LMFDB - Embedded newform 2842.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.1019601.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 10x^{3} - x^{2} + 24x + 7 $ x^5 - 10x^3 - x^2 + 24x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.48141$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.714579 q^{3} +1.00000 q^{4} -0.233169 q^{5} +0.714579 q^{6} +1.00000 q^{8} -2.48938 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.714579 q^{3} +1.00000 q^{4} -0.233169 q^{5} +0.714579 q^{6} +1.00000 q^{8} -2.48938 q^{9} -0.233169 q^{10} +0.293388 q^{11} +0.714579 q^{12} -4.15740 q^{13} -0.166617 q^{15} +1.00000 q^{16} -0.609435 q^{17} -2.48938 q^{18} -6.67740 q^{19} -0.233169 q^{20} +0.293388 q^{22} -1.48774 q^{23} +0.714579 q^{24} -4.94563 q^{25} -4.15740 q^{26} -3.92259 q^{27} -1.00000 q^{29} -0.166617 q^{30} +1.35175 q^{31} +1.00000 q^{32} +0.209649 q^{33} -0.609435 q^{34} -2.48938 q^{36} +0.637171 q^{37} -6.67740 q^{38} -2.97079 q^{39} -0.233169 q^{40} -3.31605 q^{41} -3.29502 q^{43} +0.293388 q^{44} +0.580445 q^{45} -1.48774 q^{46} -2.18092 q^{47} +0.714579 q^{48} -4.94563 q^{50} -0.435489 q^{51} -4.15740 q^{52} +11.9922 q^{53} -3.92259 q^{54} -0.0684089 q^{55} -4.77153 q^{57} -1.00000 q^{58} -4.30113 q^{59} -0.166617 q^{60} -3.64803 q^{61} +1.35175 q^{62} +1.00000 q^{64} +0.969374 q^{65} +0.209649 q^{66} +4.95649 q^{67} -0.609435 q^{68} -1.06311 q^{69} +4.21106 q^{71} -2.48938 q^{72} -5.84298 q^{73} +0.637171 q^{74} -3.53404 q^{75} -6.67740 q^{76} -2.97079 q^{78} +2.10678 q^{79} -0.233169 q^{80} +4.66513 q^{81} -3.31605 q^{82} -6.73621 q^{83} +0.142101 q^{85} -3.29502 q^{86} -0.714579 q^{87} +0.293388 q^{88} +12.6247 q^{89} +0.580445 q^{90} -1.48774 q^{92} +0.965932 q^{93} -2.18092 q^{94} +1.55696 q^{95} +0.714579 q^{96} -5.70498 q^{97} -0.730354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 7 q^{5} - 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 7 * q^5 - 3 * q^6 + 5 * q^8 + 8 * q^9	$ 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 7 q^{5} - 3 q^{6} + 5 q^{8} + 8 q^{9} - 7 q^{10} - 3 q^{12} - 10 q^{13} - 10 q^{15} + 5 q^{16} - 8 q^{17} + 8 q^{18} - 2 q^{19} - 7 q^{20} + q^{23} - 3 q^{24} + 12 q^{25} - 10 q^{26} - 15 q^{27} - 5 q^{29} - 10 q^{30} - 11 q^{31} + 5 q^{32} - 9 q^{33} - 8 q^{34} + 8 q^{36} - 8 q^{37} - 2 q^{38} + 18 q^{39} - 7 q^{40} - 23 q^{41} - 3 q^{43} - 4 q^{45} + q^{46} - 16 q^{47} - 3 q^{48} + 12 q^{50} + 7 q^{51} - 10 q^{52} + 7 q^{53} - 15 q^{54} - 6 q^{55} - 34 q^{57} - 5 q^{58} + 9 q^{59} - 10 q^{60} - 15 q^{61} - 11 q^{62} + 5 q^{64} + 5 q^{65} - 9 q^{66} - 4 q^{67} - 8 q^{68} - 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} + 34 q^{75} - 2 q^{76} + 18 q^{78} - 13 q^{79} - 7 q^{80} + 17 q^{81} - 23 q^{82} - 28 q^{83} - 7 q^{85} - 3 q^{86} + 3 q^{87} - 17 q^{89} - 4 q^{90} + q^{92} + 17 q^{93} - 16 q^{94} - 9 q^{95} - 3 q^{96} - 42 q^{97} - 42 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 7 * q^5 - 3 * q^6 + 5 * q^8 + 8 * q^9 - 7 * q^10 - 3 * q^12 - 10 * q^13 - 10 * q^15 + 5 * q^16 - 8 * q^17 + 8 * q^18 - 2 * q^19 - 7 * q^20 + q^23 - 3 * q^24 + 12 * q^25 - 10 * q^26 - 15 * q^27 - 5 * q^29 - 10 * q^30 - 11 * q^31 + 5 * q^32 - 9 * q^33 - 8 * q^34 + 8 * q^36 - 8 * q^37 - 2 * q^38 + 18 * q^39 - 7 * q^40 - 23 * q^41 - 3 * q^43 - 4 * q^45 + q^46 - 16 * q^47 - 3 * q^48 + 12 * q^50 + 7 * q^51 - 10 * q^52 + 7 * q^53 - 15 * q^54 - 6 * q^55 - 34 * q^57 - 5 * q^58 + 9 * q^59 - 10 * q^60 - 15 * q^61 - 11 * q^62 + 5 * q^64 + 5 * q^65 - 9 * q^66 - 4 * q^67 - 8 * q^68 - 14 * q^69 - 22 * q^71 + 8 * q^72 - 8 * q^74 + 34 * q^75 - 2 * q^76 + 18 * q^78 - 13 * q^79 - 7 * q^80 + 17 * q^81 - 23 * q^82 - 28 * q^83 - 7 * q^85 - 3 * q^86 + 3 * q^87 - 17 * q^89 - 4 * q^90 + q^92 + 17 * q^93 - 16 * q^94 - 9 * q^95 - 3 * q^96 - 42 * q^97 - 42 * 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
$3$	0.714579	0.412562	0.206281	−	0.978493i	$-0.433864\pi$
$3$	0.714579	0.412562	0.206281	+	0.978493i	$0.433864\pi$
$4$	1.00000	0.500000
$5$	−0.233169	−0.104276	−0.0521381	−	0.998640i	$-0.516604\pi$
$5$	−0.233169	−0.104276	−0.0521381	+	0.998640i	$0.516604\pi$
$6$	0.714579	0.291726
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.48938	−0.829792
$10$	−0.233169	−0.0737344
$11$	0.293388	0.0884599	0.0442299	−	0.999021i	$-0.485917\pi$
$11$	0.293388	0.0884599	0.0442299	+	0.999021i	$0.485917\pi$
$12$	0.714579	0.206281
$13$	−4.15740	−1.15305	−0.576527	−	0.817078i	$-0.695592\pi$
$13$	−4.15740	−1.15305	−0.576527	+	0.817078i	$0.695592\pi$
$14$	0	0
$15$	−0.166617	−0.0430204
$16$	1.00000	0.250000
$17$	−0.609435	−0.147810	−0.0739048	−	0.997265i	$-0.523546\pi$
$17$	−0.609435	−0.147810	−0.0739048	+	0.997265i	$0.523546\pi$
$18$	−2.48938	−0.586752
$19$	−6.67740	−1.53190	−0.765950	−	0.642900i	$-0.777731\pi$
$19$	−6.67740	−1.53190	−0.765950	+	0.642900i	$0.777731\pi$
$20$	−0.233169	−0.0521381
$21$	0	0
$22$	0.293388	0.0625506
$23$	−1.48774	−0.310216	−0.155108	−	0.987898i	$-0.549572\pi$
$23$	−1.48774	−0.310216	−0.155108	+	0.987898i	$0.549572\pi$
$24$	0.714579	0.145863
$25$	−4.94563	−0.989126
$26$	−4.15740	−0.815333
$27$	−3.92259	−0.754903
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.166617	−0.0304200
$31$	1.35175	0.242781	0.121391	−	0.992605i	$-0.461265\pi$
$31$	1.35175	0.242781	0.121391	+	0.992605i	$0.461265\pi$
$32$	1.00000	0.176777
$33$	0.209649	0.0364952
$34$	−0.609435	−0.104517
$35$	0	0
$36$	−2.48938	−0.414896
$37$	0.637171	0.104750	0.0523752	−	0.998627i	$-0.483321\pi$
$37$	0.637171	0.104750	0.0523752	+	0.998627i	$0.483321\pi$
$38$	−6.67740	−1.08322
$39$	−2.97079	−0.475707
$40$	−0.233169	−0.0368672
$41$	−3.31605	−0.517880	−0.258940	−	0.965893i	$-0.583373\pi$
$41$	−3.31605	−0.517880	−0.258940	+	0.965893i	$0.583373\pi$
$42$	0	0
$43$	−3.29502	−0.502486	−0.251243	−	0.967924i	$-0.580839\pi$
$43$	−3.29502	−0.502486	−0.251243	+	0.967924i	$0.580839\pi$
$44$	0.293388	0.0442299
$45$	0.580445	0.0865276
$46$	−1.48774	−0.219356
$47$	−2.18092	−0.318119	−0.159060	−	0.987269i	$-0.550846\pi$
$47$	−2.18092	−0.318119	−0.159060	+	0.987269i	$0.550846\pi$
$48$	0.714579	0.103141
$49$	0	0
$50$	−4.94563	−0.699418
$51$	−0.435489	−0.0609807
$52$	−4.15740	−0.576527
$53$	11.9922	1.64725	0.823627	−	0.567132i	$-0.191947\pi$
$53$	11.9922	1.64725	0.823627	+	0.567132i	$0.191947\pi$
$54$	−3.92259	−0.533797
$55$	−0.0684089	−0.00922426
$56$	0	0
$57$	−4.77153	−0.632004
$58$	−1.00000	−0.131306
$59$	−4.30113	−0.559960	−0.279980	−	0.960006i	$-0.590328\pi$
$59$	−4.30113	−0.559960	−0.279980	+	0.960006i	$0.590328\pi$
$60$	−0.166617	−0.0215102
$61$	−3.64803	−0.467082	−0.233541	−	0.972347i	$-0.575031\pi$
$61$	−3.64803	−0.467082	−0.233541	+	0.972347i	$0.575031\pi$
$62$	1.35175	0.171672
$63$	0	0
$64$	1.00000	0.125000
$65$	0.969374	0.120236
$66$	0.209649	0.0258060
$67$	4.95649	0.605531	0.302766	−	0.953065i	$-0.402090\pi$
$67$	4.95649	0.605531	0.302766	+	0.953065i	$0.402090\pi$
$68$	−0.609435	−0.0739048
$69$	−1.06311	−0.127983
$70$	0	0
$71$	4.21106	0.499761	0.249881	−	0.968277i	$-0.419609\pi$
$71$	4.21106	0.499761	0.249881	+	0.968277i	$0.419609\pi$
$72$	−2.48938	−0.293376
$73$	−5.84298	−0.683870	−0.341935	−	0.939724i	$-0.611082\pi$
$73$	−5.84298	−0.683870	−0.341935	+	0.939724i	$0.611082\pi$
$74$	0.637171	0.0740697
$75$	−3.53404	−0.408076
$76$	−6.67740	−0.765950
$77$	0	0
$78$	−2.97079	−0.336375
$79$	2.10678	0.237031	0.118516	−	0.992952i	$-0.462186\pi$
$79$	2.10678	0.237031	0.118516	+	0.992952i	$0.462186\pi$
$80$	−0.233169	−0.0260690
$81$	4.66513	0.518348
$82$	−3.31605	−0.366196
$83$	−6.73621	−0.739395	−0.369697	−	0.929152i	$-0.620539\pi$
$83$	−6.73621	−0.739395	−0.369697	+	0.929152i	$0.620539\pi$
$84$	0	0
$85$	0.142101	0.0154130
$86$	−3.29502	−0.355312
$87$	−0.714579	−0.0766109
$88$	0.293388	0.0312753
$89$	12.6247	1.33821	0.669106	−	0.743167i	$-0.266677\pi$
$89$	12.6247	1.33821	0.669106	+	0.743167i	$0.266677\pi$
$90$	0.580445	0.0611842
$91$	0	0
$92$	−1.48774	−0.155108
$93$	0.965932	0.100162
$94$	−2.18092	−0.224944
$95$	1.55696	0.159741
$96$	0.714579	0.0729314
$97$	−5.70498	−0.579253	−0.289626	−	0.957140i	$-0.593531\pi$
$97$	−5.70498	−0.579253	−0.289626	+	0.957140i	$0.593531\pi$
$98$	0	0
$99$	−0.730354	−0.0734033
$100$	−4.94563	−0.494563
$101$	−15.7339	−1.56558	−0.782789	−	0.622287i	$-0.786204\pi$
$101$	−15.7339	−1.56558	−0.782789	+	0.622287i	$0.786204\pi$
$102$	−0.435489	−0.0431199
$103$	4.89549	0.482367	0.241184	−	0.970479i	$-0.422464\pi$
$103$	4.89549	0.482367	0.241184	+	0.970479i	$0.422464\pi$
$104$	−4.15740	−0.407666
$105$	0	0
$106$	11.9922	1.16478
$107$	11.2315	1.08579	0.542894	−	0.839801i	$-0.317329\pi$
$107$	11.2315	1.08579	0.542894	+	0.839801i	$0.317329\pi$
$108$	−3.92259	−0.377452
$109$	15.1865	1.45461	0.727304	−	0.686316i	$-0.240773\pi$
$109$	15.1865	1.45461	0.727304	+	0.686316i	$0.240773\pi$
$110$	−0.0684089	−0.00652253
$111$	0.455309	0.0432160
$112$	0	0
$113$	−10.2976	−0.968717	−0.484359	−	0.874870i	$-0.660947\pi$
$113$	−10.2976	−0.968717	−0.484359	+	0.874870i	$0.660947\pi$
$114$	−4.77153	−0.446895
$115$	0.346895	0.0323481
$116$	−1.00000	−0.0928477
$117$	10.3493	0.956796
$118$	−4.30113	−0.395951
$119$	0	0
$120$	−0.166617	−0.0152100
$121$	−10.9139	−0.992175
$122$	−3.64803	−0.330277
$123$	−2.36958	−0.213658
$124$	1.35175	0.121391
$125$	2.31901	0.207419
$126$	0	0
$127$	−15.3053	−1.35813	−0.679065	−	0.734078i	$-0.737615\pi$
$127$	−15.3053	−1.35813	−0.679065	+	0.734078i	$0.737615\pi$
$128$	1.00000	0.0883883
$129$	−2.35455	−0.207307
$130$	0.969374	0.0850198
$131$	−12.2176	−1.06745	−0.533726	−	0.845657i	$-0.679209\pi$
$131$	−12.2176	−1.06745	−0.533726	+	0.845657i	$0.679209\pi$
$132$	0.209649	0.0182476
$133$	0	0
$134$	4.95649	0.428175
$135$	0.914626	0.0787184
$136$	−0.609435	−0.0522586
$137$	17.8291	1.52324	0.761622	−	0.648022i	$-0.224404\pi$
$137$	17.8291	1.52324	0.761622	+	0.648022i	$0.224404\pi$
$138$	−1.06311	−0.0904978
$139$	−7.99852	−0.678426	−0.339213	−	0.940710i	$-0.610161\pi$
$139$	−7.99852	−0.678426	−0.339213	+	0.940710i	$0.610161\pi$
$140$	0	0
$141$	−1.55844	−0.131244
$142$	4.21106	0.353384
$143$	−1.21973	−0.101999
$144$	−2.48938	−0.207448
$145$	0.233169	0.0193636
$146$	−5.84298	−0.483569
$147$	0	0
$148$	0.637171	0.0523752
$149$	7.81597	0.640309	0.320155	−	0.947365i	$-0.396265\pi$
$149$	7.81597	0.640309	0.320155	+	0.947365i	$0.396265\pi$
$150$	−3.53404	−0.288553
$151$	−16.2176	−1.31977	−0.659883	−	0.751368i	$-0.729394\pi$
$151$	−16.2176	−1.31977	−0.659883	+	0.751368i	$0.729394\pi$
$152$	−6.67740	−0.541609
$153$	1.51711	0.122651
$154$	0	0
$155$	−0.315186	−0.0253163
$156$	−2.97079	−0.237853
$157$	23.6455	1.88711	0.943556	−	0.331212i	$-0.107457\pi$
$157$	23.6455	1.88711	0.943556	+	0.331212i	$0.107457\pi$
$158$	2.10678	0.167606
$159$	8.56937	0.679595
$160$	−0.233169	−0.0184336
$161$	0	0
$162$	4.66513	0.366527
$163$	−13.6125	−1.06621	−0.533106	−	0.846048i	$-0.678975\pi$
$163$	−13.6125	−1.06621	−0.533106	+	0.846048i	$0.678975\pi$
$164$	−3.31605	−0.258940
$165$	−0.0488836	−0.00380558
$166$	−6.73621	−0.522831
$167$	3.59710	0.278352	0.139176	−	0.990268i	$-0.455555\pi$
$167$	3.59710	0.278352	0.139176	+	0.990268i	$0.455555\pi$
$168$	0	0
$169$	4.28394	0.329534
$170$	0.142101	0.0108987
$171$	16.6226	1.27116
$172$	−3.29502	−0.251243
$173$	−12.3956	−0.942423	−0.471212	−	0.882020i	$-0.656183\pi$
$173$	−12.3956	−0.942423	−0.471212	+	0.882020i	$0.656183\pi$
$174$	−0.714579	−0.0541721
$175$	0	0
$176$	0.293388	0.0221150
$177$	−3.07350	−0.231018
$178$	12.6247	0.946259
$179$	9.58344	0.716300	0.358150	−	0.933664i	$-0.383408\pi$
$179$	9.58344	0.716300	0.358150	+	0.933664i	$0.383408\pi$
$180$	0.580445	0.0432638
$181$	−0.148655	−0.0110495	−0.00552473	−	0.999985i	$-0.501759\pi$
$181$	−0.148655	−0.0110495	−0.00552473	+	0.999985i	$0.501759\pi$
$182$	0	0
$183$	−2.60680	−0.192700
$184$	−1.48774	−0.109678
$185$	−0.148568	−0.0109230
$186$	0.965932	0.0708256
$187$	−0.178801	−0.0130752
$188$	−2.18092	−0.159060
$189$	0	0
$190$	1.55696	0.112954
$191$	10.2831	0.744058	0.372029	−	0.928221i	$-0.378662\pi$
$191$	10.2831	0.744058	0.372029	+	0.928221i	$0.378662\pi$
$192$	0.714579	0.0515703
$193$	12.4681	0.897476	0.448738	−	0.893663i	$-0.351874\pi$
$193$	12.4681	0.897476	0.448738	+	0.893663i	$0.351874\pi$
$194$	−5.70498	−0.409593
$195$	0.692694	0.0496049
$196$	0	0
$197$	−19.0312	−1.35591	−0.677957	−	0.735101i	$-0.737135\pi$
$197$	−19.0312	−1.35591	−0.677957	+	0.735101i	$0.737135\pi$
$198$	−0.730354	−0.0519040
$199$	10.6083	0.752005	0.376003	−	0.926619i	$-0.377298\pi$
$199$	10.6083	0.752005	0.376003	+	0.926619i	$0.377298\pi$
$200$	−4.94563	−0.349709
$201$	3.54180	0.249819
$202$	−15.7339	−1.10703
$203$	0	0
$204$	−0.435489	−0.0304903
$205$	0.773198	0.0540025
$206$	4.89549	0.341085
$207$	3.70355	0.257415
$208$	−4.15740	−0.288264
$209$	−1.95907	−0.135512
$210$	0	0
$211$	−8.69020	−0.598258	−0.299129	−	0.954213i	$-0.596696\pi$
$211$	−8.69020	−0.598258	−0.299129	+	0.954213i	$0.596696\pi$
$212$	11.9922	0.823627
$213$	3.00914	0.206183
$214$	11.2315	0.767767
$215$	0.768296	0.0523974
$216$	−3.92259	−0.266899
$217$	0	0
$218$	15.1865	1.02856
$219$	−4.17527	−0.282139
$220$	−0.0684089	−0.00461213
$221$	2.53366	0.170433
$222$	0.455309	0.0305583
$223$	−9.99383	−0.669236	−0.334618	−	0.942354i	$-0.608607\pi$
$223$	−9.99383	−0.669236	−0.334618	+	0.942354i	$0.608607\pi$
$224$	0	0
$225$	12.3115	0.820770
$226$	−10.2976	−0.684986
$227$	25.3090	1.67982	0.839910	−	0.542726i	$-0.182608\pi$
$227$	25.3090	1.67982	0.839910	+	0.542726i	$0.182608\pi$
$228$	−4.77153	−0.316002
$229$	−18.4785	−1.22109	−0.610545	−	0.791981i	$-0.709050\pi$
$229$	−18.4785	−1.22109	−0.610545	+	0.791981i	$0.709050\pi$
$230$	0.346895	0.0228736
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	−9.35908	−0.613134	−0.306567	−	0.951849i	$-0.599180\pi$
$233$	−9.35908	−0.613134	−0.306567	+	0.951849i	$0.599180\pi$
$234$	10.3493	0.676557
$235$	0.508521	0.0331723
$236$	−4.30113	−0.279980
$237$	1.50546	0.0977901
$238$	0	0
$239$	−17.5424	−1.13473	−0.567363	−	0.823468i	$-0.692036\pi$
$239$	−17.5424	−1.13473	−0.567363	+	0.823468i	$0.692036\pi$
$240$	−0.166617	−0.0107551
$241$	−3.04226	−0.195969	−0.0979845	−	0.995188i	$-0.531240\pi$
$241$	−3.04226	−0.195969	−0.0979845	+	0.995188i	$0.531240\pi$
$242$	−10.9139	−0.701574
$243$	15.1014	0.968754
$244$	−3.64803	−0.233541
$245$	0	0
$246$	−2.36958	−0.151079
$247$	27.7606	1.76636
$248$	1.35175	0.0858362
$249$	−4.81355	−0.305046
$250$	2.31901	0.146667
$251$	17.2275	1.08739	0.543694	−	0.839283i	$-0.317025\pi$
$251$	17.2275	1.08739	0.543694	+	0.839283i	$0.317025\pi$
$252$	0	0
$253$	−0.436486	−0.0274416
$254$	−15.3053	−0.960343
$255$	0.101542	0.00635883
$256$	1.00000	0.0625000
$257$	−20.6454	−1.28783	−0.643913	−	0.765098i	$-0.722690\pi$
$257$	−20.6454	−1.28783	−0.643913	+	0.765098i	$0.722690\pi$
$258$	−2.35455	−0.146588
$259$	0	0
$260$	0.969374	0.0601180
$261$	2.48938	0.154089
$262$	−12.2176	−0.754803
$263$	−16.5706	−1.02179	−0.510894	−	0.859644i	$-0.670686\pi$
$263$	−16.5706	−1.02179	−0.510894	+	0.859644i	$0.670686\pi$
$264$	0.209649	0.0129030
$265$	−2.79620	−0.171769
$266$	0	0
$267$	9.02132	0.552096
$268$	4.95649	0.302766
$269$	2.62826	0.160248	0.0801239	−	0.996785i	$-0.474468\pi$
$269$	2.62826	0.160248	0.0801239	+	0.996785i	$0.474468\pi$
$270$	0.914626	0.0556623
$271$	12.6224	0.766756	0.383378	−	0.923592i	$-0.374761\pi$
$271$	12.6224	0.766756	0.383378	+	0.923592i	$0.374761\pi$
$272$	−0.609435	−0.0369524
$273$	0	0
$274$	17.8291	1.07710
$275$	−1.45099	−0.0874980
$276$	−1.06311	−0.0639916
$277$	19.4595	1.16921	0.584605	−	0.811318i	$-0.301249\pi$
$277$	19.4595	1.16921	0.584605	+	0.811318i	$0.301249\pi$
$278$	−7.99852	−0.479720
$279$	−3.36502	−0.201458
$280$	0	0
$281$	15.9906	0.953917	0.476958	−	0.878926i	$-0.341739\pi$
$281$	15.9906	0.953917	0.476958	+	0.878926i	$0.341739\pi$
$282$	−1.55844	−0.0928035
$283$	−27.9827	−1.66340	−0.831699	−	0.555227i	$-0.812631\pi$
$283$	−27.9827	−1.66340	−0.831699	+	0.555227i	$0.812631\pi$
$284$	4.21106	0.249881
$285$	1.11257	0.0659030
$286$	−1.21973	−0.0721242
$287$	0	0
$288$	−2.48938	−0.146688
$289$	−16.6286	−0.978152
$290$	0.233169	0.0136921
$291$	−4.07666	−0.238978
$292$	−5.84298	−0.341935
$293$	−20.6845	−1.20840	−0.604202	−	0.796832i	$-0.706508\pi$
$293$	−20.6845	−1.20840	−0.604202	+	0.796832i	$0.706508\pi$
$294$	0	0
$295$	1.00289	0.0583905
$296$	0.637171	0.0370348
$297$	−1.15084	−0.0667786
$298$	7.81597	0.452767
$299$	6.18513	0.357695
$300$	−3.53404	−0.204038
$301$	0	0
$302$	−16.2176	−0.933215
$303$	−11.2431	−0.645899
$304$	−6.67740	−0.382975
$305$	0.850606	0.0487055
$306$	1.51711	0.0867276
$307$	28.6540	1.63537	0.817686	−	0.575664i	$-0.195256\pi$
$307$	28.6540	1.63537	0.817686	+	0.575664i	$0.195256\pi$
$308$	0	0
$309$	3.49822	0.199007
$310$	−0.315186	−0.0179013
$311$	−10.4647	−0.593399	−0.296699	−	0.954971i	$-0.595886\pi$
$311$	−10.4647	−0.593399	−0.296699	+	0.954971i	$0.595886\pi$
$312$	−2.97079	−0.168188
$313$	31.4172	1.77580	0.887901	−	0.460034i	$-0.152163\pi$
$313$	31.4172	1.77580	0.887901	+	0.460034i	$0.152163\pi$
$314$	23.6455	1.33439
$315$	0	0
$316$	2.10678	0.118516
$317$	12.7478	0.715986	0.357993	−	0.933724i	$-0.383461\pi$
$317$	12.7478	0.715986	0.357993	+	0.933724i	$0.383461\pi$
$318$	8.56937	0.480546
$319$	−0.293388	−0.0164266
$320$	−0.233169	−0.0130345
$321$	8.02577	0.447955
$322$	0	0
$323$	4.06944	0.226430
$324$	4.66513	0.259174
$325$	20.5610	1.14052
$326$	−13.6125	−0.753926
$327$	10.8520	0.600116
$328$	−3.31605	−0.183098
$329$	0	0
$330$	−0.0488836	−0.00269095
$331$	−10.2619	−0.564046	−0.282023	−	0.959408i	$-0.591006\pi$
$331$	−10.2619	−0.564046	−0.282023	+	0.959408i	$0.591006\pi$
$332$	−6.73621	−0.369697
$333$	−1.58616	−0.0869210
$334$	3.59710	0.196825
$335$	−1.15570	−0.0631425
$336$	0	0
$337$	−26.9868	−1.47007	−0.735033	−	0.678031i	$-0.762833\pi$
$337$	−26.9868	−1.47007	−0.735033	+	0.678031i	$0.762833\pi$
$338$	4.28394	0.233016
$339$	−7.35845	−0.399656
$340$	0.142101	0.00770652
$341$	0.396588	0.0214764
$342$	16.6226	0.898845
$343$	0	0
$344$	−3.29502	−0.177656
$345$	0.247884	0.0133456
$346$	−12.3956	−0.666394
$347$	0.0299869	0.00160978	0.000804890	−	1.00000i	$-0.499744\pi$
$347$	0.0299869	0.00160978	0.000804890		1.00000i	$0.499744\pi$
$348$	−0.714579	−0.0383054
$349$	−6.30027	−0.337246	−0.168623	−	0.985681i	$-0.553932\pi$
$349$	−6.30027	−0.337246	−0.168623	+	0.985681i	$0.553932\pi$
$350$	0	0
$351$	16.3078	0.870444
$352$	0.293388	0.0156376
$353$	−27.6344	−1.47083	−0.735415	−	0.677617i	$-0.763013\pi$
$353$	−27.6344	−1.47083	−0.735415	+	0.677617i	$0.763013\pi$
$354$	−3.07350	−0.163355
$355$	−0.981888	−0.0521132
$356$	12.6247	0.669106
$357$	0	0
$358$	9.58344	0.506501
$359$	−18.4797	−0.975322	−0.487661	−	0.873033i	$-0.662150\pi$
$359$	−18.4797	−0.975322	−0.487661	+	0.873033i	$0.662150\pi$
$360$	0.580445	0.0305921
$361$	25.5877	1.34672
$362$	−0.148655	−0.00781314
$363$	−7.79886	−0.409334
$364$	0	0
$365$	1.36240	0.0713113
$366$	−2.60680	−0.136260
$367$	17.7335	0.925683	0.462841	−	0.886441i	$-0.346830\pi$
$367$	17.7335	0.925683	0.462841	+	0.886441i	$0.346830\pi$
$368$	−1.48774	−0.0775539
$369$	8.25489	0.429732
$370$	−0.148568	−0.00772370
$371$	0	0
$372$	0.965932	0.0500812
$373$	14.2392	0.737279	0.368639	−	0.929573i	$-0.379824\pi$
$373$	14.2392	0.737279	0.368639	+	0.929573i	$0.379824\pi$
$374$	−0.178801	−0.00924558
$375$	1.65712	0.0855731
$376$	−2.18092	−0.112472
$377$	4.15740	0.214117
$378$	0	0
$379$	33.9879	1.74584	0.872920	−	0.487863i	$-0.162224\pi$
$379$	33.9879	1.74584	0.872920	+	0.487863i	$0.162224\pi$
$380$	1.55696	0.0798704
$381$	−10.9369	−0.560313
$382$	10.2831	0.526128
$383$	17.0812	0.872807	0.436404	−	0.899751i	$-0.356252\pi$
$383$	17.0812	0.872807	0.436404	+	0.899751i	$0.356252\pi$
$384$	0.714579	0.0364657
$385$	0	0
$386$	12.4681	0.634611
$387$	8.20256	0.416959
$388$	−5.70498	−0.289626
$389$	−11.3176	−0.573827	−0.286913	−	0.957957i	$-0.592629\pi$
$389$	−11.3176	−0.573827	−0.286913	+	0.957957i	$0.592629\pi$
$390$	0.692694	0.0350759
$391$	0.906682	0.0458529
$392$	0	0
$393$	−8.73040	−0.440391
$394$	−19.0312	−0.958776
$395$	−0.491235	−0.0247167
$396$	−0.730354	−0.0367017
$397$	−10.2515	−0.514506	−0.257253	−	0.966344i	$-0.582817\pi$
$397$	−10.2515	−0.514506	−0.257253	+	0.966344i	$0.582817\pi$
$398$	10.6083	0.531748
$399$	0	0
$400$	−4.94563	−0.247282
$401$	−17.6102	−0.879410	−0.439705	−	0.898142i	$-0.644917\pi$
$401$	−17.6102	−0.879410	−0.439705	+	0.898142i	$0.644917\pi$
$402$	3.54180	0.176649
$403$	−5.61976	−0.279940
$404$	−15.7339	−0.782789
$405$	−1.08776	−0.0540513
$406$	0	0
$407$	0.186939	0.00926620
$408$	−0.435489	−0.0215599
$409$	38.8959	1.92328	0.961639	−	0.274317i	$-0.0884519\pi$
$409$	38.8959	1.92328	0.961639	+	0.274317i	$0.0884519\pi$
$410$	0.773198	0.0381855
$411$	12.7403	0.628433
$412$	4.89549	0.241184
$413$	0	0
$414$	3.70355	0.182020
$415$	1.57067	0.0771013
$416$	−4.15740	−0.203833
$417$	−5.71558	−0.279893
$418$	−1.95907	−0.0958212
$419$	12.6437	0.617683	0.308842	−	0.951113i	$-0.400059\pi$
$419$	12.6437	0.617683	0.308842	+	0.951113i	$0.400059\pi$
$420$	0	0
$421$	−10.7981	−0.526267	−0.263133	−	0.964759i	$-0.584756\pi$
$421$	−10.7981	−0.526267	−0.263133	+	0.964759i	$0.584756\pi$
$422$	−8.69020	−0.423032
$423$	5.42912	0.263973
$424$	11.9922	0.582392
$425$	3.01404	0.146202
$426$	3.00914	0.145793
$427$	0	0
$428$	11.2315	0.542894
$429$	−0.871594	−0.0420810
$430$	0.768296	0.0370505
$431$	−36.1812	−1.74279	−0.871394	−	0.490583i	$-0.836784\pi$
$431$	−36.1812	−1.74279	−0.871394	+	0.490583i	$0.836784\pi$
$432$	−3.92259	−0.188726
$433$	−10.6350	−0.511084	−0.255542	−	0.966798i	$-0.582254\pi$
$433$	−10.6350	−0.511084	−0.255542	+	0.966798i	$0.582254\pi$
$434$	0	0
$435$	0.166617	0.00798869
$436$	15.1865	0.727304
$437$	9.93425	0.475219
$438$	−4.17527	−0.199502
$439$	2.97507	0.141992	0.0709961	−	0.997477i	$-0.477382\pi$
$439$	2.97507	0.141992	0.0709961	+	0.997477i	$0.477382\pi$
$440$	−0.0684089	−0.00326127
$441$	0	0
$442$	2.53366	0.120514
$443$	−27.9429	−1.32761	−0.663804	−	0.747907i	$-0.731059\pi$
$443$	−27.9429	−1.32761	−0.663804	+	0.747907i	$0.731059\pi$
$444$	0.455309	0.0216080
$445$	−2.94368	−0.139544
$446$	−9.99383	−0.473221
$447$	5.58513	0.264167
$448$	0	0
$449$	−0.604431	−0.0285248	−0.0142624	−	0.999898i	$-0.504540\pi$
$449$	−0.604431	−0.0285248	−0.0142624	+	0.999898i	$0.504540\pi$
$450$	12.3115	0.580372
$451$	−0.972889	−0.0458116
$452$	−10.2976	−0.484359
$453$	−11.5887	−0.544486
$454$	25.3090	1.18781
$455$	0	0
$456$	−4.77153	−0.223447
$457$	−7.10311	−0.332270	−0.166135	−	0.986103i	$-0.553129\pi$
$457$	−7.10311	−0.332270	−0.166135	+	0.986103i	$0.553129\pi$
$458$	−18.4785	−0.863442
$459$	2.39057	0.111582
$460$	0.346895	0.0161741
$461$	−3.81028	−0.177462	−0.0887312	−	0.996056i	$-0.528281\pi$
$461$	−3.81028	−0.177462	−0.0887312	+	0.996056i	$0.528281\pi$
$462$	0	0
$463$	−3.42327	−0.159093	−0.0795464	−	0.996831i	$-0.525347\pi$
$463$	−3.42327	−0.159093	−0.0795464	+	0.996831i	$0.525347\pi$
$464$	−1.00000	−0.0464238
$465$	−0.225225	−0.0104446
$466$	−9.35908	−0.433551
$467$	−22.8701	−1.05830	−0.529151	−	0.848528i	$-0.677490\pi$
$467$	−22.8701	−1.05830	−0.529151	+	0.848528i	$0.677490\pi$
$468$	10.3493	0.478398
$469$	0	0
$470$	0.508521	0.0234563
$471$	16.8965	0.778552
$472$	−4.30113	−0.197976
$473$	−0.966721	−0.0444499
$474$	1.50546	0.0691481
$475$	33.0240	1.51524
$476$	0	0
$477$	−29.8531	−1.36688
$478$	−17.5424	−0.802372
$479$	4.57219	0.208909	0.104454	−	0.994530i	$-0.466690\pi$
$479$	4.57219	0.208909	0.104454	+	0.994530i	$0.466690\pi$
$480$	−0.166617	−0.00760501
$481$	−2.64897	−0.120783
$482$	−3.04226	−0.138571
$483$	0	0
$484$	−10.9139	−0.496087
$485$	1.33022	0.0604022
$486$	15.1014	0.685013
$487$	21.6569	0.981367	0.490683	−	0.871338i	$-0.336747\pi$
$487$	21.6569	0.981367	0.490683	+	0.871338i	$0.336747\pi$
$488$	−3.64803	−0.165138
$489$	−9.72719	−0.439879
$490$	0	0
$491$	32.0537	1.44656	0.723281	−	0.690554i	$-0.242633\pi$
$491$	32.0537	1.44656	0.723281	+	0.690554i	$0.242633\pi$
$492$	−2.36958	−0.106829
$493$	0.609435	0.0274476
$494$	27.7606	1.24901
$495$	0.170296	0.00765422
$496$	1.35175	0.0606954
$497$	0	0
$498$	−4.81355	−0.215700
$499$	24.6113	1.10175	0.550877	−	0.834587i	$-0.314293\pi$
$499$	24.6113	1.10175	0.550877	+	0.834587i	$0.314293\pi$
$500$	2.31901	0.103709
$501$	2.57041	0.114838
$502$	17.2275	0.768900
$503$	35.0600	1.56325	0.781623	−	0.623751i	$-0.214392\pi$
$503$	35.0600	1.56325	0.781623	+	0.623751i	$0.214392\pi$
$504$	0	0
$505$	3.66864	0.163253
$506$	−0.436486	−0.0194042
$507$	3.06122	0.135953
$508$	−15.3053	−0.679065
$509$	31.7592	1.40770	0.703851	−	0.710348i	$-0.251462\pi$
$509$	31.7592	1.40770	0.703851	+	0.710348i	$0.251462\pi$
$510$	0.101542	0.00449638
$511$	0	0
$512$	1.00000	0.0441942
$513$	26.1927	1.15644
$514$	−20.6454	−0.910631
$515$	−1.14148	−0.0502994
$516$	−2.35455	−0.103653
$517$	−0.639855	−0.0281408
$518$	0	0
$519$	−8.85766	−0.388808
$520$	0.969374	0.0425099
$521$	14.1681	0.620716	0.310358	−	0.950620i	$-0.399551\pi$
$521$	14.1681	0.620716	0.310358	+	0.950620i	$0.399551\pi$
$522$	2.48938	0.108957
$523$	19.7029	0.861547	0.430774	−	0.902460i	$-0.358241\pi$
$523$	19.7029	0.861547	0.430774	+	0.902460i	$0.358241\pi$
$524$	−12.2176	−0.533726
$525$	0	0
$526$	−16.5706	−0.722513
$527$	−0.823804	−0.0358855
$528$	0.209649	0.00912380
$529$	−20.7866	−0.903766
$530$	−2.79620	−0.121459
$531$	10.7071	0.464650
$532$	0	0
$533$	13.7861	0.597143
$534$	9.02132	0.390391
$535$	−2.61883	−0.113222
$536$	4.95649	0.214088
$537$	6.84812	0.295518
$538$	2.62826	0.113312
$539$	0	0
$540$	0.914626	0.0393592
$541$	−13.2854	−0.571184	−0.285592	−	0.958351i	$-0.592190\pi$
$541$	−13.2854	−0.571184	−0.285592	+	0.958351i	$0.592190\pi$
$542$	12.6224	0.542178
$543$	−0.106226	−0.00455859
$544$	−0.609435	−0.0261293
$545$	−3.54103	−0.151681
$546$	0	0
$547$	−3.77149	−0.161257	−0.0806287	−	0.996744i	$-0.525693\pi$
$547$	−3.77149	−0.161257	−0.0806287	+	0.996744i	$0.525693\pi$
$548$	17.8291	0.761622
$549$	9.08132	0.387581
$550$	−1.45099	−0.0618704
$551$	6.67740	0.284467
$552$	−1.06311	−0.0452489
$553$	0	0
$554$	19.4595	0.826757
$555$	−0.106164	−0.00450640
$556$	−7.99852	−0.339213
$557$	−41.3443	−1.75181	−0.875907	−	0.482480i	$-0.839736\pi$
$557$	−41.3443	−1.75181	−0.875907	+	0.482480i	$0.839736\pi$
$558$	−3.36502	−0.142452
$559$	13.6987	0.579394
$560$	0	0
$561$	−0.127767	−0.00539434
$562$	15.9906	0.674521
$563$	6.62591	0.279249	0.139624	−	0.990205i	$-0.455410\pi$
$563$	6.62591	0.279249	0.139624	+	0.990205i	$0.455410\pi$
$564$	−1.55844	−0.0656220
$565$	2.40108	0.101014
$566$	−27.9827	−1.17620
$567$	0	0
$568$	4.21106	0.176692
$569$	−13.9549	−0.585022	−0.292511	−	0.956262i	$-0.594491\pi$
$569$	−13.9549	−0.585022	−0.292511	+	0.956262i	$0.594491\pi$
$570$	1.11257	0.0466005
$571$	−2.11161	−0.0883682	−0.0441841	−	0.999023i	$-0.514069\pi$
$571$	−2.11161	−0.0883682	−0.0441841	+	0.999023i	$0.514069\pi$
$572$	−1.21973	−0.0509995
$573$	7.34807	0.306970
$574$	0	0
$575$	7.35782	0.306842
$576$	−2.48938	−0.103724
$577$	−2.79762	−0.116466	−0.0582331	−	0.998303i	$-0.518547\pi$
$577$	−2.79762	−0.116466	−0.0582331	+	0.998303i	$0.518547\pi$
$578$	−16.6286	−0.691658
$579$	8.90946	0.370265
$580$	0.233169	0.00968180
$581$	0	0
$582$	−4.07666	−0.168983
$583$	3.51837	0.145716
$584$	−5.84298	−0.241784
$585$	−2.41314	−0.0997710
$586$	−20.6845	−0.854470
$587$	−6.93586	−0.286274	−0.143137	−	0.989703i	$-0.545719\pi$
$587$	−6.93586	−0.286274	−0.143137	+	0.989703i	$0.545719\pi$
$588$	0	0
$589$	−9.02617	−0.371917
$590$	1.00289	0.0412883
$591$	−13.5993	−0.559399
$592$	0.637171	0.0261876
$593$	−3.39084	−0.139245	−0.0696225	−	0.997573i	$-0.522179\pi$
$593$	−3.39084	−0.139245	−0.0696225	+	0.997573i	$0.522179\pi$
$594$	−1.15084	−0.0472196
$595$	0	0
$596$	7.81597	0.320155
$597$	7.58049	0.310249
$598$	6.18513	0.252929
$599$	−30.7247	−1.25538	−0.627689	−	0.778464i	$-0.715999\pi$
$599$	−30.7247	−1.25538	−0.627689	+	0.778464i	$0.715999\pi$
$600$	−3.53404	−0.144277
$601$	−32.5720	−1.32864	−0.664320	−	0.747448i	$-0.731279\pi$
$601$	−32.5720	−1.32864	−0.664320	+	0.747448i	$0.731279\pi$
$602$	0	0
$603$	−12.3386	−0.502465
$604$	−16.2176	−0.659883
$605$	2.54478	0.103460
$606$	−11.2431	−0.456719
$607$	1.92006	0.0779329	0.0389664	−	0.999241i	$-0.487593\pi$
$607$	1.92006	0.0779329	0.0389664	+	0.999241i	$0.487593\pi$
$608$	−6.67740	−0.270804
$609$	0	0
$610$	0.850606	0.0344400
$611$	9.06693	0.366809
$612$	1.51711	0.0613257
$613$	−28.8055	−1.16344	−0.581722	−	0.813388i	$-0.697621\pi$
$613$	−28.8055	−1.16344	−0.581722	+	0.813388i	$0.697621\pi$
$614$	28.6540	1.15638
$615$	0.552511	0.0222794
$616$	0	0
$617$	41.9416	1.68850	0.844252	−	0.535946i	$-0.180045\pi$
$617$	41.9416	1.68850	0.844252	+	0.535946i	$0.180045\pi$
$618$	3.49822	0.140719
$619$	0.752705	0.0302538	0.0151269	−	0.999886i	$-0.495185\pi$
$619$	0.752705	0.0302538	0.0151269	+	0.999886i	$0.495185\pi$
$620$	−0.315186	−0.0126582
$621$	5.83581	0.234183
$622$	−10.4647	−0.419596
$623$	0	0
$624$	−2.97079	−0.118927
$625$	24.1874	0.967498
$626$	31.4172	1.25568
$627$	−1.39991	−0.0559070
$628$	23.6455	0.943556
$629$	−0.388314	−0.0154831
$630$	0	0
$631$	−36.3961	−1.44891	−0.724453	−	0.689325i	$-0.757907\pi$
$631$	−36.3961	−1.44891	−0.724453	+	0.689325i	$0.757907\pi$
$632$	2.10678	0.0838032
$633$	−6.20983	−0.246819
$634$	12.7478	0.506279
$635$	3.56873	0.141621
$636$	8.56937	0.339797
$637$	0	0
$638$	−0.293388	−0.0116153
$639$	−10.4829	−0.414698
$640$	−0.233169	−0.00921680
$641$	−20.4574	−0.808021	−0.404010	−	0.914754i	$-0.632384\pi$
$641$	−20.4574	−0.808021	−0.404010	+	0.914754i	$0.632384\pi$
$642$	8.02577	0.316752
$643$	36.0350	1.42108	0.710541	−	0.703656i	$-0.248450\pi$
$643$	36.0350	1.42108	0.710541	+	0.703656i	$0.248450\pi$
$644$	0	0
$645$	0.549008	0.0216172
$646$	4.06944	0.160110
$647$	−42.7775	−1.68176	−0.840879	−	0.541223i	$-0.817961\pi$
$647$	−42.7775	−1.68176	−0.840879	+	0.541223i	$0.817961\pi$
$648$	4.66513	0.183264
$649$	−1.26190	−0.0495340
$650$	20.5610	0.806467
$651$	0	0
$652$	−13.6125	−0.533106
$653$	28.0322	1.09699	0.548493	−	0.836155i	$-0.315202\pi$
$653$	28.0322	1.09699	0.548493	+	0.836155i	$0.315202\pi$
$654$	10.8520	0.424346
$655$	2.84875	0.111310
$656$	−3.31605	−0.129470
$657$	14.5454	0.567470
$658$	0	0
$659$	36.2772	1.41316	0.706579	−	0.707634i	$-0.250238\pi$
$659$	36.2772	1.41316	0.706579	+	0.707634i	$0.250238\pi$
$660$	−0.0488836	−0.00190279
$661$	6.03049	0.234559	0.117279	−	0.993099i	$-0.462583\pi$
$661$	6.03049	0.234559	0.117279	+	0.993099i	$0.462583\pi$
$662$	−10.2619	−0.398841
$663$	1.81050	0.0703141
$664$	−6.73621	−0.261415
$665$	0	0
$666$	−1.58616	−0.0614624
$667$	1.48774	0.0576056
$668$	3.59710	0.139176
$669$	−7.14138	−0.276102
$670$	−1.15570	−0.0446485
$671$	−1.07029	−0.0413180
$672$	0	0
$673$	16.7412	0.645327	0.322663	−	0.946514i	$-0.395422\pi$
$673$	16.7412	0.645327	0.322663	+	0.946514i	$0.395422\pi$
$674$	−26.9868	−1.03949
$675$	19.3997	0.746695
$676$	4.28394	0.164767
$677$	−40.9926	−1.57547	−0.787737	−	0.616011i	$-0.788748\pi$
$677$	−40.9926	−1.57547	−0.787737	+	0.616011i	$0.788748\pi$
$678$	−7.35845	−0.282600
$679$	0	0
$680$	0.142101	0.00544933
$681$	18.0853	0.693030
$682$	0.396588	0.0151861
$683$	−34.1468	−1.30659	−0.653296	−	0.757102i	$-0.726614\pi$
$683$	−34.1468	−1.30659	−0.653296	+	0.757102i	$0.726614\pi$
$684$	16.6226	0.635580
$685$	−4.15719	−0.158838
$686$	0	0
$687$	−13.2043	−0.503776
$688$	−3.29502	−0.125622
$689$	−49.8563	−1.89937
$690$	0.247884	0.00943677
$691$	22.6343	0.861051	0.430525	−	0.902579i	$-0.358328\pi$
$691$	22.6343	0.861051	0.430525	+	0.902579i	$0.358328\pi$
$692$	−12.3956	−0.471212
$693$	0	0
$694$	0.0299869	0.00113829
$695$	1.86500	0.0707437
$696$	−0.714579	−0.0270860
$697$	2.02091	0.0765476
$698$	−6.30027	−0.238469
$699$	−6.68780	−0.252956
$700$	0	0
$701$	−15.1951	−0.573911	−0.286955	−	0.957944i	$-0.592643\pi$
$701$	−15.1951	−0.573911	−0.286955	+	0.957944i	$0.592643\pi$
$702$	16.3078	0.615497
$703$	−4.25465	−0.160467
$704$	0.293388	0.0110575
$705$	0.363378	0.0136856
$706$	−27.6344	−1.04003
$707$	0	0
$708$	−3.07350	−0.115509
$709$	8.01561	0.301033	0.150516	−	0.988608i	$-0.451906\pi$
$709$	8.01561	0.301033	0.150516	+	0.988608i	$0.451906\pi$
$710$	−0.981888	−0.0368496
$711$	−5.24457	−0.196687
$712$	12.6247	0.473129
$713$	−2.01106	−0.0753146
$714$	0	0
$715$	0.284403	0.0106361
$716$	9.58344	0.358150
$717$	−12.5354	−0.468145
$718$	−18.4797	−0.689657
$719$	−2.17601	−0.0811515	−0.0405757	−	0.999176i	$-0.512919\pi$
$719$	−2.17601	−0.0811515	−0.0405757	+	0.999176i	$0.512919\pi$
$720$	0.580445	0.0216319
$721$	0	0
$722$	25.5877	0.952274
$723$	−2.17393	−0.0808494
$724$	−0.148655	−0.00552473
$725$	4.94563	0.183676
$726$	−7.79886	−0.289443
$727$	53.7791	1.99456	0.997278	−	0.0737366i	$-0.0234924\pi$
$727$	53.7791	1.99456	0.997278	+	0.0737366i	$0.0234924\pi$
$728$	0	0
$729$	−3.20426	−0.118676
$730$	1.36240	0.0504247
$731$	2.00810	0.0742724
$732$	−2.60680	−0.0963502
$733$	−26.7745	−0.988938	−0.494469	−	0.869195i	$-0.664637\pi$
$733$	−26.7745	−0.988938	−0.494469	+	0.869195i	$0.664637\pi$
$734$	17.7335	0.654556
$735$	0	0
$736$	−1.48774	−0.0548389
$737$	1.45418	0.0535652
$738$	8.25489	0.303867
$739$	29.2936	1.07758	0.538791	−	0.842440i	$-0.318881\pi$
$739$	29.2936	1.07758	0.538791	+	0.842440i	$0.318881\pi$
$740$	−0.148568	−0.00546148
$741$	19.8371	0.728735
$742$	0	0
$743$	6.53498	0.239745	0.119873	−	0.992789i	$-0.461751\pi$
$743$	6.53498	0.239745	0.119873	+	0.992789i	$0.461751\pi$
$744$	0.965932	0.0354128
$745$	−1.82244	−0.0667690
$746$	14.2392	0.521335
$747$	16.7690	0.613544
$748$	−0.178801	−0.00653761
$749$	0	0
$750$	1.65712	0.0605093
$751$	30.1997	1.10200	0.551002	−	0.834504i	$-0.314246\pi$
$751$	30.1997	1.10200	0.551002	+	0.834504i	$0.314246\pi$
$752$	−2.18092	−0.0795298
$753$	12.3104	0.448616
$754$	4.15740	0.151403
$755$	3.78142	0.137620
$756$	0	0
$757$	−26.5008	−0.963189	−0.481595	−	0.876394i	$-0.659942\pi$
$757$	−26.5008	−0.963189	−0.481595	+	0.876394i	$0.659942\pi$
$758$	33.9879	1.23450
$759$	−0.311904	−0.0113214
$760$	1.55696	0.0564769
$761$	−4.37410	−0.158561	−0.0792805	−	0.996852i	$-0.525262\pi$
$761$	−4.37410	−0.158561	−0.0792805	+	0.996852i	$0.525262\pi$
$762$	−10.9369	−0.396201
$763$	0	0
$764$	10.2831	0.372029
$765$	−0.353743	−0.0127896
$766$	17.0812	0.617168
$767$	17.8815	0.645664
$768$	0.714579	0.0257851
$769$	−43.7523	−1.57775	−0.788874	−	0.614555i	$-0.789335\pi$
$769$	−43.7523	−1.57775	−0.788874	+	0.614555i	$0.789335\pi$
$770$	0	0
$771$	−14.7528	−0.531309
$772$	12.4681	0.448738
$773$	−14.3435	−0.515901	−0.257950	−	0.966158i	$-0.583047\pi$
$773$	−14.3435	−0.515901	−0.257950	+	0.966158i	$0.583047\pi$
$774$	8.20256	0.294835
$775$	−6.68526	−0.240142
$776$	−5.70498	−0.204797
$777$	0	0
$778$	−11.3176	−0.405757
$779$	22.1426	0.793340
$780$	0.692694	0.0248024
$781$	1.23548	0.0442088
$782$	0.906682	0.0324229
$783$	3.92259	0.140182
$784$	0	0
$785$	−5.51338	−0.196781
$786$	−8.73040	−0.311403
$787$	31.6417	1.12791	0.563953	−	0.825807i	$-0.309280\pi$
$787$	31.6417	1.12791	0.563953	+	0.825807i	$0.309280\pi$
$788$	−19.0312	−0.677957
$789$	−11.8410	−0.421551
$790$	−0.491235	−0.0174773
$791$	0	0
$792$	−0.730354	−0.0259520
$793$	15.1663	0.538571
$794$	−10.2515	−0.363811
$795$	−1.99811	−0.0708656
$796$	10.6083	0.376003
$797$	12.6909	0.449536	0.224768	−	0.974412i	$-0.427838\pi$
$797$	12.6909	0.449536	0.224768	+	0.974412i	$0.427838\pi$
$798$	0	0
$799$	1.32913	0.0470211
$800$	−4.94563	−0.174855
$801$	−31.4276	−1.11044
$802$	−17.6102	−0.621837
$803$	−1.71426	−0.0604950
$804$	3.54180	0.124910
$805$	0	0
$806$	−5.61976	−0.197948
$807$	1.87810	0.0661122
$808$	−15.7339	−0.553516
$809$	10.5845	0.372132	0.186066	−	0.982537i	$-0.440426\pi$
$809$	10.5845	0.372132	0.186066	+	0.982537i	$0.440426\pi$
$810$	−1.08776	−0.0382201
$811$	47.2614	1.65957	0.829786	−	0.558082i	$-0.188463\pi$
$811$	47.2614	1.65957	0.829786	+	0.558082i	$0.188463\pi$
$812$	0	0
$813$	9.01969	0.316334
$814$	0.186939	0.00655219
$815$	3.17400	0.111181
$816$	−0.435489	−0.0152452
$817$	22.0022	0.769759
$818$	38.8959	1.35996
$819$	0	0
$820$	0.773198	0.0270012
$821$	−0.820326	−0.0286296	−0.0143148	−	0.999898i	$-0.504557\pi$
$821$	−0.820326	−0.0286296	−0.0143148	+	0.999898i	$0.504557\pi$
$822$	12.7403	0.444369
$823$	41.1702	1.43510	0.717551	−	0.696506i	$-0.245263\pi$
$823$	41.1702	1.43510	0.717551	+	0.696506i	$0.245263\pi$
$824$	4.89549	0.170543
$825$	−1.03685	−0.0360984
$826$	0	0
$827$	−24.2372	−0.842810	−0.421405	−	0.906872i	$-0.638463\pi$
$827$	−24.2372	−0.842810	−0.421405	+	0.906872i	$0.638463\pi$
$828$	3.70355	0.128707
$829$	29.7746	1.03411	0.517057	−	0.855951i	$-0.327028\pi$
$829$	29.7746	1.03411	0.517057	+	0.855951i	$0.327028\pi$
$830$	1.57067	0.0545188
$831$	13.9054	0.482372
$832$	−4.15740	−0.144132
$833$	0	0
$834$	−5.71558	−0.197914
$835$	−0.838731	−0.0290255
$836$	−1.95907	−0.0677559
$837$	−5.30236	−0.183277
$838$	12.6437	0.436768
$839$	−14.8726	−0.513459	−0.256730	−	0.966483i	$-0.582645\pi$
$839$	−14.8726	−0.513459	−0.256730	+	0.966483i	$0.582645\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−10.7981	−0.372127
$843$	11.4265	0.393550
$844$	−8.69020	−0.299129
$845$	−0.998882	−0.0343626
$846$	5.42912	0.186657
$847$	0	0
$848$	11.9922	0.411814
$849$	−19.9958	−0.686255
$850$	3.01404	0.103381
$851$	−0.947946	−0.0324952
$852$	3.00914	0.103091
$853$	−48.2468	−1.65194	−0.825970	−	0.563715i	$-0.809372\pi$
$853$	−48.2468	−1.65194	−0.825970	+	0.563715i	$0.809372\pi$
$854$	0	0
$855$	−3.87586	−0.132552
$856$	11.2315	0.383884
$857$	22.2883	0.761355	0.380677	−	0.924708i	$-0.375691\pi$
$857$	22.2883	0.761355	0.380677	+	0.924708i	$0.375691\pi$
$858$	−0.871594	−0.0297557
$859$	−33.0107	−1.12631	−0.563155	−	0.826351i	$-0.690413\pi$
$859$	−33.0107	−1.12631	−0.563155	+	0.826351i	$0.690413\pi$
$860$	0.768296	0.0261987
$861$	0	0
$862$	−36.1812	−1.23234
$863$	2.98200	0.101509	0.0507543	−	0.998711i	$-0.483837\pi$
$863$	2.98200	0.101509	0.0507543	+	0.998711i	$0.483837\pi$
$864$	−3.92259	−0.133449
$865$	2.89028	0.0982723
$866$	−10.6350	−0.361391
$867$	−11.8824	−0.403549
$868$	0	0
$869$	0.618104	0.0209677
$870$	0.166617	0.00564886
$871$	−20.6061	−0.698211
$872$	15.1865	0.514281
$873$	14.2018	0.480659
$874$	9.93425	0.336031
$875$	0	0
$876$	−4.17527	−0.141069
$877$	−9.60117	−0.324208	−0.162104	−	0.986774i	$-0.551828\pi$
$877$	−9.60117	−0.324208	−0.162104	+	0.986774i	$0.551828\pi$
$878$	2.97507	0.100404
$879$	−14.7807	−0.498541
$880$	−0.0684089	−0.00230606
$881$	−11.0461	−0.372153	−0.186076	−	0.982535i	$-0.559577\pi$
$881$	−11.0461	−0.372153	−0.186076	+	0.982535i	$0.559577\pi$
$882$	0	0
$883$	−30.8011	−1.03654	−0.518269	−	0.855218i	$-0.673423\pi$
$883$	−30.8011	−1.03654	−0.518269	+	0.855218i	$0.673423\pi$
$884$	2.53366	0.0852163
$885$	0.716643	0.0240897
$886$	−27.9429	−0.938760
$887$	39.0735	1.31196	0.655980	−	0.754778i	$-0.272256\pi$
$887$	39.0735	1.31196	0.655980	+	0.754778i	$0.272256\pi$
$888$	0.455309	0.0152792
$889$	0	0
$890$	−2.94368	−0.0986723
$891$	1.36869	0.0458530
$892$	−9.99383	−0.334618
$893$	14.5628	0.487327
$894$	5.58513	0.186795
$895$	−2.23456	−0.0746930
$896$	0	0
$897$	4.41976	0.147572
$898$	−0.604431	−0.0201701
$899$	−1.35175	−0.0450834
$900$	12.3115	0.410385
$901$	−7.30846	−0.243480
$902$	−0.972889	−0.0323937
$903$	0	0
$904$	−10.2976	−0.342493
$905$	0.0346617	0.00115219
$906$	−11.5887	−0.385009
$907$	−0.412413	−0.0136939	−0.00684697	−	0.999977i	$-0.502179\pi$
$907$	−0.412413	−0.0136939	−0.00684697	+	0.999977i	$0.502179\pi$
$908$	25.3090	0.839910
$909$	39.1675	1.29911
$910$	0	0
$911$	31.6863	1.04981	0.524907	−	0.851160i	$-0.324100\pi$
$911$	31.6863	1.04981	0.524907	+	0.851160i	$0.324100\pi$
$912$	−4.77153	−0.158001
$913$	−1.97632	−0.0654068
$914$	−7.10311	−0.234950
$915$	0.607825	0.0200941
$916$	−18.4785	−0.610545
$917$	0	0
$918$	2.39057	0.0789004
$919$	−55.1497	−1.81922	−0.909611	−	0.415462i	$-0.863620\pi$
$919$	−55.1497	−1.81922	−0.909611	+	0.415462i	$0.863620\pi$
$920$	0.346895	0.0114368
$921$	20.4756	0.674693
$922$	−3.81028	−0.125485
$923$	−17.5071	−0.576252
$924$	0	0
$925$	−3.15122	−0.103611
$926$	−3.42327	−0.112496
$927$	−12.1867	−0.400265
$928$	−1.00000	−0.0328266
$929$	−39.6996	−1.30250	−0.651251	−	0.758863i	$-0.725755\pi$
$929$	−39.6996	−1.30250	−0.651251	+	0.758863i	$0.725755\pi$
$930$	−0.225225	−0.00738542
$931$	0	0
$932$	−9.35908	−0.306567
$933$	−7.47785	−0.244814
$934$	−22.8701	−0.748333
$935$	0.0416908	0.00136343
$936$	10.3493	0.338278
$937$	−2.47672	−0.0809108	−0.0404554	−	0.999181i	$-0.512881\pi$
$937$	−2.47672	−0.0809108	−0.0404554	+	0.999181i	$0.512881\pi$
$938$	0	0
$939$	22.4500	0.732629
$940$	0.508521	0.0165861
$941$	−25.1780	−0.820780	−0.410390	−	0.911910i	$-0.634607\pi$
$941$	−25.1780	−0.820780	−0.410390	+	0.911910i	$0.634607\pi$
$942$	16.8965	0.550519
$943$	4.93342	0.160654
$944$	−4.30113	−0.139990
$945$	0	0
$946$	−0.966721	−0.0314308
$947$	−38.1720	−1.24042	−0.620212	−	0.784434i	$-0.712953\pi$
$947$	−38.1720	−1.24042	−0.620212	+	0.784434i	$0.712953\pi$
$948$	1.50546	0.0488951
$949$	24.2916	0.788539
$950$	33.0240	1.07144
$951$	9.10929	0.295389
$952$	0	0
$953$	41.3605	1.33980	0.669900	−	0.742452i	$-0.266337\pi$
$953$	41.3605	1.33980	0.669900	+	0.742452i	$0.266337\pi$
$954$	−29.8531	−0.966529
$955$	−2.39769	−0.0775875
$956$	−17.5424	−0.567363
$957$	−0.209649	−0.00677699
$958$	4.57219	0.147721
$959$	0	0
$960$	−0.166617	−0.00537755
$961$	−29.1728	−0.941057
$962$	−2.64897	−0.0854063
$963$	−27.9594	−0.900978
$964$	−3.04226	−0.0979845
$965$	−2.90718	−0.0935853
$966$	0	0
$967$	7.05786	0.226965	0.113483	−	0.993540i	$-0.463799\pi$
$967$	7.05786	0.226965	0.113483	+	0.993540i	$0.463799\pi$
$968$	−10.9139	−0.350787
$969$	2.90794	0.0934164
$970$	1.33022	0.0427108
$971$	−35.4988	−1.13921	−0.569605	−	0.821919i	$-0.692904\pi$
$971$	−35.4988	−1.13921	−0.569605	+	0.821919i	$0.692904\pi$
$972$	15.1014	0.484377
$973$	0	0
$974$	21.6569	0.693931
$975$	14.6924	0.470534
$976$	−3.64803	−0.116771
$977$	14.8701	0.475735	0.237868	−	0.971298i	$-0.423552\pi$
$977$	14.8701	0.475735	0.237868	+	0.971298i	$0.423552\pi$
$978$	−9.72719	−0.311041
$979$	3.70393	0.118378
$980$	0	0
$981$	−37.8050	−1.20702
$982$	32.0537	1.02287
$983$	−36.7682	−1.17272	−0.586362	−	0.810049i	$-0.699440\pi$
$983$	−36.7682	−1.17272	−0.586362	+	0.810049i	$0.699440\pi$
$984$	−2.36958	−0.0755393
$985$	4.43747	0.141390
$986$	0.609435	0.0194084
$987$	0	0
$988$	27.7606	0.883182
$989$	4.90214	0.155879
$990$	0.170296	0.00541235
$991$	−26.9622	−0.856483	−0.428242	−	0.903664i	$-0.640867\pi$
$991$	−26.9622	−0.856483	−0.428242	+	0.903664i	$0.640867\pi$
$992$	1.35175	0.0429181
$993$	−7.33295	−0.232704
$994$	0	0
$995$	−2.47353	−0.0784162
$996$	−4.81355	−0.152523
$997$	−7.46930	−0.236555	−0.118278	−	0.992981i	$-0.537737\pi$
$997$	−7.46930	−0.236555	−0.118278	+	0.992981i	$0.537737\pi$
$998$	24.6113	0.779058
$999$	−2.49936	−0.0790764

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.x.1.4		5
7.3	odd	6		406.2.e.a.233.4	✓	10
7.5	odd	6		406.2.e.a.291.4	yes	10
7.6	odd	2		2842.2.a.z.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.4	✓	10	7.3	odd	6
406.2.e.a.291.4	yes	10	7.5	odd	6
2842.2.a.x.1.4		5	1.1	even	1	trivial
2842.2.a.z.1.2		5	7.6	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.714579 q^{3} +1.00000 q^{4} -0.233169 q^{5} +0.714579 q^{6} +1.00000 q^{8} -2.48938 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.714579 q^{3} +1.00000 q^{4} -0.233169 q^{5} +0.714579 q^{6} +1.00000 q^{8} -2.48938 q^{9} -0.233169 q^{10} +0.293388 q^{11} +0.714579 q^{12} -4.15740 q^{13} -0.166617 q^{15} +1.00000 q^{16} -0.609435 q^{17} -2.48938 q^{18} -6.67740 q^{19} -0.233169 q^{20} +0.293388 q^{22} -1.48774 q^{23} +0.714579 q^{24} -4.94563 q^{25} -4.15740 q^{26} -3.92259 q^{27} -1.00000 q^{29} -0.166617 q^{30} +1.35175 q^{31} +1.00000 q^{32} +0.209649 q^{33} -0.609435 q^{34} -2.48938 q^{36} +0.637171 q^{37} -6.67740 q^{38} -2.97079 q^{39} -0.233169 q^{40} -3.31605 q^{41} -3.29502 q^{43} +0.293388 q^{44} +0.580445 q^{45} -1.48774 q^{46} -2.18092 q^{47} +0.714579 q^{48} -4.94563 q^{50} -0.435489 q^{51} -4.15740 q^{52} +11.9922 q^{53} -3.92259 q^{54} -0.0684089 q^{55} -4.77153 q^{57} -1.00000 q^{58} -4.30113 q^{59} -0.166617 q^{60} -3.64803 q^{61} +1.35175 q^{62} +1.00000 q^{64} +0.969374 q^{65} +0.209649 q^{66} +4.95649 q^{67} -0.609435 q^{68} -1.06311 q^{69} +4.21106 q^{71} -2.48938 q^{72} -5.84298 q^{73} +0.637171 q^{74} -3.53404 q^{75} -6.67740 q^{76} -2.97079 q^{78} +2.10678 q^{79} -0.233169 q^{80} +4.66513 q^{81} -3.31605 q^{82} -6.73621 q^{83} +0.142101 q^{85} -3.29502 q^{86} -0.714579 q^{87} +0.293388 q^{88} +12.6247 q^{89} +0.580445 q^{90} -1.48774 q^{92} +0.965932 q^{93} -2.18092 q^{94} +1.55696 q^{95} +0.714579 q^{96} -5.70498 q^{97} -0.730354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 7 q^{5} - 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 7 * q^5 - 3 * q^6 + 5 * q^8 + 8 * q^9	\( 5 q + 5 q^{2} - 3 q^{3} + 5 q^{4} - 7 q^{5} - 3 q^{6} + 5 q^{8} + 8 q^{9} - 7 q^{10} - 3 q^{12} - 10 q^{13} - 10 q^{15} + 5 q^{16} - 8 q^{17} + 8 q^{18} - 2 q^{19} - 7 q^{20} + q^{23} - 3 q^{24} + 12 q^{25} - 10 q^{26} - 15 q^{27} - 5 q^{29} - 10 q^{30} - 11 q^{31} + 5 q^{32} - 9 q^{33} - 8 q^{34} + 8 q^{36} - 8 q^{37} - 2 q^{38} + 18 q^{39} - 7 q^{40} - 23 q^{41} - 3 q^{43} - 4 q^{45} + q^{46} - 16 q^{47} - 3 q^{48} + 12 q^{50} + 7 q^{51} - 10 q^{52} + 7 q^{53} - 15 q^{54} - 6 q^{55} - 34 q^{57} - 5 q^{58} + 9 q^{59} - 10 q^{60} - 15 q^{61} - 11 q^{62} + 5 q^{64} + 5 q^{65} - 9 q^{66} - 4 q^{67} - 8 q^{68} - 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} + 34 q^{75} - 2 q^{76} + 18 q^{78} - 13 q^{79} - 7 q^{80} + 17 q^{81} - 23 q^{82} - 28 q^{83} - 7 q^{85} - 3 q^{86} + 3 q^{87} - 17 q^{89} - 4 q^{90} + q^{92} + 17 q^{93} - 16 q^{94} - 9 q^{95} - 3 q^{96} - 42 q^{97} - 42 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 3 * q^3 + 5 * q^4 - 7 * q^5 - 3 * q^6 + 5 * q^8 + 8 * q^9 - 7 * q^10 - 3 * q^12 - 10 * q^13 - 10 * q^15 + 5 * q^16 - 8 * q^17 + 8 * q^18 - 2 * q^19 - 7 * q^20 + q^23 - 3 * q^24 + 12 * q^25 - 10 * q^26 - 15 * q^27 - 5 * q^29 - 10 * q^30 - 11 * q^31 + 5 * q^32 - 9 * q^33 - 8 * q^34 + 8 * q^36 - 8 * q^37 - 2 * q^38 + 18 * q^39 - 7 * q^40 - 23 * q^41 - 3 * q^43 - 4 * q^45 + q^46 - 16 * q^47 - 3 * q^48 + 12 * q^50 + 7 * q^51 - 10 * q^52 + 7 * q^53 - 15 * q^54 - 6 * q^55 - 34 * q^57 - 5 * q^58 + 9 * q^59 - 10 * q^60 - 15 * q^61 - 11 * q^62 + 5 * q^64 + 5 * q^65 - 9 * q^66 - 4 * q^67 - 8 * q^68 - 14 * q^69 - 22 * q^71 + 8 * q^72 - 8 * q^74 + 34 * q^75 - 2 * q^76 + 18 * q^78 - 13 * q^79 - 7 * q^80 + 17 * q^81 - 23 * q^82 - 28 * q^83 - 7 * q^85 - 3 * q^86 + 3 * q^87 - 17 * q^89 - 4 * q^90 + q^92 + 17 * q^93 - 16 * q^94 - 9 * q^95 - 3 * q^96 - 42 * q^97 - 42 * q^99

Introduction

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