LMFDB - Embedded newform 1666.2.a.x.1.1

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.334904$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.80853 q^{3} +1.00000 q^{4} -1.66510 q^{5} -2.80853 q^{6} +1.00000 q^{8} +4.88784 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.80853 q^{3} +1.00000 q^{4} -1.66510 q^{5} -2.80853 q^{6} +1.00000 q^{8} +4.88784 q^{9} -1.66510 q^{10} -0.605684 q^{11} -2.80853 q^{12} -0.466962 q^{13} +4.67647 q^{15} +1.00000 q^{16} +1.00000 q^{17} +4.88784 q^{18} +5.85970 q^{19} -1.66510 q^{20} -0.605684 q^{22} +2.35480 q^{23} -2.80853 q^{24} -2.22746 q^{25} -0.466962 q^{26} -5.30205 q^{27} -0.0547002 q^{29} +4.67647 q^{30} -10.1399 q^{31} +1.00000 q^{32} +1.70108 q^{33} +1.00000 q^{34} +4.88784 q^{36} -4.92069 q^{37} +5.85970 q^{38} +1.31148 q^{39} -1.66510 q^{40} -2.85657 q^{41} -6.32666 q^{43} -0.605684 q^{44} -8.13872 q^{45} +2.35480 q^{46} +10.6881 q^{47} -2.80853 q^{48} -2.22746 q^{50} -2.80853 q^{51} -0.466962 q^{52} -9.39274 q^{53} -5.30205 q^{54} +1.00852 q^{55} -16.4571 q^{57} -0.0547002 q^{58} -4.86323 q^{59} +4.67647 q^{60} -8.39745 q^{61} -10.1399 q^{62} +1.00000 q^{64} +0.777537 q^{65} +1.70108 q^{66} +2.03979 q^{67} +1.00000 q^{68} -6.61353 q^{69} -12.2212 q^{71} +4.88784 q^{72} -5.33019 q^{73} -4.92069 q^{74} +6.25587 q^{75} +5.85970 q^{76} +1.31148 q^{78} +11.7194 q^{79} -1.66510 q^{80} +0.227455 q^{81} -2.85657 q^{82} +3.70108 q^{83} -1.66510 q^{85} -6.32666 q^{86} +0.153627 q^{87} -0.605684 q^{88} -17.5260 q^{89} -8.13872 q^{90} +2.35480 q^{92} +28.4782 q^{93} +10.6881 q^{94} -9.75696 q^{95} -2.80853 q^{96} +14.4666 q^{97} -2.96049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 8 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 8 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 8 q^{25} - 8 q^{26} - 4 q^{27} - 4 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 16 q^{33} + 4 q^{34} + 8 q^{36} - 24 q^{37} - 8 q^{38} - 20 q^{39} - 8 q^{40} - 20 q^{41} - 4 q^{44} - 28 q^{45} + 4 q^{46} - 4 q^{48} + 8 q^{50} - 4 q^{51} - 8 q^{52} - 4 q^{54} + 16 q^{55} - 12 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 8 q^{61} - 4 q^{62} + 4 q^{64} + 4 q^{65} - 16 q^{66} + 4 q^{68} + 16 q^{69} + 8 q^{72} - 24 q^{73} - 24 q^{74} + 16 q^{75} - 8 q^{76} - 20 q^{78} - 16 q^{79} - 8 q^{80} - 16 q^{81} - 20 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 4 q^{88} - 8 q^{89} - 28 q^{90} + 4 q^{92} + 24 q^{93} + 12 q^{95} - 4 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 - 4 * q^12 - 8 * q^13 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 8 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 8 * q^25 - 8 * q^26 - 4 * q^27 - 4 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 16 * q^33 + 4 * q^34 + 8 * q^36 - 24 * q^37 - 8 * q^38 - 20 * q^39 - 8 * q^40 - 20 * q^41 - 4 * q^44 - 28 * q^45 + 4 * q^46 - 4 * q^48 + 8 * q^50 - 4 * q^51 - 8 * q^52 - 4 * q^54 + 16 * q^55 - 12 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 8 * q^61 - 4 * q^62 + 4 * q^64 + 4 * q^65 - 16 * q^66 + 4 * q^68 + 16 * q^69 + 8 * q^72 - 24 * q^73 - 24 * q^74 + 16 * q^75 - 8 * q^76 - 20 * q^78 - 16 * q^79 - 8 * q^80 - 16 * q^81 - 20 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 4 * q^88 - 8 * q^89 - 28 * q^90 + 4 * q^92 + 24 * q^93 + 12 * q^95 - 4 * q^96 - 4 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.80853	−1.62151	−0.810753	−	0.585389i	$-0.800942\pi$
$3$	−2.80853	−1.62151	−0.810753	+	0.585389i	$0.800942\pi$
$4$	1.00000	0.500000
$5$	−1.66510	−0.744654	−0.372327	−	0.928102i	$-0.621440\pi$
$5$	−1.66510	−0.744654	−0.372327	+	0.928102i	$0.621440\pi$
$6$	−2.80853	−1.14658
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	4.88784	1.62928
$10$	−1.66510	−0.526550
$11$	−0.605684	−0.182621	−0.0913103	−	0.995822i	$-0.529106\pi$
$11$	−0.605684	−0.182621	−0.0913103	+	0.995822i	$0.529106\pi$
$12$	−2.80853	−0.810753
$13$	−0.466962	−0.129512	−0.0647560	−	0.997901i	$-0.520627\pi$
$13$	−0.466962	−0.129512	−0.0647560	+	0.997901i	$0.520627\pi$
$14$	0	0
$15$	4.67647	1.20746
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.88784	1.15207
$19$	5.85970	1.34431	0.672154	−	0.740412i	$-0.265369\pi$
$19$	5.85970	1.34431	0.672154	+	0.740412i	$0.265369\pi$
$20$	−1.66510	−0.372327
$21$	0	0
$22$	−0.605684	−0.129132
$23$	2.35480	0.491010	0.245505	−	0.969395i	$-0.421046\pi$
$23$	2.35480	0.491010	0.245505	+	0.969395i	$0.421046\pi$
$24$	−2.80853	−0.573289
$25$	−2.22746	−0.445491
$26$	−0.466962	−0.0915788
$27$	−5.30205	−1.02038
$28$	0	0
$29$	−0.0547002	−0.0101576	−0.00507879	−	0.999987i	$-0.501617\pi$
$29$	−0.0547002	−0.0101576	−0.00507879	+	0.999987i	$0.501617\pi$
$30$	4.67647	0.853803
$31$	−10.1399	−1.82118	−0.910590	−	0.413310i	$-0.864372\pi$
$31$	−10.1399	−1.82118	−0.910590	+	0.413310i	$0.864372\pi$
$32$	1.00000	0.176777
$33$	1.70108	0.296120
$34$	1.00000	0.171499
$35$	0	0
$36$	4.88784	0.814640
$37$	−4.92069	−0.808957	−0.404478	−	0.914548i	$-0.632547\pi$
$37$	−4.92069	−0.808957	−0.404478	+	0.914548i	$0.632547\pi$
$38$	5.85970	0.950569
$39$	1.31148	0.210004
$40$	−1.66510	−0.263275
$41$	−2.85657	−0.446121	−0.223060	−	0.974805i	$-0.571605\pi$
$41$	−2.85657	−0.446121	−0.223060	+	0.974805i	$0.571605\pi$
$42$	0	0
$43$	−6.32666	−0.964807	−0.482403	−	0.875949i	$-0.660236\pi$
$43$	−6.32666	−0.964807	−0.482403	+	0.875949i	$0.660236\pi$
$44$	−0.605684	−0.0913103
$45$	−8.13872	−1.21325
$46$	2.35480	0.347197
$47$	10.6881	1.55902	0.779512	−	0.626388i	$-0.215467\pi$
$47$	10.6881	1.55902	0.779512	+	0.626388i	$0.215467\pi$
$48$	−2.80853	−0.405376
$49$	0	0
$50$	−2.22746	−0.315010
$51$	−2.80853	−0.393273
$52$	−0.466962	−0.0647560
$53$	−9.39274	−1.29019	−0.645096	−	0.764102i	$-0.723183\pi$
$53$	−9.39274	−1.29019	−0.645096	+	0.764102i	$0.723183\pi$
$54$	−5.30205	−0.721518
$55$	1.00852	0.135989
$56$	0	0
$57$	−16.4571	−2.17980
$58$	−0.0547002	−0.00718249
$59$	−4.86323	−0.633139	−0.316569	−	0.948569i	$-0.602531\pi$
$59$	−4.86323	−0.633139	−0.316569	+	0.948569i	$0.602531\pi$
$60$	4.67647	0.603730
$61$	−8.39745	−1.07518	−0.537592	−	0.843205i	$-0.680666\pi$
$61$	−8.39745	−1.07518	−0.537592	+	0.843205i	$0.680666\pi$
$62$	−10.1399	−1.28777
$63$	0	0
$64$	1.00000	0.125000
$65$	0.777537	0.0964416
$66$	1.70108	0.209389
$67$	2.03979	0.249201	0.124600	−	0.992207i	$-0.460235\pi$
$67$	2.03979	0.249201	0.124600	+	0.992207i	$0.460235\pi$
$68$	1.00000	0.121268
$69$	−6.61353	−0.796175
$70$	0	0
$71$	−12.2212	−1.45039	−0.725193	−	0.688546i	$-0.758249\pi$
$71$	−12.2212	−1.45039	−0.725193	+	0.688546i	$0.758249\pi$
$72$	4.88784	0.576037
$73$	−5.33019	−0.623852	−0.311926	−	0.950106i	$-0.600974\pi$
$73$	−5.33019	−0.623852	−0.311926	+	0.950106i	$0.600974\pi$
$74$	−4.92069	−0.572019
$75$	6.25587	0.722366
$76$	5.85970	0.672154
$77$	0	0
$78$	1.31148	0.148496
$79$	11.7194	1.31854	0.659268	−	0.751908i	$-0.270866\pi$
$79$	11.7194	1.31854	0.659268	+	0.751908i	$0.270866\pi$
$80$	−1.66510	−0.186163
$81$	0.227455	0.0252728
$82$	−2.85657	−0.315455
$83$	3.70108	0.406246	0.203123	−	0.979153i	$-0.434891\pi$
$83$	3.70108	0.406246	0.203123	+	0.979153i	$0.434891\pi$
$84$	0	0
$85$	−1.66510	−0.180605
$86$	−6.32666	−0.682222
$87$	0.153627	0.0164706
$88$	−0.605684	−0.0645661
$89$	−17.5260	−1.85775	−0.928875	−	0.370393i	$-0.879223\pi$
$89$	−17.5260	−1.85775	−0.928875	+	0.370393i	$0.879223\pi$
$90$	−8.13872	−0.857897
$91$	0	0
$92$	2.35480	0.245505
$93$	28.4782	2.95305
$94$	10.6881	1.10240
$95$	−9.75696	−1.00104
$96$	−2.80853	−0.286644
$97$	14.4666	1.46886	0.734429	−	0.678686i	$-0.237450\pi$
$97$	14.4666	1.46886	0.734429	+	0.678686i	$0.237450\pi$
$98$	0	0
$99$	−2.96049	−0.297540
$100$	−2.22746	−0.222746
$101$	−12.0840	−1.20241	−0.601203	−	0.799097i	$-0.705312\pi$
$101$	−12.0840	−1.20241	−0.601203	+	0.799097i	$0.705312\pi$
$102$	−2.80853	−0.278086
$103$	9.33962	0.920260	0.460130	−	0.887852i	$-0.347803\pi$
$103$	9.33962	0.920260	0.460130	+	0.887852i	$0.347803\pi$
$104$	−0.466962	−0.0457894
$105$	0	0
$106$	−9.39274	−0.912303
$107$	−13.7210	−1.32646	−0.663229	−	0.748417i	$-0.730814\pi$
$107$	−13.7210	−1.32646	−0.663229	+	0.748417i	$0.730814\pi$
$108$	−5.30205	−0.510190
$109$	2.68695	0.257363	0.128681	−	0.991686i	$-0.458926\pi$
$109$	2.68695	0.257363	0.128681	+	0.991686i	$0.458926\pi$
$110$	1.00852	0.0961588
$111$	13.8199	1.31173
$112$	0	0
$113$	−6.13990	−0.577594	−0.288797	−	0.957390i	$-0.593255\pi$
$113$	−6.13990	−0.577594	−0.288797	+	0.957390i	$0.593255\pi$
$114$	−16.4571	−1.54135
$115$	−3.92097	−0.365632
$116$	−0.0547002	−0.00507879
$117$	−2.28244	−0.211011
$118$	−4.86323	−0.447697
$119$	0	0
$120$	4.67647	0.426902
$121$	−10.6331	−0.966650
$122$	−8.39745	−0.760269
$123$	8.02275	0.723387
$124$	−10.1399	−0.910590
$125$	12.0344	1.07639
$126$	0	0
$127$	−10.9241	−0.969358	−0.484679	−	0.874692i	$-0.661063\pi$
$127$	−10.9241	−0.969358	−0.484679	+	0.874692i	$0.661063\pi$
$128$	1.00000	0.0883883
$129$	17.7686	1.56444
$130$	0.777537	0.0681945
$131$	−22.4770	−1.96383	−0.981914	−	0.189327i	$-0.939369\pi$
$131$	−22.4770	−1.96383	−0.981914	+	0.189327i	$0.939369\pi$
$132$	1.70108	0.148060
$133$	0	0
$134$	2.03979	0.176211
$135$	8.82843	0.759830
$136$	1.00000	0.0857493
$137$	14.6600	1.25249	0.626244	−	0.779627i	$-0.284592\pi$
$137$	14.6600	1.25249	0.626244	+	0.779627i	$0.284592\pi$
$138$	−6.61353	−0.562981
$139$	−5.24236	−0.444651	−0.222326	−	0.974972i	$-0.571365\pi$
$139$	−5.24236	−0.444651	−0.222326	+	0.974972i	$0.571365\pi$
$140$	0	0
$141$	−30.0179	−2.52797
$142$	−12.2212	−1.02558
$143$	0.282831	0.0236515
$144$	4.88784	0.407320
$145$	0.0910812	0.00756388
$146$	−5.33019	−0.441130
$147$	0	0
$148$	−4.92069	−0.404478
$149$	−13.8249	−1.13258	−0.566290	−	0.824206i	$-0.691622\pi$
$149$	−13.8249	−1.13258	−0.566290	+	0.824206i	$0.691622\pi$
$150$	6.25587	0.510790
$151$	12.5576	1.02193	0.510963	−	0.859602i	$-0.329289\pi$
$151$	12.5576	1.02193	0.510963	+	0.859602i	$0.329289\pi$
$152$	5.85970	0.475284
$153$	4.88784	0.395158
$154$	0	0
$155$	16.8839	1.35615
$156$	1.31148	0.105002
$157$	−10.8860	−0.868796	−0.434398	−	0.900721i	$-0.643039\pi$
$157$	−10.8860	−0.868796	−0.434398	+	0.900721i	$0.643039\pi$
$158$	11.7194	0.932345
$159$	26.3798	2.09205
$160$	−1.66510	−0.131637
$161$	0	0
$162$	0.227455	0.0178706
$163$	−0.160197	−0.0125476	−0.00627381	−	0.999980i	$-0.501997\pi$
$163$	−0.160197	−0.0125476	−0.00627381	+	0.999980i	$0.501997\pi$
$164$	−2.85657	−0.223060
$165$	−2.83246	−0.220507
$166$	3.70108	0.287260
$167$	4.09069	0.316547	0.158273	−	0.987395i	$-0.449407\pi$
$167$	4.09069	0.316547	0.158273	+	0.987395i	$0.449407\pi$
$168$	0	0
$169$	−12.7819	−0.983227
$170$	−1.66510	−0.127707
$171$	28.6413	2.19025
$172$	−6.32666	−0.482403
$173$	−13.2938	−1.01071	−0.505355	−	0.862912i	$-0.668638\pi$
$173$	−13.2938	−1.01071	−0.505355	+	0.862912i	$0.668638\pi$
$174$	0.153627	0.0116465
$175$	0	0
$176$	−0.605684	−0.0456551
$177$	13.6585	1.02664
$178$	−17.5260	−1.31363
$179$	−7.60764	−0.568621	−0.284311	−	0.958732i	$-0.591765\pi$
$179$	−7.60764	−0.568621	−0.284311	+	0.958732i	$0.591765\pi$
$180$	−8.13872	−0.606625
$181$	0.384123	0.0285516	0.0142758	−	0.999898i	$-0.495456\pi$
$181$	0.384123	0.0285516	0.0142758	+	0.999898i	$0.495456\pi$
$182$	0	0
$183$	23.5845	1.74342
$184$	2.35480	0.173598
$185$	8.19342	0.602392
$186$	28.4782	2.08812
$187$	−0.605684	−0.0442920
$188$	10.6881	0.779512
$189$	0	0
$190$	−9.75696	−0.707845
$191$	2.51119	0.181703	0.0908516	−	0.995864i	$-0.471041\pi$
$191$	2.51119	0.181703	0.0908516	+	0.995864i	$0.471041\pi$
$192$	−2.80853	−0.202688
$193$	23.7007	1.70601	0.853006	−	0.521901i	$-0.174777\pi$
$193$	23.7007	1.70601	0.853006	+	0.521901i	$0.174777\pi$
$194$	14.4666	1.03864
$195$	−2.18373	−0.156380
$196$	0	0
$197$	5.58734	0.398082	0.199041	−	0.979991i	$-0.436217\pi$
$197$	5.58734	0.398082	0.199041	+	0.979991i	$0.436217\pi$
$198$	−2.96049	−0.210393
$199$	24.5175	1.73800	0.868998	−	0.494815i	$-0.164764\pi$
$199$	24.5175	1.73800	0.868998	+	0.494815i	$0.164764\pi$
$200$	−2.22746	−0.157505
$201$	−5.72882	−0.404080
$202$	−12.0840	−0.850229
$203$	0	0
$204$	−2.80853	−0.196636
$205$	4.75646	0.332205
$206$	9.33962	0.650722
$207$	11.5099	0.799993
$208$	−0.466962	−0.0323780
$209$	−3.54913	−0.245498
$210$	0	0
$211$	18.7965	1.29400	0.647001	−	0.762489i	$-0.276023\pi$
$211$	18.7965	1.29400	0.647001	+	0.762489i	$0.276023\pi$
$212$	−9.39274	−0.645096
$213$	34.3235	2.35181
$214$	−13.7210	−0.937947
$215$	10.5345	0.718447
$216$	−5.30205	−0.360759
$217$	0	0
$218$	2.68695	0.181983
$219$	14.9700	1.01158
$220$	1.00852	0.0679945
$221$	−0.466962	−0.0314113
$222$	13.8199	0.927531
$223$	27.4673	1.83935	0.919674	−	0.392682i	$-0.128453\pi$
$223$	27.4673	1.83935	0.919674	+	0.392682i	$0.128453\pi$
$224$	0	0
$225$	−10.8874	−0.725830
$226$	−6.13990	−0.408420
$227$	−3.16556	−0.210106	−0.105053	−	0.994467i	$-0.533501\pi$
$227$	−3.16556	−0.210106	−0.105053	+	0.994467i	$0.533501\pi$
$228$	−16.4571	−1.08990
$229$	10.9522	0.723745	0.361872	−	0.932228i	$-0.382138\pi$
$229$	10.9522	0.723745	0.361872	+	0.932228i	$0.382138\pi$
$230$	−3.92097	−0.258541
$231$	0	0
$232$	−0.0547002	−0.00359125
$233$	−8.81194	−0.577290	−0.288645	−	0.957436i	$-0.593205\pi$
$233$	−8.81194	−0.577290	−0.288645	+	0.957436i	$0.593205\pi$
$234$	−2.28244	−0.149207
$235$	−17.7968	−1.16093
$236$	−4.86323	−0.316569
$237$	−32.9143	−2.13801
$238$	0	0
$239$	21.0331	1.36052	0.680259	−	0.732971i	$-0.261867\pi$
$239$	21.0331	1.36052	0.680259	+	0.732971i	$0.261867\pi$
$240$	4.67647	0.301865
$241$	−15.5210	−0.999795	−0.499897	−	0.866085i	$-0.666629\pi$
$241$	−15.5210	−0.999795	−0.499897	+	0.866085i	$0.666629\pi$
$242$	−10.6331	−0.683525
$243$	15.2673	0.979401
$244$	−8.39745	−0.537592
$245$	0	0
$246$	8.02275	0.511512
$247$	−2.73626	−0.174104
$248$	−10.1399	−0.643885
$249$	−10.3946	−0.658731
$250$	12.0344	0.761123
$251$	−14.5334	−0.917341	−0.458670	−	0.888606i	$-0.651674\pi$
$251$	−14.5334	−0.917341	−0.458670	+	0.888606i	$0.651674\pi$
$252$	0	0
$253$	−1.42627	−0.0896685
$254$	−10.9241	−0.685439
$255$	4.67647	0.292852
$256$	1.00000	0.0625000
$257$	4.20784	0.262478	0.131239	−	0.991351i	$-0.458105\pi$
$257$	4.20784	0.262478	0.131239	+	0.991351i	$0.458105\pi$
$258$	17.7686	1.10623
$259$	0	0
$260$	0.777537	0.0482208
$261$	−0.267366	−0.0165495
$262$	−22.4770	−1.38864
$263$	−7.75253	−0.478042	−0.239021	−	0.971014i	$-0.576826\pi$
$263$	−7.75253	−0.478042	−0.239021	+	0.971014i	$0.576826\pi$
$264$	1.70108	0.104694
$265$	15.6398	0.960746
$266$	0	0
$267$	49.2222	3.01235
$268$	2.03979	0.124600
$269$	9.23753	0.563222	0.281611	−	0.959529i	$-0.409131\pi$
$269$	9.23753	0.563222	0.281611	+	0.959529i	$0.409131\pi$
$270$	8.82843	0.537281
$271$	3.30481	0.200753	0.100377	−	0.994950i	$-0.467995\pi$
$271$	3.30481	0.200753	0.100377	+	0.994950i	$0.467995\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	14.6600	0.885642
$275$	1.34913	0.0813558
$276$	−6.61353	−0.398088
$277$	4.77596	0.286960	0.143480	−	0.989653i	$-0.454171\pi$
$277$	4.77596	0.286960	0.143480	+	0.989653i	$0.454171\pi$
$278$	−5.24236	−0.314416
$279$	−49.5622	−2.96721
$280$	0	0
$281$	6.88431	0.410683	0.205342	−	0.978690i	$-0.434169\pi$
$281$	6.88431	0.410683	0.205342	+	0.978690i	$0.434169\pi$
$282$	−30.0179	−1.78754
$283$	−28.1661	−1.67430	−0.837150	−	0.546974i	$-0.815780\pi$
$283$	−28.1661	−1.67430	−0.837150	+	0.546974i	$0.815780\pi$
$284$	−12.2212	−0.725193
$285$	27.4027	1.62320
$286$	0.282831	0.0167242
$287$	0	0
$288$	4.88784	0.288019
$289$	1.00000	0.0588235
$290$	0.0910812	0.00534847
$291$	−40.6298	−2.38176
$292$	−5.33019	−0.311926
$293$	−5.78011	−0.337678	−0.168839	−	0.985644i	$-0.554002\pi$
$293$	−5.78011	−0.337678	−0.168839	+	0.985644i	$0.554002\pi$
$294$	0	0
$295$	8.09774	0.471469
$296$	−4.92069	−0.286009
$297$	3.21137	0.186342
$298$	−13.8249	−0.800855
$299$	−1.09960	−0.0635917
$300$	6.25587	0.361183
$301$	0	0
$302$	12.5576	0.722611
$303$	33.9383	1.94971
$304$	5.85970	0.336077
$305$	13.9826	0.800639
$306$	4.88784	0.279419
$307$	16.9352	0.966543	0.483271	−	0.875471i	$-0.339448\pi$
$307$	16.9352	0.966543	0.483271	+	0.875471i	$0.339448\pi$
$308$	0	0
$309$	−26.2306	−1.49221
$310$	16.8839	0.958942
$311$	−9.05902	−0.513690	−0.256845	−	0.966453i	$-0.582683\pi$
$311$	−9.05902	−0.513690	−0.256845	+	0.966453i	$0.582683\pi$
$312$	1.31148	0.0742478
$313$	−14.6909	−0.830378	−0.415189	−	0.909735i	$-0.636285\pi$
$313$	−14.6909	−0.830378	−0.415189	+	0.909735i	$0.636285\pi$
$314$	−10.8860	−0.614331
$315$	0	0
$316$	11.7194	0.659268
$317$	−15.3849	−0.864102	−0.432051	−	0.901849i	$-0.642210\pi$
$317$	−15.3849	−0.864102	−0.432051	+	0.901849i	$0.642210\pi$
$318$	26.3798	1.47930
$319$	0.0331311	0.00185498
$320$	−1.66510	−0.0930817
$321$	38.5358	2.15086
$322$	0	0
$323$	5.85970	0.326042
$324$	0.227455	0.0126364
$325$	1.04014	0.0576964
$326$	−0.160197	−0.00887250
$327$	−7.54637	−0.417315
$328$	−2.85657	−0.157727
$329$	0	0
$330$	−2.83246	−0.155922
$331$	16.4196	0.902502	0.451251	−	0.892397i	$-0.350978\pi$
$331$	16.4196	0.902502	0.451251	+	0.892397i	$0.350978\pi$
$332$	3.70108	0.203123
$333$	−24.0515	−1.31802
$334$	4.09069	0.223832
$335$	−3.39645	−0.185568
$336$	0	0
$337$	−25.1175	−1.36824	−0.684119	−	0.729370i	$-0.739813\pi$
$337$	−25.1175	−1.36824	−0.684119	+	0.729370i	$0.739813\pi$
$338$	−12.7819	−0.695246
$339$	17.2441	0.936571
$340$	−1.66510	−0.0903025
$341$	6.14158	0.332585
$342$	28.6413	1.54874
$343$	0	0
$344$	−6.32666	−0.341111
$345$	11.0122	0.592875
$346$	−13.2938	−0.714680
$347$	26.8668	1.44228	0.721142	−	0.692787i	$-0.243617\pi$
$347$	26.8668	1.44228	0.721142	+	0.692787i	$0.243617\pi$
$348$	0.153627	0.00823529
$349$	−27.5228	−1.47326	−0.736631	−	0.676294i	$-0.763585\pi$
$349$	−27.5228	−1.47326	−0.736631	+	0.676294i	$0.763585\pi$
$350$	0	0
$351$	2.47586	0.132151
$352$	−0.605684	−0.0322831
$353$	−17.8217	−0.948556	−0.474278	−	0.880375i	$-0.657291\pi$
$353$	−17.8217	−0.948556	−0.474278	+	0.880375i	$0.657291\pi$
$354$	13.6585	0.725942
$355$	20.3494	1.08003
$356$	−17.5260	−0.928875
$357$	0	0
$358$	−7.60764	−0.402076
$359$	−26.8651	−1.41788	−0.708942	−	0.705267i	$-0.750827\pi$
$359$	−26.8651	−1.41788	−0.708942	+	0.705267i	$0.750827\pi$
$360$	−8.13872	−0.428948
$361$	15.3361	0.807162
$362$	0.384123	0.0201890
$363$	29.8635	1.56743
$364$	0	0
$365$	8.87528	0.464553
$366$	23.5845	1.23278
$367$	−1.85930	−0.0970549	−0.0485274	−	0.998822i	$-0.515453\pi$
$367$	−1.85930	−0.0970549	−0.0485274	+	0.998822i	$0.515453\pi$
$368$	2.35480	0.122753
$369$	−13.9624	−0.726855
$370$	8.19342	0.425956
$371$	0	0
$372$	28.4782	1.47653
$373$	27.5741	1.42773	0.713867	−	0.700282i	$-0.246942\pi$
$373$	27.5741	1.42773	0.713867	+	0.700282i	$0.246942\pi$
$374$	−0.605684	−0.0313192
$375$	−33.7990	−1.74537
$376$	10.6881	0.551198
$377$	0.0255429	0.00131553
$378$	0	0
$379$	−24.8176	−1.27479	−0.637396	−	0.770536i	$-0.719989\pi$
$379$	−24.8176	−1.27479	−0.637396	+	0.770536i	$0.719989\pi$
$380$	−9.75696	−0.500522
$381$	30.6807	1.57182
$382$	2.51119	0.128484
$383$	20.2704	1.03577	0.517884	−	0.855451i	$-0.326720\pi$
$383$	20.2704	1.03577	0.517884	+	0.855451i	$0.326720\pi$
$384$	−2.80853	−0.143322
$385$	0	0
$386$	23.7007	1.20633
$387$	−30.9237	−1.57194
$388$	14.4666	0.734429
$389$	−30.8972	−1.56655	−0.783276	−	0.621674i	$-0.786453\pi$
$389$	−30.8972	−1.56655	−0.783276	+	0.621674i	$0.786453\pi$
$390$	−2.18373	−0.110578
$391$	2.35480	0.119087
$392$	0	0
$393$	63.1274	3.18436
$394$	5.58734	0.281486
$395$	−19.5139	−0.981852
$396$	−2.96049	−0.148770
$397$	20.1543	1.01151	0.505757	−	0.862676i	$-0.331213\pi$
$397$	20.1543	1.01151	0.505757	+	0.862676i	$0.331213\pi$
$398$	24.5175	1.22895
$399$	0	0
$400$	−2.22746	−0.111373
$401$	9.65147	0.481971	0.240986	−	0.970529i	$-0.422529\pi$
$401$	9.65147	0.481971	0.240986	+	0.970529i	$0.422529\pi$
$402$	−5.72882	−0.285728
$403$	4.73495	0.235865
$404$	−12.0840	−0.601203
$405$	−0.378735	−0.0188195
$406$	0	0
$407$	2.98038	0.147732
$408$	−2.80853	−0.139043
$409$	12.7761	0.631735	0.315868	−	0.948803i	$-0.397704\pi$
$409$	12.7761	0.631735	0.315868	+	0.948803i	$0.397704\pi$
$410$	4.75646	0.234905
$411$	−41.1730	−2.03091
$412$	9.33962	0.460130
$413$	0	0
$414$	11.5099	0.565680
$415$	−6.16266	−0.302513
$416$	−0.466962	−0.0228947
$417$	14.7233	0.721004
$418$	−3.54913	−0.173593
$419$	−6.02932	−0.294552	−0.147276	−	0.989095i	$-0.547050\pi$
$419$	−6.02932	−0.294552	−0.147276	+	0.989095i	$0.547050\pi$
$420$	0	0
$421$	9.29276	0.452901	0.226451	−	0.974023i	$-0.427288\pi$
$421$	9.29276	0.452901	0.226451	+	0.974023i	$0.427288\pi$
$422$	18.7965	0.914998
$423$	52.2418	2.54009
$424$	−9.39274	−0.456152
$425$	−2.22746	−0.108047
$426$	34.3235	1.66298
$427$	0	0
$428$	−13.7210	−0.663229
$429$	−0.794340	−0.0383511
$430$	10.5345	0.508019
$431$	−9.46619	−0.455970	−0.227985	−	0.973665i	$-0.573214\pi$
$431$	−9.46619	−0.455970	−0.227985	+	0.973665i	$0.573214\pi$
$432$	−5.30205	−0.255095
$433$	15.8262	0.760557	0.380279	−	0.924872i	$-0.375828\pi$
$433$	15.8262	0.760557	0.380279	+	0.924872i	$0.375828\pi$
$434$	0	0
$435$	−0.255804	−0.0122649
$436$	2.68695	0.128681
$437$	13.7984	0.660068
$438$	14.9700	0.715294
$439$	−2.28910	−0.109253	−0.0546264	−	0.998507i	$-0.517397\pi$
$439$	−2.28910	−0.109253	−0.0546264	+	0.998507i	$0.517397\pi$
$440$	1.00852	0.0480794
$441$	0	0
$442$	−0.466962	−0.0222111
$443$	−38.8878	−1.84762	−0.923808	−	0.382856i	$-0.874940\pi$
$443$	−38.8878	−1.84762	−0.923808	+	0.382856i	$0.874940\pi$
$444$	13.8199	0.655864
$445$	29.1824	1.38338
$446$	27.4673	1.30062
$447$	38.8276	1.83648
$448$	0	0
$449$	−3.56394	−0.168193	−0.0840963	−	0.996458i	$-0.526800\pi$
$449$	−3.56394	−0.168193	−0.0840963	+	0.996458i	$0.526800\pi$
$450$	−10.8874	−0.513239
$451$	1.73018	0.0814708
$452$	−6.13990	−0.288797
$453$	−35.2685	−1.65706
$454$	−3.16556	−0.148567
$455$	0	0
$456$	−16.4571	−0.770676
$457$	−28.0196	−1.31070	−0.655351	−	0.755325i	$-0.727479\pi$
$457$	−28.0196	−1.31070	−0.655351	+	0.755325i	$0.727479\pi$
$458$	10.9522	0.511765
$459$	−5.30205	−0.247479
$460$	−3.92097	−0.182816
$461$	0.872654	0.0406435	0.0203218	−	0.999793i	$-0.493531\pi$
$461$	0.872654	0.0406435	0.0203218	+	0.999793i	$0.493531\pi$
$462$	0	0
$463$	18.1653	0.844212	0.422106	−	0.906546i	$-0.361291\pi$
$463$	18.1653	0.844212	0.422106	+	0.906546i	$0.361291\pi$
$464$	−0.0547002	−0.00253939
$465$	−47.4190	−2.19900
$466$	−8.81194	−0.408205
$467$	−33.1132	−1.53230	−0.766149	−	0.642663i	$-0.777829\pi$
$467$	−33.1132	−1.53230	−0.766149	+	0.642663i	$0.777829\pi$
$468$	−2.28244	−0.105506
$469$	0	0
$470$	−17.7968	−0.820903
$471$	30.5736	1.40876
$472$	−4.86323	−0.223848
$473$	3.83196	0.176194
$474$	−32.9143	−1.51180
$475$	−13.0522	−0.598877
$476$	0	0
$477$	−45.9102	−2.10208
$478$	21.0331	0.962032
$479$	−20.5151	−0.937358	−0.468679	−	0.883368i	$-0.655270\pi$
$479$	−20.5151	−0.937358	−0.468679	+	0.883368i	$0.655270\pi$
$480$	4.67647	0.213451
$481$	2.29778	0.104770
$482$	−15.5210	−0.706962
$483$	0	0
$484$	−10.6331	−0.483325
$485$	−24.0882	−1.09379
$486$	15.2673	0.692541
$487$	−24.1962	−1.09643	−0.548217	−	0.836336i	$-0.684693\pi$
$487$	−24.1962	−1.09643	−0.548217	+	0.836336i	$0.684693\pi$
$488$	−8.39745	−0.380135
$489$	0.449919	0.0203460
$490$	0	0
$491$	23.2878	1.05096	0.525482	−	0.850805i	$-0.323885\pi$
$491$	23.2878	1.05096	0.525482	+	0.850805i	$0.323885\pi$
$492$	8.02275	0.361694
$493$	−0.0547002	−0.00246357
$494$	−2.73626	−0.123110
$495$	4.92949	0.221564
$496$	−10.1399	−0.455295
$497$	0	0
$498$	−10.3946	−0.465793
$499$	11.3630	0.508679	0.254339	−	0.967115i	$-0.418142\pi$
$499$	11.3630	0.508679	0.254339	+	0.967115i	$0.418142\pi$
$500$	12.0344	0.538195
$501$	−11.4888	−0.513282
$502$	−14.5334	−0.648658
$503$	26.6972	1.19037	0.595184	−	0.803590i	$-0.297079\pi$
$503$	26.6972	1.19037	0.595184	+	0.803590i	$0.297079\pi$
$504$	0	0
$505$	20.1211	0.895375
$506$	−1.42627	−0.0634052
$507$	35.8985	1.59431
$508$	−10.9241	−0.484679
$509$	−19.6385	−0.870463	−0.435231	−	0.900319i	$-0.643333\pi$
$509$	−19.6385	−0.870463	−0.435231	+	0.900319i	$0.643333\pi$
$510$	4.67647	0.207078
$511$	0	0
$512$	1.00000	0.0441942
$513$	−31.0684	−1.37171
$514$	4.20784	0.185600
$515$	−15.5514	−0.685275
$516$	17.7686	0.782220
$517$	−6.47363	−0.284710
$518$	0	0
$519$	37.3361	1.63887
$520$	0.777537	0.0340972
$521$	−24.7590	−1.08471	−0.542356	−	0.840149i	$-0.682468\pi$
$521$	−24.7590	−1.08471	−0.542356	+	0.840149i	$0.682468\pi$
$522$	−0.267366	−0.0117023
$523$	−13.8856	−0.607175	−0.303588	−	0.952804i	$-0.598185\pi$
$523$	−13.8856	−0.607175	−0.303588	+	0.952804i	$0.598185\pi$
$524$	−22.4770	−0.981914
$525$	0	0
$526$	−7.75253	−0.338026
$527$	−10.1399	−0.441701
$528$	1.70108	0.0740300
$529$	−17.4549	−0.758909
$530$	15.6398	0.679350
$531$	−23.7707	−1.03156
$532$	0	0
$533$	1.33391	0.0577780
$534$	49.2222	2.13005
$535$	22.8467	0.987751
$536$	2.03979	0.0881057
$537$	21.3663	0.922023
$538$	9.23753	0.398258
$539$	0	0
$540$	8.82843	0.379915
$541$	4.05706	0.174427	0.0872134	−	0.996190i	$-0.472204\pi$
$541$	4.05706	0.174427	0.0872134	+	0.996190i	$0.472204\pi$
$542$	3.30481	0.141954
$543$	−1.07882	−0.0462966
$544$	1.00000	0.0428746
$545$	−4.47402	−0.191646
$546$	0	0
$547$	−34.3385	−1.46821	−0.734105	−	0.679036i	$-0.762398\pi$
$547$	−34.3385	−1.46821	−0.734105	+	0.679036i	$0.762398\pi$
$548$	14.6600	0.626244
$549$	−41.0454	−1.75177
$550$	1.34913	0.0575273
$551$	−0.320527	−0.0136549
$552$	−6.61353	−0.281491
$553$	0	0
$554$	4.77596	0.202911
$555$	−23.0115	−0.976782
$556$	−5.24236	−0.222326
$557$	0.188990	0.00800776	0.00400388	−	0.999992i	$-0.498726\pi$
$557$	0.188990	0.00800776	0.00400388	+	0.999992i	$0.498726\pi$
$558$	−49.5622	−2.09814
$559$	2.95431	0.124954
$560$	0	0
$561$	1.70108	0.0718197
$562$	6.88431	0.290397
$563$	21.1292	0.890488	0.445244	−	0.895409i	$-0.353117\pi$
$563$	21.1292	0.890488	0.445244	+	0.895409i	$0.353117\pi$
$564$	−30.0179	−1.26398
$565$	10.2235	0.430107
$566$	−28.1661	−1.18391
$567$	0	0
$568$	−12.2212	−0.512789
$569$	38.7025	1.62250	0.811248	−	0.584703i	$-0.198789\pi$
$569$	38.7025	1.62250	0.811248	+	0.584703i	$0.198789\pi$
$570$	27.4027	1.14777
$571$	−38.7121	−1.62005	−0.810025	−	0.586396i	$-0.800546\pi$
$571$	−38.7121	−1.62005	−0.810025	+	0.586396i	$0.800546\pi$
$572$	0.282831	0.0118258
$573$	−7.05275	−0.294633
$574$	0	0
$575$	−5.24521	−0.218741
$576$	4.88784	0.203660
$577$	−27.7359	−1.15466	−0.577330	−	0.816511i	$-0.695905\pi$
$577$	−27.7359	−1.15466	−0.577330	+	0.816511i	$0.695905\pi$
$578$	1.00000	0.0415945
$579$	−66.5641	−2.76631
$580$	0.0910812	0.00378194
$581$	0	0
$582$	−40.6298	−1.68416
$583$	5.68903	0.235616
$584$	−5.33019	−0.220565
$585$	3.80047	0.157130
$586$	−5.78011	−0.238774
$587$	−6.49914	−0.268248	−0.134124	−	0.990965i	$-0.542822\pi$
$587$	−6.49914	−0.268248	−0.134124	+	0.990965i	$0.542822\pi$
$588$	0	0
$589$	−59.4168	−2.44823
$590$	8.09774	0.333379
$591$	−15.6922	−0.645492
$592$	−4.92069	−0.202239
$593$	−41.6985	−1.71235	−0.856176	−	0.516685i	$-0.827166\pi$
$593$	−41.6985	−1.71235	−0.856176	+	0.516685i	$0.827166\pi$
$594$	3.21137	0.131764
$595$	0	0
$596$	−13.8249	−0.566290
$597$	−68.8580	−2.81817
$598$	−1.09960	−0.0449661
$599$	24.2941	0.992630	0.496315	−	0.868143i	$-0.334686\pi$
$599$	24.2941	0.992630	0.496315	+	0.868143i	$0.334686\pi$
$600$	6.25587	0.255395
$601$	24.5103	0.999795	0.499897	−	0.866085i	$-0.333371\pi$
$601$	24.5103	0.999795	0.499897	+	0.866085i	$0.333371\pi$
$602$	0	0
$603$	9.97019	0.406017
$604$	12.5576	0.510963
$605$	17.7052	0.719819
$606$	33.9383	1.37865
$607$	43.7757	1.77680	0.888400	−	0.459070i	$-0.151817\pi$
$607$	43.7757	1.77680	0.888400	+	0.459070i	$0.151817\pi$
$608$	5.85970	0.237642
$609$	0	0
$610$	13.9826	0.566137
$611$	−4.99095	−0.201912
$612$	4.88784	0.197579
$613$	−3.22079	−0.130087	−0.0650433	−	0.997882i	$-0.520719\pi$
$613$	−3.22079	−0.130087	−0.0650433	+	0.997882i	$0.520719\pi$
$614$	16.9352	0.683449
$615$	−13.3587	−0.538673
$616$	0	0
$617$	40.0930	1.61409	0.807043	−	0.590493i	$-0.201067\pi$
$617$	40.0930	1.61409	0.807043	+	0.590493i	$0.201067\pi$
$618$	−26.2306	−1.05515
$619$	−4.54051	−0.182499	−0.0912493	−	0.995828i	$-0.529086\pi$
$619$	−4.54051	−0.182499	−0.0912493	+	0.995828i	$0.529086\pi$
$620$	16.8839	0.678074
$621$	−12.4853	−0.501017
$622$	−9.05902	−0.363233
$623$	0	0
$624$	1.31148	0.0525011
$625$	−8.90117	−0.356047
$626$	−14.6909	−0.587166
$627$	9.96782	0.398077
$628$	−10.8860	−0.434398
$629$	−4.92069	−0.196201
$630$	0	0
$631$	−22.5416	−0.897365	−0.448683	−	0.893691i	$-0.648107\pi$
$631$	−22.5416	−0.897365	−0.448683	+	0.893691i	$0.648107\pi$
$632$	11.7194	0.466173
$633$	−52.7905	−2.09823
$634$	−15.3849	−0.611012
$635$	18.1897	0.721836
$636$	26.3798	1.04603
$637$	0	0
$638$	0.0331311	0.00131167
$639$	−59.7351	−2.36308
$640$	−1.66510	−0.0658187
$641$	28.6322	1.13091	0.565453	−	0.824781i	$-0.308701\pi$
$641$	28.6322	1.13091	0.565453	+	0.824781i	$0.308701\pi$
$642$	38.5358	1.52089
$643$	−4.00880	−0.158092	−0.0790459	−	0.996871i	$-0.525187\pi$
$643$	−4.00880	−0.158092	−0.0790459	+	0.996871i	$0.525187\pi$
$644$	0	0
$645$	−29.5865	−1.16497
$646$	5.85970	0.230547
$647$	36.8865	1.45016	0.725080	−	0.688665i	$-0.241803\pi$
$647$	36.8865	1.45016	0.725080	+	0.688665i	$0.241803\pi$
$648$	0.227455	0.00893529
$649$	2.94558	0.115624
$650$	1.04014	0.0407975
$651$	0	0
$652$	−0.160197	−0.00627381
$653$	−20.5749	−0.805160	−0.402580	−	0.915385i	$-0.631886\pi$
$653$	−20.5749	−0.805160	−0.402580	+	0.915385i	$0.631886\pi$
$654$	−7.54637	−0.295086
$655$	37.4264	1.46237
$656$	−2.85657	−0.111530
$657$	−26.0531	−1.01643
$658$	0	0
$659$	−4.22432	−0.164556	−0.0822781	−	0.996609i	$-0.526220\pi$
$659$	−4.22432	−0.164556	−0.0822781	+	0.996609i	$0.526220\pi$
$660$	−2.83246	−0.110253
$661$	28.5075	1.10881	0.554407	−	0.832246i	$-0.312945\pi$
$661$	28.5075	1.10881	0.554407	+	0.832246i	$0.312945\pi$
$662$	16.4196	0.638165
$663$	1.31148	0.0509335
$664$	3.70108	0.143630
$665$	0	0
$666$	−24.0515	−0.931978
$667$	−0.128808	−0.00498747
$668$	4.09069	0.158273
$669$	−77.1428	−2.98251
$670$	−3.39645	−0.131216
$671$	5.08620	0.196351
$672$	0	0
$673$	14.3792	0.554278	0.277139	−	0.960830i	$-0.410614\pi$
$673$	14.3792	0.554278	0.277139	+	0.960830i	$0.410614\pi$
$674$	−25.1175	−0.967491
$675$	11.8101	0.454570
$676$	−12.7819	−0.491613
$677$	−5.74469	−0.220786	−0.110393	−	0.993888i	$-0.535211\pi$
$677$	−5.74469	−0.220786	−0.110393	+	0.993888i	$0.535211\pi$
$678$	17.2441	0.662256
$679$	0	0
$680$	−1.66510	−0.0638535
$681$	8.89058	0.340688
$682$	6.14158	0.235173
$683$	41.2277	1.57753	0.788767	−	0.614692i	$-0.210720\pi$
$683$	41.2277	1.57753	0.788767	+	0.614692i	$0.210720\pi$
$684$	28.6413	1.09513
$685$	−24.4103	−0.932669
$686$	0	0
$687$	−30.7597	−1.17356
$688$	−6.32666	−0.241202
$689$	4.38605	0.167095
$690$	11.0122	0.419226
$691$	26.3147	1.00106	0.500529	−	0.865720i	$-0.333139\pi$
$691$	26.3147	1.00106	0.500529	+	0.865720i	$0.333139\pi$
$692$	−13.2938	−0.505355
$693$	0	0
$694$	26.8668	1.01985
$695$	8.72903	0.331111
$696$	0.153627	0.00582323
$697$	−2.85657	−0.108200
$698$	−27.5228	−1.04175
$699$	24.7486	0.936078
$700$	0	0
$701$	1.13178	0.0427467	0.0213733	−	0.999772i	$-0.493196\pi$
$701$	1.13178	0.0427467	0.0213733	+	0.999772i	$0.493196\pi$
$702$	2.47586	0.0934452
$703$	−28.8338	−1.08749
$704$	−0.605684	−0.0228276
$705$	49.9827	1.88246
$706$	−17.8217	−0.670730
$707$	0	0
$708$	13.6585	0.513319
$709$	27.3873	1.02855	0.514275	−	0.857625i	$-0.328061\pi$
$709$	27.3873	1.02855	0.514275	+	0.857625i	$0.328061\pi$
$710$	20.3494	0.763700
$711$	57.2825	2.14826
$712$	−17.5260	−0.656814
$713$	−23.8775	−0.894218
$714$	0	0
$715$	−0.470941	−0.0176122
$716$	−7.60764	−0.284311
$717$	−59.0721	−2.20609
$718$	−26.8651	−1.00260
$719$	−13.6037	−0.507334	−0.253667	−	0.967292i	$-0.581637\pi$
$719$	−13.6037	−0.507334	−0.253667	+	0.967292i	$0.581637\pi$
$720$	−8.13872	−0.303312
$721$	0	0
$722$	15.3361	0.570750
$723$	43.5912	1.62117
$724$	0.384123	0.0142758
$725$	0.121842	0.00452511
$726$	29.8635	1.10834
$727$	−2.10993	−0.0782529	−0.0391265	−	0.999234i	$-0.512458\pi$
$727$	−2.10993	−0.0782529	−0.0391265	+	0.999234i	$0.512458\pi$
$728$	0	0
$729$	−43.5612	−1.61338
$730$	8.87528	0.328489
$731$	−6.32666	−0.234000
$732$	23.5845	0.871708
$733$	33.4509	1.23554	0.617768	−	0.786361i	$-0.288037\pi$
$733$	33.4509	1.23554	0.617768	+	0.786361i	$0.288037\pi$
$734$	−1.85930	−0.0686282
$735$	0	0
$736$	2.35480	0.0867991
$737$	−1.23547	−0.0455091
$738$	−13.9624	−0.513964
$739$	38.9857	1.43411	0.717056	−	0.697016i	$-0.245489\pi$
$739$	38.9857	1.43411	0.717056	+	0.697016i	$0.245489\pi$
$740$	8.19342	0.301196
$741$	7.68486	0.282310
$742$	0	0
$743$	42.9387	1.57527	0.787634	−	0.616143i	$-0.211306\pi$
$743$	42.9387	1.57527	0.787634	+	0.616143i	$0.211306\pi$
$744$	28.4782	1.04406
$745$	23.0198	0.843380
$746$	27.5741	1.00956
$747$	18.0903	0.661889
$748$	−0.605684	−0.0221460
$749$	0	0
$750$	−33.7990	−1.23416
$751$	−33.2850	−1.21459	−0.607294	−	0.794477i	$-0.707745\pi$
$751$	−33.2850	−1.21459	−0.607294	+	0.794477i	$0.707745\pi$
$752$	10.6881	0.389756
$753$	40.8175	1.48747
$754$	0.0255429	0.000930219 0
$755$	−20.9097	−0.760981
$756$	0	0
$757$	36.7059	1.33410	0.667049	−	0.745014i	$-0.267557\pi$
$757$	36.7059	1.33410	0.667049	+	0.745014i	$0.267557\pi$
$758$	−24.8176	−0.901414
$759$	4.00571	0.145398
$760$	−9.75696	−0.353922
$761$	4.81956	0.174709	0.0873545	−	0.996177i	$-0.472159\pi$
$761$	4.81956	0.174709	0.0873545	+	0.996177i	$0.472159\pi$
$762$	30.6807	1.11144
$763$	0	0
$764$	2.51119	0.0908516
$765$	−8.13872	−0.294256
$766$	20.2704	0.732399
$767$	2.27094	0.0819990
$768$	−2.80853	−0.101344
$769$	−41.7516	−1.50560	−0.752800	−	0.658249i	$-0.771297\pi$
$769$	−41.7516	−1.50560	−0.752800	+	0.658249i	$0.771297\pi$
$770$	0	0
$771$	−11.8178	−0.425609
$772$	23.7007	0.853006
$773$	−50.1623	−1.80421	−0.902106	−	0.431515i	$-0.857979\pi$
$773$	−50.1623	−1.80421	−0.902106	+	0.431515i	$0.857979\pi$
$774$	−30.9237	−1.11153
$775$	22.5862	0.811320
$776$	14.4666	0.519319
$777$	0	0
$778$	−30.8972	−1.10772
$779$	−16.7386	−0.599723
$780$	−2.18373	−0.0781902
$781$	7.40216	0.264870
$782$	2.35480	0.0842075
$783$	0.290024	0.0103646
$784$	0	0
$785$	18.1262	0.646952
$786$	63.1274	2.25168
$787$	6.17852	0.220240	0.110120	−	0.993918i	$-0.464876\pi$
$787$	6.17852	0.220240	0.110120	+	0.993918i	$0.464876\pi$
$788$	5.58734	0.199041
$789$	21.7732	0.775147
$790$	−19.5139	−0.694274
$791$	0	0
$792$	−2.96049	−0.105196
$793$	3.92129	0.139249
$794$	20.1543	0.715249
$795$	−43.9249	−1.55785
$796$	24.5175	0.868998
$797$	−18.0018	−0.637658	−0.318829	−	0.947812i	$-0.603290\pi$
$797$	−18.0018	−0.637658	−0.318829	+	0.947812i	$0.603290\pi$
$798$	0	0
$799$	10.6881	0.378119
$800$	−2.22746	−0.0787524
$801$	−85.6642	−3.02679
$802$	9.65147	0.340805
$803$	3.22841	0.113928
$804$	−5.72882	−0.202040
$805$	0	0
$806$	4.73495	0.166782
$807$	−25.9439	−0.913268
$808$	−12.0840	−0.425114
$809$	28.7309	1.01012	0.505062	−	0.863083i	$-0.331470\pi$
$809$	28.7309	1.01012	0.505062	+	0.863083i	$0.331470\pi$
$810$	−0.378735	−0.0133074
$811$	47.9659	1.68431	0.842154	−	0.539236i	$-0.181287\pi$
$811$	47.9659	1.68431	0.842154	+	0.539236i	$0.181287\pi$
$812$	0	0
$813$	−9.28167	−0.325522
$814$	2.98038	0.104462
$815$	0.266744	0.00934363
$816$	−2.80853	−0.0983182
$817$	−37.0723	−1.29700
$818$	12.7761	0.446704
$819$	0	0
$820$	4.75646	0.166103
$821$	30.7799	1.07422	0.537112	−	0.843511i	$-0.319515\pi$
$821$	30.7799	1.07422	0.537112	+	0.843511i	$0.319515\pi$
$822$	−41.1730	−1.43607
$823$	26.0992	0.909760	0.454880	−	0.890553i	$-0.349682\pi$
$823$	26.0992	0.909760	0.454880	+	0.890553i	$0.349682\pi$
$824$	9.33962	0.325361
$825$	−3.78908	−0.131919
$826$	0	0
$827$	−11.8000	−0.410326	−0.205163	−	0.978728i	$-0.565773\pi$
$827$	−11.8000	−0.410326	−0.205163	+	0.978728i	$0.565773\pi$
$828$	11.5099	0.399996
$829$	−3.62911	−0.126044	−0.0630221	−	0.998012i	$-0.520074\pi$
$829$	−3.62911	−0.126044	−0.0630221	+	0.998012i	$0.520074\pi$
$830$	−6.16266	−0.213909
$831$	−13.4134	−0.465306
$832$	−0.466962	−0.0161890
$833$	0	0
$834$	14.7233	0.509827
$835$	−6.81138	−0.235718
$836$	−3.54913	−0.122749
$837$	53.7623	1.85830
$838$	−6.02932	−0.208279
$839$	−39.9648	−1.37974	−0.689869	−	0.723934i	$-0.742332\pi$
$839$	−39.9648	−1.37974	−0.689869	+	0.723934i	$0.742332\pi$
$840$	0	0
$841$	−28.9970	−0.999897
$842$	9.29276	0.320250
$843$	−19.3348	−0.665925
$844$	18.7965	0.647001
$845$	21.2832	0.732163
$846$	52.2418	1.79611
$847$	0	0
$848$	−9.39274	−0.322548
$849$	79.1052	2.71488
$850$	−2.22746	−0.0764011
$851$	−11.5872	−0.397206
$852$	34.3235	1.17590
$853$	−29.1445	−0.997888	−0.498944	−	0.866634i	$-0.666279\pi$
$853$	−29.1445	−0.997888	−0.498944	+	0.866634i	$0.666279\pi$
$854$	0	0
$855$	−47.6905	−1.63098
$856$	−13.7210	−0.468973
$857$	−10.5760	−0.361268	−0.180634	−	0.983550i	$-0.557815\pi$
$857$	−10.5760	−0.361268	−0.180634	+	0.983550i	$0.557815\pi$
$858$	−0.794340	−0.0271183
$859$	−31.9526	−1.09021	−0.545105	−	0.838368i	$-0.683510\pi$
$859$	−31.9526	−1.09021	−0.545105	+	0.838368i	$0.683510\pi$
$860$	10.5345	0.359223
$861$	0	0
$862$	−9.46619	−0.322420
$863$	−11.6641	−0.397050	−0.198525	−	0.980096i	$-0.563615\pi$
$863$	−11.6641	−0.397050	−0.198525	+	0.980096i	$0.563615\pi$
$864$	−5.30205	−0.180380
$865$	22.1355	0.752629
$866$	15.8262	0.537795
$867$	−2.80853	−0.0953827
$868$	0	0
$869$	−7.09825	−0.240792
$870$	−0.255804	−0.00867257
$871$	−0.952507	−0.0322745
$872$	2.68695	0.0909914
$873$	70.7103	2.39318
$874$	13.7984	0.466739
$875$	0	0
$876$	14.9700	0.505790
$877$	53.9086	1.82036	0.910182	−	0.414208i	$-0.135941\pi$
$877$	53.9086	1.82036	0.910182	+	0.414208i	$0.135941\pi$
$878$	−2.28910	−0.0772534
$879$	16.2336	0.547546
$880$	1.00852	0.0339973
$881$	8.01718	0.270106	0.135053	−	0.990838i	$-0.456880\pi$
$881$	8.01718	0.270106	0.135053	+	0.990838i	$0.456880\pi$
$882$	0	0
$883$	39.2465	1.32075	0.660374	−	0.750937i	$-0.270398\pi$
$883$	39.2465	1.32075	0.660374	+	0.750937i	$0.270398\pi$
$884$	−0.466962	−0.0157056
$885$	−22.7428	−0.764489
$886$	−38.8878	−1.30646
$887$	−27.3825	−0.919415	−0.459708	−	0.888070i	$-0.652046\pi$
$887$	−27.3825	−0.919415	−0.459708	+	0.888070i	$0.652046\pi$
$888$	13.8199	0.463766
$889$	0	0
$890$	29.1824	0.978197
$891$	−0.137766	−0.00461533
$892$	27.4673	0.919674
$893$	62.6292	2.09581
$894$	38.8276	1.29859
$895$	12.6674	0.423426
$896$	0	0
$897$	3.08827	0.103114
$898$	−3.56394	−0.118930
$899$	0.554655	0.0184988
$900$	−10.8874	−0.362915
$901$	−9.39274	−0.312917
$902$	1.73018	0.0576086
$903$	0	0
$904$	−6.13990	−0.204210
$905$	−0.639601	−0.0212611
$906$	−35.2685	−1.17172
$907$	−10.7700	−0.357612	−0.178806	−	0.983884i	$-0.557224\pi$
$907$	−10.7700	−0.357612	−0.178806	+	0.983884i	$0.557224\pi$
$908$	−3.16556	−0.105053
$909$	−59.0648	−1.95905
$910$	0	0
$911$	−9.30261	−0.308209	−0.154105	−	0.988055i	$-0.549249\pi$
$911$	−9.30261	−0.308209	−0.154105	+	0.988055i	$0.549249\pi$
$912$	−16.4571	−0.544950
$913$	−2.24168	−0.0741889
$914$	−28.0196	−0.926806
$915$	−39.2704	−1.29824
$916$	10.9522	0.361872
$917$	0	0
$918$	−5.30205	−0.174994
$919$	−36.2727	−1.19653	−0.598264	−	0.801299i	$-0.704143\pi$
$919$	−36.2727	−1.19653	−0.598264	+	0.801299i	$0.704143\pi$
$920$	−3.92097	−0.129271
$921$	−47.5630	−1.56725
$922$	0.872654	0.0287393
$923$	5.70682	0.187842
$924$	0	0
$925$	10.9606	0.360383
$926$	18.1653	0.596948
$927$	45.6505	1.49936
$928$	−0.0547002	−0.00179562
$929$	−18.4133	−0.604121	−0.302061	−	0.953289i	$-0.597674\pi$
$929$	−18.4133	−0.604121	−0.302061	+	0.953289i	$0.597674\pi$
$930$	−47.4190	−1.55493
$931$	0	0
$932$	−8.81194	−0.288645
$933$	25.4425	0.832951
$934$	−33.1132	−1.08350
$935$	1.00852	0.0329822
$936$	−2.28244	−0.0746037
$937$	−12.2641	−0.400651	−0.200326	−	0.979729i	$-0.564200\pi$
$937$	−12.2641	−0.400651	−0.200326	+	0.979729i	$0.564200\pi$
$938$	0	0
$939$	41.2598	1.34646
$940$	−17.7968	−0.580466
$941$	−26.7849	−0.873161	−0.436581	−	0.899665i	$-0.643811\pi$
$941$	−26.7849	−0.873161	−0.436581	+	0.899665i	$0.643811\pi$
$942$	30.5736	0.996142
$943$	−6.72665	−0.219050
$944$	−4.86323	−0.158285
$945$	0	0
$946$	3.83196	0.124588
$947$	24.2470	0.787921	0.393960	−	0.919127i	$-0.371105\pi$
$947$	24.2470	0.787921	0.393960	+	0.919127i	$0.371105\pi$
$948$	−32.9143	−1.06901
$949$	2.48900	0.0807963
$950$	−13.0522	−0.423470
$951$	43.2089	1.40115
$952$	0	0
$953$	46.2298	1.49753	0.748765	−	0.662836i	$-0.230647\pi$
$953$	46.2298	1.49753	0.748765	+	0.662836i	$0.230647\pi$
$954$	−45.9102	−1.48640
$955$	−4.18137	−0.135306
$956$	21.0331	0.680259
$957$	−0.0930495	−0.00300786
$958$	−20.5151	−0.662813
$959$	0	0
$960$	4.67647	0.150932
$961$	71.8177	2.31670
$962$	2.29778	0.0740833
$963$	−67.0659	−2.16117
$964$	−15.5210	−0.499897
$965$	−39.4639	−1.27039
$966$	0	0
$967$	−43.1653	−1.38810	−0.694051	−	0.719926i	$-0.744176\pi$
$967$	−43.1653	−1.38810	−0.694051	+	0.719926i	$0.744176\pi$
$968$	−10.6331	−0.341762
$969$	−16.4571	−0.528680
$970$	−24.0882	−0.773426
$971$	−0.0801180	−0.00257111	−0.00128555	−	0.999999i	$-0.500409\pi$
$971$	−0.0801180	−0.00257111	−0.00128555	+	0.999999i	$0.500409\pi$
$972$	15.2673	0.489700
$973$	0	0
$974$	−24.1962	−0.775296
$975$	−2.92126	−0.0935551
$976$	−8.39745	−0.268796
$977$	41.2027	1.31819	0.659095	−	0.752059i	$-0.270939\pi$
$977$	41.2027	1.31819	0.659095	+	0.752059i	$0.270939\pi$
$978$	0.449919	0.0143868
$979$	10.6152	0.339263
$980$	0	0
$981$	13.1334	0.419316
$982$	23.2878	0.743144
$983$	28.9541	0.923492	0.461746	−	0.887012i	$-0.347223\pi$
$983$	28.9541	0.923492	0.461746	+	0.887012i	$0.347223\pi$
$984$	8.02275	0.255756
$985$	−9.30346	−0.296433
$986$	−0.0547002	−0.00174201
$987$	0	0
$988$	−2.73626	−0.0870520
$989$	−14.8980	−0.473730
$990$	4.92949	0.156670
$991$	−11.9647	−0.380070	−0.190035	−	0.981777i	$-0.560860\pi$
$991$	−11.9647	−0.380070	−0.190035	+	0.981777i	$0.560860\pi$
$992$	−10.1399	−0.321942
$993$	−46.1149	−1.46341
$994$	0	0
$995$	−40.8239	−1.29421
$996$	−10.3946	−0.329365
$997$	57.1938	1.81135	0.905673	−	0.423977i	$-0.139366\pi$
$997$	57.1938	1.81135	0.905673	+	0.423977i	$0.139366\pi$
$998$	11.3630	0.359690
$999$	26.0898	0.825444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1666.2.a.x.1.1	✓	4
7.6	odd	2		1666.2.a.y.1.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1666.2.a.x.1.1	✓	4	1.1	even	1	trivial
1666.2.a.y.1.4	yes	4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.80853 q^{3} +1.00000 q^{4} -1.66510 q^{5} -2.80853 q^{6} +1.00000 q^{8} +4.88784 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.80853 q^{3} +1.00000 q^{4} -1.66510 q^{5} -2.80853 q^{6} +1.00000 q^{8} +4.88784 q^{9} -1.66510 q^{10} -0.605684 q^{11} -2.80853 q^{12} -0.466962 q^{13} +4.67647 q^{15} +1.00000 q^{16} +1.00000 q^{17} +4.88784 q^{18} +5.85970 q^{19} -1.66510 q^{20} -0.605684 q^{22} +2.35480 q^{23} -2.80853 q^{24} -2.22746 q^{25} -0.466962 q^{26} -5.30205 q^{27} -0.0547002 q^{29} +4.67647 q^{30} -10.1399 q^{31} +1.00000 q^{32} +1.70108 q^{33} +1.00000 q^{34} +4.88784 q^{36} -4.92069 q^{37} +5.85970 q^{38} +1.31148 q^{39} -1.66510 q^{40} -2.85657 q^{41} -6.32666 q^{43} -0.605684 q^{44} -8.13872 q^{45} +2.35480 q^{46} +10.6881 q^{47} -2.80853 q^{48} -2.22746 q^{50} -2.80853 q^{51} -0.466962 q^{52} -9.39274 q^{53} -5.30205 q^{54} +1.00852 q^{55} -16.4571 q^{57} -0.0547002 q^{58} -4.86323 q^{59} +4.67647 q^{60} -8.39745 q^{61} -10.1399 q^{62} +1.00000 q^{64} +0.777537 q^{65} +1.70108 q^{66} +2.03979 q^{67} +1.00000 q^{68} -6.61353 q^{69} -12.2212 q^{71} +4.88784 q^{72} -5.33019 q^{73} -4.92069 q^{74} +6.25587 q^{75} +5.85970 q^{76} +1.31148 q^{78} +11.7194 q^{79} -1.66510 q^{80} +0.227455 q^{81} -2.85657 q^{82} +3.70108 q^{83} -1.66510 q^{85} -6.32666 q^{86} +0.153627 q^{87} -0.605684 q^{88} -17.5260 q^{89} -8.13872 q^{90} +2.35480 q^{92} +28.4782 q^{93} +10.6881 q^{94} -9.75696 q^{95} -2.80853 q^{96} +14.4666 q^{97} -2.96049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 8 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 8 q^{5} - 4 q^{6} + 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} - 4 q^{12} - 8 q^{13} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 8 q^{18} - 8 q^{19} - 8 q^{20} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 8 q^{25} - 8 q^{26} - 4 q^{27} - 4 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 16 q^{33} + 4 q^{34} + 8 q^{36} - 24 q^{37} - 8 q^{38} - 20 q^{39} - 8 q^{40} - 20 q^{41} - 4 q^{44} - 28 q^{45} + 4 q^{46} - 4 q^{48} + 8 q^{50} - 4 q^{51} - 8 q^{52} - 4 q^{54} + 16 q^{55} - 12 q^{57} - 4 q^{58} - 16 q^{59} + 4 q^{60} + 8 q^{61} - 4 q^{62} + 4 q^{64} + 4 q^{65} - 16 q^{66} + 4 q^{68} + 16 q^{69} + 8 q^{72} - 24 q^{73} - 24 q^{74} + 16 q^{75} - 8 q^{76} - 20 q^{78} - 16 q^{79} - 8 q^{80} - 16 q^{81} - 20 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 4 q^{88} - 8 q^{89} - 28 q^{90} + 4 q^{92} + 24 q^{93} + 12 q^{95} - 4 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 8 * q^5 - 4 * q^6 + 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 - 4 * q^12 - 8 * q^13 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 8 * q^18 - 8 * q^19 - 8 * q^20 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 8 * q^25 - 8 * q^26 - 4 * q^27 - 4 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 16 * q^33 + 4 * q^34 + 8 * q^36 - 24 * q^37 - 8 * q^38 - 20 * q^39 - 8 * q^40 - 20 * q^41 - 4 * q^44 - 28 * q^45 + 4 * q^46 - 4 * q^48 + 8 * q^50 - 4 * q^51 - 8 * q^52 - 4 * q^54 + 16 * q^55 - 12 * q^57 - 4 * q^58 - 16 * q^59 + 4 * q^60 + 8 * q^61 - 4 * q^62 + 4 * q^64 + 4 * q^65 - 16 * q^66 + 4 * q^68 + 16 * q^69 + 8 * q^72 - 24 * q^73 - 24 * q^74 + 16 * q^75 - 8 * q^76 - 20 * q^78 - 16 * q^79 - 8 * q^80 - 16 * q^81 - 20 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 4 * q^88 - 8 * q^89 - 28 * q^90 + 4 * q^92 + 24 * q^93 + 12 * q^95 - 4 * q^96 - 4 * q^97 - 8 * q^99

Introduction

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