LMFDB - Embedded newform 6015.2.a.h.1.18

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:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-0.407003 q^{2} +1.00000 q^{3} -1.83435 q^{4} -1.00000 q^{5} -0.407003 q^{6} -1.58531 q^{7} +1.56059 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.407003 q^{2} +1.00000 q^{3} -1.83435 q^{4} -1.00000 q^{5} -0.407003 q^{6} -1.58531 q^{7} +1.56059 q^{8} +1.00000 q^{9} +0.407003 q^{10} +4.33658 q^{11} -1.83435 q^{12} +2.76107 q^{13} +0.645226 q^{14} -1.00000 q^{15} +3.03353 q^{16} -5.25871 q^{17} -0.407003 q^{18} +6.29974 q^{19} +1.83435 q^{20} -1.58531 q^{21} -1.76500 q^{22} +7.73192 q^{23} +1.56059 q^{24} +1.00000 q^{25} -1.12376 q^{26} +1.00000 q^{27} +2.90801 q^{28} +0.364508 q^{29} +0.407003 q^{30} -0.365455 q^{31} -4.35584 q^{32} +4.33658 q^{33} +2.14031 q^{34} +1.58531 q^{35} -1.83435 q^{36} -4.41609 q^{37} -2.56401 q^{38} +2.76107 q^{39} -1.56059 q^{40} +1.08394 q^{41} +0.645226 q^{42} +0.643776 q^{43} -7.95480 q^{44} -1.00000 q^{45} -3.14692 q^{46} -5.45445 q^{47} +3.03353 q^{48} -4.48679 q^{49} -0.407003 q^{50} -5.25871 q^{51} -5.06476 q^{52} +5.96839 q^{53} -0.407003 q^{54} -4.33658 q^{55} -2.47402 q^{56} +6.29974 q^{57} -0.148356 q^{58} -0.379200 q^{59} +1.83435 q^{60} -9.16252 q^{61} +0.148741 q^{62} -1.58531 q^{63} -4.29422 q^{64} -2.76107 q^{65} -1.76500 q^{66} +6.96755 q^{67} +9.64630 q^{68} +7.73192 q^{69} -0.645226 q^{70} -12.5284 q^{71} +1.56059 q^{72} -3.96243 q^{73} +1.79736 q^{74} +1.00000 q^{75} -11.5559 q^{76} -6.87482 q^{77} -1.12376 q^{78} +5.36993 q^{79} -3.03353 q^{80} +1.00000 q^{81} -0.441167 q^{82} +0.852315 q^{83} +2.90801 q^{84} +5.25871 q^{85} -0.262019 q^{86} +0.364508 q^{87} +6.76763 q^{88} +0.678376 q^{89} +0.407003 q^{90} -4.37715 q^{91} -14.1830 q^{92} -0.365455 q^{93} +2.21998 q^{94} -6.29974 q^{95} -4.35584 q^{96} +10.9255 q^{97} +1.82614 q^{98} +4.33658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * 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 $

$2$	−0.407003	−0.287795	−0.143897	−	0.989593i	$-0.545964\pi$
$2$	−0.407003	−0.287795	−0.143897	+	0.989593i	$0.545964\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.83435	−0.917174
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.407003	−0.166158
$7$	−1.58531	−0.599191	−0.299595	−	0.954066i	$-0.596852\pi$
$7$	−1.58531	−0.599191	−0.299595	+	0.954066i	$0.596852\pi$
$8$	1.56059	0.551753
$9$	1.00000	0.333333
$10$	0.407003	0.128706
$11$	4.33658	1.30753	0.653764	−	0.756698i	$-0.273189\pi$
$11$	4.33658	1.30753	0.653764	+	0.756698i	$0.273189\pi$
$12$	−1.83435	−0.529531
$13$	2.76107	0.765782	0.382891	−	0.923794i	$-0.374928\pi$
$13$	2.76107	0.765782	0.382891	+	0.923794i	$0.374928\pi$
$14$	0.645226	0.172444
$15$	−1.00000	−0.258199
$16$	3.03353	0.758383
$17$	−5.25871	−1.27542	−0.637712	−	0.770275i	$-0.720119\pi$
$17$	−5.25871	−1.27542	−0.637712	+	0.770275i	$0.720119\pi$
$18$	−0.407003	−0.0959316
$19$	6.29974	1.44526	0.722630	−	0.691235i	$-0.242933\pi$
$19$	6.29974	1.44526	0.722630	+	0.691235i	$0.242933\pi$
$20$	1.83435	0.410173
$21$	−1.58531	−0.345943
$22$	−1.76500	−0.376300
$23$	7.73192	1.61222	0.806109	−	0.591768i	$-0.201570\pi$
$23$	7.73192	1.61222	0.806109	+	0.591768i	$0.201570\pi$
$24$	1.56059	0.318554
$25$	1.00000	0.200000
$26$	−1.12376	−0.220388
$27$	1.00000	0.192450
$28$	2.90801	0.549562
$29$	0.364508	0.0676874	0.0338437	−	0.999427i	$-0.489225\pi$
$29$	0.364508	0.0676874	0.0338437	+	0.999427i	$0.489225\pi$
$30$	0.407003	0.0743083
$31$	−0.365455	−0.0656376	−0.0328188	−	0.999461i	$-0.510448\pi$
$31$	−0.365455	−0.0656376	−0.0328188	+	0.999461i	$0.510448\pi$
$32$	−4.35584	−0.770011
$33$	4.33658	0.754902
$34$	2.14031	0.367060
$35$	1.58531	0.267966
$36$	−1.83435	−0.305725
$37$	−4.41609	−0.726001	−0.363000	−	0.931789i	$-0.618248\pi$
$37$	−4.41609	−0.726001	−0.363000	+	0.931789i	$0.618248\pi$
$38$	−2.56401	−0.415938
$39$	2.76107	0.442124
$40$	−1.56059	−0.246751
$41$	1.08394	0.169283	0.0846414	−	0.996411i	$-0.473026\pi$
$41$	1.08394	0.169283	0.0846414	+	0.996411i	$0.473026\pi$
$42$	0.645226	0.0995605
$43$	0.643776	0.0981750	0.0490875	−	0.998794i	$-0.484369\pi$
$43$	0.643776	0.0981750	0.0490875	+	0.998794i	$0.484369\pi$
$44$	−7.95480	−1.19923
$45$	−1.00000	−0.149071
$46$	−3.14692	−0.463987
$47$	−5.45445	−0.795613	−0.397807	−	0.917469i	$-0.630228\pi$
$47$	−5.45445	−0.795613	−0.397807	+	0.917469i	$0.630228\pi$
$48$	3.03353	0.437853
$49$	−4.48679	−0.640970
$50$	−0.407003	−0.0575589
$51$	−5.25871	−0.736366
$52$	−5.06476	−0.702356
$53$	5.96839	0.819822	0.409911	−	0.912126i	$-0.365560\pi$
$53$	5.96839	0.819822	0.409911	+	0.912126i	$0.365560\pi$
$54$	−0.407003	−0.0553861
$55$	−4.33658	−0.584744
$56$	−2.47402	−0.330605
$57$	6.29974	0.834421
$58$	−0.148356	−0.0194801
$59$	−0.379200	−0.0493677	−0.0246838	−	0.999695i	$-0.507858\pi$
$59$	−0.379200	−0.0493677	−0.0246838	+	0.999695i	$0.507858\pi$
$60$	1.83435	0.236813
$61$	−9.16252	−1.17314	−0.586570	−	0.809898i	$-0.699522\pi$
$61$	−9.16252	−1.17314	−0.586570	+	0.809898i	$0.699522\pi$
$62$	0.148741	0.0188901
$63$	−1.58531	−0.199730
$64$	−4.29422	−0.536778
$65$	−2.76107	−0.342468
$66$	−1.76500	−0.217257
$67$	6.96755	0.851221	0.425611	−	0.904906i	$-0.360059\pi$
$67$	6.96755	0.851221	0.425611	+	0.904906i	$0.360059\pi$
$68$	9.64630	1.16979
$69$	7.73192	0.930814
$70$	−0.645226	−0.0771193
$71$	−12.5284	−1.48685	−0.743426	−	0.668818i	$-0.766801\pi$
$71$	−12.5284	−1.48685	−0.743426	+	0.668818i	$0.766801\pi$
$72$	1.56059	0.183918
$73$	−3.96243	−0.463768	−0.231884	−	0.972743i	$-0.574489\pi$
$73$	−3.96243	−0.463768	−0.231884	+	0.972743i	$0.574489\pi$
$74$	1.79736	0.208939
$75$	1.00000	0.115470
$76$	−11.5559	−1.32555
$77$	−6.87482	−0.783459
$78$	−1.12376	−0.127241
$79$	5.36993	0.604164	0.302082	−	0.953282i	$-0.402318\pi$
$79$	5.36993	0.604164	0.302082	+	0.953282i	$0.402318\pi$
$80$	−3.03353	−0.339159
$81$	1.00000	0.111111
$82$	−0.441167	−0.0487187
$83$	0.852315	0.0935537	0.0467769	−	0.998905i	$-0.485105\pi$
$83$	0.852315	0.0935537	0.0467769	+	0.998905i	$0.485105\pi$
$84$	2.90801	0.317290
$85$	5.25871	0.570387
$86$	−0.262019	−0.0282542
$87$	0.364508	0.0390793
$88$	6.76763	0.721432
$89$	0.678376	0.0719078	0.0359539	−	0.999353i	$-0.488553\pi$
$89$	0.678376	0.0719078	0.0359539	+	0.999353i	$0.488553\pi$
$90$	0.407003	0.0429019
$91$	−4.37715	−0.458850
$92$	−14.1830	−1.47868
$93$	−0.365455	−0.0378959
$94$	2.21998	0.228973
$95$	−6.29974	−0.646340
$96$	−4.35584	−0.444566
$97$	10.9255	1.10932	0.554658	−	0.832078i	$-0.312849\pi$
$97$	10.9255	1.10932	0.554658	+	0.832078i	$0.312849\pi$
$98$	1.82614	0.184468
$99$	4.33658	0.435843
$100$	−1.83435	−0.183435
$101$	−0.665404	−0.0662101	−0.0331051	−	0.999452i	$-0.510540\pi$
$101$	−0.665404	−0.0662101	−0.0331051	+	0.999452i	$0.510540\pi$
$102$	2.14031	0.211922
$103$	10.2420	1.00917	0.504587	−	0.863361i	$-0.331645\pi$
$103$	10.2420	1.00917	0.504587	+	0.863361i	$0.331645\pi$
$104$	4.30890	0.422522
$105$	1.58531	0.154710
$106$	−2.42915	−0.235940
$107$	5.53927	0.535502	0.267751	−	0.963488i	$-0.413720\pi$
$107$	5.53927	0.535502	0.267751	+	0.963488i	$0.413720\pi$
$108$	−1.83435	−0.176510
$109$	2.63811	0.252685	0.126342	−	0.991987i	$-0.459676\pi$
$109$	2.63811	0.252685	0.126342	+	0.991987i	$0.459676\pi$
$110$	1.76500	0.168286
$111$	−4.41609	−0.419157
$112$	−4.80909	−0.454416
$113$	3.38070	0.318030	0.159015	−	0.987276i	$-0.449168\pi$
$113$	3.38070	0.318030	0.159015	+	0.987276i	$0.449168\pi$
$114$	−2.56401	−0.240142
$115$	−7.73192	−0.721005
$116$	−0.668635	−0.0620812
$117$	2.76107	0.255261
$118$	0.154336	0.0142078
$119$	8.33668	0.764222
$120$	−1.56059	−0.142462
$121$	7.80592	0.709630
$122$	3.72918	0.337624
$123$	1.08394	0.0977355
$124$	0.670371	0.0602011
$125$	−1.00000	−0.0894427
$126$	0.645226	0.0574813
$127$	6.50986	0.577657	0.288828	−	0.957381i	$-0.406734\pi$
$127$	6.50986	0.577657	0.288828	+	0.957381i	$0.406734\pi$
$128$	10.4594	0.924493
$129$	0.643776	0.0566814
$130$	1.12376	0.0985605
$131$	7.04666	0.615670	0.307835	−	0.951440i	$-0.400396\pi$
$131$	7.04666	0.615670	0.307835	+	0.951440i	$0.400396\pi$
$132$	−7.95480	−0.692376
$133$	−9.98704	−0.865986
$134$	−2.83581	−0.244977
$135$	−1.00000	−0.0860663
$136$	−8.20669	−0.703718
$137$	14.7630	1.26129	0.630645	−	0.776071i	$-0.282790\pi$
$137$	14.7630	1.26129	0.630645	+	0.776071i	$0.282790\pi$
$138$	−3.14692	−0.267883
$139$	1.34440	0.114031	0.0570153	−	0.998373i	$-0.481842\pi$
$139$	1.34440	0.114031	0.0570153	+	0.998373i	$0.481842\pi$
$140$	−2.90801	−0.245772
$141$	−5.45445	−0.459347
$142$	5.09912	0.427908
$143$	11.9736	1.00128
$144$	3.03353	0.252794
$145$	−0.364508	−0.0302707
$146$	1.61272	0.133470
$147$	−4.48679	−0.370064
$148$	8.10065	0.665869
$149$	−8.50215	−0.696523	−0.348261	−	0.937397i	$-0.613228\pi$
$149$	−8.50215	−0.696523	−0.348261	+	0.937397i	$0.613228\pi$
$150$	−0.407003	−0.0332317
$151$	5.67003	0.461421	0.230710	−	0.973022i	$-0.425895\pi$
$151$	5.67003	0.461421	0.230710	+	0.973022i	$0.425895\pi$
$152$	9.83132	0.797426
$153$	−5.25871	−0.425141
$154$	2.79807	0.225475
$155$	0.365455	0.0293540
$156$	−5.06476	−0.405505
$157$	0.609948	0.0486791	0.0243396	−	0.999704i	$-0.492252\pi$
$157$	0.609948	0.0486791	0.0243396	+	0.999704i	$0.492252\pi$
$158$	−2.18558	−0.173875
$159$	5.96839	0.473324
$160$	4.35584	0.344359
$161$	−12.2575	−0.966026
$162$	−0.407003	−0.0319772
$163$	9.60451	0.752283	0.376141	−	0.926562i	$-0.377251\pi$
$163$	9.60451	0.752283	0.376141	+	0.926562i	$0.377251\pi$
$164$	−1.98832	−0.155262
$165$	−4.33658	−0.337602
$166$	−0.346895	−0.0269243
$167$	15.2764	1.18213	0.591063	−	0.806625i	$-0.298709\pi$
$167$	15.2764	1.18213	0.591063	+	0.806625i	$0.298709\pi$
$168$	−2.47402	−0.190875
$169$	−5.37651	−0.413578
$170$	−2.14031	−0.164154
$171$	6.29974	0.481753
$172$	−1.18091	−0.0900436
$173$	11.8007	0.897194	0.448597	−	0.893734i	$-0.351924\pi$
$173$	11.8007	0.897194	0.448597	+	0.893734i	$0.351924\pi$
$174$	−0.148356	−0.0112468
$175$	−1.58531	−0.119838
$176$	13.1552	0.991607
$177$	−0.379200	−0.0285024
$178$	−0.276101	−0.0206947
$179$	1.04569	0.0781585	0.0390793	−	0.999236i	$-0.487558\pi$
$179$	1.04569	0.0781585	0.0390793	+	0.999236i	$0.487558\pi$
$180$	1.83435	0.136724
$181$	−5.19308	−0.385999	−0.192999	−	0.981199i	$-0.561822\pi$
$181$	−5.19308	−0.385999	−0.192999	+	0.981199i	$0.561822\pi$
$182$	1.78151	0.132054
$183$	−9.16252	−0.677313
$184$	12.0664	0.889545
$185$	4.41609	0.324677
$186$	0.148741	0.0109062
$187$	−22.8048	−1.66765
$188$	10.0054	0.729716
$189$	−1.58531	−0.115314
$190$	2.56401	0.186013
$191$	10.3694	0.750303	0.375151	−	0.926964i	$-0.377591\pi$
$191$	10.3694	0.750303	0.375151	+	0.926964i	$0.377591\pi$
$192$	−4.29422	−0.309909
$193$	−10.7596	−0.774495	−0.387247	−	0.921976i	$-0.626574\pi$
$193$	−10.7596	−0.774495	−0.387247	+	0.921976i	$0.626574\pi$
$194$	−4.44671	−0.319255
$195$	−2.76107	−0.197724
$196$	8.23034	0.587882
$197$	−12.7042	−0.905138	−0.452569	−	0.891729i	$-0.649492\pi$
$197$	−12.7042	−0.905138	−0.452569	+	0.891729i	$0.649492\pi$
$198$	−1.76500	−0.125433
$199$	−4.11646	−0.291808	−0.145904	−	0.989299i	$-0.546609\pi$
$199$	−4.11646	−0.291808	−0.145904	+	0.989299i	$0.546609\pi$
$200$	1.56059	0.110351
$201$	6.96755	0.491453
$202$	0.270821	0.0190549
$203$	−0.577858	−0.0405577
$204$	9.64630	0.675376
$205$	−1.08394	−0.0757056
$206$	−4.16852	−0.290435
$207$	7.73192	0.537406
$208$	8.37578	0.580756
$209$	27.3193	1.88972
$210$	−0.645226	−0.0445248
$211$	−6.25170	−0.430385	−0.215193	−	0.976572i	$-0.569038\pi$
$211$	−6.25170	−0.430385	−0.215193	+	0.976572i	$0.569038\pi$
$212$	−10.9481	−0.751919
$213$	−12.5284	−0.858435
$214$	−2.25450	−0.154115
$215$	−0.643776	−0.0439052
$216$	1.56059	0.106185
$217$	0.579359	0.0393294
$218$	−1.07372	−0.0727213
$219$	−3.96243	−0.267756
$220$	7.95480	0.536312
$221$	−14.5196	−0.976697
$222$	1.79736	0.120631
$223$	12.4887	0.836306	0.418153	−	0.908377i	$-0.362678\pi$
$223$	12.4887	0.836306	0.418153	+	0.908377i	$0.362678\pi$
$224$	6.90536	0.461384
$225$	1.00000	0.0666667
$226$	−1.37596	−0.0915272
$227$	18.5386	1.23045	0.615225	−	0.788352i	$-0.289065\pi$
$227$	18.5386	1.23045	0.615225	+	0.788352i	$0.289065\pi$
$228$	−11.5559	−0.765309
$229$	−15.5717	−1.02901	−0.514504	−	0.857488i	$-0.672024\pi$
$229$	−15.5717	−1.02901	−0.514504	+	0.857488i	$0.672024\pi$
$230$	3.14692	0.207502
$231$	−6.87482	−0.452330
$232$	0.568848	0.0373467
$233$	−6.21772	−0.407336	−0.203668	−	0.979040i	$-0.565286\pi$
$233$	−6.21772	−0.407336	−0.203668	+	0.979040i	$0.565286\pi$
$234$	−1.12376	−0.0734627
$235$	5.45445	0.355809
$236$	0.695585	0.0452788
$237$	5.36993	0.348814
$238$	−3.39305	−0.219939
$239$	1.78966	0.115764	0.0578818	−	0.998323i	$-0.481565\pi$
$239$	1.78966	0.115764	0.0578818	+	0.998323i	$0.481565\pi$
$240$	−3.03353	−0.195814
$241$	−3.97830	−0.256265	−0.128132	−	0.991757i	$-0.540898\pi$
$241$	−3.97830	−0.256265	−0.128132	+	0.991757i	$0.540898\pi$
$242$	−3.17704	−0.204228
$243$	1.00000	0.0641500
$244$	16.8073	1.07597
$245$	4.48679	0.286651
$246$	−0.441167	−0.0281278
$247$	17.3940	1.10675
$248$	−0.570326	−0.0362157
$249$	0.852315	0.0540133
$250$	0.407003	0.0257411
$251$	12.3565	0.779935	0.389967	−	0.920829i	$-0.372486\pi$
$251$	12.3565	0.779935	0.389967	+	0.920829i	$0.372486\pi$
$252$	2.90801	0.183187
$253$	33.5301	2.10802
$254$	−2.64953	−0.166246
$255$	5.25871	0.329313
$256$	4.33142	0.270714
$257$	6.79334	0.423757	0.211879	−	0.977296i	$-0.432042\pi$
$257$	6.79334	0.423757	0.211879	+	0.977296i	$0.432042\pi$
$258$	−0.262019	−0.0163126
$259$	7.00087	0.435013
$260$	5.06476	0.314103
$261$	0.364508	0.0225625
$262$	−2.86801	−0.177187
$263$	−9.63494	−0.594116	−0.297058	−	0.954859i	$-0.596005\pi$
$263$	−9.63494	−0.594116	−0.297058	+	0.954859i	$0.596005\pi$
$264$	6.76763	0.416519
$265$	−5.96839	−0.366635
$266$	4.06476	0.249226
$267$	0.678376	0.0415160
$268$	−12.7809	−0.780718
$269$	5.27146	0.321406	0.160703	−	0.987003i	$-0.448624\pi$
$269$	5.27146	0.321406	0.160703	+	0.987003i	$0.448624\pi$
$270$	0.407003	0.0247694
$271$	23.0438	1.39981	0.699905	−	0.714236i	$-0.253226\pi$
$271$	23.0438	1.39981	0.699905	+	0.714236i	$0.253226\pi$
$272$	−15.9524	−0.967259
$273$	−4.37715	−0.264917
$274$	−6.00860	−0.362993
$275$	4.33658	0.261506
$276$	−14.1830	−0.853719
$277$	5.64105	0.338938	0.169469	−	0.985536i	$-0.445795\pi$
$277$	5.64105	0.338938	0.169469	+	0.985536i	$0.445795\pi$
$278$	−0.547175	−0.0328174
$279$	−0.365455	−0.0218792
$280$	2.47402	0.147851
$281$	−6.81691	−0.406662	−0.203331	−	0.979110i	$-0.565177\pi$
$281$	−6.81691	−0.406662	−0.203331	+	0.979110i	$0.565177\pi$
$282$	2.21998	0.132198
$283$	12.9043	0.767084	0.383542	−	0.923523i	$-0.374704\pi$
$283$	12.9043	0.767084	0.383542	+	0.923523i	$0.374704\pi$
$284$	22.9815	1.36370
$285$	−6.29974	−0.373164
$286$	−4.87329	−0.288163
$287$	−1.71838	−0.101433
$288$	−4.35584	−0.256670
$289$	10.6540	0.626705
$290$	0.148356	0.00871176
$291$	10.9255	0.640464
$292$	7.26848	0.425356
$293$	−10.0598	−0.587702	−0.293851	−	0.955851i	$-0.594937\pi$
$293$	−10.0598	−0.587702	−0.293851	+	0.955851i	$0.594937\pi$
$294$	1.82614	0.106503
$295$	0.379200	0.0220779
$296$	−6.89171	−0.400573
$297$	4.33658	0.251634
$298$	3.46040	0.200456
$299$	21.3483	1.23461
$300$	−1.83435	−0.105906
$301$	−1.02059	−0.0588256
$302$	−2.30772	−0.132794
$303$	−0.665404	−0.0382264
$304$	19.1105	1.09606
$305$	9.16252	0.524645
$306$	2.14031	0.122353
$307$	32.3553	1.84661	0.923306	−	0.384064i	$-0.125476\pi$
$307$	32.3553	1.84661	0.923306	+	0.384064i	$0.125476\pi$
$308$	12.6108	0.718568
$309$	10.2420	0.582647
$310$	−0.148741	−0.00844793
$311$	6.58316	0.373297	0.186648	−	0.982427i	$-0.440237\pi$
$311$	6.58316	0.373297	0.186648	+	0.982427i	$0.440237\pi$
$312$	4.30890	0.243943
$313$	−25.3899	−1.43512	−0.717562	−	0.696495i	$-0.754742\pi$
$313$	−25.3899	−1.43512	−0.717562	+	0.696495i	$0.754742\pi$
$314$	−0.248251	−0.0140096
$315$	1.58531	0.0893221
$316$	−9.85032	−0.554124
$317$	−10.8150	−0.607430	−0.303715	−	0.952763i	$-0.598227\pi$
$317$	−10.8150	−0.607430	−0.303715	+	0.952763i	$0.598227\pi$
$318$	−2.42915	−0.136220
$319$	1.58072	0.0885032
$320$	4.29422	0.240054
$321$	5.53927	0.309172
$322$	4.98884	0.278017
$323$	−33.1285	−1.84332
$324$	−1.83435	−0.101908
$325$	2.76107	0.153156
$326$	−3.90906	−0.216503
$327$	2.63811	0.145888
$328$	1.69159	0.0934022
$329$	8.64699	0.476724
$330$	1.76500	0.0971601
$331$	31.4830	1.73046	0.865232	−	0.501372i	$-0.167171\pi$
$331$	31.4830	1.73046	0.865232	+	0.501372i	$0.167171\pi$
$332$	−1.56344	−0.0858051
$333$	−4.41609	−0.242000
$334$	−6.21756	−0.340209
$335$	−6.96755	−0.380678
$336$	−4.80909	−0.262357
$337$	4.42865	0.241244	0.120622	−	0.992699i	$-0.461511\pi$
$337$	4.42865	0.241244	0.120622	+	0.992699i	$0.461511\pi$
$338$	2.18826	0.119026
$339$	3.38070	0.183614
$340$	−9.64630	−0.523144
$341$	−1.58482	−0.0858230
$342$	−2.56401	−0.138646
$343$	18.2101	0.983254
$344$	1.00467	0.0541683
$345$	−7.73192	−0.416273
$346$	−4.80294	−0.258208
$347$	5.40946	0.290395	0.145198	−	0.989403i	$-0.453618\pi$
$347$	5.40946	0.290395	0.145198	+	0.989403i	$0.453618\pi$
$348$	−0.668635	−0.0358426
$349$	30.0296	1.60745	0.803723	−	0.595004i	$-0.202849\pi$
$349$	30.0296	1.60745	0.803723	+	0.595004i	$0.202849\pi$
$350$	0.645226	0.0344888
$351$	2.76107	0.147375
$352$	−18.8894	−1.00681
$353$	−34.9622	−1.86085	−0.930426	−	0.366480i	$-0.880563\pi$
$353$	−34.9622	−1.86085	−0.930426	+	0.366480i	$0.880563\pi$
$354$	0.154336	0.00820285
$355$	12.5284	0.664941
$356$	−1.24438	−0.0659519
$357$	8.33668	0.441224
$358$	−0.425599	−0.0224936
$359$	−14.2835	−0.753854	−0.376927	−	0.926243i	$-0.623019\pi$
$359$	−14.2835	−0.753854	−0.376927	+	0.926243i	$0.623019\pi$
$360$	−1.56059	−0.0822504
$361$	20.6867	1.08878
$362$	2.11360	0.111088
$363$	7.80592	0.409705
$364$	8.02921	0.420845
$365$	3.96243	0.207403
$366$	3.72918	0.194927
$367$	4.69297	0.244971	0.122486	−	0.992470i	$-0.460913\pi$
$367$	4.69297	0.244971	0.122486	+	0.992470i	$0.460913\pi$
$368$	23.4550	1.22268
$369$	1.08394	0.0564276
$370$	−1.79736	−0.0934404
$371$	−9.46175	−0.491230
$372$	0.670371	0.0347571
$373$	6.93207	0.358929	0.179465	−	0.983764i	$-0.442563\pi$
$373$	6.93207	0.358929	0.179465	+	0.983764i	$0.442563\pi$
$374$	9.28162	0.479941
$375$	−1.00000	−0.0516398
$376$	−8.51217	−0.438982
$377$	1.00643	0.0518338
$378$	0.645226	0.0331868
$379$	13.9808	0.718144	0.359072	−	0.933310i	$-0.383093\pi$
$379$	13.9808	0.718144	0.359072	+	0.933310i	$0.383093\pi$
$380$	11.5559	0.592806
$381$	6.50986	0.333510
$382$	−4.22037	−0.215933
$383$	−4.72261	−0.241314	−0.120657	−	0.992694i	$-0.538500\pi$
$383$	−4.72261	−0.241314	−0.120657	+	0.992694i	$0.538500\pi$
$384$	10.4594	0.533756
$385$	6.87482	0.350373
$386$	4.37920	0.222895
$387$	0.643776	0.0327250
$388$	−20.0412	−1.01744
$389$	−10.1904	−0.516676	−0.258338	−	0.966055i	$-0.583175\pi$
$389$	−10.1904	−0.516676	−0.258338	+	0.966055i	$0.583175\pi$
$390$	1.12376	0.0569039
$391$	−40.6599	−2.05626
$392$	−7.00205	−0.353657
$393$	7.04666	0.355457
$394$	5.17066	0.260494
$395$	−5.36993	−0.270190
$396$	−7.95480	−0.399744
$397$	11.3243	0.568352	0.284176	−	0.958772i	$-0.408280\pi$
$397$	11.3243	0.568352	0.284176	+	0.958772i	$0.408280\pi$
$398$	1.67541	0.0839808
$399$	−9.98704	−0.499977
$400$	3.03353	0.151677
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−2.83581	−0.141438
$403$	−1.00904	−0.0502641
$404$	1.22058	0.0607262
$405$	−1.00000	−0.0496904
$406$	0.235190	0.0116723
$407$	−19.1507	−0.949266
$408$	−8.20669	−0.406292
$409$	−1.29667	−0.0641164	−0.0320582	−	0.999486i	$-0.510206\pi$
$409$	−1.29667	−0.0641164	−0.0320582	+	0.999486i	$0.510206\pi$
$410$	0.441167	0.0217877
$411$	14.7630	0.728207
$412$	−18.7874	−0.925588
$413$	0.601150	0.0295807
$414$	−3.14692	−0.154662
$415$	−0.852315	−0.0418385
$416$	−12.0268	−0.589661
$417$	1.34440	0.0658356
$418$	−11.1191	−0.543851
$419$	8.26078	0.403565	0.201783	−	0.979430i	$-0.435327\pi$
$419$	8.26078	0.403565	0.201783	+	0.979430i	$0.435327\pi$
$420$	−2.90801	−0.141896
$421$	−16.0563	−0.782534	−0.391267	−	0.920277i	$-0.627963\pi$
$421$	−16.0563	−0.782534	−0.391267	+	0.920277i	$0.627963\pi$
$422$	2.54446	0.123863
$423$	−5.45445	−0.265204
$424$	9.31422	0.452339
$425$	−5.25871	−0.255085
$426$	5.09912	0.247053
$427$	14.5254	0.702935
$428$	−10.1610	−0.491148
$429$	11.9736	0.578090
$430$	0.262019	0.0126357
$431$	4.80974	0.231677	0.115839	−	0.993268i	$-0.463044\pi$
$431$	4.80974	0.231677	0.115839	+	0.993268i	$0.463044\pi$
$432$	3.03353	0.145951
$433$	27.5148	1.32228	0.661139	−	0.750263i	$-0.270073\pi$
$433$	27.5148	1.32228	0.661139	+	0.750263i	$0.270073\pi$
$434$	−0.235801	−0.0113188
$435$	−0.364508	−0.0174768
$436$	−4.83920	−0.231756
$437$	48.7091	2.33007
$438$	1.61272	0.0770589
$439$	3.12428	0.149114	0.0745569	−	0.997217i	$-0.476246\pi$
$439$	3.12428	0.149114	0.0745569	+	0.997217i	$0.476246\pi$
$440$	−6.76763	−0.322634
$441$	−4.48679	−0.213657
$442$	5.90954	0.281088
$443$	33.9932	1.61506	0.807532	−	0.589824i	$-0.200803\pi$
$443$	33.9932	1.61506	0.807532	+	0.589824i	$0.200803\pi$
$444$	8.10065	0.384440
$445$	−0.678376	−0.0321581
$446$	−5.08295	−0.240684
$447$	−8.50215	−0.402138
$448$	6.80767	0.321632
$449$	−12.5728	−0.593348	−0.296674	−	0.954979i	$-0.595877\pi$
$449$	−12.5728	−0.593348	−0.296674	+	0.954979i	$0.595877\pi$
$450$	−0.407003	−0.0191863
$451$	4.70059	0.221342
$452$	−6.20138	−0.291688
$453$	5.67003	0.266401
$454$	−7.54527	−0.354117
$455$	4.37715	0.205204
$456$	9.83132	0.460394
$457$	−28.3521	−1.32626	−0.663128	−	0.748506i	$-0.730772\pi$
$457$	−28.3521	−1.32626	−0.663128	+	0.748506i	$0.730772\pi$
$458$	6.33774	0.296143
$459$	−5.25871	−0.245455
$460$	14.1830	0.661288
$461$	−32.1457	−1.49717	−0.748587	−	0.663036i	$-0.769268\pi$
$461$	−32.1457	−1.49717	−0.748587	+	0.663036i	$0.769268\pi$
$462$	2.79807	0.130178
$463$	−6.56104	−0.304918	−0.152459	−	0.988310i	$-0.548719\pi$
$463$	−6.56104	−0.304918	−0.152459	+	0.988310i	$0.548719\pi$
$464$	1.10575	0.0513330
$465$	0.365455	0.0169476
$466$	2.53063	0.117229
$467$	14.5189	0.671855	0.335928	−	0.941888i	$-0.390950\pi$
$467$	14.5189	0.671855	0.335928	+	0.941888i	$0.390950\pi$
$468$	−5.06476	−0.234119
$469$	−11.0457	−0.510044
$470$	−2.21998	−0.102400
$471$	0.609948	0.0281049
$472$	−0.591777	−0.0272387
$473$	2.79179	0.128367
$474$	−2.18558	−0.100387
$475$	6.29974	0.289052
$476$	−15.2924	−0.700925
$477$	5.96839	0.273274
$478$	−0.728398	−0.0333161
$479$	−29.0955	−1.32941	−0.664703	−	0.747108i	$-0.731442\pi$
$479$	−29.0955	−1.32941	−0.664703	+	0.747108i	$0.731442\pi$
$480$	4.35584	0.198816
$481$	−12.1931	−0.555958
$482$	1.61918	0.0737516
$483$	−12.2575	−0.557735
$484$	−14.3188	−0.650854
$485$	−10.9255	−0.496101
$486$	−0.407003	−0.0184620
$487$	−16.8998	−0.765803	−0.382902	−	0.923789i	$-0.625075\pi$
$487$	−16.8998	−0.765803	−0.382902	+	0.923789i	$0.625075\pi$
$488$	−14.2990	−0.647283
$489$	9.60451	0.434331
$490$	−1.82614	−0.0824965
$491$	8.63197	0.389555	0.194778	−	0.980847i	$-0.437601\pi$
$491$	8.63197	0.389555	0.194778	+	0.980847i	$0.437601\pi$
$492$	−1.98832	−0.0896405
$493$	−1.91684	−0.0863301
$494$	−7.07941	−0.318518
$495$	−4.33658	−0.194915
$496$	−1.10862	−0.0497784
$497$	19.8615	0.890908
$498$	−0.346895	−0.0155447
$499$	23.0256	1.03077	0.515384	−	0.856960i	$-0.327649\pi$
$499$	23.0256	1.03077	0.515384	+	0.856960i	$0.327649\pi$
$500$	1.83435	0.0820346
$501$	15.2764	0.682501
$502$	−5.02913	−0.224461
$503$	16.8623	0.751853	0.375927	−	0.926649i	$-0.377325\pi$
$503$	16.8623	0.751853	0.375927	+	0.926649i	$0.377325\pi$
$504$	−2.47402	−0.110202
$505$	0.665404	0.0296101
$506$	−13.6469	−0.606677
$507$	−5.37651	−0.238779
$508$	−11.9413	−0.529812
$509$	−7.50502	−0.332654	−0.166327	−	0.986071i	$-0.553191\pi$
$509$	−7.50502	−0.332654	−0.166327	+	0.986071i	$0.553191\pi$
$510$	−2.14031	−0.0947745
$511$	6.28169	0.277885
$512$	−22.6818	−1.00240
$513$	6.29974	0.278140
$514$	−2.76491	−0.121955
$515$	−10.2420	−0.451316
$516$	−1.18091	−0.0519867
$517$	−23.6537	−1.04029
$518$	−2.84938	−0.125194
$519$	11.8007	0.517995
$520$	−4.30890	−0.188958
$521$	−7.87283	−0.344915	−0.172458	−	0.985017i	$-0.555171\pi$
$521$	−7.87283	−0.344915	−0.172458	+	0.985017i	$0.555171\pi$
$522$	−0.148356	−0.00649336
$523$	28.9790	1.26716	0.633582	−	0.773676i	$-0.281584\pi$
$523$	28.9790	1.26716	0.633582	+	0.773676i	$0.281584\pi$
$524$	−12.9260	−0.564677
$525$	−1.58531	−0.0691886
$526$	3.92145	0.170983
$527$	1.92182	0.0837157
$528$	13.1552	0.572504
$529$	36.7826	1.59924
$530$	2.42915	0.105516
$531$	−0.379200	−0.0164559
$532$	18.3197	0.794260
$533$	2.99283	0.129634
$534$	−0.276101	−0.0119481
$535$	−5.53927	−0.239484
$536$	10.8735	0.469664
$537$	1.04569	0.0451248
$538$	−2.14550	−0.0924990
$539$	−19.4573	−0.838087
$540$	1.83435	0.0789378
$541$	25.8659	1.11206	0.556031	−	0.831161i	$-0.312323\pi$
$541$	25.8659	1.11206	0.556031	+	0.831161i	$0.312323\pi$
$542$	−9.37888	−0.402858
$543$	−5.19308	−0.222856
$544$	22.9061	0.982090
$545$	−2.63811	−0.113004
$546$	1.78151	0.0762417
$547$	−4.73151	−0.202305	−0.101152	−	0.994871i	$-0.532253\pi$
$547$	−4.73151	−0.202305	−0.101152	+	0.994871i	$0.532253\pi$
$548$	−27.0805	−1.15682
$549$	−9.16252	−0.391047
$550$	−1.76500	−0.0752599
$551$	2.29631	0.0978259
$552$	12.0664	0.513579
$553$	−8.51300	−0.362010
$554$	−2.29592	−0.0975444
$555$	4.41609	0.187453
$556$	−2.46610	−0.104586
$557$	−38.1825	−1.61785	−0.808923	−	0.587915i	$-0.799949\pi$
$557$	−38.1825	−1.61785	−0.808923	+	0.587915i	$0.799949\pi$
$558$	0.148741	0.00629672
$559$	1.77751	0.0751806
$560$	4.80909	0.203221
$561$	−22.8048	−0.962819
$562$	2.77450	0.117035
$563$	−24.6123	−1.03728	−0.518642	−	0.854991i	$-0.673562\pi$
$563$	−24.6123	−1.03728	−0.518642	+	0.854991i	$0.673562\pi$
$564$	10.0054	0.421302
$565$	−3.38070	−0.142227
$566$	−5.25211	−0.220763
$567$	−1.58531	−0.0665768
$568$	−19.5518	−0.820375
$569$	−31.2573	−1.31037	−0.655187	−	0.755467i	$-0.727410\pi$
$569$	−31.2573	−1.31037	−0.655187	+	0.755467i	$0.727410\pi$
$570$	2.56401	0.107395
$571$	0.472255	0.0197632	0.00988162	−	0.999951i	$-0.496855\pi$
$571$	0.472255	0.0197632	0.00988162	+	0.999951i	$0.496855\pi$
$572$	−21.9637	−0.918350
$573$	10.3694	0.433187
$574$	0.699386	0.0291918
$575$	7.73192	0.322443
$576$	−4.29422	−0.178926
$577$	2.23699	0.0931271	0.0465635	−	0.998915i	$-0.485173\pi$
$577$	2.23699	0.0931271	0.0465635	+	0.998915i	$0.485173\pi$
$578$	−4.33621	−0.180362
$579$	−10.7596	−0.447155
$580$	0.668635	0.0277635
$581$	−1.35118	−0.0560565
$582$	−4.44671	−0.184322
$583$	25.8824	1.07194
$584$	−6.18374	−0.255885
$585$	−2.76107	−0.114156
$586$	4.09439	0.169138
$587$	−25.7231	−1.06171	−0.530853	−	0.847464i	$-0.678128\pi$
$587$	−25.7231	−1.06171	−0.530853	+	0.847464i	$0.678128\pi$
$588$	8.23034	0.339414
$589$	−2.30227	−0.0948634
$590$	−0.154336	−0.00635390
$591$	−12.7042	−0.522582
$592$	−13.3963	−0.550586
$593$	−15.1400	−0.621724	−0.310862	−	0.950455i	$-0.600618\pi$
$593$	−15.1400	−0.621724	−0.310862	+	0.950455i	$0.600618\pi$
$594$	−1.76500	−0.0724189
$595$	−8.33668	−0.341771
$596$	15.5959	0.638833
$597$	−4.11646	−0.168476
$598$	−8.68884	−0.355313
$599$	−46.4692	−1.89868	−0.949341	−	0.314249i	$-0.898247\pi$
$599$	−46.4692	−1.89868	−0.949341	+	0.314249i	$0.898247\pi$
$600$	1.56059	0.0637109
$601$	5.55182	0.226463	0.113232	−	0.993569i	$-0.463880\pi$
$601$	5.55182	0.226463	0.113232	+	0.993569i	$0.463880\pi$
$602$	0.415381	0.0169297
$603$	6.96755	0.283740
$604$	−10.4008	−0.423203
$605$	−7.80592	−0.317356
$606$	0.270821	0.0110014
$607$	11.2601	0.457034	0.228517	−	0.973540i	$-0.426612\pi$
$607$	11.2601	0.457034	0.228517	+	0.973540i	$0.426612\pi$
$608$	−27.4407	−1.11287
$609$	−0.577858	−0.0234160
$610$	−3.72918	−0.150990
$611$	−15.0601	−0.609266
$612$	9.64630	0.389929
$613$	27.5070	1.11100	0.555499	−	0.831517i	$-0.312527\pi$
$613$	27.5070	1.11100	0.555499	+	0.831517i	$0.312527\pi$
$614$	−13.1687	−0.531445
$615$	−1.08394	−0.0437086
$616$	−10.7288	−0.432275
$617$	14.2257	0.572706	0.286353	−	0.958124i	$-0.407557\pi$
$617$	14.2257	0.572706	0.286353	+	0.958124i	$0.407557\pi$
$618$	−4.16852	−0.167683
$619$	32.5161	1.30693	0.653466	−	0.756956i	$-0.273314\pi$
$619$	32.5161	1.30693	0.653466	+	0.756956i	$0.273314\pi$
$620$	−0.670371	−0.0269228
$621$	7.73192	0.310271
$622$	−2.67937	−0.107433
$623$	−1.07544	−0.0430865
$624$	8.37578	0.335300
$625$	1.00000	0.0400000
$626$	10.3338	0.413021
$627$	27.3193	1.09103
$628$	−1.11886	−0.0446472
$629$	23.2229	0.925959
$630$	−0.645226	−0.0257064
$631$	14.5212	0.578081	0.289041	−	0.957317i	$-0.406664\pi$
$631$	14.5212	0.578081	0.289041	+	0.957317i	$0.406664\pi$
$632$	8.38027	0.333349
$633$	−6.25170	−0.248483
$634$	4.40173	0.174815
$635$	−6.50986	−0.258336
$636$	−10.9481	−0.434121
$637$	−12.3883	−0.490844
$638$	−0.643357	−0.0254707
$639$	−12.5284	−0.495618
$640$	−10.4594	−0.413446
$641$	−10.4880	−0.414249	−0.207125	−	0.978315i	$-0.566411\pi$
$641$	−10.4880	−0.414249	−0.207125	+	0.978315i	$0.566411\pi$
$642$	−2.25450	−0.0889781
$643$	−13.5595	−0.534734	−0.267367	−	0.963595i	$-0.586154\pi$
$643$	−13.5595	−0.534734	−0.267367	+	0.963595i	$0.586154\pi$
$644$	22.4845	0.886014
$645$	−0.643776	−0.0253487
$646$	13.4834	0.530497
$647$	−8.73668	−0.343474	−0.171737	−	0.985143i	$-0.554938\pi$
$647$	−8.73668	−0.343474	−0.171737	+	0.985143i	$0.554938\pi$
$648$	1.56059	0.0613058
$649$	−1.64443	−0.0645496
$650$	−1.12376	−0.0440776
$651$	0.579359	0.0227069
$652$	−17.6180	−0.689975
$653$	0.673796	0.0263677	0.0131838	−	0.999913i	$-0.495803\pi$
$653$	0.673796	0.0263677	0.0131838	+	0.999913i	$0.495803\pi$
$654$	−1.07372	−0.0419857
$655$	−7.04666	−0.275336
$656$	3.28816	0.128381
$657$	−3.96243	−0.154589
$658$	−3.51935	−0.137199
$659$	−7.94409	−0.309458	−0.154729	−	0.987957i	$-0.549450\pi$
$659$	−7.94409	−0.309458	−0.154729	+	0.987957i	$0.549450\pi$
$660$	7.95480	0.309640
$661$	51.3632	1.99780	0.998898	−	0.0469413i	$-0.0149474\pi$
$661$	51.3632	1.99780	0.998898	+	0.0469413i	$0.0149474\pi$
$662$	−12.8137	−0.498018
$663$	−14.5196	−0.563896
$664$	1.33012	0.0516185
$665$	9.98704	0.387281
$666$	1.79736	0.0696464
$667$	2.81835	0.109127
$668$	−28.0223	−1.08422
$669$	12.4887	0.482842
$670$	2.83581	0.109557
$671$	−39.7340	−1.53391
$672$	6.90536	0.266380
$673$	7.43599	0.286637	0.143318	−	0.989677i	$-0.454223\pi$
$673$	7.43599	0.286637	0.143318	+	0.989677i	$0.454223\pi$
$674$	−1.80248	−0.0694288
$675$	1.00000	0.0384900
$676$	9.86240	0.379323
$677$	41.8074	1.60679	0.803395	−	0.595446i	$-0.203025\pi$
$677$	41.8074	1.60679	0.803395	+	0.595446i	$0.203025\pi$
$678$	−1.37596	−0.0528433
$679$	−17.3203	−0.664692
$680$	8.20669	0.314712
$681$	18.5386	0.710400
$682$	0.645028	0.0246994
$683$	9.40402	0.359835	0.179917	−	0.983682i	$-0.442417\pi$
$683$	9.40402	0.359835	0.179917	+	0.983682i	$0.442417\pi$
$684$	−11.5559	−0.441852
$685$	−14.7630	−0.564066
$686$	−7.41158	−0.282975
$687$	−15.5717	−0.594098
$688$	1.95292	0.0744542
$689$	16.4791	0.627805
$690$	3.14692	0.119801
$691$	11.2005	0.426087	0.213044	−	0.977043i	$-0.431662\pi$
$691$	11.2005	0.426087	0.213044	+	0.977043i	$0.431662\pi$
$692$	−21.6467	−0.822884
$693$	−6.87482	−0.261153
$694$	−2.20167	−0.0835742
$695$	−1.34440	−0.0509960
$696$	0.568848	0.0215621
$697$	−5.70012	−0.215907
$698$	−12.2221	−0.462614
$699$	−6.21772	−0.235176
$700$	2.90801	0.109912
$701$	4.62859	0.174820	0.0874098	−	0.996172i	$-0.472141\pi$
$701$	4.62859	0.174820	0.0874098	+	0.996172i	$0.472141\pi$
$702$	−1.12376	−0.0424137
$703$	−27.8202	−1.04926
$704$	−18.6222	−0.701852
$705$	5.45445	0.205426
$706$	14.2297	0.535543
$707$	1.05487	0.0396725
$708$	0.695585	0.0261417
$709$	0.430137	0.0161541	0.00807707	−	0.999967i	$-0.497429\pi$
$709$	0.430137	0.0161541	0.00807707	+	0.999967i	$0.497429\pi$
$710$	−5.09912	−0.191366
$711$	5.36993	0.201388
$712$	1.05867	0.0396753
$713$	−2.82567	−0.105822
$714$	−3.39305	−0.126982
$715$	−11.9736	−0.447787
$716$	−1.91816	−0.0716850
$717$	1.78966	0.0668361
$718$	5.81343	0.216955
$719$	−11.2346	−0.418979	−0.209489	−	0.977811i	$-0.567180\pi$
$719$	−11.2346	−0.418979	−0.209489	+	0.977811i	$0.567180\pi$
$720$	−3.03353	−0.113053
$721$	−16.2367	−0.604688
$722$	−8.41957	−0.313344
$723$	−3.97830	−0.147954
$724$	9.52592	0.354028
$725$	0.364508	0.0135375
$726$	−3.17704	−0.117911
$727$	−5.84421	−0.216750	−0.108375	−	0.994110i	$-0.534565\pi$
$727$	−5.84421	−0.216750	−0.108375	+	0.994110i	$0.534565\pi$
$728$	−6.83094	−0.253171
$729$	1.00000	0.0370370
$730$	−1.61272	−0.0596896
$731$	−3.38543	−0.125215
$732$	16.8073	0.621214
$733$	45.3166	1.67381	0.836904	−	0.547350i	$-0.184363\pi$
$733$	45.3166	1.67381	0.836904	+	0.547350i	$0.184363\pi$
$734$	−1.91005	−0.0705014
$735$	4.48679	0.165498
$736$	−33.6790	−1.24142
$737$	30.2153	1.11300
$738$	−0.441167	−0.0162396
$739$	26.1668	0.962562	0.481281	−	0.876566i	$-0.340172\pi$
$739$	26.1668	0.962562	0.481281	+	0.876566i	$0.340172\pi$
$740$	−8.10065	−0.297786
$741$	17.3940	0.638985
$742$	3.85096	0.141373
$743$	−9.40464	−0.345023	−0.172511	−	0.985008i	$-0.555188\pi$
$743$	−9.40464	−0.345023	−0.172511	+	0.985008i	$0.555188\pi$
$744$	−0.570326	−0.0209091
$745$	8.50215	0.311495
$746$	−2.82138	−0.103298
$747$	0.852315	0.0311846
$748$	41.8319	1.52953
$749$	−8.78147	−0.320868
$750$	0.407003	0.0148617
$751$	−37.9356	−1.38429	−0.692146	−	0.721758i	$-0.743334\pi$
$751$	−37.9356	−1.38429	−0.692146	+	0.721758i	$0.743334\pi$
$752$	−16.5462	−0.603379
$753$	12.3565	0.450296
$754$	−0.409620	−0.0149175
$755$	−5.67003	−0.206354
$756$	2.90801	0.105763
$757$	10.8115	0.392952	0.196476	−	0.980509i	$-0.437050\pi$
$757$	10.8115	0.392952	0.196476	+	0.980509i	$0.437050\pi$
$758$	−5.69022	−0.206678
$759$	33.5301	1.21707
$760$	−9.83132	−0.356620
$761$	32.3528	1.17279	0.586394	−	0.810026i	$-0.300547\pi$
$761$	32.3528	1.17279	0.586394	+	0.810026i	$0.300547\pi$
$762$	−2.64953	−0.0959824
$763$	−4.18221	−0.151406
$764$	−19.0211	−0.688158
$765$	5.25871	0.190129
$766$	1.92212	0.0694489
$767$	−1.04700	−0.0378049
$768$	4.33142	0.156297
$769$	−40.3925	−1.45659	−0.728296	−	0.685263i	$-0.759687\pi$
$769$	−40.3925	−1.45659	−0.728296	+	0.685263i	$0.759687\pi$
$770$	−2.79807	−0.100836
$771$	6.79334	0.244656
$772$	19.7369	0.710347
$773$	44.1414	1.58766	0.793828	−	0.608142i	$-0.208085\pi$
$773$	44.1414	1.58766	0.793828	+	0.608142i	$0.208085\pi$
$774$	−0.262019	−0.00941808
$775$	−0.365455	−0.0131275
$776$	17.0502	0.612068
$777$	7.00087	0.251155
$778$	4.14754	0.148697
$779$	6.82853	0.244658
$780$	5.06476	0.181347
$781$	−54.3306	−1.94410
$782$	16.5487	0.591781
$783$	0.364508	0.0130264
$784$	−13.6108	−0.486101
$785$	−0.609948	−0.0217700
$786$	−2.86801	−0.102299
$787$	36.6560	1.30664	0.653322	−	0.757080i	$-0.273375\pi$
$787$	36.6560	1.30664	0.653322	+	0.757080i	$0.273375\pi$
$788$	23.3040	0.830169
$789$	−9.63494	−0.343013
$790$	2.18558	0.0777594
$791$	−5.35946	−0.190560
$792$	6.76763	0.240477
$793$	−25.2983	−0.898370
$794$	−4.60904	−0.163569
$795$	−5.96839	−0.211677
$796$	7.55102	0.267639
$797$	−43.5194	−1.54153	−0.770767	−	0.637117i	$-0.780127\pi$
$797$	−43.5194	−1.54153	−0.770767	+	0.637117i	$0.780127\pi$
$798$	4.06476	0.143891
$799$	28.6833	1.01474
$800$	−4.35584	−0.154002
$801$	0.678376	0.0239693
$802$	0.407003	0.0143718
$803$	−17.1834	−0.606389
$804$	−12.7809	−0.450748
$805$	12.2575	0.432020
$806$	0.410684	0.0144657
$807$	5.27146	0.185564
$808$	−1.03842	−0.0365316
$809$	38.4418	1.35154	0.675771	−	0.737112i	$-0.263811\pi$
$809$	38.4418	1.35154	0.675771	+	0.737112i	$0.263811\pi$
$810$	0.407003	0.0143006
$811$	17.6539	0.619913	0.309956	−	0.950751i	$-0.399686\pi$
$811$	17.6539	0.619913	0.309956	+	0.950751i	$0.399686\pi$
$812$	1.05999	0.0371985
$813$	23.0438	0.808180
$814$	7.79441	0.273194
$815$	−9.60451	−0.336431
$816$	−15.9524	−0.558447
$817$	4.05562	0.141888
$818$	0.527751	0.0184524
$819$	−4.37715	−0.152950
$820$	1.98832	0.0694352
$821$	15.2989	0.533936	0.266968	−	0.963705i	$-0.413978\pi$
$821$	15.2989	0.533936	0.266968	+	0.963705i	$0.413978\pi$
$822$	−6.00860	−0.209574
$823$	12.6599	0.441296	0.220648	−	0.975353i	$-0.429183\pi$
$823$	12.6599	0.441296	0.220648	+	0.975353i	$0.429183\pi$
$824$	15.9836	0.556814
$825$	4.33658	0.150980
$826$	−0.244670	−0.00851316
$827$	20.5644	0.715095	0.357548	−	0.933895i	$-0.383613\pi$
$827$	20.5644	0.715095	0.357548	+	0.933895i	$0.383613\pi$
$828$	−14.1830	−0.492895
$829$	12.4732	0.433212	0.216606	−	0.976259i	$-0.430501\pi$
$829$	12.4732	0.433212	0.216606	+	0.976259i	$0.430501\pi$
$830$	0.346895	0.0120409
$831$	5.64105	0.195686
$832$	−11.8566	−0.411055
$833$	23.5947	0.817509
$834$	−0.547175	−0.0189471
$835$	−15.2764	−0.528663
$836$	−50.1132	−1.73320
$837$	−0.365455	−0.0126320
$838$	−3.36216	−0.116144
$839$	−22.9516	−0.792377	−0.396188	−	0.918169i	$-0.629667\pi$
$839$	−22.9516	−0.792377	−0.396188	+	0.918169i	$0.629667\pi$
$840$	2.47402	0.0853619
$841$	−28.8671	−0.995418
$842$	6.53494	0.225209
$843$	−6.81691	−0.234787
$844$	11.4678	0.394738
$845$	5.37651	0.184958
$846$	2.21998	0.0763244
$847$	−12.3748	−0.425203
$848$	18.1053	0.621739
$849$	12.9043	0.442876
$850$	2.14031	0.0734120
$851$	−34.1449	−1.17047
$852$	22.9815	0.787334
$853$	−12.0711	−0.413306	−0.206653	−	0.978414i	$-0.566257\pi$
$853$	−12.0711	−0.413306	−0.206653	+	0.978414i	$0.566257\pi$
$854$	−5.91190	−0.202301
$855$	−6.29974	−0.215447
$856$	8.64455	0.295464
$857$	−39.0721	−1.33468	−0.667339	−	0.744754i	$-0.732567\pi$
$857$	−39.0721	−1.33468	−0.667339	+	0.744754i	$0.732567\pi$
$858$	−4.87329	−0.166371
$859$	16.1263	0.550223	0.275111	−	0.961412i	$-0.411285\pi$
$859$	16.1263	0.550223	0.275111	+	0.961412i	$0.411285\pi$
$860$	1.18091	0.0402687
$861$	−1.71838	−0.0585622
$862$	−1.95758	−0.0666754
$863$	−10.3719	−0.353063	−0.176531	−	0.984295i	$-0.556488\pi$
$863$	−10.3719	−0.353063	−0.176531	+	0.984295i	$0.556488\pi$
$864$	−4.35584	−0.148189
$865$	−11.8007	−0.401238
$866$	−11.1986	−0.380545
$867$	10.6540	0.361829
$868$	−1.06275	−0.0360719
$869$	23.2871	0.789962
$870$	0.148356	0.00502973
$871$	19.2379	0.651850
$872$	4.11701	0.139419
$873$	10.9255	0.369772
$874$	−19.8248	−0.670582
$875$	1.58531	0.0535933
$876$	7.26848	0.245579
$877$	−18.3896	−0.620973	−0.310486	−	0.950578i	$-0.600492\pi$
$877$	−18.3896	−0.620973	−0.310486	+	0.950578i	$0.600492\pi$
$878$	−1.27159	−0.0429142
$879$	−10.0598	−0.339310
$880$	−13.1552	−0.443460
$881$	−21.5480	−0.725972	−0.362986	−	0.931795i	$-0.618243\pi$
$881$	−21.5480	−0.725972	−0.362986	+	0.931795i	$0.618243\pi$
$882$	1.82614	0.0614893
$883$	52.8375	1.77812	0.889061	−	0.457788i	$-0.151358\pi$
$883$	52.8375	1.77812	0.889061	+	0.457788i	$0.151358\pi$
$884$	26.6341	0.895801
$885$	0.379200	0.0127467
$886$	−13.8353	−0.464807
$887$	25.6922	0.862659	0.431330	−	0.902194i	$-0.358045\pi$
$887$	25.6922	0.862659	0.431330	+	0.902194i	$0.358045\pi$
$888$	−6.89171	−0.231271
$889$	−10.3201	−0.346126
$890$	0.276101	0.00925494
$891$	4.33658	0.145281
$892$	−22.9087	−0.767038
$893$	−34.3616	−1.14987
$894$	3.46040	0.115733
$895$	−1.04569	−0.0349535
$896$	−16.5815	−0.553948
$897$	21.3483	0.712801
$898$	5.11718	0.170762
$899$	−0.133211	−0.00444284
$900$	−1.83435	−0.0611449
$901$	−31.3860	−1.04562
$902$	−1.91315	−0.0637011
$903$	−1.02059	−0.0339629
$904$	5.27589	0.175474
$905$	5.19308	0.172624
$906$	−2.30772	−0.0766689
$907$	−32.6184	−1.08308	−0.541538	−	0.840676i	$-0.682158\pi$
$907$	−32.6184	−1.08308	−0.541538	+	0.840676i	$0.682158\pi$
$908$	−34.0062	−1.12854
$909$	−0.665404	−0.0220700
$910$	−1.78151	−0.0590565
$911$	6.53242	0.216429	0.108214	−	0.994128i	$-0.465487\pi$
$911$	6.53242	0.216429	0.108214	+	0.994128i	$0.465487\pi$
$912$	19.1105	0.632811
$913$	3.69613	0.122324
$914$	11.5394	0.381689
$915$	9.16252	0.302904
$916$	28.5640	0.943780
$917$	−11.1711	−0.368904
$918$	2.14031	0.0706408
$919$	54.8648	1.80982	0.904912	−	0.425599i	$-0.139937\pi$
$919$	54.8648	1.80982	0.904912	+	0.425599i	$0.139937\pi$
$920$	−12.0664	−0.397817
$921$	32.3553	1.06614
$922$	13.0834	0.430879
$923$	−34.5919	−1.13861
$924$	12.6108	0.414866
$925$	−4.41609	−0.145200
$926$	2.67037	0.0877536
$927$	10.2420	0.336391
$928$	−1.58774	−0.0521201
$929$	54.5922	1.79111	0.895557	−	0.444947i	$-0.146778\pi$
$929$	54.5922	1.79111	0.895557	+	0.444947i	$0.146778\pi$
$930$	−0.148741	−0.00487742
$931$	−28.2656	−0.926369
$932$	11.4055	0.373598
$933$	6.58316	0.215523
$934$	−5.90924	−0.193356
$935$	22.8048	0.745797
$936$	4.30890	0.140841
$937$	60.4195	1.97382	0.986910	−	0.161271i	$-0.0515594\pi$
$937$	60.4195	1.97382	0.986910	+	0.161271i	$0.0515594\pi$
$938$	4.49564	0.146788
$939$	−25.3899	−0.828569
$940$	−10.0054	−0.326339
$941$	18.1067	0.590262	0.295131	−	0.955457i	$-0.404637\pi$
$941$	18.1067	0.590262	0.295131	+	0.955457i	$0.404637\pi$
$942$	−0.248251	−0.00808844
$943$	8.38093	0.272921
$944$	−1.15032	−0.0374396
$945$	1.58531	0.0515701
$946$	−1.13627	−0.0369432
$947$	2.77241	0.0900913	0.0450456	−	0.998985i	$-0.485657\pi$
$947$	2.77241	0.0900913	0.0450456	+	0.998985i	$0.485657\pi$
$948$	−9.85032	−0.319924
$949$	−10.9405	−0.355145
$950$	−2.56401	−0.0831876
$951$	−10.8150	−0.350700
$952$	13.0102	0.421661
$953$	−25.5883	−0.828885	−0.414443	−	0.910075i	$-0.636023\pi$
$953$	−25.5883	−0.828885	−0.414443	+	0.910075i	$0.636023\pi$
$954$	−2.42915	−0.0786468
$955$	−10.3694	−0.335546
$956$	−3.28286	−0.106175
$957$	1.58072	0.0510973
$958$	11.8419	0.382596
$959$	−23.4040	−0.755754
$960$	4.29422	0.138595
$961$	−30.8664	−0.995692
$962$	4.96264	0.160002
$963$	5.53927	0.178501
$964$	7.29758	0.235039
$965$	10.7596	0.346365
$966$	4.98884	0.160513
$967$	−24.6709	−0.793362	−0.396681	−	0.917957i	$-0.629838\pi$
$967$	−24.6709	−0.793362	−0.396681	+	0.917957i	$0.629838\pi$
$968$	12.1819	0.391540
$969$	−33.1285	−1.06424
$970$	4.44671	0.142775
$971$	−19.7287	−0.633125	−0.316563	−	0.948572i	$-0.602529\pi$
$971$	−19.7287	−0.633125	−0.316563	+	0.948572i	$0.602529\pi$
$972$	−1.83435	−0.0588368
$973$	−2.13129	−0.0683260
$974$	6.87827	0.220394
$975$	2.76107	0.0884249
$976$	−27.7948	−0.889690
$977$	−30.6365	−0.980150	−0.490075	−	0.871680i	$-0.663031\pi$
$977$	−30.6365	−0.980150	−0.490075	+	0.871680i	$0.663031\pi$
$978$	−3.90906	−0.124998
$979$	2.94183	0.0940214
$980$	−8.23034	−0.262909
$981$	2.63811	0.0842282
$982$	−3.51324	−0.112112
$983$	10.5741	0.337263	0.168631	−	0.985679i	$-0.446065\pi$
$983$	10.5741	0.337263	0.168631	+	0.985679i	$0.446065\pi$
$984$	1.69159	0.0539258
$985$	12.7042	0.404790
$986$	0.780160	0.0248454
$987$	8.64699	0.275237
$988$	−31.9067	−1.01509
$989$	4.97763	0.158279
$990$	1.76500	0.0560954
$991$	13.5005	0.428859	0.214429	−	0.976739i	$-0.431211\pi$
$991$	13.5005	0.428859	0.214429	+	0.976739i	$0.431211\pi$
$992$	1.59186	0.0505417
$993$	31.4830	0.999084
$994$	−8.08368	−0.256399
$995$	4.11646	0.130501
$996$	−1.56344	−0.0495396
$997$	1.62784	0.0515541	0.0257771	−	0.999668i	$-0.491794\pi$
$997$	1.62784	0.0515541	0.0257771	+	0.999668i	$0.491794\pi$
$998$	−9.37149	−0.296649
$999$	−4.41609	−0.139719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.18	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.18	✓	39	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)

\(f(q)\)	\(=\)	\(q-0.407003 q^{2} +1.00000 q^{3} -1.83435 q^{4} -1.00000 q^{5} -0.407003 q^{6} -1.58531 q^{7} +1.56059 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.407003 q^{2} +1.00000 q^{3} -1.83435 q^{4} -1.00000 q^{5} -0.407003 q^{6} -1.58531 q^{7} +1.56059 q^{8} +1.00000 q^{9} +0.407003 q^{10} +4.33658 q^{11} -1.83435 q^{12} +2.76107 q^{13} +0.645226 q^{14} -1.00000 q^{15} +3.03353 q^{16} -5.25871 q^{17} -0.407003 q^{18} +6.29974 q^{19} +1.83435 q^{20} -1.58531 q^{21} -1.76500 q^{22} +7.73192 q^{23} +1.56059 q^{24} +1.00000 q^{25} -1.12376 q^{26} +1.00000 q^{27} +2.90801 q^{28} +0.364508 q^{29} +0.407003 q^{30} -0.365455 q^{31} -4.35584 q^{32} +4.33658 q^{33} +2.14031 q^{34} +1.58531 q^{35} -1.83435 q^{36} -4.41609 q^{37} -2.56401 q^{38} +2.76107 q^{39} -1.56059 q^{40} +1.08394 q^{41} +0.645226 q^{42} +0.643776 q^{43} -7.95480 q^{44} -1.00000 q^{45} -3.14692 q^{46} -5.45445 q^{47} +3.03353 q^{48} -4.48679 q^{49} -0.407003 q^{50} -5.25871 q^{51} -5.06476 q^{52} +5.96839 q^{53} -0.407003 q^{54} -4.33658 q^{55} -2.47402 q^{56} +6.29974 q^{57} -0.148356 q^{58} -0.379200 q^{59} +1.83435 q^{60} -9.16252 q^{61} +0.148741 q^{62} -1.58531 q^{63} -4.29422 q^{64} -2.76107 q^{65} -1.76500 q^{66} +6.96755 q^{67} +9.64630 q^{68} +7.73192 q^{69} -0.645226 q^{70} -12.5284 q^{71} +1.56059 q^{72} -3.96243 q^{73} +1.79736 q^{74} +1.00000 q^{75} -11.5559 q^{76} -6.87482 q^{77} -1.12376 q^{78} +5.36993 q^{79} -3.03353 q^{80} +1.00000 q^{81} -0.441167 q^{82} +0.852315 q^{83} +2.90801 q^{84} +5.25871 q^{85} -0.262019 q^{86} +0.364508 q^{87} +6.76763 q^{88} +0.678376 q^{89} +0.407003 q^{90} -4.37715 q^{91} -14.1830 q^{92} -0.365455 q^{93} +2.21998 q^{94} -6.29974 q^{95} -4.35584 q^{96} +10.9255 q^{97} +1.82614 q^{98} +4.33658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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