LMFDB - Embedded newform 4235.2.a.u.1.4

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:	$4$
Coefficient field:	4.4.15952.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 2x + 1 $ x^4 - 6x^2 - 2x + 1
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			1.4
Root			$-2.21161$ 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)

$f(q)$	$=$	$q+2.21161 q^{2} -1.45216 q^{3} +2.89124 q^{4} +1.00000 q^{5} -3.21161 q^{6} +1.00000 q^{7} +1.97107 q^{8} -0.891236 q^{9} +O(q^{10})$	\(q+2.21161 q^{2} -1.45216 q^{3} +2.89124 q^{4} +1.00000 q^{5} -3.21161 q^{6} +1.00000 q^{7} +1.97107 q^{8} -0.891236 q^{9} +2.21161 q^{10} -4.19853 q^{12} -6.19853 q^{13} +2.21161 q^{14} -1.45216 q^{15} -1.42323 q^{16} +6.75354 q^{17} -1.97107 q^{18} -6.55501 q^{19} +2.89124 q^{20} -1.45216 q^{21} -1.75946 q^{23} -2.86230 q^{24} +1.00000 q^{25} -13.7088 q^{26} +5.65069 q^{27} +2.89124 q^{28} +3.32754 q^{29} -3.21161 q^{30} +5.76662 q^{31} -7.08977 q^{32} +14.9362 q^{34} +1.00000 q^{35} -2.57677 q^{36} -9.70159 q^{37} -14.4971 q^{38} +9.00125 q^{39} +1.97107 q^{40} -7.98415 q^{41} -3.21161 q^{42} -5.27837 q^{43} -0.891236 q^{45} -3.89124 q^{46} -11.9493 q^{47} +2.06675 q^{48} +1.00000 q^{49} +2.21161 q^{50} -9.80721 q^{51} -17.9214 q^{52} +5.33623 q^{53} +12.4971 q^{54} +1.97107 q^{56} +9.51891 q^{57} +7.35924 q^{58} -14.1637 q^{59} -4.19853 q^{60} -10.9362 q^{61} +12.7535 q^{62} -0.891236 q^{63} -12.8334 q^{64} -6.19853 q^{65} +7.27837 q^{67} +19.5261 q^{68} +2.55501 q^{69} +2.21161 q^{70} +8.82029 q^{71} -1.75669 q^{72} -0.811402 q^{73} -21.4562 q^{74} -1.45216 q^{75} -18.9521 q^{76} +19.9073 q^{78} +4.53199 q^{79} -1.42323 q^{80} -5.53199 q^{81} -17.6579 q^{82} +0.639032 q^{83} -4.19853 q^{84} +6.75354 q^{85} -11.6737 q^{86} -4.83212 q^{87} +10.1001 q^{89} -1.97107 q^{90} -6.19853 q^{91} -5.08700 q^{92} -8.37405 q^{93} -26.4272 q^{94} -6.55501 q^{95} +10.2955 q^{96} -7.25363 q^{97} +2.21161 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 4 * q^9	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 4 q^{9} - 8 q^{12} - 16 q^{13} - 2 q^{15} + 12 q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} + 4 q^{20} - 2 q^{21} - 2 q^{23} + 10 q^{24} + 4 q^{25} + 2 q^{26} + 10 q^{27} + 4 q^{28} - 12 q^{29} - 4 q^{30} - 6 q^{31} - 12 q^{32} + 8 q^{34} + 4 q^{35} - 28 q^{36} - 6 q^{37} - 10 q^{38} - 12 q^{39} - 6 q^{40} - 18 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 2 q^{48} + 4 q^{49} - 4 q^{51} - 30 q^{52} + 34 q^{53} + 2 q^{54} - 6 q^{56} + 28 q^{57} + 32 q^{58} - 10 q^{59} - 8 q^{60} + 8 q^{61} + 22 q^{62} + 4 q^{63} - 16 q^{64} - 16 q^{65} + 14 q^{67} + 44 q^{68} - 10 q^{69} + 12 q^{72} - 2 q^{73} - 48 q^{74} - 2 q^{75} - 38 q^{76} + 14 q^{78} + 8 q^{79} + 12 q^{80} - 12 q^{81} - 34 q^{82} + 10 q^{83} - 8 q^{84} - 2 q^{85} - 24 q^{86} - 32 q^{87} + 10 q^{89} + 6 q^{90} - 16 q^{91} + 10 q^{92} - 26 q^{93} - 54 q^{94} - 6 q^{95} - 8 q^{96} - 34 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 4 * q^9 - 8 * q^12 - 16 * q^13 - 2 * q^15 + 12 * q^16 - 2 * q^17 + 6 * q^18 - 6 * q^19 + 4 * q^20 - 2 * q^21 - 2 * q^23 + 10 * q^24 + 4 * q^25 + 2 * q^26 + 10 * q^27 + 4 * q^28 - 12 * q^29 - 4 * q^30 - 6 * q^31 - 12 * q^32 + 8 * q^34 + 4 * q^35 - 28 * q^36 - 6 * q^37 - 10 * q^38 - 12 * q^39 - 6 * q^40 - 18 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^45 - 8 * q^46 + 4 * q^47 + 2 * q^48 + 4 * q^49 - 4 * q^51 - 30 * q^52 + 34 * q^53 + 2 * q^54 - 6 * q^56 + 28 * q^57 + 32 * q^58 - 10 * q^59 - 8 * q^60 + 8 * q^61 + 22 * q^62 + 4 * q^63 - 16 * q^64 - 16 * q^65 + 14 * q^67 + 44 * q^68 - 10 * q^69 + 12 * q^72 - 2 * q^73 - 48 * q^74 - 2 * q^75 - 38 * q^76 + 14 * q^78 + 8 * q^79 + 12 * q^80 - 12 * q^81 - 34 * q^82 + 10 * q^83 - 8 * q^84 - 2 * q^85 - 24 * q^86 - 32 * q^87 + 10 * q^89 + 6 * q^90 - 16 * q^91 + 10 * q^92 - 26 * q^93 - 54 * q^94 - 6 * q^95 - 8 * q^96 - 34 * 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 $

$2$	2.21161	1.56385	0.781924	−	0.623374i	$-0.214239\pi$
$2$	2.21161	1.56385	0.781924	+	0.623374i	$0.214239\pi$
$3$	−1.45216	−0.838404	−0.419202	−	0.907893i	$-0.637690\pi$
$3$	−1.45216	−0.838404	−0.419202	+	0.907893i	$0.637690\pi$
$4$	2.89124	1.44562
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.21161	−1.31114
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.97107	0.696878
$9$	−0.891236	−0.297079
$10$	2.21161	0.699374
$11$	0	0
$11$	0	0
$12$	−4.19853	−1.21201
$13$	−6.19853	−1.71916	−0.859582	−	0.510998i	$-0.829276\pi$
$13$	−6.19853	−1.71916	−0.859582	+	0.510998i	$0.829276\pi$
$14$	2.21161	0.591079
$15$	−1.45216	−0.374946
$16$	−1.42323	−0.355807
$17$	6.75354	1.63797	0.818987	−	0.573812i	$-0.194536\pi$
$17$	6.75354	1.63797	0.818987	+	0.573812i	$0.194536\pi$
$18$	−1.97107	−0.464585
$19$	−6.55501	−1.50382	−0.751911	−	0.659265i	$-0.770868\pi$
$19$	−6.55501	−1.50382	−0.751911	+	0.659265i	$0.770868\pi$
$20$	2.89124	0.646500
$21$	−1.45216	−0.316887
$22$	0	0
$23$	−1.75946	−0.366872	−0.183436	−	0.983032i	$-0.558722\pi$
$23$	−1.75946	−0.366872	−0.183436	+	0.983032i	$0.558722\pi$
$24$	−2.86230	−0.584266
$25$	1.00000	0.200000
$26$	−13.7088	−2.68851
$27$	5.65069	1.08748
$28$	2.89124	0.546392
$29$	3.32754	0.617910	0.308955	−	0.951077i	$-0.400021\pi$
$29$	3.32754	0.617910	0.308955	+	0.951077i	$0.400021\pi$
$30$	−3.21161	−0.586358
$31$	5.76662	1.03572	0.517858	−	0.855467i	$-0.326730\pi$
$31$	5.76662	1.03572	0.517858	+	0.855467i	$0.326730\pi$
$32$	−7.08977	−1.25331
$33$	0	0
$34$	14.9362	2.56154
$35$	1.00000	0.169031
$36$	−2.57677	−0.429462
$37$	−9.70159	−1.59493	−0.797466	−	0.603364i	$-0.793827\pi$
$37$	−9.70159	−1.59493	−0.797466	+	0.603364i	$0.793827\pi$
$38$	−14.4971	−2.35175
$39$	9.00125	1.44135
$40$	1.97107	0.311653
$41$	−7.98415	−1.24691	−0.623457	−	0.781857i	$-0.714273\pi$
$41$	−7.98415	−1.24691	−0.623457	+	0.781857i	$0.714273\pi$
$42$	−3.21161	−0.495563
$43$	−5.27837	−0.804943	−0.402472	−	0.915432i	$-0.631849\pi$
$43$	−5.27837	−0.804943	−0.402472	+	0.915432i	$0.631849\pi$
$44$	0	0
$45$	−0.891236	−0.132858
$46$	−3.89124	−0.573731
$47$	−11.9493	−1.74299	−0.871493	−	0.490409i	$-0.836848\pi$
$47$	−11.9493	−1.74299	−0.871493	+	0.490409i	$0.836848\pi$
$48$	2.06675	0.298310
$49$	1.00000	0.142857
$50$	2.21161	0.312769
$51$	−9.80721	−1.37328
$52$	−17.9214	−2.48525
$53$	5.33623	0.732987	0.366494	−	0.930421i	$-0.380558\pi$
$53$	5.33623	0.732987	0.366494	+	0.930421i	$0.380558\pi$
$54$	12.4971	1.70065
$55$	0	0
$56$	1.97107	0.263395
$57$	9.51891	1.26081
$58$	7.35924	0.966316
$59$	−14.1637	−1.84395	−0.921977	−	0.387244i	$-0.873427\pi$
$59$	−14.1637	−1.84395	−0.921977	+	0.387244i	$0.873427\pi$
$60$	−4.19853	−0.542028
$61$	−10.9362	−1.40024	−0.700120	−	0.714025i	$-0.746870\pi$
$61$	−10.9362	−1.40024	−0.700120	+	0.714025i	$0.746870\pi$
$62$	12.7535	1.61970
$63$	−0.891236	−0.112285
$64$	−12.8334	−1.60417
$65$	−6.19853	−0.768833
$66$	0	0
$67$	7.27837	0.889194	0.444597	−	0.895731i	$-0.353347\pi$
$67$	7.27837	0.889194	0.444597	+	0.895731i	$0.353347\pi$
$68$	19.5261	2.36788
$69$	2.55501	0.307587
$70$	2.21161	0.264338
$71$	8.82029	1.04678	0.523388	−	0.852094i	$-0.324668\pi$
$71$	8.82029	1.04678	0.523388	+	0.852094i	$0.324668\pi$
$72$	−1.75669	−0.207028
$73$	−0.811402	−0.0949674	−0.0474837	−	0.998872i	$-0.515120\pi$
$73$	−0.811402	−0.0949674	−0.0474837	+	0.998872i	$0.515120\pi$
$74$	−21.4562	−2.49423
$75$	−1.45216	−0.167681
$76$	−18.9521	−2.17395
$77$	0	0
$78$	19.9073	2.25406
$79$	4.53199	0.509889	0.254944	−	0.966956i	$-0.417943\pi$
$79$	4.53199	0.509889	0.254944	+	0.966956i	$0.417943\pi$
$80$	−1.42323	−0.159122
$81$	−5.53199	−0.614666
$82$	−17.6579	−1.94998
$83$	0.639032	0.0701429	0.0350715	−	0.999385i	$-0.488834\pi$
$83$	0.639032	0.0701429	0.0350715	+	0.999385i	$0.488834\pi$
$84$	−4.19853	−0.458097
$85$	6.75354	0.732524
$86$	−11.6737	−1.25881
$87$	−4.83212	−0.518058
$88$	0	0
$89$	10.1001	1.07061	0.535303	−	0.844660i	$-0.320197\pi$
$89$	10.1001	1.07061	0.535303	+	0.844660i	$0.320197\pi$
$90$	−1.97107	−0.207769
$91$	−6.19853	−0.649783
$92$	−5.08700	−0.530356
$93$	−8.37405	−0.868348
$94$	−26.4272	−2.72576
$95$	−6.55501	−0.672530
$96$	10.2955	1.05078
$97$	−7.25363	−0.736494	−0.368247	−	0.929728i	$-0.620042\pi$
$97$	−7.25363	−0.736494	−0.368247	+	0.929728i	$0.620042\pi$
$98$	2.21161	0.223407
$99$	0	0
$100$	2.89124	0.289124
$101$	−18.1898	−1.80996	−0.904979	−	0.425457i	$-0.860114\pi$
$101$	−18.1898	−1.80996	−0.904979	+	0.425457i	$0.860114\pi$
$102$	−21.6898	−2.14761
$103$	3.79136	0.373574	0.186787	−	0.982400i	$-0.440193\pi$
$103$	3.79136	0.373574	0.186787	+	0.982400i	$0.440193\pi$
$104$	−12.2177	−1.19805
$105$	−1.45216	−0.141716
$106$	11.8017	1.14628
$107$	3.73644	0.361215	0.180608	−	0.983555i	$-0.442194\pi$
$107$	3.73644	0.361215	0.180608	+	0.983555i	$0.442194\pi$
$108$	16.3375	1.57207
$109$	9.50708	0.910613	0.455307	−	0.890335i	$-0.349530\pi$
$109$	9.50708	0.910613	0.455307	+	0.890335i	$0.349530\pi$
$110$	0	0
$111$	14.0883	1.33720
$112$	−1.42323	−0.134482
$113$	−12.8465	−1.20849	−0.604246	−	0.796797i	$-0.706526\pi$
$113$	−12.8465	−1.20849	−0.604246	+	0.796797i	$0.706526\pi$
$114$	21.0522	1.97171
$115$	−1.75946	−0.164070
$116$	9.62072	0.893261
$117$	5.52435	0.510727
$118$	−31.3246	−2.88366
$119$	6.75354	0.619096
$120$	−2.86230	−0.261291
$121$	0	0
$122$	−24.1867	−2.18976
$123$	11.5943	1.04542
$124$	16.6727	1.49725
$125$	1.00000	0.0894427
$126$	−1.97107	−0.175597
$127$	10.1478	0.900475	0.450237	−	0.892909i	$-0.351339\pi$
$127$	10.1478	0.900475	0.450237	+	0.892909i	$0.351339\pi$
$128$	−14.2029	−1.25537
$129$	7.66502	0.674868
$130$	−13.7088	−1.20234
$131$	−4.96218	−0.433548	−0.216774	−	0.976222i	$-0.569553\pi$
$131$	−4.96218	−0.433548	−0.216774	+	0.976222i	$0.569553\pi$
$132$	0	0
$133$	−6.55501	−0.568391
$134$	16.0969	1.39056
$135$	5.65069	0.486334
$136$	13.3117	1.14147
$137$	2.61774	0.223649	0.111824	−	0.993728i	$-0.464331\pi$
$137$	2.61774	0.223649	0.111824	+	0.993728i	$0.464331\pi$
$138$	5.65069	0.481019
$139$	−5.94214	−0.504006	−0.252003	−	0.967727i	$-0.581089\pi$
$139$	−5.94214	−0.504006	−0.252003	+	0.967727i	$0.581089\pi$
$140$	2.89124	0.244354
$141$	17.3523	1.46133
$142$	19.5071	1.63700
$143$	0	0
$144$	1.26843	0.105703
$145$	3.32754	0.276338
$146$	−1.79451	−0.148515
$147$	−1.45216	−0.119772
$148$	−28.0496	−2.30566
$149$	0.686788	0.0562639	0.0281319	−	0.999604i	$-0.491044\pi$
$149$	0.686788	0.0562639	0.0281319	+	0.999604i	$0.491044\pi$
$150$	−3.21161	−0.262227
$151$	14.9751	1.21866	0.609328	−	0.792918i	$-0.291439\pi$
$151$	14.9751	1.21866	0.609328	+	0.792918i	$0.291439\pi$
$152$	−12.9204	−1.04798
$153$	−6.01900	−0.486607
$154$	0	0
$155$	5.76662	0.463186
$156$	26.0247	2.08365
$157$	0.746374	0.0595671	0.0297836	−	0.999556i	$-0.490518\pi$
$157$	0.746374	0.0595671	0.0297836	+	0.999556i	$0.490518\pi$
$158$	10.0230	0.797388
$159$	−7.74905	−0.614540
$160$	−7.08977	−0.560495
$161$	−1.75946	−0.138665
$162$	−12.2346	−0.961243
$163$	−22.1447	−1.73451	−0.867253	−	0.497868i	$-0.834117\pi$
$163$	−22.1447	−1.73451	−0.867253	+	0.497868i	$0.834117\pi$
$164$	−23.0841	−1.80256
$165$	0	0
$166$	1.41329	0.109693
$167$	−16.4393	−1.27211	−0.636055	−	0.771644i	$-0.719435\pi$
$167$	−16.4393	−1.27211	−0.636055	+	0.771644i	$0.719435\pi$
$168$	−2.86230	−0.220832
$169$	25.4218	1.95552
$170$	14.9362	1.14556
$171$	5.84206	0.446753
$172$	−15.2610	−1.16364
$173$	7.23463	0.550039	0.275019	−	0.961439i	$-0.411316\pi$
$173$	7.23463	0.550039	0.275019	+	0.961439i	$0.411316\pi$
$174$	−10.6868	−0.810163
$175$	1.00000	0.0755929
$176$	0	0
$177$	20.5679	1.54598
$178$	22.3375	1.67426
$179$	1.80863	0.135184	0.0675918	−	0.997713i	$-0.478468\pi$
$179$	1.80863	0.135184	0.0675918	+	0.997713i	$0.478468\pi$
$180$	−2.57677	−0.192061
$181$	−9.25363	−0.687817	−0.343908	−	0.939003i	$-0.611751\pi$
$181$	−9.25363	−0.687817	−0.343908	+	0.939003i	$0.611751\pi$
$182$	−13.7088	−1.01616
$183$	15.8811	1.17397
$184$	−3.46801	−0.255665
$185$	−9.70159	−0.713275
$186$	−18.5202	−1.35796
$187$	0	0
$188$	−34.5483	−2.51969
$189$	5.65069	0.411027
$190$	−14.4971	−1.05173
$191$	−16.7886	−1.21478	−0.607390	−	0.794404i	$-0.707783\pi$
$191$	−16.7886	−1.21478	−0.607390	+	0.794404i	$0.707783\pi$
$192$	18.6361	1.34494
$193$	1.33069	0.0957853	0.0478926	−	0.998852i	$-0.484749\pi$
$193$	1.33069	0.0957853	0.0478926	+	0.998852i	$0.484749\pi$
$194$	−16.0422	−1.15176
$195$	9.00125	0.644593
$196$	2.89124	0.206517
$197$	−5.59425	−0.398574	−0.199287	−	0.979941i	$-0.563863\pi$
$197$	−5.59425	−0.398574	−0.199287	+	0.979941i	$0.563863\pi$
$198$	0	0
$199$	8.05807	0.571221	0.285611	−	0.958346i	$-0.407804\pi$
$199$	8.05807	0.571221	0.285611	+	0.958346i	$0.407804\pi$
$200$	1.97107	0.139376
$201$	−10.5693	−0.745504
$202$	−40.2289	−2.83050
$203$	3.32754	0.233548
$204$	−28.3550	−1.98524
$205$	−7.98415	−0.557637
$206$	8.38503	0.584213
$207$	1.56809	0.108990
$208$	8.82192	0.611690
$209$	0	0
$210$	−3.21161	−0.221622
$211$	2.13350	0.146876	0.0734382	−	0.997300i	$-0.476603\pi$
$211$	2.13350	0.146876	0.0734382	+	0.997300i	$0.476603\pi$
$212$	15.4283	1.05962
$213$	−12.8085	−0.877621
$214$	8.26356	0.564885
$215$	−5.27837	−0.359982
$216$	11.1379	0.757838
$217$	5.76662	0.391464
$218$	21.0260	1.42406
$219$	1.17828	0.0796211
$220$	0	0
$221$	−41.8620	−2.81595
$222$	31.1578	2.09117
$223$	15.5421	1.04078	0.520389	−	0.853929i	$-0.325787\pi$
$223$	15.5421	1.04078	0.520389	+	0.853929i	$0.325787\pi$
$224$	−7.08977	−0.473705
$225$	−0.891236	−0.0594157
$226$	−28.4114	−1.88990
$227$	20.5592	1.36456	0.682282	−	0.731089i	$-0.260988\pi$
$227$	20.5592	1.36456	0.682282	+	0.731089i	$0.260988\pi$
$228$	27.5214	1.82265
$229$	26.3274	1.73976	0.869881	−	0.493262i	$-0.164196\pi$
$229$	26.3274	1.73976	0.869881	+	0.493262i	$0.164196\pi$
$230$	−3.89124	−0.256580
$231$	0	0
$232$	6.55882	0.430608
$233$	0.0808778	0.00529848	0.00264924	−	0.999996i	$-0.499157\pi$
$233$	0.0808778	0.00529848	0.00264924	+	0.999996i	$0.499157\pi$
$234$	12.2177	0.798698
$235$	−11.9493	−0.779487
$236$	−40.9506	−2.66565
$237$	−6.58117	−0.427493
$238$	14.9362	0.968172
$239$	6.87815	0.444911	0.222455	−	0.974943i	$-0.428593\pi$
$239$	6.87815	0.444911	0.222455	+	0.974943i	$0.428593\pi$
$240$	2.06675	0.133408
$241$	−9.65928	−0.622209	−0.311104	−	0.950376i	$-0.600699\pi$
$241$	−9.65928	−0.622209	−0.311104	+	0.950376i	$0.600699\pi$
$242$	0	0
$243$	−8.91874	−0.572138
$244$	−31.6192	−2.02421
$245$	1.00000	0.0638877
$246$	25.6420	1.63487
$247$	40.6314	2.58532
$248$	11.3664	0.721768
$249$	−0.927976	−0.0588081
$250$	2.21161	0.139875
$251$	−9.31723	−0.588098	−0.294049	−	0.955790i	$-0.595003\pi$
$251$	−9.31723	−0.588098	−0.294049	+	0.955790i	$0.595003\pi$
$252$	−2.57677	−0.162321
$253$	0	0
$254$	22.4431	1.40821
$255$	−9.80721	−0.614151
$256$	−5.74465	−0.359041
$257$	−6.12624	−0.382145	−0.191072	−	0.981576i	$-0.561196\pi$
$257$	−6.12624	−0.382145	−0.191072	+	0.981576i	$0.561196\pi$
$258$	16.9521	1.05539
$259$	−9.70159	−0.602828
$260$	−17.9214	−1.11144
$261$	−2.96563	−0.183568
$262$	−10.9744	−0.678002
$263$	−7.97384	−0.491688	−0.245844	−	0.969309i	$-0.579065\pi$
$263$	−7.97384	−0.491688	−0.245844	+	0.969309i	$0.579065\pi$
$264$	0	0
$265$	5.33623	0.327802
$266$	−14.4971	−0.888877
$267$	−14.6669	−0.897601
$268$	21.0435	1.28543
$269$	−26.7084	−1.62844	−0.814219	−	0.580557i	$-0.802835\pi$
$269$	−26.7084	−1.62844	−0.814219	+	0.580557i	$0.802835\pi$
$270$	12.4971	0.760552
$271$	−17.7706	−1.07949	−0.539745	−	0.841829i	$-0.681479\pi$
$271$	−17.7706	−1.07949	−0.539745	+	0.841829i	$0.681479\pi$
$272$	−9.61183	−0.582803
$273$	9.00125	0.544781
$274$	5.78943	0.349752
$275$	0	0
$276$	7.38713	0.444653
$277$	30.2465	1.81734	0.908668	−	0.417520i	$-0.137101\pi$
$277$	30.2465	1.81734	0.908668	+	0.417520i	$0.137101\pi$
$278$	−13.1417	−0.788188
$279$	−5.13942	−0.307689
$280$	1.97107	0.117794
$281$	−26.8925	−1.60427	−0.802136	−	0.597142i	$-0.796303\pi$
$281$	−26.8925	−1.60427	−0.802136	+	0.597142i	$0.796303\pi$
$282$	38.3766	2.28529
$283$	−12.1795	−0.723998	−0.361999	−	0.932178i	$-0.617906\pi$
$283$	−12.1795	−0.723998	−0.361999	+	0.932178i	$0.617906\pi$
$284$	25.5015	1.51324
$285$	9.51891	0.563852
$286$	0	0
$287$	−7.98415	−0.471290
$288$	6.31865	0.372330
$289$	28.6103	1.68296
$290$	7.35924	0.432150
$291$	10.5334	0.617480
$292$	−2.34596	−0.137287
$293$	−7.02339	−0.410311	−0.205156	−	0.978729i	$-0.565770\pi$
$293$	−7.02339	−0.410311	−0.205156	+	0.978729i	$0.565770\pi$
$294$	−3.21161	−0.187305
$295$	−14.1637	−0.824642
$296$	−19.1225	−1.11147
$297$	0	0
$298$	1.51891	0.0879881
$299$	10.9060	0.630713
$300$	−4.19853	−0.242402
$301$	−5.27837	−0.304240
$302$	33.1191	1.90579
$303$	26.4145	1.51748
$304$	9.32927	0.535070
$305$	−10.9362	−0.626206
$306$	−13.3117	−0.760979
$307$	4.02159	0.229524	0.114762	−	0.993393i	$-0.463389\pi$
$307$	4.02159	0.229524	0.114762	+	0.993393i	$0.463389\pi$
$308$	0	0
$309$	−5.50566	−0.313206
$310$	12.7535	0.724352
$311$	4.14209	0.234877	0.117438	−	0.993080i	$-0.462532\pi$
$311$	4.14209	0.234877	0.117438	+	0.993080i	$0.462532\pi$
$312$	17.7421	1.00445
$313$	2.35103	0.132888	0.0664441	−	0.997790i	$-0.478835\pi$
$313$	2.35103	0.132888	0.0664441	+	0.997790i	$0.478835\pi$
$314$	1.65069	0.0931539
$315$	−0.891236	−0.0502154
$316$	13.1031	0.737105
$317$	−0.0198694	−0.00111598	−0.000557988	−	1.00000i	$-0.500178\pi$
$317$	−0.0198694	−0.00111598	−0.000557988		1.00000i	$0.500178\pi$
$318$	−17.1379	−0.961046
$319$	0	0
$320$	−12.8334	−0.717407
$321$	−5.42590	−0.302844
$322$	−3.89124	−0.216850
$323$	−44.2695	−2.46322
$324$	−15.9943	−0.888572
$325$	−6.19853	−0.343833
$326$	−48.9755	−2.71250
$327$	−13.8058	−0.763462
$328$	−15.7373	−0.868948
$329$	−11.9493	−0.658786
$330$	0	0
$331$	9.11555	0.501036	0.250518	−	0.968112i	$-0.419399\pi$
$331$	9.11555	0.501036	0.250518	+	0.968112i	$0.419399\pi$
$332$	1.84759	0.101400
$333$	8.64641	0.473820
$334$	−36.3573	−1.98939
$335$	7.27837	0.397660
$336$	2.06675	0.112751
$337$	−0.637610	−0.0347328	−0.0173664	−	0.999849i	$-0.505528\pi$
$337$	−0.637610	−0.0347328	−0.0173664	+	0.999849i	$0.505528\pi$
$338$	56.2232	3.05814
$339$	18.6551	1.01321
$340$	19.5261	1.05895
$341$	0	0
$342$	12.9204	0.698654
$343$	1.00000	0.0539949
$344$	−10.4040	−0.560947
$345$	2.55501	0.137557
$346$	16.0002	0.860176
$347$	−5.42620	−0.291294	−0.145647	−	0.989337i	$-0.546526\pi$
$347$	−5.42620	−0.291294	−0.145647	+	0.989337i	$0.546526\pi$
$348$	−13.9708	−0.748914
$349$	−20.0842	−1.07508	−0.537542	−	0.843237i	$-0.680647\pi$
$349$	−20.0842	−1.07508	−0.537542	+	0.843237i	$0.680647\pi$
$350$	2.21161	0.118216
$351$	−35.0260	−1.86955
$352$	0	0
$353$	15.0117	0.798990	0.399495	−	0.916735i	$-0.369185\pi$
$353$	15.0117	0.798990	0.399495	+	0.916735i	$0.369185\pi$
$354$	45.4883	2.41768
$355$	8.82029	0.468133
$356$	29.2017	1.54769
$357$	−9.80721	−0.519053
$358$	4.00000	0.211407
$359$	5.58968	0.295012	0.147506	−	0.989061i	$-0.452875\pi$
$359$	5.58968	0.295012	0.147506	+	0.989061i	$0.452875\pi$
$360$	−1.75669	−0.0925855
$361$	23.9681	1.26148
$362$	−20.4654	−1.07564
$363$	0	0
$364$	−17.9214	−0.939338
$365$	−0.811402	−0.0424707
$366$	35.1229	1.83590
$367$	26.4503	1.38069	0.690346	−	0.723479i	$-0.257458\pi$
$367$	26.4503	1.38069	0.690346	+	0.723479i	$0.257458\pi$
$368$	2.50411	0.130536
$369$	7.11576	0.370432
$370$	−21.4562	−1.11545
$371$	5.33623	0.277043
$372$	−24.2113	−1.25530
$373$	−21.7595	−1.12666	−0.563331	−	0.826231i	$-0.690480\pi$
$373$	−21.7595	−1.12666	−0.563331	+	0.826231i	$0.690480\pi$
$374$	0	0
$375$	−1.45216	−0.0749891
$376$	−23.5529	−1.21465
$377$	−20.6259	−1.06229
$378$	12.4971	0.642784
$379$	4.28972	0.220348	0.110174	−	0.993912i	$-0.464859\pi$
$379$	4.28972	0.220348	0.110174	+	0.993912i	$0.464859\pi$
$380$	−18.9521	−0.972221
$381$	−14.7363	−0.754962
$382$	−37.1299	−1.89973
$383$	17.8319	0.911165	0.455583	−	0.890193i	$-0.349431\pi$
$383$	17.8319	0.911165	0.455583	+	0.890193i	$0.349431\pi$
$384$	20.6249	1.05251
$385$	0	0
$386$	2.94298	0.149793
$387$	4.70427	0.239131
$388$	−20.9719	−1.06469
$389$	26.6694	1.35219	0.676097	−	0.736813i	$-0.263670\pi$
$389$	26.6694	1.35219	0.676097	+	0.736813i	$0.263670\pi$
$390$	19.9073	1.00804
$391$	−11.8826	−0.600927
$392$	1.97107	0.0995540
$393$	7.20587	0.363488
$394$	−12.3723	−0.623309
$395$	4.53199	0.228029
$396$	0	0
$397$	−0.514512	−0.0258226	−0.0129113	−	0.999917i	$-0.504110\pi$
$397$	−0.514512	−0.0258226	−0.0129113	+	0.999917i	$0.504110\pi$
$398$	17.8213	0.893303
$399$	9.51891	0.476542
$400$	−1.42323	−0.0711614
$401$	5.03437	0.251405	0.125702	−	0.992068i	$-0.459882\pi$
$401$	5.03437	0.251405	0.125702	+	0.992068i	$0.459882\pi$
$402$	−23.3753	−1.16585
$403$	−35.7446	−1.78056
$404$	−52.5911	−2.61651
$405$	−5.53199	−0.274887
$406$	7.35924	0.365233
$407$	0	0
$408$	−19.3307	−0.957012
$409$	−25.4435	−1.25810	−0.629049	−	0.777365i	$-0.716556\pi$
$409$	−25.4435	−1.25810	−0.629049	+	0.777365i	$0.716556\pi$
$410$	−17.6579	−0.872059
$411$	−3.80137	−0.187508
$412$	10.9617	0.540045
$413$	−14.1637	−0.696949
$414$	3.46801	0.170443
$415$	0.639032	0.0313689
$416$	43.9462	2.15464
$417$	8.62893	0.422560
$418$	0	0
$419$	−3.24961	−0.158754	−0.0793768	−	0.996845i	$-0.525293\pi$
$419$	−3.24961	−0.158754	−0.0793768	+	0.996845i	$0.525293\pi$
$420$	−4.19853	−0.204867
$421$	36.8737	1.79711	0.898557	−	0.438857i	$-0.144616\pi$
$421$	36.8737	1.79711	0.898557	+	0.438857i	$0.144616\pi$
$422$	4.71849	0.229692
$423$	10.6496	0.517804
$424$	10.5181	0.510803
$425$	6.75354	0.327595
$426$	−28.3274	−1.37247
$427$	−10.9362	−0.529241
$428$	10.8029	0.522179
$429$	0	0
$430$	−11.6737	−0.562956
$431$	2.29459	0.110527	0.0552633	−	0.998472i	$-0.482400\pi$
$431$	2.29459	0.110527	0.0552633	+	0.998472i	$0.482400\pi$
$432$	−8.04222	−0.386931
$433$	19.3213	0.928520	0.464260	−	0.885699i	$-0.346320\pi$
$433$	19.3213	0.928520	0.464260	+	0.885699i	$0.346320\pi$
$434$	12.7535	0.612190
$435$	−4.83212	−0.231683
$436$	27.4872	1.31640
$437$	11.5332	0.551710
$438$	2.60591	0.124515
$439$	−21.4610	−1.02428	−0.512140	−	0.858902i	$-0.671147\pi$
$439$	−21.4610	−1.02428	−0.512140	+	0.858902i	$0.671147\pi$
$440$	0	0
$441$	−0.891236	−0.0424398
$442$	−92.5827	−4.40371
$443$	25.8000	1.22579	0.612896	−	0.790163i	$-0.290004\pi$
$443$	25.8000	1.22579	0.612896	+	0.790163i	$0.290004\pi$
$444$	40.7325	1.93308
$445$	10.1001	0.478790
$446$	34.3732	1.62762
$447$	−0.997326	−0.0471719
$448$	−12.8334	−0.606320
$449$	18.5408	0.874994	0.437497	−	0.899220i	$-0.355865\pi$
$449$	18.5408	0.874994	0.437497	+	0.899220i	$0.355865\pi$
$450$	−1.97107	−0.0929171
$451$	0	0
$452$	−37.1421	−1.74702
$453$	−21.7462	−1.02173
$454$	45.4691	2.13397
$455$	−6.19853	−0.290592
$456$	18.7624	0.878631
$457$	−10.9155	−0.510606	−0.255303	−	0.966861i	$-0.582175\pi$
$457$	−10.9155	−0.510606	−0.255303	+	0.966861i	$0.582175\pi$
$458$	58.2260	2.72072
$459$	38.1622	1.78126
$460$	−5.08700	−0.237183
$461$	−20.2160	−0.941554	−0.470777	−	0.882252i	$-0.656026\pi$
$461$	−20.2160	−0.941554	−0.470777	+	0.882252i	$0.656026\pi$
$462$	0	0
$463$	32.5425	1.51238	0.756189	−	0.654353i	$-0.227059\pi$
$463$	32.5425	1.51238	0.756189	+	0.654353i	$0.227059\pi$
$464$	−4.73585	−0.219856
$465$	−8.37405	−0.388337
$466$	0.178870	0.00828601
$467$	30.5276	1.41265	0.706325	−	0.707888i	$-0.250352\pi$
$467$	30.5276	1.41265	0.706325	+	0.707888i	$0.250352\pi$
$468$	15.9722	0.738316
$469$	7.27837	0.336084
$470$	−26.4272	−1.21900
$471$	−1.08385	−0.0499413
$472$	−27.9176	−1.28501
$473$	0	0
$474$	−14.5550	−0.668534
$475$	−6.55501	−0.300764
$476$	19.5261	0.894976
$477$	−4.75584	−0.217755
$478$	15.2118	0.695773
$479$	13.0560	0.596542	0.298271	−	0.954481i	$-0.403590\pi$
$479$	13.0560	0.596542	0.298271	+	0.954481i	$0.403590\pi$
$480$	10.2955	0.469922
$481$	60.1356	2.74195
$482$	−21.3626	−0.973040
$483$	2.55501	0.116257
$484$	0	0
$485$	−7.25363	−0.329370
$486$	−19.7248	−0.894736
$487$	2.07534	0.0940427	0.0470213	−	0.998894i	$-0.485027\pi$
$487$	2.07534	0.0940427	0.0470213	+	0.998894i	$0.485027\pi$
$488$	−21.5561	−0.975797
$489$	32.1576	1.45422
$490$	2.21161	0.0999105
$491$	24.4163	1.10189	0.550945	−	0.834541i	$-0.314267\pi$
$491$	24.4163	1.10189	0.550945	+	0.834541i	$0.314267\pi$
$492$	33.5217	1.51128
$493$	22.4727	1.01212
$494$	89.8610	4.04304
$495$	0	0
$496$	−8.20722	−0.368515
$497$	8.82029	0.395644
$498$	−2.05233	−0.0919669
$499$	4.60906	0.206330	0.103165	−	0.994664i	$-0.467103\pi$
$499$	4.60906	0.206330	0.103165	+	0.994664i	$0.467103\pi$
$500$	2.89124	0.129300
$501$	23.8724	1.06654
$502$	−20.6061	−0.919696
$503$	30.2653	1.34946	0.674731	−	0.738064i	$-0.264260\pi$
$503$	30.2653	1.34946	0.674731	+	0.738064i	$0.264260\pi$
$504$	−1.75669	−0.0782491
$505$	−18.1898	−0.809438
$506$	0	0
$507$	−36.9165	−1.63952
$508$	29.3398	1.30174
$509$	−5.34741	−0.237020	−0.118510	−	0.992953i	$-0.537812\pi$
$509$	−5.34741	−0.237020	−0.118510	+	0.992953i	$0.537812\pi$
$510$	−21.6898	−0.960439
$511$	−0.811402	−0.0358943
$512$	15.7009	0.693889
$513$	−37.0403	−1.63537
$514$	−13.5489	−0.597616
$515$	3.79136	0.167067
$516$	22.1614	0.975601
$517$	0	0
$518$	−21.4562	−0.942730
$519$	−10.5058	−0.461155
$520$	−12.2177	−0.535783
$521$	15.8247	0.693292	0.346646	−	0.937996i	$-0.387320\pi$
$521$	15.8247	0.693292	0.346646	+	0.937996i	$0.387320\pi$
$522$	−6.55882	−0.287072
$523$	36.1406	1.58032	0.790159	−	0.612902i	$-0.209998\pi$
$523$	36.1406	1.58032	0.790159	+	0.612902i	$0.209998\pi$
$524$	−14.3468	−0.626744
$525$	−1.45216	−0.0633774
$526$	−17.6350	−0.768925
$527$	38.9451	1.69648
$528$	0	0
$529$	−19.9043	−0.865405
$530$	11.8017	0.512632
$531$	12.6232	0.547799
$532$	−18.9521	−0.821677
$533$	49.4900	2.14365
$534$	−32.4376	−1.40371
$535$	3.73644	0.161540
$536$	14.3462	0.619660
$537$	−2.62642	−0.113339
$538$	−59.0686	−2.54663
$539$	0	0
$540$	16.3375	0.703053
$541$	−19.5594	−0.840925	−0.420462	−	0.907310i	$-0.638132\pi$
$541$	−19.5594	−0.840925	−0.420462	+	0.907310i	$0.638132\pi$
$542$	−39.3018	−1.68816
$543$	13.4377	0.576668
$544$	−47.8810	−2.05288
$545$	9.50708	0.407239
$546$	19.9073	0.851953
$547$	−24.1043	−1.03063	−0.515313	−	0.857002i	$-0.672324\pi$
$547$	−24.1043	−1.03063	−0.515313	+	0.857002i	$0.672324\pi$
$548$	7.56850	0.323310
$549$	9.74675	0.415981
$550$	0	0
$551$	−21.8121	−0.929226
$552$	5.03610	0.214351
$553$	4.53199	0.192720
$554$	66.8936	2.84204
$555$	14.0883	0.598013
$556$	−17.1801	−0.728599
$557$	−33.6176	−1.42442	−0.712211	−	0.701965i	$-0.752306\pi$
$557$	−33.6176	−1.42442	−0.712211	+	0.701965i	$0.752306\pi$
$558$	−11.3664	−0.481179
$559$	32.7181	1.38383
$560$	−1.42323	−0.0601423
$561$	0	0
$562$	−59.4758	−2.50884
$563$	10.5711	0.445517	0.222759	−	0.974874i	$-0.428494\pi$
$563$	10.5711	0.445517	0.222759	+	0.974874i	$0.428494\pi$
$564$	50.1695	2.11252
$565$	−12.8465	−0.540454
$566$	−26.9364	−1.13222
$567$	−5.53199	−0.232322
$568$	17.3854	0.729475
$569$	−31.6316	−1.32607	−0.663033	−	0.748590i	$-0.730731\pi$
$569$	−31.6316	−1.32607	−0.663033	+	0.748590i	$0.730731\pi$
$570$	21.0522	0.881778
$571$	13.9160	0.582365	0.291183	−	0.956667i	$-0.405951\pi$
$571$	13.9160	0.582365	0.291183	+	0.956667i	$0.405951\pi$
$572$	0	0
$573$	24.3797	1.01848
$574$	−17.6579	−0.737025
$575$	−1.75946	−0.0733744
$576$	11.4376	0.476565
$577$	45.7055	1.90275	0.951373	−	0.308042i	$-0.0996736\pi$
$577$	45.7055	1.90275	0.951373	+	0.308042i	$0.0996736\pi$
$578$	63.2750	2.63189
$579$	−1.93237	−0.0803068
$580$	9.62072	0.399478
$581$	0.639032	0.0265115
$582$	23.2958	0.965644
$583$	0	0
$584$	−1.59933	−0.0661807
$585$	5.52435	0.228404
$586$	−15.5330	−0.641664
$587$	12.8553	0.530597	0.265298	−	0.964166i	$-0.414530\pi$
$587$	12.8553	0.530597	0.265298	+	0.964166i	$0.414530\pi$
$588$	−4.19853	−0.173145
$589$	−37.8003	−1.55753
$590$	−31.3246	−1.28961
$591$	8.12374	0.334166
$592$	13.8076	0.567488
$593$	−15.4564	−0.634718	−0.317359	−	0.948306i	$-0.602796\pi$
$593$	−15.4564	−0.634718	−0.317359	+	0.948306i	$0.602796\pi$
$594$	0	0
$595$	6.75354	0.276868
$596$	1.98567	0.0813361
$597$	−11.7016	−0.478914
$598$	24.1200	0.986338
$599$	−34.2496	−1.39940	−0.699701	−	0.714436i	$-0.746684\pi$
$599$	−34.2496	−1.39940	−0.699701	+	0.714436i	$0.746684\pi$
$600$	−2.86230	−0.116853
$601$	25.5119	1.04065	0.520325	−	0.853968i	$-0.325811\pi$
$601$	25.5119	1.04065	0.520325	+	0.853968i	$0.325811\pi$
$602$	−11.6737	−0.475785
$603$	−6.48674	−0.264160
$604$	43.2965	1.76171
$605$	0	0
$606$	58.4188	2.37310
$607$	−1.52063	−0.0617206	−0.0308603	−	0.999524i	$-0.509825\pi$
$607$	−1.52063	−0.0617206	−0.0308603	+	0.999524i	$0.509825\pi$
$608$	46.4735	1.88475
$609$	−4.83212	−0.195807
$610$	−24.1867	−0.979291
$611$	74.0682	2.99648
$612$	−17.4023	−0.703448
$613$	−41.1735	−1.66298	−0.831492	−	0.555537i	$-0.812513\pi$
$613$	−41.1735	−1.66298	−0.831492	+	0.555537i	$0.812513\pi$
$614$	8.89421	0.358941
$615$	11.5943	0.467525
$616$	0	0
$617$	42.9037	1.72724	0.863618	−	0.504146i	$-0.168193\pi$
$617$	42.9037	1.72724	0.863618	+	0.504146i	$0.168193\pi$
$618$	−12.1764	−0.489806
$619$	−41.9939	−1.68788	−0.843939	−	0.536439i	$-0.819769\pi$
$619$	−41.9939	−1.68788	−0.843939	+	0.536439i	$0.819769\pi$
$620$	16.6727	0.669590
$621$	−9.94214	−0.398964
$622$	9.16071	0.367311
$623$	10.1001	0.404651
$624$	−12.8108	−0.512844
$625$	1.00000	0.0400000
$626$	5.19958	0.207817
$627$	0	0
$628$	2.15794	0.0861113
$629$	−65.5201	−2.61246
$630$	−1.97107	−0.0785293
$631$	0.0696914	0.00277437	0.00138719	−	0.999999i	$-0.499558\pi$
$631$	0.0696914	0.00277437	0.00138719	+	0.999999i	$0.499558\pi$
$632$	8.93287	0.355330
$633$	−3.09819	−0.123142
$634$	−0.0439434	−0.00174522
$635$	10.1478	0.402705
$636$	−22.4043	−0.888389
$637$	−6.19853	−0.245595
$638$	0	0
$639$	−7.86096	−0.310975
$640$	−14.2029	−0.561420
$641$	−9.52913	−0.376378	−0.188189	−	0.982133i	$-0.560262\pi$
$641$	−9.52913	−0.376378	−0.188189	+	0.982133i	$0.560262\pi$
$642$	−12.0000	−0.473602
$643$	−33.6596	−1.32740	−0.663702	−	0.747997i	$-0.731016\pi$
$643$	−33.6596	−1.32740	−0.663702	+	0.747997i	$0.731016\pi$
$644$	−5.08700	−0.200456
$645$	7.66502	0.301810
$646$	−97.9071	−3.85210
$647$	45.7694	1.79938	0.899691	−	0.436528i	$-0.143792\pi$
$647$	45.7694	1.79938	0.899691	+	0.436528i	$0.143792\pi$
$648$	−10.9039	−0.428347
$649$	0	0
$650$	−13.7088	−0.537702
$651$	−8.37405	−0.328205
$652$	−64.0255	−2.50743
$653$	10.7743	0.421629	0.210815	−	0.977526i	$-0.432388\pi$
$653$	10.7743	0.421629	0.210815	+	0.977526i	$0.432388\pi$
$654$	−30.5331	−1.19394
$655$	−4.96218	−0.193888
$656$	11.3633	0.443661
$657$	0.723151	0.0282128
$658$	−26.4272	−1.03024
$659$	−16.8298	−0.655594	−0.327797	−	0.944748i	$-0.606306\pi$
$659$	−16.8298	−0.655594	−0.327797	+	0.944748i	$0.606306\pi$
$660$	0	0
$661$	−30.3814	−1.18170	−0.590850	−	0.806781i	$-0.701208\pi$
$661$	−30.3814	−1.18170	−0.590850	+	0.806781i	$0.701208\pi$
$662$	20.1601	0.783544
$663$	60.7903	2.36090
$664$	1.25958	0.0488811
$665$	−6.55501	−0.254192
$666$	19.1225	0.740982
$667$	−5.85467	−0.226694
$668$	−47.5298	−1.83898
$669$	−22.5696	−0.872593
$670$	16.0969	0.621879
$671$	0	0
$672$	10.2955	0.397156
$673$	−17.0093	−0.655659	−0.327830	−	0.944737i	$-0.606317\pi$
$673$	−17.0093	−0.655659	−0.327830	+	0.944737i	$0.606317\pi$
$674$	−1.41015	−0.0543168
$675$	5.65069	0.217495
$676$	73.5004	2.82694
$677$	11.5295	0.443116	0.221558	−	0.975147i	$-0.428886\pi$
$677$	11.5295	0.443116	0.221558	+	0.975147i	$0.428886\pi$
$678$	41.2579	1.58450
$679$	−7.25363	−0.278369
$680$	13.3117	0.510480
$681$	−29.8553	−1.14406
$682$	0	0
$683$	−4.61429	−0.176561	−0.0882805	−	0.996096i	$-0.528137\pi$
$683$	−4.61429	−0.176561	−0.0882805	+	0.996096i	$0.528137\pi$
$684$	16.8908	0.645834
$685$	2.61774	0.100019
$686$	2.21161	0.0844398
$687$	−38.2315	−1.45862
$688$	7.51232	0.286404
$689$	−33.0768	−1.26012
$690$	5.65069	0.215118
$691$	−16.3453	−0.621804	−0.310902	−	0.950442i	$-0.600631\pi$
$691$	−16.3453	−0.621804	−0.310902	+	0.950442i	$0.600631\pi$
$692$	20.9170	0.795146
$693$	0	0
$694$	−12.0007	−0.455539
$695$	−5.94214	−0.225398
$696$	−9.52445	−0.361023
$697$	−53.9213	−2.04241
$698$	−44.4186	−1.68127
$699$	−0.117447	−0.00444227
$700$	2.89124	0.109278
$701$	−21.3419	−0.806072	−0.403036	−	0.915184i	$-0.632045\pi$
$701$	−21.3419	−0.806072	−0.403036	+	0.915184i	$0.632045\pi$
$702$	−77.4640	−2.92369
$703$	63.5940	2.39849
$704$	0	0
$705$	17.3523	0.653525
$706$	33.2000	1.24950
$707$	−18.1898	−0.684100
$708$	59.4667	2.23490
$709$	17.1857	0.645421	0.322710	−	0.946498i	$-0.395406\pi$
$709$	17.1857	0.645421	0.322710	+	0.946498i	$0.395406\pi$
$710$	19.5071	0.732088
$711$	−4.03907	−0.151477
$712$	19.9080	0.746082
$713$	−10.1461	−0.379975
$714$	−21.6898	−0.811719
$715$	0	0
$716$	5.22919	0.195424
$717$	−9.98817	−0.373015
$718$	12.3622	0.461354
$719$	−19.5770	−0.730098	−0.365049	−	0.930988i	$-0.618948\pi$
$719$	−19.5770	−0.730098	−0.365049	+	0.930988i	$0.618948\pi$
$720$	1.26843	0.0472716
$721$	3.79136	0.141198
$722$	53.0082	1.97276
$723$	14.0268	0.521663
$724$	−26.7544	−0.994320
$725$	3.32754	0.123582
$726$	0	0
$727$	−20.7261	−0.768687	−0.384344	−	0.923190i	$-0.625572\pi$
$727$	−20.7261	−0.768687	−0.384344	+	0.923190i	$0.625572\pi$
$728$	−12.2177	−0.452819
$729$	29.5474	1.09435
$730$	−1.79451	−0.0664177
$731$	−35.6477	−1.31848
$732$	45.9161	1.69711
$733$	10.2931	0.380183	0.190092	−	0.981766i	$-0.439121\pi$
$733$	10.2931	0.380183	0.190092	+	0.981766i	$0.439121\pi$
$734$	58.4978	2.15919
$735$	−1.45216	−0.0535637
$736$	12.4741	0.459803
$737$	0	0
$738$	15.7373	0.579298
$739$	14.2200	0.523092	0.261546	−	0.965191i	$-0.415768\pi$
$739$	14.2200	0.523092	0.261546	+	0.965191i	$0.415768\pi$
$740$	−28.0496	−1.03112
$741$	−59.0033	−2.16754
$742$	11.8017	0.433253
$743$	−1.42306	−0.0522069	−0.0261034	−	0.999659i	$-0.508310\pi$
$743$	−1.42306	−0.0522069	−0.0261034	+	0.999659i	$0.508310\pi$
$744$	−16.5058	−0.605133
$745$	0.686788	0.0251620
$746$	−48.1235	−1.76193
$747$	−0.569528	−0.0208380
$748$	0	0
$749$	3.73644	0.136527
$750$	−3.21161	−0.117272
$751$	−17.8201	−0.650265	−0.325133	−	0.945668i	$-0.605409\pi$
$751$	−17.8201	−0.650265	−0.325133	+	0.945668i	$0.605409\pi$
$752$	17.0066	0.620166
$753$	13.5301	0.493064
$754$	−45.6165	−1.66126
$755$	14.9751	0.544999
$756$	16.3375	0.594188
$757$	−22.5791	−0.820652	−0.410326	−	0.911939i	$-0.634585\pi$
$757$	−22.5791	−0.820652	−0.410326	+	0.911939i	$0.634585\pi$
$758$	9.48721	0.344591
$759$	0	0
$760$	−12.9204	−0.468671
$761$	13.6408	0.494478	0.247239	−	0.968954i	$-0.420477\pi$
$761$	13.6408	0.494478	0.247239	+	0.968954i	$0.420477\pi$
$762$	−32.5909	−1.18064
$763$	9.50708	0.344179
$764$	−48.5398	−1.75611
$765$	−6.01900	−0.217617
$766$	39.4372	1.42492
$767$	87.7941	3.17006
$768$	8.34214	0.301021
$769$	20.8163	0.750654	0.375327	−	0.926892i	$-0.377530\pi$
$769$	20.8163	0.750654	0.375327	+	0.926892i	$0.377530\pi$
$770$	0	0
$771$	8.89628	0.320392
$772$	3.84734	0.138469
$773$	9.30561	0.334699	0.167350	−	0.985898i	$-0.446479\pi$
$773$	9.30561	0.334699	0.167350	+	0.985898i	$0.446479\pi$
$774$	10.4040	0.373965
$775$	5.76662	0.207143
$776$	−14.2974	−0.513247
$777$	14.0883	0.505413
$778$	58.9825	2.11462
$779$	52.3362	1.87514
$780$	26.0247	0.931835
$781$	0	0
$782$	−26.2796	−0.939757
$783$	18.8029	0.671962
$784$	−1.42323	−0.0508296
$785$	0.746374	0.0266392
$786$	15.9366	0.568440
$787$	−15.0205	−0.535421	−0.267711	−	0.963499i	$-0.586267\pi$
$787$	−15.0205	−0.535421	−0.267711	+	0.963499i	$0.586267\pi$
$788$	−16.1743	−0.576186
$789$	11.5793	0.412233
$790$	10.0230	0.356603
$791$	−12.8465	−0.456767
$792$	0	0
$793$	67.7885	2.40724
$794$	−1.13790	−0.0403826
$795$	−7.74905	−0.274830
$796$	23.2978	0.825768
$797$	−40.8706	−1.44771	−0.723855	−	0.689953i	$-0.757631\pi$
$797$	−40.8706	−1.44771	−0.723855	+	0.689953i	$0.757631\pi$
$798$	21.0522	0.745238
$799$	−80.7001	−2.85496
$800$	−7.08977	−0.250661
$801$	−9.00155	−0.318054
$802$	11.1341	0.393158
$803$	0	0
$804$	−30.5585	−1.07771
$805$	−1.75946	−0.0620127
$806$	−79.0532	−2.78453
$807$	38.7848	1.36529
$808$	−35.8535	−1.26132
$809$	−16.2670	−0.571918	−0.285959	−	0.958242i	$-0.592312\pi$
$809$	−16.2670	−0.571918	−0.285959	+	0.958242i	$0.592312\pi$
$810$	−12.2346	−0.429881
$811$	−25.1784	−0.884133	−0.442067	−	0.896982i	$-0.645755\pi$
$811$	−25.1784	−0.884133	−0.442067	+	0.896982i	$0.645755\pi$
$812$	9.62072	0.337621
$813$	25.8058	0.905049
$814$	0	0
$815$	−22.1447	−0.775695
$816$	13.9579	0.488624
$817$	34.5997	1.21049
$818$	−56.2711	−1.96747
$819$	5.52435	0.193037
$820$	−23.0841	−0.806130
$821$	24.5153	0.855590	0.427795	−	0.903876i	$-0.359291\pi$
$821$	24.5153	0.855590	0.427795	+	0.903876i	$0.359291\pi$
$822$	−8.40717	−0.293234
$823$	−9.15460	−0.319109	−0.159555	−	0.987189i	$-0.551006\pi$
$823$	−9.15460	−0.319109	−0.159555	+	0.987189i	$0.551006\pi$
$824$	7.47304	0.260336
$825$	0	0
$826$	−31.3246	−1.08992
$827$	24.3588	0.847037	0.423519	−	0.905887i	$-0.360795\pi$
$827$	24.3588	0.847037	0.423519	+	0.905887i	$0.360795\pi$
$828$	4.53372	0.157558
$829$	−15.1100	−0.524793	−0.262396	−	0.964960i	$-0.584513\pi$
$829$	−15.1100	−0.524793	−0.262396	+	0.964960i	$0.584513\pi$
$830$	1.41329	0.0490561
$831$	−43.9227	−1.52366
$832$	79.5481	2.75783
$833$	6.75354	0.233996
$834$	19.0839	0.660820
$835$	−16.4393	−0.568905
$836$	0	0
$837$	32.5854	1.12632
$838$	−7.18687	−0.248266
$839$	0.170947	0.00590175	0.00295087	−	0.999996i	$-0.499061\pi$
$839$	0.170947	0.00590175	0.00295087	+	0.999996i	$0.499061\pi$
$840$	−2.86230	−0.0987589
$841$	−17.9274	−0.618188
$842$	81.5504	2.81041
$843$	39.0522	1.34503
$844$	6.16846	0.212327
$845$	25.4218	0.874537
$846$	23.5529	0.809766
$847$	0	0
$848$	−7.59467	−0.260802
$849$	17.6866	0.607003
$850$	14.9362	0.512308
$851$	17.0695	0.585136
$852$	−37.0323	−1.26871
$853$	−39.4944	−1.35226	−0.676131	−	0.736782i	$-0.736345\pi$
$853$	−39.4944	−1.35226	−0.676131	+	0.736782i	$0.736345\pi$
$854$	−24.1867	−0.827652
$855$	5.84206	0.199794
$856$	7.36478	0.251723
$857$	−32.2687	−1.10228	−0.551138	−	0.834414i	$-0.685806\pi$
$857$	−32.2687	−1.10228	−0.551138	+	0.834414i	$0.685806\pi$
$858$	0	0
$859$	17.6791	0.603205	0.301602	−	0.953434i	$-0.402478\pi$
$859$	17.6791	0.603205	0.301602	+	0.953434i	$0.402478\pi$
$860$	−15.2610	−0.520396
$861$	11.5943	0.395131
$862$	5.07476	0.172847
$863$	−27.6057	−0.939710	−0.469855	−	0.882744i	$-0.655694\pi$
$863$	−27.6057	−0.939710	−0.469855	+	0.882744i	$0.655694\pi$
$864$	−40.0621	−1.36294
$865$	7.23463	0.245985
$866$	42.7311	1.45206
$867$	−41.5467	−1.41100
$868$	16.6727	0.565907
$869$	0	0
$870$	−10.6868	−0.362316
$871$	−45.1152	−1.52867
$872$	18.7391	0.634586
$873$	6.46469	0.218797
$874$	25.5071	0.862790
$875$	1.00000	0.0338062
$876$	3.40670	0.115102
$877$	3.64582	0.123111	0.0615553	−	0.998104i	$-0.480394\pi$
$877$	3.64582	0.123111	0.0615553	+	0.998104i	$0.480394\pi$
$878$	−47.4636	−1.60182
$879$	10.1991	0.344006
$880$	0	0
$881$	−24.0883	−0.811554	−0.405777	−	0.913972i	$-0.632999\pi$
$881$	−24.0883	−0.811554	−0.405777	+	0.913972i	$0.632999\pi$
$882$	−1.97107	−0.0663693
$883$	8.40021	0.282690	0.141345	−	0.989960i	$-0.454857\pi$
$883$	8.40021	0.282690	0.141345	+	0.989960i	$0.454857\pi$
$884$	−121.033	−4.07078
$885$	20.5679	0.691383
$886$	57.0595	1.91695
$887$	−48.8895	−1.64155	−0.820774	−	0.571254i	$-0.806457\pi$
$887$	−48.8895	−1.64155	−0.820774	+	0.571254i	$0.806457\pi$
$888$	27.7689	0.931864
$889$	10.1478	0.340348
$890$	22.3375	0.748754
$891$	0	0
$892$	44.9360	1.50457
$893$	78.3278	2.62114
$894$	−2.20570	−0.0737696
$895$	1.80863	0.0604560
$896$	−14.2029	−0.474487
$897$	−15.8373	−0.528792
$898$	41.0051	1.36836
$899$	19.1887	0.639979
$900$	−2.57677	−0.0858924
$901$	36.0384	1.20061
$902$	0	0
$903$	7.66502	0.255076
$904$	−25.3213	−0.842172
$905$	−9.25363	−0.307601
$906$	−48.0942	−1.59782
$907$	9.06429	0.300975	0.150487	−	0.988612i	$-0.451916\pi$
$907$	9.06429	0.300975	0.150487	+	0.988612i	$0.451916\pi$
$908$	59.4416	1.97264
$909$	16.2114	0.537700
$910$	−13.7088	−0.454441
$911$	38.1305	1.26332	0.631659	−	0.775246i	$-0.282374\pi$
$911$	38.1305	1.26332	0.631659	+	0.775246i	$0.282374\pi$
$912$	−13.5476	−0.448605
$913$	0	0
$914$	−24.1409	−0.798509
$915$	15.8811	0.525014
$916$	76.1186	2.51503
$917$	−4.96218	−0.163866
$918$	84.4000	2.78561
$919$	28.5711	0.942472	0.471236	−	0.882007i	$-0.343808\pi$
$919$	28.5711	0.942472	0.471236	+	0.882007i	$0.343808\pi$
$920$	−3.46801	−0.114337
$921$	−5.83999	−0.192434
$922$	−44.7100	−1.47245
$923$	−54.6729	−1.79958
$924$	0	0
$925$	−9.70159	−0.318986
$926$	71.9715	2.36513
$927$	−3.37900	−0.110981
$928$	−23.5915	−0.774430
$929$	−7.79299	−0.255680	−0.127840	−	0.991795i	$-0.540804\pi$
$929$	−7.79299	−0.255680	−0.127840	+	0.991795i	$0.540804\pi$
$930$	−18.5202	−0.607300
$931$	−6.55501	−0.214832
$932$	0.233837	0.00765958
$933$	−6.01498	−0.196921
$934$	67.5153	2.20917
$935$	0	0
$936$	10.8889	0.355914
$937$	−0.427891	−0.0139786	−0.00698929	−	0.999976i	$-0.502225\pi$
$937$	−0.427891	−0.0139786	−0.00698929	+	0.999976i	$0.502225\pi$
$938$	16.0969	0.525584
$939$	−3.41407	−0.111414
$940$	−34.5483	−1.12684
$941$	−50.7330	−1.65385	−0.826925	−	0.562313i	$-0.809912\pi$
$941$	−50.7330	−1.65385	−0.826925	+	0.562313i	$0.809912\pi$
$942$	−2.39706	−0.0781006
$943$	14.0478	0.457458
$944$	20.1582	0.656092
$945$	5.65069	0.183817
$946$	0	0
$947$	−23.7388	−0.771408	−0.385704	−	0.922623i	$-0.626041\pi$
$947$	−23.7388	−0.771408	−0.385704	+	0.922623i	$0.626041\pi$
$948$	−19.0277	−0.617991
$949$	5.02950	0.163265
$950$	−14.4971	−0.470350
$951$	0.0288535	0.000935639 0
$952$	13.3117	0.431435
$953$	−4.55359	−0.147505	−0.0737525	−	0.997277i	$-0.523497\pi$
$953$	−4.55359	−0.147505	−0.0737525	+	0.997277i	$0.523497\pi$
$954$	−10.5181	−0.340535
$955$	−16.7886	−0.543266
$956$	19.8864	0.643171
$957$	0	0
$958$	28.8748	0.932901
$959$	2.61774	0.0845312
$960$	18.6361	0.601477
$961$	2.25393	0.0727073
$962$	132.997	4.28799
$963$	−3.33005	−0.107309
$964$	−27.9273	−0.899476
$965$	1.33069	0.0428365
$966$	5.65069	0.181808
$967$	−38.9252	−1.25175	−0.625876	−	0.779923i	$-0.715258\pi$
$967$	−38.9252	−1.25175	−0.625876	+	0.779923i	$0.715258\pi$
$968$	0	0
$969$	64.2863	2.06518
$970$	−16.0422	−0.515085
$971$	6.67820	0.214314	0.107157	−	0.994242i	$-0.465825\pi$
$971$	6.67820	0.214314	0.107157	+	0.994242i	$0.465825\pi$
$972$	−25.7862	−0.827092
$973$	−5.94214	−0.190496
$974$	4.58985	0.147068
$975$	9.00125	0.288271
$976$	15.5647	0.498215
$977$	34.5917	1.10669	0.553343	−	0.832953i	$-0.313352\pi$
$977$	34.5917	1.10669	0.553343	+	0.832953i	$0.313352\pi$
$978$	71.1202	2.27417
$979$	0	0
$980$	2.89124	0.0923571
$981$	−8.47305	−0.270524
$982$	53.9994	1.72319
$983$	−6.03257	−0.192409	−0.0962046	−	0.995362i	$-0.530670\pi$
$983$	−6.03257	−0.192409	−0.0962046	+	0.995362i	$0.530670\pi$
$984$	22.8531	0.728529
$985$	−5.59425	−0.178248
$986$	49.7010	1.58280
$987$	17.3523	0.552329
$988$	117.475	3.73738
$989$	9.28705	0.295311
$990$	0	0
$991$	13.1912	0.419032	0.209516	−	0.977805i	$-0.432811\pi$
$991$	13.1912	0.419032	0.209516	+	0.977805i	$0.432811\pi$
$992$	−40.8840	−1.29807
$993$	−13.2372	−0.420071
$994$	19.5071	0.618727
$995$	8.05807	0.255458
$996$	−2.68300	−0.0850141
$997$	−2.69777	−0.0854392	−0.0427196	−	0.999087i	$-0.513602\pi$
$997$	−2.69777	−0.0854392	−0.0427196	+	0.999087i	$0.513602\pi$
$998$	10.1935	0.322668
$999$	−54.8207	−1.73445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.u.1.4	✓	4
11.10	odd	2		4235.2.a.v.1.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.u.1.4	✓	4	1.1	even	1	trivial
4235.2.a.v.1.1	yes	4	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)

\(f(q)\)	\(=\)	\(q+2.21161 q^{2} -1.45216 q^{3} +2.89124 q^{4} +1.00000 q^{5} -3.21161 q^{6} +1.00000 q^{7} +1.97107 q^{8} -0.891236 q^{9} +O(q^{10})\)	\(q+2.21161 q^{2} -1.45216 q^{3} +2.89124 q^{4} +1.00000 q^{5} -3.21161 q^{6} +1.00000 q^{7} +1.97107 q^{8} -0.891236 q^{9} +2.21161 q^{10} -4.19853 q^{12} -6.19853 q^{13} +2.21161 q^{14} -1.45216 q^{15} -1.42323 q^{16} +6.75354 q^{17} -1.97107 q^{18} -6.55501 q^{19} +2.89124 q^{20} -1.45216 q^{21} -1.75946 q^{23} -2.86230 q^{24} +1.00000 q^{25} -13.7088 q^{26} +5.65069 q^{27} +2.89124 q^{28} +3.32754 q^{29} -3.21161 q^{30} +5.76662 q^{31} -7.08977 q^{32} +14.9362 q^{34} +1.00000 q^{35} -2.57677 q^{36} -9.70159 q^{37} -14.4971 q^{38} +9.00125 q^{39} +1.97107 q^{40} -7.98415 q^{41} -3.21161 q^{42} -5.27837 q^{43} -0.891236 q^{45} -3.89124 q^{46} -11.9493 q^{47} +2.06675 q^{48} +1.00000 q^{49} +2.21161 q^{50} -9.80721 q^{51} -17.9214 q^{52} +5.33623 q^{53} +12.4971 q^{54} +1.97107 q^{56} +9.51891 q^{57} +7.35924 q^{58} -14.1637 q^{59} -4.19853 q^{60} -10.9362 q^{61} +12.7535 q^{62} -0.891236 q^{63} -12.8334 q^{64} -6.19853 q^{65} +7.27837 q^{67} +19.5261 q^{68} +2.55501 q^{69} +2.21161 q^{70} +8.82029 q^{71} -1.75669 q^{72} -0.811402 q^{73} -21.4562 q^{74} -1.45216 q^{75} -18.9521 q^{76} +19.9073 q^{78} +4.53199 q^{79} -1.42323 q^{80} -5.53199 q^{81} -17.6579 q^{82} +0.639032 q^{83} -4.19853 q^{84} +6.75354 q^{85} -11.6737 q^{86} -4.83212 q^{87} +10.1001 q^{89} -1.97107 q^{90} -6.19853 q^{91} -5.08700 q^{92} -8.37405 q^{93} -26.4272 q^{94} -6.55501 q^{95} +10.2955 q^{96} -7.25363 q^{97} +2.21161 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 4 * q^9	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 4 q^{9} - 8 q^{12} - 16 q^{13} - 2 q^{15} + 12 q^{16} - 2 q^{17} + 6 q^{18} - 6 q^{19} + 4 q^{20} - 2 q^{21} - 2 q^{23} + 10 q^{24} + 4 q^{25} + 2 q^{26} + 10 q^{27} + 4 q^{28} - 12 q^{29} - 4 q^{30} - 6 q^{31} - 12 q^{32} + 8 q^{34} + 4 q^{35} - 28 q^{36} - 6 q^{37} - 10 q^{38} - 12 q^{39} - 6 q^{40} - 18 q^{41} - 4 q^{42} - 6 q^{43} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 2 q^{48} + 4 q^{49} - 4 q^{51} - 30 q^{52} + 34 q^{53} + 2 q^{54} - 6 q^{56} + 28 q^{57} + 32 q^{58} - 10 q^{59} - 8 q^{60} + 8 q^{61} + 22 q^{62} + 4 q^{63} - 16 q^{64} - 16 q^{65} + 14 q^{67} + 44 q^{68} - 10 q^{69} + 12 q^{72} - 2 q^{73} - 48 q^{74} - 2 q^{75} - 38 q^{76} + 14 q^{78} + 8 q^{79} + 12 q^{80} - 12 q^{81} - 34 q^{82} + 10 q^{83} - 8 q^{84} - 2 q^{85} - 24 q^{86} - 32 q^{87} + 10 q^{89} + 6 q^{90} - 16 q^{91} + 10 q^{92} - 26 q^{93} - 54 q^{94} - 6 q^{95} - 8 q^{96} - 34 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 4 * q^9 - 8 * q^12 - 16 * q^13 - 2 * q^15 + 12 * q^16 - 2 * q^17 + 6 * q^18 - 6 * q^19 + 4 * q^20 - 2 * q^21 - 2 * q^23 + 10 * q^24 + 4 * q^25 + 2 * q^26 + 10 * q^27 + 4 * q^28 - 12 * q^29 - 4 * q^30 - 6 * q^31 - 12 * q^32 + 8 * q^34 + 4 * q^35 - 28 * q^36 - 6 * q^37 - 10 * q^38 - 12 * q^39 - 6 * q^40 - 18 * q^41 - 4 * q^42 - 6 * q^43 + 4 * q^45 - 8 * q^46 + 4 * q^47 + 2 * q^48 + 4 * q^49 - 4 * q^51 - 30 * q^52 + 34 * q^53 + 2 * q^54 - 6 * q^56 + 28 * q^57 + 32 * q^58 - 10 * q^59 - 8 * q^60 + 8 * q^61 + 22 * q^62 + 4 * q^63 - 16 * q^64 - 16 * q^65 + 14 * q^67 + 44 * q^68 - 10 * q^69 + 12 * q^72 - 2 * q^73 - 48 * q^74 - 2 * q^75 - 38 * q^76 + 14 * q^78 + 8 * q^79 + 12 * q^80 - 12 * q^81 - 34 * q^82 + 10 * q^83 - 8 * q^84 - 2 * q^85 - 24 * q^86 - 32 * q^87 + 10 * q^89 + 6 * q^90 - 16 * q^91 + 10 * q^92 - 26 * q^93 - 54 * q^94 - 6 * q^95 - 8 * q^96 - 34 * q^97

Introduction

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Database

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