LMFDB - Embedded newform 8035.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79540 q^{2} -1.02268 q^{3} +5.81427 q^{4} -1.00000 q^{5} +2.85879 q^{6} +3.00451 q^{7} -10.6624 q^{8} -1.95413 q^{9} +O(q^{10})$	\(q-2.79540 q^{2} -1.02268 q^{3} +5.81427 q^{4} -1.00000 q^{5} +2.85879 q^{6} +3.00451 q^{7} -10.6624 q^{8} -1.95413 q^{9} +2.79540 q^{10} -1.06207 q^{11} -5.94611 q^{12} +4.88500 q^{13} -8.39882 q^{14} +1.02268 q^{15} +18.1772 q^{16} +1.92118 q^{17} +5.46259 q^{18} +6.61422 q^{19} -5.81427 q^{20} -3.07264 q^{21} +2.96892 q^{22} +4.90252 q^{23} +10.9042 q^{24} +1.00000 q^{25} -13.6555 q^{26} +5.06647 q^{27} +17.4690 q^{28} -8.72927 q^{29} -2.85879 q^{30} +6.70228 q^{31} -29.4877 q^{32} +1.08616 q^{33} -5.37046 q^{34} -3.00451 q^{35} -11.3619 q^{36} -9.25787 q^{37} -18.4894 q^{38} -4.99577 q^{39} +10.6624 q^{40} +2.97387 q^{41} +8.58927 q^{42} -8.88574 q^{43} -6.17518 q^{44} +1.95413 q^{45} -13.7045 q^{46} -12.0581 q^{47} -18.5894 q^{48} +2.02710 q^{49} -2.79540 q^{50} -1.96474 q^{51} +28.4027 q^{52} +1.78842 q^{53} -14.1628 q^{54} +1.06207 q^{55} -32.0354 q^{56} -6.76421 q^{57} +24.4018 q^{58} -4.41573 q^{59} +5.94611 q^{60} +2.71518 q^{61} -18.7356 q^{62} -5.87122 q^{63} +46.0755 q^{64} -4.88500 q^{65} -3.03625 q^{66} -9.24560 q^{67} +11.1702 q^{68} -5.01369 q^{69} +8.39882 q^{70} +3.62788 q^{71} +20.8358 q^{72} -15.2961 q^{73} +25.8795 q^{74} -1.02268 q^{75} +38.4569 q^{76} -3.19102 q^{77} +13.9652 q^{78} -5.41366 q^{79} -18.1772 q^{80} +0.681036 q^{81} -8.31317 q^{82} -1.97185 q^{83} -17.8652 q^{84} -1.92118 q^{85} +24.8392 q^{86} +8.92722 q^{87} +11.3243 q^{88} +13.2194 q^{89} -5.46259 q^{90} +14.6770 q^{91} +28.5046 q^{92} -6.85427 q^{93} +33.7073 q^{94} -6.61422 q^{95} +30.1563 q^{96} -10.1235 q^{97} -5.66656 q^{98} +2.07543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * 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 $

$2$	−2.79540	−1.97665	−0.988324	−	0.152370i	$-0.951310\pi$
$2$	−2.79540	−1.97665	−0.988324	+	0.152370i	$0.951310\pi$
$3$	−1.02268	−0.590442	−0.295221	−	0.955429i	$-0.595393\pi$
$3$	−1.02268	−0.590442	−0.295221	+	0.955429i	$0.595393\pi$
$4$	5.81427	2.90713
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.85879	1.16710
$7$	3.00451	1.13560	0.567800	−	0.823167i	$-0.307795\pi$
$7$	3.00451	1.13560	0.567800	+	0.823167i	$0.307795\pi$
$8$	−10.6624	−3.76973
$9$	−1.95413	−0.651378
$10$	2.79540	0.883983
$11$	−1.06207	−0.320227	−0.160114	−	0.987099i	$-0.551186\pi$
$11$	−1.06207	−0.320227	−0.160114	+	0.987099i	$0.551186\pi$
$12$	−5.94611	−1.71650
$13$	4.88500	1.35485	0.677427	−	0.735590i	$-0.263095\pi$
$13$	4.88500	1.35485	0.677427	+	0.735590i	$0.263095\pi$
$14$	−8.39882	−2.24468
$15$	1.02268	0.264054
$16$	18.1772	4.54429
$17$	1.92118	0.465954	0.232977	−	0.972482i	$-0.425153\pi$
$17$	1.92118	0.465954	0.232977	+	0.972482i	$0.425153\pi$
$18$	5.46259	1.28754
$19$	6.61422	1.51741	0.758703	−	0.651436i	$-0.225833\pi$
$19$	6.61422	1.51741	0.758703	+	0.651436i	$0.225833\pi$
$20$	−5.81427	−1.30011
$21$	−3.07264	−0.670506
$22$	2.96892	0.632976
$23$	4.90252	1.02225	0.511123	−	0.859507i	$-0.329230\pi$
$23$	4.90252	1.02225	0.511123	+	0.859507i	$0.329230\pi$
$24$	10.9042	2.22581
$25$	1.00000	0.200000
$26$	−13.6555	−2.67807
$27$	5.06647	0.975043
$28$	17.4690	3.30134
$29$	−8.72927	−1.62099	−0.810493	−	0.585749i	$-0.800800\pi$
$29$	−8.72927	−1.62099	−0.810493	+	0.585749i	$0.800800\pi$
$30$	−2.85879	−0.521941
$31$	6.70228	1.20377	0.601883	−	0.798584i	$-0.294417\pi$
$31$	6.70228	1.20377	0.601883	+	0.798584i	$0.294417\pi$
$32$	−29.4877	−5.21273
$33$	1.08616	0.189076
$34$	−5.37046	−0.921026
$35$	−3.00451	−0.507855
$36$	−11.3619	−1.89364
$37$	−9.25787	−1.52198	−0.760992	−	0.648761i	$-0.775288\pi$
$37$	−9.25787	−1.52198	−0.760992	+	0.648761i	$0.775288\pi$
$38$	−18.4894	−2.99938
$39$	−4.99577	−0.799963
$40$	10.6624	1.68587
$41$	2.97387	0.464441	0.232220	−	0.972663i	$-0.425401\pi$
$41$	2.97387	0.464441	0.232220	+	0.972663i	$0.425401\pi$
$42$	8.58927	1.32535
$43$	−8.88574	−1.35506	−0.677531	−	0.735494i	$-0.736950\pi$
$43$	−8.88574	−1.35506	−0.677531	+	0.735494i	$0.736950\pi$
$44$	−6.17518	−0.930944
$45$	1.95413	0.291305
$46$	−13.7045	−2.02062
$47$	−12.0581	−1.75886	−0.879430	−	0.476029i	$-0.842076\pi$
$47$	−12.0581	−1.75886	−0.879430	+	0.476029i	$0.842076\pi$
$48$	−18.5894	−2.68314
$49$	2.02710	0.289586
$50$	−2.79540	−0.395329
$51$	−1.96474	−0.275119
$52$	28.4027	3.93874
$53$	1.78842	0.245659	0.122829	−	0.992428i	$-0.460803\pi$
$53$	1.78842	0.245659	0.122829	+	0.992428i	$0.460803\pi$
$54$	−14.1628	−1.92732
$55$	1.06207	0.143210
$56$	−32.0354	−4.28090
$57$	−6.76421	−0.895941
$58$	24.4018	3.20412
$59$	−4.41573	−0.574879	−0.287439	−	0.957799i	$-0.592804\pi$
$59$	−4.41573	−0.574879	−0.287439	+	0.957799i	$0.592804\pi$
$60$	5.94611	0.767640
$61$	2.71518	0.347644	0.173822	−	0.984777i	$-0.444388\pi$
$61$	2.71518	0.347644	0.173822	+	0.984777i	$0.444388\pi$
$62$	−18.7356	−2.37942
$63$	−5.87122	−0.739704
$64$	46.0755	5.75944
$65$	−4.88500	−0.605909
$66$	−3.03625	−0.373736
$67$	−9.24560	−1.12953	−0.564765	−	0.825252i	$-0.691033\pi$
$67$	−9.24560	−1.12953	−0.564765	+	0.825252i	$0.691033\pi$
$68$	11.1702	1.35459
$69$	−5.01369	−0.603578
$70$	8.39882	1.00385
$71$	3.62788	0.430551	0.215275	−	0.976553i	$-0.430935\pi$
$71$	3.62788	0.430551	0.215275	+	0.976553i	$0.430935\pi$
$72$	20.8358	2.45552
$73$	−15.2961	−1.79027	−0.895137	−	0.445792i	$-0.852922\pi$
$73$	−15.2961	−1.79027	−0.895137	+	0.445792i	$0.852922\pi$
$74$	25.8795	3.00843
$75$	−1.02268	−0.118088
$76$	38.4569	4.41130
$77$	−3.19102	−0.363650
$78$	13.9652	1.58125
$79$	−5.41366	−0.609084	−0.304542	−	0.952499i	$-0.598503\pi$
$79$	−5.41366	−0.609084	−0.304542	+	0.952499i	$0.598503\pi$
$80$	−18.1772	−2.03227
$81$	0.681036	0.0756707
$82$	−8.31317	−0.918036
$83$	−1.97185	−0.216438	−0.108219	−	0.994127i	$-0.534515\pi$
$83$	−1.97185	−0.216438	−0.108219	+	0.994127i	$0.534515\pi$
$84$	−17.8652	−1.94925
$85$	−1.92118	−0.208381
$86$	24.8392	2.67848
$87$	8.92722	0.957098
$88$	11.3243	1.20717
$89$	13.2194	1.40125	0.700624	−	0.713530i	$-0.252905\pi$
$89$	13.2194	1.40125	0.700624	+	0.713530i	$0.252905\pi$
$90$	−5.46259	−0.575807
$91$	14.6770	1.53857
$92$	28.5046	2.97181
$93$	−6.85427	−0.710754
$94$	33.7073	3.47664
$95$	−6.61422	−0.678605
$96$	30.1563	3.07782
$97$	−10.1235	−1.02789	−0.513943	−	0.857824i	$-0.671816\pi$
$97$	−10.1235	−1.02789	−0.513943	+	0.857824i	$0.671816\pi$
$98$	−5.66656	−0.572409
$99$	2.07543	0.208589
$100$	5.81427	0.581427
$101$	−15.7903	−1.57120	−0.785598	−	0.618737i	$-0.787645\pi$
$101$	−15.7903	−1.57120	−0.785598	+	0.618737i	$0.787645\pi$
$102$	5.49224	0.543813
$103$	5.53925	0.545798	0.272899	−	0.962043i	$-0.412017\pi$
$103$	5.53925	0.545798	0.272899	+	0.962043i	$0.412017\pi$
$104$	−52.0858	−5.10744
$105$	3.07264	0.299859
$106$	−4.99936	−0.485581
$107$	−12.8768	−1.24484	−0.622421	−	0.782682i	$-0.713851\pi$
$107$	−12.8768	−1.24484	−0.622421	+	0.782682i	$0.713851\pi$
$108$	29.4578	2.83458
$109$	16.3472	1.56578	0.782888	−	0.622163i	$-0.213746\pi$
$109$	16.3472	1.56578	0.782888	+	0.622163i	$0.213746\pi$
$110$	−2.96892	−0.283076
$111$	9.46781	0.898644
$112$	54.6136	5.16050
$113$	5.22821	0.491829	0.245914	−	0.969292i	$-0.420912\pi$
$113$	5.22821	0.491829	0.245914	+	0.969292i	$0.420912\pi$
$114$	18.9087	1.77096
$115$	−4.90252	−0.457163
$116$	−50.7543	−4.71242
$117$	−9.54593	−0.882522
$118$	12.3437	1.13633
$119$	5.77220	0.529137
$120$	−10.9042	−0.995412
$121$	−9.87200	−0.897454
$122$	−7.59003	−0.687169
$123$	−3.04131	−0.274226
$124$	38.9689	3.49951
$125$	−1.00000	−0.0894427
$126$	16.4124	1.46213
$127$	−17.5151	−1.55421	−0.777107	−	0.629369i	$-0.783313\pi$
$127$	−17.5151	−1.55421	−0.777107	+	0.629369i	$0.783313\pi$
$128$	−69.8243	−6.17165
$129$	9.08723	0.800086
$130$	13.6555	1.19767
$131$	4.21207	0.368010	0.184005	−	0.982925i	$-0.441094\pi$
$131$	4.21207	0.368010	0.184005	+	0.982925i	$0.441094\pi$
$132$	6.31521	0.549669
$133$	19.8725	1.72317
$134$	25.8452	2.23268
$135$	−5.06647	−0.436053
$136$	−20.4844	−1.75652
$137$	7.46379	0.637674	0.318837	−	0.947810i	$-0.396708\pi$
$137$	7.46379	0.637674	0.318837	+	0.947810i	$0.396708\pi$
$138$	14.0153	1.19306
$139$	−7.12043	−0.603947	−0.301973	−	0.953316i	$-0.597645\pi$
$139$	−7.12043	−0.603947	−0.301973	+	0.953316i	$0.597645\pi$
$140$	−17.4690	−1.47640
$141$	12.3316	1.03850
$142$	−10.1414	−0.851047
$143$	−5.18823	−0.433861
$144$	−35.5206	−2.96005
$145$	8.72927	0.724927
$146$	42.7587	3.53874
$147$	−2.07307	−0.170984
$148$	−53.8277	−4.42461
$149$	−0.866457	−0.0709829	−0.0354915	−	0.999370i	$-0.511300\pi$
$149$	−0.866457	−0.0709829	−0.0354915	+	0.999370i	$0.511300\pi$
$150$	2.85879	0.233419
$151$	−19.5593	−1.59171	−0.795855	−	0.605487i	$-0.792978\pi$
$151$	−19.5593	−1.59171	−0.795855	+	0.605487i	$0.792978\pi$
$152$	−70.5235	−5.72021
$153$	−3.75424	−0.303512
$154$	8.92017	0.718808
$155$	−6.70228	−0.538340
$156$	−29.0467	−2.32560
$157$	12.0715	0.963407	0.481704	−	0.876334i	$-0.340018\pi$
$157$	12.0715	0.963407	0.481704	+	0.876334i	$0.340018\pi$
$158$	15.1334	1.20394
$159$	−1.82898	−0.145047
$160$	29.4877	2.33121
$161$	14.7297	1.16086
$162$	−1.90377	−0.149574
$163$	−24.6406	−1.93000	−0.965000	−	0.262248i	$-0.915536\pi$
$163$	−24.6406	−1.93000	−0.965000	+	0.262248i	$0.915536\pi$
$164$	17.2909	1.35019
$165$	−1.08616	−0.0845573
$166$	5.51210	0.427822
$167$	19.5571	1.51338	0.756688	−	0.653776i	$-0.226816\pi$
$167$	19.5571	1.51338	0.756688	+	0.653776i	$0.226816\pi$
$168$	32.7618	2.52763
$169$	10.8632	0.835630
$170$	5.37046	0.411896
$171$	−12.9251	−0.988405
$172$	−51.6641	−3.93935
$173$	4.28562	0.325830	0.162915	−	0.986640i	$-0.447910\pi$
$173$	4.28562	0.325830	0.162915	+	0.986640i	$0.447910\pi$
$174$	−24.9552	−1.89185
$175$	3.00451	0.227120
$176$	−19.3055	−1.45521
$177$	4.51586	0.339433
$178$	−36.9534	−2.76977
$179$	9.31271	0.696065	0.348032	−	0.937483i	$-0.386850\pi$
$179$	9.31271	0.696065	0.348032	+	0.937483i	$0.386850\pi$
$180$	11.3619	0.846863
$181$	−5.57935	−0.414710	−0.207355	−	0.978266i	$-0.566486\pi$
$181$	−5.57935	−0.414710	−0.207355	+	0.978266i	$0.566486\pi$
$182$	−41.0282	−3.04121
$183$	−2.77675	−0.205264
$184$	−52.2727	−3.85359
$185$	9.25787	0.680652
$186$	19.1604	1.40491
$187$	−2.04043	−0.149211
$188$	−70.1092	−5.11324
$189$	15.2223	1.10726
$190$	18.4894	1.34136
$191$	17.0729	1.23535	0.617677	−	0.786432i	$-0.288074\pi$
$191$	17.0729	1.23535	0.617677	+	0.786432i	$0.288074\pi$
$192$	−47.1204	−3.40062
$193$	7.33901	0.528274	0.264137	−	0.964485i	$-0.414913\pi$
$193$	7.33901	0.528274	0.264137	+	0.964485i	$0.414913\pi$
$194$	28.2993	2.03177
$195$	4.99577	0.357754
$196$	11.7861	0.841865
$197$	−19.0616	−1.35808	−0.679041	−	0.734100i	$-0.737604\pi$
$197$	−19.0616	−1.35808	−0.679041	+	0.734100i	$0.737604\pi$
$198$	−5.80167	−0.412307
$199$	−15.0242	−1.06503	−0.532517	−	0.846419i	$-0.678754\pi$
$199$	−15.0242	−1.06503	−0.532517	+	0.846419i	$0.678754\pi$
$200$	−10.6624	−0.753946
$201$	9.45525	0.666922
$202$	44.1403	3.10570
$203$	−26.2272	−1.84079
$204$	−11.4235	−0.799808
$205$	−2.97387	−0.207704
$206$	−15.4844	−1.07885
$207$	−9.58018	−0.665869
$208$	88.7954	6.15686
$209$	−7.02479	−0.485915
$210$	−8.58927	−0.592716
$211$	−16.4787	−1.13444	−0.567219	−	0.823567i	$-0.691981\pi$
$211$	−16.4787	−1.13444	−0.567219	+	0.823567i	$0.691981\pi$
$212$	10.3984	0.714163
$213$	−3.71015	−0.254215
$214$	35.9957	2.46062
$215$	8.88574	0.606002
$216$	−54.0208	−3.67565
$217$	20.1371	1.36700
$218$	−45.6969	−3.09499
$219$	15.6430	1.05705
$220$	6.17518	0.416331
$221$	9.38494	0.631300
$222$	−26.4663	−1.77630
$223$	−15.2428	−1.02073	−0.510366	−	0.859957i	$-0.670490\pi$
$223$	−15.2428	−1.02073	−0.510366	+	0.859957i	$0.670490\pi$
$224$	−88.5961	−5.91958
$225$	−1.95413	−0.130276
$226$	−14.6150	−0.972172
$227$	−18.6579	−1.23837	−0.619186	−	0.785245i	$-0.712537\pi$
$227$	−18.6579	−1.23837	−0.619186	+	0.785245i	$0.712537\pi$
$228$	−39.3289	−2.60462
$229$	−3.07555	−0.203238	−0.101619	−	0.994823i	$-0.532402\pi$
$229$	−3.07555	−0.203238	−0.101619	+	0.994823i	$0.532402\pi$
$230$	13.7045	0.903649
$231$	3.26338	0.214714
$232$	93.0751	6.11068
$233$	8.92792	0.584888	0.292444	−	0.956283i	$-0.405532\pi$
$233$	8.92792	0.584888	0.292444	+	0.956283i	$0.405532\pi$
$234$	26.6847	1.74443
$235$	12.0581	0.786586
$236$	−25.6742	−1.67125
$237$	5.53642	0.359629
$238$	−16.1356	−1.04592
$239$	25.2527	1.63346	0.816729	−	0.577021i	$-0.195785\pi$
$239$	25.2527	1.63346	0.816729	+	0.577021i	$0.195785\pi$
$240$	18.5894	1.19994
$241$	7.66119	0.493500	0.246750	−	0.969079i	$-0.420637\pi$
$241$	7.66119	0.493500	0.246750	+	0.969079i	$0.420637\pi$
$242$	27.5962	1.77395
$243$	−15.8959	−1.01972
$244$	15.7868	1.01065
$245$	−2.02710	−0.129507
$246$	8.50168	0.542047
$247$	32.3104	2.05586
$248$	−71.4625	−4.53787
$249$	2.01656	0.127794
$250$	2.79540	0.176797
$251$	−0.878788	−0.0554686	−0.0277343	−	0.999615i	$-0.508829\pi$
$251$	−0.878788	−0.0554686	−0.0277343	+	0.999615i	$0.508829\pi$
$252$	−34.1368	−2.15042
$253$	−5.20684	−0.327351
$254$	48.9617	3.07213
$255$	1.96474	0.123037
$256$	103.036	6.43973
$257$	2.15466	0.134404	0.0672021	−	0.997739i	$-0.478593\pi$
$257$	2.15466	0.134404	0.0672021	+	0.997739i	$0.478593\pi$
$258$	−25.4025	−1.58149
$259$	−27.8154	−1.72837
$260$	−28.4027	−1.76146
$261$	17.0582	1.05587
$262$	−11.7744	−0.727427
$263$	4.51877	0.278639	0.139320	−	0.990247i	$-0.455508\pi$
$263$	4.51877	0.278639	0.139320	+	0.990247i	$0.455508\pi$
$264$	−11.5811	−0.712765
$265$	−1.78842	−0.109862
$266$	−55.5517	−3.40609
$267$	−13.5191	−0.827357
$268$	−53.7564	−3.28369
$269$	−11.8146	−0.720350	−0.360175	−	0.932885i	$-0.617283\pi$
$269$	−11.8146	−0.720350	−0.360175	+	0.932885i	$0.617283\pi$
$270$	14.1628	0.861922
$271$	23.8026	1.44590	0.722951	−	0.690899i	$-0.242785\pi$
$271$	23.8026	1.44590	0.722951	+	0.690899i	$0.242785\pi$
$272$	34.9216	2.11743
$273$	−15.0099	−0.908438
$274$	−20.8643	−1.26046
$275$	−1.06207	−0.0640455
$276$	−29.1510	−1.75468
$277$	6.86866	0.412698	0.206349	−	0.978478i	$-0.433842\pi$
$277$	6.86866	0.412698	0.206349	+	0.978478i	$0.433842\pi$
$278$	19.9045	1.19379
$279$	−13.0972	−0.784106
$280$	32.0354	1.91448
$281$	12.4974	0.745533	0.372767	−	0.927925i	$-0.378409\pi$
$281$	12.4974	0.745533	0.372767	+	0.927925i	$0.378409\pi$
$282$	−34.4717	−2.05276
$283$	−5.42187	−0.322297	−0.161149	−	0.986930i	$-0.551520\pi$
$283$	−5.42187	−0.322297	−0.161149	+	0.986930i	$0.551520\pi$
$284$	21.0935	1.25167
$285$	6.76421	0.400677
$286$	14.5032	0.857591
$287$	8.93504	0.527419
$288$	57.6229	3.39546
$289$	−13.3091	−0.782887
$290$	−24.4018	−1.43292
$291$	10.3531	0.606908
$292$	−88.9356	−5.20457
$293$	0.983571	0.0574608	0.0287304	−	0.999587i	$-0.490854\pi$
$293$	0.983571	0.0574608	0.0287304	+	0.999587i	$0.490854\pi$
$294$	5.79506	0.337975
$295$	4.41573	0.257094
$296$	98.7112	5.73747
$297$	−5.38097	−0.312236
$298$	2.42209	0.140308
$299$	23.9488	1.38500
$300$	−5.94611	−0.343299
$301$	−26.6973	−1.53881
$302$	54.6760	3.14625
$303$	16.1484	0.927701
$304$	120.228	6.89554
$305$	−2.71518	−0.155471
$306$	10.4946	0.599936
$307$	6.75293	0.385410	0.192705	−	0.981257i	$-0.438274\pi$
$307$	6.75293	0.385410	0.192705	+	0.981257i	$0.438274\pi$
$308$	−18.5534	−1.05718
$309$	−5.66486	−0.322262
$310$	18.7356	1.06411
$311$	−22.5750	−1.28011	−0.640057	−	0.768328i	$-0.721089\pi$
$311$	−22.5750	−1.28011	−0.640057	+	0.768328i	$0.721089\pi$
$312$	53.2669	3.01565
$313$	28.7878	1.62718	0.813590	−	0.581438i	$-0.197510\pi$
$313$	28.7878	1.62718	0.813590	+	0.581438i	$0.197510\pi$
$314$	−33.7446	−1.90432
$315$	5.87122	0.330806
$316$	−31.4765	−1.77069
$317$	4.41079	0.247735	0.123867	−	0.992299i	$-0.460470\pi$
$317$	4.41079	0.247735	0.123867	+	0.992299i	$0.460470\pi$
$318$	5.11273	0.286707
$319$	9.27113	0.519084
$320$	−46.0755	−2.57570
$321$	13.1688	0.735008
$322$	−41.1754	−2.29462
$323$	12.7071	0.707041
$324$	3.95973	0.219985
$325$	4.88500	0.270971
$326$	68.8804	3.81493
$327$	−16.7179	−0.924500
$328$	−31.7086	−1.75082
$329$	−36.2288	−1.99736
$330$	3.03625	0.167140
$331$	−4.90141	−0.269406	−0.134703	−	0.990886i	$-0.543008\pi$
$331$	−4.90141	−0.269406	−0.134703	+	0.990886i	$0.543008\pi$
$332$	−11.4648	−0.629215
$333$	18.0911	0.991387
$334$	−54.6700	−2.99141
$335$	9.24560	0.505141
$336$	−55.8520	−3.04698
$337$	−13.7626	−0.749699	−0.374850	−	0.927086i	$-0.622306\pi$
$337$	−13.7626	−0.749699	−0.374850	+	0.927086i	$0.622306\pi$
$338$	−30.3670	−1.65175
$339$	−5.34677	−0.290397
$340$	−11.1702	−0.605791
$341$	−7.11832	−0.385479
$342$	36.1308	1.95373
$343$	−14.9411	−0.806746
$344$	94.7434	5.10822
$345$	5.01369	0.269928
$346$	−11.9800	−0.644051
$347$	23.1918	1.24500	0.622500	−	0.782620i	$-0.286117\pi$
$347$	23.1918	1.24500	0.622500	+	0.782620i	$0.286117\pi$
$348$	51.9052	2.78241
$349$	−9.59248	−0.513474	−0.256737	−	0.966481i	$-0.582647\pi$
$349$	−9.59248	−0.513474	−0.256737	+	0.966481i	$0.582647\pi$
$350$	−8.39882	−0.448936
$351$	24.7497	1.32104
$352$	31.3181	1.66926
$353$	0.368461	0.0196112	0.00980560	−	0.999952i	$-0.496879\pi$
$353$	0.368461	0.0196112	0.00980560	+	0.999952i	$0.496879\pi$
$354$	−12.6236	−0.670939
$355$	−3.62788	−0.192548
$356$	76.8609	4.07362
$357$	−5.90309	−0.312425
$358$	−26.0328	−1.37587
$359$	4.05598	0.214067	0.107033	−	0.994255i	$-0.465865\pi$
$359$	4.05598	0.214067	0.107033	+	0.994255i	$0.465865\pi$
$360$	−20.8358	−1.09814
$361$	24.7479	1.30252
$362$	15.5965	0.819735
$363$	10.0959	0.529895
$364$	85.3362	4.47283
$365$	15.2961	0.800635
$366$	7.76214	0.405734
$367$	−35.3278	−1.84410	−0.922049	−	0.387074i	$-0.873486\pi$
$367$	−35.3278	−1.84410	−0.922049	+	0.387074i	$0.873486\pi$
$368$	89.1140	4.64539
$369$	−5.81134	−0.302526
$370$	−25.8795	−1.34541
$371$	5.37334	0.278970
$372$	−39.8525	−2.06626
$373$	−7.84604	−0.406253	−0.203126	−	0.979153i	$-0.565110\pi$
$373$	−7.84604	−0.406253	−0.203126	+	0.979153i	$0.565110\pi$
$374$	5.70383	0.294938
$375$	1.02268	0.0528108
$376$	128.569	6.63043
$377$	−42.6425	−2.19620
$378$	−42.5524	−2.18866
$379$	−1.05879	−0.0543864	−0.0271932	−	0.999630i	$-0.508657\pi$
$379$	−1.05879	−0.0543864	−0.0271932	+	0.999630i	$0.508657\pi$
$380$	−38.4569	−1.97279
$381$	17.9123	0.917674
$382$	−47.7257	−2.44186
$383$	−33.8744	−1.73090	−0.865450	−	0.500995i	$-0.832968\pi$
$383$	−33.8744	−1.73090	−0.865450	+	0.500995i	$0.832968\pi$
$384$	71.4076	3.64400
$385$	3.19102	0.162629
$386$	−20.5155	−1.04421
$387$	17.3639	0.882658
$388$	−58.8608	−2.98820
$389$	−17.1641	−0.870253	−0.435126	−	0.900369i	$-0.643296\pi$
$389$	−17.1641	−0.870253	−0.435126	+	0.900369i	$0.643296\pi$
$390$	−13.9652	−0.707154
$391$	9.41862	0.476320
$392$	−21.6138	−1.09166
$393$	−4.30758	−0.217289
$394$	53.2848	2.68445
$395$	5.41366	0.272391
$396$	12.0671	0.606396
$397$	−29.9604	−1.50367	−0.751834	−	0.659353i	$-0.770830\pi$
$397$	−29.9604	−1.50367	−0.751834	+	0.659353i	$0.770830\pi$
$398$	41.9985	2.10520
$399$	−20.3232	−1.01743
$400$	18.1772	0.908859
$401$	8.29910	0.414438	0.207219	−	0.978295i	$-0.433559\pi$
$401$	8.29910	0.414438	0.207219	+	0.978295i	$0.433559\pi$
$402$	−26.4312	−1.31827
$403$	32.7406	1.63093
$404$	−91.8092	−4.56768
$405$	−0.681036	−0.0338410
$406$	73.3156	3.63859
$407$	9.83254	0.487381
$408$	20.9489	1.03712
$409$	12.7878	0.632316	0.316158	−	0.948707i	$-0.397607\pi$
$409$	12.7878	0.632316	0.316158	+	0.948707i	$0.397607\pi$
$410$	8.31317	0.410558
$411$	−7.63304	−0.376510
$412$	32.2067	1.58671
$413$	−13.2671	−0.652832
$414$	26.7805	1.31619
$415$	1.97185	0.0967942
$416$	−144.047	−7.06249
$417$	7.28189	0.356596
$418$	19.6371	0.960482
$419$	34.6397	1.69226	0.846129	−	0.532978i	$-0.178927\pi$
$419$	34.6397	1.69226	0.846129	+	0.532978i	$0.178927\pi$
$420$	17.8652	0.871732
$421$	16.0586	0.782647	0.391323	−	0.920253i	$-0.372017\pi$
$421$	16.0586	0.782647	0.391323	+	0.920253i	$0.372017\pi$
$422$	46.0644	2.24238
$423$	23.5632	1.14568
$424$	−19.0689	−0.926067
$425$	1.92118	0.0931908
$426$	10.3714	0.502494
$427$	8.15781	0.394784
$428$	−74.8689	−3.61892
$429$	5.30588	0.256170
$430$	−24.8392	−1.19785
$431$	−33.0614	−1.59251	−0.796257	−	0.604959i	$-0.793190\pi$
$431$	−33.0614	−1.59251	−0.796257	+	0.604959i	$0.793190\pi$
$432$	92.0942	4.43088
$433$	−8.35997	−0.401754	−0.200877	−	0.979616i	$-0.564379\pi$
$433$	−8.35997	−0.401754	−0.200877	+	0.979616i	$0.564379\pi$
$434$	−56.2913	−2.70207
$435$	−8.92722	−0.428027
$436$	95.0469	4.55192
$437$	32.4264	1.55116
$438$	−43.7284	−2.08942
$439$	41.6356	1.98716	0.993580	−	0.113136i	$-0.0360895\pi$
$439$	41.6356	1.98716	0.993580	+	0.113136i	$0.0360895\pi$
$440$	−11.3243	−0.539863
$441$	−3.96123	−0.188630
$442$	−26.2347	−1.24786
$443$	−1.68958	−0.0802742	−0.0401371	−	0.999194i	$-0.512779\pi$
$443$	−1.68958	−0.0802742	−0.0401371	+	0.999194i	$0.512779\pi$
$444$	55.0484	2.61248
$445$	−13.2194	−0.626657
$446$	42.6097	2.01763
$447$	0.886105	0.0419113
$448$	138.435	6.54042
$449$	−4.91539	−0.231971	−0.115986	−	0.993251i	$-0.537003\pi$
$449$	−4.91539	−0.231971	−0.115986	+	0.993251i	$0.537003\pi$
$450$	5.46259	0.257509
$451$	−3.15847	−0.148727
$452$	30.3982	1.42981
$453$	20.0028	0.939814
$454$	52.1564	2.44782
$455$	−14.6770	−0.688070
$456$	72.1227	3.37746
$457$	19.8570	0.928871	0.464436	−	0.885607i	$-0.346257\pi$
$457$	19.8570	0.928871	0.464436	+	0.885607i	$0.346257\pi$
$458$	8.59739	0.401730
$459$	9.73360	0.454325
$460$	−28.5046	−1.32903
$461$	−13.4510	−0.626476	−0.313238	−	0.949675i	$-0.601414\pi$
$461$	−13.4510	−0.626476	−0.313238	+	0.949675i	$0.601414\pi$
$462$	−9.12244	−0.424415
$463$	8.34639	0.387890	0.193945	−	0.981012i	$-0.437872\pi$
$463$	8.34639	0.387890	0.193945	+	0.981012i	$0.437872\pi$
$464$	−158.674	−7.36623
$465$	6.85427	0.317859
$466$	−24.9571	−1.15612
$467$	9.23198	0.427205	0.213603	−	0.976921i	$-0.431480\pi$
$467$	9.23198	0.427205	0.213603	+	0.976921i	$0.431480\pi$
$468$	−55.5026	−2.56561
$469$	−27.7785	−1.28269
$470$	−33.7073	−1.55480
$471$	−12.3452	−0.568836
$472$	47.0823	2.16714
$473$	9.43731	0.433928
$474$	−15.4765	−0.710860
$475$	6.61422	0.303481
$476$	33.5611	1.53827
$477$	−3.49482	−0.160017
$478$	−70.5913	−3.22877
$479$	−38.6092	−1.76410	−0.882049	−	0.471157i	$-0.843836\pi$
$479$	−38.6092	−1.76410	−0.882049	+	0.471157i	$0.843836\pi$
$480$	−30.1563	−1.37644
$481$	−45.2247	−2.06207
$482$	−21.4161	−0.975476
$483$	−15.0637	−0.685423
$484$	−57.3984	−2.60902
$485$	10.1235	0.459685
$486$	44.4354	2.01563
$487$	38.0422	1.72386	0.861928	−	0.507031i	$-0.169257\pi$
$487$	38.0422	1.72386	0.861928	+	0.507031i	$0.169257\pi$
$488$	−28.9504	−1.31052
$489$	25.1994	1.13955
$490$	5.66656	0.255989
$491$	12.4565	0.562154	0.281077	−	0.959685i	$-0.409308\pi$
$491$	12.4565	0.562154	0.281077	+	0.959685i	$0.409308\pi$
$492$	−17.6830	−0.797210
$493$	−16.7705	−0.755304
$494$	−90.3207	−4.06372
$495$	−2.07543	−0.0932838
$496$	121.829	5.47027
$497$	10.9000	0.488933
$498$	−5.63710	−0.252604
$499$	−21.0623	−0.942878	−0.471439	−	0.881899i	$-0.656265\pi$
$499$	−21.0623	−0.942878	−0.471439	+	0.881899i	$0.656265\pi$
$500$	−5.81427	−0.260022
$501$	−20.0006	−0.893561
$502$	2.45656	0.109642
$503$	9.29547	0.414465	0.207232	−	0.978292i	$-0.433554\pi$
$503$	9.29547	0.414465	0.207232	+	0.978292i	$0.433554\pi$
$504$	62.6013	2.78849
$505$	15.7903	0.702660
$506$	14.5552	0.647058
$507$	−11.1095	−0.493391
$508$	−101.837	−4.51831
$509$	−2.79761	−0.124002	−0.0620010	−	0.998076i	$-0.519748\pi$
$509$	−2.79761	−0.124002	−0.0620010	+	0.998076i	$0.519748\pi$
$510$	−5.49224	−0.243201
$511$	−45.9574	−2.03303
$512$	−148.378	−6.55743
$513$	33.5108	1.47954
$514$	−6.02315	−0.265670
$515$	−5.53925	−0.244088
$516$	52.8356	2.32596
$517$	12.8066	0.563235
$518$	77.7552	3.41637
$519$	−4.38280	−0.192384
$520$	52.0858	2.28411
$521$	−7.87793	−0.345139	−0.172569	−	0.984997i	$-0.555207\pi$
$521$	−7.87793	−0.345139	−0.172569	+	0.984997i	$0.555207\pi$
$522$	−47.6844	−2.08709
$523$	−21.8253	−0.954352	−0.477176	−	0.878808i	$-0.658340\pi$
$523$	−21.8253	−0.954352	−0.477176	+	0.878808i	$0.658340\pi$
$524$	24.4901	1.06986
$525$	−3.07264	−0.134101
$526$	−12.6318	−0.550771
$527$	12.8763	0.560899
$528$	19.7433	0.859216
$529$	1.03473	0.0449884
$530$	4.99936	0.217158
$531$	8.62892	0.374463
$532$	115.544	5.00947
$533$	14.5274	0.629250
$534$	37.7914	1.63539
$535$	12.8768	0.556711
$536$	98.5803	4.25802
$537$	−9.52389	−0.410986
$538$	33.0266	1.42388
$539$	−2.15293	−0.0927334
$540$	−29.4578	−1.26766
$541$	0.372994	0.0160363	0.00801814	−	0.999968i	$-0.497448\pi$
$541$	0.372994	0.0160363	0.00801814	+	0.999968i	$0.497448\pi$
$542$	−66.5377	−2.85804
$543$	5.70587	0.244862
$544$	−56.6511	−2.42889
$545$	−16.3472	−0.700236
$546$	41.9586	1.79566
$547$	−15.2115	−0.650395	−0.325198	−	0.945646i	$-0.605431\pi$
$547$	−15.2115	−0.650395	−0.325198	+	0.945646i	$0.605431\pi$
$548$	43.3965	1.85380
$549$	−5.30583	−0.226447
$550$	2.96892	0.126595
$551$	−57.7373	−2.45969
$552$	53.4581	2.27533
$553$	−16.2654	−0.691676
$554$	−19.2007	−0.815758
$555$	−9.46781	−0.401886
$556$	−41.4001	−1.75575
$557$	26.5741	1.12598	0.562991	−	0.826463i	$-0.309651\pi$
$557$	26.5741	1.12598	0.562991	+	0.826463i	$0.309651\pi$
$558$	36.6118	1.54990
$559$	−43.4068	−1.83591
$560$	−54.6136	−2.30784
$561$	2.08670	0.0881006
$562$	−34.9353	−1.47366
$563$	−25.6130	−1.07946	−0.539729	−	0.841839i	$-0.681473\pi$
$563$	−25.6130	−1.07946	−0.539729	+	0.841839i	$0.681473\pi$
$564$	71.6990	3.01907
$565$	−5.22821	−0.219953
$566$	15.1563	0.637067
$567$	2.04618	0.0859316
$568$	−38.6820	−1.62306
$569$	−29.2870	−1.22778	−0.613888	−	0.789393i	$-0.710395\pi$
$569$	−29.2870	−1.22778	−0.613888	+	0.789393i	$0.710395\pi$
$570$	−18.9087	−0.791997
$571$	15.5931	0.652551	0.326276	−	0.945275i	$-0.394206\pi$
$571$	15.5931	0.652551	0.326276	+	0.945275i	$0.394206\pi$
$572$	−30.1657	−1.26129
$573$	−17.4601	−0.729405
$574$	−24.9770	−1.04252
$575$	4.90252	0.204449
$576$	−90.0377	−3.75157
$577$	−32.9270	−1.37077	−0.685384	−	0.728181i	$-0.740366\pi$
$577$	−32.9270	−1.37077	−0.685384	+	0.728181i	$0.740366\pi$
$578$	37.2042	1.54749
$579$	−7.50543	−0.311915
$580$	50.7543	2.10746
$581$	−5.92444	−0.245787
$582$	−28.9410	−1.19964
$583$	−1.89944	−0.0786666
$584$	163.093	6.74885
$585$	9.54593	0.394676
$586$	−2.74947	−0.113580
$587$	25.9933	1.07286	0.536428	−	0.843946i	$-0.319773\pi$
$587$	25.9933	1.07286	0.536428	+	0.843946i	$0.319773\pi$
$588$	−12.0534	−0.497073
$589$	44.3304	1.82660
$590$	−12.3437	−0.508183
$591$	19.4938	0.801870
$592$	−168.282	−6.91635
$593$	40.6704	1.67013	0.835066	−	0.550150i	$-0.185430\pi$
$593$	40.6704	1.67013	0.835066	+	0.550150i	$0.185430\pi$
$594$	15.0420	0.617179
$595$	−5.77220	−0.236637
$596$	−5.03781	−0.206357
$597$	15.3648	0.628841
$598$	−66.9465	−2.73765
$599$	0.951188	0.0388645	0.0194322	−	0.999811i	$-0.493814\pi$
$599$	0.951188	0.0388645	0.0194322	+	0.999811i	$0.493814\pi$
$600$	10.9042	0.445162
$601$	−38.0503	−1.55210	−0.776052	−	0.630668i	$-0.782781\pi$
$601$	−38.0503	−1.55210	−0.776052	+	0.630668i	$0.782781\pi$
$602$	74.6297	3.04168
$603$	18.0671	0.735750
$604$	−113.723	−4.62732
$605$	9.87200	0.401354
$606$	−45.1412	−1.83374
$607$	5.39535	0.218990	0.109495	−	0.993987i	$-0.465077\pi$
$607$	5.39535	0.218990	0.109495	+	0.993987i	$0.465077\pi$
$608$	−195.038	−7.90984
$609$	26.8220	1.08688
$610$	7.59003	0.307311
$611$	−58.9039	−2.38300
$612$	−21.8281	−0.882350
$613$	−4.62555	−0.186824	−0.0934120	−	0.995628i	$-0.529777\pi$
$613$	−4.62555	−0.186824	−0.0934120	+	0.995628i	$0.529777\pi$
$614$	−18.8771	−0.761819
$615$	3.04131	0.122637
$616$	34.0239	1.37086
$617$	−19.0244	−0.765895	−0.382948	−	0.923770i	$-0.625091\pi$
$617$	−19.0244	−0.765895	−0.382948	+	0.923770i	$0.625091\pi$
$618$	15.8355	0.636999
$619$	21.4336	0.861487	0.430744	−	0.902474i	$-0.358251\pi$
$619$	21.4336	0.861487	0.430744	+	0.902474i	$0.358251\pi$
$620$	−38.9689	−1.56503
$621$	24.8385	0.996735
$622$	63.1063	2.53033
$623$	39.7177	1.59126
$624$	−90.8090	−3.63527
$625$	1.00000	0.0400000
$626$	−80.4734	−3.21636
$627$	7.18409	0.286905
$628$	70.1867	2.80075
$629$	−17.7860	−0.709175
$630$	−16.4124	−0.653886
$631$	20.9696	0.834786	0.417393	−	0.908726i	$-0.362944\pi$
$631$	20.9696	0.834786	0.417393	+	0.908726i	$0.362944\pi$
$632$	57.7227	2.29608
$633$	16.8523	0.669820
$634$	−12.3299	−0.489684
$635$	17.5151	0.695065
$636$	−10.6342	−0.421672
$637$	9.90239	0.392347
$638$	−25.9165	−1.02605
$639$	−7.08937	−0.280451
$640$	69.8243	2.76005
$641$	−42.7516	−1.68859	−0.844294	−	0.535881i	$-0.819980\pi$
$641$	−42.7516	−1.68859	−0.844294	+	0.535881i	$0.819980\pi$
$642$	−36.8119	−1.45285
$643$	34.2235	1.34964	0.674821	−	0.737982i	$-0.264221\pi$
$643$	34.2235	1.34964	0.674821	+	0.737982i	$0.264221\pi$
$644$	85.6424	3.37478
$645$	−9.08723	−0.357810
$646$	−35.5214	−1.39757
$647$	−23.9033	−0.939735	−0.469867	−	0.882737i	$-0.655698\pi$
$647$	−23.9033	−0.939735	−0.469867	+	0.882737i	$0.655698\pi$
$648$	−7.26149	−0.285258
$649$	4.68983	0.184092
$650$	−13.6555	−0.535614
$651$	−20.5937	−0.807132
$652$	−143.267	−5.61077
$653$	23.4326	0.916987	0.458493	−	0.888698i	$-0.348389\pi$
$653$	23.4326	0.916987	0.458493	+	0.888698i	$0.348389\pi$
$654$	46.7331	1.82741
$655$	−4.21207	−0.164579
$656$	54.0566	2.11056
$657$	29.8906	1.16614
$658$	101.274	3.94807
$659$	30.7808	1.19905	0.599525	−	0.800356i	$-0.295356\pi$
$659$	30.7808	1.19905	0.599525	+	0.800356i	$0.295356\pi$
$660$	−6.31521	−0.245819
$661$	−29.7915	−1.15875	−0.579377	−	0.815060i	$-0.696704\pi$
$661$	−29.7915	−1.15875	−0.579377	+	0.815060i	$0.696704\pi$
$662$	13.7014	0.532521
$663$	−9.59776	−0.372746
$664$	21.0246	0.815914
$665$	−19.8725	−0.770623
$666$	−50.5719	−1.95962
$667$	−42.7955	−1.65705
$668$	113.710	4.39959
$669$	15.5884	0.602684
$670$	−25.8452	−0.998485
$671$	−2.88373	−0.111325
$672$	90.6052	3.49517
$673$	−24.9203	−0.960608	−0.480304	−	0.877102i	$-0.659474\pi$
$673$	−24.9203	−0.960608	−0.480304	+	0.877102i	$0.659474\pi$
$674$	38.4721	1.48189
$675$	5.06647	0.195009
$676$	63.1615	2.42929
$677$	9.85158	0.378627	0.189314	−	0.981917i	$-0.439374\pi$
$677$	9.85158	0.378627	0.189314	+	0.981917i	$0.439374\pi$
$678$	14.9464	0.574012
$679$	−30.4162	−1.16727
$680$	20.4844	0.785540
$681$	19.0810	0.731187
$682$	19.8986	0.761955
$683$	2.20482	0.0843651	0.0421825	−	0.999110i	$-0.486569\pi$
$683$	2.20482	0.0843651	0.0421825	+	0.999110i	$0.486569\pi$
$684$	−75.1498	−2.87342
$685$	−7.46379	−0.285177
$686$	41.7665	1.59465
$687$	3.14529	0.120000
$688$	−161.518	−6.15780
$689$	8.73644	0.332832
$690$	−14.0153	−0.533553
$691$	−23.4700	−0.892842	−0.446421	−	0.894823i	$-0.647302\pi$
$691$	−23.4700	−0.892842	−0.446421	+	0.894823i	$0.647302\pi$
$692$	24.9178	0.947231
$693$	6.23567	0.236873
$694$	−64.8303	−2.46093
$695$	7.12043	0.270093
$696$	−95.1857	−3.60800
$697$	5.71334	0.216408
$698$	26.8148	1.01496
$699$	−9.13038	−0.345343
$700$	17.4690	0.660268
$701$	31.2122	1.17887	0.589434	−	0.807817i	$-0.299351\pi$
$701$	31.2122	1.17887	0.589434	+	0.807817i	$0.299351\pi$
$702$	−69.1854	−2.61123
$703$	−61.2336	−2.30947
$704$	−48.9356	−1.84433
$705$	−12.3316	−0.464434
$706$	−1.03000	−0.0387644
$707$	−47.4423	−1.78425
$708$	26.2564	0.986777
$709$	22.0949	0.829790	0.414895	−	0.909869i	$-0.363818\pi$
$709$	22.0949	0.829790	0.414895	+	0.909869i	$0.363818\pi$
$710$	10.1414	0.380600
$711$	10.5790	0.396744
$712$	−140.950	−5.28233
$713$	32.8581	1.23055
$714$	16.5015	0.617554
$715$	5.18823	0.194029
$716$	54.1466	2.02355
$717$	−25.8253	−0.964463
$718$	−11.3381	−0.423134
$719$	9.71027	0.362132	0.181066	−	0.983471i	$-0.442045\pi$
$719$	9.71027	0.362132	0.181066	+	0.983471i	$0.442045\pi$
$720$	35.5206	1.32378
$721$	16.6427	0.619808
$722$	−69.1804	−2.57463
$723$	−7.83491	−0.291384
$724$	−32.4398	−1.20562
$725$	−8.72927	−0.324197
$726$	−28.2220	−1.04742
$727$	−28.3868	−1.05281	−0.526404	−	0.850235i	$-0.676460\pi$
$727$	−28.3868	−1.05281	−0.526404	+	0.850235i	$0.676460\pi$
$728$	−156.493	−5.80000
$729$	14.2133	0.526417
$730$	−42.7587	−1.58257
$731$	−17.0711	−0.631397
$732$	−16.1448	−0.596729
$733$	9.35398	0.345497	0.172748	−	0.984966i	$-0.444735\pi$
$733$	9.35398	0.345497	0.172748	+	0.984966i	$0.444735\pi$
$734$	98.7554	3.64513
$735$	2.07307	0.0764663
$736$	−144.564	−5.32870
$737$	9.81951	0.361706
$738$	16.2450	0.597988
$739$	−6.68436	−0.245888	−0.122944	−	0.992414i	$-0.539234\pi$
$739$	−6.68436	−0.245888	−0.122944	+	0.992414i	$0.539234\pi$
$740$	53.8277	1.97875
$741$	−33.0431	−1.21387
$742$	−15.0206	−0.551425
$743$	13.8899	0.509572	0.254786	−	0.966997i	$-0.417995\pi$
$743$	13.8899	0.509572	0.254786	+	0.966997i	$0.417995\pi$
$744$	73.0830	2.67935
$745$	0.866457	0.0317445
$746$	21.9328	0.803018
$747$	3.85325	0.140983
$748$	−11.8636	−0.433777
$749$	−38.6884	−1.41364
$750$	−2.85879	−0.104388
$751$	19.7024	0.718952	0.359476	−	0.933154i	$-0.382955\pi$
$751$	19.7024	0.718952	0.359476	+	0.933154i	$0.382955\pi$
$752$	−219.183	−7.99277
$753$	0.898716	0.0327510
$754$	119.203	4.34111
$755$	19.5593	0.711835
$756$	88.5065	3.21895
$757$	−13.3591	−0.485545	−0.242773	−	0.970083i	$-0.578057\pi$
$757$	−13.3591	−0.485545	−0.242773	+	0.970083i	$0.578057\pi$
$758$	2.95975	0.107503
$759$	5.32491	0.193282
$760$	70.5235	2.55816
$761$	0.305294	0.0110669	0.00553345	−	0.999985i	$-0.498239\pi$
$761$	0.305294	0.0110669	0.00553345	+	0.999985i	$0.498239\pi$
$762$	−50.0720	−1.81392
$763$	49.1153	1.77809
$764$	99.2665	3.59134
$765$	3.75424	0.135735
$766$	94.6925	3.42138
$767$	−21.5708	−0.778877
$768$	−105.372	−3.80229
$769$	47.5679	1.71534	0.857671	−	0.514198i	$-0.171910\pi$
$769$	47.5679	1.71534	0.857671	+	0.514198i	$0.171910\pi$
$770$	−8.92017	−0.321461
$771$	−2.20352	−0.0793580
$772$	42.6710	1.53576
$773$	35.4152	1.27380	0.636898	−	0.770948i	$-0.280217\pi$
$773$	35.4152	1.27380	0.636898	+	0.770948i	$0.280217\pi$
$774$	−48.5391	−1.74470
$775$	6.70228	0.240753
$776$	107.941	3.87485
$777$	28.4462	1.02050
$778$	47.9805	1.72018
$779$	19.6698	0.704746
$780$	29.0467	1.04004
$781$	−3.85308	−0.137874
$782$	−26.3288	−0.941516
$783$	−44.2266	−1.58053
$784$	36.8470	1.31596
$785$	−12.0715	−0.430849
$786$	12.0414	0.429504
$787$	−1.78203	−0.0635226	−0.0317613	−	0.999495i	$-0.510112\pi$
$787$	−1.78203	−0.0635226	−0.0317613	+	0.999495i	$0.510112\pi$
$788$	−110.829	−3.94813
$789$	−4.62124	−0.164520
$790$	−15.1334	−0.538420
$791$	15.7082	0.558521
$792$	−22.1291	−0.786324
$793$	13.2637	0.471006
$794$	83.7512	2.97222
$795$	1.82898	0.0648671
$796$	−87.3545	−3.09620
$797$	24.7629	0.877145	0.438573	−	0.898696i	$-0.355484\pi$
$797$	24.7629	0.877145	0.438573	+	0.898696i	$0.355484\pi$
$798$	56.8114	2.01110
$799$	−23.1658	−0.819547
$800$	−29.4877	−1.04255
$801$	−25.8324	−0.912742
$802$	−23.1993	−0.819197
$803$	16.2456	0.573294
$804$	54.9754	1.93883
$805$	−14.7297	−0.519154
$806$	−91.5232	−3.22377
$807$	12.0825	0.425325
$808$	168.363	5.92299
$809$	0.670866	0.0235864	0.0117932	−	0.999930i	$-0.496246\pi$
$809$	0.670866	0.0235864	0.0117932	+	0.999930i	$0.496246\pi$
$810$	1.90377	0.0668917
$811$	13.1144	0.460510	0.230255	−	0.973130i	$-0.426044\pi$
$811$	13.1144	0.460510	0.230255	+	0.973130i	$0.426044\pi$
$812$	−152.492	−5.35142
$813$	−24.3423	−0.853722
$814$	−27.4859	−0.963380
$815$	24.6406	0.863123
$816$	−35.7135	−1.25022
$817$	−58.7722	−2.05618
$818$	−35.7470	−1.24986
$819$	−28.6809	−1.00219
$820$	−17.2909	−0.603824
$821$	−11.5223	−0.402132	−0.201066	−	0.979578i	$-0.564441\pi$
$821$	−11.5223	−0.402132	−0.201066	+	0.979578i	$0.564441\pi$
$822$	21.3374	0.744227
$823$	32.8063	1.14356	0.571778	−	0.820408i	$-0.306254\pi$
$823$	32.8063	1.14356	0.571778	+	0.820408i	$0.306254\pi$
$824$	−59.0617	−2.05751
$825$	1.08616	0.0378152
$826$	37.0869	1.29042
$827$	−6.20874	−0.215899	−0.107950	−	0.994156i	$-0.534428\pi$
$827$	−6.20874	−0.215899	−0.107950	+	0.994156i	$0.534428\pi$
$828$	−55.7018	−1.93577
$829$	−31.4770	−1.09324	−0.546620	−	0.837380i	$-0.684086\pi$
$829$	−31.4770	−1.09324	−0.546620	+	0.837380i	$0.684086\pi$
$830$	−5.51210	−0.191328
$831$	−7.02442	−0.243674
$832$	225.079	7.80320
$833$	3.89442	0.134934
$834$	−20.3558	−0.704864
$835$	−19.5571	−0.676802
$836$	−40.8440	−1.41262
$837$	33.9570	1.17372
$838$	−96.8317	−3.34500
$839$	−26.1837	−0.903961	−0.451981	−	0.892028i	$-0.649282\pi$
$839$	−26.1837	−0.903961	−0.451981	+	0.892028i	$0.649282\pi$
$840$	−32.7618	−1.13039
$841$	47.2002	1.62759
$842$	−44.8901	−1.54702
$843$	−12.7808	−0.440194
$844$	−95.8113	−3.29796
$845$	−10.8632	−0.373705
$846$	−65.8686	−2.26461
$847$	−29.6606	−1.01915
$848$	32.5085	1.11635
$849$	5.54482	0.190298
$850$	−5.37046	−0.184205
$851$	−45.3869	−1.55584
$852$	−21.5718	−0.739038
$853$	−16.8754	−0.577804	−0.288902	−	0.957359i	$-0.593290\pi$
$853$	−16.8754	−0.577804	−0.288902	+	0.957359i	$0.593290\pi$
$854$	−22.8043	−0.780349
$855$	12.9251	0.442028
$856$	137.297	4.69272
$857$	−42.8522	−1.46380	−0.731902	−	0.681409i	$-0.761367\pi$
$857$	−42.8522	−1.46380	−0.731902	+	0.681409i	$0.761367\pi$
$858$	−14.8321	−0.506358
$859$	52.5644	1.79347	0.896737	−	0.442565i	$-0.145931\pi$
$859$	52.5644	1.79347	0.896737	+	0.442565i	$0.145931\pi$
$860$	51.6641	1.76173
$861$	−9.13765	−0.311410
$862$	92.4200	3.14784
$863$	0.823465	0.0280311	0.0140155	−	0.999902i	$-0.495539\pi$
$863$	0.823465	0.0280311	0.0140155	+	0.999902i	$0.495539\pi$
$864$	−149.399	−5.08264
$865$	−4.28562	−0.145716
$866$	23.3695	0.794127
$867$	13.6109	0.462250
$868$	117.083	3.97404
$869$	5.74971	0.195045
$870$	24.9552	0.846059
$871$	−45.1647	−1.53035
$872$	−174.300	−5.90255
$873$	19.7827	0.669542
$874$	−90.6447	−3.06610
$875$	−3.00451	−0.101571
$876$	90.9524	3.07300
$877$	−53.3478	−1.80143	−0.900714	−	0.434414i	$-0.856956\pi$
$877$	−53.3478	−1.80143	−0.900714	+	0.434414i	$0.856956\pi$
$878$	−116.388	−3.92791
$879$	−1.00587	−0.0339273
$880$	19.3055	0.650788
$881$	−49.9175	−1.68176	−0.840882	−	0.541218i	$-0.817963\pi$
$881$	−49.9175	−1.68176	−0.840882	+	0.541218i	$0.817963\pi$
$882$	11.0732	0.372855
$883$	−54.6855	−1.84031	−0.920156	−	0.391552i	$-0.871938\pi$
$883$	−54.6855	−1.84031	−0.920156	+	0.391552i	$0.871938\pi$
$884$	54.5666	1.83527
$885$	−4.51586	−0.151799
$886$	4.72304	0.158674
$887$	−36.9054	−1.23916	−0.619580	−	0.784933i	$-0.712697\pi$
$887$	−36.9054	−1.23916	−0.619580	+	0.784933i	$0.712697\pi$
$888$	−100.950	−3.38765
$889$	−52.6243	−1.76496
$890$	36.9534	1.23868
$891$	−0.723311	−0.0242318
$892$	−88.6257	−2.96741
$893$	−79.7551	−2.66890
$894$	−2.47702	−0.0828439
$895$	−9.31271	−0.311290
$896$	−209.788	−7.00852
$897$	−24.4919	−0.817760
$898$	13.7405	0.458526
$899$	−58.5061	−1.95129
$900$	−11.3619	−0.378728
$901$	3.43588	0.114466
$902$	8.82920	0.293980
$903$	27.3027	0.908578
$904$	−55.7453	−1.85406
$905$	5.57935	0.185464
$906$	−55.9159	−1.85768
$907$	2.44474	0.0811762	0.0405881	−	0.999176i	$-0.487077\pi$
$907$	2.44474	0.0811762	0.0405881	+	0.999176i	$0.487077\pi$
$908$	−108.482	−3.60011
$909$	30.8564	1.02344
$910$	41.0282	1.36007
$911$	−18.8169	−0.623433	−0.311716	−	0.950175i	$-0.600904\pi$
$911$	−18.8169	−0.623433	−0.311716	+	0.950175i	$0.600904\pi$
$912$	−122.954	−4.07142
$913$	2.09425	0.0693095
$914$	−55.5083	−1.83605
$915$	2.77675	0.0917967
$916$	−17.8821	−0.590840
$917$	12.6552	0.417912
$918$	−27.2093	−0.898041
$919$	−21.9883	−0.725328	−0.362664	−	0.931920i	$-0.618133\pi$
$919$	−21.9883	−0.725328	−0.362664	+	0.931920i	$0.618133\pi$
$920$	52.2727	1.72338
$921$	−6.90606	−0.227562
$922$	37.6010	1.23832
$923$	17.7222	0.583333
$924$	18.9741	0.624203
$925$	−9.25787	−0.304397
$926$	−23.3315	−0.766721
$927$	−10.8244	−0.355521
$928$	257.406	8.44977
$929$	26.4583	0.868068	0.434034	−	0.900897i	$-0.357090\pi$
$929$	26.4583	0.868068	0.434034	+	0.900897i	$0.357090\pi$
$930$	−19.1604	−0.628295
$931$	13.4077	0.439420
$932$	51.9093	1.70035
$933$	23.0870	0.755833
$934$	−25.8071	−0.844434
$935$	2.04043	0.0667293
$936$	101.783	3.32687
$937$	8.72219	0.284941	0.142471	−	0.989799i	$-0.454495\pi$
$937$	8.72219	0.284941	0.142471	+	0.989799i	$0.454495\pi$
$938$	77.6521	2.53543
$939$	−29.4406	−0.960757
$940$	70.1092	2.28671
$941$	−58.5782	−1.90960	−0.954798	−	0.297256i	$-0.903929\pi$
$941$	−58.5782	−1.90960	−0.954798	+	0.297256i	$0.903929\pi$
$942$	34.5098	1.12439
$943$	14.5795	0.474773
$944$	−80.2655	−2.61242
$945$	−15.2223	−0.495181
$946$	−26.3811	−0.857723
$947$	−46.2362	−1.50247	−0.751237	−	0.660033i	$-0.770542\pi$
$947$	−46.2362	−1.50247	−0.751237	+	0.660033i	$0.770542\pi$
$948$	32.1902	1.04549
$949$	−74.7214	−2.42556
$950$	−18.4894	−0.599875
$951$	−4.51081	−0.146273
$952$	−61.5456	−1.99470
$953$	54.3484	1.76052	0.880258	−	0.474495i	$-0.157369\pi$
$953$	54.3484	1.76052	0.880258	+	0.474495i	$0.157369\pi$
$954$	9.76941	0.316296
$955$	−17.0729	−0.552467
$956$	146.826	4.74868
$957$	−9.48137	−0.306489
$958$	107.928	3.48700
$959$	22.4250	0.724143
$960$	47.1204	1.52080
$961$	13.9206	0.449052
$962$	126.421	4.07598
$963$	25.1629	0.810863
$964$	44.5442	1.43467
$965$	−7.33901	−0.236251
$966$	42.1091	1.35484
$967$	50.2427	1.61570	0.807848	−	0.589391i	$-0.200632\pi$
$967$	50.2427	1.61570	0.807848	+	0.589391i	$0.200632\pi$
$968$	105.259	3.38316
$969$	−12.9952	−0.417467
$970$	−28.2993	−0.908634
$971$	−19.4159	−0.623086	−0.311543	−	0.950232i	$-0.600846\pi$
$971$	−19.4159	−0.623086	−0.311543	+	0.950232i	$0.600846\pi$
$972$	−92.4230	−2.96447
$973$	−21.3934	−0.685842
$974$	−106.343	−3.40745
$975$	−4.99577	−0.159993
$976$	49.3544	1.57979
$977$	−37.9595	−1.21443	−0.607216	−	0.794537i	$-0.707714\pi$
$977$	−37.9595	−1.21443	−0.607216	+	0.794537i	$0.707714\pi$
$978$	−70.4423	−2.25250
$979$	−14.0399	−0.448718
$980$	−11.7861	−0.376494
$981$	−31.9446	−1.01991
$982$	−34.8209	−1.11118
$983$	−30.4960	−0.972672	−0.486336	−	0.873772i	$-0.661667\pi$
$983$	−30.4960	−0.972672	−0.486336	+	0.873772i	$0.661667\pi$
$984$	32.4277	1.03376
$985$	19.0616	0.607353
$986$	46.8802	1.49297
$987$	37.0504	1.17933
$988$	187.862	5.97667
$989$	−43.5625	−1.38521
$990$	5.80167	0.184389
$991$	10.4271	0.331228	0.165614	−	0.986191i	$-0.447039\pi$
$991$	10.4271	0.331228	0.165614	+	0.986191i	$0.447039\pi$
$992$	−197.635	−6.27491
$993$	5.01256	0.159069
$994$	−30.4700	−0.966448
$995$	15.0242	0.476298
$996$	11.7248	0.371515
$997$	4.32383	0.136937	0.0684685	−	0.997653i	$-0.478189\pi$
$997$	4.32383	0.136937	0.0684685	+	0.997653i	$0.478189\pi$
$998$	58.8776	1.86374
$999$	−46.9048	−1.48400

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.2	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.2	✓	140	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79540 q^{2} -1.02268 q^{3} +5.81427 q^{4} -1.00000 q^{5} +2.85879 q^{6} +3.00451 q^{7} -10.6624 q^{8} -1.95413 q^{9} +O(q^{10})\)	\(q-2.79540 q^{2} -1.02268 q^{3} +5.81427 q^{4} -1.00000 q^{5} +2.85879 q^{6} +3.00451 q^{7} -10.6624 q^{8} -1.95413 q^{9} +2.79540 q^{10} -1.06207 q^{11} -5.94611 q^{12} +4.88500 q^{13} -8.39882 q^{14} +1.02268 q^{15} +18.1772 q^{16} +1.92118 q^{17} +5.46259 q^{18} +6.61422 q^{19} -5.81427 q^{20} -3.07264 q^{21} +2.96892 q^{22} +4.90252 q^{23} +10.9042 q^{24} +1.00000 q^{25} -13.6555 q^{26} +5.06647 q^{27} +17.4690 q^{28} -8.72927 q^{29} -2.85879 q^{30} +6.70228 q^{31} -29.4877 q^{32} +1.08616 q^{33} -5.37046 q^{34} -3.00451 q^{35} -11.3619 q^{36} -9.25787 q^{37} -18.4894 q^{38} -4.99577 q^{39} +10.6624 q^{40} +2.97387 q^{41} +8.58927 q^{42} -8.88574 q^{43} -6.17518 q^{44} +1.95413 q^{45} -13.7045 q^{46} -12.0581 q^{47} -18.5894 q^{48} +2.02710 q^{49} -2.79540 q^{50} -1.96474 q^{51} +28.4027 q^{52} +1.78842 q^{53} -14.1628 q^{54} +1.06207 q^{55} -32.0354 q^{56} -6.76421 q^{57} +24.4018 q^{58} -4.41573 q^{59} +5.94611 q^{60} +2.71518 q^{61} -18.7356 q^{62} -5.87122 q^{63} +46.0755 q^{64} -4.88500 q^{65} -3.03625 q^{66} -9.24560 q^{67} +11.1702 q^{68} -5.01369 q^{69} +8.39882 q^{70} +3.62788 q^{71} +20.8358 q^{72} -15.2961 q^{73} +25.8795 q^{74} -1.02268 q^{75} +38.4569 q^{76} -3.19102 q^{77} +13.9652 q^{78} -5.41366 q^{79} -18.1772 q^{80} +0.681036 q^{81} -8.31317 q^{82} -1.97185 q^{83} -17.8652 q^{84} -1.92118 q^{85} +24.8392 q^{86} +8.92722 q^{87} +11.3243 q^{88} +13.2194 q^{89} -5.46259 q^{90} +14.6770 q^{91} +28.5046 q^{92} -6.85427 q^{93} +33.7073 q^{94} -6.61422 q^{95} +30.1563 q^{96} -10.1235 q^{97} -5.66656 q^{98} +2.07543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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