LMFDB - Embedded newform 8027.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.81318 q^{2} -2.25224 q^{3} +5.91397 q^{4} +2.72187 q^{5} +6.33595 q^{6} -2.92129 q^{7} -11.0107 q^{8} +2.07257 q^{9} +O(q^{10})$	\(q-2.81318 q^{2} -2.25224 q^{3} +5.91397 q^{4} +2.72187 q^{5} +6.33595 q^{6} -2.92129 q^{7} -11.0107 q^{8} +2.07257 q^{9} -7.65711 q^{10} +5.30687 q^{11} -13.3197 q^{12} -0.142199 q^{13} +8.21812 q^{14} -6.13030 q^{15} +19.1471 q^{16} +1.04850 q^{17} -5.83052 q^{18} +2.88618 q^{19} +16.0971 q^{20} +6.57945 q^{21} -14.9292 q^{22} +1.00000 q^{23} +24.7987 q^{24} +2.40858 q^{25} +0.400031 q^{26} +2.08879 q^{27} -17.2765 q^{28} +0.921678 q^{29} +17.2456 q^{30} -1.77450 q^{31} -31.8429 q^{32} -11.9523 q^{33} -2.94961 q^{34} -7.95138 q^{35} +12.2571 q^{36} +1.86389 q^{37} -8.11935 q^{38} +0.320266 q^{39} -29.9697 q^{40} -0.623949 q^{41} -18.5092 q^{42} +3.15660 q^{43} +31.3847 q^{44} +5.64127 q^{45} -2.81318 q^{46} -7.57547 q^{47} -43.1239 q^{48} +1.53396 q^{49} -6.77576 q^{50} -2.36147 q^{51} -0.840960 q^{52} -8.04608 q^{53} -5.87613 q^{54} +14.4446 q^{55} +32.1655 q^{56} -6.50037 q^{57} -2.59284 q^{58} -12.7118 q^{59} -36.2544 q^{60} -8.44327 q^{61} +4.99199 q^{62} -6.05459 q^{63} +51.2856 q^{64} -0.387047 q^{65} +33.6241 q^{66} +3.10309 q^{67} +6.20079 q^{68} -2.25224 q^{69} +22.3687 q^{70} +8.36962 q^{71} -22.8205 q^{72} +4.22035 q^{73} -5.24347 q^{74} -5.42469 q^{75} +17.0688 q^{76} -15.5029 q^{77} -0.900964 q^{78} +5.10658 q^{79} +52.1161 q^{80} -10.9222 q^{81} +1.75528 q^{82} +7.17873 q^{83} +38.9107 q^{84} +2.85388 q^{85} -8.88007 q^{86} -2.07584 q^{87} -58.4324 q^{88} -7.44496 q^{89} -15.8699 q^{90} +0.415405 q^{91} +5.91397 q^{92} +3.99660 q^{93} +21.3112 q^{94} +7.85582 q^{95} +71.7178 q^{96} +0.814372 q^{97} -4.31530 q^{98} +10.9989 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.81318	−1.98922	−0.994609	−	0.103697i	$-0.966933\pi$
$2$	−2.81318	−1.98922	−0.994609	+	0.103697i	$0.966933\pi$
$3$	−2.25224	−1.30033	−0.650165	−	0.759793i	$-0.725300\pi$
$3$	−2.25224	−1.30033	−0.650165	+	0.759793i	$0.725300\pi$
$4$	5.91397	2.95699
$5$	2.72187	1.21726	0.608629	−	0.793455i	$-0.291720\pi$
$5$	2.72187	1.21726	0.608629	+	0.793455i	$0.291720\pi$
$6$	6.33595	2.58664
$7$	−2.92129	−1.10415	−0.552073	−	0.833796i	$-0.686163\pi$
$7$	−2.92129	−1.10415	−0.552073	+	0.833796i	$0.686163\pi$
$8$	−11.0107	−3.89287
$9$	2.07257	0.690858
$10$	−7.65711	−2.42139
$11$	5.30687	1.60008	0.800041	−	0.599945i	$-0.204811\pi$
$11$	5.30687	1.60008	0.800041	+	0.599945i	$0.204811\pi$
$12$	−13.3197	−3.84506
$13$	−0.142199	−0.0394389	−0.0197194	−	0.999806i	$-0.506277\pi$
$13$	−0.142199	−0.0394389	−0.0197194	+	0.999806i	$0.506277\pi$
$14$	8.21812	2.19639
$15$	−6.13030	−1.58284
$16$	19.1471	4.78679
$17$	1.04850	0.254298	0.127149	−	0.991884i	$-0.459417\pi$
$17$	1.04850	0.254298	0.127149	+	0.991884i	$0.459417\pi$
$18$	−5.83052	−1.37427
$19$	2.88618	0.662136	0.331068	−	0.943607i	$-0.392591\pi$
$19$	2.88618	0.662136	0.331068	+	0.943607i	$0.392591\pi$
$20$	16.0971	3.59941
$21$	6.57945	1.43575
$22$	−14.9292	−3.18291
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	24.7987	5.06202
$25$	2.40858	0.481716
$26$	0.400031	0.0784525
$27$	2.08879	0.401987
$28$	−17.2765	−3.26494
$29$	0.921678	0.171151	0.0855757	−	0.996332i	$-0.472727\pi$
$29$	0.921678	0.171151	0.0855757	+	0.996332i	$0.472727\pi$
$30$	17.2456	3.14861
$31$	−1.77450	−0.318710	−0.159355	−	0.987221i	$-0.550941\pi$
$31$	−1.77450	−0.318710	−0.159355	+	0.987221i	$0.550941\pi$
$32$	−31.8429	−5.62909
$33$	−11.9523	−2.08063
$34$	−2.94961	−0.505855
$35$	−7.95138	−1.34403
$36$	12.2571	2.04286
$37$	1.86389	0.306422	0.153211	−	0.988193i	$-0.451039\pi$
$37$	1.86389	0.306422	0.153211	+	0.988193i	$0.451039\pi$
$38$	−8.11935	−1.31713
$39$	0.320266	0.0512835
$40$	−29.9697	−4.73863
$41$	−0.623949	−0.0974445	−0.0487222	−	0.998812i	$-0.515515\pi$
$41$	−0.623949	−0.0974445	−0.0487222	+	0.998812i	$0.515515\pi$
$42$	−18.5092	−2.85603
$43$	3.15660	0.481376	0.240688	−	0.970602i	$-0.422627\pi$
$43$	3.15660	0.481376	0.240688	+	0.970602i	$0.422627\pi$
$44$	31.3847	4.73142
$45$	5.64127	0.840952
$46$	−2.81318	−0.414781
$47$	−7.57547	−1.10500	−0.552498	−	0.833514i	$-0.686325\pi$
$47$	−7.57547	−1.10500	−0.552498	+	0.833514i	$0.686325\pi$
$48$	−43.1239	−6.22440
$49$	1.53396	0.219137
$50$	−6.77576	−0.958237
$51$	−2.36147	−0.330672
$52$	−0.840960	−0.116620
$53$	−8.04608	−1.10521	−0.552607	−	0.833442i	$-0.686367\pi$
$53$	−8.04608	−1.10521	−0.552607	+	0.833442i	$0.686367\pi$
$54$	−5.87613	−0.799640
$55$	14.4446	1.94771
$56$	32.1655	4.29830
$57$	−6.50037	−0.860995
$58$	−2.59284	−0.340457
$59$	−12.7118	−1.65493	−0.827465	−	0.561518i	$-0.810218\pi$
$59$	−12.7118	−1.65493	−0.827465	+	0.561518i	$0.810218\pi$
$60$	−36.2544	−4.68043
$61$	−8.44327	−1.08105	−0.540525	−	0.841328i	$-0.681774\pi$
$61$	−8.44327	−1.08105	−0.540525	+	0.841328i	$0.681774\pi$
$62$	4.99199	0.633984
$63$	−6.05459	−0.762807
$64$	51.2856	6.41069
$65$	−0.387047	−0.0480073
$66$	33.6241	4.13884
$67$	3.10309	0.379103	0.189552	−	0.981871i	$-0.439297\pi$
$67$	3.10309	0.379103	0.189552	+	0.981871i	$0.439297\pi$
$68$	6.20079	0.751957
$69$	−2.25224	−0.271138
$70$	22.3687	2.67357
$71$	8.36962	0.993291	0.496646	−	0.867953i	$-0.334565\pi$
$71$	8.36962	0.993291	0.496646	+	0.867953i	$0.334565\pi$
$72$	−22.8205	−2.68942
$73$	4.22035	0.493954	0.246977	−	0.969021i	$-0.420563\pi$
$73$	4.22035	0.493954	0.246977	+	0.969021i	$0.420563\pi$
$74$	−5.24347	−0.609541
$75$	−5.42469	−0.626389
$76$	17.0688	1.95793
$77$	−15.5029	−1.76672
$78$	−0.900964	−0.102014
$79$	5.10658	0.574535	0.287267	−	0.957850i	$-0.407253\pi$
$79$	5.10658	0.574535	0.287267	+	0.957850i	$0.407253\pi$
$80$	52.1161	5.82675
$81$	−10.9222	−1.21357
$82$	1.75528	0.193838
$83$	7.17873	0.787968	0.393984	−	0.919117i	$-0.371097\pi$
$83$	7.17873	0.787968	0.393984	+	0.919117i	$0.371097\pi$
$84$	38.9107	4.24550
$85$	2.85388	0.309546
$86$	−8.88007	−0.957562
$87$	−2.07584	−0.222553
$88$	−58.4324	−6.22892
$89$	−7.44496	−0.789164	−0.394582	−	0.918861i	$-0.629111\pi$
$89$	−7.44496	−0.789164	−0.394582	+	0.918861i	$0.629111\pi$
$90$	−15.8699	−1.67284
$91$	0.415405	0.0435462
$92$	5.91397	0.616574
$93$	3.99660	0.414428
$94$	21.3112	2.19808
$95$	7.85582	0.805990
$96$	71.7178	7.31967
$97$	0.814372	0.0826870	0.0413435	−	0.999145i	$-0.486836\pi$
$97$	0.814372	0.0826870	0.0413435	+	0.999145i	$0.486836\pi$
$98$	−4.31530	−0.435911
$99$	10.9989	1.10543
$100$	14.2443	1.42443
$101$	−12.1128	−1.20527	−0.602633	−	0.798019i	$-0.705882\pi$
$101$	−12.1128	−1.20527	−0.602633	+	0.798019i	$0.705882\pi$
$102$	6.64323	0.657778
$103$	−5.56349	−0.548187	−0.274093	−	0.961703i	$-0.588378\pi$
$103$	−5.56349	−0.548187	−0.274093	+	0.961703i	$0.588378\pi$
$104$	1.56571	0.153531
$105$	17.9084	1.74768
$106$	22.6351	2.19851
$107$	−4.06025	−0.392519	−0.196259	−	0.980552i	$-0.562879\pi$
$107$	−4.06025	−0.392519	−0.196259	+	0.980552i	$0.562879\pi$
$108$	12.3530	1.18867
$109$	−1.38820	−0.132965	−0.0664827	−	0.997788i	$-0.521178\pi$
$109$	−1.38820	−0.132965	−0.0664827	+	0.997788i	$0.521178\pi$
$110$	−40.6353	−3.87442
$111$	−4.19793	−0.398450
$112$	−55.9344	−5.28531
$113$	0.217657	0.0204755	0.0102377	−	0.999948i	$-0.496741\pi$
$113$	0.217657	0.0204755	0.0102377	+	0.999948i	$0.496741\pi$
$114$	18.2867	1.71271
$115$	2.72187	0.253816
$116$	5.45078	0.506092
$117$	−0.294717	−0.0272466
$118$	35.7604	3.29202
$119$	−3.06297	−0.280782
$120$	67.4989	6.16178
$121$	17.1629	1.56026
$122$	23.7524	2.15044
$123$	1.40528	0.126710
$124$	−10.4944	−0.942422
$125$	−7.05352	−0.630886
$126$	17.0327	1.51739
$127$	−12.2886	−1.09044	−0.545219	−	0.838293i	$-0.683554\pi$
$127$	−12.2886	−1.09044	−0.545219	+	0.838293i	$0.683554\pi$
$128$	−80.5896	−7.12318
$129$	−7.10940	−0.625948
$130$	1.08883	0.0954969
$131$	13.2964	1.16171	0.580856	−	0.814006i	$-0.302718\pi$
$131$	13.2964	1.16171	0.580856	+	0.814006i	$0.302718\pi$
$132$	−70.6858	−6.15241
$133$	−8.43139	−0.731094
$134$	−8.72956	−0.754119
$135$	5.68540	0.489322
$136$	−11.5447	−0.989951
$137$	−8.01150	−0.684468	−0.342234	−	0.939615i	$-0.611184\pi$
$137$	−8.01150	−0.684468	−0.342234	+	0.939615i	$0.611184\pi$
$138$	6.33595	0.539352
$139$	2.61203	0.221550	0.110775	−	0.993846i	$-0.464667\pi$
$139$	2.61203	0.221550	0.110775	+	0.993846i	$0.464667\pi$
$140$	−47.0243	−3.97428
$141$	17.0618	1.43686
$142$	−23.5452	−1.97587
$143$	−0.754631	−0.0631054
$144$	39.6839	3.30699
$145$	2.50869	0.208335
$146$	−11.8726	−0.982583
$147$	−3.45484	−0.284950
$148$	11.0230	0.906087
$149$	20.0237	1.64041	0.820203	−	0.572073i	$-0.193861\pi$
$149$	20.0237	1.64041	0.820203	+	0.572073i	$0.193861\pi$
$150$	15.2606	1.24602
$151$	−21.3638	−1.73856	−0.869280	−	0.494321i	$-0.835417\pi$
$151$	−21.3638	−1.73856	−0.869280	+	0.494321i	$0.835417\pi$
$152$	−31.7789	−2.57761
$153$	2.17309	0.175684
$154$	43.6125	3.51440
$155$	−4.82997	−0.387952
$156$	1.89404	0.151645
$157$	−5.38010	−0.429379	−0.214689	−	0.976682i	$-0.568874\pi$
$157$	−5.38010	−0.429379	−0.214689	+	0.976682i	$0.568874\pi$
$158$	−14.3657	−1.14287
$159$	18.1217	1.43714
$160$	−86.6723	−6.85205
$161$	−2.92129	−0.230230
$162$	30.7260	2.41406
$163$	−12.4901	−0.978297	−0.489149	−	0.872200i	$-0.662692\pi$
$163$	−12.4901	−0.978297	−0.489149	+	0.872200i	$0.662692\pi$
$164$	−3.69002	−0.288142
$165$	−32.5327	−2.53267
$166$	−20.1951	−1.56744
$167$	−19.7859	−1.53108	−0.765540	−	0.643389i	$-0.777528\pi$
$167$	−19.7859	−1.53108	−0.765540	+	0.643389i	$0.777528\pi$
$168$	−72.4444	−5.58921
$169$	−12.9798	−0.998445
$170$	−8.02847	−0.615755
$171$	5.98183	0.457442
$172$	18.6680	1.42342
$173$	2.02324	0.153824	0.0769122	−	0.997038i	$-0.475494\pi$
$173$	2.02324	0.153824	0.0769122	+	0.997038i	$0.475494\pi$
$174$	5.83970	0.442707
$175$	−7.03616	−0.531884
$176$	101.611	7.65925
$177$	28.6299	2.15195
$178$	20.9440	1.56982
$179$	−2.11950	−0.158419	−0.0792093	−	0.996858i	$-0.525240\pi$
$179$	−2.11950	−0.158419	−0.0792093	+	0.996858i	$0.525240\pi$
$180$	33.3624	2.48668
$181$	−10.0016	−0.743414	−0.371707	−	0.928350i	$-0.621227\pi$
$181$	−10.0016	−0.743414	−0.371707	+	0.928350i	$0.621227\pi$
$182$	−1.16861	−0.0866230
$183$	19.0163	1.40572
$184$	−11.0107	−0.811720
$185$	5.07328	0.372995
$186$	−11.2432	−0.824388
$187$	5.56425	0.406898
$188$	−44.8012	−3.26746
$189$	−6.10196	−0.443852
$190$	−22.0998	−1.60329
$191$	−5.14215	−0.372073	−0.186036	−	0.982543i	$-0.559564\pi$
$191$	−5.14215	−0.372073	−0.186036	+	0.982543i	$0.559564\pi$
$192$	−115.507	−8.33602
$193$	4.20808	0.302905	0.151452	−	0.988465i	$-0.451605\pi$
$193$	4.20808	0.302905	0.151452	+	0.988465i	$0.451605\pi$
$194$	−2.29097	−0.164482
$195$	0.871721	0.0624253
$196$	9.07178	0.647985
$197$	15.7912	1.12508	0.562539	−	0.826770i	$-0.309824\pi$
$197$	15.7912	1.12508	0.562539	+	0.826770i	$0.309824\pi$
$198$	−30.9418	−2.19894
$199$	−22.3875	−1.58701	−0.793503	−	0.608566i	$-0.791745\pi$
$199$	−22.3875	−1.58701	−0.793503	+	0.608566i	$0.791745\pi$
$200$	−26.5202	−1.87526
$201$	−6.98890	−0.492959
$202$	34.0754	2.39754
$203$	−2.69249	−0.188976
$204$	−13.9657	−0.977792
$205$	−1.69831	−0.118615
$206$	15.6511	1.09046
$207$	2.07257	0.144054
$208$	−2.72270	−0.188785
$209$	15.3166	1.05947
$210$	−50.3795	−3.47652
$211$	−28.8472	−1.98593	−0.992963	−	0.118428i	$-0.962214\pi$
$211$	−28.8472	−1.98593	−0.992963	+	0.118428i	$0.962214\pi$
$212$	−47.5843	−3.26810
$213$	−18.8504	−1.29161
$214$	11.4222	0.780805
$215$	8.59184	0.585959
$216$	−22.9990	−1.56489
$217$	5.18384	0.351902
$218$	3.90526	0.264497
$219$	−9.50522	−0.642303
$220$	85.4251	5.75936
$221$	−0.149095	−0.0100292
$222$	11.8095	0.792604
$223$	−0.316463	−0.0211919	−0.0105960	−	0.999944i	$-0.503373\pi$
$223$	−0.316463	−0.0211919	−0.0105960	+	0.999944i	$0.503373\pi$
$224$	93.0225	6.21533
$225$	4.99195	0.332797
$226$	−0.612309	−0.0407302
$227$	22.6544	1.50362	0.751812	−	0.659377i	$-0.229180\pi$
$227$	22.6544	1.50362	0.751812	+	0.659377i	$0.229180\pi$
$228$	−38.4430	−2.54595
$229$	−22.2174	−1.46817	−0.734083	−	0.679059i	$-0.762388\pi$
$229$	−22.2174	−1.46817	−0.734083	+	0.679059i	$0.762388\pi$
$230$	−7.65711	−0.504895
$231$	34.9163	2.29732
$232$	−10.1483	−0.666270
$233$	−20.7548	−1.35969	−0.679847	−	0.733354i	$-0.737954\pi$
$233$	−20.7548	−1.35969	−0.679847	+	0.733354i	$0.737954\pi$
$234$	0.829093	0.0541995
$235$	−20.6195	−1.34507
$236$	−75.1770	−4.89361
$237$	−11.5012	−0.747085
$238$	8.61669	0.558537
$239$	13.3259	0.861978	0.430989	−	0.902357i	$-0.358165\pi$
$239$	13.3259	0.861978	0.430989	+	0.902357i	$0.358165\pi$
$240$	−117.378	−7.57670
$241$	−0.0145858	−0.000939551 0	−0.000469775	−	1.00000i	$-0.500150\pi$
$241$	−0.0145858	−0.000939551 0	−0.000469775		1.00000i	$0.500150\pi$
$242$	−48.2823	−3.10370
$243$	18.3329	1.17606
$244$	−49.9333	−3.19665
$245$	4.17523	0.266746
$246$	−3.95331	−0.252054
$247$	−0.410412	−0.0261139
$248$	19.5385	1.24070
$249$	−16.1682	−1.02462
$250$	19.8428	1.25497
$251$	17.1809	1.08445	0.542226	−	0.840233i	$-0.317582\pi$
$251$	17.1809	1.08445	0.542226	+	0.840233i	$0.317582\pi$
$252$	−35.8067	−2.25561
$253$	5.30687	0.333640
$254$	34.5701	2.16912
$255$	−6.42761	−0.402512
$256$	124.142	7.75886
$257$	13.8082	0.861333	0.430667	−	0.902511i	$-0.358278\pi$
$257$	13.8082	0.861333	0.430667	+	0.902511i	$0.358278\pi$
$258$	20.0000	1.24515
$259$	−5.44498	−0.338335
$260$	−2.28899	−0.141957
$261$	1.91024	0.118241
$262$	−37.4052	−2.31090
$263$	4.89609	0.301906	0.150953	−	0.988541i	$-0.451766\pi$
$263$	4.89609	0.301906	0.150953	+	0.988541i	$0.451766\pi$
$264$	131.604	8.09965
$265$	−21.9004	−1.34533
$266$	23.7190	1.45431
$267$	16.7678	1.02617
$268$	18.3516	1.12100
$269$	18.7975	1.14611	0.573053	−	0.819518i	$-0.305759\pi$
$269$	18.7975	1.14611	0.573053	+	0.819518i	$0.305759\pi$
$270$	−15.9941	−0.973368
$271$	23.5581	1.43105	0.715525	−	0.698587i	$-0.246187\pi$
$271$	23.5581	1.43105	0.715525	+	0.698587i	$0.246187\pi$
$272$	20.0758	1.21727
$273$	−0.935590	−0.0566245
$274$	22.5378	1.36156
$275$	12.7820	0.770784
$276$	−13.3197	−0.801750
$277$	8.32086	0.499952	0.249976	−	0.968252i	$-0.419577\pi$
$277$	8.32086	0.499952	0.249976	+	0.968252i	$0.419577\pi$
$278$	−7.34811	−0.440710
$279$	−3.67779	−0.220183
$280$	87.5504	5.23214
$281$	29.2354	1.74404	0.872019	−	0.489472i	$-0.162811\pi$
$281$	29.2354	1.74404	0.872019	+	0.489472i	$0.162811\pi$
$282$	−47.9978	−2.85823
$283$	13.9662	0.830206	0.415103	−	0.909774i	$-0.363746\pi$
$283$	13.9662	0.830206	0.415103	+	0.909774i	$0.363746\pi$
$284$	49.4977	2.93715
$285$	−17.6932	−1.04805
$286$	2.12291	0.125530
$287$	1.82274	0.107593
$288$	−65.9968	−3.88890
$289$	−15.9007	−0.935332
$290$	−7.05739	−0.414424
$291$	−1.83416	−0.107520
$292$	24.9590	1.46062
$293$	−2.36723	−0.138295	−0.0691476	−	0.997606i	$-0.522028\pi$
$293$	−2.36723	−0.138295	−0.0691476	+	0.997606i	$0.522028\pi$
$294$	9.71907	0.566828
$295$	−34.5998	−2.01448
$296$	−20.5228	−1.19286
$297$	11.0849	0.643212
$298$	−56.3303	−3.26312
$299$	−0.142199	−0.00822357
$300$	−32.0815	−1.85222
$301$	−9.22134	−0.531509
$302$	60.1001	3.45837
$303$	27.2808	1.56724
$304$	55.2622	3.16950
$305$	−22.9815	−1.31592
$306$	−6.11329	−0.349473
$307$	14.5777	0.831991	0.415995	−	0.909367i	$-0.363433\pi$
$307$	14.5777	0.831991	0.415995	+	0.909367i	$0.363433\pi$
$308$	−91.6839	−5.22418
$309$	12.5303	0.712824
$310$	13.5876	0.771721
$311$	23.3597	1.32461	0.662305	−	0.749235i	$-0.269578\pi$
$311$	23.3597	1.32461	0.662305	+	0.749235i	$0.269578\pi$
$312$	−3.52635	−0.199640
$313$	−18.6226	−1.05261	−0.526306	−	0.850295i	$-0.676423\pi$
$313$	−18.6226	−1.05261	−0.526306	+	0.850295i	$0.676423\pi$
$314$	15.1352	0.854128
$315$	−16.4798	−0.928533
$316$	30.2002	1.69889
$317$	−30.3862	−1.70666	−0.853329	−	0.521373i	$-0.825420\pi$
$317$	−30.3862	−1.70666	−0.853329	+	0.521373i	$0.825420\pi$
$318$	−50.9795	−2.85879
$319$	4.89123	0.273856
$320$	139.593	7.80346
$321$	9.14464	0.510404
$322$	8.21812	0.457978
$323$	3.02616	0.168380
$324$	−64.5934	−3.58852
$325$	−0.342497	−0.0189983
$326$	35.1368	1.94605
$327$	3.12656	0.172899
$328$	6.87012	0.379339
$329$	22.1302	1.22008
$330$	91.5203	5.03803
$331$	9.77294	0.537170	0.268585	−	0.963256i	$-0.413444\pi$
$331$	9.77294	0.537170	0.268585	+	0.963256i	$0.413444\pi$
$332$	42.4548	2.33001
$333$	3.86306	0.211694
$334$	55.6613	3.04565
$335$	8.44622	0.461466
$336$	125.978	6.87264
$337$	−11.1219	−0.605850	−0.302925	−	0.953014i	$-0.597963\pi$
$337$	−11.1219	−0.605850	−0.302925	+	0.953014i	$0.597963\pi$
$338$	36.5144	1.98612
$339$	−0.490216	−0.0266249
$340$	16.8778	0.915325
$341$	−9.41706	−0.509962
$342$	−16.8279	−0.909951
$343$	15.9679	0.862186
$344$	−34.7564	−1.87394
$345$	−6.13030	−0.330044
$346$	−5.69174	−0.305990
$347$	−10.9560	−0.588147	−0.294074	−	0.955783i	$-0.595011\pi$
$347$	−10.9560	−0.588147	−0.294074	+	0.955783i	$0.595011\pi$
$348$	−12.2765	−0.658087
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	19.7940	1.05803
$351$	−0.297023	−0.0158539
$352$	−168.986	−9.00700
$353$	16.7791	0.893061	0.446531	−	0.894768i	$-0.352659\pi$
$353$	16.7791	0.893061	0.446531	+	0.894768i	$0.352659\pi$
$354$	−80.5410	−4.28071
$355$	22.7810	1.20909
$356$	−44.0293	−2.33355
$357$	6.89854	0.365109
$358$	5.96252	0.315129
$359$	−13.3921	−0.706808	−0.353404	−	0.935471i	$-0.614976\pi$
$359$	−13.3921	−0.706808	−0.353404	+	0.935471i	$0.614976\pi$
$360$	−62.1144	−3.27372
$361$	−10.6699	−0.561576
$362$	28.1363	1.47881
$363$	−38.6549	−2.02886
$364$	2.45669	0.128766
$365$	11.4872	0.601270
$366$	−53.4961	−2.79629
$367$	−19.0824	−0.996095	−0.498048	−	0.867150i	$-0.665950\pi$
$367$	−19.0824	−0.996095	−0.498048	+	0.867150i	$0.665950\pi$
$368$	19.1471	0.998114
$369$	−1.29318	−0.0673203
$370$	−14.2720	−0.741968
$371$	23.5050	1.22032
$372$	23.6358	1.22546
$373$	3.27615	0.169632	0.0848162	−	0.996397i	$-0.472970\pi$
$373$	3.27615	0.169632	0.0848162	+	0.996397i	$0.472970\pi$
$374$	−15.6532	−0.809409
$375$	15.8862	0.820359
$376$	83.4114	4.30161
$377$	−0.131062	−0.00675001
$378$	17.1659	0.882919
$379$	−3.18940	−0.163829	−0.0819143	−	0.996639i	$-0.526103\pi$
$379$	−3.18940	−0.163829	−0.0819143	+	0.996639i	$0.526103\pi$
$380$	46.4591	2.38330
$381$	27.6769	1.41793
$382$	14.4658	0.740134
$383$	35.8169	1.83016	0.915080	−	0.403273i	$-0.132127\pi$
$383$	35.8169	1.83016	0.915080	+	0.403273i	$0.132127\pi$
$384$	181.507	9.26248
$385$	−42.1970	−2.15056
$386$	−11.8381	−0.602543
$387$	6.54228	0.332563
$388$	4.81618	0.244504
$389$	1.47209	0.0746381	0.0373191	−	0.999303i	$-0.488118\pi$
$389$	1.47209	0.0746381	0.0373191	+	0.999303i	$0.488118\pi$
$390$	−2.45231	−0.124177
$391$	1.04850	0.0530248
$392$	−16.8900	−0.853072
$393$	−29.9467	−1.51061
$394$	−44.4236	−2.23803
$395$	13.8994	0.699357
$396$	65.0471	3.26874
$397$	−8.48594	−0.425897	−0.212948	−	0.977063i	$-0.568307\pi$
$397$	−8.48594	−0.425897	−0.212948	+	0.977063i	$0.568307\pi$
$398$	62.9800	3.15690
$399$	18.9895	0.950664
$400$	46.1174	2.30587
$401$	−7.64214	−0.381630	−0.190815	−	0.981626i	$-0.561113\pi$
$401$	−7.64214	−0.381630	−0.190815	+	0.981626i	$0.561113\pi$
$402$	19.6610	0.980603
$403$	0.252332	0.0125696
$404$	−71.6346	−3.56395
$405$	−29.7287	−1.47723
$406$	7.57446	0.375914
$407$	9.89144	0.490301
$408$	26.0014	1.28726
$409$	−28.5982	−1.41409	−0.707046	−	0.707168i	$-0.749972\pi$
$409$	−28.5982	−1.41409	−0.707046	+	0.707168i	$0.749972\pi$
$410$	4.77765	0.235951
$411$	18.0438	0.890035
$412$	−32.9023	−1.62098
$413$	37.1348	1.82728
$414$	−5.83052	−0.286554
$415$	19.5396	0.959160
$416$	4.52803	0.222005
$417$	−5.88291	−0.288087
$418$	−43.0884	−2.10752
$419$	32.8234	1.60353	0.801764	−	0.597641i	$-0.203895\pi$
$419$	32.8234	1.60353	0.801764	+	0.597641i	$0.203895\pi$
$420$	105.910	5.16787
$421$	−25.7903	−1.25694	−0.628471	−	0.777833i	$-0.716319\pi$
$421$	−25.7903	−1.25694	−0.628471	+	0.777833i	$0.716319\pi$
$422$	81.1524	3.95044
$423$	−15.7007	−0.763395
$424$	88.5931	4.30246
$425$	2.52539	0.122499
$426$	53.0295	2.56929
$427$	24.6653	1.19364
$428$	−24.0122	−1.16067
$429$	1.69961	0.0820579
$430$	−24.1704	−1.16560
$431$	−32.6582	−1.57309	−0.786545	−	0.617533i	$-0.788132\pi$
$431$	−32.6582	−1.57309	−0.786545	+	0.617533i	$0.788132\pi$
$432$	39.9943	1.92423
$433$	−4.00465	−0.192451	−0.0962257	−	0.995360i	$-0.530677\pi$
$433$	−4.00465	−0.192451	−0.0962257	+	0.995360i	$0.530677\pi$
$434$	−14.5831	−0.700010
$435$	−5.65016	−0.270904
$436$	−8.20978	−0.393177
$437$	2.88618	0.138065
$438$	26.7399	1.27768
$439$	19.3618	0.924087	0.462043	−	0.886857i	$-0.347116\pi$
$439$	19.3618	0.924087	0.462043	+	0.886857i	$0.347116\pi$
$440$	−159.045	−7.58220
$441$	3.17924	0.151392
$442$	0.419432	0.0199503
$443$	13.5772	0.645074	0.322537	−	0.946557i	$-0.395464\pi$
$443$	13.5772	0.645074	0.322537	+	0.946557i	$0.395464\pi$
$444$	−24.8265	−1.17821
$445$	−20.2642	−0.960616
$446$	0.890268	0.0421554
$447$	−45.0981	−2.13307
$448$	−149.820	−7.07834
$449$	−4.52255	−0.213432	−0.106716	−	0.994290i	$-0.534034\pi$
$449$	−4.52255	−0.213432	−0.106716	+	0.994290i	$0.534034\pi$
$450$	−14.0433	−0.662005
$451$	−3.31122	−0.155919
$452$	1.28722	0.0605457
$453$	48.1163	2.26070
$454$	−63.7308	−2.99104
$455$	1.13068	0.0530070
$456$	71.5737	3.35175
$457$	−20.8635	−0.975954	−0.487977	−	0.872856i	$-0.662265\pi$
$457$	−20.8635	−0.975954	−0.487977	+	0.872856i	$0.662265\pi$
$458$	62.5015	2.92050
$459$	2.19009	0.102225
$460$	16.0971	0.750530
$461$	−33.7704	−1.57284	−0.786422	−	0.617689i	$-0.788069\pi$
$461$	−33.7704	−1.57284	−0.786422	+	0.617689i	$0.788069\pi$
$462$	−98.2257	−4.56988
$463$	−18.3509	−0.852838	−0.426419	−	0.904526i	$-0.640225\pi$
$463$	−18.3509	−0.852838	−0.426419	+	0.904526i	$0.640225\pi$
$464$	17.6475	0.819265
$465$	10.8782	0.504466
$466$	58.3870	2.70473
$467$	−15.6396	−0.723716	−0.361858	−	0.932233i	$-0.617858\pi$
$467$	−15.6396	−0.723716	−0.361858	+	0.932233i	$0.617858\pi$
$468$	−1.74295	−0.0805680
$469$	−9.06505	−0.418585
$470$	58.0062	2.67563
$471$	12.1173	0.558334
$472$	139.965	6.44243
$473$	16.7517	0.770242
$474$	32.3550	1.48611
$475$	6.95160	0.318961
$476$	−18.1143	−0.830269
$477$	−16.6761	−0.763546
$478$	−37.4880	−1.71466
$479$	25.3603	1.15874	0.579371	−	0.815064i	$-0.303298\pi$
$479$	25.3603	1.15874	0.579371	+	0.815064i	$0.303298\pi$
$480$	195.207	8.90992
$481$	−0.265044	−0.0120849
$482$	0.0410323	0.00186897
$483$	6.57945	0.299375
$484$	101.501	4.61368
$485$	2.21662	0.100651
$486$	−51.5738	−2.33944
$487$	−9.60926	−0.435437	−0.217719	−	0.976012i	$-0.569861\pi$
$487$	−9.60926	−0.435437	−0.217719	+	0.976012i	$0.569861\pi$
$488$	92.9664	4.20839
$489$	28.1306	1.27211
$490$	−11.7457	−0.530616
$491$	35.5532	1.60449	0.802246	−	0.596994i	$-0.203638\pi$
$491$	35.5532	1.60449	0.802246	+	0.596994i	$0.203638\pi$
$492$	8.31080	0.374680
$493$	0.966378	0.0435235
$494$	1.15456	0.0519462
$495$	29.9375	1.34559
$496$	−33.9767	−1.52560
$497$	−24.4501	−1.09674
$498$	45.4840	2.03819
$499$	18.9734	0.849364	0.424682	−	0.905343i	$-0.360386\pi$
$499$	18.9734	0.849364	0.424682	+	0.905343i	$0.360386\pi$
$500$	−41.7143	−1.86552
$501$	44.5625	1.99091
$502$	−48.3331	−2.15721
$503$	−10.7004	−0.477107	−0.238554	−	0.971129i	$-0.576673\pi$
$503$	−10.7004	−0.477107	−0.238554	+	0.971129i	$0.576673\pi$
$504$	66.6654	2.96951
$505$	−32.9694	−1.46712
$506$	−14.9292	−0.663683
$507$	29.2335	1.29831
$508$	−72.6746	−3.22441
$509$	−7.48992	−0.331985	−0.165993	−	0.986127i	$-0.553083\pi$
$509$	−7.48992	−0.331985	−0.165993	+	0.986127i	$0.553083\pi$
$510$	18.0820	0.800685
$511$	−12.3289	−0.545397
$512$	−188.054	−8.31088
$513$	6.02862	0.266170
$514$	−38.8450	−1.71338
$515$	−15.1431	−0.667285
$516$	−42.0448	−1.85092
$517$	−40.2021	−1.76809
$518$	15.3177	0.673021
$519$	−4.55682	−0.200022
$520$	4.26166	0.186886
$521$	1.71698	0.0752223	0.0376111	−	0.999292i	$-0.488025\pi$
$521$	1.71698	0.0752223	0.0376111	+	0.999292i	$0.488025\pi$
$522$	−5.37386	−0.235207
$523$	30.2123	1.32109	0.660546	−	0.750785i	$-0.270325\pi$
$523$	30.2123	1.32109	0.660546	+	0.750785i	$0.270325\pi$
$524$	78.6346	3.43517
$525$	15.8471	0.691625
$526$	−13.7736	−0.600556
$527$	−1.86056	−0.0810474
$528$	−228.853	−9.95955
$529$	1.00000	0.0434783
$530$	61.6097	2.67615
$531$	−26.3460	−1.14332
$532$	−49.8630	−2.16184
$533$	0.0887248	0.00384310
$534$	−47.1709	−2.04128
$535$	−11.0515	−0.477796
$536$	−34.1673	−1.47580
$537$	4.77361	0.205996
$538$	−52.8808	−2.27985
$539$	8.14052	0.350637
$540$	33.6233	1.44692
$541$	−25.4038	−1.09219	−0.546097	−	0.837722i	$-0.683887\pi$
$541$	−25.4038	−1.09219	−0.546097	+	0.837722i	$0.683887\pi$
$542$	−66.2730	−2.84667
$543$	22.5260	0.966683
$544$	−33.3873	−1.43147
$545$	−3.77850	−0.161853
$546$	2.63198	0.112638
$547$	36.3215	1.55300	0.776498	−	0.630120i	$-0.216994\pi$
$547$	36.3215	1.55300	0.776498	+	0.630120i	$0.216994\pi$
$548$	−47.3798	−2.02396
$549$	−17.4993	−0.746852
$550$	−35.9581	−1.53326
$551$	2.66013	0.113325
$552$	24.7987	1.05550
$553$	−14.9178	−0.634370
$554$	−23.4081	−0.994513
$555$	−11.4262	−0.485016
$556$	15.4475	0.655119
$557$	43.2189	1.83124	0.915622	−	0.402040i	$-0.131699\pi$
$557$	43.2189	1.83124	0.915622	+	0.402040i	$0.131699\pi$
$558$	10.3463	0.437993
$559$	−0.448864	−0.0189849
$560$	−152.246	−6.43358
$561$	−12.5320	−0.529102
$562$	−82.2444	−3.46927
$563$	3.40462	0.143488	0.0717438	−	0.997423i	$-0.477144\pi$
$563$	3.40462	0.143488	0.0717438	+	0.997423i	$0.477144\pi$
$564$	100.903	4.24878
$565$	0.592435	0.0249239
$566$	−39.2895	−1.65146
$567$	31.9068	1.33996
$568$	−92.1555	−3.86676
$569$	−16.6970	−0.699974	−0.349987	−	0.936755i	$-0.613814\pi$
$569$	−16.6970	−0.699974	−0.349987	+	0.936755i	$0.613814\pi$
$570$	49.7740	2.08480
$571$	46.5634	1.94862	0.974309	−	0.225214i	$-0.0723082\pi$
$571$	46.5634	1.94862	0.974309	+	0.225214i	$0.0723082\pi$
$572$	−4.46287	−0.186602
$573$	11.5813	0.483817
$574$	−5.12769	−0.214026
$575$	2.40858	0.100445
$576$	106.293	4.42888
$577$	38.7010	1.61114	0.805571	−	0.592499i	$-0.201858\pi$
$577$	38.7010	1.61114	0.805571	+	0.592499i	$0.201858\pi$
$578$	44.7314	1.86058
$579$	−9.47761	−0.393876
$580$	14.8363	0.616045
$581$	−20.9712	−0.870031
$582$	5.15982	0.213881
$583$	−42.6995	−1.76843
$584$	−46.4690	−1.92290
$585$	−0.802183	−0.0331662
$586$	6.65945	0.275099
$587$	−40.8370	−1.68552	−0.842761	−	0.538287i	$-0.819072\pi$
$587$	−40.8370	−1.68552	−0.842761	+	0.538287i	$0.819072\pi$
$588$	−20.4318	−0.842594
$589$	−5.12154	−0.211029
$590$	97.3353	4.00723
$591$	−35.5656	−1.46297
$592$	35.6882	1.46678
$593$	−26.8984	−1.10459	−0.552293	−	0.833650i	$-0.686247\pi$
$593$	−26.8984	−1.10459	−0.552293	+	0.833650i	$0.686247\pi$
$594$	−31.1839	−1.27949
$595$	−8.33701	−0.341784
$596$	118.420	4.85066
$597$	50.4219	2.06363
$598$	0.400031	0.0163585
$599$	−43.4855	−1.77677	−0.888384	−	0.459102i	$-0.848171\pi$
$599$	−43.4855	−1.77677	−0.888384	+	0.459102i	$0.848171\pi$
$600$	59.7297	2.43845
$601$	−11.4288	−0.466191	−0.233095	−	0.972454i	$-0.574885\pi$
$601$	−11.4288	−0.466191	−0.233095	+	0.972454i	$0.574885\pi$
$602$	25.9413	1.05729
$603$	6.43139	0.261906
$604$	−126.345	−5.14090
$605$	46.7152	1.89924
$606$	−76.7458	−3.11759
$607$	9.24755	0.375346	0.187673	−	0.982232i	$-0.439905\pi$
$607$	9.24755	0.375346	0.187673	+	0.982232i	$0.439905\pi$
$608$	−91.9045	−3.72722
$609$	6.06413	0.245731
$610$	64.6511	2.61764
$611$	1.07722	0.0435798
$612$	12.8516	0.519495
$613$	−32.8738	−1.32776	−0.663881	−	0.747839i	$-0.731092\pi$
$613$	−32.8738	−1.32776	−0.663881	+	0.747839i	$0.731092\pi$
$614$	−41.0096	−1.65501
$615$	3.82499	0.154239
$616$	170.698	6.87763
$617$	−34.1493	−1.37480	−0.687400	−	0.726279i	$-0.741248\pi$
$617$	−34.1493	−1.37480	−0.687400	+	0.726279i	$0.741248\pi$
$618$	−35.2500	−1.41796
$619$	38.8857	1.56295	0.781474	−	0.623938i	$-0.214468\pi$
$619$	38.8857	1.56295	0.781474	+	0.623938i	$0.214468\pi$
$620$	−28.5643	−1.14717
$621$	2.08879	0.0838201
$622$	−65.7151	−2.63494
$623$	21.7489	0.871352
$624$	6.13217	0.245483
$625$	−31.2416	−1.24967
$626$	52.3887	2.09387
$627$	−34.4966	−1.37766
$628$	−31.8178	−1.26967
$629$	1.95429	0.0779226
$630$	46.3607	1.84705
$631$	−25.5907	−1.01875	−0.509375	−	0.860544i	$-0.670124\pi$
$631$	−25.5907	−1.01875	−0.509375	+	0.860544i	$0.670124\pi$
$632$	−56.2270	−2.23659
$633$	64.9708	2.58236
$634$	85.4817	3.39491
$635$	−33.4480	−1.32734
$636$	107.171	4.24961
$637$	−0.218127	−0.00864251
$638$	−13.7599	−0.544759
$639$	17.3466	0.686223
$640$	−219.354	−8.67074
$641$	−29.2989	−1.15724	−0.578619	−	0.815598i	$-0.696408\pi$
$641$	−29.2989	−1.15724	−0.578619	+	0.815598i	$0.696408\pi$
$642$	−25.7255	−1.01530
$643$	37.9271	1.49570	0.747850	−	0.663867i	$-0.231086\pi$
$643$	37.9271	1.49570	0.747850	+	0.663867i	$0.231086\pi$
$644$	−17.2765	−0.680788
$645$	−19.3509	−0.761940
$646$	−8.51313	−0.334944
$647$	8.18141	0.321644	0.160822	−	0.986983i	$-0.448585\pi$
$647$	8.18141	0.321644	0.160822	+	0.986983i	$0.448585\pi$
$648$	120.261	4.72429
$649$	−67.4597	−2.64802
$650$	0.963505	0.0377918
$651$	−11.6752	−0.457589
$652$	−73.8659	−2.89281
$653$	43.7720	1.71293	0.856466	−	0.516204i	$-0.172655\pi$
$653$	43.7720	1.71293	0.856466	+	0.516204i	$0.172655\pi$
$654$	−8.79556	−0.343934
$655$	36.1911	1.41410
$656$	−11.9468	−0.466446
$657$	8.74698	0.341252
$658$	−62.2562	−2.42700
$659$	−12.9899	−0.506016	−0.253008	−	0.967464i	$-0.581420\pi$
$659$	−12.9899	−0.506016	−0.253008	+	0.967464i	$0.581420\pi$
$660$	−192.398	−7.48907
$661$	−17.7405	−0.690025	−0.345013	−	0.938598i	$-0.612125\pi$
$661$	−17.7405	−0.690025	−0.345013	+	0.938598i	$0.612125\pi$
$662$	−27.4930	−1.06855
$663$	0.335798	0.0130413
$664$	−79.0429	−3.06746
$665$	−22.9492	−0.889930
$666$	−10.8675	−0.421106
$667$	0.921678	0.0356875
$668$	−117.013	−4.52738
$669$	0.712750	0.0275565
$670$	−23.7607	−0.917957
$671$	−44.8074	−1.72977
$672$	−209.509	−8.08198
$673$	−3.05553	−0.117782	−0.0588911	−	0.998264i	$-0.518756\pi$
$673$	−3.05553	−0.117782	−0.0588911	+	0.998264i	$0.518756\pi$
$674$	31.2880	1.20517
$675$	5.03100	0.193643
$676$	−76.7621	−2.95239
$677$	14.1617	0.544276	0.272138	−	0.962258i	$-0.412269\pi$
$677$	14.1617	0.544276	0.272138	+	0.962258i	$0.412269\pi$
$678$	1.37906	0.0529626
$679$	−2.37902	−0.0912984
$680$	−31.4232	−1.20503
$681$	−51.0231	−1.95521
$682$	26.4919	1.01443
$683$	−25.4932	−0.975471	−0.487736	−	0.872991i	$-0.662177\pi$
$683$	−25.4932	−0.975471	−0.487736	+	0.872991i	$0.662177\pi$
$684$	35.3764	1.35265
$685$	−21.8063	−0.833174
$686$	−44.9206	−1.71508
$687$	50.0388	1.90910
$688$	60.4398	2.30425
$689$	1.14414	0.0435884
$690$	17.2456	0.656530
$691$	−22.7104	−0.863945	−0.431973	−	0.901887i	$-0.642182\pi$
$691$	−22.7104	−0.863945	−0.431973	+	0.901887i	$0.642182\pi$
$692$	11.9654	0.454857
$693$	−32.1310	−1.22055
$694$	30.8211	1.16995
$695$	7.10961	0.269683
$696$	22.8564	0.866371
$697$	−0.654210	−0.0247800
$698$	−2.81318	−0.106480
$699$	46.7448	1.76805
$700$	−41.6117	−1.57277
$701$	7.58368	0.286432	0.143216	−	0.989691i	$-0.454256\pi$
$701$	7.58368	0.286432	0.143216	+	0.989691i	$0.454256\pi$
$702$	0.835579	0.0315369
$703$	5.37954	0.202893
$704$	272.166	10.2576
$705$	46.4399	1.74903
$706$	−47.2026	−1.77649
$707$	35.3849	1.33079
$708$	169.316	6.36330
$709$	17.5637	0.659619	0.329810	−	0.944047i	$-0.393015\pi$
$709$	17.5637	0.659619	0.329810	+	0.944047i	$0.393015\pi$
$710$	−64.0871	−2.40515
$711$	10.5837	0.396922
$712$	81.9743	3.07212
$713$	−1.77450	−0.0664556
$714$	−19.4068	−0.726282
$715$	−2.05401	−0.0768155
$716$	−12.5347	−0.468442
$717$	−30.0130	−1.12086
$718$	37.6744	1.40600
$719$	−7.86971	−0.293491	−0.146745	−	0.989174i	$-0.546880\pi$
$719$	−7.86971	−0.293491	−0.146745	+	0.989174i	$0.546880\pi$
$720$	108.014	4.02546
$721$	16.2526	0.605278
$722$	30.0165	1.11710
$723$	0.0328506	0.00122173
$724$	−59.1493	−2.19827
$725$	2.21993	0.0824462
$726$	108.743	4.03584
$727$	0.309533	0.0114799	0.00573996	−	0.999984i	$-0.498173\pi$
$727$	0.309533	0.0114799	0.00573996	+	0.999984i	$0.498173\pi$
$728$	−4.57390	−0.169520
$729$	−8.52365	−0.315691
$730$	−32.3157	−1.19606
$731$	3.30969	0.122413
$732$	112.462	4.15670
$733$	44.2936	1.63602	0.818011	−	0.575203i	$-0.195077\pi$
$733$	44.2936	1.63602	0.818011	+	0.575203i	$0.195077\pi$
$734$	53.6823	1.98145
$735$	−9.40361	−0.346858
$736$	−31.8429	−1.17375
$737$	16.4677	0.606596
$738$	3.63795	0.133915
$739$	26.6385	0.979913	0.489957	−	0.871747i	$-0.337013\pi$
$739$	26.6385	0.979913	0.489957	+	0.871747i	$0.337013\pi$
$740$	30.0032	1.10294
$741$	0.924345	0.0339567
$742$	−66.1237	−2.42748
$743$	7.42155	0.272270	0.136135	−	0.990690i	$-0.456532\pi$
$743$	7.42155	0.272270	0.136135	+	0.990690i	$0.456532\pi$
$744$	−44.0054	−1.61332
$745$	54.5019	1.99680
$746$	−9.21639	−0.337436
$747$	14.8784	0.544374
$748$	32.9068	1.20319
$749$	11.8612	0.433398
$750$	−44.6907	−1.63187
$751$	−36.9442	−1.34811	−0.674056	−	0.738680i	$-0.735449\pi$
$751$	−36.9442	−1.34811	−0.674056	+	0.738680i	$0.735449\pi$
$752$	−145.049	−5.28938
$753$	−38.6956	−1.41014
$754$	0.368700	0.0134272
$755$	−58.1494	−2.11627
$756$	−36.0868	−1.31247
$757$	14.0961	0.512330	0.256165	−	0.966633i	$-0.417541\pi$
$757$	14.0961	0.512330	0.256165	+	0.966633i	$0.417541\pi$
$758$	8.97236	0.325891
$759$	−11.9523	−0.433842
$760$	−86.4981	−3.13762
$761$	21.2631	0.770788	0.385394	−	0.922752i	$-0.374066\pi$
$761$	21.2631	0.770788	0.385394	+	0.922752i	$0.374066\pi$
$762$	−77.8600	−2.82057
$763$	4.05534	0.146813
$764$	−30.4105	−1.10021
$765$	5.91487	0.213852
$766$	−100.759	−3.64059
$767$	1.80760	0.0652686
$768$	−279.597	−10.0891
$769$	−14.7049	−0.530272	−0.265136	−	0.964211i	$-0.585417\pi$
$769$	−14.7049	−0.530272	−0.265136	+	0.964211i	$0.585417\pi$
$770$	118.708	4.27793
$771$	−31.0994	−1.12002
$772$	24.8865	0.895685
$773$	−22.9930	−0.827001	−0.413500	−	0.910504i	$-0.635694\pi$
$773$	−22.9930	−0.827001	−0.413500	+	0.910504i	$0.635694\pi$
$774$	−18.4046	−0.661539
$775$	−4.27403	−0.153528
$776$	−8.96682	−0.321890
$777$	12.2634	0.439947
$778$	−4.14126	−0.148471
$779$	−1.80083	−0.0645215
$780$	5.15534	0.184591
$781$	44.4165	1.58935
$782$	−2.94961	−0.105478
$783$	1.92519	0.0688006
$784$	29.3709	1.04896
$785$	−14.6439	−0.522665
$786$	84.2453	3.00493
$787$	1.76103	0.0627738	0.0313869	−	0.999507i	$-0.490008\pi$
$787$	1.76103	0.0627738	0.0313869	+	0.999507i	$0.490008\pi$
$788$	93.3890	3.32684
$789$	−11.0272	−0.392577
$790$	−39.1016	−1.39117
$791$	−0.635841	−0.0226079
$792$	−121.105	−4.30330
$793$	1.20062	0.0426354
$794$	23.8725	0.847202
$795$	49.3249	1.74937
$796$	−132.399	−4.69276
$797$	1.18783	0.0420750	0.0210375	−	0.999779i	$-0.493303\pi$
$797$	1.18783	0.0420750	0.0210375	+	0.999779i	$0.493303\pi$
$798$	−53.4208	−1.89108
$799$	−7.94287	−0.280999
$800$	−76.6962	−2.71162
$801$	−15.4302	−0.545200
$802$	21.4987	0.759146
$803$	22.3968	0.790367
$804$	−41.3322	−1.45767
$805$	−7.95138	−0.280249
$806$	−0.709856	−0.0250036
$807$	−42.3365	−1.49032
$808$	133.370	4.69195
$809$	−2.91231	−0.102391	−0.0511957	−	0.998689i	$-0.516303\pi$
$809$	−2.91231	−0.102391	−0.0511957	+	0.998689i	$0.516303\pi$
$810$	83.6322	2.93853
$811$	−52.2026	−1.83308	−0.916541	−	0.399940i	$-0.869031\pi$
$811$	−52.2026	−1.83308	−0.916541	+	0.399940i	$0.869031\pi$
$812$	−15.9233	−0.558799
$813$	−53.0584	−1.86084
$814$	−27.8264	−0.975315
$815$	−33.9963	−1.19084
$816$	−45.2154	−1.58285
$817$	9.11052	0.318737
$818$	80.4519	2.81294
$819$	0.860956	0.0300843
$820$	−10.0438	−0.350743
$821$	38.6585	1.34919	0.674595	−	0.738188i	$-0.264318\pi$
$821$	38.6585	1.34919	0.674595	+	0.738188i	$0.264318\pi$
$822$	−50.7604	−1.77047
$823$	12.9508	0.451435	0.225718	−	0.974193i	$-0.427527\pi$
$823$	12.9508	0.451435	0.225718	+	0.974193i	$0.427527\pi$
$824$	61.2580	2.13402
$825$	−28.7881	−1.00227
$826$	−104.467	−3.63486
$827$	29.9113	1.04012	0.520058	−	0.854131i	$-0.325910\pi$
$827$	29.9113	1.04012	0.520058	+	0.854131i	$0.325910\pi$
$828$	12.2571	0.425965
$829$	28.3250	0.983770	0.491885	−	0.870660i	$-0.336308\pi$
$829$	28.3250	0.983770	0.491885	+	0.870660i	$0.336308\pi$
$830$	−54.9683	−1.90798
$831$	−18.7405	−0.650102
$832$	−7.29275	−0.252831
$833$	1.60835	0.0557261
$834$	16.5497	0.573069
$835$	−53.8547	−1.86372
$836$	90.5820	3.13284
$837$	−3.70656	−0.128117
$838$	−92.3381	−3.18977
$839$	42.5527	1.46908	0.734541	−	0.678564i	$-0.237397\pi$
$839$	42.5527	1.46908	0.734541	+	0.678564i	$0.237397\pi$
$840$	−197.184	−6.80350
$841$	−28.1505	−0.970707
$842$	72.5528	2.50033
$843$	−65.8451	−2.26782
$844$	−170.602	−5.87236
$845$	−35.3293	−1.21536
$846$	44.1689	1.51856
$847$	−50.1378	−1.72276
$848$	−154.059	−5.29042
$849$	−31.4552	−1.07954
$850$	−7.10437	−0.243678
$851$	1.86389	0.0638935
$852$	−111.481	−3.81926
$853$	9.78227	0.334939	0.167469	−	0.985877i	$-0.446440\pi$
$853$	9.78227	0.334939	0.167469	+	0.985877i	$0.446440\pi$
$854$	−69.3879	−2.37440
$855$	16.2818	0.556824
$856$	44.7062	1.52803
$857$	−11.4939	−0.392626	−0.196313	−	0.980541i	$-0.562897\pi$
$857$	−11.4939	−0.392626	−0.196313	+	0.980541i	$0.562897\pi$
$858$	−4.78130	−0.163231
$859$	−6.69622	−0.228472	−0.114236	−	0.993454i	$-0.536442\pi$
$859$	−6.69622	−0.228472	−0.114236	+	0.993454i	$0.536442\pi$
$860$	50.8120	1.73267
$861$	−4.10524	−0.139906
$862$	91.8733	3.12922
$863$	6.11113	0.208025	0.104013	−	0.994576i	$-0.466832\pi$
$863$	6.11113	0.208025	0.104013	+	0.994576i	$0.466832\pi$
$864$	−66.5131	−2.26282
$865$	5.50700	0.187244
$866$	11.2658	0.382828
$867$	35.8120	1.21624
$868$	30.6571	1.04057
$869$	27.0999	0.919303
$870$	15.8949	0.538888
$871$	−0.441256	−0.0149514
$872$	15.2851	0.517618
$873$	1.68785	0.0571249
$874$	−8.11935	−0.274641
$875$	20.6054	0.696589
$876$	−56.2137	−1.89928
$877$	−52.2842	−1.76551	−0.882755	−	0.469833i	$-0.844314\pi$
$877$	−52.2842	−1.76551	−0.882755	+	0.469833i	$0.844314\pi$
$878$	−54.4681	−1.83821
$879$	5.33157	0.179829
$880$	276.573	9.32328
$881$	0.431514	0.0145381	0.00726903	−	0.999974i	$-0.497686\pi$
$881$	0.431514	0.0145381	0.00726903	+	0.999974i	$0.497686\pi$
$882$	−8.94377	−0.301152
$883$	−48.0621	−1.61742	−0.808709	−	0.588209i	$-0.799833\pi$
$883$	−48.0621	−1.61742	−0.808709	+	0.588209i	$0.799833\pi$
$884$	−0.881746	−0.0296563
$885$	77.9268	2.61948
$886$	−38.1952	−1.28319
$887$	−23.1296	−0.776614	−0.388307	−	0.921530i	$-0.626940\pi$
$887$	−23.1296	−0.776614	−0.388307	+	0.921530i	$0.626940\pi$
$888$	46.2222	1.55112
$889$	35.8987	1.20400
$890$	57.0069	1.91087
$891$	−57.9625	−1.94182
$892$	−1.87156	−0.0626643
$893$	−21.8642	−0.731658
$894$	126.869	4.24314
$895$	−5.76900	−0.192836
$896$	235.426	7.86502
$897$	0.320266	0.0106934
$898$	12.7227	0.424563
$899$	−1.63552	−0.0545476
$900$	29.5223	0.984076
$901$	−8.43630	−0.281054
$902$	9.31505	0.310157
$903$	20.7687	0.691138
$904$	−2.39656	−0.0797084
$905$	−27.2231	−0.904926
$906$	−135.360	−4.49703
$907$	−21.7096	−0.720855	−0.360427	−	0.932787i	$-0.617369\pi$
$907$	−21.7096	−0.720855	−0.360427	+	0.932787i	$0.617369\pi$
$908$	133.977	4.44620
$909$	−25.1046	−0.832667
$910$	−3.18080	−0.105442
$911$	33.5066	1.11012	0.555062	−	0.831809i	$-0.312695\pi$
$911$	33.5066	1.11012	0.555062	+	0.831809i	$0.312695\pi$
$912$	−124.464	−4.12140
$913$	38.0966	1.26081
$914$	58.6928	1.94139
$915$	51.7598	1.71113
$916$	−131.393	−4.34135
$917$	−38.8427	−1.28270
$918$	−6.16111	−0.203347
$919$	−0.656300	−0.0216494	−0.0108247	−	0.999941i	$-0.503446\pi$
$919$	−0.656300	−0.0216494	−0.0108247	+	0.999941i	$0.503446\pi$
$920$	−29.9697	−0.988073
$921$	−32.8323	−1.08186
$922$	95.0022	3.12873
$923$	−1.19015	−0.0391743
$924$	206.494	6.79315
$925$	4.48933	0.147608
$926$	51.6243	1.69648
$927$	−11.5307	−0.378719
$928$	−29.3489	−0.963426
$929$	−15.8635	−0.520465	−0.260232	−	0.965546i	$-0.583799\pi$
$929$	−15.8635	−0.520465	−0.260232	+	0.965546i	$0.583799\pi$
$930$	−30.6024	−1.00349
$931$	4.42728	0.145098
$932$	−122.743	−4.02060
$933$	−52.6117	−1.72243
$934$	43.9971	1.43963
$935$	15.1452	0.495300
$936$	3.24505	0.106068
$937$	−50.8729	−1.66194	−0.830972	−	0.556314i	$-0.812215\pi$
$937$	−50.8729	−1.66194	−0.830972	+	0.556314i	$0.812215\pi$
$938$	25.5016	0.832657
$939$	41.9425	1.36874
$940$	−121.943	−3.97734
$941$	−28.2584	−0.921199	−0.460599	−	0.887608i	$-0.652366\pi$
$941$	−28.2584	−0.921199	−0.460599	+	0.887608i	$0.652366\pi$
$942$	−34.0880	−1.11065
$943$	−0.623949	−0.0203186
$944$	−243.394	−7.92180
$945$	−16.6087	−0.540282
$946$	−47.1254	−1.53218
$947$	−30.5233	−0.991873	−0.495936	−	0.868359i	$-0.665175\pi$
$947$	−30.5233	−0.991873	−0.495936	+	0.868359i	$0.665175\pi$
$948$	−68.0179	−2.20912
$949$	−0.600129	−0.0194810
$950$	−19.5561	−0.634483
$951$	68.4369	2.21922
$952$	33.7255	1.09305
$953$	−46.6519	−1.51120	−0.755602	−	0.655031i	$-0.772656\pi$
$953$	−46.6519	−1.51120	−0.755602	+	0.655031i	$0.772656\pi$
$954$	46.9128	1.51886
$955$	−13.9963	−0.452908
$956$	78.8088	2.54886
$957$	−11.0162	−0.356103
$958$	−71.3431	−2.30499
$959$	23.4039	0.755753
$960$	−314.396	−10.1471
$961$	−27.8511	−0.898424
$962$	0.745615	0.0240396
$963$	−8.41516	−0.271175
$964$	−0.0862598	−0.00277824
$965$	11.4539	0.368713
$966$	−18.5092	−0.595522
$967$	38.7390	1.24576	0.622880	−	0.782317i	$-0.285962\pi$
$967$	38.7390	1.24576	0.622880	+	0.782317i	$0.285962\pi$
$968$	−188.976	−6.07391
$969$	−6.81563	−0.218950
$970$	−6.23573	−0.200217
$971$	−13.0488	−0.418755	−0.209378	−	0.977835i	$-0.567144\pi$
$971$	−13.0488	−0.418755	−0.209378	+	0.977835i	$0.567144\pi$
$972$	108.421	3.47759
$973$	−7.63051	−0.244623
$974$	27.0326	0.866179
$975$	0.771384	0.0247041
$976$	−161.665	−5.17476
$977$	−41.7883	−1.33693	−0.668464	−	0.743745i	$-0.733048\pi$
$977$	−41.7883	−1.33693	−0.668464	+	0.743745i	$0.733048\pi$
$978$	−79.1364	−2.53050
$979$	−39.5095	−1.26273
$980$	24.6922	0.788764
$981$	−2.87715	−0.0918602
$982$	−100.017	−3.19168
$983$	21.1812	0.675576	0.337788	−	0.941222i	$-0.390321\pi$
$983$	21.1812	0.675576	0.337788	+	0.941222i	$0.390321\pi$
$984$	−15.4731	−0.493266
$985$	42.9817	1.36951
$986$	−2.71859	−0.0865777
$987$	−49.8424	−1.58650
$988$	−2.42717	−0.0772184
$989$	3.15660	0.100374
$990$	−84.2196	−2.67667
$991$	8.55149	0.271647	0.135824	−	0.990733i	$-0.456632\pi$
$991$	8.55149	0.271647	0.135824	+	0.990733i	$0.456632\pi$
$992$	56.5054	1.79405
$993$	−22.0110	−0.698498
$994$	68.7826	2.18165
$995$	−60.9358	−1.93179
$996$	−95.6184	−3.02978
$997$	53.3351	1.68914	0.844570	−	0.535445i	$-0.179856\pi$
$997$	53.3351	1.68914	0.844570	+	0.535445i	$0.179856\pi$
$998$	−53.3755	−1.68957
$999$	3.89328	0.123178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.1	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.1	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.81318 q^{2} -2.25224 q^{3} +5.91397 q^{4} +2.72187 q^{5} +6.33595 q^{6} -2.92129 q^{7} -11.0107 q^{8} +2.07257 q^{9} +O(q^{10})\)	\(q-2.81318 q^{2} -2.25224 q^{3} +5.91397 q^{4} +2.72187 q^{5} +6.33595 q^{6} -2.92129 q^{7} -11.0107 q^{8} +2.07257 q^{9} -7.65711 q^{10} +5.30687 q^{11} -13.3197 q^{12} -0.142199 q^{13} +8.21812 q^{14} -6.13030 q^{15} +19.1471 q^{16} +1.04850 q^{17} -5.83052 q^{18} +2.88618 q^{19} +16.0971 q^{20} +6.57945 q^{21} -14.9292 q^{22} +1.00000 q^{23} +24.7987 q^{24} +2.40858 q^{25} +0.400031 q^{26} +2.08879 q^{27} -17.2765 q^{28} +0.921678 q^{29} +17.2456 q^{30} -1.77450 q^{31} -31.8429 q^{32} -11.9523 q^{33} -2.94961 q^{34} -7.95138 q^{35} +12.2571 q^{36} +1.86389 q^{37} -8.11935 q^{38} +0.320266 q^{39} -29.9697 q^{40} -0.623949 q^{41} -18.5092 q^{42} +3.15660 q^{43} +31.3847 q^{44} +5.64127 q^{45} -2.81318 q^{46} -7.57547 q^{47} -43.1239 q^{48} +1.53396 q^{49} -6.77576 q^{50} -2.36147 q^{51} -0.840960 q^{52} -8.04608 q^{53} -5.87613 q^{54} +14.4446 q^{55} +32.1655 q^{56} -6.50037 q^{57} -2.59284 q^{58} -12.7118 q^{59} -36.2544 q^{60} -8.44327 q^{61} +4.99199 q^{62} -6.05459 q^{63} +51.2856 q^{64} -0.387047 q^{65} +33.6241 q^{66} +3.10309 q^{67} +6.20079 q^{68} -2.25224 q^{69} +22.3687 q^{70} +8.36962 q^{71} -22.8205 q^{72} +4.22035 q^{73} -5.24347 q^{74} -5.42469 q^{75} +17.0688 q^{76} -15.5029 q^{77} -0.900964 q^{78} +5.10658 q^{79} +52.1161 q^{80} -10.9222 q^{81} +1.75528 q^{82} +7.17873 q^{83} +38.9107 q^{84} +2.85388 q^{85} -8.88007 q^{86} -2.07584 q^{87} -58.4324 q^{88} -7.44496 q^{89} -15.8699 q^{90} +0.415405 q^{91} +5.91397 q^{92} +3.99660 q^{93} +21.3112 q^{94} +7.85582 q^{95} +71.7178 q^{96} +0.814372 q^{97} -4.31530 q^{98} +10.9989 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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