LMFDB - Embedded newform 6014.2.a.f.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.191955 q^{3} +1.00000 q^{4} -1.50666 q^{5} -0.191955 q^{6} -2.08203 q^{7} -1.00000 q^{8} -2.96315 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.191955 q^{3} +1.00000 q^{4} -1.50666 q^{5} -0.191955 q^{6} -2.08203 q^{7} -1.00000 q^{8} -2.96315 q^{9} +1.50666 q^{10} +5.27833 q^{11} +0.191955 q^{12} -2.65205 q^{13} +2.08203 q^{14} -0.289211 q^{15} +1.00000 q^{16} +1.37810 q^{17} +2.96315 q^{18} +4.07561 q^{19} -1.50666 q^{20} -0.399657 q^{21} -5.27833 q^{22} +0.484659 q^{23} -0.191955 q^{24} -2.72998 q^{25} +2.65205 q^{26} -1.14466 q^{27} -2.08203 q^{28} -2.92567 q^{29} +0.289211 q^{30} +1.00000 q^{31} -1.00000 q^{32} +1.01320 q^{33} -1.37810 q^{34} +3.13690 q^{35} -2.96315 q^{36} +8.02843 q^{37} -4.07561 q^{38} -0.509075 q^{39} +1.50666 q^{40} -7.48629 q^{41} +0.399657 q^{42} +3.22344 q^{43} +5.27833 q^{44} +4.46446 q^{45} -0.484659 q^{46} +0.0207396 q^{47} +0.191955 q^{48} -2.66516 q^{49} +2.72998 q^{50} +0.264535 q^{51} -2.65205 q^{52} +11.5544 q^{53} +1.14466 q^{54} -7.95263 q^{55} +2.08203 q^{56} +0.782335 q^{57} +2.92567 q^{58} -9.10741 q^{59} -0.289211 q^{60} +4.03281 q^{61} -1.00000 q^{62} +6.16937 q^{63} +1.00000 q^{64} +3.99573 q^{65} -1.01320 q^{66} -8.31825 q^{67} +1.37810 q^{68} +0.0930330 q^{69} -3.13690 q^{70} -6.45884 q^{71} +2.96315 q^{72} +2.97971 q^{73} -8.02843 q^{74} -0.524035 q^{75} +4.07561 q^{76} -10.9896 q^{77} +0.509075 q^{78} +6.72788 q^{79} -1.50666 q^{80} +8.66974 q^{81} +7.48629 q^{82} -9.10612 q^{83} -0.399657 q^{84} -2.07633 q^{85} -3.22344 q^{86} -0.561599 q^{87} -5.27833 q^{88} +10.8126 q^{89} -4.46446 q^{90} +5.52164 q^{91} +0.484659 q^{92} +0.191955 q^{93} -0.0207396 q^{94} -6.14054 q^{95} -0.191955 q^{96} +1.00000 q^{97} +2.66516 q^{98} -15.6405 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.191955	0.110826	0.0554128	−	0.998464i	$-0.482353\pi$
$3$	0.191955	0.110826	0.0554128	+	0.998464i	$0.482353\pi$
$4$	1.00000	0.500000
$5$	−1.50666	−0.673798	−0.336899	−	0.941541i	$-0.609378\pi$
$5$	−1.50666	−0.673798	−0.336899	+	0.941541i	$0.609378\pi$
$6$	−0.191955	−0.0783655
$7$	−2.08203	−0.786933	−0.393466	−	0.919339i	$-0.628724\pi$
$7$	−2.08203	−0.786933	−0.393466	+	0.919339i	$0.628724\pi$
$8$	−1.00000	−0.353553
$9$	−2.96315	−0.987718
$10$	1.50666	0.476447
$11$	5.27833	1.59148	0.795738	−	0.605641i	$-0.207083\pi$
$11$	5.27833	1.59148	0.795738	+	0.605641i	$0.207083\pi$
$12$	0.191955	0.0554128
$13$	−2.65205	−0.735546	−0.367773	−	0.929916i	$-0.619880\pi$
$13$	−2.65205	−0.735546	−0.367773	+	0.929916i	$0.619880\pi$
$14$	2.08203	0.556446
$15$	−0.289211	−0.0746740
$16$	1.00000	0.250000
$17$	1.37810	0.334239	0.167120	−	0.985937i	$-0.446553\pi$
$17$	1.37810	0.334239	0.167120	+	0.985937i	$0.446553\pi$
$18$	2.96315	0.698422
$19$	4.07561	0.935008	0.467504	−	0.883991i	$-0.345153\pi$
$19$	4.07561	0.935008	0.467504	+	0.883991i	$0.345153\pi$
$20$	−1.50666	−0.336899
$21$	−0.399657	−0.0872122
$22$	−5.27833	−1.12534
$23$	0.484659	0.101058	0.0505292	−	0.998723i	$-0.483909\pi$
$23$	0.484659	0.101058	0.0505292	+	0.998723i	$0.483909\pi$
$24$	−0.191955	−0.0391827
$25$	−2.72998	−0.545996
$26$	2.65205	0.520110
$27$	−1.14466	−0.220290
$28$	−2.08203	−0.393466
$29$	−2.92567	−0.543284	−0.271642	−	0.962398i	$-0.587567\pi$
$29$	−2.92567	−0.543284	−0.271642	+	0.962398i	$0.587567\pi$
$30$	0.289211	0.0528025
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	1.01320	0.176376
$34$	−1.37810	−0.236343
$35$	3.13690	0.530234
$36$	−2.96315	−0.493859
$37$	8.02843	1.31987	0.659933	−	0.751325i	$-0.270585\pi$
$37$	8.02843	1.31987	0.659933	+	0.751325i	$0.270585\pi$
$38$	−4.07561	−0.661151
$39$	−0.509075	−0.0815173
$40$	1.50666	0.238224
$41$	−7.48629	−1.16916	−0.584581	−	0.811335i	$-0.698741\pi$
$41$	−7.48629	−1.16916	−0.584581	+	0.811335i	$0.698741\pi$
$42$	0.399657	0.0616684
$43$	3.22344	0.491570	0.245785	−	0.969324i	$-0.420954\pi$
$43$	3.22344	0.491570	0.245785	+	0.969324i	$0.420954\pi$
$44$	5.27833	0.795738
$45$	4.46446	0.665522
$46$	−0.484659	−0.0714591
$47$	0.0207396	0.00302518	0.00151259	−	0.999999i	$-0.499519\pi$
$47$	0.0207396	0.00302518	0.00151259	+	0.999999i	$0.499519\pi$
$48$	0.191955	0.0277064
$49$	−2.66516	−0.380737
$50$	2.72998	0.386078
$51$	0.264535	0.0370422
$52$	−2.65205	−0.367773
$53$	11.5544	1.58712	0.793558	−	0.608495i	$-0.208226\pi$
$53$	11.5544	1.58712	0.793558	+	0.608495i	$0.208226\pi$
$54$	1.14466	0.155768
$55$	−7.95263	−1.07233
$56$	2.08203	0.278223
$57$	0.782335	0.103623
$58$	2.92567	0.384160
$59$	−9.10741	−1.18568	−0.592842	−	0.805319i	$-0.701994\pi$
$59$	−9.10741	−1.18568	−0.592842	+	0.805319i	$0.701994\pi$
$60$	−0.289211	−0.0373370
$61$	4.03281	0.516349	0.258174	−	0.966098i	$-0.416879\pi$
$61$	4.03281	0.516349	0.258174	+	0.966098i	$0.416879\pi$
$62$	−1.00000	−0.127000
$63$	6.16937	0.777267
$64$	1.00000	0.125000
$65$	3.99573	0.495610
$66$	−1.01320	−0.124717
$67$	−8.31825	−1.01624	−0.508118	−	0.861288i	$-0.669659\pi$
$67$	−8.31825	−1.01624	−0.508118	+	0.861288i	$0.669659\pi$
$68$	1.37810	0.167120
$69$	0.0930330	0.0111999
$70$	−3.13690	−0.374932
$71$	−6.45884	−0.766523	−0.383262	−	0.923640i	$-0.625199\pi$
$71$	−6.45884	−0.766523	−0.383262	+	0.923640i	$0.625199\pi$
$72$	2.96315	0.349211
$73$	2.97971	0.348749	0.174374	−	0.984679i	$-0.444210\pi$
$73$	2.97971	0.348749	0.174374	+	0.984679i	$0.444210\pi$
$74$	−8.02843	−0.933286
$75$	−0.524035	−0.0605103
$76$	4.07561	0.467504
$77$	−10.9896	−1.25238
$78$	0.509075	0.0576414
$79$	6.72788	0.756946	0.378473	−	0.925612i	$-0.376449\pi$
$79$	6.72788	0.756946	0.378473	+	0.925612i	$0.376449\pi$
$80$	−1.50666	−0.168449
$81$	8.66974	0.963304
$82$	7.48629	0.826722
$83$	−9.10612	−0.999527	−0.499763	−	0.866162i	$-0.666580\pi$
$83$	−9.10612	−0.999527	−0.499763	+	0.866162i	$0.666580\pi$
$84$	−0.399657	−0.0436061
$85$	−2.07633	−0.225210
$86$	−3.22344	−0.347592
$87$	−0.561599	−0.0602097
$88$	−5.27833	−0.562671
$89$	10.8126	1.14613	0.573065	−	0.819510i	$-0.305754\pi$
$89$	10.8126	1.14613	0.573065	+	0.819510i	$0.305754\pi$
$90$	−4.46446	−0.470595
$91$	5.52164	0.578826
$92$	0.484659	0.0505292
$93$	0.191955	0.0199049
$94$	−0.0207396	−0.00213913
$95$	−6.14054	−0.630007
$96$	−0.191955	−0.0195914
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	2.66516	0.269222
$99$	−15.6405	−1.57193
$100$	−2.72998	−0.272998
$101$	2.50536	0.249293	0.124646	−	0.992201i	$-0.460220\pi$
$101$	2.50536	0.249293	0.124646	+	0.992201i	$0.460220\pi$
$102$	−0.264535	−0.0261928
$103$	13.5118	1.33135	0.665676	−	0.746241i	$-0.268143\pi$
$103$	13.5118	1.33135	0.665676	+	0.746241i	$0.268143\pi$
$104$	2.65205	0.260055
$105$	0.602146	0.0587634
$106$	−11.5544	−1.12226
$107$	13.0034	1.25709	0.628544	−	0.777774i	$-0.283651\pi$
$107$	13.0034	1.25709	0.628544	+	0.777774i	$0.283651\pi$
$108$	−1.14466	−0.110145
$109$	6.84132	0.655280	0.327640	−	0.944803i	$-0.393747\pi$
$109$	6.84132	0.655280	0.327640	+	0.944803i	$0.393747\pi$
$110$	7.95263	0.758254
$111$	1.54110	0.146275
$112$	−2.08203	−0.196733
$113$	12.0621	1.13470	0.567351	−	0.823476i	$-0.307968\pi$
$113$	12.0621	1.13470	0.567351	+	0.823476i	$0.307968\pi$
$114$	−0.782335	−0.0732724
$115$	−0.730216	−0.0680930
$116$	−2.92567	−0.271642
$117$	7.85843	0.726512
$118$	9.10741	0.838406
$119$	−2.86925	−0.263024
$120$	0.289211	0.0264012
$121$	16.8607	1.53279
$122$	−4.03281	−0.365114
$123$	−1.43703	−0.129573
$124$	1.00000	0.0898027
$125$	11.6464	1.04169
$126$	−6.16937	−0.549611
$127$	−12.9406	−1.14830	−0.574148	−	0.818752i	$-0.694666\pi$
$127$	−12.9406	−1.14830	−0.574148	+	0.818752i	$0.694666\pi$
$128$	−1.00000	−0.0883883
$129$	0.618756	0.0544785
$130$	−3.99573	−0.350449
$131$	−0.367342	−0.0320948	−0.0160474	−	0.999871i	$-0.505108\pi$
$131$	−0.367342	−0.0320948	−0.0160474	+	0.999871i	$0.505108\pi$
$132$	1.01320	0.0881880
$133$	−8.48553	−0.735789
$134$	8.31825	0.718587
$135$	1.72461	0.148431
$136$	−1.37810	−0.118171
$137$	−5.80751	−0.496169	−0.248085	−	0.968738i	$-0.579801\pi$
$137$	−5.80751	−0.496169	−0.248085	+	0.968738i	$0.579801\pi$
$138$	−0.0930330	−0.00791949
$139$	−15.0843	−1.27944	−0.639718	−	0.768610i	$-0.720949\pi$
$139$	−15.0843	−1.27944	−0.639718	+	0.768610i	$0.720949\pi$
$140$	3.13690	0.265117
$141$	0.00398108	0.000335267 0
$142$	6.45884	0.542014
$143$	−13.9984	−1.17060
$144$	−2.96315	−0.246929
$145$	4.40799	0.366063
$146$	−2.97971	−0.246603
$147$	−0.511591	−0.0421954
$148$	8.02843	0.659933
$149$	−14.2830	−1.17011	−0.585055	−	0.810993i	$-0.698927\pi$
$149$	−14.2830	−1.17011	−0.585055	+	0.810993i	$0.698927\pi$
$150$	0.524035	0.0427873
$151$	−4.91746	−0.400177	−0.200088	−	0.979778i	$-0.564123\pi$
$151$	−4.91746	−0.400177	−0.200088	+	0.979778i	$0.564123\pi$
$152$	−4.07561	−0.330575
$153$	−4.08353	−0.330134
$154$	10.9896	0.885569
$155$	−1.50666	−0.121018
$156$	−0.509075	−0.0407587
$157$	−19.0170	−1.51772	−0.758861	−	0.651253i	$-0.774244\pi$
$157$	−19.0170	−1.51772	−0.758861	+	0.651253i	$0.774244\pi$
$158$	−6.72788	−0.535242
$159$	2.21793	0.175893
$160$	1.50666	0.119112
$161$	−1.00907	−0.0795262
$162$	−8.66974	−0.681159
$163$	−7.57423	−0.593259	−0.296630	−	0.954993i	$-0.595863\pi$
$163$	−7.57423	−0.593259	−0.296630	+	0.954993i	$0.595863\pi$
$164$	−7.48629	−0.584581
$165$	−1.52655	−0.118842
$166$	9.10612	0.706772
$167$	−2.84496	−0.220150	−0.110075	−	0.993923i	$-0.535109\pi$
$167$	−2.84496	−0.220150	−0.110075	+	0.993923i	$0.535109\pi$
$168$	0.399657	0.0308342
$169$	−5.96663	−0.458972
$170$	2.07633	0.159247
$171$	−12.0766	−0.923524
$172$	3.22344	0.245785
$173$	−11.2322	−0.853966	−0.426983	−	0.904260i	$-0.640424\pi$
$173$	−11.2322	−0.853966	−0.426983	+	0.904260i	$0.640424\pi$
$174$	0.561599	0.0425747
$175$	5.68390	0.429662
$176$	5.27833	0.397869
$177$	−1.74822	−0.131404
$178$	−10.8126	−0.810437
$179$	−23.6111	−1.76478	−0.882388	−	0.470523i	$-0.844065\pi$
$179$	−23.6111	−1.76478	−0.882388	+	0.470523i	$0.844065\pi$
$180$	4.46446	0.332761
$181$	18.6592	1.38693	0.693463	−	0.720492i	$-0.256084\pi$
$181$	18.6592	1.38693	0.693463	+	0.720492i	$0.256084\pi$
$182$	−5.52164	−0.409291
$183$	0.774121	0.0572246
$184$	−0.484659	−0.0357296
$185$	−12.0961	−0.889323
$186$	−0.191955	−0.0140749
$187$	7.27408	0.531934
$188$	0.0207396	0.00151259
$189$	2.38321	0.173353
$190$	6.14054	0.445482
$191$	−6.70479	−0.485142	−0.242571	−	0.970134i	$-0.577991\pi$
$191$	−6.70479	−0.485142	−0.242571	+	0.970134i	$0.577991\pi$
$192$	0.191955	0.0138532
$193$	−17.7373	−1.27676	−0.638381	−	0.769721i	$-0.720395\pi$
$193$	−17.7373	−1.27676	−0.638381	+	0.769721i	$0.720395\pi$
$194$	−1.00000	−0.0717958
$195$	0.767003	0.0549262
$196$	−2.66516	−0.190368
$197$	−0.955852	−0.0681016	−0.0340508	−	0.999420i	$-0.510841\pi$
$197$	−0.955852	−0.0681016	−0.0340508	+	0.999420i	$0.510841\pi$
$198$	15.6405	1.11152
$199$	−5.89079	−0.417587	−0.208793	−	0.977960i	$-0.566954\pi$
$199$	−5.89079	−0.417587	−0.208793	+	0.977960i	$0.566954\pi$
$200$	2.72998	0.193039
$201$	−1.59673	−0.112625
$202$	−2.50536	−0.176277
$203$	6.09133	0.427528
$204$	0.264535	0.0185211
$205$	11.2793	0.787779
$206$	−13.5118	−0.941409
$207$	−1.43612	−0.0998172
$208$	−2.65205	−0.183887
$209$	21.5124	1.48804
$210$	−0.602146	−0.0415520
$211$	−23.6964	−1.63133	−0.815664	−	0.578526i	$-0.803628\pi$
$211$	−23.6964	−1.63133	−0.815664	+	0.578526i	$0.803628\pi$
$212$	11.5544	0.793558
$213$	−1.23981	−0.0849503
$214$	−13.0034	−0.888895
$215$	−4.85662	−0.331219
$216$	1.14466	0.0778842
$217$	−2.08203	−0.141337
$218$	−6.84132	−0.463353
$219$	0.571972	0.0386503
$220$	−7.95263	−0.536166
$221$	−3.65480	−0.245848
$222$	−1.54110	−0.103432
$223$	−11.7320	−0.785635	−0.392817	−	0.919617i	$-0.628500\pi$
$223$	−11.7320	−0.785635	−0.392817	+	0.919617i	$0.628500\pi$
$224$	2.08203	0.139111
$225$	8.08935	0.539290
$226$	−12.0621	−0.802356
$227$	−2.30954	−0.153290	−0.0766449	−	0.997058i	$-0.524421\pi$
$227$	−2.30954	−0.153290	−0.0766449	+	0.997058i	$0.524421\pi$
$228$	0.782335	0.0518114
$229$	−17.2094	−1.13723	−0.568614	−	0.822605i	$-0.692520\pi$
$229$	−17.2094	−1.13723	−0.568614	+	0.822605i	$0.692520\pi$
$230$	0.730216	0.0481490
$231$	−2.10952	−0.138796
$232$	2.92567	0.192080
$233$	12.3315	0.807860	0.403930	−	0.914790i	$-0.367644\pi$
$233$	12.3315	0.807860	0.403930	+	0.914790i	$0.367644\pi$
$234$	−7.85843	−0.513722
$235$	−0.0312475	−0.00203836
$236$	−9.10741	−0.592842
$237$	1.29145	0.0838889
$238$	2.86925	0.185986
$239$	5.76345	0.372807	0.186403	−	0.982473i	$-0.440317\pi$
$239$	5.76345	0.372807	0.186403	+	0.982473i	$0.440317\pi$
$240$	−0.289211	−0.0186685
$241$	−9.34315	−0.601845	−0.300922	−	0.953649i	$-0.597295\pi$
$241$	−9.34315	−0.601845	−0.300922	+	0.953649i	$0.597295\pi$
$242$	−16.8607	−1.08385
$243$	5.09818	0.327049
$244$	4.03281	0.258174
$245$	4.01548	0.256540
$246$	1.43703	0.0916219
$247$	−10.8087	−0.687742
$248$	−1.00000	−0.0635001
$249$	−1.74797	−0.110773
$250$	−11.6464	−0.736585
$251$	−9.87050	−0.623020	−0.311510	−	0.950243i	$-0.600835\pi$
$251$	−9.87050	−0.623020	−0.311510	+	0.950243i	$0.600835\pi$
$252$	6.16937	0.388634
$253$	2.55819	0.160832
$254$	12.9406	0.811967
$255$	−0.398563	−0.0249590
$256$	1.00000	0.0625000
$257$	−10.8749	−0.678355	−0.339177	−	0.940722i	$-0.610149\pi$
$257$	−10.8749	−0.678355	−0.339177	+	0.940722i	$0.610149\pi$
$258$	−0.618756	−0.0385221
$259$	−16.7154	−1.03865
$260$	3.99573	0.247805
$261$	8.66921	0.536611
$262$	0.367342	0.0226945
$263$	18.0050	1.11023	0.555117	−	0.831772i	$-0.312674\pi$
$263$	18.0050	1.11023	0.555117	+	0.831772i	$0.312674\pi$
$264$	−1.01320	−0.0623584
$265$	−17.4085	−1.06940
$266$	8.48553	0.520281
$267$	2.07553	0.127021
$268$	−8.31825	−0.508118
$269$	−19.6740	−1.19955	−0.599773	−	0.800170i	$-0.704743\pi$
$269$	−19.6740	−1.19955	−0.599773	+	0.800170i	$0.704743\pi$
$270$	−1.72461	−0.104956
$271$	−3.37907	−0.205264	−0.102632	−	0.994719i	$-0.532726\pi$
$271$	−3.37907	−0.205264	−0.102632	+	0.994719i	$0.532726\pi$
$272$	1.37810	0.0835598
$273$	1.05991	0.0641486
$274$	5.80751	0.350845
$275$	−14.4097	−0.868940
$276$	0.0930330	0.00559993
$277$	13.6323	0.819085	0.409542	−	0.912291i	$-0.365688\pi$
$277$	13.6323	0.819085	0.409542	+	0.912291i	$0.365688\pi$
$278$	15.0843	0.904698
$279$	−2.96315	−0.177399
$280$	−3.13690	−0.187466
$281$	11.4901	0.685439	0.342720	−	0.939438i	$-0.388652\pi$
$281$	11.4901	0.685439	0.342720	+	0.939438i	$0.388652\pi$
$282$	−0.00398108	−0.000237070 0
$283$	11.6331	0.691516	0.345758	−	0.938324i	$-0.387622\pi$
$283$	11.6331	0.691516	0.345758	+	0.938324i	$0.387622\pi$
$284$	−6.45884	−0.383262
$285$	−1.17871	−0.0698208
$286$	13.9984	0.827742
$287$	15.5867	0.920052
$288$	2.96315	0.174605
$289$	−15.1008	−0.888284
$290$	−4.40799	−0.258846
$291$	0.191955	0.0112526
$292$	2.97971	0.174374
$293$	−7.68691	−0.449074	−0.224537	−	0.974466i	$-0.572087\pi$
$293$	−7.68691	−0.449074	−0.224537	+	0.974466i	$0.572087\pi$
$294$	0.511591	0.0298366
$295$	13.7218	0.798912
$296$	−8.02843	−0.466643
$297$	−6.04189	−0.350586
$298$	14.2830	0.827393
$299$	−1.28534	−0.0743332
$300$	−0.524035	−0.0302552
$301$	−6.71129	−0.386832
$302$	4.91746	0.282968
$303$	0.480918	0.0276280
$304$	4.07561	0.233752
$305$	−6.07607	−0.347915
$306$	4.08353	0.233440
$307$	9.72109	0.554812	0.277406	−	0.960753i	$-0.410525\pi$
$307$	9.72109	0.554812	0.277406	+	0.960753i	$0.410525\pi$
$308$	−10.9896	−0.626192
$309$	2.59365	0.147548
$310$	1.50666	0.0855724
$311$	−20.2690	−1.14935	−0.574674	−	0.818383i	$-0.694871\pi$
$311$	−20.2690	−1.14935	−0.574674	+	0.818383i	$0.694871\pi$
$312$	0.509075	0.0288207
$313$	−19.7901	−1.11861	−0.559303	−	0.828964i	$-0.688931\pi$
$313$	−19.7901	−1.11861	−0.559303	+	0.828964i	$0.688931\pi$
$314$	19.0170	1.07319
$315$	−9.29513	−0.523721
$316$	6.72788	0.378473
$317$	−9.30012	−0.522347	−0.261174	−	0.965292i	$-0.584109\pi$
$317$	−9.30012	−0.522347	−0.261174	+	0.965292i	$0.584109\pi$
$318$	−2.21793	−0.124375
$319$	−15.4427	−0.864623
$320$	−1.50666	−0.0842247
$321$	2.49608	0.139317
$322$	1.00907	0.0562335
$323$	5.61661	0.312516
$324$	8.66974	0.481652
$325$	7.24005	0.401606
$326$	7.57423	0.419498
$327$	1.31323	0.0726217
$328$	7.48629	0.413361
$329$	−0.0431804	−0.00238061
$330$	1.52655	0.0840339
$331$	14.5828	0.801543	0.400771	−	0.916178i	$-0.368742\pi$
$331$	14.5828	0.801543	0.400771	+	0.916178i	$0.368742\pi$
$332$	−9.10612	−0.499763
$333$	−23.7895	−1.30365
$334$	2.84496	0.155670
$335$	12.5328	0.684738
$336$	−0.399657	−0.0218031
$337$	1.33381	0.0726572	0.0363286	−	0.999340i	$-0.488434\pi$
$337$	1.33381	0.0726572	0.0363286	+	0.999340i	$0.488434\pi$
$338$	5.96663	0.324542
$339$	2.31538	0.125754
$340$	−2.07633	−0.112605
$341$	5.27833	0.285837
$342$	12.0766	0.653030
$343$	20.1231	1.08655
$344$	−3.22344	−0.173796
$345$	−0.140169	−0.00754644
$346$	11.2322	0.603845
$347$	−28.8415	−1.54829	−0.774147	−	0.633006i	$-0.781821\pi$
$347$	−28.8415	−1.54829	−0.774147	+	0.633006i	$0.781821\pi$
$348$	−0.561599	−0.0301048
$349$	−9.86681	−0.528158	−0.264079	−	0.964501i	$-0.585068\pi$
$349$	−9.86681	−0.528158	−0.264079	+	0.964501i	$0.585068\pi$
$350$	−5.68390	−0.303817
$351$	3.03569	0.162033
$352$	−5.27833	−0.281336
$353$	24.1257	1.28408	0.642041	−	0.766670i	$-0.278088\pi$
$353$	24.1257	1.28408	0.642041	+	0.766670i	$0.278088\pi$
$354$	1.74822	0.0929167
$355$	9.73126	0.516482
$356$	10.8126	0.573065
$357$	−0.550768	−0.0291498
$358$	23.6111	1.24788
$359$	15.1297	0.798516	0.399258	−	0.916839i	$-0.369268\pi$
$359$	15.1297	0.798516	0.399258	+	0.916839i	$0.369268\pi$
$360$	−4.46446	−0.235298
$361$	−2.38944	−0.125760
$362$	−18.6592	−0.980705
$363$	3.23651	0.169873
$364$	5.52164	0.289413
$365$	−4.48941	−0.234986
$366$	−0.774121	−0.0404639
$367$	−15.6686	−0.817892	−0.408946	−	0.912559i	$-0.634104\pi$
$367$	−15.6686	−0.817892	−0.408946	+	0.912559i	$0.634104\pi$
$368$	0.484659	0.0252646
$369$	22.1830	1.15480
$370$	12.0961	0.628846
$371$	−24.0565	−1.24895
$372$	0.191955	0.00995243
$373$	−13.3839	−0.692992	−0.346496	−	0.938051i	$-0.612629\pi$
$373$	−13.3839	−0.692992	−0.346496	+	0.938051i	$0.612629\pi$
$374$	−7.27408	−0.376134
$375$	2.23560	0.115446
$376$	−0.0207396	−0.00106956
$377$	7.75903	0.399610
$378$	−2.38321	−0.122579
$379$	−29.6675	−1.52391	−0.761957	−	0.647627i	$-0.775761\pi$
$379$	−29.6675	−1.52391	−0.761957	+	0.647627i	$0.775761\pi$
$380$	−6.14054	−0.315003
$381$	−2.48402	−0.127260
$382$	6.70479	0.343047
$383$	−5.74217	−0.293411	−0.146706	−	0.989180i	$-0.546867\pi$
$383$	−5.74217	−0.293411	−0.146706	+	0.989180i	$0.546867\pi$
$384$	−0.191955	−0.00979568
$385$	16.5576	0.843854
$386$	17.7373	0.902806
$387$	−9.55154	−0.485532
$388$	1.00000	0.0507673
$389$	−8.24198	−0.417885	−0.208943	−	0.977928i	$-0.567002\pi$
$389$	−8.24198	−0.417885	−0.208943	+	0.977928i	$0.567002\pi$
$390$	−0.767003	−0.0388387
$391$	0.667911	0.0337777
$392$	2.66516	0.134611
$393$	−0.0705133	−0.00355693
$394$	0.955852	0.0481551
$395$	−10.1366	−0.510029
$396$	−15.6405	−0.785964
$397$	5.57808	0.279956	0.139978	−	0.990155i	$-0.455297\pi$
$397$	5.57808	0.279956	0.139978	+	0.990155i	$0.455297\pi$
$398$	5.89079	0.295278
$399$	−1.62884	−0.0815442
$400$	−2.72998	−0.136499
$401$	−38.7177	−1.93347	−0.966735	−	0.255778i	$-0.917668\pi$
$401$	−38.7177	−1.93347	−0.966735	+	0.255778i	$0.917668\pi$
$402$	1.59673	0.0796378
$403$	−2.65205	−0.132108
$404$	2.50536	0.124646
$405$	−13.0623	−0.649072
$406$	−6.09133	−0.302308
$407$	42.3767	2.10053
$408$	−0.264535	−0.0130964
$409$	4.51200	0.223104	0.111552	−	0.993759i	$-0.464418\pi$
$409$	4.51200	0.223104	0.111552	+	0.993759i	$0.464418\pi$
$410$	−11.2793	−0.557044
$411$	−1.11478	−0.0549882
$412$	13.5118	0.665676
$413$	18.9619	0.933054
$414$	1.43612	0.0705814
$415$	13.7198	0.673479
$416$	2.65205	0.130027
$417$	−2.89552	−0.141794
$418$	−21.5124	−1.05220
$419$	36.9093	1.80313	0.901567	−	0.432639i	$-0.142417\pi$
$419$	36.9093	1.80313	0.901567	+	0.432639i	$0.142417\pi$
$420$	0.602146	0.0293817
$421$	−35.5371	−1.73197	−0.865987	−	0.500066i	$-0.833309\pi$
$421$	−35.5371	−1.73197	−0.865987	+	0.500066i	$0.833309\pi$
$422$	23.6964	1.15352
$423$	−0.0614546	−0.00298802
$424$	−11.5544	−0.561130
$425$	−3.76220	−0.182493
$426$	1.23981	0.0600689
$427$	−8.39643	−0.406332
$428$	13.0034	0.628544
$429$	−2.68707	−0.129733
$430$	4.85662	0.234207
$431$	39.8051	1.91734	0.958672	−	0.284513i	$-0.0918319\pi$
$431$	39.8051	1.91734	0.958672	+	0.284513i	$0.0918319\pi$
$432$	−1.14466	−0.0550725
$433$	8.05411	0.387056	0.193528	−	0.981095i	$-0.438007\pi$
$433$	8.05411	0.387056	0.193528	+	0.981095i	$0.438007\pi$
$434$	2.08203	0.0999406
$435$	0.846137	0.0405692
$436$	6.84132	0.327640
$437$	1.97528	0.0944905
$438$	−0.571972	−0.0273299
$439$	−27.4669	−1.31093	−0.655463	−	0.755227i	$-0.727526\pi$
$439$	−27.4669	−1.31093	−0.655463	+	0.755227i	$0.727526\pi$
$440$	7.95263	0.379127
$441$	7.89727	0.376060
$442$	3.65480	0.173841
$443$	26.8960	1.27787	0.638934	−	0.769262i	$-0.279376\pi$
$443$	26.8960	1.27787	0.638934	+	0.769262i	$0.279376\pi$
$444$	1.54110	0.0731374
$445$	−16.2909	−0.772261
$446$	11.7320	0.555528
$447$	−2.74170	−0.129678
$448$	−2.08203	−0.0983666
$449$	4.24365	0.200270	0.100135	−	0.994974i	$-0.468073\pi$
$449$	4.24365	0.200270	0.100135	+	0.994974i	$0.468073\pi$
$450$	−8.08935	−0.381336
$451$	−39.5151	−1.86069
$452$	12.0621	0.567351
$453$	−0.943932	−0.0443498
$454$	2.30954	0.108392
$455$	−8.31923	−0.390011
$456$	−0.782335	−0.0366362
$457$	21.9779	1.02808	0.514041	−	0.857766i	$-0.328148\pi$
$457$	21.9779	1.02808	0.514041	+	0.857766i	$0.328148\pi$
$458$	17.2094	0.804141
$459$	−1.57746	−0.0736295
$460$	−0.730216	−0.0340465
$461$	−41.3985	−1.92812	−0.964061	−	0.265681i	$-0.914403\pi$
$461$	−41.3985	−1.92812	−0.964061	+	0.265681i	$0.914403\pi$
$462$	2.10952	0.0981437
$463$	−13.8742	−0.644791	−0.322395	−	0.946605i	$-0.604488\pi$
$463$	−13.8742	−0.644791	−0.322395	+	0.946605i	$0.604488\pi$
$464$	−2.92567	−0.135821
$465$	−0.289211	−0.0134118
$466$	−12.3315	−0.571244
$467$	−3.61877	−0.167457	−0.0837283	−	0.996489i	$-0.526683\pi$
$467$	−3.61877	−0.167457	−0.0837283	+	0.996489i	$0.526683\pi$
$468$	7.85843	0.363256
$469$	17.3188	0.799709
$470$	0.0312475	0.00144134
$471$	−3.65042	−0.168202
$472$	9.10741	0.419203
$473$	17.0144	0.782321
$474$	−1.29145	−0.0593184
$475$	−11.1263	−0.510511
$476$	−2.86925	−0.131512
$477$	−34.2374	−1.56762
$478$	−5.76345	−0.263614
$479$	23.5000	1.07374	0.536872	−	0.843664i	$-0.319606\pi$
$479$	23.5000	1.07374	0.536872	+	0.843664i	$0.319606\pi$
$480$	0.289211	0.0132006
$481$	−21.2918	−0.970822
$482$	9.34315	0.425569
$483$	−0.193697	−0.00881353
$484$	16.8607	0.766397
$485$	−1.50666	−0.0684138
$486$	−5.09818	−0.231258
$487$	36.9421	1.67401	0.837003	−	0.547198i	$-0.184305\pi$
$487$	36.9421	1.67401	0.837003	+	0.547198i	$0.184305\pi$
$488$	−4.03281	−0.182557
$489$	−1.45391	−0.0657483
$490$	−4.01548	−0.181401
$491$	20.8694	0.941824	0.470912	−	0.882180i	$-0.343925\pi$
$491$	20.8694	0.941824	0.470912	+	0.882180i	$0.343925\pi$
$492$	−1.43703	−0.0647865
$493$	−4.03188	−0.181587
$494$	10.8087	0.486307
$495$	23.5649	1.05916
$496$	1.00000	0.0449013
$497$	13.4475	0.603202
$498$	1.74797	0.0783284
$499$	−25.9142	−1.16008	−0.580039	−	0.814588i	$-0.696963\pi$
$499$	−25.9142	−1.16008	−0.580039	+	0.814588i	$0.696963\pi$
$500$	11.6464	0.520845
$501$	−0.546106	−0.0243982
$502$	9.87050	0.440542
$503$	−32.3219	−1.44116	−0.720582	−	0.693370i	$-0.756125\pi$
$503$	−32.3219	−1.44116	−0.720582	+	0.693370i	$0.756125\pi$
$504$	−6.16937	−0.274806
$505$	−3.77473	−0.167973
$506$	−2.55819	−0.113725
$507$	−1.14533	−0.0508658
$508$	−12.9406	−0.574148
$509$	6.17883	0.273872	0.136936	−	0.990580i	$-0.456275\pi$
$509$	6.17883	0.273872	0.136936	+	0.990580i	$0.456275\pi$
$510$	0.398563	0.0176487
$511$	−6.20384	−0.274442
$512$	−1.00000	−0.0441942
$513$	−4.66518	−0.205973
$514$	10.8749	0.479669
$515$	−20.3576	−0.897063
$516$	0.618756	0.0272392
$517$	0.109470	0.00481450
$518$	16.7154	0.734433
$519$	−2.15608	−0.0946413
$520$	−3.99573	−0.175224
$521$	−1.96929	−0.0862763	−0.0431381	−	0.999069i	$-0.513736\pi$
$521$	−1.96929	−0.0862763	−0.0431381	+	0.999069i	$0.513736\pi$
$522$	−8.66921	−0.379441
$523$	−17.8460	−0.780349	−0.390175	−	0.920741i	$-0.627585\pi$
$523$	−17.8460	−0.780349	−0.390175	+	0.920741i	$0.627585\pi$
$524$	−0.367342	−0.0160474
$525$	1.09106	0.0476176
$526$	−18.0050	−0.785054
$527$	1.37810	0.0600311
$528$	1.01320	0.0440940
$529$	−22.7651	−0.989787
$530$	17.4085	0.756177
$531$	26.9867	1.17112
$532$	−8.48553	−0.367894
$533$	19.8540	0.859973
$534$	−2.07553	−0.0898171
$535$	−19.5917	−0.847023
$536$	8.31825	0.359294
$537$	−4.53228	−0.195582
$538$	19.6740	0.848208
$539$	−14.0676	−0.605933
$540$	1.72461	0.0742154
$541$	−4.55345	−0.195768	−0.0978840	−	0.995198i	$-0.531207\pi$
$541$	−4.55345	−0.195768	−0.0978840	+	0.995198i	$0.531207\pi$
$542$	3.37907	0.145144
$543$	3.58173	0.153707
$544$	−1.37810	−0.0590857
$545$	−10.3075	−0.441526
$546$	−1.05991	−0.0453599
$547$	−4.76985	−0.203944	−0.101972	−	0.994787i	$-0.532515\pi$
$547$	−4.76985	−0.203944	−0.101972	+	0.994787i	$0.532515\pi$
$548$	−5.80751	−0.248085
$549$	−11.9498	−0.510007
$550$	14.4097	0.614433
$551$	−11.9239	−0.507975
$552$	−0.0930330	−0.00395975
$553$	−14.0076	−0.595666
$554$	−13.6323	−0.579180
$555$	−2.32191	−0.0985596
$556$	−15.0843	−0.639718
$557$	14.6431	0.620449	0.310224	−	0.950663i	$-0.399596\pi$
$557$	14.6431	0.620449	0.310224	+	0.950663i	$0.399596\pi$
$558$	2.96315	0.125440
$559$	−8.54872	−0.361572
$560$	3.13690	0.132558
$561$	1.39630	0.0589518
$562$	−11.4901	−0.484679
$563$	−27.1199	−1.14297	−0.571484	−	0.820613i	$-0.693632\pi$
$563$	−27.1199	−1.14297	−0.571484	+	0.820613i	$0.693632\pi$
$564$	0.00398108	0.000167634 0
$565$	−18.1734	−0.764560
$566$	−11.6331	−0.488976
$567$	−18.0506	−0.758055
$568$	6.45884	0.271007
$569$	−5.43884	−0.228008	−0.114004	−	0.993480i	$-0.536368\pi$
$569$	−5.43884	−0.228008	−0.114004	+	0.993480i	$0.536368\pi$
$570$	1.17871	0.0493708
$571$	−25.2771	−1.05781	−0.528907	−	0.848680i	$-0.677398\pi$
$571$	−25.2771	−1.05781	−0.528907	+	0.848680i	$0.677398\pi$
$572$	−13.9984	−0.585302
$573$	−1.28702	−0.0537661
$574$	−15.5867	−0.650575
$575$	−1.32311	−0.0551776
$576$	−2.96315	−0.123465
$577$	20.5327	0.854789	0.427394	−	0.904065i	$-0.359432\pi$
$577$	20.5327	0.854789	0.427394	+	0.904065i	$0.359432\pi$
$578$	15.1008	0.628112
$579$	−3.40478	−0.141498
$580$	4.40799	0.183032
$581$	18.9592	0.786560
$582$	−0.191955	−0.00795681
$583$	60.9878	2.52586
$584$	−2.97971	−0.123301
$585$	−11.8400	−0.489522
$586$	7.68691	0.317543
$587$	26.1228	1.07820	0.539101	−	0.842241i	$-0.318764\pi$
$587$	26.1228	1.07820	0.539101	+	0.842241i	$0.318764\pi$
$588$	−0.511591	−0.0210977
$589$	4.07561	0.167932
$590$	−13.7218	−0.564916
$591$	−0.183481	−0.00754740
$592$	8.02843	0.329966
$593$	−27.3721	−1.12404	−0.562020	−	0.827124i	$-0.689975\pi$
$593$	−27.3721	−1.12404	−0.562020	+	0.827124i	$0.689975\pi$
$594$	6.04189	0.247902
$595$	4.32298	0.177225
$596$	−14.2830	−0.585055
$597$	−1.13077	−0.0462793
$598$	1.28534	0.0525615
$599$	36.7111	1.49997	0.749987	−	0.661453i	$-0.230060\pi$
$599$	36.7111	1.49997	0.749987	+	0.661453i	$0.230060\pi$
$600$	0.524035	0.0213936
$601$	−36.6813	−1.49626	−0.748130	−	0.663552i	$-0.769048\pi$
$601$	−36.6813	−1.49626	−0.748130	+	0.663552i	$0.769048\pi$
$602$	6.71129	0.273532
$603$	24.6482	1.00375
$604$	−4.91746	−0.200088
$605$	−25.4034	−1.03279
$606$	−0.480918	−0.0195360
$607$	2.62406	0.106507	0.0532536	−	0.998581i	$-0.483041\pi$
$607$	2.62406	0.106507	0.0532536	+	0.998581i	$0.483041\pi$
$608$	−4.07561	−0.165288
$609$	1.16926	0.0473810
$610$	6.07607	0.246013
$611$	−0.0550024	−0.00222516
$612$	−4.08353	−0.165067
$613$	39.7243	1.60445	0.802225	−	0.597022i	$-0.203649\pi$
$613$	39.7243	1.60445	0.802225	+	0.597022i	$0.203649\pi$
$614$	−9.72109	−0.392311
$615$	2.16512	0.0873060
$616$	10.9896	0.442785
$617$	−18.2486	−0.734662	−0.367331	−	0.930090i	$-0.619728\pi$
$617$	−18.2486	−0.734662	−0.367331	+	0.930090i	$0.619728\pi$
$618$	−2.59365	−0.104332
$619$	−26.8552	−1.07940	−0.539701	−	0.841857i	$-0.681463\pi$
$619$	−26.8552	−1.07940	−0.539701	+	0.841857i	$0.681463\pi$
$620$	−1.50666	−0.0605088
$621$	−0.554770	−0.0222622
$622$	20.2690	0.812711
$623$	−22.5121	−0.901928
$624$	−0.509075	−0.0203793
$625$	−3.89729	−0.155892
$626$	19.7901	0.790973
$627$	4.12942	0.164913
$628$	−19.0170	−0.758861
$629$	11.0640	0.441151
$630$	9.29513	0.370327
$631$	34.7546	1.38356	0.691780	−	0.722108i	$-0.256827\pi$
$631$	34.7546	1.38356	0.691780	+	0.722108i	$0.256827\pi$
$632$	−6.72788	−0.267621
$633$	−4.54865	−0.180793
$634$	9.30012	0.369355
$635$	19.4971	0.773719
$636$	2.21793	0.0879465
$637$	7.06813	0.280050
$638$	15.4427	0.611380
$639$	19.1385	0.757108
$640$	1.50666	0.0595559
$641$	3.49697	0.138122	0.0690610	−	0.997612i	$-0.478000\pi$
$641$	3.49697	0.138122	0.0690610	+	0.997612i	$0.478000\pi$
$642$	−2.49608	−0.0985122
$643$	31.2124	1.23090	0.615449	−	0.788177i	$-0.288975\pi$
$643$	31.2124	1.23090	0.615449	+	0.788177i	$0.288975\pi$
$644$	−1.00907	−0.0397631
$645$	−0.932254	−0.0367075
$646$	−5.61661	−0.220982
$647$	4.68987	0.184378	0.0921888	−	0.995742i	$-0.470614\pi$
$647$	4.68987	0.184378	0.0921888	+	0.995742i	$0.470614\pi$
$648$	−8.66974	−0.340579
$649$	−48.0719	−1.88699
$650$	−7.24005	−0.283978
$651$	−0.399657	−0.0156638
$652$	−7.57423	−0.296630
$653$	−6.50882	−0.254710	−0.127355	−	0.991857i	$-0.540649\pi$
$653$	−6.50882	−0.254710	−0.127355	+	0.991857i	$0.540649\pi$
$654$	−1.31323	−0.0513513
$655$	0.553459	0.0216254
$656$	−7.48629	−0.292291
$657$	−8.82934	−0.344465
$658$	0.0431804	0.00168335
$659$	−30.0804	−1.17177	−0.585883	−	0.810396i	$-0.699252\pi$
$659$	−30.0804	−1.17177	−0.585883	+	0.810396i	$0.699252\pi$
$660$	−1.52655	−0.0594209
$661$	−7.45529	−0.289977	−0.144989	−	0.989433i	$-0.546315\pi$
$661$	−7.45529	−0.289977	−0.144989	+	0.989433i	$0.546315\pi$
$662$	−14.5828	−0.566776
$663$	−0.701559	−0.0272463
$664$	9.10612	0.353386
$665$	12.7848	0.495773
$666$	23.7895	0.921823
$667$	−1.41795	−0.0549034
$668$	−2.84496	−0.110075
$669$	−2.25203	−0.0870684
$670$	−12.5328	−0.484183
$671$	21.2865	0.821757
$672$	0.399657	0.0154171
$673$	−2.78935	−0.107522	−0.0537608	−	0.998554i	$-0.517121\pi$
$673$	−2.78935	−0.107522	−0.0537608	+	0.998554i	$0.517121\pi$
$674$	−1.33381	−0.0513764
$675$	3.12490	0.120277
$676$	−5.96663	−0.229486
$677$	−46.5088	−1.78748	−0.893739	−	0.448587i	$-0.851928\pi$
$677$	−46.5088	−1.78748	−0.893739	+	0.448587i	$0.851928\pi$
$678$	−2.31538	−0.0889215
$679$	−2.08203	−0.0799009
$680$	2.07633	0.0796237
$681$	−0.443329	−0.0169884
$682$	−5.27833	−0.202118
$683$	46.1538	1.76603	0.883013	−	0.469349i	$-0.155511\pi$
$683$	46.1538	1.76603	0.883013	+	0.469349i	$0.155511\pi$
$684$	−12.0766	−0.461762
$685$	8.74993	0.334318
$686$	−20.1231	−0.768305
$687$	−3.30343	−0.126034
$688$	3.22344	0.122892
$689$	−30.6428	−1.16740
$690$	0.140169	0.00533614
$691$	−35.3742	−1.34570	−0.672849	−	0.739780i	$-0.734930\pi$
$691$	−35.3742	−1.34570	−0.672849	+	0.739780i	$0.734930\pi$
$692$	−11.2322	−0.426983
$693$	32.5639	1.23700
$694$	28.8415	1.09481
$695$	22.7269	0.862081
$696$	0.561599	0.0212873
$697$	−10.3169	−0.390780
$698$	9.86681	0.373464
$699$	2.36709	0.0895315
$700$	5.68390	0.214831
$701$	41.6665	1.57372	0.786862	−	0.617130i	$-0.211705\pi$
$701$	41.6665	1.57372	0.786862	+	0.617130i	$0.211705\pi$
$702$	−3.03569	−0.114575
$703$	32.7207	1.23409
$704$	5.27833	0.198934
$705$	−0.00599812	−0.000225902 0
$706$	−24.1257	−0.907984
$707$	−5.21624	−0.196177
$708$	−1.74822	−0.0657020
$709$	−9.42342	−0.353904	−0.176952	−	0.984219i	$-0.556624\pi$
$709$	−9.42342	−0.353904	−0.176952	+	0.984219i	$0.556624\pi$
$710$	−9.73126	−0.365208
$711$	−19.9358	−0.747649
$712$	−10.8126	−0.405218
$713$	0.484659	0.0181506
$714$	0.550768	0.0206120
$715$	21.0908	0.788750
$716$	−23.6111	−0.882388
$717$	1.10633	0.0413165
$718$	−15.1297	−0.564636
$719$	−17.5973	−0.656270	−0.328135	−	0.944631i	$-0.606420\pi$
$719$	−17.5973	−0.656270	−0.328135	+	0.944631i	$0.606420\pi$
$720$	4.46446	0.166381
$721$	−28.1319	−1.04769
$722$	2.38944	0.0889256
$723$	−1.79347	−0.0666998
$724$	18.6592	0.693463
$725$	7.98703	0.296631
$726$	−3.23651	−0.120118
$727$	−50.4636	−1.87159	−0.935795	−	0.352543i	$-0.885317\pi$
$727$	−50.4636	−1.87159	−0.935795	+	0.352543i	$0.885317\pi$
$728$	−5.52164	−0.204646
$729$	−25.0306	−0.927059
$730$	4.48941	0.166160
$731$	4.44223	0.164302
$732$	0.774121	0.0286123
$733$	47.0758	1.73878	0.869392	−	0.494123i	$-0.164511\pi$
$733$	47.0758	1.73878	0.869392	+	0.494123i	$0.164511\pi$
$734$	15.6686	0.578337
$735$	0.770793	0.0284311
$736$	−0.484659	−0.0178648
$737$	−43.9064	−1.61731
$738$	−22.1830	−0.816568
$739$	−13.8478	−0.509398	−0.254699	−	0.967020i	$-0.581976\pi$
$739$	−13.8478	−0.509398	−0.254699	+	0.967020i	$0.581976\pi$
$740$	−12.0961	−0.444661
$741$	−2.07479	−0.0762193
$742$	24.0565	0.883144
$743$	1.45207	0.0532714	0.0266357	−	0.999645i	$-0.491521\pi$
$743$	1.45207	0.0532714	0.0266357	+	0.999645i	$0.491521\pi$
$744$	−0.191955	−0.00703743
$745$	21.5196	0.788418
$746$	13.3839	0.490019
$747$	26.9828	0.987250
$748$	7.27408	0.265967
$749$	−27.0735	−0.989243
$750$	−2.23560	−0.0816325
$751$	−38.8147	−1.41637	−0.708184	−	0.706028i	$-0.750485\pi$
$751$	−38.8147	−1.41637	−0.708184	+	0.706028i	$0.750485\pi$
$752$	0.0207396	0.000756295 0
$753$	−1.89470	−0.0690465
$754$	−7.75903	−0.282567
$755$	7.40892	0.269638
$756$	2.38321	0.0866767
$757$	14.8675	0.540369	0.270185	−	0.962809i	$-0.412915\pi$
$757$	14.8675	0.540369	0.270185	+	0.962809i	$0.412915\pi$
$758$	29.6675	1.07757
$759$	0.491058	0.0178243
$760$	6.14054	0.222741
$761$	23.2676	0.843449	0.421724	−	0.906724i	$-0.361425\pi$
$761$	23.2676	0.843449	0.421724	+	0.906724i	$0.361425\pi$
$762$	2.48402	0.0899867
$763$	−14.2438	−0.515661
$764$	−6.70479	−0.242571
$765$	6.15249	0.222444
$766$	5.74217	0.207473
$767$	24.1533	0.872126
$768$	0.191955	0.00692660
$769$	−8.36074	−0.301496	−0.150748	−	0.988572i	$-0.548168\pi$
$769$	−8.36074	−0.301496	−0.150748	+	0.988572i	$0.548168\pi$
$770$	−16.5576	−0.596695
$771$	−2.08749	−0.0751790
$772$	−17.7373	−0.638381
$773$	8.72956	0.313980	0.156990	−	0.987600i	$-0.449821\pi$
$773$	8.72956	0.313980	0.156990	+	0.987600i	$0.449821\pi$
$774$	9.55154	0.343323
$775$	−2.72998	−0.0980638
$776$	−1.00000	−0.0358979
$777$	−3.20862	−0.115108
$778$	8.24198	0.295489
$779$	−30.5112	−1.09318
$780$	0.767003	0.0274631
$781$	−34.0919	−1.21990
$782$	−0.667911	−0.0238844
$783$	3.34890	0.119680
$784$	−2.66516	−0.0951842
$785$	28.6521	1.02264
$786$	0.0705133	0.00251513
$787$	−50.4183	−1.79722	−0.898609	−	0.438751i	$-0.855421\pi$
$787$	−50.4183	−1.79722	−0.898609	+	0.438751i	$0.855421\pi$
$788$	−0.955852	−0.0340508
$789$	3.45615	0.123042
$790$	10.1366	0.360645
$791$	−25.1135	−0.892935
$792$	15.6405	0.555761
$793$	−10.6952	−0.379799
$794$	−5.57808	−0.197959
$795$	−3.34166	−0.118516
$796$	−5.89079	−0.208793
$797$	31.1099	1.10197	0.550984	−	0.834515i	$-0.314252\pi$
$797$	31.1099	1.10197	0.550984	+	0.834515i	$0.314252\pi$
$798$	1.62884	0.0576604
$799$	0.0285813	0.00101113
$800$	2.72998	0.0965194
$801$	−32.0393	−1.13205
$802$	38.7177	1.36717
$803$	15.7279	0.555025
$804$	−1.59673	−0.0563124
$805$	1.52033	0.0535846
$806$	2.65205	0.0934145
$807$	−3.77654	−0.132940
$808$	−2.50536	−0.0881384
$809$	44.3094	1.55784	0.778918	−	0.627126i	$-0.215769\pi$
$809$	44.3094	1.55784	0.778918	+	0.627126i	$0.215769\pi$
$810$	13.0623	0.458963
$811$	−36.2738	−1.27375	−0.636873	−	0.770969i	$-0.719772\pi$
$811$	−36.2738	−1.27375	−0.636873	+	0.770969i	$0.719772\pi$
$812$	6.09133	0.213764
$813$	−0.648631	−0.0227485
$814$	−42.3767	−1.48530
$815$	11.4118	0.399737
$816$	0.264535	0.00926056
$817$	13.1375	0.459622
$818$	−4.51200	−0.157758
$819$	−16.3615	−0.571716
$820$	11.2793	0.393890
$821$	34.8808	1.21735	0.608674	−	0.793421i	$-0.291702\pi$
$821$	34.8808	1.21735	0.608674	+	0.793421i	$0.291702\pi$
$822$	1.11478	0.0388825
$823$	33.5991	1.17119	0.585595	−	0.810604i	$-0.300861\pi$
$823$	33.5991	1.17119	0.585595	+	0.810604i	$0.300861\pi$
$824$	−13.5118	−0.470704
$825$	−2.76603	−0.0963007
$826$	−18.9619	−0.659769
$827$	−32.7448	−1.13865	−0.569324	−	0.822113i	$-0.692795\pi$
$827$	−32.7448	−1.13865	−0.569324	+	0.822113i	$0.692795\pi$
$828$	−1.43612	−0.0499086
$829$	−15.7633	−0.547483	−0.273741	−	0.961803i	$-0.588261\pi$
$829$	−15.7633	−0.547483	−0.273741	+	0.961803i	$0.588261\pi$
$830$	−13.7198	−0.476221
$831$	2.61679	0.0907755
$832$	−2.65205	−0.0919433
$833$	−3.67286	−0.127257
$834$	2.89552	0.100264
$835$	4.28639	0.148337
$836$	21.5124	0.744021
$837$	−1.14466	−0.0395652
$838$	−36.9093	−1.27501
$839$	19.7556	0.682040	0.341020	−	0.940056i	$-0.389228\pi$
$839$	19.7556	0.682040	0.341020	+	0.940056i	$0.389228\pi$
$840$	−0.602146	−0.0207760
$841$	−20.4404	−0.704843
$842$	35.5371	1.22469
$843$	2.20558	0.0759642
$844$	−23.6964	−0.815664
$845$	8.98967	0.309254
$846$	0.0614546	0.00211285
$847$	−35.1045	−1.20621
$848$	11.5544	0.396779
$849$	2.23304	0.0766376
$850$	3.76220	0.129042
$851$	3.89105	0.133384
$852$	−1.23981	−0.0424752
$853$	−13.4108	−0.459176	−0.229588	−	0.973288i	$-0.573738\pi$
$853$	−13.4108	−0.459176	−0.229588	+	0.973288i	$0.573738\pi$
$854$	8.39643	0.287320
$855$	18.1954	0.622269
$856$	−13.0034	−0.444447
$857$	18.6901	0.638441	0.319221	−	0.947680i	$-0.396579\pi$
$857$	18.6901	0.638441	0.319221	+	0.947680i	$0.396579\pi$
$858$	2.68707	0.0917349
$859$	55.3213	1.88754	0.943769	−	0.330605i	$-0.107253\pi$
$859$	55.3213	1.88754	0.943769	+	0.330605i	$0.107253\pi$
$860$	−4.85662	−0.165609
$861$	2.99195	0.101965
$862$	−39.8051	−1.35577
$863$	−25.1981	−0.857753	−0.428876	−	0.903363i	$-0.641090\pi$
$863$	−25.1981	−0.857753	−0.428876	+	0.903363i	$0.641090\pi$
$864$	1.14466	0.0389421
$865$	16.9230	0.575401
$866$	−8.05411	−0.273690
$867$	−2.89869	−0.0984445
$868$	−2.08203	−0.0706687
$869$	35.5120	1.20466
$870$	−0.846137	−0.0286867
$871$	22.0604	0.747489
$872$	−6.84132	−0.231676
$873$	−2.96315	−0.100288
$874$	−1.97528	−0.0668149
$875$	−24.2482	−0.819739
$876$	0.571972	0.0193251
$877$	1.48863	0.0502675	0.0251338	−	0.999684i	$-0.491999\pi$
$877$	1.48863	0.0502675	0.0251338	+	0.999684i	$0.491999\pi$
$878$	27.4669	0.926965
$879$	−1.47554	−0.0497689
$880$	−7.95263	−0.268083
$881$	−38.3498	−1.29204	−0.646019	−	0.763322i	$-0.723567\pi$
$881$	−38.3498	−1.29204	−0.646019	+	0.763322i	$0.723567\pi$
$882$	−7.89727	−0.265915
$883$	−47.8443	−1.61009	−0.805044	−	0.593215i	$-0.797858\pi$
$883$	−47.8443	−1.61009	−0.805044	+	0.593215i	$0.797858\pi$
$884$	−3.65480	−0.122924
$885$	2.63397	0.0885398
$886$	−26.8960	−0.903588
$887$	44.3990	1.49077	0.745386	−	0.666633i	$-0.232265\pi$
$887$	44.3990	1.49077	0.745386	+	0.666633i	$0.232265\pi$
$888$	−1.54110	−0.0517159
$889$	26.9428	0.903631
$890$	16.2909	0.546071
$891$	45.7617	1.53307
$892$	−11.7320	−0.392817
$893$	0.0845264	0.00282857
$894$	2.74170	0.0916963
$895$	35.5738	1.18910
$896$	2.08203	0.0695557
$897$	−0.246728	−0.00823801
$898$	−4.24365	−0.141612
$899$	−2.92567	−0.0975766
$900$	8.08935	0.269645
$901$	15.9231	0.530477
$902$	39.5151	1.31571
$903$	−1.28827	−0.0428709
$904$	−12.0621	−0.401178
$905$	−28.1130	−0.934508
$906$	0.943932	0.0313600
$907$	−32.0860	−1.06540	−0.532700	−	0.846304i	$-0.678822\pi$
$907$	−32.0860	−1.06540	−0.532700	+	0.846304i	$0.678822\pi$
$908$	−2.30954	−0.0766449
$909$	−7.42377	−0.246231
$910$	8.31923	0.275780
$911$	43.0093	1.42496	0.712480	−	0.701692i	$-0.247572\pi$
$911$	43.0093	1.42496	0.712480	+	0.701692i	$0.247572\pi$
$912$	0.782335	0.0259057
$913$	−48.0651	−1.59072
$914$	−21.9779	−0.726963
$915$	−1.16633	−0.0385578
$916$	−17.2094	−0.568614
$917$	0.764817	0.0252565
$918$	1.57746	0.0520639
$919$	−17.0239	−0.561567	−0.280784	−	0.959771i	$-0.590594\pi$
$919$	−17.0239	−0.561567	−0.280784	+	0.959771i	$0.590594\pi$
$920$	0.730216	0.0240745
$921$	1.86602	0.0614873
$922$	41.3985	1.36339
$923$	17.1292	0.563813
$924$	−2.10952	−0.0693981
$925$	−21.9175	−0.720642
$926$	13.8742	0.455936
$927$	−40.0374	−1.31500
$928$	2.92567	0.0960399
$929$	−27.6647	−0.907650	−0.453825	−	0.891091i	$-0.649941\pi$
$929$	−27.6647	−0.907650	−0.453825	+	0.891091i	$0.649941\pi$
$930$	0.289211	0.00948361
$931$	−10.8621	−0.355992
$932$	12.3315	0.403930
$933$	−3.89074	−0.127377
$934$	3.61877	0.118410
$935$	−10.9596	−0.358416
$936$	−7.85843	−0.256861
$937$	−44.9445	−1.46827	−0.734137	−	0.679002i	$-0.762413\pi$
$937$	−44.9445	−1.46827	−0.734137	+	0.679002i	$0.762413\pi$
$938$	−17.3188	−0.565480
$939$	−3.79883	−0.123970
$940$	−0.0312475	−0.00101918
$941$	−29.2984	−0.955101	−0.477550	−	0.878604i	$-0.658475\pi$
$941$	−29.2984	−0.955101	−0.477550	+	0.878604i	$0.658475\pi$
$942$	3.65042	0.118937
$943$	−3.62830	−0.118154
$944$	−9.10741	−0.296421
$945$	−3.59069	−0.116805
$946$	−17.0144	−0.553184
$947$	−12.8450	−0.417405	−0.208703	−	0.977979i	$-0.566924\pi$
$947$	−12.8450	−0.417405	−0.208703	+	0.977979i	$0.566924\pi$
$948$	1.29145	0.0419445
$949$	−7.90235	−0.256521
$950$	11.1263	0.360986
$951$	−1.78521	−0.0578894
$952$	2.86925	0.0929930
$953$	20.4357	0.661978	0.330989	−	0.943635i	$-0.392618\pi$
$953$	20.4357	0.661978	0.330989	+	0.943635i	$0.392618\pi$
$954$	34.2374	1.10848
$955$	10.1018	0.326888
$956$	5.76345	0.186403
$957$	−2.96430	−0.0958222
$958$	−23.5000	−0.759252
$959$	12.0914	0.390452
$960$	−0.289211	−0.00933425
$961$	1.00000	0.0322581
$962$	21.2918	0.686475
$963$	−38.5311	−1.24165
$964$	−9.34315	−0.300922
$965$	26.7241	0.860279
$966$	0.193697	0.00623211
$967$	−24.9041	−0.800863	−0.400431	−	0.916327i	$-0.631140\pi$
$967$	−24.9041	−0.800863	−0.400431	+	0.916327i	$0.631140\pi$
$968$	−16.8607	−0.541924
$969$	1.07814	0.0346348
$970$	1.50666	0.0483759
$971$	33.4219	1.07256	0.536280	−	0.844040i	$-0.319829\pi$
$971$	33.4219	1.07256	0.536280	+	0.844040i	$0.319829\pi$
$972$	5.09818	0.163524
$973$	31.4060	1.00683
$974$	−36.9421	−1.18370
$975$	1.38977	0.0445082
$976$	4.03281	0.129087
$977$	−7.55845	−0.241816	−0.120908	−	0.992664i	$-0.538581\pi$
$977$	−7.55845	−0.241816	−0.120908	+	0.992664i	$0.538581\pi$
$978$	1.45391	0.0464911
$979$	57.0723	1.82404
$980$	4.01548	0.128270
$981$	−20.2719	−0.647231
$982$	−20.8694	−0.665970
$983$	3.31523	0.105739	0.0528697	−	0.998601i	$-0.483163\pi$
$983$	3.31523	0.105739	0.0528697	+	0.998601i	$0.483163\pi$
$984$	1.43703	0.0458110
$985$	1.44014	0.0458867
$986$	4.03188	0.128401
$987$	−0.00828872	−0.000263833 0
$988$	−10.8087	−0.343871
$989$	1.56227	0.0496773
$990$	−23.5649	−0.748941
$991$	−34.2506	−1.08801	−0.544003	−	0.839083i	$-0.683092\pi$
$991$	−34.2506	−1.08801	−0.544003	+	0.839083i	$0.683092\pi$
$992$	−1.00000	−0.0317500
$993$	2.79925	0.0888314
$994$	−13.4475	−0.426528
$995$	8.87540	0.281369
$996$	−1.74797	−0.0553865
$997$	−39.6775	−1.25660	−0.628300	−	0.777971i	$-0.716249\pi$
$997$	−39.6775	−1.25660	−0.628300	+	0.777971i	$0.716249\pi$
$998$	25.9142	0.820300
$999$	−9.18982	−0.290753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.12	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.12	✓	22	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.191955 q^{3} +1.00000 q^{4} -1.50666 q^{5} -0.191955 q^{6} -2.08203 q^{7} -1.00000 q^{8} -2.96315 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.191955 q^{3} +1.00000 q^{4} -1.50666 q^{5} -0.191955 q^{6} -2.08203 q^{7} -1.00000 q^{8} -2.96315 q^{9} +1.50666 q^{10} +5.27833 q^{11} +0.191955 q^{12} -2.65205 q^{13} +2.08203 q^{14} -0.289211 q^{15} +1.00000 q^{16} +1.37810 q^{17} +2.96315 q^{18} +4.07561 q^{19} -1.50666 q^{20} -0.399657 q^{21} -5.27833 q^{22} +0.484659 q^{23} -0.191955 q^{24} -2.72998 q^{25} +2.65205 q^{26} -1.14466 q^{27} -2.08203 q^{28} -2.92567 q^{29} +0.289211 q^{30} +1.00000 q^{31} -1.00000 q^{32} +1.01320 q^{33} -1.37810 q^{34} +3.13690 q^{35} -2.96315 q^{36} +8.02843 q^{37} -4.07561 q^{38} -0.509075 q^{39} +1.50666 q^{40} -7.48629 q^{41} +0.399657 q^{42} +3.22344 q^{43} +5.27833 q^{44} +4.46446 q^{45} -0.484659 q^{46} +0.0207396 q^{47} +0.191955 q^{48} -2.66516 q^{49} +2.72998 q^{50} +0.264535 q^{51} -2.65205 q^{52} +11.5544 q^{53} +1.14466 q^{54} -7.95263 q^{55} +2.08203 q^{56} +0.782335 q^{57} +2.92567 q^{58} -9.10741 q^{59} -0.289211 q^{60} +4.03281 q^{61} -1.00000 q^{62} +6.16937 q^{63} +1.00000 q^{64} +3.99573 q^{65} -1.01320 q^{66} -8.31825 q^{67} +1.37810 q^{68} +0.0930330 q^{69} -3.13690 q^{70} -6.45884 q^{71} +2.96315 q^{72} +2.97971 q^{73} -8.02843 q^{74} -0.524035 q^{75} +4.07561 q^{76} -10.9896 q^{77} +0.509075 q^{78} +6.72788 q^{79} -1.50666 q^{80} +8.66974 q^{81} +7.48629 q^{82} -9.10612 q^{83} -0.399657 q^{84} -2.07633 q^{85} -3.22344 q^{86} -0.561599 q^{87} -5.27833 q^{88} +10.8126 q^{89} -4.46446 q^{90} +5.52164 q^{91} +0.484659 q^{92} +0.191955 q^{93} -0.0207396 q^{94} -6.14054 q^{95} -0.191955 q^{96} +1.00000 q^{97} +2.66516 q^{98} -15.6405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

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