LMFDB - Embedded newform 5577.2.a.y.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 7x^{5} + 21x^{4} + 13x^{3} - 33x^{2} - 7x + 7 $ x^7 - 3x^6 - 7x^5 + 21x^4 + 13x^3 - 33x^2 - 7x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.36814$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36814 q^{2} +1.00000 q^{3} -0.128197 q^{4} +2.18365 q^{5} -1.36814 q^{6} -4.27070 q^{7} +2.91167 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.36814 q^{2} +1.00000 q^{3} -0.128197 q^{4} +2.18365 q^{5} -1.36814 q^{6} -4.27070 q^{7} +2.91167 q^{8} +1.00000 q^{9} -2.98753 q^{10} +1.00000 q^{11} -0.128197 q^{12} +5.84291 q^{14} +2.18365 q^{15} -3.72717 q^{16} -3.79173 q^{17} -1.36814 q^{18} -3.17118 q^{19} -0.279937 q^{20} -4.27070 q^{21} -1.36814 q^{22} -4.94243 q^{23} +2.91167 q^{24} -0.231676 q^{25} +1.00000 q^{27} +0.547491 q^{28} -7.35483 q^{29} -2.98753 q^{30} +0.0727448 q^{31} -0.724050 q^{32} +1.00000 q^{33} +5.18761 q^{34} -9.32571 q^{35} -0.128197 q^{36} +3.66658 q^{37} +4.33862 q^{38} +6.35806 q^{40} -4.16722 q^{41} +5.84291 q^{42} +7.11697 q^{43} -0.128197 q^{44} +2.18365 q^{45} +6.76193 q^{46} +11.6337 q^{47} -3.72717 q^{48} +11.2389 q^{49} +0.316965 q^{50} -3.79173 q^{51} +5.11268 q^{53} -1.36814 q^{54} +2.18365 q^{55} -12.4349 q^{56} -3.17118 q^{57} +10.0624 q^{58} +5.62765 q^{59} -0.279937 q^{60} -5.40800 q^{61} -0.0995250 q^{62} -4.27070 q^{63} +8.44494 q^{64} -1.36814 q^{66} +10.1145 q^{67} +0.486088 q^{68} -4.94243 q^{69} +12.7589 q^{70} +9.62239 q^{71} +2.91167 q^{72} +6.44736 q^{73} -5.01639 q^{74} -0.231676 q^{75} +0.406536 q^{76} -4.27070 q^{77} +10.1209 q^{79} -8.13884 q^{80} +1.00000 q^{81} +5.70134 q^{82} -7.80918 q^{83} +0.547491 q^{84} -8.27981 q^{85} -9.73700 q^{86} -7.35483 q^{87} +2.91167 q^{88} +2.87912 q^{89} -2.98753 q^{90} +0.633605 q^{92} +0.0727448 q^{93} -15.9166 q^{94} -6.92475 q^{95} -0.724050 q^{96} +3.79281 q^{97} -15.3764 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9	$ 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9} + 7 q^{11} + 9 q^{12} + 8 q^{14} + 6 q^{15} + 17 q^{16} - 2 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20} + 6 q^{21} + 3 q^{22} + 4 q^{23} + 15 q^{24} + 13 q^{25} + 7 q^{27} + 12 q^{28} - 12 q^{29} - 10 q^{31} + 33 q^{32} + 7 q^{33} + 28 q^{34} - 4 q^{35} + 9 q^{36} + 6 q^{37} + 16 q^{38} - 10 q^{40} + 2 q^{41} + 8 q^{42} - 16 q^{43} + 9 q^{44} + 6 q^{45} - 26 q^{46} + 18 q^{47} + 17 q^{48} + 23 q^{49} + 39 q^{50} - 2 q^{51} + 10 q^{53} + 3 q^{54} + 6 q^{55} + 16 q^{56} + 8 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 10 q^{61} - 36 q^{62} + 6 q^{63} + 29 q^{64} + 3 q^{66} + 8 q^{67} - 10 q^{68} + 4 q^{69} - 20 q^{70} + 36 q^{71} + 15 q^{72} + 20 q^{73} + 13 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} - 20 q^{80} + 7 q^{81} - 10 q^{82} + 30 q^{83} + 12 q^{84} - 40 q^{85} + 6 q^{86} - 12 q^{87} + 15 q^{88} + 34 q^{89} - 12 q^{92} - 10 q^{93} + 32 q^{94} + 18 q^{95} + 33 q^{96} + 16 q^{97} + q^{98} + 7 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9 + 7 * q^11 + 9 * q^12 + 8 * q^14 + 6 * q^15 + 17 * q^16 - 2 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 6 * q^21 + 3 * q^22 + 4 * q^23 + 15 * q^24 + 13 * q^25 + 7 * q^27 + 12 * q^28 - 12 * q^29 - 10 * q^31 + 33 * q^32 + 7 * q^33 + 28 * q^34 - 4 * q^35 + 9 * q^36 + 6 * q^37 + 16 * q^38 - 10 * q^40 + 2 * q^41 + 8 * q^42 - 16 * q^43 + 9 * q^44 + 6 * q^45 - 26 * q^46 + 18 * q^47 + 17 * q^48 + 23 * q^49 + 39 * q^50 - 2 * q^51 + 10 * q^53 + 3 * q^54 + 6 * q^55 + 16 * q^56 + 8 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 10 * q^61 - 36 * q^62 + 6 * q^63 + 29 * q^64 + 3 * q^66 + 8 * q^67 - 10 * q^68 + 4 * q^69 - 20 * q^70 + 36 * q^71 + 15 * q^72 + 20 * q^73 + 13 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 - 20 * q^80 + 7 * q^81 - 10 * q^82 + 30 * q^83 + 12 * q^84 - 40 * q^85 + 6 * q^86 - 12 * q^87 + 15 * q^88 + 34 * q^89 - 12 * q^92 - 10 * q^93 + 32 * q^94 + 18 * q^95 + 33 * q^96 + 16 * q^97 + q^98 + 7 * 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 $

$2$	−1.36814	−0.967420	−0.483710	−	0.875228i	$-0.660711\pi$
$2$	−1.36814	−0.967420	−0.483710	+	0.875228i	$0.660711\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.128197	−0.0640985
$5$	2.18365	0.976558	0.488279	−	0.872688i	$-0.337625\pi$
$5$	2.18365	0.976558	0.488279	+	0.872688i	$0.337625\pi$
$6$	−1.36814	−0.558540
$7$	−4.27070	−1.61417	−0.807087	−	0.590433i	$-0.798957\pi$
$7$	−4.27070	−1.61417	−0.807087	+	0.590433i	$0.798957\pi$
$8$	2.91167	1.02943
$9$	1.00000	0.333333
$10$	−2.98753	−0.944741
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.128197	−0.0370073
$13$	0	0
$13$	0	0
$14$	5.84291	1.56158
$15$	2.18365	0.563816
$16$	−3.72717	−0.931793
$17$	−3.79173	−0.919629	−0.459815	−	0.888015i	$-0.652084\pi$
$17$	−3.79173	−0.919629	−0.459815	+	0.888015i	$0.652084\pi$
$18$	−1.36814	−0.322473
$19$	−3.17118	−0.727519	−0.363760	−	0.931493i	$-0.618507\pi$
$19$	−3.17118	−0.727519	−0.363760	+	0.931493i	$0.618507\pi$
$20$	−0.279937	−0.0625959
$21$	−4.27070	−0.931943
$22$	−1.36814	−0.291688
$23$	−4.94243	−1.03057	−0.515284	−	0.857020i	$-0.672313\pi$
$23$	−4.94243	−1.03057	−0.515284	+	0.857020i	$0.672313\pi$
$24$	2.91167	0.594342
$25$	−0.231676	−0.0463352
$26$	0	0
$27$	1.00000	0.192450
$28$	0.547491	0.103466
$29$	−7.35483	−1.36576	−0.682879	−	0.730531i	$-0.739272\pi$
$29$	−7.35483	−1.36576	−0.682879	+	0.730531i	$0.739272\pi$
$30$	−2.98753	−0.545447
$31$	0.0727448	0.0130654	0.00653268	−	0.999979i	$-0.497921\pi$
$31$	0.0727448	0.0130654	0.00653268	+	0.999979i	$0.497921\pi$
$32$	−0.724050	−0.127995
$33$	1.00000	0.174078
$34$	5.18761	0.889668
$35$	−9.32571	−1.57633
$36$	−0.128197	−0.0213662
$37$	3.66658	0.602782	0.301391	−	0.953501i	$-0.402549\pi$
$37$	3.66658	0.602782	0.301391	+	0.953501i	$0.402549\pi$
$38$	4.33862	0.703817
$39$	0	0
$40$	6.35806	1.00530
$41$	−4.16722	−0.650811	−0.325405	−	0.945575i	$-0.605501\pi$
$41$	−4.16722	−0.650811	−0.325405	+	0.945575i	$0.605501\pi$
$42$	5.84291	0.901581
$43$	7.11697	1.08533	0.542664	−	0.839950i	$-0.317416\pi$
$43$	7.11697	1.08533	0.542664	+	0.839950i	$0.317416\pi$
$44$	−0.128197	−0.0193264
$45$	2.18365	0.325519
$46$	6.76193	0.996992
$47$	11.6337	1.69695	0.848477	−	0.529232i	$-0.177520\pi$
$47$	11.6337	1.69695	0.848477	+	0.529232i	$0.177520\pi$
$48$	−3.72717	−0.537971
$49$	11.2389	1.60556
$50$	0.316965	0.0448256
$51$	−3.79173	−0.530948
$52$	0	0
$53$	5.11268	0.702281	0.351140	−	0.936323i	$-0.385794\pi$
$53$	5.11268	0.702281	0.351140	+	0.936323i	$0.385794\pi$
$54$	−1.36814	−0.186180
$55$	2.18365	0.294443
$56$	−12.4349	−1.66168
$57$	−3.17118	−0.420034
$58$	10.0624	1.32126
$59$	5.62765	0.732658	0.366329	−	0.930485i	$-0.380614\pi$
$59$	5.62765	0.732658	0.366329	+	0.930485i	$0.380614\pi$
$60$	−0.279937	−0.0361398
$61$	−5.40800	−0.692424	−0.346212	−	0.938156i	$-0.612532\pi$
$61$	−5.40800	−0.692424	−0.346212	+	0.938156i	$0.612532\pi$
$62$	−0.0995250	−0.0126397
$63$	−4.27070	−0.538058
$64$	8.44494	1.05562
$65$	0	0
$66$	−1.36814	−0.168406
$67$	10.1145	1.23569	0.617843	−	0.786302i	$-0.288007\pi$
$67$	10.1145	1.23569	0.617843	+	0.786302i	$0.288007\pi$
$68$	0.486088	0.0589469
$69$	−4.94243	−0.594998
$70$	12.7589	1.52498
$71$	9.62239	1.14197	0.570984	−	0.820961i	$-0.306562\pi$
$71$	9.62239	1.14197	0.570984	+	0.820961i	$0.306562\pi$
$72$	2.91167	0.343143
$73$	6.44736	0.754607	0.377303	−	0.926090i	$-0.376851\pi$
$73$	6.44736	0.754607	0.377303	+	0.926090i	$0.376851\pi$
$74$	−5.01639	−0.583144
$75$	−0.231676	−0.0267516
$76$	0.406536	0.0466329
$77$	−4.27070	−0.486692
$78$	0	0
$79$	10.1209	1.13869	0.569347	−	0.822097i	$-0.307196\pi$
$79$	10.1209	1.13869	0.569347	+	0.822097i	$0.307196\pi$
$80$	−8.13884	−0.909949
$81$	1.00000	0.111111
$82$	5.70134	0.629607
$83$	−7.80918	−0.857169	−0.428585	−	0.903502i	$-0.640988\pi$
$83$	−7.80918	−0.857169	−0.428585	+	0.903502i	$0.640988\pi$
$84$	0.547491	0.0597362
$85$	−8.27981	−0.898071
$86$	−9.73700	−1.04997
$87$	−7.35483	−0.788521
$88$	2.91167	0.310385
$89$	2.87912	0.305187	0.152593	−	0.988289i	$-0.451238\pi$
$89$	2.87912	0.305187	0.152593	+	0.988289i	$0.451238\pi$
$90$	−2.98753	−0.314914
$91$	0	0
$92$	0.633605	0.0660579
$93$	0.0727448	0.00754329
$94$	−15.9166	−1.64167
$95$	−6.92475	−0.710465
$96$	−0.724050	−0.0738980
$97$	3.79281	0.385101	0.192551	−	0.981287i	$-0.438324\pi$
$97$	3.79281	0.385101	0.192551	+	0.981287i	$0.438324\pi$
$98$	−15.3764	−1.55325
$99$	1.00000	0.100504
$100$	0.0297002	0.00297002
$101$	12.8641	1.28003	0.640014	−	0.768363i	$-0.278928\pi$
$101$	12.8641	1.28003	0.640014	+	0.768363i	$0.278928\pi$
$102$	5.18761	0.513650
$103$	−16.9975	−1.67482	−0.837409	−	0.546577i	$-0.815930\pi$
$103$	−16.9975	−1.67482	−0.837409	+	0.546577i	$0.815930\pi$
$104$	0	0
$105$	−9.32571	−0.910096
$106$	−6.99486	−0.679400
$107$	−12.6819	−1.22600	−0.613001	−	0.790082i	$-0.710038\pi$
$107$	−12.6819	−1.22600	−0.613001	+	0.790082i	$0.710038\pi$
$108$	−0.128197	−0.0123358
$109$	8.89607	0.852089	0.426045	−	0.904702i	$-0.359907\pi$
$109$	8.89607	0.852089	0.426045	+	0.904702i	$0.359907\pi$
$110$	−2.98753	−0.284850
$111$	3.66658	0.348017
$112$	15.9176	1.50408
$113$	1.36552	0.128457	0.0642287	−	0.997935i	$-0.479541\pi$
$113$	1.36552	0.128457	0.0642287	+	0.997935i	$0.479541\pi$
$114$	4.33862	0.406349
$115$	−10.7925	−1.00641
$116$	0.942868	0.0875431
$117$	0	0
$118$	−7.69941	−0.708788
$119$	16.1933	1.48444
$120$	6.35806	0.580409
$121$	1.00000	0.0909091
$122$	7.39890	0.669865
$123$	−4.16722	−0.375746
$124$	−0.00932567	−0.000837470 0
$125$	−11.4241	−1.02181
$126$	5.84291	0.520528
$127$	10.4027	0.923093	0.461546	−	0.887116i	$-0.347295\pi$
$127$	10.4027	0.923093	0.461546	+	0.887116i	$0.347295\pi$
$128$	−10.1058	−0.893231
$129$	7.11697	0.626614
$130$	0	0
$131$	−12.0678	−1.05437	−0.527183	−	0.849752i	$-0.676752\pi$
$131$	−12.0678	−1.05437	−0.527183	+	0.849752i	$0.676752\pi$
$132$	−0.128197	−0.0111581
$133$	13.5432	1.17434
$134$	−13.8381	−1.19543
$135$	2.18365	0.187939
$136$	−11.0403	−0.946694
$137$	3.96114	0.338423	0.169211	−	0.985580i	$-0.445878\pi$
$137$	3.96114	0.338423	0.169211	+	0.985580i	$0.445878\pi$
$138$	6.76193	0.575613
$139$	18.2437	1.54741	0.773703	−	0.633548i	$-0.218402\pi$
$139$	18.2437	1.54741	0.773703	+	0.633548i	$0.218402\pi$
$140$	1.19553	0.101041
$141$	11.6337	0.979737
$142$	−13.1648	−1.10476
$143$	0	0
$144$	−3.72717	−0.310598
$145$	−16.0604	−1.33374
$146$	−8.82089	−0.730022
$147$	11.2389	0.926968
$148$	−0.470045	−0.0386375
$149$	13.8984	1.13860	0.569299	−	0.822131i	$-0.307215\pi$
$149$	13.8984	1.13860	0.569299	+	0.822131i	$0.307215\pi$
$150$	0.316965	0.0258801
$151$	−2.29739	−0.186959	−0.0934795	−	0.995621i	$-0.529799\pi$
$151$	−2.29739	−0.186959	−0.0934795	+	0.995621i	$0.529799\pi$
$152$	−9.23344	−0.748931
$153$	−3.79173	−0.306543
$154$	5.84291	0.470835
$155$	0.158849	0.0127591
$156$	0	0
$157$	−15.6293	−1.24736	−0.623678	−	0.781682i	$-0.714362\pi$
$157$	−15.6293	−1.24736	−0.623678	+	0.781682i	$0.714362\pi$
$158$	−13.8468	−1.10160
$159$	5.11268	0.405462
$160$	−1.58107	−0.124995
$161$	21.1076	1.66351
$162$	−1.36814	−0.107491
$163$	1.25583	0.0983643	0.0491822	−	0.998790i	$-0.484339\pi$
$163$	1.25583	0.0983643	0.0491822	+	0.998790i	$0.484339\pi$
$164$	0.534226	0.0417160
$165$	2.18365	0.169997
$166$	10.6840	0.829243
$167$	17.3823	1.34509	0.672543	−	0.740058i	$-0.265202\pi$
$167$	17.3823	1.34509	0.672543	+	0.740058i	$0.265202\pi$
$168$	−12.4349	−0.959371
$169$	0	0
$170$	11.3279	0.868812
$171$	−3.17118	−0.242506
$172$	−0.912375	−0.0695679
$173$	−12.0899	−0.919178	−0.459589	−	0.888132i	$-0.652003\pi$
$173$	−12.0899	−0.919178	−0.459589	+	0.888132i	$0.652003\pi$
$174$	10.0624	0.762831
$175$	0.989418	0.0747930
$176$	−3.72717	−0.280946
$177$	5.62765	0.423000
$178$	−3.93904	−0.295244
$179$	−5.13094	−0.383504	−0.191752	−	0.981443i	$-0.561417\pi$
$179$	−5.13094	−0.383504	−0.191752	+	0.981443i	$0.561417\pi$
$180$	−0.279937	−0.0208653
$181$	−23.3170	−1.73314	−0.866568	−	0.499059i	$-0.833679\pi$
$181$	−23.3170	−1.73314	−0.866568	+	0.499059i	$0.833679\pi$
$182$	0	0
$183$	−5.40800	−0.399771
$184$	−14.3907	−1.06090
$185$	8.00653	0.588652
$186$	−0.0995250	−0.00729753
$187$	−3.79173	−0.277279
$188$	−1.49141	−0.108772
$189$	−4.27070	−0.310648
$190$	9.47402	0.687318
$191$	11.1231	0.804838	0.402419	−	0.915456i	$-0.368169\pi$
$191$	11.1231	0.804838	0.402419	+	0.915456i	$0.368169\pi$
$192$	8.44494	0.609461
$193$	23.1664	1.66756	0.833778	−	0.552099i	$-0.186173\pi$
$193$	23.1664	1.66756	0.833778	+	0.552099i	$0.186173\pi$
$194$	−5.18909	−0.372555
$195$	0	0
$196$	−1.44079	−0.102914
$197$	9.18435	0.654358	0.327179	−	0.944962i	$-0.393902\pi$
$197$	9.18435	0.654358	0.327179	+	0.944962i	$0.393902\pi$
$198$	−1.36814	−0.0972294
$199$	6.38937	0.452930	0.226465	−	0.974019i	$-0.427283\pi$
$199$	6.38937	0.452930	0.226465	+	0.974019i	$0.427283\pi$
$200$	−0.674563	−0.0476988
$201$	10.1145	0.713423
$202$	−17.5999	−1.23833
$203$	31.4103	2.20457
$204$	0.486088	0.0340330
$205$	−9.09975	−0.635554
$206$	23.2550	1.62025
$207$	−4.94243	−0.343522
$208$	0	0
$209$	−3.17118	−0.219355
$210$	12.7589	0.880446
$211$	22.4436	1.54508	0.772541	−	0.634965i	$-0.218985\pi$
$211$	22.4436	1.54508	0.772541	+	0.634965i	$0.218985\pi$
$212$	−0.655431	−0.0450152
$213$	9.62239	0.659315
$214$	17.3505	1.18606
$215$	15.5410	1.05989
$216$	2.91167	0.198114
$217$	−0.310671	−0.0210897
$218$	−12.1711	−0.824328
$219$	6.44736	0.435673
$220$	−0.279937	−0.0188734
$221$	0	0
$222$	−5.01639	−0.336678
$223$	−16.5344	−1.10722	−0.553611	−	0.832775i	$-0.686751\pi$
$223$	−16.5344	−1.10722	−0.553611	+	0.832775i	$0.686751\pi$
$224$	3.09220	0.206606
$225$	−0.231676	−0.0154451
$226$	−1.86822	−0.124272
$227$	−19.9826	−1.32630	−0.663148	−	0.748489i	$-0.730780\pi$
$227$	−19.9826	−1.32630	−0.663148	+	0.748489i	$0.730780\pi$
$228$	0.406536	0.0269235
$229$	15.8459	1.04713	0.523564	−	0.851986i	$-0.324602\pi$
$229$	15.8459	1.04713	0.523564	+	0.851986i	$0.324602\pi$
$230$	14.7657	0.973620
$231$	−4.27070	−0.280992
$232$	−21.4148	−1.40595
$233$	15.9195	1.04292	0.521460	−	0.853276i	$-0.325388\pi$
$233$	15.9195	1.04292	0.521460	+	0.853276i	$0.325388\pi$
$234$	0	0
$235$	25.4040	1.65717
$236$	−0.721449	−0.0469623
$237$	10.1209	0.657425
$238$	−22.1547	−1.43608
$239$	16.9898	1.09898	0.549491	−	0.835500i	$-0.314822\pi$
$239$	16.9898	1.09898	0.549491	+	0.835500i	$0.314822\pi$
$240$	−8.13884	−0.525360
$241$	−21.9883	−1.41639	−0.708197	−	0.706015i	$-0.750491\pi$
$241$	−21.9883	−1.41639	−0.708197	+	0.706015i	$0.750491\pi$
$242$	−1.36814	−0.0879473
$243$	1.00000	0.0641500
$244$	0.693290	0.0443834
$245$	24.5418	1.56792
$246$	5.70134	0.363504
$247$	0	0
$248$	0.211809	0.0134499
$249$	−7.80918	−0.494887
$250$	15.6298	0.988516
$251$	11.9461	0.754029	0.377015	−	0.926207i	$-0.376951\pi$
$251$	11.9461	0.754029	0.377015	+	0.926207i	$0.376951\pi$
$252$	0.547491	0.0344887
$253$	−4.94243	−0.310728
$254$	−14.2324	−0.893019
$255$	−8.27981	−0.518502
$256$	−3.06382	−0.191489
$257$	28.3671	1.76949	0.884746	−	0.466074i	$-0.154332\pi$
$257$	28.3671	1.76949	0.884746	+	0.466074i	$0.154332\pi$
$258$	−9.73700	−0.606199
$259$	−15.6589	−0.972995
$260$	0	0
$261$	−7.35483	−0.455253
$262$	16.5104	1.02001
$263$	−1.37798	−0.0849699	−0.0424849	−	0.999097i	$-0.513527\pi$
$263$	−1.37798	−0.0849699	−0.0424849	+	0.999097i	$0.513527\pi$
$264$	2.91167	0.179201
$265$	11.1643	0.685818
$266$	−18.5289	−1.13608
$267$	2.87912	0.176200
$268$	−1.29665	−0.0792056
$269$	−14.6274	−0.891847	−0.445923	−	0.895071i	$-0.647125\pi$
$269$	−14.6274	−0.891847	−0.445923	+	0.895071i	$0.647125\pi$
$270$	−2.98753	−0.181816
$271$	13.3040	0.808158	0.404079	−	0.914724i	$-0.367592\pi$
$271$	13.3040	0.808158	0.404079	+	0.914724i	$0.367592\pi$
$272$	14.1324	0.856904
$273$	0	0
$274$	−5.41938	−0.327397
$275$	−0.231676	−0.0139706
$276$	0.633605	0.0381385
$277$	22.1581	1.33135	0.665676	−	0.746241i	$-0.268143\pi$
$277$	22.1581	1.33135	0.665676	+	0.746241i	$0.268143\pi$
$278$	−24.9598	−1.49699
$279$	0.0727448	0.00435512
$280$	−27.1534	−1.62273
$281$	−2.12589	−0.126820	−0.0634100	−	0.997988i	$-0.520198\pi$
$281$	−2.12589	−0.126820	−0.0634100	+	0.997988i	$0.520198\pi$
$282$	−15.9166	−0.947817
$283$	−31.1036	−1.84892	−0.924458	−	0.381283i	$-0.875482\pi$
$283$	−31.1036	−1.84892	−0.924458	+	0.381283i	$0.875482\pi$
$284$	−1.23356	−0.0731984
$285$	−6.92475	−0.410187
$286$	0	0
$287$	17.7970	1.05052
$288$	−0.724050	−0.0426650
$289$	−2.62279	−0.154282
$290$	21.9728	1.29029
$291$	3.79281	0.222338
$292$	−0.826533	−0.0483692
$293$	16.9009	0.987363	0.493682	−	0.869643i	$-0.335651\pi$
$293$	16.9009	0.987363	0.493682	+	0.869643i	$0.335651\pi$
$294$	−15.3764	−0.896767
$295$	12.2888	0.715483
$296$	10.6759	0.620523
$297$	1.00000	0.0580259
$298$	−19.0149	−1.10150
$299$	0	0
$300$	0.0297002	0.00171474
$301$	−30.3945	−1.75191
$302$	3.14315	0.180868
$303$	12.8641	0.739025
$304$	11.8195	0.677897
$305$	−11.8092	−0.676192
$306$	5.18761	0.296556
$307$	−24.6110	−1.40462	−0.702312	−	0.711869i	$-0.747849\pi$
$307$	−24.6110	−1.40462	−0.702312	+	0.711869i	$0.747849\pi$
$308$	0.547491	0.0311962
$309$	−16.9975	−0.966956
$310$	−0.217328	−0.0123434
$311$	−1.00504	−0.0569904	−0.0284952	−	0.999594i	$-0.509072\pi$
$311$	−1.00504	−0.0569904	−0.0284952	+	0.999594i	$0.509072\pi$
$312$	0	0
$313$	−13.8744	−0.784227	−0.392114	−	0.919917i	$-0.628256\pi$
$313$	−13.8744	−0.784227	−0.392114	+	0.919917i	$0.628256\pi$
$314$	21.3831	1.20672
$315$	−9.32571	−0.525444
$316$	−1.29747	−0.0729886
$317$	15.6405	0.878460	0.439230	−	0.898375i	$-0.355251\pi$
$317$	15.6405	0.878460	0.439230	+	0.898375i	$0.355251\pi$
$318$	−6.99486	−0.392252
$319$	−7.35483	−0.411792
$320$	18.4408	1.03087
$321$	−12.6819	−0.707832
$322$	−28.8782	−1.60932
$323$	12.0243	0.669048
$324$	−0.128197	−0.00712206
$325$	0	0
$326$	−1.71815	−0.0951596
$327$	8.89607	0.491954
$328$	−12.1336	−0.669964
$329$	−49.6842	−2.73918
$330$	−2.98753	−0.164458
$331$	23.1426	1.27203	0.636017	−	0.771675i	$-0.280581\pi$
$331$	23.1426	1.27203	0.636017	+	0.771675i	$0.280581\pi$
$332$	1.00111	0.0549433
$333$	3.66658	0.200927
$334$	−23.7814	−1.30126
$335$	22.0866	1.20672
$336$	15.9176	0.868378
$337$	15.1946	0.827705	0.413853	−	0.910344i	$-0.364183\pi$
$337$	15.1946	0.827705	0.413853	+	0.910344i	$0.364183\pi$
$338$	0	0
$339$	1.36552	0.0741650
$340$	1.06145	0.0575650
$341$	0.0727448	0.00393935
$342$	4.33862	0.234606
$343$	−18.1030	−0.977472
$344$	20.7223	1.11727
$345$	−10.7925	−0.581050
$346$	16.5407	0.889231
$347$	16.6545	0.894061	0.447030	−	0.894519i	$-0.352482\pi$
$347$	16.6545	0.894061	0.447030	+	0.894519i	$0.352482\pi$
$348$	0.942868	0.0505430
$349$	−29.1080	−1.55812	−0.779058	−	0.626952i	$-0.784302\pi$
$349$	−29.1080	−1.55812	−0.779058	+	0.626952i	$0.784302\pi$
$350$	−1.35366	−0.0723562
$351$	0	0
$352$	−0.724050	−0.0385920
$353$	29.1723	1.55268	0.776342	−	0.630312i	$-0.217073\pi$
$353$	29.1723	1.55268	0.776342	+	0.630312i	$0.217073\pi$
$354$	−7.69941	−0.409219
$355$	21.0119	1.11520
$356$	−0.369095	−0.0195620
$357$	16.1933	0.857043
$358$	7.01983	0.371010
$359$	−18.0809	−0.954271	−0.477136	−	0.878830i	$-0.658325\pi$
$359$	−18.0809	−0.954271	−0.477136	+	0.878830i	$0.658325\pi$
$360$	6.35806	0.335099
$361$	−8.94359	−0.470715
$362$	31.9008	1.67667
$363$	1.00000	0.0524864
$364$	0	0
$365$	14.0788	0.736917
$366$	7.39890	0.386747
$367$	18.1338	0.946578	0.473289	−	0.880907i	$-0.343067\pi$
$367$	18.1338	0.946578	0.473289	+	0.880907i	$0.343067\pi$
$368$	18.4213	0.960275
$369$	−4.16722	−0.216937
$370$	−10.9540	−0.569474
$371$	−21.8347	−1.13360
$372$	−0.00932567	−0.000483513 0
$373$	−15.8564	−0.821012	−0.410506	−	0.911858i	$-0.634648\pi$
$373$	−15.8564	−0.821012	−0.410506	+	0.911858i	$0.634648\pi$
$374$	5.18761	0.268245
$375$	−11.4241	−0.589940
$376$	33.8736	1.74690
$377$	0	0
$378$	5.84291	0.300527
$379$	−18.3431	−0.942224	−0.471112	−	0.882073i	$-0.656147\pi$
$379$	−18.3431	−0.942224	−0.471112	+	0.882073i	$0.656147\pi$
$380$	0.887733	0.0455397
$381$	10.4027	0.532948
$382$	−15.2179	−0.778617
$383$	16.1019	0.822768	0.411384	−	0.911462i	$-0.365046\pi$
$383$	16.1019	0.822768	0.411384	+	0.911462i	$0.365046\pi$
$384$	−10.1058	−0.515707
$385$	−9.32571	−0.475282
$386$	−31.6949	−1.61323
$387$	7.11697	0.361776
$388$	−0.486227	−0.0246844
$389$	32.7166	1.65880	0.829400	−	0.558655i	$-0.188683\pi$
$389$	32.7166	1.65880	0.829400	+	0.558655i	$0.188683\pi$
$390$	0	0
$391$	18.7403	0.947740
$392$	32.7239	1.65281
$393$	−12.0678	−0.608738
$394$	−12.5655	−0.633039
$395$	22.1006	1.11200
$396$	−0.128197	−0.00644214
$397$	3.51685	0.176506	0.0882529	−	0.996098i	$-0.471872\pi$
$397$	3.51685	0.176506	0.0882529	+	0.996098i	$0.471872\pi$
$398$	−8.74154	−0.438174
$399$	13.5432	0.678007
$400$	0.863496	0.0431748
$401$	−18.6231	−0.929992	−0.464996	−	0.885313i	$-0.653944\pi$
$401$	−18.6231	−0.929992	−0.464996	+	0.885313i	$0.653944\pi$
$402$	−13.8381	−0.690180
$403$	0	0
$404$	−1.64914	−0.0820480
$405$	2.18365	0.108506
$406$	−42.9736	−2.13275
$407$	3.66658	0.181746
$408$	−11.0403	−0.546574
$409$	17.6809	0.874262	0.437131	−	0.899398i	$-0.355995\pi$
$409$	17.6809	0.874262	0.437131	+	0.899398i	$0.355995\pi$
$410$	12.4497	0.614848
$411$	3.96114	0.195388
$412$	2.17903	0.107353
$413$	−24.0340	−1.18264
$414$	6.76193	0.332331
$415$	−17.0525	−0.837075
$416$	0	0
$417$	18.2437	0.893395
$418$	4.33862	0.212209
$419$	−1.93036	−0.0943044	−0.0471522	−	0.998888i	$-0.515015\pi$
$419$	−1.93036	−0.0943044	−0.0471522	+	0.998888i	$0.515015\pi$
$420$	1.19553	0.0583358
$421$	−7.21742	−0.351756	−0.175878	−	0.984412i	$-0.556276\pi$
$421$	−7.21742	−0.351756	−0.175878	+	0.984412i	$0.556276\pi$
$422$	−30.7060	−1.49474
$423$	11.6337	0.565651
$424$	14.8864	0.722949
$425$	0.878452	0.0426112
$426$	−13.1648	−0.637835
$427$	23.0960	1.11769
$428$	1.62578	0.0785849
$429$	0	0
$430$	−21.2622	−1.02535
$431$	−29.7876	−1.43482	−0.717408	−	0.696653i	$-0.754672\pi$
$431$	−29.7876	−1.43482	−0.717408	+	0.696653i	$0.754672\pi$
$432$	−3.72717	−0.179324
$433$	−25.2468	−1.21329	−0.606643	−	0.794975i	$-0.707484\pi$
$433$	−25.2468	−1.21329	−0.606643	+	0.794975i	$0.707484\pi$
$434$	0.425041	0.0204026
$435$	−16.0604	−0.770036
$436$	−1.14045	−0.0546177
$437$	15.6733	0.749758
$438$	−8.82089	−0.421478
$439$	−9.07110	−0.432940	−0.216470	−	0.976289i	$-0.569454\pi$
$439$	−9.07110	−0.432940	−0.216470	+	0.976289i	$0.569454\pi$
$440$	6.35806	0.303109
$441$	11.2389	0.535185
$442$	0	0
$443$	−12.0753	−0.573715	−0.286858	−	0.957973i	$-0.592611\pi$
$443$	−12.0753	−0.573715	−0.286858	+	0.957973i	$0.592611\pi$
$444$	−0.470045	−0.0223074
$445$	6.28700	0.298032
$446$	22.6213	1.07115
$447$	13.8984	0.657370
$448$	−36.0658	−1.70395
$449$	8.94438	0.422111	0.211056	−	0.977474i	$-0.432310\pi$
$449$	8.94438	0.422111	0.211056	+	0.977474i	$0.432310\pi$
$450$	0.316965	0.0149419
$451$	−4.16722	−0.196227
$452$	−0.175056	−0.00823394
$453$	−2.29739	−0.107941
$454$	27.3390	1.28308
$455$	0	0
$456$	−9.23344	−0.432395
$457$	−28.4975	−1.33305	−0.666527	−	0.745481i	$-0.732220\pi$
$457$	−28.4975	−1.33305	−0.666527	+	0.745481i	$0.732220\pi$
$458$	−21.6794	−1.01301
$459$	−3.79173	−0.176983
$460$	1.38357	0.0645093
$461$	−19.2580	−0.896932	−0.448466	−	0.893800i	$-0.648030\pi$
$461$	−19.2580	−0.896932	−0.448466	+	0.893800i	$0.648030\pi$
$462$	5.84291	0.271837
$463$	36.3639	1.68997	0.844987	−	0.534787i	$-0.179608\pi$
$463$	36.3639	1.68997	0.844987	+	0.534787i	$0.179608\pi$
$464$	27.4127	1.27260
$465$	0.158849	0.00736645
$466$	−21.7801	−1.00894
$467$	1.70345	0.0788264	0.0394132	−	0.999223i	$-0.487451\pi$
$467$	1.70345	0.0788264	0.0394132	+	0.999223i	$0.487451\pi$
$468$	0	0
$469$	−43.1961	−1.99461
$470$	−34.7562	−1.60318
$471$	−15.6293	−0.720161
$472$	16.3859	0.754220
$473$	7.11697	0.327239
$474$	−13.8468	−0.636006
$475$	0.734687	0.0337097
$476$	−2.07594	−0.0951505
$477$	5.11268	0.234094
$478$	−23.2444	−1.06318
$479$	−24.5812	−1.12314	−0.561571	−	0.827429i	$-0.689803\pi$
$479$	−24.5812	−1.12314	−0.561571	+	0.827429i	$0.689803\pi$
$480$	−1.58107	−0.0721657
$481$	0	0
$482$	30.0831	1.37025
$483$	21.1076	0.960431
$484$	−0.128197	−0.00582714
$485$	8.28216	0.376074
$486$	−1.36814	−0.0620600
$487$	40.5270	1.83646	0.918228	−	0.396053i	$-0.129620\pi$
$487$	40.5270	1.83646	0.918228	+	0.396053i	$0.129620\pi$
$488$	−15.7463	−0.712802
$489$	1.25583	0.0567907
$490$	−33.5766	−1.51683
$491$	16.8245	0.759277	0.379639	−	0.925135i	$-0.376048\pi$
$491$	16.8245	0.759277	0.379639	+	0.925135i	$0.376048\pi$
$492$	0.534226	0.0240848
$493$	27.8875	1.25599
$494$	0	0
$495$	2.18365	0.0981477
$496$	−0.271132	−0.0121742
$497$	−41.0943	−1.84333
$498$	10.6840	0.478764
$499$	28.5150	1.27651	0.638254	−	0.769826i	$-0.279657\pi$
$499$	28.5150	1.27651	0.638254	+	0.769826i	$0.279657\pi$
$500$	1.46454	0.0654963
$501$	17.3823	0.776586
$502$	−16.3439	−0.729463
$503$	27.4200	1.22260	0.611299	−	0.791400i	$-0.290647\pi$
$503$	27.4200	1.22260	0.611299	+	0.791400i	$0.290647\pi$
$504$	−12.4349	−0.553893
$505$	28.0908	1.25002
$506$	6.76193	0.300604
$507$	0	0
$508$	−1.33360	−0.0591689
$509$	−25.4659	−1.12876	−0.564378	−	0.825516i	$-0.690884\pi$
$509$	−25.4659	−1.12876	−0.564378	+	0.825516i	$0.690884\pi$
$510$	11.3279	0.501609
$511$	−27.5348	−1.21807
$512$	24.4032	1.07848
$513$	−3.17118	−0.140011
$514$	−38.8101	−1.71184
$515$	−37.1167	−1.63556
$516$	−0.912375	−0.0401651
$517$	11.6337	0.511651
$518$	21.4235	0.941295
$519$	−12.0899	−0.530688
$520$	0	0
$521$	2.38806	0.104623	0.0523113	−	0.998631i	$-0.483341\pi$
$521$	2.38806	0.104623	0.0523113	+	0.998631i	$0.483341\pi$
$522$	10.0624	0.440421
$523$	45.6041	1.99413	0.997064	−	0.0765769i	$-0.0243991\pi$
$523$	45.6041	1.99413	0.997064	+	0.0765769i	$0.0243991\pi$
$524$	1.54705	0.0675833
$525$	0.989418	0.0431818
$526$	1.88527	0.0822015
$527$	−0.275829	−0.0120153
$528$	−3.72717	−0.162204
$529$	1.42760	0.0620694
$530$	−15.2743	−0.663474
$531$	5.62765	0.244219
$532$	−1.73620	−0.0752736
$533$	0	0
$534$	−3.93904	−0.170459
$535$	−27.6927	−1.19726
$536$	29.4501	1.27205
$537$	−5.13094	−0.221416
$538$	20.0123	0.862791
$539$	11.2389	0.484093
$540$	−0.279937	−0.0120466
$541$	−29.4997	−1.26829	−0.634145	−	0.773214i	$-0.718648\pi$
$541$	−29.4997	−1.26829	−0.634145	+	0.773214i	$0.718648\pi$
$542$	−18.2017	−0.781828
$543$	−23.3170	−1.00063
$544$	2.74540	0.117708
$545$	19.4259	0.832114
$546$	0	0
$547$	7.75142	0.331427	0.165713	−	0.986174i	$-0.447007\pi$
$547$	7.75142	0.331427	0.165713	+	0.986174i	$0.447007\pi$
$548$	−0.507806	−0.0216924
$549$	−5.40800	−0.230808
$550$	0.316965	0.0135154
$551$	23.3235	0.993616
$552$	−14.3907	−0.612509
$553$	−43.2235	−1.83805
$554$	−30.3153	−1.28798
$555$	8.00653	0.339858
$556$	−2.33878	−0.0991865
$557$	−20.2857	−0.859534	−0.429767	−	0.902940i	$-0.641404\pi$
$557$	−20.2857	−0.859534	−0.429767	+	0.902940i	$0.641404\pi$
$558$	−0.0995250	−0.00421323
$559$	0	0
$560$	34.7585	1.46882
$561$	−3.79173	−0.160087
$562$	2.90851	0.122688
$563$	−32.7633	−1.38081	−0.690403	−	0.723425i	$-0.742567\pi$
$563$	−32.7633	−1.38081	−0.690403	+	0.723425i	$0.742567\pi$
$564$	−1.49141	−0.0627997
$565$	2.98182	0.125446
$566$	42.5540	1.78868
$567$	−4.27070	−0.179353
$568$	28.0172	1.17558
$569$	27.8002	1.16545	0.582723	−	0.812671i	$-0.301987\pi$
$569$	27.8002	1.16545	0.582723	+	0.812671i	$0.301987\pi$
$570$	9.47402	0.396823
$571$	43.4425	1.81801	0.909007	−	0.416782i	$-0.136842\pi$
$571$	43.4425	1.81801	0.909007	+	0.416782i	$0.136842\pi$
$572$	0	0
$573$	11.1231	0.464674
$574$	−24.3487	−1.01630
$575$	1.14504	0.0477515
$576$	8.44494	0.351873
$577$	25.7084	1.07025	0.535127	−	0.844772i	$-0.320264\pi$
$577$	25.7084	1.07025	0.535127	+	0.844772i	$0.320264\pi$
$578$	3.58834	0.149255
$579$	23.1664	0.962764
$580$	2.05889	0.0854909
$581$	33.3507	1.38362
$582$	−5.18909	−0.215095
$583$	5.11268	0.211746
$584$	18.7726	0.776815
$585$	0	0
$586$	−23.1228	−0.955195
$587$	1.44805	0.0597673	0.0298837	−	0.999553i	$-0.490486\pi$
$587$	1.44805	0.0597673	0.0298837	+	0.999553i	$0.490486\pi$
$588$	−1.44079	−0.0594173
$589$	−0.230687	−0.00950530
$590$	−16.8128	−0.692173
$591$	9.18435	0.377794
$592$	−13.6660	−0.561668
$593$	4.27539	0.175569	0.0877845	−	0.996139i	$-0.472021\pi$
$593$	4.27539	0.175569	0.0877845	+	0.996139i	$0.472021\pi$
$594$	−1.36814	−0.0561354
$595$	35.3606	1.44964
$596$	−1.78173	−0.0729824
$597$	6.38937	0.261499
$598$	0	0
$599$	15.9807	0.652953	0.326476	−	0.945205i	$-0.394139\pi$
$599$	15.9807	0.652953	0.326476	+	0.945205i	$0.394139\pi$
$600$	−0.674563	−0.0275389
$601$	−25.2647	−1.03057	−0.515283	−	0.857020i	$-0.672313\pi$
$601$	−25.2647	−1.03057	−0.515283	+	0.857020i	$0.672313\pi$
$602$	41.5838	1.69483
$603$	10.1145	0.411895
$604$	0.294519	0.0119838
$605$	2.18365	0.0887780
$606$	−17.5999	−0.714948
$607$	41.6506	1.69055	0.845273	−	0.534334i	$-0.179437\pi$
$607$	41.6506	1.69055	0.845273	+	0.534334i	$0.179437\pi$
$608$	2.29610	0.0931190
$609$	31.4103	1.27281
$610$	16.1566	0.654162
$611$	0	0
$612$	0.486088	0.0196490
$613$	16.1620	0.652777	0.326388	−	0.945236i	$-0.394168\pi$
$613$	16.1620	0.652777	0.326388	+	0.945236i	$0.394168\pi$
$614$	33.6713	1.35886
$615$	−9.09975	−0.366937
$616$	−12.4349	−0.501015
$617$	8.12561	0.327125	0.163562	−	0.986533i	$-0.447701\pi$
$617$	8.12561	0.327125	0.163562	+	0.986533i	$0.447701\pi$
$618$	23.2550	0.935453
$619$	7.09593	0.285209	0.142605	−	0.989780i	$-0.454452\pi$
$619$	7.09593	0.285209	0.142605	+	0.989780i	$0.454452\pi$
$620$	−0.0203640	−0.000817838 0
$621$	−4.94243	−0.198333
$622$	1.37503	0.0551337
$623$	−12.2959	−0.492624
$624$	0	0
$625$	−23.7879	−0.951518
$626$	18.9821	0.758677
$627$	−3.17118	−0.126645
$628$	2.00363	0.0799536
$629$	−13.9027	−0.554337
$630$	12.7589	0.508325
$631$	3.62153	0.144171	0.0720854	−	0.997398i	$-0.477035\pi$
$631$	3.62153	0.144171	0.0720854	+	0.997398i	$0.477035\pi$
$632$	29.4688	1.17221
$633$	22.4436	0.892053
$634$	−21.3984	−0.849840
$635$	22.7159	0.901453
$636$	−0.655431	−0.0259895
$637$	0	0
$638$	10.0624	0.398375
$639$	9.62239	0.380656
$640$	−22.0674	−0.872291
$641$	−8.81244	−0.348070	−0.174035	−	0.984739i	$-0.555681\pi$
$641$	−8.81244	−0.348070	−0.174035	+	0.984739i	$0.555681\pi$
$642$	17.3505	0.684771
$643$	−47.2262	−1.86242	−0.931210	−	0.364484i	$-0.881245\pi$
$643$	−47.2262	−1.86242	−0.931210	+	0.364484i	$0.881245\pi$
$644$	−2.70594	−0.106629
$645$	15.5410	0.611925
$646$	−16.4509	−0.647251
$647$	41.0552	1.61405	0.807023	−	0.590520i	$-0.201077\pi$
$647$	41.0552	1.61405	0.807023	+	0.590520i	$0.201077\pi$
$648$	2.91167	0.114381
$649$	5.62765	0.220905
$650$	0	0
$651$	−0.310671	−0.0121762
$652$	−0.160994	−0.00630501
$653$	36.9362	1.44542	0.722712	−	0.691149i	$-0.242895\pi$
$653$	36.9362	1.44542	0.722712	+	0.691149i	$0.242895\pi$
$654$	−12.1711	−0.475926
$655$	−26.3518	−1.02965
$656$	15.5320	0.606421
$657$	6.44736	0.251536
$658$	67.9748	2.64994
$659$	39.7980	1.55031	0.775154	−	0.631772i	$-0.217672\pi$
$659$	39.7980	1.55031	0.775154	+	0.631772i	$0.217672\pi$
$660$	−0.279937	−0.0108965
$661$	−21.8622	−0.850342	−0.425171	−	0.905113i	$-0.639786\pi$
$661$	−21.8622	−0.850342	−0.425171	+	0.905113i	$0.639786\pi$
$662$	−31.6623	−1.23059
$663$	0	0
$664$	−22.7378	−0.882396
$665$	29.5736	1.14681
$666$	−5.01639	−0.194381
$667$	36.3507	1.40751
$668$	−2.22836	−0.0862180
$669$	−16.5344	−0.639255
$670$	−30.2175	−1.16740
$671$	−5.40800	−0.208774
$672$	3.09220	0.119284
$673$	−32.3152	−1.24566	−0.622830	−	0.782357i	$-0.714017\pi$
$673$	−32.3152	−1.24566	−0.622830	+	0.782357i	$0.714017\pi$
$674$	−20.7884	−0.800739
$675$	−0.231676	−0.00891721
$676$	0	0
$677$	−21.1472	−0.812753	−0.406376	−	0.913706i	$-0.633208\pi$
$677$	−21.1472	−0.812753	−0.406376	+	0.913706i	$0.633208\pi$
$678$	−1.86822	−0.0717487
$679$	−16.1979	−0.621620
$680$	−24.1081	−0.924502
$681$	−19.9826	−0.765737
$682$	−0.0995250	−0.00381101
$683$	−24.7401	−0.946654	−0.473327	−	0.880887i	$-0.656947\pi$
$683$	−24.7401	−0.946654	−0.473327	+	0.880887i	$0.656947\pi$
$684$	0.406536	0.0155443
$685$	8.64973	0.330489
$686$	24.7675	0.945626
$687$	15.8459	0.604560
$688$	−26.5262	−1.01130
$689$	0	0
$690$	14.7657	0.562120
$691$	22.7394	0.865047	0.432523	−	0.901623i	$-0.357623\pi$
$691$	22.7394	0.865047	0.432523	+	0.901623i	$0.357623\pi$
$692$	1.54989	0.0589180
$693$	−4.27070	−0.162231
$694$	−22.7857	−0.864932
$695$	39.8377	1.51113
$696$	−21.4148	−0.811727
$697$	15.8010	0.598505
$698$	39.8238	1.50735
$699$	15.9195	0.602130
$700$	−0.126840	−0.00479412
$701$	−23.8173	−0.899567	−0.449783	−	0.893138i	$-0.648499\pi$
$701$	−23.8173	−0.899567	−0.449783	+	0.893138i	$0.648499\pi$
$702$	0	0
$703$	−11.6274	−0.438536
$704$	8.44494	0.318281
$705$	25.4040	0.956769
$706$	−39.9117	−1.50210
$707$	−54.9389	−2.06619
$708$	−0.721449	−0.0271137
$709$	15.8902	0.596770	0.298385	−	0.954446i	$-0.403552\pi$
$709$	15.8902	0.596770	0.298385	+	0.954446i	$0.403552\pi$
$710$	−28.7472	−1.07886
$711$	10.1209	0.379565
$712$	8.38305	0.314168
$713$	−0.359536	−0.0134647
$714$	−22.1547	−0.829120
$715$	0	0
$716$	0.657771	0.0245821
$717$	16.9898	0.634497
$718$	24.7371	0.923181
$719$	4.64051	0.173062	0.0865309	−	0.996249i	$-0.472422\pi$
$719$	4.64051	0.173062	0.0865309	+	0.996249i	$0.472422\pi$
$720$	−8.13884	−0.303316
$721$	72.5914	2.70345
$722$	12.2361	0.455379
$723$	−21.9883	−0.817755
$724$	2.98917	0.111091
$725$	1.70394	0.0632826
$726$	−1.36814	−0.0507764
$727$	−14.5583	−0.539938	−0.269969	−	0.962869i	$-0.587013\pi$
$727$	−14.5583	−0.539938	−0.269969	+	0.962869i	$0.587013\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−19.2617	−0.712908
$731$	−26.9856	−0.998100
$732$	0.693290	0.0256247
$733$	34.2475	1.26496	0.632480	−	0.774576i	$-0.282037\pi$
$733$	34.2475	1.26496	0.632480	+	0.774576i	$0.282037\pi$
$734$	−24.8096	−0.915738
$735$	24.5418	0.905238
$736$	3.57856	0.131908
$737$	10.1145	0.372573
$738$	5.70134	0.209869
$739$	−30.5325	−1.12316	−0.561578	−	0.827424i	$-0.689806\pi$
$739$	−30.5325	−1.12316	−0.561578	+	0.827424i	$0.689806\pi$
$740$	−1.02641	−0.0377317
$741$	0	0
$742$	29.8729	1.09667
$743$	2.86476	0.105098	0.0525490	−	0.998618i	$-0.483265\pi$
$743$	2.86476	0.105098	0.0525490	+	0.998618i	$0.483265\pi$
$744$	0.211809	0.00776529
$745$	30.3491	1.11191
$746$	21.6937	0.794263
$747$	−7.80918	−0.285723
$748$	0.486088	0.0177732
$749$	54.1604	1.97898
$750$	15.6298	0.570720
$751$	38.1810	1.39324	0.696621	−	0.717439i	$-0.254686\pi$
$751$	38.1810	1.39324	0.696621	+	0.717439i	$0.254686\pi$
$752$	−43.3609	−1.58121
$753$	11.9461	0.435339
$754$	0	0
$755$	−5.01670	−0.182576
$756$	0.547491	0.0199121
$757$	−38.9456	−1.41550	−0.707750	−	0.706463i	$-0.750290\pi$
$757$	−38.9456	−1.41550	−0.707750	+	0.706463i	$0.750290\pi$
$758$	25.0960	0.911526
$759$	−4.94243	−0.179399
$760$	−20.1626	−0.731374
$761$	−26.9359	−0.976427	−0.488214	−	0.872724i	$-0.662351\pi$
$761$	−26.9359	−0.976427	−0.488214	+	0.872724i	$0.662351\pi$
$762$	−14.2324	−0.515585
$763$	−37.9925	−1.37542
$764$	−1.42595	−0.0515889
$765$	−8.27981	−0.299357
$766$	−22.0296	−0.795962
$767$	0	0
$768$	−3.06382	−0.110556
$769$	3.83575	0.138321	0.0691603	−	0.997606i	$-0.477968\pi$
$769$	3.83575	0.138321	0.0691603	+	0.997606i	$0.477968\pi$
$770$	12.7589	0.459798
$771$	28.3671	1.02162
$772$	−2.96987	−0.106888
$773$	21.7215	0.781267	0.390633	−	0.920546i	$-0.372256\pi$
$773$	21.7215	0.781267	0.390633	+	0.920546i	$0.372256\pi$
$774$	−9.73700	−0.349989
$775$	−0.0168532	−0.000605385 0
$776$	11.0434	0.396435
$777$	−15.6589	−0.561759
$778$	−44.7609	−1.60476
$779$	13.2150	0.473478
$780$	0	0
$781$	9.62239	0.344316
$782$	−25.6394	−0.916863
$783$	−7.35483	−0.262840
$784$	−41.8893	−1.49605
$785$	−34.1290	−1.21811
$786$	16.5104	0.588905
$787$	32.8705	1.17171	0.585853	−	0.810417i	$-0.300760\pi$
$787$	32.8705	1.17171	0.585853	+	0.810417i	$0.300760\pi$
$788$	−1.17741	−0.0419434
$789$	−1.37798	−0.0490574
$790$	−30.2366	−1.07577
$791$	−5.83174	−0.207353
$792$	2.91167	0.103462
$793$	0	0
$794$	−4.81154	−0.170755
$795$	11.1643	0.395957
$796$	−0.819098	−0.0290322
$797$	−2.27867	−0.0807147	−0.0403573	−	0.999185i	$-0.512850\pi$
$797$	−2.27867	−0.0807147	−0.0403573	+	0.999185i	$0.512850\pi$
$798$	−18.5289	−0.655918
$799$	−44.1120	−1.56057
$800$	0.167745	0.00593068
$801$	2.87912	0.101729
$802$	25.4789	0.899693
$803$	6.44736	0.227523
$804$	−1.29665	−0.0457294
$805$	46.0917	1.62452
$806$	0	0
$807$	−14.6274	−0.514908
$808$	37.4561	1.31770
$809$	25.3935	0.892786	0.446393	−	0.894837i	$-0.352708\pi$
$809$	25.3935	0.892786	0.446393	+	0.894837i	$0.352708\pi$
$810$	−2.98753	−0.104971
$811$	−32.7178	−1.14888	−0.574439	−	0.818548i	$-0.694780\pi$
$811$	−32.7178	−1.14888	−0.574439	+	0.818548i	$0.694780\pi$
$812$	−4.02671	−0.141310
$813$	13.3040	0.466590
$814$	−5.01639	−0.175824
$815$	2.74230	0.0960584
$816$	14.1324	0.494734
$817$	−22.5692	−0.789597
$818$	−24.1899	−0.845779
$819$	0	0
$820$	1.16656	0.0407381
$821$	−31.2361	−1.09015	−0.545073	−	0.838388i	$-0.683498\pi$
$821$	−31.2361	−1.09015	−0.545073	+	0.838388i	$0.683498\pi$
$822$	−5.41938	−0.189023
$823$	8.94424	0.311777	0.155888	−	0.987775i	$-0.450176\pi$
$823$	8.94424	0.311777	0.155888	+	0.987775i	$0.450176\pi$
$824$	−49.4912	−1.72411
$825$	−0.231676	−0.00806592
$826$	32.8819	1.14411
$827$	−28.6667	−0.996838	−0.498419	−	0.866936i	$-0.666086\pi$
$827$	−28.6667	−0.996838	−0.498419	+	0.866936i	$0.666086\pi$
$828$	0.633605	0.0220193
$829$	39.5515	1.37368	0.686839	−	0.726809i	$-0.258998\pi$
$829$	39.5515	1.37368	0.686839	+	0.726809i	$0.258998\pi$
$830$	23.3302	0.809803
$831$	22.1581	0.768656
$832$	0	0
$833$	−42.6148	−1.47652
$834$	−24.9598	−0.864289
$835$	37.9569	1.31355
$836$	0.406536	0.0140604
$837$	0.0727448	0.00251443
$838$	2.64100	0.0912320
$839$	45.1833	1.55990	0.779951	−	0.625840i	$-0.215244\pi$
$839$	45.1833	1.55990	0.779951	+	0.625840i	$0.215244\pi$
$840$	−27.1534	−0.936881
$841$	25.0936	0.865296
$842$	9.87443	0.340295
$843$	−2.12589	−0.0732195
$844$	−2.87720	−0.0990375
$845$	0	0
$846$	−15.9166	−0.547222
$847$	−4.27070	−0.146743
$848$	−19.0558	−0.654380
$849$	−31.1036	−1.06747
$850$	−1.20184	−0.0412229
$851$	−18.1218	−0.621208
$852$	−1.23356	−0.0422611
$853$	−13.2579	−0.453943	−0.226972	−	0.973901i	$-0.572882\pi$
$853$	−13.2579	−0.453943	−0.226972	+	0.973901i	$0.572882\pi$
$854$	−31.5985	−1.08128
$855$	−6.92475	−0.236822
$856$	−36.9254	−1.26208
$857$	38.9268	1.32971	0.664857	−	0.746971i	$-0.268493\pi$
$857$	38.9268	1.32971	0.664857	+	0.746971i	$0.268493\pi$
$858$	0	0
$859$	−21.2750	−0.725893	−0.362947	−	0.931810i	$-0.618229\pi$
$859$	−21.2750	−0.725893	−0.362947	+	0.931810i	$0.618229\pi$
$860$	−1.99231	−0.0679371
$861$	17.7970	0.606519
$862$	40.7535	1.38807
$863$	−8.94497	−0.304490	−0.152245	−	0.988343i	$-0.548650\pi$
$863$	−8.94497	−0.304490	−0.152245	+	0.988343i	$0.548650\pi$
$864$	−0.724050	−0.0246327
$865$	−26.4001	−0.897630
$866$	34.5412	1.17376
$867$	−2.62279	−0.0890746
$868$	0.0398271	0.00135182
$869$	10.1209	0.343329
$870$	21.9728	0.744948
$871$	0	0
$872$	25.9024	0.877166
$873$	3.79281	0.128367
$874$	−21.4433	−0.725331
$875$	48.7891	1.64937
$876$	−0.826533	−0.0279260
$877$	11.5696	0.390679	0.195340	−	0.980736i	$-0.437419\pi$
$877$	11.5696	0.390679	0.195340	+	0.980736i	$0.437419\pi$
$878$	12.4105	0.418835
$879$	16.9009	0.570055
$880$	−8.13884	−0.274360
$881$	−13.2958	−0.447947	−0.223974	−	0.974595i	$-0.571903\pi$
$881$	−13.2958	−0.447947	−0.223974	+	0.974595i	$0.571903\pi$
$882$	−15.3764	−0.517749
$883$	−18.7422	−0.630726	−0.315363	−	0.948971i	$-0.602126\pi$
$883$	−18.7422	−0.630726	−0.315363	+	0.948971i	$0.602126\pi$
$884$	0	0
$885$	12.2888	0.413084
$886$	16.5207	0.555024
$887$	41.6306	1.39782	0.698910	−	0.715210i	$-0.253669\pi$
$887$	41.6306	1.39782	0.698910	+	0.715210i	$0.253669\pi$
$888$	10.6759	0.358259
$889$	−44.4269	−1.49003
$890$	−8.60148	−0.288322
$891$	1.00000	0.0335013
$892$	2.11966	0.0709713
$893$	−36.8927	−1.23457
$894$	−19.0149	−0.635953
$895$	−11.2042	−0.374514
$896$	43.1586	1.44183
$897$	0	0
$898$	−12.2372	−0.408359
$899$	−0.535026	−0.0178441
$900$	0.0297002	0.000990005 0
$901$	−19.3859	−0.645838
$902$	5.70134	0.189834
$903$	−30.3945	−1.01146
$904$	3.97595	0.132238
$905$	−50.9161	−1.69251
$906$	3.14315	0.104424
$907$	37.0540	1.23036	0.615179	−	0.788387i	$-0.289084\pi$
$907$	37.0540	1.23036	0.615179	+	0.788387i	$0.289084\pi$
$908$	2.56172	0.0850136
$909$	12.8641	0.426676
$910$	0	0
$911$	−43.8739	−1.45361	−0.726804	−	0.686845i	$-0.758995\pi$
$911$	−43.8739	−1.45361	−0.726804	+	0.686845i	$0.758995\pi$
$912$	11.8195	0.391384
$913$	−7.80918	−0.258446
$914$	38.9885	1.28962
$915$	−11.8092	−0.390400
$916$	−2.03140	−0.0671194
$917$	51.5378	1.70193
$918$	5.18761	0.171217
$919$	−30.1561	−0.994759	−0.497380	−	0.867533i	$-0.665704\pi$
$919$	−30.1561	−0.994759	−0.497380	+	0.867533i	$0.665704\pi$
$920$	−31.4243	−1.03603
$921$	−24.6110	−0.810961
$922$	26.3475	0.867710
$923$	0	0
$924$	0.547491	0.0180111
$925$	−0.849459	−0.0279300
$926$	−49.7508	−1.63491
$927$	−16.9975	−0.558272
$928$	5.32527	0.174810
$929$	−29.2684	−0.960264	−0.480132	−	0.877196i	$-0.659411\pi$
$929$	−29.2684	−0.960264	−0.480132	+	0.877196i	$0.659411\pi$
$930$	−0.217328	−0.00712645
$931$	−35.6406	−1.16807
$932$	−2.04083	−0.0668496
$933$	−1.00504	−0.0329034
$934$	−2.33056	−0.0762583
$935$	−8.27981	−0.270779
$936$	0	0
$937$	−14.7979	−0.483427	−0.241713	−	0.970348i	$-0.577709\pi$
$937$	−14.7979	−0.483427	−0.241713	+	0.970348i	$0.577709\pi$
$938$	59.0983	1.92963
$939$	−13.8744	−0.452774
$940$	−3.25672	−0.106222
$941$	17.5021	0.570553	0.285276	−	0.958445i	$-0.407915\pi$
$941$	17.5021	0.570553	0.285276	+	0.958445i	$0.407915\pi$
$942$	21.3831	0.696698
$943$	20.5962	0.670704
$944$	−20.9752	−0.682686
$945$	−9.32571	−0.303365
$946$	−9.73700	−0.316577
$947$	32.5998	1.05935	0.529675	−	0.848201i	$-0.322314\pi$
$947$	32.5998	1.05935	0.529675	+	0.848201i	$0.322314\pi$
$948$	−1.29747	−0.0421400
$949$	0	0
$950$	−1.00515	−0.0326115
$951$	15.6405	0.507179
$952$	47.1496	1.52813
$953$	−44.8368	−1.45241	−0.726204	−	0.687479i	$-0.758717\pi$
$953$	−44.8368	−1.45241	−0.726204	+	0.687479i	$0.758717\pi$
$954$	−6.99486	−0.226467
$955$	24.2889	0.785971
$956$	−2.17805	−0.0704431
$957$	−7.35483	−0.237748
$958$	33.6304	1.08655
$959$	−16.9168	−0.546273
$960$	18.4408	0.595174
$961$	−30.9947	−0.999829
$962$	0	0
$963$	−12.6819	−0.408667
$964$	2.81884	0.0907887
$965$	50.5874	1.62847
$966$	−28.8782	−0.929140
$967$	21.7225	0.698550	0.349275	−	0.937020i	$-0.386428\pi$
$967$	21.7225	0.698550	0.349275	+	0.937020i	$0.386428\pi$
$968$	2.91167	0.0935846
$969$	12.0243	0.386275
$970$	−11.3311	−0.363821
$971$	−28.7521	−0.922699	−0.461349	−	0.887219i	$-0.652635\pi$
$971$	−28.7521	−0.922699	−0.461349	+	0.887219i	$0.652635\pi$
$972$	−0.128197	−0.00411192
$973$	−77.9132	−2.49778
$974$	−55.4466	−1.77662
$975$	0	0
$976$	20.1566	0.645196
$977$	13.7868	0.441077	0.220539	−	0.975378i	$-0.429218\pi$
$977$	13.7868	0.441077	0.220539	+	0.975378i	$0.429218\pi$
$978$	−1.71815	−0.0549404
$979$	2.87912	0.0920172
$980$	−3.14619	−0.100501
$981$	8.89607	0.284030
$982$	−23.0182	−0.734540
$983$	−32.5478	−1.03811	−0.519056	−	0.854740i	$-0.673716\pi$
$983$	−32.5478	−1.03811	−0.519056	+	0.854740i	$0.673716\pi$
$984$	−12.1336	−0.386804
$985$	20.0554	0.639018
$986$	−38.1540	−1.21507
$987$	−49.6842	−1.58146
$988$	0	0
$989$	−35.1751	−1.11850
$990$	−2.98753	−0.0949501
$991$	−3.97937	−0.126409	−0.0632044	−	0.998001i	$-0.520132\pi$
$991$	−3.97937	−0.126409	−0.0632044	+	0.998001i	$0.520132\pi$
$992$	−0.0526709	−0.00167230
$993$	23.1426	0.734409
$994$	56.2227	1.78328
$995$	13.9521	0.442312
$996$	1.00111	0.0317215
$997$	−24.9767	−0.791021	−0.395511	−	0.918461i	$-0.629432\pi$
$997$	−24.9767	−0.791021	−0.395511	+	0.918461i	$0.629432\pi$
$998$	−39.0125	−1.23492
$999$	3.66658	0.116006

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.y.1.2		7
13.5	odd	4		429.2.b.b.298.10	yes	14
13.8	odd	4		429.2.b.b.298.5	✓	14
13.12	even	2		5577.2.a.x.1.6		7
39.5	even	4		1287.2.b.c.298.5		14
39.8	even	4		1287.2.b.c.298.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.b.298.5	✓	14	13.8	odd	4
429.2.b.b.298.10	yes	14	13.5	odd	4
1287.2.b.c.298.5		14	39.5	even	4
1287.2.b.c.298.10		14	39.8	even	4
5577.2.a.x.1.6		7	13.12	even	2
5577.2.a.y.1.2		7	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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36814 q^{2} +1.00000 q^{3} -0.128197 q^{4} +2.18365 q^{5} -1.36814 q^{6} -4.27070 q^{7} +2.91167 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.36814 q^{2} +1.00000 q^{3} -0.128197 q^{4} +2.18365 q^{5} -1.36814 q^{6} -4.27070 q^{7} +2.91167 q^{8} +1.00000 q^{9} -2.98753 q^{10} +1.00000 q^{11} -0.128197 q^{12} +5.84291 q^{14} +2.18365 q^{15} -3.72717 q^{16} -3.79173 q^{17} -1.36814 q^{18} -3.17118 q^{19} -0.279937 q^{20} -4.27070 q^{21} -1.36814 q^{22} -4.94243 q^{23} +2.91167 q^{24} -0.231676 q^{25} +1.00000 q^{27} +0.547491 q^{28} -7.35483 q^{29} -2.98753 q^{30} +0.0727448 q^{31} -0.724050 q^{32} +1.00000 q^{33} +5.18761 q^{34} -9.32571 q^{35} -0.128197 q^{36} +3.66658 q^{37} +4.33862 q^{38} +6.35806 q^{40} -4.16722 q^{41} +5.84291 q^{42} +7.11697 q^{43} -0.128197 q^{44} +2.18365 q^{45} +6.76193 q^{46} +11.6337 q^{47} -3.72717 q^{48} +11.2389 q^{49} +0.316965 q^{50} -3.79173 q^{51} +5.11268 q^{53} -1.36814 q^{54} +2.18365 q^{55} -12.4349 q^{56} -3.17118 q^{57} +10.0624 q^{58} +5.62765 q^{59} -0.279937 q^{60} -5.40800 q^{61} -0.0995250 q^{62} -4.27070 q^{63} +8.44494 q^{64} -1.36814 q^{66} +10.1145 q^{67} +0.486088 q^{68} -4.94243 q^{69} +12.7589 q^{70} +9.62239 q^{71} +2.91167 q^{72} +6.44736 q^{73} -5.01639 q^{74} -0.231676 q^{75} +0.406536 q^{76} -4.27070 q^{77} +10.1209 q^{79} -8.13884 q^{80} +1.00000 q^{81} +5.70134 q^{82} -7.80918 q^{83} +0.547491 q^{84} -8.27981 q^{85} -9.73700 q^{86} -7.35483 q^{87} +2.91167 q^{88} +2.87912 q^{89} -2.98753 q^{90} +0.633605 q^{92} +0.0727448 q^{93} -15.9166 q^{94} -6.92475 q^{95} -0.724050 q^{96} +3.79281 q^{97} -15.3764 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9	\( 7 q + 3 q^{2} + 7 q^{3} + 9 q^{4} + 6 q^{5} + 3 q^{6} + 6 q^{7} + 15 q^{8} + 7 q^{9} + 7 q^{11} + 9 q^{12} + 8 q^{14} + 6 q^{15} + 17 q^{16} - 2 q^{17} + 3 q^{18} + 8 q^{19} - 2 q^{20} + 6 q^{21} + 3 q^{22} + 4 q^{23} + 15 q^{24} + 13 q^{25} + 7 q^{27} + 12 q^{28} - 12 q^{29} - 10 q^{31} + 33 q^{32} + 7 q^{33} + 28 q^{34} - 4 q^{35} + 9 q^{36} + 6 q^{37} + 16 q^{38} - 10 q^{40} + 2 q^{41} + 8 q^{42} - 16 q^{43} + 9 q^{44} + 6 q^{45} - 26 q^{46} + 18 q^{47} + 17 q^{48} + 23 q^{49} + 39 q^{50} - 2 q^{51} + 10 q^{53} + 3 q^{54} + 6 q^{55} + 16 q^{56} + 8 q^{57} + 10 q^{58} + 2 q^{59} - 2 q^{60} - 10 q^{61} - 36 q^{62} + 6 q^{63} + 29 q^{64} + 3 q^{66} + 8 q^{67} - 10 q^{68} + 4 q^{69} - 20 q^{70} + 36 q^{71} + 15 q^{72} + 20 q^{73} + 13 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} - 20 q^{80} + 7 q^{81} - 10 q^{82} + 30 q^{83} + 12 q^{84} - 40 q^{85} + 6 q^{86} - 12 q^{87} + 15 q^{88} + 34 q^{89} - 12 q^{92} - 10 q^{93} + 32 q^{94} + 18 q^{95} + 33 q^{96} + 16 q^{97} + q^{98} + 7 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 + 7 * q^3 + 9 * q^4 + 6 * q^5 + 3 * q^6 + 6 * q^7 + 15 * q^8 + 7 * q^9 + 7 * q^11 + 9 * q^12 + 8 * q^14 + 6 * q^15 + 17 * q^16 - 2 * q^17 + 3 * q^18 + 8 * q^19 - 2 * q^20 + 6 * q^21 + 3 * q^22 + 4 * q^23 + 15 * q^24 + 13 * q^25 + 7 * q^27 + 12 * q^28 - 12 * q^29 - 10 * q^31 + 33 * q^32 + 7 * q^33 + 28 * q^34 - 4 * q^35 + 9 * q^36 + 6 * q^37 + 16 * q^38 - 10 * q^40 + 2 * q^41 + 8 * q^42 - 16 * q^43 + 9 * q^44 + 6 * q^45 - 26 * q^46 + 18 * q^47 + 17 * q^48 + 23 * q^49 + 39 * q^50 - 2 * q^51 + 10 * q^53 + 3 * q^54 + 6 * q^55 + 16 * q^56 + 8 * q^57 + 10 * q^58 + 2 * q^59 - 2 * q^60 - 10 * q^61 - 36 * q^62 + 6 * q^63 + 29 * q^64 + 3 * q^66 + 8 * q^67 - 10 * q^68 + 4 * q^69 - 20 * q^70 + 36 * q^71 + 15 * q^72 + 20 * q^73 + 13 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 - 20 * q^80 + 7 * q^81 - 10 * q^82 + 30 * q^83 + 12 * q^84 - 40 * q^85 + 6 * q^86 - 12 * q^87 + 15 * q^88 + 34 * q^89 - 12 * q^92 - 10 * q^93 + 32 * q^94 + 18 * q^95 + 33 * q^96 + 16 * q^97 + q^98 + 7 * q^99

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