LMFDB - Embedded newform 6015.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65304 q^{2} -1.00000 q^{3} +5.03861 q^{4} -1.00000 q^{5} +2.65304 q^{6} -2.89459 q^{7} -8.06155 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.65304 q^{2} -1.00000 q^{3} +5.03861 q^{4} -1.00000 q^{5} +2.65304 q^{6} -2.89459 q^{7} -8.06155 q^{8} +1.00000 q^{9} +2.65304 q^{10} -1.27940 q^{11} -5.03861 q^{12} +5.27510 q^{13} +7.67945 q^{14} +1.00000 q^{15} +11.3104 q^{16} +2.30304 q^{17} -2.65304 q^{18} +1.21819 q^{19} -5.03861 q^{20} +2.89459 q^{21} +3.39429 q^{22} +0.302101 q^{23} +8.06155 q^{24} +1.00000 q^{25} -13.9950 q^{26} -1.00000 q^{27} -14.5847 q^{28} -4.64856 q^{29} -2.65304 q^{30} +6.71827 q^{31} -13.8838 q^{32} +1.27940 q^{33} -6.11005 q^{34} +2.89459 q^{35} +5.03861 q^{36} -9.19888 q^{37} -3.23192 q^{38} -5.27510 q^{39} +8.06155 q^{40} +1.18004 q^{41} -7.67945 q^{42} -9.11290 q^{43} -6.44639 q^{44} -1.00000 q^{45} -0.801485 q^{46} -11.4035 q^{47} -11.3104 q^{48} +1.37864 q^{49} -2.65304 q^{50} -2.30304 q^{51} +26.5792 q^{52} -6.42289 q^{53} +2.65304 q^{54} +1.27940 q^{55} +23.3349 q^{56} -1.21819 q^{57} +12.3328 q^{58} +3.28210 q^{59} +5.03861 q^{60} +1.11864 q^{61} -17.8238 q^{62} -2.89459 q^{63} +14.2134 q^{64} -5.27510 q^{65} -3.39429 q^{66} +15.3320 q^{67} +11.6041 q^{68} -0.302101 q^{69} -7.67945 q^{70} +8.34401 q^{71} -8.06155 q^{72} -3.82903 q^{73} +24.4050 q^{74} -1.00000 q^{75} +6.13801 q^{76} +3.70333 q^{77} +13.9950 q^{78} +10.5723 q^{79} -11.3104 q^{80} +1.00000 q^{81} -3.13068 q^{82} -6.63777 q^{83} +14.5847 q^{84} -2.30304 q^{85} +24.1769 q^{86} +4.64856 q^{87} +10.3139 q^{88} +3.66282 q^{89} +2.65304 q^{90} -15.2692 q^{91} +1.52217 q^{92} -6.71827 q^{93} +30.2538 q^{94} -1.21819 q^{95} +13.8838 q^{96} +7.98020 q^{97} -3.65759 q^{98} -1.27940 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - 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 $

$2$	−2.65304	−1.87598	−0.937991	−	0.346661i	$-0.887316\pi$
$2$	−2.65304	−1.87598	−0.937991	+	0.346661i	$0.887316\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.03861	2.51931
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.65304	1.08310
$7$	−2.89459	−1.09405	−0.547026	−	0.837116i	$-0.684240\pi$
$7$	−2.89459	−1.09405	−0.547026	+	0.837116i	$0.684240\pi$
$8$	−8.06155	−2.85019
$9$	1.00000	0.333333
$10$	2.65304	0.838964
$11$	−1.27940	−0.385753	−0.192877	−	0.981223i	$-0.561782\pi$
$11$	−1.27940	−0.385753	−0.192877	+	0.981223i	$0.561782\pi$
$12$	−5.03861	−1.45452
$13$	5.27510	1.46305	0.731525	−	0.681815i	$-0.238809\pi$
$13$	5.27510	1.46305	0.731525	+	0.681815i	$0.238809\pi$
$14$	7.67945	2.05242
$15$	1.00000	0.258199
$16$	11.3104	2.82759
$17$	2.30304	0.558569	0.279285	−	0.960208i	$-0.409903\pi$
$17$	2.30304	0.558569	0.279285	+	0.960208i	$0.409903\pi$
$18$	−2.65304	−0.625327
$19$	1.21819	0.279473	0.139736	−	0.990189i	$-0.455374\pi$
$19$	1.21819	0.279473	0.139736	+	0.990189i	$0.455374\pi$
$20$	−5.03861	−1.12667
$21$	2.89459	0.631651
$22$	3.39429	0.723666
$23$	0.302101	0.0629923	0.0314962	−	0.999504i	$-0.489973\pi$
$23$	0.302101	0.0629923	0.0314962	+	0.999504i	$0.489973\pi$
$24$	8.06155	1.64556
$25$	1.00000	0.200000
$26$	−13.9950	−2.74465
$27$	−1.00000	−0.192450
$28$	−14.5847	−2.75625
$29$	−4.64856	−0.863216	−0.431608	−	0.902061i	$-0.642054\pi$
$29$	−4.64856	−0.863216	−0.431608	+	0.902061i	$0.642054\pi$
$30$	−2.65304	−0.484376
$31$	6.71827	1.20664	0.603319	−	0.797500i	$-0.293845\pi$
$31$	6.71827	1.20664	0.603319	+	0.797500i	$0.293845\pi$
$32$	−13.8838	−2.45433
$33$	1.27940	0.222715
$34$	−6.11005	−1.04787
$35$	2.89459	0.489275
$36$	5.03861	0.839768
$37$	−9.19888	−1.51229	−0.756143	−	0.654406i	$-0.772919\pi$
$37$	−9.19888	−1.51229	−0.756143	+	0.654406i	$0.772919\pi$
$38$	−3.23192	−0.524286
$39$	−5.27510	−0.844692
$40$	8.06155	1.27464
$41$	1.18004	0.184291	0.0921453	−	0.995746i	$-0.470628\pi$
$41$	1.18004	0.184291	0.0921453	+	0.995746i	$0.470628\pi$
$42$	−7.67945	−1.18497
$43$	−9.11290	−1.38970	−0.694852	−	0.719153i	$-0.744530\pi$
$43$	−9.11290	−1.38970	−0.694852	+	0.719153i	$0.744530\pi$
$44$	−6.44639	−0.971830
$45$	−1.00000	−0.149071
$46$	−0.801485	−0.118172
$47$	−11.4035	−1.66337	−0.831683	−	0.555250i	$-0.812623\pi$
$47$	−11.4035	−1.66337	−0.831683	+	0.555250i	$0.812623\pi$
$48$	−11.3104	−1.63251
$49$	1.37864	0.196949
$50$	−2.65304	−0.375196
$51$	−2.30304	−0.322490
$52$	26.5792	3.68587
$53$	−6.42289	−0.882252	−0.441126	−	0.897445i	$-0.645421\pi$
$53$	−6.42289	−0.882252	−0.441126	+	0.897445i	$0.645421\pi$
$54$	2.65304	0.361033
$55$	1.27940	0.172514
$56$	23.3349	3.11825
$57$	−1.21819	−0.161354
$58$	12.3328	1.61938
$59$	3.28210	0.427293	0.213647	−	0.976911i	$-0.431466\pi$
$59$	3.28210	0.427293	0.213647	+	0.976911i	$0.431466\pi$
$60$	5.03861	0.650482
$61$	1.11864	0.143227	0.0716133	−	0.997432i	$-0.477185\pi$
$61$	1.11864	0.143227	0.0716133	+	0.997432i	$0.477185\pi$
$62$	−17.8238	−2.26363
$63$	−2.89459	−0.364684
$64$	14.2134	1.77667
$65$	−5.27510	−0.654296
$66$	−3.39429	−0.417809
$67$	15.3320	1.87310	0.936551	−	0.350533i	$-0.113999\pi$
$67$	15.3320	1.87310	0.936551	+	0.350533i	$0.113999\pi$
$68$	11.6041	1.40721
$69$	−0.302101	−0.0363686
$70$	−7.67945	−0.917870
$71$	8.34401	0.990252	0.495126	−	0.868821i	$-0.335122\pi$
$71$	8.34401	0.990252	0.495126	+	0.868821i	$0.335122\pi$
$72$	−8.06155	−0.950063
$73$	−3.82903	−0.448154	−0.224077	−	0.974571i	$-0.571937\pi$
$73$	−3.82903	−0.448154	−0.224077	+	0.974571i	$0.571937\pi$
$74$	24.4050	2.83702
$75$	−1.00000	−0.115470
$76$	6.13801	0.704078
$77$	3.70333	0.422034
$78$	13.9950	1.58463
$79$	10.5723	1.18947	0.594736	−	0.803921i	$-0.297256\pi$
$79$	10.5723	1.18947	0.594736	+	0.803921i	$0.297256\pi$
$80$	−11.3104	−1.26454
$81$	1.00000	0.111111
$82$	−3.13068	−0.345726
$83$	−6.63777	−0.728590	−0.364295	−	0.931284i	$-0.618690\pi$
$83$	−6.63777	−0.728590	−0.364295	+	0.931284i	$0.618690\pi$
$84$	14.5847	1.59132
$85$	−2.30304	−0.249800
$86$	24.1769	2.60706
$87$	4.64856	0.498378
$88$	10.3139	1.09947
$89$	3.66282	0.388258	0.194129	−	0.980976i	$-0.437812\pi$
$89$	3.66282	0.388258	0.194129	+	0.980976i	$0.437812\pi$
$90$	2.65304	0.279655
$91$	−15.2692	−1.60065
$92$	1.52217	0.158697
$93$	−6.71827	−0.696653
$94$	30.2538	3.12044
$95$	−1.21819	−0.124984
$96$	13.8838	1.41701
$97$	7.98020	0.810267	0.405134	−	0.914258i	$-0.367225\pi$
$97$	7.98020	0.810267	0.405134	+	0.914258i	$0.367225\pi$
$98$	−3.65759	−0.369473
$99$	−1.27940	−0.128584
$100$	5.03861	0.503861
$101$	−14.1413	−1.40711	−0.703555	−	0.710641i	$-0.748405\pi$
$101$	−14.1413	−1.40711	−0.703555	+	0.710641i	$0.748405\pi$
$102$	6.11005	0.604985
$103$	13.7967	1.35943	0.679715	−	0.733476i	$-0.262104\pi$
$103$	13.7967	1.35943	0.679715	+	0.733476i	$0.262104\pi$
$104$	−42.5255	−4.16997
$105$	−2.89459	−0.282483
$106$	17.0402	1.65509
$107$	5.97146	0.577283	0.288642	−	0.957437i	$-0.406796\pi$
$107$	5.97146	0.577283	0.288642	+	0.957437i	$0.406796\pi$
$108$	−5.03861	−0.484841
$109$	18.3336	1.75604	0.878021	−	0.478623i	$-0.158864\pi$
$109$	18.3336	1.75604	0.878021	+	0.478623i	$0.158864\pi$
$110$	−3.39429	−0.323633
$111$	9.19888	0.873119
$112$	−32.7389	−3.09353
$113$	−13.2003	−1.24178	−0.620891	−	0.783897i	$-0.713229\pi$
$113$	−13.2003	−1.24178	−0.620891	+	0.783897i	$0.713229\pi$
$114$	3.23192	0.302697
$115$	−0.302101	−0.0281710
$116$	−23.4223	−2.17470
$117$	5.27510	0.487683
$118$	−8.70754	−0.801594
$119$	−6.66635	−0.611104
$120$	−8.06155	−0.735915
$121$	−9.36314	−0.851194
$122$	−2.96778	−0.268690
$123$	−1.18004	−0.106400
$124$	33.8508	3.03989
$125$	−1.00000	−0.0894427
$126$	7.67945	0.684140
$127$	−10.1523	−0.900872	−0.450436	−	0.892809i	$-0.648732\pi$
$127$	−10.1523	−0.900872	−0.450436	+	0.892809i	$0.648732\pi$
$128$	−9.94115	−0.878681
$129$	9.11290	0.802346
$130$	13.9950	1.22745
$131$	11.6618	1.01889	0.509446	−	0.860502i	$-0.329850\pi$
$131$	11.6618	1.01889	0.509446	+	0.860502i	$0.329850\pi$
$132$	6.44639	0.561087
$133$	−3.52617	−0.305758
$134$	−40.6764	−3.51390
$135$	1.00000	0.0860663
$136$	−18.5661	−1.59203
$137$	−4.05687	−0.346602	−0.173301	−	0.984869i	$-0.555443\pi$
$137$	−4.05687	−0.346602	−0.173301	+	0.984869i	$0.555443\pi$
$138$	0.801485	0.0682269
$139$	2.50295	0.212298	0.106149	−	0.994350i	$-0.466148\pi$
$139$	2.50295	0.212298	0.106149	+	0.994350i	$0.466148\pi$
$140$	14.5847	1.23263
$141$	11.4035	0.960345
$142$	−22.1370	−1.85769
$143$	−6.74896	−0.564376
$144$	11.3104	0.942531
$145$	4.64856	0.386042
$146$	10.1586	0.840728
$147$	−1.37864	−0.113709
$148$	−46.3496	−3.80991
$149$	14.4273	1.18193	0.590963	−	0.806698i	$-0.298748\pi$
$149$	14.4273	1.18193	0.590963	+	0.806698i	$0.298748\pi$
$150$	2.65304	0.216620
$151$	6.04843	0.492214	0.246107	−	0.969243i	$-0.420849\pi$
$151$	6.04843	0.492214	0.246107	+	0.969243i	$0.420849\pi$
$152$	−9.82053	−0.796550
$153$	2.30304	0.186190
$154$	−9.82508	−0.791728
$155$	−6.71827	−0.539625
$156$	−26.5792	−2.12804
$157$	−0.175800	−0.0140304	−0.00701519	−	0.999975i	$-0.502233\pi$
$157$	−0.175800	−0.0140304	−0.00701519	+	0.999975i	$0.502233\pi$
$158$	−28.0486	−2.23143
$159$	6.42289	0.509368
$160$	13.8838	1.09761
$161$	−0.874457	−0.0689169
$162$	−2.65304	−0.208442
$163$	2.21762	0.173698	0.0868489	−	0.996221i	$-0.472320\pi$
$163$	2.21762	0.173698	0.0868489	+	0.996221i	$0.472320\pi$
$164$	5.94574	0.464284
$165$	−1.27940	−0.0996011
$166$	17.6103	1.36682
$167$	20.0636	1.55257	0.776285	−	0.630382i	$-0.217102\pi$
$167$	20.0636	1.55257	0.776285	+	0.630382i	$0.217102\pi$
$168$	−23.3349	−1.80032
$169$	14.8267	1.14051
$170$	6.11005	0.468620
$171$	1.21819	0.0931576
$172$	−45.9164	−3.50109
$173$	15.5652	1.18340	0.591701	−	0.806157i	$-0.298456\pi$
$173$	15.5652	1.18340	0.591701	+	0.806157i	$0.298456\pi$
$174$	−12.3328	−0.934947
$175$	−2.89459	−0.218810
$176$	−14.4705	−1.09075
$177$	−3.28210	−0.246698
$178$	−9.71760	−0.728365
$179$	15.4897	1.15775	0.578877	−	0.815415i	$-0.303491\pi$
$179$	15.4897	1.15775	0.578877	+	0.815415i	$0.303491\pi$
$180$	−5.03861	−0.375556
$181$	−13.3312	−0.990904	−0.495452	−	0.868635i	$-0.664997\pi$
$181$	−13.3312	−0.990904	−0.495452	+	0.868635i	$0.664997\pi$
$182$	40.5099	3.00279
$183$	−1.11864	−0.0826919
$184$	−2.43540	−0.179540
$185$	9.19888	0.676315
$186$	17.8238	1.30691
$187$	−2.94651	−0.215470
$188$	−57.4576	−4.19053
$189$	2.89459	0.210550
$190$	3.23192	0.234468
$191$	−25.2998	−1.83063	−0.915314	−	0.402742i	$-0.868057\pi$
$191$	−25.2998	−1.83063	−0.915314	+	0.402742i	$0.868057\pi$
$192$	−14.2134	−1.02576
$193$	−25.5672	−1.84037	−0.920185	−	0.391484i	$-0.871962\pi$
$193$	−25.5672	−1.84037	−0.920185	+	0.391484i	$0.871962\pi$
$194$	−21.1718	−1.52005
$195$	5.27510	0.377758
$196$	6.94644	0.496175
$197$	−6.10569	−0.435012	−0.217506	−	0.976059i	$-0.569792\pi$
$197$	−6.10569	−0.435012	−0.217506	+	0.976059i	$0.569792\pi$
$198$	3.39429	0.241222
$199$	−7.50008	−0.531667	−0.265833	−	0.964019i	$-0.585647\pi$
$199$	−7.50008	−0.531667	−0.265833	+	0.964019i	$0.585647\pi$
$200$	−8.06155	−0.570038
$201$	−15.3320	−1.08144
$202$	37.5173	2.63971
$203$	13.4557	0.944402
$204$	−11.6041	−0.812451
$205$	−1.18004	−0.0824172
$206$	−36.6032	−2.55026
$207$	0.302101	0.0209974
$208$	59.6634	4.13691
$209$	−1.55856	−0.107808
$210$	7.67945	0.529933
$211$	−5.85120	−0.402813	−0.201406	−	0.979508i	$-0.564551\pi$
$211$	−5.85120	−0.402813	−0.201406	+	0.979508i	$0.564551\pi$
$212$	−32.3624	−2.22266
$213$	−8.34401	−0.571722
$214$	−15.8425	−1.08297
$215$	9.11290	0.621495
$216$	8.06155	0.548519
$217$	−19.4466	−1.32012
$218$	−48.6398	−3.29430
$219$	3.82903	0.258742
$220$	6.44639	0.434616
$221$	12.1488	0.817214
$222$	−24.4050	−1.63795
$223$	22.0445	1.47621	0.738105	−	0.674685i	$-0.235721\pi$
$223$	22.0445	1.47621	0.738105	+	0.674685i	$0.235721\pi$
$224$	40.1878	2.68516
$225$	1.00000	0.0666667
$226$	35.0210	2.32956
$227$	−6.32931	−0.420091	−0.210046	−	0.977692i	$-0.567361\pi$
$227$	−6.32931	−0.420091	−0.210046	+	0.977692i	$0.567361\pi$
$228$	−6.13801	−0.406499
$229$	11.3474	0.749856	0.374928	−	0.927054i	$-0.377667\pi$
$229$	11.3474	0.749856	0.374928	+	0.927054i	$0.377667\pi$
$230$	0.801485	0.0528483
$231$	−3.70333	−0.243661
$232$	37.4746	2.46033
$233$	−10.8870	−0.713229	−0.356615	−	0.934252i	$-0.616069\pi$
$233$	−10.8870	−0.713229	−0.356615	+	0.934252i	$0.616069\pi$
$234$	−13.9950	−0.914884
$235$	11.4035	0.743880
$236$	16.5372	1.07648
$237$	−10.5723	−0.686742
$238$	17.6861	1.14642
$239$	−19.2866	−1.24755	−0.623774	−	0.781605i	$-0.714402\pi$
$239$	−19.2866	−1.24755	−0.623774	+	0.781605i	$0.714402\pi$
$240$	11.3104	0.730082
$241$	−13.2813	−0.855526	−0.427763	−	0.903891i	$-0.640698\pi$
$241$	−13.2813	−0.855526	−0.427763	+	0.903891i	$0.640698\pi$
$242$	24.8408	1.59682
$243$	−1.00000	−0.0641500
$244$	5.63637	0.360831
$245$	−1.37864	−0.0880783
$246$	3.13068	0.199605
$247$	6.42610	0.408883
$248$	−54.1597	−3.43914
$249$	6.63777	0.420652
$250$	2.65304	0.167793
$251$	21.8005	1.37604	0.688018	−	0.725693i	$-0.258481\pi$
$251$	21.8005	1.37604	0.688018	+	0.725693i	$0.258481\pi$
$252$	−14.5847	−0.918750
$253$	−0.386507	−0.0242995
$254$	26.9345	1.69002
$255$	2.30304	0.144222
$256$	−2.05254	−0.128284
$257$	16.3403	1.01928	0.509640	−	0.860388i	$-0.329778\pi$
$257$	16.3403	1.01928	0.509640	+	0.860388i	$0.329778\pi$
$258$	−24.1769	−1.50519
$259$	26.6270	1.65452
$260$	−26.5792	−1.64837
$261$	−4.64856	−0.287739
$262$	−30.9391	−1.91142
$263$	−6.80909	−0.419866	−0.209933	−	0.977716i	$-0.567325\pi$
$263$	−6.80909	−0.419866	−0.209933	+	0.977716i	$0.567325\pi$
$264$	−10.3139	−0.634779
$265$	6.42289	0.394555
$266$	9.35507	0.573596
$267$	−3.66282	−0.224161
$268$	77.2519	4.71891
$269$	−1.95596	−0.119257	−0.0596286	−	0.998221i	$-0.518992\pi$
$269$	−1.95596	−0.119257	−0.0596286	+	0.998221i	$0.518992\pi$
$270$	−2.65304	−0.161459
$271$	−6.73429	−0.409079	−0.204539	−	0.978858i	$-0.565570\pi$
$271$	−6.73429	−0.409079	−0.204539	+	0.978858i	$0.565570\pi$
$272$	26.0483	1.57941
$273$	15.2692	0.924137
$274$	10.7630	0.650219
$275$	−1.27940	−0.0771507
$276$	−1.52217	−0.0916237
$277$	−15.1293	−0.909034	−0.454517	−	0.890738i	$-0.650188\pi$
$277$	−15.1293	−0.909034	−0.454517	+	0.890738i	$0.650188\pi$
$278$	−6.64043	−0.398267
$279$	6.71827	0.402213
$280$	−23.3349	−1.39453
$281$	−14.0947	−0.840816	−0.420408	−	0.907335i	$-0.638113\pi$
$281$	−14.0947	−0.840816	−0.420408	+	0.907335i	$0.638113\pi$
$282$	−30.2538	−1.80159
$283$	20.1452	1.19751	0.598754	−	0.800933i	$-0.295663\pi$
$283$	20.1452	1.19751	0.598754	+	0.800933i	$0.295663\pi$
$284$	42.0422	2.49475
$285$	1.21819	0.0721596
$286$	17.9052	1.05876
$287$	−3.41572	−0.201623
$288$	−13.8838	−0.818108
$289$	−11.6960	−0.688000
$290$	−12.3328	−0.724207
$291$	−7.98020	−0.467808
$292$	−19.2930	−1.12904
$293$	−18.0099	−1.05215	−0.526076	−	0.850437i	$-0.676337\pi$
$293$	−18.0099	−1.05215	−0.526076	+	0.850437i	$0.676337\pi$
$294$	3.65759	0.213315
$295$	−3.28210	−0.191091
$296$	74.1572	4.31030
$297$	1.27940	0.0742383
$298$	−38.2760	−2.21727
$299$	1.59361	0.0921609
$300$	−5.03861	−0.290904
$301$	26.3781	1.52041
$302$	−16.0467	−0.923385
$303$	14.1413	0.812395
$304$	13.7782	0.790236
$305$	−1.11864	−0.0640529
$306$	−6.11005	−0.349288
$307$	28.2053	1.60976	0.804881	−	0.593437i	$-0.202229\pi$
$307$	28.2053	1.60976	0.804881	+	0.593437i	$0.202229\pi$
$308$	18.6597	1.06323
$309$	−13.7967	−0.784867
$310$	17.8238	1.01233
$311$	17.8410	1.01167	0.505835	−	0.862630i	$-0.331185\pi$
$311$	17.8410	1.01167	0.505835	+	0.862630i	$0.331185\pi$
$312$	42.5255	2.40753
$313$	1.88817	0.106726	0.0533629	−	0.998575i	$-0.483006\pi$
$313$	1.88817	0.106726	0.0533629	+	0.998575i	$0.483006\pi$
$314$	0.466405	0.0263207
$315$	2.89459	0.163092
$316$	53.2695	2.99665
$317$	−5.87846	−0.330167	−0.165084	−	0.986280i	$-0.552789\pi$
$317$	−5.87846	−0.330167	−0.165084	+	0.986280i	$0.552789\pi$
$318$	−17.0402	−0.955566
$319$	5.94736	0.332988
$320$	−14.2134	−0.794553
$321$	−5.97146	−0.333295
$322$	2.31997	0.129287
$323$	2.80555	0.156105
$324$	5.03861	0.279923
$325$	5.27510	0.292610
$326$	−5.88344	−0.325854
$327$	−18.3336	−1.01385
$328$	−9.51291	−0.525263
$329$	33.0084	1.81981
$330$	3.39429	0.186850
$331$	−10.6758	−0.586795	−0.293398	−	0.955990i	$-0.594786\pi$
$331$	−10.6758	−0.586795	−0.293398	+	0.955990i	$0.594786\pi$
$332$	−33.4451	−1.83554
$333$	−9.19888	−0.504096
$334$	−53.2296	−2.91259
$335$	−15.3320	−0.837676
$336$	32.7389	1.78605
$337$	1.42857	0.0778192	0.0389096	−	0.999243i	$-0.487612\pi$
$337$	1.42857	0.0778192	0.0389096	+	0.999243i	$0.487612\pi$
$338$	−39.3357	−2.13958
$339$	13.2003	0.716943
$340$	−11.6041	−0.629322
$341$	−8.59535	−0.465464
$342$	−3.23192	−0.174762
$343$	16.2715	0.878579
$344$	73.4641	3.96092
$345$	0.302101	0.0162646
$346$	−41.2952	−2.22004
$347$	−2.69004	−0.144409	−0.0722043	−	0.997390i	$-0.523003\pi$
$347$	−2.69004	−0.144409	−0.0722043	+	0.997390i	$0.523003\pi$
$348$	23.4223	1.25557
$349$	−0.445750	−0.0238605	−0.0119302	−	0.999929i	$-0.503798\pi$
$349$	−0.445750	−0.0238605	−0.0119302	+	0.999929i	$0.503798\pi$
$350$	7.67945	0.410484
$351$	−5.27510	−0.281564
$352$	17.7629	0.946764
$353$	20.9066	1.11275	0.556374	−	0.830932i	$-0.312192\pi$
$353$	20.9066	1.11275	0.556374	+	0.830932i	$0.312192\pi$
$354$	8.70754	0.462800
$355$	−8.34401	−0.442854
$356$	18.4555	0.978141
$357$	6.66635	0.352821
$358$	−41.0947	−2.17192
$359$	26.7037	1.40937	0.704684	−	0.709521i	$-0.251089\pi$
$359$	26.7037	1.40937	0.704684	+	0.709521i	$0.251089\pi$
$360$	8.06155	0.424881
$361$	−17.5160	−0.921895
$362$	35.3683	1.85892
$363$	9.36314	0.491437
$364$	−76.9358	−4.03253
$365$	3.82903	0.200420
$366$	2.96778	0.155128
$367$	−20.5556	−1.07299	−0.536496	−	0.843903i	$-0.680252\pi$
$367$	−20.5556	−1.07299	−0.536496	+	0.843903i	$0.680252\pi$
$368$	3.41687	0.178117
$369$	1.18004	0.0614302
$370$	−24.4050	−1.26875
$371$	18.5916	0.965229
$372$	−33.8508	−1.75508
$373$	28.1096	1.45546	0.727730	−	0.685864i	$-0.240575\pi$
$373$	28.1096	1.45546	0.727730	+	0.685864i	$0.240575\pi$
$374$	7.81720	0.404218
$375$	1.00000	0.0516398
$376$	91.9296	4.74091
$377$	−24.5216	−1.26293
$378$	−7.67945	−0.394988
$379$	−7.00982	−0.360070	−0.180035	−	0.983660i	$-0.557621\pi$
$379$	−7.00982	−0.360070	−0.180035	+	0.983660i	$0.557621\pi$
$380$	−6.13801	−0.314873
$381$	10.1523	0.520119
$382$	67.1213	3.43422
$383$	−9.71422	−0.496373	−0.248187	−	0.968712i	$-0.579835\pi$
$383$	−9.71422	−0.496373	−0.248187	+	0.968712i	$0.579835\pi$
$384$	9.94115	0.507307
$385$	−3.70333	−0.188739
$386$	67.8309	3.45250
$387$	−9.11290	−0.463235
$388$	40.2091	2.04131
$389$	−29.6820	−1.50494	−0.752469	−	0.658628i	$-0.771137\pi$
$389$	−29.6820	−1.50494	−0.752469	+	0.658628i	$0.771137\pi$
$390$	−13.9950	−0.708666
$391$	0.695750	0.0351856
$392$	−11.1140	−0.561342
$393$	−11.6618	−0.588258
$394$	16.1986	0.816075
$395$	−10.5723	−0.531948
$396$	−6.44639	−0.323943
$397$	17.4142	0.873995	0.436997	−	0.899463i	$-0.356042\pi$
$397$	17.4142	0.873995	0.436997	+	0.899463i	$0.356042\pi$
$398$	19.8980	0.997397
$399$	3.52617	0.176529
$400$	11.3104	0.565519
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	40.6764	2.02875
$403$	35.4396	1.76537
$404$	−71.2524	−3.54494
$405$	−1.00000	−0.0496904
$406$	−35.6984	−1.77168
$407$	11.7690	0.583370
$408$	18.5661	0.919158
$409$	−33.7138	−1.66704	−0.833520	−	0.552489i	$-0.813678\pi$
$409$	−33.7138	−1.66704	−0.833520	+	0.552489i	$0.813678\pi$
$410$	3.13068	0.154613
$411$	4.05687	0.200111
$412$	69.5162	3.42482
$413$	−9.50033	−0.467481
$414$	−0.801485	−0.0393908
$415$	6.63777	0.325835
$416$	−73.2382	−3.59080
$417$	−2.50295	−0.122570
$418$	4.13491	0.202245
$419$	22.7806	1.11290	0.556452	−	0.830880i	$-0.312162\pi$
$419$	22.7806	1.11290	0.556452	+	0.830880i	$0.312162\pi$
$420$	−14.5847	−0.711661
$421$	−3.03015	−0.147681	−0.0738403	−	0.997270i	$-0.523526\pi$
$421$	−3.03015	−0.147681	−0.0738403	+	0.997270i	$0.523526\pi$
$422$	15.5234	0.755669
$423$	−11.4035	−0.554456
$424$	51.7785	2.51458
$425$	2.30304	0.111714
$426$	22.1370	1.07254
$427$	−3.23799	−0.156697
$428$	30.0879	1.45435
$429$	6.74896	0.325843
$430$	−24.1769	−1.16591
$431$	9.39410	0.452498	0.226249	−	0.974070i	$-0.427354\pi$
$431$	9.39410	0.452498	0.226249	+	0.974070i	$0.427354\pi$
$432$	−11.3104	−0.544171
$433$	0.988256	0.0474925	0.0237463	−	0.999718i	$-0.492441\pi$
$433$	0.988256	0.0474925	0.0237463	+	0.999718i	$0.492441\pi$
$434$	51.5927	2.47653
$435$	−4.64856	−0.222881
$436$	92.3759	4.42400
$437$	0.368017	0.0176047
$438$	−10.1586	−0.485394
$439$	16.7649	0.800143	0.400072	−	0.916484i	$-0.368985\pi$
$439$	16.7649	0.800143	0.400072	+	0.916484i	$0.368985\pi$
$440$	−10.3139	−0.491698
$441$	1.37864	0.0656497
$442$	−32.2311	−1.53308
$443$	−2.46481	−0.117107	−0.0585534	−	0.998284i	$-0.518649\pi$
$443$	−2.46481	−0.117107	−0.0585534	+	0.998284i	$0.518649\pi$
$444$	46.3496	2.19965
$445$	−3.66282	−0.173634
$446$	−58.4850	−2.76934
$447$	−14.4273	−0.682386
$448$	−41.1419	−1.94377
$449$	−27.5361	−1.29951	−0.649753	−	0.760145i	$-0.725128\pi$
$449$	−27.5361	−1.29951	−0.649753	+	0.760145i	$0.725128\pi$
$450$	−2.65304	−0.125065
$451$	−1.50974	−0.0710907
$452$	−66.5113	−3.12843
$453$	−6.04843	−0.284180
$454$	16.7919	0.788083
$455$	15.2692	0.715833
$456$	9.82053	0.459889
$457$	−7.81385	−0.365517	−0.182758	−	0.983158i	$-0.558503\pi$
$457$	−7.81385	−0.365517	−0.182758	+	0.983158i	$0.558503\pi$
$458$	−30.1050	−1.40672
$459$	−2.30304	−0.107497
$460$	−1.52217	−0.0709714
$461$	−26.5120	−1.23479	−0.617394	−	0.786654i	$-0.711811\pi$
$461$	−26.5120	−1.23479	−0.617394	+	0.786654i	$0.711811\pi$
$462$	9.82508	0.457104
$463$	−37.1663	−1.72726	−0.863631	−	0.504124i	$-0.831815\pi$
$463$	−37.1663	−1.72726	−0.863631	+	0.504124i	$0.831815\pi$
$464$	−52.5769	−2.44082
$465$	6.71827	0.311552
$466$	28.8835	1.33800
$467$	−20.3525	−0.941801	−0.470901	−	0.882186i	$-0.656071\pi$
$467$	−20.3525	−0.941801	−0.470901	+	0.882186i	$0.656071\pi$
$468$	26.5792	1.22862
$469$	−44.3798	−2.04927
$470$	−30.2538	−1.39551
$471$	0.175800	0.00810045
$472$	−26.4588	−1.21787
$473$	11.6590	0.536083
$474$	28.0486	1.28832
$475$	1.21819	0.0558946
$476$	−33.5892	−1.53956
$477$	−6.42289	−0.294084
$478$	51.1682	2.34038
$479$	1.82640	0.0834504	0.0417252	−	0.999129i	$-0.486715\pi$
$479$	1.82640	0.0834504	0.0417252	+	0.999129i	$0.486715\pi$
$480$	−13.8838	−0.633704
$481$	−48.5250	−2.21255
$482$	35.2359	1.60495
$483$	0.874457	0.0397892
$484$	−47.1772	−2.14442
$485$	−7.98020	−0.362362
$486$	2.65304	0.120344
$487$	25.1373	1.13908	0.569540	−	0.821963i	$-0.307121\pi$
$487$	25.1373	1.13908	0.569540	+	0.821963i	$0.307121\pi$
$488$	−9.01793	−0.408223
$489$	−2.21762	−0.100284
$490$	3.65759	0.165233
$491$	−10.0423	−0.453205	−0.226602	−	0.973987i	$-0.572762\pi$
$491$	−10.0423	−0.453205	−0.226602	+	0.973987i	$0.572762\pi$
$492$	−5.94574	−0.268055
$493$	−10.7058	−0.482166
$494$	−17.0487	−0.767056
$495$	1.27940	0.0575047
$496$	75.9862	3.41188
$497$	−24.1525	−1.08339
$498$	−17.6103	−0.789134
$499$	6.68974	0.299474	0.149737	−	0.988726i	$-0.452157\pi$
$499$	6.68974	0.299474	0.149737	+	0.988726i	$0.452157\pi$
$500$	−5.03861	−0.225334
$501$	−20.0636	−0.896377
$502$	−57.8376	−2.58142
$503$	−36.0744	−1.60848	−0.804238	−	0.594308i	$-0.797426\pi$
$503$	−36.0744	−1.60848	−0.804238	+	0.594308i	$0.797426\pi$
$504$	23.3349	1.03942
$505$	14.1413	0.629279
$506$	1.02542	0.0455854
$507$	−14.8267	−0.658476
$508$	−51.1536	−2.26957
$509$	−20.9501	−0.928598	−0.464299	−	0.885678i	$-0.653694\pi$
$509$	−20.9501	−0.928598	−0.464299	+	0.885678i	$0.653694\pi$
$510$	−6.11005	−0.270558
$511$	11.0835	0.490303
$512$	25.3278	1.11934
$513$	−1.21819	−0.0537846
$514$	−43.3515	−1.91215
$515$	−13.7967	−0.607955
$516$	45.9164	2.02135
$517$	14.5896	0.641649
$518$	−70.6424	−3.10385
$519$	−15.5652	−0.683238
$520$	42.5255	1.86487
$521$	−14.7681	−0.647001	−0.323501	−	0.946228i	$-0.604860\pi$
$521$	−14.7681	−0.647001	−0.323501	+	0.946228i	$0.604860\pi$
$522$	12.3328	0.539792
$523$	−32.6528	−1.42781	−0.713904	−	0.700244i	$-0.753075\pi$
$523$	−32.6528	−1.42781	−0.713904	+	0.700244i	$0.753075\pi$
$524$	58.7591	2.56690
$525$	2.89459	0.126330
$526$	18.0648	0.787662
$527$	15.4725	0.673991
$528$	14.4705	0.629747
$529$	−22.9087	−0.996032
$530$	−17.0402	−0.740178
$531$	3.28210	0.142431
$532$	−17.7670	−0.770297
$533$	6.22480	0.269626
$534$	9.71760	0.420522
$535$	−5.97146	−0.258169
$536$	−123.600	−5.33869
$537$	−15.4897	−0.668429
$538$	5.18925	0.223724
$539$	−1.76383	−0.0759737
$540$	5.03861	0.216827
$541$	−23.9291	−1.02879	−0.514397	−	0.857552i	$-0.671984\pi$
$541$	−23.9291	−1.02879	−0.514397	+	0.857552i	$0.671984\pi$
$542$	17.8663	0.767424
$543$	13.3312	0.572098
$544$	−31.9749	−1.37091
$545$	−18.3336	−0.785326
$546$	−40.5099	−1.73366
$547$	−20.8202	−0.890206	−0.445103	−	0.895479i	$-0.646833\pi$
$547$	−20.8202	−0.890206	−0.445103	+	0.895479i	$0.646833\pi$
$548$	−20.4410	−0.873196
$549$	1.11864	0.0477422
$550$	3.39429	0.144733
$551$	−5.66285	−0.241245
$552$	2.43540	0.103657
$553$	−30.6024	−1.30134
$554$	40.1387	1.70533
$555$	−9.19888	−0.390471
$556$	12.6114	0.534843
$557$	41.2298	1.74696	0.873482	−	0.486857i	$-0.161857\pi$
$557$	41.2298	1.74696	0.873482	+	0.486857i	$0.161857\pi$
$558$	−17.8238	−0.754543
$559$	−48.0715	−2.03321
$560$	32.7389	1.38347
$561$	2.94651	0.124402
$562$	37.3936	1.57736
$563$	−24.5618	−1.03516	−0.517578	−	0.855636i	$-0.673166\pi$
$563$	−24.5618	−1.03516	−0.517578	+	0.855636i	$0.673166\pi$
$564$	57.4576	2.41940
$565$	13.2003	0.555342
$566$	−53.4460	−2.24650
$567$	−2.89459	−0.121561
$568$	−67.2657	−2.82240
$569$	−20.6287	−0.864799	−0.432399	−	0.901682i	$-0.642333\pi$
$569$	−20.6287	−0.864799	−0.432399	+	0.901682i	$0.642333\pi$
$570$	−3.23192	−0.135370
$571$	−29.6690	−1.24161	−0.620805	−	0.783965i	$-0.713194\pi$
$571$	−29.6690	−1.24161	−0.620805	+	0.783965i	$0.713194\pi$
$572$	−34.0054	−1.42184
$573$	25.2998	1.05691
$574$	9.06203	0.378242
$575$	0.302101	0.0125985
$576$	14.2134	0.592225
$577$	23.7944	0.990573	0.495286	−	0.868730i	$-0.335063\pi$
$577$	23.7944	0.990573	0.495286	+	0.868730i	$0.335063\pi$
$578$	31.0300	1.29068
$579$	25.5672	1.06254
$580$	23.4223	0.972557
$581$	19.2136	0.797115
$582$	21.1718	0.877599
$583$	8.21744	0.340332
$584$	30.8679	1.27732
$585$	−5.27510	−0.218099
$586$	47.7811	1.97382
$587$	−22.1084	−0.912510	−0.456255	−	0.889849i	$-0.650810\pi$
$587$	−22.1084	−0.912510	−0.456255	+	0.889849i	$0.650810\pi$
$588$	−6.94644	−0.286467
$589$	8.18416	0.337223
$590$	8.70754	0.358484
$591$	6.10569	0.251154
$592$	−104.043	−4.27613
$593$	−14.3196	−0.588036	−0.294018	−	0.955800i	$-0.594993\pi$
$593$	−14.3196	−0.588036	−0.294018	+	0.955800i	$0.594993\pi$
$594$	−3.39429	−0.139270
$595$	6.66635	0.273294
$596$	72.6933	2.97763
$597$	7.50008	0.306958
$598$	−4.22791	−0.172892
$599$	15.6212	0.638264	0.319132	−	0.947710i	$-0.396609\pi$
$599$	15.6212	0.638264	0.319132	+	0.947710i	$0.396609\pi$
$600$	8.06155	0.329111
$601$	−15.5875	−0.635826	−0.317913	−	0.948120i	$-0.602982\pi$
$601$	−15.5875	−0.635826	−0.317913	+	0.948120i	$0.602982\pi$
$602$	−69.9821	−2.85226
$603$	15.3320	0.624367
$604$	30.4757	1.24004
$605$	9.36314	0.380666
$606$	−37.5173	−1.52404
$607$	5.16957	0.209826	0.104913	−	0.994481i	$-0.466544\pi$
$607$	5.16957	0.209826	0.104913	+	0.994481i	$0.466544\pi$
$608$	−16.9131	−0.685917
$609$	−13.4557	−0.545251
$610$	2.96778	0.120162
$611$	−60.1544	−2.43359
$612$	11.6041	0.469069
$613$	9.88542	0.399268	0.199634	−	0.979870i	$-0.436025\pi$
$613$	9.88542	0.399268	0.199634	+	0.979870i	$0.436025\pi$
$614$	−74.8297	−3.01988
$615$	1.18004	0.0475836
$616$	−29.8546	−1.20288
$617$	16.7525	0.674430	0.337215	−	0.941428i	$-0.390515\pi$
$617$	16.7525	0.674430	0.337215	+	0.941428i	$0.390515\pi$
$618$	36.6032	1.47240
$619$	−16.0056	−0.643321	−0.321660	−	0.946855i	$-0.604241\pi$
$619$	−16.0056	−0.643321	−0.321660	+	0.946855i	$0.604241\pi$
$620$	−33.8508	−1.35948
$621$	−0.302101	−0.0121229
$622$	−47.3328	−1.89787
$623$	−10.6024	−0.424774
$624$	−59.6634	−2.38845
$625$	1.00000	0.0400000
$626$	−5.00939	−0.200215
$627$	1.55856	0.0622427
$628$	−0.885789	−0.0353468
$629$	−21.1854	−0.844717
$630$	−7.67945	−0.305957
$631$	−35.8528	−1.42728	−0.713638	−	0.700514i	$-0.752954\pi$
$631$	−35.8528	−1.42728	−0.713638	+	0.700514i	$0.752954\pi$
$632$	−85.2288	−3.39022
$633$	5.85120	0.232564
$634$	15.5958	0.619387
$635$	10.1523	0.402882
$636$	32.3624	1.28325
$637$	7.27248	0.288146
$638$	−15.7786	−0.624680
$639$	8.34401	0.330084
$640$	9.94115	0.392958
$641$	26.0826	1.03020	0.515101	−	0.857130i	$-0.327754\pi$
$641$	26.0826	1.03020	0.515101	+	0.857130i	$0.327754\pi$
$642$	15.8425	0.625254
$643$	−5.62951	−0.222006	−0.111003	−	0.993820i	$-0.535406\pi$
$643$	−5.62951	−0.222006	−0.111003	+	0.993820i	$0.535406\pi$
$644$	−4.40605	−0.173623
$645$	−9.11290	−0.358820
$646$	−7.44323	−0.292850
$647$	31.6489	1.24425	0.622123	−	0.782919i	$-0.286270\pi$
$647$	31.6489	1.24425	0.622123	+	0.782919i	$0.286270\pi$
$648$	−8.06155	−0.316688
$649$	−4.19912	−0.164830
$650$	−13.9950	−0.548931
$651$	19.4466	0.762174
$652$	11.1737	0.437598
$653$	−10.2456	−0.400941	−0.200471	−	0.979700i	$-0.564247\pi$
$653$	−10.2456	−0.400941	−0.200471	+	0.979700i	$0.564247\pi$
$654$	48.6398	1.90197
$655$	−11.6618	−0.455663
$656$	13.3466	0.521099
$657$	−3.82903	−0.149385
$658$	−87.5724	−3.41393
$659$	1.39282	0.0542566	0.0271283	−	0.999632i	$-0.491364\pi$
$659$	1.39282	0.0542566	0.0271283	+	0.999632i	$0.491364\pi$
$660$	−6.44639	−0.250926
$661$	20.3527	0.791630	0.395815	−	0.918330i	$-0.370462\pi$
$661$	20.3527	0.791630	0.395815	+	0.918330i	$0.370462\pi$
$662$	28.3233	1.10082
$663$	−12.1488	−0.471819
$664$	53.5107	2.07662
$665$	3.52617	0.136739
$666$	24.4050	0.945674
$667$	−1.40433	−0.0543760
$668$	101.093	3.91140
$669$	−22.0445	−0.852291
$670$	40.6764	1.57146
$671$	−1.43118	−0.0552501
$672$	−40.1878	−1.55028
$673$	−45.4808	−1.75316	−0.876578	−	0.481260i	$-0.840179\pi$
$673$	−45.4808	−1.75316	−0.876578	+	0.481260i	$0.840179\pi$
$674$	−3.79005	−0.145987
$675$	−1.00000	−0.0384900
$676$	74.7058	2.87330
$677$	38.9275	1.49611	0.748053	−	0.663639i	$-0.230989\pi$
$677$	38.9275	1.49611	0.748053	+	0.663639i	$0.230989\pi$
$678$	−35.0210	−1.34497
$679$	−23.0994	−0.886474
$680$	18.5661	0.711976
$681$	6.32931	0.242540
$682$	22.8038	0.873203
$683$	−5.14062	−0.196700	−0.0983501	−	0.995152i	$-0.531357\pi$
$683$	−5.14062	−0.196700	−0.0983501	+	0.995152i	$0.531357\pi$
$684$	6.13801	0.234693
$685$	4.05687	0.155005
$686$	−43.1690	−1.64820
$687$	−11.3474	−0.432930
$688$	−103.070	−3.92952
$689$	−33.8814	−1.29078
$690$	−0.801485	−0.0305120
$691$	−7.57178	−0.288044	−0.144022	−	0.989574i	$-0.546004\pi$
$691$	−7.57178	−0.288044	−0.144022	+	0.989574i	$0.546004\pi$
$692$	78.4271	2.98135
$693$	3.70333	0.140678
$694$	7.13677	0.270908
$695$	−2.50295	−0.0949425
$696$	−37.4746	−1.42047
$697$	2.71767	0.102939
$698$	1.18259	0.0447618
$699$	10.8870	0.411783
$700$	−14.5847	−0.551250
$701$	−36.7906	−1.38956	−0.694781	−	0.719222i	$-0.744499\pi$
$701$	−36.7906	−1.38956	−0.694781	+	0.719222i	$0.744499\pi$
$702$	13.9950	0.528209
$703$	−11.2060	−0.422643
$704$	−18.1846	−0.685358
$705$	−11.4035	−0.429479
$706$	−55.4661	−2.08749
$707$	40.9332	1.53945
$708$	−16.5372	−0.621507
$709$	−28.7766	−1.08073	−0.540364	−	0.841432i	$-0.681713\pi$
$709$	−28.7766	−1.08073	−0.540364	+	0.841432i	$0.681713\pi$
$710$	22.1370	0.830786
$711$	10.5723	0.396491
$712$	−29.5280	−1.10661
$713$	2.02960	0.0760089
$714$	−17.6861	−0.661885
$715$	6.74896	0.252397
$716$	78.0465	2.91673
$717$	19.2866	0.720272
$718$	−70.8460	−2.64395
$719$	−30.9173	−1.15302	−0.576510	−	0.817090i	$-0.695586\pi$
$719$	−30.9173	−1.15302	−0.576510	+	0.817090i	$0.695586\pi$
$720$	−11.3104	−0.421513
$721$	−39.9358	−1.48729
$722$	46.4706	1.72946
$723$	13.2813	0.493938
$724$	−67.1710	−2.49639
$725$	−4.64856	−0.172643
$726$	−24.8408	−0.921927
$727$	32.0966	1.19040	0.595198	−	0.803579i	$-0.297074\pi$
$727$	32.0966	1.19040	0.595198	+	0.803579i	$0.297074\pi$
$728$	123.094	4.56216
$729$	1.00000	0.0370370
$730$	−10.1586	−0.375985
$731$	−20.9874	−0.776246
$732$	−5.63637	−0.208326
$733$	25.7708	0.951867	0.475933	−	0.879481i	$-0.342110\pi$
$733$	25.7708	0.951867	0.475933	+	0.879481i	$0.342110\pi$
$734$	54.5347	2.01291
$735$	1.37864	0.0508520
$736$	−4.19429	−0.154604
$737$	−19.6157	−0.722555
$738$	−3.13068	−0.115242
$739$	38.1006	1.40155	0.700776	−	0.713381i	$-0.252837\pi$
$739$	38.1006	1.40155	0.700776	+	0.713381i	$0.252837\pi$
$740$	46.3496	1.70384
$741$	−6.42610	−0.236069
$742$	−49.3243	−1.81075
$743$	−41.0443	−1.50577	−0.752884	−	0.658153i	$-0.771338\pi$
$743$	−41.0443	−1.50577	−0.752884	+	0.658153i	$0.771338\pi$
$744$	54.1597	1.98559
$745$	−14.4273	−0.528574
$746$	−74.5759	−2.73042
$747$	−6.63777	−0.242863
$748$	−14.8463	−0.542835
$749$	−17.2849	−0.631578
$750$	−2.65304	−0.0968753
$751$	−8.61597	−0.314401	−0.157201	−	0.987567i	$-0.550247\pi$
$751$	−8.61597	−0.314401	−0.157201	+	0.987567i	$0.550247\pi$
$752$	−128.978	−4.70333
$753$	−21.8005	−0.794455
$754$	65.0568	2.36923
$755$	−6.04843	−0.220125
$756$	14.5847	0.530441
$757$	33.2873	1.20985	0.604924	−	0.796283i	$-0.293204\pi$
$757$	33.2873	1.20985	0.604924	+	0.796283i	$0.293204\pi$
$758$	18.5973	0.675485
$759$	0.386507	0.0140293
$760$	9.82053	0.356228
$761$	29.4180	1.06640	0.533200	−	0.845989i	$-0.320989\pi$
$761$	29.4180	1.06640	0.533200	+	0.845989i	$0.320989\pi$
$762$	−26.9345	−0.975733
$763$	−53.0683	−1.92120
$764$	−127.476	−4.61191
$765$	−2.30304	−0.0832666
$766$	25.7722	0.931187
$767$	17.3134	0.625151
$768$	2.05254	0.0740648
$769$	13.2480	0.477734	0.238867	−	0.971052i	$-0.423224\pi$
$769$	13.2480	0.477734	0.238867	+	0.971052i	$0.423224\pi$
$770$	9.82508	0.354071
$771$	−16.3403	−0.588482
$772$	−128.823	−4.63645
$773$	−8.71355	−0.313405	−0.156702	−	0.987646i	$-0.550086\pi$
$773$	−8.71355	−0.313405	−0.156702	+	0.987646i	$0.550086\pi$
$774$	24.1769	0.869020
$775$	6.71827	0.241328
$776$	−64.3328	−2.30941
$777$	−26.6270	−0.955237
$778$	78.7475	2.82324
$779$	1.43751	0.0515042
$780$	26.5792	0.951687
$781$	−10.6753	−0.381993
$782$	−1.84585	−0.0660075
$783$	4.64856	0.166126
$784$	15.5930	0.556892
$785$	0.175800	0.00627458
$786$	30.9391	1.10356
$787$	−8.14974	−0.290507	−0.145253	−	0.989394i	$-0.546400\pi$
$787$	−8.14974	−0.290507	−0.145253	+	0.989394i	$0.546400\pi$
$788$	−30.7642	−1.09593
$789$	6.80909	0.242410
$790$	28.0486	0.997925
$791$	38.2095	1.35857
$792$	10.3139	0.366490
$793$	5.90091	0.209548
$794$	−46.2006	−1.63960
$795$	−6.42289	−0.227796
$796$	−37.7900	−1.33943
$797$	15.5796	0.551857	0.275928	−	0.961178i	$-0.411015\pi$
$797$	15.5796	0.551857	0.275928	+	0.961178i	$0.411015\pi$
$798$	−9.35507	−0.331166
$799$	−26.2626	−0.929106
$800$	−13.8838	−0.490865
$801$	3.66282	0.129419
$802$	2.65304	0.0936820
$803$	4.89885	0.172877
$804$	−77.2519	−2.72447
$805$	0.874457	0.0308206
$806$	−94.0225	−3.31180
$807$	1.95596	0.0688532
$808$	114.001	4.01053
$809$	−40.5061	−1.42412	−0.712060	−	0.702118i	$-0.752238\pi$
$809$	−40.5061	−1.42412	−0.712060	+	0.702118i	$0.752238\pi$
$810$	2.65304	0.0932183
$811$	−31.1682	−1.09446	−0.547231	−	0.836982i	$-0.684318\pi$
$811$	−31.1682	−1.09446	−0.547231	+	0.836982i	$0.684318\pi$
$812$	67.7979	2.37924
$813$	6.73429	0.236182
$814$	−31.2237	−1.09439
$815$	−2.21762	−0.0776800
$816$	−26.0483	−0.911871
$817$	−11.1013	−0.388385
$818$	89.4440	3.12734
$819$	−15.2692	−0.533551
$820$	−5.94574	−0.207634
$821$	−2.76759	−0.0965894	−0.0482947	−	0.998833i	$-0.515379\pi$
$821$	−2.76759	−0.0965894	−0.0482947	+	0.998833i	$0.515379\pi$
$822$	−10.7630	−0.375404
$823$	20.3452	0.709188	0.354594	−	0.935020i	$-0.384619\pi$
$823$	20.3452	0.709188	0.354594	+	0.935020i	$0.384619\pi$
$824$	−111.223	−3.87463
$825$	1.27940	0.0445430
$826$	25.2047	0.876985
$827$	17.7808	0.618298	0.309149	−	0.951014i	$-0.399956\pi$
$827$	17.7808	0.618298	0.309149	+	0.951014i	$0.399956\pi$
$828$	1.52217	0.0528990
$829$	−39.6827	−1.37824	−0.689119	−	0.724648i	$-0.742002\pi$
$829$	−39.6827	−1.37824	−0.689119	+	0.724648i	$0.742002\pi$
$830$	−17.6103	−0.611261
$831$	15.1293	0.524831
$832$	74.9771	2.59936
$833$	3.17507	0.110010
$834$	6.64043	0.229939
$835$	−20.0636	−0.694331
$836$	−7.85296	−0.271600
$837$	−6.71827	−0.232218
$838$	−60.4377	−2.08779
$839$	28.1869	0.973120	0.486560	−	0.873647i	$-0.338251\pi$
$839$	28.1869	0.973120	0.486560	+	0.873647i	$0.338251\pi$
$840$	23.3349	0.805130
$841$	−7.39091	−0.254859
$842$	8.03911	0.277046
$843$	14.0947	0.485446
$844$	−29.4819	−1.01481
$845$	−14.8267	−0.510053
$846$	30.2538	1.04015
$847$	27.1024	0.931251
$848$	−72.6453	−2.49465
$849$	−20.1452	−0.691381
$850$	−6.11005	−0.209573
$851$	−2.77899	−0.0952625
$852$	−42.0422	−1.44034
$853$	−32.2211	−1.10323	−0.551615	−	0.834099i	$-0.685988\pi$
$853$	−32.2211	−1.10323	−0.551615	+	0.834099i	$0.685988\pi$
$854$	8.59051	0.293961
$855$	−1.21819	−0.0416614
$856$	−48.1392	−1.64537
$857$	6.48649	0.221574	0.110787	−	0.993844i	$-0.464663\pi$
$857$	6.48649	0.221574	0.110787	+	0.993844i	$0.464663\pi$
$858$	−17.9052	−0.611275
$859$	−22.9195	−0.782003	−0.391002	−	0.920390i	$-0.627871\pi$
$859$	−22.9195	−0.782003	−0.391002	+	0.920390i	$0.627871\pi$
$860$	45.9164	1.56573
$861$	3.41572	0.116407
$862$	−24.9229	−0.848877
$863$	50.8707	1.73166	0.865830	−	0.500339i	$-0.166791\pi$
$863$	50.8707	1.73166	0.865830	+	0.500339i	$0.166791\pi$
$864$	13.8838	0.472335
$865$	−15.5652	−0.529234
$866$	−2.62188	−0.0890951
$867$	11.6960	0.397217
$868$	−97.9840	−3.32580
$869$	−13.5261	−0.458843
$870$	12.3328	0.418121
$871$	80.8778	2.74044
$872$	−147.797	−5.00505
$873$	7.98020	0.270089
$874$	−0.976364	−0.0330260
$875$	2.89459	0.0978550
$876$	19.2930	0.651849
$877$	−22.2806	−0.752364	−0.376182	−	0.926546i	$-0.622763\pi$
$877$	−22.2806	−0.752364	−0.376182	+	0.926546i	$0.622763\pi$
$878$	−44.4778	−1.50105
$879$	18.0099	0.607460
$880$	14.4705	0.487800
$881$	51.1580	1.72356	0.861779	−	0.507284i	$-0.169351\pi$
$881$	51.1580	1.72356	0.861779	+	0.507284i	$0.169351\pi$
$882$	−3.65759	−0.123158
$883$	17.5576	0.590862	0.295431	−	0.955364i	$-0.404537\pi$
$883$	17.5576	0.590862	0.295431	+	0.955364i	$0.404537\pi$
$884$	61.2129	2.05881
$885$	3.28210	0.110327
$886$	6.53924	0.219690
$887$	5.48446	0.184150	0.0920750	−	0.995752i	$-0.470650\pi$
$887$	5.48446	0.184150	0.0920750	+	0.995752i	$0.470650\pi$
$888$	−74.1572	−2.48855
$889$	29.3868	0.985601
$890$	9.71760	0.325735
$891$	−1.27940	−0.0428615
$892$	111.074	3.71903
$893$	−13.8916	−0.464866
$894$	38.2760	1.28014
$895$	−15.4897	−0.517763
$896$	28.7755	0.961323
$897$	−1.59361	−0.0532091
$898$	73.0542	2.43785
$899$	−31.2303	−1.04159
$900$	5.03861	0.167954
$901$	−14.7922	−0.492799
$902$	4.00539	0.133365
$903$	−26.3781	−0.877808
$904$	106.415	3.53931
$905$	13.3312	0.443146
$906$	16.0467	0.533116
$907$	−17.3626	−0.576514	−0.288257	−	0.957553i	$-0.593076\pi$
$907$	−17.3626	−0.576514	−0.288257	+	0.957553i	$0.593076\pi$
$908$	−31.8909	−1.05834
$909$	−14.1413	−0.469037
$910$	−40.5099	−1.34289
$911$	−3.32414	−0.110134	−0.0550668	−	0.998483i	$-0.517537\pi$
$911$	−3.32414	−0.110134	−0.0550668	+	0.998483i	$0.517537\pi$
$912$	−13.7782	−0.456243
$913$	8.49235	0.281056
$914$	20.7304	0.685702
$915$	1.11864	0.0369809
$916$	57.1750	1.88912
$917$	−33.7560	−1.11472
$918$	6.11005	0.201662
$919$	−8.92336	−0.294354	−0.147177	−	0.989110i	$-0.547019\pi$
$919$	−8.92336	−0.294354	−0.147177	+	0.989110i	$0.547019\pi$
$920$	2.43540	0.0802927
$921$	−28.2053	−0.929396
$922$	70.3374	2.31644
$923$	44.0155	1.44879
$924$	−18.6597	−0.613858
$925$	−9.19888	−0.302457
$926$	98.6035	3.24031
$927$	13.7967	0.453143
$928$	64.5395	2.11861
$929$	44.1531	1.44862	0.724308	−	0.689476i	$-0.242159\pi$
$929$	44.1531	1.44862	0.724308	+	0.689476i	$0.242159\pi$
$930$	−17.8238	−0.584467
$931$	1.67945	0.0550419
$932$	−54.8552	−1.79684
$933$	−17.8410	−0.584088
$934$	53.9960	1.76680
$935$	2.94651	0.0963611
$936$	−42.5255	−1.38999
$937$	−1.34652	−0.0439890	−0.0219945	−	0.999758i	$-0.507002\pi$
$937$	−1.34652	−0.0439890	−0.0219945	+	0.999758i	$0.507002\pi$
$938$	117.741	3.84439
$939$	−1.88817	−0.0616181
$940$	57.4576	1.87406
$941$	9.02224	0.294117	0.147058	−	0.989128i	$-0.453020\pi$
$941$	9.02224	0.294117	0.147058	+	0.989128i	$0.453020\pi$
$942$	−0.466405	−0.0151963
$943$	0.356489	0.0116089
$944$	37.1218	1.20821
$945$	−2.89459	−0.0941610
$946$	−30.9319	−1.00568
$947$	−49.0883	−1.59516	−0.797578	−	0.603216i	$-0.793886\pi$
$947$	−49.0883	−1.59516	−0.797578	+	0.603216i	$0.793886\pi$
$948$	−53.2695	−1.73011
$949$	−20.1985	−0.655671
$950$	−3.23192	−0.104857
$951$	5.87846	0.190622
$952$	53.7411	1.74176
$953$	26.4425	0.856557	0.428278	−	0.903647i	$-0.359120\pi$
$953$	26.4425	0.856557	0.428278	+	0.903647i	$0.359120\pi$
$954$	17.0402	0.551696
$955$	25.2998	0.818681
$956$	−97.1778	−3.14296
$957$	−5.94736	−0.192251
$958$	−4.84551	−0.156551
$959$	11.7430	0.379201
$960$	14.2134	0.458735
$961$	14.1352	0.455974
$962$	128.739	4.15070
$963$	5.97146	0.192428
$964$	−66.9195	−2.15533
$965$	25.5672	0.823038
$966$	−2.31997	−0.0746437
$967$	−17.5619	−0.564754	−0.282377	−	0.959303i	$-0.591123\pi$
$967$	−17.5619	−0.564754	−0.282377	+	0.959303i	$0.591123\pi$
$968$	75.4814	2.42606
$969$	−2.80555	−0.0901272
$970$	21.1718	0.679785
$971$	25.7422	0.826106	0.413053	−	0.910707i	$-0.364462\pi$
$971$	25.7422	0.826106	0.413053	+	0.910707i	$0.364462\pi$
$972$	−5.03861	−0.161614
$973$	−7.24502	−0.232265
$974$	−66.6902	−2.13689
$975$	−5.27510	−0.168938
$976$	12.6522	0.404987
$977$	18.0106	0.576210	0.288105	−	0.957599i	$-0.406975\pi$
$977$	18.0106	0.576210	0.288105	+	0.957599i	$0.406975\pi$
$978$	5.88344	0.188132
$979$	−4.68621	−0.149772
$980$	−6.94644	−0.221896
$981$	18.3336	0.585347
$982$	26.6427	0.850204
$983$	9.39466	0.299643	0.149822	−	0.988713i	$-0.452130\pi$
$983$	9.39466	0.299643	0.149822	+	0.988713i	$0.452130\pi$
$984$	9.51291	0.303261
$985$	6.10569	0.194543
$986$	28.4029	0.904534
$987$	−33.0084	−1.05067
$988$	32.3786	1.03010
$989$	−2.75301	−0.0875407
$990$	−3.39429	−0.107878
$991$	−1.89497	−0.0601957	−0.0300978	−	0.999547i	$-0.509582\pi$
$991$	−1.89497	−0.0601957	−0.0300978	+	0.999547i	$0.509582\pi$
$992$	−93.2749	−2.96148
$993$	10.6758	0.338787
$994$	64.0774	2.03241
$995$	7.50008	0.237769
$996$	33.4451	1.05975
$997$	−8.26643	−0.261800	−0.130900	−	0.991396i	$-0.541787\pi$
$997$	−8.26643	−0.261800	−0.130900	+	0.991396i	$0.541787\pi$
$998$	−17.7481	−0.561807
$999$	9.19888	0.291040

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.f.1.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.f.1.3	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65304 q^{2} -1.00000 q^{3} +5.03861 q^{4} -1.00000 q^{5} +2.65304 q^{6} -2.89459 q^{7} -8.06155 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.65304 q^{2} -1.00000 q^{3} +5.03861 q^{4} -1.00000 q^{5} +2.65304 q^{6} -2.89459 q^{7} -8.06155 q^{8} +1.00000 q^{9} +2.65304 q^{10} -1.27940 q^{11} -5.03861 q^{12} +5.27510 q^{13} +7.67945 q^{14} +1.00000 q^{15} +11.3104 q^{16} +2.30304 q^{17} -2.65304 q^{18} +1.21819 q^{19} -5.03861 q^{20} +2.89459 q^{21} +3.39429 q^{22} +0.302101 q^{23} +8.06155 q^{24} +1.00000 q^{25} -13.9950 q^{26} -1.00000 q^{27} -14.5847 q^{28} -4.64856 q^{29} -2.65304 q^{30} +6.71827 q^{31} -13.8838 q^{32} +1.27940 q^{33} -6.11005 q^{34} +2.89459 q^{35} +5.03861 q^{36} -9.19888 q^{37} -3.23192 q^{38} -5.27510 q^{39} +8.06155 q^{40} +1.18004 q^{41} -7.67945 q^{42} -9.11290 q^{43} -6.44639 q^{44} -1.00000 q^{45} -0.801485 q^{46} -11.4035 q^{47} -11.3104 q^{48} +1.37864 q^{49} -2.65304 q^{50} -2.30304 q^{51} +26.5792 q^{52} -6.42289 q^{53} +2.65304 q^{54} +1.27940 q^{55} +23.3349 q^{56} -1.21819 q^{57} +12.3328 q^{58} +3.28210 q^{59} +5.03861 q^{60} +1.11864 q^{61} -17.8238 q^{62} -2.89459 q^{63} +14.2134 q^{64} -5.27510 q^{65} -3.39429 q^{66} +15.3320 q^{67} +11.6041 q^{68} -0.302101 q^{69} -7.67945 q^{70} +8.34401 q^{71} -8.06155 q^{72} -3.82903 q^{73} +24.4050 q^{74} -1.00000 q^{75} +6.13801 q^{76} +3.70333 q^{77} +13.9950 q^{78} +10.5723 q^{79} -11.3104 q^{80} +1.00000 q^{81} -3.13068 q^{82} -6.63777 q^{83} +14.5847 q^{84} -2.30304 q^{85} +24.1769 q^{86} +4.64856 q^{87} +10.3139 q^{88} +3.66282 q^{89} +2.65304 q^{90} -15.2692 q^{91} +1.52217 q^{92} -6.71827 q^{93} +30.2538 q^{94} -1.21819 q^{95} +13.8838 q^{96} +7.98020 q^{97} -3.65759 q^{98} -1.27940 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9	\( 36 q - 7 q^{2} - 36 q^{3} + 45 q^{4} - 36 q^{5} + 7 q^{6} + 2 q^{7} - 24 q^{8} + 36 q^{9} + 7 q^{10} - q^{11} - 45 q^{12} - 8 q^{13} - 4 q^{14} + 36 q^{15} + 63 q^{16} - 50 q^{17} - 7 q^{18} + 15 q^{19} - 45 q^{20} - 2 q^{21} + 7 q^{22} - 32 q^{23} + 24 q^{24} + 36 q^{25} - 12 q^{26} - 36 q^{27} - 10 q^{28} + 7 q^{29} - 7 q^{30} + 7 q^{31} - 50 q^{32} + q^{33} + 8 q^{34} - 2 q^{35} + 45 q^{36} - 10 q^{37} - 48 q^{38} + 8 q^{39} + 24 q^{40} - 31 q^{41} + 4 q^{42} + 27 q^{43} - 9 q^{44} - 36 q^{45} + 23 q^{46} - 46 q^{47} - 63 q^{48} + 48 q^{49} - 7 q^{50} + 50 q^{51} - 14 q^{52} - 39 q^{53} + 7 q^{54} + q^{55} - 29 q^{56} - 15 q^{57} - 26 q^{58} - 9 q^{59} + 45 q^{60} + 5 q^{61} - 65 q^{62} + 2 q^{63} + 90 q^{64} + 8 q^{65} - 7 q^{66} + 18 q^{67} - 128 q^{68} + 32 q^{69} + 4 q^{70} + 4 q^{71} - 24 q^{72} - 45 q^{73} - 22 q^{74} - 36 q^{75} + 26 q^{76} - 38 q^{77} + 12 q^{78} + 25 q^{79} - 63 q^{80} + 36 q^{81} - 5 q^{82} - 71 q^{83} + 10 q^{84} + 50 q^{85} + 3 q^{86} - 7 q^{87} - 9 q^{88} - 39 q^{89} + 7 q^{90} + 19 q^{91} - 95 q^{92} - 7 q^{93} + 16 q^{94} - 15 q^{95} + 50 q^{96} - 61 q^{97} - 76 q^{98} - q^{99}+O(q^{100}) \) 36 * q - 7 * q^2 - 36 * q^3 + 45 * q^4 - 36 * q^5 + 7 * q^6 + 2 * q^7 - 24 * q^8 + 36 * q^9 + 7 * q^10 - q^11 - 45 * q^12 - 8 * q^13 - 4 * q^14 + 36 * q^15 + 63 * q^16 - 50 * q^17 - 7 * q^18 + 15 * q^19 - 45 * q^20 - 2 * q^21 + 7 * q^22 - 32 * q^23 + 24 * q^24 + 36 * q^25 - 12 * q^26 - 36 * q^27 - 10 * q^28 + 7 * q^29 - 7 * q^30 + 7 * q^31 - 50 * q^32 + q^33 + 8 * q^34 - 2 * q^35 + 45 * q^36 - 10 * q^37 - 48 * q^38 + 8 * q^39 + 24 * q^40 - 31 * q^41 + 4 * q^42 + 27 * q^43 - 9 * q^44 - 36 * q^45 + 23 * q^46 - 46 * q^47 - 63 * q^48 + 48 * q^49 - 7 * q^50 + 50 * q^51 - 14 * q^52 - 39 * q^53 + 7 * q^54 + q^55 - 29 * q^56 - 15 * q^57 - 26 * q^58 - 9 * q^59 + 45 * q^60 + 5 * q^61 - 65 * q^62 + 2 * q^63 + 90 * q^64 + 8 * q^65 - 7 * q^66 + 18 * q^67 - 128 * q^68 + 32 * q^69 + 4 * q^70 + 4 * q^71 - 24 * q^72 - 45 * q^73 - 22 * q^74 - 36 * q^75 + 26 * q^76 - 38 * q^77 + 12 * q^78 + 25 * q^79 - 63 * q^80 + 36 * q^81 - 5 * q^82 - 71 * q^83 + 10 * q^84 + 50 * q^85 + 3 * q^86 - 7 * q^87 - 9 * q^88 - 39 * q^89 + 7 * q^90 + 19 * q^91 - 95 * q^92 - 7 * q^93 + 16 * q^94 - 15 * q^95 + 50 * q^96 - 61 * q^97 - 76 * q^98 - q^99

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