LMFDB - Embedded newform 4015.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.11520 q^{2} +0.824774 q^{3} +2.47406 q^{4} -1.00000 q^{5} -1.74456 q^{6} +0.827865 q^{7} -1.00272 q^{8} -2.31975 q^{9} +O(q^{10})$	\(q-2.11520 q^{2} +0.824774 q^{3} +2.47406 q^{4} -1.00000 q^{5} -1.74456 q^{6} +0.827865 q^{7} -1.00272 q^{8} -2.31975 q^{9} +2.11520 q^{10} +1.00000 q^{11} +2.04054 q^{12} +6.12707 q^{13} -1.75110 q^{14} -0.824774 q^{15} -2.82716 q^{16} +2.24003 q^{17} +4.90672 q^{18} -1.94946 q^{19} -2.47406 q^{20} +0.682802 q^{21} -2.11520 q^{22} -4.61905 q^{23} -0.827018 q^{24} +1.00000 q^{25} -12.9599 q^{26} -4.38759 q^{27} +2.04818 q^{28} +1.17583 q^{29} +1.74456 q^{30} -7.54708 q^{31} +7.98544 q^{32} +0.824774 q^{33} -4.73809 q^{34} -0.827865 q^{35} -5.73918 q^{36} +2.15280 q^{37} +4.12349 q^{38} +5.05345 q^{39} +1.00272 q^{40} -5.98039 q^{41} -1.44426 q^{42} -6.75944 q^{43} +2.47406 q^{44} +2.31975 q^{45} +9.77020 q^{46} +0.151070 q^{47} -2.33177 q^{48} -6.31464 q^{49} -2.11520 q^{50} +1.84752 q^{51} +15.1587 q^{52} -10.7003 q^{53} +9.28062 q^{54} -1.00000 q^{55} -0.830117 q^{56} -1.60787 q^{57} -2.48712 q^{58} +4.22161 q^{59} -2.04054 q^{60} +3.88540 q^{61} +15.9636 q^{62} -1.92044 q^{63} -11.2365 q^{64} -6.12707 q^{65} -1.74456 q^{66} +8.84825 q^{67} +5.54195 q^{68} -3.80967 q^{69} +1.75110 q^{70} +9.01270 q^{71} +2.32606 q^{72} +1.00000 q^{73} -4.55360 q^{74} +0.824774 q^{75} -4.82308 q^{76} +0.827865 q^{77} -10.6890 q^{78} +8.75713 q^{79} +2.82716 q^{80} +3.34047 q^{81} +12.6497 q^{82} -0.0896414 q^{83} +1.68929 q^{84} -2.24003 q^{85} +14.2976 q^{86} +0.969798 q^{87} -1.00272 q^{88} -15.0105 q^{89} -4.90672 q^{90} +5.07238 q^{91} -11.4278 q^{92} -6.22464 q^{93} -0.319543 q^{94} +1.94946 q^{95} +6.58618 q^{96} +15.6292 q^{97} +13.3567 q^{98} -2.31975 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * 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 $

$2$	−2.11520	−1.49567	−0.747835	−	0.663885i	$-0.768907\pi$
$2$	−2.11520	−1.49567	−0.747835	+	0.663885i	$0.768907\pi$
$3$	0.824774	0.476184	0.238092	−	0.971243i	$-0.423478\pi$
$3$	0.824774	0.476184	0.238092	+	0.971243i	$0.423478\pi$
$4$	2.47406	1.23703
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.74456	−0.712213
$7$	0.827865	0.312903	0.156452	−	0.987686i	$-0.449994\pi$
$7$	0.827865	0.312903	0.156452	+	0.987686i	$0.449994\pi$
$8$	−1.00272	−0.354515
$9$	−2.31975	−0.773249
$10$	2.11520	0.668884
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.04054	0.589052
$13$	6.12707	1.69934	0.849671	−	0.527313i	$-0.176800\pi$
$13$	6.12707	1.69934	0.849671	+	0.527313i	$0.176800\pi$
$14$	−1.75110	−0.468000
$15$	−0.824774	−0.212956
$16$	−2.82716	−0.706790
$17$	2.24003	0.543286	0.271643	−	0.962398i	$-0.412433\pi$
$17$	2.24003	0.543286	0.271643	+	0.962398i	$0.412433\pi$
$18$	4.90672	1.15653
$19$	−1.94946	−0.447237	−0.223619	−	0.974677i	$-0.571787\pi$
$19$	−1.94946	−0.447237	−0.223619	+	0.974677i	$0.571787\pi$
$20$	−2.47406	−0.553216
$21$	0.682802	0.149000
$22$	−2.11520	−0.450961
$23$	−4.61905	−0.963139	−0.481569	−	0.876408i	$-0.659933\pi$
$23$	−4.61905	−0.963139	−0.481569	+	0.876408i	$0.659933\pi$
$24$	−0.827018	−0.168814
$25$	1.00000	0.200000
$26$	−12.9599	−2.54166
$27$	−4.38759	−0.844392
$28$	2.04818	0.387070
$29$	1.17583	0.218347	0.109173	−	0.994023i	$-0.465180\pi$
$29$	1.17583	0.218347	0.109173	+	0.994023i	$0.465180\pi$
$30$	1.74456	0.318511
$31$	−7.54708	−1.35550	−0.677748	−	0.735295i	$-0.737044\pi$
$31$	−7.54708	−1.35550	−0.677748	+	0.735295i	$0.737044\pi$
$32$	7.98544	1.41164
$33$	0.824774	0.143575
$34$	−4.73809	−0.812576
$35$	−0.827865	−0.139935
$36$	−5.73918	−0.956531
$37$	2.15280	0.353918	0.176959	−	0.984218i	$-0.443374\pi$
$37$	2.15280	0.353918	0.176959	+	0.984218i	$0.443374\pi$
$38$	4.12349	0.668919
$39$	5.05345	0.809199
$40$	1.00272	0.158544
$41$	−5.98039	−0.933980	−0.466990	−	0.884263i	$-0.654662\pi$
$41$	−5.98039	−0.933980	−0.466990	+	0.884263i	$0.654662\pi$
$42$	−1.44426	−0.222854
$43$	−6.75944	−1.03081	−0.515403	−	0.856948i	$-0.672358\pi$
$43$	−6.75944	−1.03081	−0.515403	+	0.856948i	$0.672358\pi$
$44$	2.47406	0.372978
$45$	2.31975	0.345808
$46$	9.77020	1.44054
$47$	0.151070	0.0220358	0.0110179	−	0.999939i	$-0.496493\pi$
$47$	0.151070	0.0220358	0.0110179	+	0.999939i	$0.496493\pi$
$48$	−2.33177	−0.336562
$49$	−6.31464	−0.902091
$50$	−2.11520	−0.299134
$51$	1.84752	0.258704
$52$	15.1587	2.10213
$53$	−10.7003	−1.46980	−0.734898	−	0.678177i	$-0.762770\pi$
$53$	−10.7003	−1.46980	−0.734898	+	0.678177i	$0.762770\pi$
$54$	9.28062	1.26293
$55$	−1.00000	−0.134840
$56$	−0.830117	−0.110929
$57$	−1.60787	−0.212967
$58$	−2.48712	−0.326575
$59$	4.22161	0.549607	0.274804	−	0.961500i	$-0.411387\pi$
$59$	4.22161	0.549607	0.274804	+	0.961500i	$0.411387\pi$
$60$	−2.04054	−0.263432
$61$	3.88540	0.497474	0.248737	−	0.968571i	$-0.419984\pi$
$61$	3.88540	0.497474	0.248737	+	0.968571i	$0.419984\pi$
$62$	15.9636	2.02737
$63$	−1.92044	−0.241952
$64$	−11.2365	−1.40456
$65$	−6.12707	−0.759969
$66$	−1.74456	−0.214740
$67$	8.84825	1.08099	0.540493	−	0.841349i	$-0.318238\pi$
$67$	8.84825	1.08099	0.540493	+	0.841349i	$0.318238\pi$
$68$	5.54195	0.672060
$69$	−3.80967	−0.458631
$70$	1.75110	0.209296
$71$	9.01270	1.06961	0.534805	−	0.844975i	$-0.320385\pi$
$71$	9.01270	1.06961	0.534805	+	0.844975i	$0.320385\pi$
$72$	2.32606	0.274129
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−4.55360	−0.529345
$75$	0.824774	0.0952367
$76$	−4.82308	−0.553245
$77$	0.827865	0.0943440
$78$	−10.6890	−1.21029
$79$	8.75713	0.985254	0.492627	−	0.870240i	$-0.336037\pi$
$79$	8.75713	0.985254	0.492627	+	0.870240i	$0.336037\pi$
$80$	2.82716	0.316086
$81$	3.34047	0.371164
$82$	12.6497	1.39693
$83$	−0.0896414	−0.00983942	−0.00491971	−	0.999988i	$-0.501566\pi$
$83$	−0.0896414	−0.00983942	−0.00491971	+	0.999988i	$0.501566\pi$
$84$	1.68929	0.184317
$85$	−2.24003	−0.242965
$86$	14.2976	1.54174
$87$	0.969798	0.103973
$88$	−1.00272	−0.106890
$89$	−15.0105	−1.59111	−0.795556	−	0.605880i	$-0.792821\pi$
$89$	−15.0105	−1.59111	−0.795556	+	0.605880i	$0.792821\pi$
$90$	−4.90672	−0.517214
$91$	5.07238	0.531730
$92$	−11.4278	−1.19143
$93$	−6.22464	−0.645465
$94$	−0.319543	−0.0329583
$95$	1.94946	0.200011
$96$	6.58618	0.672200
$97$	15.6292	1.58690	0.793452	−	0.608633i	$-0.208282\pi$
$97$	15.6292	1.58690	0.793452	+	0.608633i	$0.208282\pi$
$98$	13.3567	1.34923
$99$	−2.31975	−0.233143
$100$	2.47406	0.247406
$101$	−16.1945	−1.61141	−0.805705	−	0.592317i	$-0.798213\pi$
$101$	−16.1945	−1.61141	−0.805705	+	0.592317i	$0.798213\pi$
$102$	−3.90786	−0.386936
$103$	−8.60944	−0.848314	−0.424157	−	0.905589i	$-0.639429\pi$
$103$	−8.60944	−0.848314	−0.424157	+	0.905589i	$0.639429\pi$
$104$	−6.14374	−0.602443
$105$	−0.682802	−0.0666346
$106$	22.6332	2.19833
$107$	−11.8020	−1.14094	−0.570469	−	0.821319i	$-0.693238\pi$
$107$	−11.8020	−1.14094	−0.570469	+	0.821319i	$0.693238\pi$
$108$	−10.8551	−1.04454
$109$	13.1159	1.25627	0.628136	−	0.778104i	$-0.283818\pi$
$109$	13.1159	1.25627	0.628136	+	0.778104i	$0.283818\pi$
$110$	2.11520	0.201676
$111$	1.77558	0.168530
$112$	−2.34051	−0.221157
$113$	0.612633	0.0576317	0.0288158	−	0.999585i	$-0.490826\pi$
$113$	0.612633	0.0576317	0.0288158	+	0.999585i	$0.490826\pi$
$114$	3.40095	0.318528
$115$	4.61905	0.430729
$116$	2.90908	0.270101
$117$	−14.2132	−1.31402
$118$	−8.92954	−0.822031
$119$	1.85444	0.169996
$120$	0.827018	0.0754961
$121$	1.00000	0.0909091
$122$	−8.21838	−0.744057
$123$	−4.93247	−0.444746
$124$	−18.6719	−1.67679
$125$	−1.00000	−0.0894427
$126$	4.06210	0.361881
$127$	−4.88916	−0.433843	−0.216921	−	0.976189i	$-0.569602\pi$
$127$	−4.88916	−0.433843	−0.216921	+	0.976189i	$0.569602\pi$
$128$	7.79643	0.689113
$129$	−5.57502	−0.490853
$130$	12.9599	1.13666
$131$	−13.3123	−1.16310	−0.581549	−	0.813511i	$-0.697553\pi$
$131$	−13.3123	−1.16310	−0.581549	+	0.813511i	$0.697553\pi$
$132$	2.04054	0.177606
$133$	−1.61389	−0.139942
$134$	−18.7158	−1.61680
$135$	4.38759	0.377624
$136$	−2.24612	−0.192603
$137$	−14.1345	−1.20759	−0.603796	−	0.797139i	$-0.706346\pi$
$137$	−14.1345	−1.20759	−0.603796	+	0.797139i	$0.706346\pi$
$138$	8.05821	0.685960
$139$	18.3988	1.56057	0.780284	−	0.625425i	$-0.215074\pi$
$139$	18.3988	1.56057	0.780284	+	0.625425i	$0.215074\pi$
$140$	−2.04818	−0.173103
$141$	0.124599	0.0104931
$142$	−19.0636	−1.59978
$143$	6.12707	0.512371
$144$	6.55830	0.546525
$145$	−1.17583	−0.0976477
$146$	−2.11520	−0.175055
$147$	−5.20815	−0.429561
$148$	5.32615	0.437807
$149$	−4.23845	−0.347227	−0.173614	−	0.984814i	$-0.555544\pi$
$149$	−4.23845	−0.347227	−0.173614	+	0.984814i	$0.555544\pi$
$150$	−1.74456	−0.142443
$151$	−5.08106	−0.413491	−0.206745	−	0.978395i	$-0.566287\pi$
$151$	−5.08106	−0.413491	−0.206745	+	0.978395i	$0.566287\pi$
$152$	1.95477	0.158552
$153$	−5.19629	−0.420095
$154$	−1.75110	−0.141107
$155$	7.54708	0.606196
$156$	12.5025	1.00100
$157$	0.401127	0.0320134	0.0160067	−	0.999872i	$-0.494905\pi$
$157$	0.401127	0.0320134	0.0160067	+	0.999872i	$0.494905\pi$
$158$	−18.5231	−1.47362
$159$	−8.82532	−0.699893
$160$	−7.98544	−0.631304
$161$	−3.82395	−0.301369
$162$	−7.06575	−0.555138
$163$	−8.12504	−0.636402	−0.318201	−	0.948023i	$-0.603079\pi$
$163$	−8.12504	−0.636402	−0.318201	+	0.948023i	$0.603079\pi$
$164$	−14.7958	−1.15536
$165$	−0.824774	−0.0642086
$166$	0.189609	0.0147165
$167$	6.95319	0.538054	0.269027	−	0.963133i	$-0.413298\pi$
$167$	6.95319	0.538054	0.269027	+	0.963133i	$0.413298\pi$
$168$	−0.684659	−0.0528226
$169$	24.5409	1.88777
$170$	4.73809	0.363395
$171$	4.52226	0.345826
$172$	−16.7232	−1.27514
$173$	−24.3172	−1.84880	−0.924401	−	0.381421i	$-0.875435\pi$
$173$	−24.3172	−1.84880	−0.924401	+	0.381421i	$0.875435\pi$
$174$	−2.05131	−0.155510
$175$	0.827865	0.0625807
$176$	−2.82716	−0.213105
$177$	3.48188	0.261714
$178$	31.7502	2.37978
$179$	9.69553	0.724678	0.362339	−	0.932046i	$-0.381978\pi$
$179$	9.69553	0.724678	0.362339	+	0.932046i	$0.381978\pi$
$180$	5.73918	0.427774
$181$	−15.8353	−1.17703	−0.588515	−	0.808487i	$-0.700287\pi$
$181$	−15.8353	−1.17703	−0.588515	+	0.808487i	$0.700287\pi$
$182$	−10.7291	−0.795293
$183$	3.20458	0.236889
$184$	4.63162	0.341447
$185$	−2.15280	−0.158277
$186$	13.1663	0.965402
$187$	2.24003	0.163807
$188$	0.373756	0.0272589
$189$	−3.63233	−0.264213
$190$	−4.12349	−0.299150
$191$	−6.10008	−0.441386	−0.220693	−	0.975343i	$-0.570832\pi$
$191$	−6.10008	−0.441386	−0.220693	+	0.975343i	$0.570832\pi$
$192$	−9.26754	−0.668827
$193$	4.08667	0.294165	0.147082	−	0.989124i	$-0.453012\pi$
$193$	4.08667	0.294165	0.147082	+	0.989124i	$0.453012\pi$
$194$	−33.0588	−2.37348
$195$	−5.05345	−0.361885
$196$	−15.6228	−1.11591
$197$	−5.86681	−0.417993	−0.208996	−	0.977916i	$-0.567020\pi$
$197$	−5.86681	−0.417993	−0.208996	+	0.977916i	$0.567020\pi$
$198$	4.90672	0.348706
$199$	16.6657	1.18140	0.590701	−	0.806891i	$-0.298851\pi$
$199$	16.6657	1.18140	0.590701	+	0.806891i	$0.298851\pi$
$200$	−1.00272	−0.0709031
$201$	7.29781	0.514748
$202$	34.2545	2.41014
$203$	0.973432	0.0683215
$204$	4.57086	0.320024
$205$	5.98039	0.417689
$206$	18.2107	1.26880
$207$	10.7150	0.744746
$208$	−17.3222	−1.20108
$209$	−1.94946	−0.134847
$210$	1.44426	0.0996634
$211$	2.50375	0.172365	0.0861826	−	0.996279i	$-0.472533\pi$
$211$	2.50375	0.172365	0.0861826	+	0.996279i	$0.472533\pi$
$212$	−26.4731	−1.81818
$213$	7.43344	0.509331
$214$	24.9634	1.70647
$215$	6.75944	0.460990
$216$	4.39953	0.299350
$217$	−6.24796	−0.424139
$218$	−27.7426	−1.87897
$219$	0.824774	0.0557331
$220$	−2.47406	−0.166801
$221$	13.7248	0.923229
$222$	−3.75569	−0.252065
$223$	−22.6474	−1.51658	−0.758289	−	0.651918i	$-0.773965\pi$
$223$	−22.6474	−1.51658	−0.758289	+	0.651918i	$0.773965\pi$
$224$	6.61086	0.441707
$225$	−2.31975	−0.154650
$226$	−1.29584	−0.0861979
$227$	16.7119	1.10921	0.554603	−	0.832115i	$-0.312870\pi$
$227$	16.7119	1.10921	0.554603	+	0.832115i	$0.312870\pi$
$228$	−3.97795	−0.263446
$229$	−7.76788	−0.513316	−0.256658	−	0.966502i	$-0.582621\pi$
$229$	−7.76788	−0.513316	−0.256658	+	0.966502i	$0.582621\pi$
$230$	−9.77020	−0.644228
$231$	0.682802	0.0449250
$232$	−1.17903	−0.0774073
$233$	−28.6401	−1.87627	−0.938137	−	0.346266i	$-0.887450\pi$
$233$	−28.6401	−1.87627	−0.938137	+	0.346266i	$0.887450\pi$
$234$	30.0638	1.96533
$235$	−0.151070	−0.00985472
$236$	10.4445	0.679879
$237$	7.22266	0.469162
$238$	−3.92250	−0.254258
$239$	5.65644	0.365885	0.182942	−	0.983124i	$-0.441438\pi$
$239$	5.65644	0.365885	0.182942	+	0.983124i	$0.441438\pi$
$240$	2.33177	0.150515
$241$	−1.17445	−0.0756531	−0.0378266	−	0.999284i	$-0.512043\pi$
$241$	−1.17445	−0.0756531	−0.0378266	+	0.999284i	$0.512043\pi$
$242$	−2.11520	−0.135970
$243$	15.9179	1.02113
$244$	9.61269	0.615390
$245$	6.31464	0.403428
$246$	10.4331	0.665193
$247$	−11.9445	−0.760009
$248$	7.56761	0.480544
$249$	−0.0739339	−0.00468537
$250$	2.11520	0.133777
$251$	20.2478	1.27803	0.639016	−	0.769194i	$-0.279342\pi$
$251$	20.2478	1.27803	0.639016	+	0.769194i	$0.279342\pi$
$252$	−4.75127	−0.299302
$253$	−4.61905	−0.290397
$254$	10.3415	0.648886
$255$	−1.84752	−0.115696
$256$	5.98194	0.373871
$257$	−0.371738	−0.0231884	−0.0115942	−	0.999933i	$-0.503691\pi$
$257$	−0.371738	−0.0231884	−0.0115942	+	0.999933i	$0.503691\pi$
$258$	11.7923	0.734154
$259$	1.78223	0.110742
$260$	−15.1587	−0.940103
$261$	−2.72764	−0.168837
$262$	28.1581	1.73961
$263$	−4.68370	−0.288810	−0.144405	−	0.989519i	$-0.546127\pi$
$263$	−4.68370	−0.288810	−0.144405	+	0.989519i	$0.546127\pi$
$264$	−0.827018	−0.0508995
$265$	10.7003	0.657313
$266$	3.41370	0.209307
$267$	−12.3803	−0.757661
$268$	21.8911	1.33721
$269$	−9.45147	−0.576266	−0.288133	−	0.957590i	$-0.593035\pi$
$269$	−9.45147	−0.576266	−0.288133	+	0.957590i	$0.593035\pi$
$270$	−9.28062	−0.564800
$271$	−12.7498	−0.774493	−0.387246	−	0.921976i	$-0.626574\pi$
$271$	−12.7498	−0.774493	−0.387246	+	0.921976i	$0.626574\pi$
$272$	−6.33291	−0.383989
$273$	4.18357	0.253201
$274$	29.8972	1.80616
$275$	1.00000	0.0603023
$276$	−9.42534	−0.567339
$277$	5.66400	0.340317	0.170159	−	0.985417i	$-0.445572\pi$
$277$	5.66400	0.340317	0.170159	+	0.985417i	$0.445572\pi$
$278$	−38.9171	−2.33410
$279$	17.5073	1.04814
$280$	0.830117	0.0496090
$281$	0.0361771	0.00215815	0.00107907	−	0.999999i	$-0.499657\pi$
$281$	0.0361771	0.00215815	0.00107907	+	0.999999i	$0.499657\pi$
$282$	−0.263551	−0.0156942
$283$	−24.8316	−1.47608	−0.738042	−	0.674755i	$-0.764249\pi$
$283$	−24.8316	−1.47608	−0.738042	+	0.674755i	$0.764249\pi$
$284$	22.2979	1.32314
$285$	1.60787	0.0952417
$286$	−12.9599	−0.766338
$287$	−4.95096	−0.292246
$288$	−18.5242	−1.09155
$289$	−11.9823	−0.704840
$290$	2.48712	0.146049
$291$	12.8906	0.755658
$292$	2.47406	0.144783
$293$	−3.94204	−0.230297	−0.115148	−	0.993348i	$-0.536734\pi$
$293$	−3.94204	−0.230297	−0.115148	+	0.993348i	$0.536734\pi$
$294$	11.0163	0.642482
$295$	−4.22161	−0.245792
$296$	−2.15866	−0.125469
$297$	−4.38759	−0.254594
$298$	8.96515	0.519337
$299$	−28.3012	−1.63670
$300$	2.04054	0.117810
$301$	−5.59591	−0.322543
$302$	10.7474	0.618445
$303$	−13.3568	−0.767327
$304$	5.51144	0.316103
$305$	−3.88540	−0.222477
$306$	10.9912	0.628324
$307$	8.69983	0.496526	0.248263	−	0.968693i	$-0.420140\pi$
$307$	8.69983	0.496526	0.248263	+	0.968693i	$0.420140\pi$
$308$	2.04818	0.116706
$309$	−7.10085	−0.403953
$310$	−15.9636	−0.906669
$311$	18.4221	1.04462	0.522311	−	0.852755i	$-0.325070\pi$
$311$	18.4221	1.04462	0.522311	+	0.852755i	$0.325070\pi$
$312$	−5.06720	−0.286873
$313$	14.4041	0.814168	0.407084	−	0.913391i	$-0.366546\pi$
$313$	14.4041	0.814168	0.407084	+	0.913391i	$0.366546\pi$
$314$	−0.848461	−0.0478814
$315$	1.92044	0.108204
$316$	21.6656	1.21879
$317$	−1.64194	−0.0922203	−0.0461101	−	0.998936i	$-0.514683\pi$
$317$	−1.64194	−0.0922203	−0.0461101	+	0.998936i	$0.514683\pi$
$318$	18.6673	1.04681
$319$	1.17583	0.0658341
$320$	11.2365	0.628137
$321$	−9.73394	−0.543296
$322$	8.08840	0.450749
$323$	−4.36684	−0.242978
$324$	8.26451	0.459140
$325$	6.12707	0.339869
$326$	17.1861	0.951847
$327$	10.8176	0.598216
$328$	5.99666	0.331110
$329$	0.125066	0.00689509
$330$	1.74456	0.0960348
$331$	−2.62836	−0.144468	−0.0722340	−	0.997388i	$-0.523013\pi$
$331$	−2.62836	−0.144468	−0.0722340	+	0.997388i	$0.523013\pi$
$332$	−0.221778	−0.0121716
$333$	−4.99396	−0.273667
$334$	−14.7074	−0.804751
$335$	−8.84825	−0.483431
$336$	−1.93039	−0.105311
$337$	4.00470	0.218150	0.109075	−	0.994034i	$-0.465211\pi$
$337$	4.00470	0.218150	0.109075	+	0.994034i	$0.465211\pi$
$338$	−51.9089	−2.82347
$339$	0.505284	0.0274433
$340$	−5.54195	−0.300554
$341$	−7.54708	−0.408697
$342$	−9.56547	−0.517241
$343$	−11.0227	−0.595171
$344$	6.77784	0.365436
$345$	3.80967	0.205106
$346$	51.4357	2.76520
$347$	−25.0253	−1.34343	−0.671715	−	0.740810i	$-0.734442\pi$
$347$	−25.0253	−1.34343	−0.671715	+	0.740810i	$0.734442\pi$
$348$	2.39933	0.128618
$349$	−35.4360	−1.89685	−0.948424	−	0.317004i	$-0.897323\pi$
$349$	−35.4360	−1.89685	−0.948424	+	0.317004i	$0.897323\pi$
$350$	−1.75110	−0.0936001
$351$	−26.8831	−1.43491
$352$	7.98544	0.425625
$353$	−18.8403	−1.00277	−0.501385	−	0.865224i	$-0.667176\pi$
$353$	−18.8403	−1.00277	−0.501385	+	0.865224i	$0.667176\pi$
$354$	−7.36485	−0.391437
$355$	−9.01270	−0.478344
$356$	−37.1369	−1.96825
$357$	1.52949	0.0809493
$358$	−20.5079	−1.08388
$359$	27.9176	1.47343	0.736716	−	0.676202i	$-0.236375\pi$
$359$	27.9176	1.47343	0.736716	+	0.676202i	$0.236375\pi$
$360$	−2.32606	−0.122594
$361$	−15.1996	−0.799979
$362$	33.4948	1.76045
$363$	0.824774	0.0432894
$364$	12.5494	0.657765
$365$	−1.00000	−0.0523424
$366$	−6.77831	−0.354308
$367$	−14.6189	−0.763100	−0.381550	−	0.924348i	$-0.624610\pi$
$367$	−14.6189	−0.763100	−0.381550	+	0.924348i	$0.624610\pi$
$368$	13.0588	0.680737
$369$	13.8730	0.722199
$370$	4.55360	0.236730
$371$	−8.85839	−0.459905
$372$	−15.4001	−0.798458
$373$	7.39667	0.382985	0.191493	−	0.981494i	$-0.438667\pi$
$373$	7.39667	0.382985	0.191493	+	0.981494i	$0.438667\pi$
$374$	−4.73809	−0.245001
$375$	−0.824774	−0.0425912
$376$	−0.151481	−0.00781204
$377$	7.20441	0.371046
$378$	7.68309	0.395176
$379$	−5.83226	−0.299583	−0.149792	−	0.988718i	$-0.547860\pi$
$379$	−5.83226	−0.299583	−0.149792	+	0.988718i	$0.547860\pi$
$380$	4.82308	0.247419
$381$	−4.03245	−0.206589
$382$	12.9029	0.660168
$383$	−17.6802	−0.903418	−0.451709	−	0.892165i	$-0.649186\pi$
$383$	−17.6802	−0.903418	−0.451709	+	0.892165i	$0.649186\pi$
$384$	6.43029	0.328144
$385$	−0.827865	−0.0421919
$386$	−8.64411	−0.439974
$387$	15.6802	0.797070
$388$	38.6675	1.96304
$389$	6.51062	0.330101	0.165051	−	0.986285i	$-0.447221\pi$
$389$	6.51062	0.330101	0.165051	+	0.986285i	$0.447221\pi$
$390$	10.6890	0.541260
$391$	−10.3468	−0.523260
$392$	6.33182	0.319805
$393$	−10.9796	−0.553848
$394$	12.4094	0.625179
$395$	−8.75713	−0.440619
$396$	−5.73918	−0.288405
$397$	1.69173	0.0849056	0.0424528	−	0.999098i	$-0.486483\pi$
$397$	1.69173	0.0849056	0.0424528	+	0.999098i	$0.486483\pi$
$398$	−35.2513	−1.76699
$399$	−1.33110	−0.0666381
$400$	−2.82716	−0.141358
$401$	18.8440	0.941023	0.470511	−	0.882394i	$-0.344069\pi$
$401$	18.8440	0.941023	0.470511	+	0.882394i	$0.344069\pi$
$402$	−15.4363	−0.769892
$403$	−46.2415	−2.30345
$404$	−40.0660	−1.99336
$405$	−3.34047	−0.165989
$406$	−2.05900	−0.102186
$407$	2.15280	0.106710
$408$	−1.85254	−0.0917145
$409$	−4.28795	−0.212025	−0.106013	−	0.994365i	$-0.533808\pi$
$409$	−4.28795	−0.212025	−0.106013	+	0.994365i	$0.533808\pi$
$410$	−12.6497	−0.624724
$411$	−11.6578	−0.575035
$412$	−21.3002	−1.04939
$413$	3.49492	0.171974
$414$	−22.6644	−1.11389
$415$	0.0896414	0.00440032
$416$	48.9273	2.39886
$417$	15.1749	0.743117
$418$	4.12349	0.201687
$419$	−4.03059	−0.196907	−0.0984536	−	0.995142i	$-0.531390\pi$
$419$	−4.03059	−0.196907	−0.0984536	+	0.995142i	$0.531390\pi$
$420$	−1.68929	−0.0824289
$421$	−33.1294	−1.61463	−0.807315	−	0.590121i	$-0.799080\pi$
$421$	−33.1294	−1.61463	−0.807315	+	0.590121i	$0.799080\pi$
$422$	−5.29592	−0.257802
$423$	−0.350444	−0.0170392
$424$	10.7294	0.521066
$425$	2.24003	0.108657
$426$	−15.7232	−0.761791
$427$	3.21659	0.155661
$428$	−29.1987	−1.41137
$429$	5.05345	0.243983
$430$	−14.2976	−0.689489
$431$	−19.0881	−0.919440	−0.459720	−	0.888064i	$-0.652050\pi$
$431$	−19.0881	−0.919440	−0.459720	+	0.888064i	$0.652050\pi$
$432$	12.4044	0.596808
$433$	25.5852	1.22955	0.614774	−	0.788703i	$-0.289247\pi$
$433$	25.5852	1.22955	0.614774	+	0.788703i	$0.289247\pi$
$434$	13.2157	0.634372
$435$	−0.969798	−0.0464982
$436$	32.4494	1.55404
$437$	9.00466	0.430751
$438$	−1.74456	−0.0833583
$439$	10.7910	0.515026	0.257513	−	0.966275i	$-0.417097\pi$
$439$	10.7910	0.515026	0.257513	+	0.966275i	$0.417097\pi$
$440$	1.00272	0.0478028
$441$	14.6484	0.697541
$442$	−29.0306	−1.38085
$443$	−3.42386	−0.162673	−0.0813363	−	0.996687i	$-0.525919\pi$
$443$	−3.42386	−0.162673	−0.0813363	+	0.996687i	$0.525919\pi$
$444$	4.39287	0.208476
$445$	15.0105	0.711567
$446$	47.9036	2.26830
$447$	−3.49576	−0.165344
$448$	−9.30226	−0.439491
$449$	4.68094	0.220907	0.110454	−	0.993881i	$-0.464770\pi$
$449$	4.68094	0.220907	0.110454	+	0.993881i	$0.464770\pi$
$450$	4.90672	0.231305
$451$	−5.98039	−0.281606
$452$	1.51569	0.0712920
$453$	−4.19073	−0.196897
$454$	−35.3489	−1.65901
$455$	−5.07238	−0.237797
$456$	1.61224	0.0755001
$457$	6.87059	0.321392	0.160696	−	0.987004i	$-0.448626\pi$
$457$	6.87059	0.321392	0.160696	+	0.987004i	$0.448626\pi$
$458$	16.4306	0.767751
$459$	−9.82831	−0.458746
$460$	11.4278	0.532823
$461$	−20.0665	−0.934591	−0.467296	−	0.884101i	$-0.654772\pi$
$461$	−20.0665	−0.934591	−0.467296	+	0.884101i	$0.654772\pi$
$462$	−1.44426	−0.0671930
$463$	7.57643	0.352106	0.176053	−	0.984381i	$-0.443667\pi$
$463$	7.57643	0.352106	0.176053	+	0.984381i	$0.443667\pi$
$464$	−3.32427	−0.154325
$465$	6.22464	0.288661
$466$	60.5794	2.80628
$467$	−17.3491	−0.802818	−0.401409	−	0.915899i	$-0.631479\pi$
$467$	−17.3491	−0.802818	−0.401409	+	0.915899i	$0.631479\pi$
$468$	−35.1644	−1.62547
$469$	7.32515	0.338244
$470$	0.319543	0.0147394
$471$	0.330839	0.0152442
$472$	−4.23310	−0.194844
$473$	−6.75944	−0.310800
$474$	−15.2773	−0.701711
$475$	−1.94946	−0.0894474
$476$	4.58798	0.210290
$477$	24.8220	1.13652
$478$	−11.9645	−0.547243
$479$	−8.28398	−0.378505	−0.189252	−	0.981928i	$-0.560606\pi$
$479$	−8.28398	−0.378505	−0.189252	+	0.981928i	$0.560606\pi$
$480$	−6.58618	−0.300617
$481$	13.1904	0.601429
$482$	2.48420	0.113152
$483$	−3.15389	−0.143507
$484$	2.47406	0.112457
$485$	−15.6292	−0.709685
$486$	−33.6695	−1.52728
$487$	−22.0963	−1.00128	−0.500640	−	0.865656i	$-0.666902\pi$
$487$	−22.0963	−1.00128	−0.500640	+	0.865656i	$0.666902\pi$
$488$	−3.89597	−0.176362
$489$	−6.70132	−0.303044
$490$	−13.3567	−0.603394
$491$	−31.6243	−1.42718	−0.713592	−	0.700561i	$-0.752933\pi$
$491$	−31.6243	−1.42718	−0.713592	+	0.700561i	$0.752933\pi$
$492$	−12.2032	−0.550163
$493$	2.63390	0.118625
$494$	25.2649	1.13672
$495$	2.31975	0.104265
$496$	21.3368	0.958051
$497$	7.46129	0.334685
$498$	0.156385	0.00700777
$499$	16.1613	0.723478	0.361739	−	0.932279i	$-0.382183\pi$
$499$	16.1613	0.723478	0.361739	+	0.932279i	$0.382183\pi$
$500$	−2.47406	−0.110643
$501$	5.73481	0.256213
$502$	−42.8281	−1.91151
$503$	−3.09687	−0.138083	−0.0690413	−	0.997614i	$-0.521994\pi$
$503$	−3.09687	−0.138083	−0.0690413	+	0.997614i	$0.521994\pi$
$504$	1.92566	0.0857758
$505$	16.1945	0.720644
$506$	9.77020	0.434338
$507$	20.2407	0.898923
$508$	−12.0961	−0.536676
$509$	−37.6697	−1.66968	−0.834840	−	0.550492i	$-0.814440\pi$
$509$	−37.6697	−1.66968	−0.834840	+	0.550492i	$0.814440\pi$
$510$	3.90786	0.173043
$511$	0.827865	0.0366226
$512$	−28.2458	−1.24830
$513$	8.55344	0.377644
$514$	0.786299	0.0346821
$515$	8.60944	0.379377
$516$	−13.7929	−0.607198
$517$	0.151070	0.00664405
$518$	−3.76976	−0.165634
$519$	−20.0562	−0.880370
$520$	6.14374	0.269421
$521$	5.26003	0.230446	0.115223	−	0.993340i	$-0.463242\pi$
$521$	5.26003	0.230446	0.115223	+	0.993340i	$0.463242\pi$
$522$	5.76949	0.252524
$523$	35.8193	1.56627	0.783135	−	0.621852i	$-0.213620\pi$
$523$	35.8193	1.56627	0.783135	+	0.621852i	$0.213620\pi$
$524$	−32.9353	−1.43879
$525$	0.682802	0.0297999
$526$	9.90695	0.431964
$527$	−16.9056	−0.736422
$528$	−2.33177	−0.101477
$529$	−1.66437	−0.0723639
$530$	−22.6332	−0.983123
$531$	−9.79307	−0.424983
$532$	−3.99286	−0.173112
$533$	−36.6423	−1.58715
$534$	26.1867	1.13321
$535$	11.8020	0.510243
$536$	−8.87232	−0.383226
$537$	7.99662	0.345080
$538$	19.9917	0.861904
$539$	−6.31464	−0.271991
$540$	10.8551	0.467131
$541$	−26.0702	−1.12085	−0.560424	−	0.828206i	$-0.689362\pi$
$541$	−26.0702	−1.12085	−0.560424	+	0.828206i	$0.689362\pi$
$542$	26.9683	1.15839
$543$	−13.0606	−0.560482
$544$	17.8876	0.766924
$545$	−13.1159	−0.561822
$546$	−8.84907	−0.378705
$547$	−16.4087	−0.701584	−0.350792	−	0.936453i	$-0.614088\pi$
$547$	−16.4087	−0.701584	−0.350792	+	0.936453i	$0.614088\pi$
$548$	−34.9695	−1.49382
$549$	−9.01315	−0.384672
$550$	−2.11520	−0.0901923
$551$	−2.29224	−0.0976529
$552$	3.82004	0.162592
$553$	7.24972	0.308290
$554$	−11.9805	−0.509002
$555$	−1.77558	−0.0753690
$556$	45.5197	1.93047
$557$	15.6256	0.662076	0.331038	−	0.943617i	$-0.392601\pi$
$557$	15.6256	0.662076	0.331038	+	0.943617i	$0.392601\pi$
$558$	−37.0314	−1.56766
$559$	−41.4156	−1.75169
$560$	2.34051	0.0989044
$561$	1.84752	0.0780022
$562$	−0.0765218	−0.00322788
$563$	−34.7228	−1.46339	−0.731695	−	0.681632i	$-0.761271\pi$
$563$	−34.7228	−1.46339	−0.731695	+	0.681632i	$0.761271\pi$
$564$	0.308264	0.0129803
$565$	−0.612633	−0.0257737
$566$	52.5237	2.20773
$567$	2.76546	0.116138
$568$	−9.03722	−0.379193
$569$	29.0364	1.21727	0.608635	−	0.793450i	$-0.291717\pi$
$569$	29.0364	1.21727	0.608635	+	0.793450i	$0.291717\pi$
$570$	−3.40095	−0.142450
$571$	−12.0731	−0.505244	−0.252622	−	0.967565i	$-0.581293\pi$
$571$	−12.0731	−0.505244	−0.252622	+	0.967565i	$0.581293\pi$
$572$	15.1587	0.633817
$573$	−5.03119	−0.210181
$574$	10.4722	0.437103
$575$	−4.61905	−0.192628
$576$	26.0657	1.08607
$577$	6.18071	0.257306	0.128653	−	0.991690i	$-0.458935\pi$
$577$	6.18071	0.257306	0.128653	+	0.991690i	$0.458935\pi$
$578$	25.3449	1.05421
$579$	3.37058	0.140077
$580$	−2.90908	−0.120793
$581$	−0.0742110	−0.00307879
$582$	−27.2661	−1.13021
$583$	−10.7003	−0.443160
$584$	−1.00272	−0.0414929
$585$	14.2132	0.587646
$586$	8.33820	0.344448
$587$	−37.1615	−1.53382	−0.766909	−	0.641756i	$-0.778206\pi$
$587$	−37.1615	−1.53382	−0.766909	+	0.641756i	$0.778206\pi$
$588$	−12.8853	−0.531379
$589$	14.7127	0.606228
$590$	8.92954	0.367623
$591$	−4.83879	−0.199041
$592$	−6.08631	−0.250146
$593$	−44.0427	−1.80862	−0.904308	−	0.426881i	$-0.859612\pi$
$593$	−44.0427	−1.80862	−0.904308	+	0.426881i	$0.859612\pi$
$594$	9.28062	0.380788
$595$	−1.85444	−0.0760246
$596$	−10.4862	−0.429530
$597$	13.7455	0.562564
$598$	59.8627	2.44797
$599$	4.93228	0.201528	0.100764	−	0.994910i	$-0.467871\pi$
$599$	4.93228	0.201528	0.100764	+	0.994910i	$0.467871\pi$
$600$	−0.827018	−0.0337629
$601$	13.3427	0.544260	0.272130	−	0.962260i	$-0.412272\pi$
$601$	13.3427	0.544260	0.272130	+	0.962260i	$0.412272\pi$
$602$	11.8364	0.482417
$603$	−20.5257	−0.835871
$604$	−12.5708	−0.511499
$605$	−1.00000	−0.0406558
$606$	28.2522	1.14767
$607$	−32.8901	−1.33497	−0.667485	−	0.744623i	$-0.732629\pi$
$607$	−32.8901	−1.33497	−0.667485	+	0.744623i	$0.732629\pi$
$608$	−15.5673	−0.631338
$609$	0.802861	0.0325336
$610$	8.21838	0.332753
$611$	0.925616	0.0374464
$612$	−12.8559	−0.519670
$613$	29.0716	1.17419	0.587095	−	0.809518i	$-0.300272\pi$
$613$	29.0716	1.17419	0.587095	+	0.809518i	$0.300272\pi$
$614$	−18.4018	−0.742638
$615$	4.93247	0.198896
$616$	−0.830117	−0.0334464
$617$	−19.6068	−0.789341	−0.394670	−	0.918823i	$-0.629141\pi$
$617$	−19.6068	−0.789341	−0.394670	+	0.918823i	$0.629141\pi$
$618$	15.0197	0.604180
$619$	−33.4922	−1.34616	−0.673082	−	0.739568i	$-0.735030\pi$
$619$	−33.4922	−1.34616	−0.673082	+	0.739568i	$0.735030\pi$
$620$	18.6719	0.749881
$621$	20.2665	0.813267
$622$	−38.9664	−1.56241
$623$	−12.4267	−0.497864
$624$	−14.2869	−0.571934
$625$	1.00000	0.0400000
$626$	−30.4675	−1.21773
$627$	−1.60787	−0.0642120
$628$	0.992409	0.0396014
$629$	4.82233	0.192279
$630$	−4.06210	−0.161838
$631$	26.3470	1.04886	0.524429	−	0.851454i	$-0.324279\pi$
$631$	26.3470	1.04886	0.524429	+	0.851454i	$0.324279\pi$
$632$	−8.78096	−0.349288
$633$	2.06503	0.0820775
$634$	3.47302	0.137931
$635$	4.88916	0.194020
$636$	−21.8343	−0.865787
$637$	−38.6902	−1.53296
$638$	−2.48712	−0.0984660
$639$	−20.9072	−0.827075
$640$	−7.79643	−0.308181
$641$	22.0437	0.870676	0.435338	−	0.900267i	$-0.356629\pi$
$641$	22.0437	0.870676	0.435338	+	0.900267i	$0.356629\pi$
$642$	20.5892	0.812591
$643$	−48.6260	−1.91762	−0.958810	−	0.284047i	$-0.908323\pi$
$643$	−48.6260	−1.91762	−0.958810	+	0.284047i	$0.908323\pi$
$644$	−9.46066	−0.372802
$645$	5.57502	0.219516
$646$	9.23673	0.363414
$647$	−5.07076	−0.199352	−0.0996762	−	0.995020i	$-0.531781\pi$
$647$	−5.07076	−0.199352	−0.0996762	+	0.995020i	$0.531781\pi$
$648$	−3.34956	−0.131583
$649$	4.22161	0.165713
$650$	−12.9599	−0.508331
$651$	−5.15316	−0.201968
$652$	−20.1018	−0.787247
$653$	5.86630	0.229566	0.114783	−	0.993391i	$-0.463383\pi$
$653$	5.86630	0.229566	0.114783	+	0.993391i	$0.463383\pi$
$654$	−22.8814	−0.894733
$655$	13.3123	0.520154
$656$	16.9075	0.660128
$657$	−2.31975	−0.0905020
$658$	−0.264538	−0.0103128
$659$	31.8713	1.24153	0.620766	−	0.783996i	$-0.286822\pi$
$659$	31.8713	1.24153	0.620766	+	0.783996i	$0.286822\pi$
$660$	−2.04054	−0.0794278
$661$	13.8474	0.538603	0.269302	−	0.963056i	$-0.413207\pi$
$661$	13.8474	0.538603	0.269302	+	0.963056i	$0.413207\pi$
$662$	5.55951	0.216076
$663$	11.3198	0.439627
$664$	0.0898853	0.00348823
$665$	1.61389	0.0625840
$666$	10.5632	0.409316
$667$	−5.43124	−0.210298
$668$	17.2026	0.665588
$669$	−18.6789	−0.722170
$670$	18.7158	0.723054
$671$	3.88540	0.149994
$672$	5.45247	0.210334
$673$	−28.3566	−1.09307	−0.546534	−	0.837437i	$-0.684053\pi$
$673$	−28.3566	−1.09307	−0.546534	+	0.837437i	$0.684053\pi$
$674$	−8.47074	−0.326281
$675$	−4.38759	−0.168878
$676$	60.7157	2.33522
$677$	12.1492	0.466931	0.233466	−	0.972365i	$-0.424993\pi$
$677$	12.1492	0.466931	0.233466	+	0.972365i	$0.424993\pi$
$678$	−1.06877	−0.0410460
$679$	12.9389	0.496548
$680$	2.24612	0.0861348
$681$	13.7835	0.528186
$682$	15.9636	0.611276
$683$	−8.78586	−0.336182	−0.168091	−	0.985772i	$-0.553760\pi$
$683$	−8.78586	−0.336182	−0.168091	+	0.985772i	$0.553760\pi$
$684$	11.1883	0.427796
$685$	14.1345	0.540051
$686$	23.3152	0.890179
$687$	−6.40674	−0.244433
$688$	19.1100	0.728563
$689$	−65.5613	−2.49769
$690$	−8.05821	−0.306771
$691$	16.7245	0.636230	0.318115	−	0.948052i	$-0.396950\pi$
$691$	16.7245	0.636230	0.318115	+	0.948052i	$0.396950\pi$
$692$	−60.1621	−2.28702
$693$	−1.92044	−0.0729514
$694$	52.9335	2.00933
$695$	−18.3988	−0.697907
$696$	−0.972436	−0.0368601
$697$	−13.3962	−0.507418
$698$	74.9542	2.83706
$699$	−23.6216	−0.893450
$700$	2.04818	0.0774141
$701$	8.71755	0.329257	0.164629	−	0.986356i	$-0.447357\pi$
$701$	8.71755	0.329257	0.164629	+	0.986356i	$0.447357\pi$
$702$	56.8629	2.14615
$703$	−4.19680	−0.158285
$704$	−11.2365	−0.423490
$705$	−0.124599	−0.00469266
$706$	39.8510	1.49981
$707$	−13.4068	−0.504216
$708$	8.61436	0.323747
$709$	−13.7876	−0.517803	−0.258902	−	0.965904i	$-0.583361\pi$
$709$	−13.7876	−0.517803	−0.258902	+	0.965904i	$0.583361\pi$
$710$	19.0636	0.715445
$711$	−20.3143	−0.761847
$712$	15.0514	0.564074
$713$	34.8603	1.30553
$714$	−3.23518	−0.121073
$715$	−6.12707	−0.229139
$716$	23.9873	0.896447
$717$	4.66529	0.174228
$718$	−59.0511	−2.20377
$719$	34.4490	1.28473	0.642366	−	0.766398i	$-0.277953\pi$
$719$	34.4490	1.28473	0.642366	+	0.766398i	$0.277953\pi$
$720$	−6.55830	−0.244413
$721$	−7.12746	−0.265440
$722$	32.1501	1.19650
$723$	−0.968658	−0.0360248
$724$	−39.1774	−1.45602
$725$	1.17583	0.0436694
$726$	−1.74456	−0.0647467
$727$	49.8027	1.84708	0.923540	−	0.383503i	$-0.125282\pi$
$727$	49.8027	1.84708	0.923540	+	0.383503i	$0.125282\pi$
$728$	−5.08618	−0.188507
$729$	3.10726	0.115084
$730$	2.11520	0.0782869
$731$	−15.1413	−0.560022
$732$	7.92830	0.293038
$733$	−33.6374	−1.24243	−0.621213	−	0.783642i	$-0.713360\pi$
$733$	−33.6374	−1.24243	−0.621213	+	0.783642i	$0.713360\pi$
$734$	30.9218	1.14135
$735$	5.20815	0.192106
$736$	−36.8852	−1.35960
$737$	8.84825	0.325929
$738$	−29.3441	−1.08017
$739$	0.276253	0.0101621	0.00508106	−	0.999987i	$-0.498383\pi$
$739$	0.276253	0.0101621	0.00508106	+	0.999987i	$0.498383\pi$
$740$	−5.32615	−0.195793
$741$	−9.85150	−0.361904
$742$	18.7372	0.687865
$743$	40.5744	1.48853	0.744266	−	0.667883i	$-0.232800\pi$
$743$	40.5744	1.48853	0.744266	+	0.667883i	$0.232800\pi$
$744$	6.24157	0.228827
$745$	4.23845	0.155285
$746$	−15.6454	−0.572819
$747$	0.207945	0.00760832
$748$	5.54195	0.202634
$749$	−9.77042	−0.357003
$750$	1.74456	0.0637023
$751$	−20.5155	−0.748621	−0.374311	−	0.927303i	$-0.622121\pi$
$751$	−20.5155	−0.748621	−0.374311	+	0.927303i	$0.622121\pi$
$752$	−0.427099	−0.0155747
$753$	16.6999	0.608578
$754$	−15.2387	−0.554963
$755$	5.08106	0.184919
$756$	−8.98659	−0.326839
$757$	30.1446	1.09563	0.547813	−	0.836601i	$-0.315461\pi$
$757$	30.1446	1.09563	0.547813	+	0.836601i	$0.315461\pi$
$758$	12.3364	0.448078
$759$	−3.80967	−0.138282
$760$	−1.95477	−0.0709068
$761$	−3.93368	−0.142596	−0.0712979	−	0.997455i	$-0.522714\pi$
$761$	−3.93368	−0.142596	−0.0712979	+	0.997455i	$0.522714\pi$
$762$	8.52943	0.308989
$763$	10.8582	0.393092
$764$	−15.0919	−0.546007
$765$	5.19629	0.187872
$766$	37.3972	1.35122
$767$	25.8661	0.933971
$768$	4.93375	0.178031
$769$	2.96825	0.107038	0.0535190	−	0.998567i	$-0.482956\pi$
$769$	2.96825	0.107038	0.0535190	+	0.998567i	$0.482956\pi$
$770$	1.75110	0.0631051
$771$	−0.306600	−0.0110419
$772$	10.1106	0.363890
$773$	26.2479	0.944072	0.472036	−	0.881579i	$-0.343519\pi$
$773$	26.2479	0.944072	0.472036	+	0.881579i	$0.343519\pi$
$774$	−33.1667	−1.19215
$775$	−7.54708	−0.271099
$776$	−15.6717	−0.562582
$777$	1.46994	0.0527337
$778$	−13.7712	−0.493723
$779$	11.6585	0.417711
$780$	−12.5025	−0.447662
$781$	9.01270	0.322500
$782$	21.8855	0.782624
$783$	−5.15908	−0.184370
$784$	17.8525	0.637589
$785$	−0.401127	−0.0143168
$786$	23.2240	0.828374
$787$	39.0436	1.39175	0.695877	−	0.718161i	$-0.255016\pi$
$787$	39.0436	1.39175	0.695877	+	0.718161i	$0.255016\pi$
$788$	−14.5148	−0.517069
$789$	−3.86300	−0.137526
$790$	18.5231	0.659021
$791$	0.507177	0.0180332
$792$	2.32606	0.0826529
$793$	23.8061	0.845379
$794$	−3.57834	−0.126991
$795$	8.82532	0.313002
$796$	41.2319	1.46143
$797$	−37.6438	−1.33341	−0.666705	−	0.745322i	$-0.732296\pi$
$797$	−37.6438	−1.33341	−0.666705	+	0.745322i	$0.732296\pi$
$798$	2.81553	0.0996686
$799$	0.338401	0.0119718
$800$	7.98544	0.282328
$801$	34.8206	1.23033
$802$	−39.8587	−1.40746
$803$	1.00000	0.0352892
$804$	18.0552	0.636757
$805$	3.82395	0.134777
$806$	97.8098	3.44520
$807$	−7.79533	−0.274408
$808$	16.2385	0.571270
$809$	−41.5247	−1.45993	−0.729965	−	0.683485i	$-0.760464\pi$
$809$	−41.5247	−1.45993	−0.729965	+	0.683485i	$0.760464\pi$
$810$	7.06575	0.248265
$811$	22.7405	0.798525	0.399263	−	0.916837i	$-0.369266\pi$
$811$	22.7405	0.798525	0.399263	+	0.916837i	$0.369266\pi$
$812$	2.40832	0.0845156
$813$	−10.5157	−0.368801
$814$	−4.55360	−0.159604
$815$	8.12504	0.284608
$816$	−5.22322	−0.182849
$817$	13.1773	0.461015
$818$	9.06985	0.317120
$819$	−11.7666	−0.411160
$820$	14.7958	0.516692
$821$	−2.19280	−0.0765293	−0.0382647	−	0.999268i	$-0.512183\pi$
$821$	−2.19280	−0.0765293	−0.0382647	+	0.999268i	$0.512183\pi$
$822$	24.6585	0.860063
$823$	27.5360	0.959844	0.479922	−	0.877311i	$-0.340665\pi$
$823$	27.5360	0.959844	0.479922	+	0.877311i	$0.340665\pi$
$824$	8.63287	0.300740
$825$	0.824774	0.0287150
$826$	−7.39245	−0.257216
$827$	18.8854	0.656711	0.328355	−	0.944554i	$-0.393506\pi$
$827$	18.8854	0.656711	0.328355	+	0.944554i	$0.393506\pi$
$828$	26.5096	0.921272
$829$	27.0161	0.938308	0.469154	−	0.883116i	$-0.344559\pi$
$829$	27.0161	0.938308	0.469154	+	0.883116i	$0.344559\pi$
$830$	−0.189609	−0.00658143
$831$	4.67152	0.162053
$832$	−68.8465	−2.38682
$833$	−14.1450	−0.490094
$834$	−32.0979	−1.11146
$835$	−6.95319	−0.240625
$836$	−4.82308	−0.166810
$837$	33.1135	1.14457
$838$	8.52549	0.294508
$839$	18.3076	0.632048	0.316024	−	0.948751i	$-0.397652\pi$
$839$	18.3076	0.632048	0.316024	+	0.948751i	$0.397652\pi$
$840$	0.684659	0.0236230
$841$	−27.6174	−0.952325
$842$	70.0752	2.41495
$843$	0.0298380	0.00102767
$844$	6.19442	0.213221
$845$	−24.5409	−0.844234
$846$	0.741259	0.0254850
$847$	0.827865	0.0284458
$848$	30.2514	1.03884
$849$	−20.4804	−0.702887
$850$	−4.73809	−0.162515
$851$	−9.94390	−0.340872
$852$	18.3907	0.630056
$853$	11.4478	0.391965	0.195983	−	0.980607i	$-0.437210\pi$
$853$	11.4478	0.391965	0.195983	+	0.980607i	$0.437210\pi$
$854$	−6.80371	−0.232818
$855$	−4.52226	−0.154658
$856$	11.8341	0.404480
$857$	17.1362	0.585360	0.292680	−	0.956210i	$-0.405453\pi$
$857$	17.1362	0.585360	0.292680	+	0.956210i	$0.405453\pi$
$858$	−10.6890	−0.364918
$859$	−33.9076	−1.15691	−0.578456	−	0.815713i	$-0.696345\pi$
$859$	−33.9076	−1.15691	−0.578456	+	0.815713i	$0.696345\pi$
$860$	16.7232	0.570258
$861$	−4.08342	−0.139163
$862$	40.3750	1.37518
$863$	3.73976	0.127303	0.0636515	−	0.997972i	$-0.479725\pi$
$863$	3.73976	0.127303	0.0636515	+	0.997972i	$0.479725\pi$
$864$	−35.0368	−1.19198
$865$	24.3172	0.826810
$866$	−54.1178	−1.83900
$867$	−9.88268	−0.335633
$868$	−15.4578	−0.524672
$869$	8.75713	0.297065
$870$	2.05131	0.0695460
$871$	54.2138	1.83696
$872$	−13.1515	−0.445367
$873$	−36.2558	−1.22707
$874$	−19.0466	−0.644262
$875$	−0.827865	−0.0279869
$876$	2.04054	0.0689434
$877$	59.0975	1.99558	0.997791	−	0.0664334i	$-0.0211620\pi$
$877$	59.0975	1.99558	0.997791	+	0.0664334i	$0.0211620\pi$
$878$	−22.8251	−0.770309
$879$	−3.25130	−0.109664
$880$	2.82716	0.0953035
$881$	43.8484	1.47729	0.738646	−	0.674094i	$-0.235466\pi$
$881$	43.8484	1.47729	0.738646	+	0.674094i	$0.235466\pi$
$882$	−30.9842	−1.04329
$883$	53.7796	1.80983	0.904914	−	0.425595i	$-0.139935\pi$
$883$	53.7796	1.80983	0.904914	+	0.425595i	$0.139935\pi$
$884$	33.9559	1.14206
$885$	−3.48188	−0.117042
$886$	7.24214	0.243304
$887$	−28.4357	−0.954779	−0.477389	−	0.878692i	$-0.658417\pi$
$887$	−28.4357	−0.954779	−0.477389	+	0.878692i	$0.658417\pi$
$888$	−1.78041	−0.0597465
$889$	−4.04756	−0.135751
$890$	−31.7502	−1.06427
$891$	3.34047	0.111910
$892$	−56.0308	−1.87605
$893$	−0.294505	−0.00985524
$894$	7.39422	0.247300
$895$	−9.69553	−0.324086
$896$	6.45439	0.215626
$897$	−23.3421	−0.779371
$898$	−9.90110	−0.330404
$899$	−8.87411	−0.295968
$900$	−5.73918	−0.191306
$901$	−23.9689	−0.798520
$902$	12.6497	0.421189
$903$	−4.61536	−0.153590
$904$	−0.614300	−0.0204313
$905$	15.8353	0.526383
$906$	8.86421	0.294494
$907$	18.9605	0.629575	0.314787	−	0.949162i	$-0.398067\pi$
$907$	18.9605	0.629575	0.314787	+	0.949162i	$0.398067\pi$
$908$	41.3461	1.37212
$909$	37.5671	1.24602
$910$	10.7291	0.355666
$911$	−28.9288	−0.958452	−0.479226	−	0.877691i	$-0.659083\pi$
$911$	−28.9288	−0.958452	−0.479226	+	0.877691i	$0.659083\pi$
$912$	4.54569	0.150523
$913$	−0.0896414	−0.00296670
$914$	−14.5326	−0.480697
$915$	−3.20458	−0.105940
$916$	−19.2182	−0.634986
$917$	−11.0208	−0.363938
$918$	20.7888	0.686133
$919$	6.58834	0.217329	0.108665	−	0.994078i	$-0.465343\pi$
$919$	6.58834	0.217329	0.108665	+	0.994078i	$0.465343\pi$
$920$	−4.63162	−0.152700
$921$	7.17539	0.236437
$922$	42.4446	1.39784
$923$	55.2214	1.81763
$924$	1.68929	0.0555735
$925$	2.15280	0.0707837
$926$	−16.0256	−0.526635
$927$	19.9717	0.655958
$928$	9.38955	0.308227
$929$	49.5992	1.62730	0.813649	−	0.581357i	$-0.197478\pi$
$929$	49.5992	1.62730	0.813649	+	0.581357i	$0.197478\pi$
$930$	−13.1663	−0.431741
$931$	12.3101	0.403449
$932$	−70.8571	−2.32100
$933$	15.1941	0.497432
$934$	36.6967	1.20075
$935$	−2.24003	−0.0732567
$936$	14.2519	0.465839
$937$	−36.0497	−1.17769	−0.588847	−	0.808245i	$-0.700418\pi$
$937$	−36.0497	−1.17769	−0.588847	+	0.808245i	$0.700418\pi$
$938$	−15.4941	−0.505901
$939$	11.8801	0.387693
$940$	−0.373756	−0.0121906
$941$	36.4451	1.18808	0.594039	−	0.804436i	$-0.297533\pi$
$941$	36.4451	1.18808	0.594039	+	0.804436i	$0.297533\pi$
$942$	−0.699789	−0.0228004
$943$	27.6237	0.899552
$944$	−11.9352	−0.388457
$945$	3.63233	0.118160
$946$	14.2976	0.464854
$947$	−0.638177	−0.0207380	−0.0103690	−	0.999946i	$-0.503301\pi$
$947$	−0.638177	−0.0207380	−0.0103690	+	0.999946i	$0.503301\pi$
$948$	17.8693	0.580366
$949$	6.12707	0.198893
$950$	4.12349	0.133784
$951$	−1.35423	−0.0439138
$952$	−1.85948	−0.0602662
$953$	−36.8738	−1.19446	−0.597231	−	0.802070i	$-0.703732\pi$
$953$	−36.8738	−1.19446	−0.597231	+	0.802070i	$0.703732\pi$
$954$	−52.5033	−1.69986
$955$	6.10008	0.197394
$956$	13.9944	0.452610
$957$	0.969798	0.0313491
$958$	17.5222	0.566118
$959$	−11.7015	−0.377860
$960$	9.26754	0.299108
$961$	25.9584	0.837368
$962$	−27.9002	−0.899538
$963$	27.3775	0.882229
$964$	−2.90566	−0.0935850
$965$	−4.08667	−0.131555
$966$	6.67111	0.214639
$967$	5.42617	0.174494	0.0872470	−	0.996187i	$-0.472193\pi$
$967$	5.42617	0.174494	0.0872470	+	0.996187i	$0.472193\pi$
$968$	−1.00272	−0.0322287
$969$	−3.60166	−0.115702
$970$	33.0588	1.06145
$971$	−25.7079	−0.825004	−0.412502	−	0.910957i	$-0.635345\pi$
$971$	−25.7079	−0.825004	−0.412502	+	0.910957i	$0.635345\pi$
$972$	39.3818	1.26317
$973$	15.2317	0.488307
$974$	46.7380	1.49758
$975$	5.05345	0.161840
$976$	−10.9846	−0.351610
$977$	−58.6101	−1.87510	−0.937552	−	0.347845i	$-0.886913\pi$
$977$	−58.6101	−1.87510	−0.937552	+	0.347845i	$0.886913\pi$
$978$	14.1746	0.453254
$979$	−15.0105	−0.479738
$980$	15.6228	0.499051
$981$	−30.4255	−0.971411
$982$	66.8916	2.13460
$983$	−50.1730	−1.60027	−0.800136	−	0.599819i	$-0.795239\pi$
$983$	−50.1730	−1.60027	−0.800136	+	0.599819i	$0.795239\pi$
$984$	4.94589	0.157669
$985$	5.86681	0.186932
$986$	−5.57121	−0.177424
$987$	0.103151	0.00328333
$988$	−29.5513	−0.940153
$989$	31.2222	0.992809
$990$	−4.90672	−0.155946
$991$	33.1541	1.05318	0.526588	−	0.850121i	$-0.323471\pi$
$991$	33.1541	1.05318	0.526588	+	0.850121i	$0.323471\pi$
$992$	−60.2667	−1.91347
$993$	−2.16781	−0.0687933
$994$	−15.7821	−0.500578
$995$	−16.6657	−0.528339
$996$	−0.182917	−0.00579593
$997$	1.97527	0.0625574	0.0312787	−	0.999511i	$-0.490042\pi$
$997$	1.97527	0.0625574	0.0312787	+	0.999511i	$0.490042\pi$
$998$	−34.1843	−1.08208
$999$	−9.44561	−0.298846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.7	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.7	✓	31	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.11520 q^{2} +0.824774 q^{3} +2.47406 q^{4} -1.00000 q^{5} -1.74456 q^{6} +0.827865 q^{7} -1.00272 q^{8} -2.31975 q^{9} +O(q^{10})\)	\(q-2.11520 q^{2} +0.824774 q^{3} +2.47406 q^{4} -1.00000 q^{5} -1.74456 q^{6} +0.827865 q^{7} -1.00272 q^{8} -2.31975 q^{9} +2.11520 q^{10} +1.00000 q^{11} +2.04054 q^{12} +6.12707 q^{13} -1.75110 q^{14} -0.824774 q^{15} -2.82716 q^{16} +2.24003 q^{17} +4.90672 q^{18} -1.94946 q^{19} -2.47406 q^{20} +0.682802 q^{21} -2.11520 q^{22} -4.61905 q^{23} -0.827018 q^{24} +1.00000 q^{25} -12.9599 q^{26} -4.38759 q^{27} +2.04818 q^{28} +1.17583 q^{29} +1.74456 q^{30} -7.54708 q^{31} +7.98544 q^{32} +0.824774 q^{33} -4.73809 q^{34} -0.827865 q^{35} -5.73918 q^{36} +2.15280 q^{37} +4.12349 q^{38} +5.05345 q^{39} +1.00272 q^{40} -5.98039 q^{41} -1.44426 q^{42} -6.75944 q^{43} +2.47406 q^{44} +2.31975 q^{45} +9.77020 q^{46} +0.151070 q^{47} -2.33177 q^{48} -6.31464 q^{49} -2.11520 q^{50} +1.84752 q^{51} +15.1587 q^{52} -10.7003 q^{53} +9.28062 q^{54} -1.00000 q^{55} -0.830117 q^{56} -1.60787 q^{57} -2.48712 q^{58} +4.22161 q^{59} -2.04054 q^{60} +3.88540 q^{61} +15.9636 q^{62} -1.92044 q^{63} -11.2365 q^{64} -6.12707 q^{65} -1.74456 q^{66} +8.84825 q^{67} +5.54195 q^{68} -3.80967 q^{69} +1.75110 q^{70} +9.01270 q^{71} +2.32606 q^{72} +1.00000 q^{73} -4.55360 q^{74} +0.824774 q^{75} -4.82308 q^{76} +0.827865 q^{77} -10.6890 q^{78} +8.75713 q^{79} +2.82716 q^{80} +3.34047 q^{81} +12.6497 q^{82} -0.0896414 q^{83} +1.68929 q^{84} -2.24003 q^{85} +14.2976 q^{86} +0.969798 q^{87} -1.00272 q^{88} -15.0105 q^{89} -4.90672 q^{90} +5.07238 q^{91} -11.4278 q^{92} -6.22464 q^{93} -0.319543 q^{94} +1.94946 q^{95} +6.58618 q^{96} +15.6292 q^{97} +13.3567 q^{98} -2.31975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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