LMFDB - Embedded newform 8047.2.a.c.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8047,2,Mod(1,8047)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8047, 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("8047.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8047 = 13 \cdot 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8047.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:	$64.2556185065$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8047.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42822 q^{2} +2.05739 q^{3} +3.89625 q^{4} +1.53452 q^{5} -4.99579 q^{6} +1.53522 q^{7} -4.60451 q^{8} +1.23285 q^{9} +O(q^{10})$	\(q-2.42822 q^{2} +2.05739 q^{3} +3.89625 q^{4} +1.53452 q^{5} -4.99579 q^{6} +1.53522 q^{7} -4.60451 q^{8} +1.23285 q^{9} -3.72615 q^{10} +6.13938 q^{11} +8.01610 q^{12} -1.00000 q^{13} -3.72784 q^{14} +3.15710 q^{15} +3.38826 q^{16} -3.53429 q^{17} -2.99363 q^{18} -6.93943 q^{19} +5.97887 q^{20} +3.15854 q^{21} -14.9078 q^{22} -2.61012 q^{23} -9.47327 q^{24} -2.64525 q^{25} +2.42822 q^{26} -3.63571 q^{27} +5.98159 q^{28} -8.21506 q^{29} -7.66614 q^{30} -3.68024 q^{31} +0.981582 q^{32} +12.6311 q^{33} +8.58203 q^{34} +2.35582 q^{35} +4.80349 q^{36} -3.79993 q^{37} +16.8505 q^{38} -2.05739 q^{39} -7.06571 q^{40} +6.73124 q^{41} -7.66962 q^{42} -5.52012 q^{43} +23.9206 q^{44} +1.89183 q^{45} +6.33794 q^{46} +10.9792 q^{47} +6.97097 q^{48} -4.64311 q^{49} +6.42324 q^{50} -7.27141 q^{51} -3.89625 q^{52} +5.00677 q^{53} +8.82831 q^{54} +9.42101 q^{55} -7.06892 q^{56} -14.2771 q^{57} +19.9480 q^{58} -10.7930 q^{59} +12.3009 q^{60} +2.61800 q^{61} +8.93643 q^{62} +1.89269 q^{63} -9.16001 q^{64} -1.53452 q^{65} -30.6711 q^{66} -8.34550 q^{67} -13.7705 q^{68} -5.37003 q^{69} -5.72045 q^{70} -12.3484 q^{71} -5.67667 q^{72} +5.92499 q^{73} +9.22707 q^{74} -5.44231 q^{75} -27.0377 q^{76} +9.42529 q^{77} +4.99579 q^{78} -7.49898 q^{79} +5.19935 q^{80} -11.1786 q^{81} -16.3449 q^{82} +4.03813 q^{83} +12.3065 q^{84} -5.42344 q^{85} +13.4041 q^{86} -16.9016 q^{87} -28.2689 q^{88} -15.1230 q^{89} -4.59379 q^{90} -1.53522 q^{91} -10.1697 q^{92} -7.57169 q^{93} -26.6599 q^{94} -10.6487 q^{95} +2.01950 q^{96} +9.60392 q^{97} +11.2745 q^{98} +7.56895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) $ 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * 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 $

$2$	−2.42822	−1.71701	−0.858505	−	0.512805i	$-0.828606\pi$
$2$	−2.42822	−1.71701	−0.858505	+	0.512805i	$0.828606\pi$
$3$	2.05739	1.18783	0.593917	−	0.804526i	$-0.297581\pi$
$3$	2.05739	1.18783	0.593917	+	0.804526i	$0.297581\pi$
$4$	3.89625	1.94812
$5$	1.53452	0.686258	0.343129	−	0.939288i	$-0.388513\pi$
$5$	1.53452	0.686258	0.343129	+	0.939288i	$0.388513\pi$
$6$	−4.99579	−2.03952
$7$	1.53522	0.580257	0.290129	−	0.956988i	$-0.406302\pi$
$7$	1.53522	0.580257	0.290129	+	0.956988i	$0.406302\pi$
$8$	−4.60451	−1.62794
$9$	1.23285	0.410950
$10$	−3.72615	−1.17831
$11$	6.13938	1.85109	0.925547	−	0.378633i	$-0.123606\pi$
$11$	6.13938	1.85109	0.925547	+	0.378633i	$0.123606\pi$
$12$	8.01610	2.31405
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.72784	−0.996308
$15$	3.15710	0.815161
$16$	3.38826	0.847065
$17$	−3.53429	−0.857191	−0.428596	−	0.903496i	$-0.640992\pi$
$17$	−3.53429	−0.857191	−0.428596	+	0.903496i	$0.640992\pi$
$18$	−2.99363	−0.705606
$19$	−6.93943	−1.59201	−0.796007	−	0.605287i	$-0.793058\pi$
$19$	−6.93943	−1.59201	−0.796007	+	0.605287i	$0.793058\pi$
$20$	5.97887	1.33692
$21$	3.15854	0.689250
$22$	−14.9078	−3.17835
$23$	−2.61012	−0.544247	−0.272124	−	0.962262i	$-0.587726\pi$
$23$	−2.61012	−0.544247	−0.272124	+	0.962262i	$0.587726\pi$
$24$	−9.47327	−1.93372
$25$	−2.64525	−0.529050
$26$	2.42822	0.476213
$27$	−3.63571	−0.699693
$28$	5.98159	1.13041
$29$	−8.21506	−1.52550	−0.762749	−	0.646695i	$-0.776151\pi$
$29$	−8.21506	−1.52550	−0.762749	+	0.646695i	$0.776151\pi$
$30$	−7.66614	−1.39964
$31$	−3.68024	−0.660991	−0.330495	−	0.943808i	$-0.607216\pi$
$31$	−3.68024	−0.660991	−0.330495	+	0.943808i	$0.607216\pi$
$32$	0.981582	0.173521
$33$	12.6311	2.19879
$34$	8.58203	1.47181
$35$	2.35582	0.398206
$36$	4.80349	0.800582
$37$	−3.79993	−0.624705	−0.312353	−	0.949966i	$-0.601117\pi$
$37$	−3.79993	−0.624705	−0.312353	+	0.949966i	$0.601117\pi$
$38$	16.8505	2.73351
$39$	−2.05739	−0.329446
$40$	−7.06571	−1.11719
$41$	6.73124	1.05124	0.525622	−	0.850718i	$-0.323833\pi$
$41$	6.73124	1.05124	0.525622	+	0.850718i	$0.323833\pi$
$42$	−7.66962	−1.18345
$43$	−5.52012	−0.841811	−0.420905	−	0.907105i	$-0.638288\pi$
$43$	−5.52012	−0.841811	−0.420905	+	0.907105i	$0.638288\pi$
$44$	23.9206	3.60616
$45$	1.89183	0.282018
$46$	6.33794	0.934478
$47$	10.9792	1.60148	0.800741	−	0.599011i	$-0.204439\pi$
$47$	10.9792	1.60148	0.800741	+	0.599011i	$0.204439\pi$
$48$	6.97097	1.00617
$49$	−4.64311	−0.663301
$50$	6.42324	0.908384
$51$	−7.27141	−1.01820
$52$	−3.89625	−0.540313
$53$	5.00677	0.687733	0.343867	−	0.939019i	$-0.388263\pi$
$53$	5.00677	0.687733	0.343867	+	0.939019i	$0.388263\pi$
$54$	8.82831	1.20138
$55$	9.42101	1.27033
$56$	−7.06892	−0.944624
$57$	−14.2771	−1.89105
$58$	19.9480	2.61930
$59$	−10.7930	−1.40512	−0.702562	−	0.711623i	$-0.747961\pi$
$59$	−10.7930	−1.40512	−0.702562	+	0.711623i	$0.747961\pi$
$60$	12.3009	1.58804
$61$	2.61800	0.335200	0.167600	−	0.985855i	$-0.446398\pi$
$61$	2.61800	0.335200	0.167600	+	0.985855i	$0.446398\pi$
$62$	8.93643	1.13493
$63$	1.89269	0.238457
$64$	−9.16001	−1.14500
$65$	−1.53452	−0.190334
$66$	−30.6711	−3.77535
$67$	−8.34550	−1.01956	−0.509782	−	0.860303i	$-0.670274\pi$
$67$	−8.34550	−1.01956	−0.509782	+	0.860303i	$0.670274\pi$
$68$	−13.7705	−1.66992
$69$	−5.37003	−0.646476
$70$	−5.72045	−0.683724
$71$	−12.3484	−1.46549	−0.732746	−	0.680503i	$-0.761761\pi$
$71$	−12.3484	−1.46549	−0.732746	+	0.680503i	$0.761761\pi$
$72$	−5.67667	−0.669002
$73$	5.92499	0.693468	0.346734	−	0.937964i	$-0.387291\pi$
$73$	5.92499	0.693468	0.346734	+	0.937964i	$0.387291\pi$
$74$	9.22707	1.07263
$75$	−5.44231	−0.628423
$76$	−27.0377	−3.10144
$77$	9.42529	1.07411
$78$	4.99579	0.565662
$79$	−7.49898	−0.843701	−0.421850	−	0.906665i	$-0.638619\pi$
$79$	−7.49898	−0.843701	−0.421850	+	0.906665i	$0.638619\pi$
$80$	5.19935	0.581305
$81$	−11.1786	−1.24207
$82$	−16.3449	−1.80500
$83$	4.03813	0.443242	0.221621	−	0.975133i	$-0.428865\pi$
$83$	4.03813	0.443242	0.221621	+	0.975133i	$0.428865\pi$
$84$	12.3065	1.34274
$85$	−5.42344	−0.588255
$86$	13.4041	1.44540
$87$	−16.9016	−1.81204
$88$	−28.2689	−3.01347
$89$	−15.1230	−1.60304	−0.801519	−	0.597970i	$-0.795974\pi$
$89$	−15.1230	−1.60304	−0.801519	+	0.597970i	$0.795974\pi$
$90$	−4.59379	−0.484228
$91$	−1.53522	−0.160934
$92$	−10.1697	−1.06026
$93$	−7.57169	−0.785147
$94$	−26.6599	−2.74976
$95$	−10.6487	−1.09253
$96$	2.01950	0.206114
$97$	9.60392	0.975130	0.487565	−	0.873087i	$-0.337885\pi$
$97$	9.60392	0.975130	0.487565	+	0.873087i	$0.337885\pi$
$98$	11.2745	1.13890
$99$	7.56895	0.760708
$100$	−10.3065	−1.03065
$101$	−5.08585	−0.506061	−0.253030	−	0.967458i	$-0.581427\pi$
$101$	−5.08585	−0.506061	−0.253030	+	0.967458i	$0.581427\pi$
$102$	17.6566	1.74826
$103$	14.1837	1.39756	0.698780	−	0.715337i	$-0.253727\pi$
$103$	14.1837	1.39756	0.698780	+	0.715337i	$0.253727\pi$
$104$	4.60451	0.451509
$105$	4.84684	0.473003
$106$	−12.1575	−1.18085
$107$	−1.92439	−0.186038	−0.0930191	−	0.995664i	$-0.529652\pi$
$107$	−1.92439	−0.186038	−0.0930191	+	0.995664i	$0.529652\pi$
$108$	−14.1656	−1.36309
$109$	−17.0604	−1.63409	−0.817045	−	0.576574i	$-0.804389\pi$
$109$	−17.0604	−1.63409	−0.817045	+	0.576574i	$0.804389\pi$
$110$	−22.8763	−2.18117
$111$	−7.81794	−0.742046
$112$	5.20171	0.491516
$113$	−5.45602	−0.513259	−0.256630	−	0.966510i	$-0.582612\pi$
$113$	−5.45602	−0.513259	−0.256630	+	0.966510i	$0.582612\pi$
$114$	34.6680	3.24695
$115$	−4.00528	−0.373494
$116$	−32.0079	−2.97186
$117$	−1.23285	−0.113977
$118$	26.2077	2.41261
$119$	−5.42590	−0.497392
$120$	−14.5369	−1.32703
$121$	26.6920	2.42655
$122$	−6.35707	−0.575542
$123$	13.8488	1.24870
$124$	−14.3391	−1.28769
$125$	−11.7318	−1.04932
$126$	−4.59587	−0.409433
$127$	6.84699	0.607573	0.303786	−	0.952740i	$-0.401749\pi$
$127$	6.84699	0.607573	0.303786	+	0.952740i	$0.401749\pi$
$128$	20.2794	1.79246
$129$	−11.3570	−0.999931
$130$	3.72615	0.326805
$131$	14.8229	1.29509	0.647543	−	0.762029i	$-0.275797\pi$
$131$	14.8229	1.29509	0.647543	+	0.762029i	$0.275797\pi$
$132$	49.2139	4.28352
$133$	−10.6535	−0.923778
$134$	20.2647	1.75060
$135$	−5.57908	−0.480170
$136$	16.2737	1.39546
$137$	−18.3730	−1.56972	−0.784858	−	0.619676i	$-0.787264\pi$
$137$	−18.3730	−1.56972	−0.784858	+	0.619676i	$0.787264\pi$
$138$	13.0396	1.11001
$139$	15.7598	1.33673	0.668363	−	0.743835i	$-0.266995\pi$
$139$	15.7598	1.33673	0.668363	+	0.743835i	$0.266995\pi$
$140$	9.17886	0.775756
$141$	22.5885	1.90230
$142$	29.9847	2.51626
$143$	−6.13938	−0.513401
$144$	4.17722	0.348101
$145$	−12.6062	−1.04689
$146$	−14.3872	−1.19069
$147$	−9.55268	−0.787892
$148$	−14.8055	−1.21700
$149$	−22.5557	−1.84784	−0.923919	−	0.382587i	$-0.875033\pi$
$149$	−22.5557	−1.84784	−0.923919	+	0.382587i	$0.875033\pi$
$150$	13.2151	1.07901
$151$	9.28412	0.755531	0.377765	−	0.925901i	$-0.376693\pi$
$151$	9.28412	0.755531	0.377765	+	0.925901i	$0.376693\pi$
$152$	31.9527	2.59170
$153$	−4.35725	−0.352263
$154$	−22.8867	−1.84426
$155$	−5.64740	−0.453610
$156$	−8.01610	−0.641802
$157$	−14.3172	−1.14264	−0.571320	−	0.820727i	$-0.693569\pi$
$157$	−14.3172	−1.14264	−0.571320	+	0.820727i	$0.693569\pi$
$158$	18.2092	1.44864
$159$	10.3009	0.816913
$160$	1.50626	0.119080
$161$	−4.00710	−0.315804
$162$	27.1442	2.13265
$163$	−13.6882	−1.07215	−0.536073	−	0.844172i	$-0.680093\pi$
$163$	−13.6882	−1.07215	−0.536073	+	0.844172i	$0.680093\pi$
$164$	26.2266	2.04795
$165$	19.3827	1.50894
$166$	−9.80546	−0.761051
$167$	−20.1888	−1.56226	−0.781129	−	0.624369i	$-0.785356\pi$
$167$	−20.1888	−1.56226	−0.781129	+	0.624369i	$0.785356\pi$
$168$	−14.5435	−1.12206
$169$	1.00000	0.0769231
$170$	13.1693	1.01004
$171$	−8.55528	−0.654239
$172$	−21.5078	−1.63995
$173$	14.8887	1.13197	0.565983	−	0.824417i	$-0.308497\pi$
$173$	14.8887	1.13197	0.565983	+	0.824417i	$0.308497\pi$
$174$	41.0407	3.11129
$175$	−4.06103	−0.306985
$176$	20.8018	1.56800
$177$	−22.2053	−1.66905
$178$	36.7220	2.75243
$179$	13.7751	1.02960	0.514798	−	0.857311i	$-0.327867\pi$
$179$	13.7751	1.02960	0.514798	+	0.857311i	$0.327867\pi$
$180$	7.37106	0.549406
$181$	8.13406	0.604600	0.302300	−	0.953213i	$-0.402246\pi$
$181$	8.13406	0.604600	0.302300	+	0.953213i	$0.402246\pi$
$182$	3.72784	0.276326
$183$	5.38624	0.398162
$184$	12.0183	0.886002
$185$	−5.83107	−0.428709
$186$	18.3857	1.34811
$187$	−21.6984	−1.58674
$188$	42.7777	3.11989
$189$	−5.58161	−0.406002
$190$	25.8574	1.87589
$191$	−6.75320	−0.488644	−0.244322	−	0.969694i	$-0.578565\pi$
$191$	−6.75320	−0.488644	−0.244322	+	0.969694i	$0.578565\pi$
$192$	−18.8457	−1.36007
$193$	26.3662	1.89788	0.948940	−	0.315456i	$-0.102157\pi$
$193$	26.3662	1.89788	0.948940	+	0.315456i	$0.102157\pi$
$194$	−23.3204	−1.67431
$195$	−3.15710	−0.226085
$196$	−18.0907	−1.29219
$197$	−23.9946	−1.70954	−0.854771	−	0.519005i	$-0.826302\pi$
$197$	−23.9946	−1.70954	−0.854771	+	0.519005i	$0.826302\pi$
$198$	−18.3791	−1.30614
$199$	0.641296	0.0454603	0.0227301	−	0.999742i	$-0.492764\pi$
$199$	0.641296	0.0454603	0.0227301	+	0.999742i	$0.492764\pi$
$200$	12.1801	0.861261
$201$	−17.1699	−1.21107
$202$	12.3496	0.868911
$203$	−12.6119	−0.885181
$204$	−28.3312	−1.98358
$205$	10.3292	0.721425
$206$	−34.4411	−2.39962
$207$	−3.21789	−0.223659
$208$	−3.38826	−0.234933
$209$	−42.6038	−2.94697
$210$	−11.7692	−0.812151
$211$	−2.42611	−0.167020	−0.0835102	−	0.996507i	$-0.526613\pi$
$211$	−2.42611	−0.167020	−0.0835102	+	0.996507i	$0.526613\pi$
$212$	19.5076	1.33979
$213$	−25.4056	−1.74076
$214$	4.67285	0.319430
$215$	−8.47073	−0.577699
$216$	16.7407	1.13906
$217$	−5.64997	−0.383545
$218$	41.4264	2.80575
$219$	12.1900	0.823725
$220$	36.7066	2.47476
$221$	3.53429	0.237742
$222$	18.9837	1.27410
$223$	5.33022	0.356938	0.178469	−	0.983946i	$-0.442886\pi$
$223$	5.33022	0.356938	0.178469	+	0.983946i	$0.442886\pi$
$224$	1.50694	0.100687
$225$	−3.26120	−0.217413
$226$	13.2484	0.881271
$227$	−13.3349	−0.885068	−0.442534	−	0.896752i	$-0.645920\pi$
$227$	−13.3349	−0.885068	−0.442534	+	0.896752i	$0.645920\pi$
$228$	−55.6272	−3.68400
$229$	26.7555	1.76805	0.884026	−	0.467438i	$-0.154823\pi$
$229$	26.7555	1.76805	0.884026	+	0.467438i	$0.154823\pi$
$230$	9.72570	0.641293
$231$	19.3915	1.27587
$232$	37.8263	2.48342
$233$	−18.5651	−1.21624	−0.608121	−	0.793844i	$-0.708077\pi$
$233$	−18.5651	−1.21624	−0.608121	+	0.793844i	$0.708077\pi$
$234$	2.99363	0.195700
$235$	16.8478	1.09903
$236$	−42.0521	−2.73736
$237$	−15.4283	−1.00218
$238$	13.1753	0.854027
$239$	4.04111	0.261397	0.130699	−	0.991422i	$-0.458278\pi$
$239$	4.04111	0.261397	0.130699	+	0.991422i	$0.458278\pi$
$240$	10.6971	0.690494
$241$	21.0517	1.35606	0.678030	−	0.735034i	$-0.262834\pi$
$241$	21.0517	1.35606	0.678030	+	0.735034i	$0.262834\pi$
$242$	−64.8141	−4.16641
$243$	−12.0917	−0.775680
$244$	10.2004	0.653012
$245$	−7.12494	−0.455196
$246$	−33.6279	−2.14404
$247$	6.93943	0.441545
$248$	16.9457	1.07605
$249$	8.30800	0.526498
$250$	28.4874	1.80170
$251$	18.1791	1.14745	0.573726	−	0.819047i	$-0.305497\pi$
$251$	18.1791	1.14745	0.573726	+	0.819047i	$0.305497\pi$
$252$	7.37440	0.464544
$253$	−16.0245	−1.00745
$254$	−16.6260	−1.04321
$255$	−11.1581	−0.698749
$256$	−30.9227	−1.93267
$257$	0.849631	0.0529985	0.0264992	−	0.999649i	$-0.491564\pi$
$257$	0.849631	0.0529985	0.0264992	+	0.999649i	$0.491564\pi$
$258$	27.5774	1.71689
$259$	−5.83372	−0.362490
$260$	−5.97887	−0.370794
$261$	−10.1279	−0.626904
$262$	−35.9934	−2.22368
$263$	−9.46369	−0.583556	−0.291778	−	0.956486i	$-0.594247\pi$
$263$	−9.46369	−0.583556	−0.291778	+	0.956486i	$0.594247\pi$
$264$	−58.1600	−3.57950
$265$	7.68299	0.471963
$266$	25.8691	1.58614
$267$	−31.1140	−1.90414
$268$	−32.5161	−1.98624
$269$	2.74106	0.167125	0.0835626	−	0.996503i	$-0.473370\pi$
$269$	2.74106	0.167125	0.0835626	+	0.996503i	$0.473370\pi$
$270$	13.5472	0.824457
$271$	20.1087	1.22152	0.610758	−	0.791817i	$-0.290865\pi$
$271$	20.1087	1.22152	0.610758	+	0.791817i	$0.290865\pi$
$272$	−11.9751	−0.726097
$273$	−3.15854	−0.191163
$274$	44.6138	2.69522
$275$	−16.2402	−0.979321
$276$	−20.9230	−1.25942
$277$	4.78739	0.287647	0.143823	−	0.989603i	$-0.454060\pi$
$277$	4.78739	0.287647	0.143823	+	0.989603i	$0.454060\pi$
$278$	−38.2682	−2.29517
$279$	−4.53719	−0.271634
$280$	−10.8474	−0.648256
$281$	0.682134	0.0406927	0.0203464	−	0.999793i	$-0.493523\pi$
$281$	0.682134	0.0406927	0.0203464	+	0.999793i	$0.493523\pi$
$282$	−54.8498	−3.26626
$283$	−27.9099	−1.65907	−0.829535	−	0.558454i	$-0.811395\pi$
$283$	−27.9099	−1.65907	−0.829535	+	0.558454i	$0.811395\pi$
$284$	−48.1126	−2.85496
$285$	−21.9085	−1.29775
$286$	14.9078	0.881515
$287$	10.3339	0.609992
$288$	1.21014	0.0713084
$289$	−4.50879	−0.265223
$290$	30.6105	1.79751
$291$	19.7590	1.15829
$292$	23.0852	1.35096
$293$	27.1144	1.58404	0.792019	−	0.610496i	$-0.209030\pi$
$293$	27.1144	1.58404	0.792019	+	0.610496i	$0.209030\pi$
$294$	23.1960	1.35282
$295$	−16.5620	−0.964277
$296$	17.4968	1.01698
$297$	−22.3210	−1.29520
$298$	54.7703	3.17276
$299$	2.61012	0.150947
$300$	−21.2046	−1.22425
$301$	−8.47458	−0.488467
$302$	−22.5439	−1.29725
$303$	−10.4636	−0.601116
$304$	−23.5126	−1.34854
$305$	4.01737	0.230034
$306$	10.5804	0.604839
$307$	−4.95393	−0.282736	−0.141368	−	0.989957i	$-0.545150\pi$
$307$	−4.95393	−0.282736	−0.141368	+	0.989957i	$0.545150\pi$
$308$	36.7233	2.09250
$309$	29.1814	1.66007
$310$	13.7131	0.778853
$311$	14.5040	0.822448	0.411224	−	0.911534i	$-0.365101\pi$
$311$	14.5040	0.822448	0.411224	+	0.911534i	$0.365101\pi$
$312$	9.47327	0.536318
$313$	−16.9256	−0.956690	−0.478345	−	0.878172i	$-0.658763\pi$
$313$	−16.9256	−0.956690	−0.478345	+	0.878172i	$0.658763\pi$
$314$	34.7654	1.96193
$315$	2.90438	0.163643
$316$	−29.2179	−1.64363
$317$	18.6632	1.04823	0.524115	−	0.851648i	$-0.324396\pi$
$317$	18.6632	1.04823	0.524115	+	0.851648i	$0.324396\pi$
$318$	−25.0128	−1.40265
$319$	−50.4354	−2.82384
$320$	−14.0562	−0.785767
$321$	−3.95923	−0.220983
$322$	9.73011	0.542238
$323$	24.5260	1.36466
$324$	−43.5547	−2.41971
$325$	2.64525	0.146732
$326$	33.2380	1.84088
$327$	−35.0999	−1.94103
$328$	−30.9941	−1.71136
$329$	16.8555	0.929272
$330$	−47.0654	−2.59086
$331$	0.573241	0.0315082	0.0157541	−	0.999876i	$-0.494985\pi$
$331$	0.573241	0.0315082	0.0157541	+	0.999876i	$0.494985\pi$
$332$	15.7336	0.863491
$333$	−4.68475	−0.256723
$334$	49.0229	2.68241
$335$	−12.8063	−0.699685
$336$	10.7019	0.583839
$337$	30.7908	1.67728	0.838642	−	0.544683i	$-0.183350\pi$
$337$	30.7908	1.67728	0.838642	+	0.544683i	$0.183350\pi$
$338$	−2.42822	−0.132078
$339$	−11.2252	−0.609667
$340$	−21.1311	−1.14599
$341$	−22.5944	−1.22356
$342$	20.7741	1.12333
$343$	−17.8747	−0.965143
$344$	25.4174	1.37042
$345$	−8.24042	−0.443649
$346$	−36.1530	−1.94360
$347$	27.5448	1.47868	0.739342	−	0.673330i	$-0.235137\pi$
$347$	27.5448	1.47868	0.739342	+	0.673330i	$0.235137\pi$
$348$	−65.8527	−3.53008
$349$	12.2907	0.657905	0.328953	−	0.944346i	$-0.393304\pi$
$349$	12.2907	0.657905	0.328953	+	0.944346i	$0.393304\pi$
$350$	9.86107	0.527096
$351$	3.63571	0.194060
$352$	6.02631	0.321203
$353$	−25.1499	−1.33860	−0.669298	−	0.742994i	$-0.733405\pi$
$353$	−25.1499	−1.33860	−0.669298	+	0.742994i	$0.733405\pi$
$354$	53.9194	2.86578
$355$	−18.9489	−1.00571
$356$	−58.9231	−3.12292
$357$	−11.1632	−0.590819
$358$	−33.4489	−1.76783
$359$	−6.99704	−0.369289	−0.184645	−	0.982805i	$-0.559113\pi$
$359$	−6.99704	−0.369289	−0.184645	+	0.982805i	$0.559113\pi$
$360$	−8.71097	−0.459108
$361$	29.1557	1.53451
$362$	−19.7513	−1.03810
$363$	54.9159	2.88234
$364$	−5.98159	−0.313520
$365$	9.09202	0.475898
$366$	−13.0790	−0.683649
$367$	−15.3081	−0.799076	−0.399538	−	0.916717i	$-0.630829\pi$
$367$	−15.3081	−0.799076	−0.399538	+	0.916717i	$0.630829\pi$
$368$	−8.84376	−0.461013
$369$	8.29862	0.432009
$370$	14.1591	0.736098
$371$	7.68648	0.399062
$372$	−29.5012	−1.52956
$373$	0.383384	0.0198509	0.00992543	−	0.999951i	$-0.496841\pi$
$373$	0.383384	0.0198509	0.00992543	+	0.999951i	$0.496841\pi$
$374$	52.6884	2.72445
$375$	−24.1369	−1.24642
$376$	−50.5539	−2.60712
$377$	8.21506	0.423097
$378$	13.5534	0.697110
$379$	11.0792	0.569099	0.284550	−	0.958661i	$-0.408156\pi$
$379$	11.0792	0.569099	0.284550	+	0.958661i	$0.408156\pi$
$380$	−41.4900	−2.12839
$381$	14.0869	0.721695
$382$	16.3982	0.839007
$383$	10.0092	0.511445	0.255722	−	0.966750i	$-0.417687\pi$
$383$	10.0092	0.511445	0.255722	+	0.966750i	$0.417687\pi$
$384$	41.7225	2.12914
$385$	14.4633	0.737117
$386$	−64.0229	−3.25868
$387$	−6.80549	−0.345942
$388$	37.4192	1.89967
$389$	−11.9101	−0.603867	−0.301934	−	0.953329i	$-0.597632\pi$
$389$	−11.9101	−0.603867	−0.301934	+	0.953329i	$0.597632\pi$
$390$	7.66614	0.388190
$391$	9.22492	0.466524
$392$	21.3792	1.07981
$393$	30.4966	1.53835
$394$	58.2641	2.93530
$395$	−11.5073	−0.578997
$396$	29.4905	1.48195
$397$	−14.5698	−0.731237	−0.365619	−	0.930765i	$-0.619143\pi$
$397$	−14.5698	−0.731237	−0.365619	+	0.930765i	$0.619143\pi$
$398$	−1.55721	−0.0780557
$399$	−21.9185	−1.09730
$400$	−8.96279	−0.448139
$401$	4.51760	0.225598	0.112799	−	0.993618i	$-0.464018\pi$
$401$	4.51760	0.225598	0.112799	+	0.993618i	$0.464018\pi$
$402$	41.6924	2.07943
$403$	3.68024	0.183326
$404$	−19.8157	−0.985869
$405$	−17.1538	−0.852381
$406$	30.6244	1.51987
$407$	−23.3292	−1.15639
$408$	33.4813	1.65757
$409$	20.4085	1.00913	0.504567	−	0.863373i	$-0.331652\pi$
$409$	20.4085	1.00913	0.504567	+	0.863373i	$0.331652\pi$
$410$	−25.0816	−1.23869
$411$	−37.8005	−1.86456
$412$	55.2632	2.72262
$413$	−16.5695	−0.815333
$414$	7.81374	0.384024
$415$	6.19659	0.304179
$416$	−0.981582	−0.0481260
$417$	32.4240	1.58781
$418$	103.451	5.05998
$419$	24.2798	1.18615	0.593073	−	0.805149i	$-0.297915\pi$
$419$	24.2798	1.18615	0.593073	+	0.805149i	$0.297915\pi$
$420$	18.8845	0.921469
$421$	−26.9254	−1.31227	−0.656133	−	0.754645i	$-0.727809\pi$
$421$	−26.9254	−1.31227	−0.656133	+	0.754645i	$0.727809\pi$
$422$	5.89113	0.286776
$423$	13.5357	0.658129
$424$	−23.0537	−1.11959
$425$	9.34908	0.453497
$426$	61.6903	2.98890
$427$	4.01919	0.194502
$428$	−7.49792	−0.362426
$429$	−12.6311	−0.609835
$430$	20.5688	0.991916
$431$	−5.89176	−0.283796	−0.141898	−	0.989881i	$-0.545321\pi$
$431$	−5.89176	−0.283796	−0.141898	+	0.989881i	$0.545321\pi$
$432$	−12.3187	−0.592686
$433$	−14.3597	−0.690084	−0.345042	−	0.938587i	$-0.612135\pi$
$433$	−14.3597	−0.690084	−0.345042	+	0.938587i	$0.612135\pi$
$434$	13.7194	0.658550
$435$	−25.9358	−1.24353
$436$	−66.4716	−3.18341
$437$	18.1127	0.866450
$438$	−29.6000	−1.41434
$439$	1.52102	0.0725944	0.0362972	−	0.999341i	$-0.488444\pi$
$439$	1.52102	0.0725944	0.0362972	+	0.999341i	$0.488444\pi$
$440$	−43.3791	−2.06802
$441$	−5.72426	−0.272584
$442$	−8.58203	−0.408206
$443$	−11.1632	−0.530380	−0.265190	−	0.964196i	$-0.585435\pi$
$443$	−11.1632	−0.530380	−0.265190	+	0.964196i	$0.585435\pi$
$444$	−30.4606	−1.44560
$445$	−23.2066	−1.10010
$446$	−12.9430	−0.612866
$447$	−46.4060	−2.19493
$448$	−14.0626	−0.664396
$449$	30.1519	1.42296	0.711479	−	0.702707i	$-0.248026\pi$
$449$	30.1519	1.42296	0.711479	+	0.702707i	$0.248026\pi$
$450$	7.91890	0.373301
$451$	41.3257	1.94595
$452$	−21.2580	−0.999893
$453$	19.1010	0.897446
$454$	32.3801	1.51967
$455$	−2.35582	−0.110443
$456$	65.7391	3.07851
$457$	12.3588	0.578121	0.289060	−	0.957311i	$-0.406657\pi$
$457$	12.3588	0.578121	0.289060	+	0.957311i	$0.406657\pi$
$458$	−64.9682	−3.03576
$459$	12.8497	0.599771
$460$	−15.6056	−0.727613
$461$	11.7849	0.548876	0.274438	−	0.961605i	$-0.411508\pi$
$461$	11.7849	0.548876	0.274438	+	0.961605i	$0.411508\pi$
$462$	−47.0868	−2.19067
$463$	−19.4649	−0.904609	−0.452305	−	0.891863i	$-0.649398\pi$
$463$	−19.4649	−0.904609	−0.452305	+	0.891863i	$0.649398\pi$
$464$	−27.8347	−1.29220
$465$	−11.6189	−0.538814
$466$	45.0802	2.08830
$467$	7.98200	0.369363	0.184682	−	0.982798i	$-0.440875\pi$
$467$	7.98200	0.369363	0.184682	+	0.982798i	$0.440875\pi$
$468$	−4.80349	−0.222042
$469$	−12.8121	−0.591610
$470$	−40.9102	−1.88705
$471$	−29.4561	−1.35727
$472$	49.6963	2.28746
$473$	−33.8901	−1.55827
$474$	37.4633	1.72075
$475$	18.3565	0.842255
$476$	−21.1407	−0.968981
$477$	6.17260	0.282624
$478$	−9.81269	−0.448822
$479$	−10.3141	−0.471263	−0.235632	−	0.971842i	$-0.575716\pi$
$479$	−10.3141	−0.471263	−0.235632	+	0.971842i	$0.575716\pi$
$480$	3.09896	0.141447
$481$	3.79993	0.173262
$482$	−51.1182	−2.32837
$483$	−8.24416	−0.375122
$484$	103.999	4.72722
$485$	14.7374	0.669191
$486$	29.3612	1.33185
$487$	3.24724	0.147146	0.0735732	−	0.997290i	$-0.476560\pi$
$487$	3.24724	0.147146	0.0735732	+	0.997290i	$0.476560\pi$
$488$	−12.0546	−0.545686
$489$	−28.1620	−1.27353
$490$	17.3009	0.781576
$491$	−15.3194	−0.691354	−0.345677	−	0.938354i	$-0.612351\pi$
$491$	−15.3194	−0.691354	−0.345677	+	0.938354i	$0.612351\pi$
$492$	53.9583	2.43263
$493$	29.0344	1.30764
$494$	−16.8505	−0.758138
$495$	11.6147	0.522042
$496$	−12.4696	−0.559902
$497$	−18.9575	−0.850362
$498$	−20.1737	−0.904003
$499$	2.24255	0.100390	0.0501952	−	0.998739i	$-0.484016\pi$
$499$	2.24255	0.100390	0.0501952	+	0.998739i	$0.484016\pi$
$500$	−45.7100	−2.04421
$501$	−41.5363	−1.85570
$502$	−44.1427	−1.97019
$503$	27.8786	1.24305	0.621523	−	0.783396i	$-0.286514\pi$
$503$	27.8786	1.24305	0.621523	+	0.783396i	$0.286514\pi$
$504$	−8.71492	−0.388194
$505$	−7.80433	−0.347288
$506$	38.9111	1.72981
$507$	2.05739	0.0913719
$508$	26.6776	1.18363
$509$	30.8776	1.36863	0.684313	−	0.729188i	$-0.260102\pi$
$509$	30.8776	1.36863	0.684313	+	0.729188i	$0.260102\pi$
$510$	27.0944	1.19976
$511$	9.09615	0.402390
$512$	34.5284	1.52595
$513$	25.2298	1.11392
$514$	−2.06309	−0.0909990
$515$	21.7651	0.959087
$516$	−44.2498	−1.94799
$517$	67.4056	2.96449
$518$	14.1656	0.622399
$519$	30.6318	1.34459
$520$	7.06571	0.309852
$521$	45.3234	1.98565	0.992827	−	0.119564i	$-0.0381496\pi$
$521$	45.3234	1.98565	0.992827	+	0.119564i	$0.0381496\pi$
$522$	24.5929	1.07640
$523$	−31.0037	−1.35570	−0.677848	−	0.735202i	$-0.737087\pi$
$523$	−31.0037	−1.35570	−0.677848	+	0.735202i	$0.737087\pi$
$524$	57.7539	2.52299
$525$	−8.35512	−0.364647
$526$	22.9799	1.00197
$527$	13.0070	0.566595
$528$	42.7975	1.86252
$529$	−16.1873	−0.703795
$530$	−18.6560	−0.810365
$531$	−13.3061	−0.577436
$532$	−41.5088	−1.79963
$533$	−6.73124	−0.291563
$534$	75.5515	3.26943
$535$	−2.95302	−0.127670
$536$	38.4269	1.65979
$537$	28.3407	1.22299
$538$	−6.65589	−0.286956
$539$	−28.5058	−1.22783
$540$	−21.7375	−0.935432
$541$	22.5637	0.970089	0.485045	−	0.874489i	$-0.338803\pi$
$541$	22.5637	0.970089	0.485045	+	0.874489i	$0.338803\pi$
$542$	−48.8283	−2.09736
$543$	16.7349	0.718164
$544$	−3.46919	−0.148740
$545$	−26.1795	−1.12141
$546$	7.66962	0.328230
$547$	27.0455	1.15638	0.578190	−	0.815902i	$-0.303759\pi$
$547$	27.0455	1.15638	0.578190	+	0.815902i	$0.303759\pi$
$548$	−71.5860	−3.05800
$549$	3.22760	0.137751
$550$	39.4348	1.68150
$551$	57.0078	2.42861
$552$	24.7264	1.05242
$553$	−11.5126	−0.489564
$554$	−11.6248	−0.493892
$555$	−11.9968	−0.509235
$556$	61.4040	2.60411
$557$	1.43730	0.0609005	0.0304503	−	0.999536i	$-0.490306\pi$
$557$	1.43730	0.0609005	0.0304503	+	0.999536i	$0.490306\pi$
$558$	11.0173	0.466399
$559$	5.52012	0.233476
$560$	7.98213	0.337307
$561$	−44.6420	−1.88479
$562$	−1.65637	−0.0698698
$563$	13.5903	0.572763	0.286382	−	0.958116i	$-0.407547\pi$
$563$	13.5903	0.572763	0.286382	+	0.958116i	$0.407547\pi$
$564$	88.0104	3.70591
$565$	−8.37237	−0.352228
$566$	67.7713	2.84864
$567$	−17.1616	−0.720720
$568$	56.8585	2.38573
$569$	38.4607	1.61236	0.806178	−	0.591674i	$-0.201533\pi$
$569$	38.4607	1.61236	0.806178	+	0.591674i	$0.201533\pi$
$570$	53.1987	2.22825
$571$	5.33215	0.223144	0.111572	−	0.993756i	$-0.464412\pi$
$571$	5.33215	0.223144	0.111572	+	0.993756i	$0.464412\pi$
$572$	−23.9206	−1.00017
$573$	−13.8940	−0.580428
$574$	−25.0930	−1.04736
$575$	6.90441	0.287934
$576$	−11.2929	−0.470539
$577$	2.67750	0.111466	0.0557330	−	0.998446i	$-0.482250\pi$
$577$	2.67750	0.111466	0.0557330	+	0.998446i	$0.482250\pi$
$578$	10.9483	0.455390
$579$	54.2455	2.25437
$580$	−49.1168	−2.03946
$581$	6.19940	0.257195
$582$	−47.9792	−1.98880
$583$	30.7385	1.27306
$584$	−27.2817	−1.12892
$585$	−1.89183	−0.0782177
$586$	−65.8396	−2.71981
$587$	−2.13330	−0.0880506	−0.0440253	−	0.999030i	$-0.514018\pi$
$587$	−2.13330	−0.0880506	−0.0440253	+	0.999030i	$0.514018\pi$
$588$	−37.2196	−1.53491
$589$	25.5388	1.05231
$590$	40.2162	1.65567
$591$	−49.3662	−2.03065
$592$	−12.8752	−0.529166
$593$	−3.30120	−0.135564	−0.0677820	−	0.997700i	$-0.521592\pi$
$593$	−3.30120	−0.135564	−0.0677820	+	0.997700i	$0.521592\pi$
$594$	54.2004	2.22387
$595$	−8.32616	−0.341339
$596$	−87.8828	−3.59982
$597$	1.31940	0.0539992
$598$	−6.33794	−0.259178
$599$	−5.98350	−0.244479	−0.122240	−	0.992501i	$-0.539008\pi$
$599$	−5.98350	−0.244479	−0.122240	+	0.992501i	$0.539008\pi$
$600$	25.0591	1.02304
$601$	−12.6554	−0.516225	−0.258112	−	0.966115i	$-0.583100\pi$
$601$	−12.6554	−0.516225	−0.258112	+	0.966115i	$0.583100\pi$
$602$	20.5781	0.838703
$603$	−10.2888	−0.418990
$604$	36.1732	1.47187
$605$	40.9595	1.66524
$606$	25.4078	1.03212
$607$	15.6693	0.635998	0.317999	−	0.948091i	$-0.396989\pi$
$607$	15.6693	0.635998	0.317999	+	0.948091i	$0.396989\pi$
$608$	−6.81162	−0.276248
$609$	−25.9476	−1.05145
$610$	−9.75505	−0.394971
$611$	−10.9792	−0.444171
$612$	−16.9769	−0.686252
$613$	−2.65310	−0.107158	−0.0535789	−	0.998564i	$-0.517063\pi$
$613$	−2.65310	−0.107158	−0.0535789	+	0.998564i	$0.517063\pi$
$614$	12.0292	0.485460
$615$	21.2512	0.856933
$616$	−43.3988	−1.74859
$617$	24.9890	1.00602	0.503009	−	0.864281i	$-0.332226\pi$
$617$	24.9890	1.00602	0.503009	+	0.864281i	$0.332226\pi$
$618$	−70.8587	−2.85036
$619$	−1.00000	−0.0401934
$619$	−1.00000	−0.0401934
$620$	−22.0037	−0.883689
$621$	9.48964	0.380806
$622$	−35.2190	−1.41215
$623$	−23.2171	−0.930174
$624$	−6.97097	−0.279062
$625$	−4.77642	−0.191057
$626$	41.0990	1.64265
$627$	−87.6527	−3.50051
$628$	−55.7835	−2.22601
$629$	13.4301	0.535492
$630$	−7.05246	−0.280977
$631$	−33.1678	−1.32039	−0.660194	−	0.751095i	$-0.729526\pi$
$631$	−33.1678	−1.32039	−0.660194	+	0.751095i	$0.729526\pi$
$632$	34.5291	1.37349
$633$	−4.99146	−0.198393
$634$	−45.3183	−1.79982
$635$	10.5068	0.416952
$636$	40.1348	1.59145
$637$	4.64311	0.183967
$638$	122.468	4.84856
$639$	−15.2238	−0.602244
$640$	31.1191	1.23009
$641$	0.341958	0.0135065	0.00675327	−	0.999977i	$-0.497850\pi$
$641$	0.341958	0.0135065	0.00675327	+	0.999977i	$0.497850\pi$
$642$	9.61387	0.379429
$643$	−11.7832	−0.464685	−0.232342	−	0.972634i	$-0.574639\pi$
$643$	−11.7832	−0.464685	−0.232342	+	0.972634i	$0.574639\pi$
$644$	−15.6127	−0.615225
$645$	−17.4276	−0.686211
$646$	−59.5544	−2.34314
$647$	−43.4227	−1.70712	−0.853561	−	0.520993i	$-0.825562\pi$
$647$	−43.4227	−1.70712	−0.853561	+	0.520993i	$0.825562\pi$
$648$	51.4721	2.02202
$649$	−66.2621	−2.60102
$650$	−6.42324	−0.251940
$651$	−11.6242	−0.455587
$652$	−53.3328	−2.08867
$653$	−30.6007	−1.19750	−0.598750	−	0.800936i	$-0.704336\pi$
$653$	−30.6007	−1.19750	−0.598750	+	0.800936i	$0.704336\pi$
$654$	85.2302	3.33277
$655$	22.7461	0.888764
$656$	22.8072	0.890472
$657$	7.30463	0.284981
$658$	−40.9288	−1.59557
$659$	−44.1736	−1.72076	−0.860379	−	0.509655i	$-0.829773\pi$
$659$	−44.1736	−1.72076	−0.860379	+	0.509655i	$0.829773\pi$
$660$	75.5198	2.93960
$661$	34.9909	1.36099	0.680495	−	0.732753i	$-0.261765\pi$
$661$	34.9909	1.36099	0.680495	+	0.732753i	$0.261765\pi$
$662$	−1.39195	−0.0540998
$663$	7.27141	0.282398
$664$	−18.5936	−0.721572
$665$	−16.3481	−0.633950
$666$	11.3756	0.440796
$667$	21.4423	0.830248
$668$	−78.6607	−3.04347
$669$	10.9663	0.423983
$670$	31.0966	1.20137
$671$	16.0729	0.620487
$672$	3.10036	0.119599
$673$	10.6199	0.409368	0.204684	−	0.978828i	$-0.434383\pi$
$673$	10.6199	0.409368	0.204684	+	0.978828i	$0.434383\pi$
$674$	−74.7669	−2.87991
$675$	9.61737	0.370173
$676$	3.89625	0.149856
$677$	46.4822	1.78646	0.893228	−	0.449603i	$-0.148435\pi$
$677$	46.4822	1.78646	0.893228	+	0.449603i	$0.148435\pi$
$678$	27.2571	1.04680
$679$	14.7441	0.565826
$680$	24.9723	0.957643
$681$	−27.4351	−1.05131
$682$	54.8642	2.10086
$683$	−37.4952	−1.43471	−0.717357	−	0.696706i	$-0.754648\pi$
$683$	−37.4952	−1.43471	−0.717357	+	0.696706i	$0.754648\pi$
$684$	−33.3335	−1.27454
$685$	−28.1938	−1.07723
$686$	43.4037	1.65716
$687$	55.0464	2.10015
$688$	−18.7036	−0.713068
$689$	−5.00677	−0.190743
$690$	20.0095	0.761750
$691$	−6.50268	−0.247374	−0.123687	−	0.992321i	$-0.539472\pi$
$691$	−6.50268	−0.247374	−0.123687	+	0.992321i	$0.539472\pi$
$692$	58.0100	2.20521
$693$	11.6200	0.441406
$694$	−66.8849	−2.53892
$695$	24.1837	0.917340
$696$	77.8234	2.94989
$697$	−23.7902	−0.901117
$698$	−29.8445	−1.12963
$699$	−38.1957	−1.44469
$700$	−15.8228	−0.598045
$701$	−16.9804	−0.641339	−0.320669	−	0.947191i	$-0.603908\pi$
$701$	−16.9804	−0.641339	−0.320669	+	0.947191i	$0.603908\pi$
$702$	−8.82831	−0.333203
$703$	26.3694	0.994539
$704$	−56.2368	−2.11951
$705$	34.6625	1.30547
$706$	61.0696	2.29838
$707$	−7.80788	−0.293645
$708$	−86.5174	−3.25152
$709$	47.9222	1.79975	0.899877	−	0.436144i	$-0.143656\pi$
$709$	47.9222	1.79975	0.899877	+	0.436144i	$0.143656\pi$
$710$	46.0122	1.72681
$711$	−9.24512	−0.346719
$712$	69.6341	2.60965
$713$	9.60586	0.359742
$714$	27.1067	1.01444
$715$	−9.42101	−0.352326
$716$	53.6711	2.00578
$717$	8.31413	0.310497
$718$	16.9903	0.634074
$719$	−42.5031	−1.58510	−0.792549	−	0.609809i	$-0.791246\pi$
$719$	−42.5031	−1.58510	−0.792549	+	0.609809i	$0.791246\pi$
$720$	6.41002	0.238887
$721$	21.7750	0.810944
$722$	−70.7964	−2.63477
$723$	43.3116	1.61077
$724$	31.6923	1.17784
$725$	21.7309	0.807064
$726$	−133.348	−4.94900
$727$	−34.3465	−1.27384	−0.636920	−	0.770930i	$-0.719792\pi$
$727$	−34.3465	−1.27384	−0.636920	+	0.770930i	$0.719792\pi$
$728$	7.06892	0.261992
$729$	8.65865	0.320691
$730$	−22.0774	−0.817122
$731$	19.5097	0.721593
$732$	20.9861	0.775670
$733$	11.1689	0.412533	0.206267	−	0.978496i	$-0.433869\pi$
$733$	11.1689	0.412533	0.206267	+	0.978496i	$0.433869\pi$
$734$	37.1714	1.37202
$735$	−14.6588	−0.540697
$736$	−2.56204	−0.0944382
$737$	−51.2362	−1.88731
$738$	−20.1509	−0.741764
$739$	−12.8695	−0.473410	−0.236705	−	0.971582i	$-0.576068\pi$
$739$	−12.8695	−0.473410	−0.236705	+	0.971582i	$0.576068\pi$
$740$	−22.7193	−0.835178
$741$	14.2771	0.524483
$742$	−18.6645	−0.685194
$743$	2.47692	0.0908693	0.0454346	−	0.998967i	$-0.485533\pi$
$743$	2.47692	0.0908693	0.0454346	+	0.998967i	$0.485533\pi$
$744$	34.8639	1.27817
$745$	−34.6122	−1.26809
$746$	−0.930939	−0.0340841
$747$	4.97841	0.182151
$748$	−84.5423	−3.09117
$749$	−2.95436	−0.107950
$750$	58.6096	2.14012
$751$	−1.28227	−0.0467906	−0.0233953	−	0.999726i	$-0.507448\pi$
$751$	−1.28227	−0.0467906	−0.0233953	+	0.999726i	$0.507448\pi$
$752$	37.2004	1.35656
$753$	37.4014	1.36298
$754$	−19.9480	−0.726462
$755$	14.2467	0.518489
$756$	−21.7473	−0.790943
$757$	−4.42727	−0.160912	−0.0804559	−	0.996758i	$-0.525638\pi$
$757$	−4.42727	−0.160912	−0.0804559	+	0.996758i	$0.525638\pi$
$758$	−26.9027	−0.977150
$759$	−32.9687	−1.19669
$760$	49.0320	1.77858
$761$	−36.4178	−1.32015	−0.660073	−	0.751201i	$-0.729475\pi$
$761$	−36.4178	−1.32015	−0.660073	+	0.751201i	$0.729475\pi$
$762$	−34.2062	−1.23916
$763$	−26.1914	−0.948193
$764$	−26.3121	−0.951940
$765$	−6.68629	−0.241743
$766$	−24.3045	−0.878156
$767$	10.7930	0.389711
$768$	−63.6200	−2.29569
$769$	24.0581	0.867559	0.433779	−	0.901019i	$-0.357180\pi$
$769$	24.0581	0.867559	0.433779	+	0.901019i	$0.357180\pi$
$770$	−35.1200	−1.26564
$771$	1.74802	0.0629534
$772$	102.729	3.69731
$773$	−39.2063	−1.41015	−0.705077	−	0.709131i	$-0.749087\pi$
$773$	−39.2063	−1.41015	−0.705077	+	0.709131i	$0.749087\pi$
$774$	16.5252	0.593986
$775$	9.73515	0.349697
$776$	−44.2213	−1.58745
$777$	−12.0022	−0.430578
$778$	28.9204	1.03685
$779$	−46.7110	−1.67360
$780$	−12.3009	−0.440442
$781$	−75.8119	−2.71276
$782$	−22.4001	−0.801027
$783$	29.8676	1.06738
$784$	−15.7321	−0.561859
$785$	−21.9701	−0.784146
$786$	−74.0523	−2.64136
$787$	2.00728	0.0715516	0.0357758	−	0.999360i	$-0.488610\pi$
$787$	2.00728	0.0715516	0.0357758	+	0.999360i	$0.488610\pi$
$788$	−93.4888	−3.33040
$789$	−19.4705	−0.693168
$790$	27.9423	0.994143
$791$	−8.37617	−0.297822
$792$	−34.8513	−1.23839
$793$	−2.61800	−0.0929678
$794$	35.3787	1.25554
$795$	15.8069	0.560613
$796$	2.49865	0.0885622
$797$	29.0568	1.02925	0.514623	−	0.857417i	$-0.327932\pi$
$797$	29.0568	1.02925	0.514623	+	0.857417i	$0.327932\pi$
$798$	53.2228	1.88407
$799$	−38.8037	−1.37278
$800$	−2.59653	−0.0918011
$801$	−18.6444	−0.658769
$802$	−10.9697	−0.387355
$803$	36.3758	1.28367
$804$	−66.8984	−2.35932
$805$	−6.14897	−0.216723
$806$	−8.93643	−0.314772
$807$	5.63942	0.198517
$808$	23.4178	0.823836
$809$	−20.5790	−0.723520	−0.361760	−	0.932271i	$-0.617824\pi$
$809$	−20.5790	−0.723520	−0.361760	+	0.932271i	$0.617824\pi$
$810$	41.6533	1.46355
$811$	0.796470	0.0279678	0.0139839	−	0.999902i	$-0.495549\pi$
$811$	0.796470	0.0279678	0.0139839	+	0.999902i	$0.495549\pi$
$812$	−49.1391	−1.72444
$813$	41.3714	1.45096
$814$	56.6485	1.98553
$815$	−21.0049	−0.735768
$816$	−24.6374	−0.862483
$817$	38.3065	1.34017
$818$	−49.5562	−1.73269
$819$	−1.89269	−0.0661361
$820$	40.2452	1.40542
$821$	56.5836	1.97478	0.987391	−	0.158303i	$-0.0506022\pi$
$821$	56.5836	1.97478	0.987391	+	0.158303i	$0.0506022\pi$
$822$	91.7879	3.20147
$823$	−35.0026	−1.22011	−0.610056	−	0.792358i	$-0.708853\pi$
$823$	−35.0026	−1.22011	−0.610056	+	0.792358i	$0.708853\pi$
$824$	−65.3089	−2.27514
$825$	−33.4124	−1.16327
$826$	40.2345	1.39994
$827$	−4.69730	−0.163341	−0.0816706	−	0.996659i	$-0.526026\pi$
$827$	−4.69730	−0.163341	−0.0816706	+	0.996659i	$0.526026\pi$
$828$	−12.5377	−0.435715
$829$	9.58459	0.332887	0.166443	−	0.986051i	$-0.446772\pi$
$829$	9.58459	0.332887	0.166443	+	0.986051i	$0.446772\pi$
$830$	−15.0467	−0.522278
$831$	9.84953	0.341676
$832$	9.16001	0.317566
$833$	16.4101	0.568576
$834$	−78.7326	−2.72629
$835$	−30.9802	−1.07211
$836$	−165.995	−5.74106
$837$	13.3803	0.462491
$838$	−58.9567	−2.03662
$839$	−43.3704	−1.49731	−0.748655	−	0.662959i	$-0.769300\pi$
$839$	−43.3704	−1.49731	−0.748655	+	0.662959i	$0.769300\pi$
$840$	−22.3173	−0.770021
$841$	38.4872	1.32714
$842$	65.3809	2.25317
$843$	1.40342	0.0483362
$844$	−9.45273	−0.325377
$845$	1.53452	0.0527891
$846$	−32.8677	−1.13002
$847$	40.9781	1.40802
$848$	16.9642	0.582555
$849$	−57.4215	−1.97070
$850$	−22.7016	−0.778659
$851$	9.91827	0.339994
$852$	−98.9864	−3.39122
$853$	23.4120	0.801612	0.400806	−	0.916163i	$-0.368730\pi$
$853$	23.4120	0.801612	0.400806	+	0.916163i	$0.368730\pi$
$854$	−9.75948	−0.333963
$855$	−13.1283	−0.448977
$856$	8.86089	0.302859
$857$	30.0317	1.02586	0.512931	−	0.858430i	$-0.328560\pi$
$857$	30.0317	1.02586	0.512931	+	0.858430i	$0.328560\pi$
$858$	30.6711	1.04709
$859$	12.4486	0.424740	0.212370	−	0.977189i	$-0.431882\pi$
$859$	12.4486	0.424740	0.212370	+	0.977189i	$0.431882\pi$
$860$	−33.0041	−1.12543
$861$	21.2609	0.724569
$862$	14.3065	0.487281
$863$	−31.7150	−1.07959	−0.539795	−	0.841796i	$-0.681498\pi$
$863$	−31.7150	−1.07959	−0.539795	+	0.841796i	$0.681498\pi$
$864$	−3.56875	−0.121411
$865$	22.8470	0.776820
$866$	34.8686	1.18488
$867$	−9.27633	−0.315041
$868$	−22.0137	−0.747193
$869$	−46.0391	−1.56177
$870$	62.9778	2.13515
$871$	8.34550	0.282776
$872$	78.5548	2.66020
$873$	11.8402	0.400730
$874$	−43.9817	−1.48770
$875$	−18.0108	−0.608877
$876$	47.4953	1.60472
$877$	9.79260	0.330673	0.165336	−	0.986237i	$-0.447129\pi$
$877$	9.79260	0.330673	0.165336	+	0.986237i	$0.447129\pi$
$878$	−3.69338	−0.124645
$879$	55.7848	1.88157
$880$	31.9208	1.07605
$881$	−46.8648	−1.57892	−0.789458	−	0.613805i	$-0.789638\pi$
$881$	−46.8648	−1.57892	−0.789458	+	0.613805i	$0.789638\pi$
$882$	13.8998	0.468029
$883$	−15.8468	−0.533288	−0.266644	−	0.963795i	$-0.585915\pi$
$883$	−15.8468	−0.533288	−0.266644	+	0.963795i	$0.585915\pi$
$884$	13.7705	0.463151
$885$	−34.0745	−1.14540
$886$	27.1067	0.910667
$887$	−20.8881	−0.701354	−0.350677	−	0.936496i	$-0.614049\pi$
$887$	−20.8881	−0.701354	−0.350677	+	0.936496i	$0.614049\pi$
$888$	35.9978	1.20801
$889$	10.5116	0.352548
$890$	56.3507	1.88888
$891$	−68.6299	−2.29919
$892$	20.7679	0.695360
$893$	−76.1894	−2.54958
$894$	112.684	3.76871
$895$	21.1381	0.706569
$896$	31.1332	1.04009
$897$	5.37003	0.179300
$898$	−73.2155	−2.44323
$899$	30.2334	1.00834
$900$	−12.7064	−0.423548
$901$	−17.6954	−0.589519
$902$	−100.348	−3.34122
$903$	−17.4355	−0.580218
$904$	25.1223	0.835555
$905$	12.4819	0.414911
$906$	−46.3815	−1.54092
$907$	48.5013	1.61046	0.805230	−	0.592963i	$-0.202042\pi$
$907$	48.5013	1.61046	0.805230	+	0.592963i	$0.202042\pi$
$908$	−51.9561	−1.72422
$909$	−6.27009	−0.207966
$910$	5.72045	0.189631
$911$	44.7574	1.48288	0.741439	−	0.671020i	$-0.234144\pi$
$911$	44.7574	1.48288	0.741439	+	0.671020i	$0.234144\pi$
$912$	−48.3745	−1.60184
$913$	24.7916	0.820483
$914$	−30.0099	−0.992639
$915$	8.26529	0.273242
$916$	104.246	3.44438
$917$	22.7564	0.751484
$918$	−31.2018	−1.02981
$919$	−28.8214	−0.950731	−0.475366	−	0.879788i	$-0.657684\pi$
$919$	−28.8214	−0.950731	−0.475366	+	0.879788i	$0.657684\pi$
$920$	18.4423	0.608026
$921$	−10.1922	−0.335843
$922$	−28.6163	−0.942426
$923$	12.3484	0.406454
$924$	75.5540	2.48555
$925$	10.0518	0.330500
$926$	47.2650	1.55322
$927$	17.4864	0.574328
$928$	−8.06375	−0.264705
$929$	17.3097	0.567914	0.283957	−	0.958837i	$-0.408353\pi$
$929$	17.3097	0.567914	0.283957	+	0.958837i	$0.408353\pi$
$930$	28.2132	0.925149
$931$	32.2205	1.05599
$932$	−72.3344	−2.36939
$933$	29.8404	0.976932
$934$	−19.3821	−0.634200
$935$	−33.2966	−1.08891
$936$	5.67667	0.185548
$937$	22.1479	0.723541	0.361770	−	0.932267i	$-0.382172\pi$
$937$	22.1479	0.723541	0.361770	+	0.932267i	$0.382172\pi$
$938$	31.1107	1.01580
$939$	−34.8225	−1.13639
$940$	65.6433	2.14105
$941$	10.4111	0.339393	0.169697	−	0.985496i	$-0.445721\pi$
$941$	10.4111	0.339393	0.169697	+	0.985496i	$0.445721\pi$
$942$	71.5260	2.33044
$943$	−17.5693	−0.572137
$944$	−36.5693	−1.19023
$945$	−8.56509	−0.278622
$946$	82.2927	2.67557
$947$	−49.2193	−1.59941	−0.799707	−	0.600391i	$-0.795012\pi$
$947$	−49.2193	−1.59941	−0.799707	+	0.600391i	$0.795012\pi$
$948$	−60.1126	−1.95237
$949$	−5.92499	−0.192333
$950$	−44.5737	−1.44616
$951$	38.3974	1.24512
$952$	24.9836	0.809724
$953$	−46.7841	−1.51549	−0.757743	−	0.652553i	$-0.773698\pi$
$953$	−46.7841	−1.51549	−0.757743	+	0.652553i	$0.773698\pi$
$954$	−14.9884	−0.485269
$955$	−10.3629	−0.335336
$956$	15.7452	0.509235
$957$	−103.765	−3.35425
$958$	25.0449	0.809164
$959$	−28.2066	−0.910839
$960$	−28.9191	−0.933361
$961$	−17.4558	−0.563092
$962$	−9.22707	−0.297493
$963$	−2.37249	−0.0764524
$964$	82.0227	2.64177
$965$	40.4595	1.30244
$966$	20.0186	0.644089
$967$	23.9685	0.770773	0.385387	−	0.922755i	$-0.374068\pi$
$967$	23.9685	0.770773	0.385387	+	0.922755i	$0.374068\pi$
$968$	−122.904	−3.95028
$969$	50.4595	1.62099
$970$	−35.7856	−1.14901
$971$	30.0669	0.964892	0.482446	−	0.875926i	$-0.339748\pi$
$971$	30.0669	0.964892	0.482446	+	0.875926i	$0.339748\pi$
$972$	−47.1121	−1.51112
$973$	24.1947	0.775646
$974$	−7.88500	−0.252652
$975$	5.44231	0.174293
$976$	8.87045	0.283936
$977$	−40.8852	−1.30803	−0.654017	−	0.756480i	$-0.726918\pi$
$977$	−40.8852	−1.30803	−0.654017	+	0.756480i	$0.726918\pi$
$978$	68.3836	2.18667
$979$	−92.8461	−2.96737
$980$	−27.7606	−0.886778
$981$	−21.0329	−0.671530
$982$	37.1988	1.18706
$983$	−17.9216	−0.571609	−0.285805	−	0.958288i	$-0.592261\pi$
$983$	−17.9216	−0.571609	−0.285805	+	0.958288i	$0.592261\pi$
$984$	−63.7669	−2.03281
$985$	−36.8201	−1.17319
$986$	−70.5019	−2.24524
$987$	34.6783	1.10382
$988$	27.0377	0.860185
$989$	14.4082	0.458153
$990$	−28.2030	−0.896351
$991$	−49.7989	−1.58191	−0.790957	−	0.611872i	$-0.790417\pi$
$991$	−49.7989	−1.58191	−0.790957	+	0.611872i	$0.790417\pi$
$992$	−3.61246	−0.114696
$993$	1.17938	0.0374265
$994$	46.0331	1.46008
$995$	0.984081	0.0311975
$996$	32.3700	1.02568
$997$	17.5677	0.556374	0.278187	−	0.960527i	$-0.410267\pi$
$997$	17.5677	0.556374	0.278187	+	0.960527i	$0.410267\pi$
$998$	−5.44540	−0.172371
$999$	13.8155	0.437102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8047.2.a.c.1.14	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8047.2.a.c.1.14	✓	151	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:	\( N \)	\(=\)	\( 8047 = 13 \cdot 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8047.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42822 q^{2} +2.05739 q^{3} +3.89625 q^{4} +1.53452 q^{5} -4.99579 q^{6} +1.53522 q^{7} -4.60451 q^{8} +1.23285 q^{9} +O(q^{10})\)	\(q-2.42822 q^{2} +2.05739 q^{3} +3.89625 q^{4} +1.53452 q^{5} -4.99579 q^{6} +1.53522 q^{7} -4.60451 q^{8} +1.23285 q^{9} -3.72615 q^{10} +6.13938 q^{11} +8.01610 q^{12} -1.00000 q^{13} -3.72784 q^{14} +3.15710 q^{15} +3.38826 q^{16} -3.53429 q^{17} -2.99363 q^{18} -6.93943 q^{19} +5.97887 q^{20} +3.15854 q^{21} -14.9078 q^{22} -2.61012 q^{23} -9.47327 q^{24} -2.64525 q^{25} +2.42822 q^{26} -3.63571 q^{27} +5.98159 q^{28} -8.21506 q^{29} -7.66614 q^{30} -3.68024 q^{31} +0.981582 q^{32} +12.6311 q^{33} +8.58203 q^{34} +2.35582 q^{35} +4.80349 q^{36} -3.79993 q^{37} +16.8505 q^{38} -2.05739 q^{39} -7.06571 q^{40} +6.73124 q^{41} -7.66962 q^{42} -5.52012 q^{43} +23.9206 q^{44} +1.89183 q^{45} +6.33794 q^{46} +10.9792 q^{47} +6.97097 q^{48} -4.64311 q^{49} +6.42324 q^{50} -7.27141 q^{51} -3.89625 q^{52} +5.00677 q^{53} +8.82831 q^{54} +9.42101 q^{55} -7.06892 q^{56} -14.2771 q^{57} +19.9480 q^{58} -10.7930 q^{59} +12.3009 q^{60} +2.61800 q^{61} +8.93643 q^{62} +1.89269 q^{63} -9.16001 q^{64} -1.53452 q^{65} -30.6711 q^{66} -8.34550 q^{67} -13.7705 q^{68} -5.37003 q^{69} -5.72045 q^{70} -12.3484 q^{71} -5.67667 q^{72} +5.92499 q^{73} +9.22707 q^{74} -5.44231 q^{75} -27.0377 q^{76} +9.42529 q^{77} +4.99579 q^{78} -7.49898 q^{79} +5.19935 q^{80} -11.1786 q^{81} -16.3449 q^{82} +4.03813 q^{83} +12.3065 q^{84} -5.42344 q^{85} +13.4041 q^{86} -16.9016 q^{87} -28.2689 q^{88} -15.1230 q^{89} -4.59379 q^{90} -1.53522 q^{91} -10.1697 q^{92} -7.57169 q^{93} -26.6599 q^{94} -10.6487 q^{95} +2.01950 q^{96} +9.60392 q^{97} +11.2745 q^{98} +7.56895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9}+O(q^{10}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9	\( 151 q - 13 q^{2} - 16 q^{3} + 151 q^{4} - 43 q^{5} - 17 q^{6} - 18 q^{7} - 39 q^{8} + 135 q^{9} - 3 q^{10} - 27 q^{11} - 52 q^{12} - 151 q^{13} - 9 q^{14} - 14 q^{15} + 143 q^{16} - 111 q^{17} - 37 q^{18} - 17 q^{19} - 107 q^{20} - 29 q^{21} - 16 q^{22} - 47 q^{23} - 46 q^{24} + 122 q^{25} + 13 q^{26} - 55 q^{27} - 44 q^{28} + 37 q^{29} - 14 q^{30} - 27 q^{31} - 86 q^{32} - 94 q^{33} - 10 q^{34} - 47 q^{35} + 124 q^{36} - 59 q^{37} - 80 q^{38} + 16 q^{39} + 5 q^{40} - 129 q^{41} - 77 q^{42} - 11 q^{43} - 99 q^{44} - 122 q^{45} - 17 q^{46} - 130 q^{47} - 111 q^{48} + 99 q^{49} - 72 q^{50} + 15 q^{51} - 151 q^{52} - 43 q^{53} - 49 q^{54} - 40 q^{55} - 50 q^{56} - 85 q^{57} - 73 q^{58} - 74 q^{59} - 43 q^{60} - 7 q^{61} - 110 q^{62} - 70 q^{63} + 141 q^{64} + 43 q^{65} - 16 q^{66} - 39 q^{67} - 222 q^{68} + 19 q^{69} - 52 q^{70} - 72 q^{71} - 106 q^{72} - 143 q^{73} + 20 q^{74} - 73 q^{75} - 88 q^{76} - 86 q^{77} + 17 q^{78} + 10 q^{79} - 239 q^{80} + 103 q^{81} - 96 q^{82} - 96 q^{83} - 75 q^{84} - 24 q^{85} - 109 q^{86} - 65 q^{87} - 45 q^{88} - 237 q^{89} - 79 q^{90} + 18 q^{91} - 153 q^{92} - 137 q^{93} - 23 q^{94} + 10 q^{95} - 109 q^{96} - 160 q^{97} - 119 q^{98} - 86 q^{99}+O(q^{100}) \) 151 * q - 13 * q^2 - 16 * q^3 + 151 * q^4 - 43 * q^5 - 17 * q^6 - 18 * q^7 - 39 * q^8 + 135 * q^9 - 3 * q^10 - 27 * q^11 - 52 * q^12 - 151 * q^13 - 9 * q^14 - 14 * q^15 + 143 * q^16 - 111 * q^17 - 37 * q^18 - 17 * q^19 - 107 * q^20 - 29 * q^21 - 16 * q^22 - 47 * q^23 - 46 * q^24 + 122 * q^25 + 13 * q^26 - 55 * q^27 - 44 * q^28 + 37 * q^29 - 14 * q^30 - 27 * q^31 - 86 * q^32 - 94 * q^33 - 10 * q^34 - 47 * q^35 + 124 * q^36 - 59 * q^37 - 80 * q^38 + 16 * q^39 + 5 * q^40 - 129 * q^41 - 77 * q^42 - 11 * q^43 - 99 * q^44 - 122 * q^45 - 17 * q^46 - 130 * q^47 - 111 * q^48 + 99 * q^49 - 72 * q^50 + 15 * q^51 - 151 * q^52 - 43 * q^53 - 49 * q^54 - 40 * q^55 - 50 * q^56 - 85 * q^57 - 73 * q^58 - 74 * q^59 - 43 * q^60 - 7 * q^61 - 110 * q^62 - 70 * q^63 + 141 * q^64 + 43 * q^65 - 16 * q^66 - 39 * q^67 - 222 * q^68 + 19 * q^69 - 52 * q^70 - 72 * q^71 - 106 * q^72 - 143 * q^73 + 20 * q^74 - 73 * q^75 - 88 * q^76 - 86 * q^77 + 17 * q^78 + 10 * q^79 - 239 * q^80 + 103 * q^81 - 96 * q^82 - 96 * q^83 - 75 * q^84 - 24 * q^85 - 109 * q^86 - 65 * q^87 - 45 * q^88 - 237 * q^89 - 79 * q^90 + 18 * q^91 - 153 * q^92 - 137 * q^93 - 23 * q^94 + 10 * q^95 - 109 * q^96 - 160 * q^97 - 119 * q^98 - 86 * q^99

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