Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [154,2,Mod(153,154)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(154, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("154.153");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 154 = 2 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 154.c (of order \(2\), degree \(1\), 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: | \(1.22969619113\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 153.6 | ||
Root | \(0.323042 + 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 154.153 |
Dual form | 154.2.c.a.153.3 |
$q$-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 \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).
\(n\) | \(45\) | \(57\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 0.646084i | − | 0.373017i | −0.982453 | − | 0.186508i | \(-0.940283\pi\) | ||
0.982453 | − | 0.186508i | \(-0.0597171\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 3.09557i | − | 1.38438i | −0.721714 | − | 0.692191i | \(-0.756645\pi\) | ||
0.721714 | − | 0.692191i | \(-0.243355\pi\) | |||||||
\(6\) | 0.646084 | 0.263763 | ||||||||
\(7\) | 2.44949 | − | 1.00000i | 0.925820 | − | 0.377964i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.58258 | 0.860859 | ||||||||
\(10\) | 3.09557 | 0.978906 | ||||||||
\(11\) | −1.79129 | + | 2.79129i | −0.540094 | + | 0.841605i | ||||
\(12\) | 0.646084i | 0.186508i | ||||||||
\(13\) | 0.646084 | 0.179191 | 0.0895957 | − | 0.995978i | \(-0.471443\pi\) | ||||
0.0895957 | + | 0.995978i | \(0.471443\pi\) | |||||||
\(14\) | 1.00000 | + | 2.44949i | 0.267261 | + | 0.654654i | ||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.74166 | −0.907485 | −0.453743 | − | 0.891133i | \(-0.649911\pi\) | ||||
−0.453743 | + | 0.891133i | \(0.649911\pi\) | |||||||
\(18\) | 2.58258i | 0.608719i | ||||||||
\(19\) | −1.80341 | −0.413730 | −0.206865 | − | 0.978370i | \(-0.566326\pi\) | ||||
−0.206865 | + | 0.978370i | \(0.566326\pi\) | |||||||
\(20\) | 3.09557i | 0.692191i | ||||||||
\(21\) | −0.646084 | − | 1.58258i | −0.140987 | − | 0.345346i | ||||
\(22\) | −2.79129 | − | 1.79129i | −0.595105 | − | 0.381904i | ||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | −0.646084 | −0.131881 | ||||||||
\(25\) | −4.58258 | −0.916515 | ||||||||
\(26\) | 0.646084i | 0.126707i | ||||||||
\(27\) | − | 3.60681i | − | 0.694131i | ||||||
\(28\) | −2.44949 | + | 1.00000i | −0.462910 | + | 0.188982i | ||||
\(29\) | − | 1.58258i | − | 0.293877i | −0.989146 | − | 0.146938i | \(-0.953058\pi\) | ||
0.989146 | − | 0.146938i | \(-0.0469419\pi\) | |||||||
\(30\) | − | 2.00000i | − | 0.365148i | ||||||
\(31\) | 8.64064i | 1.55190i | 0.630792 | + | 0.775952i | \(0.282730\pi\) | ||||
−0.630792 | + | 0.775952i | \(0.717270\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.80341 | + | 1.15732i | 0.313933 | + | 0.201464i | ||||
\(34\) | − | 3.74166i | − | 0.641689i | ||||||
\(35\) | −3.09557 | − | 7.58258i | −0.523247 | − | 1.28169i | ||||
\(36\) | −2.58258 | −0.430429 | ||||||||
\(37\) | 3.58258 | 0.588972 | 0.294486 | − | 0.955656i | \(-0.404852\pi\) | ||||
0.294486 | + | 0.955656i | \(0.404852\pi\) | |||||||
\(38\) | − | 1.80341i | − | 0.292551i | ||||||
\(39\) | − | 0.417424i | − | 0.0668414i | ||||||
\(40\) | −3.09557 | −0.489453 | ||||||||
\(41\) | −9.93280 | −1.55124 | −0.775622 | − | 0.631198i | \(-0.782564\pi\) | ||||
−0.775622 | + | 0.631198i | \(0.782564\pi\) | |||||||
\(42\) | 1.58258 | − | 0.646084i | 0.244197 | − | 0.0996929i | ||||
\(43\) | 7.16515i | 1.09268i | 0.837565 | + | 0.546338i | \(0.183978\pi\) | ||||
−0.837565 | + | 0.546338i | \(0.816022\pi\) | |||||||
\(44\) | 1.79129 | − | 2.79129i | 0.270047 | − | 0.420802i | ||||
\(45\) | − | 7.99455i | − | 1.19176i | ||||||
\(46\) | 4.00000i | 0.589768i | ||||||||
\(47\) | 9.93280i | 1.44885i | 0.689354 | + | 0.724424i | \(0.257894\pi\) | ||||
−0.689354 | + | 0.724424i | \(0.742106\pi\) | |||||||
\(48\) | − | 0.646084i | − | 0.0932542i | ||||||
\(49\) | 5.00000 | − | 4.89898i | 0.714286 | − | 0.699854i | ||||
\(50\) | − | 4.58258i | − | 0.648074i | ||||||
\(51\) | 2.41742i | 0.338507i | ||||||||
\(52\) | −0.646084 | −0.0895957 | ||||||||
\(53\) | −11.5826 | −1.59099 | −0.795495 | − | 0.605961i | \(-0.792789\pi\) | ||||
−0.795495 | + | 0.605961i | \(0.792789\pi\) | |||||||
\(54\) | 3.60681 | 0.490825 | ||||||||
\(55\) | 8.64064 | + | 5.54506i | 1.16510 | + | 0.747696i | ||||
\(56\) | −1.00000 | − | 2.44949i | −0.133631 | − | 0.327327i | ||||
\(57\) | 1.16515i | 0.154328i | ||||||||
\(58\) | 1.58258 | 0.207802 | ||||||||
\(59\) | 0.646084i | 0.0841129i | 0.999115 | + | 0.0420565i | \(0.0133909\pi\) | ||||
−0.999115 | + | 0.0420565i | \(0.986609\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | 1.93825 | 0.248168 | 0.124084 | − | 0.992272i | \(-0.460401\pi\) | ||||
0.124084 | + | 0.992272i | \(0.460401\pi\) | |||||||
\(62\) | −8.64064 | −1.09736 | ||||||||
\(63\) | 6.32599 | − | 2.58258i | 0.797000 | − | 0.325374i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 2.00000i | − | 0.248069i | ||||||
\(66\) | −1.15732 | + | 1.80341i | −0.142457 | + | 0.221984i | ||||
\(67\) | −7.58258 | −0.926359 | −0.463180 | − | 0.886264i | \(-0.653291\pi\) | ||||
−0.463180 | + | 0.886264i | \(0.653291\pi\) | |||||||
\(68\) | 3.74166 | 0.453743 | ||||||||
\(69\) | − | 2.58434i | − | 0.311117i | ||||||
\(70\) | 7.58258 | − | 3.09557i | 0.906291 | − | 0.369992i | ||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | − | 2.58258i | − | 0.304359i | ||||||
\(73\) | 16.1240 | 1.88717 | 0.943583 | − | 0.331136i | \(-0.107432\pi\) | ||||
0.943583 | + | 0.331136i | \(0.107432\pi\) | |||||||
\(74\) | 3.58258i | 0.416466i | ||||||||
\(75\) | 2.96073i | 0.341875i | ||||||||
\(76\) | 1.80341 | 0.206865 | ||||||||
\(77\) | −1.59645 | + | 8.62852i | −0.181933 | + | 0.983311i | ||||
\(78\) | 0.417424 | 0.0472640 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | − | 3.09557i | − | 0.346096i | ||||||
\(81\) | 5.41742 | 0.601936 | ||||||||
\(82\) | − | 9.93280i | − | 1.09689i | ||||||
\(83\) | 12.8935 | 1.41525 | 0.707625 | − | 0.706589i | \(-0.249767\pi\) | ||||
0.707625 | + | 0.706589i | \(0.249767\pi\) | |||||||
\(84\) | 0.646084 | + | 1.58258i | 0.0704935 | + | 0.172673i | ||||
\(85\) | 11.5826i | 1.25631i | ||||||||
\(86\) | −7.16515 | −0.772638 | ||||||||
\(87\) | −1.02248 | −0.109621 | ||||||||
\(88\) | 2.79129 | + | 1.79129i | 0.297552 | + | 0.190952i | ||||
\(89\) | − | 9.79796i | − | 1.03858i | −0.854598 | − | 0.519291i | \(-0.826196\pi\) | ||
0.854598 | − | 0.519291i | \(-0.173804\pi\) | |||||||
\(90\) | 7.99455 | 0.842700 | ||||||||
\(91\) | 1.58258 | − | 0.646084i | 0.165899 | − | 0.0677280i | ||||
\(92\) | −4.00000 | −0.417029 | ||||||||
\(93\) | 5.58258 | 0.578886 | ||||||||
\(94\) | −9.93280 | −1.02449 | ||||||||
\(95\) | 5.58258i | 0.572760i | ||||||||
\(96\) | 0.646084 | 0.0659407 | ||||||||
\(97\) | 8.50579i | 0.863632i | 0.901962 | + | 0.431816i | \(0.142127\pi\) | ||||
−0.901962 | + | 0.431816i | \(0.857873\pi\) | |||||||
\(98\) | 4.89898 | + | 5.00000i | 0.494872 | + | 0.505076i | ||||
\(99\) | −4.62614 | + | 7.20871i | −0.464944 | + | 0.724503i | ||||
\(100\) | 4.58258 | 0.458258 | ||||||||
\(101\) | −11.7362 | −1.16780 | −0.583898 | − | 0.811827i | \(-0.698473\pi\) | ||||
−0.583898 | + | 0.811827i | \(0.698473\pi\) | |||||||
\(102\) | −2.41742 | −0.239361 | ||||||||
\(103\) | − | 6.05630i | − | 0.596745i | −0.954449 | − | 0.298373i | \(-0.903556\pi\) | ||
0.954449 | − | 0.298373i | \(-0.0964438\pi\) | |||||||
\(104\) | − | 0.646084i | − | 0.0633537i | ||||||
\(105\) | −4.89898 | + | 2.00000i | −0.478091 | + | 0.195180i | ||||
\(106\) | − | 11.5826i | − | 1.12500i | ||||||
\(107\) | − | 17.5826i | − | 1.69977i | −0.526967 | − | 0.849886i | \(-0.676671\pi\) | ||
0.526967 | − | 0.849886i | \(-0.323329\pi\) | |||||||
\(108\) | 3.60681i | 0.347066i | ||||||||
\(109\) | − | 17.1652i | − | 1.64412i | −0.569398 | − | 0.822062i | \(-0.692824\pi\) | ||
0.569398 | − | 0.822062i | \(-0.307176\pi\) | |||||||
\(110\) | −5.54506 | + | 8.64064i | −0.528701 | + | 0.823852i | ||||
\(111\) | − | 2.31464i | − | 0.219696i | ||||||
\(112\) | 2.44949 | − | 1.00000i | 0.231455 | − | 0.0944911i | ||||
\(113\) | 10.7477 | 1.01106 | 0.505531 | − | 0.862809i | \(-0.331297\pi\) | ||||
0.505531 | + | 0.862809i | \(0.331297\pi\) | |||||||
\(114\) | −1.16515 | −0.109126 | ||||||||
\(115\) | − | 12.3823i | − | 1.15465i | ||||||
\(116\) | 1.58258i | 0.146938i | ||||||||
\(117\) | 1.66856 | 0.154258 | ||||||||
\(118\) | −0.646084 | −0.0594768 | ||||||||
\(119\) | −9.16515 | + | 3.74166i | −0.840168 | + | 0.342997i | ||||
\(120\) | 2.00000i | 0.182574i | ||||||||
\(121\) | −4.58258 | − | 10.0000i | −0.416598 | − | 0.909091i | ||||
\(122\) | 1.93825i | 0.175481i | ||||||||
\(123\) | 6.41742i | 0.578640i | ||||||||
\(124\) | − | 8.64064i | − | 0.775952i | ||||||
\(125\) | − | 1.29217i | − | 0.115575i | ||||||
\(126\) | 2.58258 | + | 6.32599i | 0.230074 | + | 0.563564i | ||||
\(127\) | 3.58258i | 0.317902i | 0.987286 | + | 0.158951i | \(0.0508112\pi\) | ||||
−0.987286 | + | 0.158951i | \(0.949189\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 4.62929 | 0.407586 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | −16.7700 | −1.46520 | −0.732602 | − | 0.680657i | \(-0.761694\pi\) | ||||
−0.732602 | + | 0.680657i | \(0.761694\pi\) | |||||||
\(132\) | −1.80341 | − | 1.15732i | −0.156966 | − | 0.100732i | ||||
\(133\) | −4.41742 | + | 1.80341i | −0.383039 | + | 0.156375i | ||||
\(134\) | − | 7.58258i | − | 0.655035i | ||||||
\(135\) | −11.1652 | −0.960943 | ||||||||
\(136\) | 3.74166i | 0.320844i | ||||||||
\(137\) | −3.16515 | −0.270417 | −0.135209 | − | 0.990817i | \(-0.543170\pi\) | ||||
−0.135209 | + | 0.990817i | \(0.543170\pi\) | |||||||
\(138\) | 2.58434 | 0.219993 | ||||||||
\(139\) | −15.4779 | −1.31282 | −0.656408 | − | 0.754406i | \(-0.727925\pi\) | ||||
−0.656408 | + | 0.754406i | \(0.727925\pi\) | |||||||
\(140\) | 3.09557 | + | 7.58258i | 0.261624 | + | 0.640845i | ||||
\(141\) | 6.41742 | 0.540445 | ||||||||
\(142\) | 2.00000i | 0.167836i | ||||||||
\(143\) | −1.15732 | + | 1.80341i | −0.0967801 | + | 0.150808i | ||||
\(144\) | 2.58258 | 0.215215 | ||||||||
\(145\) | −4.89898 | −0.406838 | ||||||||
\(146\) | 16.1240i | 1.33443i | ||||||||
\(147\) | −3.16515 | − | 3.23042i | −0.261057 | − | 0.266440i | ||||
\(148\) | −3.58258 | −0.294486 | ||||||||
\(149\) | 14.0000i | 1.14692i | 0.819232 | + | 0.573462i | \(0.194400\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | −2.96073 | −0.241742 | ||||||||
\(151\) | − | 5.58258i | − | 0.454304i | −0.973859 | − | 0.227152i | \(-0.927059\pi\) | ||
0.973859 | − | 0.227152i | \(-0.0729414\pi\) | |||||||
\(152\) | 1.80341i | 0.146276i | ||||||||
\(153\) | −9.66311 | −0.781216 | ||||||||
\(154\) | −8.62852 | − | 1.59645i | −0.695306 | − | 0.128646i | ||||
\(155\) | 26.7477 | 2.14843 | ||||||||
\(156\) | 0.417424i | 0.0334207i | ||||||||
\(157\) | 13.1632i | 1.05054i | 0.850936 | + | 0.525270i | \(0.176036\pi\) | ||||
−0.850936 | + | 0.525270i | \(0.823964\pi\) | |||||||
\(158\) | −4.00000 | −0.318223 | ||||||||
\(159\) | 7.48331i | 0.593465i | ||||||||
\(160\) | 3.09557 | 0.244727 | ||||||||
\(161\) | 9.79796 | − | 4.00000i | 0.772187 | − | 0.315244i | ||||
\(162\) | 5.41742i | 0.425633i | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 9.93280 | 0.775622 | ||||||||
\(165\) | 3.58258 | − | 5.58258i | 0.278903 | − | 0.434603i | ||||
\(166\) | 12.8935i | 1.00073i | ||||||||
\(167\) | 1.29217 | 0.0999909 | 0.0499955 | − | 0.998749i | \(-0.484079\pi\) | ||||
0.0499955 | + | 0.998749i | \(0.484079\pi\) | |||||||
\(168\) | −1.58258 | + | 0.646084i | −0.122098 | + | 0.0498464i | ||||
\(169\) | −12.5826 | −0.967890 | ||||||||
\(170\) | −11.5826 | −0.888343 | ||||||||
\(171\) | −4.65743 | −0.356163 | ||||||||
\(172\) | − | 7.16515i | − | 0.546338i | ||||||
\(173\) | 10.7137 | 0.814550 | 0.407275 | − | 0.913306i | \(-0.366479\pi\) | ||||
0.407275 | + | 0.913306i | \(0.366479\pi\) | |||||||
\(174\) | − | 1.02248i | − | 0.0775137i | ||||||
\(175\) | −11.2250 | + | 4.58258i | −0.848528 | + | 0.346410i | ||||
\(176\) | −1.79129 | + | 2.79129i | −0.135023 | + | 0.210401i | ||||
\(177\) | 0.417424 | 0.0313755 | ||||||||
\(178\) | 9.79796 | 0.734388 | ||||||||
\(179\) | 11.1652 | 0.834523 | 0.417261 | − | 0.908787i | \(-0.362990\pi\) | ||||
0.417261 | + | 0.908787i | \(0.362990\pi\) | |||||||
\(180\) | 7.99455i | 0.595879i | ||||||||
\(181\) | − | 5.41022i | − | 0.402138i | −0.979577 | − | 0.201069i | \(-0.935558\pi\) | ||
0.979577 | − | 0.201069i | \(-0.0644416\pi\) | |||||||
\(182\) | 0.646084 | + | 1.58258i | 0.0478909 | + | 0.117308i | ||||
\(183\) | − | 1.25227i | − | 0.0925707i | ||||||
\(184\) | − | 4.00000i | − | 0.294884i | ||||||
\(185\) | − | 11.0901i | − | 0.815362i | ||||||
\(186\) | 5.58258i | 0.409334i | ||||||||
\(187\) | 6.70239 | − | 10.4440i | 0.490127 | − | 0.763744i | ||||
\(188\) | − | 9.93280i | − | 0.724424i | ||||||
\(189\) | −3.60681 | − | 8.83485i | −0.262357 | − | 0.642641i | ||||
\(190\) | −5.58258 | −0.405003 | ||||||||
\(191\) | −18.0000 | −1.30243 | −0.651217 | − | 0.758891i | \(-0.725741\pi\) | ||||
−0.651217 | + | 0.758891i | \(0.725741\pi\) | |||||||
\(192\) | 0.646084i | 0.0466271i | ||||||||
\(193\) | − | 16.3303i | − | 1.17548i | −0.809050 | − | 0.587740i | \(-0.800018\pi\) | ||
0.809050 | − | 0.587740i | \(-0.199982\pi\) | |||||||
\(194\) | −8.50579 | −0.610680 | ||||||||
\(195\) | −1.29217 | −0.0925340 | ||||||||
\(196\) | −5.00000 | + | 4.89898i | −0.357143 | + | 0.349927i | ||||
\(197\) | − | 8.74773i | − | 0.623250i | −0.950205 | − | 0.311625i | \(-0.899127\pi\) | ||
0.950205 | − | 0.311625i | \(-0.100873\pi\) | |||||||
\(198\) | −7.20871 | − | 4.62614i | −0.512301 | − | 0.328765i | ||||
\(199\) | 9.66311i | 0.685000i | 0.939518 | + | 0.342500i | \(0.111274\pi\) | ||||
−0.939518 | + | 0.342500i | \(0.888726\pi\) | |||||||
\(200\) | 4.58258i | 0.324037i | ||||||||
\(201\) | 4.89898i | 0.345547i | ||||||||
\(202\) | − | 11.7362i | − | 0.825757i | ||||||
\(203\) | −1.58258 | − | 3.87650i | −0.111075 | − | 0.272077i | ||||
\(204\) | − | 2.41742i | − | 0.169254i | ||||||
\(205\) | 30.7477i | 2.14751i | ||||||||
\(206\) | 6.05630 | 0.421963 | ||||||||
\(207\) | 10.3303 | 0.718006 | ||||||||
\(208\) | 0.646084 | 0.0447979 | ||||||||
\(209\) | 3.23042 | − | 5.03383i | 0.223453 | − | 0.348197i | ||||
\(210\) | −2.00000 | − | 4.89898i | −0.138013 | − | 0.338062i | ||||
\(211\) | − | 16.7477i | − | 1.15296i | −0.817111 | − | 0.576481i | \(-0.804426\pi\) | ||
0.817111 | − | 0.576481i | \(-0.195574\pi\) | |||||||
\(212\) | 11.5826 | 0.795495 | ||||||||
\(213\) | − | 1.29217i | − | 0.0885379i | ||||||
\(214\) | 17.5826 | 1.20192 | ||||||||
\(215\) | 22.1803 | 1.51268 | ||||||||
\(216\) | −3.60681 | −0.245412 | ||||||||
\(217\) | 8.64064 | + | 21.1652i | 0.586565 | + | 1.43678i | ||||
\(218\) | 17.1652 | 1.16257 | ||||||||
\(219\) | − | 10.4174i | − | 0.703944i | ||||||
\(220\) | −8.64064 | − | 5.54506i | −0.582552 | − | 0.373848i | ||||
\(221\) | −2.41742 | −0.162614 | ||||||||
\(222\) | 2.31464 | 0.155349 | ||||||||
\(223\) | − | 16.1240i | − | 1.07974i | −0.841749 | − | 0.539870i | \(-0.818473\pi\) | ||
0.841749 | − | 0.539870i | \(-0.181527\pi\) | |||||||
\(224\) | 1.00000 | + | 2.44949i | 0.0668153 | + | 0.163663i | ||||
\(225\) | −11.8348 | −0.788990 | ||||||||
\(226\) | 10.7477i | 0.714928i | ||||||||
\(227\) | −0.511238 | −0.0339321 | −0.0169660 | − | 0.999856i | \(-0.505401\pi\) | ||||
−0.0169660 | + | 0.999856i | \(0.505401\pi\) | |||||||
\(228\) | − | 1.16515i | − | 0.0771640i | ||||||
\(229\) | 5.67991i | 0.375339i | 0.982232 | + | 0.187669i | \(0.0600934\pi\) | ||||
−0.982232 | + | 0.187669i | \(0.939907\pi\) | |||||||
\(230\) | 12.3823 | 0.816464 | ||||||||
\(231\) | 5.57475 | + | 1.03144i | 0.366791 | + | 0.0678639i | ||||
\(232\) | −1.58258 | −0.103901 | ||||||||
\(233\) | 27.1652i | 1.77965i | 0.456304 | + | 0.889824i | \(0.349173\pi\) | ||||
−0.456304 | + | 0.889824i | \(0.650827\pi\) | |||||||
\(234\) | 1.66856i | 0.109077i | ||||||||
\(235\) | 30.7477 | 2.00576 | ||||||||
\(236\) | − | 0.646084i | − | 0.0420565i | ||||||
\(237\) | 2.58434 | 0.167871 | ||||||||
\(238\) | −3.74166 | − | 9.16515i | −0.242536 | − | 0.594089i | ||||
\(239\) | 8.41742i | 0.544478i | 0.962230 | + | 0.272239i | \(0.0877641\pi\) | ||||
−0.962230 | + | 0.272239i | \(0.912236\pi\) | |||||||
\(240\) | −2.00000 | −0.129099 | ||||||||
\(241\) | −3.47197 | −0.223649 | −0.111825 | − | 0.993728i | \(-0.535669\pi\) | ||||
−0.111825 | + | 0.993728i | \(0.535669\pi\) | |||||||
\(242\) | 10.0000 | − | 4.58258i | 0.642824 | − | 0.294579i | ||||
\(243\) | − | 14.3205i | − | 0.918663i | ||||||
\(244\) | −1.93825 | −0.124084 | ||||||||
\(245\) | −15.1652 | − | 15.4779i | −0.968866 | − | 0.988845i | ||||
\(246\) | −6.41742 | −0.409160 | ||||||||
\(247\) | −1.16515 | −0.0741368 | ||||||||
\(248\) | 8.64064 | 0.548681 | ||||||||
\(249\) | − | 8.33030i | − | 0.527911i | ||||||
\(250\) | 1.29217 | 0.0817239 | ||||||||
\(251\) | − | 24.1185i | − | 1.52235i | −0.648549 | − | 0.761173i | \(-0.724624\pi\) | ||
0.648549 | − | 0.761173i | \(-0.275376\pi\) | |||||||
\(252\) | −6.32599 | + | 2.58258i | −0.398500 | + | 0.162687i | ||||
\(253\) | −7.16515 | + | 11.1652i | −0.450469 | + | 0.701947i | ||||
\(254\) | −3.58258 | −0.224791 | ||||||||
\(255\) | 7.48331 | 0.468623 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.89898i | 0.305590i | 0.988258 | + | 0.152795i | \(0.0488274\pi\) | ||||
−0.988258 | + | 0.152795i | \(0.951173\pi\) | |||||||
\(258\) | 4.62929i | 0.288207i | ||||||||
\(259\) | 8.77548 | − | 3.58258i | 0.545282 | − | 0.222610i | ||||
\(260\) | 2.00000i | 0.124035i | ||||||||
\(261\) | − | 4.08712i | − | 0.252986i | ||||||
\(262\) | − | 16.7700i | − | 1.03606i | ||||||
\(263\) | 8.33030i | 0.513668i | 0.966455 | + | 0.256834i | \(0.0826794\pi\) | ||||
−0.966455 | + | 0.256834i | \(0.917321\pi\) | |||||||
\(264\) | 1.15732 | − | 1.80341i | 0.0712283 | − | 0.110992i | ||||
\(265\) | 35.8547i | 2.20254i | ||||||||
\(266\) | −1.80341 | − | 4.41742i | −0.110574 | − | 0.270850i | ||||
\(267\) | −6.33030 | −0.387408 | ||||||||
\(268\) | 7.58258 | 0.463180 | ||||||||
\(269\) | 16.5003i | 1.00604i | 0.864274 | + | 0.503022i | \(0.167778\pi\) | ||||
−0.864274 | + | 0.503022i | \(0.832222\pi\) | |||||||
\(270\) | − | 11.1652i | − | 0.679489i | ||||||
\(271\) | −4.89898 | −0.297592 | −0.148796 | − | 0.988868i | \(-0.547540\pi\) | ||||
−0.148796 | + | 0.988868i | \(0.547540\pi\) | |||||||
\(272\) | −3.74166 | −0.226871 | ||||||||
\(273\) | −0.417424 | − | 1.02248i | −0.0252637 | − | 0.0618831i | ||||
\(274\) | − | 3.16515i | − | 0.191214i | ||||||
\(275\) | 8.20871 | − | 12.7913i | 0.495004 | − | 0.771344i | ||||
\(276\) | 2.58434i | 0.155559i | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | − | 15.4779i | − | 0.928301i | ||||||
\(279\) | 22.3151i | 1.33597i | ||||||||
\(280\) | −7.58258 | + | 3.09557i | −0.453146 | + | 0.184996i | ||||
\(281\) | − | 11.1652i | − | 0.666057i | −0.942917 | − | 0.333029i | \(-0.891929\pi\) | ||
0.942917 | − | 0.333029i | \(-0.108071\pi\) | |||||||
\(282\) | 6.41742i | 0.382152i | ||||||||
\(283\) | −18.0622 | −1.07369 | −0.536843 | − | 0.843682i | \(-0.680383\pi\) | ||||
−0.536843 | + | 0.843682i | \(0.680383\pi\) | |||||||
\(284\) | −2.00000 | −0.118678 | ||||||||
\(285\) | 3.60681 | 0.213649 | ||||||||
\(286\) | −1.80341 | − | 1.15732i | −0.106638 | − | 0.0684339i | ||||
\(287\) | −24.3303 | + | 9.93280i | −1.43617 | + | 0.586315i | ||||
\(288\) | 2.58258i | 0.152180i | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | − | 4.89898i | − | 0.287678i | ||||||
\(291\) | 5.49545 | 0.322149 | ||||||||
\(292\) | −16.1240 | −0.943583 | ||||||||
\(293\) | 25.1410 | 1.46875 | 0.734376 | − | 0.678743i | \(-0.237475\pi\) | ||||
0.734376 | + | 0.678743i | \(0.237475\pi\) | |||||||
\(294\) | 3.23042 | − | 3.16515i | 0.188402 | − | 0.184595i | ||||
\(295\) | 2.00000 | 0.116445 | ||||||||
\(296\) | − | 3.58258i | − | 0.208233i | ||||||
\(297\) | 10.0677 | + | 6.46084i | 0.584184 | + | 0.374896i | ||||
\(298\) | −14.0000 | −0.810998 | ||||||||
\(299\) | 2.58434 | 0.149456 | ||||||||
\(300\) | − | 2.96073i | − | 0.170938i | ||||||
\(301\) | 7.16515 | + | 17.5510i | 0.412992 | + | 1.01162i | ||||
\(302\) | 5.58258 | 0.321241 | ||||||||
\(303\) | 7.58258i | 0.435608i | ||||||||
\(304\) | −1.80341 | −0.103432 | ||||||||
\(305\) | − | 6.00000i | − | 0.343559i | ||||||
\(306\) | − | 9.66311i | − | 0.552403i | ||||||
\(307\) | −10.5789 | −0.603769 | −0.301885 | − | 0.953344i | \(-0.597616\pi\) | ||||
−0.301885 | + | 0.953344i | \(0.597616\pi\) | |||||||
\(308\) | 1.59645 | − | 8.62852i | 0.0909664 | − | 0.491655i | ||||
\(309\) | −3.91288 | −0.222596 | ||||||||
\(310\) | 26.7477i | 1.51917i | ||||||||
\(311\) | − | 5.03383i | − | 0.285442i | −0.989763 | − | 0.142721i | \(-0.954415\pi\) | ||
0.989763 | − | 0.142721i | \(-0.0455852\pi\) | |||||||
\(312\) | −0.417424 | −0.0236320 | ||||||||
\(313\) | 23.4724i | 1.32674i | 0.748292 | + | 0.663370i | \(0.230874\pi\) | ||||
−0.748292 | + | 0.663370i | \(0.769126\pi\) | |||||||
\(314\) | −13.1632 | −0.742844 | ||||||||
\(315\) | −7.99455 | − | 19.5826i | −0.450442 | − | 1.10335i | ||||
\(316\) | − | 4.00000i | − | 0.225018i | ||||||
\(317\) | 9.16515 | 0.514766 | 0.257383 | − | 0.966309i | \(-0.417140\pi\) | ||||
0.257383 | + | 0.966309i | \(0.417140\pi\) | |||||||
\(318\) | −7.48331 | −0.419643 | ||||||||
\(319\) | 4.41742 | + | 2.83485i | 0.247328 | + | 0.158721i | ||||
\(320\) | 3.09557i | 0.173048i | ||||||||
\(321\) | −11.3598 | −0.634043 | ||||||||
\(322\) | 4.00000 | + | 9.79796i | 0.222911 | + | 0.546019i | ||||
\(323\) | 6.74773 | 0.375454 | ||||||||
\(324\) | −5.41742 | −0.300968 | ||||||||
\(325\) | −2.96073 | −0.164232 | ||||||||
\(326\) | 4.00000i | 0.221540i | ||||||||
\(327\) | −11.0901 | −0.613285 | ||||||||
\(328\) | 9.93280i | 0.548447i | ||||||||
\(329\) | 9.93280 | + | 24.3303i | 0.547613 | + | 1.34137i | ||||
\(330\) | 5.58258 | + | 3.58258i | 0.307311 | + | 0.197214i | ||||
\(331\) | −23.5826 | −1.29622 | −0.648108 | − | 0.761549i | \(-0.724439\pi\) | ||||
−0.648108 | + | 0.761549i | \(0.724439\pi\) | |||||||
\(332\) | −12.8935 | −0.707625 | ||||||||
\(333\) | 9.25227 | 0.507021 | ||||||||
\(334\) | 1.29217i | 0.0707043i | ||||||||
\(335\) | 23.4724i | 1.28244i | ||||||||
\(336\) | −0.646084 | − | 1.58258i | −0.0352468 | − | 0.0863366i | ||||
\(337\) | − | 10.8348i | − | 0.590212i | −0.955465 | − | 0.295106i | \(-0.904645\pi\) | ||
0.955465 | − | 0.295106i | \(-0.0953549\pi\) | |||||||
\(338\) | − | 12.5826i | − | 0.684402i | ||||||
\(339\) | − | 6.94393i | − | 0.377143i | ||||||
\(340\) | − | 11.5826i | − | 0.628153i | ||||||
\(341\) | −24.1185 | − | 15.4779i | −1.30609 | − | 0.838174i | ||||
\(342\) | − | 4.65743i | − | 0.251845i | ||||||
\(343\) | 7.34847 | − | 17.0000i | 0.396780 | − | 0.917914i | ||||
\(344\) | 7.16515 | 0.386319 | ||||||||
\(345\) | −8.00000 | −0.430706 | ||||||||
\(346\) | 10.7137i | 0.575974i | ||||||||
\(347\) | 19.1652i | 1.02884i | 0.857539 | + | 0.514420i | \(0.171993\pi\) | ||||
−0.857539 | + | 0.514420i | \(0.828007\pi\) | |||||||
\(348\) | 1.02248 | 0.0548105 | ||||||||
\(349\) | 24.1185 | 1.29103 | 0.645517 | − | 0.763746i | \(-0.276642\pi\) | ||||
0.645517 | + | 0.763746i | \(0.276642\pi\) | |||||||
\(350\) | −4.58258 | − | 11.2250i | −0.244949 | − | 0.600000i | ||||
\(351\) | − | 2.33030i | − | 0.124382i | ||||||
\(352\) | −2.79129 | − | 1.79129i | −0.148776 | − | 0.0954760i | ||||
\(353\) | − | 7.48331i | − | 0.398297i | −0.979969 | − | 0.199148i | \(-0.936182\pi\) | ||
0.979969 | − | 0.199148i | \(-0.0638176\pi\) | |||||||
\(354\) | 0.417424i | 0.0221859i | ||||||||
\(355\) | − | 6.19115i | − | 0.328592i | ||||||
\(356\) | 9.79796i | 0.519291i | ||||||||
\(357\) | 2.41742 | + | 5.92146i | 0.127944 | + | 0.313397i | ||||
\(358\) | 11.1652i | 0.590097i | ||||||||
\(359\) | 9.58258i | 0.505749i | 0.967499 | + | 0.252875i | \(0.0813760\pi\) | ||||
−0.967499 | + | 0.252875i | \(0.918624\pi\) | |||||||
\(360\) | −7.99455 | −0.421350 | ||||||||
\(361\) | −15.7477 | −0.828828 | ||||||||
\(362\) | 5.41022 | 0.284355 | ||||||||
\(363\) | −6.46084 | + | 2.96073i | −0.339106 | + | 0.155398i | ||||
\(364\) | −1.58258 | + | 0.646084i | −0.0829495 | + | 0.0338640i | ||||
\(365\) | − | 49.9129i | − | 2.61256i | ||||||
\(366\) | 1.25227 | 0.0654574 | ||||||||
\(367\) | − | 21.0229i | − | 1.09739i | −0.836023 | − | 0.548694i | \(-0.815125\pi\) | ||
0.836023 | − | 0.548694i | \(-0.184875\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | −25.6522 | −1.33540 | ||||||||
\(370\) | 11.0901 | 0.576548 | ||||||||
\(371\) | −28.3714 | + | 11.5826i | −1.47297 | + | 0.601337i | ||||
\(372\) | −5.58258 | −0.289443 | ||||||||
\(373\) | − | 9.58258i | − | 0.496167i | −0.968739 | − | 0.248083i | \(-0.920199\pi\) | ||
0.968739 | − | 0.248083i | \(-0.0798007\pi\) | |||||||
\(374\) | 10.4440 | + | 6.70239i | 0.540049 | + | 0.346572i | ||||
\(375\) | −0.834849 | −0.0431114 | ||||||||
\(376\) | 9.93280 | 0.512245 | ||||||||
\(377\) | − | 1.02248i | − | 0.0526602i | ||||||
\(378\) | 8.83485 | − | 3.60681i | 0.454416 | − | 0.185514i | ||||
\(379\) | −22.3303 | −1.14703 | −0.573515 | − | 0.819195i | \(-0.694421\pi\) | ||||
−0.573515 | + | 0.819195i | \(0.694421\pi\) | |||||||
\(380\) | − | 5.58258i | − | 0.286380i | ||||||
\(381\) | 2.31464 | 0.118583 | ||||||||
\(382\) | − | 18.0000i | − | 0.920960i | ||||||
\(383\) | − | 19.7308i | − | 1.00819i | −0.863647 | − | 0.504097i | \(-0.831825\pi\) | ||
0.863647 | − | 0.504097i | \(-0.168175\pi\) | |||||||
\(384\) | −0.646084 | −0.0329703 | ||||||||
\(385\) | 26.7102 | + | 4.94194i | 1.36128 | + | 0.251865i | ||||
\(386\) | 16.3303 | 0.831191 | ||||||||
\(387\) | 18.5045i | 0.940639i | ||||||||
\(388\) | − | 8.50579i | − | 0.431816i | ||||||
\(389\) | 10.0000 | 0.507020 | 0.253510 | − | 0.967333i | \(-0.418415\pi\) | ||||
0.253510 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(390\) | − | 1.29217i | − | 0.0654315i | ||||||
\(391\) | −14.9666 | −0.756895 | ||||||||
\(392\) | −4.89898 | − | 5.00000i | −0.247436 | − | 0.252538i | ||||
\(393\) | 10.8348i | 0.546546i | ||||||||
\(394\) | 8.74773 | 0.440704 | ||||||||
\(395\) | 12.3823 | 0.623021 | ||||||||
\(396\) | 4.62614 | − | 7.20871i | 0.232472 | − | 0.362251i | ||||
\(397\) | 27.5905i | 1.38473i | 0.721549 | + | 0.692363i | \(0.243430\pi\) | ||||
−0.721549 | + | 0.692363i | \(0.756570\pi\) | |||||||
\(398\) | −9.66311 | −0.484368 | ||||||||
\(399\) | 1.16515 | + | 2.85403i | 0.0583305 | + | 0.142880i | ||||
\(400\) | −4.58258 | −0.229129 | ||||||||
\(401\) | 7.58258 | 0.378656 | 0.189328 | − | 0.981914i | \(-0.439369\pi\) | ||||
0.189328 | + | 0.981914i | \(0.439369\pi\) | |||||||
\(402\) | −4.89898 | −0.244339 | ||||||||
\(403\) | 5.58258i | 0.278088i | ||||||||
\(404\) | 11.7362 | 0.583898 | ||||||||
\(405\) | − | 16.7700i | − | 0.833310i | ||||||
\(406\) | 3.87650 | − | 1.58258i | 0.192388 | − | 0.0785419i | ||||
\(407\) | −6.41742 | + | 10.0000i | −0.318100 | + | 0.495682i | ||||
\(408\) | 2.41742 | 0.119680 | ||||||||
\(409\) | −5.03383 | −0.248907 | −0.124453 | − | 0.992225i | \(-0.539718\pi\) | ||||
−0.124453 | + | 0.992225i | \(0.539718\pi\) | |||||||
\(410\) | −30.7477 | −1.51852 | ||||||||
\(411\) | 2.04495i | 0.100870i | ||||||||
\(412\) | 6.05630i | 0.298373i | ||||||||
\(413\) | 0.646084 | + | 1.58258i | 0.0317917 | + | 0.0778735i | ||||
\(414\) | 10.3303i | 0.507707i | ||||||||
\(415\) | − | 39.9129i | − | 1.95925i | ||||||
\(416\) | 0.646084i | 0.0316769i | ||||||||
\(417\) | 10.0000i | 0.489702i | ||||||||
\(418\) | 5.03383 | + | 3.23042i | 0.246212 | + | 0.158005i | ||||
\(419\) | − | 13.0284i | − | 0.636478i | −0.948011 | − | 0.318239i | \(-0.896909\pi\) | ||
0.948011 | − | 0.318239i | \(-0.103091\pi\) | |||||||
\(420\) | 4.89898 | − | 2.00000i | 0.239046 | − | 0.0975900i | ||||
\(421\) | 7.58258 | 0.369552 | 0.184776 | − | 0.982781i | \(-0.440844\pi\) | ||||
0.184776 | + | 0.982781i | \(0.440844\pi\) | |||||||
\(422\) | 16.7477 | 0.815267 | ||||||||
\(423\) | 25.6522i | 1.24725i | ||||||||
\(424\) | 11.5826i | 0.562500i | ||||||||
\(425\) | 17.1464 | 0.831724 | ||||||||
\(426\) | 1.29217 | 0.0626057 | ||||||||
\(427\) | 4.74773 | − | 1.93825i | 0.229759 | − | 0.0937986i | ||||
\(428\) | 17.5826i | 0.849886i | ||||||||
\(429\) | 1.16515 | + | 0.747727i | 0.0562540 | + | 0.0361006i | ||||
\(430\) | 22.1803i | 1.06963i | ||||||||
\(431\) | 27.9129i | 1.34452i | 0.740317 | + | 0.672258i | \(0.234675\pi\) | ||||
−0.740317 | + | 0.672258i | \(0.765325\pi\) | |||||||
\(432\) | − | 3.60681i | − | 0.173533i | ||||||
\(433\) | − | 35.5850i | − | 1.71011i | −0.518540 | − | 0.855054i | \(-0.673524\pi\) | ||
0.518540 | − | 0.855054i | \(-0.326476\pi\) | |||||||
\(434\) | −21.1652 | + | 8.64064i | −1.01596 | + | 0.414764i | ||||
\(435\) | 3.16515i | 0.151757i | ||||||||
\(436\) | 17.1652i | 0.822062i | ||||||||
\(437\) | −7.21362 | −0.345074 | ||||||||
\(438\) | 10.4174 | 0.497764 | ||||||||
\(439\) | 17.2813 | 0.824790 | 0.412395 | − | 0.911005i | \(-0.364692\pi\) | ||||
0.412395 | + | 0.911005i | \(0.364692\pi\) | |||||||
\(440\) | 5.54506 | − | 8.64064i | 0.264351 | − | 0.411926i | ||||
\(441\) | 12.9129 | − | 12.6520i | 0.614899 | − | 0.602475i | ||||
\(442\) | − | 2.41742i | − | 0.114985i | ||||||
\(443\) | 15.1652 | 0.720518 | 0.360259 | − | 0.932852i | \(-0.382688\pi\) | ||||
0.360259 | + | 0.932852i | \(0.382688\pi\) | |||||||
\(444\) | 2.31464i | 0.109848i | ||||||||
\(445\) | −30.3303 | −1.43779 | ||||||||
\(446\) | 16.1240 | 0.763491 | ||||||||
\(447\) | 9.04517 | 0.427822 | ||||||||
\(448\) | −2.44949 | + | 1.00000i | −0.115728 | + | 0.0472456i | ||||
\(449\) | 31.1652 | 1.47077 | 0.735387 | − | 0.677647i | \(-0.237000\pi\) | ||||
0.735387 | + | 0.677647i | \(0.237000\pi\) | |||||||
\(450\) | − | 11.8348i | − | 0.557900i | ||||||
\(451\) | 17.7925 | − | 27.7253i | 0.837817 | − | 1.30553i | ||||
\(452\) | −10.7477 | −0.505531 | ||||||||
\(453\) | −3.60681 | −0.169463 | ||||||||
\(454\) | − | 0.511238i | − | 0.0239936i | ||||||
\(455\) | −2.00000 | − | 4.89898i | −0.0937614 | − | 0.229668i | ||||
\(456\) | 1.16515 | 0.0545632 | ||||||||
\(457\) | − | 33.1652i | − | 1.55140i | −0.631102 | − | 0.775700i | \(-0.717397\pi\) | ||
0.631102 | − | 0.775700i | \(-0.282603\pi\) | |||||||
\(458\) | −5.67991 | −0.265405 | ||||||||
\(459\) | 13.4955i | 0.629914i | ||||||||
\(460\) | 12.3823i | 0.577327i | ||||||||
\(461\) | 30.0400 | 1.39910 | 0.699550 | − | 0.714583i | \(-0.253384\pi\) | ||||
0.699550 | + | 0.714583i | \(0.253384\pi\) | |||||||
\(462\) | −1.03144 | + | 5.57475i | −0.0479871 | + | 0.259361i | ||||
\(463\) | 5.16515 | 0.240045 | 0.120022 | − | 0.992771i | \(-0.461703\pi\) | ||||
0.120022 | + | 0.992771i | \(0.461703\pi\) | |||||||
\(464\) | − | 1.58258i | − | 0.0734692i | ||||||
\(465\) | − | 17.2813i | − | 0.801400i | ||||||
\(466\) | −27.1652 | −1.25840 | ||||||||
\(467\) | 11.7362i | 0.543087i | 0.962426 | + | 0.271544i | \(0.0875341\pi\) | ||||
−0.962426 | + | 0.271544i | \(0.912466\pi\) | |||||||
\(468\) | −1.66856 | −0.0771292 | ||||||||
\(469\) | −18.5734 | + | 7.58258i | −0.857642 | + | 0.350131i | ||||
\(470\) | 30.7477i | 1.41829i | ||||||||
\(471\) | 8.50455 | 0.391869 | ||||||||
\(472\) | 0.646084 | 0.0297384 | ||||||||
\(473\) | −20.0000 | − | 12.8348i | −0.919601 | − | 0.590147i | ||||
\(474\) | 2.58434i | 0.118702i | ||||||||
\(475\) | 8.26424 | 0.379190 | ||||||||
\(476\) | 9.16515 | − | 3.74166i | 0.420084 | − | 0.171499i | ||||
\(477\) | −29.9129 | −1.36962 | ||||||||
\(478\) | −8.41742 | −0.385004 | ||||||||
\(479\) | 30.9557 | 1.41440 | 0.707202 | − | 0.707012i | \(-0.249957\pi\) | ||||
0.707202 | + | 0.707012i | \(0.249957\pi\) | |||||||
\(480\) | − | 2.00000i | − | 0.0912871i | ||||||
\(481\) | 2.31464 | 0.105539 | ||||||||
\(482\) | − | 3.47197i | − | 0.158144i | ||||||
\(483\) | −2.58434 | − | 6.33030i | −0.117591 | − | 0.288039i | ||||
\(484\) | 4.58258 | + | 10.0000i | 0.208299 | + | 0.454545i | ||||
\(485\) | 26.3303 | 1.19560 | ||||||||
\(486\) | 14.3205 | 0.649593 | ||||||||
\(487\) | 21.4955 | 0.974052 | 0.487026 | − | 0.873387i | \(-0.338082\pi\) | ||||
0.487026 | + | 0.873387i | \(0.338082\pi\) | |||||||
\(488\) | − | 1.93825i | − | 0.0877405i | ||||||
\(489\) | − | 2.58434i | − | 0.116868i | ||||||
\(490\) | 15.4779 | − | 15.1652i | 0.699219 | − | 0.685092i | ||||
\(491\) | − | 33.4955i | − | 1.51163i | −0.654786 | − | 0.755814i | \(-0.727241\pi\) | ||
0.654786 | − | 0.755814i | \(-0.272759\pi\) | |||||||
\(492\) | − | 6.41742i | − | 0.289320i | ||||||
\(493\) | 5.92146i | 0.266689i | ||||||||
\(494\) | − | 1.16515i | − | 0.0524226i | ||||||
\(495\) | 22.3151 | + | 14.3205i | 1.00299 | + | 0.643661i | ||||
\(496\) | 8.64064i | 0.387976i | ||||||||
\(497\) | 4.89898 | − | 2.00000i | 0.219749 | − | 0.0897123i | ||||
\(498\) | 8.33030 | 0.373290 | ||||||||
\(499\) | −17.9129 | −0.801891 | −0.400945 | − | 0.916102i | \(-0.631318\pi\) | ||||
−0.400945 | + | 0.916102i | \(0.631318\pi\) | |||||||
\(500\) | 1.29217i | 0.0577875i | ||||||||
\(501\) | − | 0.834849i | − | 0.0372983i | ||||||
\(502\) | 24.1185 | 1.07646 | ||||||||
\(503\) | −17.0116 | −0.758509 | −0.379254 | − | 0.925292i | \(-0.623820\pi\) | ||||
−0.379254 | + | 0.925292i | \(0.623820\pi\) | |||||||
\(504\) | −2.58258 | − | 6.32599i | −0.115037 | − | 0.281782i | ||||
\(505\) | 36.3303i | 1.61668i | ||||||||
\(506\) | −11.1652 | − | 7.16515i | −0.496352 | − | 0.318530i | ||||
\(507\) | 8.12940i | 0.361039i | ||||||||
\(508\) | − | 3.58258i | − | 0.158951i | ||||||
\(509\) | − | 0.780929i | − | 0.0346141i | −0.999850 | − | 0.0173070i | \(-0.994491\pi\) | ||
0.999850 | − | 0.0173070i | \(-0.00550928\pi\) | |||||||
\(510\) | 7.48331i | 0.331367i | ||||||||
\(511\) | 39.4955 | − | 16.1240i | 1.74718 | − | 0.713282i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 6.50455i | 0.287183i | ||||||||
\(514\) | −4.89898 | −0.216085 | ||||||||
\(515\) | −18.7477 | −0.826124 | ||||||||
\(516\) | −4.62929 | −0.203793 | ||||||||
\(517\) | −27.7253 | − | 17.7925i | −1.21936 | − | 0.782514i | ||||
\(518\) | 3.58258 | + | 8.77548i | 0.157409 | + | 0.385573i | ||||
\(519\) | − | 6.92197i | − | 0.303841i | ||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | 28.1017i | 1.23116i | 0.788075 | + | 0.615579i | \(0.211078\pi\) | ||||
−0.788075 | + | 0.615579i | \(0.788922\pi\) | |||||||
\(522\) | 4.08712 | 0.178888 | ||||||||
\(523\) | −14.4554 | −0.632090 | −0.316045 | − | 0.948744i | \(-0.602355\pi\) | ||||
−0.316045 | + | 0.948744i | \(0.602355\pi\) | |||||||
\(524\) | 16.7700 | 0.732602 | ||||||||
\(525\) | 2.96073 | + | 7.25227i | 0.129217 | + | 0.316515i | ||||
\(526\) | −8.33030 | −0.363218 | ||||||||
\(527\) | − | 32.3303i | − | 1.40833i | ||||||
\(528\) | 1.80341 | + | 1.15732i | 0.0784832 | + | 0.0503660i | ||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −35.8547 | −1.55743 | ||||||||
\(531\) | 1.66856i | 0.0724094i | ||||||||
\(532\) | 4.41742 | − | 1.80341i | 0.191520 | − | 0.0781876i | ||||
\(533\) | −6.41742 | −0.277970 | ||||||||
\(534\) | − | 6.33030i | − | 0.273939i | ||||||
\(535\) | −54.4282 | −2.35313 | ||||||||
\(536\) | 7.58258i | 0.327517i | ||||||||
\(537\) | − | 7.21362i | − | 0.311291i | ||||||
\(538\) | −16.5003 | −0.711380 | ||||||||
\(539\) | 4.71802 | + | 22.7319i | 0.203220 | + | 0.979133i | ||||
\(540\) | 11.1652 | 0.480472 | ||||||||
\(541\) | 36.7477i | 1.57991i | 0.613166 | + | 0.789954i | \(0.289896\pi\) | ||||
−0.613166 | + | 0.789954i | \(0.710104\pi\) | |||||||
\(542\) | − | 4.89898i | − | 0.210429i | ||||||
\(543\) | −3.49545 | −0.150004 | ||||||||
\(544\) | − | 3.74166i | − | 0.160422i | ||||||
\(545\) | −53.1360 | −2.27610 | ||||||||
\(546\) | 1.02248 | − | 0.417424i | 0.0437580 | − | 0.0178641i | ||||
\(547\) | 24.7477i | 1.05814i | 0.848579 | + | 0.529068i | \(0.177458\pi\) | ||||
−0.848579 | + | 0.529068i | \(0.822542\pi\) | |||||||
\(548\) | 3.16515 | 0.135209 | ||||||||
\(549\) | 5.00568 | 0.213637 | ||||||||
\(550\) | 12.7913 | + | 8.20871i | 0.545422 | + | 0.350021i | ||||
\(551\) | 2.85403i | 0.121586i | ||||||||
\(552\) | −2.58434 | −0.109997 | ||||||||
\(553\) | 4.00000 | + | 9.79796i | 0.170097 | + | 0.416652i | ||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | −7.16515 | −0.304144 | ||||||||
\(556\) | 15.4779 | 0.656408 | ||||||||
\(557\) | 35.9129i | 1.52168i | 0.648941 | + | 0.760839i | \(0.275212\pi\) | ||||
−0.648941 | + | 0.760839i | \(0.724788\pi\) | |||||||
\(558\) | −22.3151 | −0.944673 | ||||||||
\(559\) | 4.62929i | 0.195798i | ||||||||
\(560\) | −3.09557 | − | 7.58258i | −0.130812 | − | 0.320422i | ||||
\(561\) | −6.74773 | − | 4.33030i | −0.284889 | − | 0.182826i | ||||
\(562\) | 11.1652 | 0.470973 | ||||||||
\(563\) | 23.7140 | 0.999425 | 0.499712 | − | 0.866191i | \(-0.333439\pi\) | ||||
0.499712 | + | 0.866191i | \(0.333439\pi\) | |||||||
\(564\) | −6.41742 | −0.270222 | ||||||||
\(565\) | − | 33.2704i | − | 1.39970i | ||||||
\(566\) | − | 18.0622i | − | 0.759211i | ||||||
\(567\) | 13.2699 | − | 5.41742i | 0.557284 | − | 0.227510i | ||||
\(568\) | − | 2.00000i | − | 0.0839181i | ||||||
\(569\) | − | 39.4955i | − | 1.65574i | −0.560923 | − | 0.827868i | \(-0.689554\pi\) | ||
0.560923 | − | 0.827868i | \(-0.310446\pi\) | |||||||
\(570\) | 3.60681i | 0.151073i | ||||||||
\(571\) | 5.58258i | 0.233624i | 0.993154 | + | 0.116812i | \(0.0372674\pi\) | ||||
−0.993154 | + | 0.116812i | \(0.962733\pi\) | |||||||
\(572\) | 1.15732 | − | 1.80341i | 0.0483901 | − | 0.0754042i | ||||
\(573\) | 11.6295i | 0.485830i | ||||||||
\(574\) | −9.93280 | − | 24.3303i | −0.414587 | − | 1.01553i | ||||
\(575\) | −18.3303 | −0.764426 | ||||||||
\(576\) | −2.58258 | −0.107607 | ||||||||
\(577\) | − | 29.6636i | − | 1.23491i | −0.786606 | − | 0.617455i | \(-0.788164\pi\) | ||
0.786606 | − | 0.617455i | \(-0.211836\pi\) | |||||||
\(578\) | − | 3.00000i | − | 0.124784i | ||||||
\(579\) | −10.5507 | −0.438474 | ||||||||
\(580\) | 4.89898 | 0.203419 | ||||||||
\(581\) | 31.5826 | − | 12.8935i | 1.31027 | − | 0.534914i | ||||
\(582\) | 5.49545i | 0.227794i | ||||||||
\(583\) | 20.7477 | − | 32.3303i | 0.859283 | − | 1.33898i | ||||
\(584\) | − | 16.1240i | − | 0.667214i | ||||||
\(585\) | − | 5.16515i | − | 0.213553i | ||||||
\(586\) | 25.1410i | 1.03856i | ||||||||
\(587\) | 39.0851i | 1.61322i | 0.591087 | + | 0.806608i | \(0.298699\pi\) | ||||
−0.591087 | + | 0.806608i | \(0.701301\pi\) | |||||||
\(588\) | 3.16515 | + | 3.23042i | 0.130529 | + | 0.133220i | ||||
\(589\) | − | 15.5826i | − | 0.642069i | ||||||
\(590\) | 2.00000i | 0.0823387i | ||||||||
\(591\) | −5.65176 | −0.232483 | ||||||||
\(592\) | 3.58258 | 0.147243 | ||||||||
\(593\) | −14.8318 | −0.609068 | −0.304534 | − | 0.952501i | \(-0.598501\pi\) | ||||
−0.304534 | + | 0.952501i | \(0.598501\pi\) | |||||||
\(594\) | −6.46084 | + | 10.0677i | −0.265091 | + | 0.413081i | ||||
\(595\) | 11.5826 | + | 28.3714i | 0.474839 | + | 1.16311i | ||||
\(596\) | − | 14.0000i | − | 0.573462i | ||||||
\(597\) | 6.24318 | 0.255516 | ||||||||
\(598\) | 2.58434i | 0.105681i | ||||||||
\(599\) | −21.1652 | −0.864785 | −0.432392 | − | 0.901686i | \(-0.642330\pi\) | ||||
−0.432392 | + | 0.901686i | \(0.642330\pi\) | |||||||
\(600\) | 2.96073 | 0.120871 | ||||||||
\(601\) | 21.0229 | 0.857543 | 0.428772 | − | 0.903413i | \(-0.358947\pi\) | ||||
0.428772 | + | 0.903413i | \(0.358947\pi\) | |||||||
\(602\) | −17.5510 | + | 7.16515i | −0.715324 | + | 0.292030i | ||||
\(603\) | −19.5826 | −0.797464 | ||||||||
\(604\) | 5.58258i | 0.227152i | ||||||||
\(605\) | −30.9557 | + | 14.1857i | −1.25853 | + | 0.576731i | ||||
\(606\) | −7.58258 | −0.308021 | ||||||||
\(607\) | 2.04495 | 0.0830021 | 0.0415010 | − | 0.999138i | \(-0.486786\pi\) | ||||
0.0415010 | + | 0.999138i | \(0.486786\pi\) | |||||||
\(608\) | − | 1.80341i | − | 0.0731378i | ||||||
\(609\) | −2.50455 | + | 1.02248i | −0.101489 | + | 0.0414328i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 6.41742i | 0.259621i | ||||||||
\(612\) | 9.66311 | 0.390608 | ||||||||
\(613\) | − | 31.9129i | − | 1.28895i | −0.764626 | − | 0.644475i | \(-0.777076\pi\) | ||
0.764626 | − | 0.644475i | \(-0.222924\pi\) | |||||||
\(614\) | − | 10.5789i | − | 0.426929i | ||||||
\(615\) | 19.8656 | 0.801059 | ||||||||
\(616\) | 8.62852 | + | 1.59645i | 0.347653 | + | 0.0643229i | ||||
\(617\) | −19.9129 | −0.801662 | −0.400831 | − | 0.916152i | \(-0.631279\pi\) | ||||
−0.400831 | + | 0.916152i | \(0.631279\pi\) | |||||||
\(618\) | − | 3.91288i | − | 0.157399i | ||||||
\(619\) | 17.9274i | 0.720561i | 0.932844 | + | 0.360281i | \(0.117319\pi\) | ||||
−0.932844 | + | 0.360281i | \(0.882681\pi\) | |||||||
\(620\) | −26.7477 | −1.07421 | ||||||||
\(621\) | − | 14.4272i | − | 0.578945i | ||||||
\(622\) | 5.03383 | 0.201838 | ||||||||
\(623\) | −9.79796 | − | 24.0000i | −0.392547 | − | 0.961540i | ||||
\(624\) | − | 0.417424i | − | 0.0167103i | ||||||
\(625\) | −26.9129 | −1.07652 | ||||||||
\(626\) | −23.4724 | −0.938147 | ||||||||
\(627\) | −3.25227 | − | 2.08712i | −0.129883 | − | 0.0833516i | ||||
\(628\) | − | 13.1632i | − | 0.525270i | ||||||
\(629\) | −13.4048 | −0.534483 | ||||||||
\(630\) | 19.5826 | − | 7.99455i | 0.780188 | − | 0.318511i | ||||
\(631\) | 13.1652 | 0.524096 | 0.262048 | − | 0.965055i | \(-0.415602\pi\) | ||||
0.262048 | + | 0.965055i | \(0.415602\pi\) | |||||||
\(632\) | 4.00000 | 0.159111 | ||||||||
\(633\) | −10.8204 | −0.430074 | ||||||||
\(634\) | 9.16515i | 0.363995i | ||||||||
\(635\) | 11.0901 | 0.440098 | ||||||||
\(636\) | − | 7.48331i | − | 0.296733i | ||||||
\(637\) | 3.23042 | − | 3.16515i | 0.127994 | − | 0.125408i | ||||
\(638\) | −2.83485 | + | 4.41742i | −0.112233 | + | 0.174888i | ||||
\(639\) | 5.16515 | 0.204330 | ||||||||
\(640\) | −3.09557 | −0.122363 | ||||||||
\(641\) | −15.9129 | −0.628521 | −0.314260 | − | 0.949337i | \(-0.601757\pi\) | ||||
−0.314260 | + | 0.949337i | \(0.601757\pi\) | |||||||
\(642\) | − | 11.3598i | − | 0.448336i | ||||||
\(643\) | 9.42157i | 0.371550i | 0.982592 | + | 0.185775i | \(0.0594796\pi\) | ||||
−0.982592 | + | 0.185775i | \(0.940520\pi\) | |||||||
\(644\) | −9.79796 | + | 4.00000i | −0.386094 | + | 0.157622i | ||||
\(645\) | − | 14.3303i | − | 0.564255i | ||||||
\(646\) | 6.74773i | 0.265486i | ||||||||
\(647\) | 30.0681i | 1.18210i | 0.806635 | + | 0.591050i | \(0.201286\pi\) | ||||
−0.806635 | + | 0.591050i | \(0.798714\pi\) | |||||||
\(648\) | − | 5.41742i | − | 0.212817i | ||||||
\(649\) | −1.80341 | − | 1.15732i | −0.0707899 | − | 0.0454289i | ||||
\(650\) | − | 2.96073i | − | 0.116129i | ||||||
\(651\) | 13.6745 | − | 5.58258i | 0.535944 | − | 0.218798i | ||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −6.00000 | −0.234798 | −0.117399 | − | 0.993085i | \(-0.537456\pi\) | ||||
−0.117399 | + | 0.993085i | \(0.537456\pi\) | |||||||
\(654\) | − | 11.0901i | − | 0.433658i | ||||||
\(655\) | 51.9129i | 2.02840i | ||||||||
\(656\) | −9.93280 | −0.387811 | ||||||||
\(657\) | 41.6413 | 1.62458 | ||||||||
\(658\) | −24.3303 | + | 9.93280i | −0.948494 | + | 0.387221i | ||||
\(659\) | 6.33030i | 0.246594i | 0.992370 | + | 0.123297i | \(0.0393467\pi\) | ||||
−0.992370 | + | 0.123297i | \(0.960653\pi\) | |||||||
\(660\) | −3.58258 | + | 5.58258i | −0.139452 | + | 0.217301i | ||||
\(661\) | − | 8.26424i | − | 0.321442i | −0.987000 | − | 0.160721i | \(-0.948618\pi\) | ||
0.987000 | − | 0.160721i | \(-0.0513819\pi\) | |||||||
\(662\) | − | 23.5826i | − | 0.916563i | ||||||
\(663\) | 1.56186i | 0.0606576i | ||||||||
\(664\) | − | 12.8935i | − | 0.500366i | ||||||
\(665\) | 5.58258 | + | 13.6745i | 0.216483 | + | 0.530273i | ||||
\(666\) | 9.25227i | 0.358518i | ||||||||
\(667\) | − | 6.33030i | − | 0.245110i | ||||||
\(668\) | −1.29217 | −0.0499955 | ||||||||
\(669\) | −10.4174 | −0.402761 | ||||||||
\(670\) | −23.4724 | −0.906819 | ||||||||
\(671\) | −3.47197 | + | 5.41022i | −0.134034 | + | 0.208859i | ||||
\(672\) | 1.58258 | − | 0.646084i | 0.0610492 | − | 0.0249232i | ||||
\(673\) | 18.3303i | 0.706581i | 0.935514 | + | 0.353291i | \(0.114937\pi\) | ||||
−0.935514 | + | 0.353291i | \(0.885063\pi\) | |||||||
\(674\) | 10.8348 | 0.417343 | ||||||||
\(675\) | 16.5285i | 0.636182i | ||||||||
\(676\) | 12.5826 | 0.483945 | ||||||||
\(677\) | 5.27537 | 0.202749 | 0.101375 | − | 0.994848i | \(-0.467676\pi\) | ||||
0.101375 | + | 0.994848i | \(0.467676\pi\) | |||||||
\(678\) | 6.94393 | 0.266680 | ||||||||
\(679\) | 8.50579 | + | 20.8348i | 0.326422 | + | 0.799568i | ||||
\(680\) | 11.5826 | 0.444172 | ||||||||
\(681\) | 0.330303i | 0.0126572i | ||||||||
\(682\) | 15.4779 | − | 24.1185i | 0.592678 | − | 0.923545i | ||||
\(683\) | −9.49545 | −0.363333 | −0.181667 | − | 0.983360i | \(-0.558149\pi\) | ||||
−0.181667 | + | 0.983360i | \(0.558149\pi\) | |||||||
\(684\) | 4.65743 | 0.178081 | ||||||||
\(685\) | 9.79796i | 0.374361i | ||||||||
\(686\) | 17.0000 | + | 7.34847i | 0.649063 | + | 0.280566i | ||||
\(687\) | 3.66970 | 0.140008 | ||||||||
\(688\) | 7.16515i | 0.273169i | ||||||||
\(689\) | −7.48331 | −0.285092 | ||||||||
\(690\) | − | 8.00000i | − | 0.304555i | ||||||
\(691\) | 3.98320i | 0.151528i | 0.997126 | + | 0.0757641i | \(0.0241396\pi\) | ||||
−0.997126 | + | 0.0757641i | \(0.975860\pi\) | |||||||
\(692\) | −10.7137 | −0.407275 | ||||||||
\(693\) | −4.12296 | + | 22.2838i | −0.156618 | + | 0.846492i | ||||
\(694\) | −19.1652 | −0.727499 | ||||||||
\(695\) | 47.9129i | 1.81744i | ||||||||
\(696\) | 1.02248i | 0.0387569i | ||||||||
\(697\) | 37.1652 | 1.40773 | ||||||||
\(698\) | 24.1185i | 0.912899i | ||||||||
\(699\) | 17.5510 | 0.663838 | ||||||||
\(700\) | 11.2250 | − | 4.58258i | 0.424264 | − | 0.173205i | ||||
\(701\) | − | 12.3303i | − | 0.465709i | −0.972512 | − | 0.232855i | \(-0.925193\pi\) | ||
0.972512 | − | 0.232855i | \(-0.0748066\pi\) | |||||||
\(702\) | 2.33030 | 0.0879516 | ||||||||
\(703\) | −6.46084 | −0.243675 | ||||||||
\(704\) | 1.79129 | − | 2.79129i | 0.0675117 | − | 0.105201i | ||||
\(705\) | − | 19.8656i | − | 0.748182i | ||||||
\(706\) | 7.48331 | 0.281638 | ||||||||
\(707\) | −28.7477 | + | 11.7362i | −1.08117 | + | 0.441386i | ||||
\(708\) | −0.417424 | −0.0156878 | ||||||||
\(709\) | 52.3303 | 1.96531 | 0.982653 | − | 0.185454i | \(-0.0593757\pi\) | ||||
0.982653 | + | 0.185454i | \(0.0593757\pi\) | |||||||
\(710\) | 6.19115 | 0.232350 | ||||||||
\(711\) | 10.3303i | 0.387417i | ||||||||
\(712\) | −9.79796 | −0.367194 | ||||||||
\(713\) | 34.5625i | 1.29438i | ||||||||
\(714\) | −5.92146 | + | 2.41742i | −0.221605 | + | 0.0904698i | ||||
\(715\) | 5.58258 | + | 3.58258i | 0.208776 | + | 0.133981i | ||||
\(716\) | −11.1652 | −0.417261 | ||||||||
\(717\) | 5.43836 | 0.203099 | ||||||||
\(718\) | −9.58258 | −0.357619 | ||||||||
\(719\) | 23.3376i | 0.870345i | 0.900347 | + | 0.435172i | \(0.143313\pi\) | ||||
−0.900347 | + | 0.435172i | \(0.856687\pi\) | |||||||
\(720\) | − | 7.99455i | − | 0.297939i | ||||||
\(721\) | −6.05630 | − | 14.8348i | −0.225548 | − | 0.552479i | ||||
\(722\) | − | 15.7477i | − | 0.586070i | ||||||
\(723\) | 2.24318i | 0.0834248i | ||||||||
\(724\) | 5.41022i | 0.201069i | ||||||||
\(725\) | 7.25227i | 0.269343i | ||||||||
\(726\) | −2.96073 | − | 6.46084i | −0.109883 | − | 0.239784i | ||||
\(727\) | − | 37.5514i | − | 1.39271i | −0.717700 | − | 0.696353i | \(-0.754805\pi\) | ||
0.717700 | − | 0.696353i | \(-0.245195\pi\) | |||||||
\(728\) | −0.646084 | − | 1.58258i | −0.0239455 | − | 0.0586542i | ||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | 49.9129 | 1.84736 | ||||||||
\(731\) | − | 26.8095i | − | 0.991587i | ||||||
\(732\) | 1.25227i | 0.0462853i | ||||||||
\(733\) | 10.7137 | 0.395721 | 0.197860 | − | 0.980230i | \(-0.436601\pi\) | ||||
0.197860 | + | 0.980230i | \(0.436601\pi\) | |||||||
\(734\) | 21.0229 | 0.775971 | ||||||||
\(735\) | −10.0000 | + | 9.79796i | −0.368856 | + | 0.361403i | ||||
\(736\) | 4.00000i | 0.147442i | ||||||||
\(737\) | 13.5826 | − | 21.1652i | 0.500321 | − | 0.779628i | ||||
\(738\) | − | 25.6522i | − | 0.944271i | ||||||
\(739\) | − | 1.58258i | − | 0.0582160i | −0.999576 | − | 0.0291080i | \(-0.990733\pi\) | ||
0.999576 | − | 0.0291080i | \(-0.00926667\pi\) | |||||||
\(740\) | 11.0901i | 0.407681i | ||||||||
\(741\) | 0.752785i | 0.0276543i | ||||||||
\(742\) | −11.5826 | − | 28.3714i | −0.425210 | − | 1.04155i | ||||
\(743\) | − | 1.91288i | − | 0.0701767i | −0.999384 | − | 0.0350884i | \(-0.988829\pi\) | ||
0.999384 | − | 0.0350884i | \(-0.0111713\pi\) | |||||||
\(744\) | − | 5.58258i | − | 0.204667i | ||||||
\(745\) | 43.3380 | 1.58778 | ||||||||
\(746\) | 9.58258 | 0.350843 | ||||||||
\(747\) | 33.2985 | 1.21833 | ||||||||
\(748\) | −6.70239 | + | 10.4440i | −0.245063 | + | 0.381872i | ||||
\(749\) | −17.5826 | − | 43.0683i | −0.642453 | − | 1.57368i | ||||
\(750\) | − | 0.834849i | − | 0.0304844i | ||||||
\(751\) | −41.4955 | −1.51419 | −0.757095 | − | 0.653304i | \(-0.773382\pi\) | ||||
−0.757095 | + | 0.653304i | \(0.773382\pi\) | |||||||
\(752\) | 9.93280i | 0.362212i | ||||||||
\(753\) | −15.5826 | −0.567861 | ||||||||
\(754\) | 1.02248 | 0.0372364 | ||||||||
\(755\) | −17.2813 | −0.628930 | ||||||||
\(756\) | 3.60681 | + | 8.83485i | 0.131178 | + | 0.321320i | ||||
\(757\) | −30.8348 | −1.12071 | −0.560356 | − | 0.828252i | \(-0.689336\pi\) | ||||
−0.560356 | + | 0.828252i | \(0.689336\pi\) | |||||||
\(758\) | − | 22.3303i | − | 0.811073i | ||||||
\(759\) | 7.21362 | + | 4.62929i | 0.261838 | + | 0.168033i | ||||
\(760\) | 5.58258 | 0.202501 | ||||||||
\(761\) | 28.2366 | 1.02357 | 0.511787 | − | 0.859112i | \(-0.328984\pi\) | ||||
0.511787 | + | 0.859112i | \(0.328984\pi\) | |||||||
\(762\) | 2.31464i | 0.0838507i | ||||||||
\(763\) | −17.1652 | − | 42.0459i | −0.621420 | − | 1.52216i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 29.9129i | 1.08150i | ||||||||
\(766\) | 19.7308 | 0.712901 | ||||||||
\(767\) | 0.417424i | 0.0150723i | ||||||||
\(768\) | − | 0.646084i | − | 0.0233135i | ||||||
\(769\) | −15.1015 | −0.544573 | −0.272287 | − | 0.962216i | \(-0.587780\pi\) | ||||
−0.272287 | + | 0.962216i | \(0.587780\pi\) | |||||||
\(770\) | −4.94194 | + | 26.7102i | −0.178095 | + | 0.962569i | ||||
\(771\) | 3.16515 | 0.113990 | ||||||||
\(772\) | 16.3303i | 0.587740i | ||||||||
\(773\) | − | 10.0395i | − | 0.361096i | −0.983566 | − | 0.180548i | \(-0.942213\pi\) | ||
0.983566 | − | 0.180548i | \(-0.0577871\pi\) | |||||||
\(774\) | −18.5045 | −0.665132 | ||||||||
\(775\) | − | 39.5964i | − | 1.42234i | ||||||
\(776\) | 8.50579 | 0.305340 | ||||||||
\(777\) | −2.31464 | − | 5.66970i | −0.0830374 | − | 0.203399i | ||||
\(778\) | 10.0000i | 0.358517i | ||||||||
\(779\) | 17.9129 | 0.641795 | ||||||||
\(780\) | 1.29217 | 0.0462670 | ||||||||
\(781\) | −3.58258 | + | 5.58258i | −0.128195 | + | 0.199760i | ||||
\(782\) | − | 14.9666i | − | 0.535206i | ||||||
\(783\) | −5.70805 | −0.203989 | ||||||||
\(784\) | 5.00000 | − | 4.89898i | 0.178571 | − | 0.174964i | ||||
\(785\) | 40.7477 | 1.45435 | ||||||||
\(786\) | −10.8348 | −0.386466 | ||||||||
\(787\) | 23.2309 | 0.828091 | 0.414046 | − | 0.910256i | \(-0.364115\pi\) | ||||
0.414046 | + | 0.910256i | \(0.364115\pi\) | |||||||
\(788\) | 8.74773i | 0.311625i | ||||||||
\(789\) | 5.38207 | 0.191607 | ||||||||
\(790\) | 12.3823i | 0.440542i | ||||||||
\(791\) | 26.3264 | − | 10.7477i | 0.936061 | − | 0.382145i | ||||
\(792\) | 7.20871 | + | 4.62614i | 0.256150 | + | 0.164383i | ||||
\(793\) | 1.25227 | 0.0444695 | ||||||||
\(794\) | −27.5905 | −0.979149 | ||||||||
\(795\) | 23.1652 | 0.821583 | ||||||||
\(796\) | − | 9.66311i | − | 0.342500i | ||||||
\(797\) | − | 25.0061i | − | 0.885763i | −0.896580 | − | 0.442881i | \(-0.853956\pi\) | ||
0.896580 | − | 0.442881i | \(-0.146044\pi\) | |||||||
\(798\) | −2.85403 | + | 1.16515i | −0.101031 | + | 0.0412459i | ||||
\(799\) | − | 37.1652i | − | 1.31481i | ||||||
\(800\) | − | 4.58258i | − | 0.162019i | ||||||
\(801\) | − | 25.3040i | − | 0.894072i | ||||||
\(802\) | 7.58258i | 0.267750i | ||||||||
\(803\) | −28.8826 | + | 45.0066i | −1.01925 | + | 1.58825i | ||||
\(804\) | − | 4.89898i | − | 0.172774i | ||||||
\(805\) | −12.3823 | − | 30.3303i | −0.436419 | − | 1.06900i | ||||
\(806\) | −5.58258 | −0.196638 | ||||||||
\(807\) | 10.6606 | 0.375271 | ||||||||
\(808\) | 11.7362i | 0.412878i | ||||||||
\(809\) | − | 14.8348i | − | 0.521566i | −0.965398 | − | 0.260783i | \(-0.916019\pi\) | ||
0.965398 | − | 0.260783i | \(-0.0839806\pi\) | |||||||
\(810\) | 16.7700 | 0.589239 | ||||||||
\(811\) | 3.36526 | 0.118170 | 0.0590852 | − | 0.998253i | \(-0.481182\pi\) | ||||
0.0590852 | + | 0.998253i | \(0.481182\pi\) | |||||||
\(812\) | 1.58258 | + | 3.87650i | 0.0555375 | + | 0.136039i | ||||
\(813\) | 3.16515i | 0.111007i | ||||||||
\(814\) | −10.0000 | − | 6.41742i | −0.350500 | − | 0.224931i | ||||
\(815\) | − | 12.3823i | − | 0.433733i | ||||||
\(816\) | 2.41742i | 0.0846268i | ||||||||
\(817\) | − | 12.9217i | − | 0.452072i | ||||||
\(818\) | − | 5.03383i | − | 0.176004i | ||||||
\(819\) | 4.08712 | − | 1.66856i | 0.142816 | − | 0.0583042i | ||||
\(820\) | − | 30.7477i | − | 1.07376i | ||||||
\(821\) | 43.4955i | 1.51800i | 0.651090 | + | 0.759001i | \(0.274312\pi\) | ||||
−0.651090 | + | 0.759001i | \(0.725688\pi\) | |||||||
\(822\) | −2.04495 | −0.0713259 | ||||||||
\(823\) | −3.66970 | −0.127918 | −0.0639588 | − | 0.997953i | \(-0.520373\pi\) | ||||
−0.0639588 | + | 0.997953i | \(0.520373\pi\) | |||||||
\(824\) | −6.05630 | −0.210981 | ||||||||
\(825\) | −8.26424 | − | 5.30352i | −0.287724 | − | 0.184645i | ||||
\(826\) | −1.58258 | + | 0.646084i | −0.0550649 | + | 0.0224801i | ||||
\(827\) | − | 3.16515i | − | 0.110063i | −0.998485 | − | 0.0550315i | \(-0.982474\pi\) | ||
0.998485 | − | 0.0550315i | \(-0.0175259\pi\) | |||||||
\(828\) | −10.3303 | −0.359003 | ||||||||
\(829\) | − | 7.99455i | − | 0.277662i | −0.990316 | − | 0.138831i | \(-0.955665\pi\) | ||
0.990316 | − | 0.138831i | \(-0.0443345\pi\) | |||||||
\(830\) | 39.9129 | 1.38540 | ||||||||
\(831\) | −1.29217 | −0.0448248 | ||||||||
\(832\) | −0.646084 | −0.0223989 | ||||||||
\(833\) | −18.7083 | + | 18.3303i | −0.648204 | + | 0.635107i | ||||
\(834\) | −10.0000 | −0.346272 | ||||||||
\(835\) | − | 4.00000i | − | 0.138426i | ||||||
\(836\) | −3.23042 | + | 5.03383i | −0.111726 | + | 0.174098i | ||||
\(837\) | 31.1652 | 1.07723 | ||||||||
\(838\) | 13.0284 | 0.450058 | ||||||||
\(839\) | 9.66311i | 0.333608i | 0.985990 | + | 0.166804i | \(0.0533447\pi\) | ||||
−0.985990 | + | 0.166804i | \(0.946655\pi\) | |||||||
\(840\) | 2.00000 | + | 4.89898i | 0.0690066 | + | 0.169031i | ||||
\(841\) | 26.4955 | 0.913636 | ||||||||
\(842\) | 7.58258i | 0.261313i | ||||||||
\(843\) | −7.21362 | −0.248450 | ||||||||
\(844\) | 16.7477i | 0.576481i | ||||||||
\(845\) | 38.9503i | 1.33993i | ||||||||
\(846\) | −25.6522 | −0.881941 | ||||||||
\(847\) | −21.2250 | − | 19.9123i | −0.729299 | − | 0.684195i | ||||
\(848\) | −11.5826 | −0.397747 | ||||||||
\(849\) | 11.6697i | 0.400503i | ||||||||
\(850\) | 17.1464i | 0.588118i | ||||||||
\(851\) | 14.3303 | 0.491236 | ||||||||
\(852\) | 1.29217i | 0.0442689i | ||||||||
\(853\) | 11.4665 | 0.392606 | 0.196303 | − | 0.980543i | \(-0.437106\pi\) | ||||
0.196303 | + | 0.980543i | \(0.437106\pi\) | |||||||
\(854\) | 1.93825 | + | 4.74773i | 0.0663256 | + | 0.162464i | ||||
\(855\) | 14.4174i | 0.493066i | ||||||||
\(856\) | −17.5826 | −0.600960 | ||||||||
\(857\) | −31.0906 | −1.06203 | −0.531017 | − | 0.847361i | \(-0.678190\pi\) | ||||
−0.531017 | + | 0.847361i | \(0.678190\pi\) | |||||||
\(858\) | −0.747727 | + | 1.16515i | −0.0255270 | + | 0.0397776i | ||||
\(859\) | 24.3882i | 0.832115i | 0.909338 | + | 0.416057i | \(0.136588\pi\) | ||||
−0.909338 | + | 0.416057i | \(0.863412\pi\) | |||||||
\(860\) | −22.1803 | −0.756340 | ||||||||
\(861\) | 6.41742 | + | 15.7194i | 0.218705 | + | 0.535716i | ||||
\(862\) | −27.9129 | −0.950716 | ||||||||
\(863\) | −14.8348 | −0.504984 | −0.252492 | − | 0.967599i | \(-0.581250\pi\) | ||||
−0.252492 | + | 0.967599i | \(0.581250\pi\) | |||||||
\(864\) | 3.60681 | 0.122706 | ||||||||
\(865\) | − | 33.1652i | − | 1.12765i | ||||||
\(866\) | 35.5850 | 1.20923 | ||||||||
\(867\) | 1.93825i | 0.0658265i | ||||||||
\(868\) | −8.64064 | − | 21.1652i | −0.293282 | − | 0.718392i | ||||
\(869\) | −11.1652 | − | 7.16515i | −0.378752 | − | 0.243061i | ||||
\(870\) | −3.16515 | −0.107309 | ||||||||
\(871\) | −4.89898 | −0.165996 | ||||||||
\(872\) | −17.1652 | −0.581285 | ||||||||
\(873\) | 21.9668i | 0.743465i | ||||||||
\(874\) | − | 7.21362i | − | 0.244004i | ||||||
\(875\) | −1.29217 | − | 3.16515i | −0.0436832 | − | 0.107002i | ||||
\(876\) | 10.4174i | 0.351972i | ||||||||
\(877\) | 6.83485i | 0.230796i | 0.993319 | + | 0.115398i | \(0.0368144\pi\) | ||||
−0.993319 | + | 0.115398i | \(0.963186\pi\) | |||||||
\(878\) | 17.2813i | 0.583215i | ||||||||
\(879\) | − | 16.2432i | − | 0.547869i | ||||||
\(880\) | 8.64064 | + | 5.54506i | 0.291276 | + | 0.186924i | ||||
\(881\) | − | 7.21362i | − | 0.243033i | −0.992589 | − | 0.121517i | \(-0.961224\pi\) | ||
0.992589 | − | 0.121517i | \(-0.0387758\pi\) | |||||||
\(882\) | 12.6520 | + | 12.9129i | 0.426015 | + | 0.434799i | ||||
\(883\) | 12.8348 | 0.431927 | 0.215964 | − | 0.976401i | \(-0.430711\pi\) | ||||
0.215964 | + | 0.976401i | \(0.430711\pi\) | |||||||
\(884\) | 2.41742 | 0.0813068 | ||||||||
\(885\) | − | 1.29217i | − | 0.0434357i | ||||||
\(886\) | 15.1652i | 0.509483i | ||||||||
\(887\) | −53.4057 | −1.79319 | −0.896594 | − | 0.442854i | \(-0.853966\pi\) | ||||
−0.896594 | + | 0.442854i | \(0.853966\pi\) | |||||||
\(888\) | −2.31464 | −0.0776744 | ||||||||
\(889\) | 3.58258 | + | 8.77548i | 0.120156 | + | 0.294320i | ||||
\(890\) | − | 30.3303i | − | 1.01667i | ||||||
\(891\) | −9.70417 | + | 15.1216i | −0.325102 | + | 0.506592i | ||||
\(892\) | 16.1240i | 0.539870i | ||||||||
\(893\) | − | 17.9129i | − | 0.599432i | ||||||
\(894\) | 9.04517i | 0.302516i | ||||||||
\(895\) | − | 34.5625i | − | 1.15530i | ||||||
\(896\) | −1.00000 | − | 2.44949i | −0.0334077 | − | 0.0818317i | ||||
\(897\) | − | 1.66970i | − | 0.0557496i | ||||||
\(898\) | 31.1652i | 1.03999i | ||||||||
\(899\) | 13.6745 | 0.456069 | ||||||||
\(900\) | 11.8348 | 0.394495 | ||||||||
\(901\) | 43.3380 | 1.44380 | ||||||||
\(902\) | 27.7253 | + | 17.7925i | 0.923152 | + | 0.592426i | ||||
\(903\) | 11.3394 | − | 4.62929i | 0.377351 | − | 0.154053i | ||||
\(904\) | − | 10.7477i | − | 0.357464i | ||||||
\(905\) | −16.7477 | −0.556713 | ||||||||
\(906\) | − | 3.60681i | − | 0.119828i | ||||||
\(907\) | 5.91288 | 0.196334 | 0.0981670 | − | 0.995170i | \(-0.468702\pi\) | ||||
0.0981670 | + | 0.995170i | \(0.468702\pi\) | |||||||
\(908\) | 0.511238 | 0.0169660 | ||||||||
\(909\) | −30.3097 | −1.00531 | ||||||||
\(910\) | 4.89898 | − | 2.00000i | 0.162400 | − | 0.0662994i | ||||
\(911\) | 3.16515 | 0.104866 | 0.0524331 | − | 0.998624i | \(-0.483302\pi\) | ||||
0.0524331 | + | 0.998624i | \(0.483302\pi\) | |||||||
\(912\) | 1.16515i | 0.0385820i | ||||||||
\(913\) | −23.0960 | + | 35.9896i | −0.764367 | + | 1.19108i | ||||
\(914\) | 33.1652 | 1.09701 | ||||||||
\(915\) | −3.87650 | −0.128153 | ||||||||
\(916\) | − | 5.67991i | − | 0.187669i | ||||||
\(917\) | −41.0780 | + | 16.7700i | −1.35652 | + | 0.553795i | ||||
\(918\) | −13.4955 | −0.445416 | ||||||||
\(919\) | − | 19.4955i | − | 0.643096i | −0.946893 | − | 0.321548i | \(-0.895797\pi\) | ||
0.946893 | − | 0.321548i | \(-0.104203\pi\) | |||||||
\(920\) | −12.3823 | −0.408232 | ||||||||
\(921\) | 6.83485i | 0.225216i | ||||||||
\(922\) | 30.0400i | 0.989313i | ||||||||
\(923\) | 1.29217 | 0.0425322 | ||||||||
\(924\) | −5.57475 | − | 1.03144i | −0.183396 | − | 0.0339320i | ||||
\(925\) | −16.4174 | −0.539802 | ||||||||
\(926\) | 5.16515i | 0.169737i | ||||||||
\(927\) | − | 15.6409i | − | 0.513713i | ||||||
\(928\) | 1.58258 | 0.0519506 | ||||||||
\(929\) | − | 43.6077i | − | 1.43072i | −0.698755 | − | 0.715361i | \(-0.746262\pi\) | ||
0.698755 | − | 0.715361i | \(-0.253738\pi\) | |||||||
\(930\) | 17.2813 | 0.566675 | ||||||||
\(931\) | −9.01703 | + | 8.83485i | −0.295521 | + | 0.289550i | ||||
\(932\) | − | 27.1652i | − | 0.889824i | ||||||
\(933\) | −3.25227 | −0.106475 | ||||||||
\(934\) | −11.7362 | −0.384021 | ||||||||
\(935\) | −32.3303 | − | 20.7477i | −1.05731 | − | 0.678523i | ||||
\(936\) | − | 1.66856i | − | 0.0545386i | ||||||
\(937\) | 30.0681 | 0.982282 | 0.491141 | − | 0.871080i | \(-0.336580\pi\) | ||||
0.491141 | + | 0.871080i | \(0.336580\pi\) | |||||||
\(938\) | −7.58258 | − | 18.5734i | −0.247580 | − | 0.606444i | ||||
\(939\) | 15.1652 | 0.494896 | ||||||||
\(940\) | −30.7477 | −1.00288 | ||||||||
\(941\) | −5.27537 | −0.171972 | −0.0859861 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859861 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(942\) | 8.50455i | 0.277093i | ||||||||
\(943\) | −39.7312 | −1.29383 | ||||||||
\(944\) | 0.646084i | 0.0210282i | ||||||||
\(945\) | −27.3489 | + | 11.1652i | −0.889661 | + | 0.363202i | ||||
\(946\) | 12.8348 | − | 20.0000i | 0.417297 | − | 0.650256i | ||||
\(947\) | 3.58258 | 0.116418 | 0.0582090 | − | 0.998304i | \(-0.481461\pi\) | ||||
0.0582090 | + | 0.998304i | \(0.481461\pi\) | |||||||
\(948\) | −2.58434 | −0.0839353 | ||||||||
\(949\) | 10.4174 | 0.338164 | ||||||||
\(950\) | 8.26424i | 0.268127i | ||||||||
\(951\) | − | 5.92146i | − | 0.192016i | ||||||
\(952\) | 3.74166 | + | 9.16515i | 0.121268 | + | 0.297044i | ||||
\(953\) | 18.3303i | 0.593777i | 0.954912 | + | 0.296888i | \(0.0959489\pi\) | ||||
−0.954912 | + | 0.296888i | \(0.904051\pi\) | |||||||
\(954\) | − | 29.9129i | − | 0.968465i | ||||||
\(955\) | 55.7203i | 1.80307i | ||||||||
\(956\) | − | 8.41742i | − | 0.272239i | ||||||
\(957\) | 1.83155 | − | 2.85403i | 0.0592056 | − | 0.0922576i | ||||
\(958\) | 30.9557i | 1.00013i | ||||||||
\(959\) | −7.75301 | + | 3.16515i | −0.250358 | + | 0.102208i | ||||
\(960\) | 2.00000 | 0.0645497 | ||||||||
\(961\) | −43.6606 | −1.40841 | ||||||||
\(962\) | 2.31464i | 0.0746271i | ||||||||
\(963\) | − | 45.4083i | − | 1.46326i | ||||||
\(964\) | 3.47197 | 0.111825 | ||||||||
\(965\) | −50.5517 | −1.62732 | ||||||||
\(966\) | 6.33030 | − | 2.58434i | 0.203674 | − | 0.0831496i | ||||
\(967\) | 22.4174i | 0.720896i | 0.932779 | + | 0.360448i | \(0.117376\pi\) | ||||
−0.932779 | + | 0.360448i | \(0.882624\pi\) | |||||||
\(968\) | −10.0000 | + | 4.58258i | −0.321412 | + | 0.147290i | ||||
\(969\) | − | 4.35960i | − | 0.140050i | ||||||
\(970\) | 26.3303i | 0.845415i | ||||||||
\(971\) | − | 14.0509i | − | 0.450913i | −0.974253 | − | 0.225457i | \(-0.927613\pi\) | ||
0.974253 | − | 0.225457i | \(-0.0723874\pi\) | |||||||
\(972\) | 14.3205i | 0.459332i | ||||||||
\(973\) | −37.9129 | + | 15.4779i | −1.21543 | + | 0.496198i | ||||
\(974\) | 21.4955i | 0.688759i | ||||||||
\(975\) | 1.91288i | 0.0612611i | ||||||||
\(976\) | 1.93825 | 0.0620419 | ||||||||
\(977\) | 9.16515 | 0.293219 | 0.146610 | − | 0.989194i | \(-0.453164\pi\) | ||||
0.146610 | + | 0.989194i | \(0.453164\pi\) | |||||||
\(978\) | 2.58434 | 0.0826379 | ||||||||
\(979\) | 27.3489 | + | 17.5510i | 0.874075 | + | 0.560931i | ||||
\(980\) | 15.1652 | + | 15.4779i | 0.484433 | + | 0.494422i | ||||
\(981\) | − | 44.3303i | − | 1.41536i | ||||||
\(982\) | 33.4955 | 1.06888 | ||||||||
\(983\) | − | 50.6865i | − | 1.61665i | −0.588738 | − | 0.808324i | \(-0.700375\pi\) | ||
0.588738 | − | 0.808324i | \(-0.299625\pi\) | |||||||
\(984\) | 6.41742 | 0.204580 | ||||||||
\(985\) | −27.0792 | −0.862816 | ||||||||
\(986\) | −5.92146 | −0.188578 | ||||||||
\(987\) | 15.7194 | − | 6.41742i | 0.500354 | − | 0.204269i | ||||
\(988\) | 1.16515 | 0.0370684 | ||||||||
\(989\) | 28.6606i | 0.911354i | ||||||||
\(990\) | −14.3205 | + | 22.3151i | −0.455137 | + | 0.709220i | ||||
\(991\) | 46.6606 | 1.48222 | 0.741111 | − | 0.671382i | \(-0.234299\pi\) | ||||
0.741111 | + | 0.671382i | \(0.234299\pi\) | |||||||
\(992\) | −8.64064 | −0.274340 | ||||||||
\(993\) | 15.2363i | 0.483510i | ||||||||
\(994\) | 2.00000 | + | 4.89898i | 0.0634361 | + | 0.155386i | ||||
\(995\) | 29.9129 | 0.948302 | ||||||||
\(996\) | 8.33030i | 0.263956i | ||||||||
\(997\) | 22.5566 | 0.714376 | 0.357188 | − | 0.934032i | \(-0.383736\pi\) | ||||
0.357188 | + | 0.934032i | \(0.383736\pi\) | |||||||
\(998\) | − | 17.9129i | − | 0.567022i | ||||||
\(999\) | − | 12.9217i | − | 0.408824i |
(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 | 154.2.c.a.153.6 | yes | 8 | |
3.2 | odd | 2 | 1386.2.e.b.307.4 | 8 | |||
4.3 | odd | 2 | 1232.2.e.e.769.5 | 8 | |||
7.2 | even | 3 | 1078.2.i.b.1011.7 | 16 | |||
7.3 | odd | 6 | 1078.2.i.b.901.3 | 16 | |||
7.4 | even | 3 | 1078.2.i.b.901.2 | 16 | |||
7.5 | odd | 6 | 1078.2.i.b.1011.6 | 16 | |||
7.6 | odd | 2 | inner | 154.2.c.a.153.7 | yes | 8 | |
11.10 | odd | 2 | inner | 154.2.c.a.153.2 | ✓ | 8 | |
21.20 | even | 2 | 1386.2.e.b.307.1 | 8 | |||
28.27 | even | 2 | 1232.2.e.e.769.4 | 8 | |||
33.32 | even | 2 | 1386.2.e.b.307.8 | 8 | |||
44.43 | even | 2 | 1232.2.e.e.769.6 | 8 | |||
77.10 | even | 6 | 1078.2.i.b.901.7 | 16 | |||
77.32 | odd | 6 | 1078.2.i.b.901.6 | 16 | |||
77.54 | even | 6 | 1078.2.i.b.1011.2 | 16 | |||
77.65 | odd | 6 | 1078.2.i.b.1011.3 | 16 | |||
77.76 | even | 2 | inner | 154.2.c.a.153.3 | yes | 8 | |
231.230 | odd | 2 | 1386.2.e.b.307.5 | 8 | |||
308.307 | odd | 2 | 1232.2.e.e.769.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.c.a.153.2 | ✓ | 8 | 11.10 | odd | 2 | inner | |
154.2.c.a.153.3 | yes | 8 | 77.76 | even | 2 | inner | |
154.2.c.a.153.6 | yes | 8 | 1.1 | even | 1 | trivial | |
154.2.c.a.153.7 | yes | 8 | 7.6 | odd | 2 | inner | |
1078.2.i.b.901.2 | 16 | 7.4 | even | 3 | |||
1078.2.i.b.901.3 | 16 | 7.3 | odd | 6 | |||
1078.2.i.b.901.6 | 16 | 77.32 | odd | 6 | |||
1078.2.i.b.901.7 | 16 | 77.10 | even | 6 | |||
1078.2.i.b.1011.2 | 16 | 77.54 | even | 6 | |||
1078.2.i.b.1011.3 | 16 | 77.65 | odd | 6 | |||
1078.2.i.b.1011.6 | 16 | 7.5 | odd | 6 | |||
1078.2.i.b.1011.7 | 16 | 7.2 | even | 3 | |||
1232.2.e.e.769.3 | 8 | 308.307 | odd | 2 | |||
1232.2.e.e.769.4 | 8 | 28.27 | even | 2 | |||
1232.2.e.e.769.5 | 8 | 4.3 | odd | 2 | |||
1232.2.e.e.769.6 | 8 | 44.43 | even | 2 | |||
1386.2.e.b.307.1 | 8 | 21.20 | even | 2 | |||
1386.2.e.b.307.4 | 8 | 3.2 | odd | 2 | |||
1386.2.e.b.307.5 | 8 | 231.230 | odd | 2 | |||
1386.2.e.b.307.8 | 8 | 33.32 | even | 2 |