LMFDB - Embedded newform 6014.2.a.i.1.5

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:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.09814 q^{3} +1.00000 q^{4} +3.98650 q^{5} -2.09814 q^{6} +1.58307 q^{7} +1.00000 q^{8} +1.40217 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.09814 q^{3} +1.00000 q^{4} +3.98650 q^{5} -2.09814 q^{6} +1.58307 q^{7} +1.00000 q^{8} +1.40217 q^{9} +3.98650 q^{10} +3.27907 q^{11} -2.09814 q^{12} +2.09529 q^{13} +1.58307 q^{14} -8.36422 q^{15} +1.00000 q^{16} +3.89492 q^{17} +1.40217 q^{18} -2.88949 q^{19} +3.98650 q^{20} -3.32150 q^{21} +3.27907 q^{22} +5.91146 q^{23} -2.09814 q^{24} +10.8922 q^{25} +2.09529 q^{26} +3.35246 q^{27} +1.58307 q^{28} -5.07254 q^{29} -8.36422 q^{30} -1.00000 q^{31} +1.00000 q^{32} -6.87994 q^{33} +3.89492 q^{34} +6.31092 q^{35} +1.40217 q^{36} -4.99481 q^{37} -2.88949 q^{38} -4.39621 q^{39} +3.98650 q^{40} +0.0545720 q^{41} -3.32150 q^{42} +9.91490 q^{43} +3.27907 q^{44} +5.58975 q^{45} +5.91146 q^{46} +0.311181 q^{47} -2.09814 q^{48} -4.49388 q^{49} +10.8922 q^{50} -8.17207 q^{51} +2.09529 q^{52} -2.78066 q^{53} +3.35246 q^{54} +13.0720 q^{55} +1.58307 q^{56} +6.06254 q^{57} -5.07254 q^{58} -3.95399 q^{59} -8.36422 q^{60} -4.74267 q^{61} -1.00000 q^{62} +2.21974 q^{63} +1.00000 q^{64} +8.35289 q^{65} -6.87994 q^{66} +11.2037 q^{67} +3.89492 q^{68} -12.4030 q^{69} +6.31092 q^{70} +7.07124 q^{71} +1.40217 q^{72} +4.23578 q^{73} -4.99481 q^{74} -22.8533 q^{75} -2.88949 q^{76} +5.19101 q^{77} -4.39621 q^{78} -15.6024 q^{79} +3.98650 q^{80} -11.2404 q^{81} +0.0545720 q^{82} +14.1369 q^{83} -3.32150 q^{84} +15.5271 q^{85} +9.91490 q^{86} +10.6429 q^{87} +3.27907 q^{88} -2.06651 q^{89} +5.58975 q^{90} +3.31700 q^{91} +5.91146 q^{92} +2.09814 q^{93} +0.311181 q^{94} -11.5190 q^{95} -2.09814 q^{96} -1.00000 q^{97} -4.49388 q^{98} +4.59782 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * 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
$3$	−2.09814	−1.21136	−0.605679	−	0.795709i	$-0.707099\pi$
$3$	−2.09814	−1.21136	−0.605679	+	0.795709i	$0.707099\pi$
$4$	1.00000	0.500000
$5$	3.98650	1.78282	0.891409	−	0.453201i	$-0.149718\pi$
$5$	3.98650	1.78282	0.891409	+	0.453201i	$0.149718\pi$
$6$	−2.09814	−0.856560
$7$	1.58307	0.598345	0.299173	−	0.954199i	$-0.403289\pi$
$7$	1.58307	0.598345	0.299173	+	0.954199i	$0.403289\pi$
$8$	1.00000	0.353553
$9$	1.40217	0.467390
$10$	3.98650	1.26064
$11$	3.27907	0.988677	0.494339	−	0.869269i	$-0.335410\pi$
$11$	3.27907	0.988677	0.494339	+	0.869269i	$0.335410\pi$
$12$	−2.09814	−0.605679
$13$	2.09529	0.581130	0.290565	−	0.956855i	$-0.406157\pi$
$13$	2.09529	0.581130	0.290565	+	0.956855i	$0.406157\pi$
$14$	1.58307	0.423094
$15$	−8.36422	−2.15963
$16$	1.00000	0.250000
$17$	3.89492	0.944657	0.472328	−	0.881423i	$-0.343414\pi$
$17$	3.89492	0.944657	0.472328	+	0.881423i	$0.343414\pi$
$18$	1.40217	0.330495
$19$	−2.88949	−0.662895	−0.331447	−	0.943474i	$-0.607537\pi$
$19$	−2.88949	−0.662895	−0.331447	+	0.943474i	$0.607537\pi$
$20$	3.98650	0.891409
$21$	−3.32150	−0.724811
$22$	3.27907	0.699101
$23$	5.91146	1.23262	0.616312	−	0.787502i	$-0.288626\pi$
$23$	5.91146	1.23262	0.616312	+	0.787502i	$0.288626\pi$
$24$	−2.09814	−0.428280
$25$	10.8922	2.17844
$26$	2.09529	0.410921
$27$	3.35246	0.645182
$28$	1.58307	0.299173
$29$	−5.07254	−0.941947	−0.470974	−	0.882147i	$-0.656097\pi$
$29$	−5.07254	−0.941947	−0.470974	+	0.882147i	$0.656097\pi$
$30$	−8.36422	−1.52709
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	−6.87994	−1.19764
$34$	3.89492	0.667973
$35$	6.31092	1.06674
$36$	1.40217	0.233695
$37$	−4.99481	−0.821142	−0.410571	−	0.911829i	$-0.634671\pi$
$37$	−4.99481	−0.821142	−0.410571	+	0.911829i	$0.634671\pi$
$38$	−2.88949	−0.468737
$39$	−4.39621	−0.703957
$40$	3.98650	0.630321
$41$	0.0545720	0.00852271	0.00426136	−	0.999991i	$-0.498644\pi$
$41$	0.0545720	0.00852271	0.00426136	+	0.999991i	$0.498644\pi$
$42$	−3.32150	−0.512519
$43$	9.91490	1.51201	0.756004	−	0.654567i	$-0.227149\pi$
$43$	9.91490	1.51201	0.756004	+	0.654567i	$0.227149\pi$
$44$	3.27907	0.494339
$45$	5.58975	0.833271
$46$	5.91146	0.871597
$47$	0.311181	0.0453903	0.0226952	−	0.999742i	$-0.492775\pi$
$47$	0.311181	0.0453903	0.0226952	+	0.999742i	$0.492775\pi$
$48$	−2.09814	−0.302840
$49$	−4.49388	−0.641983
$50$	10.8922	1.54039
$51$	−8.17207	−1.14432
$52$	2.09529	0.290565
$53$	−2.78066	−0.381952	−0.190976	−	0.981595i	$-0.561165\pi$
$53$	−2.78066	−0.381952	−0.190976	+	0.981595i	$0.561165\pi$
$54$	3.35246	0.456212
$55$	13.0720	1.76263
$56$	1.58307	0.211547
$57$	6.06254	0.803003
$58$	−5.07254	−0.666057
$59$	−3.95399	−0.514765	−0.257383	−	0.966310i	$-0.582860\pi$
$59$	−3.95399	−0.514765	−0.257383	+	0.966310i	$0.582860\pi$
$60$	−8.36422	−1.07982
$61$	−4.74267	−0.607237	−0.303618	−	0.952794i	$-0.598195\pi$
$61$	−4.74267	−0.607237	−0.303618	+	0.952794i	$0.598195\pi$
$62$	−1.00000	−0.127000
$63$	2.21974	0.279661
$64$	1.00000	0.125000
$65$	8.35289	1.03605
$66$	−6.87994	−0.846862
$67$	11.2037	1.36875	0.684377	−	0.729128i	$-0.260074\pi$
$67$	11.2037	1.36875	0.684377	+	0.729128i	$0.260074\pi$
$68$	3.89492	0.472328
$69$	−12.4030	−1.49315
$70$	6.31092	0.754299
$71$	7.07124	0.839202	0.419601	−	0.907709i	$-0.362170\pi$
$71$	7.07124	0.839202	0.419601	+	0.907709i	$0.362170\pi$
$72$	1.40217	0.165247
$73$	4.23578	0.495761	0.247881	−	0.968791i	$-0.420266\pi$
$73$	4.23578	0.495761	0.247881	+	0.968791i	$0.420266\pi$
$74$	−4.99481	−0.580635
$75$	−22.8533	−2.63887
$76$	−2.88949	−0.331447
$77$	5.19101	0.591570
$78$	−4.39621	−0.497773
$79$	−15.6024	−1.75541	−0.877703	−	0.479204i	$-0.840925\pi$
$79$	−15.6024	−1.75541	−0.877703	+	0.479204i	$0.840925\pi$
$80$	3.98650	0.445704
$81$	−11.2404	−1.24894
$82$	0.0545720	0.00602647
$83$	14.1369	1.55172	0.775861	−	0.630904i	$-0.217316\pi$
$83$	14.1369	1.55172	0.775861	+	0.630904i	$0.217316\pi$
$84$	−3.32150	−0.362405
$85$	15.5271	1.68415
$86$	9.91490	1.06915
$87$	10.6429	1.14104
$88$	3.27907	0.349550
$89$	−2.06651	−0.219049	−0.109525	−	0.993984i	$-0.534933\pi$
$89$	−2.06651	−0.219049	−0.109525	+	0.993984i	$0.534933\pi$
$90$	5.58975	0.589212
$91$	3.31700	0.347716
$92$	5.91146	0.616312
$93$	2.09814	0.217566
$94$	0.311181	0.0320958
$95$	−11.5190	−1.18182
$96$	−2.09814	−0.214140
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	−4.49388	−0.453951
$99$	4.59782	0.462098
$100$	10.8922	1.08922
$101$	−11.7200	−1.16619	−0.583094	−	0.812405i	$-0.698158\pi$
$101$	−11.7200	−1.16619	−0.583094	+	0.812405i	$0.698158\pi$
$102$	−8.17207	−0.809155
$103$	9.06347	0.893050	0.446525	−	0.894771i	$-0.352661\pi$
$103$	9.06347	0.893050	0.446525	+	0.894771i	$0.352661\pi$
$104$	2.09529	0.205460
$105$	−13.2412	−1.29221
$106$	−2.78066	−0.270081
$107$	−9.64932	−0.932835	−0.466417	−	0.884565i	$-0.654455\pi$
$107$	−9.64932	−0.932835	−0.466417	+	0.884565i	$0.654455\pi$
$108$	3.35246	0.322591
$109$	−18.0250	−1.72648	−0.863242	−	0.504790i	$-0.831570\pi$
$109$	−18.0250	−1.72648	−0.863242	+	0.504790i	$0.831570\pi$
$110$	13.0720	1.24637
$111$	10.4798	0.994698
$112$	1.58307	0.149586
$113$	−15.1956	−1.42948	−0.714741	−	0.699389i	$-0.753455\pi$
$113$	−15.1956	−1.42948	−0.714741	+	0.699389i	$0.753455\pi$
$114$	6.06254	0.567809
$115$	23.5660	2.19754
$116$	−5.07254	−0.470974
$117$	2.93796	0.271614
$118$	−3.95399	−0.363994
$119$	6.16594	0.565231
$120$	−8.36422	−0.763545
$121$	−0.247687	−0.0225170
$122$	−4.74267	−0.429381
$123$	−0.114499	−0.0103241
$124$	−1.00000	−0.0898027
$125$	23.4892	2.10094
$126$	2.21974	0.197750
$127$	−19.2078	−1.70442	−0.852209	−	0.523201i	$-0.824738\pi$
$127$	−19.2078	−1.70442	−0.852209	+	0.523201i	$0.824738\pi$
$128$	1.00000	0.0883883
$129$	−20.8028	−1.83158
$130$	8.35289	0.732597
$131$	−17.3902	−1.51939	−0.759696	−	0.650278i	$-0.774652\pi$
$131$	−17.3902	−1.51939	−0.759696	+	0.650278i	$0.774652\pi$
$132$	−6.87994	−0.598822
$133$	−4.57427	−0.396640
$134$	11.2037	0.967856
$135$	13.3646	1.15024
$136$	3.89492	0.333987
$137$	15.7084	1.34206	0.671030	−	0.741430i	$-0.265852\pi$
$137$	15.7084	1.34206	0.671030	+	0.741430i	$0.265852\pi$
$138$	−12.4030	−1.05582
$139$	−6.32947	−0.536859	−0.268429	−	0.963299i	$-0.586505\pi$
$139$	−6.32947	−0.536859	−0.268429	+	0.963299i	$0.586505\pi$
$140$	6.31092	0.533370
$141$	−0.652899	−0.0549840
$142$	7.07124	0.593405
$143$	6.87062	0.574550
$144$	1.40217	0.116848
$145$	−20.2217	−1.67932
$146$	4.23578	0.350556
$147$	9.42877	0.777672
$148$	−4.99481	−0.410571
$149$	20.1819	1.65337	0.826683	−	0.562668i	$-0.190225\pi$
$149$	20.1819	1.65337	0.826683	+	0.562668i	$0.190225\pi$
$150$	−22.8533	−1.86596
$151$	−4.52905	−0.368569	−0.184284	−	0.982873i	$-0.558997\pi$
$151$	−4.52905	−0.368569	−0.184284	+	0.982873i	$0.558997\pi$
$152$	−2.88949	−0.234369
$153$	5.46134	0.441523
$154$	5.19101	0.418303
$155$	−3.98650	−0.320203
$156$	−4.39621	−0.351978
$157$	−3.07532	−0.245437	−0.122719	−	0.992442i	$-0.539161\pi$
$157$	−3.07532	−0.245437	−0.122719	+	0.992442i	$0.539161\pi$
$158$	−15.6024	−1.24126
$159$	5.83419	0.462681
$160$	3.98650	0.315161
$161$	9.35827	0.737535
$162$	−11.2404	−0.883132
$163$	16.9420	1.32700	0.663500	−	0.748177i	$-0.269070\pi$
$163$	16.9420	1.32700	0.663500	+	0.748177i	$0.269070\pi$
$164$	0.0545720	0.00426136
$165$	−27.4269	−2.13518
$166$	14.1369	1.09723
$167$	−8.54549	−0.661270	−0.330635	−	0.943759i	$-0.607263\pi$
$167$	−8.54549	−0.661270	−0.330635	+	0.943759i	$0.607263\pi$
$168$	−3.32150	−0.256259
$169$	−8.60975	−0.662288
$170$	15.5271	1.19087
$171$	−4.05156	−0.309830
$172$	9.91490	0.756004
$173$	6.74172	0.512563	0.256282	−	0.966602i	$-0.417503\pi$
$173$	6.74172	0.512563	0.256282	+	0.966602i	$0.417503\pi$
$174$	10.6429	0.806834
$175$	17.2431	1.30346
$176$	3.27907	0.247169
$177$	8.29600	0.623565
$178$	−2.06651	−0.154891
$179$	18.9576	1.41696	0.708479	−	0.705732i	$-0.249382\pi$
$179$	18.9576	1.41696	0.708479	+	0.705732i	$0.249382\pi$
$180$	5.58975	0.416636
$181$	2.90087	0.215620	0.107810	−	0.994172i	$-0.465616\pi$
$181$	2.90087	0.215620	0.107810	+	0.994172i	$0.465616\pi$
$182$	3.31700	0.245872
$183$	9.95077	0.735582
$184$	5.91146	0.435798
$185$	−19.9118	−1.46395
$186$	2.09814	0.153843
$187$	12.7717	0.933961
$188$	0.311181	0.0226952
$189$	5.30719	0.386041
$190$	−11.5190	−0.835673
$191$	8.87080	0.641869	0.320934	−	0.947101i	$-0.396003\pi$
$191$	8.87080	0.641869	0.320934	+	0.947101i	$0.396003\pi$
$192$	−2.09814	−0.151420
$193$	5.41672	0.389904	0.194952	−	0.980813i	$-0.437545\pi$
$193$	5.41672	0.389904	0.194952	+	0.980813i	$0.437545\pi$
$194$	−1.00000	−0.0717958
$195$	−17.5255	−1.25503
$196$	−4.49388	−0.320991
$197$	2.02450	0.144240	0.0721198	−	0.997396i	$-0.477024\pi$
$197$	2.02450	0.144240	0.0721198	+	0.997396i	$0.477024\pi$
$198$	4.59782	0.326753
$199$	−10.4873	−0.743424	−0.371712	−	0.928348i	$-0.621229\pi$
$199$	−10.4873	−0.743424	−0.371712	+	0.928348i	$0.621229\pi$
$200$	10.8922	0.770194
$201$	−23.5070	−1.65805
$202$	−11.7200	−0.824619
$203$	−8.03020	−0.563610
$204$	−8.17207	−0.572159
$205$	0.217551	0.0151944
$206$	9.06347	0.631482
$207$	8.28887	0.576116
$208$	2.09529	0.145282
$209$	−9.47485	−0.655389
$210$	−13.2412	−0.913727
$211$	−5.36798	−0.369547	−0.184774	−	0.982781i	$-0.559155\pi$
$211$	−5.36798	−0.369547	−0.184774	+	0.982781i	$0.559155\pi$
$212$	−2.78066	−0.190976
$213$	−14.8364	−1.01657
$214$	−9.64932	−0.659614
$215$	39.5258	2.69563
$216$	3.35246	0.228106
$217$	−1.58307	−0.107466
$218$	−18.0250	−1.22081
$219$	−8.88725	−0.600545
$220$	13.0720	0.881316
$221$	8.16100	0.548968
$222$	10.4798	0.703357
$223$	14.7021	0.984527	0.492263	−	0.870446i	$-0.336170\pi$
$223$	14.7021	0.984527	0.492263	+	0.870446i	$0.336170\pi$
$224$	1.58307	0.105773
$225$	15.2727	1.01818
$226$	−15.1956	−1.01080
$227$	−13.5200	−0.897356	−0.448678	−	0.893693i	$-0.648105\pi$
$227$	−13.5200	−0.897356	−0.448678	+	0.893693i	$0.648105\pi$
$228$	6.06254	0.401502
$229$	−6.39759	−0.422764	−0.211382	−	0.977403i	$-0.567796\pi$
$229$	−6.39759	−0.422764	−0.211382	+	0.977403i	$0.567796\pi$
$230$	23.5660	1.55390
$231$	−10.8914	−0.716604
$232$	−5.07254	−0.333029
$233$	−17.6923	−1.15906	−0.579531	−	0.814950i	$-0.696764\pi$
$233$	−17.6923	−1.15906	−0.579531	+	0.814950i	$0.696764\pi$
$234$	2.93796	0.192060
$235$	1.24052	0.0809227
$236$	−3.95399	−0.257383
$237$	32.7359	2.12643
$238$	6.16594	0.399679
$239$	−12.6558	−0.818638	−0.409319	−	0.912391i	$-0.634234\pi$
$239$	−12.6558	−0.818638	−0.409319	+	0.912391i	$0.634234\pi$
$240$	−8.36422	−0.539908
$241$	−6.49499	−0.418379	−0.209190	−	0.977875i	$-0.567083\pi$
$241$	−6.49499	−0.418379	−0.209190	+	0.977875i	$0.567083\pi$
$242$	−0.247687	−0.0159219
$243$	13.5266	0.867729
$244$	−4.74267	−0.303618
$245$	−17.9149	−1.14454
$246$	−0.114499	−0.00730022
$247$	−6.05433	−0.385228
$248$	−1.00000	−0.0635001
$249$	−29.6610	−1.87969
$250$	23.4892	1.48559
$251$	10.5969	0.668873	0.334437	−	0.942418i	$-0.391454\pi$
$251$	10.5969	0.668873	0.334437	+	0.942418i	$0.391454\pi$
$252$	2.21974	0.139830
$253$	19.3841	1.21867
$254$	−19.2078	−1.20521
$255$	−32.5779	−2.04011
$256$	1.00000	0.0625000
$257$	13.9082	0.867572	0.433786	−	0.901016i	$-0.357177\pi$
$257$	13.9082	0.867572	0.433786	+	0.901016i	$0.357177\pi$
$258$	−20.8028	−1.29513
$259$	−7.90715	−0.491326
$260$	8.35289	0.518024
$261$	−7.11257	−0.440257
$262$	−17.3902	−1.07437
$263$	5.83540	0.359826	0.179913	−	0.983682i	$-0.442418\pi$
$263$	5.83540	0.359826	0.179913	+	0.983682i	$0.442418\pi$
$264$	−6.87994	−0.423431
$265$	−11.0851	−0.680951
$266$	−4.57427	−0.280467
$267$	4.33581	0.265347
$268$	11.2037	0.684377
$269$	7.16249	0.436705	0.218352	−	0.975870i	$-0.429932\pi$
$269$	7.16249	0.436705	0.218352	+	0.975870i	$0.429932\pi$
$270$	13.3646	0.813343
$271$	18.9899	1.15356	0.576778	−	0.816901i	$-0.304310\pi$
$271$	18.9899	1.15356	0.576778	+	0.816901i	$0.304310\pi$
$272$	3.89492	0.236164
$273$	−6.95952	−0.421209
$274$	15.7084	0.948980
$275$	35.7163	2.15377
$276$	−12.4030	−0.746575
$277$	−29.5974	−1.77834	−0.889168	−	0.457581i	$-0.848716\pi$
$277$	−29.5974	−1.77834	−0.889168	+	0.457581i	$0.848716\pi$
$278$	−6.32947	−0.379616
$279$	−1.40217	−0.0839458
$280$	6.31092	0.377150
$281$	−20.1004	−1.19909	−0.599545	−	0.800341i	$-0.704652\pi$
$281$	−20.1004	−1.19909	−0.599545	+	0.800341i	$0.704652\pi$
$282$	−0.652899	−0.0388796
$283$	−15.1574	−0.901016	−0.450508	−	0.892772i	$-0.648757\pi$
$283$	−15.1574	−0.901016	−0.450508	+	0.892772i	$0.648757\pi$
$284$	7.07124	0.419601
$285$	24.1683	1.43161
$286$	6.87062	0.406268
$287$	0.0863914	0.00509953
$288$	1.40217	0.0826237
$289$	−1.82960	−0.107624
$290$	−20.2217	−1.18746
$291$	2.09814	0.122995
$292$	4.23578	0.247881
$293$	−16.1284	−0.942228	−0.471114	−	0.882072i	$-0.656148\pi$
$293$	−16.1284	−0.942228	−0.471114	+	0.882072i	$0.656148\pi$
$294$	9.42877	0.549897
$295$	−15.7626	−0.917732
$296$	−4.99481	−0.290318
$297$	10.9930	0.637876
$298$	20.1819	1.16911
$299$	12.3862	0.716315
$300$	−22.8533	−1.31943
$301$	15.6960	0.904703
$302$	−4.52905	−0.260617
$303$	24.5902	1.41267
$304$	−2.88949	−0.165724
$305$	−18.9067	−1.08259
$306$	5.46134	0.312204
$307$	−23.7040	−1.35286	−0.676430	−	0.736507i	$-0.736474\pi$
$307$	−23.7040	−1.35286	−0.676430	+	0.736507i	$0.736474\pi$
$308$	5.19101	0.295785
$309$	−19.0164	−1.08180
$310$	−3.98650	−0.226418
$311$	27.6780	1.56947	0.784736	−	0.619830i	$-0.212798\pi$
$311$	27.6780	1.56947	0.784736	+	0.619830i	$0.212798\pi$
$312$	−4.39621	−0.248886
$313$	0.252364	0.0142644	0.00713222	−	0.999975i	$-0.497730\pi$
$313$	0.252364	0.0142644	0.00713222	+	0.999975i	$0.497730\pi$
$314$	−3.07532	−0.173550
$315$	8.84899	0.498584
$316$	−15.6024	−0.877703
$317$	19.9126	1.11840	0.559201	−	0.829032i	$-0.311108\pi$
$317$	19.9126	1.11840	0.559201	+	0.829032i	$0.311108\pi$
$318$	5.83419	0.327165
$319$	−16.6332	−0.931282
$320$	3.98650	0.222852
$321$	20.2456	1.13000
$322$	9.35827	0.521516
$323$	−11.2543	−0.626208
$324$	−11.2404	−0.624468
$325$	22.8223	1.26595
$326$	16.9420	0.938330
$327$	37.8189	2.09139
$328$	0.0545720	0.00301323
$329$	0.492621	0.0271591
$330$	−27.4269	−1.50980
$331$	22.9446	1.26115	0.630574	−	0.776129i	$-0.282819\pi$
$331$	22.9446	1.26115	0.630574	+	0.776129i	$0.282819\pi$
$332$	14.1369	0.775861
$333$	−7.00358	−0.383794
$334$	−8.54549	−0.467588
$335$	44.6637	2.44024
$336$	−3.32150	−0.181203
$337$	−0.0455247	−0.00247989	−0.00123994	−	0.999999i	$-0.500395\pi$
$337$	−0.0455247	−0.00247989	−0.00123994	+	0.999999i	$0.500395\pi$
$338$	−8.60975	−0.468308
$339$	31.8824	1.73162
$340$	15.5271	0.842075
$341$	−3.27907	−0.177572
$342$	−4.05156	−0.219083
$343$	−18.1956	−0.982473
$344$	9.91490	0.534576
$345$	−49.4447	−2.66201
$346$	6.74172	0.362437
$347$	23.0761	1.23879	0.619394	−	0.785080i	$-0.287378\pi$
$347$	23.0761	1.23879	0.619394	+	0.785080i	$0.287378\pi$
$348$	10.6429	0.570518
$349$	−6.25871	−0.335021	−0.167511	−	0.985870i	$-0.553573\pi$
$349$	−6.25871	−0.335021	−0.167511	+	0.985870i	$0.553573\pi$
$350$	17.2431	0.921684
$351$	7.02439	0.374934
$352$	3.27907	0.174775
$353$	6.81508	0.362730	0.181365	−	0.983416i	$-0.441948\pi$
$353$	6.81508	0.362730	0.181365	+	0.983416i	$0.441948\pi$
$354$	8.29600	0.440927
$355$	28.1895	1.49614
$356$	−2.06651	−0.109525
$357$	−12.9370	−0.684697
$358$	18.9576	1.00194
$359$	22.0473	1.16361	0.581806	−	0.813328i	$-0.302346\pi$
$359$	22.0473	1.16361	0.581806	+	0.813328i	$0.302346\pi$
$360$	5.58975	0.294606
$361$	−10.6508	−0.560571
$362$	2.90087	0.152466
$363$	0.519680	0.0272761
$364$	3.31700	0.173858
$365$	16.8860	0.883851
$366$	9.95077	0.520135
$367$	32.3974	1.69113	0.845564	−	0.533873i	$-0.179264\pi$
$367$	32.3974	1.69113	0.845564	+	0.533873i	$0.179264\pi$
$368$	5.91146	0.308156
$369$	0.0765192	0.00398343
$370$	−19.9118	−1.03517
$371$	−4.40198	−0.228539
$372$	2.09814	0.108783
$373$	5.88461	0.304694	0.152347	−	0.988327i	$-0.451317\pi$
$373$	5.88461	0.304694	0.152347	+	0.988327i	$0.451317\pi$
$374$	12.7717	0.660410
$375$	−49.2835	−2.54499
$376$	0.311181	0.0160479
$377$	−10.6285	−0.547394
$378$	5.30719	0.272972
$379$	35.7682	1.83729	0.918645	−	0.395083i	$-0.129284\pi$
$379$	35.7682	1.83729	0.918645	+	0.395083i	$0.129284\pi$
$380$	−11.5190	−0.590910
$381$	40.3006	2.06466
$382$	8.87080	0.453870
$383$	21.6884	1.10823	0.554113	−	0.832441i	$-0.313057\pi$
$383$	21.6884	1.10823	0.554113	+	0.832441i	$0.313057\pi$
$384$	−2.09814	−0.107070
$385$	20.6940	1.05466
$386$	5.41672	0.275704
$387$	13.9024	0.706698
$388$	−1.00000	−0.0507673
$389$	21.0275	1.06614	0.533068	−	0.846072i	$-0.321039\pi$
$389$	21.0275	1.06614	0.533068	+	0.846072i	$0.321039\pi$
$390$	−17.5255	−0.887437
$391$	23.0247	1.16441
$392$	−4.49388	−0.226975
$393$	36.4871	1.84053
$394$	2.02450	0.101993
$395$	−62.1990	−3.12957
$396$	4.59782	0.231049
$397$	−20.8252	−1.04519	−0.522593	−	0.852582i	$-0.675035\pi$
$397$	−20.8252	−1.04519	−0.522593	+	0.852582i	$0.675035\pi$
$398$	−10.4873	−0.525680
$399$	9.59745	0.480473
$400$	10.8922	0.544609
$401$	2.87029	0.143335	0.0716677	−	0.997429i	$-0.477168\pi$
$401$	2.87029	0.143335	0.0716677	+	0.997429i	$0.477168\pi$
$402$	−23.5070	−1.17242
$403$	−2.09529	−0.104374
$404$	−11.7200	−0.583094
$405$	−44.8100	−2.22663
$406$	−8.03020	−0.398532
$407$	−16.3783	−0.811845
$408$	−8.17207	−0.404578
$409$	−10.9325	−0.540578	−0.270289	−	0.962779i	$-0.587119\pi$
$409$	−10.9325	−0.540578	−0.270289	+	0.962779i	$0.587119\pi$
$410$	0.217551	0.0107441
$411$	−32.9584	−1.62572
$412$	9.06347	0.446525
$413$	−6.25945	−0.308007
$414$	8.28887	0.407376
$415$	56.3566	2.76644
$416$	2.09529	0.102730
$417$	13.2801	0.650329
$418$	−9.47485	−0.463430
$419$	20.7569	1.01404	0.507020	−	0.861934i	$-0.330747\pi$
$419$	20.7569	1.01404	0.507020	+	0.861934i	$0.330747\pi$
$420$	−13.2412	−0.646103
$421$	5.72546	0.279042	0.139521	−	0.990219i	$-0.455444\pi$
$421$	5.72546	0.279042	0.139521	+	0.990219i	$0.455444\pi$
$422$	−5.36798	−0.261309
$423$	0.436328	0.0212150
$424$	−2.78066	−0.135041
$425$	42.4242	2.05788
$426$	−14.8364	−0.718827
$427$	−7.50799	−0.363337
$428$	−9.64932	−0.466417
$429$	−14.4155	−0.695986
$430$	39.5258	1.90610
$431$	−28.1348	−1.35521	−0.677603	−	0.735428i	$-0.736981\pi$
$431$	−28.1348	−1.35521	−0.677603	+	0.735428i	$0.736981\pi$
$432$	3.35246	0.161295
$433$	14.7114	0.706985	0.353492	−	0.935437i	$-0.384994\pi$
$433$	14.7114	0.706985	0.353492	+	0.935437i	$0.384994\pi$
$434$	−1.58307	−0.0759899
$435$	42.4278	2.03426
$436$	−18.0250	−0.863242
$437$	−17.0811	−0.817100
$438$	−8.88725	−0.424649
$439$	−31.7022	−1.51307	−0.756533	−	0.653956i	$-0.773108\pi$
$439$	−31.7022	−1.51307	−0.756533	+	0.653956i	$0.773108\pi$
$440$	13.0720	0.623184
$441$	−6.30119	−0.300057
$442$	8.16100	0.388179
$443$	−12.9825	−0.616817	−0.308409	−	0.951254i	$-0.599796\pi$
$443$	−12.9825	−0.616817	−0.308409	+	0.951254i	$0.599796\pi$
$444$	10.4798	0.497349
$445$	−8.23813	−0.390525
$446$	14.7021	0.696165
$447$	−42.3444	−2.00282
$448$	1.58307	0.0747932
$449$	22.6929	1.07094	0.535472	−	0.844553i	$-0.320134\pi$
$449$	22.6929	1.07094	0.535472	+	0.844553i	$0.320134\pi$
$450$	15.2727	0.719962
$451$	0.178946	0.00842622
$452$	−15.1956	−0.714741
$453$	9.50256	0.446469
$454$	−13.5200	−0.634527
$455$	13.2232	0.619914
$456$	6.06254	0.283905
$457$	4.95142	0.231618	0.115809	−	0.993272i	$-0.463054\pi$
$457$	4.95142	0.231618	0.115809	+	0.993272i	$0.463054\pi$
$458$	−6.39759	−0.298940
$459$	13.0576	0.609475
$460$	23.5660	1.09877
$461$	32.4773	1.51262	0.756309	−	0.654215i	$-0.227001\pi$
$461$	32.4773	1.51262	0.756309	+	0.654215i	$0.227001\pi$
$462$	−10.8914	−0.506716
$463$	31.3873	1.45869	0.729345	−	0.684146i	$-0.239825\pi$
$463$	31.3873	1.45869	0.729345	+	0.684146i	$0.239825\pi$
$464$	−5.07254	−0.235487
$465$	8.36422	0.387881
$466$	−17.6923	−0.819581
$467$	1.86473	0.0862892	0.0431446	−	0.999069i	$-0.486262\pi$
$467$	1.86473	0.0862892	0.0431446	+	0.999069i	$0.486262\pi$
$468$	2.93796	0.135807
$469$	17.7363	0.818988
$470$	1.24052	0.0572210
$471$	6.45243	0.297312
$472$	−3.95399	−0.181997
$473$	32.5117	1.49489
$474$	32.7359	1.50361
$475$	−31.4729	−1.44407
$476$	6.16594	0.282615
$477$	−3.89895	−0.178521
$478$	−12.6558	−0.578864
$479$	26.2801	1.20077	0.600384	−	0.799712i	$-0.295014\pi$
$479$	26.2801	1.20077	0.600384	+	0.799712i	$0.295014\pi$
$480$	−8.36422	−0.381772
$481$	−10.4656	−0.477190
$482$	−6.49499	−0.295839
$483$	−19.6349	−0.893419
$484$	−0.247687	−0.0112585
$485$	−3.98650	−0.181018
$486$	13.5266	0.613577
$487$	−23.4541	−1.06281	−0.531403	−	0.847119i	$-0.678335\pi$
$487$	−23.4541	−1.06281	−0.531403	+	0.847119i	$0.678335\pi$
$488$	−4.74267	−0.214691
$489$	−35.5466	−1.60747
$490$	−17.9149	−0.809311
$491$	−21.8003	−0.983834	−0.491917	−	0.870642i	$-0.663704\pi$
$491$	−21.8003	−0.983834	−0.491917	+	0.870642i	$0.663704\pi$
$492$	−0.114499	−0.00516203
$493$	−19.7571	−0.889817
$494$	−6.05433	−0.272397
$495$	18.3292	0.823836
$496$	−1.00000	−0.0449013
$497$	11.1943	0.502132
$498$	−29.6610	−1.32914
$499$	19.2554	0.861988	0.430994	−	0.902355i	$-0.358163\pi$
$499$	19.2554	0.861988	0.430994	+	0.902355i	$0.358163\pi$
$500$	23.4892	1.05047
$501$	17.9296	0.801035
$502$	10.5969	0.472965
$503$	24.4373	1.08961	0.544803	−	0.838564i	$-0.316604\pi$
$503$	24.4373	1.08961	0.544803	+	0.838564i	$0.316604\pi$
$504$	2.21974	0.0988750
$505$	−46.7220	−2.07910
$506$	19.3841	0.861728
$507$	18.0644	0.802269
$508$	−19.2078	−0.852209
$509$	36.6637	1.62509	0.812544	−	0.582899i	$-0.198082\pi$
$509$	36.6637	1.62509	0.812544	+	0.582899i	$0.198082\pi$
$510$	−32.5779	−1.44258
$511$	6.70555	0.296636
$512$	1.00000	0.0441942
$513$	−9.68691	−0.427687
$514$	13.9082	0.613466
$515$	36.1315	1.59215
$516$	−20.8028	−0.915792
$517$	1.02038	0.0448764
$518$	−7.90715	−0.347420
$519$	−14.1450	−0.620898
$520$	8.35289	0.366298
$521$	−28.0279	−1.22792	−0.613962	−	0.789335i	$-0.710425\pi$
$521$	−28.0279	−1.22792	−0.613962	+	0.789335i	$0.710425\pi$
$522$	−7.11257	−0.311309
$523$	31.7877	1.38998	0.694989	−	0.719020i	$-0.255409\pi$
$523$	31.7877	1.38998	0.694989	+	0.719020i	$0.255409\pi$
$524$	−17.3902	−0.759696
$525$	−36.1784	−1.57895
$526$	5.83540	0.254436
$527$	−3.89492	−0.169665
$528$	−6.87994	−0.299411
$529$	11.9453	0.519362
$530$	−11.0851	−0.481505
$531$	−5.54416	−0.240596
$532$	−4.57427	−0.198320
$533$	0.114344	0.00495280
$534$	4.33581	0.187629
$535$	−38.4670	−1.66307
$536$	11.2037	0.483928
$537$	−39.7756	−1.71644
$538$	7.16249	0.308797
$539$	−14.7358	−0.634714
$540$	13.3646	0.575120
$541$	12.0380	0.517554	0.258777	−	0.965937i	$-0.416681\pi$
$541$	12.0380	0.517554	0.258777	+	0.965937i	$0.416681\pi$
$542$	18.9899	0.815687
$543$	−6.08641	−0.261193
$544$	3.89492	0.166993
$545$	−71.8568	−3.07801
$546$	−6.95952	−0.297840
$547$	−40.9270	−1.74991	−0.874955	−	0.484204i	$-0.839109\pi$
$547$	−40.9270	−1.74991	−0.874955	+	0.484204i	$0.839109\pi$
$548$	15.7084	0.671030
$549$	−6.65003	−0.283817
$550$	35.7163	1.52295
$551$	14.6571	0.624412
$552$	−12.4030	−0.527908
$553$	−24.6997	−1.05034
$554$	−29.5974	−1.25747
$555$	41.7777	1.77336
$556$	−6.32947	−0.268429
$557$	−34.6831	−1.46957	−0.734784	−	0.678301i	$-0.762717\pi$
$557$	−34.6831	−1.46957	−0.734784	+	0.678301i	$0.762717\pi$
$558$	−1.40217	−0.0593586
$559$	20.7746	0.878673
$560$	6.31092	0.266685
$561$	−26.7968	−1.13136
$562$	−20.1004	−0.847884
$563$	−5.99859	−0.252810	−0.126405	−	0.991979i	$-0.540344\pi$
$563$	−5.99859	−0.252810	−0.126405	+	0.991979i	$0.540344\pi$
$564$	−0.652899	−0.0274920
$565$	−60.5773	−2.54850
$566$	−15.1574	−0.637115
$567$	−17.7944	−0.747295
$568$	7.07124	0.296703
$569$	22.3448	0.936742	0.468371	−	0.883532i	$-0.344841\pi$
$569$	22.3448	0.936742	0.468371	+	0.883532i	$0.344841\pi$
$570$	24.1683	1.01230
$571$	−25.2689	−1.05747	−0.528735	−	0.848787i	$-0.677333\pi$
$571$	−25.2689	−1.05747	−0.528735	+	0.848787i	$0.677333\pi$
$572$	6.87062	0.287275
$573$	−18.6121	−0.777533
$574$	0.0863914	0.00360591
$575$	64.3887	2.68519
$576$	1.40217	0.0584238
$577$	25.0426	1.04254	0.521268	−	0.853393i	$-0.325459\pi$
$577$	25.0426	1.04254	0.521268	+	0.853393i	$0.325459\pi$
$578$	−1.82960	−0.0761015
$579$	−11.3650	−0.472313
$580$	−20.2217	−0.839660
$581$	22.3797	0.928465
$582$	2.09814	0.0869705
$583$	−9.11797	−0.377628
$584$	4.23578	0.175278
$585$	11.7122	0.484239
$586$	−16.1284	−0.666256
$587$	−37.6545	−1.55417	−0.777083	−	0.629398i	$-0.783302\pi$
$587$	−37.6545	−1.55417	−0.777083	+	0.629398i	$0.783302\pi$
$588$	9.42877	0.388836
$589$	2.88949	0.119059
$590$	−15.7626	−0.648935
$591$	−4.24767	−0.174726
$592$	−4.99481	−0.205286
$593$	3.45736	0.141977	0.0709884	−	0.997477i	$-0.477385\pi$
$593$	3.45736	0.141977	0.0709884	+	0.997477i	$0.477385\pi$
$594$	10.9930	0.451047
$595$	24.5805	1.00770
$596$	20.1819	0.826683
$597$	22.0037	0.900553
$598$	12.3862	0.506511
$599$	−46.6833	−1.90743	−0.953715	−	0.300713i	$-0.902775\pi$
$599$	−46.6833	−1.90743	−0.953715	+	0.300713i	$0.902775\pi$
$600$	−22.8533	−0.932981
$601$	23.4163	0.955170	0.477585	−	0.878586i	$-0.341512\pi$
$601$	23.4163	0.955170	0.477585	+	0.878586i	$0.341512\pi$
$602$	15.6960	0.639722
$603$	15.7096	0.639742
$604$	−4.52905	−0.184284
$605$	−0.987403	−0.0401436
$606$	24.5902	0.998910
$607$	−26.0126	−1.05582	−0.527910	−	0.849301i	$-0.677024\pi$
$607$	−26.0126	−1.05582	−0.527910	+	0.849301i	$0.677024\pi$
$608$	−2.88949	−0.117184
$609$	16.8484	0.682734
$610$	−18.9067	−0.765508
$611$	0.652014	0.0263777
$612$	5.46134	0.220762
$613$	40.1251	1.62064	0.810319	−	0.585988i	$-0.199294\pi$
$613$	40.1251	1.62064	0.810319	+	0.585988i	$0.199294\pi$
$614$	−23.7040	−0.956617
$615$	−0.456452	−0.0184059
$616$	5.19101	0.209152
$617$	−35.5387	−1.43074	−0.715368	−	0.698748i	$-0.753741\pi$
$617$	−35.5387	−1.43074	−0.715368	+	0.698748i	$0.753741\pi$
$618$	−19.0164	−0.764951
$619$	−15.2975	−0.614860	−0.307430	−	0.951571i	$-0.599469\pi$
$619$	−15.2975	−0.614860	−0.307430	+	0.951571i	$0.599469\pi$
$620$	−3.98650	−0.160102
$621$	19.8179	0.795266
$622$	27.6780	1.10978
$623$	−3.27143	−0.131067
$624$	−4.39621	−0.175989
$625$	39.1788	1.56715
$626$	0.252364	0.0100865
$627$	19.8795	0.793911
$628$	−3.07532	−0.122719
$629$	−19.4544	−0.775697
$630$	8.84899	0.352552
$631$	8.09128	0.322109	0.161054	−	0.986946i	$-0.448511\pi$
$631$	8.09128	0.322109	0.161054	+	0.986946i	$0.448511\pi$
$632$	−15.6024	−0.620630
$633$	11.2628	0.447654
$634$	19.9126	0.790830
$635$	−76.5720	−3.03867
$636$	5.83419	0.231341
$637$	−9.41600	−0.373075
$638$	−16.6332	−0.658516
$639$	9.91508	0.392235
$640$	3.98650	0.157580
$641$	14.6286	0.577794	0.288897	−	0.957360i	$-0.406711\pi$
$641$	14.6286	0.577794	0.288897	+	0.957360i	$0.406711\pi$
$642$	20.2456	0.799029
$643$	−27.8405	−1.09792	−0.548962	−	0.835847i	$-0.684977\pi$
$643$	−27.8405	−1.09792	−0.548962	+	0.835847i	$0.684977\pi$
$644$	9.35827	0.368767
$645$	−82.9304	−3.26538
$646$	−11.2543	−0.442796
$647$	−5.56847	−0.218919	−0.109460	−	0.993991i	$-0.534912\pi$
$647$	−5.56847	−0.218919	−0.109460	+	0.993991i	$0.534912\pi$
$648$	−11.2404	−0.441566
$649$	−12.9654	−0.508937
$650$	22.8223	0.895165
$651$	3.32150	0.130180
$652$	16.9420	0.663500
$653$	−12.4233	−0.486160	−0.243080	−	0.970006i	$-0.578158\pi$
$653$	−12.4233	−0.486160	−0.243080	+	0.970006i	$0.578158\pi$
$654$	37.8189	1.47884
$655$	−69.3262	−2.70880
$656$	0.0545720	0.00213068
$657$	5.93929	0.231714
$658$	0.492621	0.0192044
$659$	13.9759	0.544425	0.272213	−	0.962237i	$-0.412245\pi$
$659$	13.9759	0.544425	0.272213	+	0.962237i	$0.412245\pi$
$660$	−27.4269	−1.06759
$661$	20.5173	0.798030	0.399015	−	0.916944i	$-0.369352\pi$
$661$	20.5173	0.798030	0.399015	+	0.916944i	$0.369352\pi$
$662$	22.9446	0.891767
$663$	−17.1229	−0.664997
$664$	14.1369	0.548617
$665$	−18.2353	−0.707136
$666$	−7.00358	−0.271383
$667$	−29.9861	−1.16107
$668$	−8.54549	−0.330635
$669$	−30.8470	−1.19261
$670$	44.6637	1.72551
$671$	−15.5516	−0.600361
$672$	−3.32150	−0.128130
$673$	1.72964	0.0666729	0.0333364	−	0.999444i	$-0.489387\pi$
$673$	1.72964	0.0666729	0.0333364	+	0.999444i	$0.489387\pi$
$674$	−0.0455247	−0.00175354
$675$	36.5156	1.40549
$676$	−8.60975	−0.331144
$677$	7.40839	0.284728	0.142364	−	0.989814i	$-0.454530\pi$
$677$	7.40839	0.284728	0.142364	+	0.989814i	$0.454530\pi$
$678$	31.8824	1.22444
$679$	−1.58307	−0.0607528
$680$	15.5271	0.595437
$681$	28.3669	1.08702
$682$	−3.27907	−0.125562
$683$	2.93227	0.112200	0.0561000	−	0.998425i	$-0.482133\pi$
$683$	2.93227	0.112200	0.0561000	+	0.998425i	$0.482133\pi$
$684$	−4.05156	−0.154915
$685$	62.6216	2.39265
$686$	−18.1956	−0.694713
$687$	13.4230	0.512119
$688$	9.91490	0.378002
$689$	−5.82629	−0.221964
$690$	−49.4447	−1.88233
$691$	−46.9385	−1.78563	−0.892813	−	0.450428i	$-0.851271\pi$
$691$	−46.9385	−1.78563	−0.892813	+	0.450428i	$0.851271\pi$
$692$	6.74172	0.256282
$693$	7.27868	0.276494
$694$	23.0761	0.875956
$695$	−25.2324	−0.957121
$696$	10.6429	0.403417
$697$	0.212554	0.00805104
$698$	−6.25871	−0.236896
$699$	37.1209	1.40404
$700$	17.2431	0.651729
$701$	39.5760	1.49476	0.747382	−	0.664394i	$-0.231310\pi$
$701$	39.5760	1.49476	0.747382	+	0.664394i	$0.231310\pi$
$702$	7.02439	0.265119
$703$	14.4325	0.544331
$704$	3.27907	0.123585
$705$	−2.60278	−0.0980264
$706$	6.81508	0.256489
$707$	−18.5537	−0.697783
$708$	8.29600	0.311783
$709$	12.4440	0.467344	0.233672	−	0.972315i	$-0.424926\pi$
$709$	12.4440	0.467344	0.233672	+	0.972315i	$0.424926\pi$
$710$	28.1895	1.05793
$711$	−21.8772	−0.820460
$712$	−2.06651	−0.0774456
$713$	−5.91146	−0.221386
$714$	−12.9370	−0.484154
$715$	27.3897	1.02432
$716$	18.9576	0.708479
$717$	26.5536	0.991664
$718$	22.0473	0.822798
$719$	−9.09952	−0.339355	−0.169677	−	0.985500i	$-0.554273\pi$
$719$	−9.09952	−0.339355	−0.169677	+	0.985500i	$0.554273\pi$
$720$	5.58975	0.208318
$721$	14.3481	0.534352
$722$	−10.6508	−0.396383
$723$	13.6274	0.506807
$724$	2.90087	0.107810
$725$	−55.2511	−2.05197
$726$	0.519680	0.0192871
$727$	29.9894	1.11224	0.556122	−	0.831101i	$-0.312289\pi$
$727$	29.9894	1.11224	0.556122	+	0.831101i	$0.312289\pi$
$728$	3.31700	0.122936
$729$	5.34075	0.197806
$730$	16.8860	0.624977
$731$	38.6177	1.42833
$732$	9.95077	0.367791
$733$	−32.2361	−1.19067	−0.595334	−	0.803478i	$-0.702980\pi$
$733$	−32.2361	−1.19067	−0.595334	+	0.803478i	$0.702980\pi$
$734$	32.3974	1.19581
$735$	37.5878	1.38645
$736$	5.91146	0.217899
$737$	36.7379	1.35326
$738$	0.0765192	0.00281671
$739$	1.58859	0.0584371	0.0292186	−	0.999573i	$-0.490698\pi$
$739$	1.58859	0.0584371	0.0292186	+	0.999573i	$0.490698\pi$
$740$	−19.9118	−0.731973
$741$	12.7028	0.466649
$742$	−4.40198	−0.161602
$743$	25.3208	0.928929	0.464465	−	0.885592i	$-0.346247\pi$
$743$	25.3208	0.928929	0.464465	+	0.885592i	$0.346247\pi$
$744$	2.09814	0.0769214
$745$	80.4552	2.94765
$746$	5.88461	0.215451
$747$	19.8223	0.725260
$748$	12.7717	0.466980
$749$	−15.2756	−0.558157
$750$	−49.2835	−1.79958
$751$	−46.3146	−1.69004	−0.845022	−	0.534731i	$-0.820413\pi$
$751$	−46.3146	−1.69004	−0.845022	+	0.534731i	$0.820413\pi$
$752$	0.311181	0.0113476
$753$	−22.2338	−0.810246
$754$	−10.6285	−0.387066
$755$	−18.0551	−0.657091
$756$	5.30719	0.193021
$757$	−20.7999	−0.755985	−0.377993	−	0.925809i	$-0.623386\pi$
$757$	−20.7999	−0.755985	−0.377993	+	0.925809i	$0.623386\pi$
$758$	35.7682	1.29916
$759$	−40.6705	−1.47624
$760$	−11.5190	−0.417837
$761$	−40.7165	−1.47597	−0.737985	−	0.674817i	$-0.764223\pi$
$761$	−40.7165	−1.47597	−0.737985	+	0.674817i	$0.764223\pi$
$762$	40.3006	1.45994
$763$	−28.5349	−1.03303
$764$	8.87080	0.320934
$765$	21.7716	0.787155
$766$	21.6884	0.783634
$767$	−8.28476	−0.299145
$768$	−2.09814	−0.0757099
$769$	−19.8033	−0.714125	−0.357062	−	0.934081i	$-0.616222\pi$
$769$	−19.8033	−0.714125	−0.357062	+	0.934081i	$0.616222\pi$
$770$	20.6940	0.745759
$771$	−29.1813	−1.05094
$772$	5.41672	0.194952
$773$	13.4439	0.483545	0.241773	−	0.970333i	$-0.422271\pi$
$773$	13.4439	0.483545	0.241773	+	0.970333i	$0.422271\pi$
$774$	13.9024	0.499711
$775$	−10.8922	−0.391259
$776$	−1.00000	−0.0358979
$777$	16.5903	0.595173
$778$	21.0275	0.753873
$779$	−0.157685	−0.00564966
$780$	−17.5255	−0.627513
$781$	23.1871	0.829700
$782$	23.0247	0.823360
$783$	−17.0055	−0.607727
$784$	−4.49388	−0.160496
$785$	−12.2598	−0.437569
$786$	36.4871	1.30145
$787$	−42.1285	−1.50172	−0.750860	−	0.660462i	$-0.770361\pi$
$787$	−42.1285	−1.50172	−0.750860	+	0.660462i	$0.770361\pi$
$788$	2.02450	0.0721198
$789$	−12.2435	−0.435879
$790$	−62.1990	−2.21294
$791$	−24.0557	−0.855324
$792$	4.59782	0.163376
$793$	−9.93729	−0.352883
$794$	−20.8252	−0.739058
$795$	23.2580	0.824876
$796$	−10.4873	−0.371712
$797$	5.03742	0.178435	0.0892173	−	0.996012i	$-0.471563\pi$
$797$	5.03742	0.178435	0.0892173	+	0.996012i	$0.471563\pi$
$798$	9.59745	0.339746
$799$	1.21202	0.0428783
$800$	10.8922	0.385097
$801$	−2.89759	−0.102381
$802$	2.87029	0.101353
$803$	13.8894	0.490148
$804$	−23.5070	−0.829026
$805$	37.3067	1.31489
$806$	−2.09529	−0.0738036
$807$	−15.0279	−0.529006
$808$	−11.7200	−0.412310
$809$	−32.4448	−1.14070	−0.570349	−	0.821403i	$-0.693192\pi$
$809$	−32.4448	−1.14070	−0.570349	+	0.821403i	$0.693192\pi$
$810$	−44.8100	−1.57446
$811$	−2.92359	−0.102661	−0.0513305	−	0.998682i	$-0.516346\pi$
$811$	−2.92359	−0.102661	−0.0513305	+	0.998682i	$0.516346\pi$
$812$	−8.03020	−0.281805
$813$	−39.8434	−1.39737
$814$	−16.3783	−0.574061
$815$	67.5393	2.36580
$816$	−8.17207	−0.286080
$817$	−28.6490	−1.00230
$818$	−10.9325	−0.382246
$819$	4.65100	0.162519
$820$	0.217551	0.00759722
$821$	−48.5981	−1.69609	−0.848043	−	0.529927i	$-0.822219\pi$
$821$	−48.5981	−1.69609	−0.848043	+	0.529927i	$0.822219\pi$
$822$	−32.9584	−1.14955
$823$	14.5207	0.506160	0.253080	−	0.967445i	$-0.418556\pi$
$823$	14.5207	0.506160	0.253080	+	0.967445i	$0.418556\pi$
$824$	9.06347	0.315741
$825$	−74.9375	−2.60899
$826$	−6.25945	−0.217794
$827$	−28.6531	−0.996365	−0.498182	−	0.867072i	$-0.665999\pi$
$827$	−28.6531	−0.996365	−0.498182	+	0.867072i	$0.665999\pi$
$828$	8.28887	0.288058
$829$	10.2588	0.356303	0.178151	−	0.984003i	$-0.442988\pi$
$829$	10.2588	0.356303	0.178151	+	0.984003i	$0.442988\pi$
$830$	56.3566	1.95617
$831$	62.0994	2.15420
$832$	2.09529	0.0726412
$833$	−17.5033	−0.606454
$834$	13.2801	0.459852
$835$	−34.0666	−1.17892
$836$	−9.47485	−0.327695
$837$	−3.35246	−0.115878
$838$	20.7569	0.717035
$839$	−25.4071	−0.877149	−0.438575	−	0.898695i	$-0.644516\pi$
$839$	−25.4071	−0.877149	−0.438575	+	0.898695i	$0.644516\pi$
$840$	−13.2412	−0.456864
$841$	−3.26932	−0.112735
$842$	5.72546	0.197312
$843$	42.1733	1.45253
$844$	−5.36798	−0.184774
$845$	−34.3228	−1.18074
$846$	0.436328	0.0150013
$847$	−0.392106	−0.0134729
$848$	−2.78066	−0.0954881
$849$	31.8023	1.09145
$850$	42.4242	1.45514
$851$	−29.5266	−1.01216
$852$	−14.8364	−0.508287
$853$	−32.2421	−1.10395	−0.551975	−	0.833861i	$-0.686126\pi$
$853$	−32.2421	−1.10395	−0.551975	+	0.833861i	$0.686126\pi$
$854$	−7.50799	−0.256918
$855$	−16.1515	−0.552371
$856$	−9.64932	−0.329807
$857$	−25.1140	−0.857879	−0.428940	−	0.903333i	$-0.641113\pi$
$857$	−25.1140	−0.857879	−0.428940	+	0.903333i	$0.641113\pi$
$858$	−14.4155	−0.492136
$859$	0.881443	0.0300744	0.0150372	−	0.999887i	$-0.495213\pi$
$859$	0.881443	0.0300744	0.0150372	+	0.999887i	$0.495213\pi$
$860$	39.5258	1.34782
$861$	−0.181261	−0.00617736
$862$	−28.1348	−0.958276
$863$	−41.9822	−1.42909	−0.714545	−	0.699590i	$-0.753366\pi$
$863$	−41.9822	−1.42909	−0.714545	+	0.699590i	$0.753366\pi$
$864$	3.35246	0.114053
$865$	26.8759	0.913807
$866$	14.7114	0.499914
$867$	3.83875	0.130371
$868$	−1.58307	−0.0537330
$869$	−51.1614	−1.73553
$870$	42.4278	1.43844
$871$	23.4751	0.795424
$872$	−18.0250	−0.610404
$873$	−1.40217	−0.0474563
$874$	−17.0811	−0.577777
$875$	37.1851	1.25709
$876$	−8.88725	−0.300272
$877$	54.3889	1.83658	0.918291	−	0.395907i	$-0.129570\pi$
$877$	54.3889	1.83658	0.918291	+	0.395907i	$0.129570\pi$
$878$	−31.7022	−1.06990
$879$	33.8395	1.14138
$880$	13.0720	0.440658
$881$	4.93217	0.166169	0.0830845	−	0.996543i	$-0.473523\pi$
$881$	4.93217	0.166169	0.0830845	+	0.996543i	$0.473523\pi$
$882$	−6.30119	−0.212172
$883$	−18.6291	−0.626918	−0.313459	−	0.949602i	$-0.601488\pi$
$883$	−18.6291	−0.626918	−0.313459	+	0.949602i	$0.601488\pi$
$884$	8.16100	0.274484
$885$	33.0720	1.11170
$886$	−12.9825	−0.436156
$887$	53.0518	1.78130	0.890652	−	0.454686i	$-0.150248\pi$
$887$	53.0518	1.78130	0.890652	+	0.454686i	$0.150248\pi$
$888$	10.4798	0.351679
$889$	−30.4074	−1.01983
$890$	−8.23813	−0.276143
$891$	−36.8582	−1.23480
$892$	14.7021	0.492263
$893$	−0.899153	−0.0300890
$894$	−42.3444	−1.41621
$895$	75.5745	2.52618
$896$	1.58307	0.0528867
$897$	−25.9880	−0.867714
$898$	22.6929	0.757271
$899$	5.07254	0.169179
$900$	15.2727	0.509090
$901$	−10.8304	−0.360814
$902$	0.178946	0.00595823
$903$	−32.9324	−1.09592
$904$	−15.1956	−0.505398
$905$	11.5643	0.384411
$906$	9.50256	0.315701
$907$	−46.6358	−1.54852	−0.774259	−	0.632869i	$-0.781877\pi$
$907$	−46.6358	−1.54852	−0.774259	+	0.632869i	$0.781877\pi$
$908$	−13.5200	−0.448678
$909$	−16.4335	−0.545065
$910$	13.2232	0.438346
$911$	−12.9906	−0.430396	−0.215198	−	0.976570i	$-0.569040\pi$
$911$	−12.9906	−0.430396	−0.215198	+	0.976570i	$0.569040\pi$
$912$	6.06254	0.200751
$913$	46.3558	1.53415
$914$	4.95142	0.163778
$915$	39.6687	1.31141
$916$	−6.39759	−0.211382
$917$	−27.5300	−0.909121
$918$	13.0576	0.430964
$919$	−55.0862	−1.81713	−0.908564	−	0.417746i	$-0.862820\pi$
$919$	−55.0862	−1.81713	−0.908564	+	0.417746i	$0.862820\pi$
$920$	23.5660	0.776949
$921$	49.7343	1.63880
$922$	32.4773	1.06958
$923$	14.8163	0.487685
$924$	−10.8914	−0.358302
$925$	−54.4044	−1.78881
$926$	31.3873	1.03145
$927$	12.7085	0.417403
$928$	−5.07254	−0.166514
$929$	−28.9328	−0.949254	−0.474627	−	0.880187i	$-0.657417\pi$
$929$	−28.9328	−0.949254	−0.474627	+	0.880187i	$0.657417\pi$
$930$	8.36422	0.274273
$931$	12.9850	0.425567
$932$	−17.6923	−0.579531
$933$	−58.0721	−1.90119
$934$	1.86473	0.0610157
$935$	50.9145	1.66508
$936$	2.93796	0.0960302
$937$	15.9565	0.521277	0.260639	−	0.965436i	$-0.416067\pi$
$937$	15.9565	0.521277	0.260639	+	0.965436i	$0.416067\pi$
$938$	17.7363	0.579112
$939$	−0.529493	−0.0172794
$940$	1.24052	0.0404613
$941$	−34.6112	−1.12829	−0.564146	−	0.825675i	$-0.690795\pi$
$941$	−34.6112	−1.12829	−0.564146	+	0.825675i	$0.690795\pi$
$942$	6.45243	0.210232
$943$	0.322600	0.0105053
$944$	−3.95399	−0.128691
$945$	21.1571	0.688241
$946$	32.5117	1.05705
$947$	15.8833	0.516137	0.258069	−	0.966127i	$-0.416914\pi$
$947$	15.8833	0.516137	0.258069	+	0.966127i	$0.416914\pi$
$948$	32.7359	1.06321
$949$	8.87521	0.288101
$950$	−31.4729	−1.02111
$951$	−41.7793	−1.35479
$952$	6.16594	0.199839
$953$	8.65755	0.280446	0.140223	−	0.990120i	$-0.455218\pi$
$953$	8.65755	0.280446	0.140223	+	0.990120i	$0.455218\pi$
$954$	−3.89895	−0.126233
$955$	35.3635	1.14433
$956$	−12.6558	−0.409319
$957$	34.8988	1.12812
$958$	26.2801	0.849071
$959$	24.8676	0.803015
$960$	−8.36422	−0.269954
$961$	1.00000	0.0322581
$962$	−10.4656	−0.337424
$963$	−13.5300	−0.435998
$964$	−6.49499	−0.209190
$965$	21.5937	0.695127
$966$	−19.6349	−0.631743
$967$	35.3936	1.13818	0.569091	−	0.822274i	$-0.307295\pi$
$967$	35.3936	1.13818	0.569091	+	0.822274i	$0.307295\pi$
$968$	−0.247687	−0.00796095
$969$	23.6131	0.758562
$970$	−3.98650	−0.127999
$971$	−11.3804	−0.365213	−0.182607	−	0.983186i	$-0.558453\pi$
$971$	−11.3804	−0.365213	−0.182607	+	0.983186i	$0.558453\pi$
$972$	13.5266	0.433864
$973$	−10.0200	−0.321227
$974$	−23.4541	−0.751518
$975$	−47.8843	−1.53353
$976$	−4.74267	−0.151809
$977$	8.57971	0.274489	0.137245	−	0.990537i	$-0.456175\pi$
$977$	8.57971	0.274489	0.137245	+	0.990537i	$0.456175\pi$
$978$	−35.5466	−1.13665
$979$	−6.77622	−0.216569
$980$	−17.9149	−0.572269
$981$	−25.2742	−0.806942
$982$	−21.8003	−0.695675
$983$	13.7255	0.437777	0.218888	−	0.975750i	$-0.429757\pi$
$983$	13.7255	0.437777	0.218888	+	0.975750i	$0.429757\pi$
$984$	−0.114499	−0.00365011
$985$	8.07067	0.257153
$986$	−19.7571	−0.629196
$987$	−1.03359	−0.0328994
$988$	−6.05433	−0.192614
$989$	58.6115	1.86374
$990$	18.3292	0.582540
$991$	18.5412	0.588981	0.294490	−	0.955654i	$-0.404850\pi$
$991$	18.5412	0.588981	0.294490	+	0.955654i	$0.404850\pi$
$992$	−1.00000	−0.0317500
$993$	−48.1409	−1.52770
$994$	11.1943	0.355061
$995$	−41.8076	−1.32539
$996$	−29.6610	−0.939846
$997$	1.49388	0.0473115	0.0236557	−	0.999720i	$-0.492469\pi$
$997$	1.49388	0.0473115	0.0236557	+	0.999720i	$0.492469\pi$
$998$	19.2554	0.609518
$999$	−16.7449	−0.529786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.i.1.5	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.i.1.5	✓	28	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.09814 q^{3} +1.00000 q^{4} +3.98650 q^{5} -2.09814 q^{6} +1.58307 q^{7} +1.00000 q^{8} +1.40217 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.09814 q^{3} +1.00000 q^{4} +3.98650 q^{5} -2.09814 q^{6} +1.58307 q^{7} +1.00000 q^{8} +1.40217 q^{9} +3.98650 q^{10} +3.27907 q^{11} -2.09814 q^{12} +2.09529 q^{13} +1.58307 q^{14} -8.36422 q^{15} +1.00000 q^{16} +3.89492 q^{17} +1.40217 q^{18} -2.88949 q^{19} +3.98650 q^{20} -3.32150 q^{21} +3.27907 q^{22} +5.91146 q^{23} -2.09814 q^{24} +10.8922 q^{25} +2.09529 q^{26} +3.35246 q^{27} +1.58307 q^{28} -5.07254 q^{29} -8.36422 q^{30} -1.00000 q^{31} +1.00000 q^{32} -6.87994 q^{33} +3.89492 q^{34} +6.31092 q^{35} +1.40217 q^{36} -4.99481 q^{37} -2.88949 q^{38} -4.39621 q^{39} +3.98650 q^{40} +0.0545720 q^{41} -3.32150 q^{42} +9.91490 q^{43} +3.27907 q^{44} +5.58975 q^{45} +5.91146 q^{46} +0.311181 q^{47} -2.09814 q^{48} -4.49388 q^{49} +10.8922 q^{50} -8.17207 q^{51} +2.09529 q^{52} -2.78066 q^{53} +3.35246 q^{54} +13.0720 q^{55} +1.58307 q^{56} +6.06254 q^{57} -5.07254 q^{58} -3.95399 q^{59} -8.36422 q^{60} -4.74267 q^{61} -1.00000 q^{62} +2.21974 q^{63} +1.00000 q^{64} +8.35289 q^{65} -6.87994 q^{66} +11.2037 q^{67} +3.89492 q^{68} -12.4030 q^{69} +6.31092 q^{70} +7.07124 q^{71} +1.40217 q^{72} +4.23578 q^{73} -4.99481 q^{74} -22.8533 q^{75} -2.88949 q^{76} +5.19101 q^{77} -4.39621 q^{78} -15.6024 q^{79} +3.98650 q^{80} -11.2404 q^{81} +0.0545720 q^{82} +14.1369 q^{83} -3.32150 q^{84} +15.5271 q^{85} +9.91490 q^{86} +10.6429 q^{87} +3.27907 q^{88} -2.06651 q^{89} +5.58975 q^{90} +3.31700 q^{91} +5.91146 q^{92} +2.09814 q^{93} +0.311181 q^{94} -11.5190 q^{95} -2.09814 q^{96} -1.00000 q^{97} -4.49388 q^{98} +4.59782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9	\( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 + 12 * q^3 + 28 * q^4 + 10 * q^5 + 12 * q^6 + 13 * q^7 + 28 * q^8 + 38 * q^9 + 10 * q^10 + 12 * q^11 + 12 * q^12 + 20 * q^13 + 13 * q^14 + 19 * q^15 + 28 * q^16 - 4 * q^17 + 38 * q^18 + 35 * q^19 + 10 * q^20 + 30 * q^21 + 12 * q^22 + 20 * q^23 + 12 * q^24 + 46 * q^25 + 20 * q^26 + 39 * q^27 + 13 * q^28 + 5 * q^29 + 19 * q^30 - 28 * q^31 + 28 * q^32 + 12 * q^33 - 4 * q^34 + 36 * q^35 + 38 * q^36 + 11 * q^37 + 35 * q^38 - 4 * q^39 + 10 * q^40 - 5 * q^41 + 30 * q^42 + 43 * q^43 + 12 * q^44 + 11 * q^45 + 20 * q^46 + 18 * q^47 + 12 * q^48 + 99 * q^49 + 46 * q^50 - 43 * q^51 + 20 * q^52 + 11 * q^53 + 39 * q^54 + 66 * q^55 + 13 * q^56 - 15 * q^57 + 5 * q^58 + 34 * q^59 + 19 * q^60 + 66 * q^61 - 28 * q^62 + 65 * q^63 + 28 * q^64 - 16 * q^65 + 12 * q^66 + 5 * q^67 - 4 * q^68 - 33 * q^69 + 36 * q^70 + 25 * q^71 + 38 * q^72 - 9 * q^73 + 11 * q^74 + 92 * q^75 + 35 * q^76 + 4 * q^77 - 4 * q^78 + 15 * q^79 + 10 * q^80 - 5 * q^82 - 12 * q^83 + 30 * q^84 + 88 * q^85 + 43 * q^86 + 31 * q^87 + 12 * q^88 + 8 * q^89 + 11 * q^90 + 34 * q^91 + 20 * q^92 - 12 * q^93 + 18 * q^94 + 32 * q^95 + 12 * q^96 - 28 * q^97 + 99 * q^98 + 51 * q^99

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