LMFDB - Embedded newform 4029.2.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 10 x^{16} + 120 x^{15} - 56 x^{14} - 921 x^{13} + 1181 x^{12} + 3316 x^{11} + \cdots + 138 $ x^18 - 6x^17 - 10x^16 + 120x^15 - 56x^14 - 921x^13 + 1181x^12 + 3316x^11 - 6280x^10 - 5249x^9 + 15005x^8 + 1809x^7 - 16711x^6 + 2434x^5 + 8758x^4 - 1858x^3 - 1942x^2 + 318*x + 138
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.64567$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.64567 q^{2} +1.00000 q^{3} +0.708234 q^{4} -0.419467 q^{5} -1.64567 q^{6} +1.49188 q^{7} +2.12582 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.64567 q^{2} +1.00000 q^{3} +0.708234 q^{4} -0.419467 q^{5} -1.64567 q^{6} +1.49188 q^{7} +2.12582 q^{8} +1.00000 q^{9} +0.690305 q^{10} -2.79714 q^{11} +0.708234 q^{12} -0.608370 q^{13} -2.45514 q^{14} -0.419467 q^{15} -4.91487 q^{16} +1.00000 q^{17} -1.64567 q^{18} +4.76112 q^{19} -0.297081 q^{20} +1.49188 q^{21} +4.60318 q^{22} -1.47127 q^{23} +2.12582 q^{24} -4.82405 q^{25} +1.00118 q^{26} +1.00000 q^{27} +1.05660 q^{28} -5.97897 q^{29} +0.690305 q^{30} -0.192857 q^{31} +3.83662 q^{32} -2.79714 q^{33} -1.64567 q^{34} -0.625794 q^{35} +0.708234 q^{36} +0.227267 q^{37} -7.83524 q^{38} -0.608370 q^{39} -0.891713 q^{40} -3.88634 q^{41} -2.45514 q^{42} +7.71447 q^{43} -1.98103 q^{44} -0.419467 q^{45} +2.42123 q^{46} -1.89422 q^{47} -4.91487 q^{48} -4.77430 q^{49} +7.93880 q^{50} +1.00000 q^{51} -0.430869 q^{52} -8.79892 q^{53} -1.64567 q^{54} +1.17331 q^{55} +3.17147 q^{56} +4.76112 q^{57} +9.83942 q^{58} +12.5172 q^{59} -0.297081 q^{60} -6.94692 q^{61} +0.317379 q^{62} +1.49188 q^{63} +3.51593 q^{64} +0.255191 q^{65} +4.60318 q^{66} +3.16341 q^{67} +0.708234 q^{68} -1.47127 q^{69} +1.02985 q^{70} -13.4404 q^{71} +2.12582 q^{72} -10.6477 q^{73} -0.374007 q^{74} -4.82405 q^{75} +3.37199 q^{76} -4.17300 q^{77} +1.00118 q^{78} -1.00000 q^{79} +2.06163 q^{80} +1.00000 q^{81} +6.39563 q^{82} -4.68999 q^{83} +1.05660 q^{84} -0.419467 q^{85} -12.6955 q^{86} -5.97897 q^{87} -5.94623 q^{88} +3.87182 q^{89} +0.690305 q^{90} -0.907614 q^{91} -1.04200 q^{92} -0.192857 q^{93} +3.11726 q^{94} -1.99713 q^{95} +3.83662 q^{96} -13.0588 q^{97} +7.85693 q^{98} -2.79714 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * 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 $

$2$	−1.64567	−1.16367	−0.581833	−	0.813309i	$-0.697664\pi$
$2$	−1.64567	−1.16367	−0.581833	+	0.813309i	$0.697664\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.708234	0.354117
$5$	−0.419467	−0.187591	−0.0937957	−	0.995591i	$-0.529900\pi$
$5$	−0.419467	−0.187591	−0.0937957	+	0.995591i	$0.529900\pi$
$6$	−1.64567	−0.671843
$7$	1.49188	0.563877	0.281939	−	0.959432i	$-0.409023\pi$
$7$	1.49188	0.563877	0.281939	+	0.959432i	$0.409023\pi$
$8$	2.12582	0.751592
$9$	1.00000	0.333333
$10$	0.690305	0.218294
$11$	−2.79714	−0.843370	−0.421685	−	0.906742i	$-0.638561\pi$
$11$	−2.79714	−0.843370	−0.421685	+	0.906742i	$0.638561\pi$
$12$	0.708234	0.204450
$13$	−0.608370	−0.168732	−0.0843658	−	0.996435i	$-0.526886\pi$
$13$	−0.608370	−0.168732	−0.0843658	+	0.996435i	$0.526886\pi$
$14$	−2.45514	−0.656164
$15$	−0.419467	−0.108306
$16$	−4.91487	−1.22872
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.64567	−0.387888
$19$	4.76112	1.09228	0.546138	−	0.837695i	$-0.316097\pi$
$19$	4.76112	1.09228	0.546138	+	0.837695i	$0.316097\pi$
$20$	−0.297081	−0.0664294
$21$	1.49188	0.325555
$22$	4.60318	0.981401
$23$	−1.47127	−0.306781	−0.153391	−	0.988166i	$-0.549019\pi$
$23$	−1.47127	−0.306781	−0.153391	+	0.988166i	$0.549019\pi$
$24$	2.12582	0.433932
$25$	−4.82405	−0.964809
$26$	1.00118	0.196347
$27$	1.00000	0.192450
$28$	1.05660	0.199679
$29$	−5.97897	−1.11027	−0.555133	−	0.831761i	$-0.687333\pi$
$29$	−5.97897	−1.11027	−0.555133	+	0.831761i	$0.687333\pi$
$30$	0.690305	0.126032
$31$	−0.192857	−0.0346381	−0.0173190	−	0.999850i	$-0.505513\pi$
$31$	−0.192857	−0.0346381	−0.0173190	+	0.999850i	$0.505513\pi$
$32$	3.83662	0.678225
$33$	−2.79714	−0.486920
$34$	−1.64567	−0.282230
$35$	−0.625794	−0.105779
$36$	0.708234	0.118039
$37$	0.227267	0.0373624	0.0186812	−	0.999825i	$-0.494053\pi$
$37$	0.227267	0.0373624	0.0186812	+	0.999825i	$0.494053\pi$
$38$	−7.83524	−1.27104
$39$	−0.608370	−0.0974172
$40$	−0.891713	−0.140992
$41$	−3.88634	−0.606944	−0.303472	−	0.952840i	$-0.598146\pi$
$41$	−3.88634	−0.606944	−0.303472	+	0.952840i	$0.598146\pi$
$42$	−2.45514	−0.378837
$43$	7.71447	1.17645	0.588223	−	0.808699i	$-0.299828\pi$
$43$	7.71447	1.17645	0.588223	+	0.808699i	$0.299828\pi$
$44$	−1.98103	−0.298652
$45$	−0.419467	−0.0625305
$46$	2.42123	0.356991
$47$	−1.89422	−0.276300	−0.138150	−	0.990411i	$-0.544116\pi$
$47$	−1.89422	−0.276300	−0.138150	+	0.990411i	$0.544116\pi$
$48$	−4.91487	−0.709401
$49$	−4.77430	−0.682043
$50$	7.93880	1.12272
$51$	1.00000	0.140028
$52$	−0.430869	−0.0597507
$53$	−8.79892	−1.20862	−0.604312	−	0.796748i	$-0.706552\pi$
$53$	−8.79892	−1.20862	−0.604312	+	0.796748i	$0.706552\pi$
$54$	−1.64567	−0.223948
$55$	1.17331	0.158209
$56$	3.17147	0.423805
$57$	4.76112	0.630626
$58$	9.83942	1.29198
$59$	12.5172	1.62959	0.814797	−	0.579746i	$-0.196848\pi$
$59$	12.5172	1.62959	0.814797	+	0.579746i	$0.196848\pi$
$60$	−0.297081	−0.0383530
$61$	−6.94692	−0.889462	−0.444731	−	0.895664i	$-0.646701\pi$
$61$	−6.94692	−0.889462	−0.444731	+	0.895664i	$0.646701\pi$
$62$	0.317379	0.0403071
$63$	1.49188	0.187959
$64$	3.51593	0.439491
$65$	0.255191	0.0316526
$66$	4.60318	0.566612
$67$	3.16341	0.386472	0.193236	−	0.981152i	$-0.438102\pi$
$67$	3.16341	0.386472	0.193236	+	0.981152i	$0.438102\pi$
$68$	0.708234	0.0858860
$69$	−1.47127	−0.177120
$70$	1.02985	0.123091
$71$	−13.4404	−1.59508	−0.797542	−	0.603263i	$-0.793867\pi$
$71$	−13.4404	−1.59508	−0.797542	+	0.603263i	$0.793867\pi$
$72$	2.12582	0.250531
$73$	−10.6477	−1.24621	−0.623107	−	0.782136i	$-0.714130\pi$
$73$	−10.6477	−1.24621	−0.623107	+	0.782136i	$0.714130\pi$
$74$	−0.374007	−0.0434774
$75$	−4.82405	−0.557033
$76$	3.37199	0.386794
$77$	−4.17300	−0.475557
$78$	1.00118	0.113361
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	2.06163	0.230497
$81$	1.00000	0.111111
$82$	6.39563	0.706280
$83$	−4.68999	−0.514793	−0.257397	−	0.966306i	$-0.582865\pi$
$83$	−4.68999	−0.514793	−0.257397	+	0.966306i	$0.582865\pi$
$84$	1.05660	0.115284
$85$	−0.419467	−0.0454976
$86$	−12.6955	−1.36899
$87$	−5.97897	−0.641013
$88$	−5.94623	−0.633870
$89$	3.87182	0.410412	0.205206	−	0.978719i	$-0.434213\pi$
$89$	3.87182	0.410412	0.205206	+	0.978719i	$0.434213\pi$
$90$	0.690305	0.0727646
$91$	−0.907614	−0.0951438
$92$	−1.04200	−0.108636
$93$	−0.192857	−0.0199983
$94$	3.11726	0.321521
$95$	−1.99713	−0.204902
$96$	3.83662	0.391574
$97$	−13.0588	−1.32592	−0.662962	−	0.748653i	$-0.730701\pi$
$97$	−13.0588	−1.32592	−0.662962	+	0.748653i	$0.730701\pi$
$98$	7.85693	0.793669
$99$	−2.79714	−0.281123
$100$	−3.41656	−0.341656
$101$	10.7811	1.07276	0.536379	−	0.843977i	$-0.319792\pi$
$101$	10.7811	1.07276	0.536379	+	0.843977i	$0.319792\pi$
$102$	−1.64567	−0.162946
$103$	15.9595	1.57254	0.786268	−	0.617885i	$-0.212010\pi$
$103$	15.9595	1.57254	0.786268	+	0.617885i	$0.212010\pi$
$104$	−1.29329	−0.126817
$105$	−0.625794	−0.0610713
$106$	14.4801	1.40643
$107$	−9.03537	−0.873482	−0.436741	−	0.899587i	$-0.643867\pi$
$107$	−9.03537	−0.873482	−0.436741	+	0.899587i	$0.643867\pi$
$108$	0.708234	0.0681499
$109$	5.35315	0.512739	0.256369	−	0.966579i	$-0.417474\pi$
$109$	5.35315	0.512739	0.256369	+	0.966579i	$0.417474\pi$
$110$	−1.93088	−0.184102
$111$	0.227267	0.0215712
$112$	−7.33239	−0.692846
$113$	−6.93233	−0.652139	−0.326069	−	0.945346i	$-0.605724\pi$
$113$	−6.93233	−0.652139	−0.326069	+	0.945346i	$0.605724\pi$
$114$	−7.83524	−0.733837
$115$	0.617150	0.0575495
$116$	−4.23451	−0.393165
$117$	−0.608370	−0.0562438
$118$	−20.5991	−1.89630
$119$	1.49188	0.136760
$120$	−0.891713	−0.0814019
$121$	−3.17599	−0.288727
$122$	11.4323	1.03504
$123$	−3.88634	−0.350419
$124$	−0.136588	−0.0122659
$125$	4.12087	0.368582
$126$	−2.45514	−0.218721
$127$	9.67903	0.858875	0.429438	−	0.903097i	$-0.358712\pi$
$127$	9.67903	0.858875	0.429438	+	0.903097i	$0.358712\pi$
$128$	−13.4593	−1.18965
$129$	7.71447	0.679221
$130$	−0.419961	−0.0368330
$131$	−3.75846	−0.328378	−0.164189	−	0.986429i	$-0.552501\pi$
$131$	−3.75846	−0.328378	−0.164189	+	0.986429i	$0.552501\pi$
$132$	−1.98103	−0.172427
$133$	7.10301	0.615909
$134$	−5.20593	−0.449724
$135$	−0.419467	−0.0361020
$136$	2.12582	0.182288
$137$	−20.6028	−1.76021	−0.880106	−	0.474777i	$-0.842529\pi$
$137$	−20.6028	−1.76021	−0.880106	+	0.474777i	$0.842529\pi$
$138$	2.42123	0.206109
$139$	20.8379	1.76745	0.883724	−	0.468008i	$-0.155028\pi$
$139$	20.8379	1.76745	0.883724	+	0.468008i	$0.155028\pi$
$140$	−0.443209	−0.0374580
$141$	−1.89422	−0.159522
$142$	22.1185	1.85614
$143$	1.70170	0.142303
$144$	−4.91487	−0.409573
$145$	2.50798	0.208277
$146$	17.5225	1.45018
$147$	−4.77430	−0.393777
$148$	0.160958	0.0132307
$149$	3.67808	0.301320	0.150660	−	0.988586i	$-0.451860\pi$
$149$	3.67808	0.301320	0.150660	+	0.988586i	$0.451860\pi$
$150$	7.93880	0.648200
$151$	9.85639	0.802102	0.401051	−	0.916056i	$-0.368645\pi$
$151$	9.85639	0.802102	0.401051	+	0.916056i	$0.368645\pi$
$152$	10.1213	0.820945
$153$	1.00000	0.0808452
$154$	6.86738	0.553389
$155$	0.0808970	0.00649781
$156$	−0.430869	−0.0344971
$157$	13.1969	1.05323	0.526615	−	0.850104i	$-0.323461\pi$
$157$	13.1969	1.05323	0.526615	+	0.850104i	$0.323461\pi$
$158$	1.64567	0.130923
$159$	−8.79892	−0.697799
$160$	−1.60934	−0.127229
$161$	−2.19496	−0.172987
$162$	−1.64567	−0.129296
$163$	−1.91769	−0.150205	−0.0751024	−	0.997176i	$-0.523928\pi$
$163$	−1.91769	−0.150205	−0.0751024	+	0.997176i	$0.523928\pi$
$164$	−2.75244	−0.214929
$165$	1.17331	0.0913421
$166$	7.71818	0.599047
$167$	1.09481	0.0847188	0.0423594	−	0.999102i	$-0.486513\pi$
$167$	1.09481	0.0847188	0.0423594	+	0.999102i	$0.486513\pi$
$168$	3.17147	0.244684
$169$	−12.6299	−0.971530
$170$	0.690305	0.0529440
$171$	4.76112	0.364092
$172$	5.46365	0.416599
$173$	−5.96356	−0.453401	−0.226701	−	0.973965i	$-0.572794\pi$
$173$	−5.96356	−0.453401	−0.226701	+	0.973965i	$0.572794\pi$
$174$	9.83942	0.745925
$175$	−7.19689	−0.544034
$176$	13.7476	1.03626
$177$	12.5172	0.940847
$178$	−6.37175	−0.477583
$179$	−16.8269	−1.25770	−0.628850	−	0.777526i	$-0.716474\pi$
$179$	−16.8269	−1.25770	−0.628850	+	0.777526i	$0.716474\pi$
$180$	−0.297081	−0.0221431
$181$	−6.76484	−0.502827	−0.251413	−	0.967880i	$-0.580895\pi$
$181$	−6.76484	−0.502827	−0.251413	+	0.967880i	$0.580895\pi$
$182$	1.49364	0.110716
$183$	−6.94692	−0.513531
$184$	−3.12766	−0.230574
$185$	−0.0953310	−0.00700888
$186$	0.317379	0.0232713
$187$	−2.79714	−0.204547
$188$	−1.34155	−0.0978425
$189$	1.49188	0.108518
$190$	3.28663	0.238437
$191$	−13.1999	−0.955112	−0.477556	−	0.878601i	$-0.658477\pi$
$191$	−13.1999	−0.955112	−0.477556	+	0.878601i	$0.658477\pi$
$192$	3.51593	0.253740
$193$	−7.21485	−0.519336	−0.259668	−	0.965698i	$-0.583613\pi$
$193$	−7.21485	−0.519336	−0.259668	+	0.965698i	$0.583613\pi$
$194$	21.4906	1.54293
$195$	0.255191	0.0182746
$196$	−3.38132	−0.241523
$197$	−15.7490	−1.12207	−0.561033	−	0.827793i	$-0.689596\pi$
$197$	−15.7490	−1.12207	−0.561033	+	0.827793i	$0.689596\pi$
$198$	4.60318	0.327134
$199$	−9.10312	−0.645303	−0.322652	−	0.946518i	$-0.604574\pi$
$199$	−9.10312	−0.645303	−0.322652	+	0.946518i	$0.604574\pi$
$200$	−10.2551	−0.725143
$201$	3.16341	0.223130
$202$	−17.7421	−1.24833
$203$	−8.91990	−0.626054
$204$	0.708234	0.0495863
$205$	1.63019	0.113858
$206$	−26.2641	−1.82991
$207$	−1.47127	−0.102260
$208$	2.99006	0.207323
$209$	−13.3175	−0.921193
$210$	1.02985	0.0710665
$211$	14.6073	1.00561	0.502804	−	0.864400i	$-0.332302\pi$
$211$	14.6073	1.00561	0.502804	+	0.864400i	$0.332302\pi$
$212$	−6.23169	−0.427994
$213$	−13.4404	−0.920923
$214$	14.8692	1.01644
$215$	−3.23597	−0.220691
$216$	2.12582	0.144644
$217$	−0.287719	−0.0195316
$218$	−8.80953	−0.596656
$219$	−10.6477	−0.719502
$220$	0.830978	0.0560245
$221$	−0.608370	−0.0409234
$222$	−0.374007	−0.0251017
$223$	−12.1139	−0.811209	−0.405605	−	0.914049i	$-0.632939\pi$
$223$	−12.1139	−0.811209	−0.405605	+	0.914049i	$0.632939\pi$
$224$	5.72377	0.382436
$225$	−4.82405	−0.321603
$226$	11.4083	0.758871
$227$	−2.55506	−0.169585	−0.0847926	−	0.996399i	$-0.527023\pi$
$227$	−2.55506	−0.169585	−0.0847926	+	0.996399i	$0.527023\pi$
$228$	3.37199	0.223315
$229$	25.0967	1.65844	0.829218	−	0.558925i	$-0.188786\pi$
$229$	25.0967	1.65844	0.829218	+	0.558925i	$0.188786\pi$
$230$	−1.01563	−0.0669684
$231$	−4.17300	−0.274563
$232$	−12.7102	−0.834467
$233$	6.98684	0.457723	0.228861	−	0.973459i	$-0.426500\pi$
$233$	6.98684	0.457723	0.228861	+	0.973459i	$0.426500\pi$
$234$	1.00118	0.0654490
$235$	0.794562	0.0518315
$236$	8.86507	0.577067
$237$	−1.00000	−0.0649570
$238$	−2.45514	−0.159143
$239$	2.76772	0.179029	0.0895144	−	0.995986i	$-0.471468\pi$
$239$	2.76772	0.179029	0.0895144	+	0.995986i	$0.471468\pi$
$240$	2.06163	0.133078
$241$	−12.3525	−0.795697	−0.397849	−	0.917451i	$-0.630243\pi$
$241$	−12.3525	−0.795697	−0.397849	+	0.917451i	$0.630243\pi$
$242$	5.22664	0.335981
$243$	1.00000	0.0641500
$244$	−4.92005	−0.314974
$245$	2.00266	0.127945
$246$	6.39563	0.407771
$247$	−2.89652	−0.184301
$248$	−0.409979	−0.0260337
$249$	−4.68999	−0.297216
$250$	−6.78159	−0.428906
$251$	−25.4440	−1.60601	−0.803007	−	0.595970i	$-0.796768\pi$
$251$	−25.4440	−1.60601	−0.803007	+	0.595970i	$0.796768\pi$
$252$	1.05660	0.0665595
$253$	4.11535	0.258730
$254$	−15.9285	−0.999443
$255$	−0.419467	−0.0262681
$256$	15.1177	0.944858
$257$	20.7792	1.29617	0.648085	−	0.761568i	$-0.275570\pi$
$257$	20.7792	1.29617	0.648085	+	0.761568i	$0.275570\pi$
$258$	−12.6955	−0.790386
$259$	0.339055	0.0210678
$260$	0.180735	0.0112087
$261$	−5.97897	−0.370089
$262$	6.18518	0.382122
$263$	8.27362	0.510173	0.255087	−	0.966918i	$-0.417896\pi$
$263$	8.27362	0.510173	0.255087	+	0.966918i	$0.417896\pi$
$264$	−5.94623	−0.365965
$265$	3.69086	0.226728
$266$	−11.6892	−0.716712
$267$	3.87182	0.236952
$268$	2.24043	0.136856
$269$	−5.61231	−0.342189	−0.171094	−	0.985255i	$-0.554730\pi$
$269$	−5.61231	−0.342189	−0.171094	+	0.985255i	$0.554730\pi$
$270$	0.690305	0.0420106
$271$	−8.42208	−0.511605	−0.255802	−	0.966729i	$-0.582340\pi$
$271$	−8.42208	−0.511605	−0.255802	+	0.966729i	$0.582340\pi$
$272$	−4.91487	−0.298008
$273$	−0.907614	−0.0549313
$274$	33.9054	2.04830
$275$	13.4935	0.813692
$276$	−1.04200	−0.0627213
$277$	−0.210865	−0.0126696	−0.00633481	−	0.999980i	$-0.502016\pi$
$277$	−0.210865	−0.0126696	−0.00633481	+	0.999980i	$0.502016\pi$
$278$	−34.2924	−2.05672
$279$	−0.192857	−0.0115460
$280$	−1.33033	−0.0795023
$281$	−7.40043	−0.441473	−0.220736	−	0.975334i	$-0.570846\pi$
$281$	−7.40043	−0.441473	−0.220736	+	0.975334i	$0.570846\pi$
$282$	3.11726	0.185630
$283$	−16.1470	−0.959838	−0.479919	−	0.877313i	$-0.659334\pi$
$283$	−16.1470	−0.959838	−0.479919	+	0.877313i	$0.659334\pi$
$284$	−9.51897	−0.564847
$285$	−1.99713	−0.118300
$286$	−2.80044	−0.165593
$287$	−5.79794	−0.342242
$288$	3.83662	0.226075
$289$	1.00000	0.0588235
$290$	−4.12732	−0.242364
$291$	−13.0588	−0.765523
$292$	−7.54104	−0.441306
$293$	−3.29877	−0.192716	−0.0963580	−	0.995347i	$-0.530719\pi$
$293$	−3.29877	−0.192716	−0.0963580	+	0.995347i	$0.530719\pi$
$294$	7.85693	0.458225
$295$	−5.25054	−0.305698
$296$	0.483129	0.0280813
$297$	−2.79714	−0.162307
$298$	−6.05290	−0.350635
$299$	0.895077	0.0517636
$300$	−3.41656	−0.197255
$301$	11.5090	0.663371
$302$	−16.2204	−0.933378
$303$	10.7811	0.619357
$304$	−23.4003	−1.34210
$305$	2.91401	0.166855
$306$	−1.64567	−0.0940768
$307$	−11.8120	−0.674147	−0.337074	−	0.941478i	$-0.609437\pi$
$307$	−11.8120	−0.674147	−0.337074	+	0.941478i	$0.609437\pi$
$308$	−2.95546	−0.168403
$309$	15.9595	0.907904
$310$	−0.133130	−0.00756127
$311$	4.75671	0.269729	0.134864	−	0.990864i	$-0.456940\pi$
$311$	4.75671	0.269729	0.134864	+	0.990864i	$0.456940\pi$
$312$	−1.29329	−0.0732179
$313$	−30.7486	−1.73802	−0.869008	−	0.494798i	$-0.835242\pi$
$313$	−30.7486	−1.73802	−0.869008	+	0.494798i	$0.835242\pi$
$314$	−21.7178	−1.22561
$315$	−0.625794	−0.0352595
$316$	−0.708234	−0.0398413
$317$	−9.58464	−0.538327	−0.269164	−	0.963094i	$-0.586747\pi$
$317$	−9.58464	−0.538327	−0.269164	+	0.963094i	$0.586747\pi$
$318$	14.4801	0.812005
$319$	16.7240	0.936366
$320$	−1.47482	−0.0824448
$321$	−9.03537	−0.504305
$322$	3.61218	0.201299
$323$	4.76112	0.264916
$324$	0.708234	0.0393463
$325$	2.93481	0.162794
$326$	3.15588	0.174788
$327$	5.35315	0.296030
$328$	−8.26166	−0.456174
$329$	−2.82594	−0.155799
$330$	−1.93088	−0.106292
$331$	6.25819	0.343981	0.171991	−	0.985099i	$-0.444980\pi$
$331$	6.25819	0.343981	0.171991	+	0.985099i	$0.444980\pi$
$332$	−3.32161	−0.182297
$333$	0.227267	0.0124541
$334$	−1.80170	−0.0985844
$335$	−1.32695	−0.0724988
$336$	−7.33239	−0.400015
$337$	6.73375	0.366811	0.183405	−	0.983037i	$-0.441288\pi$
$337$	6.73375	0.366811	0.183405	+	0.983037i	$0.441288\pi$
$338$	20.7846	1.13054
$339$	−6.93233	−0.376513
$340$	−0.297081	−0.0161115
$341$	0.539447	0.0292127
$342$	−7.83524	−0.423681
$343$	−17.5658	−0.948465
$344$	16.3996	0.884206
$345$	0.617150	0.0332262
$346$	9.81406	0.527607
$347$	−19.7149	−1.05835	−0.529174	−	0.848513i	$-0.677498\pi$
$347$	−19.7149	−1.05835	−0.529174	+	0.848513i	$0.677498\pi$
$348$	−4.23451	−0.226994
$349$	1.70824	0.0914400	0.0457200	−	0.998954i	$-0.485442\pi$
$349$	1.70824	0.0914400	0.0457200	+	0.998954i	$0.485442\pi$
$350$	11.8437	0.633073
$351$	−0.608370	−0.0324724
$352$	−10.7316	−0.571995
$353$	30.1829	1.60647	0.803236	−	0.595661i	$-0.203110\pi$
$353$	30.1829	1.60647	0.803236	+	0.595661i	$0.203110\pi$
$354$	−20.5991	−1.09483
$355$	5.63782	0.299224
$356$	2.74216	0.145334
$357$	1.49188	0.0789586
$358$	27.6915	1.46354
$359$	−4.09416	−0.216082	−0.108041	−	0.994146i	$-0.534458\pi$
$359$	−4.09416	−0.216082	−0.108041	+	0.994146i	$0.534458\pi$
$360$	−0.891713	−0.0469974
$361$	3.66826	0.193066
$362$	11.1327	0.585122
$363$	−3.17599	−0.166696
$364$	−0.642804	−0.0336921
$365$	4.46635	0.233779
$366$	11.4323	0.597578
$367$	15.3951	0.803615	0.401808	−	0.915724i	$-0.368382\pi$
$367$	15.3951	0.803615	0.401808	+	0.915724i	$0.368382\pi$
$368$	7.23111	0.376948
$369$	−3.88634	−0.202315
$370$	0.156884	0.00815599
$371$	−13.1269	−0.681516
$372$	−0.136588	−0.00708174
$373$	−2.21298	−0.114584	−0.0572918	−	0.998357i	$-0.518247\pi$
$373$	−2.21298	−0.114584	−0.0572918	+	0.998357i	$0.518247\pi$
$374$	4.60318	0.238025
$375$	4.12087	0.212801
$376$	−4.02677	−0.207665
$377$	3.63743	0.187337
$378$	−2.45514	−0.126279
$379$	−26.7907	−1.37615	−0.688073	−	0.725642i	$-0.741543\pi$
$379$	−26.7907	−1.37615	−0.688073	+	0.725642i	$0.741543\pi$
$380$	−1.41444	−0.0725592
$381$	9.67903	0.495872
$382$	21.7227	1.11143
$383$	−35.5739	−1.81774	−0.908871	−	0.417077i	$-0.863054\pi$
$383$	−35.5739	−1.81774	−0.908871	+	0.417077i	$0.863054\pi$
$384$	−13.4593	−0.686842
$385$	1.75044	0.0892105
$386$	11.8733	0.604333
$387$	7.71447	0.392148
$388$	−9.24872	−0.469532
$389$	−15.5194	−0.786862	−0.393431	−	0.919354i	$-0.628712\pi$
$389$	−15.5194	−0.786862	−0.393431	+	0.919354i	$0.628712\pi$
$390$	−0.419961	−0.0212656
$391$	−1.47127	−0.0744054
$392$	−10.1493	−0.512617
$393$	−3.75846	−0.189589
$394$	25.9176	1.30571
$395$	0.419467	0.0211057
$396$	−1.98103	−0.0995506
$397$	−16.1847	−0.812287	−0.406144	−	0.913809i	$-0.633127\pi$
$397$	−16.1847	−0.812287	−0.406144	+	0.913809i	$0.633127\pi$
$398$	14.9807	0.750917
$399$	7.10301	0.355595
$400$	23.7096	1.18548
$401$	−17.4275	−0.870288	−0.435144	−	0.900361i	$-0.643303\pi$
$401$	−17.4275	−0.870288	−0.435144	+	0.900361i	$0.643303\pi$
$402$	−5.20593	−0.259648
$403$	0.117328	0.00584453
$404$	7.63553	0.379882
$405$	−0.419467	−0.0208435
$406$	14.6792	0.728517
$407$	−0.635698	−0.0315104
$408$	2.12582	0.105244
$409$	1.07501	0.0531556	0.0265778	−	0.999647i	$-0.491539\pi$
$409$	1.07501	0.0531556	0.0265778	+	0.999647i	$0.491539\pi$
$410$	−2.68276	−0.132492
$411$	−20.6028	−1.01626
$412$	11.3031	0.556862
$413$	18.6741	0.918891
$414$	2.42123	0.118997
$415$	1.96730	0.0965709
$416$	−2.33409	−0.114438
$417$	20.8379	1.02044
$418$	21.9163	1.07196
$419$	−11.9780	−0.585163	−0.292582	−	0.956241i	$-0.594514\pi$
$419$	−11.9780	−0.585163	−0.292582	+	0.956241i	$0.594514\pi$
$420$	−0.443209	−0.0216264
$421$	20.9127	1.01922	0.509610	−	0.860405i	$-0.329790\pi$
$421$	20.9127	1.01922	0.509610	+	0.860405i	$0.329790\pi$
$422$	−24.0388	−1.17019
$423$	−1.89422	−0.0921000
$424$	−18.7049	−0.908392
$425$	−4.82405	−0.234001
$426$	22.1185	1.07165
$427$	−10.3640	−0.501547
$428$	−6.39916	−0.309315
$429$	1.70170	0.0821588
$430$	5.32534	0.256811
$431$	−2.12237	−0.102231	−0.0511154	−	0.998693i	$-0.516278\pi$
$431$	−2.12237	−0.102231	−0.0511154	+	0.998693i	$0.516278\pi$
$432$	−4.91487	−0.236467
$433$	14.0138	0.673460	0.336730	−	0.941601i	$-0.390679\pi$
$433$	14.0138	0.673460	0.336730	+	0.941601i	$0.390679\pi$
$434$	0.473490	0.0227283
$435$	2.50798	0.120249
$436$	3.79128	0.181570
$437$	−7.00490	−0.335090
$438$	17.5225	0.837260
$439$	35.2010	1.68005	0.840027	−	0.542545i	$-0.182539\pi$
$439$	35.2010	1.68005	0.840027	+	0.542545i	$0.182539\pi$
$440$	2.49425	0.118909
$441$	−4.77430	−0.227348
$442$	1.00118	0.0476211
$443$	−8.09102	−0.384416	−0.192208	−	0.981354i	$-0.561565\pi$
$443$	−8.09102	−0.384416	−0.192208	+	0.981354i	$0.561565\pi$
$444$	0.160958	0.00763874
$445$	−1.62410	−0.0769899
$446$	19.9356	0.943976
$447$	3.67808	0.173967
$448$	5.24534	0.247819
$449$	−25.2970	−1.19384	−0.596920	−	0.802300i	$-0.703609\pi$
$449$	−25.2970	−1.19384	−0.596920	+	0.802300i	$0.703609\pi$
$450$	7.93880	0.374238
$451$	10.8706	0.511879
$452$	−4.90971	−0.230934
$453$	9.85639	0.463094
$454$	4.20479	0.197340
$455$	0.380715	0.0178482
$456$	10.1213	0.473973
$457$	8.89196	0.415948	0.207974	−	0.978134i	$-0.433313\pi$
$457$	8.89196	0.415948	0.207974	+	0.978134i	$0.433313\pi$
$458$	−41.3009	−1.92986
$459$	1.00000	0.0466760
$460$	0.437087	0.0203793
$461$	−2.03257	−0.0946663	−0.0473331	−	0.998879i	$-0.515072\pi$
$461$	−2.03257	−0.0946663	−0.0473331	+	0.998879i	$0.515072\pi$
$462$	6.86738	0.319500
$463$	−6.83602	−0.317697	−0.158848	−	0.987303i	$-0.550778\pi$
$463$	−6.83602	−0.317697	−0.158848	+	0.987303i	$0.550778\pi$
$464$	29.3859	1.36421
$465$	0.0808970	0.00375151
$466$	−11.4980	−0.532636
$467$	−2.92453	−0.135331	−0.0676656	−	0.997708i	$-0.521555\pi$
$467$	−2.92453	−0.135331	−0.0676656	+	0.997708i	$0.521555\pi$
$468$	−0.430869	−0.0199169
$469$	4.71942	0.217923
$470$	−1.30759	−0.0603145
$471$	13.1969	0.608082
$472$	26.6092	1.22479
$473$	−21.5785	−0.992179
$474$	1.64567	0.0755882
$475$	−22.9679	−1.05384
$476$	1.05660	0.0484292
$477$	−8.79892	−0.402875
$478$	−4.55475	−0.208330
$479$	11.3377	0.518032	0.259016	−	0.965873i	$-0.416602\pi$
$479$	11.3377	0.518032	0.259016	+	0.965873i	$0.416602\pi$
$480$	−1.60934	−0.0734559
$481$	−0.138262	−0.00630422
$482$	20.3282	0.925925
$483$	−2.19496	−0.0998740
$484$	−2.24935	−0.102243
$485$	5.47776	0.248732
$486$	−1.64567	−0.0746492
$487$	−41.5288	−1.88185	−0.940924	−	0.338618i	$-0.890041\pi$
$487$	−41.5288	−1.88185	−0.940924	+	0.338618i	$0.890041\pi$
$488$	−14.7679	−0.668512
$489$	−1.91769	−0.0867207
$490$	−3.29572	−0.148886
$491$	15.1917	0.685591	0.342796	−	0.939410i	$-0.388626\pi$
$491$	15.1917	0.685591	0.342796	+	0.939410i	$0.388626\pi$
$492$	−2.75244	−0.124089
$493$	−5.97897	−0.269279
$494$	4.76673	0.214465
$495$	1.17331	0.0527364
$496$	0.947866	0.0425604
$497$	−20.0515	−0.899432
$498$	7.71818	0.345860
$499$	−29.2440	−1.30914	−0.654571	−	0.756001i	$-0.727151\pi$
$499$	−29.2440	−1.30914	−0.654571	+	0.756001i	$0.727151\pi$
$500$	2.91854	0.130521
$501$	1.09481	0.0489124
$502$	41.8725	1.86886
$503$	−12.9859	−0.579014	−0.289507	−	0.957176i	$-0.593491\pi$
$503$	−12.9859	−0.579014	−0.289507	+	0.957176i	$0.593491\pi$
$504$	3.17147	0.141268
$505$	−4.52231	−0.201240
$506$	−6.77252	−0.301075
$507$	−12.6299	−0.560913
$508$	6.85502	0.304142
$509$	−40.6636	−1.80238	−0.901191	−	0.433423i	$-0.857306\pi$
$509$	−40.6636	−1.80238	−0.901191	+	0.433423i	$0.857306\pi$
$510$	0.690305	0.0305672
$511$	−15.8850	−0.702712
$512$	2.03978	0.0901465
$513$	4.76112	0.210209
$514$	−34.1957	−1.50831
$515$	−6.69449	−0.294995
$516$	5.46365	0.240524
$517$	5.29839	0.233023
$518$	−0.557972	−0.0245159
$519$	−5.96356	−0.261771
$520$	0.542492	0.0237898
$521$	38.5383	1.68839	0.844197	−	0.536033i	$-0.180078\pi$
$521$	38.5383	1.68839	0.844197	+	0.536033i	$0.180078\pi$
$522$	9.83942	0.430660
$523$	23.5448	1.02954	0.514772	−	0.857327i	$-0.327877\pi$
$523$	23.5448	1.02954	0.514772	+	0.857327i	$0.327877\pi$
$524$	−2.66187	−0.116284
$525$	−7.19689	−0.314098
$526$	−13.6157	−0.593671
$527$	−0.192857	−0.00840097
$528$	13.7476	0.598288
$529$	−20.8354	−0.905885
$530$	−6.07394	−0.263835
$531$	12.5172	0.543198
$532$	5.03060	0.218104
$533$	2.36433	0.102411
$534$	−6.37175	−0.275733
$535$	3.79004	0.163858
$536$	6.72484	0.290469
$537$	−16.8269	−0.726134
$538$	9.23602	0.398193
$539$	13.3544	0.575214
$540$	−0.297081	−0.0127843
$541$	3.60895	0.155161	0.0775804	−	0.996986i	$-0.475281\pi$
$541$	3.60895	0.155161	0.0775804	+	0.996986i	$0.475281\pi$
$542$	13.8600	0.595337
$543$	−6.76484	−0.290307
$544$	3.83662	0.164494
$545$	−2.24547	−0.0961855
$546$	1.49364	0.0639217
$547$	−14.7752	−0.631744	−0.315872	−	0.948802i	$-0.602297\pi$
$547$	−14.7752	−0.631744	−0.315872	+	0.948802i	$0.602297\pi$
$548$	−14.5916	−0.623321
$549$	−6.94692	−0.296487
$550$	−22.2059	−0.946865
$551$	−28.4666	−1.21272
$552$	−3.12766	−0.133122
$553$	−1.49188	−0.0634411
$554$	0.347014	0.0147432
$555$	−0.0953310	−0.00404658
$556$	14.7581	0.625884
$557$	35.9393	1.52280	0.761399	−	0.648283i	$-0.224513\pi$
$557$	35.9393	1.52280	0.761399	+	0.648283i	$0.224513\pi$
$558$	0.317379	0.0134357
$559$	−4.69325	−0.198503
$560$	3.07570	0.129972
$561$	−2.79714	−0.118095
$562$	12.1787	0.513727
$563$	−2.52567	−0.106444	−0.0532222	−	0.998583i	$-0.516949\pi$
$563$	−2.52567	−0.106444	−0.0532222	+	0.998583i	$0.516949\pi$
$564$	−1.34155	−0.0564894
$565$	2.90789	0.122336
$566$	26.5726	1.11693
$567$	1.49188	0.0626530
$568$	−28.5719	−1.19885
$569$	−28.1047	−1.17821	−0.589105	−	0.808057i	$-0.700519\pi$
$569$	−28.1047	−1.17821	−0.589105	+	0.808057i	$0.700519\pi$
$570$	3.28663	0.137662
$571$	−27.3405	−1.14416	−0.572082	−	0.820197i	$-0.693864\pi$
$571$	−27.3405	−1.14416	−0.572082	+	0.820197i	$0.693864\pi$
$572$	1.20520	0.0503920
$573$	−13.1999	−0.551434
$574$	9.54151	0.398255
$575$	7.09748	0.295985
$576$	3.51593	0.146497
$577$	−25.2881	−1.05276	−0.526378	−	0.850250i	$-0.676450\pi$
$577$	−25.2881	−1.05276	−0.526378	+	0.850250i	$0.676450\pi$
$578$	−1.64567	−0.0684509
$579$	−7.21485	−0.299839
$580$	1.77624	0.0737543
$581$	−6.99690	−0.290280
$582$	21.4906	0.890812
$583$	24.6118	1.01932
$584$	−22.6350	−0.936644
$585$	0.255191	0.0105509
$586$	5.42869	0.224257
$587$	−2.33773	−0.0964885	−0.0482442	−	0.998836i	$-0.515363\pi$
$587$	−2.33773	−0.0964885	−0.0482442	+	0.998836i	$0.515363\pi$
$588$	−3.38132	−0.139443
$589$	−0.918213	−0.0378343
$590$	8.64066	0.355730
$591$	−15.7490	−0.647825
$592$	−1.11699	−0.0459079
$593$	−12.7957	−0.525455	−0.262727	−	0.964870i	$-0.584622\pi$
$593$	−12.7957	−0.525455	−0.262727	+	0.964870i	$0.584622\pi$
$594$	4.60318	0.188871
$595$	−0.625794	−0.0256551
$596$	2.60494	0.106702
$597$	−9.10312	−0.372566
$598$	−1.47300	−0.0602356
$599$	−24.3639	−0.995483	−0.497742	−	0.867325i	$-0.665837\pi$
$599$	−24.3639	−0.995483	−0.497742	+	0.867325i	$0.665837\pi$
$600$	−10.2551	−0.418661
$601$	25.3483	1.03398	0.516989	−	0.855992i	$-0.327053\pi$
$601$	25.3483	1.03398	0.516989	+	0.855992i	$0.327053\pi$
$602$	−18.9401	−0.771941
$603$	3.16341	0.128824
$604$	6.98063	0.284038
$605$	1.33222	0.0541626
$606$	−17.7421	−0.720725
$607$	33.5208	1.36057	0.680284	−	0.732948i	$-0.261856\pi$
$607$	33.5208	1.36057	0.680284	+	0.732948i	$0.261856\pi$
$608$	18.2666	0.740809
$609$	−8.91990	−0.361453
$610$	−4.79550	−0.194164
$611$	1.15238	0.0466205
$612$	0.708234	0.0286287
$613$	0.573616	0.0231681	0.0115841	−	0.999933i	$-0.496313\pi$
$613$	0.573616	0.0231681	0.0115841	+	0.999933i	$0.496313\pi$
$614$	19.4387	0.784482
$615$	1.63019	0.0657357
$616$	−8.87105	−0.357425
$617$	−16.4647	−0.662842	−0.331421	−	0.943483i	$-0.607528\pi$
$617$	−16.4647	−0.662842	−0.331421	+	0.943483i	$0.607528\pi$
$618$	−26.2641	−1.05650
$619$	10.4797	0.421216	0.210608	−	0.977571i	$-0.432456\pi$
$619$	10.4797	0.421216	0.210608	+	0.977571i	$0.432456\pi$
$620$	0.0572941	0.00230098
$621$	−1.47127	−0.0590401
$622$	−7.82799	−0.313874
$623$	5.77629	0.231422
$624$	2.99006	0.119698
$625$	22.3917	0.895667
$626$	50.6022	2.02247
$627$	−13.3175	−0.531851
$628$	9.34652	0.372967
$629$	0.227267	0.00906172
$630$	1.02985	0.0410303
$631$	3.08006	0.122615	0.0613075	−	0.998119i	$-0.480473\pi$
$631$	3.08006	0.122615	0.0613075	+	0.998119i	$0.480473\pi$
$632$	−2.12582	−0.0845607
$633$	14.6073	0.580588
$634$	15.7732	0.626433
$635$	−4.06004	−0.161118
$636$	−6.23169	−0.247103
$637$	2.90454	0.115082
$638$	−27.5223	−1.08962
$639$	−13.4404	−0.531695
$640$	5.64574	0.223167
$641$	3.76700	0.148787	0.0743937	−	0.997229i	$-0.476298\pi$
$641$	3.76700	0.148787	0.0743937	+	0.997229i	$0.476298\pi$
$642$	14.8692	0.586842
$643$	16.8442	0.664269	0.332135	−	0.943232i	$-0.392231\pi$
$643$	16.8442	0.664269	0.332135	+	0.943232i	$0.392231\pi$
$644$	−1.55454	−0.0612576
$645$	−3.23597	−0.127416
$646$	−7.83524	−0.308273
$647$	21.2764	0.836463	0.418232	−	0.908340i	$-0.362650\pi$
$647$	21.2764	0.836463	0.418232	+	0.908340i	$0.362650\pi$
$648$	2.12582	0.0835102
$649$	−35.0123	−1.37435
$650$	−4.82973	−0.189437
$651$	−0.287719	−0.0112766
$652$	−1.35817	−0.0531901
$653$	−0.915604	−0.0358303	−0.0179152	−	0.999840i	$-0.505703\pi$
$653$	−0.915604	−0.0358303	−0.0179152	+	0.999840i	$0.505703\pi$
$654$	−8.80953	−0.344480
$655$	1.57655	0.0616009
$656$	19.1009	0.745763
$657$	−10.6477	−0.415405
$658$	4.65057	0.181298
$659$	−24.6416	−0.959901	−0.479951	−	0.877296i	$-0.659345\pi$
$659$	−24.6416	−0.959901	−0.479951	+	0.877296i	$0.659345\pi$
$660$	0.830978	0.0323458
$661$	−27.6754	−1.07645	−0.538225	−	0.842801i	$-0.680905\pi$
$661$	−27.6754	−1.07645	−0.538225	+	0.842801i	$0.680905\pi$
$662$	−10.2989	−0.400279
$663$	−0.608370	−0.0236271
$664$	−9.97009	−0.386914
$665$	−2.97948	−0.115539
$666$	−0.374007	−0.0144925
$667$	8.79668	0.340609
$668$	0.775381	0.0300004
$669$	−12.1139	−0.468352
$670$	2.18372	0.0843644
$671$	19.4315	0.750146
$672$	5.72377	0.220799
$673$	−43.0950	−1.66119	−0.830596	−	0.556875i	$-0.812000\pi$
$673$	−43.0950	−1.66119	−0.830596	+	0.556875i	$0.812000\pi$
$674$	−11.0815	−0.426845
$675$	−4.82405	−0.185678
$676$	−8.94492	−0.344035
$677$	−23.1775	−0.890782	−0.445391	−	0.895336i	$-0.646935\pi$
$677$	−23.1775	−0.890782	−0.445391	+	0.895336i	$0.646935\pi$
$678$	11.4083	0.438135
$679$	−19.4822	−0.747658
$680$	−0.891713	−0.0341956
$681$	−2.55506	−0.0979101
$682$	−0.887753	−0.0339938
$683$	−21.7354	−0.831681	−0.415840	−	0.909438i	$-0.636512\pi$
$683$	−21.7354	−0.831681	−0.415840	+	0.909438i	$0.636512\pi$
$684$	3.37199	0.128931
$685$	8.64219	0.330201
$686$	28.9076	1.10370
$687$	25.0967	0.957498
$688$	−37.9156	−1.44552
$689$	5.35300	0.203933
$690$	−1.01563	−0.0386642
$691$	26.1917	0.996380	0.498190	−	0.867068i	$-0.333998\pi$
$691$	26.1917	0.996380	0.498190	+	0.867068i	$0.333998\pi$
$692$	−4.22360	−0.160557
$693$	−4.17300	−0.158519
$694$	32.4442	1.23156
$695$	−8.74082	−0.331558
$696$	−12.7102	−0.481780
$697$	−3.88634	−0.147206
$698$	−2.81120	−0.106406
$699$	6.98684	0.264266
$700$	−5.09709	−0.192652
$701$	−4.36307	−0.164791	−0.0823954	−	0.996600i	$-0.526257\pi$
$701$	−4.36307	−0.164791	−0.0823954	+	0.996600i	$0.526257\pi$
$702$	1.00118	0.0377870
$703$	1.08204	0.0408101
$704$	−9.83455	−0.370654
$705$	0.794562	0.0299249
$706$	−49.6711	−1.86940
$707$	16.0841	0.604904
$708$	8.86507	0.333170
$709$	−28.2944	−1.06262	−0.531310	−	0.847177i	$-0.678300\pi$
$709$	−28.2944	−1.06262	−0.531310	+	0.847177i	$0.678300\pi$
$710$	−9.27800	−0.348197
$711$	−1.00000	−0.0375029
$712$	8.23081	0.308463
$713$	0.283744	0.0106263
$714$	−2.45514	−0.0918814
$715$	−0.713807	−0.0266949
$716$	−11.9174	−0.445373
$717$	2.76772	0.103362
$718$	6.73765	0.251447
$719$	27.6782	1.03222	0.516112	−	0.856521i	$-0.327379\pi$
$719$	27.6782	1.03222	0.516112	+	0.856521i	$0.327379\pi$
$720$	2.06163	0.0768324
$721$	23.8096	0.886717
$722$	−6.03675	−0.224665
$723$	−12.3525	−0.459396
$724$	−4.79109	−0.178060
$725$	28.8428	1.07120
$726$	5.22664	0.193979
$727$	−7.44375	−0.276073	−0.138037	−	0.990427i	$-0.544079\pi$
$727$	−7.44375	−0.276073	−0.138037	+	0.990427i	$0.544079\pi$
$728$	−1.92943	−0.0715093
$729$	1.00000	0.0370370
$730$	−7.35014	−0.272041
$731$	7.71447	0.285330
$732$	−4.92005	−0.181850
$733$	21.6207	0.798578	0.399289	−	0.916825i	$-0.369257\pi$
$733$	21.6207	0.798578	0.399289	+	0.916825i	$0.369257\pi$
$734$	−25.3352	−0.935139
$735$	2.00266	0.0738693
$736$	−5.64471	−0.208067
$737$	−8.84851	−0.325939
$738$	6.39563	0.235427
$739$	−6.94367	−0.255427	−0.127714	−	0.991811i	$-0.540764\pi$
$739$	−6.94367	−0.255427	−0.127714	+	0.991811i	$0.540764\pi$
$740$	−0.0675167	−0.00248196
$741$	−2.89652	−0.106406
$742$	21.6026	0.793056
$743$	33.4763	1.22813	0.614064	−	0.789257i	$-0.289534\pi$
$743$	33.4763	1.22813	0.614064	+	0.789257i	$0.289534\pi$
$744$	−0.409979	−0.0150306
$745$	−1.54283	−0.0565250
$746$	3.64183	0.133337
$747$	−4.68999	−0.171598
$748$	−1.98103	−0.0724337
$749$	−13.4797	−0.492537
$750$	−6.78159	−0.247629
$751$	25.7598	0.939989	0.469995	−	0.882669i	$-0.344256\pi$
$751$	25.7598	0.939989	0.469995	+	0.882669i	$0.344256\pi$
$752$	9.30983	0.339495
$753$	−25.4440	−0.927232
$754$	−5.98601	−0.217998
$755$	−4.13443	−0.150467
$756$	1.05660	0.0384282
$757$	−29.4524	−1.07047	−0.535233	−	0.844705i	$-0.679776\pi$
$757$	−29.4524	−1.07047	−0.535233	+	0.844705i	$0.679776\pi$
$758$	44.0887	1.60137
$759$	4.11535	0.149378
$760$	−4.24555	−0.154002
$761$	44.0862	1.59812	0.799062	−	0.601249i	$-0.205330\pi$
$761$	44.0862	1.59812	0.799062	+	0.601249i	$0.205330\pi$
$762$	−15.9285	−0.577029
$763$	7.98625	0.289122
$764$	−9.34863	−0.338222
$765$	−0.419467	−0.0151659
$766$	58.5430	2.11524
$767$	−7.61506	−0.274964
$768$	15.1177	0.545514
$769$	30.7081	1.10736	0.553681	−	0.832729i	$-0.313223\pi$
$769$	30.7081	1.10736	0.553681	+	0.832729i	$0.313223\pi$
$770$	−2.88064	−0.103811
$771$	20.7792	0.748344
$772$	−5.10980	−0.183906
$773$	27.3265	0.982866	0.491433	−	0.870915i	$-0.336473\pi$
$773$	27.3265	0.982866	0.491433	+	0.870915i	$0.336473\pi$
$774$	−12.6955	−0.456330
$775$	0.930349	0.0334191
$776$	−27.7608	−0.996553
$777$	0.339055	0.0121635
$778$	25.5398	0.915644
$779$	−18.5033	−0.662950
$780$	0.180735	0.00647136
$781$	37.5948	1.34525
$782$	2.42123	0.0865829
$783$	−5.97897	−0.213671
$784$	23.4651	0.838038
$785$	−5.53568	−0.197577
$786$	6.18518	0.220618
$787$	34.3524	1.22453	0.612265	−	0.790653i	$-0.290259\pi$
$787$	34.3524	1.22453	0.612265	+	0.790653i	$0.290259\pi$
$788$	−11.1539	−0.397343
$789$	8.27362	0.294549
$790$	−0.690305	−0.0245600
$791$	−10.3422	−0.367726
$792$	−5.94623	−0.211290
$793$	4.22630	0.150080
$794$	26.6347	0.945231
$795$	3.69086	0.130901
$796$	−6.44714	−0.228513
$797$	1.85595	0.0657413	0.0328706	−	0.999460i	$-0.489535\pi$
$797$	1.85595	0.0657413	0.0328706	+	0.999460i	$0.489535\pi$
$798$	−11.6892	−0.413794
$799$	−1.89422	−0.0670126
$800$	−18.5080	−0.654358
$801$	3.87182	0.136804
$802$	28.6799	1.01272
$803$	29.7830	1.05102
$804$	2.24043	0.0790140
$805$	0.920713	0.0324509
$806$	−0.193084	−0.00680108
$807$	−5.61231	−0.197563
$808$	22.9187	0.806276
$809$	−14.6396	−0.514702	−0.257351	−	0.966318i	$-0.582850\pi$
$809$	−14.6396	−0.514702	−0.257351	+	0.966318i	$0.582850\pi$
$810$	0.690305	0.0242549
$811$	30.9349	1.08627	0.543136	−	0.839645i	$-0.317237\pi$
$811$	30.9349	1.08627	0.543136	+	0.839645i	$0.317237\pi$
$812$	−6.31738	−0.221696
$813$	−8.42208	−0.295375
$814$	1.04615	0.0366675
$815$	0.804406	0.0281771
$816$	−4.91487	−0.172055
$817$	36.7295	1.28500
$818$	−1.76911	−0.0618554
$819$	−0.907614	−0.0317146
$820$	1.15456	0.0403189
$821$	46.4665	1.62169	0.810847	−	0.585258i	$-0.199007\pi$
$821$	46.4665	1.62169	0.810847	+	0.585258i	$0.199007\pi$
$822$	33.9054	1.18259
$823$	−3.15839	−0.110094	−0.0550472	−	0.998484i	$-0.517531\pi$
$823$	−3.15839	−0.110094	−0.0550472	+	0.998484i	$0.517531\pi$
$824$	33.9271	1.18191
$825$	13.4935	0.469785
$826$	−30.7314	−1.06928
$827$	5.29042	0.183966	0.0919829	−	0.995761i	$-0.470679\pi$
$827$	5.29042	0.183966	0.0919829	+	0.995761i	$0.470679\pi$
$828$	−1.04200	−0.0362121
$829$	28.7822	0.999647	0.499824	−	0.866127i	$-0.333398\pi$
$829$	28.7822	0.999647	0.499824	+	0.866127i	$0.333398\pi$
$830$	−3.23753	−0.112376
$831$	−0.210865	−0.00731481
$832$	−2.13899	−0.0741560
$833$	−4.77430	−0.165420
$834$	−34.2924	−1.18745
$835$	−0.459236	−0.0158925
$836$	−9.43193	−0.326210
$837$	−0.192857	−0.00666610
$838$	19.7118	0.680934
$839$	−19.0878	−0.658983	−0.329492	−	0.944159i	$-0.606877\pi$
$839$	−19.0878	−0.658983	−0.329492	+	0.944159i	$0.606877\pi$
$840$	−1.33033	−0.0459007
$841$	6.74809	0.232693
$842$	−34.4154	−1.18603
$843$	−7.40043	−0.254884
$844$	10.3454	0.356103
$845$	5.29782	0.182251
$846$	3.11726	0.107174
$847$	−4.73819	−0.162806
$848$	43.2456	1.48506
$849$	−16.1470	−0.554163
$850$	7.93880	0.272298
$851$	−0.334371	−0.0114621
$852$	−9.51897	−0.326114
$853$	−35.0520	−1.20016	−0.600078	−	0.799941i	$-0.704864\pi$
$853$	−35.0520	−1.20016	−0.600078	+	0.799941i	$0.704864\pi$
$854$	17.0557	0.583633
$855$	−1.99713	−0.0683006
$856$	−19.2076	−0.656502
$857$	12.2566	0.418677	0.209339	−	0.977843i	$-0.432869\pi$
$857$	12.2566	0.418677	0.209339	+	0.977843i	$0.432869\pi$
$858$	−2.80044	−0.0956053
$859$	29.3009	0.999733	0.499866	−	0.866103i	$-0.333382\pi$
$859$	29.3009	0.999733	0.499866	+	0.866103i	$0.333382\pi$
$860$	−2.29182	−0.0781505
$861$	−5.79794	−0.197593
$862$	3.49272	0.118962
$863$	37.5531	1.27832	0.639161	−	0.769073i	$-0.279282\pi$
$863$	37.5531	1.27832	0.639161	+	0.769073i	$0.279282\pi$
$864$	3.83662	0.130525
$865$	2.50152	0.0850542
$866$	−23.0621	−0.783683
$867$	1.00000	0.0339618
$868$	−0.203772	−0.00691648
$869$	2.79714	0.0948866
$870$	−4.12732	−0.139929
$871$	−1.92452	−0.0652100
$872$	11.3798	0.385370
$873$	−13.0588	−0.441975
$874$	11.5278	0.389932
$875$	6.14783	0.207835
$876$	−7.54104	−0.254788
$877$	−31.2349	−1.05473	−0.527365	−	0.849639i	$-0.676820\pi$
$877$	−31.2349	−1.05473	−0.527365	+	0.849639i	$0.676820\pi$
$878$	−57.9293	−1.95502
$879$	−3.29877	−0.111265
$880$	−5.76667	−0.194394
$881$	47.8428	1.61186	0.805932	−	0.592008i	$-0.201665\pi$
$881$	47.8428	1.61186	0.805932	+	0.592008i	$0.201665\pi$
$882$	7.85693	0.264556
$883$	−35.4848	−1.19416	−0.597080	−	0.802182i	$-0.703673\pi$
$883$	−35.4848	−1.19416	−0.597080	+	0.802182i	$0.703673\pi$
$884$	−0.430869	−0.0144917
$885$	−5.25054	−0.176495
$886$	13.3152	0.447332
$887$	−29.4313	−0.988206	−0.494103	−	0.869403i	$-0.664503\pi$
$887$	−29.4313	−0.988206	−0.494103	+	0.869403i	$0.664503\pi$
$888$	0.483129	0.0162127
$889$	14.4399	0.484300
$890$	2.67274	0.0895905
$891$	−2.79714	−0.0937078
$892$	−8.57951	−0.287263
$893$	−9.01859	−0.301796
$894$	−6.05290	−0.202439
$895$	7.05833	0.235934
$896$	−20.0796	−0.670814
$897$	0.895077	0.0298858
$898$	41.6306	1.38923
$899$	1.15308	0.0384575
$900$	−3.41656	−0.113885
$901$	−8.79892	−0.293134
$902$	−17.8895	−0.595655
$903$	11.5090	0.382997
$904$	−14.7369	−0.490142
$905$	2.83763	0.0943260
$906$	−16.2204	−0.538886
$907$	27.0590	0.898480	0.449240	−	0.893411i	$-0.351695\pi$
$907$	27.0590	0.898480	0.449240	+	0.893411i	$0.351695\pi$
$908$	−1.80958	−0.0600530
$909$	10.7811	0.357586
$910$	−0.626531	−0.0207693
$911$	−3.63948	−0.120581	−0.0602907	−	0.998181i	$-0.519203\pi$
$911$	−3.63948	−0.120581	−0.0602907	+	0.998181i	$0.519203\pi$
$912$	−23.4003	−0.774861
$913$	13.1186	0.434161
$914$	−14.6332	−0.484025
$915$	2.91401	0.0963341
$916$	17.7743	0.587281
$917$	−5.60716	−0.185165
$918$	−1.64567	−0.0543152
$919$	28.3920	0.936565	0.468283	−	0.883579i	$-0.344873\pi$
$919$	28.3920	0.936565	0.468283	+	0.883579i	$0.344873\pi$
$920$	1.31195	0.0432537
$921$	−11.8120	−0.389219
$922$	3.34494	0.110160
$923$	8.17675	0.269141
$924$	−2.95546	−0.0972275
$925$	−1.09635	−0.0360476
$926$	11.2498	0.369693
$927$	15.9595	0.524179
$928$	−22.9390	−0.753011
$929$	39.6927	1.30227	0.651137	−	0.758960i	$-0.274292\pi$
$929$	39.6927	1.30227	0.651137	+	0.758960i	$0.274292\pi$
$930$	−0.133130	−0.00436550
$931$	−22.7310	−0.744979
$932$	4.94832	0.162088
$933$	4.75671	0.155728
$934$	4.81282	0.157480
$935$	1.17331	0.0383713
$936$	−1.29329	−0.0422724
$937$	−47.6105	−1.55537	−0.777683	−	0.628657i	$-0.783605\pi$
$937$	−47.6105	−1.55537	−0.777683	+	0.628657i	$0.783605\pi$
$938$	−7.76662	−0.253589
$939$	−30.7486	−1.00344
$940$	0.562736	0.0183544
$941$	35.6119	1.16092	0.580458	−	0.814290i	$-0.302874\pi$
$941$	35.6119	1.16092	0.580458	+	0.814290i	$0.302874\pi$
$942$	−21.7178	−0.707604
$943$	5.71785	0.186199
$944$	−61.5202	−2.00231
$945$	−0.625794	−0.0203571
$946$	35.5111	1.15456
$947$	48.0040	1.55992	0.779960	−	0.625829i	$-0.215239\pi$
$947$	48.0040	1.55992	0.779960	+	0.625829i	$0.215239\pi$
$948$	−0.708234	−0.0230024
$949$	6.47772	0.210276
$950$	37.7976	1.22631
$951$	−9.58464	−0.310803
$952$	3.17147	0.102788
$953$	24.1537	0.782414	0.391207	−	0.920303i	$-0.372058\pi$
$953$	24.1537	0.782414	0.391207	+	0.920303i	$0.372058\pi$
$954$	14.4801	0.468811
$955$	5.53693	0.179171
$956$	1.96019	0.0633972
$957$	16.7240	0.540611
$958$	−18.6581	−0.602816
$959$	−30.7368	−0.992544
$960$	−1.47482	−0.0475995
$961$	−30.9628	−0.998800
$962$	0.227534	0.00733600
$963$	−9.03537	−0.291161
$964$	−8.74849	−0.281770
$965$	3.02639	0.0974230
$966$	3.61218	0.116220
$967$	4.74650	0.152637	0.0763186	−	0.997083i	$-0.475683\pi$
$967$	4.74650	0.152637	0.0763186	+	0.997083i	$0.475683\pi$
$968$	−6.75159	−0.217004
$969$	4.76112	0.152949
$970$	−9.01459	−0.289441
$971$	28.0665	0.900697	0.450349	−	0.892853i	$-0.351300\pi$
$971$	28.0665	0.900697	0.450349	+	0.892853i	$0.351300\pi$
$972$	0.708234	0.0227166
$973$	31.0876	0.996624
$974$	68.3427	2.18984
$975$	2.93481	0.0939890
$976$	34.1432	1.09290
$977$	61.1914	1.95769	0.978843	−	0.204612i	$-0.0655933\pi$
$977$	61.1914	1.95769	0.978843	+	0.204612i	$0.0655933\pi$
$978$	3.15588	0.100914
$979$	−10.8300	−0.346130
$980$	1.41835	0.0453077
$981$	5.35315	0.170913
$982$	−25.0005	−0.797799
$983$	21.5761	0.688169	0.344085	−	0.938939i	$-0.388189\pi$
$983$	21.5761	0.688169	0.344085	+	0.938939i	$0.388189\pi$
$984$	−8.26166	−0.263372
$985$	6.60617	0.210490
$986$	9.83942	0.313351
$987$	−2.82594	−0.0899507
$988$	−2.05142	−0.0652643
$989$	−11.3501	−0.360911
$990$	−1.93088	−0.0613675
$991$	40.6337	1.29077	0.645386	−	0.763857i	$-0.276697\pi$
$991$	40.6337	1.29077	0.645386	+	0.763857i	$0.276697\pi$
$992$	−0.739918	−0.0234924
$993$	6.25819	0.198598
$994$	32.9981	1.04664
$995$	3.81846	0.121053
$996$	−3.32161	−0.105249
$997$	−20.8139	−0.659184	−0.329592	−	0.944123i	$-0.606911\pi$
$997$	−20.8139	−0.659184	−0.329592	+	0.944123i	$0.606911\pi$
$998$	48.1260	1.52340
$999$	0.227267	0.00719041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.e.1.5	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.e.1.5	✓	18	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.64567 q^{2} +1.00000 q^{3} +0.708234 q^{4} -0.419467 q^{5} -1.64567 q^{6} +1.49188 q^{7} +2.12582 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.64567 q^{2} +1.00000 q^{3} +0.708234 q^{4} -0.419467 q^{5} -1.64567 q^{6} +1.49188 q^{7} +2.12582 q^{8} +1.00000 q^{9} +0.690305 q^{10} -2.79714 q^{11} +0.708234 q^{12} -0.608370 q^{13} -2.45514 q^{14} -0.419467 q^{15} -4.91487 q^{16} +1.00000 q^{17} -1.64567 q^{18} +4.76112 q^{19} -0.297081 q^{20} +1.49188 q^{21} +4.60318 q^{22} -1.47127 q^{23} +2.12582 q^{24} -4.82405 q^{25} +1.00118 q^{26} +1.00000 q^{27} +1.05660 q^{28} -5.97897 q^{29} +0.690305 q^{30} -0.192857 q^{31} +3.83662 q^{32} -2.79714 q^{33} -1.64567 q^{34} -0.625794 q^{35} +0.708234 q^{36} +0.227267 q^{37} -7.83524 q^{38} -0.608370 q^{39} -0.891713 q^{40} -3.88634 q^{41} -2.45514 q^{42} +7.71447 q^{43} -1.98103 q^{44} -0.419467 q^{45} +2.42123 q^{46} -1.89422 q^{47} -4.91487 q^{48} -4.77430 q^{49} +7.93880 q^{50} +1.00000 q^{51} -0.430869 q^{52} -8.79892 q^{53} -1.64567 q^{54} +1.17331 q^{55} +3.17147 q^{56} +4.76112 q^{57} +9.83942 q^{58} +12.5172 q^{59} -0.297081 q^{60} -6.94692 q^{61} +0.317379 q^{62} +1.49188 q^{63} +3.51593 q^{64} +0.255191 q^{65} +4.60318 q^{66} +3.16341 q^{67} +0.708234 q^{68} -1.47127 q^{69} +1.02985 q^{70} -13.4404 q^{71} +2.12582 q^{72} -10.6477 q^{73} -0.374007 q^{74} -4.82405 q^{75} +3.37199 q^{76} -4.17300 q^{77} +1.00118 q^{78} -1.00000 q^{79} +2.06163 q^{80} +1.00000 q^{81} +6.39563 q^{82} -4.68999 q^{83} +1.05660 q^{84} -0.419467 q^{85} -12.6955 q^{86} -5.97897 q^{87} -5.94623 q^{88} +3.87182 q^{89} +0.690305 q^{90} -0.907614 q^{91} -1.04200 q^{92} -0.192857 q^{93} +3.11726 q^{94} -1.99713 q^{95} +3.83662 q^{96} -13.0588 q^{97} +7.85693 q^{98} -2.79714 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9	\( 18 q - 6 q^{2} + 18 q^{3} + 20 q^{4} - 5 q^{5} - 6 q^{6} - 13 q^{7} - 12 q^{8} + 18 q^{9} - 15 q^{10} - 27 q^{11} + 20 q^{12} - 4 q^{13} - 5 q^{14} - 5 q^{15} + 16 q^{16} + 18 q^{17} - 6 q^{18} - 30 q^{19} - 16 q^{20} - 13 q^{21} + 13 q^{22} - 21 q^{23} - 12 q^{24} + 13 q^{25} - 20 q^{26} + 18 q^{27} - 33 q^{28} - 47 q^{29} - 15 q^{30} - 18 q^{31} - 45 q^{32} - 27 q^{33} - 6 q^{34} - 17 q^{35} + 20 q^{36} + q^{37} + 5 q^{38} - 4 q^{39} - 12 q^{40} - 18 q^{41} - 5 q^{42} - 39 q^{43} - 34 q^{44} - 5 q^{45} - 7 q^{46} + 16 q^{48} + 15 q^{49} - 23 q^{50} + 18 q^{51} + 5 q^{52} - 9 q^{53} - 6 q^{54} + q^{55} - 24 q^{56} - 30 q^{57} + 41 q^{58} - 42 q^{59} - 16 q^{60} - 43 q^{61} - 54 q^{62} - 13 q^{63} + 22 q^{64} - 25 q^{65} + 13 q^{66} + 20 q^{68} - 21 q^{69} + 17 q^{70} + 9 q^{71} - 12 q^{72} + 19 q^{73} - 30 q^{74} + 13 q^{75} - 17 q^{76} - 14 q^{77} - 20 q^{78} - 18 q^{79} + 36 q^{80} + 18 q^{81} - 3 q^{82} - 61 q^{83} - 33 q^{84} - 5 q^{85} - 24 q^{86} - 47 q^{87} - 25 q^{88} + 10 q^{89} - 15 q^{90} - 52 q^{91} - 74 q^{92} - 18 q^{93} + 31 q^{94} - 37 q^{95} - 45 q^{96} - 9 q^{97} + 27 q^{98} - 27 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 + 18 * q^3 + 20 * q^4 - 5 * q^5 - 6 * q^6 - 13 * q^7 - 12 * q^8 + 18 * q^9 - 15 * q^10 - 27 * q^11 + 20 * q^12 - 4 * q^13 - 5 * q^14 - 5 * q^15 + 16 * q^16 + 18 * q^17 - 6 * q^18 - 30 * q^19 - 16 * q^20 - 13 * q^21 + 13 * q^22 - 21 * q^23 - 12 * q^24 + 13 * q^25 - 20 * q^26 + 18 * q^27 - 33 * q^28 - 47 * q^29 - 15 * q^30 - 18 * q^31 - 45 * q^32 - 27 * q^33 - 6 * q^34 - 17 * q^35 + 20 * q^36 + q^37 + 5 * q^38 - 4 * q^39 - 12 * q^40 - 18 * q^41 - 5 * q^42 - 39 * q^43 - 34 * q^44 - 5 * q^45 - 7 * q^46 + 16 * q^48 + 15 * q^49 - 23 * q^50 + 18 * q^51 + 5 * q^52 - 9 * q^53 - 6 * q^54 + q^55 - 24 * q^56 - 30 * q^57 + 41 * q^58 - 42 * q^59 - 16 * q^60 - 43 * q^61 - 54 * q^62 - 13 * q^63 + 22 * q^64 - 25 * q^65 + 13 * q^66 + 20 * q^68 - 21 * q^69 + 17 * q^70 + 9 * q^71 - 12 * q^72 + 19 * q^73 - 30 * q^74 + 13 * q^75 - 17 * q^76 - 14 * q^77 - 20 * q^78 - 18 * q^79 + 36 * q^80 + 18 * q^81 - 3 * q^82 - 61 * q^83 - 33 * q^84 - 5 * q^85 - 24 * q^86 - 47 * q^87 - 25 * q^88 + 10 * q^89 - 15 * q^90 - 52 * q^91 - 74 * q^92 - 18 * q^93 + 31 * q^94 - 37 * q^95 - 45 * q^96 - 9 * q^97 + 27 * q^98 - 27 * q^99

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