LMFDB - Embedded newform 5415.2.a.o.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5415,2,Mod(1,5415)] 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("5415.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5415, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5415 = 3 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5415.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,-2,2,2,-2,-2,-2,-6,2,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	yes
Analytic conductor:	$43.2389926945$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	5415.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.414214 q^{2} +1.00000 q^{3} -1.82843 q^{4} -1.00000 q^{5} +0.414214 q^{6} +1.82843 q^{7} -1.58579 q^{8} +1.00000 q^{9} -0.414214 q^{10} -2.82843 q^{11} -1.82843 q^{12} +1.82843 q^{13} +0.757359 q^{14} -1.00000 q^{15} +3.00000 q^{16} -1.17157 q^{17} +0.414214 q^{18} +1.82843 q^{20} +1.82843 q^{21} -1.17157 q^{22} -0.828427 q^{23} -1.58579 q^{24} +1.00000 q^{25} +0.757359 q^{26} +1.00000 q^{27} -3.34315 q^{28} -9.65685 q^{29} -0.414214 q^{30} +5.00000 q^{31} +4.41421 q^{32} -2.82843 q^{33} -0.485281 q^{34} -1.82843 q^{35} -1.82843 q^{36} +2.17157 q^{37} +1.82843 q^{39} +1.58579 q^{40} -2.82843 q^{41} +0.757359 q^{42} +7.82843 q^{43} +5.17157 q^{44} -1.00000 q^{45} -0.343146 q^{46} -3.17157 q^{47} +3.00000 q^{48} -3.65685 q^{49} +0.414214 q^{50} -1.17157 q^{51} -3.34315 q^{52} +2.00000 q^{53} +0.414214 q^{54} +2.82843 q^{55} -2.89949 q^{56} -4.00000 q^{58} +1.82843 q^{60} -8.31371 q^{61} +2.07107 q^{62} +1.82843 q^{63} -4.17157 q^{64} -1.82843 q^{65} -1.17157 q^{66} -5.48528 q^{67} +2.14214 q^{68} -0.828427 q^{69} -0.757359 q^{70} -10.0000 q^{71} -1.58579 q^{72} +9.48528 q^{73} +0.899495 q^{74} +1.00000 q^{75} -5.17157 q^{77} +0.757359 q^{78} +3.34315 q^{79} -3.00000 q^{80} +1.00000 q^{81} -1.17157 q^{82} -8.00000 q^{83} -3.34315 q^{84} +1.17157 q^{85} +3.24264 q^{86} -9.65685 q^{87} +4.48528 q^{88} -12.4853 q^{89} -0.414214 q^{90} +3.34315 q^{91} +1.51472 q^{92} +5.00000 q^{93} -1.31371 q^{94} +4.41421 q^{96} +6.00000 q^{97} -1.51472 q^{98} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} + 6 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{20} - 2 q^{21} - 8 q^{22}+ \cdots - 20 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 - 2 * q^13 + 10 * q^14 - 2 * q^15 + 6 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^20 - 2 * q^21 - 8 * q^22 + 4 * q^23 - 6 * q^24 + 2 * q^25 + 10 * q^26 + 2 * q^27 - 18 * q^28 - 8 * q^29 + 2 * q^30 + 10 * q^31 + 6 * q^32 + 16 * q^34 + 2 * q^35 + 2 * q^36 + 10 * q^37 - 2 * q^39 + 6 * q^40 + 10 * q^42 + 10 * q^43 + 16 * q^44 - 2 * q^45 - 12 * q^46 - 12 * q^47 + 6 * q^48 + 4 * q^49 - 2 * q^50 - 8 * q^51 - 18 * q^52 + 4 * q^53 - 2 * q^54 + 14 * q^56 - 8 * q^58 - 2 * q^60 + 6 * q^61 - 10 * q^62 - 2 * q^63 - 14 * q^64 + 2 * q^65 - 8 * q^66 + 6 * q^67 - 24 * q^68 + 4 * q^69 - 10 * q^70 - 20 * q^71 - 6 * q^72 + 2 * q^73 - 18 * q^74 + 2 * q^75 - 16 * q^77 + 10 * q^78 + 18 * q^79 - 6 * q^80 + 2 * q^81 - 8 * q^82 - 16 * q^83 - 18 * q^84 + 8 * q^85 - 2 * q^86 - 8 * q^87 - 8 * q^88 - 8 * q^89 + 2 * q^90 + 18 * q^91 + 20 * q^92 + 10 * q^93 + 20 * q^94 + 6 * q^96 + 12 * q^97 - 20 * q^98

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 $

$2$	0.414214	0.292893	0.146447	−	0.989219i	$-0.453216\pi$
$2$	0.414214	0.292893	0.146447	+	0.989219i	$0.453216\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.82843	−0.914214
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.414214	0.169102
$7$	1.82843	0.691080	0.345540	−	0.938404i	$-0.387696\pi$
$7$	1.82843	0.691080	0.345540	+	0.938404i	$0.387696\pi$
$8$	−1.58579	−0.560660
$9$	1.00000	0.333333
$10$	−0.414214	−0.130986
$11$	−2.82843	−0.852803	−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843	−0.852803	−0.426401	+	0.904534i	$0.640219\pi$
$12$	−1.82843	−0.527821
$13$	1.82843	0.507114	0.253557	−	0.967320i	$-0.418399\pi$
$13$	1.82843	0.507114	0.253557	+	0.967320i	$0.418399\pi$
$14$	0.757359	0.202413
$15$	−1.00000	−0.258199
$16$	3.00000	0.750000
$17$	−1.17157	−0.284148	−0.142074	−	0.989856i	$-0.545377\pi$
$17$	−1.17157	−0.284148	−0.142074	+	0.989856i	$0.545377\pi$
$18$	0.414214	0.0976311
$19$	0	0
$19$	0	0
$20$	1.82843	0.408849
$21$	1.82843	0.398996
$22$	−1.17157	−0.249780
$23$	−0.828427	−0.172739	−0.0863695	−	0.996263i	$-0.527527\pi$
$23$	−0.828427	−0.172739	−0.0863695	+	0.996263i	$0.527527\pi$
$24$	−1.58579	−0.323697
$25$	1.00000	0.200000
$26$	0.757359	0.148530
$27$	1.00000	0.192450
$28$	−3.34315	−0.631795
$29$	−9.65685	−1.79323	−0.896616	−	0.442808i	$-0.853982\pi$
$29$	−9.65685	−1.79323	−0.896616	+	0.442808i	$0.853982\pi$
$30$	−0.414214	−0.0756247
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	4.41421	0.780330
$33$	−2.82843	−0.492366
$34$	−0.485281	−0.0832251
$35$	−1.82843	−0.309061
$36$	−1.82843	−0.304738
$37$	2.17157	0.357004	0.178502	−	0.983940i	$-0.442875\pi$
$37$	2.17157	0.357004	0.178502	+	0.983940i	$0.442875\pi$
$38$	0	0
$39$	1.82843	0.292783
$40$	1.58579	0.250735
$41$	−2.82843	−0.441726	−0.220863	−	0.975305i	$-0.570887\pi$
$41$	−2.82843	−0.441726	−0.220863	+	0.975305i	$0.570887\pi$
$42$	0.757359	0.116863
$43$	7.82843	1.19382	0.596912	−	0.802307i	$-0.296394\pi$
$43$	7.82843	1.19382	0.596912	+	0.802307i	$0.296394\pi$
$44$	5.17157	0.779644
$45$	−1.00000	−0.149071
$46$	−0.343146	−0.0505941
$47$	−3.17157	−0.462621	−0.231311	−	0.972880i	$-0.574301\pi$
$47$	−3.17157	−0.462621	−0.231311	+	0.972880i	$0.574301\pi$
$48$	3.00000	0.433013
$49$	−3.65685	−0.522408
$50$	0.414214	0.0585786
$51$	−1.17157	−0.164053
$52$	−3.34315	−0.463611
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	0.414214	0.0563673
$55$	2.82843	0.381385
$56$	−2.89949	−0.387461
$57$	0	0
$58$	−4.00000	−0.525226
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	1.82843	0.236049
$61$	−8.31371	−1.06446	−0.532231	−	0.846599i	$-0.678646\pi$
$61$	−8.31371	−1.06446	−0.532231	+	0.846599i	$0.678646\pi$
$62$	2.07107	0.263026
$63$	1.82843	0.230360
$64$	−4.17157	−0.521447
$65$	−1.82843	−0.226788
$66$	−1.17157	−0.144211
$67$	−5.48528	−0.670134	−0.335067	−	0.942194i	$-0.608759\pi$
$67$	−5.48528	−0.670134	−0.335067	+	0.942194i	$0.608759\pi$
$68$	2.14214	0.259772
$69$	−0.828427	−0.0997309
$70$	−0.757359	−0.0905218
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	−1.58579	−0.186887
$73$	9.48528	1.11017	0.555084	−	0.831794i	$-0.312686\pi$
$73$	9.48528	1.11017	0.555084	+	0.831794i	$0.312686\pi$
$74$	0.899495	0.104564
$75$	1.00000	0.115470
$76$	0	0
$77$	−5.17157	−0.589355
$78$	0.757359	0.0857541
$79$	3.34315	0.376133	0.188067	−	0.982156i	$-0.439778\pi$
$79$	3.34315	0.376133	0.188067	+	0.982156i	$0.439778\pi$
$80$	−3.00000	−0.335410
$81$	1.00000	0.111111
$82$	−1.17157	−0.129379
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	−3.34315	−0.364767
$85$	1.17157	0.127075
$86$	3.24264	0.349663
$87$	−9.65685	−1.03532
$88$	4.48528	0.478133
$89$	−12.4853	−1.32344	−0.661719	−	0.749752i	$-0.730173\pi$
$89$	−12.4853	−1.32344	−0.661719	+	0.749752i	$0.730173\pi$
$90$	−0.414214	−0.0436619
$91$	3.34315	0.350457
$92$	1.51472	0.157920
$93$	5.00000	0.518476
$94$	−1.31371	−0.135499
$95$	0	0
$96$	4.41421	0.450524
$97$	6.00000	0.609208	0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000	0.609208	0.304604	+	0.952479i	$0.401476\pi$
$98$	−1.51472	−0.153010
$99$	−2.82843	−0.284268
$100$	−1.82843	−0.182843
$101$	12.1421	1.20819	0.604094	−	0.796913i	$-0.293535\pi$
$101$	12.1421	1.20819	0.604094	+	0.796913i	$0.293535\pi$
$102$	−0.485281	−0.0480500
$103$	−9.82843	−0.968424	−0.484212	−	0.874951i	$-0.660894\pi$
$103$	−9.82843	−0.968424	−0.484212	+	0.874951i	$0.660894\pi$
$104$	−2.89949	−0.284319
$105$	−1.82843	−0.178436
$106$	0.828427	0.0804640
$107$	−14.0000	−1.35343	−0.676716	−	0.736245i	$-0.736597\pi$
$107$	−14.0000	−1.35343	−0.676716	+	0.736245i	$0.736597\pi$
$108$	−1.82843	−0.175940
$109$	17.3137	1.65835	0.829176	−	0.558987i	$-0.188810\pi$
$109$	17.3137	1.65835	0.829176	+	0.558987i	$0.188810\pi$
$110$	1.17157	0.111705
$111$	2.17157	0.206117
$112$	5.48528	0.518310
$113$	−4.00000	−0.376288	−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000	−0.376288	−0.188144	+	0.982141i	$0.560247\pi$
$114$	0	0
$115$	0.828427	0.0772512
$116$	17.6569	1.63940
$117$	1.82843	0.169038
$118$	0	0
$119$	−2.14214	−0.196369
$120$	1.58579	0.144762
$121$	−3.00000	−0.272727
$122$	−3.44365	−0.311773
$123$	−2.82843	−0.255031
$124$	−9.14214	−0.820988
$125$	−1.00000	−0.0894427
$126$	0.757359	0.0674709
$127$	−12.9706	−1.15095	−0.575476	−	0.817819i	$-0.695183\pi$
$127$	−12.9706	−1.15095	−0.575476	+	0.817819i	$0.695183\pi$
$128$	−10.5563	−0.933058
$129$	7.82843	0.689255
$130$	−0.757359	−0.0664248
$131$	6.48528	0.566622	0.283311	−	0.959028i	$-0.408567\pi$
$131$	6.48528	0.566622	0.283311	+	0.959028i	$0.408567\pi$
$132$	5.17157	0.450128
$133$	0	0
$134$	−2.27208	−0.196278
$135$	−1.00000	−0.0860663
$136$	1.85786	0.159311
$137$	−10.4853	−0.895818	−0.447909	−	0.894079i	$-0.647831\pi$
$137$	−10.4853	−0.895818	−0.447909	+	0.894079i	$0.647831\pi$
$138$	−0.343146	−0.0292105
$139$	−16.3137	−1.38371	−0.691855	−	0.722036i	$-0.743206\pi$
$139$	−16.3137	−1.38371	−0.691855	+	0.722036i	$0.743206\pi$
$140$	3.34315	0.282547
$141$	−3.17157	−0.267095
$142$	−4.14214	−0.347600
$143$	−5.17157	−0.432469
$144$	3.00000	0.250000
$145$	9.65685	0.801958
$146$	3.92893	0.325161
$147$	−3.65685	−0.301612
$148$	−3.97056	−0.326378
$149$	−1.17157	−0.0959790	−0.0479895	−	0.998848i	$-0.515281\pi$
$149$	−1.17157	−0.0959790	−0.0479895	+	0.998848i	$0.515281\pi$
$150$	0.414214	0.0338204
$151$	−10.3431	−0.841713	−0.420857	−	0.907127i	$-0.638270\pi$
$151$	−10.3431	−0.841713	−0.420857	+	0.907127i	$0.638270\pi$
$152$	0	0
$153$	−1.17157	−0.0947161
$154$	−2.14214	−0.172618
$155$	−5.00000	−0.401610
$156$	−3.34315	−0.267666
$157$	−19.8284	−1.58248	−0.791240	−	0.611505i	$-0.790564\pi$
$157$	−19.8284	−1.58248	−0.791240	+	0.611505i	$0.790564\pi$
$158$	1.38478	0.110167
$159$	2.00000	0.158610
$160$	−4.41421	−0.348974
$161$	−1.51472	−0.119377
$162$	0.414214	0.0325437
$163$	15.1421	1.18602	0.593012	−	0.805194i	$-0.297939\pi$
$163$	15.1421	1.18602	0.593012	+	0.805194i	$0.297939\pi$
$164$	5.17157	0.403832
$165$	2.82843	0.220193
$166$	−3.31371	−0.257194
$167$	24.9706	1.93228	0.966140	−	0.258018i	$-0.0830694\pi$
$167$	24.9706	1.93228	0.966140	+	0.258018i	$0.0830694\pi$
$168$	−2.89949	−0.223701
$169$	−9.65685	−0.742835
$170$	0.485281	0.0372194
$171$	0	0
$172$	−14.3137	−1.09141
$173$	−7.31371	−0.556051	−0.278025	−	0.960574i	$-0.589680\pi$
$173$	−7.31371	−0.556051	−0.278025	+	0.960574i	$0.589680\pi$
$174$	−4.00000	−0.303239
$175$	1.82843	0.138216
$176$	−8.48528	−0.639602
$177$	0	0
$178$	−5.17157	−0.387626
$179$	−16.1421	−1.20652	−0.603260	−	0.797545i	$-0.706132\pi$
$179$	−16.1421	−1.20652	−0.603260	+	0.797545i	$0.706132\pi$
$180$	1.82843	0.136283
$181$	−25.3137	−1.88155	−0.940777	−	0.339027i	$-0.889902\pi$
$181$	−25.3137	−1.88155	−0.940777	+	0.339027i	$0.889902\pi$
$182$	1.38478	0.102646
$183$	−8.31371	−0.614567
$184$	1.31371	0.0968479
$185$	−2.17157	−0.159657
$186$	2.07107	0.151858
$187$	3.31371	0.242322
$188$	5.79899	0.422935
$189$	1.82843	0.132999
$190$	0	0
$191$	−16.8284	−1.21766	−0.608831	−	0.793300i	$-0.708361\pi$
$191$	−16.8284	−1.21766	−0.608831	+	0.793300i	$0.708361\pi$
$192$	−4.17157	−0.301057
$193$	24.7990	1.78507	0.892535	−	0.450978i	$-0.148925\pi$
$193$	24.7990	1.78507	0.892535	+	0.450978i	$0.148925\pi$
$194$	2.48528	0.178433
$195$	−1.82843	−0.130936
$196$	6.68629	0.477592
$197$	17.6569	1.25800	0.628999	−	0.777406i	$-0.283465\pi$
$197$	17.6569	1.25800	0.628999	+	0.777406i	$0.283465\pi$
$198$	−1.17157	−0.0832601
$199$	−17.0000	−1.20510	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	−17.0000	−1.20510	−0.602549	+	0.798082i	$0.705848\pi$
$200$	−1.58579	−0.112132
$201$	−5.48528	−0.386902
$202$	5.02944	0.353870
$203$	−17.6569	−1.23927
$204$	2.14214	0.149979
$205$	2.82843	0.197546
$206$	−4.07107	−0.283645
$207$	−0.828427	−0.0575797
$208$	5.48528	0.380336
$209$	0	0
$210$	−0.757359	−0.0522628
$211$	0.313708	0.0215966	0.0107983	−	0.999942i	$-0.496563\pi$
$211$	0.313708	0.0215966	0.0107983	+	0.999942i	$0.496563\pi$
$212$	−3.65685	−0.251154
$213$	−10.0000	−0.685189
$214$	−5.79899	−0.396411
$215$	−7.82843	−0.533894
$216$	−1.58579	−0.107899
$217$	9.14214	0.620609
$218$	7.17157	0.485720
$219$	9.48528	0.640956
$220$	−5.17157	−0.348667
$221$	−2.14214	−0.144096
$222$	0.899495	0.0603701
$223$	−5.82843	−0.390300	−0.195150	−	0.980773i	$-0.562519\pi$
$223$	−5.82843	−0.390300	−0.195150	+	0.980773i	$0.562519\pi$
$224$	8.07107	0.539271
$225$	1.00000	0.0666667
$226$	−1.65685	−0.110212
$227$	18.9706	1.25912	0.629560	−	0.776952i	$-0.283235\pi$
$227$	18.9706	1.25912	0.629560	+	0.776952i	$0.283235\pi$
$228$	0	0
$229$	−4.65685	−0.307734	−0.153867	−	0.988092i	$-0.549173\pi$
$229$	−4.65685	−0.307734	−0.153867	+	0.988092i	$0.549173\pi$
$230$	0.343146	0.0226264
$231$	−5.17157	−0.340265
$232$	15.3137	1.00539
$233$	−25.3137	−1.65836	−0.829178	−	0.558985i	$-0.811191\pi$
$233$	−25.3137	−1.65836	−0.829178	+	0.558985i	$0.811191\pi$
$234$	0.757359	0.0495101
$235$	3.17157	0.206891
$236$	0	0
$237$	3.34315	0.217161
$238$	−0.887302	−0.0575152
$239$	−24.6274	−1.59302	−0.796508	−	0.604629i	$-0.793322\pi$
$239$	−24.6274	−1.59302	−0.796508	+	0.604629i	$0.793322\pi$
$240$	−3.00000	−0.193649
$241$	−5.00000	−0.322078	−0.161039	−	0.986948i	$-0.551485\pi$
$241$	−5.00000	−0.322078	−0.161039	+	0.986948i	$0.551485\pi$
$242$	−1.24264	−0.0798800
$243$	1.00000	0.0641500
$244$	15.2010	0.973145
$245$	3.65685	0.233628
$246$	−1.17157	−0.0746968
$247$	0	0
$248$	−7.92893	−0.503488
$249$	−8.00000	−0.506979
$250$	−0.414214	−0.0261972
$251$	−16.3431	−1.03157	−0.515785	−	0.856718i	$-0.672500\pi$
$251$	−16.3431	−1.03157	−0.515785	+	0.856718i	$0.672500\pi$
$252$	−3.34315	−0.210598
$253$	2.34315	0.147312
$254$	−5.37258	−0.337106
$255$	1.17157	0.0733667
$256$	3.97056	0.248160
$257$	16.8284	1.04973	0.524864	−	0.851186i	$-0.324116\pi$
$257$	16.8284	1.04973	0.524864	+	0.851186i	$0.324116\pi$
$258$	3.24264	0.201878
$259$	3.97056	0.246719
$260$	3.34315	0.207333
$261$	−9.65685	−0.597744
$262$	2.68629	0.165960
$263$	25.7990	1.59083	0.795417	−	0.606063i	$-0.207252\pi$
$263$	25.7990	1.59083	0.795417	+	0.606063i	$0.207252\pi$
$264$	4.48528	0.276050
$265$	−2.00000	−0.122859
$266$	0	0
$267$	−12.4853	−0.764087
$268$	10.0294	0.612645
$269$	−1.65685	−0.101020	−0.0505101	−	0.998724i	$-0.516085\pi$
$269$	−1.65685	−0.101020	−0.0505101	+	0.998724i	$0.516085\pi$
$270$	−0.414214	−0.0252082
$271$	13.6569	0.829595	0.414797	−	0.909914i	$-0.363852\pi$
$271$	13.6569	0.829595	0.414797	+	0.909914i	$0.363852\pi$
$272$	−3.51472	−0.213111
$273$	3.34315	0.202336
$274$	−4.34315	−0.262379
$275$	−2.82843	−0.170561
$276$	1.51472	0.0911753
$277$	6.00000	0.360505	0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000	0.360505	0.180253	+	0.983620i	$0.442309\pi$
$278$	−6.75736	−0.405279
$279$	5.00000	0.299342
$280$	2.89949	0.173278
$281$	6.97056	0.415829	0.207914	−	0.978147i	$-0.433332\pi$
$281$	6.97056	0.415829	0.207914	+	0.978147i	$0.433332\pi$
$282$	−1.31371	−0.0782302
$283$	−20.9706	−1.24657	−0.623285	−	0.781995i	$-0.714202\pi$
$283$	−20.9706	−1.24657	−0.623285	+	0.781995i	$0.714202\pi$
$284$	18.2843	1.08497
$285$	0	0
$286$	−2.14214	−0.126667
$287$	−5.17157	−0.305268
$288$	4.41421	0.260110
$289$	−15.6274	−0.919260
$290$	4.00000	0.234888
$291$	6.00000	0.351726
$292$	−17.3431	−1.01493
$293$	5.31371	0.310430	0.155215	−	0.987881i	$-0.450393\pi$
$293$	5.31371	0.310430	0.155215	+	0.987881i	$0.450393\pi$
$294$	−1.51472	−0.0883402
$295$	0	0
$296$	−3.44365	−0.200158
$297$	−2.82843	−0.164122
$298$	−0.485281	−0.0281116
$299$	−1.51472	−0.0875984
$300$	−1.82843	−0.105564
$301$	14.3137	0.825028
$302$	−4.28427	−0.246532
$303$	12.1421	0.697547
$304$	0	0
$305$	8.31371	0.476042
$306$	−0.485281	−0.0277417
$307$	17.6569	1.00773	0.503865	−	0.863782i	$-0.331911\pi$
$307$	17.6569	1.00773	0.503865	+	0.863782i	$0.331911\pi$
$308$	9.45584	0.538797
$309$	−9.82843	−0.559120
$310$	−2.07107	−0.117629
$311$	−4.00000	−0.226819	−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000	−0.226819	−0.113410	+	0.993548i	$0.536177\pi$
$312$	−2.89949	−0.164152
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−8.21320	−0.463498
$315$	−1.82843	−0.103020
$316$	−6.11270	−0.343866
$317$	−5.31371	−0.298448	−0.149224	−	0.988803i	$-0.547677\pi$
$317$	−5.31371	−0.298448	−0.149224	+	0.988803i	$0.547677\pi$
$318$	0.828427	0.0464559
$319$	27.3137	1.52927
$320$	4.17157	0.233198
$321$	−14.0000	−0.781404
$322$	−0.627417	−0.0349646
$323$	0	0
$324$	−1.82843	−0.101579
$325$	1.82843	0.101423
$326$	6.27208	0.347378
$327$	17.3137	0.957450
$328$	4.48528	0.247658
$329$	−5.79899	−0.319709
$330$	1.17157	0.0644930
$331$	5.34315	0.293686	0.146843	−	0.989160i	$-0.453089\pi$
$331$	5.34315	0.293686	0.146843	+	0.989160i	$0.453089\pi$
$332$	14.6274	0.802784
$333$	2.17157	0.119001
$334$	10.3431	0.565952
$335$	5.48528	0.299693
$336$	5.48528	0.299247
$337$	−17.4853	−0.952484	−0.476242	−	0.879314i	$-0.658001\pi$
$337$	−17.4853	−0.952484	−0.476242	+	0.879314i	$0.658001\pi$
$338$	−4.00000	−0.217571
$339$	−4.00000	−0.217250
$340$	−2.14214	−0.116174
$341$	−14.1421	−0.765840
$342$	0	0
$343$	−19.4853	−1.05211
$344$	−12.4142	−0.669330
$345$	0.828427	0.0446010
$346$	−3.02944	−0.162864
$347$	−35.4558	−1.90337	−0.951685	−	0.307077i	$-0.900649\pi$
$347$	−35.4558	−1.90337	−0.951685	+	0.307077i	$0.900649\pi$
$348$	17.6569	0.946507
$349$	−31.6274	−1.69298	−0.846488	−	0.532407i	$-0.821288\pi$
$349$	−31.6274	−1.69298	−0.846488	+	0.532407i	$0.821288\pi$
$350$	0.757359	0.0404826
$351$	1.82843	0.0975942
$352$	−12.4853	−0.665468
$353$	−1.31371	−0.0699216	−0.0349608	−	0.999389i	$-0.511131\pi$
$353$	−1.31371	−0.0699216	−0.0349608	+	0.999389i	$0.511131\pi$
$354$	0	0
$355$	10.0000	0.530745
$356$	22.8284	1.20990
$357$	−2.14214	−0.113374
$358$	−6.68629	−0.353381
$359$	9.17157	0.484057	0.242029	−	0.970269i	$-0.422187\pi$
$359$	9.17157	0.484057	0.242029	+	0.970269i	$0.422187\pi$
$360$	1.58579	0.0835783
$361$	0	0
$362$	−10.4853	−0.551094
$363$	−3.00000	−0.157459
$364$	−6.11270	−0.320392
$365$	−9.48528	−0.496482
$366$	−3.44365	−0.180003
$367$	−34.1127	−1.78067	−0.890334	−	0.455308i	$-0.849529\pi$
$367$	−34.1127	−1.78067	−0.890334	+	0.455308i	$0.849529\pi$
$368$	−2.48528	−0.129554
$369$	−2.82843	−0.147242
$370$	−0.899495	−0.0467625
$371$	3.65685	0.189854
$372$	−9.14214	−0.473998
$373$	11.6569	0.603569	0.301785	−	0.953376i	$-0.402418\pi$
$373$	11.6569	0.603569	0.301785	+	0.953376i	$0.402418\pi$
$374$	1.37258	0.0709746
$375$	−1.00000	−0.0516398
$376$	5.02944	0.259373
$377$	−17.6569	−0.909374
$378$	0.757359	0.0389544
$379$	−1.68629	−0.0866190	−0.0433095	−	0.999062i	$-0.513790\pi$
$379$	−1.68629	−0.0866190	−0.0433095	+	0.999062i	$0.513790\pi$
$380$	0	0
$381$	−12.9706	−0.664502
$382$	−6.97056	−0.356645
$383$	33.9411	1.73431	0.867155	−	0.498038i	$-0.165946\pi$
$383$	33.9411	1.73431	0.867155	+	0.498038i	$0.165946\pi$
$384$	−10.5563	−0.538701
$385$	5.17157	0.263568
$386$	10.2721	0.522835
$387$	7.82843	0.397941
$388$	−10.9706	−0.556946
$389$	−15.4558	−0.783642	−0.391821	−	0.920041i	$-0.628155\pi$
$389$	−15.4558	−0.783642	−0.391821	+	0.920041i	$0.628155\pi$
$390$	−0.757359	−0.0383504
$391$	0.970563	0.0490835
$392$	5.79899	0.292893
$393$	6.48528	0.327139
$394$	7.31371	0.368459
$395$	−3.34315	−0.168212
$396$	5.17157	0.259881
$397$	−23.8284	−1.19591	−0.597957	−	0.801528i	$-0.704021\pi$
$397$	−23.8284	−1.19591	−0.597957	+	0.801528i	$0.704021\pi$
$398$	−7.04163	−0.352965
$399$	0	0
$400$	3.00000	0.150000
$401$	22.6274	1.12996	0.564980	−	0.825105i	$-0.308884\pi$
$401$	22.6274	1.12996	0.564980	+	0.825105i	$0.308884\pi$
$402$	−2.27208	−0.113321
$403$	9.14214	0.455402
$404$	−22.2010	−1.10454
$405$	−1.00000	−0.0496904
$406$	−7.31371	−0.362973
$407$	−6.14214	−0.304454
$408$	1.85786	0.0919780
$409$	−6.00000	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$409$	−6.00000	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$410$	1.17157	0.0578599
$411$	−10.4853	−0.517201
$412$	17.9706	0.885346
$413$	0	0
$414$	−0.343146	−0.0168647
$415$	8.00000	0.392705
$416$	8.07107	0.395717
$417$	−16.3137	−0.798886
$418$	0	0
$419$	3.31371	0.161885	0.0809426	−	0.996719i	$-0.474207\pi$
$419$	3.31371	0.161885	0.0809426	+	0.996719i	$0.474207\pi$
$420$	3.34315	0.163129
$421$	7.65685	0.373172	0.186586	−	0.982439i	$-0.440258\pi$
$421$	7.65685	0.373172	0.186586	+	0.982439i	$0.440258\pi$
$422$	0.129942	0.00632549
$423$	−3.17157	−0.154207
$424$	−3.17157	−0.154025
$425$	−1.17157	−0.0568296
$426$	−4.14214	−0.200687
$427$	−15.2010	−0.735628
$428$	25.5980	1.23733
$429$	−5.17157	−0.249686
$430$	−3.24264	−0.156374
$431$	2.48528	0.119712	0.0598559	−	0.998207i	$-0.480936\pi$
$431$	2.48528	0.119712	0.0598559	+	0.998207i	$0.480936\pi$
$432$	3.00000	0.144338
$433$	39.8284	1.91403	0.957016	−	0.290035i	$-0.0936670\pi$
$433$	39.8284	1.91403	0.957016	+	0.290035i	$0.0936670\pi$
$434$	3.78680	0.181772
$435$	9.65685	0.463011
$436$	−31.6569	−1.51609
$437$	0	0
$438$	3.92893	0.187732
$439$	−17.0000	−0.811366	−0.405683	−	0.914014i	$-0.632966\pi$
$439$	−17.0000	−0.811366	−0.405683	+	0.914014i	$0.632966\pi$
$440$	−4.48528	−0.213827
$441$	−3.65685	−0.174136
$442$	−0.887302	−0.0422046
$443$	18.1421	0.861959	0.430979	−	0.902362i	$-0.358168\pi$
$443$	18.1421	0.861959	0.430979	+	0.902362i	$0.358168\pi$
$444$	−3.97056	−0.188435
$445$	12.4853	0.591859
$446$	−2.41421	−0.114316
$447$	−1.17157	−0.0554135
$448$	−7.62742	−0.360362
$449$	−13.1716	−0.621605	−0.310802	−	0.950475i	$-0.600598\pi$
$449$	−13.1716	−0.621605	−0.310802	+	0.950475i	$0.600598\pi$
$450$	0.414214	0.0195262
$451$	8.00000	0.376705
$452$	7.31371	0.344008
$453$	−10.3431	−0.485963
$454$	7.85786	0.368788
$455$	−3.34315	−0.156729
$456$	0	0
$457$	−4.17157	−0.195138	−0.0975690	−	0.995229i	$-0.531107\pi$
$457$	−4.17157	−0.195138	−0.0975690	+	0.995229i	$0.531107\pi$
$458$	−1.92893	−0.0901331
$459$	−1.17157	−0.0546843
$460$	−1.51472	−0.0706241
$461$	30.1421	1.40386	0.701930	−	0.712246i	$-0.252322\pi$
$461$	30.1421	1.40386	0.701930	+	0.712246i	$0.252322\pi$
$462$	−2.14214	−0.0996612
$463$	−22.7990	−1.05956	−0.529779	−	0.848135i	$-0.677725\pi$
$463$	−22.7990	−1.05956	−0.529779	+	0.848135i	$0.677725\pi$
$464$	−28.9706	−1.34492
$465$	−5.00000	−0.231869
$466$	−10.4853	−0.485721
$467$	23.7990	1.10129	0.550643	−	0.834741i	$-0.314383\pi$
$467$	23.7990	1.10129	0.550643	+	0.834741i	$0.314383\pi$
$468$	−3.34315	−0.154537
$469$	−10.0294	−0.463116
$470$	1.31371	0.0605969
$471$	−19.8284	−0.913646
$472$	0	0
$473$	−22.1421	−1.01810
$474$	1.38478	0.0636049
$475$	0	0
$476$	3.91674	0.179523
$477$	2.00000	0.0915737
$478$	−10.2010	−0.466583
$479$	2.48528	0.113555	0.0567777	−	0.998387i	$-0.481917\pi$
$479$	2.48528	0.113555	0.0567777	+	0.998387i	$0.481917\pi$
$480$	−4.41421	−0.201480
$481$	3.97056	0.181042
$482$	−2.07107	−0.0943346
$483$	−1.51472	−0.0689221
$484$	5.48528	0.249331
$485$	−6.00000	−0.272446
$486$	0.414214	0.0187891
$487$	6.34315	0.287435	0.143718	−	0.989619i	$-0.454094\pi$
$487$	6.34315	0.287435	0.143718	+	0.989619i	$0.454094\pi$
$488$	13.1838	0.596801
$489$	15.1421	0.684751
$490$	1.51472	0.0684280
$491$	23.6569	1.06762	0.533809	−	0.845605i	$-0.320760\pi$
$491$	23.6569	1.06762	0.533809	+	0.845605i	$0.320760\pi$
$492$	5.17157	0.233153
$493$	11.3137	0.509544
$494$	0	0
$495$	2.82843	0.127128
$496$	15.0000	0.673520
$497$	−18.2843	−0.820162
$498$	−3.31371	−0.148491
$499$	−7.34315	−0.328724	−0.164362	−	0.986400i	$-0.552557\pi$
$499$	−7.34315	−0.328724	−0.164362	+	0.986400i	$0.552557\pi$
$500$	1.82843	0.0817697
$501$	24.9706	1.11560
$502$	−6.76955	−0.302140
$503$	13.8579	0.617892	0.308946	−	0.951080i	$-0.400024\pi$
$503$	13.8579	0.617892	0.308946	+	0.951080i	$0.400024\pi$
$504$	−2.89949	−0.129154
$505$	−12.1421	−0.540318
$506$	0.970563	0.0431468
$507$	−9.65685	−0.428876
$508$	23.7157	1.05222
$509$	−33.1127	−1.46769	−0.733847	−	0.679314i	$-0.762277\pi$
$509$	−33.1127	−1.46769	−0.733847	+	0.679314i	$0.762277\pi$
$510$	0.485281	0.0214886
$511$	17.3431	0.767216
$512$	22.7574	1.00574
$513$	0	0
$514$	6.97056	0.307458
$515$	9.82843	0.433092
$516$	−14.3137	−0.630126
$517$	8.97056	0.394525
$518$	1.64466	0.0722623
$519$	−7.31371	−0.321036
$520$	2.89949	0.127151
$521$	−6.34315	−0.277898	−0.138949	−	0.990300i	$-0.544372\pi$
$521$	−6.34315	−0.277898	−0.138949	+	0.990300i	$0.544372\pi$
$522$	−4.00000	−0.175075
$523$	29.7696	1.30173	0.650866	−	0.759193i	$-0.274406\pi$
$523$	29.7696	1.30173	0.650866	+	0.759193i	$0.274406\pi$
$524$	−11.8579	−0.518013
$525$	1.82843	0.0797991
$526$	10.6863	0.465944
$527$	−5.85786	−0.255173
$528$	−8.48528	−0.369274
$529$	−22.3137	−0.970161
$530$	−0.828427	−0.0359846
$531$	0	0
$532$	0	0
$533$	−5.17157	−0.224006
$534$	−5.17157	−0.223796
$535$	14.0000	0.605273
$536$	8.69848	0.375717
$537$	−16.1421	−0.696585
$538$	−0.686292	−0.0295881
$539$	10.3431	0.445511
$540$	1.82843	0.0786830
$541$	16.3137	0.701381	0.350691	−	0.936491i	$-0.385947\pi$
$541$	16.3137	0.701381	0.350691	+	0.936491i	$0.385947\pi$
$542$	5.65685	0.242983
$543$	−25.3137	−1.08632
$544$	−5.17157	−0.221729
$545$	−17.3137	−0.741638
$546$	1.38478	0.0592630
$547$	13.1421	0.561917	0.280959	−	0.959720i	$-0.409348\pi$
$547$	13.1421	0.561917	0.280959	+	0.959720i	$0.409348\pi$
$548$	19.1716	0.818969
$549$	−8.31371	−0.354820
$550$	−1.17157	−0.0499560
$551$	0	0
$552$	1.31371	0.0559151
$553$	6.11270	0.259938
$554$	2.48528	0.105589
$555$	−2.17157	−0.0921781
$556$	29.8284	1.26501
$557$	−9.02944	−0.382590	−0.191295	−	0.981533i	$-0.561269\pi$
$557$	−9.02944	−0.382590	−0.191295	+	0.981533i	$0.561269\pi$
$558$	2.07107	0.0876753
$559$	14.3137	0.605405
$560$	−5.48528	−0.231795
$561$	3.31371	0.139905
$562$	2.88730	0.121793
$563$	12.1421	0.511730	0.255865	−	0.966713i	$-0.417640\pi$
$563$	12.1421	0.511730	0.255865	+	0.966713i	$0.417640\pi$
$564$	5.79899	0.244182
$565$	4.00000	0.168281
$566$	−8.68629	−0.365112
$567$	1.82843	0.0767867
$568$	15.8579	0.665381
$569$	−4.97056	−0.208377	−0.104188	−	0.994558i	$-0.533224\pi$
$569$	−4.97056	−0.208377	−0.104188	+	0.994558i	$0.533224\pi$
$570$	0	0
$571$	14.3137	0.599010	0.299505	−	0.954095i	$-0.403178\pi$
$571$	14.3137	0.599010	0.299505	+	0.954095i	$0.403178\pi$
$572$	9.45584	0.395369
$573$	−16.8284	−0.703018
$574$	−2.14214	−0.0894110
$575$	−0.828427	−0.0345478
$576$	−4.17157	−0.173816
$577$	−36.3431	−1.51298	−0.756492	−	0.654002i	$-0.773089\pi$
$577$	−36.3431	−1.51298	−0.756492	+	0.654002i	$0.773089\pi$
$578$	−6.47309	−0.269245
$579$	24.7990	1.03061
$580$	−17.6569	−0.733161
$581$	−14.6274	−0.606848
$582$	2.48528	0.103018
$583$	−5.65685	−0.234283
$584$	−15.0416	−0.622427
$585$	−1.82843	−0.0755962
$586$	2.20101	0.0909229
$587$	10.6274	0.438640	0.219320	−	0.975653i	$-0.429616\pi$
$587$	10.6274	0.438640	0.219320	+	0.975653i	$0.429616\pi$
$588$	6.68629	0.275738
$589$	0	0
$590$	0	0
$591$	17.6569	0.726306
$592$	6.51472	0.267753
$593$	−9.85786	−0.404814	−0.202407	−	0.979301i	$-0.564876\pi$
$593$	−9.85786	−0.404814	−0.202407	+	0.979301i	$0.564876\pi$
$594$	−1.17157	−0.0480702
$595$	2.14214	0.0878190
$596$	2.14214	0.0877453
$597$	−17.0000	−0.695764
$598$	−0.627417	−0.0256570
$599$	16.9706	0.693398	0.346699	−	0.937976i	$-0.387302\pi$
$599$	16.9706	0.693398	0.346699	+	0.937976i	$0.387302\pi$
$600$	−1.58579	−0.0647395
$601$	35.3431	1.44168	0.720838	−	0.693103i	$-0.243757\pi$
$601$	35.3431	1.44168	0.720838	+	0.693103i	$0.243757\pi$
$602$	5.92893	0.241645
$603$	−5.48528	−0.223378
$604$	18.9117	0.769506
$605$	3.00000	0.121967
$606$	5.02944	0.204307
$607$	6.17157	0.250496	0.125248	−	0.992125i	$-0.460027\pi$
$607$	6.17157	0.250496	0.125248	+	0.992125i	$0.460027\pi$
$608$	0	0
$609$	−17.6569	−0.715492
$610$	3.44365	0.139429
$611$	−5.79899	−0.234602
$612$	2.14214	0.0865907
$613$	33.5980	1.35701	0.678505	−	0.734596i	$-0.262628\pi$
$613$	33.5980	1.35701	0.678505	+	0.734596i	$0.262628\pi$
$614$	7.31371	0.295157
$615$	2.82843	0.114053
$616$	8.20101	0.330428
$617$	25.6569	1.03291	0.516453	−	0.856316i	$-0.327252\pi$
$617$	25.6569	1.03291	0.516453	+	0.856316i	$0.327252\pi$
$618$	−4.07107	−0.163762
$619$	15.6863	0.630485	0.315243	−	0.949011i	$-0.397914\pi$
$619$	15.6863	0.630485	0.315243	+	0.949011i	$0.397914\pi$
$620$	9.14214	0.367157
$621$	−0.828427	−0.0332436
$622$	−1.65685	−0.0664338
$623$	−22.8284	−0.914602
$624$	5.48528	0.219587
$625$	1.00000	0.0400000
$626$	−2.48528	−0.0993318
$627$	0	0
$628$	36.2548	1.44673
$629$	−2.54416	−0.101442
$630$	−0.757359	−0.0301739
$631$	−13.2843	−0.528838	−0.264419	−	0.964408i	$-0.585180\pi$
$631$	−13.2843	−0.528838	−0.264419	+	0.964408i	$0.585180\pi$
$632$	−5.30152	−0.210883
$633$	0.313708	0.0124688
$634$	−2.20101	−0.0874133
$635$	12.9706	0.514721
$636$	−3.65685	−0.145004
$637$	−6.68629	−0.264921
$638$	11.3137	0.447914
$639$	−10.0000	−0.395594
$640$	10.5563	0.417276
$641$	−28.1421	−1.11155	−0.555774	−	0.831334i	$-0.687578\pi$
$641$	−28.1421	−1.11155	−0.555774	+	0.831334i	$0.687578\pi$
$642$	−5.79899	−0.228868
$643$	5.82843	0.229851	0.114925	−	0.993374i	$-0.463337\pi$
$643$	5.82843	0.229851	0.114925	+	0.993374i	$0.463337\pi$
$644$	2.76955	0.109136
$645$	−7.82843	−0.308244
$646$	0	0
$647$	−32.2843	−1.26923	−0.634613	−	0.772830i	$-0.718840\pi$
$647$	−32.2843	−1.26923	−0.634613	+	0.772830i	$0.718840\pi$
$648$	−1.58579	−0.0622956
$649$	0	0
$650$	0.757359	0.0297061
$651$	9.14214	0.358309
$652$	−27.6863	−1.08428
$653$	39.9411	1.56302	0.781509	−	0.623895i	$-0.214451\pi$
$653$	39.9411	1.56302	0.781509	+	0.623895i	$0.214451\pi$
$654$	7.17157	0.280431
$655$	−6.48528	−0.253401
$656$	−8.48528	−0.331295
$657$	9.48528	0.370056
$658$	−2.40202	−0.0936405
$659$	−7.51472	−0.292732	−0.146366	−	0.989231i	$-0.546758\pi$
$659$	−7.51472	−0.292732	−0.146366	+	0.989231i	$0.546758\pi$
$660$	−5.17157	−0.201303
$661$	6.97056	0.271123	0.135562	−	0.990769i	$-0.456716\pi$
$661$	6.97056	0.271123	0.135562	+	0.990769i	$0.456716\pi$
$662$	2.21320	0.0860186
$663$	−2.14214	−0.0831937
$664$	12.6863	0.492324
$665$	0	0
$666$	0.899495	0.0348547
$667$	8.00000	0.309761
$668$	−45.6569	−1.76652
$669$	−5.82843	−0.225340
$670$	2.27208	0.0877780
$671$	23.5147	0.907776
$672$	8.07107	0.311348
$673$	23.8284	0.918518	0.459259	−	0.888302i	$-0.348115\pi$
$673$	23.8284	0.918518	0.459259	+	0.888302i	$0.348115\pi$
$674$	−7.24264	−0.278976
$675$	1.00000	0.0384900
$676$	17.6569	0.679110
$677$	23.4558	0.901481	0.450741	−	0.892655i	$-0.351160\pi$
$677$	23.4558	0.901481	0.450741	+	0.892655i	$0.351160\pi$
$678$	−1.65685	−0.0636311
$679$	10.9706	0.421012
$680$	−1.85786	−0.0712458
$681$	18.9706	0.726954
$682$	−5.85786	−0.224309
$683$	−44.1421	−1.68905	−0.844526	−	0.535515i	$-0.820118\pi$
$683$	−44.1421	−1.68905	−0.844526	+	0.535515i	$0.820118\pi$
$684$	0	0
$685$	10.4853	0.400622
$686$	−8.07107	−0.308155
$687$	−4.65685	−0.177670
$688$	23.4853	0.895368
$689$	3.65685	0.139315
$690$	0.343146	0.0130633
$691$	31.3137	1.19123	0.595615	−	0.803270i	$-0.296908\pi$
$691$	31.3137	1.19123	0.595615	+	0.803270i	$0.296908\pi$
$692$	13.3726	0.508349
$693$	−5.17157	−0.196452
$694$	−14.6863	−0.557484
$695$	16.3137	0.618814
$696$	15.3137	0.580465
$697$	3.31371	0.125516
$698$	−13.1005	−0.495861
$699$	−25.3137	−0.957452
$700$	−3.34315	−0.126359
$701$	32.1421	1.21399	0.606996	−	0.794705i	$-0.292374\pi$
$701$	32.1421	1.21399	0.606996	+	0.794705i	$0.292374\pi$
$702$	0.757359	0.0285847
$703$	0	0
$704$	11.7990	0.444691
$705$	3.17157	0.119448
$706$	−0.544156	−0.0204796
$707$	22.2010	0.834955
$708$	0	0
$709$	31.6274	1.18779	0.593896	−	0.804542i	$-0.297589\pi$
$709$	31.6274	1.18779	0.593896	+	0.804542i	$0.297589\pi$
$710$	4.14214	0.155452
$711$	3.34315	0.125378
$712$	19.7990	0.741999
$713$	−4.14214	−0.155124
$714$	−0.887302	−0.0332064
$715$	5.17157	0.193406
$716$	29.5147	1.10302
$717$	−24.6274	−0.919728
$718$	3.79899	0.141777
$719$	−23.1716	−0.864154	−0.432077	−	0.901837i	$-0.642219\pi$
$719$	−23.1716	−0.864154	−0.432077	+	0.901837i	$0.642219\pi$
$720$	−3.00000	−0.111803
$721$	−17.9706	−0.669259
$722$	0	0
$723$	−5.00000	−0.185952
$724$	46.2843	1.72014
$725$	−9.65685	−0.358647
$726$	−1.24264	−0.0461187
$727$	36.1716	1.34153	0.670765	−	0.741670i	$-0.265966\pi$
$727$	36.1716	1.34153	0.670765	+	0.741670i	$0.265966\pi$
$728$	−5.30152	−0.196487
$729$	1.00000	0.0370370
$730$	−3.92893	−0.145416
$731$	−9.17157	−0.339223
$732$	15.2010	0.561846
$733$	3.65685	0.135069	0.0675345	−	0.997717i	$-0.478487\pi$
$733$	3.65685	0.135069	0.0675345	+	0.997717i	$0.478487\pi$
$734$	−14.1299	−0.521546
$735$	3.65685	0.134885
$736$	−3.65685	−0.134793
$737$	15.5147	0.571492
$738$	−1.17157	−0.0431262
$739$	−41.6274	−1.53129	−0.765645	−	0.643264i	$-0.777580\pi$
$739$	−41.6274	−1.53129	−0.765645	+	0.643264i	$0.777580\pi$
$740$	3.97056	0.145961
$741$	0	0
$742$	1.51472	0.0556071
$743$	−34.1421	−1.25255	−0.626277	−	0.779601i	$-0.715422\pi$
$743$	−34.1421	−1.25255	−0.626277	+	0.779601i	$0.715422\pi$
$744$	−7.92893	−0.290689
$745$	1.17157	0.0429231
$746$	4.82843	0.176781
$747$	−8.00000	−0.292705
$748$	−6.05887	−0.221534
$749$	−25.5980	−0.935330
$750$	−0.414214	−0.0151249
$751$	−26.3137	−0.960201	−0.480100	−	0.877214i	$-0.659400\pi$
$751$	−26.3137	−0.960201	−0.480100	+	0.877214i	$0.659400\pi$
$752$	−9.51472	−0.346966
$753$	−16.3431	−0.595577
$754$	−7.31371	−0.266350
$755$	10.3431	0.376426
$756$	−3.34315	−0.121589
$757$	−33.1421	−1.20457	−0.602286	−	0.798281i	$-0.705743\pi$
$757$	−33.1421	−1.20457	−0.602286	+	0.798281i	$0.705743\pi$
$758$	−0.698485	−0.0253701
$759$	2.34315	0.0850508
$760$	0	0
$761$	51.5980	1.87043	0.935213	−	0.354087i	$-0.115208\pi$
$761$	51.5980	1.87043	0.935213	+	0.354087i	$0.115208\pi$
$762$	−5.37258	−0.194628
$763$	31.6569	1.14606
$764$	30.7696	1.11320
$765$	1.17157	0.0423583
$766$	14.0589	0.507968
$767$	0	0
$768$	3.97056	0.143275
$769$	14.3137	0.516166	0.258083	−	0.966123i	$-0.416909\pi$
$769$	14.3137	0.516166	0.258083	+	0.966123i	$0.416909\pi$
$770$	2.14214	0.0771972
$771$	16.8284	0.606061
$772$	−45.3431	−1.63194
$773$	22.0000	0.791285	0.395643	−	0.918405i	$-0.370522\pi$
$773$	22.0000	0.791285	0.395643	+	0.918405i	$0.370522\pi$
$774$	3.24264	0.116554
$775$	5.00000	0.179605
$776$	−9.51472	−0.341558
$777$	3.97056	0.142443
$778$	−6.40202	−0.229524
$779$	0	0
$780$	3.34315	0.119704
$781$	28.2843	1.01209
$782$	0.402020	0.0143762
$783$	−9.65685	−0.345108
$784$	−10.9706	−0.391806
$785$	19.8284	0.707707
$786$	2.68629	0.0958168
$787$	5.48528	0.195529	0.0977646	−	0.995210i	$-0.468831\pi$
$787$	5.48528	0.195529	0.0977646	+	0.995210i	$0.468831\pi$
$788$	−32.2843	−1.15008
$789$	25.7990	0.918468
$790$	−1.38478	−0.0492681
$791$	−7.31371	−0.260046
$792$	4.48528	0.159378
$793$	−15.2010	−0.539804
$794$	−9.87006	−0.350275
$795$	−2.00000	−0.0709327
$796$	31.0833	1.10172
$797$	53.1127	1.88135	0.940674	−	0.339311i	$-0.110194\pi$
$797$	53.1127	1.88135	0.940674	+	0.339311i	$0.110194\pi$
$798$	0	0
$799$	3.71573	0.131453
$800$	4.41421	0.156066
$801$	−12.4853	−0.441146
$802$	9.37258	0.330957
$803$	−26.8284	−0.946755
$804$	10.0294	0.353711
$805$	1.51472	0.0533868
$806$	3.78680	0.133384
$807$	−1.65685	−0.0583240
$808$	−19.2548	−0.677383
$809$	3.37258	0.118574	0.0592869	−	0.998241i	$-0.481117\pi$
$809$	3.37258	0.118574	0.0592869	+	0.998241i	$0.481117\pi$
$810$	−0.414214	−0.0145540
$811$	−30.6274	−1.07547	−0.537737	−	0.843113i	$-0.680721\pi$
$811$	−30.6274	−1.07547	−0.537737	+	0.843113i	$0.680721\pi$
$812$	32.2843	1.13296
$813$	13.6569	0.478967
$814$	−2.54416	−0.0891726
$815$	−15.1421	−0.530406
$816$	−3.51472	−0.123040
$817$	0	0
$818$	−2.48528	−0.0868958
$819$	3.34315	0.116819
$820$	−5.17157	−0.180599
$821$	−52.0000	−1.81481	−0.907406	−	0.420255i	$-0.861941\pi$
$821$	−52.0000	−1.81481	−0.907406	+	0.420255i	$0.861941\pi$
$822$	−4.34315	−0.151485
$823$	25.9411	0.904251	0.452125	−	0.891954i	$-0.350666\pi$
$823$	25.9411	0.904251	0.452125	+	0.891954i	$0.350666\pi$
$824$	15.5858	0.542957
$825$	−2.82843	−0.0984732
$826$	0	0
$827$	3.31371	0.115229	0.0576145	−	0.998339i	$-0.481651\pi$
$827$	3.31371	0.115229	0.0576145	+	0.998339i	$0.481651\pi$
$828$	1.51472	0.0526401
$829$	22.0294	0.765114	0.382557	−	0.923932i	$-0.375044\pi$
$829$	22.0294	0.765114	0.382557	+	0.923932i	$0.375044\pi$
$830$	3.31371	0.115021
$831$	6.00000	0.208138
$832$	−7.62742	−0.264433
$833$	4.28427	0.148441
$834$	−6.75736	−0.233988
$835$	−24.9706	−0.864142
$836$	0	0
$837$	5.00000	0.172825
$838$	1.37258	0.0474151
$839$	5.79899	0.200203	0.100102	−	0.994977i	$-0.468083\pi$
$839$	5.79899	0.200203	0.100102	+	0.994977i	$0.468083\pi$
$840$	2.89949	0.100042
$841$	64.2548	2.21568
$842$	3.17157	0.109300
$843$	6.97056	0.240079
$844$	−0.573593	−0.0197439
$845$	9.65685	0.332206
$846$	−1.31371	−0.0451662
$847$	−5.48528	−0.188476
$848$	6.00000	0.206041
$849$	−20.9706	−0.719708
$850$	−0.485281	−0.0166450
$851$	−1.79899	−0.0616686
$852$	18.2843	0.626409
$853$	4.45584	0.152565	0.0762826	−	0.997086i	$-0.475695\pi$
$853$	4.45584	0.152565	0.0762826	+	0.997086i	$0.475695\pi$
$854$	−6.29646	−0.215461
$855$	0	0
$856$	22.2010	0.758815
$857$	−42.4853	−1.45127	−0.725635	−	0.688080i	$-0.758454\pi$
$857$	−42.4853	−1.45127	−0.725635	+	0.688080i	$0.758454\pi$
$858$	−2.14214	−0.0731313
$859$	34.9411	1.19218	0.596088	−	0.802919i	$-0.296721\pi$
$859$	34.9411	1.19218	0.596088	+	0.802919i	$0.296721\pi$
$860$	14.3137	0.488093
$861$	−5.17157	−0.176247
$862$	1.02944	0.0350628
$863$	25.3137	0.861689	0.430844	−	0.902426i	$-0.358216\pi$
$863$	25.3137	0.861689	0.430844	+	0.902426i	$0.358216\pi$
$864$	4.41421	0.150175
$865$	7.31371	0.248674
$866$	16.4975	0.560607
$867$	−15.6274	−0.530735
$868$	−16.7157	−0.567369
$869$	−9.45584	−0.320768
$870$	4.00000	0.135613
$871$	−10.0294	−0.339835
$872$	−27.4558	−0.929772
$873$	6.00000	0.203069
$874$	0	0
$875$	−1.82843	−0.0618121
$876$	−17.3431	−0.585971
$877$	44.7990	1.51275	0.756377	−	0.654136i	$-0.226967\pi$
$877$	44.7990	1.51275	0.756377	+	0.654136i	$0.226967\pi$
$878$	−7.04163	−0.237644
$879$	5.31371	0.179227
$880$	8.48528	0.286039
$881$	42.9706	1.44772	0.723858	−	0.689949i	$-0.242367\pi$
$881$	42.9706	1.44772	0.723858	+	0.689949i	$0.242367\pi$
$882$	−1.51472	−0.0510032
$883$	−33.1421	−1.11532	−0.557661	−	0.830069i	$-0.688301\pi$
$883$	−33.1421	−1.11532	−0.557661	+	0.830069i	$0.688301\pi$
$884$	3.91674	0.131734
$885$	0	0
$886$	7.51472	0.252462
$887$	−29.4558	−0.989030	−0.494515	−	0.869169i	$-0.664654\pi$
$887$	−29.4558	−0.989030	−0.494515	+	0.869169i	$0.664654\pi$
$888$	−3.44365	−0.115561
$889$	−23.7157	−0.795400
$890$	5.17157	0.173352
$891$	−2.82843	−0.0947559
$892$	10.6569	0.356818
$893$	0	0
$894$	−0.485281	−0.0162302
$895$	16.1421	0.539572
$896$	−19.3015	−0.644818
$897$	−1.51472	−0.0505750
$898$	−5.45584	−0.182064
$899$	−48.2843	−1.61037
$900$	−1.82843	−0.0609476
$901$	−2.34315	−0.0780615
$902$	3.31371	0.110334
$903$	14.3137	0.476330
$904$	6.34315	0.210970
$905$	25.3137	0.841456
$906$	−4.28427	−0.142335
$907$	30.3431	1.00753	0.503764	−	0.863841i	$-0.331948\pi$
$907$	30.3431	1.00753	0.503764	+	0.863841i	$0.331948\pi$
$908$	−34.6863	−1.15111
$909$	12.1421	0.402729
$910$	−1.38478	−0.0459049
$911$	−38.1421	−1.26371	−0.631853	−	0.775089i	$-0.717705\pi$
$911$	−38.1421	−1.26371	−0.631853	+	0.775089i	$0.717705\pi$
$912$	0	0
$913$	22.6274	0.748858
$914$	−1.72792	−0.0571546
$915$	8.31371	0.274843
$916$	8.51472	0.281334
$917$	11.8579	0.391581
$918$	−0.485281	−0.0160167
$919$	−3.00000	−0.0989609	−0.0494804	−	0.998775i	$-0.515757\pi$
$919$	−3.00000	−0.0989609	−0.0494804	+	0.998775i	$0.515757\pi$
$920$	−1.31371	−0.0433117
$921$	17.6569	0.581813
$922$	12.4853	0.411181
$923$	−18.2843	−0.601834
$924$	9.45584	0.311074
$925$	2.17157	0.0714009
$926$	−9.44365	−0.310338
$927$	−9.82843	−0.322808
$928$	−42.6274	−1.39931
$929$	−22.4853	−0.737718	−0.368859	−	0.929485i	$-0.620252\pi$
$929$	−22.4853	−0.737718	−0.368859	+	0.929485i	$0.620252\pi$
$930$	−2.07107	−0.0679130
$931$	0	0
$932$	46.2843	1.51609
$933$	−4.00000	−0.130954
$934$	9.85786	0.322559
$935$	−3.31371	−0.108370
$936$	−2.89949	−0.0947730
$937$	−35.8284	−1.17046	−0.585232	−	0.810866i	$-0.698997\pi$
$937$	−35.8284	−1.17046	−0.585232	+	0.810866i	$0.698997\pi$
$938$	−4.15433	−0.135644
$939$	−6.00000	−0.195803
$940$	−5.79899	−0.189142
$941$	10.8284	0.352997	0.176498	−	0.984301i	$-0.443523\pi$
$941$	10.8284	0.352997	0.176498	+	0.984301i	$0.443523\pi$
$942$	−8.21320	−0.267601
$943$	2.34315	0.0763033
$944$	0	0
$945$	−1.82843	−0.0594787
$946$	−9.17157	−0.298194
$947$	−57.1127	−1.85591	−0.927957	−	0.372688i	$-0.878436\pi$
$947$	−57.1127	−1.85591	−0.927957	+	0.372688i	$0.878436\pi$
$948$	−6.11270	−0.198531
$949$	17.3431	0.562982
$950$	0	0
$951$	−5.31371	−0.172309
$952$	3.39697	0.110096
$953$	−31.5980	−1.02356	−0.511779	−	0.859117i	$-0.671014\pi$
$953$	−31.5980	−1.02356	−0.511779	+	0.859117i	$0.671014\pi$
$954$	0.828427	0.0268213
$955$	16.8284	0.544555
$956$	45.0294	1.45636
$957$	27.3137	0.882927
$958$	1.02944	0.0332596
$959$	−19.1716	−0.619082
$960$	4.17157	0.134637
$961$	−6.00000	−0.193548
$962$	1.64466	0.0530260
$963$	−14.0000	−0.451144
$964$	9.14214	0.294448
$965$	−24.7990	−0.798308
$966$	−0.627417	−0.0201868
$967$	16.7990	0.540219	0.270110	−	0.962830i	$-0.412940\pi$
$967$	16.7990	0.540219	0.270110	+	0.962830i	$0.412940\pi$
$968$	4.75736	0.152907
$969$	0	0
$970$	−2.48528	−0.0797976
$971$	20.8284	0.668416	0.334208	−	0.942499i	$-0.391531\pi$
$971$	20.8284	0.668416	0.334208	+	0.942499i	$0.391531\pi$
$972$	−1.82843	−0.0586468
$973$	−29.8284	−0.956255
$974$	2.62742	0.0841879
$975$	1.82843	0.0585565
$976$	−24.9411	−0.798346
$977$	34.2843	1.09685	0.548426	−	0.836199i	$-0.315227\pi$
$977$	34.2843	1.09685	0.548426	+	0.836199i	$0.315227\pi$
$978$	6.27208	0.200559
$979$	35.3137	1.12863
$980$	−6.68629	−0.213586
$981$	17.3137	0.552784
$982$	9.79899	0.312698
$983$	36.9706	1.17918	0.589589	−	0.807703i	$-0.299290\pi$
$983$	36.9706	1.17918	0.589589	+	0.807703i	$0.299290\pi$
$984$	4.48528	0.142986
$985$	−17.6569	−0.562594
$986$	4.68629	0.149242
$987$	−5.79899	−0.184584
$988$	0	0
$989$	−6.48528	−0.206220
$990$	1.17157	0.0372350
$991$	40.6569	1.29151	0.645754	−	0.763546i	$-0.276543\pi$
$991$	40.6569	1.29151	0.645754	+	0.763546i	$0.276543\pi$
$992$	22.0711	0.700757
$993$	5.34315	0.169560
$994$	−7.57359	−0.240220
$995$	17.0000	0.538936
$996$	14.6274	0.463487
$997$	−29.4853	−0.933808	−0.466904	−	0.884308i	$-0.654631\pi$
$997$	−29.4853	−0.933808	−0.466904	+	0.884308i	$0.654631\pi$
$998$	−3.04163	−0.0962811
$999$	2.17157	0.0687055

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5415.2.a.o.1.2		2
19.8	odd	6		285.2.i.d.121.2	yes	4
19.12	odd	6		285.2.i.d.106.2	✓	4
19.18	odd	2		5415.2.a.u.1.1		2
57.8	even	6		855.2.k.f.406.1		4
57.50	even	6		855.2.k.f.676.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.d.106.2	✓	4	19.12	odd	6
285.2.i.d.121.2	yes	4	19.8	odd	6
855.2.k.f.406.1		4	57.8	even	6
855.2.k.f.676.1		4	57.50	even	6
5415.2.a.o.1.2		2	1.1	even	1	trivial
5415.2.a.u.1.1		2	19.18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)

\(f(q)\)	\(=\)	\(q+0.414214 q^{2} +1.00000 q^{3} -1.82843 q^{4} -1.00000 q^{5} +0.414214 q^{6} +1.82843 q^{7} -1.58579 q^{8} +1.00000 q^{9} -0.414214 q^{10} -2.82843 q^{11} -1.82843 q^{12} +1.82843 q^{13} +0.757359 q^{14} -1.00000 q^{15} +3.00000 q^{16} -1.17157 q^{17} +0.414214 q^{18} +1.82843 q^{20} +1.82843 q^{21} -1.17157 q^{22} -0.828427 q^{23} -1.58579 q^{24} +1.00000 q^{25} +0.757359 q^{26} +1.00000 q^{27} -3.34315 q^{28} -9.65685 q^{29} -0.414214 q^{30} +5.00000 q^{31} +4.41421 q^{32} -2.82843 q^{33} -0.485281 q^{34} -1.82843 q^{35} -1.82843 q^{36} +2.17157 q^{37} +1.82843 q^{39} +1.58579 q^{40} -2.82843 q^{41} +0.757359 q^{42} +7.82843 q^{43} +5.17157 q^{44} -1.00000 q^{45} -0.343146 q^{46} -3.17157 q^{47} +3.00000 q^{48} -3.65685 q^{49} +0.414214 q^{50} -1.17157 q^{51} -3.34315 q^{52} +2.00000 q^{53} +0.414214 q^{54} +2.82843 q^{55} -2.89949 q^{56} -4.00000 q^{58} +1.82843 q^{60} -8.31371 q^{61} +2.07107 q^{62} +1.82843 q^{63} -4.17157 q^{64} -1.82843 q^{65} -1.17157 q^{66} -5.48528 q^{67} +2.14214 q^{68} -0.828427 q^{69} -0.757359 q^{70} -10.0000 q^{71} -1.58579 q^{72} +9.48528 q^{73} +0.899495 q^{74} +1.00000 q^{75} -5.17157 q^{77} +0.757359 q^{78} +3.34315 q^{79} -3.00000 q^{80} +1.00000 q^{81} -1.17157 q^{82} -8.00000 q^{83} -3.34315 q^{84} +1.17157 q^{85} +3.24264 q^{86} -9.65685 q^{87} +4.48528 q^{88} -12.4853 q^{89} -0.414214 q^{90} +3.34315 q^{91} +1.51472 q^{92} +5.00000 q^{93} -1.31371 q^{94} +4.41421 q^{96} +6.00000 q^{97} -1.51472 q^{98} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} - 6 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} + 6 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{20} - 2 q^{21} - 8 q^{22}+ \cdots - 20 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 - 6 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 - 2 * q^13 + 10 * q^14 - 2 * q^15 + 6 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^20 - 2 * q^21 - 8 * q^22 + 4 * q^23 - 6 * q^24 + 2 * q^25 + 10 * q^26 + 2 * q^27 - 18 * q^28 - 8 * q^29 + 2 * q^30 + 10 * q^31 + 6 * q^32 + 16 * q^34 + 2 * q^35 + 2 * q^36 + 10 * q^37 - 2 * q^39 + 6 * q^40 + 10 * q^42 + 10 * q^43 + 16 * q^44 - 2 * q^45 - 12 * q^46 - 12 * q^47 + 6 * q^48 + 4 * q^49 - 2 * q^50 - 8 * q^51 - 18 * q^52 + 4 * q^53 - 2 * q^54 + 14 * q^56 - 8 * q^58 - 2 * q^60 + 6 * q^61 - 10 * q^62 - 2 * q^63 - 14 * q^64 + 2 * q^65 - 8 * q^66 + 6 * q^67 - 24 * q^68 + 4 * q^69 - 10 * q^70 - 20 * q^71 - 6 * q^72 + 2 * q^73 - 18 * q^74 + 2 * q^75 - 16 * q^77 + 10 * q^78 + 18 * q^79 - 6 * q^80 + 2 * q^81 - 8 * q^82 - 16 * q^83 - 18 * q^84 + 8 * q^85 - 2 * q^86 - 8 * q^87 - 8 * q^88 - 8 * q^89 + 2 * q^90 + 18 * q^91 + 20 * q^92 + 10 * q^93 + 20 * q^94 + 6 * q^96 + 12 * q^97 - 20 * q^98

Introduction

L-functions

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Database

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