LMFDB - Embedded newform 3234.2.a.bl.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(1,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, 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("3234.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.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:	$25.8236200137$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.27133$ of defining polynomial
Character	$\chi$	$=$	3234.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.79793 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.79793 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.79793 q^{10} +1.00000 q^{11} -1.00000 q^{12} -3.63899 q^{13} -1.79793 q^{15} +1.00000 q^{16} -6.11582 q^{17} +1.00000 q^{18} -1.84106 q^{19} +1.79793 q^{20} +1.00000 q^{22} -7.37109 q^{23} -1.00000 q^{24} -1.76744 q^{25} -3.63899 q^{26} -1.00000 q^{27} -10.4243 q^{29} -1.79793 q^{30} -7.97958 q^{31} +1.00000 q^{32} -1.00000 q^{33} -6.11582 q^{34} +1.00000 q^{36} +10.1995 q^{37} -1.84106 q^{38} +3.63899 q^{39} +1.79793 q^{40} -8.17680 q^{41} -2.28577 q^{43} +1.00000 q^{44} +1.79793 q^{45} -7.37109 q^{46} +0.669485 q^{47} -1.00000 q^{48} -1.76744 q^{50} +6.11582 q^{51} -3.63899 q^{52} +11.2848 q^{53} -1.00000 q^{54} +1.79793 q^{55} +1.84106 q^{57} -10.4243 q^{58} +13.5706 q^{59} -1.79793 q^{60} +0.274758 q^{61} -7.97958 q^{62} +1.00000 q^{64} -6.54266 q^{65} -1.00000 q^{66} +3.88163 q^{67} -6.11582 q^{68} +7.37109 q^{69} +10.8738 q^{71} +1.00000 q^{72} -3.85892 q^{73} +10.1995 q^{74} +1.76744 q^{75} -1.84106 q^{76} +3.63899 q^{78} -12.5174 q^{79} +1.79793 q^{80} +1.00000 q^{81} -8.17680 q^{82} -5.27314 q^{83} -10.9958 q^{85} -2.28577 q^{86} +10.4243 q^{87} +1.00000 q^{88} -1.98214 q^{89} +1.79793 q^{90} -7.37109 q^{92} +7.97958 q^{93} +0.669485 q^{94} -3.31010 q^{95} -1.00000 q^{96} -4.12066 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 12 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 4 q^{25} - 8 q^{26} - 4 q^{27} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} - 4 q^{34} + 4 q^{36} + 8 q^{37} - 12 q^{38} + 8 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{43} + 4 q^{44} - 4 q^{45} - 8 q^{46} - 4 q^{47} - 4 q^{48} + 4 q^{50} + 4 q^{51} - 8 q^{52} - 8 q^{53} - 4 q^{54} - 4 q^{55} + 12 q^{57} - 8 q^{58} + 4 q^{60} - 24 q^{61} - 4 q^{62} + 4 q^{64} - 16 q^{65} - 4 q^{66} - 8 q^{67} - 4 q^{68} + 8 q^{69} + 8 q^{71} + 4 q^{72} - 4 q^{73} + 8 q^{74} - 4 q^{75} - 12 q^{76} + 8 q^{78} - 8 q^{79} - 4 q^{80} + 4 q^{81} - 12 q^{82} - 4 q^{83} - 8 q^{85} - 8 q^{86} + 8 q^{87} + 4 q^{88} - 24 q^{89} - 4 q^{90} - 8 q^{92} + 4 q^{93} - 4 q^{94} + 8 q^{95} - 4 q^{96} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - 8 * q^13 + 4 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 12 * q^19 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 4 * q^25 - 8 * q^26 - 4 * q^27 - 8 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 - 4 * q^34 + 4 * q^36 + 8 * q^37 - 12 * q^38 + 8 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^43 + 4 * q^44 - 4 * q^45 - 8 * q^46 - 4 * q^47 - 4 * q^48 + 4 * q^50 + 4 * q^51 - 8 * q^52 - 8 * q^53 - 4 * q^54 - 4 * q^55 + 12 * q^57 - 8 * q^58 + 4 * q^60 - 24 * q^61 - 4 * q^62 + 4 * q^64 - 16 * q^65 - 4 * q^66 - 8 * q^67 - 4 * q^68 + 8 * q^69 + 8 * q^71 + 4 * q^72 - 4 * q^73 + 8 * q^74 - 4 * q^75 - 12 * q^76 + 8 * q^78 - 8 * q^79 - 4 * q^80 + 4 * q^81 - 12 * q^82 - 4 * q^83 - 8 * q^85 - 8 * q^86 + 8 * q^87 + 4 * q^88 - 24 * q^89 - 4 * q^90 - 8 * q^92 + 4 * q^93 - 4 * q^94 + 8 * q^95 - 4 * q^96 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.79793	0.804060	0.402030	−	0.915627i	$-0.368305\pi$
$5$	1.79793	0.804060	0.402030	+	0.915627i	$0.368305\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.79793	0.568556
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−3.63899	−1.00927	−0.504637	−	0.863331i	$-0.668374\pi$
$13$	−3.63899	−1.00927	−0.504637	+	0.863331i	$0.668374\pi$
$14$	0	0
$15$	−1.79793	−0.464224
$16$	1.00000	0.250000
$17$	−6.11582	−1.48330	−0.741652	−	0.670785i	$-0.765957\pi$
$17$	−6.11582	−1.48330	−0.741652	+	0.670785i	$0.765957\pi$
$18$	1.00000	0.235702
$19$	−1.84106	−0.422368	−0.211184	−	0.977446i	$-0.567732\pi$
$19$	−1.84106	−0.422368	−0.211184	+	0.977446i	$0.567732\pi$
$20$	1.79793	0.402030
$21$	0	0
$22$	1.00000	0.213201
$23$	−7.37109	−1.53698	−0.768489	−	0.639863i	$-0.778991\pi$
$23$	−7.37109	−1.53698	−0.768489	+	0.639863i	$0.778991\pi$
$24$	−1.00000	−0.204124
$25$	−1.76744	−0.353488
$26$	−3.63899	−0.713665
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−10.4243	−1.93574	−0.967871	−	0.251446i	$-0.919094\pi$
$29$	−10.4243	−1.93574	−0.967871	+	0.251446i	$0.919094\pi$
$30$	−1.79793	−0.328256
$31$	−7.97958	−1.43318	−0.716588	−	0.697497i	$-0.754297\pi$
$31$	−7.97958	−1.43318	−0.716588	+	0.697497i	$0.754297\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−6.11582	−1.04885
$35$	0	0
$36$	1.00000	0.166667
$37$	10.1995	1.67679	0.838395	−	0.545063i	$-0.183494\pi$
$37$	10.1995	1.67679	0.838395	+	0.545063i	$0.183494\pi$
$38$	−1.84106	−0.298659
$39$	3.63899	0.582705
$40$	1.79793	0.284278
$41$	−8.17680	−1.27700	−0.638501	−	0.769621i	$-0.720445\pi$
$41$	−8.17680	−1.27700	−0.638501	+	0.769621i	$0.720445\pi$
$42$	0	0
$43$	−2.28577	−0.348576	−0.174288	−	0.984695i	$-0.555762\pi$
$43$	−2.28577	−0.348576	−0.174288	+	0.984695i	$0.555762\pi$
$44$	1.00000	0.150756
$45$	1.79793	0.268020
$46$	−7.37109	−1.08681
$47$	0.669485	0.0976545	0.0488272	−	0.998807i	$-0.484452\pi$
$47$	0.669485	0.0976545	0.0488272	+	0.998807i	$0.484452\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−1.76744	−0.249954
$51$	6.11582	0.856386
$52$	−3.63899	−0.504637
$53$	11.2848	1.55009	0.775046	−	0.631905i	$-0.217727\pi$
$53$	11.2848	1.55009	0.775046	+	0.631905i	$0.217727\pi$
$54$	−1.00000	−0.136083
$55$	1.79793	0.242433
$56$	0	0
$57$	1.84106	0.243854
$58$	−10.4243	−1.36878
$59$	13.5706	1.76674	0.883371	−	0.468674i	$-0.155268\pi$
$59$	13.5706	1.76674	0.883371	+	0.468674i	$0.155268\pi$
$60$	−1.79793	−0.232112
$61$	0.274758	0.0351791	0.0175896	−	0.999845i	$-0.494401\pi$
$61$	0.274758	0.0351791	0.0175896	+	0.999845i	$0.494401\pi$
$62$	−7.97958	−1.01341
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.54266	−0.811517
$66$	−1.00000	−0.123091
$67$	3.88163	0.474217	0.237108	−	0.971483i	$-0.423800\pi$
$67$	3.88163	0.474217	0.237108	+	0.971483i	$0.423800\pi$
$68$	−6.11582	−0.741652
$69$	7.37109	0.887375
$70$	0	0
$71$	10.8738	1.29049	0.645244	−	0.763976i	$-0.276756\pi$
$71$	10.8738	1.29049	0.645244	+	0.763976i	$0.276756\pi$
$72$	1.00000	0.117851
$73$	−3.85892	−0.451653	−0.225826	−	0.974168i	$-0.572508\pi$
$73$	−3.85892	−0.451653	−0.225826	+	0.974168i	$0.572508\pi$
$74$	10.1995	1.18567
$75$	1.76744	0.204086
$76$	−1.84106	−0.211184
$77$	0	0
$78$	3.63899	0.412035
$79$	−12.5174	−1.40832	−0.704159	−	0.710043i	$-0.748676\pi$
$79$	−12.5174	−1.40832	−0.704159	+	0.710043i	$0.748676\pi$
$80$	1.79793	0.201015
$81$	1.00000	0.111111
$82$	−8.17680	−0.902977
$83$	−5.27314	−0.578802	−0.289401	−	0.957208i	$-0.593456\pi$
$83$	−5.27314	−0.578802	−0.289401	+	0.957208i	$0.593456\pi$
$84$	0	0
$85$	−10.9958	−1.19266
$86$	−2.28577	−0.246481
$87$	10.4243	1.11760
$88$	1.00000	0.106600
$89$	−1.98214	−0.210106	−0.105053	−	0.994467i	$-0.533501\pi$
$89$	−1.98214	−0.210106	−0.105053	+	0.994467i	$0.533501\pi$
$90$	1.79793	0.189519
$91$	0	0
$92$	−7.37109	−0.768489
$93$	7.97958	0.827444
$94$	0.669485	0.0690522
$95$	−3.31010	−0.339609
$96$	−1.00000	−0.102062
$97$	−4.12066	−0.418390	−0.209195	−	0.977874i	$-0.567084\pi$
$97$	−4.12066	−0.418390	−0.209195	+	0.977874i	$0.567084\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−1.76744	−0.176744
$101$	−6.90367	−0.686941	−0.343470	−	0.939163i	$-0.611603\pi$
$101$	−6.90367	−0.686941	−0.343470	+	0.939163i	$0.611603\pi$
$102$	6.11582	0.605556
$103$	−12.6154	−1.24303	−0.621514	−	0.783403i	$-0.713482\pi$
$103$	−12.6154	−1.24303	−0.621514	+	0.783403i	$0.713482\pi$
$104$	−3.63899	−0.356832
$105$	0	0
$106$	11.2848	1.09608
$107$	16.9417	1.63782	0.818908	−	0.573925i	$-0.194580\pi$
$107$	16.9417	1.63782	0.818908	+	0.573925i	$0.194580\pi$
$108$	−1.00000	−0.0962250
$109$	9.76326	0.935151	0.467576	−	0.883953i	$-0.345128\pi$
$109$	9.76326	0.935151	0.467576	+	0.883953i	$0.345128\pi$
$110$	1.79793	0.171426
$111$	−10.1995	−0.968095
$112$	0	0
$113$	−12.9348	−1.21681	−0.608404	−	0.793628i	$-0.708190\pi$
$113$	−12.9348	−1.21681	−0.608404	+	0.793628i	$0.708190\pi$
$114$	1.84106	0.172431
$115$	−13.2527	−1.23582
$116$	−10.4243	−0.967871
$117$	−3.63899	−0.336425
$118$	13.5706	1.24928
$119$	0	0
$120$	−1.79793	−0.164128
$121$	1.00000	0.0909091
$122$	0.274758	0.0248754
$123$	8.17680	0.737278
$124$	−7.97958	−0.716588
$125$	−12.1674	−1.08829
$126$	0	0
$127$	−7.43208	−0.659490	−0.329745	−	0.944070i	$-0.606963\pi$
$127$	−7.43208	−0.659490	−0.329745	+	0.944070i	$0.606963\pi$
$128$	1.00000	0.0883883
$129$	2.28577	0.201251
$130$	−6.54266	−0.573829
$131$	−1.64154	−0.143422	−0.0717112	−	0.997425i	$-0.522846\pi$
$131$	−1.64154	−0.143422	−0.0717112	+	0.997425i	$0.522846\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	3.88163	0.335322
$135$	−1.79793	−0.154741
$136$	−6.11582	−0.524427
$137$	14.5307	1.24144	0.620721	−	0.784032i	$-0.286840\pi$
$137$	14.5307	1.24144	0.620721	+	0.784032i	$0.286840\pi$
$138$	7.37109	0.627469
$139$	8.26535	0.701058	0.350529	−	0.936552i	$-0.386002\pi$
$139$	8.26535	0.701058	0.350529	+	0.936552i	$0.386002\pi$
$140$	0	0
$141$	−0.669485	−0.0563808
$142$	10.8738	0.912513
$143$	−3.63899	−0.304308
$144$	1.00000	0.0833333
$145$	−18.7422	−1.55645
$146$	−3.85892	−0.319367
$147$	0	0
$148$	10.1995	0.838395
$149$	−7.55045	−0.618557	−0.309278	−	0.950972i	$-0.600087\pi$
$149$	−7.55045	−0.618557	−0.309278	+	0.950972i	$0.600087\pi$
$150$	1.76744	0.144311
$151$	12.3990	1.00902	0.504509	−	0.863406i	$-0.331673\pi$
$151$	12.3990	1.00902	0.504509	+	0.863406i	$0.331673\pi$
$152$	−1.84106	−0.149330
$153$	−6.11582	−0.494434
$154$	0	0
$155$	−14.3468	−1.15236
$156$	3.63899	0.291352
$157$	−4.54011	−0.362340	−0.181170	−	0.983452i	$-0.557988\pi$
$157$	−4.54011	−0.362340	−0.181170	+	0.983452i	$0.557988\pi$
$158$	−12.5174	−0.995831
$159$	−11.2848	−0.894946
$160$	1.79793	0.142139
$161$	0	0
$162$	1.00000	0.0785674
$163$	15.8275	1.23971	0.619853	−	0.784718i	$-0.287192\pi$
$163$	15.8275	1.23971	0.619853	+	0.784718i	$0.287192\pi$
$164$	−8.17680	−0.638501
$165$	−1.79793	−0.139969
$166$	−5.27314	−0.409275
$167$	22.0844	1.70894	0.854471	−	0.519499i	$-0.173882\pi$
$167$	22.0844	1.70894	0.854471	+	0.519499i	$0.173882\pi$
$168$	0	0
$169$	0.242256	0.0186350
$170$	−10.9958	−0.843341
$171$	−1.84106	−0.140789
$172$	−2.28577	−0.174288
$173$	10.2628	0.780266	0.390133	−	0.920758i	$-0.372429\pi$
$173$	10.2628	0.780266	0.390133	+	0.920758i	$0.372429\pi$
$174$	10.4243	0.790264
$175$	0	0
$176$	1.00000	0.0753778
$177$	−13.5706	−1.02003
$178$	−1.98214	−0.148567
$179$	−12.3954	−0.926477	−0.463239	−	0.886234i	$-0.653313\pi$
$179$	−12.3954	−0.926477	−0.463239	+	0.886234i	$0.653313\pi$
$180$	1.79793	0.134010
$181$	22.4506	1.66874	0.834370	−	0.551204i	$-0.185831\pi$
$181$	22.4506	1.66874	0.834370	+	0.551204i	$0.185831\pi$
$182$	0	0
$183$	−0.274758	−0.0203107
$184$	−7.37109	−0.543404
$185$	18.3380	1.34824
$186$	7.97958	0.585092
$187$	−6.11582	−0.447233
$188$	0.669485	0.0488272
$189$	0	0
$190$	−3.31010	−0.240140
$191$	−13.7142	−0.992327	−0.496164	−	0.868229i	$-0.665258\pi$
$191$	−13.7142	−0.992327	−0.496164	+	0.868229i	$0.665258\pi$
$192$	−1.00000	−0.0721688
$193$	3.77883	0.272006	0.136003	−	0.990708i	$-0.456574\pi$
$193$	3.77883	0.272006	0.136003	+	0.990708i	$0.456574\pi$
$194$	−4.12066	−0.295846
$195$	6.54266	0.468530
$196$	0	0
$197$	−21.6316	−1.54119	−0.770594	−	0.637327i	$-0.780040\pi$
$197$	−21.6316	−1.54119	−0.770594	+	0.637327i	$0.780040\pi$
$198$	1.00000	0.0710669
$199$	17.8323	1.26410	0.632051	−	0.774927i	$-0.282213\pi$
$199$	17.8323	1.26410	0.632051	+	0.774927i	$0.282213\pi$
$200$	−1.76744	−0.124977
$201$	−3.88163	−0.273789
$202$	−6.90367	−0.485741
$203$	0	0
$204$	6.11582	0.428193
$205$	−14.7013	−1.02679
$206$	−12.6154	−0.878953
$207$	−7.37109	−0.512326
$208$	−3.63899	−0.252319
$209$	−1.84106	−0.127349
$210$	0	0
$211$	−8.27020	−0.569344	−0.284672	−	0.958625i	$-0.591885\pi$
$211$	−8.27020	−0.569344	−0.284672	+	0.958625i	$0.591885\pi$
$212$	11.2848	0.775046
$213$	−10.8738	−0.745064
$214$	16.9417	1.15811
$215$	−4.10965	−0.280276
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	9.76326	0.661252
$219$	3.85892	0.260762
$220$	1.79793	0.121217
$221$	22.2554	1.49706
$222$	−10.1995	−0.684547
$223$	9.10574	0.609765	0.304883	−	0.952390i	$-0.401383\pi$
$223$	9.10574	0.609765	0.304883	+	0.952390i	$0.401383\pi$
$224$	0	0
$225$	−1.76744	−0.117829
$226$	−12.9348	−0.860413
$227$	0.620456	0.0411811	0.0205905	−	0.999788i	$-0.493445\pi$
$227$	0.620456	0.0411811	0.0205905	+	0.999788i	$0.493445\pi$
$228$	1.84106	0.121927
$229$	−18.0011	−1.18954	−0.594772	−	0.803895i	$-0.702758\pi$
$229$	−18.0011	−1.18954	−0.594772	+	0.803895i	$0.702758\pi$
$230$	−13.2527	−0.873858
$231$	0	0
$232$	−10.4243	−0.684388
$233$	−19.8697	−1.30171	−0.650853	−	0.759204i	$-0.725588\pi$
$233$	−19.8697	−1.30171	−0.650853	+	0.759204i	$0.725588\pi$
$234$	−3.63899	−0.237888
$235$	1.20369	0.0785201
$236$	13.5706	0.883371
$237$	12.5174	0.813092
$238$	0	0
$239$	−17.4201	−1.12681	−0.563407	−	0.826180i	$-0.690510\pi$
$239$	−17.4201	−1.12681	−0.563407	+	0.826180i	$0.690510\pi$
$240$	−1.79793	−0.116056
$241$	−18.4149	−1.18621	−0.593104	−	0.805126i	$-0.702098\pi$
$241$	−18.4149	−1.18621	−0.593104	+	0.805126i	$0.702098\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	0.274758	0.0175896
$245$	0	0
$246$	8.17680	0.521334
$247$	6.69959	0.426285
$248$	−7.97958	−0.506704
$249$	5.27314	0.334171
$250$	−12.1674	−0.769534
$251$	−21.8022	−1.37614	−0.688072	−	0.725642i	$-0.741543\pi$
$251$	−21.8022	−1.37614	−0.688072	+	0.725642i	$0.741543\pi$
$252$	0	0
$253$	−7.37109	−0.463416
$254$	−7.43208	−0.466330
$255$	10.9958	0.688585
$256$	1.00000	0.0625000
$257$	4.00229	0.249656	0.124828	−	0.992178i	$-0.460162\pi$
$257$	4.00229	0.249656	0.124828	+	0.992178i	$0.460162\pi$
$258$	2.28577	0.142306
$259$	0	0
$260$	−6.54266	−0.405759
$261$	−10.4243	−0.645248
$262$	−1.64154	−0.101415
$263$	−1.13946	−0.0702619	−0.0351309	−	0.999383i	$-0.511185\pi$
$263$	−1.13946	−0.0702619	−0.0351309	+	0.999383i	$0.511185\pi$
$264$	−1.00000	−0.0615457
$265$	20.2894	1.24637
$266$	0	0
$267$	1.98214	0.121305
$268$	3.88163	0.237108
$269$	−3.85892	−0.235283	−0.117641	−	0.993056i	$-0.537533\pi$
$269$	−3.85892	−0.235283	−0.117641	+	0.993056i	$0.537533\pi$
$270$	−1.79793	−0.109419
$271$	22.0202	1.33763	0.668815	−	0.743429i	$-0.266802\pi$
$271$	22.0202	1.33763	0.668815	+	0.743429i	$0.266802\pi$
$272$	−6.11582	−0.370826
$273$	0	0
$274$	14.5307	0.877832
$275$	−1.76744	−0.106581
$276$	7.37109	0.443687
$277$	−13.1307	−0.788950	−0.394475	−	0.918907i	$-0.629073\pi$
$277$	−13.1307	−0.788950	−0.394475	+	0.918907i	$0.629073\pi$
$278$	8.26535	0.495723
$279$	−7.97958	−0.477725
$280$	0	0
$281$	−16.1064	−0.960828	−0.480414	−	0.877042i	$-0.659514\pi$
$281$	−16.1064	−0.960828	−0.480414	+	0.877042i	$0.659514\pi$
$282$	−0.669485	−0.0398673
$283$	10.6085	0.630610	0.315305	−	0.948990i	$-0.397893\pi$
$283$	10.6085	0.630610	0.315305	+	0.948990i	$0.397893\pi$
$284$	10.8738	0.645244
$285$	3.31010	0.196073
$286$	−3.63899	−0.215178
$287$	0	0
$288$	1.00000	0.0589256
$289$	20.4032	1.20019
$290$	−18.7422	−1.10058
$291$	4.12066	0.241558
$292$	−3.85892	−0.225826
$293$	3.69313	0.215755	0.107877	−	0.994164i	$-0.465595\pi$
$293$	3.69313	0.215755	0.107877	+	0.994164i	$0.465595\pi$
$294$	0	0
$295$	24.3990	1.42057
$296$	10.1995	0.592835
$297$	−1.00000	−0.0580259
$298$	−7.55045	−0.437386
$299$	26.8233	1.55123
$300$	1.76744	0.102043
$301$	0	0
$302$	12.3990	0.713484
$303$	6.90367	0.396605
$304$	−1.84106	−0.105592
$305$	0.493996	0.0282861
$306$	−6.11582	−0.349618
$307$	−19.1223	−1.09137	−0.545683	−	0.837992i	$-0.683730\pi$
$307$	−19.1223	−1.09137	−0.545683	+	0.837992i	$0.683730\pi$
$308$	0	0
$309$	12.6154	0.717662
$310$	−14.3468	−0.814841
$311$	13.1190	0.743913	0.371956	−	0.928250i	$-0.378687\pi$
$311$	13.1190	0.743913	0.371956	+	0.928250i	$0.378687\pi$
$312$	3.63899	0.206017
$313$	12.6248	0.713594	0.356797	−	0.934182i	$-0.383869\pi$
$313$	12.6248	0.713594	0.356797	+	0.934182i	$0.383869\pi$
$314$	−4.54011	−0.256213
$315$	0	0
$316$	−12.5174	−0.704159
$317$	−29.4555	−1.65438	−0.827192	−	0.561919i	$-0.810063\pi$
$317$	−29.4555	−1.65438	−0.827192	+	0.561919i	$0.810063\pi$
$318$	−11.2848	−0.632822
$319$	−10.4243	−0.583648
$320$	1.79793	0.100507
$321$	−16.9417	−0.945593
$322$	0	0
$323$	11.2596	0.626499
$324$	1.00000	0.0555556
$325$	6.43169	0.356766
$326$	15.8275	0.876604
$327$	−9.76326	−0.539910
$328$	−8.17680	−0.451489
$329$	0	0
$330$	−1.79793	−0.0989729
$331$	2.28901	0.125815	0.0629077	−	0.998019i	$-0.479963\pi$
$331$	2.28901	0.125815	0.0629077	+	0.998019i	$0.479963\pi$
$332$	−5.27314	−0.289401
$333$	10.1995	0.558930
$334$	22.0844	1.20840
$335$	6.97891	0.381299
$336$	0	0
$337$	5.35093	0.291484	0.145742	−	0.989323i	$-0.453443\pi$
$337$	5.35093	0.291484	0.145742	+	0.989323i	$0.453443\pi$
$338$	0.242256	0.0131770
$339$	12.9348	0.702524
$340$	−10.9958	−0.596332
$341$	−7.97958	−0.432119
$342$	−1.84106	−0.0995530
$343$	0	0
$344$	−2.28577	−0.123240
$345$	13.2527	0.713502
$346$	10.2628	0.551731
$347$	20.8197	1.11766	0.558830	−	0.829282i	$-0.311250\pi$
$347$	20.8197	1.11766	0.558830	+	0.829282i	$0.311250\pi$
$348$	10.4243	0.558801
$349$	23.1843	1.24103	0.620514	−	0.784195i	$-0.286924\pi$
$349$	23.1843	1.24103	0.620514	+	0.784195i	$0.286924\pi$
$350$	0	0
$351$	3.63899	0.194235
$352$	1.00000	0.0533002
$353$	−12.1243	−0.645310	−0.322655	−	0.946517i	$-0.604575\pi$
$353$	−12.1243	−0.645310	−0.322655	+	0.946517i	$0.604575\pi$
$354$	−13.5706	−0.721269
$355$	19.5504	1.03763
$356$	−1.98214	−0.105053
$357$	0	0
$358$	−12.3954	−0.655118
$359$	12.3312	0.650815	0.325408	−	0.945574i	$-0.394499\pi$
$359$	12.3312	0.650815	0.325408	+	0.945574i	$0.394499\pi$
$360$	1.79793	0.0947594
$361$	−15.6105	−0.821605
$362$	22.4506	1.17998
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−6.93808	−0.363156
$366$	−0.274758	−0.0143618
$367$	18.0860	0.944081	0.472041	−	0.881577i	$-0.343518\pi$
$367$	18.0860	0.944081	0.472041	+	0.881577i	$0.343518\pi$
$368$	−7.37109	−0.384245
$369$	−8.17680	−0.425667
$370$	18.3380	0.953349
$371$	0	0
$372$	7.97958	0.413722
$373$	6.95365	0.360046	0.180023	−	0.983662i	$-0.442383\pi$
$373$	6.95365	0.360046	0.180023	+	0.983662i	$0.442383\pi$
$374$	−6.11582	−0.316241
$375$	12.1674	0.628322
$376$	0.669485	0.0345261
$377$	37.9339	1.95370
$378$	0	0
$379$	5.14307	0.264182	0.132091	−	0.991238i	$-0.457831\pi$
$379$	5.14307	0.264182	0.132091	+	0.991238i	$0.457831\pi$
$380$	−3.31010	−0.169804
$381$	7.43208	0.380757
$382$	−13.7142	−0.701681
$383$	18.8810	0.964772	0.482386	−	0.875959i	$-0.339770\pi$
$383$	18.8810	0.964772	0.482386	+	0.875959i	$0.339770\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	3.77883	0.192337
$387$	−2.28577	−0.116192
$388$	−4.12066	−0.209195
$389$	−30.3990	−1.54129	−0.770646	−	0.637263i	$-0.780066\pi$
$389$	−30.3990	−1.54129	−0.770646	+	0.637263i	$0.780066\pi$
$390$	6.54266	0.331301
$391$	45.0802	2.27980
$392$	0	0
$393$	1.64154	0.0828049
$394$	−21.6316	−1.08978
$395$	−22.5054	−1.13237
$396$	1.00000	0.0502519
$397$	2.08009	0.104397	0.0521983	−	0.998637i	$-0.483377\pi$
$397$	2.08009	0.104397	0.0521983	+	0.998637i	$0.483377\pi$
$398$	17.8323	0.893855
$399$	0	0
$400$	−1.76744	−0.0883719
$401$	−21.8444	−1.09086	−0.545429	−	0.838157i	$-0.683633\pi$
$401$	−21.8444	−1.09086	−0.545429	+	0.838157i	$0.683633\pi$
$402$	−3.88163	−0.193598
$403$	29.0376	1.44647
$404$	−6.90367	−0.343470
$405$	1.79793	0.0893400
$406$	0	0
$407$	10.1995	0.505571
$408$	6.11582	0.302778
$409$	−33.7571	−1.66918	−0.834591	−	0.550871i	$-0.814296\pi$
$409$	−33.7571	−1.66918	−0.834591	+	0.550871i	$0.814296\pi$
$410$	−14.7013	−0.726048
$411$	−14.5307	−0.716747
$412$	−12.6154	−0.621514
$413$	0	0
$414$	−7.37109	−0.362269
$415$	−9.48074	−0.465391
$416$	−3.63899	−0.178416
$417$	−8.26535	−0.404756
$418$	−1.84106	−0.0900491
$419$	−22.7371	−1.11078	−0.555389	−	0.831590i	$-0.687431\pi$
$419$	−22.7371	−1.11078	−0.555389	+	0.831590i	$0.687431\pi$
$420$	0	0
$421$	−21.0192	−1.02441	−0.512207	−	0.858862i	$-0.671172\pi$
$421$	−21.0192	−1.02441	−0.512207	+	0.858862i	$0.671172\pi$
$422$	−8.27020	−0.402587
$423$	0.669485	0.0325515
$424$	11.2848	0.548040
$425$	10.8093	0.524329
$426$	−10.8738	−0.526840
$427$	0	0
$428$	16.9417	0.818908
$429$	3.63899	0.175692
$430$	−4.10965	−0.198185
$431$	7.03305	0.338770	0.169385	−	0.985550i	$-0.445822\pi$
$431$	7.03305	0.338770	0.169385	+	0.985550i	$0.445822\pi$
$432$	−1.00000	−0.0481125
$433$	−5.77293	−0.277429	−0.138715	−	0.990332i	$-0.544297\pi$
$433$	−5.77293	−0.277429	−0.138715	+	0.990332i	$0.544297\pi$
$434$	0	0
$435$	18.7422	0.898619
$436$	9.76326	0.467576
$437$	13.5706	0.649170
$438$	3.85892	0.184386
$439$	−31.2275	−1.49041	−0.745203	−	0.666838i	$-0.767647\pi$
$439$	−31.2275	−1.49041	−0.745203	+	0.666838i	$0.767647\pi$
$440$	1.79793	0.0857131
$441$	0	0
$442$	22.2554	1.05858
$443$	−35.8953	−1.70544	−0.852720	−	0.522369i	$-0.825048\pi$
$443$	−35.8953	−1.70544	−0.852720	+	0.522369i	$0.825048\pi$
$444$	−10.1995	−0.484048
$445$	−3.56375	−0.168938
$446$	9.10574	0.431169
$447$	7.55045	0.357124
$448$	0	0
$449$	−24.5495	−1.15856	−0.579282	−	0.815127i	$-0.696667\pi$
$449$	−24.5495	−1.15856	−0.579282	+	0.815127i	$0.696667\pi$
$450$	−1.76744	−0.0833178
$451$	−8.17680	−0.385031
$452$	−12.9348	−0.608404
$453$	−12.3990	−0.582557
$454$	0.620456	0.0291194
$455$	0	0
$456$	1.84106	0.0862155
$457$	26.2771	1.22919	0.614594	−	0.788843i	$-0.289320\pi$
$457$	26.2771	1.22919	0.614594	+	0.788843i	$0.289320\pi$
$458$	−18.0011	−0.841134
$459$	6.11582	0.285462
$460$	−13.2527	−0.617911
$461$	−20.8330	−0.970289	−0.485144	−	0.874434i	$-0.661233\pi$
$461$	−20.8330	−0.970289	−0.485144	+	0.874434i	$0.661233\pi$
$462$	0	0
$463$	17.8697	0.830474	0.415237	−	0.909713i	$-0.363699\pi$
$463$	17.8697	0.830474	0.415237	+	0.909713i	$0.363699\pi$
$464$	−10.4243	−0.483936
$465$	14.3468	0.665315
$466$	−19.8697	−0.920445
$467$	26.8642	1.24312	0.621562	−	0.783365i	$-0.286498\pi$
$467$	26.8642	1.24312	0.621562	+	0.783365i	$0.286498\pi$
$468$	−3.63899	−0.168212
$469$	0	0
$470$	1.20369	0.0555221
$471$	4.54011	0.209197
$472$	13.5706	0.624638
$473$	−2.28577	−0.105100
$474$	12.5174	0.574943
$475$	3.25396	0.149302
$476$	0	0
$477$	11.2848	0.516697
$478$	−17.4201	−0.796778
$479$	15.5050	0.708443	0.354221	−	0.935162i	$-0.384746\pi$
$479$	15.5050	0.708443	0.354221	+	0.935162i	$0.384746\pi$
$480$	−1.79793	−0.0820640
$481$	−37.1159	−1.69234
$482$	−18.4149	−0.838775
$483$	0	0
$484$	1.00000	0.0454545
$485$	−7.40867	−0.336411
$486$	−1.00000	−0.0453609
$487$	10.8858	0.493283	0.246641	−	0.969107i	$-0.420673\pi$
$487$	10.8858	0.493283	0.246641	+	0.969107i	$0.420673\pi$
$488$	0.274758	0.0124377
$489$	−15.8275	−0.715744
$490$	0	0
$491$	7.06975	0.319053	0.159527	−	0.987194i	$-0.449003\pi$
$491$	7.06975	0.319053	0.159527	+	0.987194i	$0.449003\pi$
$492$	8.17680	0.368639
$493$	63.7531	2.87129
$494$	6.69959	0.301429
$495$	1.79793	0.0808111
$496$	−7.97958	−0.358294
$497$	0	0
$498$	5.27314	0.236295
$499$	18.8678	0.844637	0.422319	−	0.906447i	$-0.361216\pi$
$499$	18.8678	0.844637	0.422319	+	0.906447i	$0.361216\pi$
$500$	−12.1674	−0.544143
$501$	−22.0844	−0.986658
$502$	−21.8022	−0.973081
$503$	−28.9752	−1.29194	−0.645969	−	0.763364i	$-0.723547\pi$
$503$	−28.9752	−1.29194	−0.645969	+	0.763364i	$0.723547\pi$
$504$	0	0
$505$	−12.4123	−0.552342
$506$	−7.37109	−0.327685
$507$	−0.242256	−0.0107589
$508$	−7.43208	−0.329745
$509$	16.3539	0.724874	0.362437	−	0.932008i	$-0.381945\pi$
$509$	16.3539	0.724874	0.362437	+	0.932008i	$0.381945\pi$
$510$	10.9958	0.486903
$511$	0	0
$512$	1.00000	0.0441942
$513$	1.84106	0.0812847
$514$	4.00229	0.176534
$515$	−22.6816	−0.999469
$516$	2.28577	0.100625
$517$	0.669485	0.0294439
$518$	0	0
$519$	−10.2628	−0.450487
$520$	−6.54266	−0.286915
$521$	21.6949	0.950470	0.475235	−	0.879859i	$-0.342363\pi$
$521$	21.6949	0.950470	0.475235	+	0.879859i	$0.342363\pi$
$522$	−10.4243	−0.456259
$523$	37.8171	1.65363	0.826814	−	0.562475i	$-0.190151\pi$
$523$	37.8171	1.65363	0.826814	+	0.562475i	$0.190151\pi$
$524$	−1.64154	−0.0717112
$525$	0	0
$526$	−1.13946	−0.0496826
$527$	48.8017	2.12583
$528$	−1.00000	−0.0435194
$529$	31.3329	1.36230
$530$	20.2894	0.881314
$531$	13.5706	0.588914
$532$	0	0
$533$	29.7553	1.28885
$534$	1.98214	0.0857754
$535$	30.4600	1.31690
$536$	3.88163	0.167661
$537$	12.3954	0.534902
$538$	−3.85892	−0.166370
$539$	0	0
$540$	−1.79793	−0.0773707
$541$	1.68212	0.0723198	0.0361599	−	0.999346i	$-0.488487\pi$
$541$	1.68212	0.0723198	0.0361599	+	0.999346i	$0.488487\pi$
$542$	22.0202	0.945847
$543$	−22.4506	−0.963448
$544$	−6.11582	−0.262213
$545$	17.5537	0.751917
$546$	0	0
$547$	13.6665	0.584339	0.292170	−	0.956366i	$-0.405623\pi$
$547$	13.6665	0.584339	0.292170	+	0.956366i	$0.405623\pi$
$548$	14.5307	0.620721
$549$	0.274758	0.0117264
$550$	−1.76744	−0.0753638
$551$	19.1917	0.817595
$552$	7.37109	0.313734
$553$	0	0
$554$	−13.1307	−0.557872
$555$	−18.3380	−0.778406
$556$	8.26535	0.350529
$557$	−8.99583	−0.381165	−0.190583	−	0.981671i	$-0.561038\pi$
$557$	−8.99583	−0.381165	−0.190583	+	0.981671i	$0.561038\pi$
$558$	−7.97958	−0.337803
$559$	8.31788	0.351809
$560$	0	0
$561$	6.11582	0.258210
$562$	−16.1064	−0.679408
$563$	−21.7461	−0.916489	−0.458244	−	0.888826i	$-0.651522\pi$
$563$	−21.7461	−0.916489	−0.458244	+	0.888826i	$0.651522\pi$
$564$	−0.669485	−0.0281904
$565$	−23.2560	−0.978386
$566$	10.6085	0.445908
$567$	0	0
$568$	10.8738	0.456256
$569$	32.4549	1.36058	0.680290	−	0.732943i	$-0.261854\pi$
$569$	32.4549	1.36058	0.680290	+	0.732943i	$0.261854\pi$
$570$	3.31010	0.138645
$571$	−20.2031	−0.845474	−0.422737	−	0.906252i	$-0.638931\pi$
$571$	−20.2031	−0.845474	−0.422737	+	0.906252i	$0.638931\pi$
$572$	−3.63899	−0.152154
$573$	13.7142	0.572920
$574$	0	0
$575$	13.0279	0.543303
$576$	1.00000	0.0416667
$577$	−24.4458	−1.01769	−0.508845	−	0.860858i	$-0.669927\pi$
$577$	−24.4458	−1.01769	−0.508845	+	0.860858i	$0.669927\pi$
$578$	20.4032	0.848661
$579$	−3.77883	−0.157043
$580$	−18.7422	−0.778226
$581$	0	0
$582$	4.12066	0.170807
$583$	11.2848	0.467370
$584$	−3.85892	−0.159683
$585$	−6.54266	−0.270506
$586$	3.69313	0.152562
$587$	−16.8894	−0.697101	−0.348550	−	0.937290i	$-0.613326\pi$
$587$	−16.8894	−0.697101	−0.348550	+	0.937290i	$0.613326\pi$
$588$	0	0
$589$	14.6909	0.605327
$590$	24.3990	1.00449
$591$	21.6316	0.889805
$592$	10.1995	0.419197
$593$	22.2781	0.914852	0.457426	−	0.889248i	$-0.348771\pi$
$593$	22.2781	0.914852	0.457426	+	0.889248i	$0.348771\pi$
$594$	−1.00000	−0.0410305
$595$	0	0
$596$	−7.55045	−0.309278
$597$	−17.8323	−0.729829
$598$	26.8233	1.09689
$599$	−6.25179	−0.255441	−0.127721	−	0.991810i	$-0.540766\pi$
$599$	−6.25179	−0.255441	−0.127721	+	0.991810i	$0.540766\pi$
$600$	1.76744	0.0721554
$601$	−31.3043	−1.27693	−0.638465	−	0.769651i	$-0.720430\pi$
$601$	−31.3043	−1.27693	−0.638465	+	0.769651i	$0.720430\pi$
$602$	0	0
$603$	3.88163	0.158072
$604$	12.3990	0.504509
$605$	1.79793	0.0730964
$606$	6.90367	0.280442
$607$	25.0348	1.01613	0.508066	−	0.861318i	$-0.330361\pi$
$607$	25.0348	1.01613	0.508066	+	0.861318i	$0.330361\pi$
$608$	−1.84106	−0.0746648
$609$	0	0
$610$	0.493996	0.0200013
$611$	−2.43625	−0.0985602
$612$	−6.11582	−0.247217
$613$	1.17157	0.0473194	0.0236597	−	0.999720i	$-0.492468\pi$
$613$	1.17157	0.0473194	0.0236597	+	0.999720i	$0.492468\pi$
$614$	−19.1223	−0.771713
$615$	14.7013	0.592815
$616$	0	0
$617$	5.06651	0.203970	0.101985	−	0.994786i	$-0.467481\pi$
$617$	5.06651	0.203970	0.101985	+	0.994786i	$0.467481\pi$
$618$	12.6154	0.507464
$619$	24.6812	0.992021	0.496010	−	0.868317i	$-0.334798\pi$
$619$	24.6812	0.992021	0.496010	+	0.868317i	$0.334798\pi$
$620$	−14.3468	−0.576180
$621$	7.37109	0.295792
$622$	13.1190	0.526026
$623$	0	0
$624$	3.63899	0.145676
$625$	−13.0390	−0.521559
$626$	12.6248	0.504587
$627$	1.84106	0.0735248
$628$	−4.54011	−0.181170
$629$	−62.3784	−2.48719
$630$	0	0
$631$	−25.8408	−1.02871	−0.514353	−	0.857579i	$-0.671968\pi$
$631$	−25.8408	−1.02871	−0.514353	+	0.857579i	$0.671968\pi$
$632$	−12.5174	−0.497915
$633$	8.27020	0.328711
$634$	−29.4555	−1.16983
$635$	−13.3624	−0.530270
$636$	−11.2848	−0.447473
$637$	0	0
$638$	−10.4243	−0.412702
$639$	10.8738	0.430163
$640$	1.79793	0.0710695
$641$	−3.19684	−0.126267	−0.0631337	−	0.998005i	$-0.520109\pi$
$641$	−3.19684	−0.126267	−0.0631337	+	0.998005i	$0.520109\pi$
$642$	−16.9417	−0.668635
$643$	−20.7623	−0.818787	−0.409393	−	0.912358i	$-0.634260\pi$
$643$	−20.7623	−0.818787	−0.409393	+	0.912358i	$0.634260\pi$
$644$	0	0
$645$	4.10965	0.161817
$646$	11.2596	0.443002
$647$	−28.4056	−1.11674	−0.558370	−	0.829592i	$-0.688573\pi$
$647$	−28.4056	−1.11674	−0.558370	+	0.829592i	$0.688573\pi$
$648$	1.00000	0.0392837
$649$	13.5706	0.532693
$650$	6.43169	0.252272
$651$	0	0
$652$	15.8275	0.619853
$653$	16.7825	0.656750	0.328375	−	0.944548i	$-0.393499\pi$
$653$	16.7825	0.656750	0.328375	+	0.944548i	$0.393499\pi$
$654$	−9.76326	−0.381774
$655$	−2.95138	−0.115320
$656$	−8.17680	−0.319251
$657$	−3.85892	−0.150551
$658$	0	0
$659$	−15.3426	−0.597662	−0.298831	−	0.954306i	$-0.596597\pi$
$659$	−15.3426	−0.597662	−0.298831	+	0.954306i	$0.596597\pi$
$660$	−1.79793	−0.0699844
$661$	6.68735	0.260108	0.130054	−	0.991507i	$-0.458485\pi$
$661$	6.68735	0.260108	0.130054	+	0.991507i	$0.458485\pi$
$662$	2.28901	0.0889649
$663$	−22.2554	−0.864328
$664$	−5.27314	−0.204637
$665$	0	0
$666$	10.1995	0.395223
$667$	76.8384	2.97519
$668$	22.0844	0.854471
$669$	−9.10574	−0.352048
$670$	6.97891	0.269619
$671$	0.274758	0.0106069
$672$	0	0
$673$	12.4921	0.481536	0.240768	−	0.970583i	$-0.422601\pi$
$673$	12.4921	0.481536	0.240768	+	0.970583i	$0.422601\pi$
$674$	5.35093	0.206110
$675$	1.76744	0.0680287
$676$	0.242256	0.00931752
$677$	−16.8830	−0.648866	−0.324433	−	0.945909i	$-0.605174\pi$
$677$	−16.8830	−0.648866	−0.324433	+	0.945909i	$0.605174\pi$
$678$	12.9348	0.496759
$679$	0	0
$680$	−10.9958	−0.421671
$681$	−0.620456	−0.0237759
$682$	−7.97958	−0.305554
$683$	−6.76970	−0.259036	−0.129518	−	0.991577i	$-0.541343\pi$
$683$	−6.76970	−0.259036	−0.129518	+	0.991577i	$0.541343\pi$
$684$	−1.84106	−0.0703946
$685$	26.1252	0.998193
$686$	0	0
$687$	18.0011	0.686783
$688$	−2.28577	−0.0871440
$689$	−41.0654	−1.56447
$690$	13.2527	0.504522
$691$	42.8876	1.63152	0.815760	−	0.578391i	$-0.196319\pi$
$691$	42.8876	1.63152	0.815760	+	0.578391i	$0.196319\pi$
$692$	10.2628	0.390133
$693$	0	0
$694$	20.8197	0.790305
$695$	14.8605	0.563693
$696$	10.4243	0.395132
$697$	50.0078	1.89418
$698$	23.1843	0.877540
$699$	19.8697	0.751540
$700$	0	0
$701$	−33.8990	−1.28035	−0.640173	−	0.768231i	$-0.721137\pi$
$701$	−33.8990	−1.28035	−0.640173	+	0.768231i	$0.721137\pi$
$702$	3.63899	0.137345
$703$	−18.7779	−0.708222
$704$	1.00000	0.0376889
$705$	−1.20369	−0.0453336
$706$	−12.1243	−0.456303
$707$	0	0
$708$	−13.5706	−0.510014
$709$	−28.6407	−1.07562	−0.537812	−	0.843065i	$-0.680749\pi$
$709$	−28.6407	−1.07562	−0.537812	+	0.843065i	$0.680749\pi$
$710$	19.5504	0.733715
$711$	−12.5174	−0.469439
$712$	−1.98214	−0.0742837
$713$	58.8182	2.20276
$714$	0	0
$715$	−6.54266	−0.244682
$716$	−12.3954	−0.463239
$717$	17.4201	0.650566
$718$	12.3312	0.460196
$719$	−2.52225	−0.0940639	−0.0470319	−	0.998893i	$-0.514976\pi$
$719$	−2.52225	−0.0940639	−0.0470319	+	0.998893i	$0.514976\pi$
$720$	1.79793	0.0670050
$721$	0	0
$722$	−15.6105	−0.580963
$723$	18.4149	0.684857
$724$	22.4506	0.834370
$725$	18.4243	0.684261
$726$	−1.00000	−0.0371135
$727$	30.0452	1.11431	0.557157	−	0.830407i	$-0.311892\pi$
$727$	30.0452	1.11431	0.557157	+	0.830407i	$0.311892\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−6.93808	−0.256790
$731$	13.9793	0.517044
$732$	−0.274758	−0.0101553
$733$	33.5866	1.24055	0.620275	−	0.784385i	$-0.287021\pi$
$733$	33.5866	1.24055	0.620275	+	0.784385i	$0.287021\pi$
$734$	18.0860	0.667566
$735$	0	0
$736$	−7.37109	−0.271702
$737$	3.88163	0.142982
$738$	−8.17680	−0.300992
$739$	−29.7380	−1.09393	−0.546965	−	0.837155i	$-0.684217\pi$
$739$	−29.7380	−1.09393	−0.546965	+	0.837155i	$0.684217\pi$
$740$	18.3380	0.674120
$741$	−6.69959	−0.246116
$742$	0	0
$743$	1.59262	0.0584276	0.0292138	−	0.999573i	$-0.490700\pi$
$743$	1.59262	0.0584276	0.0292138	+	0.999573i	$0.490700\pi$
$744$	7.97958	0.292546
$745$	−13.5752	−0.497357
$746$	6.95365	0.254591
$747$	−5.27314	−0.192934
$748$	−6.11582	−0.223616
$749$	0	0
$750$	12.1674	0.444291
$751$	0.305924	0.0111633	0.00558166	−	0.999984i	$-0.498223\pi$
$751$	0.305924	0.0111633	0.00558166	+	0.999984i	$0.498223\pi$
$752$	0.669485	0.0244136
$753$	21.8022	0.794518
$754$	37.9339	1.38147
$755$	22.2926	0.811312
$756$	0	0
$757$	40.4921	1.47171	0.735856	−	0.677138i	$-0.236780\pi$
$757$	40.4921	1.47171	0.735856	+	0.677138i	$0.236780\pi$
$758$	5.14307	0.186805
$759$	7.37109	0.267554
$760$	−3.31010	−0.120070
$761$	−48.6887	−1.76496	−0.882482	−	0.470346i	$-0.844129\pi$
$761$	−48.6887	−1.76496	−0.882482	+	0.470346i	$0.844129\pi$
$762$	7.43208	0.269236
$763$	0	0
$764$	−13.7142	−0.496164
$765$	−10.9958	−0.397555
$766$	18.8810	0.682197
$767$	−49.3833	−1.78313
$768$	−1.00000	−0.0360844
$769$	−14.7255	−0.531017	−0.265508	−	0.964109i	$-0.585540\pi$
$769$	−14.7255	−0.531017	−0.265508	+	0.964109i	$0.585540\pi$
$770$	0	0
$771$	−4.00229	−0.144139
$772$	3.77883	0.136003
$773$	−28.9612	−1.04166	−0.520830	−	0.853660i	$-0.674378\pi$
$773$	−28.9612	−1.04166	−0.520830	+	0.853660i	$0.674378\pi$
$774$	−2.28577	−0.0821602
$775$	14.1034	0.506610
$776$	−4.12066	−0.147923
$777$	0	0
$778$	−30.3990	−1.08986
$779$	15.0540	0.539365
$780$	6.54266	0.234265
$781$	10.8738	0.389097
$782$	45.0802	1.61207
$783$	10.4243	0.372534
$784$	0	0
$785$	−8.16281	−0.291343
$786$	1.64154	0.0585519
$787$	2.14203	0.0763551	0.0381775	−	0.999271i	$-0.487845\pi$
$787$	2.14203	0.0763551	0.0381775	+	0.999271i	$0.487845\pi$
$788$	−21.6316	−0.770594
$789$	1.13946	0.0405657
$790$	−22.5054	−0.800708
$791$	0	0
$792$	1.00000	0.0355335
$793$	−0.999840	−0.0355054
$794$	2.08009	0.0738196
$795$	−20.2894	−0.719590
$796$	17.8323	0.632051
$797$	−7.38735	−0.261673	−0.130837	−	0.991404i	$-0.541766\pi$
$797$	−7.38735	−0.261673	−0.130837	+	0.991404i	$0.541766\pi$
$798$	0	0
$799$	−4.09445	−0.144851
$800$	−1.76744	−0.0624884
$801$	−1.98214	−0.0700354
$802$	−21.8444	−0.771353
$803$	−3.85892	−0.136178
$804$	−3.88163	−0.136895
$805$	0	0
$806$	29.0376	1.02281
$807$	3.85892	0.135840
$808$	−6.90367	−0.242870
$809$	8.49214	0.298568	0.149284	−	0.988794i	$-0.452303\pi$
$809$	8.49214	0.298568	0.149284	+	0.988794i	$0.452303\pi$
$810$	1.79793	0.0631729
$811$	5.97995	0.209984	0.104992	−	0.994473i	$-0.466518\pi$
$811$	5.97995	0.209984	0.104992	+	0.994473i	$0.466518\pi$
$812$	0	0
$813$	−22.0202	−0.772281
$814$	10.1995	0.357493
$815$	28.4568	0.996797
$816$	6.11582	0.214096
$817$	4.20823	0.147227
$818$	−33.7571	−1.18029
$819$	0	0
$820$	−14.7013	−0.513393
$821$	20.6430	0.720445	0.360223	−	0.932866i	$-0.382701\pi$
$821$	20.6430	0.720445	0.360223	+	0.932866i	$0.382701\pi$
$822$	−14.5307	−0.506816
$823$	−32.8269	−1.14427	−0.572137	−	0.820158i	$-0.693886\pi$
$823$	−32.8269	−1.14427	−0.572137	+	0.820158i	$0.693886\pi$
$824$	−12.6154	−0.439477
$825$	1.76744	0.0615343
$826$	0	0
$827$	7.22287	0.251164	0.125582	−	0.992083i	$-0.459920\pi$
$827$	7.22287	0.251164	0.125582	+	0.992083i	$0.459920\pi$
$828$	−7.37109	−0.256163
$829$	−52.2625	−1.81515	−0.907577	−	0.419887i	$-0.862070\pi$
$829$	−52.2625	−1.81515	−0.907577	+	0.419887i	$0.862070\pi$
$830$	−9.48074	−0.329081
$831$	13.1307	0.455500
$832$	−3.63899	−0.126159
$833$	0	0
$834$	−8.26535	−0.286206
$835$	39.7062	1.37409
$836$	−1.84106	−0.0636743
$837$	7.97958	0.275815
$838$	−22.7371	−0.785439
$839$	20.5644	0.709963	0.354981	−	0.934873i	$-0.384487\pi$
$839$	20.5644	0.709963	0.354981	+	0.934873i	$0.384487\pi$
$840$	0	0
$841$	79.6659	2.74710
$842$	−21.0192	−0.724370
$843$	16.1064	0.554734
$844$	−8.27020	−0.284672
$845$	0.435559	0.0149837
$846$	0.669485	0.0230174
$847$	0	0
$848$	11.2848	0.387523
$849$	−10.6085	−0.364083
$850$	10.8093	0.370757
$851$	−75.1815	−2.57719
$852$	−10.8738	−0.372532
$853$	−24.8004	−0.849148	−0.424574	−	0.905393i	$-0.639576\pi$
$853$	−24.8004	−0.849148	−0.424574	+	0.905393i	$0.639576\pi$
$854$	0	0
$855$	−3.31010	−0.113203
$856$	16.9417	0.579055
$857$	30.1658	1.03044	0.515222	−	0.857056i	$-0.327709\pi$
$857$	30.1658	1.03044	0.515222	+	0.857056i	$0.327709\pi$
$858$	3.63899	0.124233
$859$	−26.3550	−0.899219	−0.449610	−	0.893225i	$-0.648437\pi$
$859$	−26.3550	−0.899219	−0.449610	+	0.893225i	$0.648437\pi$
$860$	−4.10965	−0.140138
$861$	0	0
$862$	7.03305	0.239547
$863$	−16.8489	−0.573545	−0.286772	−	0.957999i	$-0.592582\pi$
$863$	−16.8489	−0.573545	−0.286772	+	0.957999i	$0.592582\pi$
$864$	−1.00000	−0.0340207
$865$	18.4518	0.627381
$866$	−5.77293	−0.196172
$867$	−20.4032	−0.692929
$868$	0	0
$869$	−12.5174	−0.424624
$870$	18.7422	0.635419
$871$	−14.1252	−0.478615
$872$	9.76326	0.330626
$873$	−4.12066	−0.139463
$874$	13.5706	0.459032
$875$	0	0
$876$	3.85892	0.130381
$877$	39.3054	1.32725	0.663624	−	0.748066i	$-0.269018\pi$
$877$	39.3054	1.32725	0.663624	+	0.748066i	$0.269018\pi$
$878$	−31.2275	−1.05388
$879$	−3.69313	−0.124566
$880$	1.79793	0.0606083
$881$	−12.1055	−0.407843	−0.203922	−	0.978987i	$-0.565369\pi$
$881$	−12.1055	−0.407843	−0.203922	+	0.978987i	$0.565369\pi$
$882$	0	0
$883$	21.0614	0.708773	0.354386	−	0.935099i	$-0.384690\pi$
$883$	21.0614	0.708773	0.354386	+	0.935099i	$0.384690\pi$
$884$	22.2554	0.748530
$885$	−24.3990	−0.820164
$886$	−35.8953	−1.20593
$887$	45.1762	1.51687	0.758434	−	0.651750i	$-0.225965\pi$
$887$	45.1762	1.51687	0.758434	+	0.651750i	$0.225965\pi$
$888$	−10.1995	−0.342273
$889$	0	0
$890$	−3.56375	−0.119457
$891$	1.00000	0.0335013
$892$	9.10574	0.304883
$893$	−1.23256	−0.0412461
$894$	7.55045	0.252525
$895$	−22.2861	−0.744943
$896$	0	0
$897$	−26.8233	−0.895605
$898$	−24.5495	−0.819228
$899$	83.1815	2.77426
$900$	−1.76744	−0.0589146
$901$	−69.0160	−2.29926
$902$	−8.17680	−0.272258
$903$	0	0
$904$	−12.9348	−0.430206
$905$	40.3647	1.34177
$906$	−12.3990	−0.411930
$907$	−33.5283	−1.11329	−0.556644	−	0.830751i	$-0.687911\pi$
$907$	−33.5283	−1.11329	−0.556644	+	0.830751i	$0.687911\pi$
$908$	0.620456	0.0205905
$909$	−6.90367	−0.228980
$910$	0	0
$911$	−27.3400	−0.905813	−0.452906	−	0.891558i	$-0.649613\pi$
$911$	−27.3400	−0.905813	−0.452906	+	0.891558i	$0.649613\pi$
$912$	1.84106	0.0609635
$913$	−5.27314	−0.174515
$914$	26.2771	0.869168
$915$	−0.493996	−0.0163310
$916$	−18.0011	−0.594772
$917$	0	0
$918$	6.11582	0.201852
$919$	−12.6118	−0.416026	−0.208013	−	0.978126i	$-0.566700\pi$
$919$	−12.6118	−0.416026	−0.208013	+	0.978126i	$0.566700\pi$
$920$	−13.2527	−0.436929
$921$	19.1223	0.630101
$922$	−20.8330	−0.686098
$923$	−39.5698	−1.30246
$924$	0	0
$925$	−18.0270	−0.592725
$926$	17.8697	0.587234
$927$	−12.6154	−0.414342
$928$	−10.4243	−0.342194
$929$	53.3407	1.75005	0.875027	−	0.484075i	$-0.160844\pi$
$929$	53.3407	1.75005	0.875027	+	0.484075i	$0.160844\pi$
$930$	14.3468	0.470449
$931$	0	0
$932$	−19.8697	−0.650853
$933$	−13.1190	−0.429498
$934$	26.8642	0.879022
$935$	−10.9958	−0.359602
$936$	−3.63899	−0.118944
$937$	20.5927	0.672736	0.336368	−	0.941731i	$-0.390801\pi$
$937$	20.5927	0.672736	0.336368	+	0.941731i	$0.390801\pi$
$938$	0	0
$939$	−12.6248	−0.411993
$940$	1.20369	0.0392600
$941$	27.9554	0.911319	0.455660	−	0.890154i	$-0.349403\pi$
$941$	27.9554	0.911319	0.455660	+	0.890154i	$0.349403\pi$
$942$	4.54011	0.147925
$943$	60.2719	1.96272
$944$	13.5706	0.441686
$945$	0	0
$946$	−2.28577	−0.0743167
$947$	−44.7266	−1.45342	−0.726710	−	0.686945i	$-0.758951\pi$
$947$	−44.7266	−1.45342	−0.726710	+	0.686945i	$0.758951\pi$
$948$	12.5174	0.406546
$949$	14.0426	0.455841
$950$	3.25396	0.105572
$951$	29.4555	0.955159
$952$	0	0
$953$	−51.6527	−1.67320	−0.836598	−	0.547817i	$-0.815459\pi$
$953$	−51.6527	−1.67320	−0.836598	+	0.547817i	$0.815459\pi$
$954$	11.2848	0.365360
$955$	−24.6573	−0.797890
$956$	−17.4201	−0.563407
$957$	10.4243	0.336970
$958$	15.5050	0.500945
$959$	0	0
$960$	−1.79793	−0.0580280
$961$	32.6738	1.05399
$962$	−37.1159	−1.19667
$963$	16.9417	0.545938
$964$	−18.4149	−0.593104
$965$	6.79409	0.218709
$966$	0	0
$967$	−50.7320	−1.63143	−0.815715	−	0.578454i	$-0.803656\pi$
$967$	−50.7320	−1.63143	−0.815715	+	0.578454i	$0.803656\pi$
$968$	1.00000	0.0321412
$969$	−11.2596	−0.361710
$970$	−7.40867	−0.237878
$971$	22.7299	0.729436	0.364718	−	0.931118i	$-0.381165\pi$
$971$	22.7299	0.729436	0.364718	+	0.931118i	$0.381165\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	10.8858	0.348804
$975$	−6.43169	−0.205979
$976$	0.274758	0.00879478
$977$	−27.4811	−0.879198	−0.439599	−	0.898194i	$-0.644880\pi$
$977$	−27.4811	−0.879198	−0.439599	+	0.898194i	$0.644880\pi$
$978$	−15.8275	−0.506108
$979$	−1.98214	−0.0633494
$980$	0	0
$981$	9.76326	0.311717
$982$	7.06975	0.225605
$983$	−34.2044	−1.09095	−0.545475	−	0.838127i	$-0.683651\pi$
$983$	−34.2044	−1.09095	−0.545475	+	0.838127i	$0.683651\pi$
$984$	8.17680	0.260667
$985$	−38.8921	−1.23921
$986$	63.7531	2.03031
$987$	0	0
$988$	6.69959	0.213143
$989$	16.8486	0.535754
$990$	1.79793	0.0571421
$991$	−33.3890	−1.06064	−0.530318	−	0.847799i	$-0.677927\pi$
$991$	−33.3890	−1.06064	−0.530318	+	0.847799i	$0.677927\pi$
$992$	−7.97958	−0.253352
$993$	−2.28901	−0.0726396
$994$	0	0
$995$	32.0614	1.01641
$996$	5.27314	0.167086
$997$	−7.74406	−0.245257	−0.122628	−	0.992453i	$-0.539132\pi$
$997$	−7.74406	−0.245257	−0.122628	+	0.992453i	$0.539132\pi$
$998$	18.8678	0.597249
$999$	−10.1995	−0.322698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.a.bl.1.4	✓	4
3.2	odd	2		9702.2.a.ea.1.1		4
7.6	odd	2		3234.2.a.bm.1.1	yes	4
21.20	even	2		9702.2.a.dz.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.a.bl.1.4	✓	4	1.1	even	1	trivial
3234.2.a.bm.1.1	yes	4	7.6	odd	2
9702.2.a.dz.1.4		4	21.20	even	2
9702.2.a.ea.1.1		4	3.2	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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.79793 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.79793 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.79793 q^{10} +1.00000 q^{11} -1.00000 q^{12} -3.63899 q^{13} -1.79793 q^{15} +1.00000 q^{16} -6.11582 q^{17} +1.00000 q^{18} -1.84106 q^{19} +1.79793 q^{20} +1.00000 q^{22} -7.37109 q^{23} -1.00000 q^{24} -1.76744 q^{25} -3.63899 q^{26} -1.00000 q^{27} -10.4243 q^{29} -1.79793 q^{30} -7.97958 q^{31} +1.00000 q^{32} -1.00000 q^{33} -6.11582 q^{34} +1.00000 q^{36} +10.1995 q^{37} -1.84106 q^{38} +3.63899 q^{39} +1.79793 q^{40} -8.17680 q^{41} -2.28577 q^{43} +1.00000 q^{44} +1.79793 q^{45} -7.37109 q^{46} +0.669485 q^{47} -1.00000 q^{48} -1.76744 q^{50} +6.11582 q^{51} -3.63899 q^{52} +11.2848 q^{53} -1.00000 q^{54} +1.79793 q^{55} +1.84106 q^{57} -10.4243 q^{58} +13.5706 q^{59} -1.79793 q^{60} +0.274758 q^{61} -7.97958 q^{62} +1.00000 q^{64} -6.54266 q^{65} -1.00000 q^{66} +3.88163 q^{67} -6.11582 q^{68} +7.37109 q^{69} +10.8738 q^{71} +1.00000 q^{72} -3.85892 q^{73} +10.1995 q^{74} +1.76744 q^{75} -1.84106 q^{76} +3.63899 q^{78} -12.5174 q^{79} +1.79793 q^{80} +1.00000 q^{81} -8.17680 q^{82} -5.27314 q^{83} -10.9958 q^{85} -2.28577 q^{86} +10.4243 q^{87} +1.00000 q^{88} -1.98214 q^{89} +1.79793 q^{90} -7.37109 q^{92} +7.97958 q^{93} +0.669485 q^{94} -3.31010 q^{95} -1.00000 q^{96} -4.12066 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 12 q^{19} - 4 q^{20} + 4 q^{22} - 8 q^{23} - 4 q^{24} + 4 q^{25} - 8 q^{26} - 4 q^{27} - 8 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} - 4 q^{34} + 4 q^{36} + 8 q^{37} - 12 q^{38} + 8 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{43} + 4 q^{44} - 4 q^{45} - 8 q^{46} - 4 q^{47} - 4 q^{48} + 4 q^{50} + 4 q^{51} - 8 q^{52} - 8 q^{53} - 4 q^{54} - 4 q^{55} + 12 q^{57} - 8 q^{58} + 4 q^{60} - 24 q^{61} - 4 q^{62} + 4 q^{64} - 16 q^{65} - 4 q^{66} - 8 q^{67} - 4 q^{68} + 8 q^{69} + 8 q^{71} + 4 q^{72} - 4 q^{73} + 8 q^{74} - 4 q^{75} - 12 q^{76} + 8 q^{78} - 8 q^{79} - 4 q^{80} + 4 q^{81} - 12 q^{82} - 4 q^{83} - 8 q^{85} - 8 q^{86} + 8 q^{87} + 4 q^{88} - 24 q^{89} - 4 q^{90} - 8 q^{92} + 4 q^{93} - 4 q^{94} + 8 q^{95} - 4 q^{96} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - 8 * q^13 + 4 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 12 * q^19 - 4 * q^20 + 4 * q^22 - 8 * q^23 - 4 * q^24 + 4 * q^25 - 8 * q^26 - 4 * q^27 - 8 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 - 4 * q^34 + 4 * q^36 + 8 * q^37 - 12 * q^38 + 8 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^43 + 4 * q^44 - 4 * q^45 - 8 * q^46 - 4 * q^47 - 4 * q^48 + 4 * q^50 + 4 * q^51 - 8 * q^52 - 8 * q^53 - 4 * q^54 - 4 * q^55 + 12 * q^57 - 8 * q^58 + 4 * q^60 - 24 * q^61 - 4 * q^62 + 4 * q^64 - 16 * q^65 - 4 * q^66 - 8 * q^67 - 4 * q^68 + 8 * q^69 + 8 * q^71 + 4 * q^72 - 4 * q^73 + 8 * q^74 - 4 * q^75 - 12 * q^76 + 8 * q^78 - 8 * q^79 - 4 * q^80 + 4 * q^81 - 12 * q^82 - 4 * q^83 - 8 * q^85 - 8 * q^86 + 8 * q^87 + 4 * q^88 - 24 * q^89 - 4 * q^90 - 8 * q^92 + 4 * q^93 - 4 * q^94 + 8 * q^95 - 4 * q^96 + 4 * q^99

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