LMFDB - Embedded newform 4235.2.a.bc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.288385.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 2x^{2} + 10x + 3 $ x^5 - 7x^3 - 2x^2 + 10*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.35681$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} +0.329669 q^{6} -1.00000 q^{7} +2.92945 q^{8} -2.94096 q^{9} +O(q^{10})$	\(q-1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} +0.329669 q^{6} -1.00000 q^{7} +2.92945 q^{8} -2.94096 q^{9} -1.35681 q^{10} +0.0386517 q^{12} -2.34529 q^{13} +1.35681 q^{14} -0.242974 q^{15} -3.65654 q^{16} -0.927617 q^{17} +3.99032 q^{18} +1.95659 q^{19} -0.159077 q^{20} +0.242974 q^{21} +2.68368 q^{23} -0.711781 q^{24} +1.00000 q^{25} +3.18211 q^{26} +1.44350 q^{27} +0.159077 q^{28} +0.245772 q^{29} +0.329669 q^{30} +2.99032 q^{31} -0.897683 q^{32} +1.25860 q^{34} -1.00000 q^{35} +0.467840 q^{36} +6.23609 q^{37} -2.65471 q^{38} +0.569845 q^{39} +2.92945 q^{40} +6.05663 q^{41} -0.329669 q^{42} -9.64965 q^{43} -2.94096 q^{45} -3.64123 q^{46} +5.84459 q^{47} +0.888445 q^{48} +1.00000 q^{49} -1.35681 q^{50} +0.225387 q^{51} +0.373082 q^{52} -4.58827 q^{53} -1.95855 q^{54} -2.92945 q^{56} -0.475400 q^{57} -0.333465 q^{58} -9.66792 q^{59} +0.0386517 q^{60} -2.82941 q^{61} -4.05728 q^{62} +2.94096 q^{63} +8.53106 q^{64} -2.34529 q^{65} +15.0109 q^{67} +0.147563 q^{68} -0.652064 q^{69} +1.35681 q^{70} -2.21995 q^{71} -8.61540 q^{72} -0.100173 q^{73} -8.46116 q^{74} -0.242974 q^{75} -0.311248 q^{76} -0.773170 q^{78} -6.31847 q^{79} -3.65654 q^{80} +8.47216 q^{81} -8.21767 q^{82} -16.4112 q^{83} -0.0386517 q^{84} -0.927617 q^{85} +13.0927 q^{86} -0.0597162 q^{87} +2.73384 q^{89} +3.99032 q^{90} +2.34529 q^{91} -0.426912 q^{92} -0.726570 q^{93} -7.92997 q^{94} +1.95659 q^{95} +0.218114 q^{96} +3.11103 q^{97} -1.35681 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97}+O(q^{100}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^12 - 6 * q^13 + 2 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 5 * q^23 - 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 - 4 * q^28 - 11 * q^29 - 9 * q^30 - 2 * q^31 - 7 * q^32 + 8 * q^34 - 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 - 2 * q^39 - 6 * q^40 - 13 * q^41 + 9 * q^42 - 10 * q^43 + 7 * q^45 - 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 - 30 * q^51 + 8 * q^52 - 14 * q^53 - 16 * q^54 + 6 * q^56 - 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 - 20 * q^61 + 15 * q^62 - 7 * q^63 - 6 * q^64 - 6 * q^65 - 9 * q^67 - 3 * q^68 - 30 * q^69 - 10 * q^71 - 38 * q^72 - 15 * q^73 + 19 * q^74 + 2 * q^75 + 5 * q^76 + 21 * q^78 - 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 - 8 * q^83 - 3 * q^84 - 2 * q^85 - 29 * q^86 + 22 * q^87 + 7 * q^89 + 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 + 14 * q^94 - 7 * q^95 + 18 * q^96 + 21 * q^97

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 $

$2$	−1.35681	−0.959407	−0.479703	−	0.877431i	$-0.659256\pi$
$2$	−1.35681	−0.959407	−0.479703	+	0.877431i	$0.659256\pi$
$3$	−0.242974	−0.140281	−0.0701406	−	0.997537i	$-0.522345\pi$
$3$	−0.242974	−0.140281	−0.0701406	+	0.997537i	$0.522345\pi$
$4$	−0.159077	−0.0795386
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.329669	0.134587
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.92945	1.03572
$9$	−2.94096	−0.980321
$10$	−1.35681	−0.429060
$11$	0	0
$11$	0	0
$12$	0.0386517	0.0111578
$13$	−2.34529	−0.650467	−0.325233	−	0.945634i	$-0.605443\pi$
$13$	−2.34529	−0.650467	−0.325233	+	0.945634i	$0.605443\pi$
$14$	1.35681	0.362622
$15$	−0.242974	−0.0627357
$16$	−3.65654	−0.914135
$17$	−0.927617	−0.224980	−0.112490	−	0.993653i	$-0.535883\pi$
$17$	−0.927617	−0.224980	−0.112490	+	0.993653i	$0.535883\pi$
$18$	3.99032	0.940527
$19$	1.95659	0.448872	0.224436	−	0.974489i	$-0.427946\pi$
$19$	1.95659	0.448872	0.224436	+	0.974489i	$0.427946\pi$
$20$	−0.159077	−0.0355707
$21$	0.242974	0.0530213
$22$	0	0
$23$	2.68368	0.559585	0.279793	−	0.960060i	$-0.409734\pi$
$23$	2.68368	0.559585	0.279793	+	0.960060i	$0.409734\pi$
$24$	−0.711781	−0.145292
$25$	1.00000	0.200000
$26$	3.18211	0.624062
$27$	1.44350	0.277802
$28$	0.159077	0.0300628
$29$	0.245772	0.0456387	0.0228193	−	0.999740i	$-0.492736\pi$
$29$	0.245772	0.0456387	0.0228193	+	0.999740i	$0.492736\pi$
$30$	0.329669	0.0601890
$31$	2.99032	0.537077	0.268538	−	0.963269i	$-0.413459\pi$
$31$	2.99032	0.537077	0.268538	+	0.963269i	$0.413459\pi$
$32$	−0.897683	−0.158689
$33$	0	0
$34$	1.25860	0.215848
$35$	−1.00000	−0.169031
$36$	0.467840	0.0779734
$37$	6.23609	1.02521	0.512603	−	0.858626i	$-0.328681\pi$
$37$	6.23609	1.02521	0.512603	+	0.858626i	$0.328681\pi$
$38$	−2.65471	−0.430651
$39$	0.569845	0.0912483
$40$	2.92945	0.463187
$41$	6.05663	0.945886	0.472943	−	0.881093i	$-0.343192\pi$
$41$	6.05663	0.945886	0.472943	+	0.881093i	$0.343192\pi$
$42$	−0.329669	−0.0508690
$43$	−9.64965	−1.47156	−0.735779	−	0.677221i	$-0.763184\pi$
$43$	−9.64965	−1.47156	−0.735779	+	0.677221i	$0.763184\pi$
$44$	0	0
$45$	−2.94096	−0.438413
$46$	−3.64123	−0.536870
$47$	5.84459	0.852521	0.426260	−	0.904601i	$-0.359831\pi$
$47$	5.84459	0.852521	0.426260	+	0.904601i	$0.359831\pi$
$48$	0.888445	0.128236
$49$	1.00000	0.142857
$50$	−1.35681	−0.191881
$51$	0.225387	0.0315605
$52$	0.373082	0.0517372
$53$	−4.58827	−0.630247	−0.315123	−	0.949051i	$-0.602046\pi$
$53$	−4.58827	−0.630247	−0.315123	+	0.949051i	$0.602046\pi$
$54$	−1.95855	−0.266525
$55$	0	0
$56$	−2.92945	−0.391464
$57$	−0.475400	−0.0629683
$58$	−0.333465	−0.0437861
$59$	−9.66792	−1.25866	−0.629328	−	0.777140i	$-0.716670\pi$
$59$	−9.66792	−1.25866	−0.629328	+	0.777140i	$0.716670\pi$
$60$	0.0386517	0.00498991
$61$	−2.82941	−0.362269	−0.181134	−	0.983458i	$-0.557977\pi$
$61$	−2.82941	−0.362269	−0.181134	+	0.983458i	$0.557977\pi$
$62$	−4.05728	−0.515275
$63$	2.94096	0.370527
$64$	8.53106	1.06638
$65$	−2.34529	−0.290898
$66$	0	0
$67$	15.0109	1.83388	0.916939	−	0.399028i	$-0.130652\pi$
$67$	15.0109	1.83388	0.916939	+	0.399028i	$0.130652\pi$
$68$	0.147563	0.0178946
$69$	−0.652064	−0.0784993
$70$	1.35681	0.162169
$71$	−2.21995	−0.263459	−0.131730	−	0.991286i	$-0.542053\pi$
$71$	−2.21995	−0.263459	−0.131730	+	0.991286i	$0.542053\pi$
$72$	−8.61540	−1.01533
$73$	−0.100173	−0.0117244	−0.00586220	−	0.999983i	$-0.501866\pi$
$73$	−0.100173	−0.0117244	−0.00586220	+	0.999983i	$0.501866\pi$
$74$	−8.46116	−0.983590
$75$	−0.242974	−0.0280562
$76$	−0.311248	−0.0357026
$77$	0	0
$78$	−0.773170	−0.0875442
$79$	−6.31847	−0.710883	−0.355442	−	0.934699i	$-0.615669\pi$
$79$	−6.31847	−0.710883	−0.355442	+	0.934699i	$0.615669\pi$
$80$	−3.65654	−0.408814
$81$	8.47216	0.941351
$82$	−8.21767	−0.907490
$83$	−16.4112	−1.80136	−0.900679	−	0.434485i	$-0.856931\pi$
$83$	−16.4112	−1.80136	−0.900679	+	0.434485i	$0.856931\pi$
$84$	−0.0386517	−0.00421724
$85$	−0.927617	−0.100614
$86$	13.0927	1.41182
$87$	−0.0597162	−0.00640225
$88$	0	0
$89$	2.73384	0.289787	0.144893	−	0.989447i	$-0.453716\pi$
$89$	2.73384	0.289787	0.144893	+	0.989447i	$0.453716\pi$
$90$	3.99032	0.420616
$91$	2.34529	0.245853
$92$	−0.426912	−0.0445086
$93$	−0.726570	−0.0753418
$94$	−7.92997	−0.817914
$95$	1.95659	0.200742
$96$	0.218114	0.0222611
$97$	3.11103	0.315878	0.157939	−	0.987449i	$-0.449515\pi$
$97$	3.11103	0.315878	0.157939	+	0.987449i	$0.449515\pi$
$98$	−1.35681	−0.137058
$99$	0	0
$100$	−0.159077	−0.0159077
$101$	−14.9247	−1.48506	−0.742531	−	0.669812i	$-0.766375\pi$
$101$	−14.9247	−1.48506	−0.742531	+	0.669812i	$0.766375\pi$
$102$	−0.305807	−0.0302794
$103$	0.991937	0.0977384	0.0488692	−	0.998805i	$-0.484438\pi$
$103$	0.991937	0.0977384	0.0488692	+	0.998805i	$0.484438\pi$
$104$	−6.87041	−0.673699
$105$	0.242974	0.0237119
$106$	6.22539	0.604663
$107$	3.31075	0.320062	0.160031	−	0.987112i	$-0.448841\pi$
$107$	3.31075	0.320062	0.160031	+	0.987112i	$0.448841\pi$
$108$	−0.229628	−0.0220960
$109$	6.08363	0.582706	0.291353	−	0.956616i	$-0.405895\pi$
$109$	6.08363	0.582706	0.291353	+	0.956616i	$0.405895\pi$
$110$	0	0
$111$	−1.51521	−0.143817
$112$	3.65654	0.345511
$113$	−9.54323	−0.897751	−0.448876	−	0.893594i	$-0.648175\pi$
$113$	−9.54323	−0.897751	−0.448876	+	0.893594i	$0.648175\pi$
$114$	0.645026	0.0604122
$115$	2.68368	0.250254
$116$	−0.0390967	−0.00363004
$117$	6.89742	0.637666
$118$	13.1175	1.20756
$119$	0.927617	0.0850346
$120$	−0.711781	−0.0649764
$121$	0	0
$122$	3.83896	0.347563
$123$	−1.47160	−0.132690
$124$	−0.475691	−0.0427183
$125$	1.00000	0.0894427
$126$	−3.99032	−0.355486
$127$	−10.1792	−0.903256	−0.451628	−	0.892206i	$-0.649157\pi$
$127$	−10.1792	−0.903256	−0.451628	+	0.892206i	$0.649157\pi$
$128$	−9.77963	−0.864405
$129$	2.34462	0.206432
$130$	3.18211	0.279089
$131$	12.4893	1.09119	0.545596	−	0.838048i	$-0.316303\pi$
$131$	12.4893	1.09119	0.545596	+	0.838048i	$0.316303\pi$
$132$	0	0
$133$	−1.95659	−0.169658
$134$	−20.3669	−1.75943
$135$	1.44350	0.124237
$136$	−2.71741	−0.233016
$137$	16.6161	1.41961	0.709805	−	0.704398i	$-0.248783\pi$
$137$	16.6161	1.41961	0.709805	+	0.704398i	$0.248783\pi$
$138$	0.884725	0.0753128
$139$	−0.420472	−0.0356640	−0.0178320	−	0.999841i	$-0.505676\pi$
$139$	−0.420472	−0.0356640	−0.0178320	+	0.999841i	$0.505676\pi$
$140$	0.159077	0.0134445
$141$	−1.42008	−0.119593
$142$	3.01204	0.252764
$143$	0	0
$144$	10.7538	0.896146
$145$	0.245772	0.0204102
$146$	0.135916	0.0112485
$147$	−0.242974	−0.0200402
$148$	−0.992020	−0.0815435
$149$	−10.1747	−0.833544	−0.416772	−	0.909011i	$-0.636839\pi$
$149$	−10.1747	−0.833544	−0.416772	+	0.909011i	$0.636839\pi$
$150$	0.329669	0.0269173
$151$	5.10643	0.415555	0.207778	−	0.978176i	$-0.433377\pi$
$151$	5.10643	0.415555	0.207778	+	0.978176i	$0.433377\pi$
$152$	5.73172	0.464904
$153$	2.72809	0.220553
$154$	0	0
$155$	2.99032	0.240188
$156$	−0.0906494	−0.00725776
$157$	3.85612	0.307752	0.153876	−	0.988090i	$-0.450824\pi$
$157$	3.85612	0.307752	0.153876	+	0.988090i	$0.450824\pi$
$158$	8.57293	0.682026
$159$	1.11483	0.0884118
$160$	−0.897683	−0.0709680
$161$	−2.68368	−0.211503
$162$	−11.4951	−0.903138
$163$	−8.98048	−0.703406	−0.351703	−	0.936112i	$-0.614397\pi$
$163$	−8.98048	−0.703406	−0.351703	+	0.936112i	$0.614397\pi$
$164$	−0.963471	−0.0752345
$165$	0	0
$166$	22.2668	1.72824
$167$	0.0644782	0.00498947	0.00249474	−	0.999997i	$-0.499206\pi$
$167$	0.0644782	0.00498947	0.00249474	+	0.999997i	$0.499206\pi$
$168$	0.711781	0.0549151
$169$	−7.49961	−0.576893
$170$	1.25860	0.0965300
$171$	−5.75425	−0.440038
$172$	1.53504	0.117046
$173$	17.2202	1.30923	0.654613	−	0.755964i	$-0.272832\pi$
$173$	17.2202	1.30923	0.654613	+	0.755964i	$0.272832\pi$
$174$	0.0810233	0.00614236
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	2.34906	0.176566
$178$	−3.70930	−0.278023
$179$	−18.2017	−1.36046	−0.680230	−	0.732999i	$-0.738120\pi$
$179$	−18.2017	−1.36046	−0.680230	+	0.732999i	$0.738120\pi$
$180$	0.467840	0.0348708
$181$	−9.54258	−0.709294	−0.354647	−	0.935000i	$-0.615399\pi$
$181$	−9.54258	−0.709294	−0.354647	+	0.935000i	$0.615399\pi$
$182$	−3.18211	−0.235873
$183$	0.687473	0.0508195
$184$	7.86170	0.579572
$185$	6.23609	0.458486
$186$	0.985814	0.0722834
$187$	0	0
$188$	−0.929741	−0.0678083
$189$	−1.44350	−0.104999
$190$	−2.65471	−0.192593
$191$	10.0070	0.724078	0.362039	−	0.932163i	$-0.382081\pi$
$191$	10.0070	0.724078	0.362039	+	0.932163i	$0.382081\pi$
$192$	−2.07283	−0.149593
$193$	−13.5332	−0.974141	−0.487071	−	0.873363i	$-0.661935\pi$
$193$	−13.5332	−0.974141	−0.487071	+	0.873363i	$0.661935\pi$
$194$	−4.22107	−0.303055
$195$	0.569845	0.0408075
$196$	−0.159077	−0.0113627
$197$	−22.2486	−1.58515	−0.792575	−	0.609774i	$-0.791260\pi$
$197$	−22.2486	−1.58515	−0.792575	+	0.609774i	$0.791260\pi$
$198$	0	0
$199$	−9.44551	−0.669575	−0.334787	−	0.942294i	$-0.608664\pi$
$199$	−9.44551	−0.669575	−0.334787	+	0.942294i	$0.608664\pi$
$200$	2.92945	0.207143
$201$	−3.64727	−0.257259
$202$	20.2499	1.42478
$203$	−0.245772	−0.0172498
$204$	−0.0358540	−0.00251028
$205$	6.05663	0.423013
$206$	−1.34587	−0.0937709
$207$	−7.89260	−0.548573
$208$	8.57565	0.594615
$209$	0	0
$210$	−0.329669	−0.0227493
$211$	−4.75884	−0.327612	−0.163806	−	0.986493i	$-0.552377\pi$
$211$	−4.75884	−0.327612	−0.163806	+	0.986493i	$0.552377\pi$
$212$	0.729889	0.0501290
$213$	0.539389	0.0369584
$214$	−4.49204	−0.307070
$215$	−9.64965	−0.658101
$216$	4.22866	0.287724
$217$	−2.99032	−0.202996
$218$	−8.25431	−0.559052
$219$	0.0243395	0.00164471
$220$	0	0
$221$	2.17553	0.146342
$222$	2.05584	0.137979
$223$	19.6049	1.31284	0.656422	−	0.754394i	$-0.272069\pi$
$223$	19.6049	1.31284	0.656422	+	0.754394i	$0.272069\pi$
$224$	0.897683	0.0599789
$225$	−2.94096	−0.196064
$226$	12.9483	0.861309
$227$	−8.13362	−0.539847	−0.269924	−	0.962882i	$-0.586998\pi$
$227$	−8.13362	−0.539847	−0.269924	+	0.962882i	$0.586998\pi$
$228$	0.0756253	0.00500841
$229$	12.5891	0.831910	0.415955	−	0.909385i	$-0.363447\pi$
$229$	12.5891	0.831910	0.415955	+	0.909385i	$0.363447\pi$
$230$	−3.64123	−0.240096
$231$	0	0
$232$	0.719976	0.0472688
$233$	−2.77199	−0.181599	−0.0907996	−	0.995869i	$-0.528942\pi$
$233$	−2.77199	−0.181599	−0.0907996	+	0.995869i	$0.528942\pi$
$234$	−9.35846	−0.611782
$235$	5.84459	0.381259
$236$	1.53795	0.100112
$237$	1.53522	0.0997235
$238$	−1.25860	−0.0815827
$239$	1.04527	0.0676130	0.0338065	−	0.999428i	$-0.489237\pi$
$239$	1.04527	0.0676130	0.0338065	+	0.999428i	$0.489237\pi$
$240$	0.888445	0.0573489
$241$	−24.2918	−1.56477	−0.782385	−	0.622796i	$-0.785997\pi$
$241$	−24.2918	−1.56477	−0.782385	+	0.622796i	$0.785997\pi$
$242$	0	0
$243$	−6.38902	−0.409856
$244$	0.450094	0.0288143
$245$	1.00000	0.0638877
$246$	1.99668	0.127304
$247$	−4.58877	−0.291976
$248$	8.75998	0.556259
$249$	3.98749	0.252697
$250$	−1.35681	−0.0858120
$251$	−15.7101	−0.991610	−0.495805	−	0.868434i	$-0.665127\pi$
$251$	−15.7101	−0.991610	−0.495805	+	0.868434i	$0.665127\pi$
$252$	−0.467840	−0.0294712
$253$	0	0
$254$	13.8112	0.866590
$255$	0.225387	0.0141143
$256$	−3.79306	−0.237066
$257$	24.4875	1.52749	0.763745	−	0.645519i	$-0.223359\pi$
$257$	24.4875	1.52749	0.763745	+	0.645519i	$0.223359\pi$
$258$	−3.18119	−0.198052
$259$	−6.23609	−0.387492
$260$	0.373082	0.0231376
$261$	−0.722806	−0.0447406
$262$	−16.9455	−1.04690
$263$	21.7093	1.33865	0.669325	−	0.742969i	$-0.266583\pi$
$263$	21.7093	1.33865	0.669325	+	0.742969i	$0.266583\pi$
$264$	0	0
$265$	−4.58827	−0.281855
$266$	2.65471	0.162771
$267$	−0.664253	−0.0406516
$268$	−2.38790	−0.145864
$269$	−10.5726	−0.644621	−0.322310	−	0.946634i	$-0.604459\pi$
$269$	−10.5726	−0.644621	−0.322310	+	0.946634i	$0.604459\pi$
$270$	−1.95855	−0.119194
$271$	−23.8119	−1.44647	−0.723235	−	0.690602i	$-0.757346\pi$
$271$	−23.8119	−1.44647	−0.723235	+	0.690602i	$0.757346\pi$
$272$	3.39187	0.205662
$273$	−0.569845	−0.0344886
$274$	−22.5448	−1.36198
$275$	0	0
$276$	0.103729	0.00624373
$277$	0.357431	0.0214759	0.0107380	−	0.999942i	$-0.496582\pi$
$277$	0.357431	0.0214759	0.0107380	+	0.999942i	$0.496582\pi$
$278$	0.570499	0.0342162
$279$	−8.79441	−0.526508
$280$	−2.92945	−0.175068
$281$	6.93387	0.413640	0.206820	−	0.978379i	$-0.433689\pi$
$281$	6.93387	0.413640	0.206820	+	0.978379i	$0.433689\pi$
$282$	1.92678	0.114738
$283$	12.2813	0.730050	0.365025	−	0.930998i	$-0.381061\pi$
$283$	12.2813	0.730050	0.365025	+	0.930998i	$0.381061\pi$
$284$	0.353143	0.0209552
$285$	−0.475400	−0.0281603
$286$	0	0
$287$	−6.05663	−0.357511
$288$	2.64005	0.155567
$289$	−16.1395	−0.949384
$290$	−0.333465	−0.0195817
$291$	−0.755901	−0.0443117
$292$	0.0159353	0.000932543 0
$293$	−18.4314	−1.07678	−0.538388	−	0.842697i	$-0.680966\pi$
$293$	−18.4314	−1.07678	−0.538388	+	0.842697i	$0.680966\pi$
$294$	0.329669	0.0192267
$295$	−9.66792	−0.562888
$296$	18.2683	1.06182
$297$	0	0
$298$	13.8051	0.799708
$299$	−6.29401	−0.363992
$300$	0.0386517	0.00223155
$301$	9.64965	0.556197
$302$	−6.92843	−0.398686
$303$	3.62631	0.208326
$304$	−7.15434	−0.410329
$305$	−2.82941	−0.162011
$306$	−3.70149	−0.211600
$307$	−27.8266	−1.58815	−0.794074	−	0.607821i	$-0.792044\pi$
$307$	−27.8266	−1.58815	−0.794074	+	0.607821i	$0.792044\pi$
$308$	0	0
$309$	−0.241015	−0.0137109
$310$	−4.05728	−0.230438
$311$	−18.5140	−1.04983	−0.524916	−	0.851154i	$-0.675903\pi$
$311$	−18.5140	−1.04983	−0.524916	+	0.851154i	$0.675903\pi$
$312$	1.66933	0.0945074
$313$	−9.40487	−0.531595	−0.265797	−	0.964029i	$-0.585635\pi$
$313$	−9.40487	−0.531595	−0.265797	+	0.964029i	$0.585635\pi$
$314$	−5.23201	−0.295259
$315$	2.94096	0.165705
$316$	1.00512	0.0565427
$317$	−14.1532	−0.794924	−0.397462	−	0.917619i	$-0.630109\pi$
$317$	−14.1532	−0.794924	−0.397462	+	0.917619i	$0.630109\pi$
$318$	−1.51261	−0.0848229
$319$	0	0
$320$	8.53106	0.476901
$321$	−0.804426	−0.0448987
$322$	3.64123	0.202918
$323$	−1.81496	−0.100987
$324$	−1.34773	−0.0748737
$325$	−2.34529	−0.130093
$326$	12.1848	0.674852
$327$	−1.47817	−0.0817427
$328$	17.7426	0.979670
$329$	−5.84459	−0.322222
$330$	0	0
$331$	−24.4577	−1.34432	−0.672159	−	0.740407i	$-0.734633\pi$
$331$	−24.4577	−1.34432	−0.672159	+	0.740407i	$0.734633\pi$
$332$	2.61064	0.143278
$333$	−18.3401	−1.00503
$334$	−0.0874844	−0.00478693
$335$	15.0109	0.820135
$336$	−0.888445	−0.0484686
$337$	23.7769	1.29521	0.647605	−	0.761976i	$-0.275771\pi$
$337$	23.7769	1.29521	0.647605	+	0.761976i	$0.275771\pi$
$338$	10.1755	0.553475
$339$	2.31876	0.125938
$340$	0.147563	0.00800272
$341$	0	0
$342$	7.80740	0.422176
$343$	−1.00000	−0.0539949
$344$	−28.2682	−1.52412
$345$	−0.652064	−0.0351060
$346$	−23.3644	−1.25608
$347$	2.31154	0.124090	0.0620450	−	0.998073i	$-0.480238\pi$
$347$	2.31154	0.124090	0.0620450	+	0.998073i	$0.480238\pi$
$348$	0.00949949	0.000509226 0
$349$	−36.2674	−1.94135	−0.970675	−	0.240395i	$-0.922723\pi$
$349$	−36.2674	−1.94135	−0.970675	+	0.240395i	$0.922723\pi$
$350$	1.35681	0.0725243
$351$	−3.38543	−0.180701
$352$	0	0
$353$	−10.6567	−0.567200	−0.283600	−	0.958943i	$-0.591529\pi$
$353$	−10.6567	−0.567200	−0.283600	+	0.958943i	$0.591529\pi$
$354$	−3.18721	−0.169398
$355$	−2.21995	−0.117822
$356$	−0.434892	−0.0230492
$357$	−0.225387	−0.0119287
$358$	24.6962	1.30523
$359$	−22.4588	−1.18533	−0.592664	−	0.805450i	$-0.701924\pi$
$359$	−22.4588	−1.18533	−0.592664	+	0.805450i	$0.701924\pi$
$360$	−8.61540	−0.454072
$361$	−15.1718	−0.798514
$362$	12.9474	0.680502
$363$	0	0
$364$	−0.373082	−0.0195548
$365$	−0.100173	−0.00524331
$366$	−0.932768	−0.0487566
$367$	15.1093	0.788698	0.394349	−	0.918961i	$-0.370970\pi$
$367$	15.1093	0.788698	0.394349	+	0.918961i	$0.370970\pi$
$368$	−9.81297	−0.511537
$369$	−17.8123	−0.927272
$370$	−8.46116	−0.439875
$371$	4.58827	0.238211
$372$	0.115581	0.00599258
$373$	22.7153	1.17616	0.588078	−	0.808804i	$-0.299885\pi$
$373$	22.7153	1.17616	0.588078	+	0.808804i	$0.299885\pi$
$374$	0	0
$375$	−0.242974	−0.0125471
$376$	17.1214	0.882970
$377$	−0.576407	−0.0296865
$378$	1.95855	0.100737
$379$	−1.50696	−0.0774072	−0.0387036	−	0.999251i	$-0.512323\pi$
$379$	−1.50696	−0.0774072	−0.0387036	+	0.999251i	$0.512323\pi$
$380$	−0.311248	−0.0159667
$381$	2.47328	0.126710
$382$	−13.5775	−0.694686
$383$	−14.8062	−0.756564	−0.378282	−	0.925690i	$-0.623485\pi$
$383$	−14.8062	−0.756564	−0.378282	+	0.925690i	$0.623485\pi$
$384$	2.37620	0.121260
$385$	0	0
$386$	18.3619	0.934598
$387$	28.3793	1.44260
$388$	−0.494895	−0.0251245
$389$	−33.6017	−1.70368	−0.851838	−	0.523806i	$-0.824512\pi$
$389$	−33.6017	−1.70368	−0.851838	+	0.523806i	$0.824512\pi$
$390$	−0.773170	−0.0391510
$391$	−2.48943	−0.125896
$392$	2.92945	0.147960
$393$	−3.03457	−0.153074
$394$	30.1871	1.52080
$395$	−6.31847	−0.317917
$396$	0	0
$397$	−23.7402	−1.19149	−0.595744	−	0.803174i	$-0.703143\pi$
$397$	−23.7402	−1.19149	−0.595744	+	0.803174i	$0.703143\pi$
$398$	12.8157	0.642394
$399$	0.475400	0.0237998
$400$	−3.65654	−0.182827
$401$	25.6299	1.27990	0.639949	−	0.768417i	$-0.278955\pi$
$401$	25.6299	1.27990	0.639949	+	0.768417i	$0.278955\pi$
$402$	4.94864	0.246816
$403$	−7.01317	−0.349351
$404$	2.37418	0.118120
$405$	8.47216	0.420985
$406$	0.333465	0.0165496
$407$	0	0
$408$	0.660260	0.0326877
$409$	−26.5551	−1.31306	−0.656532	−	0.754299i	$-0.727977\pi$
$409$	−26.5551	−1.31306	−0.656532	+	0.754299i	$0.727977\pi$
$410$	−8.21767	−0.405842
$411$	−4.03728	−0.199145
$412$	−0.157795	−0.00777398
$413$	9.66792	0.475727
$414$	10.7087	0.526305
$415$	−16.4112	−0.805592
$416$	2.10533	0.103222
$417$	0.102164	0.00500298
$418$	0	0
$419$	−34.6824	−1.69435	−0.847174	−	0.531316i	$-0.821698\pi$
$419$	−34.6824	−1.69435	−0.847174	+	0.531316i	$0.821698\pi$
$420$	−0.0386517	−0.00188601
$421$	24.7907	1.20823	0.604113	−	0.796899i	$-0.293527\pi$
$421$	24.7907	1.20823	0.604113	+	0.796899i	$0.293527\pi$
$422$	6.45682	0.314313
$423$	−17.1887	−0.835744
$424$	−13.4411	−0.652757
$425$	−0.927617	−0.0449961
$426$	−0.731847	−0.0354581
$427$	2.82941	0.136925
$428$	−0.526665	−0.0254573
$429$	0	0
$430$	13.0927	0.631387
$431$	6.59999	0.317910	0.158955	−	0.987286i	$-0.449187\pi$
$431$	6.59999	0.317910	0.158955	+	0.987286i	$0.449187\pi$
$432$	−5.27822	−0.253948
$433$	20.0200	0.962101	0.481050	−	0.876693i	$-0.340255\pi$
$433$	20.0200	0.962101	0.481050	+	0.876693i	$0.340255\pi$
$434$	4.05728	0.194756
$435$	−0.0597162	−0.00286317
$436$	−0.967767	−0.0463476
$437$	5.25085	0.251182
$438$	−0.0330240	−0.00157795
$439$	26.6216	1.27058	0.635290	−	0.772274i	$-0.280881\pi$
$439$	26.6216	1.27058	0.635290	+	0.772274i	$0.280881\pi$
$440$	0	0
$441$	−2.94096	−0.140046
$442$	−2.95178	−0.140402
$443$	7.35380	0.349389	0.174695	−	0.984623i	$-0.444106\pi$
$443$	7.35380	0.349389	0.174695	+	0.984623i	$0.444106\pi$
$444$	0.241035	0.0114390
$445$	2.73384	0.129597
$446$	−26.6001	−1.25955
$447$	2.47219	0.116931
$448$	−8.53106	−0.403055
$449$	1.75184	0.0826744	0.0413372	−	0.999145i	$-0.486838\pi$
$449$	1.75184	0.0826744	0.0413372	+	0.999145i	$0.486838\pi$
$450$	3.99032	0.188105
$451$	0	0
$452$	1.51811	0.0714059
$453$	−1.24073	−0.0582946
$454$	11.0357	0.517933
$455$	2.34529	0.109949
$456$	−1.39266	−0.0652173
$457$	−17.7181	−0.828817	−0.414409	−	0.910091i	$-0.636012\pi$
$457$	−17.7181	−0.828817	−0.414409	+	0.910091i	$0.636012\pi$
$458$	−17.0809	−0.798140
$459$	−1.33902	−0.0624999
$460$	−0.426912	−0.0199049
$461$	−20.6171	−0.960235	−0.480118	−	0.877204i	$-0.659406\pi$
$461$	−20.6171	−0.960235	−0.480118	+	0.877204i	$0.659406\pi$
$462$	0	0
$463$	−13.1323	−0.610309	−0.305154	−	0.952303i	$-0.598708\pi$
$463$	−13.1323	−0.610309	−0.305154	+	0.952303i	$0.598708\pi$
$464$	−0.898675	−0.0417199
$465$	−0.726570	−0.0336939
$466$	3.76105	0.174228
$467$	30.8738	1.42867	0.714334	−	0.699805i	$-0.246730\pi$
$467$	30.8738	1.42867	0.714334	+	0.699805i	$0.246730\pi$
$468$	−1.09722	−0.0507191
$469$	−15.0109	−0.693141
$470$	−7.92997	−0.365782
$471$	−0.936938	−0.0431718
$472$	−28.3217	−1.30361
$473$	0	0
$474$	−2.08300	−0.0956754
$475$	1.95659	0.0897743
$476$	−0.147563	−0.00676353
$477$	13.4939	0.617844
$478$	−1.41823	−0.0648684
$479$	36.4945	1.66748	0.833739	−	0.552159i	$-0.186196\pi$
$479$	36.4945	1.66748	0.833739	+	0.552159i	$0.186196\pi$
$480$	0.218114	0.00995548
$481$	−14.6254	−0.666863
$482$	32.9592	1.50125
$483$	0.652064	0.0296700
$484$	0	0
$485$	3.11103	0.141265
$486$	8.66866	0.393218
$487$	−29.0277	−1.31537	−0.657685	−	0.753293i	$-0.728464\pi$
$487$	−29.0277	−1.31537	−0.657685	+	0.753293i	$0.728464\pi$
$488$	−8.28861	−0.375208
$489$	2.18203	0.0986746
$490$	−1.35681	−0.0612943
$491$	−28.1964	−1.27249	−0.636244	−	0.771488i	$-0.719513\pi$
$491$	−28.1964	−1.27249	−0.636244	+	0.771488i	$0.719513\pi$
$492$	0.234099	0.0105540
$493$	−0.227982	−0.0102678
$494$	6.22607	0.280124
$495$	0	0
$496$	−10.9342	−0.490961
$497$	2.21995	0.0995782
$498$	−5.41025	−0.242439
$499$	−12.1817	−0.545326	−0.272663	−	0.962110i	$-0.587904\pi$
$499$	−12.1817	−0.545326	−0.272663	+	0.962110i	$0.587904\pi$
$500$	−0.159077	−0.00711415
$501$	−0.0156665	−0.000699929 0
$502$	21.3155	0.951357
$503$	−9.57390	−0.426879	−0.213439	−	0.976956i	$-0.568467\pi$
$503$	−9.57390	−0.426879	−0.213439	+	0.976956i	$0.568467\pi$
$504$	8.61540	0.383761
$505$	−14.9247	−0.664140
$506$	0	0
$507$	1.82221	0.0809272
$508$	1.61927	0.0718437
$509$	−28.2988	−1.25432	−0.627161	−	0.778889i	$-0.715783\pi$
$509$	−28.2988	−1.25432	−0.627161	+	0.778889i	$0.715783\pi$
$510$	−0.305807	−0.0135413
$511$	0.100173	0.00443141
$512$	24.7057	1.09185
$513$	2.82433	0.124697
$514$	−33.2248	−1.46548
$515$	0.991937	0.0437100
$516$	−0.372975	−0.0164193
$517$	0	0
$518$	8.46116	0.371762
$519$	−4.18406	−0.183660
$520$	−6.87041	−0.301288
$521$	−6.04860	−0.264994	−0.132497	−	0.991183i	$-0.542299\pi$
$521$	−6.04860	−0.264994	−0.132497	+	0.991183i	$0.542299\pi$
$522$	0.980708	0.0429244
$523$	−15.3496	−0.671192	−0.335596	−	0.942006i	$-0.608938\pi$
$523$	−15.3496	−0.671192	−0.335596	+	0.942006i	$0.608938\pi$
$524$	−1.98676	−0.0867919
$525$	0.242974	0.0106043
$526$	−29.4553	−1.28431
$527$	−2.77387	−0.120832
$528$	0	0
$529$	−15.7979	−0.686864
$530$	6.22539	0.270414
$531$	28.4330	1.23389
$532$	0.311248	0.0134943
$533$	−14.2046	−0.615268
$534$	0.901263	0.0390015
$535$	3.31075	0.143136
$536$	43.9738	1.89938
$537$	4.42254	0.190847
$538$	14.3449	0.618453
$539$	0	0
$540$	−0.229628	−0.00988162
$541$	31.1468	1.33911	0.669553	−	0.742765i	$-0.266486\pi$
$541$	31.1468	1.33911	0.669553	+	0.742765i	$0.266486\pi$
$542$	32.3081	1.38775
$543$	2.31860	0.0995006
$544$	0.832706	0.0357020
$545$	6.08363	0.260594
$546$	0.773170	0.0330886
$547$	−2.82444	−0.120764	−0.0603821	−	0.998175i	$-0.519232\pi$
$547$	−2.82444	−0.120764	−0.0603821	+	0.998175i	$0.519232\pi$
$548$	−2.64324	−0.112914
$549$	8.32119	0.355140
$550$	0	0
$551$	0.480874	0.0204859
$552$	−1.91019	−0.0813030
$553$	6.31847	0.268689
$554$	−0.484965	−0.0206042
$555$	−1.51521	−0.0643170
$556$	0.0668875	0.00283666
$557$	−5.32104	−0.225460	−0.112730	−	0.993626i	$-0.535959\pi$
$557$	−5.32104	−0.225460	−0.112730	+	0.993626i	$0.535959\pi$
$558$	11.9323	0.505135
$559$	22.6313	0.957200
$560$	3.65654	0.154517
$561$	0	0
$562$	−9.40792	−0.396849
$563$	−1.88609	−0.0794893	−0.0397447	−	0.999210i	$-0.512654\pi$
$563$	−1.88609	−0.0794893	−0.0397447	+	0.999210i	$0.512654\pi$
$564$	0.225903	0.00951223
$565$	−9.54323	−0.401487
$566$	−16.6634	−0.700415
$567$	−8.47216	−0.355797
$568$	−6.50322	−0.272869
$569$	−4.30097	−0.180306	−0.0901529	−	0.995928i	$-0.528736\pi$
$569$	−4.30097	−0.180306	−0.0901529	+	0.995928i	$0.528736\pi$
$570$	0.645026	0.0270171
$571$	10.5416	0.441153	0.220577	−	0.975370i	$-0.429206\pi$
$571$	10.5416	0.441153	0.220577	+	0.975370i	$0.429206\pi$
$572$	0	0
$573$	−2.43143	−0.101575
$574$	8.21767	0.342999
$575$	2.68368	0.111917
$576$	−25.0895	−1.04540
$577$	−2.05286	−0.0854618	−0.0427309	−	0.999087i	$-0.513606\pi$
$577$	−2.05286	−0.0854618	−0.0427309	+	0.999087i	$0.513606\pi$
$578$	21.8982	0.910845
$579$	3.28822	0.136654
$580$	−0.0390967	−0.00162340
$581$	16.4112	0.680849
$582$	1.02561	0.0425129
$583$	0	0
$584$	−0.293453	−0.0121432
$585$	6.89742	0.285173
$586$	25.0079	1.03307
$587$	25.9972	1.07302	0.536510	−	0.843894i	$-0.319742\pi$
$587$	25.9972	1.07302	0.536510	+	0.843894i	$0.319742\pi$
$588$	0.0386517	0.00159397
$589$	5.85081	0.241079
$590$	13.1175	0.540039
$591$	5.40585	0.222367
$592$	−22.8025	−0.937177
$593$	11.1931	0.459645	0.229823	−	0.973233i	$-0.426185\pi$
$593$	11.1931	0.459645	0.229823	+	0.973233i	$0.426185\pi$
$594$	0	0
$595$	0.927617	0.0380286
$596$	1.61856	0.0662989
$597$	2.29502	0.0939287
$598$	8.53975	0.349216
$599$	33.8637	1.38363	0.691817	−	0.722073i	$-0.256811\pi$
$599$	33.8637	1.38363	0.691817	+	0.722073i	$0.256811\pi$
$600$	−0.711781	−0.0290583
$601$	−42.1489	−1.71929	−0.859645	−	0.510892i	$-0.829315\pi$
$601$	−42.1489	−1.71929	−0.859645	+	0.510892i	$0.829315\pi$
$602$	−13.0927	−0.533619
$603$	−44.1466	−1.79779
$604$	−0.812316	−0.0330527
$605$	0	0
$606$	−4.92020	−0.199870
$607$	22.4797	0.912422	0.456211	−	0.889872i	$-0.349206\pi$
$607$	22.4797	0.912422	0.456211	+	0.889872i	$0.349206\pi$
$608$	−1.75639	−0.0712312
$609$	0.0597162	0.00241982
$610$	3.83896	0.155435
$611$	−13.7073	−0.554536
$612$	−0.433977	−0.0175425
$613$	8.61975	0.348148	0.174074	−	0.984733i	$-0.444307\pi$
$613$	8.61975	0.348148	0.174074	+	0.984733i	$0.444307\pi$
$614$	37.7553	1.52368
$615$	−1.47160	−0.0593408
$616$	0	0
$617$	−1.79131	−0.0721154	−0.0360577	−	0.999350i	$-0.511480\pi$
$617$	−1.79131	−0.0721154	−0.0360577	+	0.999350i	$0.511480\pi$
$618$	0.327011	0.0131543
$619$	12.4154	0.499016	0.249508	−	0.968373i	$-0.419731\pi$
$619$	12.4154	0.499016	0.249508	+	0.968373i	$0.419731\pi$
$620$	−0.475691	−0.0191042
$621$	3.87389	0.155454
$622$	25.1199	1.00722
$623$	−2.73384	−0.109529
$624$	−2.08366	−0.0834132
$625$	1.00000	0.0400000
$626$	12.7606	0.510016
$627$	0	0
$628$	−0.613421	−0.0244782
$629$	−5.78471	−0.230651
$630$	−3.99032	−0.158978
$631$	−6.81348	−0.271240	−0.135620	−	0.990761i	$-0.543303\pi$
$631$	−6.81348	−0.271240	−0.135620	+	0.990761i	$0.543303\pi$
$632$	−18.5096	−0.736273
$633$	1.15627	0.0459578
$634$	19.2032	0.762655
$635$	−10.1792	−0.403948
$636$	−0.177344	−0.00703215
$637$	−2.34529	−0.0929238
$638$	0	0
$639$	6.52878	0.258274
$640$	−9.77963	−0.386574
$641$	−48.3163	−1.90838	−0.954190	−	0.299202i	$-0.903280\pi$
$641$	−48.3163	−1.90838	−0.954190	+	0.299202i	$0.903280\pi$
$642$	1.09145	0.0430761
$643$	−45.7624	−1.80469	−0.902346	−	0.431012i	$-0.858157\pi$
$643$	−45.7624	−1.80469	−0.902346	+	0.431012i	$0.858157\pi$
$644$	0.426912	0.0168227
$645$	2.34462	0.0923192
$646$	2.46255	0.0968879
$647$	−14.5828	−0.573310	−0.286655	−	0.958034i	$-0.592543\pi$
$647$	−14.5828	−0.573310	−0.286655	+	0.958034i	$0.592543\pi$
$648$	24.8188	0.974973
$649$	0	0
$650$	3.18211	0.124812
$651$	0.726570	0.0284765
$652$	1.42859	0.0559479
$653$	17.5533	0.686913	0.343456	−	0.939169i	$-0.388402\pi$
$653$	17.5533	0.686913	0.343456	+	0.939169i	$0.388402\pi$
$654$	2.00558	0.0784245
$655$	12.4893	0.487996
$656$	−22.1463	−0.864668
$657$	0.294606	0.0114937
$658$	7.92997	0.309142
$659$	−15.1180	−0.588915	−0.294458	−	0.955665i	$-0.595139\pi$
$659$	−15.1180	−0.588915	−0.294458	+	0.955665i	$0.595139\pi$
$660$	0	0
$661$	−38.6231	−1.50226	−0.751132	−	0.660152i	$-0.770492\pi$
$661$	−38.6231	−1.50226	−0.751132	+	0.660152i	$0.770492\pi$
$662$	33.1844	1.28975
$663$	−0.528598	−0.0205291
$664$	−48.0756	−1.86570
$665$	−1.95659	−0.0758732
$666$	24.8840	0.964234
$667$	0.659572	0.0255387
$668$	−0.0102570	−0.000396856 0
$669$	−4.76349	−0.184167
$670$	−20.3669	−0.786843
$671$	0	0
$672$	−0.218114	−0.00841392
$673$	−41.8975	−1.61503	−0.807515	−	0.589847i	$-0.799188\pi$
$673$	−41.8975	−1.61503	−0.807515	+	0.589847i	$0.799188\pi$
$674$	−32.2606	−1.24263
$675$	1.44350	0.0555604
$676$	1.19302	0.0458853
$677$	15.8363	0.608637	0.304318	−	0.952570i	$-0.401571\pi$
$677$	15.8363	0.608637	0.304318	+	0.952570i	$0.401571\pi$
$678$	−3.14611	−0.120825
$679$	−3.11103	−0.119391
$680$	−2.71741	−0.104208
$681$	1.97626	0.0757304
$682$	0	0
$683$	16.7634	0.641434	0.320717	−	0.947175i	$-0.396076\pi$
$683$	16.7634	0.641434	0.320717	+	0.947175i	$0.396076\pi$
$684$	0.915370	0.0350000
$685$	16.6161	0.634869
$686$	1.35681	0.0518031
$687$	−3.05882	−0.116701
$688$	35.2843	1.34520
$689$	10.7608	0.409955
$690$	0.884725	0.0336809
$691$	−0.259485	−0.00987129	−0.00493564	−	0.999988i	$-0.501571\pi$
$691$	−0.259485	−0.00987129	−0.00493564	+	0.999988i	$0.501571\pi$
$692$	−2.73934	−0.104134
$693$	0	0
$694$	−3.13631	−0.119053
$695$	−0.420472	−0.0159494
$696$	−0.174936	−0.00663092
$697$	−5.61823	−0.212806
$698$	49.2079	1.86254
$699$	0.673522	0.0254750
$700$	0.159077	0.00601255
$701$	14.0986	0.532498	0.266249	−	0.963904i	$-0.414216\pi$
$701$	14.0986	0.532498	0.266249	+	0.963904i	$0.414216\pi$
$702$	4.59337	0.173366
$703$	12.2014	0.460186
$704$	0	0
$705$	−1.42008	−0.0534834
$706$	14.4591	0.544176
$707$	14.9247	0.561301
$708$	−0.373681	−0.0140438
$709$	18.0034	0.676131	0.338065	−	0.941123i	$-0.390227\pi$
$709$	18.0034	0.676131	0.338065	+	0.941123i	$0.390227\pi$
$710$	3.01204	0.113040
$711$	18.5824	0.696894
$712$	8.00865	0.300137
$713$	8.02505	0.300540
$714$	0.305807	0.0114445
$715$	0	0
$716$	2.89548	0.108209
$717$	−0.253974	−0.00948483
$718$	30.4722	1.13721
$719$	−20.5769	−0.767387	−0.383694	−	0.923460i	$-0.625348\pi$
$719$	−20.5769	−0.767387	−0.383694	+	0.923460i	$0.625348\pi$
$720$	10.7538	0.400769
$721$	−0.991937	−0.0369417
$722$	20.5851	0.766100
$723$	5.90227	0.219508
$724$	1.51801	0.0564163
$725$	0.245772	0.00912774
$726$	0	0
$727$	−2.37912	−0.0882368	−0.0441184	−	0.999026i	$-0.514048\pi$
$727$	−2.37912	−0.0882368	−0.0441184	+	0.999026i	$0.514048\pi$
$728$	6.87041	0.254634
$729$	−23.8641	−0.883856
$730$	0.135916	0.00503047
$731$	8.95119	0.331072
$732$	−0.109361	−0.00404211
$733$	9.09774	0.336033	0.168016	−	0.985784i	$-0.446264\pi$
$733$	9.09774	0.336033	0.168016	+	0.985784i	$0.446264\pi$
$734$	−20.5004	−0.756682
$735$	−0.242974	−0.00896224
$736$	−2.40909	−0.0888002
$737$	0	0
$738$	24.1679	0.889631
$739$	12.3131	0.452944	0.226472	−	0.974018i	$-0.427281\pi$
$739$	12.3131	0.452944	0.226472	+	0.974018i	$0.427281\pi$
$740$	−0.992020	−0.0364674
$741$	1.11495	0.0409588
$742$	−6.22539	−0.228541
$743$	51.7175	1.89733	0.948666	−	0.316279i	$-0.102434\pi$
$743$	51.7175	1.89733	0.948666	+	0.316279i	$0.102434\pi$
$744$	−2.12845	−0.0780327
$745$	−10.1747	−0.372772
$746$	−30.8203	−1.12841
$747$	48.2646	1.76591
$748$	0	0
$749$	−3.31075	−0.120972
$750$	0.329669	0.0120378
$751$	13.7321	0.501093	0.250546	−	0.968105i	$-0.419390\pi$
$751$	13.7321	0.501093	0.250546	+	0.968105i	$0.419390\pi$
$752$	−21.3710	−0.779319
$753$	3.81714	0.139104
$754$	0.782072	0.0284814
$755$	5.10643	0.185842
$756$	0.229628	0.00835149
$757$	−49.2807	−1.79114	−0.895568	−	0.444924i	$-0.853231\pi$
$757$	−49.2807	−1.79114	−0.895568	+	0.444924i	$0.853231\pi$
$758$	2.04465	0.0742650
$759$	0	0
$760$	5.73172	0.207911
$761$	−12.4590	−0.451637	−0.225818	−	0.974169i	$-0.572506\pi$
$761$	−12.4590	−0.451637	−0.225818	+	0.974169i	$0.572506\pi$
$762$	−3.35576	−0.121566
$763$	−6.08363	−0.220242
$764$	−1.59188	−0.0575922
$765$	2.72809	0.0986343
$766$	20.0892	0.725853
$767$	22.6741	0.818714
$768$	0.921616	0.0332559
$769$	21.9501	0.791540	0.395770	−	0.918350i	$-0.370478\pi$
$769$	21.9501	0.791540	0.395770	+	0.918350i	$0.370478\pi$
$770$	0	0
$771$	−5.94983	−0.214278
$772$	2.15282	0.0774819
$773$	23.0657	0.829617	0.414808	−	0.909909i	$-0.363849\pi$
$773$	23.0657	0.829617	0.414808	+	0.909909i	$0.363849\pi$
$774$	−38.5052	−1.38404
$775$	2.99032	0.107415
$776$	9.11362	0.327160
$777$	1.51521	0.0543578
$778$	45.5910	1.63452
$779$	11.8503	0.424582
$780$	−0.0906494	−0.00324577
$781$	0	0
$782$	3.37767	0.120785
$783$	0.354772	0.0126785
$784$	−3.65654	−0.130591
$785$	3.85612	0.137631
$786$	4.11732	0.146860
$787$	46.7274	1.66565	0.832826	−	0.553534i	$-0.186721\pi$
$787$	46.7274	1.66565	0.832826	+	0.553534i	$0.186721\pi$
$788$	3.53925	0.126081
$789$	−5.27479	−0.187788
$790$	8.57293	0.305011
$791$	9.54323	0.339318
$792$	0	0
$793$	6.63579	0.235644
$794$	32.2109	1.14312
$795$	1.11483	0.0395390
$796$	1.50257	0.0532570
$797$	49.0362	1.73695	0.868475	−	0.495732i	$-0.165100\pi$
$797$	49.0362	1.73695	0.868475	+	0.495732i	$0.165100\pi$
$798$	−0.645026	−0.0228337
$799$	−5.42154	−0.191800
$800$	−0.897683	−0.0317379
$801$	−8.04013	−0.284084
$802$	−34.7749	−1.22794
$803$	0	0
$804$	0.580198	0.0204620
$805$	−2.68368	−0.0945872
$806$	9.51551	0.335169
$807$	2.56886	0.0904282
$808$	−43.7211	−1.53810
$809$	9.38528	0.329969	0.164984	−	0.986296i	$-0.447243\pi$
$809$	9.38528	0.329969	0.164984	+	0.986296i	$0.447243\pi$
$810$	−11.4951	−0.403896
$811$	−9.21722	−0.323660	−0.161830	−	0.986819i	$-0.551740\pi$
$811$	−9.21722	−0.323660	−0.161830	+	0.986819i	$0.551740\pi$
$812$	0.0390967	0.00137203
$813$	5.78568	0.202913
$814$	0	0
$815$	−8.98048	−0.314573
$816$	−0.824137	−0.0288506
$817$	−18.8804	−0.660541
$818$	36.0301	1.25976
$819$	−6.89742	−0.241015
$820$	−0.963471	−0.0336459
$821$	17.3336	0.604946	0.302473	−	0.953158i	$-0.402188\pi$
$821$	17.3336	0.604946	0.302473	+	0.953158i	$0.402188\pi$
$822$	5.47781	0.191061
$823$	−42.7706	−1.49089	−0.745445	−	0.666567i	$-0.767763\pi$
$823$	−42.7706	−1.49089	−0.745445	+	0.666567i	$0.767763\pi$
$824$	2.90583	0.101229
$825$	0	0
$826$	−13.1175	−0.456416
$827$	−19.0832	−0.663589	−0.331794	−	0.943352i	$-0.607654\pi$
$827$	−19.0832	−0.663589	−0.331794	+	0.943352i	$0.607654\pi$
$828$	1.25553	0.0436328
$829$	−40.8201	−1.41774	−0.708870	−	0.705340i	$-0.750795\pi$
$829$	−40.8201	−1.41774	−0.708870	+	0.705340i	$0.750795\pi$
$830$	22.2668	0.772890
$831$	−0.0868465	−0.00301267
$832$	−20.0078	−0.693647
$833$	−0.927617	−0.0321400
$834$	−0.138617	−0.00479990
$835$	0.0644782	0.00223136
$836$	0	0
$837$	4.31653	0.149201
$838$	47.0573	1.62557
$839$	33.0074	1.13954	0.569771	−	0.821804i	$-0.307032\pi$
$839$	33.0074	1.13954	0.569771	+	0.821804i	$0.307032\pi$
$840$	0.711781	0.0245588
$841$	−28.9396	−0.997917
$842$	−33.6362	−1.15918
$843$	−1.68475	−0.0580259
$844$	0.757022	0.0260578
$845$	−7.49961	−0.257994
$846$	23.3218	0.801818
$847$	0	0
$848$	16.7772	0.576131
$849$	−2.98405	−0.102412
$850$	1.25860	0.0431695
$851$	16.7357	0.573691
$852$	−0.0858046	−0.00293962
$853$	−48.6092	−1.66435	−0.832173	−	0.554516i	$-0.812903\pi$
$853$	−48.6092	−1.66435	−0.832173	+	0.554516i	$0.812903\pi$
$854$	−3.83896	−0.131366
$855$	−5.75425	−0.196791
$856$	9.69867	0.331494
$857$	−18.1003	−0.618294	−0.309147	−	0.951014i	$-0.600043\pi$
$857$	−18.1003	−0.618294	−0.309147	+	0.951014i	$0.600043\pi$
$858$	0	0
$859$	−7.23154	−0.246737	−0.123368	−	0.992361i	$-0.539370\pi$
$859$	−7.23154	−0.246737	−0.123368	+	0.992361i	$0.539370\pi$
$860$	1.53504	0.0523444
$861$	1.47160	0.0501521
$862$	−8.95491	−0.305005
$863$	30.3494	1.03310	0.516552	−	0.856256i	$-0.327215\pi$
$863$	30.3494	1.03310	0.516552	+	0.856256i	$0.327215\pi$
$864$	−1.29581	−0.0440842
$865$	17.2202	0.585504
$866$	−27.1633	−0.923046
$867$	3.92149	0.133181
$868$	0.475691	0.0161460
$869$	0	0
$870$	0.0810233	0.00274695
$871$	−35.2050	−1.19288
$872$	17.8217	0.603519
$873$	−9.14944	−0.309662
$874$	−7.12438	−0.240986
$875$	−1.00000	−0.0338062
$876$	−0.00387187	−0.000130818 0
$877$	−32.3026	−1.09078	−0.545391	−	0.838182i	$-0.683619\pi$
$877$	−32.3026	−1.09078	−0.545391	+	0.838182i	$0.683619\pi$
$878$	−36.1203	−1.21900
$879$	4.47836	0.151051
$880$	0	0
$881$	23.1158	0.778792	0.389396	−	0.921070i	$-0.372684\pi$
$881$	23.1158	0.778792	0.389396	+	0.921070i	$0.372684\pi$
$882$	3.99032	0.134361
$883$	47.4436	1.59661	0.798303	−	0.602257i	$-0.205732\pi$
$883$	47.4436	1.59661	0.798303	+	0.602257i	$0.205732\pi$
$884$	−0.346078	−0.0116399
$885$	2.34906	0.0789626
$886$	−9.97768	−0.335207
$887$	49.3267	1.65623	0.828114	−	0.560560i	$-0.189414\pi$
$887$	49.3267	1.65623	0.828114	+	0.560560i	$0.189414\pi$
$888$	−4.43873	−0.148954
$889$	10.1792	0.341399
$890$	−3.70930	−0.124336
$891$	0	0
$892$	−3.11870	−0.104422
$893$	11.4354	0.382672
$894$	−3.35428	−0.112184
$895$	−18.2017	−0.608416
$896$	9.77963	0.326715
$897$	1.52928	0.0510612
$898$	−2.37691	−0.0793184
$899$	0.734936	0.0245115
$900$	0.467840	0.0155947
$901$	4.25616	0.141793
$902$	0	0
$903$	−2.34462	−0.0780240
$904$	−27.9564	−0.929816
$905$	−9.54258	−0.317206
$906$	1.68343	0.0559282
$907$	32.7141	1.08625	0.543126	−	0.839651i	$-0.317240\pi$
$907$	32.7141	1.08625	0.543126	+	0.839651i	$0.317240\pi$
$908$	1.29387	0.0429387
$909$	43.8930	1.45584
$910$	−3.18211	−0.105486
$911$	−15.9930	−0.529870	−0.264935	−	0.964266i	$-0.585351\pi$
$911$	−15.9930	−0.529870	−0.264935	+	0.964266i	$0.585351\pi$
$912$	1.73832	0.0575615
$913$	0	0
$914$	24.0400	0.795173
$915$	0.687473	0.0227272
$916$	−2.00264	−0.0661689
$917$	−12.4893	−0.412432
$918$	1.81679	0.0599629
$919$	−47.6485	−1.57178	−0.785890	−	0.618366i	$-0.787795\pi$
$919$	−47.6485	−1.57178	−0.785890	+	0.618366i	$0.787795\pi$
$920$	7.86170	0.259192
$921$	6.76115	0.222787
$922$	27.9734	0.921256
$923$	5.20642	0.171371
$924$	0	0
$925$	6.23609	0.205041
$926$	17.8179	0.585534
$927$	−2.91725	−0.0958151
$928$	−0.220625	−0.00724237
$929$	53.3770	1.75124	0.875622	−	0.482998i	$-0.160452\pi$
$929$	53.3770	1.75124	0.875622	+	0.482998i	$0.160452\pi$
$930$	0.985814	0.0323261
$931$	1.95659	0.0641245
$932$	0.440961	0.0144441
$933$	4.49842	0.147272
$934$	−41.8897	−1.37067
$935$	0	0
$936$	20.2056	0.660442
$937$	−13.0806	−0.427326	−0.213663	−	0.976907i	$-0.568539\pi$
$937$	−13.0806	−0.427326	−0.213663	+	0.976907i	$0.568539\pi$
$938$	20.3669	0.665004
$939$	2.28514	0.0745727
$940$	−0.929741	−0.0303248
$941$	40.1799	1.30983	0.654913	−	0.755704i	$-0.272705\pi$
$941$	40.1799	1.30983	0.654913	+	0.755704i	$0.272705\pi$
$942$	1.27124	0.0414193
$943$	16.2540	0.529304
$944$	35.3511	1.15058
$945$	−1.44350	−0.0469571
$946$	0	0
$947$	21.1138	0.686105	0.343053	−	0.939316i	$-0.388539\pi$
$947$	21.1138	0.686105	0.343053	+	0.939316i	$0.388539\pi$
$948$	−0.244219	−0.00793187
$949$	0.234936	0.00762634
$950$	−2.65471	−0.0861301
$951$	3.43887	0.111513
$952$	2.71741	0.0880717
$953$	36.3562	1.17769	0.588846	−	0.808245i	$-0.299582\pi$
$953$	36.3562	1.17769	0.588846	+	0.808245i	$0.299582\pi$
$954$	−18.3086	−0.592764
$955$	10.0070	0.323818
$956$	−0.166279	−0.00537784
$957$	0	0
$958$	−49.5160	−1.59979
$959$	−16.6161	−0.536562
$960$	−2.07283	−0.0669002
$961$	−22.0580	−0.711548
$962$	19.8439	0.639793
$963$	−9.73679	−0.313764
$964$	3.86426	0.124460
$965$	−13.5332	−0.435649
$966$	−0.884725	−0.0284656
$967$	3.01730	0.0970299	0.0485149	−	0.998822i	$-0.484551\pi$
$967$	3.01730	0.0970299	0.0485149	+	0.998822i	$0.484551\pi$
$968$	0	0
$969$	0.440989	0.0141666
$970$	−4.22107	−0.135530
$971$	49.6294	1.59268	0.796341	−	0.604847i	$-0.206766\pi$
$971$	49.6294	1.59268	0.796341	+	0.604847i	$0.206766\pi$
$972$	1.01635	0.0325994
$973$	0.420472	0.0134797
$974$	39.3849	1.26197
$975$	0.569845	0.0182497
$976$	10.3458	0.331162
$977$	−11.0956	−0.354979	−0.177490	−	0.984123i	$-0.556798\pi$
$977$	−11.0956	−0.354979	−0.177490	+	0.984123i	$0.556798\pi$
$978$	−2.96058	−0.0946691
$979$	0	0
$980$	−0.159077	−0.00508154
$981$	−17.8917	−0.571239
$982$	38.2571	1.22083
$983$	16.2497	0.518283	0.259142	−	0.965839i	$-0.416560\pi$
$983$	16.2497	0.518283	0.259142	+	0.965839i	$0.416560\pi$
$984$	−4.31099	−0.137429
$985$	−22.2486	−0.708901
$986$	0.309328	0.00985100
$987$	1.42008	0.0452018
$988$	0.729968	0.0232234
$989$	−25.8966	−0.823463
$990$	0	0
$991$	−31.8831	−1.01280	−0.506400	−	0.862299i	$-0.669024\pi$
$991$	−31.8831	−1.01280	−0.506400	+	0.862299i	$0.669024\pi$
$992$	−2.68436	−0.0852284
$993$	5.94259	0.188582
$994$	−3.01204	−0.0955360
$995$	−9.44551	−0.299443
$996$	−0.634318	−0.0200991
$997$	10.3751	0.328584	0.164292	−	0.986412i	$-0.447466\pi$
$997$	10.3751	0.328584	0.164292	+	0.986412i	$0.447466\pi$
$998$	16.5282	0.523190
$999$	9.00180	0.284804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bc.1.2	✓	5
11.10	odd	2		4235.2.a.bd.1.4	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bc.1.2	✓	5	1.1	even	1	trivial
4235.2.a.bd.1.4	yes	5	11.10	odd	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} +0.329669 q^{6} -1.00000 q^{7} +2.92945 q^{8} -2.94096 q^{9} +O(q^{10})\)	\(q-1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} +0.329669 q^{6} -1.00000 q^{7} +2.92945 q^{8} -2.94096 q^{9} -1.35681 q^{10} +0.0386517 q^{12} -2.34529 q^{13} +1.35681 q^{14} -0.242974 q^{15} -3.65654 q^{16} -0.927617 q^{17} +3.99032 q^{18} +1.95659 q^{19} -0.159077 q^{20} +0.242974 q^{21} +2.68368 q^{23} -0.711781 q^{24} +1.00000 q^{25} +3.18211 q^{26} +1.44350 q^{27} +0.159077 q^{28} +0.245772 q^{29} +0.329669 q^{30} +2.99032 q^{31} -0.897683 q^{32} +1.25860 q^{34} -1.00000 q^{35} +0.467840 q^{36} +6.23609 q^{37} -2.65471 q^{38} +0.569845 q^{39} +2.92945 q^{40} +6.05663 q^{41} -0.329669 q^{42} -9.64965 q^{43} -2.94096 q^{45} -3.64123 q^{46} +5.84459 q^{47} +0.888445 q^{48} +1.00000 q^{49} -1.35681 q^{50} +0.225387 q^{51} +0.373082 q^{52} -4.58827 q^{53} -1.95855 q^{54} -2.92945 q^{56} -0.475400 q^{57} -0.333465 q^{58} -9.66792 q^{59} +0.0386517 q^{60} -2.82941 q^{61} -4.05728 q^{62} +2.94096 q^{63} +8.53106 q^{64} -2.34529 q^{65} +15.0109 q^{67} +0.147563 q^{68} -0.652064 q^{69} +1.35681 q^{70} -2.21995 q^{71} -8.61540 q^{72} -0.100173 q^{73} -8.46116 q^{74} -0.242974 q^{75} -0.311248 q^{76} -0.773170 q^{78} -6.31847 q^{79} -3.65654 q^{80} +8.47216 q^{81} -8.21767 q^{82} -16.4112 q^{83} -0.0386517 q^{84} -0.927617 q^{85} +13.0927 q^{86} -0.0597162 q^{87} +2.73384 q^{89} +3.99032 q^{90} +2.34529 q^{91} -0.426912 q^{92} -0.726570 q^{93} -7.92997 q^{94} +1.95659 q^{95} +0.218114 q^{96} +3.11103 q^{97} -1.35681 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97}+O(q^{100}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^12 - 6 * q^13 + 2 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 5 * q^23 - 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 - 4 * q^28 - 11 * q^29 - 9 * q^30 - 2 * q^31 - 7 * q^32 + 8 * q^34 - 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 - 2 * q^39 - 6 * q^40 - 13 * q^41 + 9 * q^42 - 10 * q^43 + 7 * q^45 - 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 - 30 * q^51 + 8 * q^52 - 14 * q^53 - 16 * q^54 + 6 * q^56 - 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 - 20 * q^61 + 15 * q^62 - 7 * q^63 - 6 * q^64 - 6 * q^65 - 9 * q^67 - 3 * q^68 - 30 * q^69 - 10 * q^71 - 38 * q^72 - 15 * q^73 + 19 * q^74 + 2 * q^75 + 5 * q^76 + 21 * q^78 - 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 - 8 * q^83 - 3 * q^84 - 2 * q^85 - 29 * q^86 + 22 * q^87 + 7 * q^89 + 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 + 14 * q^94 - 7 * q^95 + 18 * q^96 + 21 * q^97

Introduction

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Database

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