LMFDB - Embedded newform 2166.2.a.k.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,2,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, 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("2166.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2166.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:	$17.2955970778$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.618034 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.618034 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -0.618034 q^{10} -4.00000 q^{11} +1.00000 q^{12} +1.61803 q^{13} +0.618034 q^{15} +1.00000 q^{16} -4.09017 q^{17} -1.00000 q^{18} +0.618034 q^{20} +4.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} -4.61803 q^{25} -1.61803 q^{26} +1.00000 q^{27} -8.85410 q^{29} -0.618034 q^{30} +1.52786 q^{31} -1.00000 q^{32} -4.00000 q^{33} +4.09017 q^{34} +1.00000 q^{36} +5.85410 q^{37} +1.61803 q^{39} -0.618034 q^{40} +5.85410 q^{41} -10.4721 q^{43} -4.00000 q^{44} +0.618034 q^{45} +4.00000 q^{46} +4.94427 q^{47} +1.00000 q^{48} -7.00000 q^{49} +4.61803 q^{50} -4.09017 q^{51} +1.61803 q^{52} -8.61803 q^{53} -1.00000 q^{54} -2.47214 q^{55} +8.85410 q^{58} +2.47214 q^{59} +0.618034 q^{60} -9.61803 q^{61} -1.52786 q^{62} +1.00000 q^{64} +1.00000 q^{65} +4.00000 q^{66} -11.4164 q^{67} -4.09017 q^{68} -4.00000 q^{69} +6.47214 q^{71} -1.00000 q^{72} +16.0344 q^{73} -5.85410 q^{74} -4.61803 q^{75} -1.61803 q^{78} +4.00000 q^{79} +0.618034 q^{80} +1.00000 q^{81} -5.85410 q^{82} -8.00000 q^{83} -2.52786 q^{85} +10.4721 q^{86} -8.85410 q^{87} +4.00000 q^{88} -12.6180 q^{89} -0.618034 q^{90} -4.00000 q^{92} +1.52786 q^{93} -4.94427 q^{94} -1.00000 q^{96} -9.79837 q^{97} +7.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} - 8 q^{11} + 2 q^{12} + q^{13} - q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - q^{20} + 8 q^{22} - 8 q^{23} - 2 q^{24} - 7 q^{25} - q^{26} + 2 q^{27} - 11 q^{29} + q^{30} + 12 q^{31} - 2 q^{32} - 8 q^{33} - 3 q^{34} + 2 q^{36} + 5 q^{37} + q^{39} + q^{40} + 5 q^{41} - 12 q^{43} - 8 q^{44} - q^{45} + 8 q^{46} - 8 q^{47} + 2 q^{48} - 14 q^{49} + 7 q^{50} + 3 q^{51} + q^{52} - 15 q^{53} - 2 q^{54} + 4 q^{55} + 11 q^{58} - 4 q^{59} - q^{60} - 17 q^{61} - 12 q^{62} + 2 q^{64} + 2 q^{65} + 8 q^{66} + 4 q^{67} + 3 q^{68} - 8 q^{69} + 4 q^{71} - 2 q^{72} + 3 q^{73} - 5 q^{74} - 7 q^{75} - q^{78} + 8 q^{79} - q^{80} + 2 q^{81} - 5 q^{82} - 16 q^{83} - 14 q^{85} + 12 q^{86} - 11 q^{87} + 8 q^{88} - 23 q^{89} + q^{90} - 8 q^{92} + 12 q^{93} + 8 q^{94} - 2 q^{96} + 5 q^{97} + 14 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 - 8 * q^11 + 2 * q^12 + q^13 - q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - q^20 + 8 * q^22 - 8 * q^23 - 2 * q^24 - 7 * q^25 - q^26 + 2 * q^27 - 11 * q^29 + q^30 + 12 * q^31 - 2 * q^32 - 8 * q^33 - 3 * q^34 + 2 * q^36 + 5 * q^37 + q^39 + q^40 + 5 * q^41 - 12 * q^43 - 8 * q^44 - q^45 + 8 * q^46 - 8 * q^47 + 2 * q^48 - 14 * q^49 + 7 * q^50 + 3 * q^51 + q^52 - 15 * q^53 - 2 * q^54 + 4 * q^55 + 11 * q^58 - 4 * q^59 - q^60 - 17 * q^61 - 12 * q^62 + 2 * q^64 + 2 * q^65 + 8 * q^66 + 4 * q^67 + 3 * q^68 - 8 * q^69 + 4 * q^71 - 2 * q^72 + 3 * q^73 - 5 * q^74 - 7 * q^75 - q^78 + 8 * q^79 - q^80 + 2 * q^81 - 5 * q^82 - 16 * q^83 - 14 * q^85 + 12 * q^86 - 11 * q^87 + 8 * q^88 - 23 * q^89 + q^90 - 8 * q^92 + 12 * q^93 + 8 * q^94 - 2 * q^96 + 5 * q^97 + 14 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.618034	0.276393	0.138197	−	0.990405i	$-0.455869\pi$
$5$	0.618034	0.276393	0.138197	+	0.990405i	$0.455869\pi$
$6$	−1.00000	−0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.618034	−0.195440
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	1.61803	0.448762	0.224381	−	0.974502i	$-0.427964\pi$
$13$	1.61803	0.448762	0.224381	+	0.974502i	$0.427964\pi$
$14$	0	0
$15$	0.618034	0.159576
$16$	1.00000	0.250000
$17$	−4.09017	−0.992012	−0.496006	−	0.868319i	$-0.665201\pi$
$17$	−4.09017	−0.992012	−0.496006	+	0.868319i	$0.665201\pi$
$18$	−1.00000	−0.235702
$19$	0	0
$19$	0	0
$20$	0.618034	0.138197
$21$	0	0
$22$	4.00000	0.852803
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−1.00000	−0.204124
$25$	−4.61803	−0.923607
$26$	−1.61803	−0.317323
$27$	1.00000	0.192450
$28$	0	0
$29$	−8.85410	−1.64417	−0.822083	−	0.569368i	$-0.807188\pi$
$29$	−8.85410	−1.64417	−0.822083	+	0.569368i	$0.807188\pi$
$30$	−0.618034	−0.112837
$31$	1.52786	0.274412	0.137206	−	0.990543i	$-0.456188\pi$
$31$	1.52786	0.274412	0.137206	+	0.990543i	$0.456188\pi$
$32$	−1.00000	−0.176777
$33$	−4.00000	−0.696311
$34$	4.09017	0.701458
$35$	0	0
$36$	1.00000	0.166667
$37$	5.85410	0.962408	0.481204	−	0.876609i	$-0.340200\pi$
$37$	5.85410	0.962408	0.481204	+	0.876609i	$0.340200\pi$
$38$	0	0
$39$	1.61803	0.259093
$40$	−0.618034	−0.0977198
$41$	5.85410	0.914257	0.457129	−	0.889401i	$-0.348878\pi$
$41$	5.85410	0.914257	0.457129	+	0.889401i	$0.348878\pi$
$42$	0	0
$43$	−10.4721	−1.59699	−0.798493	−	0.602004i	$-0.794369\pi$
$43$	−10.4721	−1.59699	−0.798493	+	0.602004i	$0.794369\pi$
$44$	−4.00000	−0.603023
$45$	0.618034	0.0921311
$46$	4.00000	0.589768
$47$	4.94427	0.721196	0.360598	−	0.932721i	$-0.382573\pi$
$47$	4.94427	0.721196	0.360598	+	0.932721i	$0.382573\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	4.61803	0.653089
$51$	−4.09017	−0.572738
$52$	1.61803	0.224381
$53$	−8.61803	−1.18378	−0.591889	−	0.806019i	$-0.701618\pi$
$53$	−8.61803	−1.18378	−0.591889	+	0.806019i	$0.701618\pi$
$54$	−1.00000	−0.136083
$55$	−2.47214	−0.333343
$56$	0	0
$57$	0	0
$58$	8.85410	1.16260
$59$	2.47214	0.321845	0.160922	−	0.986967i	$-0.448553\pi$
$59$	2.47214	0.321845	0.160922	+	0.986967i	$0.448553\pi$
$60$	0.618034	0.0797878
$61$	−9.61803	−1.23146	−0.615732	−	0.787956i	$-0.711139\pi$
$61$	−9.61803	−1.23146	−0.615732	+	0.787956i	$0.711139\pi$
$62$	−1.52786	−0.194039
$63$	0	0
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	4.00000	0.492366
$67$	−11.4164	−1.39474	−0.697368	−	0.716713i	$-0.745646\pi$
$67$	−11.4164	−1.39474	−0.697368	+	0.716713i	$0.745646\pi$
$68$	−4.09017	−0.496006
$69$	−4.00000	−0.481543
$70$	0	0
$71$	6.47214	0.768101	0.384051	−	0.923312i	$-0.374529\pi$
$71$	6.47214	0.768101	0.384051	+	0.923312i	$0.374529\pi$
$72$	−1.00000	−0.117851
$73$	16.0344	1.87669	0.938345	−	0.345701i	$-0.112359\pi$
$73$	16.0344	1.87669	0.938345	+	0.345701i	$0.112359\pi$
$74$	−5.85410	−0.680526
$75$	−4.61803	−0.533245
$76$	0	0
$77$	0	0
$78$	−1.61803	−0.183206
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	0.618034	0.0690983
$81$	1.00000	0.111111
$82$	−5.85410	−0.646477
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	0	0
$85$	−2.52786	−0.274185
$86$	10.4721	1.12924
$87$	−8.85410	−0.949259
$88$	4.00000	0.426401
$89$	−12.6180	−1.33751	−0.668754	−	0.743483i	$-0.733172\pi$
$89$	−12.6180	−1.33751	−0.668754	+	0.743483i	$0.733172\pi$
$90$	−0.618034	−0.0651465
$91$	0	0
$92$	−4.00000	−0.417029
$93$	1.52786	0.158432
$94$	−4.94427	−0.509963
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−9.79837	−0.994874	−0.497437	−	0.867500i	$-0.665725\pi$
$97$	−9.79837	−0.994874	−0.497437	+	0.867500i	$0.665725\pi$
$98$	7.00000	0.707107
$99$	−4.00000	−0.402015
$100$	−4.61803	−0.461803
$101$	−4.90983	−0.488546	−0.244273	−	0.969706i	$-0.578549\pi$
$101$	−4.90983	−0.488546	−0.244273	+	0.969706i	$0.578549\pi$
$102$	4.09017	0.404987
$103$	15.4164	1.51902	0.759512	−	0.650493i	$-0.225438\pi$
$103$	15.4164	1.51902	0.759512	+	0.650493i	$0.225438\pi$
$104$	−1.61803	−0.158661
$105$	0	0
$106$	8.61803	0.837057
$107$	12.9443	1.25137	0.625685	−	0.780076i	$-0.284820\pi$
$107$	12.9443	1.25137	0.625685	+	0.780076i	$0.284820\pi$
$108$	1.00000	0.0962250
$109$	10.7984	1.03430	0.517148	−	0.855896i	$-0.326994\pi$
$109$	10.7984	1.03430	0.517148	+	0.855896i	$0.326994\pi$
$110$	2.47214	0.235709
$111$	5.85410	0.555647
$112$	0	0
$113$	−7.32624	−0.689194	−0.344597	−	0.938751i	$-0.611985\pi$
$113$	−7.32624	−0.689194	−0.344597	+	0.938751i	$0.611985\pi$
$114$	0	0
$115$	−2.47214	−0.230528
$116$	−8.85410	−0.822083
$117$	1.61803	0.149587
$118$	−2.47214	−0.227579
$119$	0	0
$120$	−0.618034	−0.0564185
$121$	5.00000	0.454545
$122$	9.61803	0.870776
$123$	5.85410	0.527847
$124$	1.52786	0.137206
$125$	−5.94427	−0.531672
$126$	0	0
$127$	15.4164	1.36798	0.683992	−	0.729489i	$-0.260242\pi$
$127$	15.4164	1.36798	0.683992	+	0.729489i	$0.260242\pi$
$128$	−1.00000	−0.0883883
$129$	−10.4721	−0.922020
$130$	−1.00000	−0.0877058
$131$	−11.4164	−0.997456	−0.498728	−	0.866758i	$-0.666199\pi$
$131$	−11.4164	−0.997456	−0.498728	+	0.866758i	$0.666199\pi$
$132$	−4.00000	−0.348155
$133$	0	0
$134$	11.4164	0.986227
$135$	0.618034	0.0531919
$136$	4.09017	0.350729
$137$	−0.909830	−0.0777320	−0.0388660	−	0.999244i	$-0.512375\pi$
$137$	−0.909830	−0.0777320	−0.0388660	+	0.999244i	$0.512375\pi$
$138$	4.00000	0.340503
$139$	20.9443	1.77647	0.888235	−	0.459389i	$-0.151932\pi$
$139$	20.9443	1.77647	0.888235	+	0.459389i	$0.151932\pi$
$140$	0	0
$141$	4.94427	0.416383
$142$	−6.47214	−0.543130
$143$	−6.47214	−0.541227
$144$	1.00000	0.0833333
$145$	−5.47214	−0.454436
$146$	−16.0344	−1.32702
$147$	−7.00000	−0.577350
$148$	5.85410	0.481204
$149$	−4.09017	−0.335080	−0.167540	−	0.985865i	$-0.553582\pi$
$149$	−4.09017	−0.335080	−0.167540	+	0.985865i	$0.553582\pi$
$150$	4.61803	0.377061
$151$	5.52786	0.449851	0.224926	−	0.974376i	$-0.427786\pi$
$151$	5.52786	0.449851	0.224926	+	0.974376i	$0.427786\pi$
$152$	0	0
$153$	−4.09017	−0.330671
$154$	0	0
$155$	0.944272	0.0758457
$156$	1.61803	0.129546
$157$	−19.5066	−1.55679	−0.778397	−	0.627772i	$-0.783967\pi$
$157$	−19.5066	−1.55679	−0.778397	+	0.627772i	$0.783967\pi$
$158$	−4.00000	−0.318223
$159$	−8.61803	−0.683455
$160$	−0.618034	−0.0488599
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	3.41641	0.267594	0.133797	−	0.991009i	$-0.457283\pi$
$163$	3.41641	0.267594	0.133797	+	0.991009i	$0.457283\pi$
$164$	5.85410	0.457129
$165$	−2.47214	−0.192456
$166$	8.00000	0.620920
$167$	−23.4164	−1.81202	−0.906008	−	0.423261i	$-0.860886\pi$
$167$	−23.4164	−1.81202	−0.906008	+	0.423261i	$0.860886\pi$
$168$	0	0
$169$	−10.3820	−0.798613
$170$	2.52786	0.193878
$171$	0	0
$172$	−10.4721	−0.798493
$173$	4.32624	0.328918	0.164459	−	0.986384i	$-0.447412\pi$
$173$	4.32624	0.328918	0.164459	+	0.986384i	$0.447412\pi$
$174$	8.85410	0.671228
$175$	0	0
$176$	−4.00000	−0.301511
$177$	2.47214	0.185817
$178$	12.6180	0.945762
$179$	8.00000	0.597948	0.298974	−	0.954261i	$-0.403356\pi$
$179$	8.00000	0.597948	0.298974	+	0.954261i	$0.403356\pi$
$180$	0.618034	0.0460655
$181$	−6.00000	−0.445976	−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000	−0.445976	−0.222988	+	0.974821i	$0.571581\pi$
$182$	0	0
$183$	−9.61803	−0.710986
$184$	4.00000	0.294884
$185$	3.61803	0.266003
$186$	−1.52786	−0.112028
$187$	16.3607	1.19641
$188$	4.94427	0.360598
$189$	0	0
$190$	0	0
$191$	−19.4164	−1.40492	−0.702461	−	0.711722i	$-0.747915\pi$
$191$	−19.4164	−1.40492	−0.702461	+	0.711722i	$0.747915\pi$
$192$	1.00000	0.0721688
$193$	−11.8885	−0.855756	−0.427878	−	0.903836i	$-0.640739\pi$
$193$	−11.8885	−0.855756	−0.427878	+	0.903836i	$0.640739\pi$
$194$	9.79837	0.703482
$195$	1.00000	0.0716115
$196$	−7.00000	−0.500000
$197$	12.2705	0.874238	0.437119	−	0.899404i	$-0.355999\pi$
$197$	12.2705	0.874238	0.437119	+	0.899404i	$0.355999\pi$
$198$	4.00000	0.284268
$199$	−19.4164	−1.37639	−0.688196	−	0.725525i	$-0.741597\pi$
$199$	−19.4164	−1.37639	−0.688196	+	0.725525i	$0.741597\pi$
$200$	4.61803	0.326544
$201$	−11.4164	−0.805251
$202$	4.90983	0.345454
$203$	0	0
$204$	−4.09017	−0.286369
$205$	3.61803	0.252694
$206$	−15.4164	−1.07411
$207$	−4.00000	−0.278019
$208$	1.61803	0.112190
$209$	0	0
$210$	0	0
$211$	11.4164	0.785938	0.392969	−	0.919552i	$-0.371448\pi$
$211$	11.4164	0.785938	0.392969	+	0.919552i	$0.371448\pi$
$212$	−8.61803	−0.591889
$213$	6.47214	0.443463
$214$	−12.9443	−0.884852
$215$	−6.47214	−0.441396
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−10.7984	−0.731358
$219$	16.0344	1.08351
$220$	−2.47214	−0.166671
$221$	−6.61803	−0.445177
$222$	−5.85410	−0.392902
$223$	−6.47214	−0.433406	−0.216703	−	0.976238i	$-0.569530\pi$
$223$	−6.47214	−0.433406	−0.216703	+	0.976238i	$0.569530\pi$
$224$	0	0
$225$	−4.61803	−0.307869
$226$	7.32624	0.487334
$227$	−16.9443	−1.12463	−0.562315	−	0.826923i	$-0.690089\pi$
$227$	−16.9443	−1.12463	−0.562315	+	0.826923i	$0.690089\pi$
$228$	0	0
$229$	17.5623	1.16055	0.580275	−	0.814421i	$-0.302945\pi$
$229$	17.5623	1.16055	0.580275	+	0.814421i	$0.302945\pi$
$230$	2.47214	0.163008
$231$	0	0
$232$	8.85410	0.581300
$233$	24.8541	1.62825	0.814123	−	0.580692i	$-0.197218\pi$
$233$	24.8541	1.62825	0.814123	+	0.580692i	$0.197218\pi$
$234$	−1.61803	−0.105774
$235$	3.05573	0.199334
$236$	2.47214	0.160922
$237$	4.00000	0.259828
$238$	0	0
$239$	15.4164	0.997205	0.498602	−	0.866831i	$-0.333847\pi$
$239$	15.4164	0.997205	0.498602	+	0.866831i	$0.333847\pi$
$240$	0.618034	0.0398939
$241$	7.88854	0.508146	0.254073	−	0.967185i	$-0.418230\pi$
$241$	7.88854	0.508146	0.254073	+	0.967185i	$0.418230\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	−9.61803	−0.615732
$245$	−4.32624	−0.276393
$246$	−5.85410	−0.373244
$247$	0	0
$248$	−1.52786	−0.0970195
$249$	−8.00000	−0.506979
$250$	5.94427	0.375949
$251$	6.47214	0.408518	0.204259	−	0.978917i	$-0.434522\pi$
$251$	6.47214	0.408518	0.204259	+	0.978917i	$0.434522\pi$
$252$	0	0
$253$	16.0000	1.00591
$254$	−15.4164	−0.967311
$255$	−2.52786	−0.158301
$256$	1.00000	0.0625000
$257$	−15.0902	−0.941299	−0.470649	−	0.882320i	$-0.655980\pi$
$257$	−15.0902	−0.941299	−0.470649	+	0.882320i	$0.655980\pi$
$258$	10.4721	0.651967
$259$	0	0
$260$	1.00000	0.0620174
$261$	−8.85410	−0.548055
$262$	11.4164	0.705308
$263$	13.5279	0.834164	0.417082	−	0.908869i	$-0.363053\pi$
$263$	13.5279	0.834164	0.417082	+	0.908869i	$0.363053\pi$
$264$	4.00000	0.246183
$265$	−5.32624	−0.327188
$266$	0	0
$267$	−12.6180	−0.772211
$268$	−11.4164	−0.697368
$269$	−20.2705	−1.23591	−0.617957	−	0.786212i	$-0.712040\pi$
$269$	−20.2705	−1.23591	−0.617957	+	0.786212i	$0.712040\pi$
$270$	−0.618034	−0.0376124
$271$	−8.00000	−0.485965	−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000	−0.485965	−0.242983	+	0.970031i	$0.578126\pi$
$272$	−4.09017	−0.248003
$273$	0	0
$274$	0.909830	0.0549648
$275$	18.4721	1.11391
$276$	−4.00000	−0.240772
$277$	7.09017	0.426007	0.213004	−	0.977051i	$-0.431675\pi$
$277$	7.09017	0.426007	0.213004	+	0.977051i	$0.431675\pi$
$278$	−20.9443	−1.25615
$279$	1.52786	0.0914708
$280$	0	0
$281$	−18.7426	−1.11809	−0.559046	−	0.829136i	$-0.688833\pi$
$281$	−18.7426	−1.11809	−0.559046	+	0.829136i	$0.688833\pi$
$282$	−4.94427	−0.294427
$283$	−16.9443	−1.00723	−0.503616	−	0.863927i	$-0.667997\pi$
$283$	−16.9443	−1.00723	−0.503616	+	0.863927i	$0.667997\pi$
$284$	6.47214	0.384051
$285$	0	0
$286$	6.47214	0.382705
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−0.270510	−0.0159123
$290$	5.47214	0.321335
$291$	−9.79837	−0.574391
$292$	16.0344	0.938345
$293$	−22.0000	−1.28525	−0.642627	−	0.766179i	$-0.722155\pi$
$293$	−22.0000	−1.28525	−0.642627	+	0.766179i	$0.722155\pi$
$294$	7.00000	0.408248
$295$	1.52786	0.0889557
$296$	−5.85410	−0.340263
$297$	−4.00000	−0.232104
$298$	4.09017	0.236937
$299$	−6.47214	−0.374293
$300$	−4.61803	−0.266622
$301$	0	0
$302$	−5.52786	−0.318093
$303$	−4.90983	−0.282062
$304$	0	0
$305$	−5.94427	−0.340368
$306$	4.09017	0.233819
$307$	−13.5279	−0.772076	−0.386038	−	0.922483i	$-0.626157\pi$
$307$	−13.5279	−0.772076	−0.386038	+	0.922483i	$0.626157\pi$
$308$	0	0
$309$	15.4164	0.877009
$310$	−0.944272	−0.0536310
$311$	−30.4721	−1.72792	−0.863958	−	0.503564i	$-0.832022\pi$
$311$	−30.4721	−1.72792	−0.863958	+	0.503564i	$0.832022\pi$
$312$	−1.61803	−0.0916031
$313$	−12.3262	−0.696720	−0.348360	−	0.937361i	$-0.613261\pi$
$313$	−12.3262	−0.696720	−0.348360	+	0.937361i	$0.613261\pi$
$314$	19.5066	1.10082
$315$	0	0
$316$	4.00000	0.225018
$317$	22.2148	1.24771	0.623853	−	0.781542i	$-0.285566\pi$
$317$	22.2148	1.24771	0.623853	+	0.781542i	$0.285566\pi$
$318$	8.61803	0.483275
$319$	35.4164	1.98294
$320$	0.618034	0.0345492
$321$	12.9443	0.722479
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	−7.47214	−0.414480
$326$	−3.41641	−0.189217
$327$	10.7984	0.597151
$328$	−5.85410	−0.323239
$329$	0	0
$330$	2.47214	0.136087
$331$	−33.8885	−1.86268	−0.931341	−	0.364147i	$-0.881361\pi$
$331$	−33.8885	−1.86268	−0.931341	+	0.364147i	$0.881361\pi$
$332$	−8.00000	−0.439057
$333$	5.85410	0.320803
$334$	23.4164	1.28129
$335$	−7.05573	−0.385496
$336$	0	0
$337$	33.2705	1.81236	0.906180	−	0.422892i	$-0.138985\pi$
$337$	33.2705	1.81236	0.906180	+	0.422892i	$0.138985\pi$
$338$	10.3820	0.564705
$339$	−7.32624	−0.397907
$340$	−2.52786	−0.137093
$341$	−6.11146	−0.330954
$342$	0	0
$343$	0	0
$344$	10.4721	0.564620
$345$	−2.47214	−0.133095
$346$	−4.32624	−0.232580
$347$	0	0		−	1.00000i	$-0.5\pi$
$347$	0	0			1.00000i	$0.5\pi$
$348$	−8.85410	−0.474630
$349$	15.9098	0.851634	0.425817	−	0.904809i	$-0.359987\pi$
$349$	15.9098	0.851634	0.425817	+	0.904809i	$0.359987\pi$
$350$	0	0
$351$	1.61803	0.0863643
$352$	4.00000	0.213201
$353$	−5.61803	−0.299018	−0.149509	−	0.988760i	$-0.547769\pi$
$353$	−5.61803	−0.299018	−0.149509	+	0.988760i	$0.547769\pi$
$354$	−2.47214	−0.131393
$355$	4.00000	0.212298
$356$	−12.6180	−0.668754
$357$	0	0
$358$	−8.00000	−0.422813
$359$	24.3607	1.28571	0.642854	−	0.765989i	$-0.277750\pi$
$359$	24.3607	1.28571	0.642854	+	0.765989i	$0.277750\pi$
$360$	−0.618034	−0.0325733
$361$	0	0
$362$	6.00000	0.315353
$363$	5.00000	0.262432
$364$	0	0
$365$	9.90983	0.518704
$366$	9.61803	0.502743
$367$	12.0000	0.626395	0.313197	−	0.949688i	$-0.398600\pi$
$367$	12.0000	0.626395	0.313197	+	0.949688i	$0.398600\pi$
$368$	−4.00000	−0.208514
$369$	5.85410	0.304752
$370$	−3.61803	−0.188093
$371$	0	0
$372$	1.52786	0.0792161
$373$	−25.7984	−1.33579	−0.667895	−	0.744256i	$-0.732804\pi$
$373$	−25.7984	−1.33579	−0.667895	+	0.744256i	$0.732804\pi$
$374$	−16.3607	−0.845991
$375$	−5.94427	−0.306961
$376$	−4.94427	−0.254981
$377$	−14.3262	−0.737839
$378$	0	0
$379$	19.4164	0.997354	0.498677	−	0.866788i	$-0.333819\pi$
$379$	19.4164	0.997354	0.498677	+	0.866788i	$0.333819\pi$
$380$	0	0
$381$	15.4164	0.789807
$382$	19.4164	0.993430
$383$	16.3607	0.835992	0.417996	−	0.908449i	$-0.362733\pi$
$383$	16.3607	0.835992	0.417996	+	0.908449i	$0.362733\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	11.8885	0.605111
$387$	−10.4721	−0.532329
$388$	−9.79837	−0.497437
$389$	8.85410	0.448921	0.224460	−	0.974483i	$-0.427938\pi$
$389$	8.85410	0.448921	0.224460	+	0.974483i	$0.427938\pi$
$390$	−1.00000	−0.0506370
$391$	16.3607	0.827395
$392$	7.00000	0.353553
$393$	−11.4164	−0.575882
$394$	−12.2705	−0.618179
$395$	2.47214	0.124387
$396$	−4.00000	−0.201008
$397$	7.88854	0.395915	0.197957	−	0.980211i	$-0.436569\pi$
$397$	7.88854	0.395915	0.197957	+	0.980211i	$0.436569\pi$
$398$	19.4164	0.973257
$399$	0	0
$400$	−4.61803	−0.230902
$401$	14.0000	0.699127	0.349563	−	0.936913i	$-0.386330\pi$
$401$	14.0000	0.699127	0.349563	+	0.936913i	$0.386330\pi$
$402$	11.4164	0.569399
$403$	2.47214	0.123146
$404$	−4.90983	−0.244273
$405$	0.618034	0.0307104
$406$	0	0
$407$	−23.4164	−1.16071
$408$	4.09017	0.202494
$409$	4.32624	0.213919	0.106959	−	0.994263i	$-0.465889\pi$
$409$	4.32624	0.213919	0.106959	+	0.994263i	$0.465889\pi$
$410$	−3.61803	−0.178682
$411$	−0.909830	−0.0448786
$412$	15.4164	0.759512
$413$	0	0
$414$	4.00000	0.196589
$415$	−4.94427	−0.242705
$416$	−1.61803	−0.0793306
$417$	20.9443	1.02565
$418$	0	0
$419$	−6.47214	−0.316185	−0.158092	−	0.987424i	$-0.550534\pi$
$419$	−6.47214	−0.316185	−0.158092	+	0.987424i	$0.550534\pi$
$420$	0	0
$421$	−33.5623	−1.63573	−0.817863	−	0.575412i	$-0.804842\pi$
$421$	−33.5623	−1.63573	−0.817863	+	0.575412i	$0.804842\pi$
$422$	−11.4164	−0.555742
$423$	4.94427	0.240399
$424$	8.61803	0.418529
$425$	18.8885	0.916229
$426$	−6.47214	−0.313576
$427$	0	0
$428$	12.9443	0.625685
$429$	−6.47214	−0.312478
$430$	6.47214	0.312114
$431$	0.583592	0.0281106	0.0140553	−	0.999901i	$-0.495526\pi$
$431$	0.583592	0.0281106	0.0140553	+	0.999901i	$0.495526\pi$
$432$	1.00000	0.0481125
$433$	20.9098	1.00486	0.502431	−	0.864617i	$-0.332439\pi$
$433$	20.9098	1.00486	0.502431	+	0.864617i	$0.332439\pi$
$434$	0	0
$435$	−5.47214	−0.262369
$436$	10.7984	0.517148
$437$	0	0
$438$	−16.0344	−0.766155
$439$	0.583592	0.0278533	0.0139267	−	0.999903i	$-0.495567\pi$
$439$	0.583592	0.0278533	0.0139267	+	0.999903i	$0.495567\pi$
$440$	2.47214	0.117854
$441$	−7.00000	−0.333333
$442$	6.61803	0.314788
$443$	25.5279	1.21287	0.606433	−	0.795135i	$-0.292600\pi$
$443$	25.5279	1.21287	0.606433	+	0.795135i	$0.292600\pi$
$444$	5.85410	0.277823
$445$	−7.79837	−0.369678
$446$	6.47214	0.306465
$447$	−4.09017	−0.193458
$448$	0	0
$449$	−13.7984	−0.651186	−0.325593	−	0.945510i	$-0.605564\pi$
$449$	−13.7984	−0.651186	−0.325593	+	0.945510i	$0.605564\pi$
$450$	4.61803	0.217696
$451$	−23.4164	−1.10264
$452$	−7.32624	−0.344597
$453$	5.52786	0.259722
$454$	16.9443	0.795234
$455$	0	0
$456$	0	0
$457$	−4.32624	−0.202373	−0.101186	−	0.994867i	$-0.532264\pi$
$457$	−4.32624	−0.202373	−0.101186	+	0.994867i	$0.532264\pi$
$458$	−17.5623	−0.820633
$459$	−4.09017	−0.190913
$460$	−2.47214	−0.115264
$461$	39.8885	1.85779	0.928897	−	0.370337i	$-0.120758\pi$
$461$	39.8885	1.85779	0.928897	+	0.370337i	$0.120758\pi$
$462$	0	0
$463$	−29.3050	−1.36192	−0.680958	−	0.732322i	$-0.738437\pi$
$463$	−29.3050	−1.36192	−0.680958	+	0.732322i	$0.738437\pi$
$464$	−8.85410	−0.411041
$465$	0.944272	0.0437896
$466$	−24.8541	−1.15134
$467$	34.4721	1.59518	0.797590	−	0.603200i	$-0.206108\pi$
$467$	34.4721	1.59518	0.797590	+	0.603200i	$0.206108\pi$
$468$	1.61803	0.0747936
$469$	0	0
$470$	−3.05573	−0.140950
$471$	−19.5066	−0.898816
$472$	−2.47214	−0.113789
$473$	41.8885	1.92604
$474$	−4.00000	−0.183726
$475$	0	0
$476$	0	0
$477$	−8.61803	−0.394593
$478$	−15.4164	−0.705130
$479$	−4.94427	−0.225910	−0.112955	−	0.993600i	$-0.536032\pi$
$479$	−4.94427	−0.225910	−0.112955	+	0.993600i	$0.536032\pi$
$480$	−0.618034	−0.0282093
$481$	9.47214	0.431892
$482$	−7.88854	−0.359313
$483$	0	0
$484$	5.00000	0.227273
$485$	−6.05573	−0.274976
$486$	−1.00000	−0.0453609
$487$	30.4721	1.38082	0.690412	−	0.723416i	$-0.257429\pi$
$487$	30.4721	1.38082	0.690412	+	0.723416i	$0.257429\pi$
$488$	9.61803	0.435388
$489$	3.41641	0.154495
$490$	4.32624	0.195440
$491$	−12.3607	−0.557830	−0.278915	−	0.960316i	$-0.589975\pi$
$491$	−12.3607	−0.557830	−0.278915	+	0.960316i	$0.589975\pi$
$492$	5.85410	0.263923
$493$	36.2148	1.63103
$494$	0	0
$495$	−2.47214	−0.111114
$496$	1.52786	0.0686031
$497$	0	0
$498$	8.00000	0.358489
$499$	8.94427	0.400401	0.200200	−	0.979755i	$-0.435841\pi$
$499$	8.94427	0.400401	0.200200	+	0.979755i	$0.435841\pi$
$500$	−5.94427	−0.265836
$501$	−23.4164	−1.04617
$502$	−6.47214	−0.288866
$503$	24.9443	1.11221	0.556105	−	0.831112i	$-0.312295\pi$
$503$	24.9443	1.11221	0.556105	+	0.831112i	$0.312295\pi$
$504$	0	0
$505$	−3.03444	−0.135031
$506$	−16.0000	−0.711287
$507$	−10.3820	−0.461079
$508$	15.4164	0.683992
$509$	29.9787	1.32878	0.664392	−	0.747385i	$-0.268691\pi$
$509$	29.9787	1.32878	0.664392	+	0.747385i	$0.268691\pi$
$510$	2.52786	0.111936
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	15.0902	0.665599
$515$	9.52786	0.419848
$516$	−10.4721	−0.461010
$517$	−19.7771	−0.869795
$518$	0	0
$519$	4.32624	0.189901
$520$	−1.00000	−0.0438529
$521$	8.67376	0.380004	0.190002	−	0.981784i	$-0.439150\pi$
$521$	8.67376	0.380004	0.190002	+	0.981784i	$0.439150\pi$
$522$	8.85410	0.387534
$523$	18.4721	0.807730	0.403865	−	0.914819i	$-0.367667\pi$
$523$	18.4721	0.807730	0.403865	+	0.914819i	$0.367667\pi$
$524$	−11.4164	−0.498728
$525$	0	0
$526$	−13.5279	−0.589843
$527$	−6.24922	−0.272220
$528$	−4.00000	−0.174078
$529$	−7.00000	−0.304348
$530$	5.32624	0.231357
$531$	2.47214	0.107282
$532$	0	0
$533$	9.47214	0.410284
$534$	12.6180	0.546036
$535$	8.00000	0.345870
$536$	11.4164	0.493114
$537$	8.00000	0.345225
$538$	20.2705	0.873924
$539$	28.0000	1.20605
$540$	0.618034	0.0265959
$541$	−11.1459	−0.479200	−0.239600	−	0.970872i	$-0.577016\pi$
$541$	−11.1459	−0.479200	−0.239600	+	0.970872i	$0.577016\pi$
$542$	8.00000	0.343629
$543$	−6.00000	−0.257485
$544$	4.09017	0.175365
$545$	6.67376	0.285873
$546$	0	0
$547$	12.5836	0.538036	0.269018	−	0.963135i	$-0.413301\pi$
$547$	12.5836	0.538036	0.269018	+	0.963135i	$0.413301\pi$
$548$	−0.909830	−0.0388660
$549$	−9.61803	−0.410488
$550$	−18.4721	−0.787655
$551$	0	0
$552$	4.00000	0.170251
$553$	0	0
$554$	−7.09017	−0.301232
$555$	3.61803	0.153577
$556$	20.9443	0.888235
$557$	−43.8885	−1.85962	−0.929809	−	0.368043i	$-0.880028\pi$
$557$	−43.8885	−1.85962	−0.929809	+	0.368043i	$0.880028\pi$
$558$	−1.52786	−0.0646796
$559$	−16.9443	−0.716666
$560$	0	0
$561$	16.3607	0.690748
$562$	18.7426	0.790611
$563$	29.8885	1.25965	0.629826	−	0.776736i	$-0.283126\pi$
$563$	29.8885	1.25965	0.629826	+	0.776736i	$0.283126\pi$
$564$	4.94427	0.208191
$565$	−4.52786	−0.190489
$566$	16.9443	0.712221
$567$	0	0
$568$	−6.47214	−0.271565
$569$	2.79837	0.117314	0.0586570	−	0.998278i	$-0.481318\pi$
$569$	2.79837	0.117314	0.0586570	+	0.998278i	$0.481318\pi$
$570$	0	0
$571$	8.94427	0.374306	0.187153	−	0.982331i	$-0.440074\pi$
$571$	8.94427	0.374306	0.187153	+	0.982331i	$0.440074\pi$
$572$	−6.47214	−0.270614
$573$	−19.4164	−0.811132
$574$	0	0
$575$	18.4721	0.770341
$576$	1.00000	0.0416667
$577$	27.3262	1.13761	0.568803	−	0.822474i	$-0.307407\pi$
$577$	27.3262	1.13761	0.568803	+	0.822474i	$0.307407\pi$
$578$	0.270510	0.0112517
$579$	−11.8885	−0.494071
$580$	−5.47214	−0.227218
$581$	0	0
$582$	9.79837	0.406156
$583$	34.4721	1.42769
$584$	−16.0344	−0.663510
$585$	1.00000	0.0413449
$586$	22.0000	0.908812
$587$	32.0000	1.32078	0.660391	−	0.750922i	$-0.270391\pi$
$587$	32.0000	1.32078	0.660391	+	0.750922i	$0.270391\pi$
$588$	−7.00000	−0.288675
$589$	0	0
$590$	−1.52786	−0.0629012
$591$	12.2705	0.504741
$592$	5.85410	0.240602
$593$	−10.7984	−0.443436	−0.221718	−	0.975111i	$-0.571166\pi$
$593$	−10.7984	−0.443436	−0.221718	+	0.975111i	$0.571166\pi$
$594$	4.00000	0.164122
$595$	0	0
$596$	−4.09017	−0.167540
$597$	−19.4164	−0.794661
$598$	6.47214	0.264665
$599$	43.4164	1.77395	0.886973	−	0.461821i	$-0.152804\pi$
$599$	43.4164	1.77395	0.886973	+	0.461821i	$0.152804\pi$
$600$	4.61803	0.188530
$601$	25.7771	1.05147	0.525735	−	0.850649i	$-0.323790\pi$
$601$	25.7771	1.05147	0.525735	+	0.850649i	$0.323790\pi$
$602$	0	0
$603$	−11.4164	−0.464912
$604$	5.52786	0.224926
$605$	3.09017	0.125633
$606$	4.90983	0.199448
$607$	0.583592	0.0236873	0.0118436	−	0.999930i	$-0.496230\pi$
$607$	0.583592	0.0236873	0.0118436	+	0.999930i	$0.496230\pi$
$608$	0	0
$609$	0	0
$610$	5.94427	0.240677
$611$	8.00000	0.323645
$612$	−4.09017	−0.165335
$613$	14.5066	0.585915	0.292958	−	0.956125i	$-0.405361\pi$
$613$	14.5066	0.585915	0.292958	+	0.956125i	$0.405361\pi$
$614$	13.5279	0.545940
$615$	3.61803	0.145893
$616$	0	0
$617$	−15.8885	−0.639649	−0.319824	−	0.947477i	$-0.603624\pi$
$617$	−15.8885	−0.639649	−0.319824	+	0.947477i	$0.603624\pi$
$618$	−15.4164	−0.620139
$619$	−19.4164	−0.780411	−0.390206	−	0.920728i	$-0.627596\pi$
$619$	−19.4164	−0.780411	−0.390206	+	0.920728i	$0.627596\pi$
$620$	0.944272	0.0379229
$621$	−4.00000	−0.160514
$622$	30.4721	1.22182
$623$	0	0
$624$	1.61803	0.0647732
$625$	19.4164	0.776656
$626$	12.3262	0.492656
$627$	0	0
$628$	−19.5066	−0.778397
$629$	−23.9443	−0.954721
$630$	0	0
$631$	12.3607	0.492071	0.246035	−	0.969261i	$-0.420872\pi$
$631$	12.3607	0.492071	0.246035	+	0.969261i	$0.420872\pi$
$632$	−4.00000	−0.159111
$633$	11.4164	0.453761
$634$	−22.2148	−0.882262
$635$	9.52786	0.378102
$636$	−8.61803	−0.341727
$637$	−11.3262	−0.448762
$638$	−35.4164	−1.40215
$639$	6.47214	0.256034
$640$	−0.618034	−0.0244299
$641$	2.20163	0.0869590	0.0434795	−	0.999054i	$-0.486156\pi$
$641$	2.20163	0.0869590	0.0434795	+	0.999054i	$0.486156\pi$
$642$	−12.9443	−0.510870
$643$	12.9443	0.510472	0.255236	−	0.966879i	$-0.417847\pi$
$643$	12.9443	0.510472	0.255236	+	0.966879i	$0.417847\pi$
$644$	0	0
$645$	−6.47214	−0.254840
$646$	0	0
$647$	7.05573	0.277389	0.138695	−	0.990335i	$-0.455709\pi$
$647$	7.05573	0.277389	0.138695	+	0.990335i	$0.455709\pi$
$648$	−1.00000	−0.0392837
$649$	−9.88854	−0.388159
$650$	7.47214	0.293081
$651$	0	0
$652$	3.41641	0.133797
$653$	16.6180	0.650314	0.325157	−	0.945660i	$-0.394583\pi$
$653$	16.6180	0.650314	0.325157	+	0.945660i	$0.394583\pi$
$654$	−10.7984	−0.422250
$655$	−7.05573	−0.275690
$656$	5.85410	0.228564
$657$	16.0344	0.625563
$658$	0	0
$659$	0.583592	0.0227335	0.0113668	−	0.999935i	$-0.496382\pi$
$659$	0.583592	0.0227335	0.0113668	+	0.999935i	$0.496382\pi$
$660$	−2.47214	−0.0962278
$661$	−22.0000	−0.855701	−0.427850	−	0.903850i	$-0.640729\pi$
$661$	−22.0000	−0.855701	−0.427850	+	0.903850i	$0.640729\pi$
$662$	33.8885	1.31712
$663$	−6.61803	−0.257023
$664$	8.00000	0.310460
$665$	0	0
$666$	−5.85410	−0.226842
$667$	35.4164	1.37133
$668$	−23.4164	−0.906008
$669$	−6.47214	−0.250227
$670$	7.05573	0.272587
$671$	38.4721	1.48520
$672$	0	0
$673$	9.85410	0.379848	0.189924	−	0.981799i	$-0.439176\pi$
$673$	9.85410	0.379848	0.189924	+	0.981799i	$0.439176\pi$
$674$	−33.2705	−1.28153
$675$	−4.61803	−0.177748
$676$	−10.3820	−0.399306
$677$	−17.2148	−0.661618	−0.330809	−	0.943698i	$-0.607322\pi$
$677$	−17.2148	−0.661618	−0.330809	+	0.943698i	$0.607322\pi$
$678$	7.32624	0.281362
$679$	0	0
$680$	2.52786	0.0969392
$681$	−16.9443	−0.649306
$682$	6.11146	0.234020
$683$	10.4721	0.400705	0.200353	−	0.979724i	$-0.435791\pi$
$683$	10.4721	0.400705	0.200353	+	0.979724i	$0.435791\pi$
$684$	0	0
$685$	−0.562306	−0.0214846
$686$	0	0
$687$	17.5623	0.670044
$688$	−10.4721	−0.399246
$689$	−13.9443	−0.531234
$690$	2.47214	0.0941126
$691$	−21.5279	−0.818959	−0.409479	−	0.912319i	$-0.634290\pi$
$691$	−21.5279	−0.818959	−0.409479	+	0.912319i	$0.634290\pi$
$692$	4.32624	0.164459
$693$	0	0
$694$	0	0
$695$	12.9443	0.491004
$696$	8.85410	0.335614
$697$	−23.9443	−0.906954
$698$	−15.9098	−0.602196
$699$	24.8541	0.940068
$700$	0	0
$701$	0.0344419	0.00130085	0.000650425	−	1.00000i	$-0.499793\pi$
$701$	0.0344419	0.00130085	0.000650425		1.00000i	$0.499793\pi$
$702$	−1.61803	−0.0610688
$703$	0	0
$704$	−4.00000	−0.150756
$705$	3.05573	0.115085
$706$	5.61803	0.211437
$707$	0	0
$708$	2.47214	0.0929086
$709$	−40.0902	−1.50562	−0.752809	−	0.658239i	$-0.771302\pi$
$709$	−40.0902	−1.50562	−0.752809	+	0.658239i	$0.771302\pi$
$710$	−4.00000	−0.150117
$711$	4.00000	0.150012
$712$	12.6180	0.472881
$713$	−6.11146	−0.228876
$714$	0	0
$715$	−4.00000	−0.149592
$716$	8.00000	0.298974
$717$	15.4164	0.575736
$718$	−24.3607	−0.909132
$719$	−17.5279	−0.653679	−0.326840	−	0.945080i	$-0.605984\pi$
$719$	−17.5279	−0.653679	−0.326840	+	0.945080i	$0.605984\pi$
$720$	0.618034	0.0230328
$721$	0	0
$722$	0	0
$723$	7.88854	0.293378
$724$	−6.00000	−0.222988
$725$	40.8885	1.51856
$726$	−5.00000	−0.185567
$727$	−34.8328	−1.29188	−0.645939	−	0.763389i	$-0.723534\pi$
$727$	−34.8328	−1.29188	−0.645939	+	0.763389i	$0.723534\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−9.90983	−0.366779
$731$	42.8328	1.58423
$732$	−9.61803	−0.355493
$733$	11.3262	0.418344	0.209172	−	0.977879i	$-0.432923\pi$
$733$	11.3262	0.418344	0.209172	+	0.977879i	$0.432923\pi$
$734$	−12.0000	−0.442928
$735$	−4.32624	−0.159576
$736$	4.00000	0.147442
$737$	45.6656	1.68212
$738$	−5.85410	−0.215492
$739$	−2.11146	−0.0776712	−0.0388356	−	0.999246i	$-0.512365\pi$
$739$	−2.11146	−0.0776712	−0.0388356	+	0.999246i	$0.512365\pi$
$740$	3.61803	0.133002
$741$	0	0
$742$	0	0
$743$	36.9443	1.35535	0.677677	−	0.735360i	$-0.262987\pi$
$743$	36.9443	1.35535	0.677677	+	0.735360i	$0.262987\pi$
$744$	−1.52786	−0.0560142
$745$	−2.52786	−0.0926138
$746$	25.7984	0.944546
$747$	−8.00000	−0.292705
$748$	16.3607	0.598206
$749$	0	0
$750$	5.94427	0.217054
$751$	22.8328	0.833181	0.416591	−	0.909094i	$-0.363225\pi$
$751$	22.8328	0.833181	0.416591	+	0.909094i	$0.363225\pi$
$752$	4.94427	0.180299
$753$	6.47214	0.235858
$754$	14.3262	0.521731
$755$	3.41641	0.124336
$756$	0	0
$757$	−50.3394	−1.82962	−0.914808	−	0.403889i	$-0.867658\pi$
$757$	−50.3394	−1.82962	−0.914808	+	0.403889i	$0.867658\pi$
$758$	−19.4164	−0.705236
$759$	16.0000	0.580763
$760$	0	0
$761$	−47.8885	−1.73596	−0.867979	−	0.496601i	$-0.834581\pi$
$761$	−47.8885	−1.73596	−0.867979	+	0.496601i	$0.834581\pi$
$762$	−15.4164	−0.558478
$763$	0	0
$764$	−19.4164	−0.702461
$765$	−2.52786	−0.0913951
$766$	−16.3607	−0.591135
$767$	4.00000	0.144432
$768$	1.00000	0.0360844
$769$	−45.6312	−1.64550	−0.822751	−	0.568401i	$-0.807562\pi$
$769$	−45.6312	−1.64550	−0.822751	+	0.568401i	$0.807562\pi$
$770$	0	0
$771$	−15.0902	−0.543459
$772$	−11.8885	−0.427878
$773$	−22.9656	−0.826014	−0.413007	−	0.910728i	$-0.635521\pi$
$773$	−22.9656	−0.826014	−0.413007	+	0.910728i	$0.635521\pi$
$774$	10.4721	0.376413
$775$	−7.05573	−0.253449
$776$	9.79837	0.351741
$777$	0	0
$778$	−8.85410	−0.317435
$779$	0	0
$780$	1.00000	0.0358057
$781$	−25.8885	−0.926365
$782$	−16.3607	−0.585057
$783$	−8.85410	−0.316420
$784$	−7.00000	−0.250000
$785$	−12.0557	−0.430287
$786$	11.4164	0.407210
$787$	16.5836	0.591141	0.295571	−	0.955321i	$-0.404490\pi$
$787$	16.5836	0.591141	0.295571	+	0.955321i	$0.404490\pi$
$788$	12.2705	0.437119
$789$	13.5279	0.481605
$790$	−2.47214	−0.0879547
$791$	0	0
$792$	4.00000	0.142134
$793$	−15.5623	−0.552634
$794$	−7.88854	−0.279954
$795$	−5.32624	−0.188902
$796$	−19.4164	−0.688196
$797$	−45.7984	−1.62226	−0.811131	−	0.584865i	$-0.801148\pi$
$797$	−45.7984	−1.62226	−0.811131	+	0.584865i	$0.801148\pi$
$798$	0	0
$799$	−20.2229	−0.715435
$800$	4.61803	0.163272
$801$	−12.6180	−0.445836
$802$	−14.0000	−0.494357
$803$	−64.1378	−2.26337
$804$	−11.4164	−0.402626
$805$	0	0
$806$	−2.47214	−0.0870773
$807$	−20.2705	−0.713556
$808$	4.90983	0.172727
$809$	−12.6869	−0.446048	−0.223024	−	0.974813i	$-0.571593\pi$
$809$	−12.6869	−0.446048	−0.223024	+	0.974813i	$0.571593\pi$
$810$	−0.618034	−0.0217155
$811$	−24.3607	−0.855419	−0.427710	−	0.903916i	$-0.640679\pi$
$811$	−24.3607	−0.855419	−0.427710	+	0.903916i	$0.640679\pi$
$812$	0	0
$813$	−8.00000	−0.280572
$814$	23.4164	0.820745
$815$	2.11146	0.0739611
$816$	−4.09017	−0.143185
$817$	0	0
$818$	−4.32624	−0.151263
$819$	0	0
$820$	3.61803	0.126347
$821$	0.854102	0.0298084	0.0149042	−	0.999889i	$-0.495256\pi$
$821$	0.854102	0.0298084	0.0149042	+	0.999889i	$0.495256\pi$
$822$	0.909830	0.0317340
$823$	−20.9443	−0.730071	−0.365036	−	0.930994i	$-0.618943\pi$
$823$	−20.9443	−0.730071	−0.365036	+	0.930994i	$0.618943\pi$
$824$	−15.4164	−0.537056
$825$	18.4721	0.643117
$826$	0	0
$827$	−38.8328	−1.35035	−0.675175	−	0.737658i	$-0.735932\pi$
$827$	−38.8328	−1.35035	−0.675175	+	0.737658i	$0.735932\pi$
$828$	−4.00000	−0.139010
$829$	1.49342	0.0518687	0.0259343	−	0.999664i	$-0.491744\pi$
$829$	1.49342	0.0518687	0.0259343	+	0.999664i	$0.491744\pi$
$830$	4.94427	0.171618
$831$	7.09017	0.245955
$832$	1.61803	0.0560952
$833$	28.6312	0.992012
$834$	−20.9443	−0.725241
$835$	−14.4721	−0.500829
$836$	0	0
$837$	1.52786	0.0528107
$838$	6.47214	0.223576
$839$	22.8328	0.788276	0.394138	−	0.919051i	$-0.371043\pi$
$839$	22.8328	0.788276	0.394138	+	0.919051i	$0.371043\pi$
$840$	0	0
$841$	49.3951	1.70328
$842$	33.5623	1.15663
$843$	−18.7426	−0.645531
$844$	11.4164	0.392969
$845$	−6.41641	−0.220731
$846$	−4.94427	−0.169988
$847$	0	0
$848$	−8.61803	−0.295945
$849$	−16.9443	−0.581526
$850$	−18.8885	−0.647872
$851$	−23.4164	−0.802704
$852$	6.47214	0.221732
$853$	0.270510	0.00926208	0.00463104	−	0.999989i	$-0.498526\pi$
$853$	0.270510	0.00926208	0.00463104	+	0.999989i	$0.498526\pi$
$854$	0	0
$855$	0	0
$856$	−12.9443	−0.442426
$857$	10.5623	0.360801	0.180401	−	0.983593i	$-0.442261\pi$
$857$	10.5623	0.360801	0.180401	+	0.983593i	$0.442261\pi$
$858$	6.47214	0.220955
$859$	51.1935	1.74670	0.873350	−	0.487094i	$-0.161943\pi$
$859$	51.1935	1.74670	0.873350	+	0.487094i	$0.161943\pi$
$860$	−6.47214	−0.220698
$861$	0	0
$862$	−0.583592	−0.0198772
$863$	7.41641	0.252457	0.126229	−	0.992001i	$-0.459713\pi$
$863$	7.41641	0.252457	0.126229	+	0.992001i	$0.459713\pi$
$864$	−1.00000	−0.0340207
$865$	2.67376	0.0909106
$866$	−20.9098	−0.710545
$867$	−0.270510	−0.00918700
$868$	0	0
$869$	−16.0000	−0.542763
$870$	5.47214	0.185523
$871$	−18.4721	−0.625904
$872$	−10.7984	−0.365679
$873$	−9.79837	−0.331625
$874$	0	0
$875$	0	0
$876$	16.0344	0.541754
$877$	41.9787	1.41752	0.708760	−	0.705449i	$-0.249255\pi$
$877$	41.9787	1.41752	0.708760	+	0.705449i	$0.249255\pi$
$878$	−0.583592	−0.0196953
$879$	−22.0000	−0.742042
$880$	−2.47214	−0.0833357
$881$	55.8115	1.88034	0.940169	−	0.340708i	$-0.110667\pi$
$881$	55.8115	1.88034	0.940169	+	0.340708i	$0.110667\pi$
$882$	7.00000	0.235702
$883$	0	0		−	1.00000i	$-0.5\pi$
$883$	0	0			1.00000i	$0.5\pi$
$884$	−6.61803	−0.222589
$885$	1.52786	0.0513586
$886$	−25.5279	−0.857625
$887$	29.8885	1.00356	0.501780	−	0.864996i	$-0.332679\pi$
$887$	29.8885	1.00356	0.501780	+	0.864996i	$0.332679\pi$
$888$	−5.85410	−0.196451
$889$	0	0
$890$	7.79837	0.261402
$891$	−4.00000	−0.134005
$892$	−6.47214	−0.216703
$893$	0	0
$894$	4.09017	0.136796
$895$	4.94427	0.165269
$896$	0	0
$897$	−6.47214	−0.216098
$898$	13.7984	0.460458
$899$	−13.5279	−0.451180
$900$	−4.61803	−0.153934
$901$	35.2492	1.17432
$902$	23.4164	0.779681
$903$	0	0
$904$	7.32624	0.243667
$905$	−3.70820	−0.123265
$906$	−5.52786	−0.183651
$907$	44.9443	1.49235	0.746175	−	0.665750i	$-0.231888\pi$
$907$	44.9443	1.49235	0.746175	+	0.665750i	$0.231888\pi$
$908$	−16.9443	−0.562315
$909$	−4.90983	−0.162849
$910$	0	0
$911$	−16.3607	−0.542054	−0.271027	−	0.962572i	$-0.587363\pi$
$911$	−16.3607	−0.542054	−0.271027	+	0.962572i	$0.587363\pi$
$912$	0	0
$913$	32.0000	1.05905
$914$	4.32624	0.143099
$915$	−5.94427	−0.196512
$916$	17.5623	0.580275
$917$	0	0
$918$	4.09017	0.134996
$919$	−32.0000	−1.05558	−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000	−1.05558	−0.527791	+	0.849374i	$0.676980\pi$
$920$	2.47214	0.0815039
$921$	−13.5279	−0.445758
$922$	−39.8885	−1.31366
$923$	10.4721	0.344695
$924$	0	0
$925$	−27.0344	−0.888887
$926$	29.3050	0.963020
$927$	15.4164	0.506341
$928$	8.85410	0.290650
$929$	−31.1459	−1.02186	−0.510932	−	0.859621i	$-0.670700\pi$
$929$	−31.1459	−1.02186	−0.510932	+	0.859621i	$0.670700\pi$
$930$	−0.944272	−0.0309639
$931$	0	0
$932$	24.8541	0.814123
$933$	−30.4721	−0.997613
$934$	−34.4721	−1.12796
$935$	10.1115	0.330680
$936$	−1.61803	−0.0528871
$937$	3.88854	0.127033	0.0635166	−	0.997981i	$-0.479768\pi$
$937$	3.88854	0.127033	0.0635166	+	0.997981i	$0.479768\pi$
$938$	0	0
$939$	−12.3262	−0.402252
$940$	3.05573	0.0996669
$941$	−17.7771	−0.579516	−0.289758	−	0.957100i	$-0.593575\pi$
$941$	−17.7771	−0.579516	−0.289758	+	0.957100i	$0.593575\pi$
$942$	19.5066	0.635559
$943$	−23.4164	−0.762543
$944$	2.47214	0.0804612
$945$	0	0
$946$	−41.8885	−1.36191
$947$	38.8328	1.26190	0.630948	−	0.775825i	$-0.282666\pi$
$947$	38.8328	1.26190	0.630948	+	0.775825i	$0.282666\pi$
$948$	4.00000	0.129914
$949$	25.9443	0.842187
$950$	0	0
$951$	22.2148	0.720364
$952$	0	0
$953$	−30.1591	−0.976948	−0.488474	−	0.872579i	$-0.662446\pi$
$953$	−30.1591	−0.976948	−0.488474	+	0.872579i	$0.662446\pi$
$954$	8.61803	0.279019
$955$	−12.0000	−0.388311
$956$	15.4164	0.498602
$957$	35.4164	1.14485
$958$	4.94427	0.159742
$959$	0	0
$960$	0.618034	0.0199470
$961$	−28.6656	−0.924698
$962$	−9.47214	−0.305394
$963$	12.9443	0.417123
$964$	7.88854	0.254073
$965$	−7.34752	−0.236525
$966$	0	0
$967$	−27.7771	−0.893251	−0.446625	−	0.894721i	$-0.647374\pi$
$967$	−27.7771	−0.893251	−0.446625	+	0.894721i	$0.647374\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	6.05573	0.194438
$971$	−55.4164	−1.77840	−0.889199	−	0.457521i	$-0.848737\pi$
$971$	−55.4164	−1.77840	−0.889199	+	0.457521i	$0.848737\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−30.4721	−0.976390
$975$	−7.47214	−0.239300
$976$	−9.61803	−0.307866
$977$	16.3262	0.522323	0.261161	−	0.965295i	$-0.415895\pi$
$977$	16.3262	0.522323	0.261161	+	0.965295i	$0.415895\pi$
$978$	−3.41641	−0.109245
$979$	50.4721	1.61310
$980$	−4.32624	−0.138197
$981$	10.7984	0.344766
$982$	12.3607	0.394445
$983$	1.88854	0.0602352	0.0301176	−	0.999546i	$-0.490412\pi$
$983$	1.88854	0.0602352	0.0301176	+	0.999546i	$0.490412\pi$
$984$	−5.85410	−0.186622
$985$	7.58359	0.241633
$986$	−36.2148	−1.15331
$987$	0	0
$988$	0	0
$989$	41.8885	1.33198
$990$	2.47214	0.0785696
$991$	42.8328	1.36063	0.680315	−	0.732920i	$-0.261843\pi$
$991$	42.8328	1.36063	0.680315	+	0.732920i	$0.261843\pi$
$992$	−1.52786	−0.0485097
$993$	−33.8885	−1.07542
$994$	0	0
$995$	−12.0000	−0.380426
$996$	−8.00000	−0.253490
$997$	61.3394	1.94264	0.971319	−	0.237780i	$-0.0764197\pi$
$997$	61.3394	1.94264	0.971319	+	0.237780i	$0.0764197\pi$
$998$	−8.94427	−0.283126
$999$	5.85410	0.185216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.2.a.k.1.2	✓	2
3.2	odd	2		6498.2.a.bj.1.1		2
19.18	odd	2		2166.2.a.l.1.2	yes	2
57.56	even	2		6498.2.a.bd.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2166.2.a.k.1.2	✓	2	1.1	even	1	trivial
2166.2.a.l.1.2	yes	2	19.18	odd	2
6498.2.a.bd.1.1		2	57.56	even	2
6498.2.a.bj.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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.618034 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.618034 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -0.618034 q^{10} -4.00000 q^{11} +1.00000 q^{12} +1.61803 q^{13} +0.618034 q^{15} +1.00000 q^{16} -4.09017 q^{17} -1.00000 q^{18} +0.618034 q^{20} +4.00000 q^{22} -4.00000 q^{23} -1.00000 q^{24} -4.61803 q^{25} -1.61803 q^{26} +1.00000 q^{27} -8.85410 q^{29} -0.618034 q^{30} +1.52786 q^{31} -1.00000 q^{32} -4.00000 q^{33} +4.09017 q^{34} +1.00000 q^{36} +5.85410 q^{37} +1.61803 q^{39} -0.618034 q^{40} +5.85410 q^{41} -10.4721 q^{43} -4.00000 q^{44} +0.618034 q^{45} +4.00000 q^{46} +4.94427 q^{47} +1.00000 q^{48} -7.00000 q^{49} +4.61803 q^{50} -4.09017 q^{51} +1.61803 q^{52} -8.61803 q^{53} -1.00000 q^{54} -2.47214 q^{55} +8.85410 q^{58} +2.47214 q^{59} +0.618034 q^{60} -9.61803 q^{61} -1.52786 q^{62} +1.00000 q^{64} +1.00000 q^{65} +4.00000 q^{66} -11.4164 q^{67} -4.09017 q^{68} -4.00000 q^{69} +6.47214 q^{71} -1.00000 q^{72} +16.0344 q^{73} -5.85410 q^{74} -4.61803 q^{75} -1.61803 q^{78} +4.00000 q^{79} +0.618034 q^{80} +1.00000 q^{81} -5.85410 q^{82} -8.00000 q^{83} -2.52786 q^{85} +10.4721 q^{86} -8.85410 q^{87} +4.00000 q^{88} -12.6180 q^{89} -0.618034 q^{90} -4.00000 q^{92} +1.52786 q^{93} -4.94427 q^{94} -1.00000 q^{96} -9.79837 q^{97} +7.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{10} - 8 q^{11} + 2 q^{12} + q^{13} - q^{15} + 2 q^{16} + 3 q^{17} - 2 q^{18} - q^{20} + 8 q^{22} - 8 q^{23} - 2 q^{24} - 7 q^{25} - q^{26} + 2 q^{27} - 11 q^{29} + q^{30} + 12 q^{31} - 2 q^{32} - 8 q^{33} - 3 q^{34} + 2 q^{36} + 5 q^{37} + q^{39} + q^{40} + 5 q^{41} - 12 q^{43} - 8 q^{44} - q^{45} + 8 q^{46} - 8 q^{47} + 2 q^{48} - 14 q^{49} + 7 q^{50} + 3 q^{51} + q^{52} - 15 q^{53} - 2 q^{54} + 4 q^{55} + 11 q^{58} - 4 q^{59} - q^{60} - 17 q^{61} - 12 q^{62} + 2 q^{64} + 2 q^{65} + 8 q^{66} + 4 q^{67} + 3 q^{68} - 8 q^{69} + 4 q^{71} - 2 q^{72} + 3 q^{73} - 5 q^{74} - 7 q^{75} - q^{78} + 8 q^{79} - q^{80} + 2 q^{81} - 5 q^{82} - 16 q^{83} - 14 q^{85} + 12 q^{86} - 11 q^{87} + 8 q^{88} - 23 q^{89} + q^{90} - 8 q^{92} + 12 q^{93} + 8 q^{94} - 2 q^{96} + 5 q^{97} + 14 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + q^10 - 8 * q^11 + 2 * q^12 + q^13 - q^15 + 2 * q^16 + 3 * q^17 - 2 * q^18 - q^20 + 8 * q^22 - 8 * q^23 - 2 * q^24 - 7 * q^25 - q^26 + 2 * q^27 - 11 * q^29 + q^30 + 12 * q^31 - 2 * q^32 - 8 * q^33 - 3 * q^34 + 2 * q^36 + 5 * q^37 + q^39 + q^40 + 5 * q^41 - 12 * q^43 - 8 * q^44 - q^45 + 8 * q^46 - 8 * q^47 + 2 * q^48 - 14 * q^49 + 7 * q^50 + 3 * q^51 + q^52 - 15 * q^53 - 2 * q^54 + 4 * q^55 + 11 * q^58 - 4 * q^59 - q^60 - 17 * q^61 - 12 * q^62 + 2 * q^64 + 2 * q^65 + 8 * q^66 + 4 * q^67 + 3 * q^68 - 8 * q^69 + 4 * q^71 - 2 * q^72 + 3 * q^73 - 5 * q^74 - 7 * q^75 - q^78 + 8 * q^79 - q^80 + 2 * q^81 - 5 * q^82 - 16 * q^83 - 14 * q^85 + 12 * q^86 - 11 * q^87 + 8 * q^88 - 23 * q^89 + q^90 - 8 * q^92 + 12 * q^93 + 8 * q^94 - 2 * q^96 + 5 * q^97 + 14 * q^98 - 8 * q^99

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