Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(111,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.h (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: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 111.2 | ||
Root | \(1.07046 + 0.924187i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1120.111 |
Dual form | 1120.2.h.b.111.15 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 0 | ||||||||
\(3\) | − | 2.99734i | − | 1.73052i | −0.501328 | − | 0.865258i | \(-0.667155\pi\) | ||
0.501328 | − | 0.865258i | \(-0.332845\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.183359 | − | 2.63939i | −0.0693031 | − | 0.997596i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.98405 | −1.99468 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.87706 | −1.47049 | −0.735244 | − | 0.677803i | \(-0.762932\pi\) | ||||
−0.735244 | + | 0.677803i | \(0.762932\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.42800 | −0.673406 | −0.336703 | − | 0.941611i | \(-0.609312\pi\) | ||||
−0.336703 | + | 0.941611i | \(0.609312\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.99734i | − | 0.773910i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.92955i | 0.953057i | 0.879159 | + | 0.476528i | \(0.158105\pi\) | ||||
−0.879159 | + | 0.476528i | \(0.841895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.24043i | 1.20224i | 0.799160 | + | 0.601118i | \(0.205278\pi\) | ||||
−0.799160 | + | 0.601118i | \(0.794722\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.91115 | + | 0.549588i | −1.72635 | + | 0.119930i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.114122i | 0.0237961i | 0.999929 | + | 0.0118981i | \(0.00378736\pi\) | ||||
−0.999929 | + | 0.0118981i | \(0.996213\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.94421i | 1.72131i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.60881i | − | 0.670139i | −0.942193 | − | 0.335069i | \(-0.891240\pi\) | ||
0.942193 | − | 0.335069i | \(-0.108760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.62694 | −0.831023 | −0.415511 | − | 0.909588i | \(-0.636397\pi\) | ||||
−0.415511 | + | 0.909588i | \(0.636397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.6182i | 2.54470i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.183359 | − | 2.63939i | −0.0309933 | − | 0.446138i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.83800i | − | 1.28856i | −0.764790 | − | 0.644279i | \(-0.777157\pi\) | ||
0.764790 | − | 0.644279i | \(-0.222843\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.27754i | 1.16534i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.4815i | − | 1.63694i | −0.574552 | − | 0.818468i | \(-0.694824\pi\) | ||
0.574552 | − | 0.818468i | \(-0.305176\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.76350 | −0.421430 | −0.210715 | − | 0.977548i | \(-0.567579\pi\) | ||||
−0.210715 | + | 0.977548i | \(0.567579\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.98405 | −0.892049 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0817 | 1.76229 | 0.881145 | − | 0.472846i | \(-0.156773\pi\) | ||||
0.881145 | + | 0.472846i | \(0.156773\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.93276 | + | 0.967910i | −0.990394 | + | 0.138273i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.7782 | 1.64928 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.668088i | 0.0917689i | 0.998947 | + | 0.0458845i | \(0.0146106\pi\) | ||||
−0.998947 | + | 0.0458845i | \(0.985389\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.87706 | −0.657622 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15.7073 | 2.08049 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.37541i | 0.179063i | 0.995984 | + | 0.0895314i | \(0.0285369\pi\) | ||||
−0.995984 | + | 0.0895314i | \(0.971463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.17808 | −0.150837 | −0.0754186 | − | 0.997152i | \(-0.524029\pi\) | ||||
−0.0754186 | + | 0.997152i | \(0.524029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.09723 | + | 15.7942i | 0.138238 | + | 1.98989i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.42800 | −0.301156 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.57766 | −0.314911 | −0.157456 | − | 0.987526i | \(-0.550329\pi\) | ||||
−0.157456 | + | 0.987526i | \(0.550329\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.342063 | 0.0411795 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.43699i | − | 1.11996i | −0.828505 | − | 0.559982i | \(-0.810808\pi\) | ||
0.828505 | − | 0.559982i | \(-0.189192\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.62623i | − | 0.658500i | −0.944243 | − | 0.329250i | \(-0.893204\pi\) | ||
0.944243 | − | 0.329250i | \(-0.106796\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 2.99734i | − | 0.346103i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.894251 | + | 12.8725i | 0.101909 | + | 1.46695i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.8804i | − | 1.33665i | −0.743872 | − | 0.668323i | \(-0.767013\pi\) | ||
0.743872 | − | 0.668323i | \(-0.232987\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.85669 | 0.984077 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.52348i | 0.606280i | 0.952946 | + | 0.303140i | \(0.0980350\pi\) | ||||
−0.952946 | + | 0.303140i | \(0.901965\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.92955i | 0.426220i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.8168 | −1.15969 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.21826i | 0.659135i | 0.944132 | + | 0.329567i | \(0.106903\pi\) | ||||
−0.944132 | + | 0.329567i | \(0.893097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.445195 | + | 6.40844i | 0.0466691 | + | 0.671787i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.8685i | 1.43810i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.24043i | 0.537657i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.85094i | 0.797142i | 0.917137 | + | 0.398571i | \(0.130494\pi\) | ||||
−0.917137 | + | 0.398571i | \(0.869506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 29.1845 | 2.93316 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9057 | −1.08516 | −0.542580 | − | 0.840004i | \(-0.682552\pi\) | ||||
−0.542580 | + | 0.840004i | \(0.682552\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.8202 | −1.55881 | −0.779403 | − | 0.626523i | \(-0.784477\pi\) | ||||
−0.779403 | + | 0.626523i | \(0.784477\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.91115 | + | 0.549588i | −0.772049 | + | 0.0536343i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.53444 | −0.631708 | −0.315854 | − | 0.948808i | \(-0.602291\pi\) | ||||
−0.315854 | + | 0.948808i | \(0.602291\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9309i | 1.04699i | 0.852028 | + | 0.523496i | \(0.175372\pi\) | ||||
−0.852028 | + | 0.523496i | \(0.824628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.4931 | −2.22987 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.72004 | 0.349951 | 0.174976 | − | 0.984573i | \(-0.444015\pi\) | ||||
0.174976 | + | 0.984573i | \(0.444015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.114122i | 0.0106419i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.5293 | 1.34323 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.3716 | − | 0.720518i | 0.950766 | − | 0.0660498i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.7857 | 1.16233 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −31.4166 | −2.83274 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.80326i | − | 0.337485i | −0.985660 | − | 0.168742i | \(-0.946029\pi\) | ||
0.985660 | − | 0.168742i | \(-0.0539706\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.28315i | 0.729291i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 7.68109i | − | 0.671100i | −0.942022 | − | 0.335550i | \(-0.891078\pi\) | ||
0.942022 | − | 0.335550i | \(-0.108922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.8315 | − | 0.960878i | 1.19935 | − | 0.0833187i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.94421i | 0.769795i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.9739 | −1.45018 | −0.725090 | − | 0.688655i | \(-0.758202\pi\) | ||||
−0.725090 | + | 0.688655i | \(0.758202\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.54598i | − | 0.215947i | −0.994154 | − | 0.107973i | \(-0.965564\pi\) | ||
0.994154 | − | 0.107973i | \(-0.0344362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 36.2128i | − | 3.04967i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.8415 | 0.990235 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 3.60881i | − | 0.299695i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.90116 | + | 20.7798i | 0.239283 | + | 1.71389i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 13.7925i | − | 1.12992i | −0.825118 | − | 0.564961i | \(-0.808891\pi\) | ||
0.825118 | − | 0.564961i | \(-0.191109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 0.128374i | − | 0.0104469i | −0.999986 | − | 0.00522347i | \(-0.998337\pi\) | ||
0.999986 | − | 0.00522347i | \(-0.00166269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 23.5146i | − | 1.90105i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.62694 | −0.371645 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.1585 | 1.05017 | 0.525083 | − | 0.851051i | \(-0.324034\pi\) | ||||
0.525083 | + | 0.851051i | \(0.324034\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.00249 | 0.158808 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.301213 | − | 0.0209253i | 0.0237389 | − | 0.00164914i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.158264 | −0.0123962 | −0.00619809 | − | 0.999981i | \(-0.501973\pi\) | ||||
−0.00619809 | + | 0.999981i | \(0.501973\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.6182i | 1.13802i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.7105 | 1.29310 | 0.646550 | − | 0.762871i | \(-0.276211\pi\) | ||||
0.646550 | + | 0.762871i | \(0.276211\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.10482 | −0.546524 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 31.3590i | − | 2.39808i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.19433 | 0.394918 | 0.197459 | − | 0.980311i | \(-0.436731\pi\) | ||||
0.197459 | + | 0.980311i | \(0.436731\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.183359 | − | 2.63939i | −0.0138606 | − | 0.199519i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.12256 | 0.309871 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.3274 | 1.29511 | 0.647555 | − | 0.762019i | \(-0.275792\pi\) | ||||
0.647555 | + | 0.762019i | \(0.275792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.0585 | 1.56526 | 0.782631 | − | 0.622485i | \(-0.213877\pi\) | ||||
0.782631 | + | 0.622485i | \(0.213877\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.53110i | 0.261026i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 7.83800i | − | 0.576261i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 19.1647i | − | 1.40146i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 23.6073 | − | 1.64000i | 1.71718 | − | 0.119292i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.43465i | − | 0.610310i | −0.952303 | − | 0.305155i | \(-0.901292\pi\) | ||
0.952303 | − | 0.305155i | \(-0.0987083\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.6337 | −1.84516 | −0.922578 | − | 0.385811i | \(-0.873922\pi\) | ||||
−0.922578 | + | 0.385811i | \(0.873922\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.27754i | 0.521156i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.78729i | − | 0.127339i | −0.997971 | − | 0.0636697i | \(-0.979720\pi\) | ||
0.997971 | − | 0.0636697i | \(-0.0202804\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.3178 | −1.58206 | −0.791032 | − | 0.611774i | \(-0.790456\pi\) | ||||
−0.791032 | + | 0.611774i | \(0.790456\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.72612i | 0.544958i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.52505 | + | 0.661706i | −0.668527 | + | 0.0464427i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 10.4815i | − | 0.732060i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.682913i | − | 0.0474657i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 25.5579i | − | 1.76787i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.58471 | −0.590996 | −0.295498 | − | 0.955343i | \(-0.595486\pi\) | ||||
−0.295498 | + | 0.955343i | \(0.595486\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −28.2859 | −1.93812 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.76350 | −0.188469 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.848389 | + | 12.2123i | 0.0575924 | + | 0.829024i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.8637 | −1.13954 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 9.54096i | − | 0.641794i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0359 | 0.939916 | 0.469958 | − | 0.882689i | \(-0.344269\pi\) | ||||
0.469958 | + | 0.882689i | \(0.344269\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.98405 | −0.398937 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 29.9063i | − | 1.98495i | −0.122442 | − | 0.992476i | \(-0.539073\pi\) | ||
0.122442 | − | 0.992476i | \(-0.460927\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.92103 | −0.589518 | −0.294759 | − | 0.955572i | \(-0.595239\pi\) | ||||
−0.294759 | + | 0.955572i | \(0.595239\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 38.5831 | − | 2.68037i | 2.53858 | − | 0.176356i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.565155 | 0.0370245 | 0.0185123 | − | 0.999829i | \(-0.494107\pi\) | ||||
0.0185123 | + | 0.999829i | \(0.494107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.0817 | 0.788120 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −35.6095 | −2.31309 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.51136i | − | 0.550554i | −0.961365 | − | 0.275277i | \(-0.911230\pi\) | ||
0.961365 | − | 0.275277i | \(-0.0887695\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.17523i | 0.140119i | 0.997543 | + | 0.0700595i | \(0.0223189\pi\) | ||||
−0.997543 | + | 0.0700595i | \(0.977681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.286112i | 0.0183541i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.93276 | + | 0.967910i | −0.442918 | + | 0.0618375i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 12.7238i | − | 0.809593i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.5557 | 1.04918 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.41690i | 0.594390i | 0.954817 | + | 0.297195i | \(0.0960511\pi\) | ||||
−0.954817 | + | 0.297195i | \(0.903949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.556580i | − | 0.0349919i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.7782 | 0.737580 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 4.44138i | − | 0.277045i | −0.990359 | − | 0.138523i | \(-0.955765\pi\) | ||
0.990359 | − | 0.138523i | \(-0.0442354\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.6875 | + | 1.43717i | −1.28546 | + | 0.0893011i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.5953i | 1.33671i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 13.6247i | − | 0.840132i | −0.907493 | − | 0.420066i | \(-0.862007\pi\) | ||
0.907493 | − | 0.420066i | \(-0.137993\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.668088i | 0.0410403i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.6383 | 1.14064 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2713 | −0.626253 | −0.313127 | − | 0.949711i | \(-0.601376\pi\) | ||||
−0.313127 | + | 0.949711i | \(0.601376\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.67264 | 0.162352 | 0.0811758 | − | 0.996700i | \(-0.474132\pi\) | ||||
0.0811758 | + | 0.996700i | \(0.474132\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.2083 | − | 1.33440i | 1.16254 | − | 0.0807616i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.87706 | −0.294098 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 28.1383i | − | 1.69067i | −0.534239 | − | 0.845333i | \(-0.679402\pi\) | ||
0.534239 | − | 0.845333i | \(-0.320598\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.6878 | 1.65763 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.466842 | 0.0278494 | 0.0139247 | − | 0.999903i | \(-0.495567\pi\) | ||||
0.0139247 | + | 0.999903i | \(0.495567\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.8004i | 0.642019i | 0.947076 | + | 0.321009i | \(0.104022\pi\) | ||||
−0.947076 | + | 0.321009i | \(0.895978\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.7073 | 0.930423 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.6648 | + | 1.92188i | −1.63300 | + | 0.113445i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.55860 | 0.0916824 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.5319 | 1.37947 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.34532 | 0.429118 | 0.214559 | − | 0.976711i | \(-0.431169\pi\) | ||||
0.214559 | + | 0.976711i | \(0.431169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.37541i | 0.0800793i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 43.6214i | − | 2.53117i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 0.277089i | − | 0.0160244i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.506712 | + | 7.29396i | 0.0292064 | + | 0.420417i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.6882i | 1.87789i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.17808 | −0.0674564 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.08078i | 0.289975i | 0.989433 | + | 0.144988i | \(0.0463142\pi\) | ||||
−0.989433 | + | 0.144988i | \(0.953686\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 47.4184i | 2.69754i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.8319 | 1.01116 | 0.505578 | − | 0.862781i | \(-0.331279\pi\) | ||||
0.505578 | + | 0.862781i | \(0.331279\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.54008i | 0.200097i | 0.994983 | + | 0.100049i | \(0.0318998\pi\) | ||||
−0.994983 | + | 0.100049i | \(0.968100\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.09723 | + | 15.7942i | 0.0618218 | + | 0.889904i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.86360i | 0.273167i | 0.990629 | + | 0.136583i | \(0.0436122\pi\) | ||||
−0.990629 | + | 0.136583i | \(0.956388\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.6004i | 0.985431i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.5859i | 1.09318i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.5925 | −1.14580 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.42800 | −0.134681 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.7637 | 1.81183 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.21528 | − | 31.8882i | −0.122132 | − | 1.75805i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.38870 | 0.516050 | 0.258025 | − | 0.966138i | \(-0.416928\pi\) | ||||
0.258025 | + | 0.966138i | \(0.416928\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 46.9030i | 2.57027i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.57766 | −0.140832 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.7551 | 1.07613 | 0.538064 | − | 0.842904i | \(-0.319156\pi\) | ||||
0.538064 | + | 0.842904i | \(0.319156\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 11.1502i | − | 0.605596i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 22.5658 | 1.22201 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.82587 | + | 18.1208i | 0.206578 | + | 0.978430i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.342063 | 0.0184161 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.8093 | 1.60025 | 0.800124 | − | 0.599835i | \(-0.204767\pi\) | ||||
0.800124 | + | 0.599835i | \(0.204767\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.6993 | −0.840364 | −0.420182 | − | 0.907440i | \(-0.638034\pi\) | ||||
−0.420182 | + | 0.907440i | \(0.638034\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 21.7165i | − | 1.15914i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 10.2186i | − | 0.543879i | −0.962314 | − | 0.271939i | \(-0.912335\pi\) | ||
0.962314 | − | 0.271939i | \(-0.0876651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 9.43699i | − | 0.500863i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.15964 | − | 31.0873i | −0.114300 | − | 1.64531i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.4758i | 1.23900i | 0.784995 | + | 0.619502i | \(0.212666\pi\) | ||||
−0.784995 | + | 0.619502i | \(0.787334\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.46208 | −0.445373 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 38.3230i | − | 2.01144i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 5.62623i | − | 0.294490i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5002 | −1.12230 | −0.561151 | − | 0.827714i | \(-0.689641\pi\) | ||||
−0.561151 | + | 0.827714i | \(0.689641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 62.7218i | 3.26517i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.76334 | − | 0.122500i | 0.0915483 | − | 0.00635987i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.781051i | 0.0404413i | 0.999796 | + | 0.0202206i | \(0.00643687\pi\) | ||||
−0.999796 | + | 0.0202206i | \(0.993563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 2.99734i | − | 0.154782i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.76218i | 0.451275i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.53381 | −0.232886 | −0.116443 | − | 0.993197i | \(-0.537149\pi\) | ||||
−0.116443 | + | 0.993197i | \(0.537149\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3997 | −0.584023 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.0555 | 1.84235 | 0.921176 | − | 0.389147i | \(-0.127230\pi\) | ||||
0.921176 | + | 0.389147i | \(0.127230\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.894251 | + | 12.8725i | 0.0455752 | + | 0.656041i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.5369 | 0.840619 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 21.1691i | − | 1.07332i | −0.843800 | − | 0.536658i | \(-0.819687\pi\) | ||
0.843800 | − | 0.536658i | \(-0.180313\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.448449 | −0.0226791 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23.0228 | −1.16135 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 11.8804i | − | 0.597766i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.1445 | 0.709891 | 0.354946 | − | 0.934887i | \(-0.384499\pi\) | ||||
0.354946 | + | 0.934887i | \(0.384499\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.88008 | − | 41.4578i | −0.144184 | − | 2.07549i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8168 | 0.889729 | 0.444865 | − | 0.895598i | \(-0.353252\pi\) | ||||
0.444865 | + | 0.895598i | \(0.353252\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.2342 | 0.559616 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.85669 | 0.440092 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.2264i | 1.89481i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 32.5292i | − | 1.60846i | −0.594315 | − | 0.804232i | \(-0.702577\pi\) | ||
0.594315 | − | 0.804232i | \(-0.297423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 50.8766i | 2.50956i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.63024 | − | 0.252193i | 0.178632 | − | 0.0124096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.52348i | 0.271137i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.63116 | −0.373699 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 34.4793i | − | 1.68443i | −0.539146 | − | 0.842213i | \(-0.681253\pi\) | ||
0.539146 | − | 0.842213i | \(-0.318747\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2635i | 0.597688i | 0.954302 | + | 0.298844i | \(0.0966010\pi\) | ||||
−0.954302 | + | 0.298844i | \(0.903399\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −72.2972 | −3.51521 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.92955i | 0.190611i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.216011 | + | 3.10940i | 0.0104535 | + | 0.150475i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 35.4930i | − | 1.71362i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.7718i | 1.04871i | 0.851499 | + | 0.524357i | \(0.175694\pi\) | ||||
−0.851499 | + | 0.524357i | \(0.824306\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.1597i | 1.25715i | 0.777747 | + | 0.628577i | \(0.216362\pi\) | ||||
−0.777747 | + | 0.628577i | \(0.783638\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.8168 | −0.518627 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.598049 | −0.0286086 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.5333 | −1.40955 | −0.704775 | − | 0.709431i | \(-0.748952\pi\) | ||||
−0.704775 | + | 0.709431i | \(0.748952\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 41.4860 | − | 5.79202i | 1.97552 | − | 0.275811i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.7915 | 1.03535 | 0.517673 | − | 0.855579i | \(-0.326798\pi\) | ||||
0.517673 | + | 0.855579i | \(0.326798\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.21826i | 0.294774i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −41.3407 | −1.95535 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.75711 | −0.0829231 | −0.0414615 | − | 0.999140i | \(-0.513201\pi\) | ||||
−0.0414615 | + | 0.999140i | \(0.513201\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 51.1189i | 2.40709i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.384781 | −0.0180786 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.445195 | + | 6.40844i | 0.0208711 | + | 0.300432i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.78856 | 0.177221 | 0.0886106 | − | 0.996066i | \(-0.471757\pi\) | ||||
0.0886106 | + | 0.996066i | \(0.471757\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35.1468 | −1.64051 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.3541 | 1.50688 | 0.753439 | − | 0.657517i | \(-0.228393\pi\) | ||||
0.753439 | + | 0.657517i | \(0.228393\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.2530i | 1.45245i | 0.687456 | + | 0.726226i | \(0.258727\pi\) | ||||
−0.687456 | + | 0.726226i | \(0.741273\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.8685i | 0.643137i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 22.6800i | − | 1.04950i | −0.851255 | − | 0.524752i | \(-0.824158\pi\) | ||
0.851255 | − | 0.524752i | \(-0.175842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.472636 | + | 6.80344i | 0.0218243 | + | 0.314154i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 39.4406i | − | 1.81733i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.4777 | 0.619708 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.24043i | 0.240447i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.99787i | − | 0.183050i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.8639 | −0.587765 | −0.293883 | − | 0.955842i | \(-0.594947\pi\) | ||||
−0.293883 | + | 0.955842i | \(0.594947\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.0307i | 0.867723i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0627202 | − | 0.902838i | −0.00285387 | − | 0.0410805i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.85094i | 0.356493i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 20.3133i | − | 0.920483i | −0.887794 | − | 0.460241i | \(-0.847763\pi\) | ||
0.887794 | − | 0.460241i | \(-0.152237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.474370i | 0.0214518i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.4582 | −0.742746 | −0.371373 | − | 0.928484i | \(-0.621113\pi\) | ||||
−0.371373 | + | 0.928484i | \(0.621113\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.1810 | 0.638680 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 29.1845 | 1.31175 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.9079 | + | 1.73035i | −1.11727 | + | 0.0776170i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7483 | −0.839291 | −0.419645 | − | 0.907688i | \(-0.637846\pi\) | ||||
−0.419645 | + | 0.907688i | \(0.637846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 50.0872i | − | 2.23773i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.5629 | −0.872269 | −0.436134 | − | 0.899882i | \(-0.643653\pi\) | ||||
−0.436134 | + | 0.899882i | \(0.643653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9057 | −0.485298 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.2956i | 0.945769i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.9845 | −0.885797 | −0.442898 | − | 0.896572i | \(-0.646050\pi\) | ||||
−0.442898 | + | 0.896572i | \(0.646050\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.8498 | + | 1.03162i | −0.656917 | + | 0.0456361i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.8715 | −2.06943 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.8202 | −0.697119 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.9229 | −2.59143 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15.5692i | − | 0.683411i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.35111i | − | 0.0591932i | −0.999562 | − | 0.0295966i | \(-0.990578\pi\) | ||
0.999562 | − | 0.0295966i | \(-0.00942226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.1452i | 1.23071i | 0.788252 | + | 0.615353i | \(0.210986\pi\) | ||||
−0.788252 | + | 0.615353i | \(0.789014\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.91115 | + | 0.549588i | −0.345271 | + | 0.0239860i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 18.1818i | − | 0.792012i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9870 | 0.999434 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 8.23051i | − | 0.357174i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4491i | 1.10232i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.53444 | −0.282508 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 51.9360i | − | 2.24121i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.8115 | − | 4.72055i | 1.45636 | − | 0.203329i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 0.0636523i | − | 0.00273663i | −0.999999 | − | 0.00136831i | \(-0.999564\pi\) | ||
0.999999 | − | 0.00136831i | \(-0.000435548\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 63.1194i | − | 2.70871i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.9309i | 0.468229i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.6632 | −1.14004 | −0.570018 | − | 0.821632i | \(-0.693064\pi\) | ||||
−0.570018 | + | 0.821632i | \(0.693064\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.04966 | 0.300872 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.9117 | 0.805665 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.3569 | + | 2.17837i | −1.33343 | + | 0.0926336i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23.4931 | −0.997228 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.81678i | 0.415950i | 0.978134 | + | 0.207975i | \(0.0666873\pi\) | ||||
−0.978134 | + | 0.207975i | \(0.933313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.70978 | 0.283794 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −57.4430 | −2.42525 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 30.8680i | − | 1.30093i | −0.759535 | − | 0.650466i | \(-0.774574\pi\) | ||
0.759535 | − | 0.650466i | \(-0.225426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.72004 | 0.156503 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.62395 | − | 23.3763i | −0.0681995 | − | 0.981711i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.9000 | 1.29540 | 0.647698 | − | 0.761897i | \(-0.275732\pi\) | ||||
0.647698 | + | 0.761897i | \(0.275732\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.5033 | 1.56946 | 0.784732 | − | 0.619835i | \(-0.212801\pi\) | ||||
0.784732 | + | 0.619835i | \(0.212801\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.2815 | −1.05615 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.114122i | 0.00475922i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.4216i | 0.725272i | 0.931931 | + | 0.362636i | \(0.118123\pi\) | ||||
−0.931931 | + | 0.362636i | \(0.881877\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 76.8330i | 3.19307i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.5786 | − | 1.01278i | 0.604822 | − | 0.0420171i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.25830i | − | 0.134945i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.5293 | 0.600711 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.4270i | 0.512918i | 0.966555 | + | 0.256459i | \(0.0825558\pi\) | ||||
−0.966555 | + | 0.256459i | \(0.917444\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 24.2471i | − | 0.999086i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.35713 | −0.220363 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.7257i | 0.563646i | 0.959466 | + | 0.281823i | \(0.0909391\pi\) | ||||
−0.959466 | + | 0.281823i | \(0.909061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3716 | − | 0.720518i | 0.425195 | − | 0.0295384i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 66.8940i | 2.73779i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 27.7947i | − | 1.13566i | −0.823146 | − | 0.567829i | \(-0.807783\pi\) | ||
0.823146 | − | 0.567829i | \(-0.192217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 38.9855i | − | 1.59025i | −0.606443 | − | 0.795127i | \(-0.707404\pi\) | ||
0.606443 | − | 0.795127i | \(-0.292596\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.4248 | 0.628148 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.7857 | 0.519811 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7981 | 0.478872 | 0.239436 | − | 0.970912i | \(-0.423038\pi\) | ||||
0.239436 | + | 0.970912i | \(0.423038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.98336 | + | 28.5498i | 0.0803697 | + | 1.15690i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29.3342 | −1.18674 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13.4628i | − | 0.543756i | −0.962332 | − | 0.271878i | \(-0.912355\pi\) | ||
0.962332 | − | 0.271878i | \(-0.0876447\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −31.4166 | −1.26684 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.2924 | −0.615650 | −0.307825 | − | 0.951443i | \(-0.599601\pi\) | ||||
−0.307825 | + | 0.951443i | \(0.599601\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 3.76548i | − | 0.151347i | −0.997133 | − | 0.0756736i | \(-0.975889\pi\) | ||
0.997133 | − | 0.0756736i | \(-0.0241107\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.02073 | −0.0409606 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.4124 | − | 1.14017i | 0.657550 | − | 0.0456801i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −76.6056 | −3.05933 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.7998 | 1.22807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.1777i | 0.843070i | 0.906812 | + | 0.421535i | \(0.138508\pi\) | ||||
−0.906812 | + | 0.421535i | \(0.861492\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.7313i | 1.02273i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 3.80326i | − | 0.150928i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.8327 | − | 2.35009i | 0.666937 | − | 0.0931138i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 56.4714i | 2.23397i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.5569 | 1.16743 | 0.583713 | − | 0.811960i | \(-0.301599\pi\) | ||||
0.583713 | + | 0.811960i | \(0.301599\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.8063i | 0.781085i | 0.920585 | + | 0.390543i | \(0.127713\pi\) | ||||
−0.920585 | + | 0.390543i | \(0.872287\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.28315i | 0.326149i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.4755 | −0.490461 | −0.245231 | − | 0.969465i | \(-0.578864\pi\) | ||||
−0.245231 | + | 0.969465i | \(0.578864\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.70794i | − | 0.263310i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.6044 | − | 2.54291i | 1.43464 | − | 0.0996646i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9.99757i | − | 0.391235i | −0.980680 | − | 0.195618i | \(-0.937329\pi\) | ||
0.980680 | − | 0.195618i | \(-0.0626712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 7.68109i | − | 0.300125i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 33.6676i | 1.31350i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.2870 | −1.06295 | −0.531475 | − | 0.847074i | \(-0.678362\pi\) | ||||
−0.531475 | + | 0.847074i | \(0.678362\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.2384 | −1.48730 | −0.743650 | − | 0.668569i | \(-0.766907\pi\) | ||||
−0.743650 | + | 0.668569i | \(0.766907\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.5975 | −1.11063 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.8315 | − | 0.960878i | 0.536364 | − | 0.0372613i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.411845 | 0.0159467 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 42.0705i | − | 1.62654i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.74554 | 0.221804 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.47579 | 0.326718 | 0.163359 | − | 0.986567i | \(-0.447767\pi\) | ||||
0.163359 | + | 0.986567i | \(0.447767\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.94421i | 0.344263i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.2065 | 0.891897 | 0.445948 | − | 0.895059i | \(-0.352866\pi\) | ||||
0.445948 | + | 0.895059i | \(0.352866\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7217 | − | 1.43954i | 0.795225 | − | 0.0552444i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −89.6394 | −3.43499 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7680 | 0.985986 | 0.492993 | − | 0.870033i | \(-0.335903\pi\) | ||||
0.492993 | + | 0.870033i | \(0.335903\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.9739 | −0.648540 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.7394i | 1.02017i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.62212i | − | 0.0617978i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 24.5498i | − | 0.933917i | −0.884279 | − | 0.466958i | \(-0.845350\pi\) | ||
0.884279 | − | 0.466958i | \(-0.154650\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.35124 | − | 77.0294i | −0.203277 | − | 2.92610i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 2.54598i | − | 0.0965744i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41.1877 | 1.56009 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.69396i | − | 0.0640715i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.33837i | − | 0.0883188i | −0.999024 | − | 0.0441594i | \(-0.985939\pi\) | ||
0.999024 | − | 0.0441594i | \(-0.0140610\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.0745 | 1.54915 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 36.2128i | − | 1.36385i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.99966 | + | 28.7845i | 0.0752049 | + | 1.08255i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.8318i | 1.38325i | 0.722257 | + | 0.691624i | \(0.243105\pi\) | ||||
−0.722257 | + | 0.691624i | \(0.756895\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 71.0927i | 2.66618i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 0.528036i | − | 0.0197751i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.8415 | 0.442847 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.5114 | −0.952742 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.8925 | −1.26398 | −0.631989 | − | 0.774978i | \(-0.717761\pi\) | ||||
−0.631989 | + | 0.774978i | \(0.717761\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.90076 | + | 41.7556i | 0.108030 | + | 1.55506i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.51991 | 0.242478 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 3.60881i | − | 0.134028i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.28102 | 0.158774 | 0.0793871 | − | 0.996844i | \(-0.474704\pi\) | ||||
0.0793871 | + | 0.996844i | \(0.474704\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.4276 | 1.01584 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 10.8593i | − | 0.401647i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.0426 | −1.40513 | −0.702567 | − | 0.711618i | \(-0.747963\pi\) | ||||
−0.702567 | + | 0.711618i | \(0.747963\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.90116 | + | 20.7798i | 0.107011 | + | 0.766476i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.5714 | 0.463073 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.93398 | −0.365427 | −0.182714 | − | 0.983166i | \(-0.558488\pi\) | ||||
−0.182714 | + | 0.983166i | \(0.558488\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −38.1374 | −1.40101 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.68905i | 0.0619651i | 0.999520 | + | 0.0309826i | \(0.00986363\pi\) | ||||
−0.999520 | + | 0.0309826i | \(0.990136\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.7925i | − | 0.505316i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 33.0527i | − | 1.20934i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.19815 | + | 17.2469i | 0.0437793 | + | 0.630189i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 36.9451i | − | 1.34815i | −0.738664 | − | 0.674073i | \(-0.764543\pi\) | ||
0.738664 | − | 0.674073i | \(-0.235457\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.2257 | 1.02860 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 0.128374i | − | 0.00467202i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.8391i | 1.66605i | 0.553235 | + | 0.833025i | \(0.313393\pi\) | ||||
−0.553235 | + | 0.833025i | \(0.686607\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.66826 | −0.0605540 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.9588i | 0.723506i | 0.932274 | + | 0.361753i | \(0.117822\pi\) | ||||
−0.932274 | + | 0.361753i | \(0.882178\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.8509 | − | 2.00428i | 1.04447 | − | 0.0725597i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 23.5146i | − | 0.850174i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.33949i | − | 0.120582i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.9529i | − | 0.503153i | −0.967837 | − | 0.251576i | \(-0.919051\pi\) | ||
0.967837 | − | 0.251576i | \(-0.0809490\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3123 | −0.479431 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.8775 | 1.21849 | 0.609245 | − | 0.792982i | \(-0.291473\pi\) | ||||
0.609245 | + | 0.792982i | \(0.291473\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.62694 | −0.166205 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.30767 | + | 62.0076i | 0.154537 | + | 2.22451i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 54.9276 | 1.96798 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.0247i | 1.64689i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.2779 | 1.15352 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.1585 | 0.469649 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.07748i | 0.287931i | 0.989583 | + | 0.143965i | \(0.0459854\pi\) | ||||
−0.989583 | + | 0.143965i | \(0.954015\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −40.8377 | −1.45386 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.682101 | − | 9.81862i | −0.0242527 | − | 0.349110i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.86037 | 0.101575 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.00249 | 0.0710209 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.9873 | 1.09763 | 0.548813 | − | 0.835945i | \(-0.315080\pi\) | ||||
0.548813 | + | 0.835945i | \(0.315080\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.4755i | 1.67956i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 37.2104i | − | 1.31476i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 27.4394i | 0.968316i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.301213 | − | 0.0209253i | 0.0106164 | − | 0.000737520i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.7866i | 1.08374i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −52.5895 | −1.84895 | −0.924474 | − | 0.381245i | \(-0.875495\pi\) | ||||
−0.924474 | + | 0.381245i | \(0.875495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.3872i | − | 1.31284i | −0.754395 | − | 0.656421i | \(-0.772069\pi\) | ||
0.754395 | − | 0.656421i | \(-0.227931\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.01082i | − | 0.280952i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.158264 | −0.00554374 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 14.4819i | − | 0.506659i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.66407 | − | 38.3484i | −0.0930901 | − | 1.34000i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 23.1500i | − | 0.807941i | −0.914772 | − | 0.403970i | \(-0.867630\pi\) | ||
0.914772 | − | 0.403970i | \(-0.132370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.1543i | 0.353957i | 0.984215 | + | 0.176979i | \(0.0566323\pi\) | ||||
−0.984215 | + | 0.176979i | \(0.943368\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.6182i | 0.508940i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7346 | 0.894881 | 0.447440 | − | 0.894314i | \(-0.352336\pi\) | ||||
0.447440 | + | 0.894314i | \(0.352336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.2920 | −1.01735 | −0.508677 | − | 0.860958i | \(-0.669865\pi\) | ||||
−0.508677 | + | 0.860958i | \(0.669865\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −84.3400 | −2.92572 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.80346 | − | 27.2427i | −0.131782 | − | 0.943902i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.7105 | 0.578292 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 41.3843i | − | 1.43045i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.5479 | 0.398676 | 0.199338 | − | 0.979931i | \(-0.436121\pi\) | ||||
0.199338 | + | 0.979931i | \(0.436121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9765 | 0.550914 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.39928i | − | 0.0481939i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.10482 | −0.244413 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.34436 | − | 33.7464i | −0.0805533 | − | 1.15954i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 32.3726 | 1.11102 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.894489 | 0.0306627 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.5827 | 1.21833 | 0.609164 | − | 0.793045i | \(-0.291505\pi\) | ||||
0.609164 | + | 0.793045i | \(0.291505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 31.3590i | − | 1.07245i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.71368i | − | 0.0585383i | −0.999572 | − | 0.0292691i | \(-0.990682\pi\) | ||
0.999572 | − | 0.0292691i | \(-0.00931799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7176i | 0.502158i | 0.967967 | + | 0.251079i | \(0.0807855\pi\) | ||||
−0.967967 | + | 0.251079i | \(0.919215\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.76052 | + | 82.9208i | 0.196318 | + | 2.82593i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 37.4241i | − | 1.27393i | −0.770892 | − | 0.636966i | \(-0.780189\pi\) | ||
0.770892 | − | 0.636966i | \(-0.219811\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.19433 | 0.176612 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 4.67166i | − | 0.158658i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 57.9412i | 1.96552i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.25855 | 0.212063 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 46.9804i | − | 1.59005i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.183359 | − | 2.63939i | −0.00619866 | − | 0.0892277i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 24.9933i | − | 0.843965i | −0.906604 | − | 0.421982i | \(-0.861334\pi\) | ||
0.906604 | − | 0.421982i | \(-0.138666\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 22.0164i | − | 0.742596i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.7020i | 0.933303i | 0.884441 | + | 0.466651i | \(0.154540\pi\) | ||||
−0.884441 | + | 0.466651i | \(0.845460\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.66299 | −0.123269 | −0.0616347 | − | 0.998099i | \(-0.519631\pi\) | ||||
−0.0616347 | + | 0.998099i | \(0.519631\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.12256 | 0.138579 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40.0849 | 1.34592 | 0.672960 | − | 0.739679i | \(-0.265022\pi\) | ||||
0.672960 | + | 0.739679i | \(0.265022\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.0383 | + | 0.697361i | −0.336674 | + | 0.0233887i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −43.1946 | −1.44707 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 63.3130i | 2.11869i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.3274 | 0.579190 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.830529 | −0.0277306 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.6977i | 0.556900i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.62529 | −0.0874610 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.8625 | − | 1.51879i | 0.727538 | − | 0.0505421i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0585 | 0.700007 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.0878 | 1.09866 | 0.549331 | − | 0.835605i | \(-0.314883\pi\) | ||||
0.549331 | + | 0.835605i | \(0.314883\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 65.2604 | 2.16455 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.4259i | 1.37250i | 0.727365 | + | 0.686250i | \(0.240745\pi\) | ||||
−0.727365 | + | 0.686250i | \(0.759255\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 26.9383i | − | 0.891527i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.53110i | 0.116734i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.2734 | + | 1.40840i | −0.669487 | + | 0.0465093i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.61219i | − | 0.0861682i | −0.999071 | − | 0.0430841i | \(-0.986282\pi\) | ||
0.999071 | − | 0.0430841i | \(-0.0137183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.2288 | 0.501807 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.9130i | 0.754191i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 7.83800i | − | 0.257712i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 94.6686 | 3.10932 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 29.7850i | − | 0.977213i | −0.872504 | − | 0.488606i | \(-0.837505\pi\) | ||
0.872504 | − | 0.488606i | \(-0.162495\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.07226 | − | 36.3306i | −0.166237 | − | 1.19069i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 53.4484i | − | 1.74982i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 19.1647i | − | 0.626751i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.9620i | 0.684800i | 0.939554 | + | 0.342400i | \(0.111240\pi\) | ||||
−0.939554 | + | 0.342400i | \(0.888760\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.6108 | 0.346271 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.3589 | −0.696280 | −0.348140 | − | 0.937443i | \(-0.613187\pi\) | ||||
−0.348140 | + | 0.937443i | \(0.613187\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.19617 | 0.0389527 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 23.6073 | − | 1.64000i | 0.767944 | − | 0.0533492i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54.2008 | 1.76129 | 0.880645 | − | 0.473777i | \(-0.157110\pi\) | ||||
0.880645 | + | 0.473777i | \(0.157110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.6605i | 0.443438i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.5779 | 0.472719 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.3943 | 0.854994 | 0.427497 | − | 0.904017i | \(-0.359395\pi\) | ||||
0.427497 | + | 0.904017i | \(0.359395\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 8.43465i | − | 0.272939i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 52.7542 | 1.70530 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.11231 | + | 44.8008i | 0.100502 | + | 1.44669i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.59145 | −0.309402 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 39.1024 | 1.26006 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.6337 | −0.825179 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 32.9216i | − | 1.05869i | −0.848408 | − | 0.529343i | \(-0.822438\pi\) | ||
0.848408 | − | 0.529343i | \(-0.177562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 61.7229i | 1.98282i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 32.2598i | − | 1.03527i | −0.855603 | − | 0.517633i | \(-0.826813\pi\) | ||
0.855603 | − | 0.517633i | \(-0.173187\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.71982 | + | 0.466827i | −0.215428 | + | 0.0149658i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.27754i | 0.233068i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.3881 | −0.684265 | −0.342132 | − | 0.939652i | \(-0.611149\pi\) | ||||
−0.342132 | + | 0.939652i | \(0.611149\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30.3268i | − | 0.969249i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 65.4111i | − | 2.08842i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.6503 | −0.594852 | −0.297426 | − | 0.954745i | \(-0.596128\pi\) | ||||
−0.297426 | + | 0.954745i | \(0.596128\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.78729i | − | 0.0569479i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −95.5798 | + | 6.63994i | −3.04234 | + | 0.211351i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 0.315377i | − | 0.0100284i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 13.5821i | − | 0.431448i | −0.976454 | − | 0.215724i | \(-0.930789\pi\) | ||
0.976454 | − | 0.215724i | \(-0.0692112\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 28.1411i | − | 0.893032i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.3178 | −0.707521 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.3616 | 0.803210 | 0.401605 | − | 0.915813i | \(-0.368452\pi\) | ||||
0.401605 | + | 0.915813i | \(0.368452\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 70.1047 | 2.21801 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1120.2.h.b.111.2 | 16 | ||
4.3 | odd | 2 | 280.2.h.b.251.11 | yes | 16 | ||
7.6 | odd | 2 | 1120.2.h.a.111.15 | 16 | |||
8.3 | odd | 2 | 1120.2.h.a.111.2 | 16 | |||
8.5 | even | 2 | 280.2.h.a.251.12 | yes | 16 | ||
28.27 | even | 2 | 280.2.h.a.251.11 | ✓ | 16 | ||
56.13 | odd | 2 | 280.2.h.b.251.12 | yes | 16 | ||
56.27 | even | 2 | inner | 1120.2.h.b.111.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.h.a.251.11 | ✓ | 16 | 28.27 | even | 2 | ||
280.2.h.a.251.12 | yes | 16 | 8.5 | even | 2 | ||
280.2.h.b.251.11 | yes | 16 | 4.3 | odd | 2 | ||
280.2.h.b.251.12 | yes | 16 | 56.13 | odd | 2 | ||
1120.2.h.a.111.2 | 16 | 8.3 | odd | 2 | |||
1120.2.h.a.111.15 | 16 | 7.6 | odd | 2 | |||
1120.2.h.b.111.2 | 16 | 1.1 | even | 1 | trivial | ||
1120.2.h.b.111.15 | 16 | 56.27 | even | 2 | inner |