	−	0.522138i	$-0.174865\pi$
$557$	40.2565	1.70572	0.852861	+	0.522138i	$0.174865\pi$
$558$	34.9977	1.48157
$559$	2.73865	0.115832
$560$	37.3019	1.57629
$561$	−12.0628	−0.509294
$562$	−49.0190	−2.06774
$563$	−17.5566	−0.739923	−0.369961	−	0.929047i	$-0.620629\pi$
$563$	−17.5566	−0.739923	−0.369961	+	0.929047i	$0.620629\pi$
$564$	30.6343	1.28994
$565$	35.7118	1.50241
$566$	−68.9401	−2.89777
$567$	3.02842	0.127182
$568$	−136.147	−5.71260
$569$	−46.4680	−1.94804	−0.974021	−	0.226458i	$-0.927285\pi$
$569$	−46.4680	−1.94804	−0.974021	+	0.226458i	$0.927285\pi$
$570$	8.29129	0.347284
$571$	13.9275	0.582848	0.291424	−	0.956594i	$-0.405871\pi$
$571$	13.9275	0.582848	0.291424	+	0.956594i	$0.405871\pi$
$572$	10.5760	0.442205
$573$	−19.2612	−0.804648
$574$	−23.3849	−0.976068
$575$	−14.0320	−0.585174
$576$	−48.8103	−2.03376
$577$	5.83135	0.242762	0.121381	−	0.992606i	$-0.461268\pi$
$577$	5.83135	0.242762	0.121381	+	0.992606i	$0.461268\pi$
$578$	−78.5314	−3.26647
$579$	13.3056	0.552961
$580$	80.7477	3.35286
$581$	−11.3790	−0.472082
$582$	26.9219	1.11595
$583$	1.36817	0.0566640
$584$	−50.3174	−2.08215
$585$	−4.55328	−0.188255
$586$	−44.2868	−1.82947
$587$	−35.8149	−1.47824	−0.739120	−	0.673573i	$-0.764759\pi$
$587$	−35.8149	−1.47824	−0.739120	+	0.673573i	$0.764759\pi$
$588$	−46.1181	−1.90188
$589$	8.71992	0.359298
$590$	−71.1193	−2.92794
$591$	−21.3112	−0.876628
$592$	−22.5560	−0.927045
$593$	29.8483	1.22572	0.612862	−	0.790190i	$-0.290018\pi$
$593$	29.8483	1.22572	0.612862	+	0.790190i	$0.290018\pi$
$594$	−21.2267	−0.870940
$595$	15.1511	0.621136
$596$	110.280	4.51725
$597$	−2.49802	−0.102237
$598$	−31.8020	−1.30048
$599$	25.2684	1.03244	0.516219	−	0.856457i	$-0.327339\pi$
$599$	25.2684	1.03244	0.516219	+	0.856457i	$0.327339\pi$
$600$	−22.0380	−0.899698
$601$	−37.5848	−1.53312	−0.766559	−	0.642174i	$-0.778033\pi$
$601$	−37.5848	−1.53312	−0.766559	+	0.642174i	$0.778033\pi$
$602$	−4.81611	−0.196290
$603$	−4.12706	−0.168067
$604$	5.64636	0.229747
$605$	23.5751	0.958466
$606$	54.4326	2.21117
$607$	−8.59207	−0.348741	−0.174371	−	0.984680i	$-0.555789\pi$
$607$	−8.59207	−0.348741	−0.174371	+	0.984680i	$0.555789\pi$
$608$	−22.8066	−0.924932
$609$	6.30831	0.255625
$610$	−79.5905	−3.22252
$611$	−5.67636	−0.229641
$612$	−48.9931	−1.98043
$613$	10.6718	0.431029	0.215514	−	0.976501i	$-0.430857\pi$
$613$	10.6718	0.431029	0.215514	+	0.976501i	$0.430857\pi$
$614$	20.3308	0.820483
$615$	32.8261	1.32367
$616$	−12.0108	−0.483931
$617$	−17.9580	−0.722962	−0.361481	−	0.932380i	$-0.617729\pi$
$617$	−17.9580	−0.722962	−0.361481	+	0.932380i	$0.617729\pi$
$618$	−33.0352	−1.32887
$619$	−16.6603	−0.669635	−0.334818	−	0.942283i	$-0.608675\pi$
$619$	−16.6603	−0.669635	−0.334818	+	0.942283i	$0.608675\pi$
$620$	−143.323	−5.75599
$621$	47.1333	1.89139
$622$	−16.1590	−0.647917
$623$	−0.665239	−0.0266523
$624$	−29.7170	−1.18963
$625$	−30.5617	−1.22247
$626$	32.3490	1.29293
$627$	−1.58841	−0.0634349
$628$	70.8178	2.82594
$629$	−9.16171	−0.365301
$630$	8.00727	0.319017
$631$	5.08332	0.202364	0.101182	−	0.994868i	$-0.467738\pi$
$631$	5.08332	0.202364	0.101182	+	0.994868i	$0.467738\pi$
$632$	−104.107	−4.14113
$633$	3.62127	0.143933
$634$	−37.2641	−1.47995
$635$	32.2613	1.28025
$636$	−7.38839	−0.292969
$637$	8.54541	0.338582
$638$	−20.9487	−0.829366
$639$	−17.3884	−0.687874
$640$	137.913	5.45150
$641$	12.2158	0.482497	0.241248	−	0.970463i	$-0.422443\pi$
$641$	12.2158	0.482497	0.241248	+	0.970463i	$0.422443\pi$
$642$	−3.43321	−0.135498
$643$	45.6046	1.79847	0.899235	−	0.437466i	$-0.144124\pi$
$643$	45.6046	1.79847	0.899235	+	0.437466i	$0.144124\pi$
$644$	41.2979	1.62737
$645$	6.76051	0.266195
$646$	−16.5308	−0.650396
$647$	−42.2217	−1.65991	−0.829954	−	0.557832i	$-0.811633\pi$
$647$	−42.2217	−1.65991	−0.829954	+	0.557832i	$0.811633\pi$
$648$	35.0719	1.37775
$649$	13.6247	0.534817
$650$	6.32329	0.248020
$651$	−11.1969	−0.438842
$652$	14.4232	0.564855
$653$	22.4025	0.876678	0.438339	−	0.898810i	$-0.355567\pi$
$653$	22.4025	0.876678	0.438339	+	0.898810i	$0.355567\pi$
$654$	64.5797	2.52527
$655$	34.7145	1.35641
$656$	−161.130	−6.29106
$657$	−6.42642	−0.250719
$658$	9.98230	0.389150
$659$	28.4806	1.10945	0.554723	−	0.832035i	$-0.312824\pi$
$659$	28.4806	1.10945	0.554723	+	0.832035i	$0.312824\pi$
$660$	26.1075	1.01623
$661$	−5.23118	−0.203469	−0.101735	−	0.994812i	$-0.532439\pi$
$661$	−5.23118	−0.203469	−0.101735	+	0.994812i	$0.532439\pi$
$662$	−35.0065	−1.36057
$663$	−12.0703	−0.468773
$664$	−131.780	−5.11404
$665$	1.99507	0.0773655
$666$	−4.84190	−0.187620
$667$	46.5160	1.80111
$668$	3.31488	0.128257
$669$	8.76956	0.339051
$670$	22.8878	0.884232
$671$	15.2476	0.588627
$672$	29.2851	1.12970
$673$	−32.8740	−1.26720	−0.633599	−	0.773661i	$-0.718423\pi$
$673$	−32.8740	−1.26720	−0.633599	+	0.773661i	$0.718423\pi$
$674$	7.12964	0.274623
$675$	−9.37166	−0.360715
$676$	−62.8201	−2.41616
$677$	−12.3787	−0.475754	−0.237877	−	0.971295i	$-0.576451\pi$
$677$	−12.3787	−0.475754	−0.237877	+	0.971295i	$0.576451\pi$
$678$	50.0319	1.92146
$679$	6.47801	0.248603
$680$	175.464	6.72874
$681$	5.04774	0.193430
$682$	37.1828	1.42380
$683$	49.0448	1.87665	0.938324	−	0.345758i	$-0.112378\pi$
$683$	49.0448	1.87665	0.938324	+	0.345758i	$0.112378\pi$
$684$	−6.45130	−0.246671
$685$	37.4065	1.42923
$686$	−31.8804	−1.21720
$687$	−36.6008	−1.39641
$688$	−33.1846	−1.26515
$689$	1.36903	0.0521557
$690$	−78.5050	−2.98863
$691$	−14.4057	−0.548019	−0.274009	−	0.961727i	$-0.588350\pi$
$691$	−14.4057	−0.548019	−0.274009	+	0.961727i	$0.588350\pi$
$692$	34.0720	1.29522
$693$	−1.53400	−0.0582717
$694$	−54.9831	−2.08713
$695$	−36.1976	−1.37305
$696$	73.0560	2.76918
$697$	−65.4472	−2.47899
$698$	−25.3670	−0.960156
$699$	5.38779	0.203785
$700$	−8.21140	−0.310362
$701$	13.0627	0.493370	0.246685	−	0.969096i	$-0.420659\pi$
$701$	13.0627	0.493370	0.246685	+	0.969096i	$0.420659\pi$
$702$	−21.2399	−0.801647
$703$	−1.20639	−0.0455000
$704$	−51.8578	−1.95447
$705$	−14.0124	−0.527738
$706$	−26.3752	−0.992644
$707$	13.0977	0.492590
$708$	−73.5760	−2.76515
$709$	34.1811	1.28370	0.641849	−	0.766831i	$-0.278168\pi$
$709$	34.1811	1.28370	0.641849	+	0.766831i	$0.278168\pi$
$710$	96.4322	3.61903
$711$	−13.2962	−0.498648
$712$	−7.70408	−0.288723
$713$	−82.5635	−3.09203
$714$	21.2266	0.794385
$715$	−4.83757	−0.180915
$716$	25.8008	0.964221
$717$	20.2992	0.758086
$718$	−59.2388	−2.21077
$719$	0.827451	0.0308587	0.0154294	−	0.999881i	$-0.495088\pi$
$719$	0.827451	0.0308587	0.0154294	+	0.999881i	$0.495088\pi$
$720$	55.1727	2.05617
$721$	−7.94900	−0.296036
$722$	50.3622	1.87429
$723$	−18.1274	−0.674166
$724$	88.1373	3.27560
$725$	−9.24893	−0.343497
$726$	33.0285	1.22580
$727$	16.2689	0.603380	0.301690	−	0.953406i	$-0.402449\pi$
$727$	16.2689	0.603380	0.301690	+	0.953406i	$0.402449\pi$
$728$	−12.0183	−0.445428
$729$	26.5042	0.981638
$730$	35.6395	1.31908
$731$	−13.4788	−0.498532
$732$	−82.3397	−3.04336
$733$	1.37090	0.0506355	0.0253177	−	0.999679i	$-0.491940\pi$
$733$	1.37090	0.0506355	0.0253177	+	0.999679i	$0.491940\pi$
$734$	−75.5233	−2.78762
$735$	21.0948	0.778095
$736$	215.942	7.95972
$737$	−4.38474	−0.161514
$738$	−34.5884	−1.27322
$739$	39.2350	1.44328	0.721641	−	0.692267i	$-0.243388\pi$
$739$	39.2350	1.44328	0.721641	+	0.692267i	$0.243388\pi$
$740$	19.8286	0.728914
$741$	−1.58940	−0.0583879
$742$	−2.40753	−0.0883833
$743$	18.4725	0.677689	0.338844	−	0.940842i	$-0.389964\pi$
$743$	18.4725	0.677689	0.338844	+	0.940842i	$0.389964\pi$
$744$	−129.671	−4.75395
$745$	−50.4432	−1.84810
$746$	−91.9299	−3.36579
$747$	−16.8306	−0.615799
$748$	−52.0520	−1.90321
$749$	−0.826108	−0.0301853
$750$	−31.1159	−1.13619
$751$	52.2716	1.90742	0.953710	−	0.300729i	$-0.0972300\pi$
$751$	52.2716	1.90742	0.953710	+	0.300729i	$0.0972300\pi$
$752$	68.7813	2.50820
$753$	12.0342	0.438550
$754$	−20.9617	−0.763380
$755$	−2.58270	−0.0939941
$756$	27.5820	1.00315
$757$	−26.1702	−0.951171	−0.475586	−	0.879669i	$-0.657764\pi$
$757$	−26.1702	−0.951171	−0.475586	+	0.879669i	$0.657764\pi$
$758$	48.7622	1.77112
$759$	15.0396	0.545904
$760$	23.1047	0.838097
$761$	50.2203	1.82048	0.910242	−	0.414078i	$-0.135896\pi$
$761$	50.2203	1.82048	0.910242	+	0.414078i	$0.135896\pi$
$762$	45.1977	1.63734
$763$	15.5393	0.562561
$764$	−83.1134	−3.00694
$765$	22.4099	0.810231
$766$	62.6479	2.26356
$767$	13.6332	0.492266
$768$	94.0214	3.39270
$769$	−31.7406	−1.14459	−0.572297	−	0.820047i	$-0.693947\pi$
$769$	−31.7406	−1.14459	−0.572297	+	0.820047i	$0.693947\pi$
$770$	8.50722	0.306579
$771$	−6.01673	−0.216687
$772$	57.4146	2.06640
$773$	−17.3338	−0.623454	−0.311727	−	0.950172i	$-0.600907\pi$
$773$	−17.3338	−0.623454	−0.311727	+	0.950172i	$0.600907\pi$
$774$	−7.12345	−0.256047
$775$	16.4164	0.589693
$776$	75.0213	2.69311
$777$	1.54908	0.0555731
$778$	−61.0837	−2.18996
$779$	−8.61794	−0.308770
$780$	26.1237	0.935380
$781$	−18.4741	−0.661053
$782$	156.520	5.59714
$783$	31.0670	1.11025
$784$	−103.546	−3.69807
$785$	−32.3927	−1.15615
$786$	48.6346	1.73474
$787$	0.346255	0.0123426	0.00617132	−	0.999981i	$-0.498036\pi$
$787$	0.346255	0.0123426	0.00617132	+	0.999981i	$0.498036\pi$
$788$	−91.9595	−3.27592
$789$	−26.3424	−0.937816
$790$	73.7381	2.62348
$791$	12.0388	0.428050
$792$	−17.7651	−0.631255
$793$	15.2571	0.541795
$794$	−83.9686	−2.97993
$795$	3.37952	0.119859
$796$	−10.7791	−0.382056
$797$	49.1718	1.74176	0.870878	−	0.491500i	$-0.163551\pi$
$797$	49.1718	1.74176	0.870878	+	0.491500i	$0.163551\pi$
$798$	2.79507	0.0989444
$799$	27.9374	0.988353
$800$	−42.9364	−1.51803
$801$	−0.983948	−0.0347661
$802$	−72.8939	−2.57397
$803$	−6.82767	−0.240943
$804$	23.6784	0.835072
$805$	−18.8901	−0.665787
$806$	37.2059	1.31052
$807$	−30.4089	−1.07045
$808$	151.683	5.33621
$809$	−12.5616	−0.441643	−0.220821	−	0.975314i	$-0.570874\pi$
$809$	−12.5616	−0.441643	−0.220821	+	0.975314i	$0.570874\pi$
$810$	−24.8412	−0.872831
$811$	46.0556	1.61723	0.808615	−	0.588338i	$-0.200218\pi$
$811$	46.0556	1.61723	0.808615	+	0.588338i	$0.200218\pi$
$812$	27.2208	0.955262
$813$	6.82429	0.239338
$814$	−5.14421	−0.180304
$815$	−6.59730	−0.231093
$816$	146.258	5.12006
$817$	−1.77486	−0.0620945
$818$	−14.7922	−0.517198
$819$	−1.53495	−0.0536356
$820$	141.647	4.94652
$821$	−11.1068	−0.387631	−0.193815	−	0.981038i	$-0.562086\pi$
$821$	−11.1068	−0.387631	−0.193815	+	0.981038i	$0.562086\pi$
$822$	52.4060	1.82787
$823$	−14.1847	−0.494446	−0.247223	−	0.968959i	$-0.579518\pi$
$823$	−14.1847	−0.494446	−0.247223	+	0.968959i	$0.579518\pi$
$824$	−92.0567	−3.20695
$825$	−2.99038	−0.104112
$826$	−23.9750	−0.834196
$827$	46.1191	1.60372	0.801859	−	0.597513i	$-0.203844\pi$
$827$	46.1191	1.60372	0.801859	+	0.597513i	$0.203844\pi$
$828$	61.0833	2.12279
$829$	29.6375	1.02935	0.514676	−	0.857385i	$-0.327912\pi$
$829$	29.6375	1.02935	0.514676	+	0.857385i	$0.327912\pi$
$830$	93.3388	3.23984
$831$	−20.3988	−0.707626
$832$	−51.8901	−1.79897
$833$	−42.0580	−1.45722
$834$	−50.7124	−1.75603
$835$	−1.51626	−0.0524723
$836$	−6.85409	−0.237054
$837$	−55.1424	−1.90600
$838$	−15.8679	−0.548148
$839$	48.4413	1.67238	0.836190	−	0.548441i	$-0.184778\pi$
$839$	48.4413	1.67238	0.836190	+	0.548441i	$0.184778\pi$
$840$	−29.6679	−1.02364
$841$	1.66017	0.0572474
$842$	−19.2024	−0.661758
$843$	23.1962	0.798921
$844$	15.6261	0.537871
$845$	28.7345	0.988497
$846$	14.7647	0.507621
$847$	7.94740	0.273076
$848$	−16.5887	−0.569658
$849$	32.6231	1.11962
$850$	−31.1214	−1.06745
$851$	11.4226	0.391561
$852$	99.7632	3.41783
$853$	−3.01383	−0.103192	−0.0515958	−	0.998668i	$-0.516431\pi$
$853$	−3.01383	−0.103192	−0.0515958	+	0.998668i	$0.516431\pi$
$854$	−26.8307	−0.918127
$855$	2.95088	0.100918
$856$	−9.56709	−0.326996
$857$	−27.3996	−0.935952	−0.467976	−	0.883741i	$-0.655017\pi$
$857$	−27.3996	−0.935952	−0.467976	+	0.883741i	$0.655017\pi$
$858$	−6.77738	−0.231376
$859$	37.5914	1.28260	0.641301	−	0.767290i	$-0.278395\pi$
$859$	37.5914	1.28260	0.641301	+	0.767290i	$0.278395\pi$
$860$	29.1721	0.994759
$861$	11.0660	0.377127
$862$	97.2754	3.31321
$863$	−28.7670	−0.979240	−0.489620	−	0.871936i	$-0.662864\pi$
$863$	−28.7670	−0.979240	−0.489620	+	0.871936i	$0.662864\pi$
$864$	144.223	4.90656
$865$	−15.5849	−0.529901
$866$	5.29882	0.180061
$867$	37.1618	1.26208
$868$	−48.3155	−1.63993
$869$	−14.1264	−0.479206
$870$	−51.7451	−1.75432
$871$	−4.38747	−0.148664
$872$	179.960	6.09420
$873$	9.58155	0.324286
$874$	20.6102	0.697150
$875$	−7.48719	−0.253113
$876$	36.8706	1.24574
$877$	4.66782	0.157621	0.0788105	−	0.996890i	$-0.474888\pi$
$877$	4.66782	0.157621	0.0788105	+	0.996890i	$0.474888\pi$
$878$	74.2775	2.50674
$879$	20.9570	0.706861
$880$	58.6175	1.97600
$881$	36.6606	1.23513	0.617563	−	0.786521i	$-0.288120\pi$
$881$	36.6606	1.23513	0.617563	+	0.786521i	$0.288120\pi$
$882$	−22.2273	−0.748433
$883$	−17.8823	−0.601786	−0.300893	−	0.953658i	$-0.597285\pi$
$883$	−17.8823	−0.601786	−0.300893	+	0.953658i	$0.597285\pi$
$884$	−52.0844	−1.75179
$885$	33.6543	1.13128
$886$	−70.8943	−2.38174
$887$	−45.5159	−1.52827	−0.764137	−	0.645054i	$-0.776835\pi$
$887$	−45.5159	−1.52827	−0.764137	+	0.645054i	$0.776835\pi$
$888$	17.9398	0.602021
$889$	10.8756	0.364755
$890$	5.45676	0.182911
$891$	4.75897	0.159431
$892$	37.8412	1.26702
$893$	3.67873	0.123104
$894$	−70.6703	−2.36357
$895$	−11.8015	−0.394482
$896$	46.4919	1.55318
$897$	15.0490	0.502472
$898$	78.4234	2.61702
$899$	−54.4202	−1.81502
$900$	−12.1454	−0.404846
$901$	−6.73794	−0.224473
$902$	−36.7479	−1.22357
$903$	2.27903	0.0758413
$904$	139.420	4.63705
$905$	−40.3148	−1.34011
$906$	−3.61833	−0.120211
$907$	−2.40569	−0.0798795	−0.0399397	−	0.999202i	$-0.512717\pi$
$907$	−2.40569	−0.0798795	−0.0399397	+	0.999202i	$0.512717\pi$
$908$	21.7813	0.722839
$909$	19.3727	0.642551
$910$	8.51251	0.282187
$911$	14.2468	0.472016	0.236008	−	0.971751i	$-0.424161\pi$
$911$	14.2468	0.472016	0.236008	+	0.971751i	$0.424161\pi$
$912$	19.2590	0.637728
$913$	−17.8814	−0.591789
$914$	25.6144	0.847248
$915$	37.6630	1.24510
$916$	−157.935	−5.21832
$917$	11.7026	0.386453
$918$	104.536	3.45021
$919$	−6.97491	−0.230081	−0.115041	−	0.993361i	$-0.536700\pi$
$919$	−6.97491	−0.230081	−0.115041	+	0.993361i	$0.536700\pi$
$920$	−218.764	−7.21244
$921$	−9.62071	−0.317013
$922$	−6.99363	−0.230323
$923$	−18.4855	−0.608459
$924$	8.80108	0.289534
$925$	−2.27119	−0.0746763
$926$	−37.0905	−1.21887
$927$	−11.7573	−0.386159
$928$	142.334	4.67235
$929$	−48.1874	−1.58098	−0.790488	−	0.612477i	$-0.790173\pi$
$929$	−48.1874	−1.58098	−0.790488	+	0.612477i	$0.790173\pi$
$930$	91.8449	3.01171
$931$	−5.53810	−0.181504
$932$	23.2487	0.761536
$933$	7.64660	0.250338
$934$	−24.7756	−0.810683
$935$	23.8091	0.778640
$936$	−17.7761	−0.581032
$937$	−50.7779	−1.65884	−0.829421	−	0.558624i	$-0.811329\pi$
$937$	−50.7779	−1.65884	−0.829421	+	0.558624i	$0.811329\pi$
$938$	7.71568	0.251926
$939$	−15.3079	−0.499553
$940$	−60.4646	−1.97214
$941$	56.6747	1.84754	0.923771	−	0.382944i	$-0.125090\pi$
$941$	56.6747	1.84754	0.923771	+	0.382944i	$0.125090\pi$
$942$	−45.3819	−1.47862
$943$	81.5979	2.65719
$944$	−165.196	−5.37666
$945$	−12.6163	−0.410407
$946$	−7.56821	−0.246064
$947$	26.0117	0.845268	0.422634	−	0.906301i	$-0.361106\pi$
$947$	26.0117	0.845268	0.422634	+	0.906301i	$0.361106\pi$
$948$	76.2852	2.47763
$949$	−6.83192	−0.221773
$950$	−4.09799	−0.132956
$951$	17.6337	0.571813
$952$	59.1506	1.91708
$953$	52.6861	1.70667	0.853335	−	0.521363i	$-0.174576\pi$
$953$	52.6861	1.70667	0.853335	+	0.521363i	$0.174576\pi$
$954$	−3.56095	−0.115290
$955$	38.0169	1.23020
$956$	87.5923	2.83294
$957$	9.91311	0.320445
$958$	72.9225	2.35602
$959$	12.6101	0.407200
$960$	−128.094	−4.13421
$961$	65.5930	2.11590
$962$	−5.14741	−0.165959
$963$	−1.22189	−0.0393748
$964$	−78.2211	−2.51933
$965$	−26.2620	−0.845402
$966$	−26.4648	−0.851490
$967$	18.2872	0.588076	0.294038	−	0.955794i	$-0.405001\pi$
$967$	18.2872	0.588076	0.294038	+	0.955794i	$0.405001\pi$
$968$	92.0381	2.95822
$969$	7.82254	0.251296
$970$	−53.1372	−1.70613
$971$	−30.3126	−0.972779	−0.486389	−	0.873742i	$-0.661686\pi$
$971$	−30.3126	−0.972779	−0.486389	+	0.873742i	$0.661686\pi$
$972$	69.3399	2.22408
$973$	−12.2025	−0.391195
$974$	−60.1132	−1.92615
$975$	−2.99224	−0.0958285
$976$	−184.872	−5.91762
$977$	29.2865	0.936959	0.468479	−	0.883474i	$-0.344802\pi$
$977$	29.2865	0.936959	0.468479	+	0.883474i	$0.344802\pi$
$978$	−9.24273	−0.295550
$979$	−1.04538	−0.0334105
$980$	91.0257	2.90771
$981$	22.9840	0.733823
$982$	65.0780	2.07672
$983$	−37.2045	−1.18664	−0.593319	−	0.804968i	$-0.702183\pi$
$983$	−37.2045	−1.18664	−0.593319	+	0.804968i	$0.702183\pi$
$984$	128.154	4.08540
$985$	42.0631	1.34024
$986$	103.167	3.28551
$987$	−4.72372	−0.150358
$988$	−6.85836	−0.218193
$989$	16.8050	0.534369
$990$	12.5829	0.399911
$991$	45.0889	1.43230	0.716149	−	0.697948i	$-0.245903\pi$
$991$	45.0889	1.43230	0.716149	+	0.697948i	$0.245903\pi$
$992$	−252.636	−8.02119
$993$	16.5654	0.525688
$994$	32.5082	1.03110
$995$	4.93047	0.156306
$996$	96.5629	3.05971
$997$	3.27822	0.103822	0.0519112	−	0.998652i	$-0.483469\pi$
$997$	3.27822	0.103822	0.0519112	+	0.998652i	$0.483469\pi$
$998$	23.5864	0.746614
$999$	7.62890	0.241368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.2	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.2	✓	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76521 q^{2} +1.30852 q^{3} +5.64636 q^{4} -2.58270 q^{5} -3.61833 q^{6} -0.870652 q^{7} -10.0829 q^{8} -1.28777 q^{9} +O(q^{10})\)	\(q-2.76521 q^{2} +1.30852 q^{3} +5.64636 q^{4} -2.58270 q^{5} -3.61833 q^{6} -0.870652 q^{7} -10.0829 q^{8} -1.28777 q^{9} +7.14170 q^{10} -1.36817 q^{11} +7.38839 q^{12} -1.36903 q^{13} +2.40753 q^{14} -3.37952 q^{15} +16.5887 q^{16} +6.73794 q^{17} +3.56095 q^{18} +0.887237 q^{19} -14.5829 q^{20} -1.13927 q^{21} +3.78328 q^{22} -8.40069 q^{23} -13.1938 q^{24} +1.67034 q^{25} +3.78564 q^{26} -5.61064 q^{27} -4.91602 q^{28} -5.53716 q^{29} +9.34506 q^{30} +9.82817 q^{31} -25.7053 q^{32} -1.79029 q^{33} -18.6318 q^{34} +2.24863 q^{35} -7.27122 q^{36} -1.35972 q^{37} -2.45339 q^{38} -1.79140 q^{39} +26.0412 q^{40} -9.71324 q^{41} +3.15031 q^{42} -2.00043 q^{43} -7.72521 q^{44} +3.32593 q^{45} +23.2296 q^{46} +4.14628 q^{47} +21.7067 q^{48} -6.24197 q^{49} -4.61883 q^{50} +8.81674 q^{51} -7.73002 q^{52} -1.00000 q^{53} +15.5146 q^{54} +3.53358 q^{55} +8.77873 q^{56} +1.16097 q^{57} +15.3114 q^{58} -9.95832 q^{59} -19.0820 q^{60} -11.1445 q^{61} -27.1769 q^{62} +1.12120 q^{63} +37.9029 q^{64} +3.53578 q^{65} +4.95051 q^{66} +3.20481 q^{67} +38.0449 q^{68} -10.9925 q^{69} -6.21793 q^{70} +13.5027 q^{71} +12.9845 q^{72} +4.99035 q^{73} +3.75991 q^{74} +2.18567 q^{75} +5.00966 q^{76} +1.19120 q^{77} +4.95359 q^{78} +10.3250 q^{79} -42.8436 q^{80} -3.47833 q^{81} +26.8591 q^{82} +13.0696 q^{83} -6.43271 q^{84} -17.4021 q^{85} +5.53161 q^{86} -7.24550 q^{87} +13.7952 q^{88} +0.764070 q^{89} -9.19687 q^{90} +1.19195 q^{91} -47.4334 q^{92} +12.8604 q^{93} -11.4653 q^{94} -2.29147 q^{95} -33.6359 q^{96} -7.44042 q^{97} +17.2603 q^{98} +1.76190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

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