LMFDB - Embedded newform 3822.2.a.by.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.10304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 8 $ x^4 - 2x^3 - 7x^2 + 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$3.16053$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.16053 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.16053 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -4.16053 q^{10} +3.72335 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.16053 q^{15} +1.00000 q^{16} +2.59771 q^{17} -1.00000 q^{18} +2.37069 q^{19} +4.16053 q^{20} -3.72335 q^{22} -3.95037 q^{23} -1.00000 q^{24} +12.3100 q^{25} +1.00000 q^{26} +1.00000 q^{27} -4.84035 q^{29} -4.16053 q^{30} +0.227026 q^{31} -1.00000 q^{32} +3.72335 q^{33} -2.59771 q^{34} +1.00000 q^{36} +1.04352 q^{37} -2.37069 q^{38} -1.00000 q^{39} -4.16053 q^{40} +2.35876 q^{41} +7.95037 q^{43} +3.72335 q^{44} +4.16053 q^{45} +3.95037 q^{46} -2.17246 q^{47} +1.00000 q^{48} -12.3100 q^{50} +2.59771 q^{51} -1.00000 q^{52} -4.17246 q^{53} -1.00000 q^{54} +15.4911 q^{55} +2.37069 q^{57} +4.84035 q^{58} -7.54073 q^{59} +4.16053 q^{60} +12.4525 q^{61} -0.227026 q^{62} +1.00000 q^{64} -4.16053 q^{65} -3.72335 q^{66} -6.56370 q^{67} +2.59771 q^{68} -3.95037 q^{69} -7.88388 q^{71} -1.00000 q^{72} -13.2641 q^{73} -1.04352 q^{74} +12.3100 q^{75} +2.37069 q^{76} +1.00000 q^{78} -12.3379 q^{79} +4.16053 q^{80} +1.00000 q^{81} -2.35876 q^{82} +17.9779 q^{83} +10.8079 q^{85} -7.95037 q^{86} -4.84035 q^{87} -3.72335 q^{88} +4.79594 q^{89} -4.16053 q^{90} -3.95037 q^{92} +0.227026 q^{93} +2.17246 q^{94} +9.86332 q^{95} -1.00000 q^{96} +11.6807 q^{97} +3.72335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 6 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 + 6 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{9} - 6 q^{10} + 2 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} + 2 q^{19} + 6 q^{20} - 2 q^{22} - 2 q^{23} - 4 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{27} + 6 q^{29} - 6 q^{30} - 4 q^{32} + 2 q^{33} - 2 q^{34} + 4 q^{36} + 6 q^{37} - 2 q^{38} - 4 q^{39} - 6 q^{40} + 16 q^{41} + 18 q^{43} + 2 q^{44} + 6 q^{45} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 6 q^{50} + 2 q^{51} - 4 q^{52} + 8 q^{53} - 4 q^{54} + 2 q^{55} + 2 q^{57} - 6 q^{58} + 16 q^{59} + 6 q^{60} - 2 q^{61} + 4 q^{64} - 6 q^{65} - 2 q^{66} + 12 q^{67} + 2 q^{68} - 2 q^{69} - 8 q^{71} - 4 q^{72} + 6 q^{73} - 6 q^{74} + 6 q^{75} + 2 q^{76} + 4 q^{78} - 24 q^{79} + 6 q^{80} + 4 q^{81} - 16 q^{82} + 28 q^{83} + 38 q^{85} - 18 q^{86} + 6 q^{87} - 2 q^{88} + 28 q^{89} - 6 q^{90} - 2 q^{92} - 16 q^{94} + 22 q^{95} - 4 q^{96} - 4 q^{97} + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^9 - 6 * q^10 + 2 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 + 2 * q^19 + 6 * q^20 - 2 * q^22 - 2 * q^23 - 4 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^27 + 6 * q^29 - 6 * q^30 - 4 * q^32 + 2 * q^33 - 2 * q^34 + 4 * q^36 + 6 * q^37 - 2 * q^38 - 4 * q^39 - 6 * q^40 + 16 * q^41 + 18 * q^43 + 2 * q^44 + 6 * q^45 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 6 * q^50 + 2 * q^51 - 4 * q^52 + 8 * q^53 - 4 * q^54 + 2 * q^55 + 2 * q^57 - 6 * q^58 + 16 * q^59 + 6 * q^60 - 2 * q^61 + 4 * q^64 - 6 * q^65 - 2 * q^66 + 12 * q^67 + 2 * q^68 - 2 * q^69 - 8 * q^71 - 4 * q^72 + 6 * q^73 - 6 * q^74 + 6 * q^75 + 2 * q^76 + 4 * q^78 - 24 * q^79 + 6 * q^80 + 4 * q^81 - 16 * q^82 + 28 * q^83 + 38 * q^85 - 18 * q^86 + 6 * q^87 - 2 * q^88 + 28 * q^89 - 6 * q^90 - 2 * q^92 - 16 * q^94 + 22 * q^95 - 4 * q^96 - 4 * q^97 + 2 * 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
$5$	4.16053	1.86065	0.930323	−	0.366741i	$-0.119526\pi$
$5$	4.16053	1.86065	0.930323	+	0.366741i	$0.119526\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.16053	−1.31568
$11$	3.72335	1.12263	0.561316	−	0.827602i	$-0.310295\pi$
$11$	3.72335	1.12263	0.561316	+	0.827602i	$0.310295\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	4.16053	1.07424
$16$	1.00000	0.250000
$17$	2.59771	0.630038	0.315019	−	0.949085i	$-0.397989\pi$
$17$	2.59771	0.630038	0.315019	+	0.949085i	$0.397989\pi$
$18$	−1.00000	−0.235702
$19$	2.37069	0.543873	0.271937	−	0.962315i	$-0.412336\pi$
$19$	2.37069	0.543873	0.271937	+	0.962315i	$0.412336\pi$
$20$	4.16053	0.930323
$21$	0	0
$22$	−3.72335	−0.793821
$23$	−3.95037	−0.823710	−0.411855	−	0.911249i	$-0.635119\pi$
$23$	−3.95037	−0.823710	−0.411855	+	0.911249i	$0.635119\pi$
$24$	−1.00000	−0.204124
$25$	12.3100	2.46200
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	0	0
$29$	−4.84035	−0.898831	−0.449416	−	0.893323i	$-0.648368\pi$
$29$	−4.84035	−0.898831	−0.449416	+	0.893323i	$0.648368\pi$
$30$	−4.16053	−0.759606
$31$	0.227026	0.0407750	0.0203875	−	0.999792i	$-0.493510\pi$
$31$	0.227026	0.0407750	0.0203875	+	0.999792i	$0.493510\pi$
$32$	−1.00000	−0.176777
$33$	3.72335	0.648152
$34$	−2.59771	−0.445504
$35$	0	0
$36$	1.00000	0.166667
$37$	1.04352	0.171554	0.0857772	−	0.996314i	$-0.472663\pi$
$37$	1.04352	0.171554	0.0857772	+	0.996314i	$0.472663\pi$
$38$	−2.37069	−0.384576
$39$	−1.00000	−0.160128
$40$	−4.16053	−0.657838
$41$	2.35876	0.368377	0.184188	−	0.982891i	$-0.441034\pi$
$41$	2.35876	0.368377	0.184188	+	0.982891i	$0.441034\pi$
$42$	0	0
$43$	7.95037	1.21242	0.606210	−	0.795304i	$-0.292689\pi$
$43$	7.95037	1.21242	0.606210	+	0.795304i	$0.292689\pi$
$44$	3.72335	0.561316
$45$	4.16053	0.620215
$46$	3.95037	0.582451
$47$	−2.17246	−0.316886	−0.158443	−	0.987368i	$-0.550647\pi$
$47$	−2.17246	−0.316886	−0.158443	+	0.987368i	$0.550647\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−12.3100	−1.74090
$51$	2.59771	0.363753
$52$	−1.00000	−0.138675
$53$	−4.17246	−0.573131	−0.286566	−	0.958061i	$-0.592514\pi$
$53$	−4.17246	−0.573131	−0.286566	+	0.958061i	$0.592514\pi$
$54$	−1.00000	−0.136083
$55$	15.4911	2.08882
$56$	0	0
$57$	2.37069	0.314005
$58$	4.84035	0.635570
$59$	−7.54073	−0.981720	−0.490860	−	0.871238i	$-0.663317\pi$
$59$	−7.54073	−0.981720	−0.490860	+	0.871238i	$0.663317\pi$
$60$	4.16053	0.537122
$61$	12.4525	1.59438	0.797191	−	0.603727i	$-0.206318\pi$
$61$	12.4525	1.59438	0.797191	+	0.603727i	$0.206318\pi$
$62$	−0.227026	−0.0288323
$63$	0	0
$64$	1.00000	0.125000
$65$	−4.16053	−0.516050
$66$	−3.72335	−0.458313
$67$	−6.56370	−0.801884	−0.400942	−	0.916103i	$-0.631317\pi$
$67$	−6.56370	−0.801884	−0.400942	+	0.916103i	$0.631317\pi$
$68$	2.59771	0.315019
$69$	−3.95037	−0.475569
$70$	0	0
$71$	−7.88388	−0.935644	−0.467822	−	0.883823i	$-0.654961\pi$
$71$	−7.88388	−0.935644	−0.467822	+	0.883823i	$0.654961\pi$
$72$	−1.00000	−0.117851
$73$	−13.2641	−1.55244	−0.776222	−	0.630460i	$-0.782866\pi$
$73$	−13.2641	−1.55244	−0.776222	+	0.630460i	$0.782866\pi$
$74$	−1.04352	−0.121307
$75$	12.3100	1.42144
$76$	2.37069	0.271937
$77$	0	0
$78$	1.00000	0.113228
$79$	−12.3379	−1.38813	−0.694063	−	0.719914i	$-0.744181\pi$
$79$	−12.3379	−1.38813	−0.694063	+	0.719914i	$0.744181\pi$
$80$	4.16053	0.465162
$81$	1.00000	0.111111
$82$	−2.35876	−0.260482
$83$	17.9779	1.97333	0.986666	−	0.162756i	$-0.0520383\pi$
$83$	17.9779	1.97333	0.986666	+	0.162756i	$0.0520383\pi$
$84$	0	0
$85$	10.8079	1.17228
$86$	−7.95037	−0.857311
$87$	−4.84035	−0.518941
$88$	−3.72335	−0.396910
$89$	4.79594	0.508369	0.254185	−	0.967156i	$-0.418193\pi$
$89$	4.79594	0.508369	0.254185	+	0.967156i	$0.418193\pi$
$90$	−4.16053	−0.438559
$91$	0	0
$92$	−3.95037	−0.411855
$93$	0.227026	0.0235415
$94$	2.17246	0.224072
$95$	9.86332	1.01196
$96$	−1.00000	−0.102062
$97$	11.6807	1.18600	0.592998	−	0.805204i	$-0.297944\pi$
$97$	11.6807	1.18600	0.592998	+	0.805204i	$0.297944\pi$
$98$	0	0
$99$	3.72335	0.374211
$100$	12.3100	1.23100
$101$	14.9562	1.48820	0.744099	−	0.668070i	$-0.232879\pi$
$101$	14.9562	1.48820	0.744099	+	0.668070i	$0.232879\pi$
$102$	−2.59771	−0.257212
$103$	−6.32600	−0.623320	−0.311660	−	0.950194i	$-0.600885\pi$
$103$	−6.32600	−0.623320	−0.311660	+	0.950194i	$0.600885\pi$
$104$	1.00000	0.0980581
$105$	0	0
$106$	4.17246	0.405265
$107$	18.7617	1.81376	0.906879	−	0.421391i	$-0.138458\pi$
$107$	18.7617	1.81376	0.906879	+	0.421391i	$0.138458\pi$
$108$	1.00000	0.0962250
$109$	−14.1709	−1.35733	−0.678665	−	0.734448i	$-0.737441\pi$
$109$	−14.1709	−1.35733	−0.678665	+	0.734448i	$0.737441\pi$
$110$	−15.4911	−1.47702
$111$	1.04352	0.0990470
$112$	0	0
$113$	5.50950	0.518291	0.259145	−	0.965838i	$-0.416559\pi$
$113$	5.50950	0.518291	0.259145	+	0.965838i	$0.416559\pi$
$114$	−2.37069	−0.222035
$115$	−16.4357	−1.53263
$116$	−4.84035	−0.449416
$117$	−1.00000	−0.0924500
$118$	7.54073	0.694181
$119$	0	0
$120$	−4.16053	−0.379803
$121$	2.86332	0.260302
$122$	−12.4525	−1.12740
$123$	2.35876	0.212682
$124$	0.227026	0.0203875
$125$	30.4136	2.72027
$126$	0	0
$127$	14.0481	1.24657	0.623284	−	0.781996i	$-0.285798\pi$
$127$	14.0481	1.24657	0.623284	+	0.781996i	$0.285798\pi$
$128$	−1.00000	−0.0883883
$129$	7.95037	0.699991
$130$	4.16053	0.364903
$131$	−14.9837	−1.30914	−0.654568	−	0.756003i	$-0.727149\pi$
$131$	−14.9837	−1.30914	−0.654568	+	0.756003i	$0.727149\pi$
$132$	3.72335	0.324076
$133$	0	0
$134$	6.56370	0.567018
$135$	4.16053	0.358082
$136$	−2.59771	−0.222752
$137$	14.4647	1.23580	0.617902	−	0.786255i	$-0.287983\pi$
$137$	14.4647	1.23580	0.617902	+	0.786255i	$0.287983\pi$
$138$	3.95037	0.336278
$139$	−9.39338	−0.796736	−0.398368	−	0.917226i	$-0.630423\pi$
$139$	−9.39338	−0.796736	−0.398368	+	0.917226i	$0.630423\pi$
$140$	0	0
$141$	−2.17246	−0.182954
$142$	7.88388	0.661601
$143$	−3.72335	−0.311362
$144$	1.00000	0.0833333
$145$	−20.1384	−1.67241
$146$	13.2641	1.09774
$147$	0	0
$148$	1.04352	0.0857772
$149$	−13.1495	−1.07725	−0.538624	−	0.842546i	$-0.681056\pi$
$149$	−13.1495	−1.07725	−0.538624	+	0.842546i	$0.681056\pi$
$150$	−12.3100	−1.00511
$151$	−17.4041	−1.41632	−0.708161	−	0.706051i	$-0.750475\pi$
$151$	−17.4041	−1.41632	−0.708161	+	0.706051i	$0.750475\pi$
$152$	−2.37069	−0.192288
$153$	2.59771	0.210013
$154$	0	0
$155$	0.944547	0.0758679
$156$	−1.00000	−0.0800641
$157$	−23.7013	−1.89157	−0.945783	−	0.324798i	$-0.894704\pi$
$157$	−23.7013	−1.89157	−0.945783	+	0.324798i	$0.894704\pi$
$158$	12.3379	0.981553
$159$	−4.17246	−0.330898
$160$	−4.16053	−0.328919
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	3.06408	0.239997	0.119999	−	0.992774i	$-0.461711\pi$
$163$	3.06408	0.239997	0.119999	+	0.992774i	$0.461711\pi$
$164$	2.35876	0.184188
$165$	15.4911	1.20598
$166$	−17.9779	−1.39536
$167$	−9.92488	−0.768010	−0.384005	−	0.923331i	$-0.625455\pi$
$167$	−9.92488	−0.768010	−0.384005	+	0.923331i	$0.625455\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−10.8079	−0.828926
$171$	2.37069	0.181291
$172$	7.95037	0.606210
$173$	−14.1590	−1.07649	−0.538245	−	0.842789i	$-0.680912\pi$
$173$	−14.1590	−1.07649	−0.538245	+	0.842789i	$0.680912\pi$
$174$	4.84035	0.366946
$175$	0	0
$176$	3.72335	0.280658
$177$	−7.54073	−0.566796
$178$	−4.79594	−0.359471
$179$	−10.8609	−0.811783	−0.405891	−	0.913921i	$-0.633039\pi$
$179$	−10.8609	−0.811783	−0.405891	+	0.913921i	$0.633039\pi$
$180$	4.16053	0.310108
$181$	−16.8523	−1.25262	−0.626310	−	0.779574i	$-0.715436\pi$
$181$	−16.8523	−1.25262	−0.626310	+	0.779574i	$0.715436\pi$
$182$	0	0
$183$	12.4525	0.920517
$184$	3.95037	0.291225
$185$	4.34162	0.319202
$186$	−0.227026	−0.0166463
$187$	9.67220	0.707301
$188$	−2.17246	−0.158443
$189$	0	0
$190$	−9.86332	−0.715561
$191$	11.9405	0.863984	0.431992	−	0.901877i	$-0.357811\pi$
$191$	11.9405	0.863984	0.431992	+	0.901877i	$0.357811\pi$
$192$	1.00000	0.0721688
$193$	21.9610	1.58079	0.790395	−	0.612597i	$-0.209875\pi$
$193$	21.9610	1.58079	0.790395	+	0.612597i	$0.209875\pi$
$194$	−11.6807	−0.838626
$195$	−4.16053	−0.297942
$196$	0	0
$197$	−0.823213	−0.0586515	−0.0293257	−	0.999570i	$-0.509336\pi$
$197$	−0.823213	−0.0586515	−0.0293257	+	0.999570i	$0.509336\pi$
$198$	−3.72335	−0.264607
$199$	−13.9951	−0.992083	−0.496042	−	0.868299i	$-0.665214\pi$
$199$	−13.9951	−0.992083	−0.496042	+	0.868299i	$0.665214\pi$
$200$	−12.3100	−0.870450
$201$	−6.56370	−0.462968
$202$	−14.9562	−1.05231
$203$	0	0
$204$	2.59771	0.181876
$205$	9.81370	0.685418
$206$	6.32600	0.440754
$207$	−3.95037	−0.274570
$208$	−1.00000	−0.0693375
$209$	8.82690	0.610569
$210$	0	0
$211$	25.2420	1.73773	0.868865	−	0.495048i	$-0.164850\pi$
$211$	25.2420	1.73773	0.868865	+	0.495048i	$0.164850\pi$
$212$	−4.17246	−0.286566
$213$	−7.88388	−0.540195
$214$	−18.7617	−1.28252
$215$	33.0778	2.25589
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	14.1709	0.959777
$219$	−13.2641	−0.896304
$220$	15.4911	1.04441
$221$	−2.59771	−0.174741
$222$	−1.04352	−0.0700368
$223$	−26.4969	−1.77437	−0.887183	−	0.461418i	$-0.847341\pi$
$223$	−26.4969	−1.77437	−0.887183	+	0.461418i	$0.847341\pi$
$224$	0	0
$225$	12.3100	0.820668
$226$	−5.50950	−0.366487
$227$	−6.78210	−0.450144	−0.225072	−	0.974342i	$-0.572262\pi$
$227$	−6.78210	−0.450144	−0.225072	+	0.974342i	$0.572262\pi$
$228$	2.37069	0.157003
$229$	9.90774	0.654722	0.327361	−	0.944899i	$-0.393841\pi$
$229$	9.90774	0.654722	0.327361	+	0.944899i	$0.393841\pi$
$230$	16.4357	1.08374
$231$	0	0
$232$	4.84035	0.317785
$233$	−2.38603	−0.156314	−0.0781570	−	0.996941i	$-0.524904\pi$
$233$	−2.38603	−0.156314	−0.0781570	+	0.996941i	$0.524904\pi$
$234$	1.00000	0.0653720
$235$	−9.03858	−0.589612
$236$	−7.54073	−0.490860
$237$	−12.3379	−0.801435
$238$	0	0
$239$	2.68108	0.173424	0.0867122	−	0.996233i	$-0.472364\pi$
$239$	2.68108	0.173424	0.0867122	+	0.996233i	$0.472364\pi$
$240$	4.16053	0.268561
$241$	−17.8327	−1.14871	−0.574353	−	0.818607i	$-0.694746\pi$
$241$	−17.8327	−1.14871	−0.574353	+	0.818607i	$0.694746\pi$
$242$	−2.86332	−0.184061
$243$	1.00000	0.0641500
$244$	12.4525	0.797191
$245$	0	0
$246$	−2.35876	−0.150389
$247$	−2.37069	−0.150843
$248$	−0.227026	−0.0144161
$249$	17.9779	1.13930
$250$	−30.4136	−1.92352
$251$	−0.317763	−0.0200570	−0.0100285	−	0.999950i	$-0.503192\pi$
$251$	−0.317763	−0.0200570	−0.0100285	+	0.999950i	$0.503192\pi$
$252$	0	0
$253$	−14.7086	−0.924723
$254$	−14.0481	−0.881456
$255$	10.8079	0.676815
$256$	1.00000	0.0625000
$257$	−2.13299	−0.133052	−0.0665261	−	0.997785i	$-0.521192\pi$
$257$	−2.13299	−0.133052	−0.0665261	+	0.997785i	$0.521192\pi$
$258$	−7.95037	−0.494969
$259$	0	0
$260$	−4.16053	−0.258025
$261$	−4.84035	−0.299610
$262$	14.9837	0.925699
$263$	−6.29898	−0.388412	−0.194206	−	0.980961i	$-0.562213\pi$
$263$	−6.29898	−0.388412	−0.194206	+	0.980961i	$0.562213\pi$
$264$	−3.72335	−0.229156
$265$	−17.3596	−1.06639
$266$	0	0
$267$	4.79594	0.293507
$268$	−6.56370	−0.400942
$269$	−5.76077	−0.351241	−0.175620	−	0.984458i	$-0.556193\pi$
$269$	−5.76077	−0.351241	−0.175620	+	0.984458i	$0.556193\pi$
$270$	−4.16053	−0.253202
$271$	−19.0793	−1.15899	−0.579493	−	0.814977i	$-0.696749\pi$
$271$	−19.0793	−1.15899	−0.579493	+	0.814977i	$0.696749\pi$
$272$	2.59771	0.157510
$273$	0	0
$274$	−14.4647	−0.873846
$275$	45.8345	2.76392
$276$	−3.95037	−0.237785
$277$	15.6204	0.938539	0.469270	−	0.883055i	$-0.344517\pi$
$277$	15.6204	0.938539	0.469270	+	0.883055i	$0.344517\pi$
$278$	9.39338	0.563378
$279$	0.227026	0.0135917
$280$	0	0
$281$	10.9926	0.655766	0.327883	−	0.944718i	$-0.393665\pi$
$281$	10.9926	0.655766	0.327883	+	0.944718i	$0.393665\pi$
$282$	2.17246	0.129368
$283$	1.20280	0.0714992	0.0357496	−	0.999361i	$-0.488618\pi$
$283$	1.20280	0.0714992	0.0357496	+	0.999361i	$0.488618\pi$
$284$	−7.88388	−0.467822
$285$	9.86332	0.584253
$286$	3.72335	0.220166
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−10.2519	−0.603052
$290$	20.1384	1.18257
$291$	11.6807	0.684735
$292$	−13.2641	−0.776222
$293$	6.25610	0.365485	0.182743	−	0.983161i	$-0.441503\pi$
$293$	6.25610	0.365485	0.182743	+	0.983161i	$0.441503\pi$
$294$	0	0
$295$	−31.3735	−1.82663
$296$	−1.04352	−0.0606537
$297$	3.72335	0.216051
$298$	13.1495	0.761729
$299$	3.95037	0.228456
$300$	12.3100	0.710719
$301$	0	0
$302$	17.4041	1.00149
$303$	14.9562	0.859211
$304$	2.37069	0.135968
$305$	51.8091	2.96658
$306$	−2.59771	−0.148501
$307$	23.2145	1.32492	0.662460	−	0.749098i	$-0.269513\pi$
$307$	23.2145	1.32492	0.662460	+	0.749098i	$0.269513\pi$
$308$	0	0
$309$	−6.32600	−0.359874
$310$	−0.944547	−0.0536467
$311$	3.79162	0.215003	0.107501	−	0.994205i	$-0.465715\pi$
$311$	3.79162	0.215003	0.107501	+	0.994205i	$0.465715\pi$
$312$	1.00000	0.0566139
$313$	−1.62260	−0.0917147	−0.0458573	−	0.998948i	$-0.514602\pi$
$313$	−1.62260	−0.0917147	−0.0458573	+	0.998948i	$0.514602\pi$
$314$	23.7013	1.33754
$315$	0	0
$316$	−12.3379	−0.694063
$317$	−18.5719	−1.04310	−0.521552	−	0.853219i	$-0.674647\pi$
$317$	−18.5719	−1.04310	−0.521552	+	0.853219i	$0.674647\pi$
$318$	4.17246	0.233980
$319$	−18.0223	−1.00906
$320$	4.16053	0.232581
$321$	18.7617	1.04717
$322$	0	0
$323$	6.15837	0.342661
$324$	1.00000	0.0555556
$325$	−12.3100	−0.682837
$326$	−3.06408	−0.169704
$327$	−14.1709	−0.783654
$328$	−2.35876	−0.130241
$329$	0	0
$330$	−15.4911	−0.852757
$331$	−31.3289	−1.72199	−0.860997	−	0.508610i	$-0.830160\pi$
$331$	−31.3289	−1.72199	−0.860997	+	0.508610i	$0.830160\pi$
$332$	17.9779	0.986666
$333$	1.04352	0.0571848
$334$	9.92488	0.543065
$335$	−27.3085	−1.49202
$336$	0	0
$337$	18.4577	1.00546	0.502729	−	0.864444i	$-0.332330\pi$
$337$	18.4577	1.00546	0.502729	+	0.864444i	$0.332330\pi$
$338$	−1.00000	−0.0543928
$339$	5.50950	0.299235
$340$	10.8079	0.586139
$341$	0.845296	0.0457753
$342$	−2.37069	−0.128192
$343$	0	0
$344$	−7.95037	−0.428655
$345$	−16.4357	−0.884866
$346$	14.1590	0.761193
$347$	4.75001	0.254994	0.127497	−	0.991839i	$-0.459306\pi$
$347$	4.75001	0.254994	0.127497	+	0.991839i	$0.459306\pi$
$348$	−4.84035	−0.259470
$349$	25.4433	1.36195	0.680973	−	0.732308i	$-0.261557\pi$
$349$	25.4433	1.36195	0.680973	+	0.732308i	$0.261557\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−3.72335	−0.198455
$353$	24.1382	1.28475	0.642373	−	0.766392i	$-0.277950\pi$
$353$	24.1382	1.28475	0.642373	+	0.766392i	$0.277950\pi$
$354$	7.54073	0.400785
$355$	−32.8011	−1.74090
$356$	4.79594	0.254185
$357$	0	0
$358$	10.8609	0.574017
$359$	31.0282	1.63760	0.818802	−	0.574076i	$-0.194639\pi$
$359$	31.0282	1.63760	0.818802	+	0.574076i	$0.194639\pi$
$360$	−4.16053	−0.219279
$361$	−13.3798	−0.704202
$362$	16.8523	0.885736
$363$	2.86332	0.150286
$364$	0	0
$365$	−55.1856	−2.88855
$366$	−12.4525	−0.650904
$367$	7.08794	0.369987	0.184994	−	0.982740i	$-0.440774\pi$
$367$	7.08794	0.369987	0.184994	+	0.982740i	$0.440774\pi$
$368$	−3.95037	−0.205927
$369$	2.35876	0.122792
$370$	−4.34162	−0.225710
$371$	0	0
$372$	0.227026	0.0117707
$373$	20.7994	1.07695	0.538475	−	0.842642i	$-0.319001\pi$
$373$	20.7994	1.07695	0.538475	+	0.842642i	$0.319001\pi$
$374$	−9.67220	−0.500137
$375$	30.4136	1.57055
$376$	2.17246	0.112036
$377$	4.84035	0.249291
$378$	0	0
$379$	−5.16294	−0.265203	−0.132601	−	0.991169i	$-0.542333\pi$
$379$	−5.16294	−0.265203	−0.132601	+	0.991169i	$0.542333\pi$
$380$	9.86332	0.505978
$381$	14.0481	0.719706
$382$	−11.9405	−0.610929
$383$	11.4685	0.586013	0.293007	−	0.956110i	$-0.405344\pi$
$383$	11.4685	0.586013	0.293007	+	0.956110i	$0.405344\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−21.9610	−1.11779
$387$	7.95037	0.404140
$388$	11.6807	0.592998
$389$	34.3796	1.74311	0.871556	−	0.490295i	$-0.163111\pi$
$389$	34.3796	1.74311	0.871556	+	0.490295i	$0.163111\pi$
$390$	4.16053	0.210677
$391$	−10.2619	−0.518969
$392$	0	0
$393$	−14.9837	−0.755830
$394$	0.823213	0.0414728
$395$	−51.3323	−2.58281
$396$	3.72335	0.187105
$397$	17.2916	0.867842	0.433921	−	0.900951i	$-0.357130\pi$
$397$	17.2916	0.867842	0.433921	+	0.900951i	$0.357130\pi$
$398$	13.9951	0.701509
$399$	0	0
$400$	12.3100	0.615501
$401$	12.4541	0.621926	0.310963	−	0.950422i	$-0.399349\pi$
$401$	12.4541	0.621926	0.310963	+	0.950422i	$0.399349\pi$
$402$	6.56370	0.327368
$403$	−0.227026	−0.0113090
$404$	14.9562	0.744099
$405$	4.16053	0.206738
$406$	0	0
$407$	3.88541	0.192592
$408$	−2.59771	−0.128606
$409$	29.8651	1.47673	0.738367	−	0.674399i	$-0.235597\pi$
$409$	29.8651	1.47673	0.738367	+	0.674399i	$0.235597\pi$
$410$	−9.81370	−0.484664
$411$	14.4647	0.713492
$412$	−6.32600	−0.311660
$413$	0	0
$414$	3.95037	0.194150
$415$	74.7977	3.67167
$416$	1.00000	0.0490290
$417$	−9.39338	−0.459996
$418$	−8.82690	−0.431738
$419$	−32.4084	−1.58325	−0.791626	−	0.611006i	$-0.790765\pi$
$419$	−32.4084	−1.58325	−0.791626	+	0.611006i	$0.790765\pi$
$420$	0	0
$421$	29.5732	1.44131	0.720655	−	0.693294i	$-0.243841\pi$
$421$	29.5732	1.44131	0.720655	+	0.693294i	$0.243841\pi$
$422$	−25.2420	−1.22876
$423$	−2.17246	−0.105629
$424$	4.17246	0.202633
$425$	31.9779	1.55116
$426$	7.88388	0.381975
$427$	0	0
$428$	18.7617	0.906879
$429$	−3.72335	−0.179765
$430$	−33.0778	−1.59515
$431$	19.9147	0.959258	0.479629	−	0.877471i	$-0.340771\pi$
$431$	19.9147	0.959258	0.479629	+	0.877471i	$0.340771\pi$
$432$	1.00000	0.0481125
$433$	−4.56154	−0.219214	−0.109607	−	0.993975i	$-0.534959\pi$
$433$	−4.56154	−0.219214	−0.109607	+	0.993975i	$0.534959\pi$
$434$	0	0
$435$	−20.1384	−0.965565
$436$	−14.1709	−0.678665
$437$	−9.36511	−0.447994
$438$	13.2641	0.633782
$439$	2.09376	0.0999299	0.0499649	−	0.998751i	$-0.484089\pi$
$439$	2.09376	0.0999299	0.0499649	+	0.998751i	$0.484089\pi$
$440$	−15.4911	−0.738510
$441$	0	0
$442$	2.59771	0.123561
$443$	−15.2686	−0.725435	−0.362717	−	0.931899i	$-0.618151\pi$
$443$	−15.2686	−0.725435	−0.362717	+	0.931899i	$0.618151\pi$
$444$	1.04352	0.0495235
$445$	19.9537	0.945895
$446$	26.4969	1.25467
$447$	−13.1495	−0.621950
$448$	0	0
$449$	26.3992	1.24586	0.622928	−	0.782279i	$-0.285943\pi$
$449$	26.3992	1.24586	0.622928	+	0.782279i	$0.285943\pi$
$450$	−12.3100	−0.580300
$451$	8.78249	0.413551
$452$	5.50950	0.259145
$453$	−17.4041	−0.817714
$454$	6.78210	0.318300
$455$	0	0
$456$	−2.37069	−0.111018
$457$	6.42553	0.300574	0.150287	−	0.988642i	$-0.451980\pi$
$457$	6.42553	0.300574	0.150287	+	0.988642i	$0.451980\pi$
$458$	−9.90774	−0.462958
$459$	2.59771	0.121251
$460$	−16.4357	−0.766316
$461$	−25.7009	−1.19701	−0.598505	−	0.801119i	$-0.704238\pi$
$461$	−25.7009	−1.19701	−0.598505	+	0.801119i	$0.704238\pi$
$462$	0	0
$463$	6.83910	0.317840	0.158920	−	0.987291i	$-0.449199\pi$
$463$	6.83910	0.317840	0.158920	+	0.987291i	$0.449199\pi$
$464$	−4.84035	−0.224708
$465$	0.944547	0.0438023
$466$	2.38603	0.110531
$467$	12.7472	0.589871	0.294936	−	0.955517i	$-0.404702\pi$
$467$	12.7472	0.589871	0.294936	+	0.955517i	$0.404702\pi$
$468$	−1.00000	−0.0462250
$469$	0	0
$470$	9.03858	0.416919
$471$	−23.7013	−1.09210
$472$	7.54073	0.347090
$473$	29.6020	1.36110
$474$	12.3379	0.566700
$475$	29.1832	1.33902
$476$	0	0
$477$	−4.17246	−0.191044
$478$	−2.68108	−0.122630
$479$	−6.61800	−0.302384	−0.151192	−	0.988504i	$-0.548311\pi$
$479$	−6.61800	−0.302384	−0.151192	+	0.988504i	$0.548311\pi$
$480$	−4.16053	−0.189901
$481$	−1.04352	−0.0475806
$482$	17.8327	0.812258
$483$	0	0
$484$	2.86332	0.130151
$485$	48.5980	2.20672
$486$	−1.00000	−0.0453609
$487$	−32.2292	−1.46044	−0.730222	−	0.683210i	$-0.760583\pi$
$487$	−32.2292	−1.46044	−0.730222	+	0.683210i	$0.760583\pi$
$488$	−12.4525	−0.563699
$489$	3.06408	0.138563
$490$	0	0
$491$	17.5511	0.792072	0.396036	−	0.918235i	$-0.370386\pi$
$491$	17.5511	0.792072	0.396036	+	0.918235i	$0.370386\pi$
$492$	2.35876	0.106341
$493$	−12.5739	−0.566298
$494$	2.37069	0.106662
$495$	15.4911	0.696274
$496$	0.227026	0.0101938
$497$	0	0
$498$	−17.9779	−0.805610
$499$	−14.7304	−0.659425	−0.329712	−	0.944081i	$-0.606952\pi$
$499$	−14.7304	−0.659425	−0.329712	+	0.944081i	$0.606952\pi$
$500$	30.4136	1.36014
$501$	−9.92488	−0.443411
$502$	0.317763	0.0141825
$503$	−36.6344	−1.63345	−0.816724	−	0.577029i	$-0.804212\pi$
$503$	−36.6344	−1.63345	−0.816724	+	0.577029i	$0.804212\pi$
$504$	0	0
$505$	62.2257	2.76901
$506$	14.7086	0.653878
$507$	1.00000	0.0444116
$508$	14.0481	0.623284
$509$	23.8296	1.05623	0.528114	−	0.849174i	$-0.322899\pi$
$509$	23.8296	1.05623	0.528114	+	0.849174i	$0.322899\pi$
$510$	−10.8079	−0.478581
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	2.37069	0.104668
$514$	2.13299	0.0940821
$515$	−26.3195	−1.15978
$516$	7.95037	0.349996
$517$	−8.08882	−0.355746
$518$	0	0
$519$	−14.1590	−0.621511
$520$	4.16053	0.182451
$521$	−31.4378	−1.37731	−0.688657	−	0.725087i	$-0.741800\pi$
$521$	−31.4378	−1.37731	−0.688657	+	0.725087i	$0.741800\pi$
$522$	4.84035	0.211857
$523$	−9.56282	−0.418153	−0.209076	−	0.977899i	$-0.567046\pi$
$523$	−9.56282	−0.418153	−0.209076	+	0.977899i	$0.567046\pi$
$524$	−14.9837	−0.654568
$525$	0	0
$526$	6.29898	0.274649
$527$	0.589748	0.0256898
$528$	3.72335	0.162038
$529$	−7.39454	−0.321502
$530$	17.3596	0.754055
$531$	−7.54073	−0.327240
$532$	0	0
$533$	−2.35876	−0.102169
$534$	−4.79594	−0.207541
$535$	78.0585	3.37476
$536$	6.56370	0.283509
$537$	−10.8609	−0.468683
$538$	5.76077	0.248365
$539$	0	0
$540$	4.16053	0.179041
$541$	−35.6636	−1.53330	−0.766648	−	0.642067i	$-0.778077\pi$
$541$	−35.6636	−1.53330	−0.766648	+	0.642067i	$0.778077\pi$
$542$	19.0793	0.819526
$543$	−16.8523	−0.723201
$544$	−2.59771	−0.111376
$545$	−58.9586	−2.52551
$546$	0	0
$547$	−14.1348	−0.604359	−0.302179	−	0.953251i	$-0.597714\pi$
$547$	−14.1348	−0.604359	−0.302179	+	0.953251i	$0.597714\pi$
$548$	14.4647	0.617902
$549$	12.4525	0.531461
$550$	−45.8345	−1.95439
$551$	−11.4750	−0.488850
$552$	3.95037	0.168139
$553$	0	0
$554$	−15.6204	−0.663648
$555$	4.34162	0.184291
$556$	−9.39338	−0.398368
$557$	23.6470	1.00195	0.500977	−	0.865460i	$-0.332974\pi$
$557$	23.6470	1.00195	0.500977	+	0.865460i	$0.332974\pi$
$558$	−0.227026	−0.00961076
$559$	−7.95037	−0.336265
$560$	0	0
$561$	9.67220	0.408360
$562$	−10.9926	−0.463697
$563$	35.2147	1.48412	0.742061	−	0.670332i	$-0.233848\pi$
$563$	35.2147	1.48412	0.742061	+	0.670332i	$0.233848\pi$
$564$	−2.17246	−0.0914770
$565$	22.9225	0.964355
$566$	−1.20280	−0.0505576
$567$	0	0
$568$	7.88388	0.330800
$569$	−45.4576	−1.90568	−0.952841	−	0.303469i	$-0.901855\pi$
$569$	−45.4576	−1.90568	−0.952841	+	0.303469i	$0.901855\pi$
$570$	−9.86332	−0.413129
$571$	−29.2916	−1.22582	−0.612908	−	0.790154i	$-0.710000\pi$
$571$	−29.2916	−1.22582	−0.612908	+	0.790154i	$0.710000\pi$
$572$	−3.72335	−0.155681
$573$	11.9405	0.498821
$574$	0	0
$575$	−48.6292	−2.02798
$576$	1.00000	0.0416667
$577$	−40.7604	−1.69688	−0.848439	−	0.529293i	$-0.822457\pi$
$577$	−40.7604	−1.69688	−0.848439	+	0.529293i	$0.822457\pi$
$578$	10.2519	0.426422
$579$	21.9610	0.912670
$580$	−20.1384	−0.836204
$581$	0	0
$582$	−11.6807	−0.484181
$583$	−15.5355	−0.643415
$584$	13.2641	0.548872
$585$	−4.16053	−0.172017
$586$	−6.25610	−0.258437
$587$	13.1642	0.543345	0.271672	−	0.962390i	$-0.412423\pi$
$587$	13.1642	0.543345	0.271672	+	0.962390i	$0.412423\pi$
$588$	0	0
$589$	0.538207	0.0221764
$590$	31.3735	1.29162
$591$	−0.823213	−0.0338624
$592$	1.04352	0.0428886
$593$	1.12689	0.0462757	0.0231379	−	0.999732i	$-0.492634\pi$
$593$	1.12689	0.0462757	0.0231379	+	0.999732i	$0.492634\pi$
$594$	−3.72335	−0.152771
$595$	0	0
$596$	−13.1495	−0.538624
$597$	−13.9951	−0.572780
$598$	−3.95037	−0.161543
$599$	−41.4981	−1.69557	−0.847783	−	0.530343i	$-0.822063\pi$
$599$	−41.4981	−1.69557	−0.847783	+	0.530343i	$0.822063\pi$
$600$	−12.3100	−0.502555
$601$	−28.7564	−1.17300	−0.586500	−	0.809949i	$-0.699495\pi$
$601$	−28.7564	−1.17300	−0.586500	+	0.809949i	$0.699495\pi$
$602$	0	0
$603$	−6.56370	−0.267295
$604$	−17.4041	−0.708161
$605$	11.9130	0.484330
$606$	−14.9562	−0.607554
$607$	−36.7788	−1.49280	−0.746402	−	0.665495i	$-0.768220\pi$
$607$	−36.7788	−1.49280	−0.746402	+	0.665495i	$0.768220\pi$
$608$	−2.37069	−0.0961441
$609$	0	0
$610$	−51.8091	−2.09769
$611$	2.17246	0.0878883
$612$	2.59771	0.105006
$613$	−18.9197	−0.764159	−0.382079	−	0.924129i	$-0.624792\pi$
$613$	−18.9197	−0.764159	−0.382079	+	0.924129i	$0.624792\pi$
$614$	−23.2145	−0.936859
$615$	9.81370	0.395727
$616$	0	0
$617$	40.1670	1.61706	0.808531	−	0.588454i	$-0.200263\pi$
$617$	40.1670	1.61706	0.808531	+	0.588454i	$0.200263\pi$
$618$	6.32600	0.254469
$619$	−13.7199	−0.551450	−0.275725	−	0.961237i	$-0.588918\pi$
$619$	−13.7199	−0.551450	−0.275725	+	0.961237i	$0.588918\pi$
$620$	0.944547	0.0379339
$621$	−3.95037	−0.158523
$622$	−3.79162	−0.152030
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	64.9865	2.59946
$626$	1.62260	0.0648521
$627$	8.82690	0.352512
$628$	−23.7013	−0.945783
$629$	2.71078	0.108086
$630$	0	0
$631$	−11.8728	−0.472649	−0.236325	−	0.971674i	$-0.575943\pi$
$631$	−11.8728	−0.472649	−0.236325	+	0.971674i	$0.575943\pi$
$632$	12.3379	0.490777
$633$	25.2420	1.00328
$634$	18.5719	0.737586
$635$	58.4476	2.31942
$636$	−4.17246	−0.165449
$637$	0	0
$638$	18.0223	0.713511
$639$	−7.88388	−0.311881
$640$	−4.16053	−0.164459
$641$	−7.77475	−0.307084	−0.153542	−	0.988142i	$-0.549068\pi$
$641$	−7.77475	−0.307084	−0.153542	+	0.988142i	$0.549068\pi$
$642$	−18.7617	−0.740464
$643$	34.6722	1.36734	0.683669	−	0.729793i	$-0.260383\pi$
$643$	34.6722	1.36734	0.683669	+	0.729793i	$0.260383\pi$
$644$	0	0
$645$	33.0778	1.30244
$646$	−6.15837	−0.242298
$647$	−18.0528	−0.709727	−0.354864	−	0.934918i	$-0.615473\pi$
$647$	−18.0528	−0.709727	−0.354864	+	0.934918i	$0.615473\pi$
$648$	−1.00000	−0.0392837
$649$	−28.0768	−1.10211
$650$	12.3100	0.482839
$651$	0	0
$652$	3.06408	0.119999
$653$	48.9089	1.91395	0.956976	−	0.290167i	$-0.0937110\pi$
$653$	48.9089	1.91395	0.956976	+	0.290167i	$0.0937110\pi$
$654$	14.1709	0.554127
$655$	−62.3403	−2.43584
$656$	2.35876	0.0920941
$657$	−13.2641	−0.517481
$658$	0	0
$659$	−8.13695	−0.316971	−0.158485	−	0.987361i	$-0.550661\pi$
$659$	−8.13695	−0.316971	−0.158485	+	0.987361i	$0.550661\pi$
$660$	15.4911	0.602991
$661$	−3.48275	−0.135463	−0.0677317	−	0.997704i	$-0.521576\pi$
$661$	−3.48275	−0.135463	−0.0677317	+	0.997704i	$0.521576\pi$
$662$	31.3289	1.21763
$663$	−2.59771	−0.100887
$664$	−17.9779	−0.697678
$665$	0	0
$666$	−1.04352	−0.0404358
$667$	19.1212	0.740376
$668$	−9.92488	−0.384005
$669$	−26.4969	−1.02443
$670$	27.3085	1.05502
$671$	46.3651	1.78990
$672$	0	0
$673$	16.1771	0.623580	0.311790	−	0.950151i	$-0.399072\pi$
$673$	16.1771	0.623580	0.311790	+	0.950151i	$0.399072\pi$
$674$	−18.4577	−0.710966
$675$	12.3100	0.473813
$676$	1.00000	0.0384615
$677$	31.8903	1.22564	0.612822	−	0.790221i	$-0.290034\pi$
$677$	31.8903	1.22564	0.612822	+	0.790221i	$0.290034\pi$
$678$	−5.50950	−0.211591
$679$	0	0
$680$	−10.8079	−0.414463
$681$	−6.78210	−0.259891
$682$	−0.845296	−0.0323680
$683$	−28.1675	−1.07780	−0.538900	−	0.842370i	$-0.681160\pi$
$683$	−28.1675	−1.07780	−0.538900	+	0.842370i	$0.681160\pi$
$684$	2.37069	0.0906455
$685$	60.1809	2.29940
$686$	0	0
$687$	9.90774	0.378004
$688$	7.95037	0.303105
$689$	4.17246	0.158958
$690$	16.4357	0.625695
$691$	−11.4467	−0.435453	−0.217726	−	0.976010i	$-0.569864\pi$
$691$	−11.4467	−0.435453	−0.217726	+	0.976010i	$0.569864\pi$
$692$	−14.1590	−0.538245
$693$	0	0
$694$	−4.75001	−0.180308
$695$	−39.0815	−1.48244
$696$	4.84035	0.183473
$697$	6.12739	0.232091
$698$	−25.4433	−0.963041
$699$	−2.38603	−0.0902479
$700$	0	0
$701$	34.5971	1.30671	0.653356	−	0.757051i	$-0.273360\pi$
$701$	34.5971	1.30671	0.653356	+	0.757051i	$0.273360\pi$
$702$	1.00000	0.0377426
$703$	2.47387	0.0933039
$704$	3.72335	0.140329
$705$	−9.03858	−0.340413
$706$	−24.1382	−0.908452
$707$	0	0
$708$	−7.54073	−0.283398
$709$	10.2153	0.383645	0.191823	−	0.981430i	$-0.438560\pi$
$709$	10.2153	0.383645	0.191823	+	0.981430i	$0.438560\pi$
$710$	32.8011	1.23100
$711$	−12.3379	−0.462709
$712$	−4.79594	−0.179736
$713$	−0.896836	−0.0335868
$714$	0	0
$715$	−15.4911	−0.579335
$716$	−10.8609	−0.405891
$717$	2.68108	0.100127
$718$	−31.0282	−1.15796
$719$	−36.0598	−1.34480	−0.672401	−	0.740187i	$-0.734737\pi$
$719$	−36.0598	−1.34480	−0.672401	+	0.740187i	$0.734737\pi$
$720$	4.16053	0.155054
$721$	0	0
$722$	13.3798	0.497946
$723$	−17.8327	−0.663206
$724$	−16.8523	−0.626310
$725$	−59.5849	−2.21293
$726$	−2.86332	−0.106268
$727$	−38.9895	−1.44604	−0.723020	−	0.690827i	$-0.757247\pi$
$727$	−38.9895	−1.44604	−0.723020	+	0.690827i	$0.757247\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	55.1856	2.04251
$731$	20.6528	0.763871
$732$	12.4525	0.460259
$733$	−26.2509	−0.969598	−0.484799	−	0.874625i	$-0.661107\pi$
$733$	−26.2509	−0.969598	−0.484799	+	0.874625i	$0.661107\pi$
$734$	−7.08794	−0.261620
$735$	0	0
$736$	3.95037	0.145613
$737$	−24.4390	−0.900220
$738$	−2.35876	−0.0868272
$739$	−7.60750	−0.279846	−0.139923	−	0.990162i	$-0.544686\pi$
$739$	−7.60750	−0.279846	−0.139923	+	0.990162i	$0.544686\pi$
$740$	4.34162	0.159601
$741$	−2.37069	−0.0870894
$742$	0	0
$743$	−17.4657	−0.640755	−0.320378	−	0.947290i	$-0.603810\pi$
$743$	−17.4657	−0.640755	−0.320378	+	0.947290i	$0.603810\pi$
$744$	−0.227026	−0.00832316
$745$	−54.7089	−2.00438
$746$	−20.7994	−0.761519
$747$	17.9779	0.657778
$748$	9.67220	0.353650
$749$	0	0
$750$	−30.4136	−1.11055
$751$	22.8569	0.834062	0.417031	−	0.908892i	$-0.363071\pi$
$751$	22.8569	0.834062	0.417031	+	0.908892i	$0.363071\pi$
$752$	−2.17246	−0.0792214
$753$	−0.317763	−0.0115799
$754$	−4.84035	−0.176275
$755$	−72.4101	−2.63527
$756$	0	0
$757$	34.0156	1.23632	0.618159	−	0.786053i	$-0.287879\pi$
$757$	34.0156	1.23632	0.618159	+	0.786053i	$0.287879\pi$
$758$	5.16294	0.187527
$759$	−14.7086	−0.533889
$760$	−9.86332	−0.357780
$761$	22.2357	0.806042	0.403021	−	0.915191i	$-0.367960\pi$
$761$	22.2357	0.806042	0.403021	+	0.915191i	$0.367960\pi$
$762$	−14.0481	−0.508909
$763$	0	0
$764$	11.9405	0.431992
$765$	10.8079	0.390759
$766$	−11.4685	−0.414374
$767$	7.54073	0.272280
$768$	1.00000	0.0360844
$769$	−23.2897	−0.839848	−0.419924	−	0.907559i	$-0.637943\pi$
$769$	−23.2897	−0.839848	−0.419924	+	0.907559i	$0.637943\pi$
$770$	0	0
$771$	−2.13299	−0.0768177
$772$	21.9610	0.790395
$773$	−42.6813	−1.53514	−0.767570	−	0.640965i	$-0.778534\pi$
$773$	−42.6813	−1.53514	−0.767570	+	0.640965i	$0.778534\pi$
$774$	−7.95037	−0.285770
$775$	2.79469	0.100388
$776$	−11.6807	−0.419313
$777$	0	0
$778$	−34.3796	−1.23257
$779$	5.59189	0.200350
$780$	−4.16053	−0.148971
$781$	−29.3544	−1.05038
$782$	10.2619	0.366966
$783$	−4.84035	−0.172980
$784$	0	0
$785$	−98.6099	−3.51954
$786$	14.9837	0.534452
$787$	28.2476	1.00692	0.503459	−	0.864019i	$-0.332061\pi$
$787$	28.2476	1.00692	0.503459	+	0.864019i	$0.332061\pi$
$788$	−0.823213	−0.0293257
$789$	−6.29898	−0.224250
$790$	51.3323	1.82632
$791$	0	0
$792$	−3.72335	−0.132303
$793$	−12.4525	−0.442202
$794$	−17.2916	−0.613657
$795$	−17.3596	−0.615683
$796$	−13.9951	−0.496042
$797$	43.9384	1.55638	0.778189	−	0.628030i	$-0.216138\pi$
$797$	43.9384	1.55638	0.778189	+	0.628030i	$0.216138\pi$
$798$	0	0
$799$	−5.64343	−0.199650
$800$	−12.3100	−0.435225
$801$	4.79594	0.169456
$802$	−12.4541	−0.439768
$803$	−49.3868	−1.74282
$804$	−6.56370	−0.231484
$805$	0	0
$806$	0.227026	0.00799664
$807$	−5.76077	−0.202789
$808$	−14.9562	−0.526157
$809$	11.0235	0.387565	0.193783	−	0.981044i	$-0.437924\pi$
$809$	11.0235	0.387565	0.193783	+	0.981044i	$0.437924\pi$
$810$	−4.16053	−0.146186
$811$	6.13107	0.215291	0.107646	−	0.994189i	$-0.465669\pi$
$811$	6.13107	0.215291	0.107646	+	0.994189i	$0.465669\pi$
$812$	0	0
$813$	−19.0793	−0.669141
$814$	−3.88541	−0.136183
$815$	12.7482	0.446550
$816$	2.59771	0.0909382
$817$	18.8479	0.659403
$818$	−29.8651	−1.04421
$819$	0	0
$820$	9.81370	0.342709
$821$	29.1728	1.01814	0.509069	−	0.860726i	$-0.329990\pi$
$821$	29.1728	1.01814	0.509069	+	0.860726i	$0.329990\pi$
$822$	−14.4647	−0.504515
$823$	14.3636	0.500682	0.250341	−	0.968158i	$-0.419457\pi$
$823$	14.3636	0.500682	0.250341	+	0.968158i	$0.419457\pi$
$824$	6.32600	0.220377
$825$	45.8345	1.59575
$826$	0	0
$827$	36.4855	1.26873	0.634363	−	0.773035i	$-0.281262\pi$
$827$	36.4855	1.26873	0.634363	+	0.773035i	$0.281262\pi$
$828$	−3.95037	−0.137285
$829$	50.3312	1.74807	0.874037	−	0.485859i	$-0.161493\pi$
$829$	50.3312	1.74807	0.874037	+	0.485859i	$0.161493\pi$
$830$	−74.7977	−2.59627
$831$	15.6204	0.541866
$832$	−1.00000	−0.0346688
$833$	0	0
$834$	9.39338	0.325266
$835$	−41.2928	−1.42900
$836$	8.82690	0.305285
$837$	0.227026	0.00784715
$838$	32.4084	1.11953
$839$	11.3613	0.392235	0.196118	−	0.980580i	$-0.437167\pi$
$839$	11.3613	0.392235	0.196118	+	0.980580i	$0.437167\pi$
$840$	0	0
$841$	−5.57096	−0.192102
$842$	−29.5732	−1.01916
$843$	10.9926	0.378607
$844$	25.2420	0.868865
$845$	4.16053	0.143127
$846$	2.17246	0.0746907
$847$	0	0
$848$	−4.17246	−0.143283
$849$	1.20280	0.0412801
$850$	−31.9779	−1.09683
$851$	−4.12231	−0.141311
$852$	−7.88388	−0.270097
$853$	−23.5576	−0.806597	−0.403298	−	0.915068i	$-0.632136\pi$
$853$	−23.5576	−0.806597	−0.403298	+	0.915068i	$0.632136\pi$
$854$	0	0
$855$	9.86332	0.337319
$856$	−18.7617	−0.641260
$857$	−30.5642	−1.04405	−0.522027	−	0.852929i	$-0.674824\pi$
$857$	−30.5642	−1.04405	−0.522027	+	0.852929i	$0.674824\pi$
$858$	3.72335	0.127113
$859$	2.02946	0.0692442	0.0346221	−	0.999400i	$-0.488977\pi$
$859$	2.02946	0.0692442	0.0346221	+	0.999400i	$0.488977\pi$
$860$	33.0778	1.12794
$861$	0	0
$862$	−19.9147	−0.678298
$863$	24.8805	0.846941	0.423470	−	0.905910i	$-0.360812\pi$
$863$	24.8805	0.846941	0.423470	+	0.905910i	$0.360812\pi$
$864$	−1.00000	−0.0340207
$865$	−58.9090	−2.00297
$866$	4.56154	0.155008
$867$	−10.2519	−0.348172
$868$	0	0
$869$	−45.9384	−1.55835
$870$	20.1384	0.682757
$871$	6.56370	0.222403
$872$	14.1709	0.479888
$873$	11.6807	0.395332
$874$	9.36511	0.316779
$875$	0	0
$876$	−13.2641	−0.448152
$877$	39.2704	1.32607	0.663034	−	0.748590i	$-0.269269\pi$
$877$	39.2704	1.32607	0.663034	+	0.748590i	$0.269269\pi$
$878$	−2.09376	−0.0706611
$879$	6.25610	0.211013
$880$	15.4911	0.522205
$881$	−24.5107	−0.825785	−0.412893	−	0.910780i	$-0.635482\pi$
$881$	−24.5107	−0.825785	−0.412893	+	0.910780i	$0.635482\pi$
$882$	0	0
$883$	−21.2935	−0.716585	−0.358292	−	0.933609i	$-0.616641\pi$
$883$	−21.2935	−0.716585	−0.358292	+	0.933609i	$0.616641\pi$
$884$	−2.59771	−0.0873706
$885$	−31.3735	−1.05461
$886$	15.2686	0.512960
$887$	51.4264	1.72673	0.863365	−	0.504581i	$-0.168353\pi$
$887$	51.4264	1.72673	0.863365	+	0.504581i	$0.168353\pi$
$888$	−1.04352	−0.0350184
$889$	0	0
$890$	−19.9537	−0.668849
$891$	3.72335	0.124737
$892$	−26.4969	−0.887183
$893$	−5.15022	−0.172346
$894$	13.1495	0.439785
$895$	−45.1872	−1.51044
$896$	0	0
$897$	3.95037	0.131899
$898$	−26.3992	−0.880953
$899$	−1.09888	−0.0366499
$900$	12.3100	0.410334
$901$	−10.8389	−0.361095
$902$	−8.78249	−0.292425
$903$	0	0
$904$	−5.50950	−0.183243
$905$	−70.1145	−2.33068
$906$	17.4041	0.578211
$907$	−42.5421	−1.41259	−0.706294	−	0.707918i	$-0.749634\pi$
$907$	−42.5421	−1.41259	−0.706294	+	0.707918i	$0.749634\pi$
$908$	−6.78210	−0.225072
$909$	14.9562	0.496066
$910$	0	0
$911$	22.4712	0.744503	0.372251	−	0.928132i	$-0.378586\pi$
$911$	22.4712	0.744503	0.372251	+	0.928132i	$0.378586\pi$
$912$	2.37069	0.0785013
$913$	66.9381	2.21533
$914$	−6.42553	−0.212538
$915$	51.8091	1.71276
$916$	9.90774	0.327361
$917$	0	0
$918$	−2.59771	−0.0857373
$919$	−31.8137	−1.04944	−0.524719	−	0.851276i	$-0.675829\pi$
$919$	−31.8137	−1.04944	−0.524719	+	0.851276i	$0.675829\pi$
$920$	16.4357	0.541868
$921$	23.2145	0.764942
$922$	25.7009	0.846413
$923$	7.88388	0.259501
$924$	0	0
$925$	12.8458	0.422368
$926$	−6.83910	−0.224747
$927$	−6.32600	−0.207773
$928$	4.84035	0.158892
$929$	−46.4610	−1.52434	−0.762168	−	0.647379i	$-0.775865\pi$
$929$	−46.4610	−1.52434	−0.762168	+	0.647379i	$0.775865\pi$
$930$	−0.944547	−0.0309729
$931$	0	0
$932$	−2.38603	−0.0781570
$933$	3.79162	0.124132
$934$	−12.7472	−0.417102
$935$	40.2415	1.31604
$936$	1.00000	0.0326860
$937$	−54.1421	−1.76875	−0.884373	−	0.466781i	$-0.845414\pi$
$937$	−54.1421	−1.76875	−0.884373	+	0.466781i	$0.845414\pi$
$938$	0	0
$939$	−1.62260	−0.0529515
$940$	−9.03858	−0.294806
$941$	−33.0607	−1.07775	−0.538873	−	0.842387i	$-0.681150\pi$
$941$	−33.0607	−1.07775	−0.538873	+	0.842387i	$0.681150\pi$
$942$	23.7013	0.772229
$943$	−9.31799	−0.303435
$944$	−7.54073	−0.245430
$945$	0	0
$946$	−29.6020	−0.962444
$947$	−2.10510	−0.0684065	−0.0342033	−	0.999415i	$-0.510889\pi$
$947$	−2.10510	−0.0684065	−0.0342033	+	0.999415i	$0.510889\pi$
$948$	−12.3379	−0.400717
$949$	13.2641	0.430570
$950$	−29.1832	−0.946829
$951$	−18.5719	−0.602237
$952$	0	0
$953$	−21.1158	−0.684006	−0.342003	−	0.939699i	$-0.611105\pi$
$953$	−21.1158	−0.684006	−0.342003	+	0.939699i	$0.611105\pi$
$954$	4.17246	0.135088
$955$	49.6788	1.60757
$956$	2.68108	0.0867122
$957$	−18.0223	−0.582579
$958$	6.61800	0.213818
$959$	0	0
$960$	4.16053	0.134281
$961$	−30.9485	−0.998337
$962$	1.04352	0.0336446
$963$	18.7617	0.604586
$964$	−17.8327	−0.574353
$965$	91.3696	2.94129
$966$	0	0
$967$	−20.3967	−0.655914	−0.327957	−	0.944693i	$-0.606360\pi$
$967$	−20.3967	−0.655914	−0.327957	+	0.944693i	$0.606360\pi$
$968$	−2.86332	−0.0920307
$969$	6.15837	0.197835
$970$	−48.5980	−1.56039
$971$	−12.6373	−0.405550	−0.202775	−	0.979225i	$-0.564996\pi$
$971$	−12.6373	−0.405550	−0.202775	+	0.979225i	$0.564996\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	32.2292	1.03269
$975$	−12.3100	−0.394236
$976$	12.4525	0.398596
$977$	−42.9921	−1.37544	−0.687720	−	0.725976i	$-0.741388\pi$
$977$	−42.9921	−1.37544	−0.687720	+	0.725976i	$0.741388\pi$
$978$	−3.06408	−0.0979785
$979$	17.8570	0.570711
$980$	0	0
$981$	−14.1709	−0.452443
$982$	−17.5511	−0.560079
$983$	25.8231	0.823630	0.411815	−	0.911268i	$-0.364895\pi$
$983$	25.8231	0.823630	0.411815	+	0.911268i	$0.364895\pi$
$984$	−2.35876	−0.0751945
$985$	−3.42500	−0.109130
$986$	12.5739	0.400433
$987$	0	0
$988$	−2.37069	−0.0754217
$989$	−31.4070	−0.998683
$990$	−15.4911	−0.492340
$991$	−40.0018	−1.27070	−0.635349	−	0.772225i	$-0.719144\pi$
$991$	−40.0018	−1.27070	−0.635349	+	0.772225i	$0.719144\pi$
$992$	−0.227026	−0.00720807
$993$	−31.3289	−0.994194
$994$	0	0
$995$	−58.2269	−1.84592
$996$	17.9779	0.569652
$997$	10.6586	0.337561	0.168781	−	0.985654i	$-0.446017\pi$
$997$	10.6586	0.337561	0.168781	+	0.985654i	$0.446017\pi$
$998$	14.7304	0.466284
$999$	1.04352	0.0330157

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.by.1.4	yes	4
7.6	odd	2		3822.2.a.bx.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.bx.1.1	✓	4	7.6	odd	2
3822.2.a.by.1.4	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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.16053 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.16053 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -4.16053 q^{10} +3.72335 q^{11} +1.00000 q^{12} -1.00000 q^{13} +4.16053 q^{15} +1.00000 q^{16} +2.59771 q^{17} -1.00000 q^{18} +2.37069 q^{19} +4.16053 q^{20} -3.72335 q^{22} -3.95037 q^{23} -1.00000 q^{24} +12.3100 q^{25} +1.00000 q^{26} +1.00000 q^{27} -4.84035 q^{29} -4.16053 q^{30} +0.227026 q^{31} -1.00000 q^{32} +3.72335 q^{33} -2.59771 q^{34} +1.00000 q^{36} +1.04352 q^{37} -2.37069 q^{38} -1.00000 q^{39} -4.16053 q^{40} +2.35876 q^{41} +7.95037 q^{43} +3.72335 q^{44} +4.16053 q^{45} +3.95037 q^{46} -2.17246 q^{47} +1.00000 q^{48} -12.3100 q^{50} +2.59771 q^{51} -1.00000 q^{52} -4.17246 q^{53} -1.00000 q^{54} +15.4911 q^{55} +2.37069 q^{57} +4.84035 q^{58} -7.54073 q^{59} +4.16053 q^{60} +12.4525 q^{61} -0.227026 q^{62} +1.00000 q^{64} -4.16053 q^{65} -3.72335 q^{66} -6.56370 q^{67} +2.59771 q^{68} -3.95037 q^{69} -7.88388 q^{71} -1.00000 q^{72} -13.2641 q^{73} -1.04352 q^{74} +12.3100 q^{75} +2.37069 q^{76} +1.00000 q^{78} -12.3379 q^{79} +4.16053 q^{80} +1.00000 q^{81} -2.35876 q^{82} +17.9779 q^{83} +10.8079 q^{85} -7.95037 q^{86} -4.84035 q^{87} -3.72335 q^{88} +4.79594 q^{89} -4.16053 q^{90} -3.95037 q^{92} +0.227026 q^{93} +2.17246 q^{94} +9.86332 q^{95} -1.00000 q^{96} +11.6807 q^{97} +3.72335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} - 4 q^{8} + 4 q^{9} - 6 q^{10} + 2 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} + 2 q^{19} + 6 q^{20} - 2 q^{22} - 2 q^{23} - 4 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{27} + 6 q^{29} - 6 q^{30} - 4 q^{32} + 2 q^{33} - 2 q^{34} + 4 q^{36} + 6 q^{37} - 2 q^{38} - 4 q^{39} - 6 q^{40} + 16 q^{41} + 18 q^{43} + 2 q^{44} + 6 q^{45} + 2 q^{46} + 16 q^{47} + 4 q^{48} - 6 q^{50} + 2 q^{51} - 4 q^{52} + 8 q^{53} - 4 q^{54} + 2 q^{55} + 2 q^{57} - 6 q^{58} + 16 q^{59} + 6 q^{60} - 2 q^{61} + 4 q^{64} - 6 q^{65} - 2 q^{66} + 12 q^{67} + 2 q^{68} - 2 q^{69} - 8 q^{71} - 4 q^{72} + 6 q^{73} - 6 q^{74} + 6 q^{75} + 2 q^{76} + 4 q^{78} - 24 q^{79} + 6 q^{80} + 4 q^{81} - 16 q^{82} + 28 q^{83} + 38 q^{85} - 18 q^{86} + 6 q^{87} - 2 q^{88} + 28 q^{89} - 6 q^{90} - 2 q^{92} - 16 q^{94} + 22 q^{95} - 4 q^{96} - 4 q^{97} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 - 4 * q^8 + 4 * q^9 - 6 * q^10 + 2 * q^11 + 4 * q^12 - 4 * q^13 + 6 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 + 2 * q^19 + 6 * q^20 - 2 * q^22 - 2 * q^23 - 4 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^27 + 6 * q^29 - 6 * q^30 - 4 * q^32 + 2 * q^33 - 2 * q^34 + 4 * q^36 + 6 * q^37 - 2 * q^38 - 4 * q^39 - 6 * q^40 + 16 * q^41 + 18 * q^43 + 2 * q^44 + 6 * q^45 + 2 * q^46 + 16 * q^47 + 4 * q^48 - 6 * q^50 + 2 * q^51 - 4 * q^52 + 8 * q^53 - 4 * q^54 + 2 * q^55 + 2 * q^57 - 6 * q^58 + 16 * q^59 + 6 * q^60 - 2 * q^61 + 4 * q^64 - 6 * q^65 - 2 * q^66 + 12 * q^67 + 2 * q^68 - 2 * q^69 - 8 * q^71 - 4 * q^72 + 6 * q^73 - 6 * q^74 + 6 * q^75 + 2 * q^76 + 4 * q^78 - 24 * q^79 + 6 * q^80 + 4 * q^81 - 16 * q^82 + 28 * q^83 + 38 * q^85 - 18 * q^86 + 6 * q^87 - 2 * q^88 + 28 * q^89 - 6 * q^90 - 2 * q^92 - 16 * q^94 + 22 * q^95 - 4 * q^96 - 4 * q^97 + 2 * q^99

Introduction

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