LMFDB - Embedded newform 731.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.56155 q^{3} -1.00000 q^{4} +1.56155 q^{5} +1.56155 q^{6} +3.00000 q^{8} -0.561553 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.56155 q^{3} -1.00000 q^{4} +1.56155 q^{5} +1.56155 q^{6} +3.00000 q^{8} -0.561553 q^{9} -1.56155 q^{10} -2.00000 q^{11} +1.56155 q^{12} -0.438447 q^{13} -2.43845 q^{15} -1.00000 q^{16} -1.00000 q^{17} +0.561553 q^{18} +7.12311 q^{19} -1.56155 q^{20} +2.00000 q^{22} +2.00000 q^{23} -4.68466 q^{24} -2.56155 q^{25} +0.438447 q^{26} +5.56155 q^{27} +3.12311 q^{29} +2.43845 q^{30} -6.00000 q^{31} -5.00000 q^{32} +3.12311 q^{33} +1.00000 q^{34} +0.561553 q^{36} -5.56155 q^{37} -7.12311 q^{38} +0.684658 q^{39} +4.68466 q^{40} -5.12311 q^{41} -1.00000 q^{43} +2.00000 q^{44} -0.876894 q^{45} -2.00000 q^{46} -9.56155 q^{47} +1.56155 q^{48} -7.00000 q^{49} +2.56155 q^{50} +1.56155 q^{51} +0.438447 q^{52} -10.6847 q^{53} -5.56155 q^{54} -3.12311 q^{55} -11.1231 q^{57} -3.12311 q^{58} -11.8078 q^{59} +2.43845 q^{60} +0.684658 q^{61} +6.00000 q^{62} +7.00000 q^{64} -0.684658 q^{65} -3.12311 q^{66} +5.56155 q^{67} +1.00000 q^{68} -3.12311 q^{69} +5.56155 q^{71} -1.68466 q^{72} -11.8078 q^{73} +5.56155 q^{74} +4.00000 q^{75} -7.12311 q^{76} -0.684658 q^{78} -9.12311 q^{79} -1.56155 q^{80} -7.00000 q^{81} +5.12311 q^{82} +15.8078 q^{83} -1.56155 q^{85} +1.00000 q^{86} -4.87689 q^{87} -6.00000 q^{88} -0.246211 q^{89} +0.876894 q^{90} -2.00000 q^{92} +9.36932 q^{93} +9.56155 q^{94} +11.1231 q^{95} +7.80776 q^{96} +16.2462 q^{97} +7.00000 q^{98} +1.12311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 - 2 * q^4 - q^5 - q^6 + 6 * q^8 + 3 * q^9	$ 2 q - 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - q^{6} + 6 q^{8} + 3 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} - 9 q^{15} - 2 q^{16} - 2 q^{17} - 3 q^{18} + 6 q^{19} + q^{20} + 4 q^{22} + 4 q^{23} + 3 q^{24} - q^{25} + 5 q^{26} + 7 q^{27} - 2 q^{29} + 9 q^{30} - 12 q^{31} - 10 q^{32} - 2 q^{33} + 2 q^{34} - 3 q^{36} - 7 q^{37} - 6 q^{38} - 11 q^{39} - 3 q^{40} - 2 q^{41} - 2 q^{43} + 4 q^{44} - 10 q^{45} - 4 q^{46} - 15 q^{47} - q^{48} - 14 q^{49} + q^{50} - q^{51} + 5 q^{52} - 9 q^{53} - 7 q^{54} + 2 q^{55} - 14 q^{57} + 2 q^{58} - 3 q^{59} + 9 q^{60} - 11 q^{61} + 12 q^{62} + 14 q^{64} + 11 q^{65} + 2 q^{66} + 7 q^{67} + 2 q^{68} + 2 q^{69} + 7 q^{71} + 9 q^{72} - 3 q^{73} + 7 q^{74} + 8 q^{75} - 6 q^{76} + 11 q^{78} - 10 q^{79} + q^{80} - 14 q^{81} + 2 q^{82} + 11 q^{83} + q^{85} + 2 q^{86} - 18 q^{87} - 12 q^{88} + 16 q^{89} + 10 q^{90} - 4 q^{92} - 6 q^{93} + 15 q^{94} + 14 q^{95} - 5 q^{96} + 16 q^{97} + 14 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 - 2 * q^4 - q^5 - q^6 + 6 * q^8 + 3 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 - 9 * q^15 - 2 * q^16 - 2 * q^17 - 3 * q^18 + 6 * q^19 + q^20 + 4 * q^22 + 4 * q^23 + 3 * q^24 - q^25 + 5 * q^26 + 7 * q^27 - 2 * q^29 + 9 * q^30 - 12 * q^31 - 10 * q^32 - 2 * q^33 + 2 * q^34 - 3 * q^36 - 7 * q^37 - 6 * q^38 - 11 * q^39 - 3 * q^40 - 2 * q^41 - 2 * q^43 + 4 * q^44 - 10 * q^45 - 4 * q^46 - 15 * q^47 - q^48 - 14 * q^49 + q^50 - q^51 + 5 * q^52 - 9 * q^53 - 7 * q^54 + 2 * q^55 - 14 * q^57 + 2 * q^58 - 3 * q^59 + 9 * q^60 - 11 * q^61 + 12 * q^62 + 14 * q^64 + 11 * q^65 + 2 * q^66 + 7 * q^67 + 2 * q^68 + 2 * q^69 + 7 * q^71 + 9 * q^72 - 3 * q^73 + 7 * q^74 + 8 * q^75 - 6 * q^76 + 11 * q^78 - 10 * q^79 + q^80 - 14 * q^81 + 2 * q^82 + 11 * q^83 + q^85 + 2 * q^86 - 18 * q^87 - 12 * q^88 + 16 * q^89 + 10 * q^90 - 4 * q^92 - 6 * q^93 + 15 * q^94 + 14 * q^95 - 5 * q^96 + 16 * q^97 + 14 * q^98 - 6 * 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	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−1.56155	−0.901563	−0.450781	−	0.892634i	$-0.648855\pi$
$3$	−1.56155	−0.901563	−0.450781	+	0.892634i	$0.648855\pi$
$4$	−1.00000	−0.500000
$5$	1.56155	0.698348	0.349174	−	0.937058i	$-0.386462\pi$
$5$	1.56155	0.698348	0.349174	+	0.937058i	$0.386462\pi$
$6$	1.56155	0.637501
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	3.00000	1.06066
$9$	−0.561553	−0.187184
$10$	−1.56155	−0.493806
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.56155	0.450781
$13$	−0.438447	−0.121603	−0.0608017	−	0.998150i	$-0.519366\pi$
$13$	−0.438447	−0.121603	−0.0608017	+	0.998150i	$0.519366\pi$
$14$	0	0
$15$	−2.43845	−0.629604
$16$	−1.00000	−0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.561553	0.132359
$19$	7.12311	1.63415	0.817076	−	0.576530i	$-0.195593\pi$
$19$	7.12311	1.63415	0.817076	+	0.576530i	$0.195593\pi$
$20$	−1.56155	−0.349174
$21$	0	0
$22$	2.00000	0.426401
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	−4.68466	−0.956252
$25$	−2.56155	−0.512311
$26$	0.438447	0.0859866
$27$	5.56155	1.07032
$28$	0	0
$29$	3.12311	0.579946	0.289973	−	0.957035i	$-0.406354\pi$
$29$	3.12311	0.579946	0.289973	+	0.957035i	$0.406354\pi$
$30$	2.43845	0.445198
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	−5.00000	−0.883883
$33$	3.12311	0.543663
$34$	1.00000	0.171499
$35$	0	0
$36$	0.561553	0.0935921
$37$	−5.56155	−0.914314	−0.457157	−	0.889386i	$-0.651132\pi$
$37$	−5.56155	−0.914314	−0.457157	+	0.889386i	$0.651132\pi$
$38$	−7.12311	−1.15552
$39$	0.684658	0.109633
$40$	4.68466	0.740710
$41$	−5.12311	−0.800095	−0.400047	−	0.916494i	$-0.631006\pi$
$41$	−5.12311	−0.800095	−0.400047	+	0.916494i	$0.631006\pi$
$42$	0	0
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	2.00000	0.301511
$45$	−0.876894	−0.130720
$46$	−2.00000	−0.294884
$47$	−9.56155	−1.39470	−0.697348	−	0.716733i	$-0.745637\pi$
$47$	−9.56155	−1.39470	−0.697348	+	0.716733i	$0.745637\pi$
$48$	1.56155	0.225391
$49$	−7.00000	−1.00000
$50$	2.56155	0.362258
$51$	1.56155	0.218661
$52$	0.438447	0.0608017
$53$	−10.6847	−1.46765	−0.733825	−	0.679338i	$-0.762267\pi$
$53$	−10.6847	−1.46765	−0.733825	+	0.679338i	$0.762267\pi$
$54$	−5.56155	−0.756831
$55$	−3.12311	−0.421119
$56$	0	0
$57$	−11.1231	−1.47329
$58$	−3.12311	−0.410084
$59$	−11.8078	−1.53724	−0.768620	−	0.639706i	$-0.779056\pi$
$59$	−11.8078	−1.53724	−0.768620	+	0.639706i	$0.779056\pi$
$60$	2.43845	0.314802
$61$	0.684658	0.0876615	0.0438308	−	0.999039i	$-0.486044\pi$
$61$	0.684658	0.0876615	0.0438308	+	0.999039i	$0.486044\pi$
$62$	6.00000	0.762001
$63$	0	0
$64$	7.00000	0.875000
$65$	−0.684658	−0.0849214
$66$	−3.12311	−0.384428
$67$	5.56155	0.679452	0.339726	−	0.940524i	$-0.389666\pi$
$67$	5.56155	0.679452	0.339726	+	0.940524i	$0.389666\pi$
$68$	1.00000	0.121268
$69$	−3.12311	−0.375978
$70$	0	0
$71$	5.56155	0.660035	0.330017	−	0.943975i	$-0.392945\pi$
$71$	5.56155	0.660035	0.330017	+	0.943975i	$0.392945\pi$
$72$	−1.68466	−0.198539
$73$	−11.8078	−1.38199	−0.690997	−	0.722858i	$-0.742828\pi$
$73$	−11.8078	−1.38199	−0.690997	+	0.722858i	$0.742828\pi$
$74$	5.56155	0.646517
$75$	4.00000	0.461880
$76$	−7.12311	−0.817076
$77$	0	0
$78$	−0.684658	−0.0775223
$79$	−9.12311	−1.02643	−0.513215	−	0.858260i	$-0.671546\pi$
$79$	−9.12311	−1.02643	−0.513215	+	0.858260i	$0.671546\pi$
$80$	−1.56155	−0.174587
$81$	−7.00000	−0.777778
$82$	5.12311	0.565752
$83$	15.8078	1.73513	0.867564	−	0.497326i	$-0.165685\pi$
$83$	15.8078	1.73513	0.867564	+	0.497326i	$0.165685\pi$
$84$	0	0
$85$	−1.56155	−0.169374
$86$	1.00000	0.107833
$87$	−4.87689	−0.522858
$88$	−6.00000	−0.639602
$89$	−0.246211	−0.0260983	−0.0130492	−	0.999915i	$-0.504154\pi$
$89$	−0.246211	−0.0260983	−0.0130492	+	0.999915i	$0.504154\pi$
$90$	0.876894	0.0924328
$91$	0	0
$92$	−2.00000	−0.208514
$93$	9.36932	0.971553
$94$	9.56155	0.986199
$95$	11.1231	1.14121
$96$	7.80776	0.796877
$97$	16.2462	1.64955	0.824776	−	0.565459i	$-0.191301\pi$
$97$	16.2462	1.64955	0.824776	+	0.565459i	$0.191301\pi$
$98$	7.00000	0.707107
$99$	1.12311	0.112876
$100$	2.56155	0.256155
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	−1.56155	−0.154617
$103$	−17.5616	−1.73039	−0.865196	−	0.501435i	$-0.832806\pi$
$103$	−17.5616	−1.73039	−0.865196	+	0.501435i	$0.832806\pi$
$104$	−1.31534	−0.128980
$105$	0	0
$106$	10.6847	1.03779
$107$	2.00000	0.193347	0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000	0.193347	0.0966736	+	0.995316i	$0.469180\pi$
$108$	−5.56155	−0.535161
$109$	−4.24621	−0.406713	−0.203357	−	0.979105i	$-0.565185\pi$
$109$	−4.24621	−0.406713	−0.203357	+	0.979105i	$0.565185\pi$
$110$	3.12311	0.297776
$111$	8.68466	0.824311
$112$	0	0
$113$	−11.8078	−1.11078	−0.555391	−	0.831590i	$-0.687431\pi$
$113$	−11.8078	−1.11078	−0.555391	+	0.831590i	$0.687431\pi$
$114$	11.1231	1.04177
$115$	3.12311	0.291231
$116$	−3.12311	−0.289973
$117$	0.246211	0.0227622
$118$	11.8078	1.08699
$119$	0	0
$120$	−7.31534	−0.667796
$121$	−7.00000	−0.636364
$122$	−0.684658	−0.0619861
$123$	8.00000	0.721336
$124$	6.00000	0.538816
$125$	−11.8078	−1.05612
$126$	0	0
$127$	22.0540	1.95697	0.978487	−	0.206309i	$-0.0661452\pi$
$127$	22.0540	1.95697	0.978487	+	0.206309i	$0.0661452\pi$
$128$	3.00000	0.265165
$129$	1.56155	0.137487
$130$	0.684658	0.0600485
$131$	11.8078	1.03165	0.515825	−	0.856694i	$-0.327486\pi$
$131$	11.8078	1.03165	0.515825	+	0.856694i	$0.327486\pi$
$132$	−3.12311	−0.271831
$133$	0	0
$134$	−5.56155	−0.480445
$135$	8.68466	0.747456
$136$	−3.00000	−0.257248
$137$	12.2462	1.04626	0.523132	−	0.852252i	$-0.324763\pi$
$137$	12.2462	1.04626	0.523132	+	0.852252i	$0.324763\pi$
$138$	3.12311	0.265856
$139$	−19.3693	−1.64288	−0.821442	−	0.570292i	$-0.806830\pi$
$139$	−19.3693	−1.64288	−0.821442	+	0.570292i	$0.806830\pi$
$140$	0	0
$141$	14.9309	1.25741
$142$	−5.56155	−0.466715
$143$	0.876894	0.0733296
$144$	0.561553	0.0467961
$145$	4.87689	0.405004
$146$	11.8078	0.977218
$147$	10.9309	0.901563
$148$	5.56155	0.457157
$149$	−8.24621	−0.675556	−0.337778	−	0.941226i	$-0.609675\pi$
$149$	−8.24621	−0.675556	−0.337778	+	0.941226i	$0.609675\pi$
$150$	−4.00000	−0.326599
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	21.3693	1.73328
$153$	0.561553	0.0453989
$154$	0	0
$155$	−9.36932	−0.752562
$156$	−0.684658	−0.0548165
$157$	−22.4924	−1.79509	−0.897545	−	0.440922i	$-0.854651\pi$
$157$	−22.4924	−1.79509	−0.897545	+	0.440922i	$0.854651\pi$
$158$	9.12311	0.725795
$159$	16.6847	1.32318
$160$	−7.80776	−0.617258
$161$	0	0
$162$	7.00000	0.549972
$163$	−21.5616	−1.68883	−0.844416	−	0.535689i	$-0.820052\pi$
$163$	−21.5616	−1.68883	−0.844416	+	0.535689i	$0.820052\pi$
$164$	5.12311	0.400047
$165$	4.87689	0.379666
$166$	−15.8078	−1.22692
$167$	22.0000	1.70241	0.851206	−	0.524832i	$-0.175872\pi$
$167$	22.0000	1.70241	0.851206	+	0.524832i	$0.175872\pi$
$168$	0	0
$169$	−12.8078	−0.985213
$170$	1.56155	0.119766
$171$	−4.00000	−0.305888
$172$	1.00000	0.0762493
$173$	−5.12311	−0.389503	−0.194751	−	0.980853i	$-0.562390\pi$
$173$	−5.12311	−0.389503	−0.194751	+	0.980853i	$0.562390\pi$
$174$	4.87689	0.369716
$175$	0	0
$176$	2.00000	0.150756
$177$	18.4384	1.38592
$178$	0.246211	0.0184543
$179$	8.87689	0.663490	0.331745	−	0.943369i	$-0.392363\pi$
$179$	8.87689	0.663490	0.331745	+	0.943369i	$0.392363\pi$
$180$	0.876894	0.0653598
$181$	−19.3693	−1.43971	−0.719855	−	0.694124i	$-0.755792\pi$
$181$	−19.3693	−1.43971	−0.719855	+	0.694124i	$0.755792\pi$
$182$	0	0
$183$	−1.06913	−0.0790324
$184$	6.00000	0.442326
$185$	−8.68466	−0.638509
$186$	−9.36932	−0.686992
$187$	2.00000	0.146254
$188$	9.56155	0.697348
$189$	0	0
$190$	−11.1231	−0.806955
$191$	11.1231	0.804840	0.402420	−	0.915455i	$-0.368169\pi$
$191$	11.1231	0.804840	0.402420	+	0.915455i	$0.368169\pi$
$192$	−10.9309	−0.788868
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	−16.2462	−1.16641
$195$	1.06913	0.0765620
$196$	7.00000	0.500000
$197$	17.6155	1.25505	0.627527	−	0.778595i	$-0.284067\pi$
$197$	17.6155	1.25505	0.627527	+	0.778595i	$0.284067\pi$
$198$	−1.12311	−0.0798156
$199$	−2.93087	−0.207764	−0.103882	−	0.994590i	$-0.533126\pi$
$199$	−2.93087	−0.207764	−0.103882	+	0.994590i	$0.533126\pi$
$200$	−7.68466	−0.543387
$201$	−8.68466	−0.612569
$202$	2.00000	0.140720
$203$	0	0
$204$	−1.56155	−0.109331
$205$	−8.00000	−0.558744
$206$	17.5616	1.22357
$207$	−1.12311	−0.0780612
$208$	0.438447	0.0304008
$209$	−14.2462	−0.985431
$210$	0	0
$211$	−4.19224	−0.288605	−0.144303	−	0.989534i	$-0.546094\pi$
$211$	−4.19224	−0.288605	−0.144303	+	0.989534i	$0.546094\pi$
$212$	10.6847	0.733825
$213$	−8.68466	−0.595063
$214$	−2.00000	−0.136717
$215$	−1.56155	−0.106497
$216$	16.6847	1.13525
$217$	0	0
$218$	4.24621	0.287590
$219$	18.4384	1.24595
$220$	3.12311	0.210560
$221$	0.438447	0.0294931
$222$	−8.68466	−0.582876
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	0	0
$225$	1.43845	0.0958965
$226$	11.8078	0.785441
$227$	20.4924	1.36013	0.680065	−	0.733152i	$-0.261952\pi$
$227$	20.4924	1.36013	0.680065	+	0.733152i	$0.261952\pi$
$228$	11.1231	0.736646
$229$	5.80776	0.383788	0.191894	−	0.981416i	$-0.438537\pi$
$229$	5.80776	0.383788	0.191894	+	0.981416i	$0.438537\pi$
$230$	−3.12311	−0.205931
$231$	0	0
$232$	9.36932	0.615126
$233$	19.1231	1.25280	0.626398	−	0.779503i	$-0.284528\pi$
$233$	19.1231	1.25280	0.626398	+	0.779503i	$0.284528\pi$
$234$	−0.246211	−0.0160953
$235$	−14.9309	−0.973983
$236$	11.8078	0.768620
$237$	14.2462	0.925391
$238$	0	0
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	2.43845	0.157401
$241$	−5.36932	−0.345868	−0.172934	−	0.984933i	$-0.555325\pi$
$241$	−5.36932	−0.345868	−0.172934	+	0.984933i	$0.555325\pi$
$242$	7.00000	0.449977
$243$	−5.75379	−0.369106
$244$	−0.684658	−0.0438308
$245$	−10.9309	−0.698348
$246$	−8.00000	−0.510061
$247$	−3.12311	−0.198718
$248$	−18.0000	−1.14300
$249$	−24.6847	−1.56433
$250$	11.8078	0.746789
$251$	−6.43845	−0.406391	−0.203196	−	0.979138i	$-0.565133\pi$
$251$	−6.43845	−0.406391	−0.203196	+	0.979138i	$0.565133\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	−22.0540	−1.38379
$255$	2.43845	0.152701
$256$	−17.0000	−1.06250
$257$	26.0000	1.62184	0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000	1.62184	0.810918	+	0.585160i	$0.198968\pi$
$258$	−1.56155	−0.0972180
$259$	0	0
$260$	0.684658	0.0424607
$261$	−1.75379	−0.108557
$262$	−11.8078	−0.729486
$263$	12.4924	0.770316	0.385158	−	0.922851i	$-0.374147\pi$
$263$	12.4924	0.770316	0.385158	+	0.922851i	$0.374147\pi$
$264$	9.36932	0.576642
$265$	−16.6847	−1.02493
$266$	0	0
$267$	0.384472	0.0235293
$268$	−5.56155	−0.339726
$269$	8.24621	0.502780	0.251390	−	0.967886i	$-0.419112\pi$
$269$	8.24621	0.502780	0.251390	+	0.967886i	$0.419112\pi$
$270$	−8.68466	−0.528531
$271$	−18.9309	−1.14997	−0.574984	−	0.818164i	$-0.694992\pi$
$271$	−18.9309	−1.14997	−0.574984	+	0.818164i	$0.694992\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−12.2462	−0.739821
$275$	5.12311	0.308935
$276$	3.12311	0.187989
$277$	30.9309	1.85846	0.929228	−	0.369507i	$-0.120473\pi$
$277$	30.9309	1.85846	0.929228	+	0.369507i	$0.120473\pi$
$278$	19.3693	1.16169
$279$	3.36932	0.201716
$280$	0	0
$281$	−20.9309	−1.24863	−0.624316	−	0.781172i	$-0.714622\pi$
$281$	−20.9309	−1.24863	−0.624316	+	0.781172i	$0.714622\pi$
$282$	−14.9309	−0.889120
$283$	12.2462	0.727962	0.363981	−	0.931406i	$-0.381417\pi$
$283$	12.2462	0.727962	0.363981	+	0.931406i	$0.381417\pi$
$284$	−5.56155	−0.330017
$285$	−17.3693	−1.02887
$286$	−0.876894	−0.0518519
$287$	0	0
$288$	2.80776	0.165449
$289$	1.00000	0.0588235
$290$	−4.87689	−0.286381
$291$	−25.3693	−1.48718
$292$	11.8078	0.690997
$293$	−0.246211	−0.0143838	−0.00719191	−	0.999974i	$-0.502289\pi$
$293$	−0.246211	−0.0143838	−0.00719191	+	0.999974i	$0.502289\pi$
$294$	−10.9309	−0.637501
$295$	−18.4384	−1.07353
$296$	−16.6847	−0.969776
$297$	−11.1231	−0.645428
$298$	8.24621	0.477690
$299$	−0.876894	−0.0507121
$300$	−4.00000	−0.230940
$301$	0	0
$302$	−8.00000	−0.460348
$303$	3.12311	0.179418
$304$	−7.12311	−0.408538
$305$	1.06913	0.0612182
$306$	−0.561553	−0.0321018
$307$	−14.2462	−0.813074	−0.406537	−	0.913634i	$-0.633264\pi$
$307$	−14.2462	−0.813074	−0.406537	+	0.913634i	$0.633264\pi$
$308$	0	0
$309$	27.4233	1.56006
$310$	9.36932	0.532141
$311$	15.3693	0.871514	0.435757	−	0.900064i	$-0.356481\pi$
$311$	15.3693	0.871514	0.435757	+	0.900064i	$0.356481\pi$
$312$	2.05398	0.116283
$313$	15.8078	0.893508	0.446754	−	0.894657i	$-0.352580\pi$
$313$	15.8078	0.893508	0.446754	+	0.894657i	$0.352580\pi$
$314$	22.4924	1.26932
$315$	0	0
$316$	9.12311	0.513215
$317$	−19.3693	−1.08789	−0.543945	−	0.839121i	$-0.683070\pi$
$317$	−19.3693	−1.08789	−0.543945	+	0.839121i	$0.683070\pi$
$318$	−16.6847	−0.935629
$319$	−6.24621	−0.349721
$320$	10.9309	0.611054
$321$	−3.12311	−0.174315
$322$	0	0
$323$	−7.12311	−0.396340
$324$	7.00000	0.388889
$325$	1.12311	0.0622987
$326$	21.5616	1.19418
$327$	6.63068	0.366678
$328$	−15.3693	−0.848629
$329$	0	0
$330$	−4.87689	−0.268464
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	−15.8078	−0.867564
$333$	3.12311	0.171145
$334$	−22.0000	−1.20379
$335$	8.68466	0.474494
$336$	0	0
$337$	−3.75379	−0.204482	−0.102241	−	0.994760i	$-0.532601\pi$
$337$	−3.75379	−0.204482	−0.102241	+	0.994760i	$0.532601\pi$
$338$	12.8078	0.696651
$339$	18.4384	1.00144
$340$	1.56155	0.0846871
$341$	12.0000	0.649836
$342$	4.00000	0.216295
$343$	0	0
$344$	−3.00000	−0.161749
$345$	−4.87689	−0.262563
$346$	5.12311	0.275420
$347$	−18.4384	−0.989828	−0.494914	−	0.868942i	$-0.664800\pi$
$347$	−18.4384	−0.989828	−0.494914	+	0.868942i	$0.664800\pi$
$348$	4.87689	0.261429
$349$	−10.8769	−0.582227	−0.291113	−	0.956689i	$-0.594026\pi$
$349$	−10.8769	−0.582227	−0.291113	+	0.956689i	$0.594026\pi$
$350$	0	0
$351$	−2.43845	−0.130155
$352$	10.0000	0.533002
$353$	−19.1771	−1.02069	−0.510347	−	0.859969i	$-0.670483\pi$
$353$	−19.1771	−1.02069	−0.510347	+	0.859969i	$0.670483\pi$
$354$	−18.4384	−0.979992
$355$	8.68466	0.460934
$356$	0.246211	0.0130492
$357$	0	0
$358$	−8.87689	−0.469158
$359$	−3.80776	−0.200966	−0.100483	−	0.994939i	$-0.532039\pi$
$359$	−3.80776	−0.200966	−0.100483	+	0.994939i	$0.532039\pi$
$360$	−2.63068	−0.138649
$361$	31.7386	1.67045
$362$	19.3693	1.01803
$363$	10.9309	0.573722
$364$	0	0
$365$	−18.4384	−0.965112
$366$	1.06913	0.0558843
$367$	18.4924	0.965297	0.482648	−	0.875814i	$-0.339675\pi$
$367$	18.4924	0.965297	0.482648	+	0.875814i	$0.339675\pi$
$368$	−2.00000	−0.104257
$369$	2.87689	0.149765
$370$	8.68466	0.451494
$371$	0	0
$372$	−9.36932	−0.485776
$373$	−12.6307	−0.653992	−0.326996	−	0.945026i	$-0.606036\pi$
$373$	−12.6307	−0.653992	−0.326996	+	0.945026i	$0.606036\pi$
$374$	−2.00000	−0.103418
$375$	18.4384	0.952157
$376$	−28.6847	−1.47930
$377$	−1.36932	−0.0705234
$378$	0	0
$379$	−9.12311	−0.468622	−0.234311	−	0.972162i	$-0.575283\pi$
$379$	−9.12311	−0.468622	−0.234311	+	0.972162i	$0.575283\pi$
$380$	−11.1231	−0.570603
$381$	−34.4384	−1.76434
$382$	−11.1231	−0.569108
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−4.68466	−0.239063
$385$	0	0
$386$	−2.00000	−0.101797
$387$	0.561553	0.0285453
$388$	−16.2462	−0.824776
$389$	2.49242	0.126371	0.0631854	−	0.998002i	$-0.479874\pi$
$389$	2.49242	0.126371	0.0631854	+	0.998002i	$0.479874\pi$
$390$	−1.06913	−0.0541375
$391$	−2.00000	−0.101144
$392$	−21.0000	−1.06066
$393$	−18.4384	−0.930097
$394$	−17.6155	−0.887457
$395$	−14.2462	−0.716805
$396$	−1.12311	−0.0564382
$397$	6.87689	0.345141	0.172571	−	0.984997i	$-0.444793\pi$
$397$	6.87689	0.345141	0.172571	+	0.984997i	$0.444793\pi$
$398$	2.93087	0.146911
$399$	0	0
$400$	2.56155	0.128078
$401$	−3.75379	−0.187455	−0.0937276	−	0.995598i	$-0.529878\pi$
$401$	−3.75379	−0.187455	−0.0937276	+	0.995598i	$0.529878\pi$
$402$	8.68466	0.433151
$403$	2.63068	0.131044
$404$	2.00000	0.0995037
$405$	−10.9309	−0.543159
$406$	0	0
$407$	11.1231	0.551352
$408$	4.68466	0.231925
$409$	−35.8617	−1.77325	−0.886624	−	0.462490i	$-0.846956\pi$
$409$	−35.8617	−1.77325	−0.886624	+	0.462490i	$0.846956\pi$
$410$	8.00000	0.395092
$411$	−19.1231	−0.943273
$412$	17.5616	0.865196
$413$	0	0
$414$	1.12311	0.0551976
$415$	24.6847	1.21172
$416$	2.19224	0.107483
$417$	30.2462	1.48116
$418$	14.2462	0.696805
$419$	−20.0000	−0.977064	−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000	−0.977064	−0.488532	+	0.872546i	$0.662467\pi$
$420$	0	0
$421$	12.7386	0.620843	0.310422	−	0.950599i	$-0.399530\pi$
$421$	12.7386	0.620843	0.310422	+	0.950599i	$0.399530\pi$
$422$	4.19224	0.204075
$423$	5.36932	0.261065
$424$	−32.0540	−1.55668
$425$	2.56155	0.124254
$426$	8.68466	0.420773
$427$	0	0
$428$	−2.00000	−0.0966736
$429$	−1.36932	−0.0661112
$430$	1.56155	0.0753048
$431$	−13.1231	−0.632118	−0.316059	−	0.948740i	$-0.602360\pi$
$431$	−13.1231	−0.632118	−0.316059	+	0.948740i	$0.602360\pi$
$432$	−5.56155	−0.267580
$433$	11.3693	0.546375	0.273187	−	0.961961i	$-0.411922\pi$
$433$	11.3693	0.546375	0.273187	+	0.961961i	$0.411922\pi$
$434$	0	0
$435$	−7.61553	−0.365137
$436$	4.24621	0.203357
$437$	14.2462	0.681489
$438$	−18.4384	−0.881023
$439$	15.3693	0.733537	0.366769	−	0.930312i	$-0.380464\pi$
$439$	15.3693	0.733537	0.366769	+	0.930312i	$0.380464\pi$
$440$	−9.36932	−0.446665
$441$	3.93087	0.187184
$442$	−0.438447	−0.0208548
$443$	−31.4233	−1.49297	−0.746483	−	0.665405i	$-0.768259\pi$
$443$	−31.4233	−1.49297	−0.746483	+	0.665405i	$0.768259\pi$
$444$	−8.68466	−0.412156
$445$	−0.384472	−0.0182257
$446$	16.0000	0.757622
$447$	12.8769	0.609056
$448$	0	0
$449$	−30.4384	−1.43648	−0.718240	−	0.695796i	$-0.755052\pi$
$449$	−30.4384	−1.43648	−0.718240	+	0.695796i	$0.755052\pi$
$450$	−1.43845	−0.0678091
$451$	10.2462	0.482475
$452$	11.8078	0.555391
$453$	−12.4924	−0.586945
$454$	−20.4924	−0.961757
$455$	0	0
$456$	−33.3693	−1.56266
$457$	−4.63068	−0.216614	−0.108307	−	0.994117i	$-0.534543\pi$
$457$	−4.63068	−0.216614	−0.108307	+	0.994117i	$0.534543\pi$
$458$	−5.80776	−0.271379
$459$	−5.56155	−0.259591
$460$	−3.12311	−0.145616
$461$	−17.8078	−0.829390	−0.414695	−	0.909960i	$-0.636112\pi$
$461$	−17.8078	−0.829390	−0.414695	+	0.909960i	$0.636112\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−3.12311	−0.144987
$465$	14.6307	0.678482
$466$	−19.1231	−0.885861
$467$	−32.4924	−1.50357	−0.751785	−	0.659408i	$-0.770807\pi$
$467$	−32.4924	−1.50357	−0.751785	+	0.659408i	$0.770807\pi$
$468$	−0.246211	−0.0113811
$469$	0	0
$470$	14.9309	0.688710
$471$	35.1231	1.61839
$472$	−35.4233	−1.63049
$473$	2.00000	0.0919601
$474$	−14.2462	−0.654350
$475$	−18.2462	−0.837194
$476$	0	0
$477$	6.00000	0.274721
$478$	8.00000	0.365911
$479$	31.3693	1.43330	0.716650	−	0.697433i	$-0.245674\pi$
$479$	31.3693	1.43330	0.716650	+	0.697433i	$0.245674\pi$
$480$	12.1922	0.556497
$481$	2.43845	0.111184
$482$	5.36932	0.244566
$483$	0	0
$484$	7.00000	0.318182
$485$	25.3693	1.15196
$486$	5.75379	0.260997
$487$	−26.4924	−1.20049	−0.600243	−	0.799818i	$-0.704930\pi$
$487$	−26.4924	−1.20049	−0.600243	+	0.799818i	$0.704930\pi$
$488$	2.05398	0.0929791
$489$	33.6695	1.52259
$490$	10.9309	0.493806
$491$	−5.36932	−0.242314	−0.121157	−	0.992633i	$-0.538660\pi$
$491$	−5.36932	−0.242314	−0.121157	+	0.992633i	$0.538660\pi$
$492$	−8.00000	−0.360668
$493$	−3.12311	−0.140658
$494$	3.12311	0.140515
$495$	1.75379	0.0788269
$496$	6.00000	0.269408
$497$	0	0
$498$	24.6847	1.10615
$499$	4.68466	0.209714	0.104857	−	0.994487i	$-0.466561\pi$
$499$	4.68466	0.209714	0.104857	+	0.994487i	$0.466561\pi$
$500$	11.8078	0.528059
$501$	−34.3542	−1.53483
$502$	6.43845	0.287362
$503$	39.4233	1.75780	0.878899	−	0.477008i	$-0.158279\pi$
$503$	39.4233	1.75780	0.878899	+	0.477008i	$0.158279\pi$
$504$	0	0
$505$	−3.12311	−0.138976
$506$	4.00000	0.177822
$507$	20.0000	0.888231
$508$	−22.0540	−0.978487
$509$	4.05398	0.179689	0.0898446	−	0.995956i	$-0.471363\pi$
$509$	4.05398	0.179689	0.0898446	+	0.995956i	$0.471363\pi$
$510$	−2.43845	−0.107976
$511$	0	0
$512$	11.0000	0.486136
$513$	39.6155	1.74907
$514$	−26.0000	−1.14681
$515$	−27.4233	−1.20841
$516$	−1.56155	−0.0687435
$517$	19.1231	0.841033
$518$	0	0
$519$	8.00000	0.351161
$520$	−2.05398	−0.0900728
$521$	−2.63068	−0.115252	−0.0576262	−	0.998338i	$-0.518353\pi$
$521$	−2.63068	−0.115252	−0.0576262	+	0.998338i	$0.518353\pi$
$522$	1.75379	0.0767612
$523$	39.1231	1.71073	0.855367	−	0.518023i	$-0.173332\pi$
$523$	39.1231	1.71073	0.855367	+	0.518023i	$0.173332\pi$
$524$	−11.8078	−0.515825
$525$	0	0
$526$	−12.4924	−0.544696
$527$	6.00000	0.261364
$528$	−3.12311	−0.135916
$529$	−19.0000	−0.826087
$530$	16.6847	0.724735
$531$	6.63068	0.287747
$532$	0	0
$533$	2.24621	0.0972942
$534$	−0.384472	−0.0166377
$535$	3.12311	0.135024
$536$	16.6847	0.720667
$537$	−13.8617	−0.598178
$538$	−8.24621	−0.355519
$539$	14.0000	0.603023
$540$	−8.68466	−0.373728
$541$	21.6155	0.929324	0.464662	−	0.885488i	$-0.346176\pi$
$541$	21.6155	0.929324	0.464662	+	0.885488i	$0.346176\pi$
$542$	18.9309	0.813150
$543$	30.2462	1.29799
$544$	5.00000	0.214373
$545$	−6.63068	−0.284027
$546$	0	0
$547$	34.4924	1.47479	0.737395	−	0.675462i	$-0.236056\pi$
$547$	34.4924	1.47479	0.737395	+	0.675462i	$0.236056\pi$
$548$	−12.2462	−0.523132
$549$	−0.384472	−0.0164089
$550$	−5.12311	−0.218450
$551$	22.2462	0.947720
$552$	−9.36932	−0.398785
$553$	0	0
$554$	−30.9309	−1.31413
$555$	13.5616	0.575656
$556$	19.3693	0.821442
$557$	19.1771	0.812559	0.406279	−	0.913749i	$-0.366826\pi$
$557$	19.1771	0.812559	0.406279	+	0.913749i	$0.366826\pi$
$558$	−3.36932	−0.142635
$559$	0.438447	0.0185443
$560$	0	0
$561$	−3.12311	−0.131858
$562$	20.9309	0.882915
$563$	−1.75379	−0.0739134	−0.0369567	−	0.999317i	$-0.511766\pi$
$563$	−1.75379	−0.0739134	−0.0369567	+	0.999317i	$0.511766\pi$
$564$	−14.9309	−0.628703
$565$	−18.4384	−0.775711
$566$	−12.2462	−0.514747
$567$	0	0
$568$	16.6847	0.700073
$569$	3.56155	0.149308	0.0746540	−	0.997209i	$-0.476215\pi$
$569$	3.56155	0.149308	0.0746540	+	0.997209i	$0.476215\pi$
$570$	17.3693	0.727521
$571$	−30.2462	−1.26576	−0.632882	−	0.774248i	$-0.718128\pi$
$571$	−30.2462	−1.26576	−0.632882	+	0.774248i	$0.718128\pi$
$572$	−0.876894	−0.0366648
$573$	−17.3693	−0.725614
$574$	0	0
$575$	−5.12311	−0.213648
$576$	−3.93087	−0.163786
$577$	−4.73863	−0.197272	−0.0986360	−	0.995124i	$-0.531448\pi$
$577$	−4.73863	−0.197272	−0.0986360	+	0.995124i	$0.531448\pi$
$578$	−1.00000	−0.0415945
$579$	−3.12311	−0.129792
$580$	−4.87689	−0.202502
$581$	0	0
$582$	25.3693	1.05159
$583$	21.3693	0.885027
$584$	−35.4233	−1.46583
$585$	0.384472	0.0158960
$586$	0.246211	0.0101709
$587$	−2.63068	−0.108580	−0.0542900	−	0.998525i	$-0.517290\pi$
$587$	−2.63068	−0.108580	−0.0542900	+	0.998525i	$0.517290\pi$
$588$	−10.9309	−0.450781
$589$	−42.7386	−1.76101
$590$	18.4384	0.759099
$591$	−27.5076	−1.13151
$592$	5.56155	0.228578
$593$	12.2462	0.502892	0.251446	−	0.967871i	$-0.419094\pi$
$593$	12.2462	0.502892	0.251446	+	0.967871i	$0.419094\pi$
$594$	11.1231	0.456387
$595$	0	0
$596$	8.24621	0.337778
$597$	4.57671	0.187312
$598$	0.876894	0.0358589
$599$	24.6847	1.00859	0.504294	−	0.863532i	$-0.331753\pi$
$599$	24.6847	1.00859	0.504294	+	0.863532i	$0.331753\pi$
$600$	12.0000	0.489898
$601$	2.43845	0.0994663	0.0497332	−	0.998763i	$-0.484163\pi$
$601$	2.43845	0.0994663	0.0497332	+	0.998763i	$0.484163\pi$
$602$	0	0
$603$	−3.12311	−0.127183
$604$	−8.00000	−0.325515
$605$	−10.9309	−0.444403
$606$	−3.12311	−0.126867
$607$	19.3153	0.783986	0.391993	−	0.919968i	$-0.371786\pi$
$607$	19.3153	0.783986	0.391993	+	0.919968i	$0.371786\pi$
$608$	−35.6155	−1.44440
$609$	0	0
$610$	−1.06913	−0.0432878
$611$	4.19224	0.169600
$612$	−0.561553	−0.0226994
$613$	−1.50758	−0.0608905	−0.0304452	−	0.999536i	$-0.509693\pi$
$613$	−1.50758	−0.0608905	−0.0304452	+	0.999536i	$0.509693\pi$
$614$	14.2462	0.574930
$615$	12.4924	0.503743
$616$	0	0
$617$	40.2462	1.62025	0.810126	−	0.586256i	$-0.199399\pi$
$617$	40.2462	1.62025	0.810126	+	0.586256i	$0.199399\pi$
$618$	−27.4233	−1.10313
$619$	48.7386	1.95897	0.979486	−	0.201514i	$-0.0645863\pi$
$619$	48.7386	1.95897	0.979486	+	0.201514i	$0.0645863\pi$
$620$	9.36932	0.376281
$621$	11.1231	0.446355
$622$	−15.3693	−0.616253
$623$	0	0
$624$	−0.684658	−0.0274083
$625$	−5.63068	−0.225227
$626$	−15.8078	−0.631805
$627$	22.2462	0.888428
$628$	22.4924	0.897545
$629$	5.56155	0.221754
$630$	0	0
$631$	−0.384472	−0.0153056	−0.00765279	−	0.999971i	$-0.502436\pi$
$631$	−0.384472	−0.0153056	−0.00765279	+	0.999971i	$0.502436\pi$
$632$	−27.3693	−1.08869
$633$	6.54640	0.260196
$634$	19.3693	0.769254
$635$	34.4384	1.36665
$636$	−16.6847	−0.661590
$637$	3.06913	0.121603
$638$	6.24621	0.247290
$639$	−3.12311	−0.123548
$640$	4.68466	0.185177
$641$	−15.4233	−0.609183	−0.304592	−	0.952483i	$-0.598520\pi$
$641$	−15.4233	−0.609183	−0.304592	+	0.952483i	$0.598520\pi$
$642$	3.12311	0.123259
$643$	44.2462	1.74490	0.872450	−	0.488703i	$-0.162530\pi$
$643$	44.2462	1.74490	0.872450	+	0.488703i	$0.162530\pi$
$644$	0	0
$645$	2.43845	0.0960138
$646$	7.12311	0.280255
$647$	−36.1080	−1.41955	−0.709775	−	0.704428i	$-0.751203\pi$
$647$	−36.1080	−1.41955	−0.709775	+	0.704428i	$0.751203\pi$
$648$	−21.0000	−0.824958
$649$	23.6155	0.926991
$650$	−1.12311	−0.0440518
$651$	0	0
$652$	21.5616	0.844416
$653$	−11.1231	−0.435281	−0.217640	−	0.976029i	$-0.569836\pi$
$653$	−11.1231	−0.435281	−0.217640	+	0.976029i	$0.569836\pi$
$654$	−6.63068	−0.259280
$655$	18.4384	0.720450
$656$	5.12311	0.200024
$657$	6.63068	0.258688
$658$	0	0
$659$	−46.2462	−1.80150	−0.900748	−	0.434341i	$-0.856981\pi$
$659$	−46.2462	−1.80150	−0.900748	+	0.434341i	$0.856981\pi$
$660$	−4.87689	−0.189833
$661$	−40.4384	−1.57287	−0.786437	−	0.617671i	$-0.788076\pi$
$661$	−40.4384	−1.57287	−0.786437	+	0.617671i	$0.788076\pi$
$662$	−12.0000	−0.466393
$663$	−0.684658	−0.0265899
$664$	47.4233	1.84038
$665$	0	0
$666$	−3.12311	−0.121018
$667$	6.24621	0.241854
$668$	−22.0000	−0.851206
$669$	24.9848	0.965970
$670$	−8.68466	−0.335518
$671$	−1.36932	−0.0528619
$672$	0	0
$673$	28.1922	1.08673	0.543365	−	0.839496i	$-0.317150\pi$
$673$	28.1922	1.08673	0.543365	+	0.839496i	$0.317150\pi$
$674$	3.75379	0.144591
$675$	−14.2462	−0.548337
$676$	12.8078	0.492606
$677$	−0.384472	−0.0147765	−0.00738823	−	0.999973i	$-0.502352\pi$
$677$	−0.384472	−0.0147765	−0.00738823	+	0.999973i	$0.502352\pi$
$678$	−18.4384	−0.708124
$679$	0	0
$680$	−4.68466	−0.179648
$681$	−32.0000	−1.22624
$682$	−12.0000	−0.459504
$683$	43.3693	1.65948	0.829740	−	0.558150i	$-0.188488\pi$
$683$	43.3693	1.65948	0.829740	+	0.558150i	$0.188488\pi$
$684$	4.00000	0.152944
$685$	19.1231	0.730656
$686$	0	0
$687$	−9.06913	−0.346009
$688$	1.00000	0.0381246
$689$	4.68466	0.178471
$690$	4.87689	0.185660
$691$	−0.492423	−0.0187326	−0.00936632	−	0.999956i	$-0.502981\pi$
$691$	−0.492423	−0.0187326	−0.00936632	+	0.999956i	$0.502981\pi$
$692$	5.12311	0.194751
$693$	0	0
$694$	18.4384	0.699914
$695$	−30.2462	−1.14730
$696$	−14.6307	−0.554575
$697$	5.12311	0.194051
$698$	10.8769	0.411697
$699$	−29.8617	−1.12947
$700$	0	0
$701$	28.0540	1.05958	0.529792	−	0.848128i	$-0.322270\pi$
$701$	28.0540	1.05958	0.529792	+	0.848128i	$0.322270\pi$
$702$	2.43845	0.0920333
$703$	−39.6155	−1.49413
$704$	−14.0000	−0.527645
$705$	23.3153	0.878107
$706$	19.1771	0.721739
$707$	0	0
$708$	−18.4384	−0.692959
$709$	5.50758	0.206841	0.103421	−	0.994638i	$-0.467021\pi$
$709$	5.50758	0.206841	0.103421	+	0.994638i	$0.467021\pi$
$710$	−8.68466	−0.325929
$711$	5.12311	0.192131
$712$	−0.738634	−0.0276815
$713$	−12.0000	−0.449404
$714$	0	0
$715$	1.36932	0.0512095
$716$	−8.87689	−0.331745
$717$	12.4924	0.466538
$718$	3.80776	0.142104
$719$	−6.00000	−0.223762	−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000	−0.223762	−0.111881	+	0.993722i	$0.535688\pi$
$720$	0.876894	0.0326799
$721$	0	0
$722$	−31.7386	−1.18119
$723$	8.38447	0.311822
$724$	19.3693	0.719855
$725$	−8.00000	−0.297113
$726$	−10.9309	−0.405683
$727$	−50.7386	−1.88179	−0.940896	−	0.338696i	$-0.890014\pi$
$727$	−50.7386	−1.88179	−0.940896	+	0.338696i	$0.890014\pi$
$728$	0	0
$729$	29.9848	1.11055
$730$	18.4384	0.682438
$731$	1.00000	0.0369863
$732$	1.06913	0.0395162
$733$	8.24621	0.304581	0.152290	−	0.988336i	$-0.451335\pi$
$733$	8.24621	0.304581	0.152290	+	0.988336i	$0.451335\pi$
$734$	−18.4924	−0.682568
$735$	17.0691	0.629604
$736$	−10.0000	−0.368605
$737$	−11.1231	−0.409725
$738$	−2.87689	−0.105900
$739$	−40.1080	−1.47539	−0.737697	−	0.675131i	$-0.764087\pi$
$739$	−40.1080	−1.47539	−0.737697	+	0.675131i	$0.764087\pi$
$740$	8.68466	0.319254
$741$	4.87689	0.179157
$742$	0	0
$743$	34.5464	1.26738	0.633692	−	0.773585i	$-0.281539\pi$
$743$	34.5464	1.26738	0.633692	+	0.773585i	$0.281539\pi$
$744$	28.1080	1.03049
$745$	−12.8769	−0.471773
$746$	12.6307	0.462442
$747$	−8.87689	−0.324789
$748$	−2.00000	−0.0731272
$749$	0	0
$750$	−18.4384	−0.673277
$751$	−30.0540	−1.09669	−0.548343	−	0.836254i	$-0.684741\pi$
$751$	−30.0540	−1.09669	−0.548343	+	0.836254i	$0.684741\pi$
$752$	9.56155	0.348674
$753$	10.0540	0.366387
$754$	1.36932	0.0498676
$755$	12.4924	0.454646
$756$	0	0
$757$	26.4924	0.962883	0.481442	−	0.876478i	$-0.340113\pi$
$757$	26.4924	0.962883	0.481442	+	0.876478i	$0.340113\pi$
$758$	9.12311	0.331366
$759$	6.24621	0.226723
$760$	33.3693	1.21043
$761$	54.6004	1.97926	0.989631	−	0.143633i	$-0.0458786\pi$
$761$	54.6004	1.97926	0.989631	+	0.143633i	$0.0458786\pi$
$762$	34.4384	1.24757
$763$	0	0
$764$	−11.1231	−0.402420
$765$	0.876894	0.0317042
$766$	0	0
$767$	5.17708	0.186934
$768$	26.5464	0.957911
$769$	24.5464	0.885166	0.442583	−	0.896728i	$-0.354062\pi$
$769$	24.5464	0.885166	0.442583	+	0.896728i	$0.354062\pi$
$770$	0	0
$771$	−40.6004	−1.46219
$772$	−2.00000	−0.0719816
$773$	−22.4924	−0.808996	−0.404498	−	0.914539i	$-0.632554\pi$
$773$	−22.4924	−0.808996	−0.404498	+	0.914539i	$0.632554\pi$
$774$	−0.561553	−0.0201846
$775$	15.3693	0.552082
$776$	48.7386	1.74961
$777$	0	0
$778$	−2.49242	−0.0893577
$779$	−36.4924	−1.30748
$780$	−1.06913	−0.0382810
$781$	−11.1231	−0.398016
$782$	2.00000	0.0715199
$783$	17.3693	0.620729
$784$	7.00000	0.250000
$785$	−35.1231	−1.25360
$786$	18.4384	0.657678
$787$	−34.9848	−1.24708	−0.623538	−	0.781793i	$-0.714305\pi$
$787$	−34.9848	−1.24708	−0.623538	+	0.781793i	$0.714305\pi$
$788$	−17.6155	−0.627527
$789$	−19.5076	−0.694488
$790$	14.2462	0.506857
$791$	0	0
$792$	3.36932	0.119723
$793$	−0.300187	−0.0106599
$794$	−6.87689	−0.244052
$795$	26.0540	0.924039
$796$	2.93087	0.103882
$797$	12.9309	0.458035	0.229017	−	0.973422i	$-0.426449\pi$
$797$	12.9309	0.458035	0.229017	+	0.973422i	$0.426449\pi$
$798$	0	0
$799$	9.56155	0.338263
$800$	12.8078	0.452823
$801$	0.138261	0.00488520
$802$	3.75379	0.132551
$803$	23.6155	0.833374
$804$	8.68466	0.306284
$805$	0	0
$806$	−2.63068	−0.0926619
$807$	−12.8769	−0.453288
$808$	−6.00000	−0.211079
$809$	39.3693	1.38415	0.692076	−	0.721825i	$-0.256696\pi$
$809$	39.3693	1.38415	0.692076	+	0.721825i	$0.256696\pi$
$810$	10.9309	0.384072
$811$	−7.50758	−0.263627	−0.131813	−	0.991275i	$-0.542080\pi$
$811$	−7.50758	−0.263627	−0.131813	+	0.991275i	$0.542080\pi$
$812$	0	0
$813$	29.5616	1.03677
$814$	−11.1231	−0.389865
$815$	−33.6695	−1.17939
$816$	−1.56155	−0.0546653
$817$	−7.12311	−0.249206
$818$	35.8617	1.25388
$819$	0	0
$820$	8.00000	0.279372
$821$	−16.2462	−0.566997	−0.283498	−	0.958973i	$-0.591495\pi$
$821$	−16.2462	−0.566997	−0.283498	+	0.958973i	$0.591495\pi$
$822$	19.1231	0.666995
$823$	9.50758	0.331413	0.165707	−	0.986175i	$-0.447010\pi$
$823$	9.50758	0.331413	0.165707	+	0.986175i	$0.447010\pi$
$824$	−52.6847	−1.83536
$825$	−8.00000	−0.278524
$826$	0	0
$827$	−28.7386	−0.999340	−0.499670	−	0.866216i	$-0.666545\pi$
$827$	−28.7386	−0.999340	−0.499670	+	0.866216i	$0.666545\pi$
$828$	1.12311	0.0390306
$829$	41.1231	1.42826	0.714132	−	0.700011i	$-0.246822\pi$
$829$	41.1231	1.42826	0.714132	+	0.700011i	$0.246822\pi$
$830$	−24.6847	−0.856817
$831$	−48.3002	−1.67551
$832$	−3.06913	−0.106403
$833$	7.00000	0.242536
$834$	−30.2462	−1.04734
$835$	34.3542	1.18887
$836$	14.2462	0.492716
$837$	−33.3693	−1.15341
$838$	20.0000	0.690889
$839$	19.8078	0.683840	0.341920	−	0.939729i	$-0.388923\pi$
$839$	19.8078	0.683840	0.341920	+	0.939729i	$0.388923\pi$
$840$	0	0
$841$	−19.2462	−0.663662
$842$	−12.7386	−0.439002
$843$	32.6847	1.12572
$844$	4.19224	0.144303
$845$	−20.0000	−0.688021
$846$	−5.36932	−0.184601
$847$	0	0
$848$	10.6847	0.366913
$849$	−19.1231	−0.656303
$850$	−2.56155	−0.0878605
$851$	−11.1231	−0.381295
$852$	8.68466	0.297531
$853$	−54.9848	−1.88265	−0.941323	−	0.337508i	$-0.890416\pi$
$853$	−54.9848	−1.88265	−0.941323	+	0.337508i	$0.890416\pi$
$854$	0	0
$855$	−6.24621	−0.213616
$856$	6.00000	0.205076
$857$	37.1231	1.26810	0.634051	−	0.773292i	$-0.281391\pi$
$857$	37.1231	1.26810	0.634051	+	0.773292i	$0.281391\pi$
$858$	1.36932	0.0467477
$859$	2.63068	0.0897577	0.0448789	−	0.998992i	$-0.485710\pi$
$859$	2.63068	0.0897577	0.0448789	+	0.998992i	$0.485710\pi$
$860$	1.56155	0.0532485
$861$	0	0
$862$	13.1231	0.446975
$863$	−12.4924	−0.425247	−0.212624	−	0.977134i	$-0.568201\pi$
$863$	−12.4924	−0.425247	−0.212624	+	0.977134i	$0.568201\pi$
$864$	−27.8078	−0.946039
$865$	−8.00000	−0.272008
$866$	−11.3693	−0.386345
$867$	−1.56155	−0.0530331
$868$	0	0
$869$	18.2462	0.618960
$870$	7.61553	0.258191
$871$	−2.43845	−0.0826236
$872$	−12.7386	−0.431385
$873$	−9.12311	−0.308770
$874$	−14.2462	−0.481885
$875$	0	0
$876$	−18.4384	−0.622977
$877$	−21.1231	−0.713277	−0.356638	−	0.934243i	$-0.616077\pi$
$877$	−21.1231	−0.713277	−0.356638	+	0.934243i	$0.616077\pi$
$878$	−15.3693	−0.518689
$879$	0.384472	0.0129679
$880$	3.12311	0.105280
$881$	−26.0000	−0.875962	−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000	−0.875962	−0.437981	+	0.898984i	$0.644306\pi$
$882$	−3.93087	−0.132359
$883$	−51.9157	−1.74710	−0.873551	−	0.486732i	$-0.838189\pi$
$883$	−51.9157	−1.74710	−0.873551	+	0.486732i	$0.838189\pi$
$884$	−0.438447	−0.0147466
$885$	28.7926	0.967853
$886$	31.4233	1.05569
$887$	38.2462	1.28418	0.642091	−	0.766628i	$-0.278067\pi$
$887$	38.2462	1.28418	0.642091	+	0.766628i	$0.278067\pi$
$888$	26.0540	0.874314
$889$	0	0
$890$	0.384472	0.0128875
$891$	14.0000	0.469018
$892$	16.0000	0.535720
$893$	−68.1080	−2.27915
$894$	−12.8769	−0.430668
$895$	13.8617	0.463347
$896$	0	0
$897$	1.36932	0.0457202
$898$	30.4384	1.01574
$899$	−18.7386	−0.624968
$900$	−1.43845	−0.0479482
$901$	10.6847	0.355958
$902$	−10.2462	−0.341162
$903$	0	0
$904$	−35.4233	−1.17816
$905$	−30.2462	−1.00542
$906$	12.4924	0.415033
$907$	22.0000	0.730498	0.365249	−	0.930910i	$-0.380984\pi$
$907$	22.0000	0.730498	0.365249	+	0.930910i	$0.380984\pi$
$908$	−20.4924	−0.680065
$909$	1.12311	0.0372511
$910$	0	0
$911$	31.8078	1.05384	0.526919	−	0.849915i	$-0.323347\pi$
$911$	31.8078	1.05384	0.526919	+	0.849915i	$0.323347\pi$
$912$	11.1231	0.368323
$913$	−31.6155	−1.04632
$914$	4.63068	0.153169
$915$	−1.66950	−0.0551921
$916$	−5.80776	−0.191894
$917$	0	0
$918$	5.56155	0.183559
$919$	−11.8078	−0.389502	−0.194751	−	0.980853i	$-0.562390\pi$
$919$	−11.8078	−0.389502	−0.194751	+	0.980853i	$0.562390\pi$
$920$	9.36932	0.308897
$921$	22.2462	0.733038
$922$	17.8078	0.586467
$923$	−2.43845	−0.0802625
$924$	0	0
$925$	14.2462	0.468413
$926$	8.00000	0.262896
$927$	9.86174	0.323902
$928$	−15.6155	−0.512605
$929$	−25.8617	−0.848496	−0.424248	−	0.905546i	$-0.639462\pi$
$929$	−25.8617	−0.848496	−0.424248	+	0.905546i	$0.639462\pi$
$930$	−14.6307	−0.479759
$931$	−49.8617	−1.63415
$932$	−19.1231	−0.626398
$933$	−24.0000	−0.785725
$934$	32.4924	1.06318
$935$	3.12311	0.102136
$936$	0.738634	0.0241430
$937$	34.1080	1.11426	0.557129	−	0.830426i	$-0.311903\pi$
$937$	34.1080	1.11426	0.557129	+	0.830426i	$0.311903\pi$
$938$	0	0
$939$	−24.6847	−0.805553
$940$	14.9309	0.486991
$941$	28.6307	0.933334	0.466667	−	0.884433i	$-0.345455\pi$
$941$	28.6307	0.933334	0.466667	+	0.884433i	$0.345455\pi$
$942$	−35.1231	−1.14437
$943$	−10.2462	−0.333663
$944$	11.8078	0.384310
$945$	0	0
$946$	−2.00000	−0.0650256
$947$	0.246211	0.00800079	0.00400040	−	0.999992i	$-0.498727\pi$
$947$	0.246211	0.00800079	0.00400040	+	0.999992i	$0.498727\pi$
$948$	−14.2462	−0.462695
$949$	5.17708	0.168055
$950$	18.2462	0.591985
$951$	30.2462	0.980801
$952$	0	0
$953$	−29.1231	−0.943390	−0.471695	−	0.881762i	$-0.656358\pi$
$953$	−29.1231	−0.943390	−0.471695	+	0.881762i	$0.656358\pi$
$954$	−6.00000	−0.194257
$955$	17.3693	0.562058
$956$	8.00000	0.258738
$957$	9.75379	0.315295
$958$	−31.3693	−1.01350
$959$	0	0
$960$	−17.0691	−0.550904
$961$	5.00000	0.161290
$962$	−2.43845	−0.0786187
$963$	−1.12311	−0.0361916
$964$	5.36932	0.172934
$965$	3.12311	0.100536
$966$	0	0
$967$	−24.9848	−0.803458	−0.401729	−	0.915758i	$-0.631591\pi$
$967$	−24.9848	−0.803458	−0.401729	+	0.915758i	$0.631591\pi$
$968$	−21.0000	−0.674966
$969$	11.1231	0.357326
$970$	−25.3693	−0.814560
$971$	17.1771	0.551239	0.275619	−	0.961267i	$-0.411117\pi$
$971$	17.1771	0.551239	0.275619	+	0.961267i	$0.411117\pi$
$972$	5.75379	0.184553
$973$	0	0
$974$	26.4924	0.848872
$975$	−1.75379	−0.0561662
$976$	−0.684658	−0.0219154
$977$	23.7538	0.759951	0.379976	−	0.924997i	$-0.375932\pi$
$977$	23.7538	0.759951	0.379976	+	0.924997i	$0.375932\pi$
$978$	−33.6695	−1.07663
$979$	0.492423	0.0157379
$980$	10.9309	0.349174
$981$	2.38447	0.0761303
$982$	5.36932	0.171342
$983$	−42.5464	−1.35702	−0.678510	−	0.734591i	$-0.737374\pi$
$983$	−42.5464	−1.35702	−0.678510	+	0.734591i	$0.737374\pi$
$984$	24.0000	0.765092
$985$	27.5076	0.876464
$986$	3.12311	0.0994599
$987$	0	0
$988$	3.12311	0.0993592
$989$	−2.00000	−0.0635963
$990$	−1.75379	−0.0557391
$991$	−55.9157	−1.77622	−0.888111	−	0.459630i	$-0.847982\pi$
$991$	−55.9157	−1.77622	−0.888111	+	0.459630i	$0.847982\pi$
$992$	30.0000	0.952501
$993$	−18.7386	−0.594653
$994$	0	0
$995$	−4.57671	−0.145091
$996$	24.6847	0.782163
$997$	−0.876894	−0.0277715	−0.0138858	−	0.999904i	$-0.504420\pi$
$997$	−0.876894	−0.0277715	−0.0138858	+	0.999904i	$0.504420\pi$
$998$	−4.68466	−0.148290
$999$	−30.9309	−0.978609

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.b.1.1	✓	2
3.2	odd	2		6579.2.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.b.1.1	✓	2	1.1	even	1	trivial
6579.2.a.f.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.56155 q^{3} -1.00000 q^{4} +1.56155 q^{5} +1.56155 q^{6} +3.00000 q^{8} -0.561553 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.56155 q^{3} -1.00000 q^{4} +1.56155 q^{5} +1.56155 q^{6} +3.00000 q^{8} -0.561553 q^{9} -1.56155 q^{10} -2.00000 q^{11} +1.56155 q^{12} -0.438447 q^{13} -2.43845 q^{15} -1.00000 q^{16} -1.00000 q^{17} +0.561553 q^{18} +7.12311 q^{19} -1.56155 q^{20} +2.00000 q^{22} +2.00000 q^{23} -4.68466 q^{24} -2.56155 q^{25} +0.438447 q^{26} +5.56155 q^{27} +3.12311 q^{29} +2.43845 q^{30} -6.00000 q^{31} -5.00000 q^{32} +3.12311 q^{33} +1.00000 q^{34} +0.561553 q^{36} -5.56155 q^{37} -7.12311 q^{38} +0.684658 q^{39} +4.68466 q^{40} -5.12311 q^{41} -1.00000 q^{43} +2.00000 q^{44} -0.876894 q^{45} -2.00000 q^{46} -9.56155 q^{47} +1.56155 q^{48} -7.00000 q^{49} +2.56155 q^{50} +1.56155 q^{51} +0.438447 q^{52} -10.6847 q^{53} -5.56155 q^{54} -3.12311 q^{55} -11.1231 q^{57} -3.12311 q^{58} -11.8078 q^{59} +2.43845 q^{60} +0.684658 q^{61} +6.00000 q^{62} +7.00000 q^{64} -0.684658 q^{65} -3.12311 q^{66} +5.56155 q^{67} +1.00000 q^{68} -3.12311 q^{69} +5.56155 q^{71} -1.68466 q^{72} -11.8078 q^{73} +5.56155 q^{74} +4.00000 q^{75} -7.12311 q^{76} -0.684658 q^{78} -9.12311 q^{79} -1.56155 q^{80} -7.00000 q^{81} +5.12311 q^{82} +15.8078 q^{83} -1.56155 q^{85} +1.00000 q^{86} -4.87689 q^{87} -6.00000 q^{88} -0.246211 q^{89} +0.876894 q^{90} -2.00000 q^{92} +9.36932 q^{93} +9.56155 q^{94} +11.1231 q^{95} +7.80776 q^{96} +16.2462 q^{97} +7.00000 q^{98} +1.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 - 2 * q^4 - q^5 - q^6 + 6 * q^8 + 3 * q^9	\( 2 q - 2 q^{2} + q^{3} - 2 q^{4} - q^{5} - q^{6} + 6 q^{8} + 3 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} - 9 q^{15} - 2 q^{16} - 2 q^{17} - 3 q^{18} + 6 q^{19} + q^{20} + 4 q^{22} + 4 q^{23} + 3 q^{24} - q^{25} + 5 q^{26} + 7 q^{27} - 2 q^{29} + 9 q^{30} - 12 q^{31} - 10 q^{32} - 2 q^{33} + 2 q^{34} - 3 q^{36} - 7 q^{37} - 6 q^{38} - 11 q^{39} - 3 q^{40} - 2 q^{41} - 2 q^{43} + 4 q^{44} - 10 q^{45} - 4 q^{46} - 15 q^{47} - q^{48} - 14 q^{49} + q^{50} - q^{51} + 5 q^{52} - 9 q^{53} - 7 q^{54} + 2 q^{55} - 14 q^{57} + 2 q^{58} - 3 q^{59} + 9 q^{60} - 11 q^{61} + 12 q^{62} + 14 q^{64} + 11 q^{65} + 2 q^{66} + 7 q^{67} + 2 q^{68} + 2 q^{69} + 7 q^{71} + 9 q^{72} - 3 q^{73} + 7 q^{74} + 8 q^{75} - 6 q^{76} + 11 q^{78} - 10 q^{79} + q^{80} - 14 q^{81} + 2 q^{82} + 11 q^{83} + q^{85} + 2 q^{86} - 18 q^{87} - 12 q^{88} + 16 q^{89} + 10 q^{90} - 4 q^{92} - 6 q^{93} + 15 q^{94} + 14 q^{95} - 5 q^{96} + 16 q^{97} + 14 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 - 2 * q^4 - q^5 - q^6 + 6 * q^8 + 3 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 - 9 * q^15 - 2 * q^16 - 2 * q^17 - 3 * q^18 + 6 * q^19 + q^20 + 4 * q^22 + 4 * q^23 + 3 * q^24 - q^25 + 5 * q^26 + 7 * q^27 - 2 * q^29 + 9 * q^30 - 12 * q^31 - 10 * q^32 - 2 * q^33 + 2 * q^34 - 3 * q^36 - 7 * q^37 - 6 * q^38 - 11 * q^39 - 3 * q^40 - 2 * q^41 - 2 * q^43 + 4 * q^44 - 10 * q^45 - 4 * q^46 - 15 * q^47 - q^48 - 14 * q^49 + q^50 - q^51 + 5 * q^52 - 9 * q^53 - 7 * q^54 + 2 * q^55 - 14 * q^57 + 2 * q^58 - 3 * q^59 + 9 * q^60 - 11 * q^61 + 12 * q^62 + 14 * q^64 + 11 * q^65 + 2 * q^66 + 7 * q^67 + 2 * q^68 + 2 * q^69 + 7 * q^71 + 9 * q^72 - 3 * q^73 + 7 * q^74 + 8 * q^75 - 6 * q^76 + 11 * q^78 - 10 * q^79 + q^80 - 14 * q^81 + 2 * q^82 + 11 * q^83 + q^85 + 2 * q^86 - 18 * q^87 - 12 * q^88 + 16 * q^89 + 10 * q^90 - 4 * q^92 - 6 * q^93 + 15 * q^94 + 14 * q^95 - 5 * q^96 + 16 * q^97 + 14 * q^98 - 6 * q^99

Introduction

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