LMFDB - Embedded newform 1445.2.a.n.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1445,2,Mod(1,1445)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1445.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1445, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,2,-4,6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.5383830921$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.7718912.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 7x^{4} + 4x^{3} + 9x^{2} - 2x - 1 $ x^6 - 2x^5 - 7x^4 + 4x^3 + 9x^2 - 2*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 85)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.254679$ of defining polynomial
Character	$\chi$	$=$	1445.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.51230 q^{2} -1.25468 q^{3} +4.31167 q^{4} -1.00000 q^{5} -3.15213 q^{6} -1.61485 q^{7} +5.80761 q^{8} -1.42578 q^{9} -2.51230 q^{10} -3.28669 q^{11} -5.40976 q^{12} -6.35524 q^{13} -4.05699 q^{14} +1.25468 q^{15} +5.96715 q^{16} -3.58200 q^{18} -0.747167 q^{19} -4.31167 q^{20} +2.02612 q^{21} -8.25715 q^{22} +0.143175 q^{23} -7.28669 q^{24} +1.00000 q^{25} -15.9663 q^{26} +5.55293 q^{27} -6.96269 q^{28} -8.80316 q^{29} +3.15213 q^{30} +7.21615 q^{31} +3.37606 q^{32} +4.12374 q^{33} +1.61485 q^{35} -6.14750 q^{36} -0.621115 q^{37} -1.87711 q^{38} +7.97379 q^{39} -5.80761 q^{40} +6.36239 q^{41} +5.09022 q^{42} -2.74801 q^{43} -14.1711 q^{44} +1.42578 q^{45} +0.359700 q^{46} +11.9308 q^{47} -7.48685 q^{48} -4.39226 q^{49} +2.51230 q^{50} -27.4017 q^{52} +2.71404 q^{53} +13.9507 q^{54} +3.28669 q^{55} -9.37841 q^{56} +0.937454 q^{57} -22.1162 q^{58} -12.6815 q^{59} +5.40976 q^{60} -0.464091 q^{61} +18.1292 q^{62} +2.30242 q^{63} -3.45261 q^{64} +6.35524 q^{65} +10.3601 q^{66} +1.81686 q^{67} -0.179639 q^{69} +4.05699 q^{70} -4.25738 q^{71} -8.28039 q^{72} +1.21126 q^{73} -1.56043 q^{74} -1.25468 q^{75} -3.22154 q^{76} +5.30750 q^{77} +20.0326 q^{78} -5.04874 q^{79} -5.96715 q^{80} -2.68980 q^{81} +15.9843 q^{82} -3.58494 q^{83} +8.73594 q^{84} -6.90384 q^{86} +11.0451 q^{87} -19.0878 q^{88} +10.5906 q^{89} +3.58200 q^{90} +10.2628 q^{91} +0.617325 q^{92} -9.05395 q^{93} +29.9739 q^{94} +0.747167 q^{95} -4.23587 q^{96} +6.96870 q^{97} -11.0347 q^{98} +4.68610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 4 q^{3} + 6 q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{10} - 8 q^{12} - 8 q^{14} + 4 q^{15} + 2 q^{16} + 14 q^{18} - 12 q^{19} - 6 q^{20} + 8 q^{21} - 16 q^{22} - 24 q^{24}+ \cdots - 20 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 - 4 * q^3 + 6 * q^4 - 6 * q^5 - 4 * q^6 - 8 * q^7 + 6 * q^8 + 2 * q^9 - 2 * q^10 - 8 * q^12 - 8 * q^14 + 4 * q^15 + 2 * q^16 + 14 * q^18 - 12 * q^19 - 6 * q^20 + 8 * q^21 - 16 * q^22 - 24 * q^24 + 6 * q^25 - 12 * q^26 + 8 * q^27 + 8 * q^28 - 8 * q^29 + 4 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 8 * q^35 - 10 * q^36 - 16 * q^37 - 12 * q^38 - 28 * q^39 - 6 * q^40 - 12 * q^41 - 8 * q^42 + 8 * q^43 + 4 * q^44 - 2 * q^45 - 20 * q^46 + 24 * q^47 - 8 * q^48 - 10 * q^49 + 2 * q^50 - 28 * q^52 + 12 * q^54 - 20 * q^56 + 16 * q^57 - 48 * q^58 - 16 * q^59 + 8 * q^60 + 4 * q^61 + 40 * q^62 - 20 * q^63 - 14 * q^64 - 16 * q^66 - 4 * q^67 + 8 * q^70 - 32 * q^71 - 10 * q^72 + 8 * q^73 + 8 * q^74 - 4 * q^75 - 36 * q^76 + 24 * q^77 - 4 * q^78 - 36 * q^79 - 2 * q^80 - 14 * q^81 + 28 * q^82 + 20 * q^83 - 48 * q^86 + 24 * q^87 - 12 * q^88 - 12 * q^89 - 14 * q^90 - 12 * q^91 - 28 * q^92 + 36 * q^93 + 20 * q^94 + 12 * q^95 + 44 * q^96 - 16 * q^97 - 22 * q^98 - 20 * q^99

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 $

$2$	2.51230	1.77647	0.888233	−	0.459392i	$-0.151933\pi$
$2$	2.51230	1.77647	0.888233	+	0.459392i	$0.151933\pi$
$3$	−1.25468	−0.724389	−0.362195	−	0.932103i	$-0.617972\pi$
$3$	−1.25468	−0.724389	−0.362195	+	0.932103i	$0.617972\pi$
$4$	4.31167	2.15583
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.15213	−1.28685
$7$	−1.61485	−0.610355	−0.305178	−	0.952295i	$-0.598716\pi$
$7$	−1.61485	−0.610355	−0.305178	+	0.952295i	$0.598716\pi$
$8$	5.80761	2.05330
$9$	−1.42578	−0.475261
$10$	−2.51230	−0.794460
$11$	−3.28669	−0.990973	−0.495487	−	0.868616i	$-0.665010\pi$
$11$	−3.28669	−0.990973	−0.495487	+	0.868616i	$0.665010\pi$
$12$	−5.40976	−1.56166
$13$	−6.35524	−1.76263	−0.881314	−	0.472531i	$-0.843340\pi$
$13$	−6.35524	−1.76263	−0.881314	+	0.472531i	$0.843340\pi$
$14$	−4.05699	−1.08428
$15$	1.25468	0.323957
$16$	5.96715	1.49179
$17$	0	0
$17$	0	0
$18$	−3.58200	−0.844284
$19$	−0.747167	−0.171412	−0.0857059	−	0.996320i	$-0.527315\pi$
$19$	−0.747167	−0.171412	−0.0857059	+	0.996320i	$0.527315\pi$
$20$	−4.31167	−0.964118
$21$	2.02612	0.442135
$22$	−8.25715	−1.76043
$23$	0.143175	0.0298541	0.0149271	−	0.999889i	$-0.495248\pi$
$23$	0.143175	0.0298541	0.0149271	+	0.999889i	$0.495248\pi$
$24$	−7.28669	−1.48739
$25$	1.00000	0.200000
$26$	−15.9663	−3.13125
$27$	5.55293	1.06866
$28$	−6.96269	−1.31583
$29$	−8.80316	−1.63471	−0.817353	−	0.576138i	$-0.804559\pi$
$29$	−8.80316	−1.63471	−0.817353	+	0.576138i	$0.804559\pi$
$30$	3.15213	0.575498
$31$	7.21615	1.29606	0.648029	−	0.761615i	$-0.275593\pi$
$31$	7.21615	1.29606	0.648029	+	0.761615i	$0.275593\pi$
$32$	3.37606	0.596809
$33$	4.12374	0.717850
$34$	0	0
$35$	1.61485	0.272959
$36$	−6.14750	−1.02458
$37$	−0.621115	−0.102111	−0.0510554	−	0.998696i	$-0.516258\pi$
$37$	−0.621115	−0.102111	−0.0510554	+	0.998696i	$0.516258\pi$
$38$	−1.87711	−0.304507
$39$	7.97379	1.27683
$40$	−5.80761	−0.918264
$41$	6.36239	0.993639	0.496819	−	0.867854i	$-0.334501\pi$
$41$	6.36239	0.993639	0.496819	+	0.867854i	$0.334501\pi$
$42$	5.09022	0.785438
$43$	−2.74801	−0.419068	−0.209534	−	0.977801i	$-0.567195\pi$
$43$	−2.74801	−0.419068	−0.209534	+	0.977801i	$0.567195\pi$
$44$	−14.1711	−2.13637
$45$	1.42578	0.212543
$46$	0.359700	0.0530349
$47$	11.9308	1.74029	0.870146	−	0.492794i	$-0.164024\pi$
$47$	11.9308	1.74029	0.870146	+	0.492794i	$0.164024\pi$
$48$	−7.48685	−1.08063
$49$	−4.39226	−0.627466
$50$	2.51230	0.355293
$51$	0	0
$52$	−27.4017	−3.79993
$53$	2.71404	0.372802	0.186401	−	0.982474i	$-0.440318\pi$
$53$	2.71404	0.372802	0.186401	+	0.982474i	$0.440318\pi$
$54$	13.9507	1.89844
$55$	3.28669	0.443177
$56$	−9.37841	−1.25324
$57$	0.937454	0.124169
$58$	−22.1162	−2.90400
$59$	−12.6815	−1.65099	−0.825493	−	0.564413i	$-0.809103\pi$
$59$	−12.6815	−1.65099	−0.825493	+	0.564413i	$0.809103\pi$
$60$	5.40976	0.698397
$61$	−0.464091	−0.0594207	−0.0297104	−	0.999559i	$-0.509458\pi$
$61$	−0.464091	−0.0594207	−0.0297104	+	0.999559i	$0.509458\pi$
$62$	18.1292	2.30241
$63$	2.30242	0.290078
$64$	−3.45261	−0.431576
$65$	6.35524	0.788271
$66$	10.3601	1.27524
$67$	1.81686	0.221965	0.110982	−	0.993822i	$-0.464600\pi$
$67$	1.81686	0.221965	0.110982	+	0.993822i	$0.464600\pi$
$68$	0	0
$69$	−0.179639	−0.0216260
$70$	4.05699	0.484903
$71$	−4.25738	−0.505259	−0.252629	−	0.967563i	$-0.581295\pi$
$71$	−4.25738	−0.505259	−0.252629	+	0.967563i	$0.581295\pi$
$72$	−8.28039	−0.975853
$73$	1.21126	0.141767	0.0708835	−	0.997485i	$-0.477418\pi$
$73$	1.21126	0.141767	0.0708835	+	0.997485i	$0.477418\pi$
$74$	−1.56043	−0.181396
$75$	−1.25468	−0.144878
$76$	−3.22154	−0.369535
$77$	5.30750	0.604846
$78$	20.0326	2.26824
$79$	−5.04874	−0.568028	−0.284014	−	0.958820i	$-0.591666\pi$
$79$	−5.04874	−0.568028	−0.284014	+	0.958820i	$0.591666\pi$
$80$	−5.96715	−0.667147
$81$	−2.68980	−0.298867
$82$	15.9843	1.76517
$83$	−3.58494	−0.393498	−0.196749	−	0.980454i	$-0.563038\pi$
$83$	−3.58494	−0.393498	−0.196749	+	0.980454i	$0.563038\pi$
$84$	8.73594	0.953169
$85$	0	0
$86$	−6.90384	−0.744460
$87$	11.0451	1.18416
$88$	−19.0878	−2.03477
$89$	10.5906	1.12260	0.561300	−	0.827613i	$-0.310302\pi$
$89$	10.5906	1.12260	0.561300	+	0.827613i	$0.310302\pi$
$90$	3.58200	0.377576
$91$	10.2628	1.07583
$92$	0.617325	0.0643606
$93$	−9.05395	−0.938851
$94$	29.9739	3.09157
$95$	0.747167	0.0766577
$96$	−4.23587	−0.432322
$97$	6.96870	0.707565	0.353782	−	0.935328i	$-0.384895\pi$
$97$	6.96870	0.707565	0.353782	+	0.935328i	$0.384895\pi$
$98$	−11.0347	−1.11467
$99$	4.68610	0.470971
$100$	4.31167	0.431167
$101$	−0.679421	−0.0676049	−0.0338025	−	0.999429i	$-0.510762\pi$
$101$	−0.679421	−0.0676049	−0.0338025	+	0.999429i	$0.510762\pi$
$102$	0	0
$103$	−0.156455	−0.0154160	−0.00770798	−	0.999970i	$-0.502454\pi$
$103$	−0.156455	−0.0154160	−0.00770798	+	0.999970i	$0.502454\pi$
$104$	−36.9088	−3.61921
$105$	−2.02612	−0.197729
$106$	6.81849	0.662270
$107$	−17.9652	−1.73676	−0.868379	−	0.495901i	$-0.834838\pi$
$107$	−17.9652	−1.73676	−0.868379	+	0.495901i	$0.834838\pi$
$108$	23.9424	2.30386
$109$	−5.81215	−0.556703	−0.278352	−	0.960479i	$-0.589788\pi$
$109$	−5.81215	−0.556703	−0.278352	+	0.960479i	$0.589788\pi$
$110$	8.25715	0.787289
$111$	0.779300	0.0739679
$112$	−9.63604	−0.910520
$113$	−9.29716	−0.874603	−0.437302	−	0.899315i	$-0.644066\pi$
$113$	−9.29716	−0.874603	−0.437302	+	0.899315i	$0.644066\pi$
$114$	2.35517	0.220582
$115$	−0.143175	−0.0133512
$116$	−37.9563	−3.52415
$117$	9.06119	0.837707
$118$	−31.8597	−2.93292
$119$	0	0
$120$	7.28669	0.665180
$121$	−0.197689	−0.0179717
$122$	−1.16594	−0.105559
$123$	−7.98276	−0.719781
$124$	31.1136	2.79409
$125$	−1.00000	−0.0894427
$126$	5.78438	0.515314
$127$	−15.1796	−1.34698	−0.673488	−	0.739198i	$-0.735205\pi$
$127$	−15.1796	−1.34698	−0.673488	+	0.739198i	$0.735205\pi$
$128$	−15.4261	−1.36349
$129$	3.44787	0.303568
$130$	15.9663	1.40034
$131$	−1.98251	−0.173212	−0.0866062	−	0.996243i	$-0.527602\pi$
$131$	−1.98251	−0.173212	−0.0866062	+	0.996243i	$0.527602\pi$
$132$	17.7802	1.54757
$133$	1.20656	0.104622
$134$	4.56450	0.394313
$135$	−5.55293	−0.477920
$136$	0	0
$137$	19.6088	1.67530	0.837648	−	0.546211i	$-0.183930\pi$
$137$	19.6088	1.67530	0.837648	+	0.546211i	$0.183930\pi$
$138$	−0.451308	−0.0384179
$139$	−3.61139	−0.306314	−0.153157	−	0.988202i	$-0.548944\pi$
$139$	−3.61139	−0.306314	−0.153157	+	0.988202i	$0.548944\pi$
$140$	6.96269	0.588455
$141$	−14.9694	−1.26065
$142$	−10.6958	−0.897575
$143$	20.8877	1.74672
$144$	−8.50785	−0.708987
$145$	8.80316	0.731062
$146$	3.04305	0.251844
$147$	5.51088	0.454530
$148$	−2.67804	−0.220134
$149$	1.26402	0.103553	0.0517763	−	0.998659i	$-0.483512\pi$
$149$	1.26402	0.103553	0.0517763	+	0.998659i	$0.483512\pi$
$150$	−3.15213	−0.257371
$151$	−16.2206	−1.32002	−0.660009	−	0.751258i	$-0.729447\pi$
$151$	−16.2206	−1.32002	−0.660009	+	0.751258i	$0.729447\pi$
$152$	−4.33926	−0.351960
$153$	0	0
$154$	13.3341	1.07449
$155$	−7.21615	−0.579615
$156$	34.3803	2.75263
$157$	8.52619	0.680464	0.340232	−	0.940341i	$-0.389494\pi$
$157$	8.52619	0.680464	0.340232	+	0.940341i	$0.389494\pi$
$158$	−12.6840	−1.00908
$159$	−3.40525	−0.270054
$160$	−3.37606	−0.266901
$161$	−0.231207	−0.0182216
$162$	−6.75760	−0.530927
$163$	15.4603	1.21094	0.605472	−	0.795867i	$-0.292984\pi$
$163$	15.4603	1.21094	0.605472	+	0.795867i	$0.292984\pi$
$164$	27.4325	2.14212
$165$	−4.12374	−0.321032
$166$	−9.00646	−0.699037
$167$	−3.67070	−0.284048	−0.142024	−	0.989863i	$-0.545361\pi$
$167$	−3.67070	−0.284048	−0.142024	+	0.989863i	$0.545361\pi$
$168$	11.7669	0.907836
$169$	27.3891	2.10686
$170$	0	0
$171$	1.06530	0.0814653
$172$	−11.8485	−0.903441
$173$	−9.14139	−0.695007	−0.347503	−	0.937679i	$-0.612970\pi$
$173$	−9.14139	−0.695007	−0.347503	+	0.937679i	$0.612970\pi$
$174$	27.7487	2.10363
$175$	−1.61485	−0.122071
$176$	−19.6121	−1.47832
$177$	15.9112	1.19596
$178$	26.6067	1.99426
$179$	−8.76138	−0.654857	−0.327428	−	0.944876i	$-0.606182\pi$
$179$	−8.76138	−0.654857	−0.327428	+	0.944876i	$0.606182\pi$
$180$	6.14750	0.458207
$181$	4.86717	0.361774	0.180887	−	0.983504i	$-0.442103\pi$
$181$	4.86717	0.361774	0.180887	+	0.983504i	$0.442103\pi$
$182$	25.7832	1.91118
$183$	0.582285	0.0430437
$184$	0.831507	0.0612995
$185$	0.621115	0.0456653
$186$	−22.7463	−1.66784
$187$	0	0
$188$	51.4418	3.75178
$189$	−8.96715	−0.652264
$190$	1.87711	0.136180
$191$	−11.2751	−0.815838	−0.407919	−	0.913018i	$-0.633745\pi$
$191$	−11.2751	−0.815838	−0.407919	+	0.913018i	$0.633745\pi$
$192$	4.33191	0.312629
$193$	4.58171	0.329798	0.164899	−	0.986310i	$-0.447270\pi$
$193$	4.58171	0.329798	0.164899	+	0.986310i	$0.447270\pi$
$194$	17.5075	1.25697
$195$	−7.97379	−0.571015
$196$	−18.9380	−1.35271
$197$	13.2481	0.943887	0.471944	−	0.881629i	$-0.343553\pi$
$197$	13.2481	0.943887	0.471944	+	0.881629i	$0.343553\pi$
$198$	11.7729	0.836663
$199$	2.63839	0.187031	0.0935153	−	0.995618i	$-0.470190\pi$
$199$	2.63839	0.187031	0.0935153	+	0.995618i	$0.470190\pi$
$200$	5.80761	0.410660
$201$	−2.27957	−0.160789
$202$	−1.70691	−0.120098
$203$	14.2158	0.997751
$204$	0	0
$205$	−6.36239	−0.444369
$206$	−0.393062	−0.0273860
$207$	−0.204137	−0.0141885
$208$	−37.9227	−2.62946
$209$	2.45570	0.169865
$210$	−5.09022	−0.351258
$211$	−7.13489	−0.491186	−0.245593	−	0.969373i	$-0.578983\pi$
$211$	−7.13489	−0.491186	−0.245593	+	0.969373i	$0.578983\pi$
$212$	11.7020	0.803699
$213$	5.34165	0.366004
$214$	−45.1340	−3.08529
$215$	2.74801	0.187413
$216$	32.2493	2.19429
$217$	−11.6530	−0.791057
$218$	−14.6019	−0.988965
$219$	−1.51974	−0.102694
$220$	14.1711	0.955416
$221$	0	0
$222$	1.95784	0.131402
$223$	12.1709	0.815025	0.407512	−	0.913200i	$-0.366396\pi$
$223$	12.1709	0.815025	0.407512	+	0.913200i	$0.366396\pi$
$224$	−5.45183	−0.364265
$225$	−1.42578	−0.0950521
$226$	−23.3573	−1.55370
$227$	−0.835635	−0.0554630	−0.0277315	−	0.999615i	$-0.508828\pi$
$227$	−0.835635	−0.0554630	−0.0277315	+	0.999615i	$0.508828\pi$
$228$	4.04199	0.267687
$229$	6.13420	0.405360	0.202680	−	0.979245i	$-0.435035\pi$
$229$	6.13420	0.405360	0.202680	+	0.979245i	$0.435035\pi$
$230$	−0.359700	−0.0237179
$231$	−6.65921	−0.438144
$232$	−51.1253	−3.35654
$233$	16.8371	1.10303	0.551516	−	0.834164i	$-0.314049\pi$
$233$	16.8371	1.10303	0.551516	+	0.834164i	$0.314049\pi$
$234$	22.7645	1.48816
$235$	−11.9308	−0.778282
$236$	−54.6783	−3.55925
$237$	6.33455	0.411473
$238$	0	0
$239$	6.95301	0.449753	0.224876	−	0.974387i	$-0.427802\pi$
$239$	6.95301	0.449753	0.224876	+	0.974387i	$0.427802\pi$
$240$	7.48685	0.483274
$241$	−30.7215	−1.97895	−0.989473	−	0.144714i	$-0.953774\pi$
$241$	−30.7215	−1.97895	−0.989473	+	0.144714i	$0.953774\pi$
$242$	−0.496655	−0.0319262
$243$	−13.2840	−0.852167
$244$	−2.00101	−0.128101
$245$	4.39226	0.280611
$246$	−20.0551	−1.27867
$247$	4.74843	0.302135
$248$	41.9086	2.66120
$249$	4.49795	0.285046
$250$	−2.51230	−0.158892
$251$	−22.5294	−1.42204	−0.711021	−	0.703171i	$-0.751767\pi$
$251$	−22.5294	−1.42204	−0.711021	+	0.703171i	$0.751767\pi$
$252$	9.92728	0.625360
$253$	−0.470573	−0.0295846
$254$	−38.1359	−2.39286
$255$	0	0
$256$	−31.8499	−1.99062
$257$	−1.90476	−0.118816	−0.0594079	−	0.998234i	$-0.518921\pi$
$257$	−1.90476	−0.118816	−0.0594079	+	0.998234i	$0.518921\pi$
$258$	8.66210	0.539279
$259$	1.00301	0.0623238
$260$	27.4017	1.69938
$261$	12.5514	0.776911
$262$	−4.98066	−0.307706
$263$	7.80192	0.481087	0.240543	−	0.970638i	$-0.422674\pi$
$263$	7.80192	0.481087	0.240543	+	0.970638i	$0.422674\pi$
$264$	23.9491	1.47396
$265$	−2.71404	−0.166722
$266$	3.03125	0.185858
$267$	−13.2878	−0.813199
$268$	7.83369	0.478519
$269$	13.7440	0.837987	0.418993	−	0.907989i	$-0.362383\pi$
$269$	13.7440	0.837987	0.418993	+	0.907989i	$0.362383\pi$
$270$	−13.9507	−0.849010
$271$	−12.4855	−0.758438	−0.379219	−	0.925307i	$-0.623807\pi$
$271$	−12.4855	−0.758438	−0.379219	+	0.925307i	$0.623807\pi$
$272$	0	0
$273$	−12.8765	−0.779319
$274$	49.2633	2.97611
$275$	−3.28669	−0.198195
$276$	−0.774544	−0.0466221
$277$	26.8602	1.61387	0.806935	−	0.590640i	$-0.201125\pi$
$277$	26.8602	1.61387	0.806935	+	0.590640i	$0.201125\pi$
$278$	−9.07291	−0.544157
$279$	−10.2887	−0.615966
$280$	9.37841	0.560467
$281$	15.5290	0.926385	0.463193	−	0.886258i	$-0.346704\pi$
$281$	15.5290	0.926385	0.463193	+	0.886258i	$0.346704\pi$
$282$	−37.6076	−2.23950
$283$	−10.4395	−0.620565	−0.310283	−	0.950644i	$-0.600424\pi$
$283$	−10.4395	−0.620565	−0.310283	+	0.950644i	$0.600424\pi$
$284$	−18.3564	−1.08925
$285$	−0.937454	−0.0555300
$286$	52.4762	3.10298
$287$	−10.2743	−0.606473
$288$	−4.81352	−0.283640
$289$	0	0
$290$	22.1162	1.29871
$291$	−8.74348	−0.512552
$292$	5.22254	0.305626
$293$	−7.10645	−0.415163	−0.207581	−	0.978218i	$-0.566559\pi$
$293$	−7.10645	−0.415163	−0.207581	+	0.978218i	$0.566559\pi$
$294$	13.8450	0.807457
$295$	12.6815	0.738343
$296$	−3.60720	−0.209664
$297$	−18.2508	−1.05902
$298$	3.17560	0.183958
$299$	−0.909915	−0.0526217
$300$	−5.40976	−0.312333
$301$	4.43762	0.255780
$302$	−40.7512	−2.34497
$303$	0.852455	0.0489723
$304$	−4.45845	−0.255710
$305$	0.464091	0.0265738
$306$	0	0
$307$	4.80512	0.274243	0.137121	−	0.990554i	$-0.456215\pi$
$307$	4.80512	0.274243	0.137121	+	0.990554i	$0.456215\pi$
$308$	22.8842	1.30395
$309$	0.196301	0.0111672
$310$	−18.1292	−1.02967
$311$	8.02933	0.455301	0.227651	−	0.973743i	$-0.426896\pi$
$311$	8.02933	0.455301	0.227651	+	0.973743i	$0.426896\pi$
$312$	46.3087	2.62171
$313$	−22.1020	−1.24928	−0.624640	−	0.780913i	$-0.714754\pi$
$313$	−22.1020	−1.24928	−0.624640	+	0.780913i	$0.714754\pi$
$314$	21.4204	1.20882
$315$	−2.30242	−0.129727
$316$	−21.7685	−1.22457
$317$	−15.9647	−0.896669	−0.448335	−	0.893866i	$-0.647983\pi$
$317$	−15.9647	−0.896669	−0.448335	+	0.893866i	$0.647983\pi$
$318$	−8.55501	−0.479741
$319$	28.9332	1.61995
$320$	3.45261	0.193007
$321$	22.5405	1.25809
$322$	−0.580861	−0.0323701
$323$	0	0
$324$	−11.5975	−0.644308
$325$	−6.35524	−0.352526
$326$	38.8410	2.15120
$327$	7.29238	0.403270
$328$	36.9503	2.04024
$329$	−19.2665	−1.06220
$330$	−10.3601	−0.570303
$331$	3.87911	0.213215	0.106608	−	0.994301i	$-0.466001\pi$
$331$	3.87911	0.213215	0.106608	+	0.994301i	$0.466001\pi$
$332$	−15.4571	−0.848317
$333$	0.885575	0.0485292
$334$	−9.22192	−0.504601
$335$	−1.81686	−0.0992656
$336$	12.0901	0.659571
$337$	−24.3854	−1.32836	−0.664178	−	0.747574i	$-0.731218\pi$
$337$	−24.3854	−1.32836	−0.664178	+	0.747574i	$0.731218\pi$
$338$	68.8098	3.74276
$339$	11.6649	0.633553
$340$	0	0
$341$	−23.7172	−1.28436
$342$	2.67635	0.144720
$343$	18.3968	0.993333
$344$	−15.9594	−0.860473
$345$	0.179639	0.00967144
$346$	−22.9659	−1.23466
$347$	−10.6306	−0.570681	−0.285341	−	0.958426i	$-0.592107\pi$
$347$	−10.6306	−0.570681	−0.285341	+	0.958426i	$0.592107\pi$
$348$	47.6229	2.55286
$349$	11.5579	0.618682	0.309341	−	0.950951i	$-0.399892\pi$
$349$	11.5579	0.618682	0.309341	+	0.950951i	$0.399892\pi$
$350$	−4.05699	−0.216855
$351$	−35.2903	−1.88365
$352$	−11.0961	−0.591421
$353$	11.3682	0.605070	0.302535	−	0.953138i	$-0.402167\pi$
$353$	11.3682	0.605070	0.302535	+	0.953138i	$0.402167\pi$
$354$	39.9737	2.12458
$355$	4.25738	0.225958
$356$	45.6631	2.42014
$357$	0	0
$358$	−22.0113	−1.16333
$359$	32.1310	1.69581	0.847906	−	0.530147i	$-0.177863\pi$
$359$	32.1310	1.69581	0.847906	+	0.530147i	$0.177863\pi$
$360$	8.28039	0.436415
$361$	−18.4417	−0.970618
$362$	12.2278	0.642680
$363$	0.248036	0.0130185
$364$	44.2496	2.31931
$365$	−1.21126	−0.0634001
$366$	1.46288	0.0764657
$367$	19.2552	1.00511	0.502557	−	0.864544i	$-0.332393\pi$
$367$	19.2552	1.00511	0.502557	+	0.864544i	$0.332393\pi$
$368$	0.854349	0.0445360
$369$	−9.07138	−0.472237
$370$	1.56043	0.0811229
$371$	−4.38276	−0.227542
$372$	−39.0376	−2.02401
$373$	−20.3136	−1.05180	−0.525900	−	0.850547i	$-0.676271\pi$
$373$	−20.3136	−1.05180	−0.525900	+	0.850547i	$0.676271\pi$
$374$	0	0
$375$	1.25468	0.0647913
$376$	69.2897	3.57334
$377$	55.9462	2.88138
$378$	−22.5282	−1.15873
$379$	−34.3004	−1.76189	−0.880946	−	0.473217i	$-0.843093\pi$
$379$	−34.3004	−1.76189	−0.880946	+	0.473217i	$0.843093\pi$
$380$	3.22154	0.165261
$381$	19.0456	0.975734
$382$	−28.3265	−1.44931
$383$	−21.3225	−1.08953	−0.544764	−	0.838589i	$-0.683381\pi$
$383$	−21.3225	−1.08953	−0.544764	+	0.838589i	$0.683381\pi$
$384$	19.3548	0.987697
$385$	−5.30750	−0.270495
$386$	11.5106	0.585876
$387$	3.91807	0.199166
$388$	30.0467	1.52539
$389$	−11.7682	−0.596672	−0.298336	−	0.954461i	$-0.596432\pi$
$389$	−11.7682	−0.596672	−0.298336	+	0.954461i	$0.596432\pi$
$390$	−20.0326	−1.01439
$391$	0	0
$392$	−25.5086	−1.28838
$393$	2.48741	0.125473
$394$	33.2832	1.67678
$395$	5.04874	0.254030
$396$	20.2049	1.01533
$397$	3.35896	0.168581	0.0842907	−	0.996441i	$-0.473138\pi$
$397$	3.35896	0.168581	0.0842907	+	0.996441i	$0.473138\pi$
$398$	6.62844	0.332254
$399$	−1.51385	−0.0757871
$400$	5.96715	0.298357
$401$	2.59437	0.129557	0.0647784	−	0.997900i	$-0.479366\pi$
$401$	2.59437	0.129557	0.0647784	+	0.997900i	$0.479366\pi$
$402$	−5.72698	−0.285636
$403$	−45.8604	−2.28447
$404$	−2.92944	−0.145745
$405$	2.68980	0.133657
$406$	35.7143	1.77247
$407$	2.04141	0.101189
$408$	0	0
$409$	−30.8364	−1.52476	−0.762381	−	0.647129i	$-0.775970\pi$
$409$	−30.8364	−1.52476	−0.762381	+	0.647129i	$0.775970\pi$
$410$	−15.9843	−0.789406
$411$	−24.6028	−1.21357
$412$	−0.674582	−0.0332343
$413$	20.4786	1.00769
$414$	−0.512854	−0.0252054
$415$	3.58494	0.175978
$416$	−21.4557	−1.05195
$417$	4.53114	0.221891
$418$	6.16947	0.301759
$419$	18.6672	0.911954	0.455977	−	0.889991i	$-0.349290\pi$
$419$	18.6672	0.911954	0.455977	+	0.889991i	$0.349290\pi$
$420$	−8.73594	−0.426270
$421$	29.5695	1.44113	0.720565	−	0.693388i	$-0.243883\pi$
$421$	29.5695	1.44113	0.720565	+	0.693388i	$0.243883\pi$
$422$	−17.9250	−0.872576
$423$	−17.0108	−0.827092
$424$	15.7621	0.765475
$425$	0	0
$426$	13.4198	0.650193
$427$	0.749436	0.0362678
$428$	−77.4598	−3.74416
$429$	−26.2074	−1.26530
$430$	6.90384	0.332933
$431$	16.3459	0.787355	0.393678	−	0.919249i	$-0.371203\pi$
$431$	16.3459	0.787355	0.393678	+	0.919249i	$0.371203\pi$
$432$	33.1352	1.59422
$433$	−14.3256	−0.688446	−0.344223	−	0.938888i	$-0.611858\pi$
$433$	−14.3256	−0.688446	−0.344223	+	0.938888i	$0.611858\pi$
$434$	−29.2758	−1.40529
$435$	−11.0451	−0.529574
$436$	−25.0601	−1.20016
$437$	−0.106976	−0.00511735
$438$	−3.81805	−0.182433
$439$	−30.4292	−1.45231	−0.726154	−	0.687532i	$-0.758694\pi$
$439$	−30.4292	−1.45231	−0.726154	+	0.687532i	$0.758694\pi$
$440$	19.0878	0.909975
$441$	6.26241	0.298210
$442$	0	0
$443$	26.5036	1.25922	0.629612	−	0.776909i	$-0.283214\pi$
$443$	26.5036	1.25922	0.629612	+	0.776909i	$0.283214\pi$
$444$	3.36008	0.159463
$445$	−10.5906	−0.502042
$446$	30.5770	1.44786
$447$	−1.58594	−0.0750124
$448$	5.57544	0.263415
$449$	−15.8391	−0.747492	−0.373746	−	0.927531i	$-0.621927\pi$
$449$	−15.8391	−0.747492	−0.373746	+	0.927531i	$0.621927\pi$
$450$	−3.58200	−0.168857
$451$	−20.9112	−0.984669
$452$	−40.0863	−1.88550
$453$	20.3517	0.956206
$454$	−2.09937	−0.0985283
$455$	−10.2628	−0.481126
$456$	5.44437	0.254956
$457$	−4.25348	−0.198969	−0.0994847	−	0.995039i	$-0.531719\pi$
$457$	−4.25348	−0.198969	−0.0994847	+	0.995039i	$0.531719\pi$
$458$	15.4110	0.720108
$459$	0	0
$460$	−0.617325	−0.0287829
$461$	−23.9740	−1.11658	−0.558290	−	0.829646i	$-0.688542\pi$
$461$	−23.9740	−1.11658	−0.558290	+	0.829646i	$0.688542\pi$
$462$	−16.7300	−0.778348
$463$	−23.0127	−1.06949	−0.534746	−	0.845013i	$-0.679593\pi$
$463$	−23.0127	−1.06949	−0.534746	+	0.845013i	$0.679593\pi$
$464$	−52.5297	−2.43863
$465$	9.05395	0.419867
$466$	42.2998	1.95950
$467$	21.7845	1.00807	0.504033	−	0.863684i	$-0.331849\pi$
$467$	21.7845	1.00807	0.504033	+	0.863684i	$0.331849\pi$
$468$	39.0688	1.80596
$469$	−2.93395	−0.135477
$470$	−29.9739	−1.38259
$471$	−10.6976	−0.492921
$472$	−73.6490	−3.38997
$473$	9.03186	0.415285
$474$	15.9143	0.730968
$475$	−0.747167	−0.0342824
$476$	0	0
$477$	−3.86963	−0.177178
$478$	17.4681	0.798971
$479$	−32.9304	−1.50463	−0.752313	−	0.658806i	$-0.771062\pi$
$479$	−32.9304	−1.50463	−0.752313	+	0.658806i	$0.771062\pi$
$480$	4.23587	0.193340
$481$	3.94734	0.179983
$482$	−77.1818	−3.51553
$483$	0.290090	0.0131995
$484$	−0.852369	−0.0387441
$485$	−6.96870	−0.316433
$486$	−33.3733	−1.51385
$487$	−18.6484	−0.845042	−0.422521	−	0.906353i	$-0.638855\pi$
$487$	−18.6484	−0.845042	−0.422521	+	0.906353i	$0.638855\pi$
$488$	−2.69526	−0.122009
$489$	−19.3977	−0.877195
$490$	11.0347	0.498497
$491$	−3.97306	−0.179302	−0.0896508	−	0.995973i	$-0.528575\pi$
$491$	−3.97306	−0.179302	−0.0896508	+	0.995973i	$0.528575\pi$
$492$	−34.4190	−1.55173
$493$	0	0
$494$	11.9295	0.536733
$495$	−4.68610	−0.210624
$496$	43.0598	1.93344
$497$	6.87503	0.308387
$498$	11.3002	0.506375
$499$	−34.1286	−1.52781	−0.763903	−	0.645331i	$-0.776719\pi$
$499$	−34.1286	−1.52781	−0.763903	+	0.645331i	$0.776719\pi$
$500$	−4.31167	−0.192824
$501$	4.60555	0.205761
$502$	−56.6007	−2.52621
$503$	−39.4109	−1.75725	−0.878623	−	0.477515i	$-0.841537\pi$
$503$	−39.4109	−1.75725	−0.878623	+	0.477515i	$0.841537\pi$
$504$	13.3716	0.595617
$505$	0.679421	0.0302338
$506$	−1.18222	−0.0525561
$507$	−34.3646	−1.52618
$508$	−65.4496	−2.90386
$509$	8.87274	0.393277	0.196639	−	0.980476i	$-0.436997\pi$
$509$	8.87274	0.393277	0.196639	+	0.980476i	$0.436997\pi$
$510$	0	0
$511$	−1.95600	−0.0865282
$512$	−49.1643	−2.17278
$513$	−4.14897	−0.183181
$514$	−4.78534	−0.211072
$515$	0.156455	0.00689423
$516$	14.8661	0.654443
$517$	−39.2129	−1.72458
$518$	2.51986	0.110716
$519$	11.4695	0.503455
$520$	36.9088	1.61856
$521$	17.5909	0.770673	0.385337	−	0.922776i	$-0.374085\pi$
$521$	17.5909	0.770673	0.385337	+	0.922776i	$0.374085\pi$
$522$	31.5329	1.38016
$523$	20.1681	0.881892	0.440946	−	0.897534i	$-0.354643\pi$
$523$	20.1681	0.881892	0.440946	+	0.897534i	$0.354643\pi$
$524$	−8.54791	−0.373417
$525$	2.02612	0.0884270
$526$	19.6008	0.854635
$527$	0	0
$528$	24.6069	1.07088
$529$	−22.9795	−0.999109
$530$	−6.81849	−0.296176
$531$	18.0810	0.784648
$532$	5.20229	0.225548
$533$	−40.4346	−1.75141
$534$	−33.3829	−1.44462
$535$	17.9652	0.776702
$536$	10.5516	0.455760
$537$	10.9927	0.474371
$538$	34.5291	1.48866
$539$	14.4360	0.621802
$540$	−23.9424	−1.03032
$541$	42.7378	1.83744	0.918720	−	0.394908i	$-0.129224\pi$
$541$	42.7378	1.83744	0.918720	+	0.394908i	$0.129224\pi$
$542$	−31.3673	−1.34734
$543$	−6.10674	−0.262065
$544$	0	0
$545$	5.81215	0.248965
$546$	−32.3496	−1.38443
$547$	14.2143	0.607760	0.303880	−	0.952710i	$-0.401718\pi$
$547$	14.2143	0.607760	0.303880	+	0.952710i	$0.401718\pi$
$548$	84.5468	3.61166
$549$	0.661692	0.0282403
$550$	−8.25715	−0.352086
$551$	6.57743	0.280208
$552$	−1.04327	−0.0444047
$553$	8.15295	0.346699
$554$	67.4809	2.86699
$555$	−0.779300	−0.0330795
$556$	−15.5711	−0.660363
$557$	4.00971	0.169897	0.0849484	−	0.996385i	$-0.472927\pi$
$557$	4.00971	0.169897	0.0849484	+	0.996385i	$0.472927\pi$
$558$	−25.8482	−1.09424
$559$	17.4643	0.738661
$560$	9.63604	0.407197
$561$	0	0
$562$	39.0137	1.64569
$563$	5.66772	0.238866	0.119433	−	0.992842i	$-0.461892\pi$
$563$	5.66772	0.238866	0.119433	+	0.992842i	$0.461892\pi$
$564$	−64.5430	−2.71775
$565$	9.29716	0.391134
$566$	−26.2272	−1.10241
$567$	4.34362	0.182415
$568$	−24.7252	−1.03745
$569$	−0.249161	−0.0104454	−0.00522269	−	0.999986i	$-0.501662\pi$
$569$	−0.249161	−0.0104454	−0.00522269	+	0.999986i	$0.501662\pi$
$570$	−2.35517	−0.0986472
$571$	−34.1645	−1.42974	−0.714869	−	0.699258i	$-0.753514\pi$
$571$	−34.1645	−1.42974	−0.714869	+	0.699258i	$0.753514\pi$
$572$	90.0608	3.76563
$573$	14.1466	0.590984
$574$	−25.8122	−1.07738
$575$	0.143175	0.00597083
$576$	4.92267	0.205111
$577$	28.3587	1.18059	0.590295	−	0.807188i	$-0.299011\pi$
$577$	28.3587	1.18059	0.590295	+	0.807188i	$0.299011\pi$
$578$	0	0
$579$	−5.74857	−0.238902
$580$	37.9563	1.57605
$581$	5.78914	0.240174
$582$	−21.9663	−0.910532
$583$	−8.92020	−0.369437
$584$	7.03451	0.291090
$585$	−9.06119	−0.374634
$586$	−17.8535	−0.737523
$587$	22.8461	0.942960	0.471480	−	0.881877i	$-0.343720\pi$
$587$	22.8461	0.942960	0.471480	+	0.881877i	$0.343720\pi$
$588$	23.7611	0.979891
$589$	−5.39167	−0.222160
$590$	31.8597	1.31164
$591$	−16.6221	−0.683742
$592$	−3.70629	−0.152327
$593$	−10.3077	−0.423285	−0.211642	−	0.977347i	$-0.567881\pi$
$593$	−10.3077	−0.423285	−0.211642	+	0.977347i	$0.567881\pi$
$594$	−45.8514	−1.88131
$595$	0	0
$596$	5.45004	0.223242
$597$	−3.31033	−0.135483
$598$	−2.28598	−0.0934807
$599$	−25.2157	−1.03028	−0.515142	−	0.857105i	$-0.672261\pi$
$599$	−25.2157	−1.03028	−0.515142	+	0.857105i	$0.672261\pi$
$600$	−7.28669	−0.297478
$601$	−8.56378	−0.349324	−0.174662	−	0.984628i	$-0.555883\pi$
$601$	−8.56378	−0.349324	−0.174662	+	0.984628i	$0.555883\pi$
$602$	11.1487	0.454385
$603$	−2.59044	−0.105491
$604$	−69.9380	−2.84574
$605$	0.197689	0.00803720
$606$	2.14163	0.0869976
$607$	−9.82021	−0.398590	−0.199295	−	0.979940i	$-0.563865\pi$
$607$	−9.82021	−0.398590	−0.199295	+	0.979940i	$0.563865\pi$
$608$	−2.52248	−0.102300
$609$	−17.8362	−0.722760
$610$	1.16594	0.0472074
$611$	−75.8234	−3.06749
$612$	0	0
$613$	22.3926	0.904427	0.452214	−	0.891910i	$-0.350635\pi$
$613$	22.3926	0.904427	0.452214	+	0.891910i	$0.350635\pi$
$614$	12.0719	0.487183
$615$	7.98276	0.321896
$616$	30.8239	1.24193
$617$	21.3447	0.859304	0.429652	−	0.902995i	$-0.358636\pi$
$617$	21.3447	0.859304	0.429652	+	0.902995i	$0.358636\pi$
$618$	0.493167	0.0198381
$619$	15.0557	0.605142	0.302571	−	0.953127i	$-0.402155\pi$
$619$	15.0557	0.605142	0.302571	+	0.953127i	$0.402155\pi$
$620$	−31.1136	−1.24955
$621$	0.795043	0.0319040
$622$	20.1721	0.808828
$623$	−17.1022	−0.685184
$624$	47.5808	1.90476
$625$	1.00000	0.0400000
$626$	−55.5270	−2.21930
$627$	−3.08112	−0.123048
$628$	36.7621	1.46697
$629$	0	0
$630$	−5.78438	−0.230455
$631$	−41.6046	−1.65625	−0.828127	−	0.560540i	$-0.810594\pi$
$631$	−41.6046	−1.65625	−0.828127	+	0.560540i	$0.810594\pi$
$632$	−29.3211	−1.16633
$633$	8.95199	0.355810
$634$	−40.1083	−1.59290
$635$	15.1796	0.602386
$636$	−14.6823	−0.582191
$637$	27.9139	1.10599
$638$	72.6890	2.87779
$639$	6.07010	0.240129
$640$	15.4261	0.609771
$641$	−8.86384	−0.350101	−0.175050	−	0.984559i	$-0.556009\pi$
$641$	−8.86384	−0.350101	−0.175050	+	0.984559i	$0.556009\pi$
$642$	56.6286	2.23495
$643$	−30.0257	−1.18410	−0.592050	−	0.805901i	$-0.701681\pi$
$643$	−30.0257	−1.18410	−0.592050	+	0.805901i	$0.701681\pi$
$644$	−0.996886	−0.0392828
$645$	−3.44787	−0.135760
$646$	0	0
$647$	0.383859	0.0150911	0.00754553	−	0.999972i	$-0.497598\pi$
$647$	0.383859	0.0150911	0.00754553	+	0.999972i	$0.497598\pi$
$648$	−15.6213	−0.613664
$649$	41.6800	1.63608
$650$	−15.9663	−0.626250
$651$	14.6208	0.573033
$652$	66.6597	2.61059
$653$	−1.44734	−0.0566388	−0.0283194	−	0.999599i	$-0.509016\pi$
$653$	−1.44734	−0.0566388	−0.0283194	+	0.999599i	$0.509016\pi$
$654$	18.3207	0.716395
$655$	1.98251	0.0774629
$656$	37.9653	1.48230
$657$	−1.72699	−0.0673762
$658$	−48.4033	−1.88696
$659$	21.8603	0.851555	0.425777	−	0.904828i	$-0.360001\pi$
$659$	21.8603	0.851555	0.425777	+	0.904828i	$0.360001\pi$
$660$	−17.7802	−0.692093
$661$	40.5201	1.57605	0.788024	−	0.615644i	$-0.211104\pi$
$661$	40.5201	1.57605	0.788024	+	0.615644i	$0.211104\pi$
$662$	9.74551	0.378770
$663$	0	0
$664$	−20.8200	−0.807971
$665$	−1.20656	−0.0467884
$666$	2.22483	0.0862105
$667$	−1.26040	−0.0488027
$668$	−15.8269	−0.612359
$669$	−15.2706	−0.590395
$670$	−4.56450	−0.176342
$671$	1.52532	0.0588844
$672$	6.84029	0.263870
$673$	7.93749	0.305968	0.152984	−	0.988229i	$-0.451112\pi$
$673$	7.93749	0.305968	0.152984	+	0.988229i	$0.451112\pi$
$674$	−61.2635	−2.35978
$675$	5.55293	0.213733
$676$	118.093	4.54203
$677$	−2.56547	−0.0985990	−0.0492995	−	0.998784i	$-0.515699\pi$
$677$	−2.56547	−0.0985990	−0.0492995	+	0.998784i	$0.515699\pi$
$678$	29.3059	1.12549
$679$	−11.2534	−0.431866
$680$	0	0
$681$	1.04845	0.0401768
$682$	−59.5849	−2.28162
$683$	−14.5646	−0.557299	−0.278650	−	0.960393i	$-0.589887\pi$
$683$	−14.5646	−0.557299	−0.278650	+	0.960393i	$0.589887\pi$
$684$	4.59321	0.175626
$685$	−19.6088	−0.749215
$686$	46.2183	1.76462
$687$	−7.69645	−0.293638
$688$	−16.3978	−0.625160
$689$	−17.2484	−0.657111
$690$	0.451308	0.0171810
$691$	42.9625	1.63437	0.817185	−	0.576376i	$-0.195533\pi$
$691$	42.9625	1.63437	0.817185	+	0.576376i	$0.195533\pi$
$692$	−39.4146	−1.49832
$693$	−7.56734	−0.287459
$694$	−26.7073	−1.01380
$695$	3.61139	0.136988
$696$	64.1458	2.43144
$697$	0	0
$698$	29.0370	1.09907
$699$	−21.1251	−0.799025
$700$	−6.96269	−0.263165
$701$	−46.4002	−1.75251	−0.876256	−	0.481846i	$-0.839967\pi$
$701$	−46.4002	−1.75251	−0.876256	+	0.481846i	$0.839967\pi$
$702$	−88.6598	−3.34625
$703$	0.464077	0.0175030
$704$	11.3476	0.427680
$705$	14.9694	0.563779
$706$	28.5605	1.07489
$707$	1.09716	0.0412630
$708$	68.6036	2.57828
$709$	41.5322	1.55977	0.779887	−	0.625920i	$-0.215276\pi$
$709$	41.5322	1.55977	0.779887	+	0.625920i	$0.215276\pi$
$710$	10.6958	0.401408
$711$	7.19840	0.269961
$712$	61.5060	2.30503
$713$	1.03317	0.0386927
$714$	0	0
$715$	−20.8877	−0.781156
$716$	−37.7762	−1.41176
$717$	−8.72379	−0.325796
$718$	80.7229	3.01255
$719$	0.644319	0.0240290	0.0120145	−	0.999928i	$-0.496176\pi$
$719$	0.644319	0.0240290	0.0120145	+	0.999928i	$0.496176\pi$
$720$	8.50785	0.317069
$721$	0.252651	0.00940922
$722$	−46.3313	−1.72427
$723$	38.5456	1.43353
$724$	20.9856	0.779925
$725$	−8.80316	−0.326941
$726$	0.623142	0.0231270
$727$	42.4141	1.57305	0.786525	−	0.617558i	$-0.211878\pi$
$727$	42.4141	1.57305	0.786525	+	0.617558i	$0.211878\pi$
$728$	59.6021	2.20900
$729$	24.7365	0.916167
$730$	−3.04305	−0.112628
$731$	0	0
$732$	2.51062	0.0927951
$733$	−43.4227	−1.60386	−0.801928	−	0.597421i	$-0.796192\pi$
$733$	−43.4227	−1.60386	−0.801928	+	0.597421i	$0.796192\pi$
$734$	48.3749	1.78555
$735$	−5.51088	−0.203272
$736$	0.483369	0.0178172
$737$	−5.97145	−0.219961
$738$	−22.7901	−0.838914
$739$	−28.0864	−1.03318	−0.516588	−	0.856234i	$-0.672798\pi$
$739$	−28.0864	−1.03318	−0.516588	+	0.856234i	$0.672798\pi$
$740$	2.67804	0.0984468
$741$	−5.95775	−0.218863
$742$	−11.0108	−0.404220
$743$	45.2000	1.65823	0.829114	−	0.559079i	$-0.188845\pi$
$743$	45.2000	1.65823	0.829114	+	0.559079i	$0.188845\pi$
$744$	−52.5818	−1.92774
$745$	−1.26402	−0.0463101
$746$	−51.0340	−1.86849
$747$	5.11134	0.187014
$748$	0	0
$749$	29.0110	1.06004
$750$	3.15213	0.115100
$751$	24.0654	0.878158	0.439079	−	0.898448i	$-0.355305\pi$
$751$	24.0654	0.878158	0.439079	+	0.898448i	$0.355305\pi$
$752$	71.1931	2.59614
$753$	28.2671	1.03011
$754$	140.554	5.11867
$755$	16.2206	0.590330
$756$	−38.6634	−1.40617
$757$	−18.0018	−0.654285	−0.327143	−	0.944975i	$-0.606086\pi$
$757$	−18.0018	−0.654285	−0.327143	+	0.944975i	$0.606086\pi$
$758$	−86.1730	−3.12994
$759$	0.590417	0.0214308
$760$	4.33926	0.157401
$761$	−23.4172	−0.848874	−0.424437	−	0.905458i	$-0.639528\pi$
$761$	−23.4172	−0.848874	−0.424437	+	0.905458i	$0.639528\pi$
$762$	47.8483	1.73336
$763$	9.38575	0.339787
$764$	−48.6145	−1.75881
$765$	0	0
$766$	−53.5685	−1.93551
$767$	80.5938	2.91007
$768$	39.9614	1.44198
$769$	−9.52627	−0.343526	−0.171763	−	0.985138i	$-0.554946\pi$
$769$	−9.52627	−0.343526	−0.171763	+	0.985138i	$0.554946\pi$
$770$	−13.3341	−0.480526
$771$	2.38986	0.0860688
$772$	19.7548	0.710991
$773$	20.0047	0.719519	0.359759	−	0.933045i	$-0.382859\pi$
$773$	20.0047	0.719519	0.359759	+	0.933045i	$0.382859\pi$
$774$	9.84337	0.353813
$775$	7.21615	0.259212
$776$	40.4715	1.45284
$777$	−1.25845	−0.0451467
$778$	−29.5653	−1.05997
$779$	−4.75377	−0.170321
$780$	−34.3803	−1.23101
$781$	13.9927	0.500698
$782$	0	0
$783$	−48.8833	−1.74695
$784$	−26.2093	−0.936046
$785$	−8.52619	−0.304313
$786$	6.24912	0.222899
$787$	18.1104	0.645566	0.322783	−	0.946473i	$-0.395382\pi$
$787$	18.1104	0.645566	0.322783	+	0.946473i	$0.395382\pi$
$788$	57.1214	2.03486
$789$	−9.78890	−0.348494
$790$	12.6840	0.451275
$791$	15.0135	0.533819
$792$	27.2150	0.967044
$793$	2.94941	0.104737
$794$	8.43873	0.299479
$795$	3.40525	0.120772
$796$	11.3759	0.403207
$797$	44.1981	1.56558	0.782788	−	0.622289i	$-0.213797\pi$
$797$	44.1981	1.56558	0.782788	+	0.622289i	$0.213797\pi$
$798$	−3.80324	−0.134633
$799$	0	0
$800$	3.37606	0.119362
$801$	−15.0999	−0.533527
$802$	6.51785	0.230153
$803$	−3.98102	−0.140487
$804$	−9.82877	−0.346634
$805$	0.231207	0.00814896
$806$	−115.215	−4.05828
$807$	−17.2443	−0.607029
$808$	−3.94581	−0.138813
$809$	20.3971	0.717123	0.358562	−	0.933506i	$-0.383267\pi$
$809$	20.3971	0.717123	0.358562	+	0.933506i	$0.383267\pi$
$810$	6.75760	0.237438
$811$	2.09854	0.0736896	0.0368448	−	0.999321i	$-0.488269\pi$
$811$	2.09854	0.0736896	0.0368448	+	0.999321i	$0.488269\pi$
$812$	61.2937	2.15099
$813$	15.6653	0.549404
$814$	5.12865	0.179759
$815$	−15.4603	−0.541551
$816$	0	0
$817$	2.05322	0.0718332
$818$	−77.4704	−2.70869
$819$	−14.6325	−0.511299
$820$	−27.4325	−0.957985
$821$	4.94235	0.172489	0.0862446	−	0.996274i	$-0.472513\pi$
$821$	4.94235	0.172489	0.0862446	+	0.996274i	$0.472513\pi$
$822$	−61.8096	−2.15586
$823$	−11.4540	−0.399261	−0.199631	−	0.979871i	$-0.563974\pi$
$823$	−11.4540	−0.399261	−0.199631	+	0.979871i	$0.563974\pi$
$824$	−0.908630	−0.0316536
$825$	4.12374	0.143570
$826$	51.4486	1.79012
$827$	−19.3443	−0.672666	−0.336333	−	0.941743i	$-0.609187\pi$
$827$	−19.3443	−0.672666	−0.336333	+	0.941743i	$0.609187\pi$
$828$	−0.880170	−0.0305880
$829$	−26.7634	−0.929530	−0.464765	−	0.885434i	$-0.653861\pi$
$829$	−26.7634	−0.929530	−0.464765	+	0.885434i	$0.653861\pi$
$830$	9.00646	0.312619
$831$	−33.7009	−1.16907
$832$	21.9422	0.760708
$833$	0	0
$834$	11.3836	0.394182
$835$	3.67070	0.127030
$836$	10.5882	0.366200
$837$	40.0708	1.38505
$838$	46.8978	1.62006
$839$	52.3721	1.80809	0.904043	−	0.427441i	$-0.140585\pi$
$839$	52.3721	1.80809	0.904043	+	0.427441i	$0.140585\pi$
$840$	−11.7669	−0.405996
$841$	48.4956	1.67226
$842$	74.2876	2.56012
$843$	−19.4840	−0.671063
$844$	−30.7633	−1.05892
$845$	−27.3891	−0.942215
$846$	−42.7362	−1.46930
$847$	0.319238	0.0109691
$848$	16.1951	0.556141
$849$	13.0982	0.449531
$850$	0	0
$851$	−0.0889284	−0.00304843
$852$	23.0314	0.789043
$853$	0.124531	0.00426387	0.00213193	−	0.999998i	$-0.499321\pi$
$853$	0.124531	0.00426387	0.00213193	+	0.999998i	$0.499321\pi$
$854$	1.88281	0.0644285
$855$	−1.06530	−0.0364324
$856$	−104.335	−3.56609
$857$	22.6150	0.772513	0.386257	−	0.922391i	$-0.373768\pi$
$857$	22.6150	0.772513	0.386257	+	0.922391i	$0.373768\pi$
$858$	−65.8408	−2.24777
$859$	−38.2254	−1.30423	−0.652117	−	0.758118i	$-0.726119\pi$
$859$	−38.2254	−1.30423	−0.652117	+	0.758118i	$0.726119\pi$
$860$	11.8485	0.404031
$861$	12.8909	0.439322
$862$	41.0659	1.39871
$863$	22.1777	0.754939	0.377469	−	0.926022i	$-0.376794\pi$
$863$	22.1777	0.754939	0.377469	+	0.926022i	$0.376794\pi$
$864$	18.7470	0.637787
$865$	9.14139	0.310816
$866$	−35.9904	−1.22300
$867$	0	0
$868$	−50.2438	−1.70539
$869$	16.5936	0.562901
$870$	−27.7487	−0.940770
$871$	−11.5466	−0.391241
$872$	−33.7547	−1.14308
$873$	−9.93585	−0.336278
$874$	−0.268756	−0.00909080
$875$	1.61485	0.0545918
$876$	−6.55261	−0.221392
$877$	−27.0578	−0.913676	−0.456838	−	0.889550i	$-0.651018\pi$
$877$	−27.0578	−0.913676	−0.456838	+	0.889550i	$0.651018\pi$
$878$	−76.4475	−2.57998
$879$	8.91630	0.300739
$880$	19.6121	0.661125
$881$	−36.8510	−1.24154	−0.620771	−	0.783992i	$-0.713180\pi$
$881$	−36.8510	−1.24154	−0.620771	+	0.783992i	$0.713180\pi$
$882$	15.7331	0.529760
$883$	20.6901	0.696277	0.348138	−	0.937443i	$-0.386814\pi$
$883$	20.6901	0.696277	0.348138	+	0.937443i	$0.386814\pi$
$884$	0	0
$885$	−15.9112	−0.534848
$886$	66.5851	2.23697
$887$	−14.9256	−0.501152	−0.250576	−	0.968097i	$-0.580620\pi$
$887$	−14.9256	−0.501152	−0.250576	+	0.968097i	$0.580620\pi$
$888$	4.52587	0.151878
$889$	24.5128	0.822134
$890$	−26.6067	−0.891860
$891$	8.84054	0.296169
$892$	52.4770	1.75706
$893$	−8.91433	−0.298307
$894$	−3.98436	−0.133257
$895$	8.76138	0.292861
$896$	24.9108	0.832213
$897$	1.14165	0.0381186
$898$	−39.7925	−1.32789
$899$	−63.5249	−2.11867
$900$	−6.14750	−0.204917
$901$	0	0
$902$	−52.5352	−1.74923
$903$	−5.56779	−0.185285
$904$	−53.9943	−1.79582
$905$	−4.86717	−0.161790
$906$	51.1296	1.69867
$907$	−27.3287	−0.907435	−0.453717	−	0.891146i	$-0.649902\pi$
$907$	−27.3287	−0.907435	−0.453717	+	0.891146i	$0.649902\pi$
$908$	−3.60298	−0.119569
$909$	0.968706	0.0321299
$910$	−25.7832	−0.854703
$911$	−47.3659	−1.56930	−0.784650	−	0.619939i	$-0.787157\pi$
$911$	−47.3659	−1.56930	−0.784650	+	0.619939i	$0.787157\pi$
$912$	5.59393	0.185233
$913$	11.7826	0.389947
$914$	−10.6860	−0.353463
$915$	−0.582285	−0.0192497
$916$	26.4486	0.873888
$917$	3.20145	0.105721
$918$	0	0
$919$	25.7946	0.850884	0.425442	−	0.904986i	$-0.360119\pi$
$919$	25.7946	0.850884	0.425442	+	0.904986i	$0.360119\pi$
$920$	−0.831507	−0.0274140
$921$	−6.02888	−0.198658
$922$	−60.2300	−1.98357
$923$	27.0567	0.890583
$924$	−28.7123	−0.944565
$925$	−0.621115	−0.0204222
$926$	−57.8150	−1.89992
$927$	0.223071	0.00732660
$928$	−29.7200	−0.975606
$929$	−24.7022	−0.810452	−0.405226	−	0.914217i	$-0.632807\pi$
$929$	−24.7022	−0.810452	−0.405226	+	0.914217i	$0.632807\pi$
$930$	22.7463	0.745879
$931$	3.28175	0.107555
$932$	72.5958	2.37796
$933$	−10.0742	−0.329815
$934$	54.7292	1.79080
$935$	0	0
$936$	52.6239	1.72007
$937$	37.0383	1.20999	0.604994	−	0.796230i	$-0.293175\pi$
$937$	37.0383	1.20999	0.604994	+	0.796230i	$0.293175\pi$
$938$	−7.37098	−0.240671
$939$	27.7309	0.904964
$940$	−51.4418	−1.67785
$941$	34.2914	1.11787	0.558934	−	0.829212i	$-0.311210\pi$
$941$	34.2914	1.11787	0.558934	+	0.829212i	$0.311210\pi$
$942$	−26.8757	−0.875657
$943$	0.910938	0.0296642
$944$	−75.6721	−2.46292
$945$	8.96715	0.291701
$946$	22.6908	0.737740
$947$	−37.1012	−1.20563	−0.602814	−	0.797882i	$-0.705954\pi$
$947$	−37.1012	−1.20563	−0.602814	+	0.797882i	$0.705954\pi$
$948$	27.3125	0.887068
$949$	−7.69784	−0.249882
$950$	−1.87711	−0.0609015
$951$	20.0306	0.649537
$952$	0	0
$953$	26.9203	0.872033	0.436016	−	0.899939i	$-0.356389\pi$
$953$	26.9203	0.872033	0.436016	+	0.899939i	$0.356389\pi$
$954$	−9.72168	−0.314751
$955$	11.2751	0.364854
$956$	29.9791	0.969592
$957$	−36.3019	−1.17347
$958$	−82.7311	−2.67292
$959$	−31.6653	−1.02253
$960$	−4.33191	−0.139812
$961$	21.0728	0.679768
$962$	9.91692	0.319734
$963$	25.6144	0.825413
$964$	−132.461	−4.26628
$965$	−4.58171	−0.147490
$966$	0.728794	0.0234486
$967$	26.4462	0.850452	0.425226	−	0.905087i	$-0.360195\pi$
$967$	26.4462	0.850452	0.425226	+	0.905087i	$0.360195\pi$
$968$	−1.14810	−0.0369014
$969$	0	0
$970$	−17.5075	−0.562132
$971$	9.69327	0.311072	0.155536	−	0.987830i	$-0.450290\pi$
$971$	9.69327	0.311072	0.155536	+	0.987830i	$0.450290\pi$
$972$	−57.2760	−1.83713
$973$	5.83185	0.186961
$974$	−46.8506	−1.50119
$975$	7.97379	0.255366
$976$	−2.76930	−0.0886431
$977$	5.81399	0.186006	0.0930029	−	0.995666i	$-0.470353\pi$
$977$	5.81399	0.186006	0.0930029	+	0.995666i	$0.470353\pi$
$978$	−48.7329	−1.55831
$979$	−34.8079	−1.11247
$980$	18.9380	0.604952
$981$	8.28686	0.264579
$982$	−9.98153	−0.318523
$983$	31.6929	1.01085	0.505423	−	0.862872i	$-0.331337\pi$
$983$	31.6929	1.01085	0.505423	+	0.862872i	$0.331337\pi$
$984$	−46.3608	−1.47793
$985$	−13.2481	−0.422119
$986$	0	0
$987$	24.1733	0.769443
$988$	20.4736	0.651353
$989$	−0.393448	−0.0125109
$990$	−11.7729	−0.374167
$991$	−48.4673	−1.53961	−0.769807	−	0.638277i	$-0.779648\pi$
$991$	−48.4673	−1.53961	−0.769807	+	0.638277i	$0.779648\pi$
$992$	24.3622	0.773499
$993$	−4.86704	−0.154451
$994$	17.2722	0.547840
$995$	−2.63839	−0.0836426
$996$	19.3937	0.614512
$997$	6.08879	0.192834	0.0964170	−	0.995341i	$-0.469262\pi$
$997$	6.08879	0.192834	0.0964170	+	0.995341i	$0.469262\pi$
$998$	−85.7414	−2.71410
$999$	−3.44901	−0.109122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.a.n.1.6		6
5.4	even	2		7225.2.a.bb.1.1		6
17.2	even	8		85.2.e.a.21.6	✓	12
17.4	even	4		1445.2.d.g.866.2		12
17.9	even	8		85.2.e.a.81.1	yes	12
17.13	even	4		1445.2.d.g.866.1		12
17.16	even	2		1445.2.a.o.1.6		6
51.2	odd	8		765.2.k.b.361.1		12
51.26	odd	8		765.2.k.b.676.6		12
68.19	odd	8		1360.2.bt.d.1041.4		12
68.43	odd	8		1360.2.bt.d.81.4		12
85.2	odd	8		425.2.j.b.174.1		12
85.9	even	8		425.2.e.f.251.6		12
85.19	even	8		425.2.e.f.276.1		12
85.43	odd	8		425.2.j.b.149.1		12
85.53	odd	8		425.2.j.c.174.6		12
85.77	odd	8		425.2.j.c.149.6		12
85.84	even	2		7225.2.a.z.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.6	✓	12	17.2	even	8
85.2.e.a.81.1	yes	12	17.9	even	8
425.2.e.f.251.6		12	85.9	even	8
425.2.e.f.276.1		12	85.19	even	8
425.2.j.b.149.1		12	85.43	odd	8
425.2.j.b.174.1		12	85.2	odd	8
425.2.j.c.149.6		12	85.77	odd	8
425.2.j.c.174.6		12	85.53	odd	8
765.2.k.b.361.1		12	51.2	odd	8
765.2.k.b.676.6		12	51.26	odd	8
1360.2.bt.d.81.4		12	68.43	odd	8
1360.2.bt.d.1041.4		12	68.19	odd	8
1445.2.a.n.1.6		6	1.1	even	1	trivial
1445.2.a.o.1.6		6	17.16	even	2
1445.2.d.g.866.1		12	17.13	even	4
1445.2.d.g.866.2		12	17.4	even	4
7225.2.a.z.1.1		6	85.84	even	2
7225.2.a.bb.1.1		6	5.4	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.a (trivial)

\(f(q)\)	\(=\)	\(q+2.51230 q^{2} -1.25468 q^{3} +4.31167 q^{4} -1.00000 q^{5} -3.15213 q^{6} -1.61485 q^{7} +5.80761 q^{8} -1.42578 q^{9} -2.51230 q^{10} -3.28669 q^{11} -5.40976 q^{12} -6.35524 q^{13} -4.05699 q^{14} +1.25468 q^{15} +5.96715 q^{16} -3.58200 q^{18} -0.747167 q^{19} -4.31167 q^{20} +2.02612 q^{21} -8.25715 q^{22} +0.143175 q^{23} -7.28669 q^{24} +1.00000 q^{25} -15.9663 q^{26} +5.55293 q^{27} -6.96269 q^{28} -8.80316 q^{29} +3.15213 q^{30} +7.21615 q^{31} +3.37606 q^{32} +4.12374 q^{33} +1.61485 q^{35} -6.14750 q^{36} -0.621115 q^{37} -1.87711 q^{38} +7.97379 q^{39} -5.80761 q^{40} +6.36239 q^{41} +5.09022 q^{42} -2.74801 q^{43} -14.1711 q^{44} +1.42578 q^{45} +0.359700 q^{46} +11.9308 q^{47} -7.48685 q^{48} -4.39226 q^{49} +2.51230 q^{50} -27.4017 q^{52} +2.71404 q^{53} +13.9507 q^{54} +3.28669 q^{55} -9.37841 q^{56} +0.937454 q^{57} -22.1162 q^{58} -12.6815 q^{59} +5.40976 q^{60} -0.464091 q^{61} +18.1292 q^{62} +2.30242 q^{63} -3.45261 q^{64} +6.35524 q^{65} +10.3601 q^{66} +1.81686 q^{67} -0.179639 q^{69} +4.05699 q^{70} -4.25738 q^{71} -8.28039 q^{72} +1.21126 q^{73} -1.56043 q^{74} -1.25468 q^{75} -3.22154 q^{76} +5.30750 q^{77} +20.0326 q^{78} -5.04874 q^{79} -5.96715 q^{80} -2.68980 q^{81} +15.9843 q^{82} -3.58494 q^{83} +8.73594 q^{84} -6.90384 q^{86} +11.0451 q^{87} -19.0878 q^{88} +10.5906 q^{89} +3.58200 q^{90} +10.2628 q^{91} +0.617325 q^{92} -9.05395 q^{93} +29.9739 q^{94} +0.747167 q^{95} -4.23587 q^{96} +6.96870 q^{97} -11.0347 q^{98} +4.68610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 4 q^{3} + 6 q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} + 6 q^{8} + 2 q^{9} - 2 q^{10} - 8 q^{12} - 8 q^{14} + 4 q^{15} + 2 q^{16} + 14 q^{18} - 12 q^{19} - 6 q^{20} + 8 q^{21} - 16 q^{22} - 24 q^{24}+ \cdots - 20 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 - 4 * q^3 + 6 * q^4 - 6 * q^5 - 4 * q^6 - 8 * q^7 + 6 * q^8 + 2 * q^9 - 2 * q^10 - 8 * q^12 - 8 * q^14 + 4 * q^15 + 2 * q^16 + 14 * q^18 - 12 * q^19 - 6 * q^20 + 8 * q^21 - 16 * q^22 - 24 * q^24 + 6 * q^25 - 12 * q^26 + 8 * q^27 + 8 * q^28 - 8 * q^29 + 4 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 8 * q^35 - 10 * q^36 - 16 * q^37 - 12 * q^38 - 28 * q^39 - 6 * q^40 - 12 * q^41 - 8 * q^42 + 8 * q^43 + 4 * q^44 - 2 * q^45 - 20 * q^46 + 24 * q^47 - 8 * q^48 - 10 * q^49 + 2 * q^50 - 28 * q^52 + 12 * q^54 - 20 * q^56 + 16 * q^57 - 48 * q^58 - 16 * q^59 + 8 * q^60 + 4 * q^61 + 40 * q^62 - 20 * q^63 - 14 * q^64 - 16 * q^66 - 4 * q^67 + 8 * q^70 - 32 * q^71 - 10 * q^72 + 8 * q^73 + 8 * q^74 - 4 * q^75 - 36 * q^76 + 24 * q^77 - 4 * q^78 - 36 * q^79 - 2 * q^80 - 14 * q^81 + 28 * q^82 + 20 * q^83 - 48 * q^86 + 24 * q^87 - 12 * q^88 - 12 * q^89 - 14 * q^90 - 12 * q^91 - 28 * q^92 + 36 * q^93 + 20 * q^94 + 12 * q^95 + 44 * q^96 - 16 * q^97 - 22 * q^98 - 20 * q^99

Introduction

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Database

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