LMFDB - Embedded newform 4015.2.a.h.1.5

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:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.14348 q^{2} +2.01146 q^{3} +2.59449 q^{4} +1.00000 q^{5} -4.31152 q^{6} -3.47503 q^{7} -1.27427 q^{8} +1.04598 q^{9} +O(q^{10})$	\(q-2.14348 q^{2} +2.01146 q^{3} +2.59449 q^{4} +1.00000 q^{5} -4.31152 q^{6} -3.47503 q^{7} -1.27427 q^{8} +1.04598 q^{9} -2.14348 q^{10} +1.00000 q^{11} +5.21871 q^{12} +6.08523 q^{13} +7.44863 q^{14} +2.01146 q^{15} -2.45761 q^{16} -0.860759 q^{17} -2.24204 q^{18} +5.32833 q^{19} +2.59449 q^{20} -6.98989 q^{21} -2.14348 q^{22} +5.95868 q^{23} -2.56314 q^{24} +1.00000 q^{25} -13.0435 q^{26} -3.93043 q^{27} -9.01591 q^{28} +5.45897 q^{29} -4.31152 q^{30} -4.31699 q^{31} +7.81637 q^{32} +2.01146 q^{33} +1.84501 q^{34} -3.47503 q^{35} +2.71379 q^{36} +6.22550 q^{37} -11.4211 q^{38} +12.2402 q^{39} -1.27427 q^{40} +7.88150 q^{41} +14.9826 q^{42} +7.05333 q^{43} +2.59449 q^{44} +1.04598 q^{45} -12.7723 q^{46} -9.39039 q^{47} -4.94340 q^{48} +5.07581 q^{49} -2.14348 q^{50} -1.73138 q^{51} +15.7880 q^{52} -13.5459 q^{53} +8.42479 q^{54} +1.00000 q^{55} +4.42811 q^{56} +10.7177 q^{57} -11.7012 q^{58} -13.0360 q^{59} +5.21871 q^{60} -7.65313 q^{61} +9.25337 q^{62} -3.63482 q^{63} -11.8390 q^{64} +6.08523 q^{65} -4.31152 q^{66} -4.95049 q^{67} -2.23323 q^{68} +11.9857 q^{69} +7.44863 q^{70} +9.98830 q^{71} -1.33286 q^{72} +1.00000 q^{73} -13.3442 q^{74} +2.01146 q^{75} +13.8243 q^{76} -3.47503 q^{77} -26.2366 q^{78} -14.0370 q^{79} -2.45761 q^{80} -11.0439 q^{81} -16.8938 q^{82} -15.5205 q^{83} -18.1352 q^{84} -0.860759 q^{85} -15.1186 q^{86} +10.9805 q^{87} -1.27427 q^{88} +16.0682 q^{89} -2.24204 q^{90} -21.1463 q^{91} +15.4597 q^{92} -8.68347 q^{93} +20.1281 q^{94} +5.32833 q^{95} +15.7223 q^{96} -0.440714 q^{97} -10.8799 q^{98} +1.04598 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	−2.14348	−1.51567	−0.757833	−	0.652449i	$-0.773742\pi$
$2$	−2.14348	−1.51567	−0.757833	+	0.652449i	$0.773742\pi$
$3$	2.01146	1.16132	0.580659	−	0.814147i	$-0.302795\pi$
$3$	2.01146	1.16132	0.580659	+	0.814147i	$0.302795\pi$
$4$	2.59449	1.29724
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.31152	−1.76017
$7$	−3.47503	−1.31344	−0.656718	−	0.754136i	$-0.728056\pi$
$7$	−3.47503	−1.31344	−0.656718	+	0.754136i	$0.728056\pi$
$8$	−1.27427	−0.450521
$9$	1.04598	0.348661
$10$	−2.14348	−0.677826
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	5.21871	1.50651
$13$	6.08523	1.68774	0.843869	−	0.536549i	$-0.180272\pi$
$13$	6.08523	1.68774	0.843869	+	0.536549i	$0.180272\pi$
$14$	7.44863	1.99073
$15$	2.01146	0.519357
$16$	−2.45761	−0.614403
$17$	−0.860759	−0.208765	−0.104382	−	0.994537i	$-0.533287\pi$
$17$	−0.860759	−0.208765	−0.104382	+	0.994537i	$0.533287\pi$
$18$	−2.24204	−0.528453
$19$	5.32833	1.22240	0.611201	−	0.791475i	$-0.290687\pi$
$19$	5.32833	1.22240	0.611201	+	0.791475i	$0.290687\pi$
$20$	2.59449	0.580145
$21$	−6.98989	−1.52532
$22$	−2.14348	−0.456990
$23$	5.95868	1.24247	0.621235	−	0.783624i	$-0.286631\pi$
$23$	5.95868	1.24247	0.621235	+	0.783624i	$0.286631\pi$
$24$	−2.56314	−0.523199
$25$	1.00000	0.200000
$26$	−13.0435	−2.55805
$27$	−3.93043	−0.756412
$28$	−9.01591	−1.70385
$29$	5.45897	1.01371	0.506853	−	0.862033i	$-0.330809\pi$
$29$	5.45897	1.01371	0.506853	+	0.862033i	$0.330809\pi$
$30$	−4.31152	−0.787172
$31$	−4.31699	−0.775355	−0.387677	−	0.921795i	$-0.626723\pi$
$31$	−4.31699	−0.775355	−0.387677	+	0.921795i	$0.626723\pi$
$32$	7.81637	1.38175
$33$	2.01146	0.350151
$34$	1.84501	0.316417
$35$	−3.47503	−0.587387
$36$	2.71379	0.452298
$37$	6.22550	1.02347	0.511733	−	0.859145i	$-0.329004\pi$
$37$	6.22550	1.02347	0.511733	+	0.859145i	$0.329004\pi$
$38$	−11.4211	−1.85275
$39$	12.2402	1.96000
$40$	−1.27427	−0.201479
$41$	7.88150	1.23088	0.615442	−	0.788182i	$-0.288978\pi$
$41$	7.88150	1.23088	0.615442	+	0.788182i	$0.288978\pi$
$42$	14.9826	2.31187
$43$	7.05333	1.07562	0.537812	−	0.843065i	$-0.319251\pi$
$43$	7.05333	1.07562	0.537812	+	0.843065i	$0.319251\pi$
$44$	2.59449	0.391134
$45$	1.04598	0.155926
$46$	−12.7723	−1.88317
$47$	−9.39039	−1.36973	−0.684865	−	0.728670i	$-0.740139\pi$
$47$	−9.39039	−1.36973	−0.684865	+	0.728670i	$0.740139\pi$
$48$	−4.94340	−0.713518
$49$	5.07581	0.725116
$50$	−2.14348	−0.303133
$51$	−1.73138	−0.242442
$52$	15.7880	2.18941
$53$	−13.5459	−1.86068	−0.930338	−	0.366704i	$-0.880486\pi$
$53$	−13.5459	−1.86068	−0.930338	+	0.366704i	$0.880486\pi$
$54$	8.42479	1.14647
$55$	1.00000	0.134840
$56$	4.42811	0.591731
$57$	10.7177	1.41960
$58$	−11.7012	−1.53644
$59$	−13.0360	−1.69715	−0.848574	−	0.529077i	$-0.822538\pi$
$59$	−13.0360	−1.69715	−0.848574	+	0.529077i	$0.822538\pi$
$60$	5.21871	0.673733
$61$	−7.65313	−0.979883	−0.489941	−	0.871755i	$-0.662982\pi$
$61$	−7.65313	−0.979883	−0.489941	+	0.871755i	$0.662982\pi$
$62$	9.25337	1.17518
$63$	−3.63482	−0.457944
$64$	−11.8390	−1.47987
$65$	6.08523	0.754780
$66$	−4.31152	−0.530711
$67$	−4.95049	−0.604799	−0.302400	−	0.953181i	$-0.597788\pi$
$67$	−4.95049	−0.604799	−0.302400	+	0.953181i	$0.597788\pi$
$68$	−2.23323	−0.270819
$69$	11.9857	1.44290
$70$	7.44863	0.890282
$71$	9.98830	1.18539	0.592696	−	0.805426i	$-0.298063\pi$
$71$	9.98830	1.18539	0.592696	+	0.805426i	$0.298063\pi$
$72$	−1.33286	−0.157079
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−13.3442	−1.55123
$75$	2.01146	0.232264
$76$	13.8243	1.58575
$77$	−3.47503	−0.396016
$78$	−26.2366	−2.97071
$79$	−14.0370	−1.57928	−0.789640	−	0.613570i	$-0.789733\pi$
$79$	−14.0370	−1.57928	−0.789640	+	0.613570i	$0.789733\pi$
$80$	−2.45761	−0.274770
$81$	−11.0439	−1.22710
$82$	−16.8938	−1.86561
$83$	−15.5205	−1.70360	−0.851800	−	0.523867i	$-0.824489\pi$
$83$	−15.5205	−1.70360	−0.851800	+	0.523867i	$0.824489\pi$
$84$	−18.1352	−1.97871
$85$	−0.860759	−0.0933624
$86$	−15.1186	−1.63029
$87$	10.9805	1.17723
$88$	−1.27427	−0.135837
$89$	16.0682	1.70322	0.851612	−	0.524172i	$-0.175625\pi$
$89$	16.0682	1.70322	0.851612	+	0.524172i	$0.175625\pi$
$90$	−2.24204	−0.236331
$91$	−21.1463	−2.21674
$92$	15.4597	1.61179
$93$	−8.68347	−0.900434
$94$	20.1281	2.07605
$95$	5.32833	0.546675
$96$	15.7223	1.60465
$97$	−0.440714	−0.0447477	−0.0223738	−	0.999750i	$-0.507122\pi$
$97$	−0.440714	−0.0447477	−0.0223738	+	0.999750i	$0.507122\pi$
$98$	−10.8799	−1.09903
$99$	1.04598	0.105125
$100$	2.59449	0.259449
$101$	11.1222	1.10670	0.553350	−	0.832949i	$-0.313349\pi$
$101$	11.1222	1.10670	0.553350	+	0.832949i	$0.313349\pi$
$102$	3.71118	0.367461
$103$	9.81539	0.967139	0.483570	−	0.875306i	$-0.339340\pi$
$103$	9.81539	0.967139	0.483570	+	0.875306i	$0.339340\pi$
$104$	−7.75421	−0.760362
$105$	−6.98989	−0.682143
$106$	29.0354	2.82016
$107$	10.8099	1.04503	0.522516	−	0.852629i	$-0.324993\pi$
$107$	10.8099	1.04503	0.522516	+	0.852629i	$0.324993\pi$
$108$	−10.1975	−0.981251
$109$	15.0083	1.43754	0.718770	−	0.695248i	$-0.244706\pi$
$109$	15.0083	1.43754	0.718770	+	0.695248i	$0.244706\pi$
$110$	−2.14348	−0.204372
$111$	12.5224	1.18857
$112$	8.54027	0.806980
$113$	14.5182	1.36575	0.682877	−	0.730534i	$-0.260729\pi$
$113$	14.5182	1.36575	0.682877	+	0.730534i	$0.260729\pi$
$114$	−22.9732	−2.15164
$115$	5.95868	0.555650
$116$	14.1632	1.31502
$117$	6.36504	0.588448
$118$	27.9424	2.57231
$119$	2.99116	0.274199
$120$	−2.56314	−0.233982
$121$	1.00000	0.0909091
$122$	16.4043	1.48517
$123$	15.8533	1.42945
$124$	−11.2004	−1.00582
$125$	1.00000	0.0894427
$126$	7.79114	0.694090
$127$	−3.43377	−0.304698	−0.152349	−	0.988327i	$-0.548684\pi$
$127$	−3.43377	−0.304698	−0.152349	+	0.988327i	$0.548684\pi$
$128$	9.74379	0.861238
$129$	14.1875	1.24914
$130$	−13.0435	−1.14399
$131$	−0.970461	−0.0847896	−0.0423948	−	0.999101i	$-0.513499\pi$
$131$	−0.970461	−0.0847896	−0.0423948	+	0.999101i	$0.513499\pi$
$132$	5.21871	0.454231
$133$	−18.5161	−1.60555
$134$	10.6113	0.916673
$135$	−3.93043	−0.338278
$136$	1.09684	0.0940529
$137$	−11.3261	−0.967651	−0.483825	−	0.875165i	$-0.660753\pi$
$137$	−11.3261	−0.967651	−0.483825	+	0.875165i	$0.660753\pi$
$138$	−25.6910	−2.18696
$139$	17.3886	1.47488	0.737440	−	0.675413i	$-0.236035\pi$
$139$	17.3886	1.47488	0.737440	+	0.675413i	$0.236035\pi$
$140$	−9.01591	−0.761983
$141$	−18.8884	−1.59069
$142$	−21.4097	−1.79666
$143$	6.08523	0.508872
$144$	−2.57062	−0.214218
$145$	5.45897	0.453343
$146$	−2.14348	−0.177395
$147$	10.2098	0.842090
$148$	16.1520	1.32768
$149$	7.51945	0.616017	0.308009	−	0.951384i	$-0.400337\pi$
$149$	7.51945	0.616017	0.308009	+	0.951384i	$0.400337\pi$
$150$	−4.31152	−0.352034
$151$	13.8880	1.13019	0.565095	−	0.825026i	$-0.308839\pi$
$151$	13.8880	1.13019	0.565095	+	0.825026i	$0.308839\pi$
$152$	−6.78971	−0.550719
$153$	−0.900338	−0.0727880
$154$	7.44863	0.600228
$155$	−4.31699	−0.346749
$156$	31.7571	2.54260
$157$	−6.26466	−0.499974	−0.249987	−	0.968249i	$-0.580426\pi$
$157$	−6.26466	−0.499974	−0.249987	+	0.968249i	$0.580426\pi$
$158$	30.0879	2.39366
$159$	−27.2471	−2.16084
$160$	7.81637	0.617938
$161$	−20.7066	−1.63191
$162$	23.6723	1.85987
$163$	2.44872	0.191798	0.0958991	−	0.995391i	$-0.469427\pi$
$163$	2.44872	0.191798	0.0958991	+	0.995391i	$0.469427\pi$
$164$	20.4484	1.59676
$165$	2.01146	0.156592
$166$	33.2679	2.58209
$167$	2.54186	0.196695	0.0983476	−	0.995152i	$-0.468644\pi$
$167$	2.54186	0.196695	0.0983476	+	0.995152i	$0.468644\pi$
$168$	8.90698	0.687188
$169$	24.0300	1.84846
$170$	1.84501	0.141506
$171$	5.57334	0.426204
$172$	18.2998	1.39534
$173$	0.678878	0.0516141	0.0258071	−	0.999667i	$-0.491784\pi$
$173$	0.678878	0.0516141	0.0258071	+	0.999667i	$0.491784\pi$
$174$	−23.5365	−1.78429
$175$	−3.47503	−0.262687
$176$	−2.45761	−0.185250
$177$	−26.2215	−1.97093
$178$	−34.4418	−2.58152
$179$	14.0497	1.05012	0.525060	−	0.851065i	$-0.324043\pi$
$179$	14.0497	1.05012	0.525060	+	0.851065i	$0.324043\pi$
$180$	2.71379	0.202274
$181$	6.22283	0.462539	0.231270	−	0.972890i	$-0.425712\pi$
$181$	6.22283	0.462539	0.231270	+	0.972890i	$0.425712\pi$
$182$	45.3266	3.35983
$183$	−15.3940	−1.13796
$184$	−7.59295	−0.559760
$185$	6.22550	0.457708
$186$	18.6128	1.36476
$187$	−0.860759	−0.0629449
$188$	−24.3632	−1.77687
$189$	13.6584	0.993500
$190$	−11.4211	−0.828577
$191$	25.8029	1.86703	0.933515	−	0.358539i	$-0.116725\pi$
$191$	25.8029	1.86703	0.933515	+	0.358539i	$0.116725\pi$
$192$	−23.8136	−1.71860
$193$	21.1940	1.52558	0.762788	−	0.646649i	$-0.223830\pi$
$193$	21.1940	1.52558	0.762788	+	0.646649i	$0.223830\pi$
$194$	0.944659	0.0678226
$195$	12.2402	0.876540
$196$	13.1691	0.940651
$197$	8.94792	0.637513	0.318757	−	0.947837i	$-0.396735\pi$
$197$	8.94792	0.637513	0.318757	+	0.947837i	$0.396735\pi$
$198$	−2.24204	−0.159335
$199$	1.97787	0.140208	0.0701039	−	0.997540i	$-0.477667\pi$
$199$	1.97787	0.140208	0.0701039	+	0.997540i	$0.477667\pi$
$200$	−1.27427	−0.0901043
$201$	−9.95773	−0.702364
$202$	−23.8401	−1.67739
$203$	−18.9701	−1.33144
$204$	−4.49205	−0.314507
$205$	7.88150	0.550468
$206$	−21.0390	−1.46586
$207$	6.23267	0.433201
$208$	−14.9551	−1.03695
$209$	5.32833	0.368568
$210$	14.9826	1.03390
$211$	−20.0443	−1.37991	−0.689954	−	0.723853i	$-0.742369\pi$
$211$	−20.0443	−1.37991	−0.689954	+	0.723853i	$0.742369\pi$
$212$	−35.1447	−2.41375
$213$	20.0911	1.37662
$214$	−23.1707	−1.58392
$215$	7.05333	0.481033
$216$	5.00842	0.340780
$217$	15.0017	1.01838
$218$	−32.1700	−2.17883
$219$	2.01146	0.135922
$220$	2.59449	0.174920
$221$	−5.23791	−0.352340
$222$	−26.8414	−1.80147
$223$	−5.44124	−0.364372	−0.182186	−	0.983264i	$-0.558317\pi$
$223$	−5.44124	−0.364372	−0.182186	+	0.983264i	$0.558317\pi$
$224$	−27.1621	−1.81484
$225$	1.04598	0.0697321
$226$	−31.1193	−2.07003
$227$	−21.1635	−1.40467	−0.702335	−	0.711846i	$-0.747859\pi$
$227$	−21.1635	−1.40467	−0.702335	+	0.711846i	$0.747859\pi$
$228$	27.8070	1.84157
$229$	−3.73849	−0.247046	−0.123523	−	0.992342i	$-0.539419\pi$
$229$	−3.73849	−0.247046	−0.123523	+	0.992342i	$0.539419\pi$
$230$	−12.7723	−0.842179
$231$	−6.98989	−0.459901
$232$	−6.95618	−0.456696
$233$	14.5831	0.955371	0.477686	−	0.878531i	$-0.341476\pi$
$233$	14.5831	0.955371	0.477686	+	0.878531i	$0.341476\pi$
$234$	−13.6433	−0.891891
$235$	−9.39039	−0.612562
$236$	−33.8218	−2.20161
$237$	−28.2348	−1.83405
$238$	−6.41148	−0.415594
$239$	19.1418	1.23818	0.619090	−	0.785320i	$-0.287502\pi$
$239$	19.1418	1.23818	0.619090	+	0.785320i	$0.287502\pi$
$240$	−4.94340	−0.319095
$241$	−15.2597	−0.982964	−0.491482	−	0.870888i	$-0.663545\pi$
$241$	−15.2597	−0.982964	−0.491482	+	0.870888i	$0.663545\pi$
$242$	−2.14348	−0.137788
$243$	−10.4230	−0.668637
$244$	−19.8559	−1.27115
$245$	5.07581	0.324282
$246$	−33.9813	−2.16657
$247$	32.4241	2.06310
$248$	5.50100	0.349314
$249$	−31.2190	−1.97842
$250$	−2.14348	−0.135565
$251$	15.8773	1.00217	0.501083	−	0.865399i	$-0.332935\pi$
$251$	15.8773	1.00217	0.501083	+	0.865399i	$0.332935\pi$
$252$	−9.43048	−0.594064
$253$	5.95868	0.374619
$254$	7.36020	0.461820
$255$	−1.73138	−0.108423
$256$	2.79235	0.174522
$257$	22.9203	1.42973	0.714865	−	0.699262i	$-0.246488\pi$
$257$	22.9203	1.42973	0.714865	+	0.699262i	$0.246488\pi$
$258$	−30.4106	−1.89328
$259$	−21.6338	−1.34426
$260$	15.7880	0.979133
$261$	5.70998	0.353439
$262$	2.08016	0.128513
$263$	−12.2937	−0.758062	−0.379031	−	0.925384i	$-0.623743\pi$
$263$	−12.2937	−0.758062	−0.379031	+	0.925384i	$0.623743\pi$
$264$	−2.56314	−0.157750
$265$	−13.5459	−0.832119
$266$	39.6888	2.43348
$267$	32.3206	1.97799
$268$	−12.8440	−0.784571
$269$	−11.6500	−0.710311	−0.355156	−	0.934807i	$-0.615572\pi$
$269$	−11.6500	−0.710311	−0.355156	+	0.934807i	$0.615572\pi$
$270$	8.42479	0.512716
$271$	20.2070	1.22749	0.613743	−	0.789506i	$-0.289663\pi$
$271$	20.2070	1.22749	0.613743	+	0.789506i	$0.289663\pi$
$272$	2.11541	0.128266
$273$	−42.5351	−2.57434
$274$	24.2771	1.46663
$275$	1.00000	0.0603023
$276$	31.0966	1.87180
$277$	−23.0018	−1.38204	−0.691022	−	0.722834i	$-0.742839\pi$
$277$	−23.0018	−1.38204	−0.691022	+	0.722834i	$0.742839\pi$
$278$	−37.2720	−2.23542
$279$	−4.51550	−0.270336
$280$	4.42811	0.264630
$281$	29.5901	1.76519	0.882597	−	0.470130i	$-0.155793\pi$
$281$	29.5901	1.76519	0.882597	+	0.470130i	$0.155793\pi$
$282$	40.4869	2.41096
$283$	0.968632	0.0575792	0.0287896	−	0.999585i	$-0.490835\pi$
$283$	0.968632	0.0575792	0.0287896	+	0.999585i	$0.490835\pi$
$284$	25.9145	1.53774
$285$	10.7177	0.634864
$286$	−13.0435	−0.771281
$287$	−27.3884	−1.61669
$288$	8.17578	0.481762
$289$	−16.2591	−0.956417
$290$	−11.7012	−0.687116
$291$	−0.886479	−0.0519663
$292$	2.59449	0.151831
$293$	−10.2420	−0.598346	−0.299173	−	0.954199i	$-0.596711\pi$
$293$	−10.2420	−0.598346	−0.299173	+	0.954199i	$0.596711\pi$
$294$	−21.8845	−1.27633
$295$	−13.0360	−0.758988
$296$	−7.93294	−0.461093
$297$	−3.93043	−0.228067
$298$	−16.1178	−0.933677
$299$	36.2599	2.09697
$300$	5.21871	0.301303
$301$	−24.5105	−1.41276
$302$	−29.7686	−1.71299
$303$	22.3719	1.28523
$304$	−13.0950	−0.751048
$305$	−7.65313	−0.438217
$306$	1.92985	0.110322
$307$	−0.187378	−0.0106942	−0.00534711	−	0.999986i	$-0.501702\pi$
$307$	−0.187378	−0.0106942	−0.00534711	+	0.999986i	$0.501702\pi$
$308$	−9.01591	−0.513729
$309$	19.7433	1.12316
$310$	9.25337	0.525556
$311$	8.39962	0.476299	0.238149	−	0.971229i	$-0.423459\pi$
$311$	8.39962	0.476299	0.238149	+	0.971229i	$0.423459\pi$
$312$	−15.5973	−0.883023
$313$	11.0663	0.625504	0.312752	−	0.949835i	$-0.398749\pi$
$313$	11.0663	0.625504	0.312752	+	0.949835i	$0.398749\pi$
$314$	13.4281	0.757793
$315$	−3.63482	−0.204799
$316$	−36.4187	−2.04871
$317$	−13.5612	−0.761672	−0.380836	−	0.924643i	$-0.624364\pi$
$317$	−13.5612	−0.761672	−0.380836	+	0.924643i	$0.624364\pi$
$318$	58.4035	3.27511
$319$	5.45897	0.305644
$320$	−11.8390	−0.661818
$321$	21.7437	1.21361
$322$	44.3840	2.47342
$323$	−4.58641	−0.255194
$324$	−28.6532	−1.59184
$325$	6.08523	0.337548
$326$	−5.24876	−0.290702
$327$	30.1887	1.66944
$328$	−10.0431	−0.554539
$329$	32.6319	1.79905
$330$	−4.31152	−0.237341
$331$	−17.4635	−0.959880	−0.479940	−	0.877301i	$-0.659341\pi$
$331$	−17.4635	−0.959880	−0.479940	+	0.877301i	$0.659341\pi$
$332$	−40.2678	−2.20998
$333$	6.51176	0.356842
$334$	−5.44842	−0.298124
$335$	−4.95049	−0.270474
$336$	17.1784	0.937161
$337$	−10.5428	−0.574303	−0.287152	−	0.957885i	$-0.592708\pi$
$337$	−10.5428	−0.574303	−0.287152	+	0.957885i	$0.592708\pi$
$338$	−51.5077	−2.80165
$339$	29.2027	1.58607
$340$	−2.23323	−0.121114
$341$	−4.31699	−0.233778
$342$	−11.9463	−0.645983
$343$	6.68661	0.361043
$344$	−8.98783	−0.484591
$345$	11.9857	0.645286
$346$	−1.45516	−0.0782298
$347$	−4.89240	−0.262638	−0.131319	−	0.991340i	$-0.541921\pi$
$347$	−4.89240	−0.262638	−0.131319	+	0.991340i	$0.541921\pi$
$348$	28.4888	1.52716
$349$	−20.6715	−1.10652	−0.553261	−	0.833008i	$-0.686617\pi$
$349$	−20.6715	−1.10652	−0.553261	+	0.833008i	$0.686617\pi$
$350$	7.44863	0.398146
$351$	−23.9176	−1.27663
$352$	7.81637	0.416614
$353$	10.5329	0.560611	0.280305	−	0.959911i	$-0.409564\pi$
$353$	10.5329	0.560611	0.280305	+	0.959911i	$0.409564\pi$
$354$	56.2051	2.98727
$355$	9.98830	0.530124
$356$	41.6887	2.20950
$357$	6.01661	0.318433
$358$	−30.1151	−1.59163
$359$	−9.14214	−0.482504	−0.241252	−	0.970463i	$-0.577558\pi$
$359$	−9.14214	−0.482504	−0.241252	+	0.970463i	$0.577558\pi$
$360$	−1.33286	−0.0702479
$361$	9.39110	0.494269
$362$	−13.3385	−0.701055
$363$	2.01146	0.105574
$364$	−54.8639	−2.87565
$365$	1.00000	0.0523424
$366$	32.9966	1.72476
$367$	−1.98979	−0.103866	−0.0519331	−	0.998651i	$-0.516538\pi$
$367$	−1.98979	−0.103866	−0.0519331	+	0.998651i	$0.516538\pi$
$368$	−14.6441	−0.763378
$369$	8.24391	0.429161
$370$	−13.3442	−0.693732
$371$	47.0724	2.44388
$372$	−22.5291	−1.16808
$373$	−15.4376	−0.799328	−0.399664	−	0.916662i	$-0.630873\pi$
$373$	−15.4376	−0.799328	−0.399664	+	0.916662i	$0.630873\pi$
$374$	1.84501	0.0954035
$375$	2.01146	0.103871
$376$	11.9659	0.617092
$377$	33.2191	1.71087
$378$	−29.2764	−1.50581
$379$	−7.94818	−0.408271	−0.204135	−	0.978943i	$-0.565438\pi$
$379$	−7.94818	−0.408271	−0.204135	+	0.978943i	$0.565438\pi$
$380$	13.8243	0.709171
$381$	−6.90690	−0.353851
$382$	−55.3078	−2.82979
$383$	26.8032	1.36958	0.684789	−	0.728741i	$-0.259894\pi$
$383$	26.8032	1.36958	0.684789	+	0.728741i	$0.259894\pi$
$384$	19.5993	1.00017
$385$	−3.47503	−0.177104
$386$	−45.4288	−2.31226
$387$	7.37766	0.375028
$388$	−1.14343	−0.0580486
$389$	−9.55541	−0.484478	−0.242239	−	0.970217i	$-0.577882\pi$
$389$	−9.55541	−0.484478	−0.242239	+	0.970217i	$0.577882\pi$
$390$	−26.2366	−1.32854
$391$	−5.12898	−0.259384
$392$	−6.46794	−0.326680
$393$	−1.95205	−0.0984677
$394$	−19.1797	−0.966257
$395$	−14.0370	−0.706276
$396$	2.71379	0.136373
$397$	18.9457	0.950855	0.475428	−	0.879755i	$-0.342293\pi$
$397$	18.9457	0.950855	0.475428	+	0.879755i	$0.342293\pi$
$398$	−4.23952	−0.212508
$399$	−37.2444	−1.86455
$400$	−2.45761	−0.122881
$401$	23.2141	1.15925	0.579627	−	0.814882i	$-0.303198\pi$
$401$	23.2141	1.15925	0.579627	+	0.814882i	$0.303198\pi$
$402$	21.3442	1.06455
$403$	−26.2699	−1.30860
$404$	28.8564	1.43566
$405$	−11.0439	−0.548774
$406$	40.6619	2.01801
$407$	6.22550	0.308586
$408$	2.20625	0.109225
$409$	20.7211	1.02459	0.512295	−	0.858809i	$-0.328795\pi$
$409$	20.7211	1.02459	0.512295	+	0.858809i	$0.328795\pi$
$410$	−16.8938	−0.834326
$411$	−22.7819	−1.12375
$412$	25.4659	1.25461
$413$	45.3006	2.22910
$414$	−13.3596	−0.656587
$415$	−15.5205	−0.761873
$416$	47.5644	2.33204
$417$	34.9765	1.71280
$418$	−11.4211	−0.558626
$419$	−9.83194	−0.480322	−0.240161	−	0.970733i	$-0.577200\pi$
$419$	−9.83194	−0.480322	−0.240161	+	0.970733i	$0.577200\pi$
$420$	−18.1352	−0.884905
$421$	1.39939	0.0682020	0.0341010	−	0.999418i	$-0.489143\pi$
$421$	1.39939	0.0682020	0.0341010	+	0.999418i	$0.489143\pi$
$422$	42.9645	2.09148
$423$	−9.82218	−0.477571
$424$	17.2611	0.838274
$425$	−0.860759	−0.0417529
$426$	−43.0647	−2.08649
$427$	26.5948	1.28701
$428$	28.0461	1.35566
$429$	12.2402	0.590963
$430$	−15.1186	−0.729086
$431$	24.7144	1.19045	0.595227	−	0.803558i	$-0.297062\pi$
$431$	24.7144	1.19045	0.595227	+	0.803558i	$0.297062\pi$
$432$	9.65949	0.464742
$433$	−22.0244	−1.05843	−0.529213	−	0.848489i	$-0.677513\pi$
$433$	−22.0244	−1.05843	−0.529213	+	0.848489i	$0.677513\pi$
$434$	−32.1557	−1.54352
$435$	10.9805	0.526475
$436$	38.9390	1.86484
$437$	31.7498	1.51880
$438$	−4.31152	−0.206012
$439$	−12.4472	−0.594071	−0.297035	−	0.954866i	$-0.595998\pi$
$439$	−12.4472	−0.594071	−0.297035	+	0.954866i	$0.595998\pi$
$440$	−1.27427	−0.0607483
$441$	5.30921	0.252819
$442$	11.2273	0.534030
$443$	−28.7124	−1.36416	−0.682082	−	0.731275i	$-0.738925\pi$
$443$	−28.7124	−1.36416	−0.682082	+	0.731275i	$0.738925\pi$
$444$	32.4891	1.54186
$445$	16.0682	0.761705
$446$	11.6632	0.552266
$447$	15.1251	0.715392
$448$	41.1407	1.94372
$449$	−16.6133	−0.784031	−0.392016	−	0.919959i	$-0.628222\pi$
$449$	−16.6133	−0.784031	−0.392016	+	0.919959i	$0.628222\pi$
$450$	−2.24204	−0.105691
$451$	7.88150	0.371125
$452$	37.6672	1.77171
$453$	27.9352	1.31251
$454$	45.3634	2.12901
$455$	−21.1463	−0.991355
$456$	−13.6573	−0.639560
$457$	−7.42305	−0.347236	−0.173618	−	0.984813i	$-0.555546\pi$
$457$	−7.42305	−0.347236	−0.173618	+	0.984813i	$0.555546\pi$
$458$	8.01336	0.374440
$459$	3.38316	0.157912
$460$	15.4597	0.720813
$461$	−9.94481	−0.463176	−0.231588	−	0.972814i	$-0.574392\pi$
$461$	−9.94481	−0.463176	−0.231588	+	0.972814i	$0.574392\pi$
$462$	14.9826	0.697056
$463$	−37.2609	−1.73166	−0.865830	−	0.500337i	$-0.833209\pi$
$463$	−37.2609	−1.73166	−0.865830	+	0.500337i	$0.833209\pi$
$464$	−13.4160	−0.622824
$465$	−8.68347	−0.402686
$466$	−31.2585	−1.44802
$467$	19.6412	0.908885	0.454442	−	0.890776i	$-0.349839\pi$
$467$	19.6412	0.908885	0.454442	+	0.890776i	$0.349839\pi$
$468$	16.5140	0.763360
$469$	17.2031	0.794365
$470$	20.1281	0.928439
$471$	−12.6011	−0.580629
$472$	16.6114	0.764601
$473$	7.05333	0.324313
$474$	60.5206	2.77980
$475$	5.32833	0.244481
$476$	7.76052	0.355703
$477$	−14.1688	−0.648744
$478$	−41.0300	−1.87667
$479$	−13.9792	−0.638725	−0.319362	−	0.947633i	$-0.603469\pi$
$479$	−13.9792	−0.638725	−0.319362	+	0.947633i	$0.603469\pi$
$480$	15.7223	0.717623
$481$	37.8836	1.72734
$482$	32.7088	1.48984
$483$	−41.6505	−1.89516
$484$	2.59449	0.117931
$485$	−0.440714	−0.0200118
$486$	22.3415	1.01343
$487$	−5.54233	−0.251147	−0.125574	−	0.992084i	$-0.540077\pi$
$487$	−5.54233	−0.251147	−0.125574	+	0.992084i	$0.540077\pi$
$488$	9.75213	0.441458
$489$	4.92550	0.222739
$490$	−10.8799	−0.491503
$491$	31.0809	1.40266	0.701331	−	0.712835i	$-0.252589\pi$
$491$	31.0809	1.40266	0.701331	+	0.712835i	$0.252589\pi$
$492$	41.1313	1.85434
$493$	−4.69886	−0.211626
$494$	−69.5003	−3.12697
$495$	1.04598	0.0470134
$496$	10.6095	0.476380
$497$	−34.7096	−1.55694
$498$	66.9171	2.99863
$499$	−5.75541	−0.257648	−0.128824	−	0.991667i	$-0.541120\pi$
$499$	−5.75541	−0.257648	−0.128824	+	0.991667i	$0.541120\pi$
$500$	2.59449	0.116029
$501$	5.11286	0.228426
$502$	−34.0326	−1.51895
$503$	−29.7198	−1.32514	−0.662570	−	0.749000i	$-0.730534\pi$
$503$	−29.7198	−1.32514	−0.662570	+	0.749000i	$0.730534\pi$
$504$	4.63173	0.206313
$505$	11.1222	0.494931
$506$	−12.7723	−0.567797
$507$	48.3355	2.14665
$508$	−8.90887	−0.395267
$509$	20.8070	0.922254	0.461127	−	0.887334i	$-0.347445\pi$
$509$	20.8070	0.922254	0.461127	+	0.887334i	$0.347445\pi$
$510$	3.71118	0.164334
$511$	−3.47503	−0.153726
$512$	−25.4729	−1.12575
$513$	−20.9427	−0.924641
$514$	−49.1292	−2.16699
$515$	9.81539	0.432518
$516$	36.8093	1.62044
$517$	−9.39039	−0.412989
$518$	46.3714	2.03744
$519$	1.36554	0.0599405
$520$	−7.75421	−0.340044
$521$	6.12846	0.268493	0.134246	−	0.990948i	$-0.457139\pi$
$521$	6.12846	0.268493	0.134246	+	0.990948i	$0.457139\pi$
$522$	−12.2392	−0.535696
$523$	−29.4407	−1.28735	−0.643676	−	0.765298i	$-0.722592\pi$
$523$	−29.4407	−1.28735	−0.643676	+	0.765298i	$0.722592\pi$
$524$	−2.51785	−0.109993
$525$	−6.98989	−0.305064
$526$	26.3512	1.14897
$527$	3.71589	0.161867
$528$	−4.94340	−0.215134
$529$	12.5059	0.543733
$530$	29.0354	1.26122
$531$	−13.6355	−0.591729
$532$	−48.0397	−2.08279
$533$	47.9607	2.07741
$534$	−69.2783	−2.99797
$535$	10.8099	0.467353
$536$	6.30825	0.272475
$537$	28.2604	1.21952
$538$	24.9714	1.07659
$539$	5.07581	0.218631
$540$	−10.1975	−0.438829
$541$	−30.1809	−1.29758	−0.648789	−	0.760968i	$-0.724724\pi$
$541$	−30.1809	−1.29758	−0.648789	+	0.760968i	$0.724724\pi$
$542$	−43.3131	−1.86046
$543$	12.5170	0.537155
$544$	−6.72801	−0.288461
$545$	15.0083	0.642887
$546$	91.1729	3.90184
$547$	−38.5413	−1.64791	−0.823953	−	0.566658i	$-0.808236\pi$
$547$	−38.5413	−1.64791	−0.823953	+	0.566658i	$0.808236\pi$
$548$	−29.3853	−1.25528
$549$	−8.00503	−0.341647
$550$	−2.14348	−0.0913981
$551$	29.0872	1.23916
$552$	−15.2729	−0.650059
$553$	48.7788	2.07428
$554$	49.3037	2.09472
$555$	12.5224	0.531544
$556$	45.1144	1.91328
$557$	14.1873	0.601135	0.300567	−	0.953761i	$-0.402824\pi$
$557$	14.1873	0.601135	0.300567	+	0.953761i	$0.402824\pi$
$558$	9.67885	0.409739
$559$	42.9212	1.81537
$560$	8.54027	0.360892
$561$	−1.73138	−0.0730991
$562$	−63.4256	−2.67545
$563$	33.9242	1.42973	0.714867	−	0.699261i	$-0.246487\pi$
$563$	33.9242	1.42973	0.714867	+	0.699261i	$0.246487\pi$
$564$	−49.0058	−2.06351
$565$	14.5182	0.610783
$566$	−2.07624	−0.0872708
$567$	38.3777	1.61171
$568$	−12.7278	−0.534045
$569$	26.4714	1.10974	0.554870	−	0.831937i	$-0.312768\pi$
$569$	26.4714	1.10974	0.554870	+	0.831937i	$0.312768\pi$
$570$	−22.9732	−0.962242
$571$	−36.2667	−1.51771	−0.758857	−	0.651258i	$-0.774242\pi$
$571$	−36.2667	−1.51771	−0.758857	+	0.651258i	$0.774242\pi$
$572$	15.7880	0.660131
$573$	51.9015	2.16822
$574$	58.7064	2.45036
$575$	5.95868	0.248494
$576$	−12.3833	−0.515973
$577$	−1.44734	−0.0602534	−0.0301267	−	0.999546i	$-0.509591\pi$
$577$	−1.44734	−0.0602534	−0.0301267	+	0.999546i	$0.509591\pi$
$578$	34.8510	1.44961
$579$	42.6309	1.77168
$580$	14.1632	0.588096
$581$	53.9343	2.23757
$582$	1.90015	0.0787636
$583$	−13.5459	−0.561015
$584$	−1.27427	−0.0527295
$585$	6.36504	0.263162
$586$	21.9536	0.906893
$587$	−17.9532	−0.741007	−0.370504	−	0.928831i	$-0.620815\pi$
$587$	−17.9532	−0.741007	−0.370504	+	0.928831i	$0.620815\pi$
$588$	26.4892	1.09240
$589$	−23.0024	−0.947796
$590$	27.9424	1.15037
$591$	17.9984	0.740356
$592$	−15.2999	−0.628820
$593$	−1.56421	−0.0642345	−0.0321172	−	0.999484i	$-0.510225\pi$
$593$	−1.56421	−0.0642345	−0.0321172	+	0.999484i	$0.510225\pi$
$594$	8.42479	0.345673
$595$	2.99116	0.122626
$596$	19.5091	0.799124
$597$	3.97842	0.162826
$598$	−77.7223	−3.17830
$599$	−8.21802	−0.335779	−0.167890	−	0.985806i	$-0.553695\pi$
$599$	−8.21802	−0.335779	−0.167890	+	0.985806i	$0.553695\pi$
$600$	−2.56314	−0.104640
$601$	2.34970	0.0958463	0.0479232	−	0.998851i	$-0.484740\pi$
$601$	2.34970	0.0958463	0.0479232	+	0.998851i	$0.484740\pi$
$602$	52.5377	2.14128
$603$	−5.17813	−0.210870
$604$	36.0323	1.46613
$605$	1.00000	0.0406558
$606$	−47.9535	−1.94798
$607$	12.6551	0.513654	0.256827	−	0.966457i	$-0.417323\pi$
$607$	12.6551	0.513654	0.256827	+	0.966457i	$0.417323\pi$
$608$	41.6482	1.68906
$609$	−38.1576	−1.54622
$610$	16.4043	0.664190
$611$	−57.1427	−2.31175
$612$	−2.33592	−0.0944238
$613$	29.8371	1.20511	0.602555	−	0.798078i	$-0.294150\pi$
$613$	29.8371	1.20511	0.602555	+	0.798078i	$0.294150\pi$
$614$	0.401640	0.0162089
$615$	15.8533	0.639269
$616$	4.42811	0.178414
$617$	−1.05710	−0.0425572	−0.0212786	−	0.999774i	$-0.506774\pi$
$617$	−1.05710	−0.0425572	−0.0212786	+	0.999774i	$0.506774\pi$
$618$	−42.3193	−1.70233
$619$	−5.05379	−0.203129	−0.101565	−	0.994829i	$-0.532385\pi$
$619$	−5.05379	−0.203129	−0.101565	+	0.994829i	$0.532385\pi$
$620$	−11.2004	−0.449818
$621$	−23.4202	−0.939820
$622$	−18.0044	−0.721910
$623$	−55.8374	−2.23708
$624$	−30.0817	−1.20423
$625$	1.00000	0.0400000
$626$	−23.7203	−0.948055
$627$	10.7177	0.428025
$628$	−16.2536	−0.648588
$629$	−5.35865	−0.213663
$630$	7.79114	0.310406
$631$	−18.9247	−0.753380	−0.376690	−	0.926339i	$-0.622938\pi$
$631$	−18.9247	−0.753380	−0.376690	+	0.926339i	$0.622938\pi$
$632$	17.8868	0.711500
$633$	−40.3184	−1.60251
$634$	29.0681	1.15444
$635$	−3.43377	−0.136265
$636$	−70.6923	−2.80313
$637$	30.8875	1.22381
$638$	−11.7012	−0.463254
$639$	10.4476	0.413300
$640$	9.74379	0.385157
$641$	29.9158	1.18160	0.590801	−	0.806817i	$-0.298812\pi$
$641$	29.9158	1.18160	0.590801	+	0.806817i	$0.298812\pi$
$642$	−46.6071	−1.83943
$643$	36.0543	1.42184	0.710922	−	0.703271i	$-0.248278\pi$
$643$	36.0543	1.42184	0.710922	+	0.703271i	$0.248278\pi$
$644$	−53.7229	−2.11698
$645$	14.1875	0.558633
$646$	9.83085	0.386790
$647$	5.97437	0.234877	0.117438	−	0.993080i	$-0.462532\pi$
$647$	5.97437	0.234877	0.117438	+	0.993080i	$0.462532\pi$
$648$	14.0728	0.552833
$649$	−13.0360	−0.511709
$650$	−13.0435	−0.511610
$651$	30.1753	1.18266
$652$	6.35316	0.248809
$653$	13.0849	0.512053	0.256027	−	0.966670i	$-0.417587\pi$
$653$	13.0849	0.512053	0.256027	+	0.966670i	$0.417587\pi$
$654$	−64.7088	−2.53031
$655$	−0.970461	−0.0379191
$656$	−19.3697	−0.756259
$657$	1.04598	0.0408076
$658$	−69.9456	−2.72676
$659$	46.7837	1.82244	0.911218	−	0.411925i	$-0.135144\pi$
$659$	46.7837	1.82244	0.911218	+	0.411925i	$0.135144\pi$
$660$	5.21871	0.203138
$661$	−20.5875	−0.800759	−0.400380	−	0.916349i	$-0.631122\pi$
$661$	−20.5875	−0.800759	−0.400380	+	0.916349i	$0.631122\pi$
$662$	37.4325	1.45486
$663$	−10.5359	−0.409179
$664$	19.7773	0.767508
$665$	−18.5161	−0.718023
$666$	−13.9578	−0.540853
$667$	32.5282	1.25950
$668$	6.59483	0.255161
$669$	−10.9448	−0.423152
$670$	10.6113	0.409949
$671$	−7.65313	−0.295446
$672$	−54.6355	−2.10761
$673$	−39.3176	−1.51558	−0.757791	−	0.652497i	$-0.773721\pi$
$673$	−39.3176	−1.51558	−0.757791	+	0.652497i	$0.773721\pi$
$674$	22.5983	0.870452
$675$	−3.93043	−0.151282
$676$	62.3455	2.39791
$677$	−15.1748	−0.583215	−0.291607	−	0.956538i	$-0.594190\pi$
$677$	−15.1748	−0.583215	−0.291607	+	0.956538i	$0.594190\pi$
$678$	−62.5953	−2.40396
$679$	1.53149	0.0587733
$680$	1.09684	0.0420618
$681$	−42.5696	−1.63127
$682$	9.25337	0.354330
$683$	−33.9264	−1.29816	−0.649080	−	0.760721i	$-0.724846\pi$
$683$	−33.9264	−1.29816	−0.649080	+	0.760721i	$0.724846\pi$
$684$	14.4599	0.552890
$685$	−11.3261	−0.432746
$686$	−14.3326	−0.547221
$687$	−7.51984	−0.286900
$688$	−17.3344	−0.660866
$689$	−82.4300	−3.14033
$690$	−25.6910	−0.978038
$691$	36.9312	1.40493	0.702465	−	0.711718i	$-0.252083\pi$
$691$	36.9312	1.40493	0.702465	+	0.711718i	$0.252083\pi$
$692$	1.76134	0.0669561
$693$	−3.63482	−0.138075
$694$	10.4867	0.398071
$695$	17.3886	0.659586
$696$	−13.9921	−0.530369
$697$	−6.78407	−0.256965
$698$	44.3089	1.67712
$699$	29.3334	1.10949
$700$	−9.01591	−0.340769
$701$	−29.8280	−1.12659	−0.563294	−	0.826257i	$-0.690466\pi$
$701$	−29.8280	−1.12659	−0.563294	+	0.826257i	$0.690466\pi$
$702$	51.2668	1.93494
$703$	33.1715	1.25109
$704$	−11.8390	−0.446198
$705$	−18.8884	−0.711379
$706$	−22.5771	−0.849699
$707$	−38.6499	−1.45358
$708$	−68.0313	−2.55677
$709$	29.7702	1.11804	0.559021	−	0.829153i	$-0.311177\pi$
$709$	29.7702	1.11804	0.559021	+	0.829153i	$0.311177\pi$
$710$	−21.4097	−0.803490
$711$	−14.6824	−0.550633
$712$	−20.4752	−0.767339
$713$	−25.7236	−0.963355
$714$	−12.8964	−0.482637
$715$	6.08523	0.227575
$716$	36.4517	1.36226
$717$	38.5030	1.43792
$718$	19.5959	0.731314
$719$	−1.13906	−0.0424799	−0.0212399	−	0.999774i	$-0.506761\pi$
$719$	−1.13906	−0.0424799	−0.0212399	+	0.999774i	$0.506761\pi$
$720$	−2.57062	−0.0958013
$721$	−34.1087	−1.27028
$722$	−20.1296	−0.749146
$723$	−30.6943	−1.14153
$724$	16.1450	0.600026
$725$	5.45897	0.202741
$726$	−4.31152	−0.160016
$727$	−50.2602	−1.86405	−0.932024	−	0.362397i	$-0.881958\pi$
$727$	−50.2602	−1.86405	−0.932024	+	0.362397i	$0.881958\pi$
$728$	26.9461	0.998688
$729$	12.1661	0.450595
$730$	−2.14348	−0.0793336
$731$	−6.07122	−0.224552
$732$	−39.9395	−1.47621
$733$	24.4876	0.904468	0.452234	−	0.891899i	$-0.350627\pi$
$733$	24.4876	0.904468	0.452234	+	0.891899i	$0.350627\pi$
$734$	4.26507	0.157427
$735$	10.2098	0.376594
$736$	46.5752	1.71679
$737$	−4.95049	−0.182354
$738$	−17.6706	−0.650464
$739$	15.5961	0.573713	0.286856	−	0.957974i	$-0.407390\pi$
$739$	15.5961	0.573713	0.286856	+	0.957974i	$0.407390\pi$
$740$	16.1520	0.593758
$741$	65.2199	2.39591
$742$	−100.899	−3.70410
$743$	9.05995	0.332377	0.166189	−	0.986094i	$-0.446854\pi$
$743$	9.05995	0.332377	0.166189	+	0.986094i	$0.446854\pi$
$744$	11.0651	0.405665
$745$	7.51945	0.275491
$746$	33.0901	1.21151
$747$	−16.2342	−0.593978
$748$	−2.23323	−0.0816549
$749$	−37.5647	−1.37258
$750$	−4.31152	−0.157434
$751$	18.1498	0.662295	0.331147	−	0.943579i	$-0.392564\pi$
$751$	18.1498	0.662295	0.331147	+	0.943579i	$0.392564\pi$
$752$	23.0779	0.841566
$753$	31.9366	1.16383
$754$	−71.2043	−2.59311
$755$	13.8880	0.505437
$756$	35.4364	1.28881
$757$	−13.4169	−0.487647	−0.243823	−	0.969820i	$-0.578402\pi$
$757$	−13.4169	−0.487647	−0.243823	+	0.969820i	$0.578402\pi$
$758$	17.0367	0.618802
$759$	11.9857	0.435052
$760$	−6.78971	−0.246289
$761$	40.9690	1.48513	0.742563	−	0.669776i	$-0.233610\pi$
$761$	40.9690	1.48513	0.742563	+	0.669776i	$0.233610\pi$
$762$	14.8048	0.536320
$763$	−52.1544	−1.88812
$764$	66.9452	2.42199
$765$	−0.900338	−0.0325518
$766$	−57.4519	−2.07582
$767$	−79.3273	−2.86434
$768$	5.61671	0.202675
$769$	45.1176	1.62698	0.813492	−	0.581576i	$-0.197564\pi$
$769$	45.1176	1.62698	0.813492	+	0.581576i	$0.197564\pi$
$770$	7.44863	0.268430
$771$	46.1034	1.66037
$772$	54.9875	1.97904
$773$	−19.8257	−0.713081	−0.356541	−	0.934280i	$-0.616044\pi$
$773$	−19.8257	−0.713081	−0.356541	+	0.934280i	$0.616044\pi$
$774$	−15.8138	−0.568416
$775$	−4.31699	−0.155071
$776$	0.561587	0.0201598
$777$	−43.5155	−1.56111
$778$	20.4818	0.734308
$779$	41.9952	1.50464
$780$	31.7571	1.13709
$781$	9.98830	0.357409
$782$	10.9939	0.393139
$783$	−21.4561	−0.766779
$784$	−12.4744	−0.445513
$785$	−6.26466	−0.223595
$786$	4.18416	0.149244
$787$	−20.0822	−0.715853	−0.357926	−	0.933750i	$-0.616516\pi$
$787$	−20.0822	−0.715853	−0.357926	+	0.933750i	$0.616516\pi$
$788$	23.2153	0.827010
$789$	−24.7283	−0.880352
$790$	30.0879	1.07048
$791$	−50.4510	−1.79383
$792$	−1.33286	−0.0473611
$793$	−46.5710	−1.65379
$794$	−40.6096	−1.44118
$795$	−27.2471	−0.966356
$796$	5.13157	0.181884
$797$	−50.2117	−1.77859	−0.889294	−	0.457336i	$-0.848804\pi$
$797$	−50.2117	−1.77859	−0.889294	+	0.457336i	$0.848804\pi$
$798$	79.8325	2.82604
$799$	8.08286	0.285951
$800$	7.81637	0.276350
$801$	16.8070	0.593848
$802$	−49.7588	−1.75704
$803$	1.00000	0.0352892
$804$	−25.8352	−0.911137
$805$	−20.7066	−0.729811
$806$	56.3089	1.98339
$807$	−23.4335	−0.824898
$808$	−14.1726	−0.498592
$809$	−10.4267	−0.366585	−0.183292	−	0.983058i	$-0.558675\pi$
$809$	−10.4267	−0.366585	−0.183292	+	0.983058i	$0.558675\pi$
$810$	23.6723	0.831758
$811$	51.4982	1.80835	0.904174	−	0.427165i	$-0.140488\pi$
$811$	51.4982	1.80835	0.904174	+	0.427165i	$0.140488\pi$
$812$	−49.2176	−1.72720
$813$	40.6456	1.42550
$814$	−13.3442	−0.467714
$815$	2.44872	0.0857748
$816$	4.25507	0.148957
$817$	37.5825	1.31484
$818$	−44.4151	−1.55294
$819$	−22.1187	−0.772889
$820$	20.4484	0.714091
$821$	16.4254	0.573249	0.286625	−	0.958043i	$-0.407467\pi$
$821$	16.4254	0.573249	0.286625	+	0.958043i	$0.407467\pi$
$822$	48.8325	1.70323
$823$	−32.1197	−1.11962	−0.559811	−	0.828620i	$-0.689126\pi$
$823$	−32.1197	−1.11962	−0.559811	+	0.828620i	$0.689126\pi$
$824$	−12.5074	−0.435717
$825$	2.01146	0.0700301
$826$	−97.1007	−3.37856
$827$	−11.3431	−0.394438	−0.197219	−	0.980359i	$-0.563191\pi$
$827$	−11.3431	−0.394438	−0.197219	+	0.980359i	$0.563191\pi$
$828$	16.1706	0.561967
$829$	6.84713	0.237811	0.118905	−	0.992906i	$-0.462062\pi$
$829$	6.84713	0.237811	0.118905	+	0.992906i	$0.462062\pi$
$830$	33.2679	1.15474
$831$	−46.2672	−1.60499
$832$	−72.0428	−2.49763
$833$	−4.36905	−0.151379
$834$	−74.9712	−2.59604
$835$	2.54186	0.0879648
$836$	13.8243	0.478123
$837$	16.9677	0.586488
$838$	21.0745	0.728007
$839$	−2.66868	−0.0921330	−0.0460665	−	0.998938i	$-0.514669\pi$
$839$	−2.66868	−0.0921330	−0.0460665	+	0.998938i	$0.514669\pi$
$840$	8.90698	0.307320
$841$	0.800348	0.0275982
$842$	−2.99955	−0.103371
$843$	59.5193	2.04995
$844$	−52.0047	−1.79008
$845$	24.0300	0.826658
$846$	21.0536	0.723838
$847$	−3.47503	−0.119403
$848$	33.2906	1.14321
$849$	1.94837	0.0668678
$850$	1.84501	0.0632835
$851$	37.0957	1.27163
$852$	52.1260	1.78581
$853$	47.6656	1.63204	0.816019	−	0.578025i	$-0.196176\pi$
$853$	47.6656	1.63204	0.816019	+	0.578025i	$0.196176\pi$
$854$	−57.0053	−1.95068
$855$	5.57334	0.190604
$856$	−13.7747	−0.470809
$857$	−22.7766	−0.778033	−0.389016	−	0.921231i	$-0.627185\pi$
$857$	−22.7766	−0.778033	−0.389016	+	0.921231i	$0.627185\pi$
$858$	−26.2366	−0.895702
$859$	−42.2964	−1.44313	−0.721567	−	0.692344i	$-0.756578\pi$
$859$	−42.2964	−1.44313	−0.721567	+	0.692344i	$0.756578\pi$
$860$	18.2998	0.624017
$861$	−55.0908	−1.87749
$862$	−52.9748	−1.80433
$863$	−41.6476	−1.41770	−0.708850	−	0.705359i	$-0.750786\pi$
$863$	−41.6476	−1.41770	−0.708850	+	0.705359i	$0.750786\pi$
$864$	−30.7217	−1.04517
$865$	0.678878	0.0230825
$866$	47.2088	1.60422
$867$	−32.7046	−1.11071
$868$	38.9216	1.32109
$869$	−14.0370	−0.476171
$870$	−23.5365	−0.797961
$871$	−30.1249	−1.02074
$872$	−19.1246	−0.647642
$873$	−0.460979	−0.0156018
$874$	−68.0549	−2.30199
$875$	−3.47503	−0.117477
$876$	5.21871	0.176324
$877$	−30.5965	−1.03317	−0.516586	−	0.856236i	$-0.672797\pi$
$877$	−30.5965	−1.03317	−0.516586	+	0.856236i	$0.672797\pi$
$878$	26.6802	0.900413
$879$	−20.6015	−0.694871
$880$	−2.45761	−0.0828461
$881$	12.0095	0.404609	0.202304	−	0.979323i	$-0.435157\pi$
$881$	12.0095	0.404609	0.202304	+	0.979323i	$0.435157\pi$
$882$	−11.3802	−0.383190
$883$	−41.1405	−1.38449	−0.692245	−	0.721663i	$-0.743378\pi$
$883$	−41.1405	−1.38449	−0.692245	+	0.721663i	$0.743378\pi$
$884$	−13.5897	−0.457071
$885$	−26.2215	−0.881426
$886$	61.5442	2.06762
$887$	29.9927	1.00705	0.503527	−	0.863979i	$-0.332035\pi$
$887$	29.9927	1.00705	0.503527	+	0.863979i	$0.332035\pi$
$888$	−15.9568	−0.535476
$889$	11.9324	0.400201
$890$	−34.4418	−1.15449
$891$	−11.0439	−0.369983
$892$	−14.1172	−0.472679
$893$	−50.0351	−1.67436
$894$	−32.4203	−1.08430
$895$	14.0497	0.469628
$896$	−33.8599	−1.13118
$897$	72.9355	2.43525
$898$	35.6103	1.18833
$899$	−23.5663	−0.785981
$900$	2.71379	0.0904595
$901$	11.6598	0.388443
$902$	−16.8938	−0.562502
$903$	−49.3020	−1.64067
$904$	−18.5000	−0.615301
$905$	6.22283	0.206854
$906$	−59.8785	−1.98933
$907$	−33.8969	−1.12553	−0.562764	−	0.826618i	$-0.690262\pi$
$907$	−33.8969	−1.12553	−0.562764	+	0.826618i	$0.690262\pi$
$908$	−54.9084	−1.82220
$909$	11.6336	0.385863
$910$	45.3266	1.50256
$911$	−37.1666	−1.23138	−0.615691	−	0.787987i	$-0.711123\pi$
$911$	−37.1666	−1.23138	−0.615691	+	0.787987i	$0.711123\pi$
$912$	−26.3401	−0.872206
$913$	−15.5205	−0.513655
$914$	15.9111	0.526293
$915$	−15.3940	−0.508909
$916$	−9.69946	−0.320479
$917$	3.37238	0.111366
$918$	−7.25171	−0.239342
$919$	−13.0921	−0.431867	−0.215934	−	0.976408i	$-0.569279\pi$
$919$	−13.0921	−0.431867	−0.215934	+	0.976408i	$0.569279\pi$
$920$	−7.59295	−0.250332
$921$	−0.376903	−0.0124194
$922$	21.3165	0.702020
$923$	60.7811	2.00063
$924$	−18.1352	−0.596603
$925$	6.22550	0.204693
$926$	79.8678	2.62462
$927$	10.2667	0.337203
$928$	42.6693	1.40069
$929$	−58.1511	−1.90787	−0.953937	−	0.300006i	$-0.903011\pi$
$929$	−58.1511	−1.90787	−0.953937	+	0.300006i	$0.903011\pi$
$930$	18.6128	0.610338
$931$	27.0456	0.886383
$932$	37.8357	1.23935
$933$	16.8955	0.553135
$934$	−42.1003	−1.37757
$935$	−0.860759	−0.0281498
$936$	−8.11076	−0.265109
$937$	14.2872	0.466743	0.233372	−	0.972388i	$-0.425024\pi$
$937$	14.2872	0.466743	0.233372	+	0.972388i	$0.425024\pi$
$938$	−36.8744	−1.20399
$939$	22.2594	0.726409
$940$	−24.3632	−0.794641
$941$	−29.1327	−0.949700	−0.474850	−	0.880067i	$-0.657498\pi$
$941$	−29.1327	−0.949700	−0.474850	+	0.880067i	$0.657498\pi$
$942$	27.0102	0.880040
$943$	46.9633	1.52934
$944$	32.0375	1.04273
$945$	13.6584	0.444307
$946$	−15.1186	−0.491550
$947$	41.1640	1.33765	0.668825	−	0.743420i	$-0.266798\pi$
$947$	41.1640	1.33765	0.668825	+	0.743420i	$0.266798\pi$
$948$	−73.2548	−2.37921
$949$	6.08523	0.197535
$950$	−11.4211	−0.370551
$951$	−27.2778	−0.884544
$952$	−3.81154	−0.123533
$953$	39.3961	1.27617	0.638083	−	0.769968i	$-0.279728\pi$
$953$	39.3961	1.27617	0.638083	+	0.769968i	$0.279728\pi$
$954$	30.3705	0.983280
$955$	25.8029	0.834961
$956$	49.6632	1.60622
$957$	10.9805	0.354950
$958$	29.9640	0.968094
$959$	39.3584	1.27095
$960$	−23.8136	−0.768582
$961$	−12.3636	−0.398825
$962$	−81.2025	−2.61807
$963$	11.3070	0.364362
$964$	−39.5911	−1.27514
$965$	21.1940	0.682258
$966$	89.2768	2.87243
$967$	−55.2335	−1.77619	−0.888095	−	0.459659i	$-0.847972\pi$
$967$	−55.2335	−1.77619	−0.888095	+	0.459659i	$0.847972\pi$
$968$	−1.27427	−0.0409565
$969$	−9.22539	−0.296362
$970$	0.944659	0.0303312
$971$	16.2648	0.521963	0.260982	−	0.965344i	$-0.415954\pi$
$971$	16.2648	0.521963	0.260982	+	0.965344i	$0.415954\pi$
$972$	−27.0424	−0.867385
$973$	−60.4257	−1.93716
$974$	11.8799	0.380655
$975$	12.2402	0.392000
$976$	18.8084	0.602043
$977$	7.13298	0.228204	0.114102	−	0.993469i	$-0.463601\pi$
$977$	7.13298	0.228204	0.114102	+	0.993469i	$0.463601\pi$
$978$	−10.5577	−0.337598
$979$	16.0682	0.513542
$980$	13.1691	0.420672
$981$	15.6985	0.501213
$982$	−66.6212	−2.12597
$983$	−9.56032	−0.304927	−0.152463	−	0.988309i	$-0.548721\pi$
$983$	−9.56032	−0.304927	−0.152463	+	0.988309i	$0.548721\pi$
$984$	−20.2014	−0.643997
$985$	8.94792	0.285105
$986$	10.0719	0.320754
$987$	65.6378	2.08927
$988$	84.1239	2.67634
$989$	42.0286	1.33643
$990$	−2.24204	−0.0712566
$991$	31.1509	0.989540	0.494770	−	0.869024i	$-0.335252\pi$
$991$	31.1509	0.989540	0.494770	+	0.869024i	$0.335252\pi$
$992$	−33.7432	−1.07135
$993$	−35.1271	−1.11473
$994$	74.3992	2.35980
$995$	1.97787	0.0627028
$996$	−80.9972	−2.56649
$997$	13.1014	0.414927	0.207463	−	0.978243i	$-0.433479\pi$
$997$	13.1014	0.414927	0.207463	+	0.978243i	$0.433479\pi$
$998$	12.3366	0.390508
$999$	−24.4689	−0.774162

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.5	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.5	✓	37	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)

\(f(q)\)	\(=\)	\(q-2.14348 q^{2} +2.01146 q^{3} +2.59449 q^{4} +1.00000 q^{5} -4.31152 q^{6} -3.47503 q^{7} -1.27427 q^{8} +1.04598 q^{9} +O(q^{10})\)	\(q-2.14348 q^{2} +2.01146 q^{3} +2.59449 q^{4} +1.00000 q^{5} -4.31152 q^{6} -3.47503 q^{7} -1.27427 q^{8} +1.04598 q^{9} -2.14348 q^{10} +1.00000 q^{11} +5.21871 q^{12} +6.08523 q^{13} +7.44863 q^{14} +2.01146 q^{15} -2.45761 q^{16} -0.860759 q^{17} -2.24204 q^{18} +5.32833 q^{19} +2.59449 q^{20} -6.98989 q^{21} -2.14348 q^{22} +5.95868 q^{23} -2.56314 q^{24} +1.00000 q^{25} -13.0435 q^{26} -3.93043 q^{27} -9.01591 q^{28} +5.45897 q^{29} -4.31152 q^{30} -4.31699 q^{31} +7.81637 q^{32} +2.01146 q^{33} +1.84501 q^{34} -3.47503 q^{35} +2.71379 q^{36} +6.22550 q^{37} -11.4211 q^{38} +12.2402 q^{39} -1.27427 q^{40} +7.88150 q^{41} +14.9826 q^{42} +7.05333 q^{43} +2.59449 q^{44} +1.04598 q^{45} -12.7723 q^{46} -9.39039 q^{47} -4.94340 q^{48} +5.07581 q^{49} -2.14348 q^{50} -1.73138 q^{51} +15.7880 q^{52} -13.5459 q^{53} +8.42479 q^{54} +1.00000 q^{55} +4.42811 q^{56} +10.7177 q^{57} -11.7012 q^{58} -13.0360 q^{59} +5.21871 q^{60} -7.65313 q^{61} +9.25337 q^{62} -3.63482 q^{63} -11.8390 q^{64} +6.08523 q^{65} -4.31152 q^{66} -4.95049 q^{67} -2.23323 q^{68} +11.9857 q^{69} +7.44863 q^{70} +9.98830 q^{71} -1.33286 q^{72} +1.00000 q^{73} -13.3442 q^{74} +2.01146 q^{75} +13.8243 q^{76} -3.47503 q^{77} -26.2366 q^{78} -14.0370 q^{79} -2.45761 q^{80} -11.0439 q^{81} -16.8938 q^{82} -15.5205 q^{83} -18.1352 q^{84} -0.860759 q^{85} -15.1186 q^{86} +10.9805 q^{87} -1.27427 q^{88} +16.0682 q^{89} -2.24204 q^{90} -21.1463 q^{91} +15.4597 q^{92} -8.68347 q^{93} +20.1281 q^{94} +5.32833 q^{95} +15.7223 q^{96} -0.440714 q^{97} -10.8799 q^{98} +1.04598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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