LMFDB - Embedded newform 25.16.b.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,16,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$35.6733762750$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.16.b.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-216.000i q^{2} -3348.00i q^{3} -13888.0 q^{4} -723168. q^{6} -2.82246e6i q^{7} -4.07808e6i q^{8} +3.13980e6 q^{9} +O(q^{10})$	\(q-216.000i q^{2} -3348.00i q^{3} -13888.0 q^{4} -723168. q^{6} -2.82246e6i q^{7} -4.07808e6i q^{8} +3.13980e6 q^{9} +2.05869e7 q^{11} +4.64970e7i q^{12} -1.90073e8i q^{13} -6.09650e8 q^{14} -1.33595e9 q^{16} -1.64653e9i q^{17} -6.78197e8i q^{18} -1.56326e9 q^{19} -9.44958e9 q^{21} -4.44676e9i q^{22} +9.45112e9i q^{23} -1.36534e10 q^{24} -4.10558e10 q^{26} -5.85522e10i q^{27} +3.91983e10i q^{28} +3.69026e10 q^{29} +7.15885e10 q^{31} +1.54934e11i q^{32} -6.89248e10i q^{33} -3.55650e11 q^{34} -4.36056e10 q^{36} +1.03365e12i q^{37} +3.37664e11i q^{38} -6.36366e11 q^{39} +1.64197e12 q^{41} +2.04111e12i q^{42} -4.92403e11i q^{43} -2.85910e11 q^{44} +2.04144e12 q^{46} +3.41068e12i q^{47} +4.47275e12i q^{48} -3.21870e12 q^{49} -5.51258e12 q^{51} +2.63974e12i q^{52} +6.79715e12i q^{53} -1.26473e13 q^{54} -1.15102e13 q^{56} +5.23379e12i q^{57} -7.97095e12i q^{58} -9.85886e12 q^{59} +4.93184e12 q^{61} -1.54631e13i q^{62} -8.86196e12i q^{63} -1.03106e13 q^{64} -1.48878e13 q^{66} +2.88378e13i q^{67} +2.28670e13i q^{68} +3.16423e13 q^{69} +1.25050e14 q^{71} -1.28044e13i q^{72} -8.21715e13i q^{73} +2.23269e14 q^{74} +2.17105e13 q^{76} -5.81055e13i q^{77} +1.37455e14i q^{78} +2.54131e13 q^{79} -1.50980e14 q^{81} -3.54666e14i q^{82} -2.81737e14i q^{83} +1.31236e14 q^{84} -1.06359e14 q^{86} -1.23550e14i q^{87} -8.39548e13i q^{88} -7.15619e14 q^{89} -5.36474e14 q^{91} -1.31257e14i q^{92} -2.39678e14i q^{93} +7.36708e14 q^{94} +5.18719e14 q^{96} -6.12786e14i q^{97} +6.95238e14i q^{98} +6.46387e13 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 27776 q^{4} - 1446336 q^{6} + 6279606 q^{9}+O(q^{10}) $ 2 * q - 27776 * q^4 - 1446336 * q^6 + 6279606 * q^9	$ 2 q - 27776 q^{4} - 1446336 q^{6} + 6279606 q^{9} + 41173704 q^{11} - 1219300992 q^{14} - 2671894528 q^{16} - 3126514360 q^{19} - 18899165376 q^{21} - 27306823680 q^{24} - 82111682016 q^{26} + 73805136660 q^{29} + 143176967104 q^{31} - 711300089952 q^{34} - 87211168128 q^{36} - 1272731071248 q^{39} + 3283948036404 q^{41} - 571820401152 q^{44} + 4082882143104 q^{46} - 6437392723986 q^{49} - 11025151394256 q^{51} - 25294550866560 q^{54} - 23020402728960 q^{56} - 19717713631080 q^{59} + 9863685253804 q^{61} - 20621115785216 q^{64} - 29775505174272 q^{66} + 63284673218112 q^{69} + 250100229829104 q^{71} + 446537699231328 q^{74} + 43421031431680 q^{76} + 50826157388960 q^{79} - 301960055941038 q^{81} + 262471608741888 q^{84} - 212718143221056 q^{86} - 14\!\cdots\!20 q^{89}+ \cdots + 129277319340312 q^{99}+O(q^{100}) $ 2 * q - 27776 * q^4 - 1446336 * q^6 + 6279606 * q^9 + 41173704 * q^11 - 1219300992 * q^14 - 2671894528 * q^16 - 3126514360 * q^19 - 18899165376 * q^21 - 27306823680 * q^24 - 82111682016 * q^26 + 73805136660 * q^29 + 143176967104 * q^31 - 711300089952 * q^34 - 87211168128 * q^36 - 1272731071248 * q^39 + 3283948036404 * q^41 - 571820401152 * q^44 + 4082882143104 * q^46 - 6437392723986 * q^49 - 11025151394256 * q^51 - 25294550866560 * q^54 - 23020402728960 * q^56 - 19717713631080 * q^59 + 9863685253804 * q^61 - 20621115785216 * q^64 - 29775505174272 * q^66 + 63284673218112 * q^69 + 250100229829104 * q^71 + 446537699231328 * q^74 + 43421031431680 * q^76 + 50826157388960 * q^79 - 301960055941038 * q^81 + 262471608741888 * q^84 - 212718143221056 * q^86 - 1431237129553620 * q^89 - 1072947266556256 * q^91 + 1473415899533568 * q^94 + 1037438623678464 * q^96 + 129277319340312 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 216.000i	− 1.19324i	−0.802523	−	0.596621i	$-0.796509\pi$
$2$	− 216.000i	− 1.19324i	0.802523	−	0.596621i	$-0.203491\pi$
$3$	− 3348.00i	− 0.883845i	−0.897053	−	0.441922i	$-0.854297\pi$
$3$	− 3348.00i	− 0.883845i	0.897053	−	0.441922i	$-0.145703\pi$
$4$	−13888.0	−0.423828
$5$	0	0
$5$	0	0
$6$	−723168.	−1.05464
$7$	− 2.82246e6i	− 1.29536i	−0.761911	−	0.647682i	$-0.775739\pi$
$7$	− 2.82246e6i	− 1.29536i	0.761911	−	0.647682i	$-0.224261\pi$
$8$	− 4.07808e6i	− 0.687513i
$9$	3.13980e6	0.218818
$10$	0	0
$11$	2.05869e7	0.318526	0.159263	−	0.987236i	$-0.449088\pi$
$11$	2.05869e7	0.318526	0.159263	+	0.987236i	$0.449088\pi$
$12$	4.64970e7i	0.374598i
$13$	− 1.90073e8i	− 0.840129i	−0.907494	−	0.420065i	$-0.862007\pi$
$13$	− 1.90073e8i	− 0.840129i	0.907494	−	0.420065i	$-0.137993\pi$
$14$	−6.09650e8	−1.54568
$15$	0	0
$16$	−1.33595e9	−1.24420
$17$	− 1.64653e9i	− 0.973200i	−0.873625	−	0.486600i	$-0.838237\pi$
$17$	− 1.64653e9i	− 0.973200i	0.873625	−	0.486600i	$-0.161763\pi$
$18$	− 6.78197e8i	− 0.261103i
$19$	−1.56326e9	−0.401216	−0.200608	−	0.979672i	$-0.564292\pi$
$19$	−1.56326e9	−0.401216	−0.200608	+	0.979672i	$0.564292\pi$
$20$	0	0
$21$	−9.44958e9	−1.14490
$22$	− 4.44676e9i	− 0.380079i
$23$	9.45112e9i	0.578794i	0.957209	+	0.289397i	$0.0934548\pi$
$23$	9.45112e9i	0.578794i	−0.957209	+	0.289397i	$0.906545\pi$
$24$	−1.36534e10	−0.607655
$25$	0	0
$26$	−4.10558e10	−1.00248
$27$	− 5.85522e10i	− 1.07725i
$28$	3.91983e10i	0.549012i
$29$	3.69026e10	0.397257	0.198629	−	0.980075i	$-0.436351\pi$
$29$	3.69026e10	0.397257	0.198629	+	0.980075i	$0.436351\pi$
$30$	0	0
$31$	7.15885e10	0.467337	0.233669	−	0.972316i	$-0.424927\pi$
$31$	7.15885e10	0.467337	0.233669	+	0.972316i	$0.424927\pi$
$32$	1.54934e11i	0.797117i
$33$	− 6.89248e10i	− 0.281528i
$34$	−3.55650e11	−1.16126
$35$	0	0
$36$	−4.36056e10	−0.0927413
$37$	1.03365e12i	1.79003i	0.446031	+	0.895017i	$0.352837\pi$
$37$	1.03365e12i	1.79003i	−0.446031	+	0.895017i	$0.647163\pi$
$38$	3.37664e11i	0.478748i
$39$	−6.36366e11	−0.742544
$40$	0	0
$41$	1.64197e12	1.31670	0.658351	−	0.752711i	$-0.271254\pi$
$41$	1.64197e12	1.31670	0.658351	+	0.752711i	$0.271254\pi$
$42$	2.04111e12i	1.36614i
$43$	− 4.92403e11i	− 0.276253i	−0.990415	−	0.138127i	$-0.955892\pi$
$43$	− 4.92403e11i	− 0.276253i	0.990415	−	0.138127i	$-0.0441081\pi$
$44$	−2.85910e11	−0.135000
$45$	0	0
$46$	2.04144e12	0.690642
$47$	3.41068e12i	0.981991i	0.871162	+	0.490996i	$0.163367\pi$
$47$	3.41068e12i	0.981991i	−0.871162	+	0.490996i	$0.836633\pi$
$48$	4.47275e12i	1.09968i
$49$	−3.21870e12	−0.677968
$50$	0	0
$51$	−5.51258e12	−0.860158
$52$	2.63974e12i	0.356070i
$53$	6.79715e12i	0.794800i	0.917645	+	0.397400i	$0.130087\pi$
$53$	6.79715e12i	0.794800i	−0.917645	+	0.397400i	$0.869913\pi$
$54$	−1.26473e13	−1.28542
$55$	0	0
$56$	−1.15102e13	−0.890580
$57$	5.23379e12i	0.354613i
$58$	− 7.97095e12i	− 0.474024i
$59$	−9.85886e12	−0.515747	−0.257873	−	0.966179i	$-0.583022\pi$
$59$	−9.85886e12	−0.515747	−0.257873	+	0.966179i	$0.583022\pi$
$60$	0	0
$61$	4.93184e12	0.200926	0.100463	−	0.994941i	$-0.467968\pi$
$61$	4.93184e12	0.200926	0.100463	+	0.994941i	$0.467968\pi$
$62$	− 1.54631e13i	− 0.557647i
$63$	− 8.86196e12i	− 0.283449i
$64$	−1.03106e13	−0.293044
$65$	0	0
$66$	−1.48878e13	−0.335931
$67$	2.88378e13i	0.581302i	0.956829	+	0.290651i	$0.0938718\pi$
$67$	2.88378e13i	0.581302i	−0.956829	+	0.290651i	$0.906128\pi$
$68$	2.28670e13i	0.412470i
$69$	3.16423e13	0.511564
$70$	0	0
$71$	1.25050e14	1.63172	0.815862	−	0.578247i	$-0.196263\pi$
$71$	1.25050e14	1.63172	0.815862	+	0.578247i	$0.196263\pi$
$72$	− 1.28044e13i	− 0.150440i
$73$	− 8.21715e13i	− 0.870562i	−0.900295	−	0.435281i	$-0.856649\pi$
$73$	− 8.21715e13i	− 0.870562i	0.900295	−	0.435281i	$-0.143351\pi$
$74$	2.23269e14	2.13595
$75$	0	0
$76$	2.17105e13	0.170047
$77$	− 5.81055e13i	− 0.412607i
$78$	1.37455e14i	0.886035i
$79$	2.54131e13	0.148886	0.0744430	−	0.997225i	$-0.476282\pi$
$79$	2.54131e13	0.148886	0.0744430	+	0.997225i	$0.476282\pi$
$80$	0	0
$81$	−1.50980e14	−0.733300
$82$	− 3.54666e14i	− 1.57114i
$83$	− 2.81737e14i	− 1.13961i	−0.821779	−	0.569807i	$-0.807018\pi$
$83$	− 2.81737e14i	− 1.13961i	0.821779	−	0.569807i	$-0.192982\pi$
$84$	1.31236e14	0.485241
$85$	0	0
$86$	−1.06359e14	−0.329637
$87$	− 1.23550e14i	− 0.351114i
$88$	− 8.39548e13i	− 0.218991i
$89$	−7.15619e14	−1.71497	−0.857485	−	0.514509i	$-0.827974\pi$
$89$	−7.15619e14	−1.71497	−0.857485	+	0.514509i	$0.827974\pi$
$90$	0	0
$91$	−5.36474e14	−1.08827
$92$	− 1.31257e14i	− 0.245309i
$93$	− 2.39678e14i	− 0.413054i
$94$	7.36708e14	1.17175
$95$	0	0
$96$	5.18719e14	0.704528
$97$	− 6.12786e14i	− 0.770054i	−0.922905	−	0.385027i	$-0.874192\pi$
$97$	− 6.12786e14i	− 0.770054i	0.922905	−	0.385027i	$-0.125808\pi$
$98$	6.95238e14i	0.808981i
$99$	6.46387e13	0.0696993
$100$	0	0
$101$	−8.17642e14	−0.758844	−0.379422	−	0.925224i	$-0.623877\pi$
$101$	−8.17642e14	−0.758844	−0.379422	+	0.925224i	$0.623877\pi$
$102$	1.19072e15i	1.02638i
$103$	7.41115e14i	0.593753i	0.954916	+	0.296877i	$0.0959450\pi$
$103$	7.41115e14i	0.593753i	−0.954916	+	0.296877i	$0.904055\pi$
$104$	−7.75134e14	−0.577600
$105$	0	0
$106$	1.46818e15	0.948389
$107$	2.51430e15i	1.51370i	0.653590	+	0.756849i	$0.273262\pi$
$107$	2.51430e15i	1.51370i	−0.653590	+	0.756849i	$0.726738\pi$
$108$	8.13173e14i	0.456567i
$109$	−1.26835e15	−0.664572	−0.332286	−	0.943179i	$-0.607820\pi$
$109$	−1.26835e15	−0.664572	−0.332286	+	0.943179i	$0.607820\pi$
$110$	0	0
$111$	3.46067e15	1.58211
$112$	3.77065e15i	1.61169i
$113$	− 2.05416e15i	− 0.821385i	−0.911774	−	0.410692i	$-0.865287\pi$
$113$	− 2.05416e15i	− 0.821385i	0.911774	−	0.410692i	$-0.134713\pi$
$114$	1.13050e15	0.423139
$115$	0	0
$116$	−5.12503e14	−0.168369
$117$	− 5.96793e14i	− 0.183836i
$118$	2.12951e15i	0.615411i
$119$	−4.64725e15	−1.26065
$120$	0	0
$121$	−3.75343e15	−0.898541
$122$	− 1.06528e15i	− 0.239753i
$123$	− 5.49733e15i	− 1.16376i
$124$	−9.94221e14	−0.198071
$125$	0	0
$126$	−1.91418e15	−0.338224
$127$	− 2.99068e15i	− 0.498014i	−0.968502	−	0.249007i	$-0.919896\pi$
$127$	− 2.99068e15i	− 0.498014i	0.968502	−	0.249007i	$-0.0801042\pi$
$128$	7.30396e15i	1.14679i
$129$	−1.64857e15	−0.244165
$130$	0	0
$131$	−1.62623e15	−0.214608	−0.107304	−	0.994226i	$-0.534222\pi$
$131$	−1.62623e15	−0.214608	−0.107304	+	0.994226i	$0.534222\pi$
$132$	9.57227e14i	0.119319i
$133$	4.41222e15i	0.519721i
$134$	6.22897e15	0.693634
$135$	0	0
$136$	−6.71467e15	−0.669088
$137$	− 1.05922e16i	− 0.999038i	−0.866303	−	0.499519i	$-0.833510\pi$
$137$	− 1.05922e16i	− 0.999038i	0.866303	−	0.499519i	$-0.166490\pi$
$138$	− 6.83474e15i	− 0.610421i
$139$	1.86709e16	1.57963	0.789813	−	0.613347i	$-0.210177\pi$
$139$	1.86709e16	1.57963	0.789813	+	0.613347i	$0.210177\pi$
$140$	0	0
$141$	1.14190e16	0.867928
$142$	− 2.70108e16i	− 1.94704i
$143$	− 3.91301e15i	− 0.267603i
$144$	−4.19461e15	−0.272253
$145$	0	0
$146$	−1.77490e16	−1.03879
$147$	1.07762e16i	0.599219i
$148$	− 1.43554e16i	− 0.758667i
$149$	1.25560e16	0.630889	0.315444	−	0.948944i	$-0.397846\pi$
$149$	1.25560e16	0.630889	0.315444	+	0.948944i	$0.397846\pi$
$150$	0	0
$151$	2.87588e16	1.30751	0.653753	−	0.756708i	$-0.273194\pi$
$151$	2.87588e16	1.30751	0.653753	+	0.756708i	$0.273194\pi$
$152$	6.37509e15i	0.275841i
$153$	− 5.16977e15i	− 0.212954i
$154$	−1.25508e16	−0.492340
$155$	0	0
$156$	8.83784e15	0.314711
$157$	1.45276e16i	0.493114i	0.969128	+	0.246557i	$0.0792993\pi$
$157$	1.45276e16i	0.493114i	−0.969128	+	0.246557i	$0.920701\pi$
$158$	− 5.48922e15i	− 0.177657i
$159$	2.27569e16	0.702480
$160$	0	0
$161$	2.66754e16	0.749750
$162$	3.26117e16i	0.875005i
$163$	1.67741e16i	0.429767i	0.976640	+	0.214884i	$0.0689372\pi$
$163$	1.67741e16i	0.429767i	−0.976640	+	0.214884i	$0.931063\pi$
$164$	−2.28037e16	−0.558055
$165$	0	0
$166$	−6.08551e16	−1.35984
$167$	− 6.41999e16i	− 1.37139i	−0.727889	−	0.685695i	$-0.759498\pi$
$167$	− 6.41999e16i	− 1.37139i	0.727889	−	0.685695i	$-0.240502\pi$
$168$	3.85362e16i	0.787134i
$169$	1.50580e16	0.294183
$170$	0	0
$171$	−4.90832e15	−0.0877934
$172$	6.83849e15i	0.117084i
$173$	− 7.59860e16i	− 1.24563i	−0.782370	−	0.622814i	$-0.785990\pi$
$173$	− 7.59860e16i	− 1.24563i	0.782370	−	0.622814i	$-0.214010\pi$
$174$	−2.66868e16	−0.418964
$175$	0	0
$176$	−2.75029e16	−0.396309
$177$	3.30075e16i	0.455840i
$178$	1.54574e17i	2.04638i
$179$	−9.33749e16	−1.18531	−0.592655	−	0.805456i	$-0.701920\pi$
$179$	−9.33749e16	−1.18531	−0.592655	+	0.805456i	$0.701920\pi$
$180$	0	0
$181$	7.43177e16	0.867966	0.433983	−	0.900921i	$-0.357108\pi$
$181$	7.43177e16	0.867966	0.433983	+	0.900921i	$0.357108\pi$
$182$	1.15878e17i	1.29857i
$183$	− 1.65118e16i	− 0.177587i
$184$	3.85424e16	0.397929
$185$	0	0
$186$	−5.17705e16	−0.492873
$187$	− 3.38968e16i	− 0.309990i
$188$	− 4.73676e16i	− 0.416196i
$189$	−1.65261e17	−1.39543
$190$	0	0
$191$	−9.86224e16	−0.769529	−0.384765	−	0.923015i	$-0.625717\pi$
$191$	−9.86224e16	−0.769529	−0.384765	+	0.923015i	$0.625717\pi$
$192$	3.45197e16i	0.259005i
$193$	− 8.91178e15i	− 0.0643109i	−0.999483	−	0.0321554i	$-0.989763\pi$
$193$	− 8.91178e15i	− 0.0643109i	0.999483	−	0.0321554i	$-0.0102372\pi$
$194$	−1.32362e17	−0.918861
$195$	0	0
$196$	4.47013e16	0.287342
$197$	− 3.54176e16i	− 0.219140i	−0.993979	−	0.109570i	$-0.965053\pi$
$197$	− 3.54176e16i	− 0.219140i	0.993979	−	0.109570i	$-0.0349474\pi$
$198$	− 1.39620e16i	− 0.0831682i
$199$	2.86461e17	1.64311	0.821556	−	0.570127i	$-0.193106\pi$
$199$	2.86461e17	1.64311	0.821556	+	0.570127i	$0.193106\pi$
$200$	0	0
$201$	9.65490e16	0.513780
$202$	1.76611e17i	0.905485i
$203$	− 1.04156e17i	− 0.514593i
$204$	7.65587e16	0.364559
$205$	0	0
$206$	1.60081e17	0.708492
$207$	2.96746e16i	0.126651i
$208$	2.53928e17i	1.04529i
$209$	−3.21825e16	−0.127798
$210$	0	0
$211$	3.75834e17	1.38956	0.694780	−	0.719222i	$-0.255502\pi$
$211$	3.75834e17	1.38956	0.694780	+	0.719222i	$0.255502\pi$
$212$	− 9.43988e16i	− 0.336859i
$213$	− 4.18668e17i	− 1.44219i
$214$	5.43089e17	1.80621
$215$	0	0
$216$	−2.38781e17	−0.740621
$217$	− 2.02055e17i	− 0.605372i
$218$	2.73964e17i	0.792995i
$219$	−2.75110e17	−0.769441
$220$	0	0
$221$	−3.12961e17	−0.817614
$222$	− 7.47504e17i	− 1.88784i
$223$	− 2.53078e16i	− 0.0617970i	−0.999523	−	0.0308985i	$-0.990163\pi$
$223$	− 2.53078e16i	− 0.0617970i	0.999523	−	0.0308985i	$-0.00983687\pi$
$224$	4.37295e17	1.03256
$225$	0	0
$226$	−4.43699e17	−0.980111
$227$	− 3.03692e17i	− 0.648992i	−0.945887	−	0.324496i	$-0.894805\pi$
$227$	− 3.03692e17i	− 0.648992i	0.945887	−	0.324496i	$-0.105195\pi$
$228$	− 7.26868e16i	− 0.150295i
$229$	−1.07992e17	−0.216085	−0.108042	−	0.994146i	$-0.534458\pi$
$229$	−1.07992e17	−0.216085	−0.108042	+	0.994146i	$0.534458\pi$
$230$	0	0
$231$	−1.94537e17	−0.364681
$232$	− 1.50492e17i	− 0.273119i
$233$	− 7.90506e17i	− 1.38911i	−0.719441	−	0.694554i	$-0.755602\pi$
$233$	− 7.90506e17i	− 1.38911i	0.719441	−	0.694554i	$-0.244398\pi$
$234$	−1.28907e17	−0.219360
$235$	0	0
$236$	1.36920e17	0.218588
$237$	− 8.50830e16i	− 0.131592i
$238$	1.00381e18i	1.50426i
$239$	−3.52956e17	−0.512551	−0.256275	−	0.966604i	$-0.582495\pi$
$239$	−3.52956e17	−0.512551	−0.256275	+	0.966604i	$0.582495\pi$
$240$	0	0
$241$	6.85690e16	0.0935405	0.0467703	−	0.998906i	$-0.485107\pi$
$241$	6.85690e16	0.0935405	0.0467703	+	0.998906i	$0.485107\pi$
$242$	8.10741e17i	1.07218i
$243$	− 3.34679e17i	− 0.429123i
$244$	−6.84934e16	−0.0851580
$245$	0	0
$246$	−1.18742e18	−1.38865
$247$	2.97134e17i	0.337073i
$248$	− 2.91944e17i	− 0.321300i
$249$	−9.43255e17	−1.00724
$250$	0	0
$251$	1.58806e18	1.59703	0.798515	−	0.601975i	$-0.205619\pi$
$251$	1.58806e18	1.59703	0.798515	+	0.601975i	$0.205619\pi$
$252$	1.23075e17i	0.120134i
$253$	1.94569e17i	0.184361i
$254$	−6.45986e17	−0.594251
$255$	0	0
$256$	1.23980e18	1.07535
$257$	8.28562e17i	0.697954i	0.937131	+	0.348977i	$0.113471\pi$
$257$	8.28562e17i	0.697954i	−0.937131	+	0.348977i	$0.886529\pi$
$258$	3.56090e17i	0.291348i
$259$	2.91744e18	2.31875
$260$	0	0
$261$	1.15867e17	0.0869271
$262$	3.51265e17i	0.256080i
$263$	1.40445e18i	0.995038i	0.867453	+	0.497519i	$0.165756\pi$
$263$	1.40445e18i	0.995038i	−0.867453	+	0.497519i	$0.834244\pi$
$264$	−2.81081e17	−0.193554
$265$	0	0
$266$	9.53041e17	0.620153
$267$	2.39589e18i	1.51577i
$268$	− 4.00500e17i	− 0.246372i
$269$	−1.43582e18	−0.858930	−0.429465	−	0.903083i	$-0.641298\pi$
$269$	−1.43582e18	−0.858930	−0.429465	+	0.903083i	$0.641298\pi$
$270$	0	0
$271$	5.09160e17	0.288127	0.144064	−	0.989568i	$-0.453983\pi$
$271$	5.09160e17	0.288127	0.144064	+	0.989568i	$0.453983\pi$
$272$	2.19967e18i	1.21085i
$273$	1.79611e18i	0.961865i
$274$	−2.28792e18	−1.19209
$275$	0	0
$276$	−4.39449e17	−0.216815
$277$	− 5.68946e17i	− 0.273195i	−0.990627	−	0.136598i	$-0.956383\pi$
$277$	− 5.68946e17i	− 0.273195i	0.990627	−	0.136598i	$-0.0436167\pi$
$278$	− 4.03292e18i	− 1.88488i
$279$	2.24774e17	0.102262
$280$	0	0
$281$	−4.06184e18	−1.75156	−0.875780	−	0.482710i	$-0.839652\pi$
$281$	−4.06184e18	−1.75156	−0.875780	+	0.482710i	$0.839652\pi$
$282$	− 2.46650e18i	− 1.03565i
$283$	2.78506e18i	1.13877i	0.822071	+	0.569385i	$0.192819\pi$
$283$	2.78506e18i	1.13877i	−0.822071	+	0.569385i	$0.807181\pi$
$284$	−1.73670e18	−0.691570
$285$	0	0
$286$	−8.45211e17	−0.319315
$287$	− 4.63440e18i	− 1.70561i
$288$	4.86463e17i	0.174424i
$289$	1.51369e17	0.0528813
$290$	0	0
$291$	−2.05161e18	−0.680608
$292$	1.14120e18i	0.368969i
$293$	− 3.63803e18i	− 1.14646i	−0.819395	−	0.573230i	$-0.805690\pi$
$293$	− 3.63803e18i	− 1.14646i	0.819395	−	0.573230i	$-0.194310\pi$
$294$	2.32766e18	0.715013
$295$	0	0
$296$	4.21532e18	1.23067
$297$	− 1.20541e18i	− 0.343131i
$298$	− 2.71209e18i	− 0.752803i
$299$	1.79641e18	0.486262
$300$	0	0
$301$	−1.38979e18	−0.357849
$302$	− 6.21190e18i	− 1.56017i
$303$	2.73746e18i	0.670701i
$304$	2.08843e18	0.499192
$305$	0	0
$306$	−1.11667e18	−0.254106
$307$	9.75296e17i	0.216570i	0.994120	+	0.108285i	$0.0345359\pi$
$307$	9.75296e17i	0.216570i	−0.994120	+	0.108285i	$0.965464\pi$
$308$	8.06969e17i	0.174874i
$309$	2.48125e18	0.524786
$310$	0	0
$311$	3.36692e17	0.0678468	0.0339234	−	0.999424i	$-0.489200\pi$
$311$	3.36692e17	0.0678468	0.0339234	+	0.999424i	$0.489200\pi$
$312$	2.59515e18i	0.510508i
$313$	3.65551e18i	0.702046i	0.936367	+	0.351023i	$0.114166\pi$
$313$	3.65551e18i	0.702046i	−0.936367	+	0.351023i	$0.885834\pi$
$314$	3.13797e18	0.588405
$315$	0	0
$316$	−3.52937e17	−0.0631021
$317$	7.97380e17i	0.139226i	0.997574	+	0.0696131i	$0.0221765\pi$
$317$	7.97380e17i	0.139226i	−0.997574	+	0.0696131i	$0.977824\pi$
$318$	− 4.91548e18i	− 0.838229i
$319$	7.59708e17	0.126537
$320$	0	0
$321$	8.41788e18	1.33787
$322$	− 5.76188e18i	− 0.894633i
$323$	2.57395e18i	0.390464i
$324$	2.09681e18	0.310793
$325$	0	0
$326$	3.62321e18	0.512816
$327$	4.24645e18i	0.587378i
$328$	− 6.69610e18i	− 0.905249i
$329$	9.62651e18	1.27204
$330$	0	0
$331$	−1.01585e19	−1.28269	−0.641343	−	0.767255i	$-0.721622\pi$
$331$	−1.01585e19	−1.28269	−0.641343	+	0.767255i	$0.721622\pi$
$332$	3.91276e18i	0.483000i
$333$	3.24546e18i	0.391692i
$334$	−1.38672e19	−1.63640
$335$	0	0
$336$	1.26241e19	1.42448
$337$	4.81465e18i	0.531301i	0.964069	+	0.265651i	$0.0855868\pi$
$337$	4.81465e18i	0.531301i	−0.964069	+	0.265651i	$0.914413\pi$
$338$	− 3.25253e18i	− 0.351032i
$339$	−6.87734e18	−0.725977
$340$	0	0
$341$	1.47378e18	0.148859
$342$	1.06020e18i	0.104759i
$343$	− 4.31515e18i	− 0.417148i
$344$	−2.00806e18	−0.189928
$345$	0	0
$346$	−1.64130e19	−1.48634
$347$	− 4.50275e18i	− 0.399031i	−0.979895	−	0.199516i	$-0.936063\pi$
$347$	− 4.50275e18i	− 0.399031i	0.979895	−	0.199516i	$-0.0639369\pi$
$348$	1.71586e18i	0.148812i
$349$	−2.24323e19	−1.90407	−0.952036	−	0.305986i	$-0.901014\pi$
$349$	−2.24323e19	−1.90407	−0.952036	+	0.305986i	$0.901014\pi$
$350$	0	0
$351$	−1.11292e19	−0.905026
$352$	3.18961e18i	0.253902i
$353$	8.02510e18i	0.625374i	0.949856	+	0.312687i	$0.101229\pi$
$353$	8.02510e18i	0.625374i	−0.949856	+	0.312687i	$0.898771\pi$
$354$	7.12961e18	0.543928
$355$	0	0
$356$	9.93851e18	0.726853
$357$	1.55590e19i	1.11422i
$358$	2.01690e19i	1.41436i
$359$	−1.61507e18	−0.110913	−0.0554567	−	0.998461i	$-0.517661\pi$
$359$	−1.61507e18	−0.110913	−0.0554567	+	0.998461i	$0.517661\pi$
$360$	0	0
$361$	−1.27374e19	−0.839026
$362$	− 1.60526e19i	− 1.03569i
$363$	1.25665e19i	0.794171i
$364$	7.45055e18	0.461241
$365$	0	0
$366$	−3.56655e18	−0.211905
$367$	9.97799e18i	0.580828i	0.956901	+	0.290414i	$0.0937931\pi$
$367$	9.97799e18i	0.580828i	−0.956901	+	0.290414i	$0.906207\pi$
$368$	− 1.26262e19i	− 0.720135i
$369$	5.15547e18	0.288118
$370$	0	0
$371$	1.91847e19	1.02956
$372$	3.32865e18i	0.175064i
$373$	− 2.36866e19i	− 1.22092i	−0.792048	−	0.610459i	$-0.790985\pi$
$373$	− 2.36866e19i	− 1.22092i	0.792048	−	0.610459i	$-0.209015\pi$
$374$	−7.32171e18	−0.369893
$375$	0	0
$376$	1.39090e19	0.675132
$377$	− 7.01419e18i	− 0.333747i
$378$	3.56964e19i	1.66508i
$379$	−1.86851e19	−0.854480	−0.427240	−	0.904138i	$-0.640514\pi$
$379$	−1.86851e19	−0.854480	−0.427240	+	0.904138i	$0.640514\pi$
$380$	0	0
$381$	−1.00128e19	−0.440167
$382$	2.13024e19i	0.918235i
$383$	− 3.02521e19i	− 1.27869i	−0.768921	−	0.639343i	$-0.779206\pi$
$383$	− 3.02521e19i	− 1.27869i	0.768921	−	0.639343i	$-0.220794\pi$
$384$	2.44537e19	1.01358
$385$	0	0
$386$	−1.92494e18	−0.0767385
$387$	− 1.54605e18i	− 0.0604493i
$388$	8.51037e18i	0.326370i
$389$	1.00714e18	0.0378852	0.0189426	−	0.999821i	$-0.493970\pi$
$389$	1.00714e18	0.0378852	0.0189426	+	0.999821i	$0.493970\pi$
$390$	0	0
$391$	1.55615e19	0.563283
$392$	1.31261e19i	0.466112i
$393$	5.44461e18i	0.189680i
$394$	−7.65020e18	−0.261487
$395$	0	0
$396$	−8.97702e17	−0.0295405
$397$	− 3.56324e19i	− 1.15058i	−0.817950	−	0.575290i	$-0.804889\pi$
$397$	− 3.56324e19i	− 1.15058i	0.817950	−	0.575290i	$-0.195111\pi$
$398$	− 6.18756e19i	− 1.96063i
$399$	1.47721e19	0.459353
$400$	0	0
$401$	3.94327e19	1.18106	0.590532	−	0.807014i	$-0.298918\pi$
$401$	3.94327e19	1.18106	0.590532	+	0.807014i	$0.298918\pi$
$402$	− 2.08546e19i	− 0.613065i
$403$	− 1.36071e19i	− 0.392624i
$404$	1.13554e19	0.321620
$405$	0	0
$406$	−2.24977e19	−0.614034
$407$	2.12796e19i	0.570172i
$408$	2.24807e19i	0.591370i
$409$	5.27823e19	1.36321	0.681607	−	0.731719i	$-0.261282\pi$
$409$	5.27823e19	1.36321	0.681607	+	0.731719i	$0.261282\pi$
$410$	0	0
$411$	−3.54627e19	−0.882995
$412$	− 1.02926e19i	− 0.251649i
$413$	2.78262e19i	0.668080i
$414$	6.40972e18	0.151125
$415$	0	0
$416$	2.94488e19	0.669681
$417$	− 6.25102e19i	− 1.39615i
$418$	6.95143e18i	0.152494i
$419$	−8.62630e18	−0.185874	−0.0929372	−	0.995672i	$-0.529626\pi$
$419$	−8.62630e18	−0.185874	−0.0929372	+	0.995672i	$0.529626\pi$
$420$	0	0
$421$	−4.29249e19	−0.892469	−0.446235	−	0.894916i	$-0.647235\pi$
$421$	−4.29249e19	−0.892469	−0.446235	+	0.894916i	$0.647235\pi$
$422$	− 8.11801e19i	− 1.65808i
$423$	1.07089e19i	0.214878i
$424$	2.77193e19	0.546435
$425$	0	0
$426$	−9.04322e19	−1.72088
$427$	− 1.39199e19i	− 0.260272i
$428$	− 3.49186e19i	− 0.641547i
$429$	−1.31008e19	−0.236519
$430$	0	0
$431$	5.04764e19	0.880053	0.440026	−	0.897985i	$-0.354969\pi$
$431$	5.04764e19	0.880053	0.440026	+	0.897985i	$0.354969\pi$
$432$	7.82227e19i	1.34031i
$433$	5.05734e19i	0.851653i	0.904805	+	0.425827i	$0.140017\pi$
$433$	5.05734e19i	0.851653i	−0.904805	+	0.425827i	$0.859983\pi$
$434$	−4.36440e19	−0.722356
$435$	0	0
$436$	1.76149e19	0.281664
$437$	− 1.47745e19i	− 0.232222i
$438$	5.94238e19i	0.918130i
$439$	−2.47946e19	−0.376594	−0.188297	−	0.982112i	$-0.560297\pi$
$439$	−2.47946e19	−0.376594	−0.188297	+	0.982112i	$0.560297\pi$
$440$	0	0
$441$	−1.01061e19	−0.148352
$442$	6.75996e19i	0.975612i
$443$	− 1.30654e20i	− 1.85394i	−0.375135	−	0.926970i	$-0.622404\pi$
$443$	− 1.30654e20i	− 1.85394i	0.375135	−	0.926970i	$-0.377596\pi$
$444$	−4.80617e19	−0.670544
$445$	0	0
$446$	−5.46648e18	−0.0737389
$447$	− 4.20373e19i	− 0.557608i
$448$	2.91011e19i	0.379598i
$449$	7.78280e19	0.998363	0.499181	−	0.866498i	$-0.333634\pi$
$449$	7.78280e19	0.998363	0.499181	+	0.866498i	$0.333634\pi$
$450$	0	0
$451$	3.38031e19	0.419404
$452$	2.85282e19i	0.348126i
$453$	− 9.62844e19i	− 1.15563i
$454$	−6.55975e19	−0.774405
$455$	0	0
$456$	2.13438e19	0.243801
$457$	1.18451e20i	1.33096i	0.746414	+	0.665482i	$0.231774\pi$
$457$	1.18451e20i	1.33096i	−0.746414	+	0.665482i	$0.768226\pi$
$458$	2.33262e19i	0.257841i
$459$	−9.64078e19	−1.04838
$460$	0	0
$461$	1.38643e20	1.45929	0.729644	−	0.683827i	$-0.239686\pi$
$461$	1.38643e20	1.45929	0.729644	+	0.683827i	$0.239686\pi$
$462$	4.20200e19i	0.435153i
$463$	1.75645e20i	1.78969i	0.446375	+	0.894846i	$0.352715\pi$
$463$	1.75645e20i	1.78969i	−0.446375	+	0.894846i	$0.647285\pi$
$464$	−4.92999e19	−0.494266
$465$	0	0
$466$	−1.70749e20	−1.65754
$467$	1.36631e20i	1.30519i	0.757708	+	0.652593i	$0.226319\pi$
$467$	1.36631e20i	1.30519i	−0.757708	+	0.652593i	$0.773681\pi$
$468$	8.28826e18i	0.0779147i
$469$	8.13935e19	0.752997
$470$	0	0
$471$	4.86385e19	0.435837
$472$	4.02052e19i	0.354583i
$473$	− 1.01370e19i	− 0.0879938i
$474$	−1.83779e19	−0.157021
$475$	0	0
$476$	6.45410e19	0.534298
$477$	2.13417e19i	0.173917i
$478$	7.62386e19i	0.611597i
$479$	−6.41058e19	−0.506269	−0.253134	−	0.967431i	$-0.581461\pi$
$479$	−6.41058e19	−0.506269	−0.253134	+	0.967431i	$0.581461\pi$
$480$	0	0
$481$	1.96470e20	1.50386
$482$	− 1.48109e19i	− 0.111617i
$483$	− 8.93091e19i	− 0.662662i
$484$	5.21276e19	0.380827
$485$	0	0
$486$	−7.22907e19	−0.512047
$487$	2.41343e19i	0.168332i	0.996452	+	0.0841662i	$0.0268227\pi$
$487$	2.41343e19i	0.168332i	−0.996452	+	0.0841662i	$0.973177\pi$
$488$	− 2.01124e19i	− 0.138139i
$489$	5.61598e19	0.379847
$490$	0	0
$491$	−2.80908e19	−0.184269	−0.0921346	−	0.995747i	$-0.529369\pi$
$491$	−2.80908e19	−0.184269	−0.0921346	+	0.995747i	$0.529369\pi$
$492$	7.63469e19i	0.493234i
$493$	− 6.07611e19i	− 0.386611i
$494$	6.41808e19	0.402210
$495$	0	0
$496$	−9.56384e19	−0.581460
$497$	− 3.52948e20i	− 2.11368i
$498$	2.03743e20i	1.20188i
$499$	1.71994e20	0.999443	0.499722	−	0.866186i	$-0.333436\pi$
$499$	1.71994e20	0.999443	0.499722	+	0.866186i	$0.333436\pi$
$500$	0	0
$501$	−2.14941e20	−1.21210
$502$	− 3.43020e20i	− 1.90564i
$503$	− 1.83497e20i	− 1.00431i	−0.864778	−	0.502155i	$-0.832541\pi$
$503$	− 1.83497e20i	− 1.00431i	0.864778	−	0.502155i	$-0.167459\pi$
$504$	−3.61398e19	−0.194875
$505$	0	0
$506$	4.20268e19	0.219987
$507$	− 5.04142e19i	− 0.260012i
$508$	4.15345e19i	0.211072i
$509$	−2.67204e20	−1.33801	−0.669004	−	0.743258i	$-0.733279\pi$
$509$	−2.67204e20	−1.33801	−0.669004	+	0.743258i	$0.733279\pi$
$510$	0	0
$511$	−2.31925e20	−1.12769
$512$	− 2.84604e19i	− 0.136369i
$513$	9.15321e19i	0.432209i
$514$	1.78969e20	0.832828
$515$	0	0
$516$	2.28953e19	0.103484
$517$	7.02153e19i	0.312790i
$518$	− 6.30167e20i	− 2.76683i
$519$	−2.54401e20	−1.10094
$520$	0	0
$521$	−2.01468e20	−0.847076	−0.423538	−	0.905878i	$-0.639212\pi$
$521$	−2.01468e20	−0.847076	−0.423538	+	0.905878i	$0.639212\pi$
$522$	− 2.50272e19i	− 0.103725i
$523$	3.58989e20i	1.46662i	0.679894	+	0.733311i	$0.262026\pi$
$523$	3.58989e20i	1.46662i	−0.679894	+	0.733311i	$0.737974\pi$
$524$	2.25850e19	0.0909570
$525$	0	0
$526$	3.03362e20	1.18732
$527$	− 1.17872e20i	− 0.454813i
$528$	9.20799e19i	0.350276i
$529$	1.77312e20	0.664997
$530$	0	0
$531$	−3.09549e19	−0.112855
$532$	− 6.12770e19i	− 0.220272i
$533$	− 3.12095e20i	− 1.10620i
$534$	5.17512e20	1.80868
$535$	0	0
$536$	1.17603e20	0.399652
$537$	3.12619e20i	1.04763i
$538$	3.10137e20i	1.02491i
$539$	−6.62628e19	−0.215950
$540$	0	0
$541$	2.02328e20	0.641323	0.320662	−	0.947194i	$-0.396095\pi$
$541$	2.02328e20	0.641323	0.320662	+	0.947194i	$0.396095\pi$
$542$	− 1.09979e20i	− 0.343806i
$543$	− 2.48816e20i	− 0.767147i
$544$	2.55103e20	0.775755
$545$	0	0
$546$	3.87961e20	1.14774
$547$	− 7.40963e19i	− 0.216218i	−0.994139	−	0.108109i	$-0.965520\pi$
$547$	− 7.40963e19i	− 0.216218i	0.994139	−	0.108109i	$-0.0344795\pi$
$548$	1.47104e20i	0.423420i
$549$	1.54850e19	0.0439662
$550$	0	0
$551$	−5.76882e19	−0.159386
$552$	− 1.29040e20i	− 0.351707i
$553$	− 7.17273e19i	− 0.192862i
$554$	−1.22892e20	−0.325988
$555$	0	0
$556$	−2.59302e20	−0.669490
$557$	− 2.09626e18i	− 0.00533987i	−0.999996	−	0.00266994i	$-0.999150\pi$
$557$	− 2.09626e18i	− 0.00533987i	0.999996	−	0.00266994i	$-0.000849868\pi$
$558$	− 4.85511e19i	− 0.122023i
$559$	−9.35927e19	−0.232088
$560$	0	0
$561$	−1.13487e20	−0.273983
$562$	8.77357e20i	2.09004i
$563$	6.87353e20i	1.61572i	0.589373	+	0.807861i	$0.299375\pi$
$563$	6.87353e20i	1.61572i	−0.589373	+	0.807861i	$0.700625\pi$
$564$	−1.58587e20	−0.367852
$565$	0	0
$566$	6.01573e20	1.35883
$567$	4.26134e20i	0.949891i
$568$	− 5.09964e20i	− 1.12183i
$569$	9.05218e19	0.196522	0.0982610	−	0.995161i	$-0.468672\pi$
$569$	9.05218e19	0.196522	0.0982610	+	0.995161i	$0.468672\pi$
$570$	0	0
$571$	2.05774e20	0.435130	0.217565	−	0.976046i	$-0.430189\pi$
$571$	2.05774e20	0.435130	0.217565	+	0.976046i	$0.430189\pi$
$572$	5.43439e19i	0.113418i
$573$	3.30188e20i	0.680145i
$574$	−1.00103e21	−2.03520
$575$	0	0
$576$	−3.23731e19	−0.0641233
$577$	− 5.70778e20i	− 1.11596i	−0.829854	−	0.557980i	$-0.811576\pi$
$577$	− 5.70778e20i	− 1.11596i	0.829854	−	0.557980i	$-0.188424\pi$
$578$	− 3.26956e19i	− 0.0631002i
$579$	−2.98366e19	−0.0568408
$580$	0	0
$581$	−7.95190e20	−1.47622
$582$	4.43147e20i	0.812130i
$583$	1.39932e20i	0.253164i
$584$	−3.35102e20	−0.598522
$585$	0	0
$586$	−7.85814e20	−1.36800
$587$	9.30363e20i	1.59907i	0.600621	+	0.799534i	$0.294920\pi$
$587$	9.30363e20i	1.59907i	−0.600621	+	0.799534i	$0.705080\pi$
$588$	− 1.49660e20i	− 0.253966i
$589$	−1.11911e20	−0.187503
$590$	0	0
$591$	−1.18578e20	−0.193686
$592$	− 1.38090e21i	− 2.22716i
$593$	3.54225e20i	0.564116i	0.959397	+	0.282058i	$0.0910171\pi$
$593$	3.54225e20i	0.564116i	−0.959397	+	0.282058i	$0.908983\pi$
$594$	−2.60368e20	−0.409438
$595$	0	0
$596$	−1.74377e20	−0.267388
$597$	− 9.59071e20i	− 1.45226i
$598$	− 3.88024e20i	− 0.580229i
$599$	3.30045e20	0.487385	0.243693	−	0.969853i	$-0.421641\pi$
$599$	3.30045e20	0.487385	0.243693	+	0.969853i	$0.421641\pi$
$600$	0	0
$601$	−3.35884e20	−0.483761	−0.241880	−	0.970306i	$-0.577764\pi$
$601$	−3.35884e20	−0.483761	−0.241880	+	0.970306i	$0.577764\pi$
$602$	3.00194e20i	0.427000i
$603$	9.05451e19i	0.127199i
$604$	−3.99402e20	−0.554158
$605$	0	0
$606$	5.91292e20	0.800309
$607$	1.33438e21i	1.78387i	0.452165	+	0.891934i	$0.350652\pi$
$607$	1.33438e21i	1.78387i	−0.452165	+	0.891934i	$0.649348\pi$
$608$	− 2.42202e20i	− 0.319816i
$609$	−3.48714e20	−0.454820
$610$	0	0
$611$	6.48280e20	0.825000
$612$	7.17978e19i	0.0902559i
$613$	5.68844e18i	0.00706381i	0.999994	+	0.00353191i	$0.00112424\pi$
$613$	5.68844e18i	0.00706381i	−0.999994	+	0.00353191i	$0.998876\pi$
$614$	2.10664e20	0.258421
$615$	0	0
$616$	−2.36959e20	−0.283673
$617$	− 3.98915e20i	− 0.471783i	−0.971779	−	0.235891i	$-0.924199\pi$
$617$	− 3.98915e20i	− 0.471783i	0.971779	−	0.235891i	$-0.0758010\pi$
$618$	− 5.35950e20i	− 0.626197i
$619$	5.40017e20	0.623343	0.311672	−	0.950190i	$-0.399111\pi$
$619$	5.40017e20	0.623343	0.311672	+	0.950190i	$0.399111\pi$
$620$	0	0
$621$	5.53384e20	0.623504
$622$	− 7.27254e19i	− 0.0809577i
$623$	2.01980e21i	2.22151i
$624$	8.50151e20	0.923871
$625$	0	0
$626$	7.89591e20	0.837711
$627$	1.07747e20i	0.112953i
$628$	− 2.01760e20i	− 0.208996i
$629$	1.70194e21	1.74206
$630$	0	0
$631$	9.59111e20	0.958625	0.479312	−	0.877644i	$-0.340886\pi$
$631$	9.59111e20	0.958625	0.479312	+	0.877644i	$0.340886\pi$
$632$	− 1.03637e20i	− 0.102361i
$633$	− 1.25829e21i	− 1.22816i
$634$	1.72234e20	0.166131
$635$	0	0
$636$	−3.16047e20	−0.297731
$637$	6.11788e20i	0.569581i
$638$	− 1.64097e20i	− 0.150989i
$639$	3.92633e20	0.357051
$640$	0	0
$641$	−9.25925e20	−0.822509	−0.411255	−	0.911521i	$-0.634909\pi$
$641$	−9.25925e20	−0.822509	−0.411255	+	0.911521i	$0.634909\pi$
$642$	− 1.81826e21i	− 1.59641i
$643$	− 7.65928e20i	− 0.664669i	−0.943162	−	0.332335i	$-0.892164\pi$
$643$	− 7.65928e20i	− 0.664669i	0.943162	−	0.332335i	$-0.107836\pi$
$644$	−3.70467e20	−0.317765
$645$	0	0
$646$	5.55972e20	0.465918
$647$	− 1.36075e21i	− 1.12719i	−0.826051	−	0.563596i	$-0.809418\pi$
$647$	− 1.36075e21i	− 1.12719i	0.826051	−	0.563596i	$-0.190582\pi$
$648$	6.15709e20i	0.504153i
$649$	−2.02963e20	−0.164279
$650$	0	0
$651$	−6.76481e20	−0.535055
$652$	− 2.32959e20i	− 0.182147i
$653$	− 2.71809e20i	− 0.210094i	−0.994467	−	0.105047i	$-0.966501\pi$
$653$	− 2.71809e20i	− 0.210094i	0.994467	−	0.105047i	$-0.0334994\pi$
$654$	9.17233e20	0.700885
$655$	0	0
$656$	−2.19359e21	−1.63824
$657$	− 2.58002e20i	− 0.190495i
$658$	− 2.07933e21i	− 1.51785i
$659$	−6.74316e20	−0.486657	−0.243329	−	0.969944i	$-0.578239\pi$
$659$	−6.74316e20	−0.486657	−0.243329	+	0.969944i	$0.578239\pi$
$660$	0	0
$661$	1.26727e21	0.894042	0.447021	−	0.894524i	$-0.352485\pi$
$661$	1.26727e21	0.894042	0.447021	+	0.894524i	$0.352485\pi$
$662$	2.19424e21i	1.53056i
$663$	1.04779e21i	0.722644i
$664$	−1.14894e21	−0.783499
$665$	0	0
$666$	7.01020e20	0.467384
$667$	3.48770e20i	0.229930i
$668$	8.91609e20i	0.581234i
$669$	−8.47305e19	−0.0546190
$670$	0	0
$671$	1.01531e20	0.0640000
$672$	− 1.46406e21i	− 0.912620i
$673$	− 1.13945e21i	− 0.702394i	−0.936302	−	0.351197i	$-0.885775\pi$
$673$	− 1.13945e21i	− 0.702394i	0.936302	−	0.351197i	$-0.114225\pi$
$674$	1.03997e21	0.633971
$675$	0	0
$676$	−2.09126e20	−0.124683
$677$	− 1.74431e21i	− 1.02851i	−0.857637	−	0.514256i	$-0.828068\pi$
$677$	− 1.74431e21i	− 1.02851i	0.857637	−	0.514256i	$-0.171932\pi$
$678$	1.48550e21i	0.866266i
$679$	−1.72956e21	−0.997500
$680$	0	0
$681$	−1.01676e21	−0.573608
$682$	− 3.18337e20i	− 0.177625i
$683$	− 1.43739e21i	− 0.793267i	−0.917977	−	0.396634i	$-0.870178\pi$
$683$	− 1.43739e21i	− 0.793267i	0.917977	−	0.396634i	$-0.129822\pi$
$684$	6.81667e19	0.0372093
$685$	0	0
$686$	−9.32073e20	−0.497759
$687$	3.61556e20i	0.190985i
$688$	6.57825e20i	0.343714i
$689$	1.29196e21	0.667735
$690$	0	0
$691$	−1.77548e21	−0.897903	−0.448951	−	0.893556i	$-0.648202\pi$
$691$	−1.77548e21	−0.897903	−0.448951	+	0.893556i	$0.648202\pi$
$692$	1.05529e21i	0.527932i
$693$	− 1.82440e20i	− 0.0902860i
$694$	−9.72594e20	−0.476141
$695$	0	0
$696$	−5.03846e20	−0.241395
$697$	− 2.70356e21i	− 1.28141i
$698$	4.84538e21i	2.27202i
$699$	−2.64661e21	−1.22776
$700$	0	0
$701$	1.43100e21	0.649764	0.324882	−	0.945755i	$-0.394675\pi$
$701$	1.43100e21	0.649764	0.324882	+	0.945755i	$0.394675\pi$
$702$	2.40391e21i	1.07992i
$703$	− 1.61586e21i	− 0.718191i
$704$	−2.12262e20	−0.0933420
$705$	0	0
$706$	1.73342e21	0.746223
$707$	2.30776e21i	0.982980i
$708$	− 4.58408e20i	− 0.193198i
$709$	2.41840e21	1.00851	0.504257	−	0.863554i	$-0.331766\pi$
$709$	2.41840e21	1.00851	0.504257	+	0.863554i	$0.331766\pi$
$710$	0	0
$711$	7.97921e19	0.0325790
$712$	2.91835e21i	1.17906i
$713$	6.76591e20i	0.270492i
$714$	3.36074e21	1.32953
$715$	0	0
$716$	1.29679e21	0.502368
$717$	1.18170e21i	0.453015i
$718$	3.48856e20i	0.132347i
$719$	−4.74444e21	−1.78122	−0.890611	−	0.454766i	$-0.849723\pi$
$719$	−4.74444e21	−1.78122	−0.890611	+	0.454766i	$0.849723\pi$
$720$	0	0
$721$	2.09176e21	0.769127
$722$	2.75127e21i	1.00116i
$723$	− 2.29569e20i	− 0.0826753i
$724$	−1.03212e21	−0.367868
$725$	0	0
$726$	2.71436e21	0.947639
$727$	3.59265e21i	1.24138i	0.784054	+	0.620692i	$0.213148\pi$
$727$	3.59265e21i	1.24138i	−0.784054	+	0.620692i	$0.786852\pi$
$728$	2.18778e21i	0.748202i
$729$	−3.28690e21	−1.11258
$730$	0	0
$731$	−8.10755e20	−0.268850
$732$	2.29316e20i	0.0752664i
$733$	− 2.76824e21i	− 0.899339i	−0.893195	−	0.449669i	$-0.851542\pi$
$733$	− 2.76824e21i	− 0.899339i	0.893195	−	0.449669i	$-0.148458\pi$
$734$	2.15525e21	0.693069
$735$	0	0
$736$	−1.46430e21	−0.461367
$737$	5.93680e20i	0.185160i
$738$	− 1.11358e21i	− 0.343795i
$739$	−3.55824e21	−1.08743	−0.543716	−	0.839269i	$-0.682983\pi$
$739$	−3.55824e21	−1.08743	−0.543716	+	0.839269i	$0.682983\pi$
$740$	0	0
$741$	9.94803e20	0.297921
$742$	− 4.14389e21i	− 1.22851i
$743$	− 1.94092e21i	− 0.569628i	−0.958583	−	0.284814i	$-0.908068\pi$
$743$	− 1.94092e21i	− 0.569628i	0.958583	−	0.284814i	$-0.0919319\pi$
$744$	−9.77427e20	−0.283980
$745$	0	0
$746$	−5.11630e21	−1.45685
$747$	− 8.84598e20i	− 0.249368i
$748$	4.70759e20i	0.131382i
$749$	7.09651e21	1.96079
$750$	0	0
$751$	4.75565e21	1.28798	0.643992	−	0.765032i	$-0.277277\pi$
$751$	4.75565e21	1.28798	0.643992	+	0.765032i	$0.277277\pi$
$752$	− 4.55650e21i	− 1.22179i
$753$	− 5.31681e21i	− 1.41153i
$754$	−1.51507e21	−0.398241
$755$	0	0
$756$	2.29514e21	0.591421
$757$	− 3.62137e21i	− 0.923960i	−0.886890	−	0.461980i	$-0.847139\pi$
$757$	− 3.62137e21i	− 0.923960i	0.886890	−	0.461980i	$-0.152861\pi$
$758$	4.03599e21i	1.01960i
$759$	6.51416e20	0.162947
$760$	0	0
$761$	−3.86361e21	−0.947564	−0.473782	−	0.880642i	$-0.657112\pi$
$761$	−3.86361e21	−0.947564	−0.473782	+	0.880642i	$0.657112\pi$
$762$	2.16276e21i	0.525226i
$763$	3.57987e21i	0.860862i
$764$	1.36967e21	0.326148
$765$	0	0
$766$	−6.53445e21	−1.52578
$767$	1.87391e21i	0.433294i
$768$	− 4.15085e21i	− 0.950446i
$769$	5.39327e21	1.22294	0.611469	−	0.791268i	$-0.290579\pi$
$769$	5.39327e21	1.22294	0.611469	+	0.791268i	$0.290579\pi$
$770$	0	0
$771$	2.77403e21	0.616883
$772$	1.23767e20i	0.0272568i
$773$	6.57037e21i	1.43299i	0.697591	+	0.716496i	$0.254255\pi$
$773$	6.57037e21i	1.43299i	−0.697591	+	0.716496i	$0.745745\pi$
$774$	−3.33947e20	−0.0721306
$775$	0	0
$776$	−2.49899e21	−0.529422
$777$	− 9.76758e21i	− 2.04941i
$778$	− 2.17543e20i	− 0.0452062i
$779$	−2.56683e21	−0.528282
$780$	0	0
$781$	2.57439e21	0.519746
$782$	− 3.36129e21i	− 0.672133i
$783$	− 2.16073e21i	− 0.427944i
$784$	4.30001e21	0.843527
$785$	0	0
$786$	1.17604e21	0.226335
$787$	3.72074e20i	0.0709281i	0.999371	+	0.0354641i	$0.0112909\pi$
$787$	3.72074e20i	0.0709281i	−0.999371	+	0.0354641i	$0.988709\pi$
$788$	4.91879e20i	0.0928778i
$789$	4.70211e21	0.879459
$790$	0	0
$791$	−5.79778e21	−1.06399
$792$	− 2.63602e20i	− 0.0479192i
$793$	− 9.37412e20i	− 0.168804i
$794$	−7.69660e21	−1.37292
$795$	0	0
$796$	−3.97837e21	−0.696397
$797$	− 2.61511e21i	− 0.453474i	−0.973956	−	0.226737i	$-0.927194\pi$
$797$	− 2.61511e21i	− 0.453474i	0.973956	−	0.226737i	$-0.0728058\pi$
$798$	− 3.19078e21i	− 0.548119i
$799$	5.61579e21	0.955674
$800$	0	0
$801$	−2.24690e21	−0.375267
$802$	− 8.51746e21i	− 1.40930i
$803$	− 1.69165e21i	− 0.277296i
$804$	−1.34087e21	−0.217755
$805$	0	0
$806$	−2.93913e21	−0.468495
$807$	4.80713e21i	0.759161i
$808$	3.33441e21i	0.521715i
$809$	−5.34899e21	−0.829198	−0.414599	−	0.910004i	$-0.636078\pi$
$809$	−5.34899e21	−0.829198	−0.414599	+	0.910004i	$0.636078\pi$
$810$	0	0
$811$	8.46492e21	1.28815	0.644075	−	0.764962i	$-0.277242\pi$
$811$	8.46492e21	1.28815	0.644075	+	0.764962i	$0.277242\pi$
$812$	1.44652e21i	0.218099i
$813$	− 1.70467e21i	− 0.254660i
$814$	4.59640e21	0.680354
$815$	0	0
$816$	7.36451e21	1.07021
$817$	7.69753e20i	0.110837i
$818$	− 1.14010e22i	− 1.62664i
$819$	−1.68442e21	−0.238134
$820$	0	0
$821$	7.99397e21	1.10966	0.554829	−	0.831965i	$-0.312784\pi$
$821$	7.99397e21	1.10966	0.554829	+	0.831965i	$0.312784\pi$
$822$	7.65994e21i	1.05363i
$823$	1.96841e21i	0.268297i	0.990961	+	0.134148i	$0.0428299\pi$
$823$	1.96841e21i	0.268297i	−0.990961	+	0.134148i	$0.957170\pi$
$824$	3.02232e21	0.408213
$825$	0	0
$826$	6.01046e21	0.797181
$827$	1.43539e22i	1.88659i	0.331954	+	0.943296i	$0.392292\pi$
$827$	1.43539e22i	1.88659i	−0.331954	+	0.943296i	$0.607708\pi$
$828$	− 4.12121e20i	− 0.0536782i
$829$	8.83327e21	1.14015	0.570076	−	0.821592i	$-0.306914\pi$
$829$	8.83327e21	1.14015	0.570076	+	0.821592i	$0.306914\pi$
$830$	0	0
$831$	−1.90483e21	−0.241462
$832$	1.95976e21i	0.246195i
$833$	5.29967e21i	0.659799i
$834$	−1.35022e22	−1.66594
$835$	0	0
$836$	4.46951e20	0.0541643
$837$	− 4.19166e21i	− 0.503437i
$838$	1.86328e21i	0.221793i
$839$	−1.26696e22	−1.49469	−0.747343	−	0.664439i	$-0.768671\pi$
$839$	−1.26696e22	−1.49469	−0.747343	+	0.664439i	$0.768671\pi$
$840$	0	0
$841$	−7.26739e21	−0.842187
$842$	9.27177e21i	1.06493i
$843$	1.35990e22i	1.54811i
$844$	−5.21958e21	−0.588935
$845$	0	0
$846$	2.31312e21	0.256401
$847$	1.05939e22i	1.16394i
$848$	− 9.08064e21i	− 0.988889i
$849$	9.32438e21	1.00650
$850$	0	0
$851$	−9.76917e21	−1.03606
$852$	5.81446e21i	0.611241i
$853$	6.00532e21i	0.625776i	0.949790	+	0.312888i	$0.101296\pi$
$853$	6.00532e21i	0.625776i	−0.949790	+	0.312888i	$0.898704\pi$
$854$	−3.00670e21	−0.310568
$855$	0	0
$856$	1.02535e22	1.04069
$857$	− 1.47589e22i	− 1.48491i	−0.669898	−	0.742453i	$-0.733662\pi$
$857$	− 1.47589e22i	− 1.48491i	0.669898	−	0.742453i	$-0.266338\pi$
$858$	2.82976e21i	0.282225i
$859$	−9.64956e20	−0.0954023	−0.0477012	−	0.998862i	$-0.515190\pi$
$859$	−9.64956e20	−0.0954023	−0.0477012	+	0.998862i	$0.515190\pi$
$860$	0	0
$861$	−1.55160e22	−1.50749
$862$	− 1.09029e22i	− 1.05012i
$863$	3.44391e21i	0.328829i	0.986391	+	0.164415i	$0.0525735\pi$
$863$	3.44391e21i	0.328829i	−0.986391	+	0.164415i	$0.947426\pi$
$864$	9.07173e21	0.858691
$865$	0	0
$866$	1.09239e22	1.01623
$867$	− 5.06782e20i	− 0.0467389i
$868$	2.80614e21i	0.256574i
$869$	5.23175e20	0.0474241
$870$	0	0
$871$	5.48130e21	0.488368
$872$	5.17245e21i	0.456901i
$873$	− 1.92403e21i	− 0.168502i
$874$	−3.19130e21	−0.277097
$875$	0	0
$876$	3.82073e21	0.326111
$877$	1.09850e22i	0.929617i	0.885411	+	0.464808i	$0.153877\pi$
$877$	1.09850e22i	0.929617i	−0.885411	+	0.464808i	$0.846123\pi$
$878$	5.35564e21i	0.449368i
$879$	−1.21801e22	−1.01329
$880$	0	0
$881$	−7.98462e21	−0.653033	−0.326516	−	0.945192i	$-0.605875\pi$
$881$	−7.98462e21	−0.653033	−0.326516	+	0.945192i	$0.605875\pi$
$882$	2.18291e21i	0.177020i
$883$	5.45236e21i	0.438409i	0.975679	+	0.219204i	$0.0703461\pi$
$883$	5.45236e21i	0.438409i	−0.975679	+	0.219204i	$0.929654\pi$
$884$	4.34640e21	0.346528
$885$	0	0
$886$	−2.82213e22	−2.21220
$887$	− 1.67127e22i	− 1.29903i	−0.760347	−	0.649517i	$-0.774971\pi$
$887$	− 1.67127e22i	− 1.29903i	0.760347	−	0.649517i	$-0.225029\pi$
$888$	− 1.41129e22i	− 1.08772i
$889$	−8.44105e21	−0.645109
$890$	0	0
$891$	−3.10820e21	−0.233575
$892$	3.51475e20i	0.0261913i
$893$	− 5.33178e21i	− 0.393991i
$894$	−9.08007e21	−0.665361
$895$	0	0
$896$	2.06151e22	1.48551
$897$	− 6.01436e21i	− 0.429780i
$898$	− 1.68108e22i	− 1.19129i
$899$	2.64180e21	0.185653
$900$	0	0
$901$	1.11917e22	0.773500
$902$	− 7.30146e21i	− 0.500450i
$903$	4.65300e21i	0.316283i
$904$	−8.37704e21	−0.564712
$905$	0	0
$906$	−2.07974e22	−1.37895
$907$	1.53384e22i	1.00862i	0.863523	+	0.504309i	$0.168253\pi$
$907$	1.53384e22i	1.00862i	−0.863523	+	0.504309i	$0.831747\pi$
$908$	4.21767e21i	0.275061i
$909$	−2.56723e21	−0.166049
$910$	0	0
$911$	−1.49134e22	−0.948829	−0.474415	−	0.880302i	$-0.657340\pi$
$911$	−1.49134e22	−0.948829	−0.474415	+	0.880302i	$0.657340\pi$
$912$	− 6.99206e21i	− 0.441209i
$913$	− 5.80007e21i	− 0.362997i
$914$	2.55854e22	1.58816
$915$	0	0
$916$	1.49979e21	0.0915827
$917$	4.58995e21i	0.277996i
$918$	2.08241e22i	1.25097i
$919$	5.86667e21	0.349563	0.174782	−	0.984607i	$-0.444078\pi$
$919$	5.86667e21	0.349563	0.174782	+	0.984607i	$0.444078\pi$
$920$	0	0
$921$	3.26529e21	0.191414
$922$	− 2.99469e22i	− 1.74129i
$923$	− 2.37687e22i	− 1.37086i
$924$	2.70173e21	0.154562
$925$	0	0
$926$	3.79393e22	2.13554
$927$	2.32695e21i	0.129924i
$928$	5.71747e21i	0.316660i
$929$	1.67946e22	0.922684	0.461342	−	0.887222i	$-0.347368\pi$
$929$	1.67946e22	0.922684	0.461342	+	0.887222i	$0.347368\pi$
$930$	0	0
$931$	5.03165e21	0.272012
$932$	1.09786e22i	0.588743i
$933$	− 1.12724e21i	− 0.0599661i
$934$	2.95123e22	1.55740
$935$	0	0
$936$	−2.43377e21	−0.126389
$937$	− 5.04466e21i	− 0.259887i	−0.991521	−	0.129944i	$-0.958520\pi$
$937$	− 5.04466e21i	− 0.259887i	0.991521	−	0.129944i	$-0.0414796\pi$
$938$	− 1.75810e22i	− 0.898508i
$939$	1.22387e22	0.620500
$940$	0	0
$941$	1.65425e22	0.825430	0.412715	−	0.910860i	$-0.364581\pi$
$941$	1.65425e22	0.825430	0.412715	+	0.910860i	$0.364581\pi$
$942$	− 1.05059e22i	− 0.520059i
$943$	1.55185e22i	0.762100i
$944$	1.31709e22	0.641691
$945$	0	0
$946$	−2.18960e21	−0.104998
$947$	9.81583e21i	0.466984i	0.972359	+	0.233492i	$0.0750153\pi$
$947$	9.81583e21i	0.466984i	−0.972359	+	0.233492i	$0.924985\pi$
$948$	1.18163e21i	0.0557725i
$949$	−1.56186e22	−0.731384
$950$	0	0
$951$	2.66963e21	0.123054
$952$	1.89519e22i	0.866712i
$953$	− 5.97914e21i	− 0.271295i	−0.990757	−	0.135648i	$-0.956689\pi$
$953$	− 5.97914e21i	− 0.271295i	0.990757	−	0.135648i	$-0.0433115\pi$
$954$	4.60981e21	0.207525
$955$	0	0
$956$	4.90186e21	0.217233
$957$	− 2.54350e21i	− 0.111839i
$958$	1.38469e22i	0.604101i
$959$	−2.98960e22	−1.29412
$960$	0	0
$961$	−1.83404e22	−0.781596
$962$	− 4.24375e22i	− 1.79447i
$963$	7.89441e21i	0.331225i
$964$	−9.52286e20	−0.0396451
$965$	0	0
$966$	−1.92908e22	−0.790717
$967$	1.44757e22i	0.588764i	0.955688	+	0.294382i	$0.0951137\pi$
$967$	1.44757e22i	0.588764i	−0.955688	+	0.294382i	$0.904886\pi$
$968$	1.53068e22i	0.617759i
$969$	8.61757e21	0.345109
$970$	0	0
$971$	1.77921e21	0.0701590	0.0350795	−	0.999385i	$-0.488832\pi$
$971$	1.77921e21	0.0701590	0.0350795	+	0.999385i	$0.488832\pi$
$972$	4.64802e21i	0.181874i
$973$	− 5.26978e22i	− 2.04619i
$974$	5.21301e21	0.200861
$975$	0	0
$976$	−6.58868e21	−0.249991
$977$	− 1.04088e22i	− 0.391913i	−0.980613	−	0.195957i	$-0.937219\pi$
$977$	− 1.04088e22i	− 0.391913i	0.980613	−	0.195957i	$-0.0627812\pi$
$978$	− 1.21305e22i	− 0.453250i
$979$	−1.47323e22	−0.546262
$980$	0	0
$981$	−3.98238e21	−0.145420
$982$	6.06761e21i	0.219878i
$983$	3.26461e22i	1.17403i	0.809575	+	0.587017i	$0.199698\pi$
$983$	3.26461e22i	1.17403i	−0.809575	+	0.587017i	$0.800302\pi$
$984$	−2.24185e22	−0.800100
$985$	0	0
$986$	−1.31244e22	−0.461320
$987$	− 3.22295e22i	− 1.12428i
$988$	− 4.12659e21i	− 0.142861i
$989$	4.65376e21	0.159894
$990$	0	0
$991$	−7.47327e21	−0.252906	−0.126453	−	0.991973i	$-0.540359\pi$
$991$	−7.47327e21	−0.252906	−0.126453	+	0.991973i	$0.540359\pi$
$992$	1.10915e22i	0.372523i
$993$	3.40107e22i	1.13369i
$994$	−7.62369e22	−2.52213
$995$	0	0
$996$	1.30999e22	0.426897
$997$	3.10809e22i	1.00526i	0.864500	+	0.502632i	$0.167635\pi$
$997$	3.10809e22i	1.00526i	−0.864500	+	0.502632i	$0.832365\pi$
$998$	− 3.71506e22i	− 1.19258i
$999$	6.05226e22	1.92831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.16.b.a.24.1		2
5.2	odd	4		1.16.a.a.1.1	✓	1
5.3	odd	4		25.16.a.a.1.1		1
5.4	even	2	inner	25.16.b.a.24.2		2
15.2	even	4		9.16.a.a.1.1		1
20.7	even	4		16.16.a.d.1.1		1
35.2	odd	12		49.16.c.c.18.1		2
35.12	even	12		49.16.c.b.18.1		2
35.17	even	12		49.16.c.b.30.1		2
35.27	even	4		49.16.a.a.1.1		1
35.32	odd	12		49.16.c.c.30.1		2
40.27	even	4		64.16.a.c.1.1		1
40.37	odd	4		64.16.a.i.1.1		1
55.32	even	4		121.16.a.a.1.1		1
60.47	odd	4		144.16.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.16.a.a.1.1	✓	1	5.2	odd	4
9.16.a.a.1.1		1	15.2	even	4
16.16.a.d.1.1		1	20.7	even	4
25.16.a.a.1.1		1	5.3	odd	4
25.16.b.a.24.1		2	1.1	even	1	trivial
25.16.b.a.24.2		2	5.4	even	2	inner
49.16.a.a.1.1		1	35.27	even	4
49.16.c.b.18.1		2	35.12	even	12
49.16.c.b.30.1		2	35.17	even	12
49.16.c.c.18.1		2	35.2	odd	12
49.16.c.c.30.1		2	35.32	odd	12
64.16.a.c.1.1		1	40.27	even	4
64.16.a.i.1.1		1	40.37	odd	4
121.16.a.a.1.1		1	55.32	even	4
144.16.a.f.1.1		1	60.47	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-216.000i q^{2} -3348.00i q^{3} -13888.0 q^{4} -723168. q^{6} -2.82246e6i q^{7} -4.07808e6i q^{8} +3.13980e6 q^{9} +O(q^{10})\)	\(q-216.000i q^{2} -3348.00i q^{3} -13888.0 q^{4} -723168. q^{6} -2.82246e6i q^{7} -4.07808e6i q^{8} +3.13980e6 q^{9} +2.05869e7 q^{11} +4.64970e7i q^{12} -1.90073e8i q^{13} -6.09650e8 q^{14} -1.33595e9 q^{16} -1.64653e9i q^{17} -6.78197e8i q^{18} -1.56326e9 q^{19} -9.44958e9 q^{21} -4.44676e9i q^{22} +9.45112e9i q^{23} -1.36534e10 q^{24} -4.10558e10 q^{26} -5.85522e10i q^{27} +3.91983e10i q^{28} +3.69026e10 q^{29} +7.15885e10 q^{31} +1.54934e11i q^{32} -6.89248e10i q^{33} -3.55650e11 q^{34} -4.36056e10 q^{36} +1.03365e12i q^{37} +3.37664e11i q^{38} -6.36366e11 q^{39} +1.64197e12 q^{41} +2.04111e12i q^{42} -4.92403e11i q^{43} -2.85910e11 q^{44} +2.04144e12 q^{46} +3.41068e12i q^{47} +4.47275e12i q^{48} -3.21870e12 q^{49} -5.51258e12 q^{51} +2.63974e12i q^{52} +6.79715e12i q^{53} -1.26473e13 q^{54} -1.15102e13 q^{56} +5.23379e12i q^{57} -7.97095e12i q^{58} -9.85886e12 q^{59} +4.93184e12 q^{61} -1.54631e13i q^{62} -8.86196e12i q^{63} -1.03106e13 q^{64} -1.48878e13 q^{66} +2.88378e13i q^{67} +2.28670e13i q^{68} +3.16423e13 q^{69} +1.25050e14 q^{71} -1.28044e13i q^{72} -8.21715e13i q^{73} +2.23269e14 q^{74} +2.17105e13 q^{76} -5.81055e13i q^{77} +1.37455e14i q^{78} +2.54131e13 q^{79} -1.50980e14 q^{81} -3.54666e14i q^{82} -2.81737e14i q^{83} +1.31236e14 q^{84} -1.06359e14 q^{86} -1.23550e14i q^{87} -8.39548e13i q^{88} -7.15619e14 q^{89} -5.36474e14 q^{91} -1.31257e14i q^{92} -2.39678e14i q^{93} +7.36708e14 q^{94} +5.18719e14 q^{96} -6.12786e14i q^{97} +6.95238e14i q^{98} +6.46387e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 27776 q^{4} - 1446336 q^{6} + 6279606 q^{9}+O(q^{10}) \) 2 * q - 27776 * q^4 - 1446336 * q^6 + 6279606 * q^9	\( 2 q - 27776 q^{4} - 1446336 q^{6} + 6279606 q^{9} + 41173704 q^{11} - 1219300992 q^{14} - 2671894528 q^{16} - 3126514360 q^{19} - 18899165376 q^{21} - 27306823680 q^{24} - 82111682016 q^{26} + 73805136660 q^{29} + 143176967104 q^{31} - 711300089952 q^{34} - 87211168128 q^{36} - 1272731071248 q^{39} + 3283948036404 q^{41} - 571820401152 q^{44} + 4082882143104 q^{46} - 6437392723986 q^{49} - 11025151394256 q^{51} - 25294550866560 q^{54} - 23020402728960 q^{56} - 19717713631080 q^{59} + 9863685253804 q^{61} - 20621115785216 q^{64} - 29775505174272 q^{66} + 63284673218112 q^{69} + 250100229829104 q^{71} + 446537699231328 q^{74} + 43421031431680 q^{76} + 50826157388960 q^{79} - 301960055941038 q^{81} + 262471608741888 q^{84} - 212718143221056 q^{86} - 14\!\cdots\!20 q^{89}+ \cdots + 129277319340312 q^{99}+O(q^{100}) \) 2 * q - 27776 * q^4 - 1446336 * q^6 + 6279606 * q^9 + 41173704 * q^11 - 1219300992 * q^14 - 2671894528 * q^16 - 3126514360 * q^19 - 18899165376 * q^21 - 27306823680 * q^24 - 82111682016 * q^26 + 73805136660 * q^29 + 143176967104 * q^31 - 711300089952 * q^34 - 87211168128 * q^36 - 1272731071248 * q^39 + 3283948036404 * q^41 - 571820401152 * q^44 + 4082882143104 * q^46 - 6437392723986 * q^49 - 11025151394256 * q^51 - 25294550866560 * q^54 - 23020402728960 * q^56 - 19717713631080 * q^59 + 9863685253804 * q^61 - 20621115785216 * q^64 - 29775505174272 * q^66 + 63284673218112 * q^69 + 250100229829104 * q^71 + 446537699231328 * q^74 + 43421031431680 * q^76 + 50826157388960 * q^79 - 301960055941038 * q^81 + 262471608741888 * q^84 - 212718143221056 * q^86 - 1431237129553620 * q^89 - 1072947266556256 * q^91 + 1473415899533568 * q^94 + 1037438623678464 * q^96 + 129277319340312 * q^99

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