Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,6,Mod(557,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.557");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.j (of order \(4\), degree \(2\), 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: | \(144.345437832\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 557.11 | ||
Character | \(\chi\) | \(=\) | 900.557 |
Dual form | 900.6.j.c.593.11 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 123.937 | + | 123.937i | 0.955994 | + | 0.955994i | 0.999072 | − | 0.0430780i | \(-0.0137164\pi\) |
−0.0430780 | + | 0.999072i | \(0.513716\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 296.299i | 0.738327i | 0.929364 | + | 0.369164i | \(0.120356\pi\) | ||||
−0.929364 | + | 0.369164i | \(0.879644\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.2336 | + | 16.2336i | −0.0266414 | + | 0.0266414i | −0.720302 | − | 0.693661i | \(-0.755997\pi\) |
0.693661 | + | 0.720302i | \(0.255997\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 547.265 | − | 547.265i | 0.459278 | − | 0.459278i | −0.439140 | − | 0.898418i | \(-0.644717\pi\) |
0.898418 | + | 0.439140i | \(0.144717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 262.818i | 0.167021i | 0.996507 | + | 0.0835104i | \(0.0266132\pi\) | ||||
−0.996507 | + | 0.0835104i | \(0.973387\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2434.99 | + | 2434.99i | 0.959793 | + | 0.959793i | 0.999222 | − | 0.0394291i | \(-0.0125539\pi\) |
−0.0394291 | + | 0.999222i | \(0.512554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4327.66 | −0.955561 | −0.477781 | − | 0.878479i | \(-0.658559\pi\) | ||||
−0.477781 | + | 0.878479i | \(0.658559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8473.00 | 1.58355 | 0.791777 | − | 0.610810i | \(-0.209156\pi\) | ||||
0.791777 | + | 0.610810i | \(0.209156\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 100.890 | + | 100.890i | 0.0121155 | + | 0.0121155i | 0.713139 | − | 0.701023i | \(-0.247273\pi\) |
−0.701023 | + | 0.713139i | \(0.747273\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14606.6i | 1.35703i | 0.734589 | + | 0.678513i | \(0.237375\pi\) | ||||
−0.734589 | + | 0.678513i | \(0.762625\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9268.83 | − | 9268.83i | 0.764459 | − | 0.764459i | −0.212666 | − | 0.977125i | \(-0.568215\pi\) |
0.977125 | + | 0.212666i | \(0.0682147\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1485.67 | − | 1485.67i | 0.0981017 | − | 0.0981017i | −0.656353 | − | 0.754454i | \(-0.727902\pi\) |
0.754454 | + | 0.656353i | \(0.227902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13913.6i | 0.827848i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9264.63 | + | 9264.63i | 0.453042 | + | 0.453042i | 0.896363 | − | 0.443321i | \(-0.146200\pi\) |
−0.443321 | + | 0.896363i | \(0.646200\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2053.40 | −0.0767970 | −0.0383985 | − | 0.999263i | \(-0.512226\pi\) | ||||
−0.0383985 | + | 0.999263i | \(0.512226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10864.1 | −0.373826 | −0.186913 | − | 0.982376i | \(-0.559848\pi\) | ||||
−0.186913 | + | 0.982376i | \(0.559848\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9222.90 | − | 9222.90i | −0.251004 | − | 0.251004i | 0.570378 | − | 0.821382i | \(-0.306797\pi\) |
−0.821382 | + | 0.570378i | \(0.806797\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10577.6i | 0.249024i | 0.992218 | + | 0.124512i | \(0.0397365\pi\) | ||||
−0.992218 | + | 0.124512i | \(0.960263\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −20495.6 | + | 20495.6i | −0.450146 | + | 0.450146i | −0.895403 | − | 0.445257i | \(-0.853112\pi\) |
0.445257 | + | 0.895403i | \(0.353112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −36722.4 | + | 36722.4i | −0.705836 | + | 0.705836i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 58845.3i | − | 1.06083i | −0.847740 | − | 0.530413i | \(-0.822037\pi\) | ||
0.847740 | − | 0.530413i | \(-0.177963\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −61864.1 | − | 61864.1i | −0.985698 | − | 0.985698i | 0.0142015 | − | 0.999899i | \(-0.495479\pi\) |
−0.999899 | + | 0.0142015i | \(0.995479\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 43592.7 | 0.583363 | 0.291681 | − | 0.956516i | \(-0.405785\pi\) | ||||
0.291681 | + | 0.956516i | \(0.405785\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4023.88 | −0.0509380 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 75406.9 | + | 75406.9i | 0.813733 | + | 0.813733i | 0.985191 | − | 0.171459i | \(-0.0548480\pi\) |
−0.171459 | + | 0.985191i | \(0.554848\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 136828.i | − | 1.33466i | −0.744763 | − | 0.667329i | \(-0.767437\pi\) | ||
0.744763 | − | 0.667329i | \(-0.232563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −68031.2 | + | 68031.2i | −0.631851 | + | 0.631851i | −0.948532 | − | 0.316681i | \(-0.897432\pi\) |
0.316681 | + | 0.948532i | \(0.397432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 21604.1 | − | 21604.1i | 0.182422 | − | 0.182422i | −0.609988 | − | 0.792410i | \(-0.708826\pi\) |
0.792410 | + | 0.609988i | \(0.208826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 56892.1i | 0.458655i | 0.973349 | + | 0.229327i | \(0.0736526\pi\) | ||||
−0.973349 | + | 0.229327i | \(0.926347\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −61980.0 | − | 61980.0i | −0.456621 | − | 0.456621i | 0.440924 | − | 0.897544i | \(-0.354651\pi\) |
−0.897544 | + | 0.440924i | \(0.854651\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 135653. | 0.878134 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 73257.7 | 0.454873 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 59893.7 | + | 59893.7i | 0.329512 | + | 0.329512i | 0.852401 | − | 0.522889i | \(-0.175146\pi\) |
−0.522889 | + | 0.852401i | \(0.675146\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 317743.i | 1.61770i | 0.588017 | + | 0.808849i | \(0.299909\pi\) | ||||
−0.588017 | + | 0.808849i | \(0.700091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −32572.8 | + | 32572.8i | −0.159671 | + | 0.159671i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −283098. | + | 283098.i | −1.28865 | + | 1.28865i | −0.353045 | + | 0.935606i | \(0.614854\pi\) |
−0.935606 | + | 0.353045i | \(0.885146\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 215426.i | − | 0.945716i | −0.881139 | − | 0.472858i | \(-0.843222\pi\) | ||
0.881139 | − | 0.472858i | \(-0.156778\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4810.01 | − | 4810.01i | −0.0196701 | − | 0.0196701i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −369959. | −1.36517 | −0.682587 | − | 0.730804i | \(-0.739145\pi\) | ||||
−0.682587 | + | 0.730804i | \(0.739145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 280532. | 1.00124 | 0.500621 | − | 0.865666i | \(-0.333105\pi\) | ||||
0.500621 | + | 0.865666i | \(0.333105\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 30811.3 | + | 30811.3i | 0.0997610 | + | 0.0997610i | 0.755226 | − | 0.655465i | \(-0.227527\pi\) |
−0.655465 | + | 0.755226i | \(0.727527\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 603570.i | 1.83511i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 96397.3 | − | 96397.3i | 0.284181 | − | 0.284181i | −0.550593 | − | 0.834774i | \(-0.685598\pi\) |
0.834774 | + | 0.550593i | \(0.185598\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −35684.1 | + | 35684.1i | −0.0990109 | + | 0.0990109i | −0.754877 | − | 0.655866i | \(-0.772304\pi\) |
0.655866 | + | 0.754877i | \(0.272304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 370766.i | 0.998580i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 76138.1 | + | 76138.1i | 0.193414 | + | 0.193414i | 0.797169 | − | 0.603756i | \(-0.206330\pi\) |
−0.603756 | + | 0.797169i | \(0.706330\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 411064. | 0.958907 | 0.479454 | − | 0.877567i | \(-0.340835\pi\) | ||||
0.479454 | + | 0.877567i | \(0.340835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 272889. | 0.619141 | 0.309571 | − | 0.950876i | \(-0.399815\pi\) | ||||
0.309571 | + | 0.950876i | \(0.399815\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 162154. | + | 162154.i | 0.339098 | + | 0.339098i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 868065.i | 1.72175i | 0.508820 | + | 0.860873i | \(0.330082\pi\) | ||||
−0.508820 | + | 0.860873i | \(0.669918\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23668.8 | + | 23668.8i | −0.0457387 | + | 0.0457387i | −0.729606 | − | 0.683868i | \(-0.760297\pi\) |
0.683868 | + | 0.729606i | \(0.260297\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −629819. | + | 629819.i | −1.15625 | + | 1.15625i | −0.170969 | + | 0.985276i | \(0.554690\pi\) |
−0.985276 | + | 0.170969i | \(0.945310\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 120544.i | 0.215780i | 0.994163 | + | 0.107890i | \(0.0344094\pi\) | ||||
−0.994163 | + | 0.107890i | \(0.965591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −536357. | − | 536357.i | −0.913511 | − | 0.913511i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −77872.7 | −0.123316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.16641e6 | 1.80362 | 0.901809 | − | 0.432135i | \(-0.142240\pi\) | ||||
0.901809 | + | 0.432135i | \(0.142240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.05012e6 | + | 1.05012e6i | 1.51387 | + | 1.51387i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17768.2i | 0.0244716i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −794666. | + | 794666.i | −1.07010 | + | 1.07010i | −0.0727445 | + | 0.997351i | \(0.523176\pi\) |
−0.997351 | + | 0.0727445i | \(0.976824\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −614503. | + | 614503.i | −0.791515 | + | 0.791515i | −0.981740 | − | 0.190225i | \(-0.939078\pi\) |
0.190225 | + | 0.981740i | \(0.439078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.41946e6i | − | 1.78869i | −0.447377 | − | 0.894346i | \(-0.647642\pi\) | ||
0.447377 | − | 0.894346i | \(-0.352358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −580216. | − | 580216.i | −0.700165 | − | 0.700165i | 0.264281 | − | 0.964446i | \(-0.414865\pi\) |
−0.964446 | + | 0.264281i | \(0.914865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 438358. | 0.496402 | 0.248201 | − | 0.968709i | \(-0.420161\pi\) | ||||
0.248201 | + | 0.968709i | \(0.420161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −61779.3 | −0.0685173 | −0.0342586 | − | 0.999413i | \(-0.510907\pi\) | ||||
−0.0342586 | + | 0.999413i | \(0.510907\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4266.48 | − | 4266.48i | −0.00444967 | − | 0.00444967i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 152110.i | 0.152396i | 0.997093 | + | 0.0761978i | \(0.0242780\pi\) | ||||
−0.997093 | + | 0.0761978i | \(0.975722\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −721486. | + | 721486.i | −0.708642 | + | 0.708642i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −794182. | + | 794182.i | −0.750045 | + | 0.750045i | −0.974487 | − | 0.224442i | \(-0.927944\pi\) |
0.224442 | + | 0.974487i | \(0.427944\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25007.9i | 0.0231648i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −846425. | − | 846425.i | −0.754570 | − | 0.754570i | 0.220759 | − | 0.975328i | \(-0.429147\pi\) |
−0.975328 | + | 0.220759i | \(0.929147\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.38502e6 | 1.16701 | 0.583507 | − | 0.812108i | \(-0.301680\pi\) | ||||
0.583507 | + | 0.812108i | \(0.301680\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −450412. | −0.372552 | −0.186276 | − | 0.982497i | \(-0.559642\pi\) | ||||
−0.186276 | + | 0.982497i | \(0.559642\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.25916e6 | + | 1.25916e6i | 0.986012 | + | 0.986012i | 0.999904 | − | 0.0138917i | \(-0.00442202\pi\) |
−0.0138917 | + | 0.999904i | \(0.504422\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.96636e6i | 1.48558i | 0.669522 | + | 0.742792i | \(0.266499\pi\) | ||||
−0.669522 | + | 0.742792i | \(0.733501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −963548. | + | 963548.i | −0.715167 | + | 0.715167i | −0.967611 | − | 0.252445i | \(-0.918765\pi\) |
0.252445 | + | 0.967611i | \(0.418765\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.81029e6 | + | 1.81029e6i | −1.29731 | + | 1.29731i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 820858.i | 0.578127i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.78311e6 | − | 1.78311e6i | −1.21342 | − | 1.21342i | −0.969895 | − | 0.243522i | \(-0.921697\pi\) |
−0.243522 | − | 0.969895i | \(-0.578303\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −79057.4 | −0.0511405 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.29750e6 | 1.46164 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.26197e6 | + | 1.26197e6i | 0.764193 | + | 0.764193i | 0.977077 | − | 0.212885i | \(-0.0682859\pi\) |
−0.212885 | + | 0.977077i | \(0.568286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.26700e6i | 1.32908i | 0.747253 | + | 0.664540i | \(0.231372\pi\) | ||||
−0.747253 | + | 0.664540i | \(0.768628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.03818e6 | − | 1.03818e6i | 0.598979 | − | 0.598979i | −0.341062 | − | 0.940041i | \(-0.610787\pi\) |
0.940041 | + | 0.341062i | \(0.110787\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −895082. | + | 895082.i | −0.500282 | + | 0.500282i | −0.911526 | − | 0.411244i | \(-0.865095\pi\) |
0.411244 | + | 0.911526i | \(0.365095\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.28228e6i | − | 0.705517i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 143831. | + | 143831.i | 0.0767090 | + | 0.0767090i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 368257. | 0.187569 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.59270e6 | 0.799031 | 0.399515 | − | 0.916727i | \(-0.369178\pi\) | ||||
0.399515 | + | 0.916727i | \(0.369178\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.14157e6 | − | 2.14157e6i | −1.02721 | − | 1.02721i | −0.999619 | − | 0.0275860i | \(-0.991218\pi\) |
−0.0275860 | − | 0.999619i | \(-0.508782\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.51054e6i | 1.16918i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 358594. | − | 358594.i | 0.164576 | − | 0.164576i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.35898e6 | + | 1.35898e6i | −0.605883 | + | 0.605883i | −0.941868 | − | 0.335984i | \(-0.890931\pi\) |
0.335984 | + | 0.941868i | \(0.390931\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 331480.i | − | 0.145678i | −0.997344 | − | 0.0728390i | \(-0.976794\pi\) | ||
0.997344 | − | 0.0728390i | \(-0.0232059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.53861e6 | + | 1.53861e6i | 0.657192 | + | 0.657192i | 0.954715 | − | 0.297523i | \(-0.0961604\pi\) |
−0.297523 | + | 0.954715i | \(0.596160\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.46509e6 | −1.41899 | −0.709493 | − | 0.704712i | \(-0.751076\pi\) | ||||
−0.709493 | + | 0.704712i | \(0.751076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.40703e6 | 0.972104 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.95418e6 | + | 2.95418e6i | 1.14491 | + | 1.14491i | 0.987539 | + | 0.157373i | \(0.0503026\pi\) |
0.157373 | + | 0.987539i | \(0.449697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.29646e6i | 0.866211i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.99621e6 | + | 1.99621e6i | −0.742906 | + | 0.742906i | −0.973136 | − | 0.230231i | \(-0.926052\pi\) |
0.230231 | + | 0.973136i | \(0.426052\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 70253.6 | − | 70253.6i | 0.0254575 | − | 0.0254575i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.85257e6i | 1.37769i | 0.724907 | + | 0.688847i | \(0.241883\pi\) | ||||
−0.724907 | + | 0.688847i | \(0.758117\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −114173. | − | 114173.i | −0.0397709 | − | 0.0397709i | 0.686942 | − | 0.726713i | \(-0.258953\pi\) |
−0.726713 | + | 0.686942i | \(0.758953\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.51434e6 | 1.17752 | 0.588762 | − | 0.808307i | \(-0.299616\pi\) | ||||
0.588762 | + | 0.808307i | \(0.299616\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.66517e6 | 0.881624 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.18815e6 | + | 3.18815e6i | 1.01523 | + | 1.01523i | 0.999882 | + | 0.0153441i | \(0.00488438\pi\) |
0.0153441 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.76155e6i | 1.16817i | 0.811692 | + | 0.584086i | \(0.198547\pi\) | ||||
−0.811692 | + | 0.584086i | \(0.801453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −137547. | + | 137547.i | −0.0421881 | + | 0.0421881i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29893.6 | + | 29893.6i | −0.00894524 | + | 0.00894524i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.01805e6i | − | 1.48329i | −0.670792 | − | 0.741645i | \(-0.734046\pi\) | ||
0.670792 | − | 0.741645i | \(-0.265954\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −254492. | − | 254492.i | −0.0734174 | − | 0.0734174i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.71304e6 | −0.476685 | −0.238342 | − | 0.971181i | \(-0.576604\pi\) | ||||
−0.238342 | + | 0.971181i | \(0.576604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.12412e6 | −0.309105 | −0.154552 | − | 0.987985i | \(-0.549394\pi\) | ||||
−0.154552 | + | 0.987985i | \(0.549394\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.34646e6 | − | 1.34646e6i | −0.357375 | − | 0.357375i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.16531e6i | − | 0.820773i | −0.911912 | − | 0.410386i | \(-0.865394\pi\) | ||
0.911912 | − | 0.410386i | \(-0.134606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 520810. | − | 520810.i | 0.133493 | − | 0.133493i | −0.637203 | − | 0.770696i | \(-0.719909\pi\) |
0.770696 | + | 0.637203i | \(0.219909\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −639959. | + | 639959.i | −0.160305 | + | 0.160305i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.63513e6i | 0.652589i | 0.945268 | + | 0.326295i | \(0.105800\pi\) | ||||
−0.945268 | + | 0.326295i | \(0.894200\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.89945e6 | − | 4.89945e6i | −1.18615 | − | 1.18615i | −0.978124 | − | 0.208023i | \(-0.933297\pi\) |
−0.208023 | − | 0.978124i | \(-0.566703\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.20484e6 | 0.516133 | 0.258066 | − | 0.966127i | \(-0.416915\pi\) | ||||
0.258066 | + | 0.966127i | \(0.416915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.32791e6 | −1.00193 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.27070e6 | − | 3.27070e6i | −0.732571 | − | 0.732571i | 0.238558 | − | 0.971128i | \(-0.423325\pi\) |
−0.971128 | + | 0.238558i | \(0.923325\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.76391e6i | − | 1.70148i | −0.525583 | − | 0.850742i | \(-0.676153\pi\) | ||
0.525583 | − | 0.850742i | \(-0.323847\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −171191. | + | 171191.i | −0.0371133 | + | 0.0371133i | −0.725420 | − | 0.688307i | \(-0.758354\pi\) |
0.688307 | + | 0.725420i | \(0.258354\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −921034. | + | 921034.i | −0.195426 | + | 0.195426i | −0.798036 | − | 0.602610i | \(-0.794128\pi\) |
0.602610 | + | 0.798036i | \(0.294128\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 2.28611e6i | − | 0.479917i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.74635e6 | + | 2.74635e6i | 0.564421 | + | 0.564421i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 157207. | 0.0313064 | 0.0156532 | − | 0.999877i | \(-0.495017\pi\) | ||||
0.0156532 | + | 0.999877i | \(0.495017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3275.61 | −0.000645550 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −690885. | − | 690885.i | −0.132003 | − | 0.132003i | 0.638018 | − | 0.770021i | \(-0.279754\pi\) |
−0.770021 | + | 0.638018i | \(0.779754\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.17012e6i | − | 0.593434i | −0.954965 | − | 0.296717i | \(-0.904108\pi\) | ||
0.954965 | − | 0.296717i | \(-0.0958918\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.36838e6 | + | 2.36838e6i | −0.438868 | + | 0.438868i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.31095e6 | + | 1.31095e6i | −0.238065 | + | 0.238065i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.10049e6i | − | 0.557415i | −0.960376 | − | 0.278708i | \(-0.910094\pi\) | ||
0.960376 | − | 0.278708i | \(-0.0899061\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.20877e6 | − | 3.20877e6i | −0.565481 | − | 0.565481i | 0.365378 | − | 0.930859i | \(-0.380940\pi\) |
−0.930859 | + | 0.365378i | \(0.880940\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.43063e6 | 1.10017 | 0.550084 | − | 0.835109i | \(-0.314596\pi\) | ||||
0.550084 | + | 0.835109i | \(0.314596\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.08032e6 | −0.860674 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 440202. | + | 440202.i | 0.0724312 | + | 0.0724312i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.25599e6i | 0.525519i | 0.964861 | + | 0.262759i | \(0.0846325\pi\) | ||||
−0.964861 | + | 0.262759i | \(0.915367\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 259544. | − | 259544.i | 0.0414912 | − | 0.0414912i | −0.686057 | − | 0.727548i | \(-0.740660\pi\) |
0.727548 | + | 0.686057i | \(0.240660\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.63698e6 | − | 4.63698e6i | 0.727292 | − | 0.727292i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.42202e6i | 0.842406i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −237117. | − | 237117.i | −0.0361531 | − | 0.0361531i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.12260e6 | −0.611223 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.89249e6 | −1.30626 | −0.653131 | − | 0.757245i | \(-0.726545\pi\) | ||||
−0.653131 | + | 0.757245i | \(0.726545\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.90236e6 | − | 1.90236e6i | −0.271846 | − | 0.271846i | 0.557997 | − | 0.829843i | \(-0.311570\pi\) |
−0.829843 | + | 0.557997i | \(0.811570\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.13739e6i | − | 0.159599i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.29309e6 | − | 7.29309e6i | 1.01414 | − | 1.01414i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.92347e6 | − | 6.92347e6i | 0.945553 | − | 0.945553i | −0.0530399 | − | 0.998592i | \(-0.516891\pi\) |
0.998592 | + | 0.0530399i | \(0.0168910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 300933.i | 0.0407325i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.52384e6 | + | 9.52384e6i | 1.26631 | + | 1.26631i | 0.947979 | + | 0.318334i | \(0.103123\pi\) |
0.318334 | + | 0.947979i | \(0.396877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.04760e7 | −1.35648 | −0.678241 | − | 0.734839i | \(-0.737257\pi\) | ||||
−0.678241 | + | 0.734839i | \(0.737257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.27504e6 | 0.292011 | 0.146006 | − | 0.989284i | \(-0.453358\pi\) | ||||
0.146006 | + | 0.989284i | \(0.453358\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −541993. | − | 541993.i | −0.0677726 | − | 0.0677726i | 0.672408 | − | 0.740181i | \(-0.265260\pi\) |
−0.740181 | + | 0.672408i | \(0.765260\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.53345e7i | − | 1.88464i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.74510e6 | + | 2.74510e6i | −0.334493 | + | 0.334493i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.04755e7 | − | 1.04755e7i | 1.25482 | − | 1.25482i | 0.301286 | − | 0.953534i | \(-0.402584\pi\) |
0.953534 | − | 0.301286i | \(-0.0974158\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.22686e6i | 0.264487i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.39119e6 | + | 9.39119e6i | 1.09669 | + | 1.09669i | 0.994795 | + | 0.101894i | \(0.0324904\pi\) |
0.101894 | + | 0.994795i | \(0.467510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.38639e6 | −0.385629 | −0.192814 | − | 0.981235i | \(-0.561762\pi\) | ||||
−0.192814 | + | 0.981235i | \(0.561762\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.38299e6 | 0.833770 | 0.416885 | − | 0.908959i | \(-0.363122\pi\) | ||||
0.416885 | + | 0.908959i | \(0.363122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.09377e7 | − | 1.09377e7i | −1.20491 | − | 1.20491i | −0.972654 | − | 0.232259i | \(-0.925388\pi\) |
−0.232259 | − | 0.972654i | \(-0.574612\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48235.5i | 0.00522713i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.57139e6 | − | 9.57139e6i | 1.02878 | − | 1.02878i | 0.0292102 | − | 0.999573i | \(-0.490701\pi\) |
0.999573 | − | 0.0292102i | \(-0.00929921\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.65393e6 | + | 2.65393e6i | −0.280657 | + | 0.280657i | −0.833371 | − | 0.552714i | \(-0.813592\pi\) |
0.552714 | + | 0.833371i | \(0.313592\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.23480e6i | 0.234429i | 0.993107 | + | 0.117214i | \(0.0373965\pi\) | ||||
−0.993107 | + | 0.117214i | \(0.962604\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.40274e6 | + | 5.40274e6i | 0.557691 | + | 0.557691i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 110427. | 0.0111288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.17502e6 | 0.917347 | 0.458674 | − | 0.888605i | \(-0.348325\pi\) | ||||
0.458674 | + | 0.888605i | \(0.348325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −225869. | − | 225869.i | −0.0220550 | − | 0.0220550i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 949377.i | 0.0912628i | 0.998958 | + | 0.0456314i | \(0.0145300\pi\) | ||||
−0.998958 | + | 0.0456314i | \(0.985470\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.12833e6 | + | 2.12833e6i | −0.203007 | + | 0.203007i | −0.801287 | − | 0.598280i | \(-0.795851\pi\) |
0.598280 | + | 0.801287i | \(0.295851\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.02885e7 | − | 1.02885e7i | 0.966253 | − | 0.966253i | −0.0331962 | − | 0.999449i | \(-0.510569\pi\) |
0.999449 | + | 0.0331962i | \(0.0105686\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 608422.i | − | 0.0567013i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.59428e6 | + | 4.59428e6i | 0.421633 | + | 0.421633i | 0.885766 | − | 0.464133i | \(-0.153634\pi\) |
−0.464133 | + | 0.885766i | \(0.653634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.22204e6 | −0.468411 | −0.234205 | − | 0.972187i | \(-0.575249\pi\) | ||||
−0.234205 | + | 0.972187i | \(0.575249\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.16231e7 | −1.92493 | −0.962465 | − | 0.271405i | \(-0.912512\pi\) | ||||
−0.962465 | + | 0.271405i | \(0.912512\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.05378e7 | − | 1.05378e7i | −0.917141 | − | 0.917141i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.21903e6i | − | 0.276006i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.51265e7 | − | 1.51265e7i | 1.28736 | − | 1.28736i | 0.350974 | − | 0.936385i | \(-0.385850\pi\) |
0.936385 | − | 0.350974i | \(-0.114150\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.02380e6 | − | 2.02380e6i | 0.169705 | − | 0.169705i | −0.617144 | − | 0.786850i | \(-0.711711\pi\) |
0.786850 | + | 0.617144i | \(0.211711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.86914e7i | 1.55585i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.21866e6 | − | 8.21866e6i | −0.674138 | − | 0.674138i | 0.284529 | − | 0.958667i | \(-0.408163\pi\) |
−0.958667 | + | 0.284529i | \(0.908163\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −300797. | −0.0241393 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.62147e7 | −1.29185 | −0.645926 | − | 0.763400i | \(-0.723529\pi\) | ||||
−0.645926 | + | 0.763400i | \(0.723529\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.99366e6 | + | 7.99366e6i | 0.623252 | + | 0.623252i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.49796e7i | − | 1.91995i | −0.280081 | − | 0.959976i | \(-0.590361\pi\) | ||
0.280081 | − | 0.959976i | \(-0.409639\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −26515.6 | + | 26515.6i | −0.00202355 | + | 0.00202355i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.69580e7 | − | 1.69580e7i | 1.27592 | − | 1.27592i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.44518e7i | − | 1.07971i | −0.841760 | − | 0.539853i | \(-0.818480\pi\) | ||
0.841760 | − | 0.539853i | \(-0.181520\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.06317e7 | + | 2.06317e7i | 1.51989 | + | 1.51989i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.32849e6 | 0.312258 | 0.156129 | − | 0.987737i | \(-0.450098\pi\) | ||||
0.156129 | + | 0.987737i | \(0.450098\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.68631e7 | −1.20809 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.66934e7 | − | 1.66934e7i | −1.17141 | − | 1.17141i | −0.981873 | − | 0.189538i | \(-0.939301\pi\) |
−0.189538 | − | 0.981873i | \(-0.560699\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.01450e7i | − | 0.702198i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.29281e6 | + | 7.29281e6i | −0.501343 | + | 0.501343i | −0.911855 | − | 0.410512i | \(-0.865350\pi\) |
0.410512 | + | 0.911855i | \(0.365350\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.73274e6 | − | 2.73274e6i | 0.185323 | − | 0.185323i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 7.99531e6i | − | 0.538548i | −0.963064 | − | 0.269274i | \(-0.913216\pi\) | ||
0.963064 | − | 0.269274i | \(-0.0867837\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.74977e7 | − | 1.74977e7i | −1.16281 | − | 1.16281i | −0.983858 | − | 0.178953i | \(-0.942729\pi\) |
−0.178953 | − | 0.983858i | \(-0.557271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.35509e6 | 0.348788 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.18625e7 | −0.767494 | −0.383747 | − | 0.923438i | \(-0.625366\pi\) | ||||
−0.383747 | + | 0.923438i | \(0.625366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.18681e7 | − | 1.18681e7i | −0.752733 | − | 0.752733i | 0.222255 | − | 0.974989i | \(-0.428658\pi\) |
−0.974989 | + | 0.222255i | \(0.928658\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.36406e7i | − | 0.853832i | −0.904291 | − | 0.426916i | \(-0.859600\pi\) | ||
0.904291 | − | 0.426916i | \(-0.140400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.05102e6 | + | 7.05102e6i | −0.438471 | + | 0.438471i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33334.2 | − | 33334.2i | 0.00204598 | − | 0.00204598i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.00583e6i | 0.488192i | 0.969751 | + | 0.244096i | \(0.0784912\pi\) | ||||
−0.969751 | + | 0.244096i | \(0.921509\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.94684e6 | + | 2.94684e6i | 0.177381 | + | 0.177381i | 0.790213 | − | 0.612832i | \(-0.209970\pi\) |
−0.612832 | + | 0.790213i | \(0.709970\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.83886e6 | −0.226652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.13414e6 | −0.183861 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.07512e6 | + | 5.07512e6i | 0.292085 | + | 0.292085i | 0.837904 | − | 0.545818i | \(-0.183781\pi\) |
−0.545818 | + | 0.837904i | \(0.683781\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.53632e7i | − | 0.873053i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 176364. | − | 176364.i | 0.00995924 | − | 0.00995924i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.32317e7 | + | 1.32317e7i | −0.737855 | + | 0.737855i | −0.972162 | − | 0.234308i | \(-0.924718\pi\) |
0.234308 | + | 0.972162i | \(0.424718\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.62611e6i | − | 0.0901120i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.07284e6 | − | 6.07284e6i | −0.332355 | − | 0.332355i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.80318e6 | 0.204303 | 0.102152 | − | 0.994769i | \(-0.467427\pi\) | ||||
0.102152 | + | 0.994769i | \(0.467427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.12914e7 | 0.602829 | 0.301414 | − | 0.953493i | \(-0.402541\pi\) | ||||
0.301414 | + | 0.953493i | \(0.402541\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.43601e6 | + | 2.43601e6i | 0.127681 | + | 0.127681i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.15427e7i | − | 1.11543i | −0.830032 | − | 0.557716i | \(-0.811678\pi\) | ||
0.830032 | − | 0.557716i | \(-0.188322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.73412e6 | − | 8.73412e6i | 0.449489 | − | 0.449489i | −0.445695 | − | 0.895185i | \(-0.647044\pi\) |
0.895185 | + | 0.445695i | \(0.147044\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.59254e7 | − | 1.59254e7i | 0.809705 | − | 0.809705i | −0.174884 | − | 0.984589i | \(-0.555955\pi\) |
0.984589 | + | 0.174884i | \(0.0559552\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.78306e7i | − | 1.40649i | −0.710948 | − | 0.703244i | \(-0.751734\pi\) | ||
0.710948 | − | 0.703244i | \(-0.248266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.61445e6 | + | 7.61445e6i | 0.380212 | + | 0.380212i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.50255e6 | −0.417008 | −0.208504 | − | 0.978022i | \(-0.566859\pi\) | ||||
−0.208504 | + | 0.978022i | \(0.566859\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.78247e6 | −0.0869026 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.07933e6 | + | 9.07933e6i | 0.434856 | + | 0.434856i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 491332.i | 0.0232568i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.51666e6 | − | 4.51666e6i | 0.212542 | − | 0.212542i | −0.592805 | − | 0.805346i | \(-0.701979\pi\) |
0.805346 | + | 0.592805i | \(0.201979\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.32536e7 | − | 2.32536e7i | 1.08153 | − | 1.08153i | 0.0851602 | − | 0.996367i | \(-0.472860\pi\) |
0.996367 | − | 0.0851602i | \(-0.0271402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.86671e7i | 1.78796i | 0.448105 | + | 0.893981i | \(0.352099\pi\) | ||||
−0.448105 | + | 0.893981i | \(0.647901\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.41644e7 | + | 1.41644e7i | 0.647400 | + | 0.647400i | 0.952364 | − | 0.304964i | \(-0.0986444\pi\) |
−0.304964 | + | 0.952364i | \(0.598644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.74358e7 | 0.783236 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 299442. | 0.0133742 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.20885e6 | + | 6.20885e6i | 0.272591 | + | 0.272591i | 0.830143 | − | 0.557551i | \(-0.188259\pi\) |
−0.557551 | + | 0.830143i | \(0.688259\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.69249e7i | 0.734660i | 0.930091 | + | 0.367330i | \(0.119728\pi\) | ||||
−0.930091 | + | 0.367330i | \(0.880272\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −154530. | + | 154530.i | −0.00666976 | + | 0.00666976i | −0.710434 | − | 0.703764i | \(-0.751501\pi\) |
0.703764 | + | 0.710434i | \(0.251501\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.66600e7 | − | 1.66600e7i | 0.710992 | − | 0.710992i | −0.255751 | − | 0.966743i | \(-0.582323\pi\) |
0.966743 | + | 0.255751i | \(0.0823226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.48461e7i | 0.630024i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 390460. | + | 390460.i | 0.0163850 | + | 0.0163850i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.66683e7 | −1.51318 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.01404e7 | 0.416145 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.88373e7 | − | 1.88373e7i | −0.760328 | − | 0.760328i | 0.216053 | − | 0.976382i | \(-0.430681\pi\) |
−0.976382 | + | 0.216053i | \(0.930681\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.97112e7i | 1.18611i | 0.805163 | + | 0.593054i | \(0.202078\pi\) | ||||
−0.805163 | + | 0.593054i | \(0.797922\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.83303e7 | − | 1.83303e7i | 0.727767 | − | 0.727767i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.93800e7 | + | 3.93800e7i | −1.54651 | + | 1.54651i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.68807e7i | − | 0.659329i | −0.944098 | − | 0.329665i | \(-0.893064\pi\) | ||
0.944098 | − | 0.329665i | \(-0.106936\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −171713. | − | 171713.i | −0.00663435 | − | 0.00663435i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.25540e7 | 1.23756 | 0.618779 | − | 0.785565i | \(-0.287628\pi\) | ||||
0.618779 | + | 0.785565i | \(0.287628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.65675e6 | −0.138268 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.56214e6 | − | 6.56214e6i | −0.244172 | − | 0.244172i | 0.574401 | − | 0.818574i | \(-0.305235\pi\) |
−0.818574 | + | 0.574401i | \(0.805235\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.46801e7i | 1.64490i | 0.568836 | + | 0.822451i | \(0.307394\pi\) | ||||
−0.568836 | + | 0.822451i | \(0.692606\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.55668e7 | + | 3.55668e7i | −1.30246 | + | 1.30246i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.74895e7 | + | 2.74895e7i | −0.996075 | + | 0.996075i | −0.999992 | − | 0.00391761i | \(-0.998753\pi\) |
0.00391761 | + | 0.999992i | \(0.498753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 665436.i | − | 0.0239851i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.00343e7 | + | 3.00343e7i | 1.07123 | + | 1.07123i | 0.997260 | + | 0.0739747i | \(0.0235684\pi\) |
0.0739747 | + | 0.997260i | \(0.476432\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.01725e7 | −2.46389 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.31626e7 | 1.50765 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.78773e7 | + | 1.78773e7i | 0.614803 | + | 0.614803i | 0.944194 | − | 0.329391i | \(-0.106843\pi\) |
−0.329391 | + | 0.944194i | \(0.606843\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.75062e7i | 0.595861i | 0.954588 | + | 0.297930i | \(0.0962963\pi\) | ||||
−0.954588 | + | 0.297930i | \(0.903704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.66992e7 | − | 2.66992e7i | 0.904098 | − | 0.904098i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.05445e6 | − | 6.05445e6i | 0.202926 | − | 0.202926i | −0.598326 | − | 0.801253i | \(-0.704167\pi\) |
0.801253 | + | 0.598326i | \(0.204167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.29165e7i | 0.430713i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.92434e7 | − | 3.92434e7i | −1.29534 | − | 1.29534i | −0.931439 | − | 0.363898i | \(-0.881446\pi\) |
−0.363898 | − | 0.931439i | \(-0.618554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.51390e7 | 1.46744 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.21716e6 | 0.298135 | 0.149068 | − | 0.988827i | \(-0.452373\pi\) | ||||
0.149068 | + | 0.988827i | \(0.452373\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.03016e6 | − | 3.03016e6i | −0.0965446 | − | 0.0965446i | 0.657185 | − | 0.753729i | \(-0.271747\pi\) |
−0.753729 | + | 0.657185i | \(0.771747\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 900.6.j.c.557.11 | yes | 24 | |
3.2 | odd | 2 | inner | 900.6.j.c.557.12 | yes | 24 | |
5.2 | odd | 4 | inner | 900.6.j.c.593.2 | yes | 24 | |
5.3 | odd | 4 | inner | 900.6.j.c.593.12 | yes | 24 | |
5.4 | even | 2 | inner | 900.6.j.c.557.1 | ✓ | 24 | |
15.2 | even | 4 | inner | 900.6.j.c.593.1 | yes | 24 | |
15.8 | even | 4 | inner | 900.6.j.c.593.11 | yes | 24 | |
15.14 | odd | 2 | inner | 900.6.j.c.557.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.6.j.c.557.1 | ✓ | 24 | 5.4 | even | 2 | inner | |
900.6.j.c.557.2 | yes | 24 | 15.14 | odd | 2 | inner | |
900.6.j.c.557.11 | yes | 24 | 1.1 | even | 1 | trivial | |
900.6.j.c.557.12 | yes | 24 | 3.2 | odd | 2 | inner | |
900.6.j.c.593.1 | yes | 24 | 15.2 | even | 4 | inner | |
900.6.j.c.593.2 | yes | 24 | 5.2 | odd | 4 | inner | |
900.6.j.c.593.11 | yes | 24 | 15.8 | even | 4 | inner | |
900.6.j.c.593.12 | yes | 24 | 5.3 | odd | 4 | inner |