LMFDB - Embedded newform 5586.2.a.bq.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
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:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.23607 q^{10} -0.763932 q^{11} +1.00000 q^{12} +3.23607 q^{13} +3.23607 q^{15} +1.00000 q^{16} +7.23607 q^{17} +1.00000 q^{18} -1.00000 q^{19} +3.23607 q^{20} -0.763932 q^{22} +0.763932 q^{23} +1.00000 q^{24} +5.47214 q^{25} +3.23607 q^{26} +1.00000 q^{27} -4.47214 q^{29} +3.23607 q^{30} -6.47214 q^{31} +1.00000 q^{32} -0.763932 q^{33} +7.23607 q^{34} +1.00000 q^{36} +6.00000 q^{37} -1.00000 q^{38} +3.23607 q^{39} +3.23607 q^{40} +8.94427 q^{41} -2.47214 q^{43} -0.763932 q^{44} +3.23607 q^{45} +0.763932 q^{46} -4.94427 q^{47} +1.00000 q^{48} +5.47214 q^{50} +7.23607 q^{51} +3.23607 q^{52} -13.4164 q^{53} +1.00000 q^{54} -2.47214 q^{55} -1.00000 q^{57} -4.47214 q^{58} -8.94427 q^{59} +3.23607 q^{60} -6.47214 q^{61} -6.47214 q^{62} +1.00000 q^{64} +10.4721 q^{65} -0.763932 q^{66} +4.76393 q^{67} +7.23607 q^{68} +0.763932 q^{69} -6.47214 q^{71} +1.00000 q^{72} +6.00000 q^{74} +5.47214 q^{75} -1.00000 q^{76} +3.23607 q^{78} -1.70820 q^{79} +3.23607 q^{80} +1.00000 q^{81} +8.94427 q^{82} -5.52786 q^{83} +23.4164 q^{85} -2.47214 q^{86} -4.47214 q^{87} -0.763932 q^{88} +8.94427 q^{89} +3.23607 q^{90} +0.763932 q^{92} -6.47214 q^{93} -4.94427 q^{94} -3.23607 q^{95} +1.00000 q^{96} +5.70820 q^{97} -0.763932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 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 + 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 6 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{15} + 2 q^{16} + 10 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} - 6 q^{22} + 6 q^{23} + 2 q^{24} + 2 q^{25} + 2 q^{26} + 2 q^{27} + 2 q^{30} - 4 q^{31} + 2 q^{32} - 6 q^{33} + 10 q^{34} + 2 q^{36} + 12 q^{37} - 2 q^{38} + 2 q^{39} + 2 q^{40} + 4 q^{43} - 6 q^{44} + 2 q^{45} + 6 q^{46} + 8 q^{47} + 2 q^{48} + 2 q^{50} + 10 q^{51} + 2 q^{52} + 2 q^{54} + 4 q^{55} - 2 q^{57} + 2 q^{60} - 4 q^{61} - 4 q^{62} + 2 q^{64} + 12 q^{65} - 6 q^{66} + 14 q^{67} + 10 q^{68} + 6 q^{69} - 4 q^{71} + 2 q^{72} + 12 q^{74} + 2 q^{75} - 2 q^{76} + 2 q^{78} + 10 q^{79} + 2 q^{80} + 2 q^{81} - 20 q^{83} + 20 q^{85} + 4 q^{86} - 6 q^{88} + 2 q^{90} + 6 q^{92} - 4 q^{93} + 8 q^{94} - 2 q^{95} + 2 q^{96} - 2 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 6 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^15 + 2 * q^16 + 10 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 - 6 * q^22 + 6 * q^23 + 2 * q^24 + 2 * q^25 + 2 * q^26 + 2 * q^27 + 2 * q^30 - 4 * q^31 + 2 * q^32 - 6 * q^33 + 10 * q^34 + 2 * q^36 + 12 * q^37 - 2 * q^38 + 2 * q^39 + 2 * q^40 + 4 * q^43 - 6 * q^44 + 2 * q^45 + 6 * q^46 + 8 * q^47 + 2 * q^48 + 2 * q^50 + 10 * q^51 + 2 * q^52 + 2 * q^54 + 4 * q^55 - 2 * q^57 + 2 * q^60 - 4 * q^61 - 4 * q^62 + 2 * q^64 + 12 * q^65 - 6 * q^66 + 14 * q^67 + 10 * q^68 + 6 * q^69 - 4 * q^71 + 2 * q^72 + 12 * q^74 + 2 * q^75 - 2 * q^76 + 2 * q^78 + 10 * q^79 + 2 * q^80 + 2 * q^81 - 20 * q^83 + 20 * q^85 + 4 * q^86 - 6 * q^88 + 2 * q^90 + 6 * q^92 - 4 * q^93 + 8 * q^94 - 2 * q^95 + 2 * q^96 - 2 * q^97 - 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
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.23607	1.44721	0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607	1.44721	0.723607	+	0.690212i	$0.242483\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.23607	1.02333
$11$	−0.763932	−0.230334	−0.115167	−	0.993346i	$-0.536740\pi$
$11$	−0.763932	−0.230334	−0.115167	+	0.993346i	$0.536740\pi$
$12$	1.00000	0.288675
$13$	3.23607	0.897524	0.448762	−	0.893651i	$-0.351865\pi$
$13$	3.23607	0.897524	0.448762	+	0.893651i	$0.351865\pi$
$14$	0	0
$15$	3.23607	0.835549
$16$	1.00000	0.250000
$17$	7.23607	1.75500	0.877502	−	0.479573i	$-0.159208\pi$
$17$	7.23607	1.75500	0.877502	+	0.479573i	$0.159208\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.23607	0.723607
$21$	0	0
$22$	−0.763932	−0.162871
$23$	0.763932	0.159291	0.0796454	−	0.996823i	$-0.474621\pi$
$23$	0.763932	0.159291	0.0796454	+	0.996823i	$0.474621\pi$
$24$	1.00000	0.204124
$25$	5.47214	1.09443
$26$	3.23607	0.634645
$27$	1.00000	0.192450
$28$	0	0
$29$	−4.47214	−0.830455	−0.415227	−	0.909718i	$-0.636298\pi$
$29$	−4.47214	−0.830455	−0.415227	+	0.909718i	$0.636298\pi$
$30$	3.23607	0.590822
$31$	−6.47214	−1.16243	−0.581215	−	0.813750i	$-0.697422\pi$
$31$	−6.47214	−1.16243	−0.581215	+	0.813750i	$0.697422\pi$
$32$	1.00000	0.176777
$33$	−0.763932	−0.132983
$34$	7.23607	1.24098
$35$	0	0
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	−1.00000	−0.162221
$39$	3.23607	0.518186
$40$	3.23607	0.511667
$41$	8.94427	1.39686	0.698430	−	0.715678i	$-0.253882\pi$
$41$	8.94427	1.39686	0.698430	+	0.715678i	$0.253882\pi$
$42$	0	0
$43$	−2.47214	−0.376997	−0.188499	−	0.982073i	$-0.560362\pi$
$43$	−2.47214	−0.376997	−0.188499	+	0.982073i	$0.560362\pi$
$44$	−0.763932	−0.115167
$45$	3.23607	0.482405
$46$	0.763932	0.112636
$47$	−4.94427	−0.721196	−0.360598	−	0.932721i	$-0.617427\pi$
$47$	−4.94427	−0.721196	−0.360598	+	0.932721i	$0.617427\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	5.47214	0.773877
$51$	7.23607	1.01325
$52$	3.23607	0.448762
$53$	−13.4164	−1.84289	−0.921443	−	0.388514i	$-0.872988\pi$
$53$	−13.4164	−1.84289	−0.921443	+	0.388514i	$0.872988\pi$
$54$	1.00000	0.136083
$55$	−2.47214	−0.333343
$56$	0	0
$57$	−1.00000	−0.132453
$58$	−4.47214	−0.587220
$59$	−8.94427	−1.16445	−0.582223	−	0.813029i	$-0.697817\pi$
$59$	−8.94427	−1.16445	−0.582223	+	0.813029i	$0.697817\pi$
$60$	3.23607	0.417775
$61$	−6.47214	−0.828672	−0.414336	−	0.910124i	$-0.635986\pi$
$61$	−6.47214	−0.828672	−0.414336	+	0.910124i	$0.635986\pi$
$62$	−6.47214	−0.821962
$63$	0	0
$64$	1.00000	0.125000
$65$	10.4721	1.29891
$66$	−0.763932	−0.0940335
$67$	4.76393	0.582007	0.291003	−	0.956722i	$-0.406011\pi$
$67$	4.76393	0.582007	0.291003	+	0.956722i	$0.406011\pi$
$68$	7.23607	0.877502
$69$	0.763932	0.0919666
$70$	0	0
$71$	−6.47214	−0.768101	−0.384051	−	0.923312i	$-0.625471\pi$
$71$	−6.47214	−0.768101	−0.384051	+	0.923312i	$0.625471\pi$
$72$	1.00000	0.117851
$73$	0	0		−	1.00000i	$-0.5\pi$
$73$	0	0			1.00000i	$0.5\pi$
$74$	6.00000	0.697486
$75$	5.47214	0.631868
$76$	−1.00000	−0.114708
$77$	0	0
$78$	3.23607	0.366413
$79$	−1.70820	−0.192188	−0.0960940	−	0.995372i	$-0.530635\pi$
$79$	−1.70820	−0.192188	−0.0960940	+	0.995372i	$0.530635\pi$
$80$	3.23607	0.361803
$81$	1.00000	0.111111
$82$	8.94427	0.987730
$83$	−5.52786	−0.606762	−0.303381	−	0.952869i	$-0.598115\pi$
$83$	−5.52786	−0.606762	−0.303381	+	0.952869i	$0.598115\pi$
$84$	0	0
$85$	23.4164	2.53987
$86$	−2.47214	−0.266577
$87$	−4.47214	−0.479463
$88$	−0.763932	−0.0814354
$89$	8.94427	0.948091	0.474045	−	0.880500i	$-0.342793\pi$
$89$	8.94427	0.948091	0.474045	+	0.880500i	$0.342793\pi$
$90$	3.23607	0.341112
$91$	0	0
$92$	0.763932	0.0796454
$93$	−6.47214	−0.671129
$94$	−4.94427	−0.509963
$95$	−3.23607	−0.332014
$96$	1.00000	0.102062
$97$	5.70820	0.579580	0.289790	−	0.957090i	$-0.406414\pi$
$97$	5.70820	0.579580	0.289790	+	0.957090i	$0.406414\pi$
$98$	0	0
$99$	−0.763932	−0.0767781
$100$	5.47214	0.547214
$101$	−9.70820	−0.966002	−0.483001	−	0.875620i	$-0.660453\pi$
$101$	−9.70820	−0.966002	−0.483001	+	0.875620i	$0.660453\pi$
$102$	7.23607	0.716477
$103$	−9.52786	−0.938808	−0.469404	−	0.882983i	$-0.655531\pi$
$103$	−9.52786	−0.938808	−0.469404	+	0.882983i	$0.655531\pi$
$104$	3.23607	0.317323
$105$	0	0
$106$	−13.4164	−1.30312
$107$	16.9443	1.63806	0.819032	−	0.573747i	$-0.194511\pi$
$107$	16.9443	1.63806	0.819032	+	0.573747i	$0.194511\pi$
$108$	1.00000	0.0962250
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−2.47214	−0.235709
$111$	6.00000	0.569495
$112$	0	0
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	−1.00000	−0.0936586
$115$	2.47214	0.230528
$116$	−4.47214	−0.415227
$117$	3.23607	0.299175
$118$	−8.94427	−0.823387
$119$	0	0
$120$	3.23607	0.295411
$121$	−10.4164	−0.946946
$122$	−6.47214	−0.585960
$123$	8.94427	0.806478
$124$	−6.47214	−0.581215
$125$	1.52786	0.136656
$126$	0	0
$127$	9.70820	0.861464	0.430732	−	0.902480i	$-0.358255\pi$
$127$	9.70820	0.861464	0.430732	+	0.902480i	$0.358255\pi$
$128$	1.00000	0.0883883
$129$	−2.47214	−0.217659
$130$	10.4721	0.918467
$131$	−7.41641	−0.647975	−0.323987	−	0.946061i	$-0.605024\pi$
$131$	−7.41641	−0.647975	−0.323987	+	0.946061i	$0.605024\pi$
$132$	−0.763932	−0.0664917
$133$	0	0
$134$	4.76393	0.411541
$135$	3.23607	0.278516
$136$	7.23607	0.620488
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0.763932	0.0650302
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	−4.94427	−0.416383
$142$	−6.47214	−0.543130
$143$	−2.47214	−0.206730
$144$	1.00000	0.0833333
$145$	−14.4721	−1.20185
$146$	0	0
$147$	0	0
$148$	6.00000	0.493197
$149$	14.9443	1.22428	0.612141	−	0.790748i	$-0.290308\pi$
$149$	14.9443	1.22428	0.612141	+	0.790748i	$0.290308\pi$
$150$	5.47214	0.446798
$151$	−17.7082	−1.44107	−0.720537	−	0.693417i	$-0.756104\pi$
$151$	−17.7082	−1.44107	−0.720537	+	0.693417i	$0.756104\pi$
$152$	−1.00000	−0.0811107
$153$	7.23607	0.585001
$154$	0	0
$155$	−20.9443	−1.68228
$156$	3.23607	0.259093
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	−1.70820	−0.135897
$159$	−13.4164	−1.06399
$160$	3.23607	0.255834
$161$	0	0
$162$	1.00000	0.0785674
$163$	15.4164	1.20751	0.603753	−	0.797171i	$-0.293671\pi$
$163$	15.4164	1.20751	0.603753	+	0.797171i	$0.293671\pi$
$164$	8.94427	0.698430
$165$	−2.47214	−0.192456
$166$	−5.52786	−0.429045
$167$	−20.3607	−1.57556	−0.787778	−	0.615959i	$-0.788769\pi$
$167$	−20.3607	−1.57556	−0.787778	+	0.615959i	$0.788769\pi$
$168$	0	0
$169$	−2.52786	−0.194451
$170$	23.4164	1.79596
$171$	−1.00000	−0.0764719
$172$	−2.47214	−0.188499
$173$	2.47214	0.187953	0.0939765	−	0.995574i	$-0.470042\pi$
$173$	2.47214	0.187953	0.0939765	+	0.995574i	$0.470042\pi$
$174$	−4.47214	−0.339032
$175$	0	0
$176$	−0.763932	−0.0575835
$177$	−8.94427	−0.672293
$178$	8.94427	0.670402
$179$	13.8885	1.03808	0.519039	−	0.854750i	$-0.326290\pi$
$179$	13.8885	1.03808	0.519039	+	0.854750i	$0.326290\pi$
$180$	3.23607	0.241202
$181$	9.70820	0.721605	0.360803	−	0.932642i	$-0.382503\pi$
$181$	9.70820	0.721605	0.360803	+	0.932642i	$0.382503\pi$
$182$	0	0
$183$	−6.47214	−0.478434
$184$	0.763932	0.0563178
$185$	19.4164	1.42752
$186$	−6.47214	−0.474560
$187$	−5.52786	−0.404237
$188$	−4.94427	−0.360598
$189$	0	0
$190$	−3.23607	−0.234769
$191$	16.7639	1.21300	0.606498	−	0.795085i	$-0.292574\pi$
$191$	16.7639	1.21300	0.606498	+	0.795085i	$0.292574\pi$
$192$	1.00000	0.0721688
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	5.70820	0.409825
$195$	10.4721	0.749925
$196$	0	0
$197$	−26.9443	−1.91970	−0.959850	−	0.280514i	$-0.909495\pi$
$197$	−26.9443	−1.91970	−0.959850	+	0.280514i	$0.909495\pi$
$198$	−0.763932	−0.0542903
$199$	15.4164	1.09284	0.546420	−	0.837511i	$-0.315990\pi$
$199$	15.4164	1.09284	0.546420	+	0.837511i	$0.315990\pi$
$200$	5.47214	0.386938
$201$	4.76393	0.336022
$202$	−9.70820	−0.683067
$203$	0	0
$204$	7.23607	0.506626
$205$	28.9443	2.02156
$206$	−9.52786	−0.663838
$207$	0.763932	0.0530969
$208$	3.23607	0.224381
$209$	0.763932	0.0528423
$210$	0	0
$211$	1.70820	0.117598	0.0587988	−	0.998270i	$-0.481273\pi$
$211$	1.70820	0.117598	0.0587988	+	0.998270i	$0.481273\pi$
$212$	−13.4164	−0.921443
$213$	−6.47214	−0.443463
$214$	16.9443	1.15829
$215$	−8.00000	−0.545595
$216$	1.00000	0.0680414
$217$	0	0
$218$	6.00000	0.406371
$219$	0	0
$220$	−2.47214	−0.166671
$221$	23.4164	1.57516
$222$	6.00000	0.402694
$223$	3.41641	0.228780	0.114390	−	0.993436i	$-0.463509\pi$
$223$	3.41641	0.228780	0.114390	+	0.993436i	$0.463509\pi$
$224$	0	0
$225$	5.47214	0.364809
$226$	6.00000	0.399114
$227$	19.4164	1.28871	0.644356	−	0.764726i	$-0.277125\pi$
$227$	19.4164	1.28871	0.644356	+	0.764726i	$0.277125\pi$
$228$	−1.00000	−0.0662266
$229$	−6.47214	−0.427691	−0.213845	−	0.976868i	$-0.568599\pi$
$229$	−6.47214	−0.427691	−0.213845	+	0.976868i	$0.568599\pi$
$230$	2.47214	0.163008
$231$	0	0
$232$	−4.47214	−0.293610
$233$	9.05573	0.593260	0.296630	−	0.954992i	$-0.404137\pi$
$233$	9.05573	0.593260	0.296630	+	0.954992i	$0.404137\pi$
$234$	3.23607	0.211548
$235$	−16.0000	−1.04372
$236$	−8.94427	−0.582223
$237$	−1.70820	−0.110960
$238$	0	0
$239$	−2.29180	−0.148244	−0.0741220	−	0.997249i	$-0.523615\pi$
$239$	−2.29180	−0.148244	−0.0741220	+	0.997249i	$0.523615\pi$
$240$	3.23607	0.208887
$241$	−21.7082	−1.39835	−0.699174	−	0.714951i	$-0.746449\pi$
$241$	−21.7082	−1.39835	−0.699174	+	0.714951i	$0.746449\pi$
$242$	−10.4164	−0.669592
$243$	1.00000	0.0641500
$244$	−6.47214	−0.414336
$245$	0	0
$246$	8.94427	0.570266
$247$	−3.23607	−0.205906
$248$	−6.47214	−0.410981
$249$	−5.52786	−0.350314
$250$	1.52786	0.0966306
$251$	−13.5279	−0.853871	−0.426936	−	0.904282i	$-0.640407\pi$
$251$	−13.5279	−0.853871	−0.426936	+	0.904282i	$0.640407\pi$
$252$	0	0
$253$	−0.583592	−0.0366901
$254$	9.70820	0.609147
$255$	23.4164	1.46639
$256$	1.00000	0.0625000
$257$	21.5279	1.34287	0.671436	−	0.741063i	$-0.265678\pi$
$257$	21.5279	1.34287	0.671436	+	0.741063i	$0.265678\pi$
$258$	−2.47214	−0.153908
$259$	0	0
$260$	10.4721	0.649454
$261$	−4.47214	−0.276818
$262$	−7.41641	−0.458187
$263$	−23.5967	−1.45504	−0.727519	−	0.686088i	$-0.759327\pi$
$263$	−23.5967	−1.45504	−0.727519	+	0.686088i	$0.759327\pi$
$264$	−0.763932	−0.0470168
$265$	−43.4164	−2.66705
$266$	0	0
$267$	8.94427	0.547381
$268$	4.76393	0.291003
$269$	−31.4164	−1.91549	−0.957746	−	0.287615i	$-0.907138\pi$
$269$	−31.4164	−1.91549	−0.957746	+	0.287615i	$0.907138\pi$
$270$	3.23607	0.196941
$271$	−24.0000	−1.45790	−0.728948	−	0.684569i	$-0.759990\pi$
$271$	−24.0000	−1.45790	−0.728948	+	0.684569i	$0.759990\pi$
$272$	7.23607	0.438751
$273$	0	0
$274$	6.00000	0.362473
$275$	−4.18034	−0.252084
$276$	0.763932	0.0459833
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	−4.00000	−0.239904
$279$	−6.47214	−0.387477
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	−4.94427	−0.294427
$283$	12.0000	0.713326	0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$284$	−6.47214	−0.384051
$285$	−3.23607	−0.191688
$286$	−2.47214	−0.146180
$287$	0	0
$288$	1.00000	0.0589256
$289$	35.3607	2.08004
$290$	−14.4721	−0.849833
$291$	5.70820	0.334621
$292$	0	0
$293$	2.47214	0.144424	0.0722119	−	0.997389i	$-0.476994\pi$
$293$	2.47214	0.144424	0.0722119	+	0.997389i	$0.476994\pi$
$294$	0	0
$295$	−28.9443	−1.68520
$296$	6.00000	0.348743
$297$	−0.763932	−0.0443278
$298$	14.9443	0.865698
$299$	2.47214	0.142967
$300$	5.47214	0.315934
$301$	0	0
$302$	−17.7082	−1.01899
$303$	−9.70820	−0.557722
$304$	−1.00000	−0.0573539
$305$	−20.9443	−1.19927
$306$	7.23607	0.413658
$307$	−26.8328	−1.53143	−0.765715	−	0.643180i	$-0.777615\pi$
$307$	−26.8328	−1.53143	−0.765715	+	0.643180i	$0.777615\pi$
$308$	0	0
$309$	−9.52786	−0.542021
$310$	−20.9443	−1.18955
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	3.23607	0.183206
$313$	−9.88854	−0.558934	−0.279467	−	0.960155i	$-0.590158\pi$
$313$	−9.88854	−0.558934	−0.279467	+	0.960155i	$0.590158\pi$
$314$	8.00000	0.451466
$315$	0	0
$316$	−1.70820	−0.0960940
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	−13.4164	−0.752355
$319$	3.41641	0.191282
$320$	3.23607	0.180902
$321$	16.9443	0.945737
$322$	0	0
$323$	−7.23607	−0.402626
$324$	1.00000	0.0555556
$325$	17.7082	0.982274
$326$	15.4164	0.853836
$327$	6.00000	0.331801
$328$	8.94427	0.493865
$329$	0	0
$330$	−2.47214	−0.136087
$331$	27.2361	1.49703	0.748515	−	0.663118i	$-0.230767\pi$
$331$	27.2361	1.49703	0.748515	+	0.663118i	$0.230767\pi$
$332$	−5.52786	−0.303381
$333$	6.00000	0.328798
$334$	−20.3607	−1.11409
$335$	15.4164	0.842288
$336$	0	0
$337$	−27.8885	−1.51919	−0.759593	−	0.650399i	$-0.774602\pi$
$337$	−27.8885	−1.51919	−0.759593	+	0.650399i	$0.774602\pi$
$338$	−2.52786	−0.137498
$339$	6.00000	0.325875
$340$	23.4164	1.26993
$341$	4.94427	0.267747
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	−2.47214	−0.133289
$345$	2.47214	0.133095
$346$	2.47214	0.132903
$347$	0.763932	0.0410100	0.0205050	−	0.999790i	$-0.493473\pi$
$347$	0.763932	0.0410100	0.0205050	+	0.999790i	$0.493473\pi$
$348$	−4.47214	−0.239732
$349$	−16.0000	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$350$	0	0
$351$	3.23607	0.172729
$352$	−0.763932	−0.0407177
$353$	−3.81966	−0.203300	−0.101650	−	0.994820i	$-0.532412\pi$
$353$	−3.81966	−0.203300	−0.101650	+	0.994820i	$0.532412\pi$
$354$	−8.94427	−0.475383
$355$	−20.9443	−1.11161
$356$	8.94427	0.474045
$357$	0	0
$358$	13.8885	0.734032
$359$	−21.7082	−1.14572	−0.572858	−	0.819655i	$-0.694165\pi$
$359$	−21.7082	−1.14572	−0.572858	+	0.819655i	$0.694165\pi$
$360$	3.23607	0.170556
$361$	1.00000	0.0526316
$362$	9.70820	0.510252
$363$	−10.4164	−0.546720
$364$	0	0
$365$	0	0
$366$	−6.47214	−0.338304
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	0.763932	0.0398227
$369$	8.94427	0.465620
$370$	19.4164	1.00941
$371$	0	0
$372$	−6.47214	−0.335565
$373$	30.9443	1.60223	0.801117	−	0.598508i	$-0.204240\pi$
$373$	30.9443	1.60223	0.801117	+	0.598508i	$0.204240\pi$
$374$	−5.52786	−0.285839
$375$	1.52786	0.0788986
$376$	−4.94427	−0.254981
$377$	−14.4721	−0.745353
$378$	0	0
$379$	29.1246	1.49603	0.748015	−	0.663681i	$-0.231007\pi$
$379$	29.1246	1.49603	0.748015	+	0.663681i	$0.231007\pi$
$380$	−3.23607	−0.166007
$381$	9.70820	0.497366
$382$	16.7639	0.857717
$383$	11.0557	0.564921	0.282461	−	0.959279i	$-0.408849\pi$
$383$	11.0557	0.564921	0.282461	+	0.959279i	$0.408849\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.0000	0.508987
$387$	−2.47214	−0.125666
$388$	5.70820	0.289790
$389$	−32.8328	−1.66469	−0.832345	−	0.554258i	$-0.813002\pi$
$389$	−32.8328	−1.66469	−0.832345	+	0.554258i	$0.813002\pi$
$390$	10.4721	0.530277
$391$	5.52786	0.279556
$392$	0	0
$393$	−7.41641	−0.374108
$394$	−26.9443	−1.35743
$395$	−5.52786	−0.278137
$396$	−0.763932	−0.0383890
$397$	1.88854	0.0947833	0.0473916	−	0.998876i	$-0.484909\pi$
$397$	1.88854	0.0947833	0.0473916	+	0.998876i	$0.484909\pi$
$398$	15.4164	0.772755
$399$	0	0
$400$	5.47214	0.273607
$401$	−3.52786	−0.176173	−0.0880866	−	0.996113i	$-0.528075\pi$
$401$	−3.52786	−0.176173	−0.0880866	+	0.996113i	$0.528075\pi$
$402$	4.76393	0.237603
$403$	−20.9443	−1.04331
$404$	−9.70820	−0.483001
$405$	3.23607	0.160802
$406$	0	0
$407$	−4.58359	−0.227200
$408$	7.23607	0.358239
$409$	13.7082	0.677827	0.338914	−	0.940818i	$-0.389941\pi$
$409$	13.7082	0.677827	0.338914	+	0.940818i	$0.389941\pi$
$410$	28.9443	1.42946
$411$	6.00000	0.295958
$412$	−9.52786	−0.469404
$413$	0	0
$414$	0.763932	0.0375452
$415$	−17.8885	−0.878114
$416$	3.23607	0.158661
$417$	−4.00000	−0.195881
$418$	0.763932	0.0373651
$419$	−36.3607	−1.77634	−0.888168	−	0.459519i	$-0.848022\pi$
$419$	−36.3607	−1.77634	−0.888168	+	0.459519i	$0.848022\pi$
$420$	0	0
$421$	−6.00000	−0.292422	−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000	−0.292422	−0.146211	+	0.989253i	$0.546708\pi$
$422$	1.70820	0.0831541
$423$	−4.94427	−0.240399
$424$	−13.4164	−0.651558
$425$	39.5967	1.92072
$426$	−6.47214	−0.313576
$427$	0	0
$428$	16.9443	0.819032
$429$	−2.47214	−0.119356
$430$	−8.00000	−0.385794
$431$	37.3050	1.79692	0.898458	−	0.439059i	$-0.144688\pi$
$431$	37.3050	1.79692	0.898458	+	0.439059i	$0.144688\pi$
$432$	1.00000	0.0481125
$433$	5.70820	0.274319	0.137159	−	0.990549i	$-0.456203\pi$
$433$	5.70820	0.274319	0.137159	+	0.990549i	$0.456203\pi$
$434$	0	0
$435$	−14.4721	−0.693886
$436$	6.00000	0.287348
$437$	−0.763932	−0.0365438
$438$	0	0
$439$	−17.5279	−0.836559	−0.418280	−	0.908318i	$-0.637367\pi$
$439$	−17.5279	−0.836559	−0.418280	+	0.908318i	$0.637367\pi$
$440$	−2.47214	−0.117854
$441$	0	0
$442$	23.4164	1.11380
$443$	−8.76393	−0.416387	−0.208193	−	0.978088i	$-0.566758\pi$
$443$	−8.76393	−0.416387	−0.208193	+	0.978088i	$0.566758\pi$
$444$	6.00000	0.284747
$445$	28.9443	1.37209
$446$	3.41641	0.161772
$447$	14.9443	0.706840
$448$	0	0
$449$	−27.8885	−1.31614	−0.658071	−	0.752956i	$-0.728627\pi$
$449$	−27.8885	−1.31614	−0.658071	+	0.752956i	$0.728627\pi$
$450$	5.47214	0.257959
$451$	−6.83282	−0.321745
$452$	6.00000	0.282216
$453$	−17.7082	−0.832004
$454$	19.4164	0.911257
$455$	0	0
$456$	−1.00000	−0.0468293
$457$	25.4164	1.18893	0.594465	−	0.804122i	$-0.297364\pi$
$457$	25.4164	1.18893	0.594465	+	0.804122i	$0.297364\pi$
$458$	−6.47214	−0.302423
$459$	7.23607	0.337751
$460$	2.47214	0.115264
$461$	−30.6525	−1.42763	−0.713814	−	0.700335i	$-0.753034\pi$
$461$	−30.6525	−1.42763	−0.713814	+	0.700335i	$0.753034\pi$
$462$	0	0
$463$	−22.8328	−1.06113	−0.530565	−	0.847644i	$-0.678020\pi$
$463$	−22.8328	−1.06113	−0.530565	+	0.847644i	$0.678020\pi$
$464$	−4.47214	−0.207614
$465$	−20.9443	−0.971267
$466$	9.05573	0.419499
$467$	21.5279	0.996191	0.498095	−	0.867122i	$-0.334033\pi$
$467$	21.5279	0.996191	0.498095	+	0.867122i	$0.334033\pi$
$468$	3.23607	0.149587
$469$	0	0
$470$	−16.0000	−0.738025
$471$	8.00000	0.368621
$472$	−8.94427	−0.411693
$473$	1.88854	0.0868353
$474$	−1.70820	−0.0784604
$475$	−5.47214	−0.251079
$476$	0	0
$477$	−13.4164	−0.614295
$478$	−2.29180	−0.104824
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	3.23607	0.147706
$481$	19.4164	0.885312
$482$	−21.7082	−0.988782
$483$	0	0
$484$	−10.4164	−0.473473
$485$	18.4721	0.838776
$486$	1.00000	0.0453609
$487$	4.76393	0.215874	0.107937	−	0.994158i	$-0.465575\pi$
$487$	4.76393	0.215874	0.107937	+	0.994158i	$0.465575\pi$
$488$	−6.47214	−0.292980
$489$	15.4164	0.697154
$490$	0	0
$491$	0.763932	0.0344758	0.0172379	−	0.999851i	$-0.494513\pi$
$491$	0.763932	0.0344758	0.0172379	+	0.999851i	$0.494513\pi$
$492$	8.94427	0.403239
$493$	−32.3607	−1.45745
$494$	−3.23607	−0.145598
$495$	−2.47214	−0.111114
$496$	−6.47214	−0.290607
$497$	0	0
$498$	−5.52786	−0.247710
$499$	12.3607	0.553340	0.276670	−	0.960965i	$-0.410769\pi$
$499$	12.3607	0.553340	0.276670	+	0.960965i	$0.410769\pi$
$500$	1.52786	0.0683282
$501$	−20.3607	−0.909648
$502$	−13.5279	−0.603778
$503$	41.8885	1.86772	0.933859	−	0.357642i	$-0.116419\pi$
$503$	41.8885	1.86772	0.933859	+	0.357642i	$0.116419\pi$
$504$	0	0
$505$	−31.4164	−1.39801
$506$	−0.583592	−0.0259438
$507$	−2.52786	−0.112266
$508$	9.70820	0.430732
$509$	34.4721	1.52795	0.763975	−	0.645246i	$-0.223245\pi$
$509$	34.4721	1.52795	0.763975	+	0.645246i	$0.223245\pi$
$510$	23.4164	1.03690
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	21.5279	0.949553
$515$	−30.8328	−1.35866
$516$	−2.47214	−0.108830
$517$	3.77709	0.166116
$518$	0	0
$519$	2.47214	0.108515
$520$	10.4721	0.459234
$521$	−16.9443	−0.742342	−0.371171	−	0.928565i	$-0.621044\pi$
$521$	−16.9443	−0.742342	−0.371171	+	0.928565i	$0.621044\pi$
$522$	−4.47214	−0.195740
$523$	24.9443	1.09074	0.545368	−	0.838196i	$-0.316390\pi$
$523$	24.9443	1.09074	0.545368	+	0.838196i	$0.316390\pi$
$524$	−7.41641	−0.323987
$525$	0	0
$526$	−23.5967	−1.02887
$527$	−46.8328	−2.04007
$528$	−0.763932	−0.0332459
$529$	−22.4164	−0.974626
$530$	−43.4164	−1.88589
$531$	−8.94427	−0.388148
$532$	0	0
$533$	28.9443	1.25372
$534$	8.94427	0.387056
$535$	54.8328	2.37063
$536$	4.76393	0.205771
$537$	13.8885	0.599335
$538$	−31.4164	−1.35446
$539$	0	0
$540$	3.23607	0.139258
$541$	−14.3607	−0.617414	−0.308707	−	0.951157i	$-0.599896\pi$
$541$	−14.3607	−0.617414	−0.308707	+	0.951157i	$0.599896\pi$
$542$	−24.0000	−1.03089
$543$	9.70820	0.416619
$544$	7.23607	0.310244
$545$	19.4164	0.831708
$546$	0	0
$547$	11.5967	0.495841	0.247921	−	0.968780i	$-0.420253\pi$
$547$	11.5967	0.495841	0.247921	+	0.968780i	$0.420253\pi$
$548$	6.00000	0.256307
$549$	−6.47214	−0.276224
$550$	−4.18034	−0.178250
$551$	4.47214	0.190519
$552$	0.763932	0.0325151
$553$	0	0
$554$	6.00000	0.254916
$555$	19.4164	0.824181
$556$	−4.00000	−0.169638
$557$	42.0000	1.77960	0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000	1.77960	0.889799	+	0.456354i	$0.150845\pi$
$558$	−6.47214	−0.273987
$559$	−8.00000	−0.338364
$560$	0	0
$561$	−5.52786	−0.233387
$562$	−6.00000	−0.253095
$563$	32.9443	1.38844	0.694218	−	0.719765i	$-0.255750\pi$
$563$	32.9443	1.38844	0.694218	+	0.719765i	$0.255750\pi$
$564$	−4.94427	−0.208191
$565$	19.4164	0.816854
$566$	12.0000	0.504398
$567$	0	0
$568$	−6.47214	−0.271565
$569$	−34.3607	−1.44047	−0.720237	−	0.693728i	$-0.755967\pi$
$569$	−34.3607	−1.44047	−0.720237	+	0.693728i	$0.755967\pi$
$570$	−3.23607	−0.135544
$571$	−26.8328	−1.12292	−0.561459	−	0.827504i	$-0.689760\pi$
$571$	−26.8328	−1.12292	−0.561459	+	0.827504i	$0.689760\pi$
$572$	−2.47214	−0.103365
$573$	16.7639	0.700323
$574$	0	0
$575$	4.18034	0.174332
$576$	1.00000	0.0416667
$577$	−30.8328	−1.28359	−0.641793	−	0.766878i	$-0.721809\pi$
$577$	−30.8328	−1.28359	−0.641793	+	0.766878i	$0.721809\pi$
$578$	35.3607	1.47081
$579$	10.0000	0.415586
$580$	−14.4721	−0.600923
$581$	0	0
$582$	5.70820	0.236613
$583$	10.2492	0.424479
$584$	0	0
$585$	10.4721	0.432970
$586$	2.47214	0.102123
$587$	26.4721	1.09262	0.546311	−	0.837582i	$-0.316032\pi$
$587$	26.4721	1.09262	0.546311	+	0.837582i	$0.316032\pi$
$588$	0	0
$589$	6.47214	0.266680
$590$	−28.9443	−1.19162
$591$	−26.9443	−1.10834
$592$	6.00000	0.246598
$593$	45.7082	1.87701	0.938505	−	0.345264i	$-0.112211\pi$
$593$	45.7082	1.87701	0.938505	+	0.345264i	$0.112211\pi$
$594$	−0.763932	−0.0313445
$595$	0	0
$596$	14.9443	0.612141
$597$	15.4164	0.630952
$598$	2.47214	0.101093
$599$	16.3607	0.668479	0.334240	−	0.942488i	$-0.391521\pi$
$599$	16.3607	0.668479	0.334240	+	0.942488i	$0.391521\pi$
$600$	5.47214	0.223399
$601$	−12.1803	−0.496846	−0.248423	−	0.968652i	$-0.579912\pi$
$601$	−12.1803	−0.496846	−0.248423	+	0.968652i	$0.579912\pi$
$602$	0	0
$603$	4.76393	0.194002
$604$	−17.7082	−0.720537
$605$	−33.7082	−1.37043
$606$	−9.70820	−0.394369
$607$	−27.4164	−1.11280	−0.556399	−	0.830915i	$-0.687817\pi$
$607$	−27.4164	−1.11280	−0.556399	+	0.830915i	$0.687817\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	−20.9443	−0.848009
$611$	−16.0000	−0.647291
$612$	7.23607	0.292501
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	−26.8328	−1.08288
$615$	28.9443	1.16715
$616$	0	0
$617$	7.88854	0.317581	0.158790	−	0.987312i	$-0.449241\pi$
$617$	7.88854	0.317581	0.158790	+	0.987312i	$0.449241\pi$
$618$	−9.52786	−0.383267
$619$	−12.5836	−0.505777	−0.252889	−	0.967495i	$-0.581381\pi$
$619$	−12.5836	−0.505777	−0.252889	+	0.967495i	$0.581381\pi$
$620$	−20.9443	−0.841142
$621$	0.763932	0.0306555
$622$	−24.0000	−0.962312
$623$	0	0
$624$	3.23607	0.129546
$625$	−22.4164	−0.896656
$626$	−9.88854	−0.395226
$627$	0.763932	0.0305085
$628$	8.00000	0.319235
$629$	43.4164	1.73113
$630$	0	0
$631$	−9.52786	−0.379298	−0.189649	−	0.981852i	$-0.560735\pi$
$631$	−9.52786	−0.379298	−0.189649	+	0.981852i	$0.560735\pi$
$632$	−1.70820	−0.0679487
$633$	1.70820	0.0678950
$634$	18.0000	0.714871
$635$	31.4164	1.24672
$636$	−13.4164	−0.531995
$637$	0	0
$638$	3.41641	0.135257
$639$	−6.47214	−0.256034
$640$	3.23607	0.127917
$641$	3.88854	0.153588	0.0767941	−	0.997047i	$-0.475532\pi$
$641$	3.88854	0.153588	0.0767941	+	0.997047i	$0.475532\pi$
$642$	16.9443	0.668737
$643$	−19.4164	−0.765708	−0.382854	−	0.923809i	$-0.625059\pi$
$643$	−19.4164	−0.765708	−0.382854	+	0.923809i	$0.625059\pi$
$644$	0	0
$645$	−8.00000	−0.315000
$646$	−7.23607	−0.284699
$647$	36.9443	1.45243	0.726215	−	0.687468i	$-0.241278\pi$
$647$	36.9443	1.45243	0.726215	+	0.687468i	$0.241278\pi$
$648$	1.00000	0.0392837
$649$	6.83282	0.268211
$650$	17.7082	0.694573
$651$	0	0
$652$	15.4164	0.603753
$653$	1.05573	0.0413138	0.0206569	−	0.999787i	$-0.493424\pi$
$653$	1.05573	0.0413138	0.0206569	+	0.999787i	$0.493424\pi$
$654$	6.00000	0.234619
$655$	−24.0000	−0.937758
$656$	8.94427	0.349215
$657$	0	0
$658$	0	0
$659$	−5.88854	−0.229385	−0.114693	−	0.993401i	$-0.536588\pi$
$659$	−5.88854	−0.229385	−0.114693	+	0.993401i	$0.536588\pi$
$660$	−2.47214	−0.0962278
$661$	19.5967	0.762225	0.381113	−	0.924529i	$-0.375541\pi$
$661$	19.5967	0.762225	0.381113	+	0.924529i	$0.375541\pi$
$662$	27.2361	1.05856
$663$	23.4164	0.909418
$664$	−5.52786	−0.214523
$665$	0	0
$666$	6.00000	0.232495
$667$	−3.41641	−0.132284
$668$	−20.3607	−0.787778
$669$	3.41641	0.132086
$670$	15.4164	0.595588
$671$	4.94427	0.190872
$672$	0	0
$673$	−48.8328	−1.88237	−0.941183	−	0.337896i	$-0.890285\pi$
$673$	−48.8328	−1.88237	−0.941183	+	0.337896i	$0.890285\pi$
$674$	−27.8885	−1.07423
$675$	5.47214	0.210623
$676$	−2.52786	−0.0972255
$677$	−8.94427	−0.343756	−0.171878	−	0.985118i	$-0.554984\pi$
$677$	−8.94427	−0.343756	−0.171878	+	0.985118i	$0.554984\pi$
$678$	6.00000	0.230429
$679$	0	0
$680$	23.4164	0.897978
$681$	19.4164	0.744038
$682$	4.94427	0.189326
$683$	17.3050	0.662156	0.331078	−	0.943603i	$-0.392588\pi$
$683$	17.3050	0.662156	0.331078	+	0.943603i	$0.392588\pi$
$684$	−1.00000	−0.0382360
$685$	19.4164	0.741863
$686$	0	0
$687$	−6.47214	−0.246927
$688$	−2.47214	−0.0942493
$689$	−43.4164	−1.65403
$690$	2.47214	0.0941126
$691$	−12.0000	−0.456502	−0.228251	−	0.973602i	$-0.573301\pi$
$691$	−12.0000	−0.456502	−0.228251	+	0.973602i	$0.573301\pi$
$692$	2.47214	0.0939765
$693$	0	0
$694$	0.763932	0.0289985
$695$	−12.9443	−0.491004
$696$	−4.47214	−0.169516
$697$	64.7214	2.45150
$698$	−16.0000	−0.605609
$699$	9.05573	0.342519
$700$	0	0
$701$	−13.0557	−0.493108	−0.246554	−	0.969129i	$-0.579298\pi$
$701$	−13.0557	−0.493108	−0.246554	+	0.969129i	$0.579298\pi$
$702$	3.23607	0.122138
$703$	−6.00000	−0.226294
$704$	−0.763932	−0.0287918
$705$	−16.0000	−0.602595
$706$	−3.81966	−0.143755
$707$	0	0
$708$	−8.94427	−0.336146
$709$	−26.3607	−0.989996	−0.494998	−	0.868894i	$-0.664831\pi$
$709$	−26.3607	−0.989996	−0.494998	+	0.868894i	$0.664831\pi$
$710$	−20.9443	−0.786025
$711$	−1.70820	−0.0640627
$712$	8.94427	0.335201
$713$	−4.94427	−0.185164
$714$	0	0
$715$	−8.00000	−0.299183
$716$	13.8885	0.519039
$717$	−2.29180	−0.0855887
$718$	−21.7082	−0.810143
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	3.23607	0.120601
$721$	0	0
$722$	1.00000	0.0372161
$723$	−21.7082	−0.807337
$724$	9.70820	0.360803
$725$	−24.4721	−0.908872
$726$	−10.4164	−0.386589
$727$	43.7771	1.62360	0.811801	−	0.583934i	$-0.198487\pi$
$727$	43.7771	1.62360	0.811801	+	0.583934i	$0.198487\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−17.8885	−0.661632
$732$	−6.47214	−0.239217
$733$	30.8328	1.13884	0.569418	−	0.822048i	$-0.307169\pi$
$733$	30.8328	1.13884	0.569418	+	0.822048i	$0.307169\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	0.763932	0.0281589
$737$	−3.63932	−0.134056
$738$	8.94427	0.329243
$739$	−24.9443	−0.917590	−0.458795	−	0.888542i	$-0.651719\pi$
$739$	−24.9443	−0.917590	−0.458795	+	0.888542i	$0.651719\pi$
$740$	19.4164	0.713761
$741$	−3.23607	−0.118880
$742$	0	0
$743$	49.8885	1.83023	0.915117	−	0.403189i	$-0.132098\pi$
$743$	49.8885	1.83023	0.915117	+	0.403189i	$0.132098\pi$
$744$	−6.47214	−0.237280
$745$	48.3607	1.77180
$746$	30.9443	1.13295
$747$	−5.52786	−0.202254
$748$	−5.52786	−0.202119
$749$	0	0
$750$	1.52786	0.0557897
$751$	−43.2361	−1.57771	−0.788853	−	0.614582i	$-0.789325\pi$
$751$	−43.2361	−1.57771	−0.788853	+	0.614582i	$0.789325\pi$
$752$	−4.94427	−0.180299
$753$	−13.5279	−0.492983
$754$	−14.4721	−0.527044
$755$	−57.3050	−2.08554
$756$	0	0
$757$	27.8885	1.01363	0.506813	−	0.862056i	$-0.330823\pi$
$757$	27.8885	1.01363	0.506813	+	0.862056i	$0.330823\pi$
$758$	29.1246	1.05785
$759$	−0.583592	−0.0211831
$760$	−3.23607	−0.117385
$761$	6.87539	0.249233	0.124616	−	0.992205i	$-0.460230\pi$
$761$	6.87539	0.249233	0.124616	+	0.992205i	$0.460230\pi$
$762$	9.70820	0.351691
$763$	0	0
$764$	16.7639	0.606498
$765$	23.4164	0.846622
$766$	11.0557	0.399460
$767$	−28.9443	−1.04512
$768$	1.00000	0.0360844
$769$	−22.8328	−0.823372	−0.411686	−	0.911326i	$-0.635060\pi$
$769$	−22.8328	−0.823372	−0.411686	+	0.911326i	$0.635060\pi$
$770$	0	0
$771$	21.5279	0.775307
$772$	10.0000	0.359908
$773$	10.4721	0.376657	0.188328	−	0.982106i	$-0.439693\pi$
$773$	10.4721	0.376657	0.188328	+	0.982106i	$0.439693\pi$
$774$	−2.47214	−0.0888591
$775$	−35.4164	−1.27219
$776$	5.70820	0.204913
$777$	0	0
$778$	−32.8328	−1.17711
$779$	−8.94427	−0.320462
$780$	10.4721	0.374963
$781$	4.94427	0.176920
$782$	5.52786	0.197676
$783$	−4.47214	−0.159821
$784$	0	0
$785$	25.8885	0.924002
$786$	−7.41641	−0.264535
$787$	−10.8328	−0.386148	−0.193074	−	0.981184i	$-0.561846\pi$
$787$	−10.8328	−0.386148	−0.193074	+	0.981184i	$0.561846\pi$
$788$	−26.9443	−0.959850
$789$	−23.5967	−0.840066
$790$	−5.52786	−0.196673
$791$	0	0
$792$	−0.763932	−0.0271451
$793$	−20.9443	−0.743753
$794$	1.88854	0.0670219
$795$	−43.4164	−1.53982
$796$	15.4164	0.546420
$797$	46.2492	1.63823	0.819116	−	0.573628i	$-0.194465\pi$
$797$	46.2492	1.63823	0.819116	+	0.573628i	$0.194465\pi$
$798$	0	0
$799$	−35.7771	−1.26570
$800$	5.47214	0.193469
$801$	8.94427	0.316030
$802$	−3.52786	−0.124573
$803$	0	0
$804$	4.76393	0.168011
$805$	0	0
$806$	−20.9443	−0.737731
$807$	−31.4164	−1.10591
$808$	−9.70820	−0.341533
$809$	35.8885	1.26177	0.630887	−	0.775875i	$-0.282691\pi$
$809$	35.8885	1.26177	0.630887	+	0.775875i	$0.282691\pi$
$810$	3.23607	0.113704
$811$	−34.8328	−1.22315	−0.611573	−	0.791188i	$-0.709463\pi$
$811$	−34.8328	−1.22315	−0.611573	+	0.791188i	$0.709463\pi$
$812$	0	0
$813$	−24.0000	−0.841717
$814$	−4.58359	−0.160655
$815$	49.8885	1.74752
$816$	7.23607	0.253313
$817$	2.47214	0.0864891
$818$	13.7082	0.479296
$819$	0	0
$820$	28.9443	1.01078
$821$	19.8885	0.694115	0.347057	−	0.937844i	$-0.387181\pi$
$821$	19.8885	0.694115	0.347057	+	0.937844i	$0.387181\pi$
$822$	6.00000	0.209274
$823$	−36.9443	−1.28780	−0.643898	−	0.765111i	$-0.722684\pi$
$823$	−36.9443	−1.28780	−0.643898	+	0.765111i	$0.722684\pi$
$824$	−9.52786	−0.331919
$825$	−4.18034	−0.145541
$826$	0	0
$827$	−26.8328	−0.933068	−0.466534	−	0.884503i	$-0.654498\pi$
$827$	−26.8328	−0.933068	−0.466534	+	0.884503i	$0.654498\pi$
$828$	0.763932	0.0265485
$829$	−14.6525	−0.508902	−0.254451	−	0.967086i	$-0.581895\pi$
$829$	−14.6525	−0.508902	−0.254451	+	0.967086i	$0.581895\pi$
$830$	−17.8885	−0.620920
$831$	6.00000	0.208138
$832$	3.23607	0.112190
$833$	0	0
$834$	−4.00000	−0.138509
$835$	−65.8885	−2.28017
$836$	0.763932	0.0264211
$837$	−6.47214	−0.223710
$838$	−36.3607	−1.25606
$839$	13.5279	0.467034	0.233517	−	0.972353i	$-0.424977\pi$
$839$	13.5279	0.467034	0.233517	+	0.972353i	$0.424977\pi$
$840$	0	0
$841$	−9.00000	−0.310345
$842$	−6.00000	−0.206774
$843$	−6.00000	−0.206651
$844$	1.70820	0.0587988
$845$	−8.18034	−0.281412
$846$	−4.94427	−0.169988
$847$	0	0
$848$	−13.4164	−0.460721
$849$	12.0000	0.411839
$850$	39.5967	1.35816
$851$	4.58359	0.157124
$852$	−6.47214	−0.221732
$853$	−30.4721	−1.04335	−0.521673	−	0.853146i	$-0.674692\pi$
$853$	−30.4721	−1.04335	−0.521673	+	0.853146i	$0.674692\pi$
$854$	0	0
$855$	−3.23607	−0.110671
$856$	16.9443	0.579143
$857$	12.0000	0.409912	0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000	0.409912	0.204956	+	0.978771i	$0.434295\pi$
$858$	−2.47214	−0.0843973
$859$	−3.41641	−0.116566	−0.0582832	−	0.998300i	$-0.518563\pi$
$859$	−3.41641	−0.116566	−0.0582832	+	0.998300i	$0.518563\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	37.3050	1.27061
$863$	40.7214	1.38617	0.693086	−	0.720855i	$-0.256251\pi$
$863$	40.7214	1.38617	0.693086	+	0.720855i	$0.256251\pi$
$864$	1.00000	0.0340207
$865$	8.00000	0.272008
$866$	5.70820	0.193973
$867$	35.3607	1.20091
$868$	0	0
$869$	1.30495	0.0442675
$870$	−14.4721	−0.490651
$871$	15.4164	0.522365
$872$	6.00000	0.203186
$873$	5.70820	0.193193
$874$	−0.763932	−0.0258404
$875$	0	0
$876$	0	0
$877$	−21.7771	−0.735360	−0.367680	−	0.929952i	$-0.619848\pi$
$877$	−21.7771	−0.735360	−0.367680	+	0.929952i	$0.619848\pi$
$878$	−17.5279	−0.591537
$879$	2.47214	0.0833831
$880$	−2.47214	−0.0833357
$881$	4.18034	0.140839	0.0704196	−	0.997517i	$-0.477566\pi$
$881$	4.18034	0.140839	0.0704196	+	0.997517i	$0.477566\pi$
$882$	0	0
$883$	21.5279	0.724470	0.362235	−	0.932087i	$-0.382014\pi$
$883$	21.5279	0.724470	0.362235	+	0.932087i	$0.382014\pi$
$884$	23.4164	0.787579
$885$	−28.9443	−0.972951
$886$	−8.76393	−0.294430
$887$	−20.9443	−0.703240	−0.351620	−	0.936143i	$-0.614369\pi$
$887$	−20.9443	−0.703240	−0.351620	+	0.936143i	$0.614369\pi$
$888$	6.00000	0.201347
$889$	0	0
$890$	28.9443	0.970214
$891$	−0.763932	−0.0255927
$892$	3.41641	0.114390
$893$	4.94427	0.165454
$894$	14.9443	0.499811
$895$	44.9443	1.50232
$896$	0	0
$897$	2.47214	0.0825422
$898$	−27.8885	−0.930653
$899$	28.9443	0.965346
$900$	5.47214	0.182405
$901$	−97.0820	−3.23427
$902$	−6.83282	−0.227508
$903$	0	0
$904$	6.00000	0.199557
$905$	31.4164	1.04432
$906$	−17.7082	−0.588316
$907$	−37.4853	−1.24468	−0.622339	−	0.782748i	$-0.713818\pi$
$907$	−37.4853	−1.24468	−0.622339	+	0.782748i	$0.713818\pi$
$908$	19.4164	0.644356
$909$	−9.70820	−0.322001
$910$	0	0
$911$	−22.4721	−0.744535	−0.372268	−	0.928125i	$-0.621420\pi$
$911$	−22.4721	−0.744535	−0.372268	+	0.928125i	$0.621420\pi$
$912$	−1.00000	−0.0331133
$913$	4.22291	0.139758
$914$	25.4164	0.840700
$915$	−20.9443	−0.692396
$916$	−6.47214	−0.213845
$917$	0	0
$918$	7.23607	0.238826
$919$	43.7771	1.44407	0.722036	−	0.691855i	$-0.243206\pi$
$919$	43.7771	1.44407	0.722036	+	0.691855i	$0.243206\pi$
$920$	2.47214	0.0815039
$921$	−26.8328	−0.884171
$922$	−30.6525	−1.00949
$923$	−20.9443	−0.689389
$924$	0	0
$925$	32.8328	1.07954
$926$	−22.8328	−0.750333
$927$	−9.52786	−0.312936
$928$	−4.47214	−0.146805
$929$	−39.5967	−1.29913	−0.649564	−	0.760307i	$-0.725048\pi$
$929$	−39.5967	−1.29913	−0.649564	+	0.760307i	$0.725048\pi$
$930$	−20.9443	−0.686790
$931$	0	0
$932$	9.05573	0.296630
$933$	−24.0000	−0.785725
$934$	21.5279	0.704413
$935$	−17.8885	−0.585018
$936$	3.23607	0.105774
$937$	−35.4164	−1.15700	−0.578502	−	0.815681i	$-0.696362\pi$
$937$	−35.4164	−1.15700	−0.578502	+	0.815681i	$0.696362\pi$
$938$	0	0
$939$	−9.88854	−0.322700
$940$	−16.0000	−0.521862
$941$	12.3607	0.402947	0.201473	−	0.979494i	$-0.435427\pi$
$941$	12.3607	0.402947	0.201473	+	0.979494i	$0.435427\pi$
$942$	8.00000	0.260654
$943$	6.83282	0.222507
$944$	−8.94427	−0.291111
$945$	0	0
$946$	1.88854	0.0614019
$947$	−52.1803	−1.69563	−0.847817	−	0.530290i	$-0.822083\pi$
$947$	−52.1803	−1.69563	−0.847817	+	0.530290i	$0.822083\pi$
$948$	−1.70820	−0.0554799
$949$	0	0
$950$	−5.47214	−0.177540
$951$	18.0000	0.583690
$952$	0	0
$953$	41.7771	1.35329	0.676646	−	0.736308i	$-0.263433\pi$
$953$	41.7771	1.35329	0.676646	+	0.736308i	$0.263433\pi$
$954$	−13.4164	−0.434372
$955$	54.2492	1.75546
$956$	−2.29180	−0.0741220
$957$	3.41641	0.110437
$958$	0	0
$959$	0	0
$960$	3.23607	0.104444
$961$	10.8885	0.351243
$962$	19.4164	0.626010
$963$	16.9443	0.546022
$964$	−21.7082	−0.699174
$965$	32.3607	1.04173
$966$	0	0
$967$	−35.4164	−1.13891	−0.569457	−	0.822021i	$-0.692847\pi$
$967$	−35.4164	−1.13891	−0.569457	+	0.822021i	$0.692847\pi$
$968$	−10.4164	−0.334796
$969$	−7.23607	−0.232456
$970$	18.4721	0.593105
$971$	−7.63932	−0.245157	−0.122579	−	0.992459i	$-0.539116\pi$
$971$	−7.63932	−0.245157	−0.122579	+	0.992459i	$0.539116\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	4.76393	0.152646
$975$	17.7082	0.567116
$976$	−6.47214	−0.207168
$977$	−13.4164	−0.429229	−0.214614	−	0.976699i	$-0.568849\pi$
$977$	−13.4164	−0.429229	−0.214614	+	0.976699i	$0.568849\pi$
$978$	15.4164	0.492962
$979$	−6.83282	−0.218378
$980$	0	0
$981$	6.00000	0.191565
$982$	0.763932	0.0243781
$983$	−7.41641	−0.236547	−0.118273	−	0.992981i	$-0.537736\pi$
$983$	−7.41641	−0.236547	−0.118273	+	0.992981i	$0.537736\pi$
$984$	8.94427	0.285133
$985$	−87.1935	−2.77822
$986$	−32.3607	−1.03057
$987$	0	0
$988$	−3.23607	−0.102953
$989$	−1.88854	−0.0600522
$990$	−2.47214	−0.0785696
$991$	−48.5410	−1.54196	−0.770978	−	0.636862i	$-0.780232\pi$
$991$	−48.5410	−1.54196	−0.770978	+	0.636862i	$0.780232\pi$
$992$	−6.47214	−0.205491
$993$	27.2361	0.864310
$994$	0	0
$995$	49.8885	1.58157
$996$	−5.52786	−0.175157
$997$	8.00000	0.253363	0.126681	−	0.991943i	$-0.459567\pi$
$997$	8.00000	0.253363	0.126681	+	0.991943i	$0.459567\pi$
$998$	12.3607	0.391270
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bq.1.2	yes	2
7.6	odd	2		5586.2.a.bh.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.bh.1.1	✓	2	7.6	odd	2
5586.2.a.bq.1.2	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.23607 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +3.23607 q^{10} -0.763932 q^{11} +1.00000 q^{12} +3.23607 q^{13} +3.23607 q^{15} +1.00000 q^{16} +7.23607 q^{17} +1.00000 q^{18} -1.00000 q^{19} +3.23607 q^{20} -0.763932 q^{22} +0.763932 q^{23} +1.00000 q^{24} +5.47214 q^{25} +3.23607 q^{26} +1.00000 q^{27} -4.47214 q^{29} +3.23607 q^{30} -6.47214 q^{31} +1.00000 q^{32} -0.763932 q^{33} +7.23607 q^{34} +1.00000 q^{36} +6.00000 q^{37} -1.00000 q^{38} +3.23607 q^{39} +3.23607 q^{40} +8.94427 q^{41} -2.47214 q^{43} -0.763932 q^{44} +3.23607 q^{45} +0.763932 q^{46} -4.94427 q^{47} +1.00000 q^{48} +5.47214 q^{50} +7.23607 q^{51} +3.23607 q^{52} -13.4164 q^{53} +1.00000 q^{54} -2.47214 q^{55} -1.00000 q^{57} -4.47214 q^{58} -8.94427 q^{59} +3.23607 q^{60} -6.47214 q^{61} -6.47214 q^{62} +1.00000 q^{64} +10.4721 q^{65} -0.763932 q^{66} +4.76393 q^{67} +7.23607 q^{68} +0.763932 q^{69} -6.47214 q^{71} +1.00000 q^{72} +6.00000 q^{74} +5.47214 q^{75} -1.00000 q^{76} +3.23607 q^{78} -1.70820 q^{79} +3.23607 q^{80} +1.00000 q^{81} +8.94427 q^{82} -5.52786 q^{83} +23.4164 q^{85} -2.47214 q^{86} -4.47214 q^{87} -0.763932 q^{88} +8.94427 q^{89} +3.23607 q^{90} +0.763932 q^{92} -6.47214 q^{93} -4.94427 q^{94} -3.23607 q^{95} +1.00000 q^{96} +5.70820 q^{97} -0.763932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 6 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{15} + 2 q^{16} + 10 q^{17} + 2 q^{18} - 2 q^{19} + 2 q^{20} - 6 q^{22} + 6 q^{23} + 2 q^{24} + 2 q^{25} + 2 q^{26} + 2 q^{27} + 2 q^{30} - 4 q^{31} + 2 q^{32} - 6 q^{33} + 10 q^{34} + 2 q^{36} + 12 q^{37} - 2 q^{38} + 2 q^{39} + 2 q^{40} + 4 q^{43} - 6 q^{44} + 2 q^{45} + 6 q^{46} + 8 q^{47} + 2 q^{48} + 2 q^{50} + 10 q^{51} + 2 q^{52} + 2 q^{54} + 4 q^{55} - 2 q^{57} + 2 q^{60} - 4 q^{61} - 4 q^{62} + 2 q^{64} + 12 q^{65} - 6 q^{66} + 14 q^{67} + 10 q^{68} + 6 q^{69} - 4 q^{71} + 2 q^{72} + 12 q^{74} + 2 q^{75} - 2 q^{76} + 2 q^{78} + 10 q^{79} + 2 q^{80} + 2 q^{81} - 20 q^{83} + 20 q^{85} + 4 q^{86} - 6 q^{88} + 2 q^{90} + 6 q^{92} - 4 q^{93} + 8 q^{94} - 2 q^{95} + 2 q^{96} - 2 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 6 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^15 + 2 * q^16 + 10 * q^17 + 2 * q^18 - 2 * q^19 + 2 * q^20 - 6 * q^22 + 6 * q^23 + 2 * q^24 + 2 * q^25 + 2 * q^26 + 2 * q^27 + 2 * q^30 - 4 * q^31 + 2 * q^32 - 6 * q^33 + 10 * q^34 + 2 * q^36 + 12 * q^37 - 2 * q^38 + 2 * q^39 + 2 * q^40 + 4 * q^43 - 6 * q^44 + 2 * q^45 + 6 * q^46 + 8 * q^47 + 2 * q^48 + 2 * q^50 + 10 * q^51 + 2 * q^52 + 2 * q^54 + 4 * q^55 - 2 * q^57 + 2 * q^60 - 4 * q^61 - 4 * q^62 + 2 * q^64 + 12 * q^65 - 6 * q^66 + 14 * q^67 + 10 * q^68 + 6 * q^69 - 4 * q^71 + 2 * q^72 + 12 * q^74 + 2 * q^75 - 2 * q^76 + 2 * q^78 + 10 * q^79 + 2 * q^80 + 2 * q^81 - 20 * q^83 + 20 * q^85 + 4 * q^86 - 6 * q^88 + 2 * q^90 + 6 * q^92 - 4 * q^93 + 8 * q^94 - 2 * q^95 + 2 * q^96 - 2 * q^97 - 6 * q^99

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