LMFDB - Embedded newform 1666.2.a.t.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1666,2,Mod(1,1666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1666, 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("1666.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1666 = 2 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1666.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:	$13.3030769767$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.404.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x - 1 $ x^3 - x^2 - 5*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 238)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.210756$ of defining polynomial
Character	$\chi$	$=$	1666.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.53407 q^{3} +1.00000 q^{4} +2.74483 q^{5} -2.53407 q^{6} -1.00000 q^{8} +3.42151 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.53407 q^{3} +1.00000 q^{4} +2.74483 q^{5} -2.53407 q^{6} -1.00000 q^{8} +3.42151 q^{9} -2.74483 q^{10} +4.53407 q^{11} +2.53407 q^{12} +0.534070 q^{13} +6.95558 q^{15} +1.00000 q^{16} +1.00000 q^{17} -3.42151 q^{18} +3.53407 q^{19} +2.74483 q^{20} -4.53407 q^{22} -7.27890 q^{23} -2.53407 q^{24} +2.53407 q^{25} -0.534070 q^{26} +1.06814 q^{27} -0.955582 q^{29} -6.95558 q^{30} +5.37709 q^{31} -1.00000 q^{32} +11.4897 q^{33} -1.00000 q^{34} +3.42151 q^{36} -9.16634 q^{37} -3.53407 q^{38} +1.35337 q^{39} -2.74483 q^{40} -3.88744 q^{41} -5.84302 q^{43} +4.53407 q^{44} +9.39145 q^{45} +7.27890 q^{46} -3.37709 q^{47} +2.53407 q^{48} -2.53407 q^{50} +2.53407 q^{51} +0.534070 q^{52} +12.1363 q^{53} -1.06814 q^{54} +12.4452 q^{55} +8.95558 q^{57} +0.955582 q^{58} -3.00000 q^{59} +6.95558 q^{60} +6.53407 q^{61} -5.37709 q^{62} +1.00000 q^{64} +1.46593 q^{65} -11.4897 q^{66} -14.0919 q^{67} +1.00000 q^{68} -18.4452 q^{69} +9.25517 q^{71} -3.42151 q^{72} -4.95558 q^{73} +9.16634 q^{74} +6.42151 q^{75} +3.53407 q^{76} -1.35337 q^{78} +14.4452 q^{79} +2.74483 q^{80} -7.55779 q^{81} +3.88744 q^{82} -6.64663 q^{83} +2.74483 q^{85} +5.84302 q^{86} -2.42151 q^{87} -4.53407 q^{88} -12.5134 q^{89} -9.39145 q^{90} -7.27890 q^{92} +13.6259 q^{93} +3.37709 q^{94} +9.70041 q^{95} -2.53407 q^{96} +13.7986 q^{97} +15.5134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} - q^{5} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 - q^5 - 3 * q^8 + 7 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} - q^{5} - 3 q^{8} + 7 q^{9} + q^{10} + 6 q^{11} - 6 q^{13} + 10 q^{15} + 3 q^{16} + 3 q^{17} - 7 q^{18} + 3 q^{19} - q^{20} - 6 q^{22} - 5 q^{23} + 6 q^{26} - 12 q^{27} + 8 q^{29} - 10 q^{30} + 2 q^{31} - 3 q^{32} + 16 q^{33} - 3 q^{34} + 7 q^{36} - 15 q^{37} - 3 q^{38} + 16 q^{39} + q^{40} - 16 q^{41} - 11 q^{43} + 6 q^{44} + 7 q^{45} + 5 q^{46} + 4 q^{47} - 6 q^{52} + 6 q^{53} + 12 q^{54} + 8 q^{55} + 16 q^{57} - 8 q^{58} - 9 q^{59} + 10 q^{60} + 12 q^{61} - 2 q^{62} + 3 q^{64} + 12 q^{65} - 16 q^{66} - q^{67} + 3 q^{68} - 26 q^{69} + 37 q^{71} - 7 q^{72} - 4 q^{73} + 15 q^{74} + 16 q^{75} + 3 q^{76} - 16 q^{78} + 14 q^{79} - q^{80} + 11 q^{81} + 16 q^{82} - 8 q^{83} - q^{85} + 11 q^{86} - 4 q^{87} - 6 q^{88} + 7 q^{89} - 7 q^{90} - 5 q^{92} - 8 q^{93} - 4 q^{94} + 9 q^{95} + 24 q^{97} + 2 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 - q^5 - 3 * q^8 + 7 * q^9 + q^10 + 6 * q^11 - 6 * q^13 + 10 * q^15 + 3 * q^16 + 3 * q^17 - 7 * q^18 + 3 * q^19 - q^20 - 6 * q^22 - 5 * q^23 + 6 * q^26 - 12 * q^27 + 8 * q^29 - 10 * q^30 + 2 * q^31 - 3 * q^32 + 16 * q^33 - 3 * q^34 + 7 * q^36 - 15 * q^37 - 3 * q^38 + 16 * q^39 + q^40 - 16 * q^41 - 11 * q^43 + 6 * q^44 + 7 * q^45 + 5 * q^46 + 4 * q^47 - 6 * q^52 + 6 * q^53 + 12 * q^54 + 8 * q^55 + 16 * q^57 - 8 * q^58 - 9 * q^59 + 10 * q^60 + 12 * q^61 - 2 * q^62 + 3 * q^64 + 12 * q^65 - 16 * q^66 - q^67 + 3 * q^68 - 26 * q^69 + 37 * q^71 - 7 * q^72 - 4 * q^73 + 15 * q^74 + 16 * q^75 + 3 * q^76 - 16 * q^78 + 14 * q^79 - q^80 + 11 * q^81 + 16 * q^82 - 8 * q^83 - q^85 + 11 * q^86 - 4 * q^87 - 6 * q^88 + 7 * q^89 - 7 * q^90 - 5 * q^92 - 8 * q^93 - 4 * q^94 + 9 * q^95 + 24 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.53407	1.46305	0.731523	−	0.681817i	$-0.238810\pi$
$3$	2.53407	1.46305	0.731523	+	0.681817i	$0.238810\pi$
$4$	1.00000	0.500000
$5$	2.74483	1.22752	0.613762	−	0.789491i	$-0.289656\pi$
$5$	2.74483	1.22752	0.613762	+	0.789491i	$0.289656\pi$
$6$	−2.53407	−1.03453
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	3.42151	1.14050
$10$	−2.74483	−0.867990
$11$	4.53407	1.36707	0.683537	−	0.729916i	$-0.260441\pi$
$11$	4.53407	1.36707	0.683537	+	0.729916i	$0.260441\pi$
$12$	2.53407	0.731523
$13$	0.534070	0.148124	0.0740622	−	0.997254i	$-0.476404\pi$
$13$	0.534070	0.148124	0.0740622	+	0.997254i	$0.476404\pi$
$14$	0	0
$15$	6.95558	1.79592
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.42151	−0.806458
$19$	3.53407	0.810771	0.405386	−	0.914146i	$-0.367137\pi$
$19$	3.53407	0.810771	0.405386	+	0.914146i	$0.367137\pi$
$20$	2.74483	0.613762
$21$	0	0
$22$	−4.53407	−0.966667
$23$	−7.27890	−1.51775	−0.758877	−	0.651234i	$-0.774252\pi$
$23$	−7.27890	−1.51775	−0.758877	+	0.651234i	$0.774252\pi$
$24$	−2.53407	−0.517265
$25$	2.53407	0.506814
$26$	−0.534070	−0.104740
$27$	1.06814	0.205564
$28$	0	0
$29$	−0.955582	−0.177447	−0.0887236	−	0.996056i	$-0.528279\pi$
$29$	−0.955582	−0.177447	−0.0887236	+	0.996056i	$0.528279\pi$
$30$	−6.95558	−1.26991
$31$	5.37709	0.965755	0.482877	−	0.875688i	$-0.339592\pi$
$31$	5.37709	0.965755	0.482877	+	0.875688i	$0.339592\pi$
$32$	−1.00000	−0.176777
$33$	11.4897	2.00009
$34$	−1.00000	−0.171499
$35$	0	0
$36$	3.42151	0.570252
$37$	−9.16634	−1.50694	−0.753468	−	0.657484i	$-0.771621\pi$
$37$	−9.16634	−1.50694	−0.753468	+	0.657484i	$0.771621\pi$
$38$	−3.53407	−0.573302
$39$	1.35337	0.216713
$40$	−2.74483	−0.433995
$41$	−3.88744	−0.607116	−0.303558	−	0.952813i	$-0.598175\pi$
$41$	−3.88744	−0.607116	−0.303558	+	0.952813i	$0.598175\pi$
$42$	0	0
$43$	−5.84302	−0.891053	−0.445526	−	0.895269i	$-0.646983\pi$
$43$	−5.84302	−0.891053	−0.445526	+	0.895269i	$0.646983\pi$
$44$	4.53407	0.683537
$45$	9.39145	1.40000
$46$	7.27890	1.07321
$47$	−3.37709	−0.492600	−0.246300	−	0.969194i	$-0.579215\pi$
$47$	−3.37709	−0.492600	−0.246300	+	0.969194i	$0.579215\pi$
$48$	2.53407	0.365762
$49$	0	0
$50$	−2.53407	−0.358372
$51$	2.53407	0.354841
$52$	0.534070	0.0740622
$53$	12.1363	1.66705	0.833523	−	0.552484i	$-0.186320\pi$
$53$	12.1363	1.66705	0.833523	+	0.552484i	$0.186320\pi$
$54$	−1.06814	−0.145355
$55$	12.4452	1.67812
$56$	0	0
$57$	8.95558	1.18620
$58$	0.955582	0.125474
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	6.95558	0.897962
$61$	6.53407	0.836602	0.418301	−	0.908308i	$-0.362626\pi$
$61$	6.53407	0.836602	0.418301	+	0.908308i	$0.362626\pi$
$62$	−5.37709	−0.682892
$63$	0	0
$64$	1.00000	0.125000
$65$	1.46593	0.181826
$66$	−11.4897	−1.41428
$67$	−14.0919	−1.72160	−0.860798	−	0.508948i	$-0.830035\pi$
$67$	−14.0919	−1.72160	−0.860798	+	0.508948i	$0.830035\pi$
$68$	1.00000	0.121268
$69$	−18.4452	−2.22055
$70$	0	0
$71$	9.25517	1.09839	0.549194	−	0.835695i	$-0.314935\pi$
$71$	9.25517	1.09839	0.549194	+	0.835695i	$0.314935\pi$
$72$	−3.42151	−0.403229
$73$	−4.95558	−0.580007	−0.290003	−	0.957026i	$-0.593656\pi$
$73$	−4.95558	−0.580007	−0.290003	+	0.957026i	$0.593656\pi$
$74$	9.16634	1.06557
$75$	6.42151	0.741492
$76$	3.53407	0.405386
$77$	0	0
$78$	−1.35337	−0.153239
$79$	14.4452	1.62522	0.812608	−	0.582811i	$-0.198047\pi$
$79$	14.4452	1.62522	0.812608	+	0.582811i	$0.198047\pi$
$80$	2.74483	0.306881
$81$	−7.55779	−0.839755
$82$	3.88744	0.429296
$83$	−6.64663	−0.729562	−0.364781	−	0.931093i	$-0.618856\pi$
$83$	−6.64663	−0.729562	−0.364781	+	0.931093i	$0.618856\pi$
$84$	0	0
$85$	2.74483	0.297718
$86$	5.84302	0.630069
$87$	−2.42151	−0.259613
$88$	−4.53407	−0.483334
$89$	−12.5134	−1.32642	−0.663208	−	0.748436i	$-0.730805\pi$
$89$	−12.5134	−1.32642	−0.663208	+	0.748436i	$0.730805\pi$
$90$	−9.39145	−0.989946
$91$	0	0
$92$	−7.27890	−0.758877
$93$	13.6259	1.41294
$94$	3.37709	0.348321
$95$	9.70041	0.995241
$96$	−2.53407	−0.258632
$97$	13.7986	1.40104	0.700518	−	0.713635i	$-0.252952\pi$
$97$	13.7986	1.40104	0.700518	+	0.713635i	$0.252952\pi$
$98$	0	0
$99$	15.5134	1.55915
$100$	2.53407	0.253407
$101$	9.57849	0.953095	0.476548	−	0.879149i	$-0.341888\pi$
$101$	9.57849	0.953095	0.476548	+	0.879149i	$0.341888\pi$
$102$	−2.53407	−0.250910
$103$	−18.8667	−1.85900	−0.929498	−	0.368828i	$-0.879759\pi$
$103$	−18.8667	−1.85900	−0.929498	+	0.368828i	$0.879759\pi$
$104$	−0.534070	−0.0523699
$105$	0	0
$106$	−12.1363	−1.17878
$107$	−7.09186	−0.685596	−0.342798	−	0.939409i	$-0.611375\pi$
$107$	−7.09186	−0.685596	−0.342798	+	0.939409i	$0.611375\pi$
$108$	1.06814	0.102782
$109$	−3.47529	−0.332873	−0.166436	−	0.986052i	$-0.553226\pi$
$109$	−3.47529	−0.332873	−0.166436	+	0.986052i	$0.553226\pi$
$110$	−12.4452	−1.18661
$111$	−23.2281	−2.20472
$112$	0	0
$113$	−16.4690	−1.54927	−0.774635	−	0.632409i	$-0.782066\pi$
$113$	−16.4690	−1.54927	−0.774635	+	0.632409i	$0.782066\pi$
$114$	−8.95558	−0.838767
$115$	−19.9793	−1.86308
$116$	−0.955582	−0.0887236
$117$	1.82733	0.168936
$118$	3.00000	0.276172
$119$	0	0
$120$	−6.95558	−0.634955
$121$	9.55779	0.868890
$122$	−6.53407	−0.591567
$123$	−9.85105	−0.888239
$124$	5.37709	0.482877
$125$	−6.76855	−0.605397
$126$	0	0
$127$	18.7779	1.66627	0.833135	−	0.553070i	$-0.186544\pi$
$127$	18.7779	1.66627	0.833135	+	0.553070i	$0.186544\pi$
$128$	−1.00000	−0.0883883
$129$	−14.8066	−1.30365
$130$	−1.46593	−0.128571
$131$	15.1757	1.32591	0.662953	−	0.748661i	$-0.269303\pi$
$131$	15.1757	1.32591	0.662953	+	0.748661i	$0.269303\pi$
$132$	11.4897	1.00005
$133$	0	0
$134$	14.0919	1.21735
$135$	2.93186	0.252334
$136$	−1.00000	−0.0857493
$137$	2.48965	0.212705	0.106353	−	0.994328i	$-0.466083\pi$
$137$	2.48965	0.212705	0.106353	+	0.994328i	$0.466083\pi$
$138$	18.4452	1.57016
$139$	−13.0681	−1.10843	−0.554213	−	0.832375i	$-0.686981\pi$
$139$	−13.0681	−1.10843	−0.554213	+	0.832375i	$0.686981\pi$
$140$	0	0
$141$	−8.55779	−0.720696
$142$	−9.25517	−0.776677
$143$	2.42151	0.202497
$144$	3.42151	0.285126
$145$	−2.62291	−0.217821
$146$	4.95558	0.410127
$147$	0	0
$148$	−9.16634	−0.753468
$149$	1.97628	0.161903	0.0809515	−	0.996718i	$-0.474204\pi$
$149$	1.97628	0.161903	0.0809515	+	0.996718i	$0.474204\pi$
$150$	−6.42151	−0.524314
$151$	7.69105	0.625889	0.312944	−	0.949771i	$-0.398685\pi$
$151$	7.69105	0.625889	0.312944	+	0.949771i	$0.398685\pi$
$152$	−3.53407	−0.286651
$153$	3.42151	0.276613
$154$	0	0
$155$	14.7592	1.18549
$156$	1.35337	0.108356
$157$	8.44523	0.674003	0.337002	−	0.941504i	$-0.390587\pi$
$157$	8.44523	0.674003	0.337002	+	0.941504i	$0.390587\pi$
$158$	−14.4452	−1.14920
$159$	30.7542	2.43897
$160$	−2.74483	−0.216998
$161$	0	0
$162$	7.55779	0.593796
$163$	8.33768	0.653057	0.326529	−	0.945187i	$-0.394121\pi$
$163$	8.33768	0.653057	0.326529	+	0.945187i	$0.394121\pi$
$164$	−3.88744	−0.303558
$165$	31.5371	2.45516
$166$	6.64663	0.515878
$167$	−1.14262	−0.0884182	−0.0442091	−	0.999022i	$-0.514077\pi$
$167$	−1.14262	−0.0884182	−0.0442091	+	0.999022i	$0.514077\pi$
$168$	0	0
$169$	−12.7148	−0.978059
$170$	−2.74483	−0.210519
$171$	12.0919	0.924688
$172$	−5.84302	−0.445526
$173$	−15.0825	−1.14670	−0.573351	−	0.819310i	$-0.694357\pi$
$173$	−15.0825	−1.14670	−0.573351	+	0.819310i	$0.694357\pi$
$174$	2.42151	0.183574
$175$	0	0
$176$	4.53407	0.341768
$177$	−7.60221	−0.571417
$178$	12.5134	0.937917
$179$	25.6704	1.91869	0.959346	−	0.282232i	$-0.0910749\pi$
$179$	25.6704	1.91869	0.959346	+	0.282232i	$0.0910749\pi$
$180$	9.39145	0.699998
$181$	−0.407151	−0.0302633	−0.0151316	−	0.999886i	$-0.504817\pi$
$181$	−0.407151	−0.0302633	−0.0151316	+	0.999886i	$0.504817\pi$
$182$	0	0
$183$	16.5578	1.22399
$184$	7.27890	0.536607
$185$	−25.1600	−1.84980
$186$	−13.6259	−0.999102
$187$	4.53407	0.331564
$188$	−3.37709	−0.246300
$189$	0	0
$190$	−9.70041	−0.703742
$191$	11.1807	0.809007	0.404503	−	0.914536i	$-0.367444\pi$
$191$	11.1807	0.809007	0.404503	+	0.914536i	$0.367444\pi$
$192$	2.53407	0.182881
$193$	−5.15698	−0.371207	−0.185604	−	0.982625i	$-0.559424\pi$
$193$	−5.15698	−0.371207	−0.185604	+	0.982625i	$0.559424\pi$
$194$	−13.7986	−0.990682
$195$	3.71477	0.266020
$196$	0	0
$197$	20.2345	1.44165	0.720823	−	0.693119i	$-0.243764\pi$
$197$	20.2345	1.44165	0.720823	+	0.693119i	$0.243764\pi$
$198$	−15.5134	−1.10249
$199$	−11.4152	−0.809200	−0.404600	−	0.914494i	$-0.632589\pi$
$199$	−11.4152	−0.809200	−0.404600	+	0.914494i	$0.632589\pi$
$200$	−2.53407	−0.179186
$201$	−35.7098	−2.51877
$202$	−9.57849	−0.673940
$203$	0	0
$204$	2.53407	0.177420
$205$	−10.6704	−0.745250
$206$	18.8667	1.31451
$207$	−24.9048	−1.73101
$208$	0.534070	0.0370311
$209$	16.0237	1.10838
$210$	0	0
$211$	−6.55779	−0.451457	−0.225729	−	0.974190i	$-0.572476\pi$
$211$	−6.55779	−0.451457	−0.225729	+	0.974190i	$0.572476\pi$
$212$	12.1363	0.833523
$213$	23.4533	1.60699
$214$	7.09186	0.484790
$215$	−16.0381	−1.09379
$216$	−1.06814	−0.0726777
$217$	0	0
$218$	3.47529	0.235376
$219$	−12.5578	−0.848577
$220$	12.4452	0.839058
$221$	0.534070	0.0359254
$222$	23.2281	1.55897
$223$	−16.8905	−1.13107	−0.565535	−	0.824724i	$-0.691330\pi$
$223$	−16.8905	−1.13107	−0.565535	+	0.824724i	$0.691330\pi$
$224$	0	0
$225$	8.67035	0.578023
$226$	16.4690	1.09550
$227$	22.3327	1.48227	0.741136	−	0.671355i	$-0.234287\pi$
$227$	22.3327	1.48227	0.741136	+	0.671355i	$0.234287\pi$
$228$	8.95558	0.593098
$229$	−3.18070	−0.210186	−0.105093	−	0.994462i	$-0.533514\pi$
$229$	−3.18070	−0.210186	−0.105093	+	0.994462i	$0.533514\pi$
$230$	19.9793	1.31740
$231$	0	0
$232$	0.955582	0.0627370
$233$	1.15698	0.0757960	0.0378980	−	0.999282i	$-0.487934\pi$
$233$	1.15698	0.0757960	0.0378980	+	0.999282i	$0.487934\pi$
$234$	−1.82733	−0.119456
$235$	−9.26953	−0.604678
$236$	−3.00000	−0.195283
$237$	36.6052	2.37777
$238$	0	0
$239$	21.3771	1.38277	0.691385	−	0.722487i	$-0.257001\pi$
$239$	21.3771	1.38277	0.691385	+	0.722487i	$0.257001\pi$
$240$	6.95558	0.448981
$241$	11.7148	0.754615	0.377307	−	0.926088i	$-0.376850\pi$
$241$	11.7148	0.754615	0.377307	+	0.926088i	$0.376850\pi$
$242$	−9.55779	−0.614398
$243$	−22.3564	−1.43416
$244$	6.53407	0.418301
$245$	0	0
$246$	9.85105	0.628080
$247$	1.88744	0.120095
$248$	−5.37709	−0.341446
$249$	−16.8430	−1.06738
$250$	6.76855	0.428081
$251$	−6.64663	−0.419531	−0.209766	−	0.977752i	$-0.567270\pi$
$251$	−6.64663	−0.419531	−0.209766	+	0.977752i	$0.567270\pi$
$252$	0	0
$253$	−33.0030	−2.07488
$254$	−18.7779	−1.17823
$255$	6.95558	0.435575
$256$	1.00000	0.0625000
$257$	2.38209	0.148591	0.0742955	−	0.997236i	$-0.476329\pi$
$257$	2.38209	0.148591	0.0742955	+	0.997236i	$0.476329\pi$
$258$	14.8066	0.921821
$259$	0	0
$260$	1.46593	0.0909131
$261$	−3.26953	−0.202379
$262$	−15.1757	−0.937558
$263$	8.11256	0.500242	0.250121	−	0.968215i	$-0.419530\pi$
$263$	8.11256	0.500242	0.250121	+	0.968215i	$0.419530\pi$
$264$	−11.4897	−0.707139
$265$	33.3120	2.04634
$266$	0	0
$267$	−31.7098	−1.94061
$268$	−14.0919	−0.860798
$269$	−13.2789	−0.809629	−0.404814	−	0.914399i	$-0.632664\pi$
$269$	−13.2789	−0.809629	−0.404814	+	0.914399i	$0.632664\pi$
$270$	−2.93186	−0.178427
$271$	−25.8223	−1.56859	−0.784297	−	0.620385i	$-0.786976\pi$
$271$	−25.8223	−1.56859	−0.784297	+	0.620385i	$0.786976\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	−2.48965	−0.150405
$275$	11.4897	0.692852
$276$	−18.4452	−1.11027
$277$	−7.26953	−0.436784	−0.218392	−	0.975861i	$-0.570081\pi$
$277$	−7.26953	−0.436784	−0.218392	+	0.975861i	$0.570081\pi$
$278$	13.0681	0.783775
$279$	18.3978	1.10145
$280$	0	0
$281$	−3.84802	−0.229554	−0.114777	−	0.993391i	$-0.536615\pi$
$281$	−3.84802	−0.229554	−0.114777	+	0.993391i	$0.536615\pi$
$282$	8.55779	0.509609
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	9.25517	0.549194
$285$	24.5815	1.45608
$286$	−2.42151	−0.143187
$287$	0	0
$288$	−3.42151	−0.201615
$289$	1.00000	0.0588235
$290$	2.62291	0.154022
$291$	34.9666	2.04978
$292$	−4.95558	−0.290003
$293$	22.1600	1.29460	0.647301	−	0.762235i	$-0.275898\pi$
$293$	22.1600	1.29460	0.647301	+	0.762235i	$0.275898\pi$
$294$	0	0
$295$	−8.23448	−0.479430
$296$	9.16634	0.532783
$297$	4.84302	0.281021
$298$	−1.97628	−0.114483
$299$	−3.88744	−0.224817
$300$	6.42151	0.370746
$301$	0	0
$302$	−7.69105	−0.442570
$303$	24.2726	1.39442
$304$	3.53407	0.202693
$305$	17.9349	1.02695
$306$	−3.42151	−0.195595
$307$	−10.5785	−0.603746	−0.301873	−	0.953348i	$-0.597612\pi$
$307$	−10.5785	−0.603746	−0.301873	+	0.953348i	$0.597612\pi$
$308$	0	0
$309$	−47.8097	−2.71980
$310$	−14.7592	−0.838265
$311$	15.7004	0.890288	0.445144	−	0.895459i	$-0.353152\pi$
$311$	15.7004	0.890288	0.445144	+	0.895459i	$0.353152\pi$
$312$	−1.35337	−0.0766196
$313$	−17.9399	−1.01402	−0.507011	−	0.861939i	$-0.669250\pi$
$313$	−17.9399	−1.01402	−0.507011	+	0.861939i	$0.669250\pi$
$314$	−8.44523	−0.476592
$315$	0	0
$316$	14.4452	0.812608
$317$	21.9442	1.23251	0.616256	−	0.787546i	$-0.288649\pi$
$317$	21.9442	1.23251	0.616256	+	0.787546i	$0.288649\pi$
$318$	−30.7542	−1.72461
$319$	−4.33268	−0.242583
$320$	2.74483	0.153440
$321$	−17.9713	−1.00306
$322$	0	0
$323$	3.53407	0.196641
$324$	−7.55779	−0.419877
$325$	1.35337	0.0750715
$326$	−8.33768	−0.461781
$327$	−8.80663	−0.487008
$328$	3.88744	0.214648
$329$	0	0
$330$	−31.5371	−1.73606
$331$	−2.66732	−0.146609	−0.0733047	−	0.997310i	$-0.523355\pi$
$331$	−2.66732	−0.146609	−0.0733047	+	0.997310i	$0.523355\pi$
$332$	−6.64663	−0.364781
$333$	−31.3627	−1.71867
$334$	1.14262	0.0625211
$335$	−38.6797	−2.11330
$336$	0	0
$337$	−9.86372	−0.537311	−0.268656	−	0.963236i	$-0.586579\pi$
$337$	−9.86372	−0.537311	−0.268656	+	0.963236i	$0.586579\pi$
$338$	12.7148	0.691592
$339$	−41.7335	−2.26665
$340$	2.74483	0.148859
$341$	24.3801	1.32026
$342$	−12.0919	−0.653853
$343$	0	0
$344$	5.84302	0.315035
$345$	−50.6290	−2.72577
$346$	15.0825	0.810840
$347$	4.84302	0.259987	0.129994	−	0.991515i	$-0.458504\pi$
$347$	4.84302	0.259987	0.129994	+	0.991515i	$0.458504\pi$
$348$	−2.42151	−0.129807
$349$	−0.0474447	−0.00253966	−0.00126983	−	0.999999i	$-0.500404\pi$
$349$	−0.0474447	−0.00253966	−0.00126983	+	0.999999i	$0.500404\pi$
$350$	0	0
$351$	0.570462	0.0304490
$352$	−4.53407	−0.241667
$353$	3.06511	0.163140	0.0815698	−	0.996668i	$-0.474007\pi$
$353$	3.06511	0.163140	0.0815698	+	0.996668i	$0.474007\pi$
$354$	7.60221	0.404053
$355$	25.4038	1.34830
$356$	−12.5134	−0.663208
$357$	0	0
$358$	−25.6704	−1.35672
$359$	9.82233	0.518403	0.259201	−	0.965823i	$-0.416541\pi$
$359$	9.82233	0.518403	0.259201	+	0.965823i	$0.416541\pi$
$360$	−9.39145	−0.494973
$361$	−6.51035	−0.342650
$362$	0.407151	0.0213994
$363$	24.2201	1.27123
$364$	0	0
$365$	−13.6022	−0.711972
$366$	−16.5578	−0.865490
$367$	2.18703	0.114162	0.0570811	−	0.998370i	$-0.481821\pi$
$367$	2.18703	0.114162	0.0570811	+	0.998370i	$0.481821\pi$
$368$	−7.27890	−0.379439
$369$	−13.3009	−0.692419
$370$	25.1600	1.30801
$371$	0	0
$372$	13.6259	0.706472
$373$	−8.08884	−0.418824	−0.209412	−	0.977827i	$-0.567155\pi$
$373$	−8.08884	−0.418824	−0.209412	+	0.977827i	$0.567155\pi$
$374$	−4.53407	−0.234451
$375$	−17.1520	−0.885724
$376$	3.37709	0.174160
$377$	−0.510348	−0.0262843
$378$	0	0
$379$	−26.9793	−1.38583	−0.692917	−	0.721017i	$-0.743675\pi$
$379$	−26.9793	−1.38583	−0.692917	+	0.721017i	$0.743675\pi$
$380$	9.70041	0.497620
$381$	47.5845	2.43783
$382$	−11.1807	−0.572054
$383$	6.27256	0.320513	0.160256	−	0.987075i	$-0.448768\pi$
$383$	6.27256	0.320513	0.160256	+	0.987075i	$0.448768\pi$
$384$	−2.53407	−0.129316
$385$	0	0
$386$	5.15698	0.262483
$387$	−19.9920	−1.01625
$388$	13.7986	0.700518
$389$	−5.04442	−0.255762	−0.127881	−	0.991790i	$-0.540818\pi$
$389$	−5.04442	−0.255762	−0.127881	+	0.991790i	$0.540818\pi$
$390$	−3.71477	−0.188105
$391$	−7.27890	−0.368110
$392$	0	0
$393$	38.4563	1.93986
$394$	−20.2345	−1.01940
$395$	39.6497	1.99499
$396$	15.5134	0.779576
$397$	−19.9442	−1.00097	−0.500487	−	0.865744i	$-0.666846\pi$
$397$	−19.9442	−1.00097	−0.500487	+	0.865744i	$0.666846\pi$
$398$	11.4152	0.572191
$399$	0	0
$400$	2.53407	0.126704
$401$	−20.8016	−1.03878	−0.519392	−	0.854536i	$-0.673842\pi$
$401$	−20.8016	−1.03878	−0.519392	+	0.854536i	$0.673842\pi$
$402$	35.7098	1.78104
$403$	2.87175	0.143052
$404$	9.57849	0.476548
$405$	−20.7448	−1.03082
$406$	0	0
$407$	−41.5608	−2.06009
$408$	−2.53407	−0.125455
$409$	−32.3614	−1.60017	−0.800084	−	0.599888i	$-0.795212\pi$
$409$	−32.3614	−1.60017	−0.800084	+	0.599888i	$0.795212\pi$
$410$	10.6704	0.526971
$411$	6.30895	0.311198
$412$	−18.8667	−0.929498
$413$	0	0
$414$	24.9048	1.22401
$415$	−18.2438	−0.895555
$416$	−0.534070	−0.0261849
$417$	−33.1156	−1.62168
$418$	−16.0237	−0.783746
$419$	12.5528	0.613244	0.306622	−	0.951831i	$-0.400801\pi$
$419$	12.5528	0.613244	0.306622	+	0.951831i	$0.400801\pi$
$420$	0	0
$421$	−17.7098	−0.863121	−0.431561	−	0.902084i	$-0.642037\pi$
$421$	−17.7098	−0.863121	−0.431561	+	0.902084i	$0.642037\pi$
$422$	6.55779	0.319228
$423$	−11.5548	−0.561812
$424$	−12.1363	−0.589390
$425$	2.53407	0.122920
$426$	−23.4533	−1.13631
$427$	0	0
$428$	−7.09186	−0.342798
$429$	6.13628	0.296262
$430$	16.0381	0.773425
$431$	−23.8841	−1.15046	−0.575229	−	0.817992i	$-0.695087\pi$
$431$	−23.8841	−1.15046	−0.575229	+	0.817992i	$0.695087\pi$
$432$	1.06814	0.0513909
$433$	0.329649	0.0158419	0.00792096	−	0.999969i	$-0.497479\pi$
$433$	0.329649	0.0158419	0.00792096	+	0.999969i	$0.497479\pi$
$434$	0	0
$435$	−6.64663	−0.318681
$436$	−3.47529	−0.166436
$437$	−25.7241	−1.23055
$438$	12.5578	0.600035
$439$	−35.8604	−1.71152	−0.855762	−	0.517370i	$-0.826911\pi$
$439$	−35.8604	−1.71152	−0.855762	+	0.517370i	$0.826911\pi$
$440$	−12.4452	−0.593303
$441$	0	0
$442$	−0.534070	−0.0254031
$443$	1.02372	0.0486385	0.0243193	−	0.999704i	$-0.492258\pi$
$443$	1.02372	0.0486385	0.0243193	+	0.999704i	$0.492258\pi$
$444$	−23.2281	−1.10236
$445$	−34.3470	−1.62821
$446$	16.8905	0.799787
$447$	5.00803	0.236872
$448$	0	0
$449$	26.6290	1.25670	0.628349	−	0.777931i	$-0.283731\pi$
$449$	26.6290	1.25670	0.628349	+	0.777931i	$0.283731\pi$
$450$	−8.67035	−0.408724
$451$	−17.6259	−0.829973
$452$	−16.4690	−0.774635
$453$	19.4897	0.915704
$454$	−22.3327	−1.04812
$455$	0	0
$456$	−8.95558	−0.419384
$457$	−0.180699	−0.00845273	−0.00422637	−	0.999991i	$-0.501345\pi$
$457$	−0.180699	−0.00845273	−0.00422637	+	0.999991i	$0.501345\pi$
$458$	3.18070	0.148624
$459$	1.06814	0.0498565
$460$	−19.9793	−0.931540
$461$	17.2883	0.805194	0.402597	−	0.915377i	$-0.368108\pi$
$461$	17.2883	0.805194	0.402597	+	0.915377i	$0.368108\pi$
$462$	0	0
$463$	26.5164	1.23232	0.616161	−	0.787620i	$-0.288687\pi$
$463$	26.5164	1.23232	0.616161	+	0.787620i	$0.288687\pi$
$464$	−0.955582	−0.0443618
$465$	37.4008	1.73442
$466$	−1.15698	−0.0535959
$467$	4.46593	0.206659	0.103329	−	0.994647i	$-0.467050\pi$
$467$	4.46593	0.206659	0.103329	+	0.994647i	$0.467050\pi$
$468$	1.82733	0.0844682
$469$	0	0
$470$	9.26953	0.427572
$471$	21.4008	0.986098
$472$	3.00000	0.138086
$473$	−26.4927	−1.21813
$474$	−36.6052	−1.68133
$475$	8.95558	0.410910
$476$	0	0
$477$	41.5244	1.90127
$478$	−21.3771	−0.977766
$479$	−24.7034	−1.12873	−0.564364	−	0.825526i	$-0.690879\pi$
$479$	−24.7034	−1.12873	−0.564364	+	0.825526i	$0.690879\pi$
$480$	−6.95558	−0.317477
$481$	−4.89547	−0.223214
$482$	−11.7148	−0.533593
$483$	0	0
$484$	9.55779	0.434445
$485$	37.8748	1.71980
$486$	22.3564	1.01411
$487$	−9.19506	−0.416668	−0.208334	−	0.978058i	$-0.566804\pi$
$487$	−9.19506	−0.416668	−0.208334	+	0.978058i	$0.566804\pi$
$488$	−6.53407	−0.295783
$489$	21.1283	0.955453
$490$	0	0
$491$	25.6704	1.15849	0.579243	−	0.815155i	$-0.303348\pi$
$491$	25.6704	1.15849	0.579243	+	0.815155i	$0.303348\pi$
$492$	−9.85105	−0.444120
$493$	−0.955582	−0.0430372
$494$	−1.88744	−0.0849200
$495$	42.5815	1.91390
$496$	5.37709	0.241439
$497$	0	0
$498$	16.8430	0.754754
$499$	−25.0030	−1.11929	−0.559645	−	0.828733i	$-0.689062\pi$
$499$	−25.0030	−1.11929	−0.559645	+	0.828733i	$0.689062\pi$
$500$	−6.76855	−0.302699
$501$	−2.89547	−0.129360
$502$	6.64663	0.296654
$503$	−40.7272	−1.81593	−0.907967	−	0.419041i	$-0.862366\pi$
$503$	−40.7272	−1.81593	−0.907967	+	0.419041i	$0.862366\pi$
$504$	0	0
$505$	26.2913	1.16995
$506$	33.0030	1.46716
$507$	−32.2201	−1.43095
$508$	18.7779	0.833135
$509$	−33.4058	−1.48069	−0.740343	−	0.672229i	$-0.765337\pi$
$509$	−33.4058	−1.48069	−0.740343	+	0.672229i	$0.765337\pi$
$510$	−6.95558	−0.307998
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	3.77488	0.166665
$514$	−2.38209	−0.105070
$515$	−51.7859	−2.28196
$516$	−14.8066	−0.651826
$517$	−15.3120	−0.673420
$518$	0	0
$519$	−38.2201	−1.67768
$520$	−1.46593	−0.0642853
$521$	−10.9793	−0.481012	−0.240506	−	0.970648i	$-0.577313\pi$
$521$	−10.9793	−0.481012	−0.240506	+	0.970648i	$0.577313\pi$
$522$	3.26953	0.143104
$523$	29.0681	1.27106	0.635531	−	0.772076i	$-0.280781\pi$
$523$	29.0681	1.27106	0.635531	+	0.772076i	$0.280781\pi$
$524$	15.1757	0.662953
$525$	0	0
$526$	−8.11256	−0.353724
$527$	5.37709	0.234230
$528$	11.4897	0.500023
$529$	29.9823	1.30358
$530$	−33.3120	−1.44698
$531$	−10.2645	−0.445443
$532$	0	0
$533$	−2.07617	−0.0899288
$534$	31.7098	1.37222
$535$	−19.4659	−0.841586
$536$	14.0919	0.608676
$537$	65.0505	2.80714
$538$	13.2789	0.572494
$539$	0	0
$540$	2.93186	0.126167
$541$	0.908137	0.0390439	0.0195219	−	0.999809i	$-0.493786\pi$
$541$	0.908137	0.0390439	0.0195219	+	0.999809i	$0.493786\pi$
$542$	25.8223	1.10916
$543$	−1.03175	−0.0442766
$544$	−1.00000	−0.0428746
$545$	−9.53907	−0.408609
$546$	0	0
$547$	25.9349	1.10890	0.554448	−	0.832218i	$-0.312929\pi$
$547$	25.9349	1.10890	0.554448	+	0.832218i	$0.312929\pi$
$548$	2.48965	0.106353
$549$	22.3564	0.954148
$550$	−11.4897	−0.489920
$551$	−3.37709	−0.143869
$552$	18.4452	0.785081
$553$	0	0
$554$	7.26953	0.308853
$555$	−63.7572	−2.70634
$556$	−13.0681	−0.554213
$557$	13.4008	0.567811	0.283905	−	0.958852i	$-0.408370\pi$
$557$	13.4008	0.567811	0.283905	+	0.958852i	$0.408370\pi$
$558$	−18.3978	−0.778841
$559$	−3.12058	−0.131987
$560$	0	0
$561$	11.4897	0.485093
$562$	3.84802	0.162319
$563$	30.2044	1.27296	0.636482	−	0.771291i	$-0.280389\pi$
$563$	30.2044	1.27296	0.636482	+	0.771291i	$0.280389\pi$
$564$	−8.55779	−0.360348
$565$	−45.2044	−1.90176
$566$	−8.00000	−0.336265
$567$	0	0
$568$	−9.25517	−0.388338
$569$	−23.6941	−0.993307	−0.496654	−	0.867949i	$-0.665438\pi$
$569$	−23.6941	−0.993307	−0.496654	+	0.867949i	$0.665438\pi$
$570$	−24.5815	−1.02961
$571$	12.0237	0.503177	0.251589	−	0.967834i	$-0.419047\pi$
$571$	12.0237	0.503177	0.251589	+	0.967834i	$0.419047\pi$
$572$	2.42151	0.101248
$573$	28.3327	1.18361
$574$	0	0
$575$	−18.4452	−0.769219
$576$	3.42151	0.142563
$577$	−11.2933	−0.470144	−0.235072	−	0.971978i	$-0.575533\pi$
$577$	−11.2933	−0.470144	−0.235072	+	0.971978i	$0.575533\pi$
$578$	−1.00000	−0.0415945
$579$	−13.0681	−0.543093
$580$	−2.62291	−0.108910
$581$	0	0
$582$	−34.9666	−1.44941
$583$	55.0267	2.27898
$584$	4.95558	0.205063
$585$	5.01570	0.207374
$586$	−22.1600	−0.915421
$587$	−21.3090	−0.879515	−0.439757	−	0.898117i	$-0.644936\pi$
$587$	−21.3090	−0.879515	−0.439757	+	0.898117i	$0.644936\pi$
$588$	0	0
$589$	19.0030	0.783006
$590$	8.23448	0.339008
$591$	51.2756	2.10920
$592$	−9.16634	−0.376734
$593$	−31.4008	−1.28948	−0.644738	−	0.764403i	$-0.723034\pi$
$593$	−31.4008	−1.28948	−0.644738	+	0.764403i	$0.723034\pi$
$594$	−4.84302	−0.198712
$595$	0	0
$596$	1.97628	0.0809515
$597$	−28.9269	−1.18390
$598$	3.88744	0.158969
$599$	26.3564	1.07689	0.538447	−	0.842660i	$-0.319011\pi$
$599$	26.3564	1.07689	0.538447	+	0.842660i	$0.319011\pi$
$600$	−6.42151	−0.262157
$601$	7.07314	0.288519	0.144260	−	0.989540i	$-0.453920\pi$
$601$	7.07314	0.288519	0.144260	+	0.989540i	$0.453920\pi$
$602$	0	0
$603$	−48.2155	−1.96349
$604$	7.69105	0.312944
$605$	26.2345	1.06658
$606$	−24.2726	−0.986005
$607$	23.5277	0.954961	0.477481	−	0.878642i	$-0.341550\pi$
$607$	23.5277	0.954961	0.477481	+	0.878642i	$0.341550\pi$
$608$	−3.53407	−0.143325
$609$	0	0
$610$	−17.9349	−0.726162
$611$	−1.80361	−0.0729661
$612$	3.42151	0.138306
$613$	16.8380	0.680081	0.340041	−	0.940411i	$-0.389559\pi$
$613$	16.8380	0.680081	0.340041	+	0.940411i	$0.389559\pi$
$614$	10.5785	0.426913
$615$	−27.0394	−1.09033
$616$	0	0
$617$	16.5341	0.665637	0.332818	−	0.942991i	$-0.392000\pi$
$617$	16.5341	0.665637	0.332818	+	0.942991i	$0.392000\pi$
$618$	47.8097	1.92319
$619$	−16.3090	−0.655512	−0.327756	−	0.944762i	$-0.606292\pi$
$619$	−16.3090	−0.655512	−0.327756	+	0.944762i	$0.606292\pi$
$620$	14.7592	0.592743
$621$	−7.77488	−0.311995
$622$	−15.7004	−0.629529
$623$	0	0
$624$	1.35337	0.0541782
$625$	−31.2488	−1.24995
$626$	17.9399	0.717022
$627$	40.6052	1.62162
$628$	8.44523	0.337002
$629$	−9.16634	−0.365486
$630$	0	0
$631$	20.8480	0.829947	0.414973	−	0.909834i	$-0.363791\pi$
$631$	20.8480	0.829947	0.414973	+	0.909834i	$0.363791\pi$
$632$	−14.4452	−0.574601
$633$	−16.6179	−0.660502
$634$	−21.9442	−0.871517
$635$	51.5421	2.04539
$636$	30.7542	1.21948
$637$	0	0
$638$	4.33268	0.171532
$639$	31.6667	1.25271
$640$	−2.74483	−0.108499
$641$	−11.4609	−0.452680	−0.226340	−	0.974048i	$-0.572676\pi$
$641$	−11.4609	−0.452680	−0.226340	+	0.974048i	$0.572676\pi$
$642$	17.9713	0.709270
$643$	26.0712	1.02815	0.514073	−	0.857746i	$-0.328136\pi$
$643$	26.0712	1.02815	0.514073	+	0.857746i	$0.328136\pi$
$644$	0	0
$645$	−40.6416	−1.60026
$646$	−3.53407	−0.139046
$647$	−20.4215	−0.802852	−0.401426	−	0.915891i	$-0.631485\pi$
$647$	−20.4215	−0.802852	−0.401426	+	0.915891i	$0.631485\pi$
$648$	7.55779	0.296898
$649$	−13.6022	−0.533933
$650$	−1.35337	−0.0530836
$651$	0	0
$652$	8.33768	0.326529
$653$	12.7973	0.500796	0.250398	−	0.968143i	$-0.419439\pi$
$653$	12.7973	0.500796	0.250398	+	0.968143i	$0.419439\pi$
$654$	8.80663	0.344367
$655$	41.6547	1.62758
$656$	−3.88744	−0.151779
$657$	−16.9556	−0.661500
$658$	0	0
$659$	24.0681	0.937562	0.468781	−	0.883315i	$-0.344693\pi$
$659$	24.0681	0.937562	0.468781	+	0.883315i	$0.344693\pi$
$660$	31.5371	1.22758
$661$	−17.5735	−0.683529	−0.341765	−	0.939786i	$-0.611025\pi$
$661$	−17.5735	−0.683529	−0.341765	+	0.939786i	$0.611025\pi$
$662$	2.66732	0.103669
$663$	1.35337	0.0525606
$664$	6.64663	0.257939
$665$	0	0
$666$	31.3627	1.21528
$667$	6.95558	0.269321
$668$	−1.14262	−0.0442091
$669$	−42.8016	−1.65481
$670$	38.6797	1.49433
$671$	29.6259	1.14370
$672$	0	0
$673$	−23.1994	−0.894272	−0.447136	−	0.894466i	$-0.647556\pi$
$673$	−23.1994	−0.894272	−0.447136	+	0.894466i	$0.647556\pi$
$674$	9.86372	0.379936
$675$	2.70674	0.104183
$676$	−12.7148	−0.489030
$677$	0.552793	0.0212456	0.0106228	−	0.999944i	$-0.496619\pi$
$677$	0.552793	0.0212456	0.0106228	+	0.999944i	$0.496619\pi$
$678$	41.7335	1.60277
$679$	0	0
$680$	−2.74483	−0.105259
$681$	56.5926	2.16863
$682$	−24.3801	−0.933563
$683$	−51.3120	−1.96340	−0.981699	−	0.190438i	$-0.939009\pi$
$683$	−51.3120	−1.96340	−0.981699	+	0.190438i	$0.939009\pi$
$684$	12.0919	0.462344
$685$	6.83366	0.261101
$686$	0	0
$687$	−8.06011	−0.307513
$688$	−5.84302	−0.222763
$689$	6.48163	0.246930
$690$	50.6290	1.92741
$691$	18.5992	0.707546	0.353773	−	0.935331i	$-0.384898\pi$
$691$	18.5992	0.707546	0.353773	+	0.935331i	$0.384898\pi$
$692$	−15.0825	−0.573351
$693$	0	0
$694$	−4.84302	−0.183839
$695$	−35.8698	−1.36062
$696$	2.42151	0.0917872
$697$	−3.88744	−0.147247
$698$	0.0474447	0.00179581
$699$	2.93186	0.110893
$700$	0	0
$701$	3.44221	0.130010	0.0650052	−	0.997885i	$-0.479294\pi$
$701$	3.44221	0.130010	0.0650052	+	0.997885i	$0.479294\pi$
$702$	−0.570462	−0.0215307
$703$	−32.3945	−1.22178
$704$	4.53407	0.170884
$705$	−23.4897	−0.884671
$706$	−3.06511	−0.115357
$707$	0	0
$708$	−7.60221	−0.285709
$709$	−24.8160	−0.931984	−0.465992	−	0.884789i	$-0.654302\pi$
$709$	−24.8160	−0.931984	−0.465992	+	0.884789i	$0.654302\pi$
$710$	−25.4038	−0.953389
$711$	49.4245	1.85357
$712$	12.5134	0.468959
$713$	−39.1393	−1.46578
$714$	0	0
$715$	6.64663	0.248570
$716$	25.6704	0.959346
$717$	54.1711	2.02306
$718$	−9.82233	−0.366566
$719$	9.77988	0.364728	0.182364	−	0.983231i	$-0.441625\pi$
$719$	9.77988	0.364728	0.182364	+	0.983231i	$0.441625\pi$
$720$	9.39145	0.349999
$721$	0	0
$722$	6.51035	0.242290
$723$	29.6860	1.10404
$724$	−0.407151	−0.0151316
$725$	−2.42151	−0.0899327
$726$	−24.2201	−0.898893
$727$	−1.95861	−0.0726408	−0.0363204	−	0.999340i	$-0.511564\pi$
$727$	−1.95861	−0.0726408	−0.0363204	+	0.999340i	$0.511564\pi$
$728$	0	0
$729$	−33.9793	−1.25849
$730$	13.6022	0.503440
$731$	−5.84302	−0.216112
$732$	16.5578	0.611994
$733$	41.8510	1.54580	0.772902	−	0.634526i	$-0.218804\pi$
$733$	41.8510	1.54580	0.772902	+	0.634526i	$0.218804\pi$
$734$	−2.18703	−0.0807249
$735$	0	0
$736$	7.27890	0.268304
$737$	−63.8935	−2.35355
$738$	13.3009	0.489614
$739$	2.13325	0.0784730	0.0392365	−	0.999230i	$-0.487507\pi$
$739$	2.13325	0.0784730	0.0392365	+	0.999230i	$0.487507\pi$
$740$	−25.1600	−0.924900
$741$	4.78291	0.175705
$742$	0	0
$743$	25.7098	0.943200	0.471600	−	0.881813i	$-0.343677\pi$
$743$	25.7098	0.943200	0.471600	+	0.881813i	$0.343677\pi$
$744$	−13.6259	−0.499551
$745$	5.42454	0.198740
$746$	8.08884	0.296153
$747$	−22.7415	−0.832069
$748$	4.53407	0.165782
$749$	0	0
$750$	17.1520	0.626302
$751$	16.2996	0.594781	0.297390	−	0.954756i	$-0.403884\pi$
$751$	16.2996	0.594781	0.297390	+	0.954756i	$0.403884\pi$
$752$	−3.37709	−0.123150
$753$	−16.8430	−0.613794
$754$	0.510348	0.0185858
$755$	21.1106	0.768293
$756$	0	0
$757$	−3.61988	−0.131567	−0.0657834	−	0.997834i	$-0.520955\pi$
$757$	−3.61988	−0.131567	−0.0657834	+	0.997834i	$0.520955\pi$
$758$	26.9793	0.979932
$759$	−83.6320	−3.03565
$760$	−9.70041	−0.351871
$761$	33.2438	1.20509	0.602544	−	0.798086i	$-0.294154\pi$
$761$	33.2438	1.20509	0.602544	+	0.798086i	$0.294154\pi$
$762$	−47.5845	−1.72381
$763$	0	0
$764$	11.1807	0.404503
$765$	9.39145	0.339549
$766$	−6.27256	−0.226637
$767$	−1.60221	−0.0578525
$768$	2.53407	0.0914404
$769$	−51.0535	−1.84104	−0.920518	−	0.390700i	$-0.872233\pi$
$769$	−51.0535	−1.84104	−0.920518	+	0.390700i	$0.872233\pi$
$770$	0	0
$771$	6.03639	0.217395
$772$	−5.15698	−0.185604
$773$	12.6466	0.454868	0.227434	−	0.973794i	$-0.426966\pi$
$773$	12.6466	0.454868	0.227434	+	0.973794i	$0.426966\pi$
$774$	19.9920	0.718597
$775$	13.6259	0.489458
$776$	−13.7986	−0.495341
$777$	0	0
$778$	5.04442	0.180851
$779$	−13.7385	−0.492233
$780$	3.71477	0.133010
$781$	41.9636	1.50158
$782$	7.27890	0.260293
$783$	−1.02070	−0.0364767
$784$	0	0
$785$	23.1807	0.827355
$786$	−38.4563	−1.37169
$787$	−9.42454	−0.335949	−0.167974	−	0.985791i	$-0.553723\pi$
$787$	−9.42454	−0.335949	−0.167974	+	0.985791i	$0.553723\pi$
$788$	20.2345	0.720823
$789$	20.5578	0.731877
$790$	−39.6497	−1.41067
$791$	0	0
$792$	−15.5134	−0.551244
$793$	3.48965	0.123921
$794$	19.9442	0.707795
$795$	84.4149	2.99389
$796$	−11.4152	−0.404600
$797$	5.42454	0.192147	0.0960735	−	0.995374i	$-0.469372\pi$
$797$	5.42454	0.192147	0.0960735	+	0.995374i	$0.469372\pi$
$798$	0	0
$799$	−3.37709	−0.119473
$800$	−2.53407	−0.0895929
$801$	−42.8147	−1.51278
$802$	20.8016	0.734531
$803$	−22.4690	−0.792912
$804$	−35.7098	−1.25939
$805$	0	0
$806$	−2.87175	−0.101153
$807$	−33.6497	−1.18452
$808$	−9.57849	−0.336970
$809$	−5.82733	−0.204878	−0.102439	−	0.994739i	$-0.532665\pi$
$809$	−5.82733	−0.204878	−0.102439	+	0.994739i	$0.532665\pi$
$810$	20.7448	0.728899
$811$	53.4770	1.87783	0.938915	−	0.344148i	$-0.111832\pi$
$811$	53.4770	1.87783	0.938915	+	0.344148i	$0.111832\pi$
$812$	0	0
$813$	−65.4356	−2.29493
$814$	41.5608	1.45671
$815$	22.8855	0.801643
$816$	2.53407	0.0887102
$817$	−20.6497	−0.722440
$818$	32.3614	1.13149
$819$	0	0
$820$	−10.6704	−0.372625
$821$	21.8731	0.763376	0.381688	−	0.924291i	$-0.375343\pi$
$821$	21.8731	0.763376	0.381688	+	0.924291i	$0.375343\pi$
$822$	−6.30895	−0.220050
$823$	48.5341	1.69179	0.845896	−	0.533348i	$-0.179067\pi$
$823$	48.5341	1.69179	0.845896	+	0.533348i	$0.179067\pi$
$824$	18.8667	0.657254
$825$	29.1156	1.01367
$826$	0	0
$827$	−4.64163	−0.161405	−0.0807026	−	0.996738i	$-0.525716\pi$
$827$	−4.64163	−0.161405	−0.0807026	+	0.996738i	$0.525716\pi$
$828$	−24.9048	−0.865503
$829$	5.00303	0.173762	0.0868811	−	0.996219i	$-0.472310\pi$
$829$	5.00303	0.173762	0.0868811	+	0.996219i	$0.472310\pi$
$830$	18.2438	0.633253
$831$	−18.4215	−0.639035
$832$	0.534070	0.0185156
$833$	0	0
$834$	33.1156	1.14670
$835$	−3.13628	−0.108535
$836$	16.0237	0.554192
$837$	5.74349	0.198524
$838$	−12.5528	−0.433629
$839$	34.3758	1.18678	0.593391	−	0.804914i	$-0.297789\pi$
$839$	34.3758	1.18678	0.593391	+	0.804914i	$0.297789\pi$
$840$	0	0
$841$	−28.0869	−0.968513
$842$	17.7098	0.610319
$843$	−9.75116	−0.335848
$844$	−6.55779	−0.225729
$845$	−34.8998	−1.20059
$846$	11.5548	0.397261
$847$	0	0
$848$	12.1363	0.416762
$849$	20.2726	0.695753
$850$	−2.53407	−0.0869179
$851$	66.7208	2.28716
$852$	23.4533	0.803495
$853$	−1.00303	−0.0343430	−0.0171715	−	0.999853i	$-0.505466\pi$
$853$	−1.00303	−0.0343430	−0.0171715	+	0.999853i	$0.505466\pi$
$854$	0	0
$855$	33.1901	1.13508
$856$	7.09186	0.242395
$857$	−17.4897	−0.597435	−0.298718	−	0.954342i	$-0.596559\pi$
$857$	−17.4897	−0.597435	−0.298718	+	0.954342i	$0.596559\pi$
$858$	−6.13628	−0.209489
$859$	−22.9526	−0.783131	−0.391566	−	0.920150i	$-0.628066\pi$
$859$	−22.9526	−0.783131	−0.391566	+	0.920150i	$0.628066\pi$
$860$	−16.0381	−0.546894
$861$	0	0
$862$	23.8841	0.813497
$863$	24.4877	0.833570	0.416785	−	0.909005i	$-0.363157\pi$
$863$	24.4877	0.833570	0.416785	+	0.909005i	$0.363157\pi$
$864$	−1.06814	−0.0363389
$865$	−41.3988	−1.40760
$866$	−0.329649	−0.0112019
$867$	2.53407	0.0860615
$868$	0	0
$869$	65.4957	2.22179
$870$	6.64663	0.225342
$871$	−7.52604	−0.255010
$872$	3.47529	0.117688
$873$	47.2121	1.59789
$874$	25.7241	0.870132
$875$	0	0
$876$	−12.5578	−0.424288
$877$	−15.0444	−0.508014	−0.254007	−	0.967202i	$-0.581749\pi$
$877$	−15.0444	−0.508014	−0.254007	+	0.967202i	$0.581749\pi$
$878$	35.8604	1.21023
$879$	56.1550	1.89406
$880$	12.4452	0.419529
$881$	−41.2231	−1.38884	−0.694422	−	0.719568i	$-0.744340\pi$
$881$	−41.2231	−1.38884	−0.694422	+	0.719568i	$0.744340\pi$
$882$	0	0
$883$	40.2626	1.35494	0.677472	−	0.735549i	$-0.263076\pi$
$883$	40.2626	1.35494	0.677472	+	0.735549i	$0.263076\pi$
$884$	0.534070	0.0179627
$885$	−20.8667	−0.701428
$886$	−1.02372	−0.0343926
$887$	18.8480	0.632855	0.316427	−	0.948617i	$-0.397517\pi$
$887$	18.8480	0.632855	0.316427	+	0.948617i	$0.397517\pi$
$888$	23.2281	0.779485
$889$	0	0
$890$	34.3470	1.15132
$891$	−34.2676	−1.14801
$892$	−16.8905	−0.565535
$893$	−11.9349	−0.399386
$894$	−5.00803	−0.167493
$895$	70.4606	2.35524
$896$	0	0
$897$	−9.85105	−0.328917
$898$	−26.6290	−0.888620
$899$	−5.13825	−0.171370
$900$	8.67035	0.289012
$901$	12.1363	0.404318
$902$	17.6259	0.586879
$903$	0	0
$904$	16.4690	0.547749
$905$	−1.11756	−0.0371489
$906$	−19.4897	−0.647500
$907$	27.7809	0.922451	0.461225	−	0.887283i	$-0.347410\pi$
$907$	27.7809	0.922451	0.461225	+	0.887283i	$0.347410\pi$
$908$	22.3327	0.741136
$909$	32.7729	1.08701
$910$	0	0
$911$	−10.0094	−0.331625	−0.165812	−	0.986157i	$-0.553025\pi$
$911$	−10.0094	−0.331625	−0.165812	+	0.986157i	$0.553025\pi$
$912$	8.95558	0.296549
$913$	−30.1363	−0.997365
$914$	0.180699	0.00597699
$915$	45.4483	1.50247
$916$	−3.18070	−0.105093
$917$	0	0
$918$	−1.06814	−0.0352539
$919$	−28.9616	−0.955356	−0.477678	−	0.878535i	$-0.658521\pi$
$919$	−28.9616	−0.955356	−0.477678	+	0.878535i	$0.658521\pi$
$920$	19.9793	0.658698
$921$	−26.8066	−0.883309
$922$	−17.2883	−0.569358
$923$	4.94291	0.162698
$924$	0	0
$925$	−23.2281	−0.763737
$926$	−26.5164	−0.871383
$927$	−64.5528	−2.12019
$928$	0.955582	0.0313685
$929$	13.9399	0.457353	0.228676	−	0.973502i	$-0.426560\pi$
$929$	13.9399	0.457353	0.228676	+	0.973502i	$0.426560\pi$
$930$	−37.4008	−1.22642
$931$	0	0
$932$	1.15698	0.0378980
$933$	39.7859	1.30253
$934$	−4.46593	−0.146130
$935$	12.4452	0.407003
$936$	−1.82733	−0.0597281
$937$	−13.8767	−0.453334	−0.226667	−	0.973972i	$-0.572783\pi$
$937$	−13.8767	−0.453334	−0.226667	+	0.973972i	$0.572783\pi$
$938$	0	0
$939$	−45.4609	−1.48356
$940$	−9.26953	−0.302339
$941$	−28.8347	−0.939985	−0.469992	−	0.882670i	$-0.655743\pi$
$941$	−28.8347	−0.939985	−0.469992	+	0.882670i	$0.655743\pi$
$942$	−21.4008	−0.697276
$943$	28.2963	0.921454
$944$	−3.00000	−0.0976417
$945$	0	0
$946$	26.4927	0.861351
$947$	43.3357	1.40822	0.704111	−	0.710090i	$-0.251346\pi$
$947$	43.3357	1.40822	0.704111	+	0.710090i	$0.251346\pi$
$948$	36.6052	1.18888
$949$	−2.64663	−0.0859132
$950$	−8.95558	−0.290557
$951$	55.6083	1.80322
$952$	0	0
$953$	−28.7098	−0.930001	−0.465000	−	0.885311i	$-0.653946\pi$
$953$	−28.7098	−0.930001	−0.465000	+	0.885311i	$0.653946\pi$
$954$	−41.5244	−1.34440
$955$	30.6891	0.993075
$956$	21.3771	0.691385
$957$	−10.9793	−0.354911
$958$	24.7034	0.798132
$959$	0	0
$960$	6.95558	0.224490
$961$	−2.08686	−0.0673182
$962$	4.89547	0.157836
$963$	−24.2649	−0.781925
$964$	11.7148	0.377307
$965$	−14.1550	−0.455666
$966$	0	0
$967$	−43.1680	−1.38819	−0.694095	−	0.719883i	$-0.744195\pi$
$967$	−43.1680	−1.38819	−0.694095	+	0.719883i	$0.744195\pi$
$968$	−9.55779	−0.307199
$969$	8.95558	0.287695
$970$	−37.8748	−1.21609
$971$	18.4422	0.591839	0.295919	−	0.955213i	$-0.404374\pi$
$971$	18.4422	0.591839	0.295919	+	0.955213i	$0.404374\pi$
$972$	−22.3564	−0.717082
$973$	0	0
$974$	9.19506	0.294629
$975$	3.42954	0.109833
$976$	6.53407	0.209150
$977$	29.1837	0.933670	0.466835	−	0.884344i	$-0.345394\pi$
$977$	29.1837	0.933670	0.466835	+	0.884344i	$0.345394\pi$
$978$	−21.1283	−0.675607
$979$	−56.7365	−1.81331
$980$	0	0
$981$	−11.8907	−0.379642
$982$	−25.6704	−0.819174
$983$	52.3895	1.67096	0.835482	−	0.549517i	$-0.185188\pi$
$983$	52.3895	1.67096	0.835482	+	0.549517i	$0.185188\pi$
$984$	9.85105	0.314040
$985$	55.5401	1.76966
$986$	0.955582	0.0304319
$987$	0	0
$988$	1.88744	0.0600475
$989$	42.5308	1.35240
$990$	−42.5815	−1.35333
$991$	−6.51471	−0.206947	−0.103473	−	0.994632i	$-0.532996\pi$
$991$	−6.51471	−0.206947	−0.103473	+	0.994632i	$0.532996\pi$
$992$	−5.37709	−0.170723
$993$	−6.75919	−0.214496
$994$	0	0
$995$	−31.3327	−0.993313
$996$	−16.8430	−0.533692
$997$	35.7572	1.13244	0.566221	−	0.824253i	$-0.308405\pi$
$997$	35.7572	1.13244	0.566221	+	0.824253i	$0.308405\pi$
$998$	25.0030	0.791457
$999$	−9.79094	−0.309771

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.t.1.3		3
7.2	even	3		238.2.e.e.137.1	✓	6
7.4	even	3		238.2.e.e.205.1	yes	6
7.6	odd	2		1666.2.a.u.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
238.2.e.e.137.1	✓	6	7.2	even	3
238.2.e.e.205.1	yes	6	7.4	even	3
1666.2.a.t.1.3		3	1.1	even	1	trivial
1666.2.a.u.1.1		3	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1666.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.53407 q^{3} +1.00000 q^{4} +2.74483 q^{5} -2.53407 q^{6} -1.00000 q^{8} +3.42151 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.53407 q^{3} +1.00000 q^{4} +2.74483 q^{5} -2.53407 q^{6} -1.00000 q^{8} +3.42151 q^{9} -2.74483 q^{10} +4.53407 q^{11} +2.53407 q^{12} +0.534070 q^{13} +6.95558 q^{15} +1.00000 q^{16} +1.00000 q^{17} -3.42151 q^{18} +3.53407 q^{19} +2.74483 q^{20} -4.53407 q^{22} -7.27890 q^{23} -2.53407 q^{24} +2.53407 q^{25} -0.534070 q^{26} +1.06814 q^{27} -0.955582 q^{29} -6.95558 q^{30} +5.37709 q^{31} -1.00000 q^{32} +11.4897 q^{33} -1.00000 q^{34} +3.42151 q^{36} -9.16634 q^{37} -3.53407 q^{38} +1.35337 q^{39} -2.74483 q^{40} -3.88744 q^{41} -5.84302 q^{43} +4.53407 q^{44} +9.39145 q^{45} +7.27890 q^{46} -3.37709 q^{47} +2.53407 q^{48} -2.53407 q^{50} +2.53407 q^{51} +0.534070 q^{52} +12.1363 q^{53} -1.06814 q^{54} +12.4452 q^{55} +8.95558 q^{57} +0.955582 q^{58} -3.00000 q^{59} +6.95558 q^{60} +6.53407 q^{61} -5.37709 q^{62} +1.00000 q^{64} +1.46593 q^{65} -11.4897 q^{66} -14.0919 q^{67} +1.00000 q^{68} -18.4452 q^{69} +9.25517 q^{71} -3.42151 q^{72} -4.95558 q^{73} +9.16634 q^{74} +6.42151 q^{75} +3.53407 q^{76} -1.35337 q^{78} +14.4452 q^{79} +2.74483 q^{80} -7.55779 q^{81} +3.88744 q^{82} -6.64663 q^{83} +2.74483 q^{85} +5.84302 q^{86} -2.42151 q^{87} -4.53407 q^{88} -12.5134 q^{89} -9.39145 q^{90} -7.27890 q^{92} +13.6259 q^{93} +3.37709 q^{94} +9.70041 q^{95} -2.53407 q^{96} +13.7986 q^{97} +15.5134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} - q^{5} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 - q^5 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} - q^{5} - 3 q^{8} + 7 q^{9} + q^{10} + 6 q^{11} - 6 q^{13} + 10 q^{15} + 3 q^{16} + 3 q^{17} - 7 q^{18} + 3 q^{19} - q^{20} - 6 q^{22} - 5 q^{23} + 6 q^{26} - 12 q^{27} + 8 q^{29} - 10 q^{30} + 2 q^{31} - 3 q^{32} + 16 q^{33} - 3 q^{34} + 7 q^{36} - 15 q^{37} - 3 q^{38} + 16 q^{39} + q^{40} - 16 q^{41} - 11 q^{43} + 6 q^{44} + 7 q^{45} + 5 q^{46} + 4 q^{47} - 6 q^{52} + 6 q^{53} + 12 q^{54} + 8 q^{55} + 16 q^{57} - 8 q^{58} - 9 q^{59} + 10 q^{60} + 12 q^{61} - 2 q^{62} + 3 q^{64} + 12 q^{65} - 16 q^{66} - q^{67} + 3 q^{68} - 26 q^{69} + 37 q^{71} - 7 q^{72} - 4 q^{73} + 15 q^{74} + 16 q^{75} + 3 q^{76} - 16 q^{78} + 14 q^{79} - q^{80} + 11 q^{81} + 16 q^{82} - 8 q^{83} - q^{85} + 11 q^{86} - 4 q^{87} - 6 q^{88} + 7 q^{89} - 7 q^{90} - 5 q^{92} - 8 q^{93} - 4 q^{94} + 9 q^{95} + 24 q^{97} + 2 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 - q^5 - 3 * q^8 + 7 * q^9 + q^10 + 6 * q^11 - 6 * q^13 + 10 * q^15 + 3 * q^16 + 3 * q^17 - 7 * q^18 + 3 * q^19 - q^20 - 6 * q^22 - 5 * q^23 + 6 * q^26 - 12 * q^27 + 8 * q^29 - 10 * q^30 + 2 * q^31 - 3 * q^32 + 16 * q^33 - 3 * q^34 + 7 * q^36 - 15 * q^37 - 3 * q^38 + 16 * q^39 + q^40 - 16 * q^41 - 11 * q^43 + 6 * q^44 + 7 * q^45 + 5 * q^46 + 4 * q^47 - 6 * q^52 + 6 * q^53 + 12 * q^54 + 8 * q^55 + 16 * q^57 - 8 * q^58 - 9 * q^59 + 10 * q^60 + 12 * q^61 - 2 * q^62 + 3 * q^64 + 12 * q^65 - 16 * q^66 - q^67 + 3 * q^68 - 26 * q^69 + 37 * q^71 - 7 * q^72 - 4 * q^73 + 15 * q^74 + 16 * q^75 + 3 * q^76 - 16 * q^78 + 14 * q^79 - q^80 + 11 * q^81 + 16 * q^82 - 8 * q^83 - q^85 + 11 * q^86 - 4 * q^87 - 6 * q^88 + 7 * q^89 - 7 * q^90 - 5 * q^92 - 8 * q^93 - 4 * q^94 + 9 * q^95 + 24 * q^97 + 2 * q^99

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