Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.b (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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} + \cdots + 41943040000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{50}\cdot 3^{40} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.17 | ||
Root | \(-5.24560 - 3.02855i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.6.b.c.107.18 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.45658 | − | 3.48409i | 0.787820 | − | 0.615906i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.72226 | − | 31.0543i | 0.241321 | − | 0.970445i | ||||
\(5\) | 40.4806i | 0.724139i | 0.932151 | + | 0.362069i | \(0.117930\pi\) | ||||
−0.932151 | + | 0.362069i | \(0.882070\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 148.504i | 1.14550i | 0.819731 | + | 0.572749i | \(0.194123\pi\) | ||||
−0.819731 | + | 0.572749i | \(0.805877\pi\) | |||||||
\(8\) | −73.7809 | − | 165.301i | −0.407586 | − | 0.913167i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 141.038 | + | 180.405i | 0.446001 | + | 0.570491i | ||||
\(11\) | 608.102 | 1.51529 | 0.757643 | − | 0.652670i | \(-0.226351\pi\) | ||||
0.757643 | + | 0.652670i | \(0.226351\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 883.839 | 1.45049 | 0.725245 | − | 0.688490i | \(-0.241726\pi\) | ||||
0.725245 | + | 0.688490i | \(0.241726\pi\) | |||||||
\(14\) | 517.402 | + | 661.822i | 0.705518 | + | 0.902446i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −904.733 | − | 479.618i | −0.883529 | − | 0.468377i | ||||
\(17\) | 1133.69i | 0.951415i | 0.879603 | + | 0.475708i | \(0.157808\pi\) | ||||
−0.879603 | + | 0.475708i | \(0.842192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1111.90i | − | 0.706614i | −0.935507 | − | 0.353307i | \(-0.885057\pi\) | ||
0.935507 | − | 0.353307i | \(-0.114943\pi\) | |||||||
\(20\) | 1257.09 | + | 312.602i | 0.702737 | + | 0.174750i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2710.06 | − | 2118.68i | 1.19377 | − | 0.933273i | ||||
\(23\) | −1347.14 | −0.531000 | −0.265500 | − | 0.964111i | \(-0.585537\pi\) | ||||
−0.265500 | + | 0.964111i | \(0.585537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1486.32 | 0.475623 | ||||||||
\(26\) | 3938.90 | − | 3079.37i | 1.14273 | − | 0.893365i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4611.69 | + | 1146.79i | 1.11164 | + | 0.276432i | ||||
\(29\) | − | 1856.29i | − | 0.409875i | −0.978775 | − | 0.204937i | \(-0.934301\pi\) | ||
0.978775 | − | 0.204937i | \(-0.0656991\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 606.496i | 0.113351i | 0.998393 | + | 0.0566753i | \(0.0180500\pi\) | ||||
−0.998393 | + | 0.0566753i | \(0.981950\pi\) | |||||||
\(32\) | −5703.05 | + | 1014.71i | −0.984538 | + | 0.175174i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3949.86 | + | 5052.36i | 0.585982 | + | 0.749544i | ||||
\(35\) | −6011.54 | −0.829499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13662.1 | 1.64064 | 0.820319 | − | 0.571906i | \(-0.193796\pi\) | ||||
0.820319 | + | 0.571906i | \(0.193796\pi\) | |||||||
\(38\) | −3873.96 | − | 4955.28i | −0.435208 | − | 0.556685i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6691.48 | − | 2986.69i | 0.661260 | − | 0.295148i | ||||
\(41\) | 21260.5i | 1.97522i | 0.156939 | + | 0.987608i | \(0.449837\pi\) | ||||
−0.156939 | + | 0.987608i | \(0.550163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12478.1i | − | 1.02914i | −0.857447 | − | 0.514572i | \(-0.827951\pi\) | ||
0.857447 | − | 0.514572i | \(-0.172049\pi\) | |||||||
\(44\) | 4695.92 | − | 18884.1i | 0.365670 | − | 1.47050i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6003.66 | + | 4693.57i | −0.418332 | + | 0.327046i | ||||
\(47\) | −16295.9 | −1.07606 | −0.538028 | − | 0.842927i | \(-0.680830\pi\) | ||||
−0.538028 | + | 0.842927i | \(0.680830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5246.55 | −0.312165 | ||||||||
\(50\) | 6623.92 | − | 5178.48i | 0.374705 | − | 0.292939i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6825.24 | − | 27447.0i | 0.350033 | − | 1.40762i | ||||
\(53\) | 1343.79i | 0.0657115i | 0.999460 | + | 0.0328558i | \(0.0104602\pi\) | ||||
−0.999460 | + | 0.0328558i | \(0.989540\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 24616.3i | 1.09728i | ||||||||
\(56\) | 24547.9 | − | 10956.8i | 1.04603 | − | 0.466888i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6467.48 | − | 8272.72i | −0.252444 | − | 0.322907i | ||||
\(59\) | −31250.9 | −1.16878 | −0.584389 | − | 0.811474i | \(-0.698666\pi\) | ||||
−0.584389 | + | 0.811474i | \(0.698666\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6502.94 | 0.223761 | 0.111881 | − | 0.993722i | \(-0.464313\pi\) | ||||
0.111881 | + | 0.993722i | \(0.464313\pi\) | |||||||
\(62\) | 2113.09 | + | 2702.90i | 0.0698133 | + | 0.0892999i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −21880.8 | + | 24392.1i | −0.667748 | + | 0.744387i | ||||
\(65\) | 35778.3i | 1.05036i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2355.02i | − | 0.0640924i | −0.999486 | − | 0.0320462i | \(-0.989798\pi\) | ||
0.999486 | − | 0.0320462i | \(-0.0102024\pi\) | |||||||
\(68\) | 35205.7 | + | 8754.61i | 0.923297 | + | 0.229596i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −26790.9 | + | 20944.7i | −0.653496 | + | 0.510893i | ||||
\(71\) | 26941.5 | 0.634273 | 0.317137 | − | 0.948380i | \(-0.397279\pi\) | ||||
0.317137 | + | 0.948380i | \(0.397279\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −52309.9 | −1.14889 | −0.574443 | − | 0.818545i | \(-0.694781\pi\) | ||||
−0.574443 | + | 0.818545i | \(0.694781\pi\) | |||||||
\(74\) | 60886.2 | − | 47599.9i | 1.29253 | − | 1.01048i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −34529.3 | − | 8586.40i | −0.685731 | − | 0.170521i | ||||
\(77\) | 90305.8i | 1.73576i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 35732.6i | − | 0.644165i | −0.946712 | − | 0.322082i | \(-0.895617\pi\) | ||
0.946712 | − | 0.322082i | \(-0.104383\pi\) | |||||||
\(80\) | 19415.2 | − | 36624.1i | 0.339170 | − | 0.639797i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 74073.6 | + | 94749.4i | 1.21655 | + | 1.55612i | ||||
\(83\) | −62926.7 | −1.00263 | −0.501314 | − | 0.865266i | \(-0.667150\pi\) | ||||
−0.501314 | + | 0.865266i | \(0.667150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −45892.2 | −0.688957 | ||||||||
\(86\) | −43474.7 | − | 55609.6i | −0.633856 | − | 0.810781i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −44866.3 | − | 100520.i | −0.617608 | − | 1.38371i | ||||
\(89\) | 54560.1i | 0.730130i | 0.930982 | + | 0.365065i | \(0.118953\pi\) | ||||
−0.930982 | + | 0.365065i | \(0.881047\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 131254.i | 1.66153i | ||||||||
\(92\) | −10403.0 | + | 41834.5i | −0.128141 | + | 0.515306i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −72624.2 | + | 56776.5i | −0.847738 | + | 0.662749i | ||||
\(95\) | 45010.4 | 0.511687 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −142704. | −1.53995 | −0.769973 | − | 0.638076i | \(-0.779730\pi\) | ||||
−0.769973 | + | 0.638076i | \(0.779730\pi\) | |||||||
\(98\) | −23381.7 | + | 18279.4i | −0.245930 | + | 0.192264i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11477.8 | − | 46156.6i | 0.114778 | − | 0.461566i | ||||
\(101\) | − | 81531.3i | − | 0.795282i | −0.917541 | − | 0.397641i | \(-0.869829\pi\) | ||
0.917541 | − | 0.397641i | \(-0.130171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 154038.i | − | 1.43065i | −0.698790 | − | 0.715327i | \(-0.746278\pi\) | ||
0.698790 | − | 0.715327i | \(-0.253722\pi\) | |||||||
\(104\) | −65210.4 | − | 146099.i | −0.591199 | − | 1.32454i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4681.88 | + | 5988.71i | 0.0404721 | + | 0.0517688i | ||||
\(107\) | −164110. | −1.38572 | −0.692859 | − | 0.721073i | \(-0.743649\pi\) | ||||
−0.692859 | + | 0.721073i | \(0.743649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 136782. | 1.10271 | 0.551355 | − | 0.834271i | \(-0.314111\pi\) | ||||
0.551355 | + | 0.834271i | \(0.314111\pi\) | |||||||
\(110\) | 85765.4 | + | 109705.i | 0.675819 | + | 0.864456i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 71225.4 | − | 134357.i | 0.536525 | − | 1.01208i | ||||
\(113\) | − | 172572.i | − | 1.27138i | −0.771946 | − | 0.635688i | \(-0.780716\pi\) | ||
0.771946 | − | 0.635688i | \(-0.219284\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 54533.2i | − | 0.384517i | ||||||
\(116\) | −57645.7 | − | 14334.8i | −0.397761 | − | 0.0989112i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −139272. | + | 108881.i | −0.920786 | + | 0.719857i | ||||
\(119\) | −168357. | −1.08984 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 208737. | 1.29609 | ||||||||
\(122\) | 28980.9 | − | 22656.8i | 0.176284 | − | 0.137816i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18834.3 | + | 4683.52i | 0.110001 | + | 0.0273538i | ||||
\(125\) | 186669.i | 1.06856i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 247316.i | 1.36064i | 0.732916 | + | 0.680319i | \(0.238159\pi\) | ||||
−0.732916 | + | 0.680319i | \(0.761841\pi\) | |||||||
\(128\) | −12529.3 | + | 184940.i | −0.0675929 | + | 0.997713i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 124655. | + | 159449.i | 0.646920 | + | 0.827492i | ||||
\(131\) | 356981. | 1.81747 | 0.908733 | − | 0.417377i | \(-0.137051\pi\) | ||||
0.908733 | + | 0.417377i | \(0.137051\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 165122. | 0.809425 | ||||||||
\(134\) | −8205.08 | − | 10495.3i | −0.0394749 | − | 0.0504933i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 187399. | − | 83644.3i | 0.868801 | − | 0.387783i | ||||
\(137\) | − | 256006.i | − | 1.16533i | −0.812713 | − | 0.582664i | \(-0.802010\pi\) | ||
0.812713 | − | 0.582664i | \(-0.197990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 69026.5i | 0.303025i | 0.988455 | + | 0.151513i | \(0.0484144\pi\) | ||||
−0.988455 | + | 0.151513i | \(0.951586\pi\) | |||||||
\(140\) | −46422.7 | + | 186684.i | −0.200175 | + | 0.804984i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 120067. | − | 93866.7i | 0.499693 | − | 0.390653i | ||||
\(143\) | 537464. | 2.19791 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 75143.7 | 0.296806 | ||||||||
\(146\) | −233123. | + | 182252.i | −0.905115 | + | 0.707605i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 105502. | − | 424266.i | 0.395920 | − | 1.59215i | ||||
\(149\) | − | 52137.4i | − | 0.192390i | −0.995362 | − | 0.0961952i | \(-0.969333\pi\) | ||
0.995362 | − | 0.0961952i | \(-0.0306673\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 328419.i | − | 1.17216i | −0.810254 | − | 0.586078i | \(-0.800671\pi\) | ||
0.810254 | − | 0.586078i | \(-0.199329\pi\) | |||||||
\(152\) | −183798. | + | 82037.1i | −0.645257 | + | 0.288006i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 314633. | + | 402455.i | 1.06906 | + | 1.36746i | ||||
\(155\) | −24551.3 | −0.0820816 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −312765. | −1.01267 | −0.506336 | − | 0.862336i | \(-0.669001\pi\) | ||||
−0.506336 | + | 0.862336i | \(0.669001\pi\) | |||||||
\(158\) | −124496. | − | 159245.i | −0.396745 | − | 0.507486i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −41076.2 | − | 230863.i | −0.126850 | − | 0.712942i | ||||
\(161\) | − | 200057.i | − | 0.608259i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 517503.i | − | 1.52561i | −0.646628 | − | 0.762806i | \(-0.723821\pi\) | ||
0.646628 | − | 0.762806i | \(-0.276179\pi\) | |||||||
\(164\) | 660230. | + | 164179.i | 1.91684 | + | 0.476661i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −280438. | + | 219242.i | −0.789890 | + | 0.617524i | ||||
\(167\) | 315354. | 0.875000 | 0.437500 | − | 0.899219i | \(-0.355864\pi\) | ||||
0.437500 | + | 0.899219i | \(0.355864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 409879. | 1.10392 | ||||||||
\(170\) | −204523. | + | 159893.i | −0.542774 | + | 0.424332i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −387497. | − | 96359.0i | −0.998729 | − | 0.248354i | ||||
\(173\) | − | 624427.i | − | 1.58623i | −0.609072 | − | 0.793115i | \(-0.708458\pi\) | ||
0.609072 | − | 0.793115i | \(-0.291542\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 220725.i | 0.544825i | ||||||||
\(176\) | −550170. | − | 291656.i | −1.33880 | − | 0.709725i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 190092. | + | 243152.i | 0.449691 | + | 0.575211i | ||||
\(179\) | 69186.2 | 0.161394 | 0.0806969 | − | 0.996739i | \(-0.474285\pi\) | ||||
0.0806969 | + | 0.996739i | \(0.474285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −193421. | −0.438840 | −0.219420 | − | 0.975630i | \(-0.570417\pi\) | ||||
−0.219420 | + | 0.975630i | \(0.570417\pi\) | |||||||
\(182\) | 457301. | + | 584944.i | 1.02335 | + | 1.30899i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 99393.4 | + | 222684.i | 0.216428 | + | 0.484891i | ||||
\(185\) | 553049.i | 1.18805i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 689396.i | 1.44167i | ||||||||
\(188\) | −125841. | + | 506058.i | −0.259674 | + | 1.04425i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 200593. | − | 156820.i | 0.403117 | − | 0.315151i | ||||
\(191\) | −790470. | −1.56784 | −0.783920 | − | 0.620861i | \(-0.786783\pi\) | ||||
−0.783920 | + | 0.620861i | \(0.786783\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −62439.3 | −0.120660 | −0.0603302 | − | 0.998178i | \(-0.519215\pi\) | ||||
−0.0603302 | + | 0.998178i | \(0.519215\pi\) | |||||||
\(194\) | −635970. | + | 497192.i | −1.21320 | + | 0.948461i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −40515.2 | + | 162928.i | −0.0753318 | + | 0.302939i | ||||
\(197\) | − | 965729.i | − | 1.77292i | −0.462803 | − | 0.886461i | \(-0.653156\pi\) | ||
0.462803 | − | 0.886461i | \(-0.346844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 63953.7i | 0.114481i | 0.998360 | + | 0.0572405i | \(0.0182302\pi\) | ||||
−0.998360 | + | 0.0572405i | \(0.981770\pi\) | |||||||
\(200\) | −109662. | − | 245690.i | −0.193857 | − | 0.434323i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −284062. | − | 363351.i | −0.489818 | − | 0.626539i | ||||
\(203\) | 275667. | 0.469510 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −860639. | −1.43033 | ||||||||
\(206\) | −536682. | − | 686483.i | −0.881148 | − | 1.12710i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −799639. | − | 423905.i | −1.28155 | − | 0.679377i | ||||
\(209\) | − | 676149.i | − | 1.07072i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 351620.i | 0.543710i | 0.962338 | + | 0.271855i | \(0.0876371\pi\) | ||||
−0.962338 | + | 0.271855i | \(0.912363\pi\) | |||||||
\(212\) | 41730.4 | + | 10377.1i | 0.0637694 | + | 0.0158575i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −731369. | + | 571773.i | −1.09170 | + | 0.853472i | ||||
\(215\) | 505120. | 0.745244 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −90067.4 | −0.129843 | ||||||||
\(218\) | 609578. | − | 476559.i | 0.868737 | − | 0.679165i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 764441. | + | 190094.i | 1.06485 | + | 0.264795i | ||||
\(221\) | 1.00200e6i | 1.38002i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 146682.i | − | 0.197521i | −0.995111 | − | 0.0987605i | \(-0.968512\pi\) | ||
0.995111 | − | 0.0987605i | \(-0.0314878\pi\) | |||||||
\(224\) | −150689. | − | 846928.i | −0.200661 | − | 1.12779i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −601256. | − | 769082.i | −0.783048 | − | 1.00162i | ||||
\(227\) | −647121. | −0.833529 | −0.416764 | − | 0.909015i | \(-0.636836\pi\) | ||||
−0.416764 | + | 0.909015i | \(0.636836\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 290803. | 0.366446 | 0.183223 | − | 0.983071i | \(-0.441347\pi\) | ||||
0.183223 | + | 0.983071i | \(0.441347\pi\) | |||||||
\(230\) | −189998. | − | 243032.i | −0.236826 | − | 0.302931i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −306847. | + | 136959.i | −0.374284 | + | 0.167059i | ||||
\(233\) | 1.59729e6i | 1.92750i | 0.266808 | + | 0.963750i | \(0.414031\pi\) | ||||
−0.266808 | + | 0.963750i | \(0.585969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 659669.i | − | 0.779213i | ||||||
\(236\) | −241327. | + | 970472.i | −0.282050 | + | 1.13423i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −750298. | + | 586571.i | −0.858601 | + | 0.671241i | ||||
\(239\) | −129472. | −0.146616 | −0.0733082 | − | 0.997309i | \(-0.523356\pi\) | ||||
−0.0733082 | + | 0.997309i | \(0.523356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −609709. | −0.676208 | −0.338104 | − | 0.941109i | \(-0.609786\pi\) | ||||
−0.338104 | + | 0.941109i | \(0.609786\pi\) | |||||||
\(242\) | 930252. | − | 727256.i | 1.02109 | − | 0.798269i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 50217.4 | − | 201944.i | 0.0539982 | − | 0.217148i | ||||
\(245\) | − | 212383.i | − | 0.226050i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 982743.i | − | 1.02494i | ||||||
\(248\) | 100254. | − | 44747.8i | 0.103508 | − | 0.0462001i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 650371. | + | 831906.i | 0.658129 | + | 0.841830i | ||||
\(251\) | 529459. | 0.530454 | 0.265227 | − | 0.964186i | \(-0.414553\pi\) | ||||
0.265227 | + | 0.964186i | \(0.414553\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −819200. | −0.804616 | ||||||||
\(254\) | 861670. | + | 1.10218e6i | 0.838025 | + | 1.07194i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 588509. | + | 867853.i | 0.561246 | + | 0.827649i | ||||
\(257\) | − | 82551.1i | − | 0.0779633i | −0.999240 | − | 0.0389817i | \(-0.987589\pi\) | ||
0.999240 | − | 0.0389817i | \(-0.0124114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.02888e6i | 1.87935i | ||||||||
\(260\) | 1.11107e6 | + | 276290.i | 1.01931 | + | 0.253473i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.59091e6 | − | 1.24375e6i | 1.43184 | − | 1.11939i | ||||
\(263\) | −866335. | −0.772318 | −0.386159 | − | 0.922432i | \(-0.626198\pi\) | ||||
−0.386159 | + | 0.922432i | \(0.626198\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −54397.4 | −0.0475842 | ||||||||
\(266\) | 735881. | − | 575301.i | 0.637681 | − | 0.498529i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −73133.3 | − | 18186.0i | −0.0621982 | − | 0.0154668i | ||||
\(269\) | 1.20342e6i | 1.01400i | 0.861946 | + | 0.507000i | \(0.169245\pi\) | ||||
−0.861946 | + | 0.507000i | \(0.830755\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.46736e6i | − | 1.21371i | −0.794814 | − | 0.606853i | \(-0.792432\pi\) | ||
0.794814 | − | 0.606853i | \(-0.207568\pi\) | |||||||
\(272\) | 543736. | − | 1.02568e6i | 0.445621 | − | 0.840603i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −891946. | − | 1.14091e6i | −0.717732 | − | 0.918068i | ||||
\(275\) | 903835. | 0.720705 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.23950e6 | 1.75368 | 0.876841 | − | 0.480781i | \(-0.159647\pi\) | ||||
0.876841 | + | 0.480781i | \(0.159647\pi\) | |||||||
\(278\) | 240494. | + | 307622.i | 0.186635 | + | 0.238729i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 443537. | + | 993714.i | 0.338092 | + | 0.757471i | ||||
\(281\) | 153902.i | 0.116273i | 0.998309 | + | 0.0581364i | \(0.0185158\pi\) | ||||
−0.998309 | + | 0.0581364i | \(0.981484\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.61247e6i | 1.19681i | 0.801194 | + | 0.598405i | \(0.204199\pi\) | ||||
−0.801194 | + | 0.598405i | \(0.795801\pi\) | |||||||
\(284\) | 208050. | − | 836649.i | 0.153063 | − | 0.615528i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.39525e6 | − | 1.87257e6i | 1.73156 | − | 1.35370i | ||||
\(287\) | −3.15728e6 | −2.26261 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 134615. | 0.0948090 | ||||||||
\(290\) | 334884. | − | 261807.i | 0.233830 | − | 0.182805i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −403951. | + | 1.62445e6i | −0.277250 | + | 1.11493i | ||||
\(293\) | 1.89615e6i | 1.29034i | 0.764041 | + | 0.645168i | \(0.223213\pi\) | ||||
−0.764041 | + | 0.645168i | \(0.776787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.26505e6i | − | 0.846357i | ||||||
\(296\) | −1.00800e6 | − | 2.25835e6i | −0.668700 | − | 1.49818i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −181651. | − | 232355.i | −0.118494 | − | 0.151569i | ||||
\(299\) | −1.19066e6 | −0.770210 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.85305e6 | 1.17888 | ||||||||
\(302\) | −1.14424e6 | − | 1.46363e6i | −0.721938 | − | 0.923449i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −533288. | + | 1.00597e6i | −0.330962 | + | 0.624314i | ||||
\(305\) | 263243.i | 0.162034i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 92336.2i | − | 0.0559147i | −0.999609 | − | 0.0279573i | \(-0.991100\pi\) | ||
0.999609 | − | 0.0279573i | \(-0.00890026\pi\) | |||||||
\(308\) | 2.80438e6 | + | 697364.i | 1.68446 | + | 0.418874i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −109415. | + | 85539.0i | −0.0646655 | + | 0.0505545i | ||||
\(311\) | 30371.7 | 0.0178060 | 0.00890302 | − | 0.999960i | \(-0.497166\pi\) | ||||
0.00890302 | + | 0.999960i | \(0.497166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.36319e6 | 0.786494 | 0.393247 | − | 0.919433i | \(-0.371352\pi\) | ||||
0.393247 | + | 0.919433i | \(0.371352\pi\) | |||||||
\(314\) | −1.39386e6 | + | 1.08970e6i | −0.797804 | + | 0.623711i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.10965e6 | − | 275937.i | −0.625127 | − | 0.155450i | ||||
\(317\) | 1.16441e6i | 0.650818i | 0.945573 | + | 0.325409i | \(0.105502\pi\) | ||||
−0.945573 | + | 0.325409i | \(0.894498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.12881e6i | − | 0.621077i | ||||||
\(320\) | −987406. | − | 885746.i | −0.539040 | − | 0.483542i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −697015. | − | 891569.i | −0.374630 | − | 0.479199i | ||||
\(323\) | 1.26055e6 | 0.672284 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.31367e6 | 0.689887 | ||||||||
\(326\) | −1.80303e6 | − | 2.30629e6i | −0.939632 | − | 1.20191i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.51439e6 | − | 1.56862e6i | 1.80370 | − | 0.805070i | ||||
\(329\) | − | 2.42002e6i | − | 1.23262i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 451430.i | − | 0.226475i | −0.993568 | − | 0.113237i | \(-0.963878\pi\) | ||
0.993568 | − | 0.113237i | \(-0.0361221\pi\) | |||||||
\(332\) | −485936. | + | 1.95414e6i | −0.241955 | + | 0.972995i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.40540e6 | − | 1.09872e6i | 0.689342 | − | 0.538917i | ||||
\(335\) | 95332.4 | 0.0464118 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.16248e6 | −1.03723 | −0.518617 | − | 0.855007i | \(-0.673553\pi\) | ||||
−0.518617 | + | 0.855007i | \(0.673553\pi\) | |||||||
\(338\) | 1.82666e6 | − | 1.42805e6i | 0.869693 | − | 0.679913i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −354392. | + | 1.42515e6i | −0.166259 | + | 0.668595i | ||||
\(341\) | 368811.i | 0.171759i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.71678e6i | 0.787914i | ||||||||
\(344\) | −2.06264e6 | + | 920643.i | −0.939781 | + | 0.419465i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.17556e6 | − | 2.78281e6i | −0.976968 | − | 1.24966i | ||||
\(347\) | −3.10525e6 | −1.38444 | −0.692219 | − | 0.721688i | \(-0.743367\pi\) | ||||
−0.692219 | + | 0.721688i | \(0.743367\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.35425e6 | −1.03464 | −0.517320 | − | 0.855792i | \(-0.673070\pi\) | ||||
−0.517320 | + | 0.855792i | \(0.673070\pi\) | |||||||
\(350\) | 769027. | + | 983681.i | 0.335561 | + | 0.429224i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.46803e6 | + | 617049.i | −1.49186 | + | 0.265438i | ||||
\(353\) | 1.94097e6i | 0.829052i | 0.910037 | + | 0.414526i | \(0.136053\pi\) | ||||
−0.910037 | + | 0.414526i | \(0.863947\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.09061e6i | 0.459302i | ||||||||
\(356\) | 1.69432e6 | + | 421327.i | 0.708552 | + | 0.176195i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 308334. | − | 241051.i | 0.127149 | − | 0.0994034i | ||||
\(359\) | 1.33715e6 | 0.547574 | 0.273787 | − | 0.961790i | \(-0.411724\pi\) | ||||
0.273787 | + | 0.961790i | \(0.411724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.23977e6 | 0.500696 | ||||||||
\(362\) | −861995. | + | 673895.i | −0.345727 | + | 0.270284i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.07600e6 | + | 1.01358e6i | 1.61243 | + | 0.400962i | ||||
\(365\) | − | 2.11754e6i | − | 0.831953i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.64386e6i | − | 0.637087i | −0.947908 | − | 0.318544i | \(-0.896806\pi\) | ||
0.947908 | − | 0.318544i | \(-0.103194\pi\) | |||||||
\(368\) | 1.21881e6 | + | 646114.i | 0.469154 | + | 0.248708i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.92687e6 | + | 2.46471e6i | 0.731726 | + | 0.935969i | ||||
\(371\) | −199559. | −0.0752724 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −393084. | −0.146290 | −0.0731448 | − | 0.997321i | \(-0.523304\pi\) | ||||
−0.0731448 | + | 0.997321i | \(0.523304\pi\) | |||||||
\(374\) | 2.40192e6 | + | 3.07235e6i | 0.887930 | + | 1.13577i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.20233e6 | + | 2.69373e6i | 0.438585 | + | 0.982618i | ||||
\(377\) | − | 1.64066e6i | − | 0.594519i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.30537e6i | 0.824410i | 0.911091 | + | 0.412205i | \(0.135241\pi\) | ||||
−0.911091 | + | 0.412205i | \(0.864759\pi\) | |||||||
\(380\) | 347582. | − | 1.39777e6i | 0.123481 | − | 0.496564i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.52279e6 | + | 2.75407e6i | −1.23518 | + | 0.965642i | ||||
\(383\) | 2.70064e6 | 0.940741 | 0.470370 | − | 0.882469i | \(-0.344120\pi\) | ||||
0.470370 | + | 0.882469i | \(0.344120\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.65563e6 | −1.25693 | ||||||||
\(386\) | −278266. | + | 217544.i | −0.0950587 | + | 0.0743154i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.10199e6 | + | 4.43155e6i | −0.371621 | + | 1.49443i | ||||
\(389\) | − | 1.65579e6i | − | 0.554793i | −0.960755 | − | 0.277397i | \(-0.910528\pi\) | ||
0.960755 | − | 0.277397i | \(-0.0894716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.52724e6i | − | 0.505201i | ||||||
\(392\) | 387095. | + | 867260.i | 0.127234 | + | 0.285058i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.36469e6 | − | 4.30385e6i | −1.09195 | − | 1.39674i | ||||
\(395\) | 1.44648e6 | 0.466465 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.69988e6 | −0.541306 | −0.270653 | − | 0.962677i | \(-0.587240\pi\) | ||||
−0.270653 | + | 0.962677i | \(0.587240\pi\) | |||||||
\(398\) | 222820. | + | 285015.i | 0.0705095 | + | 0.0901904i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.34473e6 | − | 712867.i | −0.420227 | − | 0.222771i | ||||
\(401\) | − | 535612.i | − | 0.166337i | −0.996535 | − | 0.0831687i | \(-0.973496\pi\) | ||
0.996535 | − | 0.0831687i | \(-0.0265040\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 536045.i | 0.164414i | ||||||||
\(404\) | −2.53189e6 | − | 629606.i | −0.771778 | − | 0.191918i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.22853e6 | − | 960449.i | 0.369890 | − | 0.289174i | ||||
\(407\) | 8.30794e6 | 2.48603 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.71273e6 | −0.506268 | −0.253134 | − | 0.967431i | \(-0.581461\pi\) | ||||
−0.253134 | + | 0.967431i | \(0.581461\pi\) | |||||||
\(410\) | −3.83551e6 | + | 2.99854e6i | −1.12684 | + | 0.880949i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.78353e6 | − | 1.18952e6i | −1.38837 | − | 0.345246i | ||||
\(413\) | − | 4.64089e6i | − | 1.33883i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.54731e6i | − | 0.726041i | ||||||
\(416\) | −5.04058e6 | + | 896844.i | −1.42806 | + | 0.254088i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.35576e6 | − | 3.01332e6i | −0.659464 | − | 0.843537i | ||||
\(419\) | 1.98989e6 | 0.553725 | 0.276863 | − | 0.960909i | \(-0.410705\pi\) | ||||
0.276863 | + | 0.960909i | \(0.410705\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 849032. | 0.233463 | 0.116732 | − | 0.993163i | \(-0.462758\pi\) | ||||
0.116732 | + | 0.993163i | \(0.462758\pi\) | |||||||
\(422\) | 1.22507e6 | + | 1.56702e6i | 0.334874 | + | 0.428346i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 222130. | − | 99145.9i | 0.0600056 | − | 0.0267831i | ||||
\(425\) | 1.68502e6i | 0.452515i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 965714.i | 0.256318i | ||||||||
\(428\) | −1.26730e6 | + | 5.09631e6i | −0.334403 | + | 1.34476i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.25111e6 | − | 1.75988e6i | 0.587118 | − | 0.459000i | ||||
\(431\) | −3.02456e6 | −0.784277 | −0.392139 | − | 0.919906i | \(-0.628265\pi\) | ||||
−0.392139 | + | 0.919906i | \(0.628265\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.32400e6 | −0.339365 | −0.169683 | − | 0.985499i | \(-0.554274\pi\) | ||||
−0.169683 | + | 0.985499i | \(0.554274\pi\) | |||||||
\(434\) | −401393. | + | 313803.i | −0.102293 | + | 0.0799709i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.05626e6 | − | 4.24765e6i | 0.266107 | − | 1.07012i | ||||
\(437\) | 1.49789e6i | 0.375212i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.74480e6i | − | 0.432100i | −0.976382 | − | 0.216050i | \(-0.930683\pi\) | ||
0.976382 | − | 0.216050i | \(-0.0693175\pi\) | |||||||
\(440\) | 4.06910e6 | − | 1.81621e6i | 1.00200 | − | 0.447234i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.49104e6 | + | 4.46548e6i | 0.849961 | + | 1.08721i | ||||
\(443\) | 4.60857e6 | 1.11572 | 0.557862 | − | 0.829934i | \(-0.311622\pi\) | ||||
0.557862 | + | 0.829934i | \(0.311622\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.20863e6 | −0.528715 | ||||||||
\(446\) | −511051. | − | 653698.i | −0.121654 | − | 0.155611i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.62233e6 | − | 3.24939e6i | −0.852694 | − | 0.764904i | ||||
\(449\) | 363410.i | 0.0850709i | 0.999095 | + | 0.0425355i | \(0.0135435\pi\) | ||||
−0.999095 | + | 0.0425355i | \(0.986456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.29286e7i | 2.99302i | ||||||||
\(452\) | −5.35910e6 | − | 1.33265e6i | −1.23380 | − | 0.306809i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.88395e6 | + | 2.25463e6i | −0.656671 | + | 0.513375i | ||||
\(455\) | −5.31324e6 | −1.20318 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.52447e6 | 0.565431 | 0.282716 | − | 0.959204i | \(-0.408765\pi\) | ||||
0.282716 | + | 0.959204i | \(0.408765\pi\) | |||||||
\(458\) | 1.29599e6 | − | 1.01318e6i | 0.288693 | − | 0.225696i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.69349e6 | − | 421119.i | −0.373153 | − | 0.0927920i | ||||
\(461\) | − | 6.13081e6i | − | 1.34359i | −0.740739 | − | 0.671793i | \(-0.765524\pi\) | ||
0.740739 | − | 0.671793i | \(-0.234476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.72811e6i | − | 1.02503i | −0.858679 | − | 0.512513i | \(-0.828715\pi\) | ||
0.858679 | − | 0.512513i | \(-0.171285\pi\) | |||||||
\(464\) | −890311. | + | 1.67945e6i | −0.191976 | + | 0.362136i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.56510e6 | + | 7.11846e6i | 1.18716 | + | 1.51852i | ||||
\(467\) | −3.47705e6 | −0.737767 | −0.368884 | − | 0.929476i | \(-0.620260\pi\) | ||||
−0.368884 | + | 0.929476i | \(0.620260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 349730. | 0.0734177 | ||||||||
\(470\) | −2.29834e6 | − | 2.93987e6i | −0.479922 | − | 0.613880i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.30572e6 | + | 5.16579e6i | 0.476377 | + | 1.06729i | ||||
\(473\) | − | 7.58794e6i | − | 1.55945i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.65265e6i | − | 0.336082i | ||||||
\(476\) | −1.30010e6 | + | 5.22821e6i | −0.263002 | + | 1.05763i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −577004. | + | 451093.i | −0.115507 | + | 0.0903018i | ||||
\(479\) | 2.90668e6 | 0.578841 | 0.289420 | − | 0.957202i | \(-0.406537\pi\) | ||||
0.289420 | + | 0.957202i | \(0.406537\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.20751e7 | 2.37973 | ||||||||
\(482\) | −2.71722e6 | + | 2.12428e6i | −0.532730 | + | 0.416480i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.61192e6 | − | 6.48216e6i | 0.312773 | − | 1.25778i | ||||
\(485\) | − | 5.77672e6i | − | 1.11513i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.40021e6i | − | 1.03178i | −0.856654 | − | 0.515892i | \(-0.827461\pi\) | ||
0.856654 | − | 0.515892i | \(-0.172539\pi\) | |||||||
\(488\) | −479792. | − | 1.07494e6i | −0.0912019 | − | 0.204331i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −739963. | − | 946504.i | −0.139226 | − | 0.178087i | ||||
\(491\) | −9.72452e6 | −1.82039 | −0.910195 | − | 0.414181i | \(-0.864068\pi\) | ||||
−0.910195 | + | 0.414181i | \(0.864068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.10445e6 | 0.389961 | ||||||||
\(494\) | −3.42396e6 | − | 4.37967e6i | −0.631265 | − | 0.807466i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 290887. | − | 548717.i | 0.0530908 | − | 0.100149i | ||||
\(497\) | 4.00094e6i | 0.726559i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.47884e6i | 0.265870i | 0.991125 | + | 0.132935i | \(0.0424402\pi\) | ||||
−0.991125 | + | 0.132935i | \(0.957560\pi\) | |||||||
\(500\) | 5.79687e6 | + | 1.44151e6i | 1.03698 | + | 0.257865i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.35958e6 | − | 1.84468e6i | 0.417902 | − | 0.326710i | ||||
\(503\) | 6.19630e6 | 1.09198 | 0.545988 | − | 0.837793i | \(-0.316155\pi\) | ||||
0.545988 | + | 0.837793i | \(0.316155\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.30043e6 | 0.575894 | ||||||||
\(506\) | −3.65083e6 | + | 2.85417e6i | −0.633893 | + | 0.495568i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.68021e6 | + | 1.90984e6i | 1.32042 | + | 0.328350i | ||||
\(509\) | 400657.i | 0.0685454i | 0.999413 | + | 0.0342727i | \(0.0109115\pi\) | ||||
−0.999413 | + | 0.0342727i | \(0.989089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.76825e6i | − | 1.31605i | ||||||
\(512\) | 5.64642e6 | + | 1.81724e6i | 0.951914 | + | 0.306364i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −287615. | − | 367896.i | −0.0480180 | − | 0.0614210i | ||||
\(515\) | 6.23554e6 | 1.03599 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.90958e6 | −1.63053 | ||||||||
\(518\) | 7.06880e6 | + | 9.04187e6i | 1.15750 | + | 1.48059i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.91419e6 | − | 2.63976e6i | 0.959151 | − | 0.428110i | ||||
\(521\) | − | 210060.i | − | 0.0339039i | −0.999856 | − | 0.0169520i | \(-0.994604\pi\) | ||
0.999856 | − | 0.0169520i | \(-0.00539624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.32849e6i | 0.851824i | 0.904765 | + | 0.425912i | \(0.140047\pi\) | ||||
−0.904765 | + | 0.425912i | \(0.859953\pi\) | |||||||
\(524\) | 2.75670e6 | − | 1.10858e7i | 0.438592 | − | 1.76375i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.86089e6 | + | 3.01839e6i | −0.608448 | + | 0.475675i | ||||
\(527\) | −687576. | −0.107844 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.62155e6 | −0.718039 | ||||||||
\(530\) | −242426. | + | 189525.i | −0.0374878 | + | 0.0293074i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.27512e6 | − | 5.12775e6i | 0.195331 | − | 0.785503i | ||||
\(533\) | 1.87909e7i | 2.86503i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.64326e6i | − | 1.00345i | ||||||
\(536\) | −389286. | + | 173755.i | −0.0585271 | + | 0.0261232i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.19283e6 | + | 5.36315e6i | 0.624528 | + | 0.798849i | ||||
\(539\) | −3.19044e6 | −0.473019 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.80721e6 | 0.706155 | 0.353077 | − | 0.935594i | \(-0.385135\pi\) | ||||
0.353077 | + | 0.935594i | \(0.385135\pi\) | |||||||
\(542\) | −5.11241e6 | − | 6.53941e6i | −0.747529 | − | 0.956182i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.15037e6 | − | 6.46546e6i | −0.166663 | − | 0.936704i | ||||
\(545\) | 5.53700e6i | 0.798515i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.22838e7i | 1.75535i | 0.479254 | + | 0.877676i | \(0.340907\pi\) | ||||
−0.479254 | + | 0.877676i | \(0.659093\pi\) | |||||||
\(548\) | −7.95006e6 | − | 1.97694e6i | −1.13089 | − | 0.281218i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.02802e6 | − | 3.14904e6i | 0.567786 | − | 0.443886i | ||||
\(551\) | −2.06401e6 | −0.289623 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.30645e6 | 0.737889 | ||||||||
\(554\) | 9.98050e6 | − | 7.80260e6i | 1.38159 | − | 1.08010i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.14357e6 | + | 533041.i | 0.294070 | + | 0.0731263i | ||||
\(557\) | 6.64124e6i | 0.907008i | 0.891254 | + | 0.453504i | \(0.149826\pi\) | ||||
−0.891254 | + | 0.453504i | \(0.850174\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.10286e7i | − | 1.49277i | ||||||
\(560\) | 5.43884e6 | + | 2.88324e6i | 0.732886 | + | 0.388518i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 536207. | + | 685876.i | 0.0716130 | + | 0.0916020i | ||||
\(563\) | 9.15547e6 | 1.21733 | 0.608667 | − | 0.793426i | \(-0.291705\pi\) | ||||
0.608667 | + | 0.793426i | \(0.291705\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.98582e6 | 0.920653 | ||||||||
\(566\) | 5.61798e6 | + | 7.18610e6i | 0.737122 | + | 0.942871i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.98777e6 | − | 4.45346e6i | −0.258521 | − | 0.579198i | ||||
\(569\) | 538876.i | 0.0697763i | 0.999391 | + | 0.0348882i | \(0.0111075\pi\) | ||||
−0.999391 | + | 0.0348882i | \(0.988893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.75530e6i | 0.610362i | 0.952294 | + | 0.305181i | \(0.0987170\pi\) | ||||
−0.952294 | + | 0.305181i | \(0.901283\pi\) | |||||||
\(572\) | 4.15044e6 | − | 1.66905e7i | 0.530400 | − | 2.13295i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.40707e7 | + | 1.10003e7i | −1.78253 | + | 1.39355i | ||||
\(575\) | −2.00229e6 | −0.252556 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −573068. | −0.0716583 | −0.0358291 | − | 0.999358i | \(-0.511407\pi\) | ||||
−0.0358291 | + | 0.999358i | \(0.511407\pi\) | |||||||
\(578\) | 599924. | − | 469011.i | 0.0746924 | − | 0.0583934i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 580280. | − | 2.33353e6i | 0.0716254 | − | 0.288034i | ||||
\(581\) | − | 9.34489e6i | − | 1.14851i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 817160.i | 0.0995717i | ||||||||
\(584\) | 3.85947e6 | + | 8.64688e6i | 0.468269 | + | 1.04912i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.60634e6 | + | 8.45033e6i | 0.794725 | + | 1.01655i | ||||
\(587\) | −3.58562e6 | −0.429505 | −0.214753 | − | 0.976668i | \(-0.568895\pi\) | ||||
−0.214753 | + | 0.976668i | \(0.568895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 674364. | 0.0800952 | ||||||||
\(590\) | −4.40756e6 | − | 5.63781e6i | −0.521276 | − | 0.666777i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.23605e7 | − | 6.55258e6i | −1.44955 | − | 0.768437i | ||||
\(593\) | − | 3.03733e6i | − | 0.354695i | −0.984148 | − | 0.177348i | \(-0.943248\pi\) | ||
0.984148 | − | 0.177348i | \(-0.0567517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6.81520e6i | − | 0.789198i | ||||||
\(596\) | −1.61909e6 | − | 402618.i | −0.186704 | − | 0.0464278i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.30627e6 | + | 4.14836e6i | −0.606787 | + | 0.474377i | ||||
\(599\) | −8.69696e6 | −0.990377 | −0.495188 | − | 0.868786i | \(-0.664901\pi\) | ||||
−0.495188 | + | 0.868786i | \(0.664901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.30820e6 | −0.260668 | −0.130334 | − | 0.991470i | \(-0.541605\pi\) | ||||
−0.130334 | + | 0.991470i | \(0.541605\pi\) | |||||||
\(602\) | 8.25827e6 | − | 6.45619e6i | 0.928748 | − | 0.726081i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.01988e7 | − | 2.53614e6i | −1.13751 | − | 0.282866i | ||||
\(605\) | 8.44978e6i | 0.938549i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.78272e7i | 1.96387i | 0.189229 | + | 0.981933i | \(0.439401\pi\) | ||||
−0.189229 | + | 0.981933i | \(0.560599\pi\) | |||||||
\(608\) | 1.12826e6 | + | 6.34123e6i | 0.123780 | + | 0.695688i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 917160. | + | 1.17316e6i | 0.0997978 | + | 0.127654i | ||||
\(611\) | −1.44030e7 | −1.56081 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.66354e6 | −0.931202 | −0.465601 | − | 0.884995i | \(-0.654162\pi\) | ||||
−0.465601 | + | 0.884995i | \(0.654162\pi\) | |||||||
\(614\) | −321707. | − | 411504.i | −0.0344382 | − | 0.0440507i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.49276e7 | − | 6.66284e6i | 1.58503 | − | 0.707469i | ||||
\(617\) | 4.06215e6i | 0.429579i | 0.976660 | + | 0.214789i | \(0.0689065\pi\) | ||||
−0.976660 | + | 0.214789i | \(0.931093\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.23718e6i | 0.444478i | 0.974992 | + | 0.222239i | \(0.0713365\pi\) | ||||
−0.974992 | + | 0.222239i | \(0.928664\pi\) | |||||||
\(620\) | −189592. | + | 762423.i | −0.0198080 | + | 0.0796557i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 135354. | − | 105818.i | 0.0140280 | − | 0.0109668i | ||||
\(623\) | −8.10242e6 | −0.836362 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.91171e6 | −0.298159 | ||||||||
\(626\) | 6.07517e6 | − | 4.74947e6i | 0.619616 | − | 0.484406i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.41525e6 | + | 9.71269e6i | −0.244379 | + | 0.982744i | ||||
\(629\) | 1.54885e7i | 1.56093i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.26919e7i | − | 1.26898i | −0.772932 | − | 0.634489i | \(-0.781211\pi\) | ||
0.772932 | − | 0.634489i | \(-0.218789\pi\) | |||||||
\(632\) | −5.90663e6 | + | 2.63638e6i | −0.588230 | + | 0.262552i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.05692e6 | + | 5.18931e6i | 0.400842 | + | 0.512727i | ||||
\(635\) | −1.00115e7 | −0.985291 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.63711e6 | −0.452792 | ||||||||
\(638\) | −3.93289e6 | − | 5.03065e6i | −0.382525 | − | 0.489297i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.48647e6 | − | 507192.i | −0.722483 | − | 0.0489466i | ||||
\(641\) | − | 5.25962e6i | − | 0.505603i | −0.967518 | − | 0.252801i | \(-0.918648\pi\) | ||
0.967518 | − | 0.252801i | \(-0.0813519\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.43696e6i | 0.232446i | 0.993223 | + | 0.116223i | \(0.0370787\pi\) | ||||
−0.993223 | + | 0.116223i | \(0.962921\pi\) | |||||||
\(644\) | −6.21261e6 | − | 1.54489e6i | −0.590282 | − | 0.146785i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.61773e6 | − | 4.39186e6i | 0.529639 | − | 0.414063i | ||||
\(647\) | −3.95714e6 | −0.371639 | −0.185819 | − | 0.982584i | \(-0.559494\pi\) | ||||
−0.185819 | + | 0.982584i | \(0.559494\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.90037e7 | −1.77103 | ||||||||
\(650\) | 5.85448e6 | − | 4.57694e6i | 0.543507 | − | 0.424905i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.60707e7 | − | 3.99629e6i | −1.48052 | − | 0.368161i | ||||
\(653\) | − | 1.87789e6i | − | 0.172340i | −0.996280 | − | 0.0861702i | \(-0.972537\pi\) | ||
0.996280 | − | 0.0861702i | \(-0.0274629\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.44508e7i | 1.31610i | ||||||||
\(656\) | 1.01969e7 | − | 1.92351e7i | 0.925146 | − | 1.74516i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.43155e6 | − | 1.07850e7i | −0.759177 | − | 0.971082i | ||||
\(659\) | 6.18082e6 | 0.554412 | 0.277206 | − | 0.960810i | \(-0.410592\pi\) | ||||
0.277206 | + | 0.960810i | \(0.410592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −468167. | −0.0416771 | −0.0208385 | − | 0.999783i | \(-0.506634\pi\) | ||||
−0.0208385 | + | 0.999783i | \(0.506634\pi\) | |||||||
\(662\) | −1.57282e6 | − | 2.01183e6i | −0.139487 | − | 0.178421i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.64278e6 | + | 1.04018e7i | 0.408656 | + | 0.915566i | ||||
\(665\) | 6.68425e6i | 0.586136i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.50069e6i | 0.217643i | ||||||||
\(668\) | 2.43525e6 | − | 9.79310e6i | 0.211155 | − | 0.849139i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 424857. | − | 332147.i | 0.0365642 | − | 0.0285853i | ||||
\(671\) | 3.95445e6 | 0.339062 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.27492e6 | −0.619142 | −0.309571 | − | 0.950876i | \(-0.600186\pi\) | ||||
−0.309571 | + | 0.950876i | \(0.600186\pi\) | |||||||
\(674\) | −9.63726e6 | + | 7.53426e6i | −0.817154 | + | 0.638838i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.16519e6 | − | 1.27285e7i | 0.266399 | − | 1.07130i | ||||
\(677\) | − | 5.70914e6i | − | 0.478739i | −0.970929 | − | 0.239370i | \(-0.923059\pi\) | ||
0.970929 | − | 0.239370i | \(-0.0769407\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.11921e7i | − | 1.76400i | ||||||
\(680\) | 3.38597e6 | + | 7.58603e6i | 0.280809 | + | 0.629132i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.28497e6 | + | 1.64364e6i | 0.105787 | + | 0.135315i | ||||
\(683\) | 6.52835e6 | 0.535490 | 0.267745 | − | 0.963490i | \(-0.413721\pi\) | ||||
0.267745 | + | 0.963490i | \(0.413721\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.03633e7 | 0.843859 | ||||||||
\(686\) | 5.98140e6 | + | 7.65096e6i | 0.485280 | + | 0.620734i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.98471e6 | + | 1.12893e7i | −0.482028 | + | 0.909279i | ||||
\(689\) | 1.18769e6i | 0.0953139i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.14706e7i | − | 0.913884i | −0.889496 | − | 0.456942i | \(-0.848945\pi\) | ||
0.889496 | − | 0.456942i | \(-0.151055\pi\) | |||||||
\(692\) | −1.93911e7 | − | 4.82198e6i | −1.53935 | − | 0.382790i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.38388e7 | + | 1.08190e7i | −1.09069 | + | 0.852683i | ||||
\(695\) | −2.79423e6 | −0.219432 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.41028e7 | −1.87925 | ||||||||
\(698\) | −1.04919e7 | + | 8.20242e6i | −0.815110 | + | 0.637240i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.85446e6 | + | 1.70450e6i | 0.528723 | + | 0.131478i | ||||
\(701\) | − | 1.82344e6i | − | 0.140151i | −0.997542 | − | 0.0700756i | \(-0.977676\pi\) | ||
0.997542 | − | 0.0700756i | \(-0.0223240\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.51909e7i | − | 1.15930i | ||||||
\(704\) | −1.33057e7 | + | 1.48329e7i | −1.01183 | + | 1.12796i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.76251e6 | + | 8.65009e6i | 0.510618 | + | 0.653144i | ||||
\(707\) | 1.21078e7 | 0.910993 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.40708e7 | 1.05124 | 0.525621 | − | 0.850719i | \(-0.323833\pi\) | ||||
0.525621 | + | 0.850719i | \(0.323833\pi\) | |||||||
\(710\) | 3.79978e6 | + | 4.86039e6i | 0.282887 | + | 0.361847i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.01884e6 | − | 4.02549e6i | 0.666731 | − | 0.297591i | ||||
\(713\) | − | 817038.i | − | 0.0601892i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.17569e7i | 1.59159i | ||||||||
\(716\) | 534274. | − | 2.14853e6i | 0.0389477 | − | 0.156624i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.95910e6 | − | 4.65874e6i | 0.431390 | − | 0.337254i | ||||
\(719\) | 3.92597e6 | 0.283220 | 0.141610 | − | 0.989923i | \(-0.454772\pi\) | ||||
0.141610 | + | 0.989923i | \(0.454772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.28753e7 | 1.63881 | ||||||||
\(722\) | 5.52515e6 | − | 4.31948e6i | 0.394458 | − | 0.308381i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.49365e6 | + | 6.00654e6i | −0.105901 | + | 0.425871i | ||||
\(725\) | − | 2.75905e6i | − | 0.194946i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.54731e6i | − | 0.599782i | −0.953973 | − | 0.299891i | \(-0.903050\pi\) | ||
0.953973 | − | 0.299891i | \(-0.0969503\pi\) | |||||||
\(728\) | 2.16964e7 | − | 9.68404e6i | 1.51726 | − | 0.677217i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.37768e6 | − | 9.43697e6i | −0.512404 | − | 0.655429i | ||||
\(731\) | 1.41462e7 | 0.979144 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.32847e7 | 0.913256 | 0.456628 | − | 0.889658i | \(-0.349057\pi\) | ||||
0.456628 | + | 0.889658i | \(0.349057\pi\) | |||||||
\(734\) | −5.72734e6 | − | 7.32598e6i | −0.392385 | − | 0.501910i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.68283e6 | − | 1.36696e6i | 0.522789 | − | 0.0930171i | ||||
\(737\) | − | 1.43209e6i | − | 0.0971183i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.75514e7i | 1.85581i | 0.372819 | + | 0.927904i | \(0.378391\pi\) | ||||
−0.372819 | + | 0.927904i | \(0.621609\pi\) | |||||||
\(740\) | 1.71745e7 | + | 4.27079e6i | 1.15294 | + | 0.286701i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −889349. | + | 695280.i | −0.0593011 | + | 0.0463607i | ||||
\(743\) | 357532. | 0.0237598 | 0.0118799 | − | 0.999929i | \(-0.496218\pi\) | ||||
0.0118799 | + | 0.999929i | \(0.496218\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.11055e6 | 0.139317 | ||||||||
\(746\) | −1.75181e6 | + | 1.36954e6i | −0.115250 | + | 0.0901006i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.14087e7 | + | 5.32369e6i | 1.39906 | + | 0.347904i | ||||
\(749\) | − | 2.43710e7i | − | 1.58734i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.39756e6i | 0.155121i | 0.996988 | + | 0.0775603i | \(0.0247130\pi\) | ||||
−0.996988 | + | 0.0775603i | \(0.975287\pi\) | |||||||
\(752\) | 1.47435e7 | + | 7.81582e6i | 0.950726 | + | 0.504000i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.71622e6 | − | 7.31175e6i | −0.366168 | − | 0.468374i | ||||
\(755\) | 1.32946e7 | 0.848804 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.85832e7 | −1.17864 | −0.589320 | − | 0.807900i | \(-0.700604\pi\) | ||||
−0.589320 | + | 0.807900i | \(0.700604\pi\) | |||||||
\(758\) | 8.03213e6 | + | 1.02741e7i | 0.507759 | + | 0.649487i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.32091e6 | − | 7.44027e6i | −0.208556 | − | 0.467256i | ||||
\(761\) | 2.59191e7i | 1.62240i | 0.584769 | + | 0.811200i | \(0.301185\pi\) | ||||
−0.584769 | + | 0.811200i | \(0.698815\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.03127e7i | 1.26315i | ||||||||
\(764\) | −6.10421e6 | + | 2.45475e7i | −0.378352 | + | 1.52150i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.20356e7 | − | 9.40927e6i | 0.741134 | − | 0.579408i | ||||
\(767\) | −2.76207e7 | −1.69530 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.70826e7 | 1.65148 | 0.825741 | − | 0.564050i | \(-0.190757\pi\) | ||||
0.825741 | + | 0.564050i | \(0.190757\pi\) | |||||||
\(770\) | −1.62916e7 | + | 1.27365e7i | −0.990233 | + | 0.774149i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −482173. | + | 1.93901e6i | −0.0291178 | + | 0.117094i | ||||
\(773\) | − | 3.16270e7i | − | 1.90375i | −0.306492 | − | 0.951873i | \(-0.599155\pi\) | ||
0.306492 | − | 0.951873i | \(-0.400845\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 901449.i | 0.0539122i | ||||||||
\(776\) | 1.05288e7 | + | 2.35890e7i | 0.627660 | + | 1.40623i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.76892e6 | − | 7.37917e6i | −0.341700 | − | 0.437077i | ||||
\(779\) | 2.36396e7 | 1.39572 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.63832e7 | 0.961105 | ||||||||
\(782\) | −5.32103e6 | − | 6.80626e6i | −0.311156 | − | 0.398008i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.74673e6 | + | 2.51634e6i | 0.275806 | + | 0.146211i | ||||
\(785\) | − | 1.26609e7i | − | 0.733316i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.34131e7i | − | 1.34748i | −0.738969 | − | 0.673739i | \(-0.764687\pi\) | ||
0.738969 | − | 0.673739i | \(-0.235313\pi\) | |||||||
\(788\) | −2.99900e7 | − | 7.45761e6i | −1.72052 | − | 0.427843i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.44634e6 | − | 5.03965e6i | 0.367490 | − | 0.287298i | ||||
\(791\) | 2.56277e7 | 1.45636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.74755e6 | 0.324564 | ||||||||
\(794\) | −7.57567e6 | + | 5.92255e6i | −0.426452 | + | 0.333394i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.98604e6 | + | 493867.i | 0.111098 | + | 0.0276266i | ||||
\(797\) | 1.66862e7i | 0.930490i | 0.885182 | + | 0.465245i | \(0.154034\pi\) | ||||
−0.885182 | + | 0.465245i | \(0.845966\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.84745e7i | − | 1.02378i | ||||||
\(800\) | −8.47657e6 | + | 1.50819e6i | −0.468269 | + | 0.0833166i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.86612e6 | − | 2.38700e6i | −0.102448 | − | 0.131044i | ||||
\(803\) | −3.18097e7 | −1.74089 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.09841e6 | 0.440464 | ||||||||
\(806\) | 1.86763e6 | + | 2.38893e6i | 0.101264 | + | 0.129529i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.34772e7 | + | 6.01545e6i | −0.726225 | + | 0.324145i | ||||
\(809\) | − | 2.53067e7i | − | 1.35945i | −0.733466 | − | 0.679726i | \(-0.762099\pi\) | ||
0.733466 | − | 0.679726i | \(-0.237901\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.91246e7i | − | 1.55492i | −0.628933 | − | 0.777460i | \(-0.716508\pi\) | ||
0.628933 | − | 0.777460i | \(-0.283492\pi\) | |||||||
\(812\) | 2.12878e6 | − | 8.56065e6i | 0.113303 | − | 0.455634i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.70250e7 | − | 2.89456e7i | 1.95855 | − | 1.53116i | ||||
\(815\) | 2.09488e7 | 1.10475 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.38744e7 | −0.727209 | ||||||||
\(818\) | −7.63291e6 | + | 5.96729e6i | −0.398848 | + | 0.311813i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.64608e6 | + | 2.67265e7i | −0.345168 | + | 1.38806i | ||||
\(821\) | − | 2.36944e7i | − | 1.22684i | −0.789756 | − | 0.613421i | \(-0.789793\pi\) | ||
0.789756 | − | 0.613421i | \(-0.210207\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.40085e7i | − | 1.23556i | −0.786350 | − | 0.617782i | \(-0.788032\pi\) | ||
0.786350 | − | 0.617782i | \(-0.211968\pi\) | |||||||
\(824\) | −2.54626e7 | + | 1.13651e7i | −1.30643 | + | 0.583114i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.61693e7 | − | 2.06825e7i | −0.824594 | − | 1.05476i | ||||
\(827\) | 1.83314e7 | 0.932035 | 0.466018 | − | 0.884775i | \(-0.345688\pi\) | ||||
0.466018 | + | 0.884775i | \(0.345688\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.28295e7 | −0.648372 | −0.324186 | − | 0.945993i | \(-0.605090\pi\) | ||||
−0.324186 | + | 0.945993i | \(0.605090\pi\) | |||||||
\(830\) | −8.87505e6 | − | 1.13523e7i | −0.447173 | − | 0.571990i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.93391e7 | + | 2.15587e7i | −0.968562 | + | 1.07973i | ||||
\(833\) | − | 5.94794e6i | − | 0.296998i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.27657e7i | 0.633621i | ||||||||
\(836\) | −2.09973e7 | − | 5.22140e6i | −1.03908 | − | 0.258387i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.86812e6 | − | 6.93296e6i | 0.436236 | − | 0.341043i | ||||
\(839\) | 1.64336e7 | 0.805985 | 0.402992 | − | 0.915203i | \(-0.367970\pi\) | ||||
0.402992 | + | 0.915203i | \(0.367970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.70653e7 | 0.832003 | ||||||||
\(842\) | 3.78378e6 | − | 2.95810e6i | 0.183927 | − | 0.143791i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.09193e7 | + | 2.71530e6i | 0.527641 | + | 0.131208i | ||||
\(845\) | 1.65921e7i | 0.799394i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.09983e7i | 1.48467i | ||||||||
\(848\) | 644506. | − | 1.21577e6i | 0.0307778 | − | 0.0580580i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.87076e6 | + | 7.50944e6i | 0.278707 | + | 0.356501i | ||||
\(851\) | −1.84048e7 | −0.871178 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.70416e6 | −0.456652 | −0.228326 | − | 0.973585i | \(-0.573325\pi\) | ||||
−0.228326 | + | 0.973585i | \(0.573325\pi\) | |||||||
\(854\) | 3.36463e6 | + | 4.30379e6i | 0.157868 | + | 0.201932i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.21082e7 | + | 2.71275e7i | 0.564799 | + | 1.26539i | ||||
\(857\) | − | 8.17649e6i | − | 0.380290i | −0.981756 | − | 0.190145i | \(-0.939104\pi\) | ||
0.981756 | − | 0.190145i | \(-0.0608958\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.67886e7i | 0.776305i | 0.921595 | + | 0.388152i | \(0.126887\pi\) | ||||
−0.921595 | + | 0.388152i | \(0.873113\pi\) | |||||||
\(860\) | 3.90067e6 | − | 1.56861e7i | 0.179843 | − | 0.723218i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.34792e7 | + | 1.05379e7i | −0.617869 | + | 0.483041i | ||||
\(863\) | −1.14812e7 | −0.524761 | −0.262381 | − | 0.964964i | \(-0.584508\pi\) | ||||
−0.262381 | + | 0.964964i | \(0.584508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.52772e7 | 1.14865 | ||||||||
\(866\) | −5.90050e6 | + | 4.61292e6i | −0.267359 | + | 0.209017i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −695524. | + | 2.79697e6i | −0.0313338 | + | 0.126005i | ||||
\(869\) | − | 2.17291e7i | − | 0.976094i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.08146e6i | − | 0.0929655i | ||||||
\(872\) | −1.00919e7 | − | 2.26101e7i | −0.449449 | − | 1.00696i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.21879e6 | + | 6.67548e6i | 0.231095 | + | 0.295600i | ||||
\(875\) | −2.77212e7 | −1.22403 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.84809e7 | −1.25042 | −0.625209 | − | 0.780458i | \(-0.714986\pi\) | ||||
−0.625209 | + | 0.780458i | \(0.714986\pi\) | |||||||
\(878\) | −6.07904e6 | − | 7.77585e6i | −0.266133 | − | 0.340417i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.18064e7 | − | 2.22712e7i | 0.513939 | − | 0.969475i | ||||
\(881\) | 4.49952e6i | 0.195311i | 0.995220 | + | 0.0976555i | \(0.0311343\pi\) | ||||
−0.995220 | + | 0.0976555i | \(0.968866\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.85783e7i | 1.23349i | 0.787164 | + | 0.616743i | \(0.211548\pi\) | ||||
−0.787164 | + | 0.616743i | \(0.788452\pi\) | |||||||
\(884\) | 3.11162e7 | + | 7.73767e6i | 1.33923 | + | 0.333027i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.05385e7 | − | 1.60567e7i | 0.878989 | − | 0.687180i | ||||
\(887\) | −3.38213e6 | −0.144338 | −0.0721691 | − | 0.997392i | \(-0.522992\pi\) | ||||
−0.0721691 | + | 0.997392i | \(0.522992\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.67275e7 | −1.55861 | ||||||||
\(890\) | −9.84292e6 | + | 7.69505e6i | −0.416533 | + | 0.325639i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.55509e6 | − | 1.13271e6i | −0.191683 | − | 0.0476659i | ||||
\(893\) | 1.81195e7i | 0.760356i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.80070e6i | 0.116872i | ||||||||
\(896\) | −2.74644e7 | − | 1.86065e6i | −1.14288 | − | 0.0774275i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.26615e6 | + | 1.61957e6i | 0.0523956 | + | 0.0670206i | ||||
\(899\) | 1.12583e6 | 0.0464596 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.52343e6 | −0.0625189 | ||||||||
\(902\) | 4.50443e7 | + | 5.76172e7i | 1.84342 | + | 2.35796i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.85263e7 | + | 1.27325e7i | −1.16098 | + | 0.518195i | ||||
\(905\) | − | 7.82978e6i | − | 0.317781i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 4.94792e7i | − | 1.99712i | −0.0536189 | − | 0.998561i | \(-0.517076\pi\) | ||
0.0536189 | − | 0.998561i | \(-0.482924\pi\) | |||||||
\(908\) | −4.99723e6 | + | 2.00958e7i | −0.201148 | + | 0.808894i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.36789e7 | + | 1.85118e7i | −0.947890 | + | 0.741046i | ||||
\(911\) | 3.42077e7 | 1.36561 | 0.682807 | − | 0.730599i | \(-0.260759\pi\) | ||||
0.682807 | + | 0.730599i | \(0.260759\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.82658e7 | −1.51927 | ||||||||
\(914\) | 1.12505e7 | − | 8.79548e6i | 0.445458 | − | 0.348252i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.24565e6 | − | 9.03066e6i | 0.0884309 | − | 0.355616i | ||||
\(917\) | 5.30132e7i | 2.08190i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.51998e7i | 1.37484i | 0.726262 | + | 0.687418i | \(0.241256\pi\) | ||||
−0.726262 | + | 0.687418i | \(0.758744\pi\) | |||||||
\(920\) | −9.01438e6 | + | 4.02350e6i | −0.351129 | + | 0.156724i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.13603e7 | − | 2.73225e7i | −0.827522 | − | 1.05850i | ||||
\(923\) | 2.38120e7 | 0.920008 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.03063e7 | 0.780325 | ||||||||
\(926\) | −1.64731e7 | − | 2.10712e7i | −0.631319 | − | 0.807536i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.88360e6 | + | 1.05865e7i | 0.0717992 | + | 0.403537i | ||||
\(929\) | − | 5.15625e7i | − | 1.96017i | −0.198568 | − | 0.980087i | \(-0.563629\pi\) | ||
0.198568 | − | 0.980087i | \(-0.436371\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.83365e6i | 0.220580i | ||||||||
\(932\) | 4.96027e7 | + | 1.23347e7i | 1.87053 | + | 0.465145i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.54958e7 | + | 1.21144e7i | −0.581228 | + | 0.454395i | ||||
\(935\) | −2.79071e7 | −1.04397 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.98027e7 | 0.736844 | 0.368422 | − | 0.929659i | \(-0.379898\pi\) | ||||
0.368422 | + | 0.929659i | \(0.379898\pi\) | |||||||
\(938\) | 1.55860e6 | − | 1.21849e6i | 0.0578400 | − | 0.0452184i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.04855e7 | − | 5.09413e6i | −0.756184 | − | 0.188040i | ||||
\(941\) | 1.34418e7i | 0.494862i | 0.968905 | + | 0.247431i | \(0.0795864\pi\) | ||||
−0.968905 | + | 0.247431i | \(0.920414\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.86410e7i | − | 1.04884i | ||||||
\(944\) | 2.82737e7 | + | 1.49885e7i | 1.03265 | + | 0.547429i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.64370e7 | − | 3.38163e7i | −0.960473 | − | 1.22856i | ||||
\(947\) | −3.05645e7 | −1.10750 | −0.553748 | − | 0.832684i | \(-0.686803\pi\) | ||||
−0.553748 | + | 0.832684i | \(0.686803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.62336e7 | −1.66645 | ||||||||
\(950\) | −5.75796e6 | − | 7.36515e6i | −0.206995 | − | 0.264772i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.24215e7 | + | 2.78296e7i | 0.444205 | + | 0.995209i | ||||
\(953\) | 5.63507e6i | 0.200987i | 0.994938 | + | 0.100493i | \(0.0320421\pi\) | ||||
−0.994938 | + | 0.100493i | \(0.967958\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 3.19987e7i | − | 1.13533i | ||||||
\(956\) | −999819. | + | 4.02067e6i | −0.0353815 | + | 0.142283i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.29539e7 | − | 1.01271e7i | 0.456022 | − | 0.356511i | ||||
\(959\) | 3.80180e7 | 1.33488 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.82613e7 | 0.987152 | ||||||||
\(962\) | 5.38136e7 | − | 4.20707e7i | 1.87480 | − | 1.46569i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.70833e6 | + | 1.89341e7i | −0.163183 | + | 0.656223i | ||||
\(965\) | − | 2.52758e6i | − | 0.0873749i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.26391e7i | 0.778560i | 0.921119 | + | 0.389280i | \(0.127276\pi\) | ||||
−0.921119 | + | 0.389280i | \(0.872724\pi\) | |||||||
\(968\) | −1.54008e7 | − | 3.45043e7i | −0.528267 | − | 1.18355i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.01266e7 | − | 2.57444e7i | −0.686817 | − | 0.878525i | ||||
\(971\) | −2.10762e6 | −0.0717372 | −0.0358686 | − | 0.999357i | \(-0.511420\pi\) | ||||
−0.0358686 | + | 0.999357i | \(0.511420\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.02507e7 | −0.347115 | ||||||||
\(974\) | −1.88148e7 | − | 2.40665e7i | −0.635481 | − | 0.812859i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.88342e6 | − | 3.11893e6i | −0.197699 | − | 0.104805i | ||||
\(977\) | 2.61881e7i | 0.877745i | 0.898549 | + | 0.438873i | \(0.144622\pi\) | ||||
−0.898549 | + | 0.438873i | \(0.855378\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.31781e7i | 1.10636i | ||||||||
\(980\) | −6.59541e6 | − | 1.64008e6i | −0.219370 | − | 0.0545506i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.33381e7 | + | 3.38811e7i | −1.43414 | + | 1.12119i | ||||
\(983\) | −4.01037e7 | −1.32373 | −0.661866 | − | 0.749622i | \(-0.730235\pi\) | ||||
−0.661866 | + | 0.749622i | \(0.730235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.90933e7 | 1.28384 | ||||||||
\(986\) | 9.37865e6 | − | 7.33209e6i | 0.307219 | − | 0.240179i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.05183e7 | − | 7.58899e6i | −0.994646 | − | 0.247339i | ||||
\(989\) | 1.68098e7i | 0.546476i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.06829e7i | 1.31592i | 0.753055 | + | 0.657958i | \(0.228580\pi\) | ||||
−0.753055 | + | 0.657958i | \(0.771420\pi\) | |||||||
\(992\) | −615420. | − | 3.45888e6i | −0.0198560 | − | 0.111598i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.39396e7 | + | 1.78305e7i | 0.447492 | + | 0.572397i | ||||
\(995\) | −2.58888e6 | −0.0829001 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.33781e7 | −0.426242 | −0.213121 | − | 0.977026i | \(-0.568363\pi\) | ||||
−0.213121 | + | 0.977026i | \(0.568363\pi\) | |||||||
\(998\) | 5.15241e6 | + | 6.59057e6i | 0.163751 | + | 0.209458i | ||||
\(999\) | 0 | 0 |
(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 | 108.6.b.c.107.17 | yes | 20 | |
3.2 | odd | 2 | inner | 108.6.b.c.107.4 | yes | 20 | |
4.3 | odd | 2 | inner | 108.6.b.c.107.3 | ✓ | 20 | |
12.11 | even | 2 | inner | 108.6.b.c.107.18 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.b.c.107.3 | ✓ | 20 | 4.3 | odd | 2 | inner | |
108.6.b.c.107.4 | yes | 20 | 3.2 | odd | 2 | inner | |
108.6.b.c.107.17 | yes | 20 | 1.1 | even | 1 | trivial | |
108.6.b.c.107.18 | yes | 20 | 12.11 | even | 2 | inner |