LMFDB - Embedded newform 8007.2.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18789 q^{2} +1.00000 q^{3} +2.78687 q^{4} +1.88275 q^{5} -2.18789 q^{6} -4.23490 q^{7} -1.72159 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18789 q^{2} +1.00000 q^{3} +2.78687 q^{4} +1.88275 q^{5} -2.18789 q^{6} -4.23490 q^{7} -1.72159 q^{8} +1.00000 q^{9} -4.11926 q^{10} -2.82858 q^{11} +2.78687 q^{12} -3.44968 q^{13} +9.26549 q^{14} +1.88275 q^{15} -1.80709 q^{16} -1.00000 q^{17} -2.18789 q^{18} +4.03133 q^{19} +5.24699 q^{20} -4.23490 q^{21} +6.18863 q^{22} +7.09312 q^{23} -1.72159 q^{24} -1.45524 q^{25} +7.54753 q^{26} +1.00000 q^{27} -11.8021 q^{28} +4.45240 q^{29} -4.11926 q^{30} -6.06536 q^{31} +7.39690 q^{32} -2.82858 q^{33} +2.18789 q^{34} -7.97327 q^{35} +2.78687 q^{36} +0.948127 q^{37} -8.82011 q^{38} -3.44968 q^{39} -3.24133 q^{40} -1.88245 q^{41} +9.26549 q^{42} +2.93590 q^{43} -7.88289 q^{44} +1.88275 q^{45} -15.5190 q^{46} +7.81020 q^{47} -1.80709 q^{48} +10.9343 q^{49} +3.18390 q^{50} -1.00000 q^{51} -9.61381 q^{52} -3.16643 q^{53} -2.18789 q^{54} -5.32553 q^{55} +7.29075 q^{56} +4.03133 q^{57} -9.74138 q^{58} -1.33133 q^{59} +5.24699 q^{60} +2.15231 q^{61} +13.2704 q^{62} -4.23490 q^{63} -12.5694 q^{64} -6.49490 q^{65} +6.18863 q^{66} -4.67577 q^{67} -2.78687 q^{68} +7.09312 q^{69} +17.4447 q^{70} +1.47881 q^{71} -1.72159 q^{72} +3.77361 q^{73} -2.07440 q^{74} -1.45524 q^{75} +11.2348 q^{76} +11.9788 q^{77} +7.54753 q^{78} +13.2228 q^{79} -3.40231 q^{80} +1.00000 q^{81} +4.11860 q^{82} +6.59385 q^{83} -11.8021 q^{84} -1.88275 q^{85} -6.42343 q^{86} +4.45240 q^{87} +4.86965 q^{88} -16.0826 q^{89} -4.11926 q^{90} +14.6090 q^{91} +19.7676 q^{92} -6.06536 q^{93} -17.0879 q^{94} +7.59000 q^{95} +7.39690 q^{96} +7.74922 q^{97} -23.9232 q^{98} -2.82858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	−2.18789	−1.54707	−0.773537	−	0.633752i	$-0.781514\pi$
$2$	−2.18789	−1.54707	−0.773537	+	0.633752i	$0.781514\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.78687	1.39344
$5$	1.88275	0.841993	0.420997	−	0.907062i	$-0.361680\pi$
$5$	1.88275	0.841993	0.420997	+	0.907062i	$0.361680\pi$
$6$	−2.18789	−0.893203
$7$	−4.23490	−1.60064	−0.800320	−	0.599573i	$-0.795337\pi$
$7$	−4.23490	−1.60064	−0.800320	+	0.599573i	$0.795337\pi$
$8$	−1.72159	−0.608673
$9$	1.00000	0.333333
$10$	−4.11926	−1.30263
$11$	−2.82858	−0.852850	−0.426425	−	0.904523i	$-0.640227\pi$
$11$	−2.82858	−0.852850	−0.426425	+	0.904523i	$0.640227\pi$
$12$	2.78687	0.804500
$13$	−3.44968	−0.956769	−0.478385	−	0.878150i	$-0.658777\pi$
$13$	−3.44968	−0.956769	−0.478385	+	0.878150i	$0.658777\pi$
$14$	9.26549	2.47631
$15$	1.88275	0.486125
$16$	−1.80709	−0.451773
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.18789	−0.515691
$19$	4.03133	0.924850	0.462425	−	0.886658i	$-0.346979\pi$
$19$	4.03133	0.924850	0.462425	+	0.886658i	$0.346979\pi$
$20$	5.24699	1.17326
$21$	−4.23490	−0.924130
$22$	6.18863	1.31942
$23$	7.09312	1.47902	0.739509	−	0.673147i	$-0.235058\pi$
$23$	7.09312	1.47902	0.739509	+	0.673147i	$0.235058\pi$
$24$	−1.72159	−0.351418
$25$	−1.45524	−0.291047
$26$	7.54753	1.48019
$27$	1.00000	0.192450
$28$	−11.8021	−2.23039
$29$	4.45240	0.826791	0.413395	−	0.910552i	$-0.364343\pi$
$29$	4.45240	0.826791	0.413395	+	0.910552i	$0.364343\pi$
$30$	−4.11926	−0.752071
$31$	−6.06536	−1.08937	−0.544686	−	0.838640i	$-0.683351\pi$
$31$	−6.06536	−1.08937	−0.544686	+	0.838640i	$0.683351\pi$
$32$	7.39690	1.30760
$33$	−2.82858	−0.492393
$34$	2.18789	0.375220
$35$	−7.97327	−1.34773
$36$	2.78687	0.464478
$37$	0.948127	0.155871	0.0779356	−	0.996958i	$-0.475167\pi$
$37$	0.948127	0.155871	0.0779356	+	0.996958i	$0.475167\pi$
$38$	−8.82011	−1.43081
$39$	−3.44968	−0.552391
$40$	−3.24133	−0.512499
$41$	−1.88245	−0.293989	−0.146995	−	0.989137i	$-0.546960\pi$
$41$	−1.88245	−0.293989	−0.146995	+	0.989137i	$0.546960\pi$
$42$	9.26549	1.42970
$43$	2.93590	0.447720	0.223860	−	0.974621i	$-0.428134\pi$
$43$	2.93590	0.447720	0.223860	+	0.974621i	$0.428134\pi$
$44$	−7.88289	−1.18839
$45$	1.88275	0.280664
$46$	−15.5190	−2.28815
$47$	7.81020	1.13923	0.569617	−	0.821910i	$-0.307091\pi$
$47$	7.81020	1.13923	0.569617	+	0.821910i	$0.307091\pi$
$48$	−1.80709	−0.260831
$49$	10.9343	1.56205
$50$	3.18390	0.450271
$51$	−1.00000	−0.140028
$52$	−9.61381	−1.33320
$53$	−3.16643	−0.434943	−0.217472	−	0.976067i	$-0.569781\pi$
$53$	−3.16643	−0.434943	−0.217472	+	0.976067i	$0.569781\pi$
$54$	−2.18789	−0.297734
$55$	−5.32553	−0.718094
$56$	7.29075	0.974267
$57$	4.03133	0.533963
$58$	−9.74138	−1.27911
$59$	−1.33133	−0.173325	−0.0866623	−	0.996238i	$-0.527620\pi$
$59$	−1.33133	−0.173325	−0.0866623	+	0.996238i	$0.527620\pi$
$60$	5.24699	0.677384
$61$	2.15231	0.275575	0.137788	−	0.990462i	$-0.456001\pi$
$61$	2.15231	0.275575	0.137788	+	0.990462i	$0.456001\pi$
$62$	13.2704	1.68534
$63$	−4.23490	−0.533547
$64$	−12.5694	−1.57118
$65$	−6.49490	−0.805593
$66$	6.18863	0.761768
$67$	−4.67577	−0.571237	−0.285618	−	0.958343i	$-0.592199\pi$
$67$	−4.67577	−0.571237	−0.285618	+	0.958343i	$0.592199\pi$
$68$	−2.78687	−0.337958
$69$	7.09312	0.853912
$70$	17.4447	2.08503
$71$	1.47881	0.175502	0.0877511	−	0.996142i	$-0.472032\pi$
$71$	1.47881	0.175502	0.0877511	+	0.996142i	$0.472032\pi$
$72$	−1.72159	−0.202891
$73$	3.77361	0.441667	0.220834	−	0.975312i	$-0.429122\pi$
$73$	3.77361	0.441667	0.220834	+	0.975312i	$0.429122\pi$
$74$	−2.07440	−0.241144
$75$	−1.45524	−0.168036
$76$	11.2348	1.28872
$77$	11.9788	1.36511
$78$	7.54753	0.854589
$79$	13.2228	1.48768	0.743840	−	0.668358i	$-0.233003\pi$
$79$	13.2228	1.48768	0.743840	+	0.668358i	$0.233003\pi$
$80$	−3.40231	−0.380390
$81$	1.00000	0.111111
$82$	4.11860	0.454823
$83$	6.59385	0.723769	0.361884	−	0.932223i	$-0.382133\pi$
$83$	6.59385	0.723769	0.361884	+	0.932223i	$0.382133\pi$
$84$	−11.8021	−1.28772
$85$	−1.88275	−0.204213
$86$	−6.42343	−0.692656
$87$	4.45240	0.477348
$88$	4.86965	0.519107
$89$	−16.0826	−1.70476	−0.852379	−	0.522925i	$-0.824841\pi$
$89$	−16.0826	−1.70476	−0.852379	+	0.522925i	$0.824841\pi$
$90$	−4.11926	−0.434208
$91$	14.6090	1.53144
$92$	19.7676	2.06092
$93$	−6.06536	−0.628949
$94$	−17.0879	−1.76248
$95$	7.59000	0.778718
$96$	7.39690	0.754943
$97$	7.74922	0.786814	0.393407	−	0.919364i	$-0.371296\pi$
$97$	7.74922	0.786814	0.393407	+	0.919364i	$0.371296\pi$
$98$	−23.9232	−2.41660
$99$	−2.82858	−0.284283
$100$	−4.05555	−0.405555
$101$	16.0824	1.60026	0.800128	−	0.599829i	$-0.204765\pi$
$101$	16.0824	1.60026	0.800128	+	0.599829i	$0.204765\pi$
$102$	2.18789	0.216634
$103$	−14.0991	−1.38923	−0.694615	−	0.719382i	$-0.744425\pi$
$103$	−14.0991	−1.38923	−0.694615	+	0.719382i	$0.744425\pi$
$104$	5.93893	0.582360
$105$	−7.97327	−0.778111
$106$	6.92782	0.672889
$107$	−8.60245	−0.831630	−0.415815	−	0.909449i	$-0.636504\pi$
$107$	−8.60245	−0.831630	−0.415815	+	0.909449i	$0.636504\pi$
$108$	2.78687	0.268167
$109$	4.25026	0.407101	0.203550	−	0.979064i	$-0.434752\pi$
$109$	4.25026	0.407101	0.203550	+	0.979064i	$0.434752\pi$
$110$	11.6517	1.11094
$111$	0.948127	0.0899922
$112$	7.65285	0.723127
$113$	2.34468	0.220569	0.110284	−	0.993900i	$-0.464824\pi$
$113$	2.34468	0.220569	0.110284	+	0.993900i	$0.464824\pi$
$114$	−8.82011	−0.826079
$115$	13.3546	1.24532
$116$	12.4083	1.15208
$117$	−3.44968	−0.318923
$118$	2.91281	0.268146
$119$	4.23490	0.388212
$120$	−3.24133	−0.295891
$121$	−2.99912	−0.272647
$122$	−4.70902	−0.426335
$123$	−1.88245	−0.169735
$124$	−16.9034	−1.51797
$125$	−12.1536	−1.08705
$126$	9.26549	0.825436
$127$	−6.49424	−0.576271	−0.288135	−	0.957590i	$-0.593035\pi$
$127$	−6.49424	−0.576271	−0.288135	+	0.957590i	$0.593035\pi$
$128$	12.7068	1.12313
$129$	2.93590	0.258492
$130$	14.2101	1.24631
$131$	−16.2039	−1.41574	−0.707869	−	0.706344i	$-0.750343\pi$
$131$	−16.2039	−1.41574	−0.707869	+	0.706344i	$0.750343\pi$
$132$	−7.88289	−0.686118
$133$	−17.0723	−1.48035
$134$	10.2301	0.883745
$135$	1.88275	0.162042
$136$	1.72159	0.147625
$137$	3.74290	0.319778	0.159889	−	0.987135i	$-0.448886\pi$
$137$	3.74290	0.319778	0.159889	+	0.987135i	$0.448886\pi$
$138$	−15.5190	−1.32106
$139$	7.95250	0.674522	0.337261	−	0.941411i	$-0.390499\pi$
$139$	7.95250	0.674522	0.337261	+	0.941411i	$0.390499\pi$
$140$	−22.2205	−1.87797
$141$	7.81020	0.657738
$142$	−3.23547	−0.271515
$143$	9.75771	0.815980
$144$	−1.80709	−0.150591
$145$	8.38278	0.696152
$146$	−8.25624	−0.683291
$147$	10.9343	0.901849
$148$	2.64231	0.217196
$149$	19.5879	1.60471	0.802353	−	0.596850i	$-0.203581\pi$
$149$	19.5879	1.60471	0.802353	+	0.596850i	$0.203581\pi$
$150$	3.18390	0.259964
$151$	6.22240	0.506372	0.253186	−	0.967418i	$-0.418522\pi$
$151$	6.22240	0.506372	0.253186	+	0.967418i	$0.418522\pi$
$152$	−6.94029	−0.562932
$153$	−1.00000	−0.0808452
$154$	−26.2082	−2.11192
$155$	−11.4196	−0.917243
$156$	−9.61381	−0.769721
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−28.9300	−2.30155
$159$	−3.16643	−0.251115
$160$	13.9265	1.10099
$161$	−30.0386	−2.36738
$162$	−2.18789	−0.171897
$163$	−7.51333	−0.588489	−0.294245	−	0.955730i	$-0.595068\pi$
$163$	−7.51333	−0.588489	−0.294245	+	0.955730i	$0.595068\pi$
$164$	−5.24614	−0.409655
$165$	−5.32553	−0.414592
$166$	−14.4266	−1.11972
$167$	2.04948	0.158594	0.0792968	−	0.996851i	$-0.474733\pi$
$167$	2.04948	0.158594	0.0792968	+	0.996851i	$0.474733\pi$
$168$	7.29075	0.562493
$169$	−1.09971	−0.0845928
$170$	4.11926	0.315933
$171$	4.03133	0.308283
$172$	8.18197	0.623869
$173$	−23.5641	−1.79154	−0.895772	−	0.444513i	$-0.853377\pi$
$173$	−23.5641	−1.79154	−0.895772	+	0.444513i	$0.853377\pi$
$174$	−9.74138	−0.738492
$175$	6.16277	0.465862
$176$	5.11151	0.385295
$177$	−1.33133	−0.100069
$178$	35.1871	2.63738
$179$	1.12270	0.0839144	0.0419572	−	0.999119i	$-0.486641\pi$
$179$	1.12270	0.0839144	0.0419572	+	0.999119i	$0.486641\pi$
$180$	5.24699	0.391088
$181$	−21.1199	−1.56983	−0.784914	−	0.619605i	$-0.787293\pi$
$181$	−21.1199	−1.56983	−0.784914	+	0.619605i	$0.787293\pi$
$182$	−31.9630	−2.36925
$183$	2.15231	0.159103
$184$	−12.2114	−0.900239
$185$	1.78509	0.131242
$186$	13.2704	0.973030
$187$	2.82858	0.206846
$188$	21.7660	1.58745
$189$	−4.23490	−0.308043
$190$	−16.6061	−1.20473
$191$	−22.4112	−1.62162	−0.810809	−	0.585310i	$-0.800973\pi$
$191$	−22.4112	−1.62162	−0.810809	+	0.585310i	$0.800973\pi$
$192$	−12.5694	−0.907121
$193$	−4.52019	−0.325371	−0.162685	−	0.986678i	$-0.552016\pi$
$193$	−4.52019	−0.325371	−0.162685	+	0.986678i	$0.552016\pi$
$194$	−16.9544	−1.21726
$195$	−6.49490	−0.465110
$196$	30.4726	2.17661
$197$	−24.5880	−1.75182	−0.875912	−	0.482471i	$-0.839739\pi$
$197$	−24.5880	−1.75182	−0.875912	+	0.482471i	$0.839739\pi$
$198$	6.18863	0.439807
$199$	−8.69617	−0.616455	−0.308227	−	0.951313i	$-0.599736\pi$
$199$	−8.69617	−0.616455	−0.308227	+	0.951313i	$0.599736\pi$
$200$	2.50532	0.177153
$201$	−4.67577	−0.329804
$202$	−35.1865	−2.47571
$203$	−18.8555	−1.32339
$204$	−2.78687	−0.195120
$205$	−3.54419	−0.247537
$206$	30.8474	2.14924
$207$	7.09312	0.493006
$208$	6.23389	0.432243
$209$	−11.4029	−0.788758
$210$	17.4447	1.20380
$211$	11.8238	0.813986	0.406993	−	0.913431i	$-0.366577\pi$
$211$	11.8238	0.813986	0.406993	+	0.913431i	$0.366577\pi$
$212$	−8.82444	−0.606065
$213$	1.47881	0.101326
$214$	18.8212	1.28659
$215$	5.52758	0.376978
$216$	−1.72159	−0.117139
$217$	25.6862	1.74369
$218$	−9.29910	−0.629815
$219$	3.77361	0.254997
$220$	−14.8416	−1.00062
$221$	3.44968	0.232051
$222$	−2.07440	−0.139225
$223$	−17.4177	−1.16638	−0.583189	−	0.812336i	$-0.698195\pi$
$223$	−17.4177	−1.16638	−0.583189	+	0.812336i	$0.698195\pi$
$224$	−31.3251	−2.09300
$225$	−1.45524	−0.0970157
$226$	−5.12991	−0.341236
$227$	21.8626	1.45107	0.725536	−	0.688185i	$-0.241592\pi$
$227$	21.8626	1.45107	0.725536	+	0.688185i	$0.241592\pi$
$228$	11.2348	0.744042
$229$	−23.9910	−1.58537	−0.792686	−	0.609630i	$-0.791318\pi$
$229$	−23.9910	−1.58537	−0.792686	+	0.609630i	$0.791318\pi$
$230$	−29.2184	−1.92661
$231$	11.9788	0.788144
$232$	−7.66520	−0.503245
$233$	−23.3784	−1.53157	−0.765786	−	0.643095i	$-0.777650\pi$
$233$	−23.3784	−1.53157	−0.765786	+	0.643095i	$0.777650\pi$
$234$	7.54753	0.493397
$235$	14.7047	0.959228
$236$	−3.71025	−0.241517
$237$	13.2228	0.858912
$238$	−9.26549	−0.600593
$239$	−20.9874	−1.35756	−0.678781	−	0.734340i	$-0.737492\pi$
$239$	−20.9874	−1.35756	−0.678781	+	0.734340i	$0.737492\pi$
$240$	−3.40231	−0.219618
$241$	11.9185	0.767737	0.383868	−	0.923388i	$-0.374592\pi$
$241$	11.9185	0.767737	0.383868	+	0.923388i	$0.374592\pi$
$242$	6.56175	0.421805
$243$	1.00000	0.0641500
$244$	5.99821	0.383996
$245$	20.5867	1.31524
$246$	4.11860	0.262592
$247$	−13.9068	−0.884868
$248$	10.4421	0.663071
$249$	6.59385	0.417868
$250$	26.5908	1.68175
$251$	−21.9973	−1.38846	−0.694230	−	0.719753i	$-0.744255\pi$
$251$	−21.9973	−1.38846	−0.694230	+	0.719753i	$0.744255\pi$
$252$	−11.8021	−0.743463
$253$	−20.0635	−1.26138
$254$	14.2087	0.891533
$255$	−1.88275	−0.117903
$256$	−2.66214	−0.166384
$257$	1.98422	0.123772	0.0618861	−	0.998083i	$-0.480288\pi$
$257$	1.98422	0.123772	0.0618861	+	0.998083i	$0.480288\pi$
$258$	−6.42343	−0.399905
$259$	−4.01522	−0.249494
$260$	−18.1005	−1.12254
$261$	4.45240	0.275597
$262$	35.4523	2.19025
$263$	−15.1935	−0.936874	−0.468437	−	0.883497i	$-0.655183\pi$
$263$	−15.1935	−0.936874	−0.468437	+	0.883497i	$0.655183\pi$
$264$	4.86965	0.299706
$265$	−5.96162	−0.366219
$266$	37.3523	2.29021
$267$	−16.0826	−0.984242
$268$	−13.0308	−0.795981
$269$	−11.1681	−0.680929	−0.340465	−	0.940257i	$-0.610584\pi$
$269$	−11.1681	−0.680929	−0.340465	+	0.940257i	$0.610584\pi$
$270$	−4.11926	−0.250690
$271$	29.3218	1.78118	0.890588	−	0.454812i	$-0.150293\pi$
$271$	29.3218	1.78118	0.890588	+	0.454812i	$0.150293\pi$
$272$	1.80709	0.109571
$273$	14.6090	0.884179
$274$	−8.18906	−0.494719
$275$	4.11625	0.248219
$276$	19.7676	1.18987
$277$	−9.78287	−0.587796	−0.293898	−	0.955837i	$-0.594953\pi$
$277$	−9.78287	−0.587796	−0.293898	+	0.955837i	$0.594953\pi$
$278$	−17.3992	−1.04354
$279$	−6.06536	−0.363124
$280$	13.7267	0.820326
$281$	18.6134	1.11038	0.555191	−	0.831723i	$-0.312645\pi$
$281$	18.6134	1.11038	0.555191	+	0.831723i	$0.312645\pi$
$282$	−17.0879	−1.01757
$283$	1.36808	0.0813237	0.0406618	−	0.999173i	$-0.487053\pi$
$283$	1.36808	0.0813237	0.0406618	+	0.999173i	$0.487053\pi$
$284$	4.12125	0.244551
$285$	7.59000	0.449593
$286$	−21.3488	−1.26238
$287$	7.97198	0.470571
$288$	7.39690	0.435867
$289$	1.00000	0.0588235
$290$	−18.3406	−1.07700
$291$	7.74922	0.454267
$292$	10.5165	0.615435
$293$	−0.159950	−0.00934437	−0.00467219	−	0.999989i	$-0.501487\pi$
$293$	−0.159950	−0.00934437	−0.00467219	+	0.999989i	$0.501487\pi$
$294$	−23.9232	−1.39523
$295$	−2.50657	−0.145938
$296$	−1.63228	−0.0948746
$297$	−2.82858	−0.164131
$298$	−42.8563	−2.48260
$299$	−24.4690	−1.41508
$300$	−4.05555	−0.234147
$301$	−12.4332	−0.716639
$302$	−13.6139	−0.783394
$303$	16.0824	0.923909
$304$	−7.28499	−0.417823
$305$	4.05227	0.232033
$306$	2.18789	0.125073
$307$	−2.25214	−0.128536	−0.0642682	−	0.997933i	$-0.520471\pi$
$307$	−2.25214	−0.128536	−0.0642682	+	0.997933i	$0.520471\pi$
$308$	33.3832	1.90219
$309$	−14.0991	−0.802072
$310$	24.9848	1.41904
$311$	−16.9471	−0.960983	−0.480491	−	0.876999i	$-0.659542\pi$
$311$	−16.9471	−0.960983	−0.480491	+	0.876999i	$0.659542\pi$
$312$	5.93893	0.336226
$313$	6.77575	0.382988	0.191494	−	0.981494i	$-0.438667\pi$
$313$	6.77575	0.382988	0.191494	+	0.981494i	$0.438667\pi$
$314$	−2.18789	−0.123470
$315$	−7.97327	−0.449243
$316$	36.8502	2.07298
$317$	0.868483	0.0487789	0.0243894	−	0.999703i	$-0.492236\pi$
$317$	0.868483	0.0487789	0.0243894	+	0.999703i	$0.492236\pi$
$318$	6.92782	0.388493
$319$	−12.5940	−0.705128
$320$	−23.6652	−1.32292
$321$	−8.60245	−0.480142
$322$	65.7213	3.66250
$323$	−4.03133	−0.224309
$324$	2.78687	0.154826
$325$	5.02010	0.278465
$326$	16.4383	0.910436
$327$	4.25026	0.235040
$328$	3.24080	0.178943
$329$	−33.0754	−1.82350
$330$	11.6517	0.641404
$331$	4.68586	0.257558	0.128779	−	0.991673i	$-0.458894\pi$
$331$	4.68586	0.257558	0.128779	+	0.991673i	$0.458894\pi$
$332$	18.3762	1.00853
$333$	0.948127	0.0519570
$334$	−4.48404	−0.245356
$335$	−8.80333	−0.480977
$336$	7.65285	0.417497
$337$	−29.3330	−1.59787	−0.798934	−	0.601419i	$-0.794602\pi$
$337$	−29.3330	−1.59787	−0.798934	+	0.601419i	$0.794602\pi$
$338$	2.40604	0.130871
$339$	2.34468	0.127346
$340$	−5.24699	−0.284558
$341$	17.1564	0.929070
$342$	−8.82011	−0.476937
$343$	−16.6615	−0.899638
$344$	−5.05441	−0.272515
$345$	13.3546	0.718988
$346$	51.5557	2.77165
$347$	−26.5955	−1.42772	−0.713860	−	0.700288i	$-0.753055\pi$
$347$	−26.5955	−1.42772	−0.713860	+	0.700288i	$0.753055\pi$
$348$	12.4083	0.665153
$349$	−5.64738	−0.302297	−0.151149	−	0.988511i	$-0.548297\pi$
$349$	−5.64738	−0.302297	−0.151149	+	0.988511i	$0.548297\pi$
$350$	−13.4835	−0.720722
$351$	−3.44968	−0.184130
$352$	−20.9227	−1.11519
$353$	17.6895	0.941516	0.470758	−	0.882262i	$-0.343980\pi$
$353$	17.6895	0.941516	0.470758	+	0.882262i	$0.343980\pi$
$354$	2.91281	0.154814
$355$	2.78423	0.147772
$356$	−44.8203	−2.37547
$357$	4.23490	0.224134
$358$	−2.45634	−0.129822
$359$	16.3229	0.861489	0.430744	−	0.902474i	$-0.358251\pi$
$359$	16.3229	0.861489	0.430744	+	0.902474i	$0.358251\pi$
$360$	−3.24133	−0.170833
$361$	−2.74838	−0.144652
$362$	46.2080	2.42864
$363$	−2.99912	−0.157413
$364$	40.7135	2.13397
$365$	7.10477	0.371881
$366$	−4.70902	−0.246145
$367$	−4.92235	−0.256945	−0.128472	−	0.991713i	$-0.541007\pi$
$367$	−4.92235	−0.256945	−0.128472	+	0.991713i	$0.541007\pi$
$368$	−12.8179	−0.668181
$369$	−1.88245	−0.0979964
$370$	−3.90558	−0.203042
$371$	13.4095	0.696188
$372$	−16.9034	−0.876399
$373$	−0.443592	−0.0229683	−0.0114842	−	0.999934i	$-0.503656\pi$
$373$	−0.443592	−0.0229683	−0.0114842	+	0.999934i	$0.503656\pi$
$374$	−6.18863	−0.320007
$375$	−12.1536	−0.627610
$376$	−13.4459	−0.693422
$377$	−15.3594	−0.791048
$378$	9.26549	0.476566
$379$	13.7476	0.706165	0.353083	−	0.935592i	$-0.385133\pi$
$379$	13.7476	0.706165	0.353083	+	0.935592i	$0.385133\pi$
$380$	21.1524	1.08509
$381$	−6.49424	−0.332710
$382$	49.0333	2.50876
$383$	−32.9438	−1.68335	−0.841675	−	0.539985i	$-0.818430\pi$
$383$	−32.9438	−1.68335	−0.841675	+	0.539985i	$0.818430\pi$
$384$	12.7068	0.648439
$385$	22.5531	1.14941
$386$	9.88969	0.503372
$387$	2.93590	0.149240
$388$	21.5961	1.09637
$389$	−7.31894	−0.371085	−0.185543	−	0.982636i	$-0.559404\pi$
$389$	−7.31894	−0.371085	−0.185543	+	0.982636i	$0.559404\pi$
$390$	14.2101	0.719559
$391$	−7.09312	−0.358715
$392$	−18.8244	−0.950777
$393$	−16.2039	−0.817377
$394$	53.7959	2.71020
$395$	24.8953	1.25262
$396$	−7.88289	−0.396130
$397$	9.70448	0.487054	0.243527	−	0.969894i	$-0.421696\pi$
$397$	9.70448	0.487054	0.243527	+	0.969894i	$0.421696\pi$
$398$	19.0263	0.953701
$399$	−17.0723	−0.854682
$400$	2.62975	0.131487
$401$	−14.1843	−0.708331	−0.354165	−	0.935183i	$-0.615235\pi$
$401$	−14.1843	−0.708331	−0.354165	+	0.935183i	$0.615235\pi$
$402$	10.2301	0.510230
$403$	20.9236	1.04228
$404$	44.8195	2.22985
$405$	1.88275	0.0935548
$406$	41.2537	2.04739
$407$	−2.68186	−0.132935
$408$	1.72159	0.0852313
$409$	−9.36389	−0.463014	−0.231507	−	0.972833i	$-0.574366\pi$
$409$	−9.36389	−0.463014	−0.231507	+	0.972833i	$0.574366\pi$
$410$	7.75431	0.382958
$411$	3.74290	0.184624
$412$	−39.2925	−1.93580
$413$	5.63805	0.277430
$414$	−15.5190	−0.762716
$415$	12.4146	0.609409
$416$	−25.5169	−1.25107
$417$	7.95250	0.389436
$418$	24.9484	1.22027
$419$	14.3834	0.702675	0.351338	−	0.936249i	$-0.385727\pi$
$419$	14.3834	0.702675	0.351338	+	0.936249i	$0.385727\pi$
$420$	−22.2205	−1.08425
$421$	30.7115	1.49678	0.748392	−	0.663256i	$-0.230826\pi$
$421$	30.7115	1.49678	0.748392	+	0.663256i	$0.230826\pi$
$422$	−25.8693	−1.25930
$423$	7.81020	0.379745
$424$	5.45130	0.264738
$425$	1.45524	0.0705893
$426$	−3.23547	−0.156759
$427$	−9.11481	−0.441097
$428$	−23.9739	−1.15882
$429$	9.75771	0.471106
$430$	−12.0937	−0.583212
$431$	−16.6451	−0.801765	−0.400883	−	0.916129i	$-0.631296\pi$
$431$	−16.6451	−0.801765	−0.400883	+	0.916129i	$0.631296\pi$
$432$	−1.80709	−0.0869438
$433$	14.7178	0.707291	0.353646	−	0.935379i	$-0.384942\pi$
$433$	14.7178	0.707291	0.353646	+	0.935379i	$0.384942\pi$
$434$	−56.1986	−2.69762
$435$	8.38278	0.401924
$436$	11.8449	0.567268
$437$	28.5947	1.36787
$438$	−8.25624	−0.394498
$439$	−12.2352	−0.583954	−0.291977	−	0.956425i	$-0.594313\pi$
$439$	−12.2352	−0.583954	−0.291977	+	0.956425i	$0.594313\pi$
$440$	9.16836	0.437085
$441$	10.9343	0.520683
$442$	−7.54753	−0.358999
$443$	−32.6376	−1.55066	−0.775330	−	0.631556i	$-0.782417\pi$
$443$	−32.6376	−1.55066	−0.775330	+	0.631556i	$0.782417\pi$
$444$	2.64231	0.125398
$445$	−30.2797	−1.43539
$446$	38.1081	1.80447
$447$	19.5879	0.926477
$448$	53.2302	2.51489
$449$	13.4223	0.633435	0.316718	−	0.948520i	$-0.397419\pi$
$449$	13.4223	0.633435	0.316718	+	0.948520i	$0.397419\pi$
$450$	3.18390	0.150090
$451$	5.32466	0.250729
$452$	6.53432	0.307349
$453$	6.22240	0.292354
$454$	−47.8330	−2.24491
$455$	27.5052	1.28947
$456$	−6.94029	−0.325009
$457$	−10.9402	−0.511760	−0.255880	−	0.966708i	$-0.582365\pi$
$457$	−10.9402	−0.511760	−0.255880	+	0.966708i	$0.582365\pi$
$458$	52.4898	2.45269
$459$	−1.00000	−0.0466760
$460$	37.2176	1.73528
$461$	−29.6276	−1.37989	−0.689946	−	0.723860i	$-0.742366\pi$
$461$	−29.6276	−1.37989	−0.689946	+	0.723860i	$0.742366\pi$
$462$	−26.2082	−1.21932
$463$	−0.622749	−0.0289416	−0.0144708	−	0.999895i	$-0.504606\pi$
$463$	−0.622749	−0.0289416	−0.0144708	+	0.999895i	$0.504606\pi$
$464$	−8.04591	−0.373522
$465$	−11.4196	−0.529571
$466$	51.1495	2.36945
$467$	−25.0738	−1.16028	−0.580138	−	0.814518i	$-0.697002\pi$
$467$	−25.0738	−1.16028	−0.580138	+	0.814518i	$0.697002\pi$
$468$	−9.61381	−0.444399
$469$	19.8014	0.914344
$470$	−32.1723	−1.48400
$471$	1.00000	0.0460776
$472$	2.29200	0.105498
$473$	−8.30443	−0.381838
$474$	−28.9300	−1.32880
$475$	−5.86653	−0.269175
$476$	11.8021	0.540949
$477$	−3.16643	−0.144981
$478$	45.9182	2.10025
$479$	41.7998	1.90988	0.954940	−	0.296798i	$-0.0959188\pi$
$479$	41.7998	1.90988	0.954940	+	0.296798i	$0.0959188\pi$
$480$	13.9265	0.635657
$481$	−3.27073	−0.149133
$482$	−26.0763	−1.18775
$483$	−30.0386	−1.36681
$484$	−8.35816	−0.379916
$485$	14.5899	0.662492
$486$	−2.18789	−0.0992448
$487$	17.3991	0.788430	0.394215	−	0.919018i	$-0.371017\pi$
$487$	17.3991	0.788430	0.394215	+	0.919018i	$0.371017\pi$
$488$	−3.70539	−0.167735
$489$	−7.51333	−0.339764
$490$	−45.0414	−2.03476
$491$	28.1789	1.27170	0.635849	−	0.771814i	$-0.280650\pi$
$491$	28.1789	1.27170	0.635849	+	0.771814i	$0.280650\pi$
$492$	−5.24614	−0.236514
$493$	−4.45240	−0.200526
$494$	30.4266	1.36896
$495$	−5.32553	−0.239365
$496$	10.9607	0.492149
$497$	−6.26260	−0.280916
$498$	−14.4266	−0.646473
$499$	18.3741	0.822539	0.411269	−	0.911514i	$-0.365086\pi$
$499$	18.3741	0.822539	0.411269	+	0.911514i	$0.365086\pi$
$500$	−33.8706	−1.51474
$501$	2.04948	0.0915640
$502$	48.1278	2.14805
$503$	−23.5000	−1.04781	−0.523906	−	0.851776i	$-0.675526\pi$
$503$	−23.5000	−1.04781	−0.523906	+	0.851776i	$0.675526\pi$
$504$	7.29075	0.324756
$505$	30.2792	1.34741
$506$	43.8967	1.95145
$507$	−1.09971	−0.0488396
$508$	−18.0986	−0.802996
$509$	−3.80681	−0.168734	−0.0843669	−	0.996435i	$-0.526887\pi$
$509$	−3.80681	−0.168734	−0.0843669	+	0.996435i	$0.526887\pi$
$510$	4.11926	0.182404
$511$	−15.9808	−0.706950
$512$	−19.5890	−0.865721
$513$	4.03133	0.177988
$514$	−4.34126	−0.191485
$515$	−26.5452	−1.16972
$516$	8.18197	0.360191
$517$	−22.0918	−0.971596
$518$	8.78486	0.385985
$519$	−23.5641	−1.03435
$520$	11.1815	0.490343
$521$	−3.09103	−0.135420	−0.0677102	−	0.997705i	$-0.521569\pi$
$521$	−3.09103	−0.135420	−0.0677102	+	0.997705i	$0.521569\pi$
$522$	−9.74138	−0.426369
$523$	−21.7874	−0.952695	−0.476347	−	0.879257i	$-0.658040\pi$
$523$	−21.7874	−0.952695	−0.476347	+	0.879257i	$0.658040\pi$
$524$	−45.1581	−1.97274
$525$	6.16277	0.268965
$526$	33.2418	1.44941
$527$	6.06536	0.264211
$528$	5.11151	0.222450
$529$	27.3124	1.18750
$530$	13.0434	0.566568
$531$	−1.33133	−0.0577749
$532$	−47.5782	−2.06278
$533$	6.49385	0.281280
$534$	35.1871	1.52269
$535$	−16.1963	−0.700227
$536$	8.04975	0.347696
$537$	1.12270	0.0484480
$538$	24.4345	1.05345
$539$	−30.9287	−1.33219
$540$	5.24699	0.225795
$541$	16.9903	0.730472	0.365236	−	0.930915i	$-0.380988\pi$
$541$	16.9903	0.730472	0.365236	+	0.930915i	$0.380988\pi$
$542$	−64.1530	−2.75561
$543$	−21.1199	−0.906341
$544$	−7.39690	−0.317139
$545$	8.00219	0.342776
$546$	−31.9630	−1.36789
$547$	1.92712	0.0823978	0.0411989	−	0.999151i	$-0.486882\pi$
$547$	1.92712	0.0823978	0.0411989	+	0.999151i	$0.486882\pi$
$548$	10.4310	0.445590
$549$	2.15231	0.0918584
$550$	−9.00592	−0.384014
$551$	17.9491	0.764658
$552$	−12.2114	−0.519753
$553$	−55.9971	−2.38124
$554$	21.4039	0.909363
$555$	1.78509	0.0757729
$556$	22.1626	0.939903
$557$	−15.4813	−0.655964	−0.327982	−	0.944684i	$-0.606369\pi$
$557$	−15.4813	−0.655964	−0.327982	+	0.944684i	$0.606369\pi$
$558$	13.2704	0.561779
$559$	−10.1279	−0.428365
$560$	14.4084	0.608868
$561$	2.82858	0.119423
$562$	−40.7241	−1.71784
$563$	23.2434	0.979593	0.489797	−	0.871837i	$-0.337071\pi$
$563$	23.2434	0.979593	0.489797	+	0.871837i	$0.337071\pi$
$564$	21.7660	0.916515
$565$	4.41446	0.185718
$566$	−2.99320	−0.125814
$567$	−4.23490	−0.177849
$568$	−2.54590	−0.106823
$569$	−8.55499	−0.358644	−0.179322	−	0.983790i	$-0.557390\pi$
$569$	−8.55499	−0.358644	−0.179322	+	0.983790i	$0.557390\pi$
$570$	−16.6061	−0.695553
$571$	16.8806	0.706433	0.353216	−	0.935542i	$-0.385088\pi$
$571$	16.8806	0.706433	0.353216	+	0.935542i	$0.385088\pi$
$572$	27.1935	1.13702
$573$	−22.4112	−0.936242
$574$	−17.4418	−0.728008
$575$	−10.3222	−0.430464
$576$	−12.5694	−0.523726
$577$	−15.3905	−0.640713	−0.320357	−	0.947297i	$-0.603803\pi$
$577$	−15.3905	−0.640713	−0.320357	+	0.947297i	$0.603803\pi$
$578$	−2.18789	−0.0910043
$579$	−4.52019	−0.187853
$580$	23.3617	0.970043
$581$	−27.9243	−1.15849
$582$	−16.9544	−0.702785
$583$	8.95652	0.370941
$584$	−6.49659	−0.268831
$585$	−6.49490	−0.268531
$586$	0.349953	0.0144564
$587$	17.2247	0.710939	0.355470	−	0.934688i	$-0.384321\pi$
$587$	17.2247	0.710939	0.355470	+	0.934688i	$0.384321\pi$
$588$	30.4726	1.25667
$589$	−24.4515	−1.00751
$590$	5.48411	0.225777
$591$	−24.5880	−1.01142
$592$	−1.71335	−0.0704184
$593$	17.8936	0.734804	0.367402	−	0.930062i	$-0.380247\pi$
$593$	17.8936	0.734804	0.367402	+	0.930062i	$0.380247\pi$
$594$	6.18863	0.253923
$595$	7.97327	0.326872
$596$	54.5890	2.23605
$597$	−8.69617	−0.355910
$598$	53.5355	2.18923
$599$	27.5913	1.12735	0.563675	−	0.825997i	$-0.309387\pi$
$599$	27.5913	1.12735	0.563675	+	0.825997i	$0.309387\pi$
$600$	2.50532	0.102279
$601$	21.4736	0.875926	0.437963	−	0.898993i	$-0.355700\pi$
$601$	21.4736	0.875926	0.437963	+	0.898993i	$0.355700\pi$
$602$	27.2026	1.10869
$603$	−4.67577	−0.190412
$604$	17.3410	0.705596
$605$	−5.64661	−0.229567
$606$	−35.1865	−1.42935
$607$	1.40781	0.0571412	0.0285706	−	0.999592i	$-0.490904\pi$
$607$	1.40781	0.0571412	0.0285706	+	0.999592i	$0.490904\pi$
$608$	29.8193	1.20933
$609$	−18.8555	−0.764062
$610$	−8.86594	−0.358971
$611$	−26.9427	−1.08998
$612$	−2.78687	−0.112653
$613$	−9.77917	−0.394977	−0.197488	−	0.980305i	$-0.563278\pi$
$613$	−9.77917	−0.394977	−0.197488	+	0.980305i	$0.563278\pi$
$614$	4.92744	0.198855
$615$	−3.54419	−0.142916
$616$	−20.6225	−0.830903
$617$	4.27814	0.172231	0.0861157	−	0.996285i	$-0.472555\pi$
$617$	4.27814	0.172231	0.0861157	+	0.996285i	$0.472555\pi$
$618$	30.8474	1.24086
$619$	24.4177	0.981428	0.490714	−	0.871321i	$-0.336736\pi$
$619$	24.4177	0.981428	0.490714	+	0.871321i	$0.336736\pi$
$620$	−31.8249	−1.27812
$621$	7.09312	0.284637
$622$	37.0785	1.48671
$623$	68.1083	2.72870
$624$	6.23389	0.249556
$625$	−15.6061	−0.624245
$626$	−14.8246	−0.592511
$627$	−11.4029	−0.455390
$628$	2.78687	0.111208
$629$	−0.948127	−0.0378043
$630$	17.4447	0.695012
$631$	6.96315	0.277199	0.138599	−	0.990349i	$-0.455740\pi$
$631$	6.96315	0.277199	0.138599	+	0.990349i	$0.455740\pi$
$632$	−22.7642	−0.905510
$633$	11.8238	0.469955
$634$	−1.90015	−0.0754645
$635$	−12.2271	−0.485216
$636$	−8.82444	−0.349912
$637$	−37.7200	−1.49452
$638$	27.5543	1.09089
$639$	1.47881	0.0585007
$640$	23.9237	0.945667
$641$	41.3401	1.63284	0.816418	−	0.577461i	$-0.195957\pi$
$641$	41.3401	1.63284	0.816418	+	0.577461i	$0.195957\pi$
$642$	18.8212	0.742814
$643$	−25.3084	−0.998064	−0.499032	−	0.866583i	$-0.666311\pi$
$643$	−25.3084	−0.998064	−0.499032	+	0.866583i	$0.666311\pi$
$644$	−83.7138	−3.29879
$645$	5.52758	0.217648
$646$	8.82011	0.347023
$647$	11.1879	0.439841	0.219920	−	0.975518i	$-0.429420\pi$
$647$	11.1879	0.439841	0.219920	+	0.975518i	$0.429420\pi$
$648$	−1.72159	−0.0676304
$649$	3.76578	0.147820
$650$	−10.9834	−0.430805
$651$	25.6862	1.00672
$652$	−20.9387	−0.820022
$653$	−10.4168	−0.407639	−0.203820	−	0.979008i	$-0.565336\pi$
$653$	−10.4168	−0.407639	−0.203820	+	0.979008i	$0.565336\pi$
$654$	−9.29910	−0.363624
$655$	−30.5079	−1.19204
$656$	3.40176	0.132817
$657$	3.77361	0.147222
$658$	72.3654	2.82110
$659$	−23.2041	−0.903902	−0.451951	−	0.892043i	$-0.649272\pi$
$659$	−23.2041	−0.903902	−0.451951	+	0.892043i	$0.649272\pi$
$660$	−14.8416	−0.577707
$661$	15.3483	0.596981	0.298490	−	0.954413i	$-0.403517\pi$
$661$	15.3483	0.596981	0.298490	+	0.954413i	$0.403517\pi$
$662$	−10.2521	−0.398461
$663$	3.44968	0.133974
$664$	−11.3519	−0.440539
$665$	−32.1429	−1.24645
$666$	−2.07440	−0.0803813
$667$	31.5814	1.22284
$668$	5.71164	0.220990
$669$	−17.4177	−0.673409
$670$	19.2607	0.744107
$671$	−6.08799	−0.235024
$672$	−31.3251	−1.20839
$673$	−10.3906	−0.400527	−0.200263	−	0.979742i	$-0.564180\pi$
$673$	−10.3906	−0.400527	−0.200263	+	0.979742i	$0.564180\pi$
$674$	64.1773	2.47202
$675$	−1.45524	−0.0560120
$676$	−3.06474	−0.117875
$677$	−36.5723	−1.40559	−0.702794	−	0.711394i	$-0.748064\pi$
$677$	−36.5723	−1.40559	−0.702794	+	0.711394i	$0.748064\pi$
$678$	−5.12991	−0.197013
$679$	−32.8171	−1.25941
$680$	3.24133	0.124299
$681$	21.8626	0.837776
$682$	−37.5363	−1.43734
$683$	3.65663	0.139917	0.0699585	−	0.997550i	$-0.477713\pi$
$683$	3.65663	0.139917	0.0699585	+	0.997550i	$0.477713\pi$
$684$	11.2348	0.429573
$685$	7.04697	0.269251
$686$	36.4536	1.39181
$687$	−23.9910	−0.915315
$688$	−5.30544	−0.202268
$689$	10.9232	0.416140
$690$	−29.2184	−1.11233
$691$	25.6964	0.977536	0.488768	−	0.872414i	$-0.337446\pi$
$691$	25.6964	0.977536	0.488768	+	0.872414i	$0.337446\pi$
$692$	−65.6701	−2.49640
$693$	11.9788	0.455035
$694$	58.1880	2.20879
$695$	14.9726	0.567943
$696$	−7.66520	−0.290549
$697$	1.88245	0.0713029
$698$	12.3559	0.467676
$699$	−23.3784	−0.884254
$700$	17.1748	0.649148
$701$	44.1837	1.66879	0.834397	−	0.551164i	$-0.185816\pi$
$701$	44.1837	1.66879	0.834397	+	0.551164i	$0.185816\pi$
$702$	7.54753	0.284863
$703$	3.82221	0.144157
$704$	35.5537	1.33998
$705$	14.7047	0.553811
$706$	−38.7027	−1.45659
$707$	−68.1072	−2.56144
$708$	−3.71025	−0.139440
$709$	−37.1353	−1.39465	−0.697323	−	0.716757i	$-0.745626\pi$
$709$	−37.1353	−1.39465	−0.697323	+	0.716757i	$0.745626\pi$
$710$	−6.09160	−0.228614
$711$	13.2228	0.495893
$712$	27.6877	1.03764
$713$	−43.0224	−1.61120
$714$	−9.26549	−0.346752
$715$	18.3714	0.687050
$716$	3.12881	0.116929
$717$	−20.9874	−0.783789
$718$	−35.7127	−1.33279
$719$	10.7049	0.399227	0.199613	−	0.979875i	$-0.436031\pi$
$719$	10.7049	0.399227	0.199613	+	0.979875i	$0.436031\pi$
$720$	−3.40231	−0.126797
$721$	59.7084	2.22366
$722$	6.01316	0.223787
$723$	11.9185	0.443253
$724$	−58.8584	−2.18745
$725$	−6.47929	−0.240635
$726$	6.56175	0.243529
$727$	−27.7585	−1.02950	−0.514752	−	0.857339i	$-0.672116\pi$
$727$	−27.7585	−1.02950	−0.514752	+	0.857339i	$0.672116\pi$
$728$	−25.1507	−0.932148
$729$	1.00000	0.0370370
$730$	−15.5445	−0.575327
$731$	−2.93590	−0.108588
$732$	5.99821	0.221700
$733$	−20.8522	−0.770193	−0.385097	−	0.922876i	$-0.625832\pi$
$733$	−20.8522	−0.770193	−0.385097	+	0.922876i	$0.625832\pi$
$734$	10.7696	0.397512
$735$	20.5867	0.759351
$736$	52.4671	1.93396
$737$	13.2258	0.487179
$738$	4.11860	0.151608
$739$	3.23412	0.118969	0.0594846	−	0.998229i	$-0.481054\pi$
$739$	3.23412	0.118969	0.0594846	+	0.998229i	$0.481054\pi$
$740$	4.97482	0.182878
$741$	−13.9068	−0.510879
$742$	−29.3386	−1.07705
$743$	30.4522	1.11718	0.558591	−	0.829444i	$-0.311342\pi$
$743$	30.4522	1.11718	0.558591	+	0.829444i	$0.311342\pi$
$744$	10.4421	0.382824
$745$	36.8793	1.35115
$746$	0.970532	0.0355337
$747$	6.59385	0.241256
$748$	7.88289	0.288227
$749$	36.4305	1.33114
$750$	26.5908	0.970959
$751$	10.2312	0.373341	0.186671	−	0.982423i	$-0.440230\pi$
$751$	10.2312	0.373341	0.186671	+	0.982423i	$0.440230\pi$
$752$	−14.1138	−0.514676
$753$	−21.9973	−0.801628
$754$	33.6046	1.22381
$755$	11.7153	0.426362
$756$	−11.8021	−0.429238
$757$	−33.3454	−1.21196	−0.605979	−	0.795481i	$-0.707219\pi$
$757$	−33.3454	−1.21196	−0.605979	+	0.795481i	$0.707219\pi$
$758$	−30.0782	−1.09249
$759$	−20.0635	−0.728258
$760$	−13.0669	−0.473985
$761$	−30.9441	−1.12172	−0.560862	−	0.827909i	$-0.689530\pi$
$761$	−30.9441	−1.12172	−0.560862	+	0.827909i	$0.689530\pi$
$762$	14.2087	0.514727
$763$	−17.9994	−0.651622
$764$	−62.4572	−2.25962
$765$	−1.88275	−0.0680711
$766$	72.0775	2.60426
$767$	4.59267	0.165832
$768$	−2.66214	−0.0960618
$769$	−3.45199	−0.124482	−0.0622410	−	0.998061i	$-0.519825\pi$
$769$	−3.45199	−0.124482	−0.0622410	+	0.998061i	$0.519825\pi$
$770$	−49.3436	−1.77822
$771$	1.98422	0.0714599
$772$	−12.5972	−0.453383
$773$	−28.3895	−1.02110	−0.510549	−	0.859849i	$-0.670558\pi$
$773$	−28.3895	−1.02110	−0.510549	+	0.859849i	$0.670558\pi$
$774$	−6.42343	−0.230885
$775$	8.82653	0.317058
$776$	−13.3410	−0.478912
$777$	−4.01522	−0.144045
$778$	16.0131	0.574096
$779$	−7.58878	−0.271896
$780$	−18.1005	−0.648100
$781$	−4.18293	−0.149677
$782$	15.5190	0.554958
$783$	4.45240	0.159116
$784$	−19.7594	−0.705692
$785$	1.88275	0.0671984
$786$	35.4523	1.26454
$787$	−0.202310	−0.00721158	−0.00360579	−	0.999993i	$-0.501148\pi$
$787$	−0.202310	−0.00721158	−0.00360579	+	0.999993i	$0.501148\pi$
$788$	−68.5236	−2.44105
$789$	−15.1935	−0.540905
$790$	−54.4681	−1.93789
$791$	−9.92948	−0.353052
$792$	4.86965	0.173036
$793$	−7.42479	−0.263662
$794$	−21.2324	−0.753508
$795$	−5.96162	−0.211437
$796$	−24.2351	−0.858990
$797$	−27.3207	−0.967750	−0.483875	−	0.875137i	$-0.660771\pi$
$797$	−27.3207	−0.967750	−0.483875	+	0.875137i	$0.660771\pi$
$798$	37.3523	1.32226
$799$	−7.81020	−0.276305
$800$	−10.7642	−0.380573
$801$	−16.0826	−0.568252
$802$	31.0337	1.09584
$803$	−10.6740	−0.376676
$804$	−13.0308	−0.459560
$805$	−56.5554	−1.99332
$806$	−45.7785	−1.61248
$807$	−11.1681	−0.393135
$808$	−27.6872	−0.974033
$809$	−23.9304	−0.841347	−0.420674	−	0.907212i	$-0.638206\pi$
$809$	−23.9304	−0.841347	−0.420674	+	0.907212i	$0.638206\pi$
$810$	−4.11926	−0.144736
$811$	7.40361	0.259976	0.129988	−	0.991516i	$-0.458506\pi$
$811$	7.40361	0.259976	0.129988	+	0.991516i	$0.458506\pi$
$812$	−52.5477	−1.84406
$813$	29.3218	1.02836
$814$	5.86761	0.205660
$815$	−14.1458	−0.495504
$816$	1.80709	0.0632609
$817$	11.8356	0.414074
$818$	20.4872	0.716317
$819$	14.6090	0.510481
$820$	−9.87720	−0.344927
$821$	−16.6659	−0.581644	−0.290822	−	0.956777i	$-0.593929\pi$
$821$	−16.6659	−0.581644	−0.290822	+	0.956777i	$0.593929\pi$
$822$	−8.18906	−0.285626
$823$	−0.0710389	−0.00247626	−0.00123813	−	0.999999i	$-0.500394\pi$
$823$	−0.0710389	−0.00247626	−0.00123813	+	0.999999i	$0.500394\pi$
$824$	24.2729	0.845587
$825$	4.11625	0.143310
$826$	−12.3354	−0.429205
$827$	15.7587	0.547984	0.273992	−	0.961732i	$-0.411656\pi$
$827$	15.7587	0.547984	0.273992	+	0.961732i	$0.411656\pi$
$828$	19.7676	0.686972
$829$	24.7596	0.859938	0.429969	−	0.902844i	$-0.358525\pi$
$829$	24.7596	0.859938	0.429969	+	0.902844i	$0.358525\pi$
$830$	−27.1618	−0.942800
$831$	−9.78287	−0.339364
$832$	43.3605	1.50326
$833$	−10.9343	−0.378853
$834$	−17.3992	−0.602485
$835$	3.85867	0.133535
$836$	−31.7785	−1.09908
$837$	−6.06536	−0.209650
$838$	−31.4693	−1.08709
$839$	−52.0084	−1.79553	−0.897764	−	0.440477i	$-0.854809\pi$
$839$	−52.0084	−1.79553	−0.897764	+	0.440477i	$0.854809\pi$
$840$	13.7267	0.473616
$841$	−9.17610	−0.316417
$842$	−67.1933	−2.31564
$843$	18.6134	0.641079
$844$	32.9515	1.13424
$845$	−2.07048	−0.0712265
$846$	−17.0879	−0.587493
$847$	12.7010	0.436410
$848$	5.72204	0.196496
$849$	1.36808	0.0469522
$850$	−3.18390	−0.109207
$851$	6.72518	0.230536
$852$	4.12125	0.141192
$853$	31.2454	1.06982	0.534910	−	0.844909i	$-0.320345\pi$
$853$	31.2454	1.06982	0.534910	+	0.844909i	$0.320345\pi$
$854$	19.9422	0.682409
$855$	7.59000	0.259573
$856$	14.8099	0.506191
$857$	−0.229233	−0.00783046	−0.00391523	−	0.999992i	$-0.501246\pi$
$857$	−0.229233	−0.00783046	−0.00391523	+	0.999992i	$0.501246\pi$
$858$	−21.3488	−0.728836
$859$	31.4090	1.07166	0.535831	−	0.844326i	$-0.319999\pi$
$859$	31.4090	1.07166	0.535831	+	0.844326i	$0.319999\pi$
$860$	15.4046	0.525294
$861$	7.97198	0.271684
$862$	36.4176	1.24039
$863$	8.20297	0.279232	0.139616	−	0.990206i	$-0.455413\pi$
$863$	8.20297	0.279232	0.139616	+	0.990206i	$0.455413\pi$
$864$	7.39690	0.251648
$865$	−44.3654	−1.50847
$866$	−32.2009	−1.09423
$867$	1.00000	0.0339618
$868$	71.5841	2.42972
$869$	−37.4017	−1.26877
$870$	−18.3406	−0.621805
$871$	16.1299	0.546542
$872$	−7.31719	−0.247791
$873$	7.74922	0.262271
$874$	−62.5621	−2.11620
$875$	51.4693	1.73998
$876$	10.5165	0.355321
$877$	23.1390	0.781349	0.390675	−	0.920529i	$-0.372242\pi$
$877$	23.1390	0.781349	0.390675	+	0.920529i	$0.372242\pi$
$878$	26.7693	0.903419
$879$	−0.159950	−0.00539498
$880$	9.62372	0.324416
$881$	−33.7002	−1.13539	−0.567694	−	0.823239i	$-0.692164\pi$
$881$	−33.7002	−1.13539	−0.567694	+	0.823239i	$0.692164\pi$
$882$	−23.9232	−0.805535
$883$	−41.1042	−1.38327	−0.691633	−	0.722249i	$-0.743108\pi$
$883$	−41.1042	−1.38327	−0.691633	+	0.722249i	$0.743108\pi$
$884$	9.61381	0.323348
$885$	−2.50657	−0.0842575
$886$	71.4076	2.39899
$887$	26.1015	0.876402	0.438201	−	0.898877i	$-0.355616\pi$
$887$	26.1015	0.876402	0.438201	+	0.898877i	$0.355616\pi$
$888$	−1.63228	−0.0547759
$889$	27.5024	0.922402
$890$	66.2487	2.22066
$891$	−2.82858	−0.0947611
$892$	−48.5410	−1.62527
$893$	31.4855	1.05362
$894$	−42.8563	−1.43333
$895$	2.11376	0.0706554
$896$	−53.8118	−1.79773
$897$	−24.4690	−0.816996
$898$	−29.3664	−0.979971
$899$	−27.0054	−0.900682
$900$	−4.05555	−0.135185
$901$	3.16643	0.105489
$902$	−11.6498	−0.387896
$903$	−12.4332	−0.413752
$904$	−4.03657	−0.134254
$905$	−39.7635	−1.32178
$906$	−13.6139	−0.452293
$907$	−39.5256	−1.31242	−0.656212	−	0.754576i	$-0.727842\pi$
$907$	−39.5256	−1.31242	−0.656212	+	0.754576i	$0.727842\pi$
$908$	60.9282	2.02197
$909$	16.0824	0.533419
$910$	−60.1785	−1.99490
$911$	23.3071	0.772199	0.386100	−	0.922457i	$-0.373822\pi$
$911$	23.3071	0.772199	0.386100	+	0.922457i	$0.373822\pi$
$912$	−7.28499	−0.241230
$913$	−18.6512	−0.617266
$914$	23.9360	0.791731
$915$	4.05227	0.133964
$916$	−66.8599	−2.20911
$917$	68.6217	2.26609
$918$	2.18789	0.0722112
$919$	−20.9166	−0.689975	−0.344988	−	0.938607i	$-0.612117\pi$
$919$	−20.9166	−0.689975	−0.344988	+	0.938607i	$0.612117\pi$
$920$	−22.9911	−0.757995
$921$	−2.25214	−0.0742105
$922$	64.8219	2.13480
$923$	−5.10141	−0.167915
$924$	33.3832	1.09823
$925$	−1.37975	−0.0453658
$926$	1.36251	0.0447747
$927$	−14.0991	−0.463077
$928$	32.9340	1.08111
$929$	−30.3691	−0.996376	−0.498188	−	0.867069i	$-0.666001\pi$
$929$	−30.3691	−0.996376	−0.498188	+	0.867069i	$0.666001\pi$
$930$	24.9848	0.819285
$931$	44.0799	1.44466
$932$	−65.1527	−2.13415
$933$	−16.9471	−0.554824
$934$	54.8588	1.79503
$935$	5.32553	0.174163
$936$	5.93893	0.194120
$937$	29.9322	0.977841	0.488920	−	0.872328i	$-0.337391\pi$
$937$	29.9322	0.977841	0.488920	+	0.872328i	$0.337391\pi$
$938$	−43.3233	−1.41456
$939$	6.77575	0.221118
$940$	40.9801	1.33662
$941$	−6.32722	−0.206262	−0.103131	−	0.994668i	$-0.532886\pi$
$941$	−6.32722	−0.206262	−0.103131	+	0.994668i	$0.532886\pi$
$942$	−2.18789	−0.0712854
$943$	−13.3524	−0.434815
$944$	2.40584	0.0783035
$945$	−7.97327	−0.259370
$946$	18.1692	0.590732
$947$	−54.3355	−1.76567	−0.882833	−	0.469686i	$-0.844367\pi$
$947$	−54.3355	−1.76567	−0.882833	+	0.469686i	$0.844367\pi$
$948$	36.8502	1.19684
$949$	−13.0177	−0.422573
$950$	12.8353	0.416433
$951$	0.868483	0.0281625
$952$	−7.29075	−0.236294
$953$	−30.2246	−0.979072	−0.489536	−	0.871983i	$-0.662834\pi$
$953$	−30.2246	−0.979072	−0.489536	+	0.871983i	$0.662834\pi$
$954$	6.92782	0.224296
$955$	−42.1948	−1.36539
$956$	−58.4892	−1.89168
$957$	−12.5940	−0.407106
$958$	−91.4534	−2.95472
$959$	−15.8508	−0.511849
$960$	−23.6652	−0.763790
$961$	5.78862	0.186730
$962$	7.15601	0.230719
$963$	−8.60245	−0.277210
$964$	33.2153	1.06979
$965$	−8.51041	−0.273960
$966$	65.7213	2.11455
$967$	31.8242	1.02340	0.511699	−	0.859165i	$-0.329016\pi$
$967$	31.8242	1.02340	0.511699	+	0.859165i	$0.329016\pi$
$968$	5.16325	0.165953
$969$	−4.03133	−0.129505
$970$	−31.9211	−1.02492
$971$	−22.4909	−0.721769	−0.360884	−	0.932611i	$-0.617525\pi$
$971$	−22.4909	−0.721769	−0.360884	+	0.932611i	$0.617525\pi$
$972$	2.78687	0.0893889
$973$	−33.6780	−1.07967
$974$	−38.0674	−1.21976
$975$	5.02010	0.160772
$976$	−3.88943	−0.124498
$977$	−39.7919	−1.27306	−0.636528	−	0.771254i	$-0.719630\pi$
$977$	−39.7919	−1.27306	−0.636528	+	0.771254i	$0.719630\pi$
$978$	16.4383	0.525640
$979$	45.4911	1.45390
$980$	57.3724	1.83269
$981$	4.25026	0.135700
$982$	−61.6524	−1.96741
$983$	38.3590	1.22346	0.611730	−	0.791066i	$-0.290474\pi$
$983$	38.3590	1.22346	0.611730	+	0.791066i	$0.290474\pi$
$984$	3.24080	0.103313
$985$	−46.2932	−1.47502
$986$	9.74138	0.310229
$987$	−33.0754	−1.05280
$988$	−38.7564	−1.23301
$989$	20.8247	0.662187
$990$	11.6517	0.370315
$991$	−48.6123	−1.54422	−0.772111	−	0.635488i	$-0.780799\pi$
$991$	−48.6123	−1.54422	−0.772111	+	0.635488i	$0.780799\pi$
$992$	−44.8649	−1.42446
$993$	4.68586	0.148701
$994$	13.7019	0.434597
$995$	−16.3727	−0.519051
$996$	18.3762	0.582272
$997$	34.2859	1.08585	0.542923	−	0.839783i	$-0.317318\pi$
$997$	34.2859	1.08585	0.542923	+	0.839783i	$0.317318\pi$
$998$	−40.2006	−1.27253
$999$	0.948127	0.0299974

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.7	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.7	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18789 q^{2} +1.00000 q^{3} +2.78687 q^{4} +1.88275 q^{5} -2.18789 q^{6} -4.23490 q^{7} -1.72159 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18789 q^{2} +1.00000 q^{3} +2.78687 q^{4} +1.88275 q^{5} -2.18789 q^{6} -4.23490 q^{7} -1.72159 q^{8} +1.00000 q^{9} -4.11926 q^{10} -2.82858 q^{11} +2.78687 q^{12} -3.44968 q^{13} +9.26549 q^{14} +1.88275 q^{15} -1.80709 q^{16} -1.00000 q^{17} -2.18789 q^{18} +4.03133 q^{19} +5.24699 q^{20} -4.23490 q^{21} +6.18863 q^{22} +7.09312 q^{23} -1.72159 q^{24} -1.45524 q^{25} +7.54753 q^{26} +1.00000 q^{27} -11.8021 q^{28} +4.45240 q^{29} -4.11926 q^{30} -6.06536 q^{31} +7.39690 q^{32} -2.82858 q^{33} +2.18789 q^{34} -7.97327 q^{35} +2.78687 q^{36} +0.948127 q^{37} -8.82011 q^{38} -3.44968 q^{39} -3.24133 q^{40} -1.88245 q^{41} +9.26549 q^{42} +2.93590 q^{43} -7.88289 q^{44} +1.88275 q^{45} -15.5190 q^{46} +7.81020 q^{47} -1.80709 q^{48} +10.9343 q^{49} +3.18390 q^{50} -1.00000 q^{51} -9.61381 q^{52} -3.16643 q^{53} -2.18789 q^{54} -5.32553 q^{55} +7.29075 q^{56} +4.03133 q^{57} -9.74138 q^{58} -1.33133 q^{59} +5.24699 q^{60} +2.15231 q^{61} +13.2704 q^{62} -4.23490 q^{63} -12.5694 q^{64} -6.49490 q^{65} +6.18863 q^{66} -4.67577 q^{67} -2.78687 q^{68} +7.09312 q^{69} +17.4447 q^{70} +1.47881 q^{71} -1.72159 q^{72} +3.77361 q^{73} -2.07440 q^{74} -1.45524 q^{75} +11.2348 q^{76} +11.9788 q^{77} +7.54753 q^{78} +13.2228 q^{79} -3.40231 q^{80} +1.00000 q^{81} +4.11860 q^{82} +6.59385 q^{83} -11.8021 q^{84} -1.88275 q^{85} -6.42343 q^{86} +4.45240 q^{87} +4.86965 q^{88} -16.0826 q^{89} -4.11926 q^{90} +14.6090 q^{91} +19.7676 q^{92} -6.06536 q^{93} -17.0879 q^{94} +7.59000 q^{95} +7.39690 q^{96} +7.74922 q^{97} -23.9232 q^{98} -2.82858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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