LMFDB - Embedded newform 4235.2.a.v.1.1

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:	$0$
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			1.1
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	$-0.785761\pi$
$2$	−2.21161	−1.56385	−0.781924	+	0.623374i	$0.785761\pi$
$3$	−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	$-0.170724\pi$
$13$	6.19853	1.71916	0.859582	+	0.510998i	$0.170724\pi$
$14$	2.21161	0.591079
$15$	−1.45216	−0.374946
$16$	−1.42323	−0.355807
$17$	−6.75354	−1.63797	−0.818987	−	0.573812i	$-0.805464\pi$
$17$	−6.75354	−1.63797	−0.818987	+	0.573812i	$0.805464\pi$
$18$	1.97107	0.464585
$19$	6.55501	1.50382	0.751911	−	0.659265i	$-0.229132\pi$
$19$	6.55501	1.50382	0.751911	+	0.659265i	$0.229132\pi$
$20$	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	$-0.599979\pi$
$29$	−3.32754	−0.617910	−0.308955	+	0.951077i	$0.599979\pi$
$30$	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	$-0.285727\pi$
$41$	7.98415	1.24691	0.623457	+	0.781857i	$0.285727\pi$
$42$	−3.21161	−0.495563
$43$	5.27837	0.804943	0.402472	−	0.915432i	$-0.368151\pi$
$43$	5.27837	0.804943	0.402472	+	0.915432i	$0.368151\pi$
$44$	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	$-0.253130\pi$
$61$	10.9362	1.40024	0.700120	+	0.714025i	$0.253130\pi$
$62$	−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	$-0.484880\pi$
$73$	0.811402	0.0949674	0.0474837	+	0.998872i	$0.484880\pi$
$74$	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	$-0.582057\pi$
$79$	−4.53199	−0.509889	−0.254944	+	0.966956i	$0.582057\pi$
$80$	−1.42323	−0.159122
$81$	−5.53199	−0.614666
$82$	−17.6579	−1.94998
$83$	−0.639032	−0.0701429	−0.0350715	−	0.999385i	$-0.511166\pi$
$83$	−0.639032	−0.0701429	−0.0350715	+	0.999385i	$0.511166\pi$
$84$	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	$-0.139886\pi$
$101$	18.1898	1.80996	0.904979	+	0.425457i	$0.139886\pi$
$102$	−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	$-0.557806\pi$
$107$	−3.73644	−0.361215	−0.180608	+	0.983555i	$0.557806\pi$
$108$	16.3375	1.57207
$109$	−9.50708	−0.910613	−0.455307	−	0.890335i	$-0.650470\pi$
$109$	−9.50708	−0.910613	−0.455307	+	0.890335i	$0.650470\pi$
$110$	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	$-0.648661\pi$
$127$	−10.1478	−0.900475	−0.450237	+	0.892909i	$0.648661\pi$
$128$	14.2029	1.25537
$129$	−7.66502	−0.674868
$130$	−13.7088	−1.20234
$131$	4.96218	0.433548	0.216774	−	0.976222i	$-0.430447\pi$
$131$	4.96218	0.433548	0.216774	+	0.976222i	$0.430447\pi$
$132$	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	$-0.418911\pi$
$139$	5.94214	0.504006	0.252003	+	0.967727i	$0.418911\pi$
$140$	−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	$-0.508956\pi$
$149$	−0.686788	−0.0562639	−0.0281319	+	0.999604i	$0.508956\pi$
$150$	3.21161	0.262227
$151$	−14.9751	−1.21866	−0.609328	−	0.792918i	$-0.708561\pi$
$151$	−14.9751	−1.21866	−0.609328	+	0.792918i	$0.708561\pi$
$152$	−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	$-0.280565\pi$
$167$	16.4393	1.27211	0.636055	+	0.771644i	$0.280565\pi$
$168$	−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	$-0.588684\pi$
$173$	−7.23463	−0.550039	−0.275019	+	0.961439i	$0.588684\pi$
$174$	−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	$-0.515251\pi$
$193$	−1.33069	−0.0957853	−0.0478926	+	0.998852i	$0.515251\pi$
$194$	16.0422	1.15176
$195$	−9.00125	−0.644593
$196$	2.89124	0.206517
$197$	5.59425	0.398574	0.199287	−	0.979941i	$-0.436137\pi$
$197$	5.59425	0.398574	0.199287	+	0.979941i	$0.436137\pi$
$198$	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	$-0.523397\pi$
$211$	−2.13350	−0.146876	−0.0734382	+	0.997300i	$0.523397\pi$
$212$	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	$-0.739012\pi$
$227$	−20.5592	−1.36456	−0.682282	+	0.731089i	$0.739012\pi$
$228$	−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	$-0.500843\pi$
$233$	−0.0808778	−0.00529848	−0.00264924	+	0.999996i	$0.500843\pi$
$234$	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	$-0.571407\pi$
$239$	−6.87815	−0.444911	−0.222455	+	0.974943i	$0.571407\pi$
$240$	2.06675	0.133408
$241$	9.65928	0.622209	0.311104	−	0.950376i	$-0.399301\pi$
$241$	9.65928	0.622209	0.311104	+	0.950376i	$0.399301\pi$
$242$	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	$-0.420935\pi$
$263$	7.97384	0.491688	0.245844	+	0.969309i	$0.420935\pi$
$264$	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	$-0.318521\pi$
$271$	17.7706	1.07949	0.539745	+	0.841829i	$0.318521\pi$
$272$	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	$-0.862899\pi$
$277$	−30.2465	−1.81734	−0.908668	+	0.417520i	$0.862899\pi$
$278$	−13.1417	−0.788188
$279$	−5.13942	−0.307689
$280$	1.97107	0.117794
$281$	26.8925	1.60427	0.802136	−	0.597142i	$-0.203697\pi$
$281$	26.8925	1.60427	0.802136	+	0.597142i	$0.203697\pi$
$282$	−38.3766	−2.28529
$283$	12.1795	0.723998	0.361999	−	0.932178i	$-0.382094\pi$
$283$	12.1795	0.723998	0.361999	+	0.932178i	$0.382094\pi$
$284$	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	$-0.434230\pi$
$293$	7.02339	0.410311	0.205156	+	0.978729i	$0.434230\pi$
$294$	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	$-0.536611\pi$
$307$	−4.02159	−0.229524	−0.114762	+	0.993393i	$0.536611\pi$
$308$	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	$-0.494472\pi$
$337$	0.637610	0.0347328	0.0173664	+	0.999849i	$0.494472\pi$
$338$	−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	$-0.453474\pi$
$347$	5.42620	0.291294	0.145647	+	0.989337i	$0.453474\pi$
$348$	13.9708	0.748914
$349$	20.0842	1.07508	0.537542	−	0.843237i	$-0.319353\pi$
$349$	20.0842	1.07508	0.537542	+	0.843237i	$0.319353\pi$
$350$	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	$-0.547125\pi$
$359$	−5.58968	−0.295012	−0.147506	+	0.989061i	$0.547125\pi$
$360$	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	$-0.309520\pi$
$373$	21.7595	1.12666	0.563331	+	0.826231i	$0.309520\pi$
$374$	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	$-0.283444\pi$
$409$	25.4435	1.25810	0.629049	+	0.777365i	$0.283444\pi$
$410$	−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	$-0.517600\pi$
$431$	−2.29459	−0.110527	−0.0552633	+	0.998472i	$0.517600\pi$
$432$	−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	$-0.328853\pi$
$439$	21.4610	1.02428	0.512140	+	0.858902i	$0.328853\pi$
$440$	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	$-0.417825\pi$
$457$	10.9155	0.510606	0.255303	+	0.966861i	$0.417825\pi$
$458$	−58.2260	−2.72072
$459$	−38.1622	−1.78126
$460$	−5.08700	−0.237183
$461$	20.2160	0.941554	0.470777	−	0.882252i	$-0.343974\pi$
$461$	20.2160	0.941554	0.470777	+	0.882252i	$0.343974\pi$
$462$	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	$-0.596410\pi$
$479$	−13.0560	−0.596542	−0.298271	+	0.954481i	$0.596410\pi$
$480$	−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	$-0.685733\pi$
$491$	−24.4163	−1.10189	−0.550945	+	0.834541i	$0.685733\pi$
$492$	−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	$-0.735740\pi$
$503$	−30.2653	−1.34946	−0.674731	+	0.738064i	$0.735740\pi$
$504$	−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	$-0.790002\pi$
$523$	−36.1406	−1.58032	−0.790159	+	0.612902i	$0.790002\pi$
$524$	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	$-0.361868\pi$
$541$	19.5594	0.840925	0.420462	+	0.907310i	$0.361868\pi$
$542$	−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	$-0.327676\pi$
$547$	24.1043	1.03063	0.515313	+	0.857002i	$0.327676\pi$
$548$	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	$-0.247694\pi$
$557$	33.6176	1.42442	0.712211	+	0.701965i	$0.247694\pi$
$558$	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	$-0.571506\pi$
$563$	−10.5711	−0.445517	−0.222759	+	0.974874i	$0.571506\pi$
$564$	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	$-0.269269\pi$
$569$	31.6316	1.32607	0.663033	+	0.748590i	$0.269269\pi$
$570$	21.0522	0.881778
$571$	−13.9160	−0.582365	−0.291183	−	0.956667i	$-0.594049\pi$
$571$	−13.9160	−0.582365	−0.291183	+	0.956667i	$0.594049\pi$
$572$	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	$-0.397204\pi$
$593$	15.4564	0.634718	0.317359	+	0.948306i	$0.397204\pi$
$594$	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	$-0.674189\pi$
$601$	−25.5119	−1.04065	−0.520325	+	0.853968i	$0.674189\pi$
$602$	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	$-0.490175\pi$
$607$	1.52063	0.0617206	0.0308603	+	0.999524i	$0.490175\pi$
$608$	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	$-0.187487\pi$
$613$	41.1735	1.66298	0.831492	+	0.555537i	$0.187487\pi$
$614$	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	$-0.393694\pi$
$659$	16.8298	0.655594	0.327797	+	0.944748i	$0.393694\pi$
$660$	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	$-0.393683\pi$
$673$	17.0093	0.655659	0.327830	+	0.944737i	$0.393683\pi$
$674$	−1.41015	−0.0543168
$675$	5.65069	0.217495
$676$	73.5004	2.82694
$677$	−11.5295	−0.443116	−0.221558	−	0.975147i	$-0.571114\pi$
$677$	−11.5295	−0.443116	−0.221558	+	0.975147i	$0.571114\pi$
$678$	−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	$-0.367955\pi$
$701$	21.3419	0.806072	0.403036	+	0.915184i	$0.367955\pi$
$702$	−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	$-0.560879\pi$
$733$	−10.2931	−0.380183	−0.190092	+	0.981766i	$0.560879\pi$
$734$	−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	$-0.584232\pi$
$739$	−14.2200	−0.523092	−0.261546	+	0.965191i	$0.584232\pi$
$740$	−28.0496	−1.03112
$741$	−59.0033	−2.16754
$742$	11.8017	0.433253
$743$	1.42306	0.0522069	0.0261034	−	0.999659i	$-0.491690\pi$
$743$	1.42306	0.0522069	0.0261034	+	0.999659i	$0.491690\pi$
$744$	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	$-0.579523\pi$
$761$	−13.6408	−0.494478	−0.247239	+	0.968954i	$0.579523\pi$
$762$	−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	$-0.622470\pi$
$769$	−20.8163	−0.750654	−0.375327	+	0.926892i	$0.622470\pi$
$770$	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	$-0.413733\pi$
$787$	15.0205	0.535421	0.267711	+	0.963499i	$0.413733\pi$
$788$	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	$-0.407688\pi$
$809$	16.2670	0.571918	0.285959	+	0.958242i	$0.407688\pi$
$810$	12.2346	0.429881
$811$	25.1784	0.884133	0.442067	−	0.896982i	$-0.354245\pi$
$811$	25.1784	0.884133	0.442067	+	0.896982i	$0.354245\pi$
$812$	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	$-0.640709\pi$
$821$	−24.5153	−0.855590	−0.427795	+	0.903876i	$0.640709\pi$
$822$	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	$-0.639205\pi$
$827$	−24.3588	−0.847037	−0.423519	+	0.905887i	$0.639205\pi$
$828$	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	$-0.263655\pi$
$853$	39.4944	1.35226	0.676131	+	0.736782i	$0.263655\pi$
$854$	24.1867	0.827652
$855$	−5.84206	−0.199794
$856$	7.36478	0.251723
$857$	32.2687	1.10228	0.551138	−	0.834414i	$-0.314194\pi$
$857$	32.2687	1.10228	0.551138	+	0.834414i	$0.314194\pi$
$858$	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	$-0.519606\pi$
$877$	−3.64582	−0.123111	−0.0615553	+	0.998104i	$0.519606\pi$
$878$	−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	$-0.193543\pi$
$887$	48.8895	1.64155	0.820774	+	0.571254i	$0.193543\pi$
$888$	−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	$-0.656192\pi$
$919$	−28.5711	−0.942472	−0.471236	+	0.882007i	$0.656192\pi$
$920$	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	$-0.497775\pi$
$937$	0.427891	0.0139786	0.00698929	+	0.999976i	$0.497775\pi$
$938$	16.0969	0.525584
$939$	−3.41407	−0.111414
$940$	−34.5483	−1.12684
$941$	50.7330	1.65385	0.826925	−	0.562313i	$-0.190088\pi$
$941$	50.7330	1.65385	0.826925	+	0.562313i	$0.190088\pi$
$942$	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	$-0.476503\pi$
$953$	4.55359	0.147505	0.0737525	+	0.997277i	$0.476503\pi$
$954$	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	$-0.284742\pi$
$967$	38.9252	1.25175	0.625876	+	0.779923i	$0.284742\pi$
$968$	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	$-0.486398\pi$
$997$	2.69777	0.0854392	0.0427196	+	0.999087i	$0.486398\pi$
$998$	−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.v.1.1	yes	4
11.10	odd	2		4235.2.a.u.1.4	✓	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
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

L-functions

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Database

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