Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,6,Mod(10,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.10");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.33036313495\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 40x^{6} + 568x^{4} + 3363x^{2} + 7056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Root | \(-3.62198i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.19 |
Dual form | 27.6.c.a.10.4 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.77467 | − | 6.53793i | 0.667275 | − | 1.15575i | −0.311389 | − | 0.950283i | \(-0.600794\pi\) |
0.978663 | − | 0.205471i | \(-0.0658725\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −12.4963 | − | 21.6443i | −0.390511 | − | 0.676384i | ||||
\(5\) | −43.7155 | − | 75.7175i | −0.782007 | − | 1.35448i | −0.930771 | − | 0.365603i | \(-0.880863\pi\) |
0.148764 | − | 0.988873i | \(-0.452471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.6033 | − | 35.6859i | 0.158925 | − | 0.275265i | −0.775557 | − | 0.631278i | \(-0.782531\pi\) |
0.934481 | + | 0.356013i | \(0.115864\pi\) | |||||||
\(8\) | 52.9007 | 0.292238 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −660.048 | −2.08725 | ||||||||
\(11\) | −3.84390 | + | 6.65783i | −0.00957834 | + | 0.0165902i | −0.870775 | − | 0.491682i | \(-0.836382\pi\) |
0.861197 | + | 0.508272i | \(0.169716\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 302.642 | + | 524.191i | 0.496673 | + | 0.860263i | 0.999993 | − | 0.00383763i | \(-0.00122156\pi\) |
−0.503320 | + | 0.864100i | \(0.667888\pi\) | |||||||
\(14\) | −155.541 | − | 269.405i | −0.212093 | − | 0.367355i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 599.566 | − | 1038.48i | 0.585514 | − | 1.01414i | ||||
\(17\) | 566.131 | 0.475111 | 0.237555 | − | 0.971374i | \(-0.423654\pi\) | ||||
0.237555 | + | 0.971374i | \(0.423654\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2060.59 | 1.30951 | 0.654755 | − | 0.755842i | \(-0.272772\pi\) | ||||
0.654755 | + | 0.755842i | \(0.272772\pi\) | |||||||
\(20\) | −1092.57 | + | 1892.38i | −0.610764 | + | 1.05787i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 29.0189 | + | 50.2623i | 0.0127828 | + | 0.0221404i | ||||
\(23\) | −137.210 | − | 237.655i | −0.0540838 | − | 0.0936759i | 0.837716 | − | 0.546106i | \(-0.183890\pi\) |
−0.891800 | + | 0.452430i | \(0.850557\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2259.59 | + | 3913.73i | −0.723070 | + | 1.25239i | ||||
\(26\) | 4569.50 | 1.32567 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1029.86 | −0.248247 | ||||||||
\(29\) | −2410.58 | + | 4175.25i | −0.532264 | + | 0.921909i | 0.467026 | + | 0.884244i | \(0.345325\pi\) |
−0.999290 | + | 0.0376653i | \(0.988008\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2230.39 | − | 3863.15i | −0.416847 | − | 0.722000i | 0.578774 | − | 0.815488i | \(-0.303531\pi\) |
−0.995620 | + | 0.0934885i | \(0.970198\pi\) | |||||||
\(32\) | −3679.92 | − | 6373.81i | −0.635278 | − | 1.10033i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2136.96 | − | 3701.32i | 0.317029 | − | 0.549111i | ||||
\(35\) | −3602.73 | −0.497121 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 242.525 | 0.0291241 | 0.0145620 | − | 0.999894i | \(-0.495365\pi\) | ||||
0.0145620 | + | 0.999894i | \(0.495365\pi\) | |||||||
\(38\) | 7778.07 | − | 13472.0i | 0.873802 | − | 1.51347i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2312.58 | − | 4005.51i | −0.228532 | − | 0.395829i | ||||
\(41\) | −1754.78 | − | 3039.37i | −0.163028 | − | 0.282373i | 0.772925 | − | 0.634497i | \(-0.218793\pi\) |
−0.935953 | + | 0.352124i | \(0.885459\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4267.58 | + | 7391.66i | −0.351974 | + | 0.609636i | −0.986595 | − | 0.163187i | \(-0.947823\pi\) |
0.634621 | + | 0.772823i | \(0.281156\pi\) | |||||||
\(44\) | 192.139 | 0.0149618 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2071.70 | −0.144355 | ||||||||
\(47\) | −8995.40 | + | 15580.5i | −0.593985 | + | 1.02881i | 0.399704 | + | 0.916644i | \(0.369113\pi\) |
−0.993689 | + | 0.112168i | \(0.964220\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7554.51 | + | 13084.8i | 0.449486 | + | 0.778533i | ||||
\(50\) | 17058.5 | + | 29546.1i | 0.964973 | + | 1.67138i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7563.83 | − | 13100.9i | 0.387912 | − | 0.671883i | ||||
\(53\) | −2025.98 | −0.0990708 | −0.0495354 | − | 0.998772i | \(-0.515774\pi\) | ||||
−0.0495354 | + | 0.998772i | \(0.515774\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 672.152 | 0.0299613 | ||||||||
\(56\) | 1089.93 | − | 1887.81i | 0.0464438 | − | 0.0804430i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 18198.3 | + | 31520.5i | 0.710333 | + | 1.23033i | ||||
\(59\) | 1009.31 | + | 1748.18i | 0.0377481 | + | 0.0653816i | 0.884282 | − | 0.466953i | \(-0.154648\pi\) |
−0.846534 | + | 0.532334i | \(0.821315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14152.6 | − | 24513.0i | 0.486981 | − | 0.843476i | −0.512907 | − | 0.858444i | \(-0.671431\pi\) |
0.999888 | + | 0.0149684i | \(0.00476476\pi\) | |||||||
\(62\) | −33676.0 | −1.11260 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −17189.8 | −0.524591 | ||||||||
\(65\) | 26460.3 | − | 45830.6i | 0.776803 | − | 1.34546i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −20947.0 | − | 36281.3i | −0.570079 | − | 0.987405i | −0.996557 | − | 0.0829074i | \(-0.973579\pi\) |
0.426479 | − | 0.904498i | \(-0.359754\pi\) | |||||||
\(68\) | −7074.57 | − | 12253.5i | −0.185536 | − | 0.321357i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −13599.1 | + | 23554.4i | −0.331716 | + | 0.574549i | ||||
\(71\) | 32656.7 | 0.768822 | 0.384411 | − | 0.923162i | \(-0.374404\pi\) | ||||
0.384411 | + | 0.923162i | \(0.374404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 32820.4 | 0.720837 | 0.360418 | − | 0.932791i | \(-0.382634\pi\) | ||||
0.360418 | + | 0.932791i | \(0.382634\pi\) | |||||||
\(74\) | 915.453 | − | 1585.61i | 0.0194337 | − | 0.0336602i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −25749.9 | − | 44600.1i | −0.511377 | − | 0.885731i | ||||
\(77\) | 158.394 | + | 274.346i | 0.00304447 | + | 0.00527317i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −44069.6 | + | 76330.8i | −0.794459 | + | 1.37604i | 0.128723 | + | 0.991681i | \(0.458912\pi\) |
−0.923182 | + | 0.384363i | \(0.874421\pi\) | |||||||
\(80\) | −104841. | −1.83150 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −26494.9 | −0.435138 | ||||||||
\(83\) | −5289.91 | + | 9162.39i | −0.0842855 | + | 0.145987i | −0.905087 | − | 0.425227i | \(-0.860194\pi\) |
0.820801 | + | 0.571214i | \(0.193527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24748.7 | − | 42866.0i | −0.371540 | − | 0.643526i | ||||
\(86\) | 32217.4 | + | 55802.2i | 0.469726 | + | 0.813590i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −203.345 | + | 352.204i | −0.00279915 | + | 0.00484828i | ||||
\(89\) | 124555. | 1.66681 | 0.833407 | − | 0.552660i | \(-0.186387\pi\) | ||||
0.833407 | + | 0.552660i | \(0.186387\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 24941.6 | 0.315734 | ||||||||
\(92\) | −3429.25 | + | 5939.64i | −0.0422406 | + | 0.0731628i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 67909.4 | + | 117623.i | 0.792702 | + | 1.37300i | ||||
\(95\) | −90080.0 | − | 156023.i | −1.02405 | − | 1.77370i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 81494.3 | − | 141152.i | 0.879423 | − | 1.52321i | 0.0274474 | − | 0.999623i | \(-0.491262\pi\) |
0.851975 | − | 0.523582i | \(-0.175405\pi\) | |||||||
\(98\) | 114063. | 1.19972 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 112947. | 1.12947 | ||||||||
\(101\) | −92925.6 | + | 160952.i | −0.906425 | + | 1.56997i | −0.0874330 | + | 0.996170i | \(0.527866\pi\) |
−0.818992 | + | 0.573804i | \(0.805467\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 24409.2 | + | 42277.9i | 0.226704 | + | 0.392663i | 0.956829 | − | 0.290650i | \(-0.0938716\pi\) |
−0.730125 | + | 0.683314i | \(0.760538\pi\) | |||||||
\(104\) | 16010.0 | + | 27730.1i | 0.145147 | + | 0.251401i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7647.42 | + | 13245.7i | −0.0661074 | + | 0.114501i | ||||
\(107\) | −131842. | −1.11325 | −0.556626 | − | 0.830763i | \(-0.687905\pi\) | ||||
−0.556626 | + | 0.830763i | \(0.687905\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −162984. | −1.31395 | −0.656976 | − | 0.753912i | \(-0.728165\pi\) | ||||
−0.656976 | + | 0.753912i | \(0.728165\pi\) | |||||||
\(110\) | 2537.16 | − | 4394.48i | 0.0199924 | − | 0.0346279i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −24706.0 | − | 42792.1i | −0.186105 | − | 0.322343i | ||||
\(113\) | 81762.9 | + | 141618.i | 0.602366 | + | 1.04333i | 0.992462 | + | 0.122554i | \(0.0391085\pi\) |
−0.390096 | + | 0.920774i | \(0.627558\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11996.4 | + | 20778.4i | −0.0845878 | + | 0.146510i | ||||
\(116\) | 120494. | 0.831419 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15239.3 | 0.100753 | ||||||||
\(119\) | 11664.2 | − | 20202.9i | 0.0755068 | − | 0.130782i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 80495.9 | + | 139423.i | 0.499817 | + | 0.865708i | ||||
\(122\) | −106843. | − | 185058.i | −0.649900 | − | 1.12566i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −55743.4 | + | 96550.4i | −0.325566 | + | 0.563897i | ||||
\(125\) | 121895. | 0.697770 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −233286. | −1.28345 | −0.641724 | − | 0.766935i | \(-0.721781\pi\) | ||||
−0.641724 | + | 0.766935i | \(0.721781\pi\) | |||||||
\(128\) | 52871.6 | − | 91576.3i | 0.285231 | − | 0.494035i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −199758. | − | 345991.i | −1.03668 | − | 1.79559i | ||||
\(131\) | −86709.6 | − | 150185.i | −0.441457 | − | 0.764626i | 0.556341 | − | 0.830954i | \(-0.312205\pi\) |
−0.997798 | + | 0.0663279i | \(0.978872\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 42455.0 | − | 73534.2i | 0.208113 | − | 0.360463i | ||||
\(134\) | −316272. | −1.52160 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 29948.8 | 0.138845 | ||||||||
\(137\) | 23981.7 | − | 41537.5i | 0.109164 | − | 0.189077i | −0.806268 | − | 0.591550i | \(-0.798516\pi\) |
0.915432 | + | 0.402473i | \(0.131849\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 95222.3 | + | 164930.i | 0.418025 | + | 0.724040i | 0.995741 | − | 0.0921980i | \(-0.0293893\pi\) |
−0.577716 | + | 0.816238i | \(0.696056\pi\) | |||||||
\(140\) | 45021.0 | + | 77978.6i | 0.194131 | + | 0.336245i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 123268. | − | 213507.i | 0.513016 | − | 0.888569i | ||||
\(143\) | −4653.30 | −0.0190292 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 421520. | 1.66494 | ||||||||
\(146\) | 123886. | − | 214577.i | 0.480996 | − | 0.833109i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3030.67 | − | 5249.28i | −0.0113733 | − | 0.0196991i | ||||
\(149\) | 24272.2 | + | 42040.6i | 0.0895660 | + | 0.155133i | 0.907328 | − | 0.420424i | \(-0.138119\pi\) |
−0.817762 | + | 0.575557i | \(0.804785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −112968. | + | 195667.i | −0.403194 | + | 0.698352i | −0.994109 | − | 0.108381i | \(-0.965433\pi\) |
0.590916 | + | 0.806733i | \(0.298767\pi\) | |||||||
\(152\) | 109007. | 0.382688 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2391.54 | 0.00812598 | ||||||||
\(155\) | −195005. | + | 337759.i | −0.651954 | + | 1.12922i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −80599.2 | − | 139602.i | −0.260965 | − | 0.452004i | 0.705534 | − | 0.708676i | \(-0.250707\pi\) |
−0.966499 | + | 0.256672i | \(0.917374\pi\) | |||||||
\(158\) | 332697. | + | 576248.i | 1.06024 | + | 1.83640i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −321739. | + | 557269.i | −0.993583 | + | 1.72094i | ||||
\(161\) | −11307.9 | −0.0343810 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −26136.5 | −0.0770510 | −0.0385255 | − | 0.999258i | \(-0.512266\pi\) | ||||
−0.0385255 | + | 0.999258i | \(0.512266\pi\) | |||||||
\(164\) | −43856.6 | + | 75961.9i | −0.127328 | + | 0.220539i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 39935.4 | + | 69170.1i | 0.112483 | + | 0.194827i | ||||
\(167\) | 63474.6 | + | 109941.i | 0.176120 | + | 0.305049i | 0.940548 | − | 0.339660i | \(-0.110312\pi\) |
−0.764428 | + | 0.644709i | \(0.776979\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2462.49 | − | 4265.15i | 0.00663219 | − | 0.0114873i | ||||
\(170\) | −373674. | −0.991676 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 213316. | 0.549798 | ||||||||
\(173\) | 265893. | − | 460540.i | 0.675447 | − | 1.16991i | −0.300891 | − | 0.953659i | \(-0.597284\pi\) |
0.976338 | − | 0.216250i | \(-0.0693826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 93110.1 | + | 161271.i | 0.229827 | + | 0.398073i | ||||
\(176\) | 4609.34 | + | 7983.61i | 0.0112165 | + | 0.0194275i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 470156. | − | 814333.i | 1.11222 | − | 1.92643i | ||||
\(179\) | −365415. | −0.852421 | −0.426211 | − | 0.904624i | \(-0.640152\pi\) | ||||
−0.426211 | + | 0.904624i | \(0.640152\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 437560. | 0.992752 | 0.496376 | − | 0.868108i | \(-0.334664\pi\) | ||||
0.496376 | + | 0.868108i | \(0.334664\pi\) | |||||||
\(182\) | 94146.6 | − | 163067.i | 0.210681 | − | 0.364911i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7258.53 | − | 12572.1i | −0.0158053 | − | 0.0273757i | ||||
\(185\) | −10602.1 | − | 18363.4i | −0.0227752 | − | 0.0394478i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2176.15 | + | 3769.20i | −0.00455077 | + | 0.00788216i | ||||
\(188\) | 449638. | 0.927830 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.36009e6 | −2.73328 | ||||||||
\(191\) | 76457.7 | − | 132429.i | 0.151648 | − | 0.262663i | −0.780185 | − | 0.625549i | \(-0.784875\pi\) |
0.931834 | + | 0.362886i | \(0.118209\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −194153. | − | 336283.i | −0.375190 | − | 0.649848i | 0.615166 | − | 0.788398i | \(-0.289089\pi\) |
−0.990355 | + | 0.138550i | \(0.955756\pi\) | |||||||
\(194\) | −615229. | − | 1.06561e6i | −1.17363 | − | 2.03279i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 188807. | − | 327024.i | 0.351058 | − | 0.608050i | ||||
\(197\) | −116484. | −0.213845 | −0.106923 | − | 0.994267i | \(-0.534100\pi\) | ||||
−0.106923 | + | 0.994267i | \(0.534100\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −904935. | −1.61989 | −0.809943 | − | 0.586508i | \(-0.800502\pi\) | ||||
−0.809943 | + | 0.586508i | \(0.800502\pi\) | |||||||
\(200\) | −119534. | + | 207039.i | −0.211309 | + | 0.365997i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 701528. | + | 1.21508e6i | 1.20967 | + | 2.09521i | ||||
\(203\) | 99331.8 | + | 172048.i | 0.169180 | + | 0.293028i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −153422. | + | 265735.i | −0.254978 | + | 0.441636i | ||||
\(206\) | 368547. | 0.605096 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 725815. | 1.16323 | ||||||||
\(209\) | −7920.71 | + | 13719.1i | −0.0125429 | + | 0.0217250i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −592009. | − | 1.02539e6i | −0.915424 | − | 1.58556i | −0.806279 | − | 0.591535i | \(-0.798522\pi\) |
−0.109145 | − | 0.994026i | \(-0.534811\pi\) | |||||||
\(212\) | 25317.3 | + | 43850.9i | 0.0386882 | + | 0.0670099i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −497660. | + | 861973.i | −0.742845 | + | 1.28665i | ||||
\(215\) | 746238. | 1.10098 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −183813. | −0.264989 | ||||||||
\(218\) | −615212. | + | 1.06558e6i | −0.876766 | + | 1.51860i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8399.44 | − | 14548.3i | −0.0117002 | − | 0.0202654i | ||||
\(221\) | 171335. | + | 296761.i | 0.235975 | + | 0.408720i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 407368. | − | 705583.i | 0.548561 | − | 0.950136i | −0.449812 | − | 0.893123i | \(-0.648509\pi\) |
0.998373 | − | 0.0570127i | \(-0.0181576\pi\) | |||||||
\(224\) | −303274. | −0.403845 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.23451e6 | 1.60777 | ||||||||
\(227\) | −187705. | + | 325115.i | −0.241775 | + | 0.418767i | −0.961220 | − | 0.275783i | \(-0.911063\pi\) |
0.719445 | + | 0.694550i | \(0.244396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −62886.2 | − | 108922.i | −0.0792441 | − | 0.137255i | 0.823680 | − | 0.567055i | \(-0.191917\pi\) |
−0.902924 | + | 0.429800i | \(0.858584\pi\) | |||||||
\(230\) | 90565.3 | + | 156864.i | 0.112887 | + | 0.195525i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −127522. | + | 220874.i | −0.155548 | + | 0.269417i | ||||
\(233\) | −423564. | −0.511128 | −0.255564 | − | 0.966792i | \(-0.582261\pi\) | ||||
−0.255564 | + | 0.966792i | \(0.582261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.57295e6 | 1.85800 | ||||||||
\(236\) | 25225.4 | − | 43691.7i | 0.0294821 | − | 0.0510644i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −88056.8 | − | 152519.i | −0.100767 | − | 0.174534i | ||||
\(239\) | −611920. | − | 1.05988e6i | −0.692947 | − | 1.20022i | −0.970868 | − | 0.239616i | \(-0.922979\pi\) |
0.277921 | − | 0.960604i | \(-0.410355\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −379300. | + | 656966.i | −0.420668 | + | 0.728619i | −0.996005 | − | 0.0892979i | \(-0.971538\pi\) |
0.575337 | + | 0.817917i | \(0.304871\pi\) | |||||||
\(242\) | 1.21538e6 | 1.33406 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −707423. | −0.760685 | ||||||||
\(245\) | 660499. | − | 1.14402e6i | 0.703002 | − | 1.21764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 623622. | + | 1.08014e6i | 0.650398 | + | 1.12652i | ||||
\(248\) | −117989. | − | 204363.i | −0.121818 | − | 0.210996i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 460116. | − | 796944.i | 0.465604 | − | 0.806450i | ||||
\(251\) | 510893. | 0.511854 | 0.255927 | − | 0.966696i | \(-0.417619\pi\) | ||||
0.255927 | + | 0.966696i | \(0.417619\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2109.69 | 0.00207213 | ||||||||
\(254\) | −880577. | + | 1.52520e6i | −0.856412 | + | 1.48335i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −674183. | − | 1.16772e6i | −0.642951 | − | 1.11362i | ||||
\(257\) | 919950. | + | 1.59340e6i | 0.868823 | + | 1.50485i | 0.863200 | + | 0.504862i | \(0.168457\pi\) |
0.00562328 | + | 0.999984i | \(0.498210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4996.81 | − | 8654.72i | 0.00462853 | − | 0.00801685i | ||||
\(260\) | −1.32263e6 | −1.21340 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.30920e6 | −1.17829 | ||||||||
\(263\) | 408180. | − | 706988.i | 0.363883 | − | 0.630264i | −0.624713 | − | 0.780854i | \(-0.714784\pi\) |
0.988596 | + | 0.150590i | \(0.0481174\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 88566.8 | + | 153402.i | 0.0774740 | + | 0.134189i | ||||
\(266\) | −320508. | − | 555135.i | −0.277737 | − | 0.481055i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −523521. | + | 906766.i | −0.445243 | + | 0.771184i | ||||
\(269\) | −1.25381e6 | −1.05646 | −0.528228 | − | 0.849103i | \(-0.677143\pi\) | ||||
−0.528228 | + | 0.849103i | \(0.677143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −347295. | −0.287260 | −0.143630 | − | 0.989631i | \(-0.545878\pi\) | ||||
−0.143630 | + | 0.989631i | \(0.545878\pi\) | |||||||
\(272\) | 339433. | − | 587915.i | 0.278184 | − | 0.481828i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −181046. | − | 313581.i | −0.145684 | − | 0.252333i | ||||
\(275\) | −17371.3 | − | 30088.0i | −0.0138516 | − | 0.0239917i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 141233. | − | 244622.i | 0.110595 | − | 0.191556i | −0.805415 | − | 0.592711i | \(-0.798058\pi\) |
0.916010 | + | 0.401155i | \(0.131391\pi\) | |||||||
\(278\) | 1.43773e6 | 1.11575 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −190587. | −0.145278 | ||||||||
\(281\) | −614335. | + | 1.06406e6i | −0.464130 | + | 0.803897i | −0.999162 | − | 0.0409352i | \(-0.986966\pi\) |
0.535032 | + | 0.844832i | \(0.320300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 223824. | + | 387674.i | 0.166127 | + | 0.287741i | 0.937055 | − | 0.349182i | \(-0.113540\pi\) |
−0.770928 | + | 0.636922i | \(0.780207\pi\) | |||||||
\(284\) | −408089. | − | 706830.i | −0.300233 | − | 0.520019i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17564.7 | + | 30422.9i | −0.0126977 | + | 0.0219931i | ||||
\(287\) | −144617. | −0.103637 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.09935e6 | −0.774270 | ||||||||
\(290\) | 1.59110e6 | − | 2.75587e6i | 1.11097 | − | 1.92426i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −410135. | − | 710375.i | −0.281494 | − | 0.487562i | ||||
\(293\) | −699361. | − | 1.21133e6i | −0.475918 | − | 0.824314i | 0.523701 | − | 0.851902i | \(-0.324551\pi\) |
−0.999619 | + | 0.0275878i | \(0.991217\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 88245.1 | − | 152845.i | 0.0590386 | − | 0.102258i | ||||
\(296\) | 12829.7 | 0.00851116 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 366478. | 0.239060 | ||||||||
\(299\) | 83051.1 | − | 143849.i | 0.0537239 | − | 0.0930525i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 175852. | + | 304585.i | 0.111875 | + | 0.193772i | ||||
\(302\) | 852836. | + | 1.47716e6i | 0.538082 | + | 0.931985i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.23546e6 | − | 2.13988e6i | 0.766735 | − | 1.32802i | ||||
\(305\) | −2.47476e6 | −1.52329 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 614731. | 0.372254 | 0.186127 | − | 0.982526i | \(-0.440406\pi\) | ||||
0.186127 | + | 0.982526i | \(0.440406\pi\) | |||||||
\(308\) | 3958.68 | − | 6856.64i | 0.00237779 | − | 0.00411846i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.47216e6 | + | 2.54986e6i | 0.870065 | + | 1.50700i | ||||
\(311\) | 1.48208e6 | + | 2.56704e6i | 0.868903 | + | 1.50498i | 0.863119 | + | 0.505001i | \(0.168508\pi\) |
0.00578452 | + | 0.999983i | \(0.498159\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 414425. | − | 717806.i | 0.239103 | − | 0.414139i | −0.721354 | − | 0.692567i | \(-0.756480\pi\) |
0.960457 | + | 0.278428i | \(0.0898132\pi\) | |||||||
\(314\) | −1.21694e6 | −0.696540 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.20283e6 | 1.24098 | ||||||||
\(317\) | 165751. | − | 287090.i | 0.0926423 | − | 0.160461i | −0.815980 | − | 0.578080i | \(-0.803802\pi\) |
0.908622 | + | 0.417619i | \(0.137135\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18532.1 | − | 32098.5i | −0.0101964 | − | 0.0176607i | ||||
\(320\) | 751461. | + | 1.30157e6i | 0.410234 | + | 0.710546i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −42683.7 | + | 73930.4i | −0.0229415 | + | 0.0397359i | ||||
\(323\) | 1.16657e6 | 0.622162 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.73539e6 | −1.43652 | ||||||||
\(326\) | −98656.8 | + | 170879.i | −0.0514142 | + | 0.0890520i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −92829.1 | − | 160785.i | −0.0476430 | − | 0.0825202i | ||||
\(329\) | 370669. | + | 642018.i | 0.188798 | + | 0.327007i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.29421e6 | + | 2.24164e6i | −0.649284 | + | 1.12459i | 0.334010 | + | 0.942570i | \(0.391598\pi\) |
−0.983294 | + | 0.182024i | \(0.941735\pi\) | |||||||
\(332\) | 264418. | 0.131658 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 958384. | 0.470082 | ||||||||
\(335\) | −1.83142e6 | + | 3.17211e6i | −0.891611 | + | 1.54432i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 880045. | + | 1.52428e6i | 0.422114 | + | 0.731124i | 0.996146 | − | 0.0877095i | \(-0.0279547\pi\) |
−0.574032 | + | 0.818833i | \(0.694621\pi\) | |||||||
\(338\) | −18590.2 | − | 32199.1i | −0.00885099 | − | 0.0153304i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −618537. | + | 1.07134e6i | −0.290181 | + | 0.502607i | ||||
\(341\) | 34293.6 | 0.0159708 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.31515e6 | 0.603587 | ||||||||
\(344\) | −225758. | + | 391024.i | −0.102860 | + | 0.178159i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.00732e6 | − | 3.47678e6i | −0.901417 | − | 1.56130i | ||||
\(347\) | −782422. | − | 1.35520e6i | −0.348833 | − | 0.604197i | 0.637209 | − | 0.770691i | \(-0.280089\pi\) |
−0.986042 | + | 0.166494i | \(0.946755\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −360712. | + | 624772.i | −0.158525 | + | 0.274573i | −0.934337 | − | 0.356391i | \(-0.884007\pi\) |
0.775812 | + | 0.630964i | \(0.217340\pi\) | |||||||
\(350\) | 1.40584e6 | 0.613432 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 56581.0 | 0.0243396 | ||||||||
\(353\) | 880430. | − | 1.52495e6i | 0.376061 | − | 0.651356i | −0.614424 | − | 0.788976i | \(-0.710612\pi\) |
0.990485 | + | 0.137619i | \(0.0439450\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.42760e6 | − | 2.47268e6i | −0.601225 | − | 1.04135i | ||||
\(356\) | −1.55648e6 | − | 2.69591e6i | −0.650908 | − | 1.12741i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.37932e6 | + | 2.38906e6i | −0.568799 | + | 0.985189i | ||||
\(359\) | 2.43938e6 | 0.998947 | 0.499474 | − | 0.866329i | \(-0.333527\pi\) | ||||
0.499474 | + | 0.866329i | \(0.333527\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.76995e6 | 0.714814 | ||||||||
\(362\) | 1.65165e6 | − | 2.86073e6i | 0.662438 | − | 1.14738i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −311679. | − | 539844.i | −0.123297 | − | 0.213558i | ||||
\(365\) | −1.43476e6 | − | 2.48508e6i | −0.563699 | − | 0.976356i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.27310e6 | − | 3.93713e6i | 0.880956 | − | 1.52586i | 0.0306760 | − | 0.999529i | \(-0.490234\pi\) |
0.850280 | − | 0.526331i | \(-0.176433\pi\) | |||||||
\(368\) | −329066. | −0.126667 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −160078. | −0.0607893 | ||||||||
\(371\) | −41741.8 | + | 72299.0i | −0.0157448 | + | 0.0272708i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 166277. | + | 288000.i | 0.0618814 | + | 0.107182i | 0.895306 | − | 0.445451i | \(-0.146957\pi\) |
−0.833425 | + | 0.552633i | \(0.813623\pi\) | |||||||
\(374\) | 16428.5 | + | 28455.0i | 0.00607323 | + | 0.0105191i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −475863. | + | 824219.i | −0.173585 | + | 0.300658i | ||||
\(377\) | −2.91817e6 | −1.05744 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 911738. | 0.326041 | 0.163021 | − | 0.986623i | \(-0.447876\pi\) | ||||
0.163021 | + | 0.986623i | \(0.447876\pi\) | |||||||
\(380\) | −2.25134e6 | + | 3.89943e6i | −0.799801 | + | 1.38530i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −577206. | − | 999750.i | −0.202382 | − | 0.350536i | ||||
\(383\) | −1.82779e6 | − | 3.16582e6i | −0.636690 | − | 1.10278i | −0.986154 | − | 0.165830i | \(-0.946970\pi\) |
0.349464 | − | 0.936950i | \(-0.386364\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13848.5 | − | 23986.4i | 0.00476159 | − | 0.00824731i | ||||
\(386\) | −2.93146e6 | −1.00142 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.07352e6 | −1.37370 | ||||||||
\(389\) | 1.41448e6 | − | 2.44995e6i | 0.473939 | − | 0.820886i | −0.525616 | − | 0.850722i | \(-0.676165\pi\) |
0.999555 | + | 0.0298360i | \(0.00949849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −77679.0 | − | 134544.i | −0.0256958 | − | 0.0445064i | ||||
\(392\) | 399639. | + | 692195.i | 0.131357 | + | 0.227517i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −439688. | + | 761563.i | −0.142694 | + | 0.247153i | ||||
\(395\) | 7.70610e6 | 2.48509 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.06659e6 | −1.61339 | −0.806695 | − | 0.590968i | \(-0.798746\pi\) | ||||
−0.806695 | + | 0.590968i | \(0.798746\pi\) | |||||||
\(398\) | −3.41584e6 | + | 5.91640e6i | −1.08091 | + | 1.87219i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.70955e6 | + | 4.69308e6i | 0.846735 | + | 1.46659i | ||||
\(401\) | 1.81834e6 | + | 3.14946e6i | 0.564695 | + | 0.978081i | 0.997078 | + | 0.0763908i | \(0.0243397\pi\) |
−0.432383 | + | 0.901690i | \(0.642327\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.35002e6 | − | 2.33830e6i | 0.414073 | − | 0.717195i | ||||
\(404\) | 4.64492e6 | 1.41587 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.49978e6 | 0.451557 | ||||||||
\(407\) | −932.241 | + | 1614.69i | −0.000278960 | + | 0.000483173i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.44052e6 | + | 4.22711e6i | 0.721397 | + | 1.24950i | 0.960440 | + | 0.278487i | \(0.0898329\pi\) |
−0.239043 | + | 0.971009i | \(0.576834\pi\) | |||||||
\(410\) | 1.15824e6 | + | 2.00613e6i | 0.340281 | + | 0.589384i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 610050. | − | 1.05664e6i | 0.177061 | − | 0.306678i | ||||
\(413\) | 83180.4 | 0.0239964 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 925005. | 0.263648 | ||||||||
\(416\) | 2.22739e6 | − | 3.85796e6i | 0.631050 | − | 1.09301i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 59796.2 | + | 103570.i | 0.0167391 | + | 0.0289930i | ||||
\(419\) | −390244. | − | 675923.i | −0.108593 | − | 0.188088i | 0.806608 | − | 0.591087i | \(-0.201301\pi\) |
−0.915200 | + | 0.402999i | \(0.867968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.38356e6 | + | 2.39639e6i | −0.380446 | + | 0.658951i | −0.991126 | − | 0.132926i | \(-0.957563\pi\) |
0.610680 | + | 0.791877i | \(0.290896\pi\) | |||||||
\(422\) | −8.93857e6 | −2.44336 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −107176. | −0.0289523 | ||||||||
\(425\) | −1.27923e6 | + | 2.21569e6i | −0.343538 | + | 0.595026i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −583180. | − | 1.01010e6i | −0.154787 | − | 0.268098i | ||||
\(428\) | 1.64754e6 | + | 2.85362e6i | 0.434737 | + | 0.752987i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.81680e6 | − | 4.87885e6i | 0.734659 | − | 1.27247i | ||||
\(431\) | −893280. | −0.231630 | −0.115815 | − | 0.993271i | \(-0.536948\pi\) | ||||
−0.115815 | + | 0.993271i | \(0.536948\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.84897e6 | 1.24288 | 0.621441 | − | 0.783461i | \(-0.286548\pi\) | ||||
0.621441 | + | 0.783461i | \(0.286548\pi\) | |||||||
\(434\) | −693835. | + | 1.20176e6i | −0.176820 | + | 0.306262i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.03671e6 | + | 3.52768e6i | 0.513112 | + | 0.888736i | ||||
\(437\) | −282735. | − | 489711.i | −0.0708232 | − | 0.122669i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 116736. | − | 202192.i | 0.0289096 | − | 0.0500729i | −0.851209 | − | 0.524827i | \(-0.824130\pi\) |
0.880118 | + | 0.474755i | \(0.157463\pi\) | |||||||
\(440\) | 35557.3 | 0.00875584 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.58693e6 | 0.629839 | ||||||||
\(443\) | −1.30744e6 | + | 2.26456e6i | −0.316529 | + | 0.548244i | −0.979761 | − | 0.200170i | \(-0.935851\pi\) |
0.663233 | + | 0.748413i | \(0.269184\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.44500e6 | − | 9.43101e6i | −1.30346 | − | 2.25766i | ||||
\(446\) | −3.07537e6 | − | 5.32669e6i | −0.732082 | − | 1.26800i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −354166. | + | 613433.i | −0.0833704 | + | 0.144402i | ||||
\(449\) | 8.32454e6 | 1.94870 | 0.974349 | − | 0.225044i | \(-0.0722526\pi\) | ||||
0.974349 | + | 0.225044i | \(0.0722526\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26980.8 | 0.00624616 | ||||||||
\(452\) | 2.04347e6 | − | 3.53940e6i | 0.470460 | − | 0.814861i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.41705e6 | + | 2.45441e6i | 0.322661 | + | 0.558865i | ||||
\(455\) | −1.09034e6 | − | 1.88852e6i | −0.246906 | − | 0.427654i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −398114. | + | 689554.i | −0.0891697 | + | 0.154446i | −0.907160 | − | 0.420785i | \(-0.861755\pi\) |
0.817991 | + | 0.575231i | \(0.195088\pi\) | |||||||
\(458\) | −949500. | −0.211510 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 599646. | 0.132130 | ||||||||
\(461\) | 700324. | − | 1.21300e6i | 0.153478 | − | 0.265832i | −0.779026 | − | 0.626992i | \(-0.784286\pi\) |
0.932504 | + | 0.361160i | \(0.117619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −574265. | − | 994656.i | −0.124497 | − | 0.215635i | 0.797039 | − | 0.603928i | \(-0.206398\pi\) |
−0.921536 | + | 0.388292i | \(0.873065\pi\) | |||||||
\(464\) | 2.89061e6 | + | 5.00668e6i | 0.623296 | + | 1.07958i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.59882e6 | + | 2.76923e6i | −0.341063 | + | 0.590738i | ||||
\(467\) | −5.64483e6 | −1.19773 | −0.598865 | − | 0.800850i | \(-0.704381\pi\) | ||||
−0.598865 | + | 0.800850i | \(0.704381\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.72631e6 | −0.362398 | ||||||||
\(470\) | 5.93739e6 | − | 1.02839e7i | 1.23980 | − | 2.14739i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 53393.3 | + | 92479.9i | 0.0110314 | + | 0.0191070i | ||||
\(473\) | −32808.3 | − | 56825.6i | −0.00674265 | − | 0.0116786i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.65611e6 | + | 8.06462e6i | −0.946867 | + | 1.64002i | ||||
\(476\) | −583037. | −0.117945 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.23920e6 | −1.84954 | ||||||||
\(479\) | −2.85304e6 | + | 4.94162e6i | −0.568159 | + | 0.984080i | 0.428589 | + | 0.903499i | \(0.359011\pi\) |
−0.996748 | + | 0.0805805i | \(0.974323\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 73398.1 | + | 127129.i | 0.0144651 | + | 0.0250543i | ||||
\(482\) | 2.86346e6 | + | 4.95967e6i | 0.561402 | + | 0.972377i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.01181e6 | − | 3.48456e6i | 0.390367 | − | 0.676136i | ||||
\(485\) | −1.42503e7 | −2.75086 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.78768e6 | −0.532624 | −0.266312 | − | 0.963887i | \(-0.585805\pi\) | ||||
−0.266312 | + | 0.963887i | \(0.585805\pi\) | |||||||
\(488\) | 748684. | − | 1.29676e6i | 0.142314 | − | 0.246496i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.98634e6 | − | 8.63659e6i | −0.938191 | − | 1.62499i | ||||
\(491\) | 479847. | + | 831119.i | 0.0898253 | + | 0.155582i | 0.907437 | − | 0.420188i | \(-0.138036\pi\) |
−0.817612 | + | 0.575770i | \(0.804702\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.36471e6 | + | 2.36374e6i | −0.252884 | + | 0.438009i | ||||
\(494\) | 9.41588e6 | 1.73597 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.34906e6 | −0.976278 | ||||||||
\(497\) | 672834. | − | 1.16538e6i | 0.122185 | − | 0.211630i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.13098e6 | + | 1.95891e6i | 0.203331 | + | 0.352179i | 0.949600 | − | 0.313466i | \(-0.101490\pi\) |
−0.746269 | + | 0.665645i | \(0.768157\pi\) | |||||||
\(500\) | −1.52325e6 | − | 2.63834e6i | −0.272487 | − | 0.471961i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.92846e6 | − | 3.34018e6i | 0.341547 | − | 0.591577i | ||||
\(503\) | 997842. | 0.175850 | 0.0879249 | − | 0.996127i | \(-0.471976\pi\) | ||||
0.0879249 | + | 0.996127i | \(0.471976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.62492e7 | 2.83532 | ||||||||
\(506\) | 7963.39 | − | 13793.0i | 0.00138268 | − | 0.00239487i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.91521e6 | + | 5.04930e6i | 0.501200 | + | 0.868104i | ||||
\(509\) | 1.03760e6 | + | 1.79718e6i | 0.177516 | + | 0.307466i | 0.941029 | − | 0.338326i | \(-0.109861\pi\) |
−0.763513 | + | 0.645792i | \(0.776527\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 676208. | − | 1.17123e6i | 0.114559 | − | 0.198421i | ||||
\(512\) | −6.79550e6 | −1.14564 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.38901e7 | 2.31897 | ||||||||
\(515\) | 2.13412e6 | − | 3.69640e6i | 0.354569 | − | 0.614131i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −69154.8 | − | 119780.i | −0.0113788 | − | 0.0197086i | ||||
\(518\) | −37722.6 | − | 65337.5i | −0.00617700 | − | 0.0106989i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.39977e6 | − | 2.42447e6i | 0.227012 | − | 0.393196i | ||||
\(521\) | 4.77686e6 | 0.770989 | 0.385494 | − | 0.922710i | \(-0.374031\pi\) | ||||
0.385494 | + | 0.922710i | \(0.374031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.14547e6 | −1.14229 | −0.571146 | − | 0.820849i | \(-0.693501\pi\) | ||||
−0.571146 | + | 0.820849i | \(0.693501\pi\) | |||||||
\(524\) | −2.16710e6 | + | 3.75353e6i | −0.344787 | + | 0.597189i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.08149e6 | − | 5.33730e6i | −0.485620 | − | 0.841119i | ||||
\(527\) | −1.26269e6 | − | 2.18705e6i | −0.198048 | − | 0.343030i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.18052e6 | − | 5.50882e6i | 0.494150 | − | 0.855893i | ||||
\(530\) | 1.33724e6 | 0.206786 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.12213e6 | −0.325082 | ||||||||
\(533\) | 1.06214e6 | − | 1.83968e6i | 0.161943 | − | 0.280494i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.76354e6 | + | 9.98274e6i | 0.870572 | + | 1.50787i | ||||
\(536\) | −1.10811e6 | − | 1.91931e6i | −0.166599 | − | 0.288557i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.73273e6 | + | 8.19732e6i | −0.704946 | + | 1.22100i | ||||
\(539\) | −116155. | −0.0172213 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.23232e6 | −0.327917 | −0.163958 | − | 0.986467i | \(-0.552426\pi\) | ||||
−0.163958 | + | 0.986467i | \(0.552426\pi\) | |||||||
\(542\) | −1.31093e6 | + | 2.27059e6i | −0.191681 | + | 0.332002i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.08332e6 | − | 3.60841e6i | −0.301827 | − | 0.522780i | ||||
\(545\) | 7.12494e6 | + | 1.23408e7i | 1.02752 | + | 1.77972i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.49201e6 | + | 4.31630e6i | −0.356108 | + | 0.616798i | −0.987307 | − | 0.158823i | \(-0.949230\pi\) |
0.631199 | + | 0.775621i | \(0.282563\pi\) | |||||||
\(548\) | −1.19873e6 | −0.170518 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −262284. | −0.0369713 | ||||||||
\(551\) | −4.96724e6 | + | 8.60351e6i | −0.697005 | + | 1.20725i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.81596e6 | + | 3.14533e6i | 0.252518 | + | 0.437374i | ||||
\(554\) | −1.06622e6 | − | 1.84674e6i | −0.147595 | − | 0.255641i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.37986e6 | − | 4.12204e6i | 0.326486 | − | 0.565490i | ||||
\(557\) | 9.32179e6 | 1.27310 | 0.636548 | − | 0.771237i | \(-0.280362\pi\) | ||||
0.636548 | + | 0.771237i | \(0.280362\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.16619e6 | −0.699263 | ||||||||
\(560\) | −2.16008e6 | + | 3.74136e6i | −0.291071 | + | 0.504150i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.63783e6 | + | 8.03296e6i | 0.619404 | + | 1.07284i | ||||
\(563\) | −6.18276e6 | − | 1.07088e7i | −0.822074 | − | 1.42387i | −0.904135 | − | 0.427247i | \(-0.859483\pi\) |
0.0820605 | − | 0.996627i | \(-0.473850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.14862e6 | − | 1.23818e7i | 0.942109 | − | 1.63178i | ||||
\(566\) | 3.37945e6 | 0.443409 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.72756e6 | 0.224679 | ||||||||
\(569\) | −1.15181e6 | + | 1.99499e6i | −0.149141 | + | 0.258321i | −0.930910 | − | 0.365248i | \(-0.880984\pi\) |
0.781769 | + | 0.623568i | \(0.214318\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.92568e6 | + | 1.02636e7i | 0.760585 | + | 1.31737i | 0.942549 | + | 0.334067i | \(0.108421\pi\) |
−0.181964 | + | 0.983305i | \(0.558245\pi\) | |||||||
\(572\) | 58149.1 | + | 100717.i | 0.00743110 | + | 0.0128710i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −545881. | + | 945494.i | −0.0691542 | + | 0.119779i | ||||
\(575\) | 1.24016e6 | 0.156426 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.25199e6 | −0.906813 | −0.453407 | − | 0.891304i | \(-0.649791\pi\) | ||||
−0.453407 | + | 0.891304i | \(0.649791\pi\) | |||||||
\(578\) | −4.14970e6 | + | 7.18749e6i | −0.516651 | + | 0.894865i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.26745e6 | − | 9.12350e6i | −0.650176 | − | 1.12614i | ||||
\(581\) | 217979. | + | 377551.i | 0.0267901 | + | 0.0464018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7787.66 | − | 13488.6i | 0.000948933 | − | 0.00164360i | ||||
\(584\) | 1.73622e6 | 0.210656 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.05594e7 | −1.27027 | ||||||||
\(587\) | 3.72719e6 | − | 6.45569e6i | 0.446464 | − | 0.773299i | −0.551689 | − | 0.834050i | \(-0.686016\pi\) |
0.998153 | + | 0.0607515i | \(0.0193497\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.59593e6 | − | 7.96038e6i | −0.545865 | − | 0.945465i | ||||
\(590\) | −666193. | − | 1.15388e6i | −0.0787899 | − | 0.136468i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 145410. | − | 251857.i | 0.0170525 | − | 0.0295359i | ||||
\(593\) | −3.98887e6 | −0.465815 | −0.232908 | − | 0.972499i | \(-0.574824\pi\) | ||||
−0.232908 | + | 0.972499i | \(0.574824\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.03962e6 | −0.236187 | ||||||||
\(596\) | 606627. | − | 1.05071e6i | 0.0699529 | − | 0.121162i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −626982. | − | 1.08596e6i | −0.0716972 | − | 0.124183i | ||||
\(599\) | −6.35985e6 | − | 1.10156e7i | −0.724236 | − | 1.25441i | −0.959288 | − | 0.282430i | \(-0.908860\pi\) |
0.235052 | − | 0.971983i | \(-0.424474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.55315e6 | + | 2.69013e6i | −0.175399 | + | 0.303800i | −0.940299 | − | 0.340349i | \(-0.889455\pi\) |
0.764900 | + | 0.644149i | \(0.222788\pi\) | |||||||
\(602\) | 2.65514e6 | 0.298604 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.64675e6 | 0.629806 | ||||||||
\(605\) | 7.03785e6 | − | 1.21899e7i | 0.781720 | − | 1.35398i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.20584e6 | − | 1.07488e7i | −0.683642 | − | 1.18410i | −0.973861 | − | 0.227143i | \(-0.927062\pi\) |
0.290219 | − | 0.956960i | \(-0.406272\pi\) | |||||||
\(608\) | −7.58282e6 | − | 1.31338e7i | −0.831902 | − | 1.44090i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.34140e6 | + | 1.61798e7i | −1.01645 | + | 1.76055i | ||||
\(611\) | −1.08895e7 | −1.18007 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.25539e6 | 0.242421 | 0.121211 | − | 0.992627i | \(-0.461322\pi\) | ||||
0.121211 | + | 0.992627i | \(0.461322\pi\) | |||||||
\(614\) | 2.32041e6 | − | 4.01906e6i | 0.248395 | − | 0.430233i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8379.15 | + | 14513.1i | 0.000889709 | + | 0.00154102i | ||||
\(617\) | 3.60754e6 | + | 6.24844e6i | 0.381503 | + | 0.660782i | 0.991277 | − | 0.131793i | \(-0.0420733\pi\) |
−0.609774 | + | 0.792575i | \(0.708740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.36680e6 | − | 1.10276e7i | 0.667874 | − | 1.15679i | −0.310623 | − | 0.950533i | \(-0.600538\pi\) |
0.978497 | − | 0.206259i | \(-0.0661290\pi\) | |||||||
\(620\) | 9.74741e6 | 1.01838 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.23775e7 | 2.31919 | ||||||||
\(623\) | 2.56625e6 | − | 4.44487e6i | 0.264898 | − | 0.458816i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.73251e6 | + | 3.00079e6i | 0.177409 | + | 0.307281i | ||||
\(626\) | −3.12864e6 | − | 5.41897e6i | −0.319095 | − | 0.552689i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.01439e6 | + | 3.48903e6i | −0.203819 | + | 0.353025i | ||||
\(629\) | 137301. | 0.0138372 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.72216e6 | 0.472136 | 0.236068 | − | 0.971737i | \(-0.424141\pi\) | ||||
0.236068 | + | 0.971737i | \(0.424141\pi\) | |||||||
\(632\) | −2.33131e6 | + | 4.03796e6i | −0.232171 | + | 0.402132i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.25132e6 | − | 2.16734e6i | −0.123636 | − | 0.214143i | ||||
\(635\) | 1.01982e7 | + | 1.76638e7i | 1.00367 | + | 1.73840i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.57262e6 | + | 7.92001e6i | −0.446495 | + | 0.773352i | ||||
\(638\) | −279810. | −0.0272152 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.24524e6 | −0.892212 | ||||||||
\(641\) | −7.33397e6 | + | 1.27028e7i | −0.705008 | + | 1.22111i | 0.261680 | + | 0.965155i | \(0.415723\pi\) |
−0.966689 | + | 0.255956i | \(0.917610\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.46256e6 | − | 1.11935e7i | −0.616420 | − | 1.06767i | −0.990134 | − | 0.140127i | \(-0.955249\pi\) |
0.373713 | − | 0.927544i | \(-0.378084\pi\) | |||||||
\(644\) | 141308. | + | 244752.i | 0.0134261 | + | 0.0232547i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.40341e6 | − | 7.62693e6i | 0.415153 | − | 0.719065i | ||||
\(647\) | 6.80424e6 | 0.639027 | 0.319513 | − | 0.947582i | \(-0.396481\pi\) | ||||
0.319513 | + | 0.947582i | \(0.396481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15518.8 | −0.00144626 | ||||||||
\(650\) | −1.03252e7 | + | 1.78838e7i | −0.958552 | + | 1.66026i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 326610. | + | 565706.i | 0.0300892 | + | 0.0521161i | ||||
\(653\) | −844518. | − | 1.46275e6i | −0.0775043 | − | 0.134241i | 0.824668 | − | 0.565617i | \(-0.191362\pi\) |
−0.902173 | + | 0.431375i | \(0.858028\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.58111e6 | + | 1.31309e7i | −0.690446 | + | 1.19589i | ||||
\(656\) | −4.20842e6 | −0.381821 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.59662e6 | 0.503920 | ||||||||
\(659\) | −3.67278e6 | + | 6.36143e6i | −0.329443 | + | 0.570613i | −0.982402 | − | 0.186781i | \(-0.940194\pi\) |
0.652958 | + | 0.757394i | \(0.273528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.43977e6 | + | 7.68990e6i | 0.395236 | + | 0.684569i | 0.993131 | − | 0.117005i | \(-0.0373294\pi\) |
−0.597895 | + | 0.801574i | \(0.703996\pi\) | |||||||
\(662\) | 9.77045e6 | + | 1.69229e7i | 0.866502 | + | 1.50082i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −279840. | + | 484697.i | −0.0246314 | + | 0.0426629i | ||||
\(665\) | −7.42377e6 | −0.650984 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.32303e6 | 0.115147 | ||||||||
\(668\) | 1.58640e6 | − | 2.74773e6i | 0.137553 | − | 0.238250i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.38260e7 | + | 2.39474e7i | 1.18990 | + | 2.06096i | ||||
\(671\) | 108802. | + | 188451.i | 0.00932894 | + | 0.0161582i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.81952e6 | − | 6.61560e6i | 0.325065 | − | 0.563030i | −0.656460 | − | 0.754361i | \(-0.727947\pi\) |
0.981526 | + | 0.191331i | \(0.0612803\pi\) | |||||||
\(674\) | 1.32875e7 | 1.12666 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −123088. | −0.0103598 | ||||||||
\(677\) | 9.78051e6 | − | 1.69403e7i | 0.820143 | − | 1.42053i | −0.0854320 | − | 0.996344i | \(-0.527227\pi\) |
0.905575 | − | 0.424186i | \(-0.139440\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.35810e6 | − | 5.81639e6i | −0.279524 | − | 0.484149i | ||||
\(680\) | −1.30923e6 | − | 2.26765e6i | −0.108578 | − | 0.188063i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 129447. | − | 224209.i | 0.0106569 | − | 0.0184583i | ||||
\(683\) | −1.08911e7 | −0.893349 | −0.446675 | − | 0.894696i | \(-0.647392\pi\) | ||||
−0.446675 | + | 0.894696i | \(0.647392\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.19349e6 | −0.341467 | ||||||||
\(686\) | 4.96426e6 | − | 8.59835e6i | 0.402758 | − | 0.697597i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.11739e6 | + | 8.86358e6i | 0.412171 | + | 0.713901i | ||||
\(689\) | −613146. | − | 1.06200e6i | −0.0492058 | − | 0.0852269i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.95944e6 | − | 1.55182e7i | 0.713815 | − | 1.23636i | −0.249599 | − | 0.968349i | \(-0.580299\pi\) |
0.963415 | − | 0.268015i | \(-0.0863677\pi\) | |||||||
\(692\) | −1.32907e7 | −1.05508 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.18136e7 | −0.931070 | ||||||||
\(695\) | 8.32539e6 | − | 1.44200e7i | 0.653796 | − | 1.13241i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −993435. | − | 1.72068e6i | −0.0774564 | − | 0.134158i | ||||
\(698\) | 2.72314e6 | + | 4.71662e6i | 0.211559 | + | 0.366431i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.32707e6 | − | 4.03060e6i | 0.179500 | − | 0.310903i | ||||
\(701\) | 1.32211e7 | 1.01619 | 0.508094 | − | 0.861302i | \(-0.330350\pi\) | ||||
0.508094 | + | 0.861302i | \(0.330350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 499745. | 0.0381382 | ||||||||
\(704\) | 66075.8 | − | 114447.i | 0.00502471 | − | 0.00870305i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.64667e6 | − | 1.15124e7i | −0.501872 | − | 0.869267i | ||||
\(707\) | 3.82914e6 | + | 6.63227e6i | 0.288107 | + | 0.499015i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 501449. | − | 868535.i | 0.0374637 | − | 0.0648891i | −0.846686 | − | 0.532094i | \(-0.821405\pi\) |
0.884149 | + | 0.467204i | \(0.154739\pi\) | |||||||
\(710\) | −2.15550e7 | −1.60473 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.58907e6 | 0.487106 | ||||||||
\(713\) | −612065. | + | 1.06013e6i | −0.0450893 | + | 0.0780970i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 203421. | + | 352336.i | 0.0148810 | + | 0.0257746i | ||||
\(716\) | 4.56635e6 | + | 7.90916e6i | 0.332879 | + | 0.576564i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.20785e6 | − | 1.59485e7i | 0.666572 | − | 1.15454i | ||||
\(719\) | −1.12752e7 | −0.813394 | −0.406697 | − | 0.913563i | \(-0.633319\pi\) | ||||
−0.406697 | + | 0.913563i | \(0.633319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.01163e6 | 0.144116 | ||||||||
\(722\) | 6.68099e6 | − | 1.15718e7i | 0.476977 | − | 0.826149i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.46789e6 | − | 9.47067e6i | −0.387680 | − | 0.671482i | ||||
\(725\) | −1.08939e7 | − | 1.88688e7i | −0.769729 | − | 1.33321i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.98334e6 | + | 1.72917e7i | −0.700551 | + | 1.21339i | 0.267722 | + | 0.963496i | \(0.413729\pi\) |
−0.968273 | + | 0.249894i | \(0.919604\pi\) | |||||||
\(728\) | 1.31943e6 | 0.0922695 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.16630e7 | −1.50457 | ||||||||
\(731\) | −2.41601e6 | + | 4.18465e6i | −0.167226 | + | 0.289645i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.06124e6 | + | 7.03427e6i | 0.279189 | + | 0.483570i | 0.971183 | − | 0.238333i | \(-0.0766011\pi\) |
−0.691994 | + | 0.721903i | \(0.743268\pi\) | |||||||
\(734\) | −1.71605e7 | − | 2.97228e7i | −1.17568 | − | 2.03634i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00985e6 | + | 1.74910e6i | −0.0687164 | + | 0.119020i | ||||
\(737\) | 322072. | 0.0218416 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −165272. | −0.0111324 | −0.00556619 | − | 0.999985i | \(-0.501772\pi\) | ||||
−0.00556619 | + | 0.999985i | \(0.501772\pi\) | |||||||
\(740\) | −264975. | + | 458950.i | −0.0177879 | + | 0.0308096i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 315124. | + | 545810.i | 0.0210122 | + | 0.0363942i | ||||
\(743\) | 1.23128e7 | + | 2.13263e7i | 0.818245 | + | 1.41724i | 0.906974 | + | 0.421186i | \(0.138386\pi\) |
−0.0887298 | + | 0.996056i | \(0.528281\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.12214e6 | − | 3.67566e6i | 0.140082 | − | 0.242630i | ||||
\(746\) | 2.51057e6 | 0.165168 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 108776. | 0.00710849 | ||||||||
\(749\) | −2.71637e6 | + | 4.70490e6i | −0.176923 | + | 0.306440i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.51225e6 | + | 2.61930e6i | 0.0978418 | + | 0.169467i | 0.910791 | − | 0.412867i | \(-0.135473\pi\) |
−0.812949 | + | 0.582334i | \(0.802139\pi\) | |||||||
\(752\) | 1.07867e7 | + | 1.86831e7i | 0.695573 | + | 1.20477i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.10152e7 | + | 1.90788e7i | −0.705606 | + | 1.22215i | ||||
\(755\) | 1.97539e7 | 1.26120 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.86322e6 | −0.562150 | −0.281075 | − | 0.959686i | \(-0.590691\pi\) | ||||
−0.281075 | + | 0.959686i | \(0.590691\pi\) | |||||||
\(758\) | 3.44152e6 | − | 5.96088e6i | 0.217559 | − | 0.376823i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.76530e6 | − | 8.25374e6i | −0.299265 | − | 0.518342i | ||||
\(761\) | 982452. | + | 1.70166e6i | 0.0614964 | + | 0.106515i | 0.895134 | − | 0.445796i | \(-0.147079\pi\) |
−0.833638 | + | 0.552311i | \(0.813746\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.35801e6 | + | 5.81624e6i | −0.208819 | + | 0.361685i | ||||
\(764\) | −3.82177e6 | −0.236881 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.75972e7 | −1.69939 | ||||||||
\(767\) | −610919. | + | 1.05814e6i | −0.0374969 | + | 0.0649465i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.90798e6 | + | 6.76883e6i | 0.238307 | + | 0.412760i | 0.960229 | − | 0.279215i | \(-0.0900742\pi\) |
−0.721922 | + | 0.691975i | \(0.756741\pi\) | |||||||
\(770\) | −104547. | − | 181081.i | −0.00635457 | − | 0.0110064i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.85241e6 | + | 8.40461e6i | −0.293031 | + | 0.507545i | ||||
\(773\) | −8.88127e6 | −0.534597 | −0.267298 | − | 0.963614i | \(-0.586131\pi\) | ||||
−0.267298 | + | 0.963614i | \(0.586131\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.01591e7 | 1.20564 | ||||||||
\(776\) | 4.31111e6 | − | 7.46706e6i | 0.257001 | − | 0.445139i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.06784e7 | − | 1.84955e7i | −0.632494 | − | 1.09551i | ||||
\(779\) | −3.61589e6 | − | 6.26290e6i | −0.213487 | − | 0.369770i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −125529. | + | 217422.i | −0.00736404 | + | 0.0127549i | ||||
\(782\) | −1.17285e6 | −0.0685846 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.81177e7 | 1.05272 | ||||||||
\(785\) | −7.04688e6 | + | 1.22055e7i | −0.408153 | + | 0.706941i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.53957e6 | + | 1.13269e7i | 0.376368 | + | 0.651888i | 0.990531 | − | 0.137291i | \(-0.0438395\pi\) |
−0.614163 | + | 0.789179i | \(0.710506\pi\) | |||||||
\(788\) | 1.45562e6 | + | 2.52121e6i | 0.0835089 | + | 0.144642i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.90880e7 | − | 5.03820e7i | 1.65824 | − | 2.87215i | ||||
\(791\) | 6.73834e6 | 0.382923 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.71327e7 | 0.967481 | ||||||||
\(794\) | −1.91247e7 | + | 3.31250e7i | −1.07657 | + | 1.86468i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.13084e7 | + | 1.95867e7i | 0.632583 | + | 1.09567i | ||||
\(797\) | −9.76620e6 | − | 1.69155e7i | −0.544603 | − | 0.943279i | −0.998632 | − | 0.0522925i | \(-0.983347\pi\) |
0.454029 | − | 0.890987i | \(-0.349986\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.09257e6 | + | 8.82060e6i | −0.282209 | + | 0.488800i | ||||
\(800\) | 3.32605e7 | 1.83740 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.74546e7 | 1.50723 | ||||||||
\(803\) | −126158. | + | 218513.i | −0.00690442 | + | 0.0119588i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 494332. | + | 856208.i | 0.0268862 | + | 0.0465682i | ||||
\(806\) | −1.01918e7 | − | 1.76526e7i | −0.552601 | − | 0.957132i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.91583e6 | + | 8.51448e6i | −0.264892 | + | 0.458806i | ||||
\(809\) | −1.72600e7 | −0.927194 | −0.463597 | − | 0.886046i | \(-0.653441\pi\) | ||||
−0.463597 | + | 0.886046i | \(0.653441\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.10857e7 | 0.591849 | 0.295924 | − | 0.955211i | \(-0.404372\pi\) | ||||
0.295924 | + | 0.955211i | \(0.404372\pi\) | |||||||
\(812\) | 2.48257e6 | − | 4.29993e6i | 0.132133 | − | 0.228861i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7037.81 | + | 12189.8i | 0.000372286 | + | 0.000644818i | ||||
\(815\) | 1.14257e6 | + | 1.97899e6i | 0.0602544 | + | 0.104364i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.79375e6 | + | 1.52312e7i | −0.460913 | + | 0.798324i | ||||
\(818\) | 3.68487e7 | 1.92548 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.66886e6 | 0.398287 | ||||||||
\(821\) | −7.48035e6 | + | 1.29563e7i | −0.387315 | + | 0.670849i | −0.992087 | − | 0.125549i | \(-0.959931\pi\) |
0.604773 | + | 0.796398i | \(0.293264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.52885e7 | − | 2.64805e7i | −0.786802 | − | 1.36278i | −0.927917 | − | 0.372787i | \(-0.878402\pi\) |
0.141115 | − | 0.989993i | \(-0.454931\pi\) | |||||||
\(824\) | 1.29126e6 | + | 2.23653e6i | 0.0662516 | + | 0.114751i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 313979. | − | 543828.i | 0.0160122 | − | 0.0277339i | ||||
\(827\) | −3.03602e7 | −1.54362 | −0.771810 | − | 0.635853i | \(-0.780648\pi\) | ||||
−0.771810 | + | 0.635853i | \(0.780648\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.09888e7 | −0.555348 | −0.277674 | − | 0.960675i | \(-0.589563\pi\) | ||||
−0.277674 | + | 0.960675i | \(0.589563\pi\) | |||||||
\(830\) | 3.49159e6 | − | 6.04762e6i | 0.175925 | − | 0.304712i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.20235e6 | − | 9.01073e6i | −0.260550 | − | 0.451286i | ||||
\(833\) | 4.27684e6 | + | 7.40771e6i | 0.213556 | + | 0.369889i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.54965e6 | − | 9.61228e6i | 0.275454 | − | 0.477101i | ||||
\(836\) | 395920. | 0.0195926 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.89218e6 | −0.289845 | ||||||||
\(839\) | −1.87744e6 | + | 3.25182e6i | −0.0920791 | + | 0.159486i | −0.908386 | − | 0.418133i | \(-0.862685\pi\) |
0.816307 | + | 0.577619i | \(0.196018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.36626e6 | − | 2.36643e6i | −0.0666105 | − | 0.115373i | ||||
\(842\) | 1.04450e7 | + | 1.80912e7i | 0.507723 | + | 0.879402i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.47959e7 | + | 2.56272e7i | −0.714966 | + | 1.23836i | ||||
\(845\) | −430596. | −0.0207457 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.63392e6 | 0.317733 | ||||||||
\(848\) | −1.21471e6 | + | 2.10394e6i | −0.0580073 | + | 0.100472i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.65733e6 | + | 1.67270e7i | 0.458469 | + | 0.794091i | ||||
\(851\) | −33276.9 | − | 57637.3i | −0.00157514 | − | 0.00272822i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.08366e7 | + | 1.87695e7i | −0.509940 | + | 0.883242i | 0.489993 | + | 0.871726i | \(0.336999\pi\) |
−0.999934 | + | 0.0115163i | \(0.996334\pi\) | |||||||
\(854\) | −8.80526e6 | −0.413140 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.97453e6 | −0.325335 | ||||||||
\(857\) | −7.00812e6 | + | 1.21384e7i | −0.325949 | + | 0.564560i | −0.981704 | − | 0.190414i | \(-0.939017\pi\) |
0.655755 | + | 0.754974i | \(0.272350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 318841. | + | 552249.i | 0.0147432 | + | 0.0255360i | 0.873303 | − | 0.487178i | \(-0.161974\pi\) |
−0.858560 | + | 0.512714i | \(0.828640\pi\) | |||||||
\(860\) | −9.32524e6 | − | 1.61518e7i | −0.429946 | − | 0.744688i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.37184e6 | + | 5.84020e6i | −0.154561 | + | 0.267707i | ||||
\(863\) | 3.79097e7 | 1.73270 | 0.866350 | − | 0.499437i | \(-0.166460\pi\) | ||||
0.866350 | + | 0.499437i | \(0.166460\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.64946e7 | −2.11282 | ||||||||
\(866\) | 1.83033e7 | − | 3.17022e7i | 0.829343 | − | 1.43646i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.29699e6 | + | 3.97851e6i | 0.103481 | + | 0.179234i | ||||
\(869\) | −338798. | − | 586816.i | −0.0152192 | − | 0.0263604i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.26789e7 | − | 2.19604e7i | 0.566285 | − | 0.980834i | ||||
\(872\) | −8.62199e6 | −0.383987 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.26893e6 | −0.189034 | ||||||||
\(875\) | 2.51145e6 | − | 4.34995e6i | 0.110893 | − | 0.192072i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.01603e7 | − | 3.49186e7i | −0.885111 | − | 1.53306i | −0.845587 | − | 0.533838i | \(-0.820749\pi\) |
−0.0395244 | − | 0.999219i | \(-0.512584\pi\) | |||||||
\(878\) | −881277. | − | 1.52642e6i | −0.0385812 | − | 0.0668247i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 402999. | − | 698016.i | 0.0175428 | − | 0.0303849i | ||||
\(881\) | 3.52506e7 | 1.53013 | 0.765063 | − | 0.643956i | \(-0.222708\pi\) | ||||
0.765063 | + | 0.643956i | \(0.222708\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.35541e6 | 0.101663 | 0.0508316 | − | 0.998707i | \(-0.483813\pi\) | ||||
0.0508316 | + | 0.998707i | \(0.483813\pi\) | |||||||
\(884\) | 4.28212e6 | − | 7.41685e6i | 0.184301 | − | 0.319219i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.87033e6 | + | 1.70959e7i | 0.422423 | + | 0.731658i | ||||
\(887\) | −1.30625e7 | − | 2.26249e7i | −0.557464 | − | 0.965556i | −0.997707 | − | 0.0676777i | \(-0.978441\pi\) |
0.440243 | − | 0.897879i | \(-0.354892\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.80644e6 | + | 8.32501e6i | −0.203972 | + | 0.353289i | ||||
\(890\) | −8.22124e7 | −3.47906 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.03624e7 | −0.856876 | ||||||||
\(893\) | −1.85359e7 | + | 3.21051e7i | −0.777829 | + | 1.34724i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.59743e7 | + | 2.76683e7i | 0.666600 | + | 1.15458i | ||||
\(896\) | −2.17865e6 | − | 3.77354e6i | −0.0906606 | − | 0.157029i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.14224e7 | − | 5.44252e7i | 1.30032 | − | 2.25221i | ||||
\(899\) | 2.15062e7 | 0.887491 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.14697e6 | −0.0470696 | ||||||||
\(902\) | 101844. | − | 176398.i | 0.00416790 | − | 0.00721901i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.32532e6 | + | 7.49167e6i | 0.176034 | + | 0.304900i | ||||
\(905\) | −1.91282e7 | − | 3.31309e7i | −0.776339 | − | 1.34466i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.18243e7 | − | 3.78008e7i | 0.880892 | − | 1.52575i | 0.0305409 | − | 0.999534i | \(-0.490277\pi\) |
0.850351 | − | 0.526216i | \(-0.176390\pi\) | |||||||
\(908\) | 9.38251e6 | 0.377663 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.64627e7 | −0.659017 | ||||||||
\(911\) | 8.65618e6 | − | 1.49929e7i | 0.345566 | − | 0.598537i | −0.639891 | − | 0.768466i | \(-0.721020\pi\) |
0.985456 | + | 0.169929i | \(0.0543538\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40667.7 | − | 70438.6i | −0.00161463 | − | 0.00279662i | ||||
\(914\) | 3.00550e6 | + | 5.20568e6i | 0.119001 | + | 0.206116i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.57170e6 | + | 2.72226e6i | −0.0618913 | + | 0.107199i | ||||
\(917\) | −7.14600e6 | −0.280634 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.03151e7 | −0.793468 | −0.396734 | − | 0.917934i | \(-0.629856\pi\) | ||||
−0.396734 | + | 0.917934i | \(0.629856\pi\) | |||||||
\(920\) | −634621. | + | 1.09920e6i | −0.0247198 | + | 0.0428159i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.28699e6 | − | 9.15733e6i | −0.204824 | − | 0.354766i | ||||
\(923\) | 9.88327e6 | + | 1.71183e7i | 0.381853 | + | 0.661389i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −548008. | + | 949178.i | −0.0210587 | + | 0.0364748i | ||||
\(926\) | −8.67065e6 | −0.332295 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.54830e7 | 1.35254 | ||||||||
\(929\) | 2.28832e7 | − | 3.96349e7i | 0.869916 | − | 1.50674i | 0.00783438 | − | 0.999969i | \(-0.497506\pi\) |
0.862082 | − | 0.506769i | \(-0.169160\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.55668e7 | + | 2.69625e7i | 0.588606 | + | 1.01950i | ||||
\(932\) | 5.29300e6 | + | 9.16775e6i | 0.199601 | + | 0.345719i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.13074e7 | + | 3.69055e7i | −0.799215 | + | 1.38428i | ||||
\(935\) | 380526. | 0.0142349 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.11001e7 | 1.52930 | 0.764652 | − | 0.644444i | \(-0.222911\pi\) | ||||
0.764652 | + | 0.644444i | \(0.222911\pi\) | |||||||
\(938\) | −6.51625e6 | + | 1.12865e7i | −0.241819 | + | 0.418843i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.96562e7 | − | 3.40455e7i | −0.725570 | − | 1.25672i | ||||
\(941\) | 1.55476e7 | + | 2.69292e7i | 0.572385 | + | 0.991400i | 0.996320 | + | 0.0857072i | \(0.0273150\pi\) |
−0.423936 | + | 0.905692i | \(0.639352\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −481547. | + | 834064.i | −0.0176344 | + | 0.0305436i | ||||
\(944\) | 2.42059e6 | 0.0884081 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −495362. | −0.0179968 | ||||||||
\(947\) | 2.10665e7 | − | 3.64883e7i | 0.763339 | − | 1.32214i | −0.177781 | − | 0.984070i | \(-0.556892\pi\) |
0.941120 | − | 0.338072i | \(-0.109775\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.93283e6 | + | 1.72042e7i | 0.358020 | + | 0.620109i | ||||
\(950\) | 3.51506e7 | + | 6.08826e7i | 1.26364 | + | 2.18869i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 617042. | − | 1.06875e6i | 0.0220660 | − | 0.0382193i | ||||
\(953\) | 1.27052e7 | 0.453158 | 0.226579 | − | 0.973993i | \(-0.427246\pi\) | ||||
0.226579 | + | 0.973993i | \(0.427246\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.33696e7 | −0.474361 | ||||||||
\(956\) | −1.52935e7 | + | 2.64892e7i | −0.541206 | + | 0.937397i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.15386e7 | + | 3.73060e7i | 0.758236 | + | 1.31330i | ||||
\(959\) | −988202. | − | 1.71162e6i | −0.0346976 | − | 0.0600980i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.36530e6 | − | 7.56093e6i | 0.152478 | − | 0.264099i | ||||
\(962\) | 1.10822e6 | 0.0386089 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.89594e7 | 0.657102 | ||||||||
\(965\) | −1.69750e7 | + | 2.94016e7i | −0.586802 | + | 1.01637i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.11678e7 | − | 3.66637e7i | −0.727964 | − | 1.26087i | −0.957743 | − | 0.287627i | \(-0.907134\pi\) |
0.229779 | − | 0.973243i | \(-0.426200\pi\) | |||||||
\(968\) | 4.25830e6 | + | 7.37558e6i | 0.146065 | + | 0.252993i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.37901e7 | + | 9.31672e7i | −1.83558 | + | 3.17932i | ||||
\(971\) | −4.04024e7 | −1.37518 | −0.687589 | − | 0.726100i | \(-0.741331\pi\) | ||||
−0.687589 | + | 0.726100i | \(0.741331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.84757e6 | 0.265737 | ||||||||
\(974\) | −1.05226e7 | + | 1.82257e7i | −0.355407 | + | 0.615583i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.69708e7 | − | 2.93944e7i | −0.570268 | − | 0.987733i | ||||
\(977\) | −1.88733e7 | − | 3.26895e7i | −0.632574 | − | 1.09565i | −0.987024 | − | 0.160576i | \(-0.948665\pi\) |
0.354449 | − | 0.935075i | \(-0.384668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −478778. | + | 829267.i | −0.0159653 | + | 0.0276527i | ||||
\(980\) | −3.30153e7 | −1.09812 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.24506e6 | 0.239753 | ||||||||
\(983\) | 2.44599e6 | − | 4.23658e6i | 0.0807367 | − | 0.139840i | −0.822830 | − | 0.568288i | \(-0.807606\pi\) |
0.903567 | + | 0.428448i | \(0.140939\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.09215e6 | + | 8.81986e6i | 0.167229 | + | 0.289649i | ||||
\(986\) | 1.03026e7 | + | 1.78447e7i | 0.337487 | + | 0.584544i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.55860e7 | − | 2.69957e7i | 0.507974 | − | 0.879837i | ||||
\(989\) | 2.34222e6 | 0.0761443 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.66907e7 | 1.18678 | 0.593392 | − | 0.804913i | \(-0.297788\pi\) | ||||
0.593392 | + | 0.804913i | \(0.297788\pi\) | |||||||
\(992\) | −1.64153e7 | + | 2.84321e7i | −0.529627 | + | 0.917340i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.07946e6 | − | 8.79788e6i | −0.163062 | − | 0.282431i | ||||
\(995\) | 3.95597e7 | + | 6.85194e7i | 1.26676 | + | 2.19410i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.25206e7 | − | 2.16863e7i | 0.398921 | − | 0.690951i | −0.594672 | − | 0.803968i | \(-0.702718\pi\) |
0.993593 | + | 0.113017i | \(0.0360515\pi\) | |||||||
\(998\) | 1.70763e7 | 0.542709 | ||||||||
\(999\) | 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 | 27.6.c.a.19.4 | 8 | ||
3.2 | odd | 2 | 9.6.c.a.7.1 | yes | 8 | ||
4.3 | odd | 2 | 432.6.i.c.289.1 | 8 | |||
9.2 | odd | 6 | 81.6.a.c.1.4 | 4 | |||
9.4 | even | 3 | inner | 27.6.c.a.10.4 | 8 | ||
9.5 | odd | 6 | 9.6.c.a.4.1 | ✓ | 8 | ||
9.7 | even | 3 | 81.6.a.d.1.1 | 4 | |||
12.11 | even | 2 | 144.6.i.c.97.4 | 8 | |||
36.23 | even | 6 | 144.6.i.c.49.4 | 8 | |||
36.31 | odd | 6 | 432.6.i.c.145.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.6.c.a.4.1 | ✓ | 8 | 9.5 | odd | 6 | ||
9.6.c.a.7.1 | yes | 8 | 3.2 | odd | 2 | ||
27.6.c.a.10.4 | 8 | 9.4 | even | 3 | inner | ||
27.6.c.a.19.4 | 8 | 1.1 | even | 1 | trivial | ||
81.6.a.c.1.4 | 4 | 9.2 | odd | 6 | |||
81.6.a.d.1.1 | 4 | 9.7 | even | 3 | |||
144.6.i.c.49.4 | 8 | 36.23 | even | 6 | |||
144.6.i.c.97.4 | 8 | 12.11 | even | 2 | |||
432.6.i.c.145.1 | 8 | 36.31 | odd | 6 | |||
432.6.i.c.289.1 | 8 | 4.3 | odd | 2 |