LMFDB - Embedded newform 4730.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.56155 q^{6} -3.00000 q^{7} -1.00000 q^{8} +3.56155 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.56155 q^{6} -3.00000 q^{7} -1.00000 q^{8} +3.56155 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.56155 q^{12} +3.56155 q^{13} +3.00000 q^{14} -2.56155 q^{15} +1.00000 q^{16} +1.43845 q^{17} -3.56155 q^{18} -1.00000 q^{19} +1.00000 q^{20} +7.68466 q^{21} +1.00000 q^{22} -9.12311 q^{23} +2.56155 q^{24} +1.00000 q^{25} -3.56155 q^{26} -1.43845 q^{27} -3.00000 q^{28} +6.12311 q^{29} +2.56155 q^{30} -2.12311 q^{31} -1.00000 q^{32} +2.56155 q^{33} -1.43845 q^{34} -3.00000 q^{35} +3.56155 q^{36} -2.56155 q^{37} +1.00000 q^{38} -9.12311 q^{39} -1.00000 q^{40} -0.438447 q^{41} -7.68466 q^{42} +1.00000 q^{43} -1.00000 q^{44} +3.56155 q^{45} +9.12311 q^{46} -2.00000 q^{47} -2.56155 q^{48} +2.00000 q^{49} -1.00000 q^{50} -3.68466 q^{51} +3.56155 q^{52} +0.561553 q^{53} +1.43845 q^{54} -1.00000 q^{55} +3.00000 q^{56} +2.56155 q^{57} -6.12311 q^{58} +9.12311 q^{59} -2.56155 q^{60} +10.3693 q^{61} +2.12311 q^{62} -10.6847 q^{63} +1.00000 q^{64} +3.56155 q^{65} -2.56155 q^{66} -5.56155 q^{67} +1.43845 q^{68} +23.3693 q^{69} +3.00000 q^{70} +12.5616 q^{71} -3.56155 q^{72} -3.56155 q^{73} +2.56155 q^{74} -2.56155 q^{75} -1.00000 q^{76} +3.00000 q^{77} +9.12311 q^{78} +3.56155 q^{79} +1.00000 q^{80} -7.00000 q^{81} +0.438447 q^{82} +7.36932 q^{83} +7.68466 q^{84} +1.43845 q^{85} -1.00000 q^{86} -15.6847 q^{87} +1.00000 q^{88} -11.6847 q^{89} -3.56155 q^{90} -10.6847 q^{91} -9.12311 q^{92} +5.43845 q^{93} +2.00000 q^{94} -1.00000 q^{95} +2.56155 q^{96} +4.87689 q^{97} -2.00000 q^{98} -3.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 6 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} - q^{12} + 3 q^{13} + 6 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} - 3 q^{18} - 2 q^{19} + 2 q^{20} + 3 q^{21} + 2 q^{22} - 10 q^{23} + q^{24} + 2 q^{25} - 3 q^{26} - 7 q^{27} - 6 q^{28} + 4 q^{29} + q^{30} + 4 q^{31} - 2 q^{32} + q^{33} - 7 q^{34} - 6 q^{35} + 3 q^{36} - q^{37} + 2 q^{38} - 10 q^{39} - 2 q^{40} - 5 q^{41} - 3 q^{42} + 2 q^{43} - 2 q^{44} + 3 q^{45} + 10 q^{46} - 4 q^{47} - q^{48} + 4 q^{49} - 2 q^{50} + 5 q^{51} + 3 q^{52} - 3 q^{53} + 7 q^{54} - 2 q^{55} + 6 q^{56} + q^{57} - 4 q^{58} + 10 q^{59} - q^{60} - 4 q^{61} - 4 q^{62} - 9 q^{63} + 2 q^{64} + 3 q^{65} - q^{66} - 7 q^{67} + 7 q^{68} + 22 q^{69} + 6 q^{70} + 21 q^{71} - 3 q^{72} - 3 q^{73} + q^{74} - q^{75} - 2 q^{76} + 6 q^{77} + 10 q^{78} + 3 q^{79} + 2 q^{80} - 14 q^{81} + 5 q^{82} - 10 q^{83} + 3 q^{84} + 7 q^{85} - 2 q^{86} - 19 q^{87} + 2 q^{88} - 11 q^{89} - 3 q^{90} - 9 q^{91} - 10 q^{92} + 15 q^{93} + 4 q^{94} - 2 q^{95} + q^{96} + 18 q^{97} - 4 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 6 * q^7 - 2 * q^8 + 3 * q^9 - 2 * q^10 - 2 * q^11 - q^12 + 3 * q^13 + 6 * q^14 - q^15 + 2 * q^16 + 7 * q^17 - 3 * q^18 - 2 * q^19 + 2 * q^20 + 3 * q^21 + 2 * q^22 - 10 * q^23 + q^24 + 2 * q^25 - 3 * q^26 - 7 * q^27 - 6 * q^28 + 4 * q^29 + q^30 + 4 * q^31 - 2 * q^32 + q^33 - 7 * q^34 - 6 * q^35 + 3 * q^36 - q^37 + 2 * q^38 - 10 * q^39 - 2 * q^40 - 5 * q^41 - 3 * q^42 + 2 * q^43 - 2 * q^44 + 3 * q^45 + 10 * q^46 - 4 * q^47 - q^48 + 4 * q^49 - 2 * q^50 + 5 * q^51 + 3 * q^52 - 3 * q^53 + 7 * q^54 - 2 * q^55 + 6 * q^56 + q^57 - 4 * q^58 + 10 * q^59 - q^60 - 4 * q^61 - 4 * q^62 - 9 * q^63 + 2 * q^64 + 3 * q^65 - q^66 - 7 * q^67 + 7 * q^68 + 22 * q^69 + 6 * q^70 + 21 * q^71 - 3 * q^72 - 3 * q^73 + q^74 - q^75 - 2 * q^76 + 6 * q^77 + 10 * q^78 + 3 * q^79 + 2 * q^80 - 14 * q^81 + 5 * q^82 - 10 * q^83 + 3 * q^84 + 7 * q^85 - 2 * q^86 - 19 * q^87 + 2 * q^88 - 11 * q^89 - 3 * q^90 - 9 * q^91 - 10 * q^92 + 15 * q^93 + 4 * q^94 - 2 * q^95 + q^96 + 18 * q^97 - 4 * q^98 - 3 * 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
$3$	−2.56155	−1.47891	−0.739457	−	0.673204i	$-0.764917\pi$
$3$	−2.56155	−1.47891	−0.739457	+	0.673204i	$0.764917\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.56155	1.04575
$7$	−3.00000	−1.13389	−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000	−1.13389	−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000	−0.353553
$9$	3.56155	1.18718
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.56155	−0.739457
$13$	3.56155	0.987797	0.493899	−	0.869520i	$-0.335571\pi$
$13$	3.56155	0.987797	0.493899	+	0.869520i	$0.335571\pi$
$14$	3.00000	0.801784
$15$	−2.56155	−0.661390
$16$	1.00000	0.250000
$17$	1.43845	0.348875	0.174437	−	0.984668i	$-0.444189\pi$
$17$	1.43845	0.348875	0.174437	+	0.984668i	$0.444189\pi$
$18$	−3.56155	−0.839466
$19$	−1.00000	−0.229416	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	−1.00000	−0.229416	−0.114708	+	0.993399i	$0.536593\pi$
$20$	1.00000	0.223607
$21$	7.68466	1.67693
$22$	1.00000	0.213201
$23$	−9.12311	−1.90230	−0.951150	−	0.308731i	$-0.900096\pi$
$23$	−9.12311	−1.90230	−0.951150	+	0.308731i	$0.900096\pi$
$24$	2.56155	0.522875
$25$	1.00000	0.200000
$26$	−3.56155	−0.698478
$27$	−1.43845	−0.276829
$28$	−3.00000	−0.566947
$29$	6.12311	1.13703	0.568516	−	0.822672i	$-0.307518\pi$
$29$	6.12311	1.13703	0.568516	+	0.822672i	$0.307518\pi$
$30$	2.56155	0.467673
$31$	−2.12311	−0.381321	−0.190661	−	0.981656i	$-0.561063\pi$
$31$	−2.12311	−0.381321	−0.190661	+	0.981656i	$0.561063\pi$
$32$	−1.00000	−0.176777
$33$	2.56155	0.445909
$34$	−1.43845	−0.246692
$35$	−3.00000	−0.507093
$36$	3.56155	0.593592
$37$	−2.56155	−0.421117	−0.210558	−	0.977581i	$-0.567528\pi$
$37$	−2.56155	−0.421117	−0.210558	+	0.977581i	$0.567528\pi$
$38$	1.00000	0.162221
$39$	−9.12311	−1.46087
$40$	−1.00000	−0.158114
$41$	−0.438447	−0.0684739	−0.0342370	−	0.999414i	$-0.510900\pi$
$41$	−0.438447	−0.0684739	−0.0342370	+	0.999414i	$0.510900\pi$
$42$	−7.68466	−1.18577
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	3.56155	0.530925
$46$	9.12311	1.34513
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	−2.56155	−0.369728
$49$	2.00000	0.285714
$50$	−1.00000	−0.141421
$51$	−3.68466	−0.515955
$52$	3.56155	0.493899
$53$	0.561553	0.0771352	0.0385676	−	0.999256i	$-0.487721\pi$
$53$	0.561553	0.0771352	0.0385676	+	0.999256i	$0.487721\pi$
$54$	1.43845	0.195748
$55$	−1.00000	−0.134840
$56$	3.00000	0.400892
$57$	2.56155	0.339286
$58$	−6.12311	−0.804003
$59$	9.12311	1.18773	0.593864	−	0.804566i	$-0.297602\pi$
$59$	9.12311	1.18773	0.593864	+	0.804566i	$0.297602\pi$
$60$	−2.56155	−0.330695
$61$	10.3693	1.32765	0.663827	−	0.747886i	$-0.268931\pi$
$61$	10.3693	1.32765	0.663827	+	0.747886i	$0.268931\pi$
$62$	2.12311	0.269635
$63$	−10.6847	−1.34614
$64$	1.00000	0.125000
$65$	3.56155	0.441756
$66$	−2.56155	−0.315305
$67$	−5.56155	−0.679452	−0.339726	−	0.940524i	$-0.610334\pi$
$67$	−5.56155	−0.679452	−0.339726	+	0.940524i	$0.610334\pi$
$68$	1.43845	0.174437
$69$	23.3693	2.81334
$70$	3.00000	0.358569
$71$	12.5616	1.49078	0.745391	−	0.666627i	$-0.232263\pi$
$71$	12.5616	1.49078	0.745391	+	0.666627i	$0.232263\pi$
$72$	−3.56155	−0.419733
$73$	−3.56155	−0.416848	−0.208424	−	0.978039i	$-0.566833\pi$
$73$	−3.56155	−0.416848	−0.208424	+	0.978039i	$0.566833\pi$
$74$	2.56155	0.297774
$75$	−2.56155	−0.295783
$76$	−1.00000	−0.114708
$77$	3.00000	0.341882
$78$	9.12311	1.03299
$79$	3.56155	0.400706	0.200353	−	0.979724i	$-0.435791\pi$
$79$	3.56155	0.400706	0.200353	+	0.979724i	$0.435791\pi$
$80$	1.00000	0.111803
$81$	−7.00000	−0.777778
$82$	0.438447	0.0484184
$83$	7.36932	0.808888	0.404444	−	0.914563i	$-0.367465\pi$
$83$	7.36932	0.808888	0.404444	+	0.914563i	$0.367465\pi$
$84$	7.68466	0.838465
$85$	1.43845	0.156022
$86$	−1.00000	−0.107833
$87$	−15.6847	−1.68157
$88$	1.00000	0.106600
$89$	−11.6847	−1.23857	−0.619286	−	0.785166i	$-0.712578\pi$
$89$	−11.6847	−1.23857	−0.619286	+	0.785166i	$0.712578\pi$
$90$	−3.56155	−0.375421
$91$	−10.6847	−1.12006
$92$	−9.12311	−0.951150
$93$	5.43845	0.563941
$94$	2.00000	0.206284
$95$	−1.00000	−0.102598
$96$	2.56155	0.261437
$97$	4.87689	0.495174	0.247587	−	0.968866i	$-0.420362\pi$
$97$	4.87689	0.495174	0.247587	+	0.968866i	$0.420362\pi$
$98$	−2.00000	−0.202031
$99$	−3.56155	−0.357950
$100$	1.00000	0.100000
$101$	−5.12311	−0.509768	−0.254884	−	0.966972i	$-0.582037\pi$
$101$	−5.12311	−0.509768	−0.254884	+	0.966972i	$0.582037\pi$
$102$	3.68466	0.364836
$103$	−19.1231	−1.88426	−0.942128	−	0.335254i	$-0.891178\pi$
$103$	−19.1231	−1.88426	−0.942128	+	0.335254i	$0.891178\pi$
$104$	−3.56155	−0.349239
$105$	7.68466	0.749946
$106$	−0.561553	−0.0545428
$107$	4.68466	0.452883	0.226442	−	0.974025i	$-0.427291\pi$
$107$	4.68466	0.452883	0.226442	+	0.974025i	$0.427291\pi$
$108$	−1.43845	−0.138415
$109$	−2.87689	−0.275557	−0.137778	−	0.990463i	$-0.543996\pi$
$109$	−2.87689	−0.275557	−0.137778	+	0.990463i	$0.543996\pi$
$110$	1.00000	0.0953463
$111$	6.56155	0.622795
$112$	−3.00000	−0.283473
$113$	8.68466	0.816984	0.408492	−	0.912762i	$-0.366055\pi$
$113$	8.68466	0.816984	0.408492	+	0.912762i	$0.366055\pi$
$114$	−2.56155	−0.239911
$115$	−9.12311	−0.850734
$116$	6.12311	0.568516
$117$	12.6847	1.17270
$118$	−9.12311	−0.839850
$119$	−4.31534	−0.395587
$120$	2.56155	0.233837
$121$	1.00000	0.0909091
$122$	−10.3693	−0.938794
$123$	1.12311	0.101267
$124$	−2.12311	−0.190661
$125$	1.00000	0.0894427
$126$	10.6847	0.951865
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.00000	−0.0883883
$129$	−2.56155	−0.225532
$130$	−3.56155	−0.312369
$131$	3.68466	0.321930	0.160965	−	0.986960i	$-0.448539\pi$
$131$	3.68466	0.321930	0.160965	+	0.986960i	$0.448539\pi$
$132$	2.56155	0.222955
$133$	3.00000	0.260133
$134$	5.56155	0.480445
$135$	−1.43845	−0.123802
$136$	−1.43845	−0.123346
$137$	14.9309	1.27563	0.637815	−	0.770189i	$-0.279838\pi$
$137$	14.9309	1.27563	0.637815	+	0.770189i	$0.279838\pi$
$138$	−23.3693	−1.98933
$139$	2.24621	0.190521	0.0952606	−	0.995452i	$-0.469632\pi$
$139$	2.24621	0.190521	0.0952606	+	0.995452i	$0.469632\pi$
$140$	−3.00000	−0.253546
$141$	5.12311	0.431443
$142$	−12.5616	−1.05414
$143$	−3.56155	−0.297832
$144$	3.56155	0.296796
$145$	6.12311	0.508496
$146$	3.56155	0.294756
$147$	−5.12311	−0.422547
$148$	−2.56155	−0.210558
$149$	4.12311	0.337778	0.168889	−	0.985635i	$-0.445982\pi$
$149$	4.12311	0.337778	0.168889	+	0.985635i	$0.445982\pi$
$150$	2.56155	0.209150
$151$	20.2462	1.64761	0.823807	−	0.566871i	$-0.191846\pi$
$151$	20.2462	1.64761	0.823807	+	0.566871i	$0.191846\pi$
$152$	1.00000	0.0811107
$153$	5.12311	0.414179
$154$	−3.00000	−0.241747
$155$	−2.12311	−0.170532
$156$	−9.12311	−0.730433
$157$	3.68466	0.294068	0.147034	−	0.989131i	$-0.453027\pi$
$157$	3.68466	0.294068	0.147034	+	0.989131i	$0.453027\pi$
$158$	−3.56155	−0.283342
$159$	−1.43845	−0.114076
$160$	−1.00000	−0.0790569
$161$	27.3693	2.15700
$162$	7.00000	0.549972
$163$	20.1771	1.58039	0.790195	−	0.612855i	$-0.209979\pi$
$163$	20.1771	1.58039	0.790195	+	0.612855i	$0.209979\pi$
$164$	−0.438447	−0.0342370
$165$	2.56155	0.199417
$166$	−7.36932	−0.571970
$167$	−15.6847	−1.21372	−0.606858	−	0.794811i	$-0.707570\pi$
$167$	−15.6847	−1.21372	−0.606858	+	0.794811i	$0.707570\pi$
$168$	−7.68466	−0.592884
$169$	−0.315342	−0.0242570
$170$	−1.43845	−0.110324
$171$	−3.56155	−0.272359
$172$	1.00000	0.0762493
$173$	−8.43845	−0.641563	−0.320782	−	0.947153i	$-0.603946\pi$
$173$	−8.43845	−0.641563	−0.320782	+	0.947153i	$0.603946\pi$
$174$	15.6847	1.18905
$175$	−3.00000	−0.226779
$176$	−1.00000	−0.0753778
$177$	−23.3693	−1.75655
$178$	11.6847	0.875802
$179$	−11.3153	−0.845748	−0.422874	−	0.906188i	$-0.638979\pi$
$179$	−11.3153	−0.845748	−0.422874	+	0.906188i	$0.638979\pi$
$180$	3.56155	0.265462
$181$	2.87689	0.213838	0.106919	−	0.994268i	$-0.465901\pi$
$181$	2.87689	0.213838	0.106919	+	0.994268i	$0.465901\pi$
$182$	10.6847	0.792000
$183$	−26.5616	−1.96349
$184$	9.12311	0.672564
$185$	−2.56155	−0.188329
$186$	−5.43845	−0.398766
$187$	−1.43845	−0.105190
$188$	−2.00000	−0.145865
$189$	4.31534	0.313895
$190$	1.00000	0.0725476
$191$	−5.36932	−0.388510	−0.194255	−	0.980951i	$-0.562229\pi$
$191$	−5.36932	−0.388510	−0.194255	+	0.980951i	$0.562229\pi$
$192$	−2.56155	−0.184864
$193$	−0.807764	−0.0581441	−0.0290721	−	0.999577i	$-0.509255\pi$
$193$	−0.807764	−0.0581441	−0.0290721	+	0.999577i	$0.509255\pi$
$194$	−4.87689	−0.350141
$195$	−9.12311	−0.653319
$196$	2.00000	0.142857
$197$	8.68466	0.618756	0.309378	−	0.950939i	$-0.399879\pi$
$197$	8.68466	0.618756	0.309378	+	0.950939i	$0.399879\pi$
$198$	3.56155	0.253109
$199$	12.5616	0.890465	0.445232	−	0.895415i	$-0.353121\pi$
$199$	12.5616	0.890465	0.445232	+	0.895415i	$0.353121\pi$
$200$	−1.00000	−0.0707107
$201$	14.2462	1.00485
$202$	5.12311	0.360460
$203$	−18.3693	−1.28927
$204$	−3.68466	−0.257978
$205$	−0.438447	−0.0306225
$206$	19.1231	1.33237
$207$	−32.4924	−2.25838
$208$	3.56155	0.246949
$209$	1.00000	0.0691714
$210$	−7.68466	−0.530292
$211$	5.43845	0.374398	0.187199	−	0.982322i	$-0.440059\pi$
$211$	5.43845	0.374398	0.187199	+	0.982322i	$0.440059\pi$
$212$	0.561553	0.0385676
$213$	−32.1771	−2.20474
$214$	−4.68466	−0.320237
$215$	1.00000	0.0681994
$216$	1.43845	0.0978739
$217$	6.36932	0.432377
$218$	2.87689	0.194848
$219$	9.12311	0.616482
$220$	−1.00000	−0.0674200
$221$	5.12311	0.344617
$222$	−6.56155	−0.440383
$223$	15.3693	1.02921	0.514603	−	0.857429i	$-0.327939\pi$
$223$	15.3693	1.02921	0.514603	+	0.857429i	$0.327939\pi$
$224$	3.00000	0.200446
$225$	3.56155	0.237437
$226$	−8.68466	−0.577695
$227$	−10.8769	−0.721925	−0.360962	−	0.932580i	$-0.617552\pi$
$227$	−10.8769	−0.721925	−0.360962	+	0.932580i	$0.617552\pi$
$228$	2.56155	0.169643
$229$	6.00000	0.396491	0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000	0.396491	0.198246	+	0.980152i	$0.436476\pi$
$230$	9.12311	0.601560
$231$	−7.68466	−0.505613
$232$	−6.12311	−0.402002
$233$	−19.9309	−1.30571	−0.652857	−	0.757481i	$-0.726430\pi$
$233$	−19.9309	−1.30571	−0.652857	+	0.757481i	$0.726430\pi$
$234$	−12.6847	−0.829222
$235$	−2.00000	−0.130466
$236$	9.12311	0.593864
$237$	−9.12311	−0.592609
$238$	4.31534	0.279722
$239$	9.80776	0.634412	0.317206	−	0.948357i	$-0.397255\pi$
$239$	9.80776	0.634412	0.317206	+	0.948357i	$0.397255\pi$
$240$	−2.56155	−0.165348
$241$	−28.7386	−1.85122	−0.925609	−	0.378481i	$-0.876447\pi$
$241$	−28.7386	−1.85122	−0.925609	+	0.378481i	$0.876447\pi$
$242$	−1.00000	−0.0642824
$243$	22.2462	1.42710
$244$	10.3693	0.663827
$245$	2.00000	0.127775
$246$	−1.12311	−0.0716066
$247$	−3.56155	−0.226616
$248$	2.12311	0.134817
$249$	−18.8769	−1.19627
$250$	−1.00000	−0.0632456
$251$	−6.00000	−0.378717	−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000	−0.378717	−0.189358	+	0.981908i	$0.560641\pi$
$252$	−10.6847	−0.673070
$253$	9.12311	0.573565
$254$	8.00000	0.501965
$255$	−3.68466	−0.230742
$256$	1.00000	0.0625000
$257$	−19.1771	−1.19623	−0.598117	−	0.801409i	$-0.704084\pi$
$257$	−19.1771	−1.19623	−0.598117	+	0.801409i	$0.704084\pi$
$258$	2.56155	0.159475
$259$	7.68466	0.477501
$260$	3.56155	0.220878
$261$	21.8078	1.34987
$262$	−3.68466	−0.227639
$263$	−7.24621	−0.446821	−0.223410	−	0.974725i	$-0.571719\pi$
$263$	−7.24621	−0.446821	−0.223410	+	0.974725i	$0.571719\pi$
$264$	−2.56155	−0.157653
$265$	0.561553	0.0344959
$266$	−3.00000	−0.183942
$267$	29.9309	1.83174
$268$	−5.56155	−0.339726
$269$	30.2462	1.84414	0.922072	−	0.387018i	$-0.126495\pi$
$269$	30.2462	1.84414	0.922072	+	0.387018i	$0.126495\pi$
$270$	1.43845	0.0875411
$271$	−7.80776	−0.474288	−0.237144	−	0.971475i	$-0.576211\pi$
$271$	−7.80776	−0.474288	−0.237144	+	0.971475i	$0.576211\pi$
$272$	1.43845	0.0872187
$273$	27.3693	1.65647
$274$	−14.9309	−0.902007
$275$	−1.00000	−0.0603023
$276$	23.3693	1.40667
$277$	−26.2462	−1.57698	−0.788491	−	0.615046i	$-0.789137\pi$
$277$	−26.2462	−1.57698	−0.788491	+	0.615046i	$0.789137\pi$
$278$	−2.24621	−0.134719
$279$	−7.56155	−0.452698
$280$	3.00000	0.179284
$281$	−18.6847	−1.11463	−0.557317	−	0.830300i	$-0.688169\pi$
$281$	−18.6847	−1.11463	−0.557317	+	0.830300i	$0.688169\pi$
$282$	−5.12311	−0.305077
$283$	0.930870	0.0553345	0.0276672	−	0.999617i	$-0.491192\pi$
$283$	0.930870	0.0553345	0.0276672	+	0.999617i	$0.491192\pi$
$284$	12.5616	0.745391
$285$	2.56155	0.151733
$286$	3.56155	0.210599
$287$	1.31534	0.0776422
$288$	−3.56155	−0.209867
$289$	−14.9309	−0.878286
$290$	−6.12311	−0.359561
$291$	−12.4924	−0.732319
$292$	−3.56155	−0.208424
$293$	−20.2462	−1.18280	−0.591398	−	0.806380i	$-0.701424\pi$
$293$	−20.2462	−1.18280	−0.591398	+	0.806380i	$0.701424\pi$
$294$	5.12311	0.298786
$295$	9.12311	0.531168
$296$	2.56155	0.148887
$297$	1.43845	0.0834672
$298$	−4.12311	−0.238845
$299$	−32.4924	−1.87909
$300$	−2.56155	−0.147891
$301$	−3.00000	−0.172917
$302$	−20.2462	−1.16504
$303$	13.1231	0.753903
$304$	−1.00000	−0.0573539
$305$	10.3693	0.593745
$306$	−5.12311	−0.292868
$307$	−27.5616	−1.57302	−0.786510	−	0.617577i	$-0.788114\pi$
$307$	−27.5616	−1.57302	−0.786510	+	0.617577i	$0.788114\pi$
$308$	3.00000	0.170941
$309$	48.9848	2.78665
$310$	2.12311	0.120584
$311$	−28.8617	−1.63660	−0.818300	−	0.574792i	$-0.805083\pi$
$311$	−28.8617	−1.63660	−0.818300	+	0.574792i	$0.805083\pi$
$312$	9.12311	0.516494
$313$	−2.49242	−0.140880	−0.0704400	−	0.997516i	$-0.522440\pi$
$313$	−2.49242	−0.140880	−0.0704400	+	0.997516i	$0.522440\pi$
$314$	−3.68466	−0.207937
$315$	−10.6847	−0.602012
$316$	3.56155	0.200353
$317$	−11.0000	−0.617822	−0.308911	−	0.951091i	$-0.599964\pi$
$317$	−11.0000	−0.617822	−0.308911	+	0.951091i	$0.599964\pi$
$318$	1.43845	0.0806641
$319$	−6.12311	−0.342828
$320$	1.00000	0.0559017
$321$	−12.0000	−0.669775
$322$	−27.3693	−1.52523
$323$	−1.43845	−0.0800373
$324$	−7.00000	−0.388889
$325$	3.56155	0.197559
$326$	−20.1771	−1.11751
$327$	7.36932	0.407524
$328$	0.438447	0.0242092
$329$	6.00000	0.330791
$330$	−2.56155	−0.141009
$331$	−16.4924	−0.906506	−0.453253	−	0.891382i	$-0.649737\pi$
$331$	−16.4924	−0.906506	−0.453253	+	0.891382i	$0.649737\pi$
$332$	7.36932	0.404444
$333$	−9.12311	−0.499943
$334$	15.6847	0.858226
$335$	−5.56155	−0.303860
$336$	7.68466	0.419232
$337$	−14.3153	−0.779806	−0.389903	−	0.920856i	$-0.627492\pi$
$337$	−14.3153	−0.779806	−0.389903	+	0.920856i	$0.627492\pi$
$338$	0.315342	0.0171523
$339$	−22.2462	−1.20825
$340$	1.43845	0.0780108
$341$	2.12311	0.114973
$342$	3.56155	0.192587
$343$	15.0000	0.809924
$344$	−1.00000	−0.0539164
$345$	23.3693	1.25816
$346$	8.43845	0.453654
$347$	14.0000	0.751559	0.375780	−	0.926709i	$-0.377375\pi$
$347$	14.0000	0.751559	0.375780	+	0.926709i	$0.377375\pi$
$348$	−15.6847	−0.840786
$349$	−20.2462	−1.08375	−0.541877	−	0.840458i	$-0.682286\pi$
$349$	−20.2462	−1.08375	−0.541877	+	0.840458i	$0.682286\pi$
$350$	3.00000	0.160357
$351$	−5.12311	−0.273451
$352$	1.00000	0.0533002
$353$	30.4924	1.62295	0.811474	−	0.584389i	$-0.198666\pi$
$353$	30.4924	1.62295	0.811474	+	0.584389i	$0.198666\pi$
$354$	23.3693	1.24207
$355$	12.5616	0.666698
$356$	−11.6847	−0.619286
$357$	11.0540	0.585038
$358$	11.3153	0.598034
$359$	−14.9309	−0.788021	−0.394011	−	0.919106i	$-0.628913\pi$
$359$	−14.9309	−0.788021	−0.394011	+	0.919106i	$0.628913\pi$
$360$	−3.56155	−0.187710
$361$	−18.0000	−0.947368
$362$	−2.87689	−0.151206
$363$	−2.56155	−0.134447
$364$	−10.6847	−0.560028
$365$	−3.56155	−0.186420
$366$	26.5616	1.38839
$367$	−28.4924	−1.48729	−0.743646	−	0.668573i	$-0.766905\pi$
$367$	−28.4924	−1.48729	−0.743646	+	0.668573i	$0.766905\pi$
$368$	−9.12311	−0.475575
$369$	−1.56155	−0.0812912
$370$	2.56155	0.133169
$371$	−1.68466	−0.0874631
$372$	5.43845	0.281970
$373$	−29.6155	−1.53343	−0.766717	−	0.641985i	$-0.778111\pi$
$373$	−29.6155	−1.53343	−0.766717	+	0.641985i	$0.778111\pi$
$374$	1.43845	0.0743803
$375$	−2.56155	−0.132278
$376$	2.00000	0.103142
$377$	21.8078	1.12316
$378$	−4.31534	−0.221957
$379$	14.4924	0.744426	0.372213	−	0.928147i	$-0.378599\pi$
$379$	14.4924	0.744426	0.372213	+	0.928147i	$0.378599\pi$
$380$	−1.00000	−0.0512989
$381$	20.4924	1.04986
$382$	5.36932	0.274718
$383$	17.8078	0.909934	0.454967	−	0.890508i	$-0.349651\pi$
$383$	17.8078	0.909934	0.454967	+	0.890508i	$0.349651\pi$
$384$	2.56155	0.130719
$385$	3.00000	0.152894
$386$	0.807764	0.0411141
$387$	3.56155	0.181044
$388$	4.87689	0.247587
$389$	−18.4924	−0.937603	−0.468802	−	0.883304i	$-0.655314\pi$
$389$	−18.4924	−0.937603	−0.468802	+	0.883304i	$0.655314\pi$
$390$	9.12311	0.461966
$391$	−13.1231	−0.663664
$392$	−2.00000	−0.101015
$393$	−9.43845	−0.476107
$394$	−8.68466	−0.437527
$395$	3.56155	0.179201
$396$	−3.56155	−0.178975
$397$	−8.24621	−0.413865	−0.206933	−	0.978355i	$-0.566348\pi$
$397$	−8.24621	−0.413865	−0.206933	+	0.978355i	$0.566348\pi$
$398$	−12.5616	−0.629654
$399$	−7.68466	−0.384714
$400$	1.00000	0.0500000
$401$	−1.49242	−0.0745280	−0.0372640	−	0.999305i	$-0.511864\pi$
$401$	−1.49242	−0.0745280	−0.0372640	+	0.999305i	$0.511864\pi$
$402$	−14.2462	−0.710536
$403$	−7.56155	−0.376668
$404$	−5.12311	−0.254884
$405$	−7.00000	−0.347833
$406$	18.3693	0.911654
$407$	2.56155	0.126971
$408$	3.68466	0.182418
$409$	−20.4924	−1.01329	−0.506643	−	0.862156i	$-0.669114\pi$
$409$	−20.4924	−1.01329	−0.506643	+	0.862156i	$0.669114\pi$
$410$	0.438447	0.0216534
$411$	−38.2462	−1.88655
$412$	−19.1231	−0.942128
$413$	−27.3693	−1.34676
$414$	32.4924	1.59692
$415$	7.36932	0.361746
$416$	−3.56155	−0.174619
$417$	−5.75379	−0.281764
$418$	−1.00000	−0.0489116
$419$	21.5616	1.05335	0.526675	−	0.850066i	$-0.323438\pi$
$419$	21.5616	1.05335	0.526675	+	0.850066i	$0.323438\pi$
$420$	7.68466	0.374973
$421$	2.93087	0.142842	0.0714209	−	0.997446i	$-0.477247\pi$
$421$	2.93087	0.142842	0.0714209	+	0.997446i	$0.477247\pi$
$422$	−5.43845	−0.264739
$423$	−7.12311	−0.346337
$424$	−0.561553	−0.0272714
$425$	1.43845	0.0697749
$426$	32.1771	1.55898
$427$	−31.1080	−1.50542
$428$	4.68466	0.226442
$429$	9.12311	0.440468
$430$	−1.00000	−0.0482243
$431$	−5.75379	−0.277150	−0.138575	−	0.990352i	$-0.544252\pi$
$431$	−5.75379	−0.277150	−0.138575	+	0.990352i	$0.544252\pi$
$432$	−1.43845	−0.0692073
$433$	3.31534	0.159325	0.0796626	−	0.996822i	$-0.474616\pi$
$433$	3.31534	0.159325	0.0796626	+	0.996822i	$0.474616\pi$
$434$	−6.36932	−0.305737
$435$	−15.6847	−0.752022
$436$	−2.87689	−0.137778
$437$	9.12311	0.436417
$438$	−9.12311	−0.435919
$439$	−34.2462	−1.63448	−0.817241	−	0.576296i	$-0.804498\pi$
$439$	−34.2462	−1.63448	−0.817241	+	0.576296i	$0.804498\pi$
$440$	1.00000	0.0476731
$441$	7.12311	0.339196
$442$	−5.12311	−0.243681
$443$	15.8078	0.751050	0.375525	−	0.926812i	$-0.377462\pi$
$443$	15.8078	0.751050	0.375525	+	0.926812i	$0.377462\pi$
$444$	6.56155	0.311398
$445$	−11.6847	−0.553906
$446$	−15.3693	−0.727758
$447$	−10.5616	−0.499544
$448$	−3.00000	−0.141737
$449$	−33.1231	−1.56318	−0.781588	−	0.623795i	$-0.785590\pi$
$449$	−33.1231	−1.56318	−0.781588	+	0.623795i	$0.785590\pi$
$450$	−3.56155	−0.167893
$451$	0.438447	0.0206457
$452$	8.68466	0.408492
$453$	−51.8617	−2.43668
$454$	10.8769	0.510478
$455$	−10.6847	−0.500905
$456$	−2.56155	−0.119956
$457$	−12.5616	−0.587605	−0.293802	−	0.955866i	$-0.594921\pi$
$457$	−12.5616	−0.587605	−0.293802	+	0.955866i	$0.594921\pi$
$458$	−6.00000	−0.280362
$459$	−2.06913	−0.0965787
$460$	−9.12311	−0.425367
$461$	−20.1771	−0.939740	−0.469870	−	0.882736i	$-0.655699\pi$
$461$	−20.1771	−0.939740	−0.469870	+	0.882736i	$0.655699\pi$
$462$	7.68466	0.357523
$463$	36.9309	1.71632	0.858162	−	0.513380i	$-0.171607\pi$
$463$	36.9309	1.71632	0.858162	+	0.513380i	$0.171607\pi$
$464$	6.12311	0.284258
$465$	5.43845	0.252202
$466$	19.9309	0.923280
$467$	−2.56155	−0.118535	−0.0592673	−	0.998242i	$-0.518876\pi$
$467$	−2.56155	−0.118535	−0.0592673	+	0.998242i	$0.518876\pi$
$468$	12.6847	0.586349
$469$	16.6847	0.770426
$470$	2.00000	0.0922531
$471$	−9.43845	−0.434901
$472$	−9.12311	−0.419925
$473$	−1.00000	−0.0459800
$474$	9.12311	0.419038
$475$	−1.00000	−0.0458831
$476$	−4.31534	−0.197793
$477$	2.00000	0.0915737
$478$	−9.80776	−0.448597
$479$	40.4924	1.85015	0.925073	−	0.379789i	$-0.124004\pi$
$479$	40.4924	1.85015	0.925073	+	0.379789i	$0.124004\pi$
$480$	2.56155	0.116918
$481$	−9.12311	−0.415978
$482$	28.7386	1.30901
$483$	−70.1080	−3.19002
$484$	1.00000	0.0454545
$485$	4.87689	0.221448
$486$	−22.2462	−1.00911
$487$	−14.6307	−0.662980	−0.331490	−	0.943459i	$-0.607551\pi$
$487$	−14.6307	−0.662980	−0.331490	+	0.943459i	$0.607551\pi$
$488$	−10.3693	−0.469397
$489$	−51.6847	−2.33726
$490$	−2.00000	−0.0903508
$491$	−19.0540	−0.859894	−0.429947	−	0.902854i	$-0.641468\pi$
$491$	−19.0540	−0.859894	−0.429947	+	0.902854i	$0.641468\pi$
$492$	1.12311	0.0506335
$493$	8.80776	0.396682
$494$	3.56155	0.160242
$495$	−3.56155	−0.160080
$496$	−2.12311	−0.0953303
$497$	−37.6847	−1.69039
$498$	18.8769	0.845894
$499$	22.0540	0.987272	0.493636	−	0.869669i	$-0.335668\pi$
$499$	22.0540	0.987272	0.493636	+	0.869669i	$0.335668\pi$
$500$	1.00000	0.0447214
$501$	40.1771	1.79498
$502$	6.00000	0.267793
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	10.6847	0.475933
$505$	−5.12311	−0.227975
$506$	−9.12311	−0.405572
$507$	0.807764	0.0358741
$508$	−8.00000	−0.354943
$509$	−1.75379	−0.0777353	−0.0388677	−	0.999244i	$-0.512375\pi$
$509$	−1.75379	−0.0777353	−0.0388677	+	0.999244i	$0.512375\pi$
$510$	3.68466	0.163159
$511$	10.6847	0.472661
$512$	−1.00000	−0.0441942
$513$	1.43845	0.0635090
$514$	19.1771	0.845865
$515$	−19.1231	−0.842665
$516$	−2.56155	−0.112766
$517$	2.00000	0.0879599
$518$	−7.68466	−0.337645
$519$	21.6155	0.948816
$520$	−3.56155	−0.156184
$521$	−12.7386	−0.558090	−0.279045	−	0.960278i	$-0.590018\pi$
$521$	−12.7386	−0.558090	−0.279045	+	0.960278i	$0.590018\pi$
$522$	−21.8078	−0.954500
$523$	−17.3693	−0.759507	−0.379754	−	0.925088i	$-0.623991\pi$
$523$	−17.3693	−0.759507	−0.379754	+	0.925088i	$0.623991\pi$
$524$	3.68466	0.160965
$525$	7.68466	0.335386
$526$	7.24621	0.315950
$527$	−3.05398	−0.133033
$528$	2.56155	0.111477
$529$	60.2311	2.61874
$530$	−0.561553	−0.0243923
$531$	32.4924	1.41005
$532$	3.00000	0.130066
$533$	−1.56155	−0.0676384
$534$	−29.9309	−1.29524
$535$	4.68466	0.202535
$536$	5.56155	0.240222
$537$	28.9848	1.25079
$538$	−30.2462	−1.30401
$539$	−2.00000	−0.0861461
$540$	−1.43845	−0.0619009
$541$	−34.1771	−1.46939	−0.734694	−	0.678399i	$-0.762674\pi$
$541$	−34.1771	−1.46939	−0.734694	+	0.678399i	$0.762674\pi$
$542$	7.80776	0.335372
$543$	−7.36932	−0.316248
$544$	−1.43845	−0.0616729
$545$	−2.87689	−0.123233
$546$	−27.3693	−1.17130
$547$	−36.0000	−1.53925	−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000	−1.53925	−0.769624	+	0.638497i	$0.779557\pi$
$548$	14.9309	0.637815
$549$	36.9309	1.57617
$550$	1.00000	0.0426401
$551$	−6.12311	−0.260853
$552$	−23.3693	−0.994664
$553$	−10.6847	−0.454358
$554$	26.2462	1.11509
$555$	6.56155	0.278522
$556$	2.24621	0.0952606
$557$	26.6847	1.13067	0.565333	−	0.824863i	$-0.308748\pi$
$557$	26.6847	1.13067	0.565333	+	0.824863i	$0.308748\pi$
$558$	7.56155	0.320106
$559$	3.56155	0.150638
$560$	−3.00000	−0.126773
$561$	3.68466	0.155566
$562$	18.6847	0.788165
$563$	−32.4384	−1.36712	−0.683559	−	0.729895i	$-0.739569\pi$
$563$	−32.4384	−1.36712	−0.683559	+	0.729895i	$0.739569\pi$
$564$	5.12311	0.215722
$565$	8.68466	0.365366
$566$	−0.930870	−0.0391274
$567$	21.0000	0.881917
$568$	−12.5616	−0.527071
$569$	32.6847	1.37021	0.685106	−	0.728443i	$-0.259756\pi$
$569$	32.6847	1.37021	0.685106	+	0.728443i	$0.259756\pi$
$570$	−2.56155	−0.107292
$571$	7.63068	0.319334	0.159667	−	0.987171i	$-0.448958\pi$
$571$	7.63068	0.319334	0.159667	+	0.987171i	$0.448958\pi$
$572$	−3.56155	−0.148916
$573$	13.7538	0.574573
$574$	−1.31534	−0.0549013
$575$	−9.12311	−0.380460
$576$	3.56155	0.148398
$577$	−43.1771	−1.79749	−0.898743	−	0.438476i	$-0.855518\pi$
$577$	−43.1771	−1.79749	−0.898743	+	0.438476i	$0.855518\pi$
$578$	14.9309	0.621042
$579$	2.06913	0.0859901
$580$	6.12311	0.254248
$581$	−22.1080	−0.917192
$582$	12.4924	0.517828
$583$	−0.561553	−0.0232571
$584$	3.56155	0.147378
$585$	12.6847	0.524446
$586$	20.2462	0.836363
$587$	8.31534	0.343211	0.171605	−	0.985166i	$-0.445105\pi$
$587$	8.31534	0.343211	0.171605	+	0.985166i	$0.445105\pi$
$588$	−5.12311	−0.211273
$589$	2.12311	0.0874810
$590$	−9.12311	−0.375592
$591$	−22.2462	−0.915087
$592$	−2.56155	−0.105279
$593$	12.0540	0.494997	0.247499	−	0.968888i	$-0.420391\pi$
$593$	12.0540	0.494997	0.247499	+	0.968888i	$0.420391\pi$
$594$	−1.43845	−0.0590202
$595$	−4.31534	−0.176912
$596$	4.12311	0.168889
$597$	−32.1771	−1.31692
$598$	32.4924	1.32871
$599$	38.5616	1.57558	0.787791	−	0.615942i	$-0.211225\pi$
$599$	38.5616	1.57558	0.787791	+	0.615942i	$0.211225\pi$
$600$	2.56155	0.104575
$601$	−9.12311	−0.372139	−0.186070	−	0.982537i	$-0.559575\pi$
$601$	−9.12311	−0.372139	−0.186070	+	0.982537i	$0.559575\pi$
$602$	3.00000	0.122271
$603$	−19.8078	−0.806635
$604$	20.2462	0.823807
$605$	1.00000	0.0406558
$606$	−13.1231	−0.533090
$607$	−20.8078	−0.844561	−0.422281	−	0.906465i	$-0.638770\pi$
$607$	−20.8078	−0.844561	−0.422281	+	0.906465i	$0.638770\pi$
$608$	1.00000	0.0405554
$609$	47.0540	1.90672
$610$	−10.3693	−0.419841
$611$	−7.12311	−0.288170
$612$	5.12311	0.207089
$613$	1.31534	0.0531261	0.0265631	−	0.999647i	$-0.491544\pi$
$613$	1.31534	0.0531261	0.0265631	+	0.999647i	$0.491544\pi$
$614$	27.5616	1.11229
$615$	1.12311	0.0452880
$616$	−3.00000	−0.120873
$617$	−4.49242	−0.180858	−0.0904291	−	0.995903i	$-0.528824\pi$
$617$	−4.49242	−0.180858	−0.0904291	+	0.995903i	$0.528824\pi$
$618$	−48.9848	−1.97046
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−2.12311	−0.0852660
$621$	13.1231	0.526612
$622$	28.8617	1.15725
$623$	35.0540	1.40441
$624$	−9.12311	−0.365217
$625$	1.00000	0.0400000
$626$	2.49242	0.0996172
$627$	−2.56155	−0.102299
$628$	3.68466	0.147034
$629$	−3.68466	−0.146917
$630$	10.6847	0.425687
$631$	−8.31534	−0.331029	−0.165514	−	0.986207i	$-0.552928\pi$
$631$	−8.31534	−0.331029	−0.165514	+	0.986207i	$0.552928\pi$
$632$	−3.56155	−0.141671
$633$	−13.9309	−0.553702
$634$	11.0000	0.436866
$635$	−8.00000	−0.317470
$636$	−1.43845	−0.0570381
$637$	7.12311	0.282228
$638$	6.12311	0.242416
$639$	44.7386	1.76983
$640$	−1.00000	−0.0395285
$641$	−18.1771	−0.717952	−0.358976	−	0.933347i	$-0.616874\pi$
$641$	−18.1771	−0.717952	−0.358976	+	0.933347i	$0.616874\pi$
$642$	12.0000	0.473602
$643$	−30.7538	−1.21281	−0.606406	−	0.795156i	$-0.707389\pi$
$643$	−30.7538	−1.21281	−0.606406	+	0.795156i	$0.707389\pi$
$644$	27.3693	1.07850
$645$	−2.56155	−0.100861
$646$	1.43845	0.0565949
$647$	−4.05398	−0.159378	−0.0796891	−	0.996820i	$-0.525393\pi$
$647$	−4.05398	−0.159378	−0.0796891	+	0.996820i	$0.525393\pi$
$648$	7.00000	0.274986
$649$	−9.12311	−0.358113
$650$	−3.56155	−0.139696
$651$	−16.3153	−0.639449
$652$	20.1771	0.790195
$653$	39.9309	1.56262	0.781308	−	0.624146i	$-0.214553\pi$
$653$	39.9309	1.56262	0.781308	+	0.624146i	$0.214553\pi$
$654$	−7.36932	−0.288163
$655$	3.68466	0.143972
$656$	−0.438447	−0.0171185
$657$	−12.6847	−0.494876
$658$	−6.00000	−0.233904
$659$	6.56155	0.255602	0.127801	−	0.991800i	$-0.459208\pi$
$659$	6.56155	0.255602	0.127801	+	0.991800i	$0.459208\pi$
$660$	2.56155	0.0997083
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	16.4924	0.640996
$663$	−13.1231	−0.509659
$664$	−7.36932	−0.285985
$665$	3.00000	0.116335
$666$	9.12311	0.353513
$667$	−55.8617	−2.16298
$668$	−15.6847	−0.606858
$669$	−39.3693	−1.52211
$670$	5.56155	0.214862
$671$	−10.3693	−0.400303
$672$	−7.68466	−0.296442
$673$	27.4924	1.05976	0.529878	−	0.848074i	$-0.322238\pi$
$673$	27.4924	1.05976	0.529878	+	0.848074i	$0.322238\pi$
$674$	14.3153	0.551406
$675$	−1.43845	−0.0553659
$676$	−0.315342	−0.0121285
$677$	32.1080	1.23401	0.617004	−	0.786960i	$-0.288346\pi$
$677$	32.1080	1.23401	0.617004	+	0.786960i	$0.288346\pi$
$678$	22.2462	0.854361
$679$	−14.6307	−0.561474
$680$	−1.43845	−0.0551619
$681$	27.8617	1.06766
$682$	−2.12311	−0.0812979
$683$	6.56155	0.251071	0.125535	−	0.992089i	$-0.459935\pi$
$683$	6.56155	0.251071	0.125535	+	0.992089i	$0.459935\pi$
$684$	−3.56155	−0.136179
$685$	14.9309	0.570479
$686$	−15.0000	−0.572703
$687$	−15.3693	−0.586376
$688$	1.00000	0.0381246
$689$	2.00000	0.0761939
$690$	−23.3693	−0.889655
$691$	−30.8769	−1.17461	−0.587306	−	0.809365i	$-0.699812\pi$
$691$	−30.8769	−1.17461	−0.587306	+	0.809365i	$0.699812\pi$
$692$	−8.43845	−0.320782
$693$	10.6847	0.405877
$694$	−14.0000	−0.531433
$695$	2.24621	0.0852036
$696$	15.6847	0.594525
$697$	−0.630683	−0.0238888
$698$	20.2462	0.766330
$699$	51.0540	1.93104
$700$	−3.00000	−0.113389
$701$	−52.6695	−1.98930	−0.994650	−	0.103304i	$-0.967059\pi$
$701$	−52.6695	−1.98930	−0.994650	+	0.103304i	$0.967059\pi$
$702$	5.12311	0.193359
$703$	2.56155	0.0966108
$704$	−1.00000	−0.0376889
$705$	5.12311	0.192947
$706$	−30.4924	−1.14760
$707$	15.3693	0.578023
$708$	−23.3693	−0.878273
$709$	−34.4924	−1.29539	−0.647695	−	0.761900i	$-0.724267\pi$
$709$	−34.4924	−1.29539	−0.647695	+	0.761900i	$0.724267\pi$
$710$	−12.5616	−0.471427
$711$	12.6847	0.475712
$712$	11.6847	0.437901
$713$	19.3693	0.725387
$714$	−11.0540	−0.413685
$715$	−3.56155	−0.133195
$716$	−11.3153	−0.422874
$717$	−25.1231	−0.938240
$718$	14.9309	0.557215
$719$	23.0540	0.859768	0.429884	−	0.902884i	$-0.358554\pi$
$719$	23.0540	0.859768	0.429884	+	0.902884i	$0.358554\pi$
$720$	3.56155	0.132731
$721$	57.3693	2.13655
$722$	18.0000	0.669891
$723$	73.6155	2.73779
$724$	2.87689	0.106919
$725$	6.12311	0.227406
$726$	2.56155	0.0950681
$727$	26.8769	0.996809	0.498404	−	0.866945i	$-0.333919\pi$
$727$	26.8769	0.996809	0.498404	+	0.866945i	$0.333919\pi$
$728$	10.6847	0.396000
$729$	−35.9848	−1.33277
$730$	3.56155	0.131819
$731$	1.43845	0.0532029
$732$	−26.5616	−0.981743
$733$	15.1231	0.558585	0.279292	−	0.960206i	$-0.409900\pi$
$733$	15.1231	0.558585	0.279292	+	0.960206i	$0.409900\pi$
$734$	28.4924	1.05167
$735$	−5.12311	−0.188969
$736$	9.12311	0.336282
$737$	5.56155	0.204862
$738$	1.56155	0.0574816
$739$	−30.9309	−1.13781	−0.568905	−	0.822403i	$-0.692633\pi$
$739$	−30.9309	−1.13781	−0.568905	+	0.822403i	$0.692633\pi$
$740$	−2.56155	−0.0941646
$741$	9.12311	0.335146
$742$	1.68466	0.0618458
$743$	9.87689	0.362348	0.181174	−	0.983451i	$-0.442010\pi$
$743$	9.87689	0.362348	0.181174	+	0.983451i	$0.442010\pi$
$744$	−5.43845	−0.199383
$745$	4.12311	0.151059
$746$	29.6155	1.08430
$747$	26.2462	0.960299
$748$	−1.43845	−0.0525948
$749$	−14.0540	−0.513521
$750$	2.56155	0.0935347
$751$	−19.1922	−0.700335	−0.350167	−	0.936687i	$-0.613875\pi$
$751$	−19.1922	−0.700335	−0.350167	+	0.936687i	$0.613875\pi$
$752$	−2.00000	−0.0729325
$753$	15.3693	0.560089
$754$	−21.8078	−0.794192
$755$	20.2462	0.736835
$756$	4.31534	0.156947
$757$	6.00000	0.218074	0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000	0.218074	0.109037	+	0.994038i	$0.465223\pi$
$758$	−14.4924	−0.526388
$759$	−23.3693	−0.848252
$760$	1.00000	0.0362738
$761$	42.4924	1.54035	0.770175	−	0.637833i	$-0.220169\pi$
$761$	42.4924	1.54035	0.770175	+	0.637833i	$0.220169\pi$
$762$	−20.4924	−0.742362
$763$	8.63068	0.312452
$764$	−5.36932	−0.194255
$765$	5.12311	0.185226
$766$	−17.8078	−0.643421
$767$	32.4924	1.17323
$768$	−2.56155	−0.0924321
$769$	2.68466	0.0968113	0.0484056	−	0.998828i	$-0.484586\pi$
$769$	2.68466	0.0968113	0.0484056	+	0.998828i	$0.484586\pi$
$770$	−3.00000	−0.108112
$771$	49.1231	1.76913
$772$	−0.807764	−0.0290721
$773$	−18.5616	−0.667613	−0.333806	−	0.942642i	$-0.608333\pi$
$773$	−18.5616	−0.667613	−0.333806	+	0.942642i	$0.608333\pi$
$774$	−3.56155	−0.128017
$775$	−2.12311	−0.0762642
$776$	−4.87689	−0.175070
$777$	−19.6847	−0.706183
$778$	18.4924	0.662985
$779$	0.438447	0.0157090
$780$	−9.12311	−0.326660
$781$	−12.5616	−0.449488
$782$	13.1231	0.469281
$783$	−8.80776	−0.314764
$784$	2.00000	0.0714286
$785$	3.68466	0.131511
$786$	9.43845	0.336658
$787$	0.684658	0.0244054	0.0122027	−	0.999926i	$-0.496116\pi$
$787$	0.684658	0.0244054	0.0122027	+	0.999926i	$0.496116\pi$
$788$	8.68466	0.309378
$789$	18.5616	0.660809
$790$	−3.56155	−0.126714
$791$	−26.0540	−0.926373
$792$	3.56155	0.126554
$793$	36.9309	1.31145
$794$	8.24621	0.292647
$795$	−1.43845	−0.0510165
$796$	12.5616	0.445232
$797$	9.31534	0.329966	0.164983	−	0.986296i	$-0.447243\pi$
$797$	9.31534	0.329966	0.164983	+	0.986296i	$0.447243\pi$
$798$	7.68466	0.272034
$799$	−2.87689	−0.101777
$800$	−1.00000	−0.0353553
$801$	−41.6155	−1.47041
$802$	1.49242	0.0526993
$803$	3.56155	0.125684
$804$	14.2462	0.502425
$805$	27.3693	0.964642
$806$	7.56155	0.266344
$807$	−77.4773	−2.72733
$808$	5.12311	0.180230
$809$	−37.4233	−1.31573	−0.657866	−	0.753135i	$-0.728541\pi$
$809$	−37.4233	−1.31573	−0.657866	+	0.753135i	$0.728541\pi$
$810$	7.00000	0.245955
$811$	5.00000	0.175574	0.0877869	−	0.996139i	$-0.472021\pi$
$811$	5.00000	0.175574	0.0877869	+	0.996139i	$0.472021\pi$
$812$	−18.3693	−0.644637
$813$	20.0000	0.701431
$814$	−2.56155	−0.0897824
$815$	20.1771	0.706772
$816$	−3.68466	−0.128989
$817$	−1.00000	−0.0349856
$818$	20.4924	0.716501
$819$	−38.0540	−1.32971
$820$	−0.438447	−0.0153112
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	38.2462	1.33399
$823$	8.38447	0.292264	0.146132	−	0.989265i	$-0.453318\pi$
$823$	8.38447	0.292264	0.146132	+	0.989265i	$0.453318\pi$
$824$	19.1231	0.666185
$825$	2.56155	0.0891818
$826$	27.3693	0.952300
$827$	−33.1771	−1.15368	−0.576840	−	0.816857i	$-0.695714\pi$
$827$	−33.1771	−1.15368	−0.576840	+	0.816857i	$0.695714\pi$
$828$	−32.4924	−1.12919
$829$	46.5464	1.61662	0.808312	−	0.588755i	$-0.200382\pi$
$829$	46.5464	1.61662	0.808312	+	0.588755i	$0.200382\pi$
$830$	−7.36932	−0.255793
$831$	67.2311	2.33222
$832$	3.56155	0.123475
$833$	2.87689	0.0996785
$834$	5.75379	0.199237
$835$	−15.6847	−0.542790
$836$	1.00000	0.0345857
$837$	3.05398	0.105561
$838$	−21.5616	−0.744831
$839$	−15.6155	−0.539108	−0.269554	−	0.962985i	$-0.586876\pi$
$839$	−15.6155	−0.539108	−0.269554	+	0.962985i	$0.586876\pi$
$840$	−7.68466	−0.265146
$841$	8.49242	0.292842
$842$	−2.93087	−0.101004
$843$	47.8617	1.64845
$844$	5.43845	0.187199
$845$	−0.315342	−0.0108481
$846$	7.12311	0.244897
$847$	−3.00000	−0.103081
$848$	0.561553	0.0192838
$849$	−2.38447	−0.0818349
$850$	−1.43845	−0.0493383
$851$	23.3693	0.801090
$852$	−32.1771	−1.10237
$853$	42.9848	1.47177	0.735887	−	0.677105i	$-0.236766\pi$
$853$	42.9848	1.47177	0.735887	+	0.677105i	$0.236766\pi$
$854$	31.1080	1.06449
$855$	−3.56155	−0.121803
$856$	−4.68466	−0.160118
$857$	15.6847	0.535778	0.267889	−	0.963450i	$-0.413674\pi$
$857$	15.6847	0.535778	0.267889	+	0.963450i	$0.413674\pi$
$858$	−9.12311	−0.311458
$859$	−25.4233	−0.867432	−0.433716	−	0.901050i	$-0.642798\pi$
$859$	−25.4233	−0.867432	−0.433716	+	0.901050i	$0.642798\pi$
$860$	1.00000	0.0340997
$861$	−3.36932	−0.114826
$862$	5.75379	0.195975
$863$	5.12311	0.174393	0.0871963	−	0.996191i	$-0.472209\pi$
$863$	5.12311	0.174393	0.0871963	+	0.996191i	$0.472209\pi$
$864$	1.43845	0.0489370
$865$	−8.43845	−0.286916
$866$	−3.31534	−0.112660
$867$	38.2462	1.29891
$868$	6.36932	0.216189
$869$	−3.56155	−0.120817
$870$	15.6847	0.531760
$871$	−19.8078	−0.671160
$872$	2.87689	0.0974239
$873$	17.3693	0.587862
$874$	−9.12311	−0.308594
$875$	−3.00000	−0.101419
$876$	9.12311	0.308241
$877$	−12.2462	−0.413525	−0.206763	−	0.978391i	$-0.566293\pi$
$877$	−12.2462	−0.413525	−0.206763	+	0.978391i	$0.566293\pi$
$878$	34.2462	1.15575
$879$	51.8617	1.74925
$880$	−1.00000	−0.0337100
$881$	29.4233	0.991296	0.495648	−	0.868524i	$-0.334931\pi$
$881$	29.4233	0.991296	0.495648	+	0.868524i	$0.334931\pi$
$882$	−7.12311	−0.239847
$883$	41.9848	1.41290	0.706451	−	0.707762i	$-0.250295\pi$
$883$	41.9848	1.41290	0.706451	+	0.707762i	$0.250295\pi$
$884$	5.12311	0.172309
$885$	−23.3693	−0.785551
$886$	−15.8078	−0.531072
$887$	19.4233	0.652170	0.326085	−	0.945340i	$-0.394270\pi$
$887$	19.4233	0.652170	0.326085	+	0.945340i	$0.394270\pi$
$888$	−6.56155	−0.220191
$889$	24.0000	0.804934
$890$	11.6847	0.391671
$891$	7.00000	0.234509
$892$	15.3693	0.514603
$893$	2.00000	0.0669274
$894$	10.5616	0.353231
$895$	−11.3153	−0.378230
$896$	3.00000	0.100223
$897$	83.2311	2.77900
$898$	33.1231	1.10533
$899$	−13.0000	−0.433574
$900$	3.56155	0.118718
$901$	0.807764	0.0269105
$902$	−0.438447	−0.0145987
$903$	7.68466	0.255729
$904$	−8.68466	−0.288847
$905$	2.87689	0.0956312
$906$	51.8617	1.72299
$907$	13.2462	0.439833	0.219917	−	0.975519i	$-0.429421\pi$
$907$	13.2462	0.439833	0.219917	+	0.975519i	$0.429421\pi$
$908$	−10.8769	−0.360962
$909$	−18.2462	−0.605189
$910$	10.6847	0.354193
$911$	−27.9309	−0.925391	−0.462695	−	0.886517i	$-0.653118\pi$
$911$	−27.9309	−0.925391	−0.462695	+	0.886517i	$0.653118\pi$
$912$	2.56155	0.0848215
$913$	−7.36932	−0.243889
$914$	12.5616	0.415499
$915$	−26.5616	−0.878098
$916$	6.00000	0.198246
$917$	−11.0540	−0.365034
$918$	2.06913	0.0682915
$919$	−40.3002	−1.32938	−0.664690	−	0.747119i	$-0.731436\pi$
$919$	−40.3002	−1.32938	−0.664690	+	0.747119i	$0.731436\pi$
$920$	9.12311	0.300780
$921$	70.6004	2.32636
$922$	20.1771	0.664497
$923$	44.7386	1.47259
$924$	−7.68466	−0.252807
$925$	−2.56155	−0.0842233
$926$	−36.9309	−1.21362
$927$	−68.1080	−2.23696
$928$	−6.12311	−0.201001
$929$	−19.4384	−0.637755	−0.318877	−	0.947796i	$-0.603306\pi$
$929$	−19.4384	−0.637755	−0.318877	+	0.947796i	$0.603306\pi$
$930$	−5.43845	−0.178334
$931$	−2.00000	−0.0655474
$932$	−19.9309	−0.652857
$933$	73.9309	2.42039
$934$	2.56155	0.0838166
$935$	−1.43845	−0.0470423
$936$	−12.6847	−0.414611
$937$	12.7386	0.416153	0.208077	−	0.978113i	$-0.433280\pi$
$937$	12.7386	0.416153	0.208077	+	0.978113i	$0.433280\pi$
$938$	−16.6847	−0.544773
$939$	6.38447	0.208349
$940$	−2.00000	−0.0652328
$941$	8.56155	0.279099	0.139549	−	0.990215i	$-0.455435\pi$
$941$	8.56155	0.279099	0.139549	+	0.990215i	$0.455435\pi$
$942$	9.43845	0.307521
$943$	4.00000	0.130258
$944$	9.12311	0.296932
$945$	4.31534	0.140378
$946$	1.00000	0.0325128
$947$	−20.3693	−0.661914	−0.330957	−	0.943646i	$-0.607371\pi$
$947$	−20.3693	−0.661914	−0.330957	+	0.943646i	$0.607371\pi$
$948$	−9.12311	−0.296305
$949$	−12.6847	−0.411761
$950$	1.00000	0.0324443
$951$	28.1771	0.913704
$952$	4.31534	0.139861
$953$	12.6155	0.408657	0.204329	−	0.978902i	$-0.434499\pi$
$953$	12.6155	0.408657	0.204329	+	0.978902i	$0.434499\pi$
$954$	−2.00000	−0.0647524
$955$	−5.36932	−0.173747
$956$	9.80776	0.317206
$957$	15.6847	0.507013
$958$	−40.4924	−1.30825
$959$	−44.7926	−1.44643
$960$	−2.56155	−0.0826738
$961$	−26.4924	−0.854594
$962$	9.12311	0.294141
$963$	16.6847	0.537656
$964$	−28.7386	−0.925609
$965$	−0.807764	−0.0260028
$966$	70.1080	2.25569
$967$	−39.9309	−1.28409	−0.642045	−	0.766667i	$-0.721914\pi$
$967$	−39.9309	−1.28409	−0.642045	+	0.766667i	$0.721914\pi$
$968$	−1.00000	−0.0321412
$969$	3.68466	0.118368
$970$	−4.87689	−0.156588
$971$	44.9848	1.44363	0.721816	−	0.692085i	$-0.243308\pi$
$971$	44.9848	1.44363	0.721816	+	0.692085i	$0.243308\pi$
$972$	22.2462	0.713548
$973$	−6.73863	−0.216031
$974$	14.6307	0.468797
$975$	−9.12311	−0.292173
$976$	10.3693	0.331914
$977$	49.3693	1.57946	0.789732	−	0.613452i	$-0.210219\pi$
$977$	49.3693	1.57946	0.789732	+	0.613452i	$0.210219\pi$
$978$	51.6847	1.65269
$979$	11.6847	0.373443
$980$	2.00000	0.0638877
$981$	−10.2462	−0.327136
$982$	19.0540	0.608037
$983$	−17.3153	−0.552274	−0.276137	−	0.961118i	$-0.589054\pi$
$983$	−17.3153	−0.552274	−0.276137	+	0.961118i	$0.589054\pi$
$984$	−1.12311	−0.0358033
$985$	8.68466	0.276716
$986$	−8.80776	−0.280496
$987$	−15.3693	−0.489211
$988$	−3.56155	−0.113308
$989$	−9.12311	−0.290098
$990$	3.56155	0.113194
$991$	11.5076	0.365550	0.182775	−	0.983155i	$-0.441492\pi$
$991$	11.5076	0.365550	0.182775	+	0.983155i	$0.441492\pi$
$992$	2.12311	0.0674087
$993$	42.2462	1.34064
$994$	37.6847	1.19528
$995$	12.5616	0.398228
$996$	−18.8769	−0.598137
$997$	30.2462	0.957907	0.478954	−	0.877840i	$-0.341016\pi$
$997$	30.2462	0.957907	0.478954	+	0.877840i	$0.341016\pi$
$998$	−22.0540	−0.698106
$999$	3.68466	0.116577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.l.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.l.1.1	✓	2	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.56155 q^{6} -3.00000 q^{7} -1.00000 q^{8} +3.56155 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.56155 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.56155 q^{6} -3.00000 q^{7} -1.00000 q^{8} +3.56155 q^{9} -1.00000 q^{10} -1.00000 q^{11} -2.56155 q^{12} +3.56155 q^{13} +3.00000 q^{14} -2.56155 q^{15} +1.00000 q^{16} +1.43845 q^{17} -3.56155 q^{18} -1.00000 q^{19} +1.00000 q^{20} +7.68466 q^{21} +1.00000 q^{22} -9.12311 q^{23} +2.56155 q^{24} +1.00000 q^{25} -3.56155 q^{26} -1.43845 q^{27} -3.00000 q^{28} +6.12311 q^{29} +2.56155 q^{30} -2.12311 q^{31} -1.00000 q^{32} +2.56155 q^{33} -1.43845 q^{34} -3.00000 q^{35} +3.56155 q^{36} -2.56155 q^{37} +1.00000 q^{38} -9.12311 q^{39} -1.00000 q^{40} -0.438447 q^{41} -7.68466 q^{42} +1.00000 q^{43} -1.00000 q^{44} +3.56155 q^{45} +9.12311 q^{46} -2.00000 q^{47} -2.56155 q^{48} +2.00000 q^{49} -1.00000 q^{50} -3.68466 q^{51} +3.56155 q^{52} +0.561553 q^{53} +1.43845 q^{54} -1.00000 q^{55} +3.00000 q^{56} +2.56155 q^{57} -6.12311 q^{58} +9.12311 q^{59} -2.56155 q^{60} +10.3693 q^{61} +2.12311 q^{62} -10.6847 q^{63} +1.00000 q^{64} +3.56155 q^{65} -2.56155 q^{66} -5.56155 q^{67} +1.43845 q^{68} +23.3693 q^{69} +3.00000 q^{70} +12.5616 q^{71} -3.56155 q^{72} -3.56155 q^{73} +2.56155 q^{74} -2.56155 q^{75} -1.00000 q^{76} +3.00000 q^{77} +9.12311 q^{78} +3.56155 q^{79} +1.00000 q^{80} -7.00000 q^{81} +0.438447 q^{82} +7.36932 q^{83} +7.68466 q^{84} +1.43845 q^{85} -1.00000 q^{86} -15.6847 q^{87} +1.00000 q^{88} -11.6847 q^{89} -3.56155 q^{90} -10.6847 q^{91} -9.12311 q^{92} +5.43845 q^{93} +2.00000 q^{94} -1.00000 q^{95} +2.56155 q^{96} +4.87689 q^{97} -2.00000 q^{98} -3.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} - 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 6 * q^7 - 2 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 6 q^{7} - 2 q^{8} + 3 q^{9} - 2 q^{10} - 2 q^{11} - q^{12} + 3 q^{13} + 6 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} - 3 q^{18} - 2 q^{19} + 2 q^{20} + 3 q^{21} + 2 q^{22} - 10 q^{23} + q^{24} + 2 q^{25} - 3 q^{26} - 7 q^{27} - 6 q^{28} + 4 q^{29} + q^{30} + 4 q^{31} - 2 q^{32} + q^{33} - 7 q^{34} - 6 q^{35} + 3 q^{36} - q^{37} + 2 q^{38} - 10 q^{39} - 2 q^{40} - 5 q^{41} - 3 q^{42} + 2 q^{43} - 2 q^{44} + 3 q^{45} + 10 q^{46} - 4 q^{47} - q^{48} + 4 q^{49} - 2 q^{50} + 5 q^{51} + 3 q^{52} - 3 q^{53} + 7 q^{54} - 2 q^{55} + 6 q^{56} + q^{57} - 4 q^{58} + 10 q^{59} - q^{60} - 4 q^{61} - 4 q^{62} - 9 q^{63} + 2 q^{64} + 3 q^{65} - q^{66} - 7 q^{67} + 7 q^{68} + 22 q^{69} + 6 q^{70} + 21 q^{71} - 3 q^{72} - 3 q^{73} + q^{74} - q^{75} - 2 q^{76} + 6 q^{77} + 10 q^{78} + 3 q^{79} + 2 q^{80} - 14 q^{81} + 5 q^{82} - 10 q^{83} + 3 q^{84} + 7 q^{85} - 2 q^{86} - 19 q^{87} + 2 q^{88} - 11 q^{89} - 3 q^{90} - 9 q^{91} - 10 q^{92} + 15 q^{93} + 4 q^{94} - 2 q^{95} + q^{96} + 18 q^{97} - 4 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + 2 * q^5 + q^6 - 6 * q^7 - 2 * q^8 + 3 * q^9 - 2 * q^10 - 2 * q^11 - q^12 + 3 * q^13 + 6 * q^14 - q^15 + 2 * q^16 + 7 * q^17 - 3 * q^18 - 2 * q^19 + 2 * q^20 + 3 * q^21 + 2 * q^22 - 10 * q^23 + q^24 + 2 * q^25 - 3 * q^26 - 7 * q^27 - 6 * q^28 + 4 * q^29 + q^30 + 4 * q^31 - 2 * q^32 + q^33 - 7 * q^34 - 6 * q^35 + 3 * q^36 - q^37 + 2 * q^38 - 10 * q^39 - 2 * q^40 - 5 * q^41 - 3 * q^42 + 2 * q^43 - 2 * q^44 + 3 * q^45 + 10 * q^46 - 4 * q^47 - q^48 + 4 * q^49 - 2 * q^50 + 5 * q^51 + 3 * q^52 - 3 * q^53 + 7 * q^54 - 2 * q^55 + 6 * q^56 + q^57 - 4 * q^58 + 10 * q^59 - q^60 - 4 * q^61 - 4 * q^62 - 9 * q^63 + 2 * q^64 + 3 * q^65 - q^66 - 7 * q^67 + 7 * q^68 + 22 * q^69 + 6 * q^70 + 21 * q^71 - 3 * q^72 - 3 * q^73 + q^74 - q^75 - 2 * q^76 + 6 * q^77 + 10 * q^78 + 3 * q^79 + 2 * q^80 - 14 * q^81 + 5 * q^82 - 10 * q^83 + 3 * q^84 + 7 * q^85 - 2 * q^86 - 19 * q^87 + 2 * q^88 - 11 * q^89 - 3 * q^90 - 9 * q^91 - 10 * q^92 + 15 * q^93 + 4 * q^94 - 2 * q^95 + q^96 + 18 * q^97 - 4 * q^98 - 3 * q^99

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