LMFDB - Embedded newform 8619.2.a.bw.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8619,2,Mod(1,8619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8619, 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("8619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8619 = 3 \cdot 13^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8619.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:	$68.8230615021$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.271243 q^{2} -1.00000 q^{3} -1.92643 q^{4} +0.00688268 q^{5} +0.271243 q^{6} -0.318502 q^{7} +1.06502 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.271243 q^{2} -1.00000 q^{3} -1.92643 q^{4} +0.00688268 q^{5} +0.271243 q^{6} -0.318502 q^{7} +1.06502 q^{8} +1.00000 q^{9} -0.00186688 q^{10} -1.42139 q^{11} +1.92643 q^{12} +0.0863913 q^{14} -0.00688268 q^{15} +3.56398 q^{16} -1.00000 q^{17} -0.271243 q^{18} +5.45062 q^{19} -0.0132590 q^{20} +0.318502 q^{21} +0.385542 q^{22} +5.80459 q^{23} -1.06502 q^{24} -4.99995 q^{25} -1.00000 q^{27} +0.613570 q^{28} -7.93198 q^{29} +0.00186688 q^{30} -7.44201 q^{31} -3.09674 q^{32} +1.42139 q^{33} +0.271243 q^{34} -0.00219214 q^{35} -1.92643 q^{36} +5.62074 q^{37} -1.47844 q^{38} +0.00733016 q^{40} -4.23517 q^{41} -0.0863913 q^{42} +0.441322 q^{43} +2.73821 q^{44} +0.00688268 q^{45} -1.57446 q^{46} -6.87013 q^{47} -3.56398 q^{48} -6.89856 q^{49} +1.35620 q^{50} +1.00000 q^{51} +12.0316 q^{53} +0.271243 q^{54} -0.00978298 q^{55} -0.339209 q^{56} -5.45062 q^{57} +2.15150 q^{58} +9.16514 q^{59} +0.0132590 q^{60} +12.7980 q^{61} +2.01859 q^{62} -0.318502 q^{63} -6.28798 q^{64} -0.385542 q^{66} -11.9404 q^{67} +1.92643 q^{68} -5.80459 q^{69} +0.000594604 q^{70} +13.0118 q^{71} +1.06502 q^{72} +3.70014 q^{73} -1.52459 q^{74} +4.99995 q^{75} -10.5002 q^{76} +0.452715 q^{77} -8.03937 q^{79} +0.0245297 q^{80} +1.00000 q^{81} +1.14876 q^{82} +1.63139 q^{83} -0.613570 q^{84} -0.00688268 q^{85} -0.119706 q^{86} +7.93198 q^{87} -1.51380 q^{88} -7.33095 q^{89} -0.00186688 q^{90} -11.1821 q^{92} +7.44201 q^{93} +1.86347 q^{94} +0.0375148 q^{95} +3.09674 q^{96} +6.25153 q^{97} +1.87119 q^{98} -1.42139 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 7 q^{2} - 24 q^{3} + 17 q^{4} - 13 q^{5} - 7 q^{6} - 12 q^{7} + 21 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 7 * q^2 - 24 * q^3 + 17 * q^4 - 13 * q^5 - 7 * q^6 - 12 * q^7 + 21 * q^8 + 24 * q^9	\( 24 q + 7 q^{2} - 24 q^{3} + 17 q^{4} - 13 q^{5} - 7 q^{6} - 12 q^{7} + 21 q^{8} + 24 q^{9} - 4 q^{10} - q^{11} - 17 q^{12} - 18 q^{14} + 13 q^{15} + 35 q^{16} - 24 q^{17} + 7 q^{18} - 16 q^{19} - 18 q^{20} + 12 q^{21} + 8 q^{22} + 3 q^{23} - 21 q^{24} + 23 q^{25} - 24 q^{27} - 30 q^{28} + 5 q^{29} + 4 q^{30} - 46 q^{31} + 44 q^{32} + q^{33} - 7 q^{34} + 11 q^{35} + 17 q^{36} - 38 q^{37} - q^{38} - 59 q^{40} - 31 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 13 q^{45} - 36 q^{46} + 49 q^{47} - 35 q^{48} + 30 q^{49} + 15 q^{50} + 24 q^{51} - 11 q^{53} - 7 q^{54} - 10 q^{55} - 38 q^{56} + 16 q^{57} - 53 q^{58} - 23 q^{59} + 18 q^{60} - 2 q^{61} - 26 q^{62} - 12 q^{63} + 57 q^{64} - 8 q^{66} - 17 q^{68} - 3 q^{69} + 10 q^{70} + 29 q^{71} + 21 q^{72} - 48 q^{73} - 66 q^{74} - 23 q^{75} - 38 q^{76} + 51 q^{77} - 26 q^{79} - 52 q^{80} + 24 q^{81} - 45 q^{82} + 8 q^{83} + 30 q^{84} + 13 q^{85} - 38 q^{86} - 5 q^{87} - 34 q^{88} - 42 q^{89} - 4 q^{90} - 10 q^{92} + 46 q^{93} + 107 q^{94} - 44 q^{96} - 60 q^{97} + 19 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 7 * q^2 - 24 * q^3 + 17 * q^4 - 13 * q^5 - 7 * q^6 - 12 * q^7 + 21 * q^8 + 24 * q^9 - 4 * q^10 - q^11 - 17 * q^12 - 18 * q^14 + 13 * q^15 + 35 * q^16 - 24 * q^17 + 7 * q^18 - 16 * q^19 - 18 * q^20 + 12 * q^21 + 8 * q^22 + 3 * q^23 - 21 * q^24 + 23 * q^25 - 24 * q^27 - 30 * q^28 + 5 * q^29 + 4 * q^30 - 46 * q^31 + 44 * q^32 + q^33 - 7 * q^34 + 11 * q^35 + 17 * q^36 - 38 * q^37 - q^38 - 59 * q^40 - 31 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 13 * q^45 - 36 * q^46 + 49 * q^47 - 35 * q^48 + 30 * q^49 + 15 * q^50 + 24 * q^51 - 11 * q^53 - 7 * q^54 - 10 * q^55 - 38 * q^56 + 16 * q^57 - 53 * q^58 - 23 * q^59 + 18 * q^60 - 2 * q^61 - 26 * q^62 - 12 * q^63 + 57 * q^64 - 8 * q^66 - 17 * q^68 - 3 * q^69 + 10 * q^70 + 29 * q^71 + 21 * q^72 - 48 * q^73 - 66 * q^74 - 23 * q^75 - 38 * q^76 + 51 * q^77 - 26 * q^79 - 52 * q^80 + 24 * q^81 - 45 * q^82 + 8 * q^83 + 30 * q^84 + 13 * q^85 - 38 * q^86 - 5 * q^87 - 34 * q^88 - 42 * q^89 - 4 * q^90 - 10 * q^92 + 46 * q^93 + 107 * q^94 - 44 * q^96 - 60 * q^97 + 19 * 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 $

$2$	−0.271243	−0.191798	−0.0958989	−	0.995391i	$-0.530573\pi$
$2$	−0.271243	−0.191798	−0.0958989	+	0.995391i	$0.530573\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.92643	−0.963214
$5$	0.00688268	0.00307803	0.00153901	−	0.999999i	$-0.499510\pi$
$5$	0.00688268	0.00307803	0.00153901	+	0.999999i	$0.499510\pi$
$6$	0.271243	0.110734
$7$	−0.318502	−0.120382	−0.0601911	−	0.998187i	$-0.519171\pi$
$7$	−0.318502	−0.120382	−0.0601911	+	0.998187i	$0.519171\pi$
$8$	1.06502	0.376540
$9$	1.00000	0.333333
$10$	−0.00186688	−0.000590359 0
$11$	−1.42139	−0.428566	−0.214283	−	0.976772i	$-0.568741\pi$
$11$	−1.42139	−0.428566	−0.214283	+	0.976772i	$0.568741\pi$
$12$	1.92643	0.556112
$13$	0	0
$13$	0	0
$14$	0.0863913	0.0230891
$15$	−0.00688268	−0.00177710
$16$	3.56398	0.890994
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.271243	−0.0639326
$19$	5.45062	1.25046	0.625229	−	0.780442i	$-0.285006\pi$
$19$	5.45062	1.25046	0.625229	+	0.780442i	$0.285006\pi$
$20$	−0.0132590	−0.00296480
$21$	0.318502	0.0695028
$22$	0.385542	0.0821979
$23$	5.80459	1.21034	0.605171	−	0.796096i	$-0.293105\pi$
$23$	5.80459	1.21034	0.605171	+	0.796096i	$0.293105\pi$
$24$	−1.06502	−0.217395
$25$	−4.99995	−0.999991
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0.613570	0.115954
$29$	−7.93198	−1.47293	−0.736466	−	0.676474i	$-0.763507\pi$
$29$	−7.93198	−1.47293	−0.736466	+	0.676474i	$0.763507\pi$
$30$	0.00186688	0.000340844 0
$31$	−7.44201	−1.33662	−0.668312	−	0.743881i	$-0.732983\pi$
$31$	−7.44201	−1.33662	−0.668312	+	0.743881i	$0.732983\pi$
$32$	−3.09674	−0.547431
$33$	1.42139	0.247432
$34$	0.271243	0.0465178
$35$	−0.00219214	−0.000370540 0
$36$	−1.92643	−0.321071
$37$	5.62074	0.924044	0.462022	−	0.886868i	$-0.347124\pi$
$37$	5.62074	0.924044	0.462022	+	0.886868i	$0.347124\pi$
$38$	−1.47844	−0.239835
$39$	0	0
$40$	0.00733016	0.00115900
$41$	−4.23517	−0.661422	−0.330711	−	0.943732i	$-0.607289\pi$
$41$	−4.23517	−0.661422	−0.330711	+	0.943732i	$0.607289\pi$
$42$	−0.0863913	−0.0133305
$43$	0.441322	0.0673010	0.0336505	−	0.999434i	$-0.489287\pi$
$43$	0.441322	0.0673010	0.0336505	+	0.999434i	$0.489287\pi$
$44$	2.73821	0.412800
$45$	0.00688268	0.00102601
$46$	−1.57446	−0.232141
$47$	−6.87013	−1.00211	−0.501055	−	0.865415i	$-0.667055\pi$
$47$	−6.87013	−1.00211	−0.501055	+	0.865415i	$0.667055\pi$
$48$	−3.56398	−0.514416
$49$	−6.89856	−0.985508
$50$	1.35620	0.191796
$51$	1.00000	0.140028
$52$	0	0
$53$	12.0316	1.65267	0.826335	−	0.563179i	$-0.190422\pi$
$53$	12.0316	1.65267	0.826335	+	0.563179i	$0.190422\pi$
$54$	0.271243	0.0369115
$55$	−0.00978298	−0.00131914
$56$	−0.339209	−0.0453287
$57$	−5.45062	−0.721952
$58$	2.15150	0.282505
$59$	9.16514	1.19320	0.596600	−	0.802539i	$-0.296518\pi$
$59$	9.16514	1.19320	0.596600	+	0.802539i	$0.296518\pi$
$60$	0.0132590	0.00171173
$61$	12.7980	1.63862	0.819308	−	0.573354i	$-0.194358\pi$
$61$	12.7980	1.63862	0.819308	+	0.573354i	$0.194358\pi$
$62$	2.01859	0.256362
$63$	−0.318502	−0.0401274
$64$	−6.28798	−0.785998
$65$	0	0
$66$	−0.385542	−0.0474570
$67$	−11.9404	−1.45876	−0.729378	−	0.684111i	$-0.760190\pi$
$67$	−11.9404	−1.45876	−0.729378	+	0.684111i	$0.760190\pi$
$68$	1.92643	0.233614
$69$	−5.80459	−0.698791
$70$	0.000594604 0	7.10687e−5 0
$71$	13.0118	1.54422	0.772111	−	0.635488i	$-0.219201\pi$
$71$	13.0118	1.54422	0.772111	+	0.635488i	$0.219201\pi$
$72$	1.06502	0.125513
$73$	3.70014	0.433069	0.216534	−	0.976275i	$-0.430525\pi$
$73$	3.70014	0.433069	0.216534	+	0.976275i	$0.430525\pi$
$74$	−1.52459	−0.177230
$75$	4.99995	0.577345
$76$	−10.5002	−1.20446
$77$	0.452715	0.0515917
$78$	0	0
$79$	−8.03937	−0.904500	−0.452250	−	0.891891i	$-0.649379\pi$
$79$	−8.03937	−0.904500	−0.452250	+	0.891891i	$0.649379\pi$
$80$	0.0245297	0.00274250
$81$	1.00000	0.111111
$82$	1.14876	0.126859
$83$	1.63139	0.179069	0.0895343	−	0.995984i	$-0.471462\pi$
$83$	1.63139	0.179069	0.0895343	+	0.995984i	$0.471462\pi$
$84$	−0.613570	−0.0669460
$85$	−0.00688268	−0.000746531 0
$86$	−0.119706	−0.0129082
$87$	7.93198	0.850398
$88$	−1.51380	−0.161372
$89$	−7.33095	−0.777080	−0.388540	−	0.921432i	$-0.627020\pi$
$89$	−7.33095	−0.777080	−0.388540	+	0.921432i	$0.627020\pi$
$90$	−0.00186688	−0.000196786 0
$91$	0	0
$92$	−11.1821	−1.16582
$93$	7.44201	0.771701
$94$	1.86347	0.192203
$95$	0.0375148	0.00384894
$96$	3.09674	0.316059
$97$	6.25153	0.634747	0.317374	−	0.948301i	$-0.397199\pi$
$97$	6.25153	0.634747	0.317374	+	0.948301i	$0.397199\pi$
$98$	1.87119	0.189018
$99$	−1.42139	−0.142855
$100$	9.63204	0.963204
$101$	−4.29051	−0.426922	−0.213461	−	0.976952i	$-0.568474\pi$
$101$	−4.29051	−0.426922	−0.213461	+	0.976952i	$0.568474\pi$
$102$	−0.271243	−0.0268571
$103$	−13.4261	−1.32291	−0.661457	−	0.749983i	$-0.730062\pi$
$103$	−13.4261	−1.32291	−0.661457	+	0.749983i	$0.730062\pi$
$104$	0	0
$105$	0.00219214	0.000213931 0
$106$	−3.26349	−0.316978
$107$	16.6563	1.61022	0.805111	−	0.593124i	$-0.202105\pi$
$107$	16.6563	1.61022	0.805111	+	0.593124i	$0.202105\pi$
$108$	1.92643	0.185371
$109$	19.3621	1.85456	0.927278	−	0.374374i	$-0.122142\pi$
$109$	19.3621	1.85456	0.927278	+	0.374374i	$0.122142\pi$
$110$	0.00265356	0.000253007 0
$111$	−5.62074	−0.533497
$112$	−1.13513	−0.107260
$113$	6.97830	0.656463	0.328232	−	0.944597i	$-0.393547\pi$
$113$	6.97830	0.656463	0.328232	+	0.944597i	$0.393547\pi$
$114$	1.47844	0.138469
$115$	0.0399511	0.00372546
$116$	15.2804	1.41875
$117$	0	0
$118$	−2.48598	−0.228853
$119$	0.318502	0.0291970
$120$	−0.00733016	−0.000669149 0
$121$	−8.97965	−0.816331
$122$	−3.47137	−0.314283
$123$	4.23517	0.381872
$124$	14.3365	1.28746
$125$	−0.0688265	−0.00615603
$126$	0.0863913	0.00769635
$127$	10.5113	0.932725	0.466363	−	0.884594i	$-0.345564\pi$
$127$	10.5113	0.932725	0.466363	+	0.884594i	$0.345564\pi$
$128$	7.89904	0.698183
$129$	−0.441322	−0.0388563
$130$	0	0
$131$	−18.4950	−1.61592	−0.807958	−	0.589240i	$-0.799427\pi$
$131$	−18.4950	−1.61592	−0.807958	+	0.589240i	$0.799427\pi$
$132$	−2.73821	−0.238330
$133$	−1.73603	−0.150533
$134$	3.23876	0.279786
$135$	−0.00688268	−0.000592367 0
$136$	−1.06502	−0.0913244
$137$	−9.75101	−0.833085	−0.416543	−	0.909116i	$-0.636758\pi$
$137$	−9.75101	−0.833085	−0.416543	+	0.909116i	$0.636758\pi$
$138$	1.57446	0.134027
$139$	3.08211	0.261421	0.130711	−	0.991421i	$-0.458274\pi$
$139$	3.08211	0.261421	0.130711	+	0.991421i	$0.458274\pi$
$140$	0.00422301	0.000356909 0
$141$	6.87013	0.578569
$142$	−3.52937	−0.296178
$143$	0	0
$144$	3.56398	0.296998
$145$	−0.0545933	−0.00453373
$146$	−1.00364	−0.0830617
$147$	6.89856	0.568983
$148$	−10.8280	−0.890052
$149$	20.6199	1.68925	0.844625	−	0.535359i	$-0.179823\pi$
$149$	20.6199	1.68925	0.844625	+	0.535359i	$0.179823\pi$
$150$	−1.35620	−0.110733
$151$	23.5613	1.91739	0.958694	−	0.284440i	$-0.0918075\pi$
$151$	23.5613	1.91739	0.958694	+	0.284440i	$0.0918075\pi$
$152$	5.80499	0.470847
$153$	−1.00000	−0.0808452
$154$	−0.122796	−0.00989518
$155$	−0.0512210	−0.00411417
$156$	0	0
$157$	8.92126	0.711994	0.355997	−	0.934487i	$-0.384141\pi$
$157$	8.92126	0.711994	0.355997	+	0.934487i	$0.384141\pi$
$158$	2.18062	0.173481
$159$	−12.0316	−0.954169
$160$	−0.0213138	−0.00168501
$161$	−1.84877	−0.145704
$162$	−0.271243	−0.0213109
$163$	−9.17334	−0.718511	−0.359256	−	0.933239i	$-0.616969\pi$
$163$	−9.17334	−0.718511	−0.359256	+	0.933239i	$0.616969\pi$
$164$	8.15875	0.637091
$165$	0.00978298	0.000761604 0
$166$	−0.442504	−0.0343450
$167$	−8.67286	−0.671126	−0.335563	−	0.942018i	$-0.608927\pi$
$167$	−8.67286	−0.671126	−0.335563	+	0.942018i	$0.608927\pi$
$168$	0.339209	0.0261706
$169$	0	0
$170$	0.00186688	0.000143183 0
$171$	5.45062	0.416819
$172$	−0.850175	−0.0648252
$173$	−21.7845	−1.65624	−0.828121	−	0.560550i	$-0.810590\pi$
$173$	−21.7845	−1.65624	−0.828121	+	0.560550i	$0.810590\pi$
$174$	−2.15150	−0.163104
$175$	1.59249	0.120381
$176$	−5.06581	−0.381849
$177$	−9.16514	−0.688894
$178$	1.98847	0.149042
$179$	4.58198	0.342473	0.171236	−	0.985230i	$-0.445224\pi$
$179$	4.58198	0.342473	0.171236	+	0.985230i	$0.445224\pi$
$180$	−0.0132590	−0.000988266 0
$181$	23.9705	1.78172	0.890858	−	0.454281i	$-0.150104\pi$
$181$	23.9705	1.78172	0.890858	+	0.454281i	$0.150104\pi$
$182$	0	0
$183$	−12.7980	−0.946055
$184$	6.18198	0.455742
$185$	0.0386858	0.00284423
$186$	−2.01859	−0.148010
$187$	1.42139	0.103942
$188$	13.2348	0.965247
$189$	0.318502	0.0231676
$190$	−0.0101756	−0.000738218 0
$191$	5.22989	0.378422	0.189211	−	0.981936i	$-0.439407\pi$
$191$	5.22989	0.378422	0.189211	+	0.981936i	$0.439407\pi$
$192$	6.28798	0.453796
$193$	−15.8515	−1.14102	−0.570508	−	0.821292i	$-0.693254\pi$
$193$	−15.8515	−1.14102	−0.570508	+	0.821292i	$0.693254\pi$
$194$	−1.69568	−0.121743
$195$	0	0
$196$	13.2896	0.949255
$197$	−4.04717	−0.288349	−0.144174	−	0.989552i	$-0.546053\pi$
$197$	−4.04717	−0.288349	−0.144174	+	0.989552i	$0.546053\pi$
$198$	0.385542	0.0273993
$199$	−8.43818	−0.598167	−0.299083	−	0.954227i	$-0.596681\pi$
$199$	−8.43818	−0.598167	−0.299083	+	0.954227i	$0.596681\pi$
$200$	−5.32503	−0.376536
$201$	11.9404	0.842213
$202$	1.16377	0.0818826
$203$	2.52635	0.177315
$204$	−1.92643	−0.134877
$205$	−0.0291493	−0.00203588
$206$	3.64174	0.253732
$207$	5.80459	0.403447
$208$	0	0
$209$	−7.74746	−0.535903
$210$	−0.000594604 0	−4.10316e−5 0
$211$	9.48816	0.653192	0.326596	−	0.945164i	$-0.394098\pi$
$211$	9.48816	0.653192	0.326596	+	0.945164i	$0.394098\pi$
$212$	−23.1780	−1.59187
$213$	−13.0118	−0.891557
$214$	−4.51790	−0.308837
$215$	0.00303748	0.000207154 0
$216$	−1.06502	−0.0724652
$217$	2.37029	0.160906
$218$	−5.25184	−0.355700
$219$	−3.70014	−0.250032
$220$	0.0188462	0.00127061
$221$	0	0
$222$	1.52459	0.102324
$223$	−23.1692	−1.55153	−0.775764	−	0.631024i	$-0.782635\pi$
$223$	−23.1692	−1.55153	−0.775764	+	0.631024i	$0.782635\pi$
$224$	0.986315	0.0659010
$225$	−4.99995	−0.333330
$226$	−1.89281	−0.125908
$227$	−20.7519	−1.37735	−0.688677	−	0.725069i	$-0.741808\pi$
$227$	−20.7519	−1.37735	−0.688677	+	0.725069i	$0.741808\pi$
$228$	10.5002	0.695394
$229$	−23.8739	−1.57763	−0.788816	−	0.614629i	$-0.789306\pi$
$229$	−23.8739	−1.57763	−0.788816	+	0.614629i	$0.789306\pi$
$230$	−0.0108365	−0.000714536 0
$231$	−0.452715	−0.0297865
$232$	−8.44769	−0.554618
$233$	−15.2349	−0.998071	−0.499035	−	0.866582i	$-0.666312\pi$
$233$	−15.2349	−0.998071	−0.499035	+	0.866582i	$0.666312\pi$
$234$	0	0
$235$	−0.0472849	−0.00308452
$236$	−17.6560	−1.14931
$237$	8.03937	0.522213
$238$	−0.0863913	−0.00559992
$239$	−22.2874	−1.44165	−0.720826	−	0.693116i	$-0.756237\pi$
$239$	−22.2874	−1.44165	−0.720826	+	0.693116i	$0.756237\pi$
$240$	−0.0245297	−0.00158339
$241$	10.8332	0.697831	0.348915	−	0.937154i	$-0.386550\pi$
$241$	10.8332	0.697831	0.348915	+	0.937154i	$0.386550\pi$
$242$	2.43567	0.156571
$243$	−1.00000	−0.0641500
$244$	−24.6544	−1.57834
$245$	−0.0474805	−0.00303342
$246$	−1.14876	−0.0732423
$247$	0	0
$248$	−7.92586	−0.503293
$249$	−1.63139	−0.103385
$250$	0.0186687	0.00118071
$251$	2.68284	0.169339	0.0846696	−	0.996409i	$-0.473017\pi$
$251$	2.68284	0.169339	0.0846696	+	0.996409i	$0.473017\pi$
$252$	0.613570	0.0386513
$253$	−8.25060	−0.518711
$254$	−2.85111	−0.178895
$255$	0.00688268	0.000431010 0
$256$	10.4334	0.652088
$257$	−2.75207	−0.171669	−0.0858346	−	0.996309i	$-0.527356\pi$
$257$	−2.75207	−0.171669	−0.0858346	+	0.996309i	$0.527356\pi$
$258$	0.119706	0.00745254
$259$	−1.79022	−0.111239
$260$	0	0
$261$	−7.93198	−0.490978
$262$	5.01664	0.309929
$263$	27.9696	1.72468	0.862339	−	0.506332i	$-0.168999\pi$
$263$	27.9696	1.72468	0.862339	+	0.506332i	$0.168999\pi$
$264$	1.51380	0.0931682
$265$	0.0828097	0.00508696
$266$	0.470886	0.0288719
$267$	7.33095	0.448647
$268$	23.0024	1.40509
$269$	5.91910	0.360894	0.180447	−	0.983585i	$-0.442246\pi$
$269$	5.91910	0.360894	0.180447	+	0.983585i	$0.442246\pi$
$270$	0.00186688	0.000113615 0
$271$	−12.5645	−0.763240	−0.381620	−	0.924319i	$-0.624634\pi$
$271$	−12.5645	−0.763240	−0.381620	+	0.924319i	$0.624634\pi$
$272$	−3.56398	−0.216098
$273$	0	0
$274$	2.64489	0.159784
$275$	7.10689	0.428562
$276$	11.1821	0.673085
$277$	5.83069	0.350332	0.175166	−	0.984539i	$-0.443954\pi$
$277$	5.83069	0.350332	0.175166	+	0.984539i	$0.443954\pi$
$278$	−0.836002	−0.0501400
$279$	−7.44201	−0.445542
$280$	−0.00233467	−0.000139523 0
$281$	−4.16768	−0.248623	−0.124311	−	0.992243i	$-0.539672\pi$
$281$	−4.16768	−0.248623	−0.124311	+	0.992243i	$0.539672\pi$
$282$	−1.86347	−0.110968
$283$	−17.8601	−1.06167	−0.530837	−	0.847474i	$-0.678123\pi$
$283$	−17.8601	−1.06167	−0.530837	+	0.847474i	$0.678123\pi$
$284$	−25.0664	−1.48742
$285$	−0.0375148	−0.00222219
$286$	0	0
$287$	1.34891	0.0796236
$288$	−3.09674	−0.182477
$289$	1.00000	0.0588235
$290$	0.0148080	0.000869559 0
$291$	−6.25153	−0.366471
$292$	−7.12806	−0.417138
$293$	10.4494	0.610459	0.305229	−	0.952279i	$-0.401267\pi$
$293$	10.4494	0.610459	0.305229	+	0.952279i	$0.401267\pi$
$294$	−1.87119	−0.109130
$295$	0.0630807	0.00367270
$296$	5.98618	0.347940
$297$	1.42139	0.0824775
$298$	−5.59301	−0.323994
$299$	0	0
$300$	−9.63204	−0.556106
$301$	−0.140562	−0.00810185
$302$	−6.39083	−0.367751
$303$	4.29051	0.246483
$304$	19.4259	1.11415
$305$	0.0880845	0.00504370
$306$	0.271243	0.0155059
$307$	−28.2902	−1.61461	−0.807304	−	0.590135i	$-0.799074\pi$
$307$	−28.2902	−1.61461	−0.807304	+	0.590135i	$0.799074\pi$
$308$	−0.872123	−0.0496938
$309$	13.4261	0.763785
$310$	0.0138933	0.000789088 0
$311$	22.6949	1.28691	0.643456	−	0.765483i	$-0.277500\pi$
$311$	22.6949	1.28691	0.643456	+	0.765483i	$0.277500\pi$
$312$	0	0
$313$	0.794040	0.0448818	0.0224409	−	0.999748i	$-0.492856\pi$
$313$	0.794040	0.0448818	0.0224409	+	0.999748i	$0.492856\pi$
$314$	−2.41983	−0.136559
$315$	−0.00219214	−0.000123513 0
$316$	15.4873	0.871227
$317$	−32.7911	−1.84173	−0.920867	−	0.389877i	$-0.872518\pi$
$317$	−32.7911	−1.84173	−0.920867	+	0.389877i	$0.872518\pi$
$318$	3.26349	0.183007
$319$	11.2745	0.631248
$320$	−0.0432782	−0.00241932
$321$	−16.6563	−0.929663
$322$	0.501467	0.0279456
$323$	−5.45062	−0.303280
$324$	−1.92643	−0.107024
$325$	0	0
$326$	2.48820	0.137809
$327$	−19.3621	−1.07073
$328$	−4.51052	−0.249052
$329$	2.18815	0.120636
$330$	−0.00265356	−0.000146074 0
$331$	−7.77000	−0.427078	−0.213539	−	0.976935i	$-0.568499\pi$
$331$	−7.77000	−0.427078	−0.213539	+	0.976935i	$0.568499\pi$
$332$	−3.14276	−0.172481
$333$	5.62074	0.308015
$334$	2.35245	0.128720
$335$	−0.0821821	−0.00449009
$336$	1.13513	0.0619265
$337$	−24.3752	−1.32780	−0.663902	−	0.747820i	$-0.731101\pi$
$337$	−24.3752	−1.32780	−0.663902	+	0.747820i	$0.731101\pi$
$338$	0	0
$339$	−6.97830	−0.379009
$340$	0.0132590	0.000719069 0
$341$	10.5780	0.572831
$342$	−1.47844	−0.0799450
$343$	4.42671	0.239020
$344$	0.470015	0.0253415
$345$	−0.0399511	−0.00215090
$346$	5.90888	0.317663
$347$	−5.88456	−0.315900	−0.157950	−	0.987447i	$-0.550488\pi$
$347$	−5.88456	−0.315900	−0.157950	+	0.987447i	$0.550488\pi$
$348$	−15.2804	−0.819115
$349$	−11.5578	−0.618673	−0.309337	−	0.950953i	$-0.600107\pi$
$349$	−11.5578	−0.618673	−0.309337	+	0.950953i	$0.600107\pi$
$350$	−0.431953	−0.0230888
$351$	0	0
$352$	4.40167	0.234610
$353$	22.4803	1.19651	0.598253	−	0.801308i	$-0.295862\pi$
$353$	22.4803	1.19651	0.598253	+	0.801308i	$0.295862\pi$
$354$	2.48598	0.132128
$355$	0.0895563	0.00475316
$356$	14.1225	0.748494
$357$	−0.318502	−0.0168569
$358$	−1.24283	−0.0656855
$359$	−24.5967	−1.29816	−0.649082	−	0.760719i	$-0.724847\pi$
$359$	−24.5967	−1.29816	−0.649082	+	0.760719i	$0.724847\pi$
$360$	0.00733016	0.000386333 0
$361$	10.7092	0.563644
$362$	−6.50184	−0.341729
$363$	8.97965	0.471309
$364$	0	0
$365$	0.0254669	0.00133300
$366$	3.47137	0.181451
$367$	−6.84500	−0.357306	−0.178653	−	0.983912i	$-0.557174\pi$
$367$	−6.84500	−0.357306	−0.178653	+	0.983912i	$0.557174\pi$
$368$	20.6874	1.07841
$369$	−4.23517	−0.220474
$370$	−0.0104932	−0.000545518 0
$371$	−3.83209	−0.198952
$372$	−14.3365	−0.743313
$373$	23.4415	1.21375	0.606876	−	0.794796i	$-0.292422\pi$
$373$	23.4415	1.21375	0.606876	+	0.794796i	$0.292422\pi$
$374$	−0.385542	−0.0199359
$375$	0.0688265	0.00355418
$376$	−7.31679	−0.377335
$377$	0	0
$378$	−0.0863913	−0.00444349
$379$	−28.2309	−1.45013	−0.725063	−	0.688683i	$-0.758189\pi$
$379$	−28.2309	−1.45013	−0.725063	+	0.688683i	$0.758189\pi$
$380$	−0.0722696	−0.00370735
$381$	−10.5113	−0.538509
$382$	−1.41857	−0.0725804
$383$	20.2683	1.03566	0.517830	−	0.855483i	$-0.326740\pi$
$383$	20.2683	1.03566	0.517830	+	0.855483i	$0.326740\pi$
$384$	−7.89904	−0.403096
$385$	0.00311589	0.000158801 0
$386$	4.29961	0.218844
$387$	0.441322	0.0224337
$388$	−12.0431	−0.611397
$389$	31.4421	1.59418	0.797088	−	0.603864i	$-0.206373\pi$
$389$	31.4421	1.59418	0.797088	+	0.603864i	$0.206373\pi$
$390$	0	0
$391$	−5.80459	−0.293551
$392$	−7.34707	−0.371083
$393$	18.4950	0.932949
$394$	1.09777	0.0553046
$395$	−0.0553324	−0.00278408
$396$	2.73821	0.137600
$397$	−17.4925	−0.877925	−0.438963	−	0.898505i	$-0.644654\pi$
$397$	−17.4925	−0.877925	−0.438963	+	0.898505i	$0.644654\pi$
$398$	2.28880	0.114727
$399$	1.73603	0.0869102
$400$	−17.8197	−0.890986
$401$	−29.9104	−1.49365	−0.746826	−	0.665020i	$-0.768423\pi$
$401$	−29.9104	−1.49365	−0.746826	+	0.665020i	$0.768423\pi$
$402$	−3.23876	−0.161535
$403$	0	0
$404$	8.26535	0.411217
$405$	0.00688268	0.000342003 0
$406$	−0.685255	−0.0340086
$407$	−7.98927	−0.396014
$408$	1.06502	0.0527261
$409$	0.625173	0.0309128	0.0154564	−	0.999881i	$-0.495080\pi$
$409$	0.625173	0.0309128	0.0154564	+	0.999881i	$0.495080\pi$
$410$	0.00790655	0.000390476 0
$411$	9.75101	0.480982
$412$	25.8644	1.27425
$413$	−2.91911	−0.143640
$414$	−1.57446	−0.0773802
$415$	0.0112283	0.000551178 0
$416$	0	0
$417$	−3.08211	−0.150932
$418$	2.10144	0.102785
$419$	16.0459	0.783892	0.391946	−	0.919988i	$-0.371802\pi$
$419$	16.0459	0.783892	0.391946	+	0.919988i	$0.371802\pi$
$420$	−0.00422301	−0.000206062 0
$421$	0.622631	0.0303452	0.0151726	−	0.999885i	$-0.495170\pi$
$421$	0.622631	0.0303452	0.0151726	+	0.999885i	$0.495170\pi$
$422$	−2.57360	−0.125281
$423$	−6.87013	−0.334037
$424$	12.8139	0.622296
$425$	4.99995	0.242533
$426$	3.52937	0.170999
$427$	−4.07618	−0.197260
$428$	−32.0871	−1.55099
$429$	0	0
$430$	−0.000823895 0	−3.97317e−5 0
$431$	−2.95119	−0.142154	−0.0710768	−	0.997471i	$-0.522644\pi$
$431$	−2.95119	−0.142154	−0.0710768	+	0.997471i	$0.522644\pi$
$432$	−3.56398	−0.171472
$433$	8.33543	0.400575	0.200288	−	0.979737i	$-0.435812\pi$
$433$	8.33543	0.400575	0.200288	+	0.979737i	$0.435812\pi$
$434$	−0.642925	−0.0308614
$435$	0.0545933	0.00261755
$436$	−37.2997	−1.78633
$437$	31.6386	1.51348
$438$	1.00364	0.0479557
$439$	−31.8986	−1.52244	−0.761219	−	0.648494i	$-0.775399\pi$
$439$	−31.8986	−1.52244	−0.761219	+	0.648494i	$0.775399\pi$
$440$	−0.0104190	−0.000496708 0
$441$	−6.89856	−0.328503
$442$	0	0
$443$	−13.7556	−0.653548	−0.326774	−	0.945103i	$-0.605962\pi$
$443$	−13.7556	−0.653548	−0.326774	+	0.945103i	$0.605962\pi$
$444$	10.8280	0.513872
$445$	−0.0504566	−0.00239187
$446$	6.28449	0.297579
$447$	−20.6199	−0.975289
$448$	2.00273	0.0946203
$449$	−22.1259	−1.04419	−0.522094	−	0.852888i	$-0.674849\pi$
$449$	−22.1259	−1.04419	−0.522094	+	0.852888i	$0.674849\pi$
$450$	1.35620	0.0639320
$451$	6.01983	0.283463
$452$	−13.4432	−0.632314
$453$	−23.5613	−1.10700
$454$	5.62881	0.264173
$455$	0	0
$456$	−5.80499	−0.271844
$457$	−13.3415	−0.624088	−0.312044	−	0.950068i	$-0.601014\pi$
$457$	−13.3415	−0.624088	−0.312044	+	0.950068i	$0.601014\pi$
$458$	6.47563	0.302586
$459$	1.00000	0.0466760
$460$	−0.0769630	−0.00358842
$461$	−2.20411	−0.102656	−0.0513279	−	0.998682i	$-0.516345\pi$
$461$	−2.20411	−0.102656	−0.0513279	+	0.998682i	$0.516345\pi$
$462$	0.122796	0.00571298
$463$	0.0836288	0.00388656	0.00194328	−	0.999998i	$-0.499381\pi$
$463$	0.0836288	0.00388656	0.00194328	+	0.999998i	$0.499381\pi$
$464$	−28.2694	−1.31237
$465$	0.0512210	0.00237532
$466$	4.13236	0.191428
$467$	19.3109	0.893602	0.446801	−	0.894633i	$-0.352563\pi$
$467$	19.3109	0.893602	0.446801	+	0.894633i	$0.352563\pi$
$468$	0	0
$469$	3.80305	0.175608
$470$	0.0128257	0.000591605 0
$471$	−8.92126	−0.411070
$472$	9.76102	0.449287
$473$	−0.627292	−0.0288429
$474$	−2.18062	−0.100159
$475$	−27.2528	−1.25045
$476$	−0.613570	−0.0281229
$477$	12.0316	0.550890
$478$	6.04530	0.276506
$479$	10.7890	0.492962	0.246481	−	0.969148i	$-0.420726\pi$
$479$	10.7890	0.492962	0.246481	+	0.969148i	$0.420726\pi$
$480$	0.0213138	0.000972839 0
$481$	0	0
$482$	−2.93844	−0.133842
$483$	1.84877	0.0841220
$484$	17.2986	0.786302
$485$	0.0430273	0.00195377
$486$	0.271243	0.0123038
$487$	11.4032	0.516727	0.258363	−	0.966048i	$-0.416817\pi$
$487$	11.4032	0.516727	0.258363	+	0.966048i	$0.416817\pi$
$488$	13.6301	0.617004
$489$	9.17334	0.414833
$490$	0.0128788	0.000581803 0
$491$	36.3438	1.64017	0.820086	−	0.572240i	$-0.193925\pi$
$491$	36.3438	1.64017	0.820086	+	0.572240i	$0.193925\pi$
$492$	−8.15875	−0.367825
$493$	7.93198	0.357239
$494$	0	0
$495$	−0.00978298	−0.000439712 0
$496$	−26.5232	−1.19092
$497$	−4.14429	−0.185897
$498$	0.442504	0.0198291
$499$	22.4463	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$499$	22.4463	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$500$	0.132589	0.00592957
$501$	8.67286	0.387475
$502$	−0.727700	−0.0324789
$503$	−10.3409	−0.461080	−0.230540	−	0.973063i	$-0.574049\pi$
$503$	−10.3409	−0.461080	−0.230540	+	0.973063i	$0.574049\pi$
$504$	−0.339209	−0.0151096
$505$	−0.0295302	−0.00131408
$506$	2.23792	0.0994875
$507$	0	0
$508$	−20.2492	−0.898414
$509$	−25.6559	−1.13718	−0.568590	−	0.822621i	$-0.692511\pi$
$509$	−25.6559	−1.13718	−0.568590	+	0.822621i	$0.692511\pi$
$510$	−0.00186688	−8.26668e−5 0
$511$	−1.17850	−0.0521338
$512$	−18.6281	−0.823252
$513$	−5.45062	−0.240651
$514$	0.746479	0.0329258
$515$	−0.0924076	−0.00407197
$516$	0.850175	0.0374269
$517$	9.76514	0.429470
$518$	0.485583	0.0213353
$519$	21.7845	0.956231
$520$	0	0
$521$	−28.8613	−1.26444	−0.632218	−	0.774790i	$-0.717855\pi$
$521$	−28.8613	−1.26444	−0.632218	+	0.774790i	$0.717855\pi$
$522$	2.15150	0.0941684
$523$	29.4307	1.28691	0.643457	−	0.765483i	$-0.277500\pi$
$523$	29.4307	1.28691	0.643457	+	0.765483i	$0.277500\pi$
$524$	35.6293	1.55647
$525$	−1.59249	−0.0695021
$526$	−7.58655	−0.330789
$527$	7.44201	0.324179
$528$	5.06581	0.220461
$529$	10.6933	0.464926
$530$	−0.0224616	−0.000975668 0
$531$	9.16514	0.397733
$532$	3.34434	0.144995
$533$	0	0
$534$	−1.98847	−0.0860495
$535$	0.114640	0.00495631
$536$	−12.7167	−0.549280
$537$	−4.58198	−0.197727
$538$	−1.60551	−0.0692186
$539$	9.80555	0.422355
$540$	0.0132590	0.000570576 0
$541$	−15.6430	−0.672546	−0.336273	−	0.941765i	$-0.609166\pi$
$541$	−15.6430	−0.672546	−0.336273	+	0.941765i	$0.609166\pi$
$542$	3.40804	0.146388
$543$	−23.9705	−1.02867
$544$	3.09674	0.132771
$545$	0.133263	0.00570837
$546$	0	0
$547$	22.3593	0.956014	0.478007	−	0.878356i	$-0.341359\pi$
$547$	22.3593	0.956014	0.478007	+	0.878356i	$0.341359\pi$
$548$	18.7846	0.802439
$549$	12.7980	0.546205
$550$	−1.92769	−0.0821972
$551$	−43.2342	−1.84184
$552$	−6.18198	−0.263123
$553$	2.56055	0.108886
$554$	−1.58153	−0.0671929
$555$	−0.0386858	−0.00164212
$556$	−5.93747	−0.251805
$557$	14.5131	0.614941	0.307470	−	0.951558i	$-0.400517\pi$
$557$	14.5131	0.614941	0.307470	+	0.951558i	$0.400517\pi$
$558$	2.01859	0.0854539
$559$	0	0
$560$	−0.00781275	−0.000330149 0
$561$	−1.42139	−0.0600112
$562$	1.13045	0.0476853
$563$	−3.83294	−0.161539	−0.0807697	−	0.996733i	$-0.525738\pi$
$563$	−3.83294	−0.161539	−0.0807697	+	0.996733i	$0.525738\pi$
$564$	−13.2348	−0.557285
$565$	0.0480294	0.00202061
$566$	4.84444	0.203627
$567$	−0.318502	−0.0133758
$568$	13.8578	0.581461
$569$	−36.7941	−1.54249	−0.771245	−	0.636538i	$-0.780366\pi$
$569$	−36.7941	−1.54249	−0.771245	+	0.636538i	$0.780366\pi$
$570$	0.0101756	0.000426211 0
$571$	−30.2379	−1.26542	−0.632709	−	0.774390i	$-0.718057\pi$
$571$	−30.2379	−1.26542	−0.632709	+	0.774390i	$0.718057\pi$
$572$	0	0
$573$	−5.22989	−0.218482
$574$	−0.365882	−0.0152716
$575$	−29.0227	−1.21033
$576$	−6.28798	−0.261999
$577$	−44.3418	−1.84597	−0.922987	−	0.384832i	$-0.874260\pi$
$577$	−44.3418	−1.84597	−0.922987	+	0.384832i	$0.874260\pi$
$578$	−0.271243	−0.0112822
$579$	15.8515	0.658766
$580$	0.105170	0.00436695
$581$	−0.519601	−0.0215567
$582$	1.69568	0.0702884
$583$	−17.1016	−0.708277
$584$	3.94071	0.163068
$585$	0	0
$586$	−2.83432	−0.117085
$587$	30.0522	1.24039	0.620194	−	0.784449i	$-0.287054\pi$
$587$	30.0522	1.24039	0.620194	+	0.784449i	$0.287054\pi$
$588$	−13.2896	−0.548053
$589$	−40.5636	−1.67139
$590$	−0.0171102	−0.000704416 0
$591$	4.04717	0.166478
$592$	20.0322	0.823318
$593$	−12.4463	−0.511107	−0.255554	−	0.966795i	$-0.582258\pi$
$593$	−12.4463	−0.511107	−0.255554	+	0.966795i	$0.582258\pi$
$594$	−0.385542	−0.0158190
$595$	0.00219214	8.98691e−5 0
$596$	−39.7228	−1.62711
$597$	8.43818	0.345352
$598$	0	0
$599$	−0.956746	−0.0390916	−0.0195458	−	0.999809i	$-0.506222\pi$
$599$	−0.956746	−0.0390916	−0.0195458	+	0.999809i	$0.506222\pi$
$600$	5.32503	0.217393
$601$	−14.1641	−0.577765	−0.288882	−	0.957365i	$-0.593284\pi$
$601$	−14.1641	−0.577765	−0.288882	+	0.957365i	$0.593284\pi$
$602$	0.0381264	0.00155392
$603$	−11.9404	−0.486252
$604$	−45.3890	−1.84685
$605$	−0.0618040	−0.00251269
$606$	−1.16377	−0.0472749
$607$	1.86891	0.0758568	0.0379284	−	0.999280i	$-0.487924\pi$
$607$	1.86891	0.0758568	0.0379284	+	0.999280i	$0.487924\pi$
$608$	−16.8791	−0.684539
$609$	−2.52635	−0.102373
$610$	−0.0238923	−0.000967371 0
$611$	0	0
$612$	1.92643	0.0778712
$613$	−3.87460	−0.156493	−0.0782467	−	0.996934i	$-0.524932\pi$
$613$	−3.87460	−0.156493	−0.0782467	+	0.996934i	$0.524932\pi$
$614$	7.67353	0.309678
$615$	0.0291493	0.00117541
$616$	0.482149	0.0194263
$617$	−27.9349	−1.12462	−0.562309	−	0.826927i	$-0.690087\pi$
$617$	−27.9349	−1.12462	−0.562309	+	0.826927i	$0.690087\pi$
$618$	−3.64174	−0.146492
$619$	18.0563	0.725746	0.362873	−	0.931839i	$-0.381796\pi$
$619$	18.0563	0.725746	0.362873	+	0.931839i	$0.381796\pi$
$620$	0.0986735	0.00396282
$621$	−5.80459	−0.232930
$622$	−6.15585	−0.246827
$623$	2.33492	0.0935466
$624$	0	0
$625$	24.9993	0.999972
$626$	−0.215378	−0.00860823
$627$	7.74746	0.309404
$628$	−17.1862	−0.685802
$629$	−5.62074	−0.224114
$630$	0.000594604 0	2.36896e−5 0
$631$	−4.46422	−0.177718	−0.0888588	−	0.996044i	$-0.528322\pi$
$631$	−4.46422	−0.177718	−0.0888588	+	0.996044i	$0.528322\pi$
$632$	−8.56206	−0.340580
$633$	−9.48816	−0.377120
$634$	8.89437	0.353240
$635$	0.0723457	0.00287095
$636$	23.1780	0.919069
$637$	0	0
$638$	−3.05812	−0.121072
$639$	13.0118	0.514741
$640$	0.0543666	0.00214903
$641$	−11.5138	−0.454768	−0.227384	−	0.973805i	$-0.573017\pi$
$641$	−11.5138	−0.454768	−0.227384	+	0.973805i	$0.573017\pi$
$642$	4.51790	0.178307
$643$	−26.5641	−1.04759	−0.523794	−	0.851845i	$-0.675484\pi$
$643$	−26.5641	−1.04759	−0.523794	+	0.851845i	$0.675484\pi$
$644$	3.56153	0.140344
$645$	−0.00303748	−0.000119601 0
$646$	1.47844	0.0581685
$647$	−5.12374	−0.201435	−0.100718	−	0.994915i	$-0.532114\pi$
$647$	−5.12374	−0.201435	−0.100718	+	0.994915i	$0.532114\pi$
$648$	1.06502	0.0418378
$649$	−13.0273	−0.511365
$650$	0	0
$651$	−2.37029	−0.0928991
$652$	17.6718	0.692080
$653$	−19.6655	−0.769572	−0.384786	−	0.923006i	$-0.625725\pi$
$653$	−19.6655	−0.769572	−0.384786	+	0.923006i	$0.625725\pi$
$654$	5.25184	0.205363
$655$	−0.127295	−0.00497383
$656$	−15.0940	−0.589323
$657$	3.70014	0.144356
$658$	−0.593519	−0.0231378
$659$	2.21540	0.0862999	0.0431499	−	0.999069i	$-0.486261\pi$
$659$	2.21540	0.0862999	0.0431499	+	0.999069i	$0.486261\pi$
$660$	−0.0188462	−0.000733587 0
$661$	19.9744	0.776916	0.388458	−	0.921466i	$-0.373008\pi$
$661$	19.9744	0.776916	0.388458	+	0.921466i	$0.373008\pi$
$662$	2.10756	0.0819126
$663$	0	0
$664$	1.73746	0.0674265
$665$	−0.0119485	−0.000463344 0
$666$	−1.52459	−0.0590765
$667$	−46.0419	−1.78275
$668$	16.7076	0.646437
$669$	23.1692	0.895775
$670$	0.0222913	0.000861189 0
$671$	−18.1910	−0.702255
$672$	−0.986315	−0.0380479
$673$	−26.9075	−1.03721	−0.518603	−	0.855015i	$-0.673548\pi$
$673$	−26.9075	−1.03721	−0.518603	+	0.855015i	$0.673548\pi$
$674$	6.61161	0.254670
$675$	4.99995	0.192448
$676$	0	0
$677$	6.71905	0.258234	0.129117	−	0.991629i	$-0.458786\pi$
$677$	6.71905	0.258234	0.129117	+	0.991629i	$0.458786\pi$
$678$	1.89281	0.0726931
$679$	−1.99112	−0.0764123
$680$	−0.00733016	−0.000281099 0
$681$	20.7519	0.795215
$682$	−2.86921	−0.109868
$683$	−25.1476	−0.962248	−0.481124	−	0.876653i	$-0.659771\pi$
$683$	−25.1476	−0.962248	−0.481124	+	0.876653i	$0.659771\pi$
$684$	−10.5002	−0.401486
$685$	−0.0671131	−0.00256426
$686$	−1.20071	−0.0458435
$687$	23.8739	0.910847
$688$	1.57286	0.0599648
$689$	0	0
$690$	0.0108365	0.000412537 0
$691$	−24.6761	−0.938725	−0.469362	−	0.883006i	$-0.655516\pi$
$691$	−24.6761	−0.938725	−0.469362	+	0.883006i	$0.655516\pi$
$692$	41.9662	1.59531
$693$	0.452715	0.0171972
$694$	1.59615	0.0605889
$695$	0.0212132	0.000804662 0
$696$	8.44769	0.320209
$697$	4.23517	0.160419
$698$	3.13497	0.118660
$699$	15.2349	0.576236
$700$	−3.06782	−0.115953
$701$	−41.8636	−1.58116	−0.790582	−	0.612356i	$-0.790222\pi$
$701$	−41.8636	−1.58116	−0.790582	+	0.612356i	$0.790222\pi$
$702$	0	0
$703$	30.6365	1.15548
$704$	8.93769	0.336852
$705$	0.0472849	0.00178085
$706$	−6.09762	−0.229487
$707$	1.36653	0.0513938
$708$	17.6560	0.663552
$709$	−28.5207	−1.07112	−0.535559	−	0.844498i	$-0.679899\pi$
$709$	−28.5207	−1.07112	−0.535559	+	0.844498i	$0.679899\pi$
$710$	−0.0242915	−0.000911645 0
$711$	−8.03937	−0.301500
$712$	−7.80758	−0.292602
$713$	−43.1978	−1.61777
$714$	0.0863913	0.00323311
$715$	0	0
$716$	−8.82684	−0.329875
$717$	22.2874	0.832338
$718$	6.67168	0.248985
$719$	−11.7552	−0.438394	−0.219197	−	0.975681i	$-0.570344\pi$
$719$	−11.7552	−0.438394	−0.219197	+	0.975681i	$0.570344\pi$
$720$	0.0245297	0.000914168 0
$721$	4.27624	0.159255
$722$	−2.90480	−0.108106
$723$	−10.8332	−0.402893
$724$	−46.1775	−1.71617
$725$	39.6595	1.47292
$726$	−2.43567	−0.0903960
$727$	−43.6953	−1.62057	−0.810284	−	0.586038i	$-0.800687\pi$
$727$	−43.6953	−1.62057	−0.810284	+	0.586038i	$0.800687\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.00690772	−0.000255666 0
$731$	−0.441322	−0.0163229
$732$	24.6544	0.911253
$733$	−21.3248	−0.787650	−0.393825	−	0.919185i	$-0.628848\pi$
$733$	−21.3248	−0.787650	−0.393825	+	0.919185i	$0.628848\pi$
$734$	1.85666	0.0685305
$735$	0.0474805	0.00175135
$736$	−17.9753	−0.662578
$737$	16.9720	0.625173
$738$	1.14876	0.0422864
$739$	−0.819899	−0.0301605	−0.0150802	−	0.999886i	$-0.504800\pi$
$739$	−0.819899	−0.0301605	−0.0150802	+	0.999886i	$0.504800\pi$
$740$	−0.0745253	−0.00273960
$741$	0	0
$742$	1.03943	0.0381586
$743$	−20.6398	−0.757200	−0.378600	−	0.925560i	$-0.623594\pi$
$743$	−20.6398	−0.757200	−0.378600	+	0.925560i	$0.623594\pi$
$744$	7.92586	0.290576
$745$	0.141920	0.00519956
$746$	−6.35833	−0.232795
$747$	1.63139	0.0596895
$748$	−2.73821	−0.100119
$749$	−5.30505	−0.193842
$750$	−0.0186687	−0.000681684 0
$751$	−4.66362	−0.170178	−0.0850890	−	0.996373i	$-0.527117\pi$
$751$	−4.66362	−0.170178	−0.0850890	+	0.996373i	$0.527117\pi$
$752$	−24.4850	−0.892875
$753$	−2.68284	−0.0977680
$754$	0	0
$755$	0.162165	0.00590177
$756$	−0.613570	−0.0223153
$757$	−16.0586	−0.583659	−0.291829	−	0.956470i	$-0.594264\pi$
$757$	−16.0586	−0.583659	−0.291829	+	0.956470i	$0.594264\pi$
$758$	7.65744	0.278131
$759$	8.25060	0.299478
$760$	0.0399539	0.00144928
$761$	11.8240	0.428621	0.214310	−	0.976766i	$-0.431250\pi$
$761$	11.8240	0.428621	0.214310	+	0.976766i	$0.431250\pi$
$762$	2.85111	0.103285
$763$	−6.16687	−0.223256
$764$	−10.0750	−0.364501
$765$	−0.00688268	−0.000248844 0
$766$	−5.49763	−0.198637
$767$	0	0
$768$	−10.4334	−0.376483
$769$	−29.2725	−1.05559	−0.527797	−	0.849370i	$-0.676982\pi$
$769$	−29.2725	−1.05559	−0.527797	+	0.849370i	$0.676982\pi$
$770$	−0.000845165 0	−3.04576e−5 0
$771$	2.75207	0.0991133
$772$	30.5368	1.09904
$773$	17.3025	0.622326	0.311163	−	0.950357i	$-0.399281\pi$
$773$	17.3025	0.622326	0.311163	+	0.950357i	$0.399281\pi$
$774$	−0.119706	−0.00430273
$775$	37.2097	1.33661
$776$	6.65798	0.239008
$777$	1.79022	0.0642236
$778$	−8.52844	−0.305759
$779$	−23.0843	−0.827081
$780$	0	0
$781$	−18.4949	−0.661801
$782$	1.57446	0.0563024
$783$	7.93198	0.283466
$784$	−24.5863	−0.878082
$785$	0.0614022	0.00219154
$786$	−5.01664	−0.178938
$787$	−31.4636	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$787$	−31.4636	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$788$	7.79657	0.277741
$789$	−27.9696	−0.995743
$790$	0.0150085	0.000533980 0
$791$	−2.22260	−0.0790265
$792$	−1.51380	−0.0537907
$793$	0	0
$794$	4.74473	0.168384
$795$	−0.0828097	−0.00293696
$796$	16.2555	0.576162
$797$	−1.23443	−0.0437259	−0.0218630	−	0.999761i	$-0.506960\pi$
$797$	−1.23443	−0.0437259	−0.0218630	+	0.999761i	$0.506960\pi$
$798$	−0.470886	−0.0166692
$799$	6.87013	0.243048
$800$	15.4835	0.547425
$801$	−7.33095	−0.259027
$802$	8.11297	0.286479
$803$	−5.25935	−0.185598
$804$	−23.0024	−0.811231
$805$	−0.0127245	−0.000448480 0
$806$	0	0
$807$	−5.91910	−0.208362
$808$	−4.56946	−0.160753
$809$	48.7732	1.71477	0.857387	−	0.514672i	$-0.172086\pi$
$809$	48.7732	1.71477	0.857387	+	0.514672i	$0.172086\pi$
$810$	−0.00186688	−6.55954e−5 0
$811$	−52.7478	−1.85223	−0.926113	−	0.377246i	$-0.876871\pi$
$811$	−52.7478	−1.85223	−0.926113	+	0.377246i	$0.876871\pi$
$812$	−4.86683	−0.170792
$813$	12.5645	0.440657
$814$	2.16703	0.0759545
$815$	−0.0631371	−0.00221160
$816$	3.56398	0.124764
$817$	2.40548	0.0841570
$818$	−0.169574	−0.00592901
$819$	0	0
$820$	0.0561540	0.00196098
$821$	5.68088	0.198264	0.0991320	−	0.995074i	$-0.468393\pi$
$821$	5.68088	0.198264	0.0991320	+	0.995074i	$0.468393\pi$
$822$	−2.64489	−0.0922513
$823$	29.2354	1.01908	0.509541	−	0.860447i	$-0.329815\pi$
$823$	29.2354	1.01908	0.509541	+	0.860447i	$0.329815\pi$
$824$	−14.2990	−0.498130
$825$	−7.10689	−0.247430
$826$	0.791789	0.0275499
$827$	13.3881	0.465549	0.232774	−	0.972531i	$-0.425220\pi$
$827$	13.3881	0.465549	0.232774	+	0.972531i	$0.425220\pi$
$828$	−11.1821	−0.388606
$829$	−16.5426	−0.574548	−0.287274	−	0.957848i	$-0.592749\pi$
$829$	−16.5426	−0.574548	−0.287274	+	0.957848i	$0.592749\pi$
$830$	−0.00304561	−0.000105715 0
$831$	−5.83069	−0.202264
$832$	0	0
$833$	6.89856	0.239021
$834$	0.836002	0.0289484
$835$	−0.0596925	−0.00206574
$836$	14.9249	0.516189
$837$	7.44201	0.257234
$838$	−4.35233	−0.150349
$839$	41.6911	1.43933	0.719667	−	0.694319i	$-0.244294\pi$
$839$	41.6911	1.43933	0.719667	+	0.694319i	$0.244294\pi$
$840$	0.00233467	8.05537e−5 0
$841$	33.9164	1.16953
$842$	−0.168884	−0.00582013
$843$	4.16768	0.143542
$844$	−18.2782	−0.629163
$845$	0	0
$846$	1.86347	0.0640675
$847$	2.86003	0.0982719
$848$	42.8804	1.47252
$849$	17.8601	0.612958
$850$	−1.35620	−0.0465173
$851$	32.6261	1.11841
$852$	25.0664	0.858760
$853$	−28.6964	−0.982548	−0.491274	−	0.871005i	$-0.663469\pi$
$853$	−28.6964	−0.982548	−0.491274	+	0.871005i	$0.663469\pi$
$854$	1.10564	0.0378341
$855$	0.0375148	0.00128298
$856$	17.7392	0.606313
$857$	16.7513	0.572213	0.286107	−	0.958198i	$-0.407639\pi$
$857$	16.7513	0.572213	0.286107	+	0.958198i	$0.407639\pi$
$858$	0	0
$859$	−5.12064	−0.174714	−0.0873571	−	0.996177i	$-0.527842\pi$
$859$	−5.12064	−0.174714	−0.0873571	+	0.996177i	$0.527842\pi$
$860$	−0.00585148	−0.000199534 0
$861$	−1.34891	−0.0459707
$862$	0.800489	0.0272648
$863$	36.6991	1.24925	0.624626	−	0.780924i	$-0.285251\pi$
$863$	36.6991	1.24925	0.624626	+	0.780924i	$0.285251\pi$
$864$	3.09674	0.105353
$865$	−0.149935	−0.00509796
$866$	−2.26093	−0.0768294
$867$	−1.00000	−0.0339618
$868$	−4.56620	−0.154987
$869$	11.4271	0.387638
$870$	−0.0148080	−0.000502040 0
$871$	0	0
$872$	20.6210	0.698314
$873$	6.25153	0.211582
$874$	−8.58175	−0.290282
$875$	0.0219213	0.000741076 0
$876$	7.12806	0.240835
$877$	−36.5447	−1.23403	−0.617013	−	0.786953i	$-0.711657\pi$
$877$	−36.5447	−1.23403	−0.617013	+	0.786953i	$0.711657\pi$
$878$	8.65228	0.292000
$879$	−10.4494	−0.352448
$880$	−0.0348663	−0.00117534
$881$	49.7618	1.67652	0.838259	−	0.545273i	$-0.183574\pi$
$881$	49.7618	1.67652	0.838259	+	0.545273i	$0.183574\pi$
$882$	1.87119	0.0630061
$883$	23.0084	0.774293	0.387146	−	0.922018i	$-0.373461\pi$
$883$	23.0084	0.774293	0.387146	+	0.922018i	$0.373461\pi$
$884$	0	0
$885$	−0.0630807	−0.00212044
$886$	3.73111	0.125349
$887$	−3.98116	−0.133674	−0.0668372	−	0.997764i	$-0.521291\pi$
$887$	−3.98116	−0.133674	−0.0668372	+	0.997764i	$0.521291\pi$
$888$	−5.98618	−0.200883
$889$	−3.34786	−0.112284
$890$	0.0136860	0.000458756 0
$891$	−1.42139	−0.0476184
$892$	44.6339	1.49445
$893$	−37.4464	−1.25310
$894$	5.59301	0.187058
$895$	0.0315363	0.00105414
$896$	−2.51586	−0.0840489
$897$	0	0
$898$	6.00151	0.200273
$899$	59.0299	1.96876
$900$	9.63204	0.321068
$901$	−12.0316	−0.400831
$902$	−1.63284	−0.0543676
$903$	0.140562	0.00467761
$904$	7.43200	0.247185
$905$	0.164982	0.00548417
$906$	6.39083	0.212321
$907$	34.6173	1.14945	0.574725	−	0.818347i	$-0.305109\pi$
$907$	34.6173	1.14945	0.574725	+	0.818347i	$0.305109\pi$
$908$	39.9771	1.32669
$909$	−4.29051	−0.142307
$910$	0	0
$911$	−9.42533	−0.312275	−0.156138	−	0.987735i	$-0.549904\pi$
$911$	−9.42533	−0.312275	−0.156138	+	0.987735i	$0.549904\pi$
$912$	−19.4259	−0.643255
$913$	−2.31885	−0.0767426
$914$	3.61878	0.119699
$915$	−0.0880845	−0.00291198
$916$	45.9914	1.51960
$917$	5.89069	0.194528
$918$	−0.271243	−0.00895235
$919$	9.82367	0.324053	0.162026	−	0.986786i	$-0.448197\pi$
$919$	9.82367	0.324053	0.162026	+	0.986786i	$0.448197\pi$
$920$	0.0425486	0.00140279
$921$	28.2902	0.932195
$922$	0.597850	0.0196892
$923$	0	0
$924$	0.872123	0.0286908
$925$	−28.1034	−0.924036
$926$	−0.0226837	−0.000745433 0
$927$	−13.4261	−0.440971
$928$	24.5633	0.806328
$929$	−2.72942	−0.0895494	−0.0447747	−	0.998997i	$-0.514257\pi$
$929$	−2.72942	−0.0895494	−0.0447747	+	0.998997i	$0.514257\pi$
$930$	−0.0138933	−0.000455580 0
$931$	−37.6014	−1.23234
$932$	29.3489	0.961355
$933$	−22.6949	−0.742999
$934$	−5.23795	−0.171391
$935$	0.00978298	0.000319938 0
$936$	0	0
$937$	−57.1445	−1.86683	−0.933414	−	0.358801i	$-0.883186\pi$
$937$	−57.1445	−1.86683	−0.933414	+	0.358801i	$0.883186\pi$
$938$	−1.03155	−0.0336813
$939$	−0.794040	−0.0259125
$940$	0.0910908	0.00297106
$941$	−29.5157	−0.962184	−0.481092	−	0.876670i	$-0.659760\pi$
$941$	−29.5157	−0.962184	−0.481092	+	0.876670i	$0.659760\pi$
$942$	2.41983	0.0788423
$943$	−24.5834	−0.800547
$944$	32.6644	1.06313
$945$	0.00219214	7.13105e−5 0
$946$	0.170148	0.00553200
$947$	42.7602	1.38952	0.694760	−	0.719242i	$-0.255511\pi$
$947$	42.7602	1.38952	0.694760	+	0.719242i	$0.255511\pi$
$948$	−15.4873	−0.503003
$949$	0	0
$950$	7.39214	0.239833
$951$	32.7911	1.06333
$952$	0.339209	0.0109938
$953$	−16.1738	−0.523921	−0.261960	−	0.965079i	$-0.584369\pi$
$953$	−16.1738	−0.523921	−0.261960	+	0.965079i	$0.584369\pi$
$954$	−3.26349	−0.105659
$955$	0.0359957	0.00116479
$956$	42.9351	1.38862
$957$	−11.2745	−0.364451
$958$	−2.92644	−0.0945491
$959$	3.10571	0.100289
$960$	0.0432782	0.00139680
$961$	24.3835	0.786565
$962$	0	0
$963$	16.6563	0.536741
$964$	−20.8695	−0.672160
$965$	−0.109101	−0.00351208
$966$	−0.501467	−0.0161344
$967$	57.2411	1.84075	0.920375	−	0.391037i	$-0.127884\pi$
$967$	57.2411	1.84075	0.920375	+	0.391037i	$0.127884\pi$
$968$	−9.56347	−0.307381
$969$	5.45062	0.175099
$970$	−0.0116709	−0.000374729 0
$971$	−40.9123	−1.31294	−0.656470	−	0.754352i	$-0.727951\pi$
$971$	−40.9123	−1.31294	−0.656470	+	0.754352i	$0.727951\pi$
$972$	1.92643	0.0617902
$973$	−0.981658	−0.0314705
$974$	−3.09303	−0.0991070
$975$	0	0
$976$	45.6118	1.46000
$977$	−21.1028	−0.675138	−0.337569	−	0.941301i	$-0.609605\pi$
$977$	−21.1028	−0.675138	−0.337569	+	0.941301i	$0.609605\pi$
$978$	−2.48820	−0.0795640
$979$	10.4202	0.333030
$980$	0.0914678	0.00292183
$981$	19.3621	0.618185
$982$	−9.85800	−0.314581
$983$	32.9357	1.05049	0.525244	−	0.850952i	$-0.323974\pi$
$983$	32.9357	1.05049	0.525244	+	0.850952i	$0.323974\pi$
$984$	4.51052	0.143790
$985$	−0.0278553	−0.000887545 0
$986$	−2.15150	−0.0685176
$987$	−2.18815	−0.0696495
$988$	0	0
$989$	2.56170	0.0814572
$990$	0.00265356	8.43358e−5 0
$991$	−51.0240	−1.62083	−0.810415	−	0.585856i	$-0.800759\pi$
$991$	−51.0240	−1.62083	−0.810415	+	0.585856i	$0.800759\pi$
$992$	23.0459	0.731709
$993$	7.77000	0.246574
$994$	1.12411	0.0356546
$995$	−0.0580773	−0.00184117
$996$	3.14276	0.0995821
$997$	36.1921	1.14622	0.573108	−	0.819480i	$-0.305738\pi$
$997$	36.1921	1.14622	0.573108	+	0.819480i	$0.305738\pi$
$998$	−6.08840	−0.192725
$999$	−5.62074	−0.177832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8619.2.a.bw.1.11	yes	24
13.12	even	2		8619.2.a.bt.1.14	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8619.2.a.bt.1.14	✓	24	13.12	even	2
8619.2.a.bw.1.11	yes	24	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:	\( N \)	\(=\)	\( 8619 = 3 \cdot 13^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8619.a (trivial)

\(f(q)\)	\(=\)	\(q-0.271243 q^{2} -1.00000 q^{3} -1.92643 q^{4} +0.00688268 q^{5} +0.271243 q^{6} -0.318502 q^{7} +1.06502 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.271243 q^{2} -1.00000 q^{3} -1.92643 q^{4} +0.00688268 q^{5} +0.271243 q^{6} -0.318502 q^{7} +1.06502 q^{8} +1.00000 q^{9} -0.00186688 q^{10} -1.42139 q^{11} +1.92643 q^{12} +0.0863913 q^{14} -0.00688268 q^{15} +3.56398 q^{16} -1.00000 q^{17} -0.271243 q^{18} +5.45062 q^{19} -0.0132590 q^{20} +0.318502 q^{21} +0.385542 q^{22} +5.80459 q^{23} -1.06502 q^{24} -4.99995 q^{25} -1.00000 q^{27} +0.613570 q^{28} -7.93198 q^{29} +0.00186688 q^{30} -7.44201 q^{31} -3.09674 q^{32} +1.42139 q^{33} +0.271243 q^{34} -0.00219214 q^{35} -1.92643 q^{36} +5.62074 q^{37} -1.47844 q^{38} +0.00733016 q^{40} -4.23517 q^{41} -0.0863913 q^{42} +0.441322 q^{43} +2.73821 q^{44} +0.00688268 q^{45} -1.57446 q^{46} -6.87013 q^{47} -3.56398 q^{48} -6.89856 q^{49} +1.35620 q^{50} +1.00000 q^{51} +12.0316 q^{53} +0.271243 q^{54} -0.00978298 q^{55} -0.339209 q^{56} -5.45062 q^{57} +2.15150 q^{58} +9.16514 q^{59} +0.0132590 q^{60} +12.7980 q^{61} +2.01859 q^{62} -0.318502 q^{63} -6.28798 q^{64} -0.385542 q^{66} -11.9404 q^{67} +1.92643 q^{68} -5.80459 q^{69} +0.000594604 q^{70} +13.0118 q^{71} +1.06502 q^{72} +3.70014 q^{73} -1.52459 q^{74} +4.99995 q^{75} -10.5002 q^{76} +0.452715 q^{77} -8.03937 q^{79} +0.0245297 q^{80} +1.00000 q^{81} +1.14876 q^{82} +1.63139 q^{83} -0.613570 q^{84} -0.00688268 q^{85} -0.119706 q^{86} +7.93198 q^{87} -1.51380 q^{88} -7.33095 q^{89} -0.00186688 q^{90} -11.1821 q^{92} +7.44201 q^{93} +1.86347 q^{94} +0.0375148 q^{95} +3.09674 q^{96} +6.25153 q^{97} +1.87119 q^{98} -1.42139 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 7 q^{2} - 24 q^{3} + 17 q^{4} - 13 q^{5} - 7 q^{6} - 12 q^{7} + 21 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 7 * q^2 - 24 * q^3 + 17 * q^4 - 13 * q^5 - 7 * q^6 - 12 * q^7 + 21 * q^8 + 24 * q^9	\( 24 q + 7 q^{2} - 24 q^{3} + 17 q^{4} - 13 q^{5} - 7 q^{6} - 12 q^{7} + 21 q^{8} + 24 q^{9} - 4 q^{10} - q^{11} - 17 q^{12} - 18 q^{14} + 13 q^{15} + 35 q^{16} - 24 q^{17} + 7 q^{18} - 16 q^{19} - 18 q^{20} + 12 q^{21} + 8 q^{22} + 3 q^{23} - 21 q^{24} + 23 q^{25} - 24 q^{27} - 30 q^{28} + 5 q^{29} + 4 q^{30} - 46 q^{31} + 44 q^{32} + q^{33} - 7 q^{34} + 11 q^{35} + 17 q^{36} - 38 q^{37} - q^{38} - 59 q^{40} - 31 q^{41} + 18 q^{42} + 3 q^{43} + 3 q^{44} - 13 q^{45} - 36 q^{46} + 49 q^{47} - 35 q^{48} + 30 q^{49} + 15 q^{50} + 24 q^{51} - 11 q^{53} - 7 q^{54} - 10 q^{55} - 38 q^{56} + 16 q^{57} - 53 q^{58} - 23 q^{59} + 18 q^{60} - 2 q^{61} - 26 q^{62} - 12 q^{63} + 57 q^{64} - 8 q^{66} - 17 q^{68} - 3 q^{69} + 10 q^{70} + 29 q^{71} + 21 q^{72} - 48 q^{73} - 66 q^{74} - 23 q^{75} - 38 q^{76} + 51 q^{77} - 26 q^{79} - 52 q^{80} + 24 q^{81} - 45 q^{82} + 8 q^{83} + 30 q^{84} + 13 q^{85} - 38 q^{86} - 5 q^{87} - 34 q^{88} - 42 q^{89} - 4 q^{90} - 10 q^{92} + 46 q^{93} + 107 q^{94} - 44 q^{96} - 60 q^{97} + 19 q^{98} - q^{99}+O(q^{100}) \) 24 * q + 7 * q^2 - 24 * q^3 + 17 * q^4 - 13 * q^5 - 7 * q^6 - 12 * q^7 + 21 * q^8 + 24 * q^9 - 4 * q^10 - q^11 - 17 * q^12 - 18 * q^14 + 13 * q^15 + 35 * q^16 - 24 * q^17 + 7 * q^18 - 16 * q^19 - 18 * q^20 + 12 * q^21 + 8 * q^22 + 3 * q^23 - 21 * q^24 + 23 * q^25 - 24 * q^27 - 30 * q^28 + 5 * q^29 + 4 * q^30 - 46 * q^31 + 44 * q^32 + q^33 - 7 * q^34 + 11 * q^35 + 17 * q^36 - 38 * q^37 - q^38 - 59 * q^40 - 31 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 13 * q^45 - 36 * q^46 + 49 * q^47 - 35 * q^48 + 30 * q^49 + 15 * q^50 + 24 * q^51 - 11 * q^53 - 7 * q^54 - 10 * q^55 - 38 * q^56 + 16 * q^57 - 53 * q^58 - 23 * q^59 + 18 * q^60 - 2 * q^61 - 26 * q^62 - 12 * q^63 + 57 * q^64 - 8 * q^66 - 17 * q^68 - 3 * q^69 + 10 * q^70 + 29 * q^71 + 21 * q^72 - 48 * q^73 - 66 * q^74 - 23 * q^75 - 38 * q^76 + 51 * q^77 - 26 * q^79 - 52 * q^80 + 24 * q^81 - 45 * q^82 + 8 * q^83 + 30 * q^84 + 13 * q^85 - 38 * q^86 - 5 * q^87 - 34 * q^88 - 42 * q^89 - 4 * q^90 - 10 * q^92 + 46 * q^93 + 107 * q^94 - 44 * q^96 - 60 * q^97 + 19 * q^98 - q^99

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