LMFDB - Embedded newform 5054.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.30278$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.30278 q^{3} +1.00000 q^{4} +2.30278 q^{5} -1.30278 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.30278 q^{3} +1.00000 q^{4} +2.30278 q^{5} -1.30278 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.30278 q^{9} -2.30278 q^{10} -0.697224 q^{11} +1.30278 q^{12} -6.60555 q^{13} -1.00000 q^{14} +3.00000 q^{15} +1.00000 q^{16} +1.30278 q^{18} +2.30278 q^{20} +1.30278 q^{21} +0.697224 q^{22} -4.60555 q^{23} -1.30278 q^{24} +0.302776 q^{25} +6.60555 q^{26} -5.60555 q^{27} +1.00000 q^{28} -0.908327 q^{29} -3.00000 q^{30} +7.21110 q^{31} -1.00000 q^{32} -0.908327 q^{33} +2.30278 q^{35} -1.30278 q^{36} +4.90833 q^{37} -8.60555 q^{39} -2.30278 q^{40} -2.30278 q^{41} -1.30278 q^{42} -6.30278 q^{43} -0.697224 q^{44} -3.00000 q^{45} +4.60555 q^{46} -3.90833 q^{47} +1.30278 q^{48} +1.00000 q^{49} -0.302776 q^{50} -6.60555 q^{52} +8.51388 q^{53} +5.60555 q^{54} -1.60555 q^{55} -1.00000 q^{56} +0.908327 q^{58} +8.30278 q^{59} +3.00000 q^{60} -7.90833 q^{61} -7.21110 q^{62} -1.30278 q^{63} +1.00000 q^{64} -15.2111 q^{65} +0.908327 q^{66} +0.788897 q^{67} -6.00000 q^{69} -2.30278 q^{70} +2.09167 q^{71} +1.30278 q^{72} +12.6056 q^{73} -4.90833 q^{74} +0.394449 q^{75} -0.697224 q^{77} +8.60555 q^{78} -14.9083 q^{79} +2.30278 q^{80} -3.39445 q^{81} +2.30278 q^{82} -9.21110 q^{83} +1.30278 q^{84} +6.30278 q^{86} -1.18335 q^{87} +0.697224 q^{88} -15.9083 q^{89} +3.00000 q^{90} -6.60555 q^{91} -4.60555 q^{92} +9.39445 q^{93} +3.90833 q^{94} -1.30278 q^{96} -13.3028 q^{97} -1.00000 q^{98} +0.908327 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 - 2 * q^8 + q^9	$ 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - q^{10} - 5 q^{11} - q^{12} - 6 q^{13} - 2 q^{14} + 6 q^{15} + 2 q^{16} - q^{18} + q^{20} - q^{21} + 5 q^{22} - 2 q^{23} + q^{24} - 3 q^{25} + 6 q^{26} - 4 q^{27} + 2 q^{28} + 9 q^{29} - 6 q^{30} - 2 q^{32} + 9 q^{33} + q^{35} + q^{36} - q^{37} - 10 q^{39} - q^{40} - q^{41} + q^{42} - 9 q^{43} - 5 q^{44} - 6 q^{45} + 2 q^{46} + 3 q^{47} - q^{48} + 2 q^{49} + 3 q^{50} - 6 q^{52} - q^{53} + 4 q^{54} + 4 q^{55} - 2 q^{56} - 9 q^{58} + 13 q^{59} + 6 q^{60} - 5 q^{61} + q^{63} + 2 q^{64} - 16 q^{65} - 9 q^{66} + 16 q^{67} - 12 q^{69} - q^{70} + 15 q^{71} - q^{72} + 18 q^{73} + q^{74} + 8 q^{75} - 5 q^{77} + 10 q^{78} - 19 q^{79} + q^{80} - 14 q^{81} + q^{82} - 4 q^{83} - q^{84} + 9 q^{86} - 24 q^{87} + 5 q^{88} - 21 q^{89} + 6 q^{90} - 6 q^{91} - 2 q^{92} + 26 q^{93} - 3 q^{94} + q^{96} - 23 q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 - 2 * q^8 + q^9 - q^10 - 5 * q^11 - q^12 - 6 * q^13 - 2 * q^14 + 6 * q^15 + 2 * q^16 - q^18 + q^20 - q^21 + 5 * q^22 - 2 * q^23 + q^24 - 3 * q^25 + 6 * q^26 - 4 * q^27 + 2 * q^28 + 9 * q^29 - 6 * q^30 - 2 * q^32 + 9 * q^33 + q^35 + q^36 - q^37 - 10 * q^39 - q^40 - q^41 + q^42 - 9 * q^43 - 5 * q^44 - 6 * q^45 + 2 * q^46 + 3 * q^47 - q^48 + 2 * q^49 + 3 * q^50 - 6 * q^52 - q^53 + 4 * q^54 + 4 * q^55 - 2 * q^56 - 9 * q^58 + 13 * q^59 + 6 * q^60 - 5 * q^61 + q^63 + 2 * q^64 - 16 * q^65 - 9 * q^66 + 16 * q^67 - 12 * q^69 - q^70 + 15 * q^71 - q^72 + 18 * q^73 + q^74 + 8 * q^75 - 5 * q^77 + 10 * q^78 - 19 * q^79 + q^80 - 14 * q^81 + q^82 - 4 * q^83 - q^84 + 9 * q^86 - 24 * q^87 + 5 * q^88 - 21 * q^89 + 6 * q^90 - 6 * q^91 - 2 * q^92 + 26 * q^93 - 3 * q^94 + q^96 - 23 * q^97 - 2 * q^98 - 9 * 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
$3$	1.30278	0.752158	0.376079	−	0.926588i	$-0.377272\pi$
$3$	1.30278	0.752158	0.376079	+	0.926588i	$0.377272\pi$
$4$	1.00000	0.500000
$5$	2.30278	1.02983	0.514916	−	0.857240i	$-0.327823\pi$
$5$	2.30278	1.02983	0.514916	+	0.857240i	$0.327823\pi$
$6$	−1.30278	−0.531856
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−1.30278	−0.434259
$10$	−2.30278	−0.728202
$11$	−0.697224	−0.210221	−0.105111	−	0.994461i	$-0.533520\pi$
$11$	−0.697224	−0.210221	−0.105111	+	0.994461i	$0.533520\pi$
$12$	1.30278	0.376079
$13$	−6.60555	−1.83205	−0.916025	−	0.401121i	$-0.868621\pi$
$13$	−6.60555	−1.83205	−0.916025	+	0.401121i	$0.868621\pi$
$14$	−1.00000	−0.267261
$15$	3.00000	0.774597
$16$	1.00000	0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	1.30278	0.307067
$19$	0	0
$19$	0	0
$20$	2.30278	0.514916
$21$	1.30278	0.284289
$22$	0.697224	0.148649
$23$	−4.60555	−0.960324	−0.480162	−	0.877180i	$-0.659422\pi$
$23$	−4.60555	−0.960324	−0.480162	+	0.877180i	$0.659422\pi$
$24$	−1.30278	−0.265928
$25$	0.302776	0.0605551
$26$	6.60555	1.29546
$27$	−5.60555	−1.07879
$28$	1.00000	0.188982
$29$	−0.908327	−0.168672	−0.0843360	−	0.996437i	$-0.526877\pi$
$29$	−0.908327	−0.168672	−0.0843360	+	0.996437i	$0.526877\pi$
$30$	−3.00000	−0.547723
$31$	7.21110	1.29515	0.647576	−	0.762001i	$-0.275783\pi$
$31$	7.21110	1.29515	0.647576	+	0.762001i	$0.275783\pi$
$32$	−1.00000	−0.176777
$33$	−0.908327	−0.158119
$34$	0	0
$35$	2.30278	0.389240
$36$	−1.30278	−0.217129
$37$	4.90833	0.806924	0.403462	−	0.914996i	$-0.367807\pi$
$37$	4.90833	0.806924	0.403462	+	0.914996i	$0.367807\pi$
$38$	0	0
$39$	−8.60555	−1.37799
$40$	−2.30278	−0.364101
$41$	−2.30278	−0.359633	−0.179817	−	0.983700i	$-0.557550\pi$
$41$	−2.30278	−0.359633	−0.179817	+	0.983700i	$0.557550\pi$
$42$	−1.30278	−0.201023
$43$	−6.30278	−0.961164	−0.480582	−	0.876950i	$-0.659575\pi$
$43$	−6.30278	−0.961164	−0.480582	+	0.876950i	$0.659575\pi$
$44$	−0.697224	−0.105111
$45$	−3.00000	−0.447214
$46$	4.60555	0.679051
$47$	−3.90833	−0.570088	−0.285044	−	0.958514i	$-0.592008\pi$
$47$	−3.90833	−0.570088	−0.285044	+	0.958514i	$0.592008\pi$
$48$	1.30278	0.188039
$49$	1.00000	0.142857
$50$	−0.302776	−0.0428189
$51$	0	0
$52$	−6.60555	−0.916025
$53$	8.51388	1.16947	0.584736	−	0.811224i	$-0.301198\pi$
$53$	8.51388	1.16947	0.584736	+	0.811224i	$0.301198\pi$
$54$	5.60555	0.762819
$55$	−1.60555	−0.216492
$56$	−1.00000	−0.133631
$57$	0	0
$58$	0.908327	0.119269
$59$	8.30278	1.08093	0.540465	−	0.841367i	$-0.318248\pi$
$59$	8.30278	1.08093	0.540465	+	0.841367i	$0.318248\pi$
$60$	3.00000	0.387298
$61$	−7.90833	−1.01256	−0.506279	−	0.862370i	$-0.668979\pi$
$61$	−7.90833	−1.01256	−0.506279	+	0.862370i	$0.668979\pi$
$62$	−7.21110	−0.915811
$63$	−1.30278	−0.164134
$64$	1.00000	0.125000
$65$	−15.2111	−1.88671
$66$	0.908327	0.111807
$67$	0.788897	0.0963792	0.0481896	−	0.998838i	$-0.484655\pi$
$67$	0.788897	0.0963792	0.0481896	+	0.998838i	$0.484655\pi$
$68$	0	0
$69$	−6.00000	−0.722315
$70$	−2.30278	−0.275234
$71$	2.09167	0.248236	0.124118	−	0.992267i	$-0.460390\pi$
$71$	2.09167	0.248236	0.124118	+	0.992267i	$0.460390\pi$
$72$	1.30278	0.153534
$73$	12.6056	1.47537	0.737684	−	0.675146i	$-0.235919\pi$
$73$	12.6056	1.47537	0.737684	+	0.675146i	$0.235919\pi$
$74$	−4.90833	−0.570581
$75$	0.394449	0.0455470
$76$	0	0
$77$	−0.697224	−0.0794561
$78$	8.60555	0.974387
$79$	−14.9083	−1.67732	−0.838659	−	0.544657i	$-0.816660\pi$
$79$	−14.9083	−1.67732	−0.838659	+	0.544657i	$0.816660\pi$
$80$	2.30278	0.257458
$81$	−3.39445	−0.377161
$82$	2.30278	0.254299
$83$	−9.21110	−1.01105	−0.505525	−	0.862812i	$-0.668701\pi$
$83$	−9.21110	−1.01105	−0.505525	+	0.862812i	$0.668701\pi$
$84$	1.30278	0.142144
$85$	0	0
$86$	6.30278	0.679646
$87$	−1.18335	−0.126868
$88$	0.697224	0.0743244
$89$	−15.9083	−1.68628	−0.843140	−	0.537695i	$-0.819295\pi$
$89$	−15.9083	−1.68628	−0.843140	+	0.537695i	$0.819295\pi$
$90$	3.00000	0.316228
$91$	−6.60555	−0.692450
$92$	−4.60555	−0.480162
$93$	9.39445	0.974159
$94$	3.90833	0.403113
$95$	0	0
$96$	−1.30278	−0.132964
$97$	−13.3028	−1.35069	−0.675346	−	0.737501i	$-0.736006\pi$
$97$	−13.3028	−1.35069	−0.675346	+	0.737501i	$0.736006\pi$
$98$	−1.00000	−0.101015
$99$	0.908327	0.0912903
$100$	0.302776	0.0302776
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	−3.39445	−0.334465	−0.167232	−	0.985917i	$-0.553483\pi$
$103$	−3.39445	−0.334465	−0.167232	+	0.985917i	$0.553483\pi$
$104$	6.60555	0.647728
$105$	3.00000	0.292770
$106$	−8.51388	−0.826941
$107$	−13.8167	−1.33571	−0.667853	−	0.744293i	$-0.732787\pi$
$107$	−13.8167	−1.33571	−0.667853	+	0.744293i	$0.732787\pi$
$108$	−5.60555	−0.539394
$109$	−17.9083	−1.71531	−0.857653	−	0.514228i	$-0.828078\pi$
$109$	−17.9083	−1.71531	−0.857653	+	0.514228i	$0.828078\pi$
$110$	1.60555	0.153083
$111$	6.39445	0.606934
$112$	1.00000	0.0944911
$113$	18.4222	1.73302	0.866508	−	0.499164i	$-0.166359\pi$
$113$	18.4222	1.73302	0.866508	+	0.499164i	$0.166359\pi$
$114$	0	0
$115$	−10.6056	−0.988973
$116$	−0.908327	−0.0843360
$117$	8.60555	0.795583
$118$	−8.30278	−0.764332
$119$	0	0
$120$	−3.00000	−0.273861
$121$	−10.5139	−0.955807
$122$	7.90833	0.715986
$123$	−3.00000	−0.270501
$124$	7.21110	0.647576
$125$	−10.8167	−0.967471
$126$	1.30278	0.116060
$127$	3.30278	0.293074	0.146537	−	0.989205i	$-0.453187\pi$
$127$	3.30278	0.293074	0.146537	+	0.989205i	$0.453187\pi$
$128$	−1.00000	−0.0883883
$129$	−8.21110	−0.722947
$130$	15.2111	1.33410
$131$	−7.81665	−0.682944	−0.341472	−	0.939892i	$-0.610925\pi$
$131$	−7.81665	−0.682944	−0.341472	+	0.939892i	$0.610925\pi$
$132$	−0.908327	−0.0790597
$133$	0	0
$134$	−0.788897	−0.0681504
$135$	−12.9083	−1.11097
$136$	0	0
$137$	−12.9083	−1.10283	−0.551416	−	0.834230i	$-0.685912\pi$
$137$	−12.9083	−1.10283	−0.551416	+	0.834230i	$0.685912\pi$
$138$	6.00000	0.510754
$139$	17.2111	1.45983	0.729913	−	0.683540i	$-0.239560\pi$
$139$	17.2111	1.45983	0.729913	+	0.683540i	$0.239560\pi$
$140$	2.30278	0.194620
$141$	−5.09167	−0.428796
$142$	−2.09167	−0.175529
$143$	4.60555	0.385136
$144$	−1.30278	−0.108565
$145$	−2.09167	−0.173704
$146$	−12.6056	−1.04324
$147$	1.30278	0.107451
$148$	4.90833	0.403462
$149$	2.78890	0.228475	0.114238	−	0.993453i	$-0.463557\pi$
$149$	2.78890	0.228475	0.114238	+	0.993453i	$0.463557\pi$
$150$	−0.394449	−0.0322066
$151$	−14.4222	−1.17366	−0.586831	−	0.809709i	$-0.699625\pi$
$151$	−14.4222	−1.17366	−0.586831	+	0.809709i	$0.699625\pi$
$152$	0	0
$153$	0	0
$154$	0.697224	0.0561839
$155$	16.6056	1.33379
$156$	−8.60555	−0.688996
$157$	−5.11943	−0.408575	−0.204287	−	0.978911i	$-0.565488\pi$
$157$	−5.11943	−0.408575	−0.204287	+	0.978911i	$0.565488\pi$
$158$	14.9083	1.18604
$159$	11.0917	0.879627
$160$	−2.30278	−0.182050
$161$	−4.60555	−0.362968
$162$	3.39445	0.266693
$163$	−13.9083	−1.08938	−0.544692	−	0.838636i	$-0.683353\pi$
$163$	−13.9083	−1.08938	−0.544692	+	0.838636i	$0.683353\pi$
$164$	−2.30278	−0.179817
$165$	−2.09167	−0.162837
$166$	9.21110	0.714920
$167$	−12.4222	−0.961259	−0.480630	−	0.876924i	$-0.659592\pi$
$167$	−12.4222	−0.961259	−0.480630	+	0.876924i	$0.659592\pi$
$168$	−1.30278	−0.100511
$169$	30.6333	2.35641
$170$	0	0
$171$	0	0
$172$	−6.30278	−0.480582
$173$	−4.60555	−0.350154	−0.175077	−	0.984555i	$-0.556017\pi$
$173$	−4.60555	−0.350154	−0.175077	+	0.984555i	$0.556017\pi$
$174$	1.18335	0.0897092
$175$	0.302776	0.0228877
$176$	−0.697224	−0.0525553
$177$	10.8167	0.813029
$178$	15.9083	1.19238
$179$	−13.8167	−1.03271	−0.516353	−	0.856376i	$-0.672711\pi$
$179$	−13.8167	−1.03271	−0.516353	+	0.856376i	$0.672711\pi$
$180$	−3.00000	−0.223607
$181$	2.18335	0.162287	0.0811434	−	0.996702i	$-0.474143\pi$
$181$	2.18335	0.162287	0.0811434	+	0.996702i	$0.474143\pi$
$182$	6.60555	0.489636
$183$	−10.3028	−0.761603
$184$	4.60555	0.339526
$185$	11.3028	0.830997
$186$	−9.39445	−0.688834
$187$	0	0
$188$	−3.90833	−0.285044
$189$	−5.60555	−0.407744
$190$	0	0
$191$	4.60555	0.333246	0.166623	−	0.986021i	$-0.446714\pi$
$191$	4.60555	0.333246	0.166623	+	0.986021i	$0.446714\pi$
$192$	1.30278	0.0940197
$193$	24.2389	1.74475	0.872376	−	0.488836i	$-0.162578\pi$
$193$	24.2389	1.74475	0.872376	+	0.488836i	$0.162578\pi$
$194$	13.3028	0.955084
$195$	−19.8167	−1.41910
$196$	1.00000	0.0714286
$197$	−3.21110	−0.228782	−0.114391	−	0.993436i	$-0.536492\pi$
$197$	−3.21110	−0.228782	−0.114391	+	0.993436i	$0.536492\pi$
$198$	−0.908327	−0.0645520
$199$	−4.90833	−0.347942	−0.173971	−	0.984751i	$-0.555660\pi$
$199$	−4.90833	−0.347942	−0.173971	+	0.984751i	$0.555660\pi$
$200$	−0.302776	−0.0214095
$201$	1.02776	0.0724923
$202$	6.00000	0.422159
$203$	−0.908327	−0.0637521
$204$	0	0
$205$	−5.30278	−0.370362
$206$	3.39445	0.236502
$207$	6.00000	0.417029
$208$	−6.60555	−0.458013
$209$	0	0
$210$	−3.00000	−0.207020
$211$	−10.7889	−0.742738	−0.371369	−	0.928485i	$-0.621112\pi$
$211$	−10.7889	−0.742738	−0.371369	+	0.928485i	$0.621112\pi$
$212$	8.51388	0.584736
$213$	2.72498	0.186713
$214$	13.8167	0.944487
$215$	−14.5139	−0.989838
$216$	5.60555	0.381409
$217$	7.21110	0.489522
$218$	17.9083	1.21290
$219$	16.4222	1.10971
$220$	−1.60555	−0.108246
$221$	0	0
$222$	−6.39445	−0.429167
$223$	9.02776	0.604543	0.302272	−	0.953222i	$-0.402255\pi$
$223$	9.02776	0.604543	0.302272	+	0.953222i	$0.402255\pi$
$224$	−1.00000	−0.0668153
$225$	−0.394449	−0.0262966
$226$	−18.4222	−1.22543
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	0	0
$229$	10.3028	0.680827	0.340413	−	0.940276i	$-0.389433\pi$
$229$	10.3028	0.680827	0.340413	+	0.940276i	$0.389433\pi$
$230$	10.6056	0.699309
$231$	−0.908327	−0.0597635
$232$	0.908327	0.0596346
$233$	19.1194	1.25256	0.626278	−	0.779600i	$-0.284578\pi$
$233$	19.1194	1.25256	0.626278	+	0.779600i	$0.284578\pi$
$234$	−8.60555	−0.562562
$235$	−9.00000	−0.587095
$236$	8.30278	0.540465
$237$	−19.4222	−1.26161
$238$	0	0
$239$	−22.6056	−1.46223	−0.731116	−	0.682253i	$-0.761000\pi$
$239$	−22.6056	−1.46223	−0.731116	+	0.682253i	$0.761000\pi$
$240$	3.00000	0.193649
$241$	−14.9083	−0.960330	−0.480165	−	0.877178i	$-0.659423\pi$
$241$	−14.9083	−0.960330	−0.480165	+	0.877178i	$0.659423\pi$
$242$	10.5139	0.675858
$243$	12.3944	0.795104
$244$	−7.90833	−0.506279
$245$	2.30278	0.147119
$246$	3.00000	0.191273
$247$	0	0
$248$	−7.21110	−0.457905
$249$	−12.0000	−0.760469
$250$	10.8167	0.684105
$251$	−4.18335	−0.264050	−0.132025	−	0.991246i	$-0.542148\pi$
$251$	−4.18335	−0.264050	−0.132025	+	0.991246i	$0.542148\pi$
$252$	−1.30278	−0.0820672
$253$	3.21110	0.201880
$254$	−3.30278	−0.207235
$255$	0	0
$256$	1.00000	0.0625000
$257$	12.4861	0.778863	0.389431	−	0.921055i	$-0.372672\pi$
$257$	12.4861	0.778863	0.389431	+	0.921055i	$0.372672\pi$
$258$	8.21110	0.511201
$259$	4.90833	0.304989
$260$	−15.2111	−0.943353
$261$	1.18335	0.0732473
$262$	7.81665	0.482914
$263$	7.81665	0.481996	0.240998	−	0.970526i	$-0.422525\pi$
$263$	7.81665	0.481996	0.240998	+	0.970526i	$0.422525\pi$
$264$	0.908327	0.0559037
$265$	19.6056	1.20436
$266$	0	0
$267$	−20.7250	−1.26835
$268$	0.788897	0.0481896
$269$	3.21110	0.195784	0.0978922	−	0.995197i	$-0.468790\pi$
$269$	3.21110	0.195784	0.0978922	+	0.995197i	$0.468790\pi$
$270$	12.9083	0.785576
$271$	15.3305	0.931263	0.465632	−	0.884979i	$-0.345827\pi$
$271$	15.3305	0.931263	0.465632	+	0.884979i	$0.345827\pi$
$272$	0	0
$273$	−8.60555	−0.520832
$274$	12.9083	0.779821
$275$	−0.211103	−0.0127300
$276$	−6.00000	−0.361158
$277$	0.605551	0.0363840	0.0181920	−	0.999835i	$-0.494209\pi$
$277$	0.605551	0.0363840	0.0181920	+	0.999835i	$0.494209\pi$
$278$	−17.2111	−1.03225
$279$	−9.39445	−0.562431
$280$	−2.30278	−0.137617
$281$	−18.4222	−1.09898	−0.549488	−	0.835501i	$-0.685177\pi$
$281$	−18.4222	−1.09898	−0.549488	+	0.835501i	$0.685177\pi$
$282$	5.09167	0.303205
$283$	23.6333	1.40485	0.702427	−	0.711756i	$-0.252100\pi$
$283$	23.6333	1.40485	0.702427	+	0.711756i	$0.252100\pi$
$284$	2.09167	0.124118
$285$	0	0
$286$	−4.60555	−0.272332
$287$	−2.30278	−0.135929
$288$	1.30278	0.0767668
$289$	−17.0000	−1.00000
$290$	2.09167	0.122827
$291$	−17.3305	−1.01593
$292$	12.6056	0.737684
$293$	7.81665	0.456654	0.228327	−	0.973585i	$-0.426675\pi$
$293$	7.81665	0.456654	0.228327	+	0.973585i	$0.426675\pi$
$294$	−1.30278	−0.0759794
$295$	19.1194	1.11318
$296$	−4.90833	−0.285291
$297$	3.90833	0.226784
$298$	−2.78890	−0.161556
$299$	30.4222	1.75936
$300$	0.394449	0.0227735
$301$	−6.30278	−0.363286
$302$	14.4222	0.829905
$303$	−7.81665	−0.449055
$304$	0	0
$305$	−18.2111	−1.04276
$306$	0	0
$307$	−29.1472	−1.66352	−0.831759	−	0.555137i	$-0.812666\pi$
$307$	−29.1472	−1.66352	−0.831759	+	0.555137i	$0.812666\pi$
$308$	−0.697224	−0.0397280
$309$	−4.42221	−0.251570
$310$	−16.6056	−0.943132
$311$	−0.275019	−0.0155949	−0.00779746	−	0.999970i	$-0.502482\pi$
$311$	−0.275019	−0.0155949	−0.00779746	+	0.999970i	$0.502482\pi$
$312$	8.60555	0.487193
$313$	14.4222	0.815191	0.407596	−	0.913163i	$-0.366367\pi$
$313$	14.4222	0.815191	0.407596	+	0.913163i	$0.366367\pi$
$314$	5.11943	0.288906
$315$	−3.00000	−0.169031
$316$	−14.9083	−0.838659
$317$	28.3305	1.59120	0.795601	−	0.605821i	$-0.207155\pi$
$317$	28.3305	1.59120	0.795601	+	0.605821i	$0.207155\pi$
$318$	−11.0917	−0.621990
$319$	0.633308	0.0354584
$320$	2.30278	0.128729
$321$	−18.0000	−1.00466
$322$	4.60555	0.256657
$323$	0	0
$324$	−3.39445	−0.188580
$325$	−2.00000	−0.110940
$326$	13.9083	0.770311
$327$	−23.3305	−1.29018
$328$	2.30278	0.127150
$329$	−3.90833	−0.215473
$330$	2.09167	0.115143
$331$	16.4222	0.902646	0.451323	−	0.892361i	$-0.350952\pi$
$331$	16.4222	0.902646	0.451323	+	0.892361i	$0.350952\pi$
$332$	−9.21110	−0.505525
$333$	−6.39445	−0.350414
$334$	12.4222	0.679713
$335$	1.81665	0.0992544
$336$	1.30278	0.0710722
$337$	−6.60555	−0.359827	−0.179914	−	0.983682i	$-0.557582\pi$
$337$	−6.60555	−0.359827	−0.179914	+	0.983682i	$0.557582\pi$
$338$	−30.6333	−1.66623
$339$	24.0000	1.30350
$340$	0	0
$341$	−5.02776	−0.272268
$342$	0	0
$343$	1.00000	0.0539949
$344$	6.30278	0.339823
$345$	−13.8167	−0.743864
$346$	4.60555	0.247596
$347$	15.6333	0.839240	0.419620	−	0.907700i	$-0.362163\pi$
$347$	15.6333	0.839240	0.419620	+	0.907700i	$0.362163\pi$
$348$	−1.18335	−0.0634340
$349$	−3.57779	−0.191515	−0.0957575	−	0.995405i	$-0.530527\pi$
$349$	−3.57779	−0.191515	−0.0957575	+	0.995405i	$0.530527\pi$
$350$	−0.302776	−0.0161840
$351$	37.0278	1.97640
$352$	0.697224	0.0371622
$353$	−15.6333	−0.832077	−0.416039	−	0.909347i	$-0.636582\pi$
$353$	−15.6333	−0.832077	−0.416039	+	0.909347i	$0.636582\pi$
$354$	−10.8167	−0.574899
$355$	4.81665	0.255641
$356$	−15.9083	−0.843140
$357$	0	0
$358$	13.8167	0.730233
$359$	28.6056	1.50974	0.754872	−	0.655873i	$-0.227699\pi$
$359$	28.6056	1.50974	0.754872	+	0.655873i	$0.227699\pi$
$360$	3.00000	0.158114
$361$	0	0
$362$	−2.18335	−0.114754
$363$	−13.6972	−0.718918
$364$	−6.60555	−0.346225
$365$	29.0278	1.51938
$366$	10.3028	0.538535
$367$	13.3028	0.694399	0.347200	−	0.937791i	$-0.387133\pi$
$367$	13.3028	0.694399	0.347200	+	0.937791i	$0.387133\pi$
$368$	−4.60555	−0.240081
$369$	3.00000	0.156174
$370$	−11.3028	−0.587603
$371$	8.51388	0.442019
$372$	9.39445	0.487079
$373$	15.0917	0.781417	0.390709	−	0.920514i	$-0.372230\pi$
$373$	15.0917	0.781417	0.390709	+	0.920514i	$0.372230\pi$
$374$	0	0
$375$	−14.0917	−0.727691
$376$	3.90833	0.201557
$377$	6.00000	0.309016
$378$	5.60555	0.288318
$379$	−9.39445	−0.482560	−0.241280	−	0.970455i	$-0.577567\pi$
$379$	−9.39445	−0.482560	−0.241280	+	0.970455i	$0.577567\pi$
$380$	0	0
$381$	4.30278	0.220438
$382$	−4.60555	−0.235641
$383$	−37.8167	−1.93234	−0.966170	−	0.257905i	$-0.916968\pi$
$383$	−37.8167	−1.93234	−0.966170	+	0.257905i	$0.916968\pi$
$384$	−1.30278	−0.0664820
$385$	−1.60555	−0.0818265
$386$	−24.2389	−1.23373
$387$	8.21110	0.417394
$388$	−13.3028	−0.675346
$389$	21.6333	1.09685	0.548426	−	0.836199i	$-0.315227\pi$
$389$	21.6333	1.09685	0.548426	+	0.836199i	$0.315227\pi$
$390$	19.8167	1.00346
$391$	0	0
$392$	−1.00000	−0.0505076
$393$	−10.1833	−0.513682
$394$	3.21110	0.161773
$395$	−34.3305	−1.72736
$396$	0.908327	0.0456451
$397$	−10.6972	−0.536878	−0.268439	−	0.963297i	$-0.586508\pi$
$397$	−10.6972	−0.536878	−0.268439	+	0.963297i	$0.586508\pi$
$398$	4.90833	0.246032
$399$	0	0
$400$	0.302776	0.0151388
$401$	24.8444	1.24067	0.620335	−	0.784337i	$-0.286997\pi$
$401$	24.8444	1.24067	0.620335	+	0.784337i	$0.286997\pi$
$402$	−1.02776	−0.0512598
$403$	−47.6333	−2.37278
$404$	−6.00000	−0.298511
$405$	−7.81665	−0.388413
$406$	0.908327	0.0450795
$407$	−3.42221	−0.169632
$408$	0	0
$409$	−16.0917	−0.795682	−0.397841	−	0.917454i	$-0.630240\pi$
$409$	−16.0917	−0.795682	−0.397841	+	0.917454i	$0.630240\pi$
$410$	5.30278	0.261885
$411$	−16.8167	−0.829504
$412$	−3.39445	−0.167232
$413$	8.30278	0.408553
$414$	−6.00000	−0.294884
$415$	−21.2111	−1.04121
$416$	6.60555	0.323864
$417$	22.4222	1.09802
$418$	0	0
$419$	12.4222	0.606864	0.303432	−	0.952853i	$-0.401867\pi$
$419$	12.4222	0.606864	0.303432	+	0.952853i	$0.401867\pi$
$420$	3.00000	0.146385
$421$	−4.78890	−0.233397	−0.116698	−	0.993167i	$-0.537231\pi$
$421$	−4.78890	−0.233397	−0.116698	+	0.993167i	$0.537231\pi$
$422$	10.7889	0.525195
$423$	5.09167	0.247566
$424$	−8.51388	−0.413470
$425$	0	0
$426$	−2.72498	−0.132026
$427$	−7.90833	−0.382711
$428$	−13.8167	−0.667853
$429$	6.00000	0.289683
$430$	14.5139	0.699921
$431$	25.5416	1.23030	0.615149	−	0.788411i	$-0.289096\pi$
$431$	25.5416	1.23030	0.615149	+	0.788411i	$0.289096\pi$
$432$	−5.60555	−0.269697
$433$	9.09167	0.436918	0.218459	−	0.975846i	$-0.429897\pi$
$433$	9.09167	0.436918	0.218459	+	0.975846i	$0.429897\pi$
$434$	−7.21110	−0.346144
$435$	−2.72498	−0.130653
$436$	−17.9083	−0.857653
$437$	0	0
$438$	−16.4222	−0.784683
$439$	−32.4222	−1.54743	−0.773714	−	0.633535i	$-0.781603\pi$
$439$	−32.4222	−1.54743	−0.773714	+	0.633535i	$0.781603\pi$
$440$	1.60555	0.0765417
$441$	−1.30278	−0.0620369
$442$	0	0
$443$	11.5139	0.547041	0.273520	−	0.961866i	$-0.411812\pi$
$443$	11.5139	0.547041	0.273520	+	0.961866i	$0.411812\pi$
$444$	6.39445	0.303467
$445$	−36.6333	−1.73659
$446$	−9.02776	−0.427477
$447$	3.63331	0.171850
$448$	1.00000	0.0472456
$449$	−25.3944	−1.19844	−0.599219	−	0.800585i	$-0.704522\pi$
$449$	−25.3944	−1.19844	−0.599219	+	0.800585i	$0.704522\pi$
$450$	0.394449	0.0185945
$451$	1.60555	0.0756025
$452$	18.4222	0.866508
$453$	−18.7889	−0.882779
$454$	−24.0000	−1.12638
$455$	−15.2111	−0.713107
$456$	0	0
$457$	−36.5139	−1.70805	−0.854024	−	0.520234i	$-0.825845\pi$
$457$	−36.5139	−1.70805	−0.854024	+	0.520234i	$0.825845\pi$
$458$	−10.3028	−0.481417
$459$	0	0
$460$	−10.6056	−0.494486
$461$	2.51388	0.117083	0.0585415	−	0.998285i	$-0.481355\pi$
$461$	2.51388	0.117083	0.0585415	+	0.998285i	$0.481355\pi$
$462$	0.908327	0.0422592
$463$	34.2389	1.59121	0.795607	−	0.605813i	$-0.207152\pi$
$463$	34.2389	1.59121	0.795607	+	0.605813i	$0.207152\pi$
$464$	−0.908327	−0.0421680
$465$	21.6333	1.00322
$466$	−19.1194	−0.885690
$467$	−13.8167	−0.639358	−0.319679	−	0.947526i	$-0.603575\pi$
$467$	−13.8167	−0.639358	−0.319679	+	0.947526i	$0.603575\pi$
$468$	8.60555	0.397792
$469$	0.788897	0.0364279
$470$	9.00000	0.415139
$471$	−6.66947	−0.307313
$472$	−8.30278	−0.382166
$473$	4.39445	0.202057
$474$	19.4222	0.892091
$475$	0	0
$476$	0	0
$477$	−11.0917	−0.507853
$478$	22.6056	1.03395
$479$	−26.7250	−1.22110	−0.610548	−	0.791979i	$-0.709051\pi$
$479$	−26.7250	−1.22110	−0.610548	+	0.791979i	$0.709051\pi$
$480$	−3.00000	−0.136931
$481$	−32.4222	−1.47833
$482$	14.9083	0.679056
$483$	−6.00000	−0.273009
$484$	−10.5139	−0.477904
$485$	−30.6333	−1.39099
$486$	−12.3944	−0.562224
$487$	9.09167	0.411983	0.205992	−	0.978554i	$-0.433958\pi$
$487$	9.09167	0.411983	0.205992	+	0.978554i	$0.433958\pi$
$488$	7.90833	0.357993
$489$	−18.1194	−0.819389
$490$	−2.30278	−0.104029
$491$	−24.8444	−1.12121	−0.560606	−	0.828082i	$-0.689432\pi$
$491$	−24.8444	−1.12121	−0.560606	+	0.828082i	$0.689432\pi$
$492$	−3.00000	−0.135250
$493$	0	0
$494$	0	0
$495$	2.09167	0.0940137
$496$	7.21110	0.323788
$497$	2.09167	0.0938244
$498$	12.0000	0.537733
$499$	10.3028	0.461216	0.230608	−	0.973047i	$-0.425929\pi$
$499$	10.3028	0.461216	0.230608	+	0.973047i	$0.425929\pi$
$500$	−10.8167	−0.483735
$501$	−16.1833	−0.723019
$502$	4.18335	0.186712
$503$	18.4861	0.824255	0.412128	−	0.911126i	$-0.364786\pi$
$503$	18.4861	0.824255	0.412128	+	0.911126i	$0.364786\pi$
$504$	1.30278	0.0580302
$505$	−13.8167	−0.614833
$506$	−3.21110	−0.142751
$507$	39.9083	1.77239
$508$	3.30278	0.146537
$509$	38.6611	1.71362	0.856811	−	0.515631i	$-0.172442\pi$
$509$	38.6611	1.71362	0.856811	+	0.515631i	$0.172442\pi$
$510$	0	0
$511$	12.6056	0.557637
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−12.4861	−0.550739
$515$	−7.81665	−0.344443
$516$	−8.21110	−0.361474
$517$	2.72498	0.119845
$518$	−4.90833	−0.215660
$519$	−6.00000	−0.263371
$520$	15.2111	0.667051
$521$	−39.2111	−1.71787	−0.858935	−	0.512085i	$-0.828873\pi$
$521$	−39.2111	−1.71787	−0.858935	+	0.512085i	$0.828873\pi$
$522$	−1.18335	−0.0517937
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	−7.81665	−0.341472
$525$	0.394449	0.0172152
$526$	−7.81665	−0.340822
$527$	0	0
$528$	−0.908327	−0.0395299
$529$	−1.78890	−0.0777781
$530$	−19.6056	−0.851611
$531$	−10.8167	−0.469403
$532$	0	0
$533$	15.2111	0.658866
$534$	20.7250	0.896858
$535$	−31.8167	−1.37555
$536$	−0.788897	−0.0340752
$537$	−18.0000	−0.776757
$538$	−3.21110	−0.138440
$539$	−0.697224	−0.0300316
$540$	−12.9083	−0.555486
$541$	−44.6056	−1.91774	−0.958871	−	0.283841i	$-0.908391\pi$
$541$	−44.6056	−1.91774	−0.958871	+	0.283841i	$0.908391\pi$
$542$	−15.3305	−0.658503
$543$	2.84441	0.122065
$544$	0	0
$545$	−41.2389	−1.76648
$546$	8.60555	0.368284
$547$	14.1833	0.606436	0.303218	−	0.952921i	$-0.401939\pi$
$547$	14.1833	0.606436	0.303218	+	0.952921i	$0.401939\pi$
$548$	−12.9083	−0.551416
$549$	10.3028	0.439712
$550$	0.211103	0.00900144
$551$	0	0
$552$	6.00000	0.255377
$553$	−14.9083	−0.633967
$554$	−0.605551	−0.0257274
$555$	14.7250	0.625041
$556$	17.2111	0.729913
$557$	44.6611	1.89235	0.946175	−	0.323655i	$-0.104912\pi$
$557$	44.6611	1.89235	0.946175	+	0.323655i	$0.104912\pi$
$558$	9.39445	0.397699
$559$	41.6333	1.76090
$560$	2.30278	0.0973100
$561$	0	0
$562$	18.4222	0.777094
$563$	27.9083	1.17620	0.588098	−	0.808790i	$-0.299877\pi$
$563$	27.9083	1.17620	0.588098	+	0.808790i	$0.299877\pi$
$564$	−5.09167	−0.214398
$565$	42.4222	1.78472
$566$	−23.6333	−0.993382
$567$	−3.39445	−0.142553
$568$	−2.09167	−0.0877647
$569$	44.2389	1.85459	0.927295	−	0.374332i	$-0.122128\pi$
$569$	44.2389	1.85459	0.927295	+	0.374332i	$0.122128\pi$
$570$	0	0
$571$	42.7527	1.78915	0.894573	−	0.446921i	$-0.147480\pi$
$571$	42.7527	1.78915	0.894573	+	0.446921i	$0.147480\pi$
$572$	4.60555	0.192568
$573$	6.00000	0.250654
$574$	2.30278	0.0961160
$575$	−1.39445	−0.0581525
$576$	−1.30278	−0.0542823
$577$	−25.6333	−1.06713	−0.533564	−	0.845760i	$-0.679148\pi$
$577$	−25.6333	−1.06713	−0.533564	+	0.845760i	$0.679148\pi$
$578$	17.0000	0.707107
$579$	31.5778	1.31233
$580$	−2.09167	−0.0868520
$581$	−9.21110	−0.382141
$582$	17.3305	0.718374
$583$	−5.93608	−0.245847
$584$	−12.6056	−0.521621
$585$	19.8167	0.819318
$586$	−7.81665	−0.322903
$587$	−10.1833	−0.420312	−0.210156	−	0.977668i	$-0.567397\pi$
$587$	−10.1833	−0.420312	−0.210156	+	0.977668i	$0.567397\pi$
$588$	1.30278	0.0537256
$589$	0	0
$590$	−19.1194	−0.787134
$591$	−4.18335	−0.172080
$592$	4.90833	0.201731
$593$	−13.8167	−0.567382	−0.283691	−	0.958916i	$-0.591559\pi$
$593$	−13.8167	−0.567382	−0.283691	+	0.958916i	$0.591559\pi$
$594$	−3.90833	−0.160361
$595$	0	0
$596$	2.78890	0.114238
$597$	−6.39445	−0.261707
$598$	−30.4222	−1.24406
$599$	−36.6972	−1.49941	−0.749704	−	0.661773i	$-0.769804\pi$
$599$	−36.6972	−1.49941	−0.749704	+	0.661773i	$0.769804\pi$
$600$	−0.394449	−0.0161033
$601$	16.4222	0.669876	0.334938	−	0.942240i	$-0.391285\pi$
$601$	16.4222	0.669876	0.334938	+	0.942240i	$0.391285\pi$
$602$	6.30278	0.256882
$603$	−1.02776	−0.0418535
$604$	−14.4222	−0.586831
$605$	−24.2111	−0.984321
$606$	7.81665	0.317530
$607$	−6.60555	−0.268111	−0.134056	−	0.990974i	$-0.542800\pi$
$607$	−6.60555	−0.268111	−0.134056	+	0.990974i	$0.542800\pi$
$608$	0	0
$609$	−1.18335	−0.0479516
$610$	18.2111	0.737346
$611$	25.8167	1.04443
$612$	0	0
$613$	5.21110	0.210474	0.105237	−	0.994447i	$-0.466440\pi$
$613$	5.21110	0.210474	0.105237	+	0.994447i	$0.466440\pi$
$614$	29.1472	1.17628
$615$	−6.90833	−0.278571
$616$	0.697224	0.0280920
$617$	34.1194	1.37360	0.686798	−	0.726848i	$-0.259016\pi$
$617$	34.1194	1.37360	0.686798	+	0.726848i	$0.259016\pi$
$618$	4.42221	0.177887
$619$	8.97224	0.360625	0.180312	−	0.983609i	$-0.442289\pi$
$619$	8.97224	0.360625	0.180312	+	0.983609i	$0.442289\pi$
$620$	16.6056	0.666895
$621$	25.8167	1.03599
$622$	0.275019	0.0110273
$623$	−15.9083	−0.637354
$624$	−8.60555	−0.344498
$625$	−26.4222	−1.05689
$626$	−14.4222	−0.576427
$627$	0	0
$628$	−5.11943	−0.204287
$629$	0	0
$630$	3.00000	0.119523
$631$	−1.21110	−0.0482132	−0.0241066	−	0.999709i	$-0.507674\pi$
$631$	−1.21110	−0.0482132	−0.0241066	+	0.999709i	$0.507674\pi$
$632$	14.9083	0.593021
$633$	−14.0555	−0.558656
$634$	−28.3305	−1.12515
$635$	7.60555	0.301817
$636$	11.0917	0.439813
$637$	−6.60555	−0.261721
$638$	−0.633308	−0.0250729
$639$	−2.72498	−0.107799
$640$	−2.30278	−0.0910252
$641$	1.81665	0.0717535	0.0358768	−	0.999356i	$-0.488578\pi$
$641$	1.81665	0.0717535	0.0358768	+	0.999356i	$0.488578\pi$
$642$	18.0000	0.710403
$643$	−38.0555	−1.50076	−0.750381	−	0.661005i	$-0.770130\pi$
$643$	−38.0555	−1.50076	−0.750381	+	0.661005i	$0.770130\pi$
$644$	−4.60555	−0.181484
$645$	−18.9083	−0.744515
$646$	0	0
$647$	38.7250	1.52244	0.761218	−	0.648496i	$-0.224602\pi$
$647$	38.7250	1.52244	0.761218	+	0.648496i	$0.224602\pi$
$648$	3.39445	0.133347
$649$	−5.78890	−0.227234
$650$	2.00000	0.0784465
$651$	9.39445	0.368197
$652$	−13.9083	−0.544692
$653$	19.8167	0.775486	0.387743	−	0.921768i	$-0.373255\pi$
$653$	19.8167	0.775486	0.387743	+	0.921768i	$0.373255\pi$
$654$	23.3305	0.912296
$655$	−18.0000	−0.703318
$656$	−2.30278	−0.0899083
$657$	−16.4222	−0.640691
$658$	3.90833	0.152362
$659$	45.2111	1.76117	0.880587	−	0.473884i	$-0.157148\pi$
$659$	45.2111	1.76117	0.880587	+	0.473884i	$0.157148\pi$
$660$	−2.09167	−0.0814183
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	−16.4222	−0.638267
$663$	0	0
$664$	9.21110	0.357460
$665$	0	0
$666$	6.39445	0.247780
$667$	4.18335	0.161980
$668$	−12.4222	−0.480630
$669$	11.7611	0.454712
$670$	−1.81665	−0.0701835
$671$	5.51388	0.212861
$672$	−1.30278	−0.0502557
$673$	−3.81665	−0.147121	−0.0735606	−	0.997291i	$-0.523436\pi$
$673$	−3.81665	−0.147121	−0.0735606	+	0.997291i	$0.523436\pi$
$674$	6.60555	0.254436
$675$	−1.69722	−0.0653262
$676$	30.6333	1.17820
$677$	−51.2111	−1.96820	−0.984101	−	0.177608i	$-0.943164\pi$
$677$	−51.2111	−1.96820	−0.984101	+	0.177608i	$0.943164\pi$
$678$	−24.0000	−0.921714
$679$	−13.3028	−0.510514
$680$	0	0
$681$	31.2666	1.19814
$682$	5.02776	0.192523
$683$	9.63331	0.368608	0.184304	−	0.982869i	$-0.440997\pi$
$683$	9.63331	0.368608	0.184304	+	0.982869i	$0.440997\pi$
$684$	0	0
$685$	−29.7250	−1.13573
$686$	−1.00000	−0.0381802
$687$	13.4222	0.512089
$688$	−6.30278	−0.240291
$689$	−56.2389	−2.14253
$690$	13.8167	0.525991
$691$	36.6056	1.39254	0.696270	−	0.717780i	$-0.254841\pi$
$691$	36.6056	1.39254	0.696270	+	0.717780i	$0.254841\pi$
$692$	−4.60555	−0.175077
$693$	0.908327	0.0345045
$694$	−15.6333	−0.593432
$695$	39.6333	1.50338
$696$	1.18335	0.0448546
$697$	0	0
$698$	3.57779	0.135422
$699$	24.9083	0.942119
$700$	0.302776	0.0114438
$701$	−13.8167	−0.521848	−0.260924	−	0.965359i	$-0.584027\pi$
$701$	−13.8167	−0.521848	−0.260924	+	0.965359i	$0.584027\pi$
$702$	−37.0278	−1.39752
$703$	0	0
$704$	−0.697224	−0.0262776
$705$	−11.7250	−0.441588
$706$	15.6333	0.588367
$707$	−6.00000	−0.225653
$708$	10.8167	0.406515
$709$	−23.8167	−0.894453	−0.447227	−	0.894421i	$-0.647588\pi$
$709$	−23.8167	−0.894453	−0.447227	+	0.894421i	$0.647588\pi$
$710$	−4.81665	−0.180766
$711$	19.4222	0.728390
$712$	15.9083	0.596190
$713$	−33.2111	−1.24377
$714$	0	0
$715$	10.6056	0.396625
$716$	−13.8167	−0.516353
$717$	−29.4500	−1.09983
$718$	−28.6056	−1.06755
$719$	42.4222	1.58208	0.791041	−	0.611764i	$-0.209540\pi$
$719$	42.4222	1.58208	0.791041	+	0.611764i	$0.209540\pi$
$720$	−3.00000	−0.111803
$721$	−3.39445	−0.126416
$722$	0	0
$723$	−19.4222	−0.722320
$724$	2.18335	0.0811434
$725$	−0.275019	−0.0102140
$726$	13.6972	0.508352
$727$	−29.1194	−1.07998	−0.539990	−	0.841671i	$-0.681572\pi$
$727$	−29.1194	−1.07998	−0.539990	+	0.841671i	$0.681572\pi$
$728$	6.60555	0.244818
$729$	26.3305	0.975205
$730$	−29.0278	−1.07437
$731$	0	0
$732$	−10.3028	−0.380802
$733$	3.88057	0.143332	0.0716661	−	0.997429i	$-0.477168\pi$
$733$	3.88057	0.143332	0.0716661	+	0.997429i	$0.477168\pi$
$734$	−13.3028	−0.491014
$735$	3.00000	0.110657
$736$	4.60555	0.169763
$737$	−0.550039	−0.0202609
$738$	−3.00000	−0.110432
$739$	−21.9361	−0.806932	−0.403466	−	0.914995i	$-0.632195\pi$
$739$	−21.9361	−0.806932	−0.403466	+	0.914995i	$0.632195\pi$
$740$	11.3028	0.415498
$741$	0	0
$742$	−8.51388	−0.312554
$743$	12.4861	0.458071	0.229036	−	0.973418i	$-0.426443\pi$
$743$	12.4861	0.458071	0.229036	+	0.973418i	$0.426443\pi$
$744$	−9.39445	−0.344417
$745$	6.42221	0.235291
$746$	−15.0917	−0.552545
$747$	12.0000	0.439057
$748$	0	0
$749$	−13.8167	−0.504850
$750$	14.0917	0.514555
$751$	−1.93608	−0.0706487	−0.0353243	−	0.999376i	$-0.511246\pi$
$751$	−1.93608	−0.0706487	−0.0353243	+	0.999376i	$0.511246\pi$
$752$	−3.90833	−0.142522
$753$	−5.44996	−0.198608
$754$	−6.00000	−0.218507
$755$	−33.2111	−1.20868
$756$	−5.60555	−0.203872
$757$	−37.2111	−1.35246	−0.676230	−	0.736690i	$-0.736388\pi$
$757$	−37.2111	−1.35246	−0.676230	+	0.736690i	$0.736388\pi$
$758$	9.39445	0.341222
$759$	4.18335	0.151846
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	−4.30278	−0.155873
$763$	−17.9083	−0.648325
$764$	4.60555	0.166623
$765$	0	0
$766$	37.8167	1.36637
$767$	−54.8444	−1.98032
$768$	1.30278	0.0470099
$769$	−32.6056	−1.17579	−0.587893	−	0.808939i	$-0.700042\pi$
$769$	−32.6056	−1.17579	−0.587893	+	0.808939i	$0.700042\pi$
$770$	1.60555	0.0578601
$771$	16.2666	0.585828
$772$	24.2389	0.872376
$773$	−20.2389	−0.727941	−0.363971	−	0.931410i	$-0.618579\pi$
$773$	−20.2389	−0.727941	−0.363971	+	0.931410i	$0.618579\pi$
$774$	−8.21110	−0.295142
$775$	2.18335	0.0784281
$776$	13.3028	0.477542
$777$	6.39445	0.229400
$778$	−21.6333	−0.775592
$779$	0	0
$780$	−19.8167	−0.709550
$781$	−1.45837	−0.0521844
$782$	0	0
$783$	5.09167	0.181962
$784$	1.00000	0.0357143
$785$	−11.7889	−0.420764
$786$	10.1833	0.363228
$787$	−13.5139	−0.481718	−0.240859	−	0.970560i	$-0.577429\pi$
$787$	−13.5139	−0.481718	−0.240859	+	0.970560i	$0.577429\pi$
$788$	−3.21110	−0.114391
$789$	10.1833	0.362537
$790$	34.3305	1.22143
$791$	18.4222	0.655018
$792$	−0.908327	−0.0322760
$793$	52.2389	1.85506
$794$	10.6972	0.379630
$795$	25.5416	0.905868
$796$	−4.90833	−0.173971
$797$	4.60555	0.163137	0.0815685	−	0.996668i	$-0.474007\pi$
$797$	4.60555	0.163137	0.0815685	+	0.996668i	$0.474007\pi$
$798$	0	0
$799$	0	0
$800$	−0.302776	−0.0107047
$801$	20.7250	0.732281
$802$	−24.8444	−0.877287
$803$	−8.78890	−0.310153
$804$	1.02776	0.0362462
$805$	−10.6056	−0.373797
$806$	47.6333	1.67781
$807$	4.18335	0.147261
$808$	6.00000	0.211079
$809$	38.7250	1.36150	0.680749	−	0.732517i	$-0.261654\pi$
$809$	38.7250	1.36150	0.680749	+	0.732517i	$0.261654\pi$
$810$	7.81665	0.274649
$811$	−44.5694	−1.56504	−0.782521	−	0.622624i	$-0.786067\pi$
$811$	−44.5694	−1.56504	−0.782521	+	0.622624i	$0.786067\pi$
$812$	−0.908327	−0.0318760
$813$	19.9722	0.700457
$814$	3.42221	0.119948
$815$	−32.0278	−1.12188
$816$	0	0
$817$	0	0
$818$	16.0917	0.562632
$819$	8.60555	0.300702
$820$	−5.30278	−0.185181
$821$	30.0000	1.04701	0.523504	−	0.852023i	$-0.324625\pi$
$821$	30.0000	1.04701	0.523504	+	0.852023i	$0.324625\pi$
$822$	16.8167	0.586548
$823$	14.0000	0.488009	0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000	0.488009	0.244005	+	0.969774i	$0.421539\pi$
$824$	3.39445	0.118251
$825$	−0.275019	−0.00957494
$826$	−8.30278	−0.288891
$827$	41.4500	1.44136	0.720678	−	0.693270i	$-0.243831\pi$
$827$	41.4500	1.44136	0.720678	+	0.693270i	$0.243831\pi$
$828$	6.00000	0.208514
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	21.2111	0.736248
$831$	0.788897	0.0273665
$832$	−6.60555	−0.229006
$833$	0	0
$834$	−22.4222	−0.776417
$835$	−28.6056	−0.989936
$836$	0	0
$837$	−40.4222	−1.39720
$838$	−12.4222	−0.429118
$839$	6.00000	0.207143	0.103572	−	0.994622i	$-0.466973\pi$
$839$	6.00000	0.207143	0.103572	+	0.994622i	$0.466973\pi$
$840$	−3.00000	−0.103510
$841$	−28.1749	−0.971550
$842$	4.78890	0.165036
$843$	−24.0000	−0.826604
$844$	−10.7889	−0.371369
$845$	70.5416	2.42671
$846$	−5.09167	−0.175055
$847$	−10.5139	−0.361261
$848$	8.51388	0.292368
$849$	30.7889	1.05667
$850$	0	0
$851$	−22.6056	−0.774908
$852$	2.72498	0.0933563
$853$	−21.0917	−0.722165	−0.361083	−	0.932534i	$-0.617593\pi$
$853$	−21.0917	−0.722165	−0.361083	+	0.932534i	$0.617593\pi$
$854$	7.90833	0.270617
$855$	0	0
$856$	13.8167	0.472244
$857$	−0.422205	−0.0144223	−0.00721113	−	0.999974i	$-0.502295\pi$
$857$	−0.422205	−0.0144223	−0.00721113	+	0.999974i	$0.502295\pi$
$858$	−6.00000	−0.204837
$859$	52.2389	1.78237	0.891183	−	0.453643i	$-0.149876\pi$
$859$	52.2389	1.78237	0.891183	+	0.453643i	$0.149876\pi$
$860$	−14.5139	−0.494919
$861$	−3.00000	−0.102240
$862$	−25.5416	−0.869952
$863$	40.9638	1.39443	0.697213	−	0.716864i	$-0.254423\pi$
$863$	40.9638	1.39443	0.697213	+	0.716864i	$0.254423\pi$
$864$	5.60555	0.190705
$865$	−10.6056	−0.360600
$866$	−9.09167	−0.308948
$867$	−22.1472	−0.752158
$868$	7.21110	0.244761
$869$	10.3944	0.352608
$870$	2.72498	0.0923855
$871$	−5.21110	−0.176571
$872$	17.9083	0.606452
$873$	17.3305	0.586550
$874$	0	0
$875$	−10.8167	−0.365670
$876$	16.4222	0.554855
$877$	−29.9083	−1.00993	−0.504966	−	0.863139i	$-0.668495\pi$
$877$	−29.9083	−1.00993	−0.504966	+	0.863139i	$0.668495\pi$
$878$	32.4222	1.09420
$879$	10.1833	0.343476
$880$	−1.60555	−0.0541231
$881$	−4.18335	−0.140941	−0.0704703	−	0.997514i	$-0.522450\pi$
$881$	−4.18335	−0.140941	−0.0704703	+	0.997514i	$0.522450\pi$
$882$	1.30278	0.0438667
$883$	−35.1194	−1.18186	−0.590931	−	0.806722i	$-0.701240\pi$
$883$	−35.1194	−1.18186	−0.590931	+	0.806722i	$0.701240\pi$
$884$	0	0
$885$	24.9083	0.837284
$886$	−11.5139	−0.386816
$887$	2.36669	0.0794658	0.0397329	−	0.999210i	$-0.487349\pi$
$887$	2.36669	0.0794658	0.0397329	+	0.999210i	$0.487349\pi$
$888$	−6.39445	−0.214584
$889$	3.30278	0.110772
$890$	36.6333	1.22795
$891$	2.36669	0.0792872
$892$	9.02776	0.302272
$893$	0	0
$894$	−3.63331	−0.121516
$895$	−31.8167	−1.06351
$896$	−1.00000	−0.0334077
$897$	39.6333	1.32332
$898$	25.3944	0.847424
$899$	−6.55004	−0.218456
$900$	−0.394449	−0.0131483
$901$	0	0
$902$	−1.60555	−0.0534590
$903$	−8.21110	−0.273248
$904$	−18.4222	−0.612713
$905$	5.02776	0.167128
$906$	18.7889	0.624219
$907$	−12.1833	−0.404541	−0.202271	−	0.979330i	$-0.564832\pi$
$907$	−12.1833	−0.404541	−0.202271	+	0.979330i	$0.564832\pi$
$908$	24.0000	0.796468
$909$	7.81665	0.259262
$910$	15.2111	0.504243
$911$	−5.09167	−0.168695	−0.0843473	−	0.996436i	$-0.526881\pi$
$911$	−5.09167	−0.168695	−0.0843473	+	0.996436i	$0.526881\pi$
$912$	0	0
$913$	6.42221	0.212544
$914$	36.5139	1.20777
$915$	−23.7250	−0.784324
$916$	10.3028	0.340413
$917$	−7.81665	−0.258129
$918$	0	0
$919$	−44.6056	−1.47140	−0.735701	−	0.677307i	$-0.763147\pi$
$919$	−44.6056	−1.47140	−0.735701	+	0.677307i	$0.763147\pi$
$920$	10.6056	0.349655
$921$	−37.9722	−1.25123
$922$	−2.51388	−0.0827902
$923$	−13.8167	−0.454781
$924$	−0.908327	−0.0298818
$925$	1.48612	0.0488634
$926$	−34.2389	−1.12516
$927$	4.42221	0.145244
$928$	0.908327	0.0298173
$929$	−19.8167	−0.650163	−0.325082	−	0.945686i	$-0.605392\pi$
$929$	−19.8167	−0.650163	−0.325082	+	0.945686i	$0.605392\pi$
$930$	−21.6333	−0.709384
$931$	0	0
$932$	19.1194	0.626278
$933$	−0.358288	−0.0117298
$934$	13.8167	0.452095
$935$	0	0
$936$	−8.60555	−0.281281
$937$	34.7889	1.13650	0.568252	−	0.822855i	$-0.307620\pi$
$937$	34.7889	1.13650	0.568252	+	0.822855i	$0.307620\pi$
$938$	−0.788897	−0.0257584
$939$	18.7889	0.613152
$940$	−9.00000	−0.293548
$941$	−6.97224	−0.227289	−0.113644	−	0.993521i	$-0.536252\pi$
$941$	−6.97224	−0.227289	−0.113644	+	0.993521i	$0.536252\pi$
$942$	6.66947	0.217303
$943$	10.6056	0.345364
$944$	8.30278	0.270232
$945$	−12.9083	−0.419908
$946$	−4.39445	−0.142876
$947$	−17.7250	−0.575984	−0.287992	−	0.957633i	$-0.592988\pi$
$947$	−17.7250	−0.575984	−0.287992	+	0.957633i	$0.592988\pi$
$948$	−19.4222	−0.630804
$949$	−83.2666	−2.70295
$950$	0	0
$951$	36.9083	1.19683
$952$	0	0
$953$	−24.4222	−0.791113	−0.395556	−	0.918442i	$-0.629448\pi$
$953$	−24.4222	−0.791113	−0.395556	+	0.918442i	$0.629448\pi$
$954$	11.0917	0.359106
$955$	10.6056	0.343188
$956$	−22.6056	−0.731116
$957$	0.825058	0.0266703
$958$	26.7250	0.863445
$959$	−12.9083	−0.416832
$960$	3.00000	0.0968246
$961$	21.0000	0.677419
$962$	32.4222	1.04533
$963$	18.0000	0.580042
$964$	−14.9083	−0.480165
$965$	55.8167	1.79680
$966$	6.00000	0.193047
$967$	−18.7889	−0.604210	−0.302105	−	0.953275i	$-0.597689\pi$
$967$	−18.7889	−0.604210	−0.302105	+	0.953275i	$0.597689\pi$
$968$	10.5139	0.337929
$969$	0	0
$970$	30.6333	0.983576
$971$	18.1472	0.582371	0.291185	−	0.956667i	$-0.405950\pi$
$971$	18.1472	0.582371	0.291185	+	0.956667i	$0.405950\pi$
$972$	12.3944	0.397552
$973$	17.2111	0.551763
$974$	−9.09167	−0.291316
$975$	−2.60555	−0.0834444
$976$	−7.90833	−0.253139
$977$	−16.6056	−0.531259	−0.265629	−	0.964075i	$-0.585580\pi$
$977$	−16.6056	−0.531259	−0.265629	+	0.964075i	$0.585580\pi$
$978$	18.1194	0.579395
$979$	11.0917	0.354491
$980$	2.30278	0.0735595
$981$	23.3305	0.744887
$982$	24.8444	0.792817
$983$	15.6333	0.498625	0.249313	−	0.968423i	$-0.419795\pi$
$983$	15.6333	0.498625	0.249313	+	0.968423i	$0.419795\pi$
$984$	3.00000	0.0956365
$985$	−7.39445	−0.235607
$986$	0	0
$987$	−5.09167	−0.162070
$988$	0	0
$989$	29.0278	0.923029
$990$	−2.09167	−0.0664777
$991$	37.3583	1.18673	0.593363	−	0.804935i	$-0.297800\pi$
$991$	37.3583	1.18673	0.593363	+	0.804935i	$0.297800\pi$
$992$	−7.21110	−0.228953
$993$	21.3944	0.678932
$994$	−2.09167	−0.0663438
$995$	−11.3028	−0.358322
$996$	−12.0000	−0.380235
$997$	−48.7250	−1.54314	−0.771568	−	0.636147i	$-0.780527\pi$
$997$	−48.7250	−1.54314	−0.771568	+	0.636147i	$0.780527\pi$
$998$	−10.3028	−0.326129
$999$	−27.5139	−0.870501

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.e.1.2		2
19.18	odd	2		266.2.a.c.1.1	✓	2
57.56	even	2		2394.2.a.q.1.1		2
76.75	even	2		2128.2.a.h.1.2		2
95.94	odd	2		6650.2.a.bl.1.2		2
133.132	even	2		1862.2.a.l.1.2		2
152.37	odd	2		8512.2.a.n.1.2		2
152.75	even	2		8512.2.a.u.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.a.c.1.1	✓	2	19.18	odd	2
1862.2.a.l.1.2		2	133.132	even	2
2128.2.a.h.1.2		2	76.75	even	2
2394.2.a.q.1.1		2	57.56	even	2
5054.2.a.e.1.2		2	1.1	even	1	trivial
6650.2.a.bl.1.2		2	95.94	odd	2
8512.2.a.n.1.2		2	152.37	odd	2
8512.2.a.u.1.1		2	152.75	even	2

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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.30278 q^{3} +1.00000 q^{4} +2.30278 q^{5} -1.30278 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.30278 q^{3} +1.00000 q^{4} +2.30278 q^{5} -1.30278 q^{6} +1.00000 q^{7} -1.00000 q^{8} -1.30278 q^{9} -2.30278 q^{10} -0.697224 q^{11} +1.30278 q^{12} -6.60555 q^{13} -1.00000 q^{14} +3.00000 q^{15} +1.00000 q^{16} +1.30278 q^{18} +2.30278 q^{20} +1.30278 q^{21} +0.697224 q^{22} -4.60555 q^{23} -1.30278 q^{24} +0.302776 q^{25} +6.60555 q^{26} -5.60555 q^{27} +1.00000 q^{28} -0.908327 q^{29} -3.00000 q^{30} +7.21110 q^{31} -1.00000 q^{32} -0.908327 q^{33} +2.30278 q^{35} -1.30278 q^{36} +4.90833 q^{37} -8.60555 q^{39} -2.30278 q^{40} -2.30278 q^{41} -1.30278 q^{42} -6.30278 q^{43} -0.697224 q^{44} -3.00000 q^{45} +4.60555 q^{46} -3.90833 q^{47} +1.30278 q^{48} +1.00000 q^{49} -0.302776 q^{50} -6.60555 q^{52} +8.51388 q^{53} +5.60555 q^{54} -1.60555 q^{55} -1.00000 q^{56} +0.908327 q^{58} +8.30278 q^{59} +3.00000 q^{60} -7.90833 q^{61} -7.21110 q^{62} -1.30278 q^{63} +1.00000 q^{64} -15.2111 q^{65} +0.908327 q^{66} +0.788897 q^{67} -6.00000 q^{69} -2.30278 q^{70} +2.09167 q^{71} +1.30278 q^{72} +12.6056 q^{73} -4.90833 q^{74} +0.394449 q^{75} -0.697224 q^{77} +8.60555 q^{78} -14.9083 q^{79} +2.30278 q^{80} -3.39445 q^{81} +2.30278 q^{82} -9.21110 q^{83} +1.30278 q^{84} +6.30278 q^{86} -1.18335 q^{87} +0.697224 q^{88} -15.9083 q^{89} +3.00000 q^{90} -6.60555 q^{91} -4.60555 q^{92} +9.39445 q^{93} +3.90833 q^{94} -1.30278 q^{96} -13.3028 q^{97} -1.00000 q^{98} +0.908327 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + q^{5} + q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - q^{10} - 5 q^{11} - q^{12} - 6 q^{13} - 2 q^{14} + 6 q^{15} + 2 q^{16} - q^{18} + q^{20} - q^{21} + 5 q^{22} - 2 q^{23} + q^{24} - 3 q^{25} + 6 q^{26} - 4 q^{27} + 2 q^{28} + 9 q^{29} - 6 q^{30} - 2 q^{32} + 9 q^{33} + q^{35} + q^{36} - q^{37} - 10 q^{39} - q^{40} - q^{41} + q^{42} - 9 q^{43} - 5 q^{44} - 6 q^{45} + 2 q^{46} + 3 q^{47} - q^{48} + 2 q^{49} + 3 q^{50} - 6 q^{52} - q^{53} + 4 q^{54} + 4 q^{55} - 2 q^{56} - 9 q^{58} + 13 q^{59} + 6 q^{60} - 5 q^{61} + q^{63} + 2 q^{64} - 16 q^{65} - 9 q^{66} + 16 q^{67} - 12 q^{69} - q^{70} + 15 q^{71} - q^{72} + 18 q^{73} + q^{74} + 8 q^{75} - 5 q^{77} + 10 q^{78} - 19 q^{79} + q^{80} - 14 q^{81} + q^{82} - 4 q^{83} - q^{84} + 9 q^{86} - 24 q^{87} + 5 q^{88} - 21 q^{89} + 6 q^{90} - 6 q^{91} - 2 q^{92} + 26 q^{93} - 3 q^{94} + q^{96} - 23 q^{97} - 2 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 + 2 * q^4 + q^5 + q^6 + 2 * q^7 - 2 * q^8 + q^9 - q^10 - 5 * q^11 - q^12 - 6 * q^13 - 2 * q^14 + 6 * q^15 + 2 * q^16 - q^18 + q^20 - q^21 + 5 * q^22 - 2 * q^23 + q^24 - 3 * q^25 + 6 * q^26 - 4 * q^27 + 2 * q^28 + 9 * q^29 - 6 * q^30 - 2 * q^32 + 9 * q^33 + q^35 + q^36 - q^37 - 10 * q^39 - q^40 - q^41 + q^42 - 9 * q^43 - 5 * q^44 - 6 * q^45 + 2 * q^46 + 3 * q^47 - q^48 + 2 * q^49 + 3 * q^50 - 6 * q^52 - q^53 + 4 * q^54 + 4 * q^55 - 2 * q^56 - 9 * q^58 + 13 * q^59 + 6 * q^60 - 5 * q^61 + q^63 + 2 * q^64 - 16 * q^65 - 9 * q^66 + 16 * q^67 - 12 * q^69 - q^70 + 15 * q^71 - q^72 + 18 * q^73 + q^74 + 8 * q^75 - 5 * q^77 + 10 * q^78 - 19 * q^79 + q^80 - 14 * q^81 + q^82 - 4 * q^83 - q^84 + 9 * q^86 - 24 * q^87 + 5 * q^88 - 21 * q^89 + 6 * q^90 - 6 * q^91 - 2 * q^92 + 26 * q^93 - 3 * q^94 + q^96 - 23 * q^97 - 2 * q^98 - 9 * q^99

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