Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(846,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.846");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 260x^{12} + 2030x^{10} + 11605x^{8} + 42100x^{6} + 106925x^{4} + 113575x^{2} + 87025 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 846.15 | ||
Root | \(1.27939 - 2.21596i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.846 |
Dual form | 847.2.b.f.846.2 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.40487i | 1.70050i | 0.526381 | + | 0.850249i | \(0.323549\pi\) | ||||
−0.526381 | + | 0.850249i | \(0.676451\pi\) | |||||||
\(3\) | − | 1.72158i | − | 0.993957i | −0.867763 | − | 0.496979i | \(-0.834443\pi\) | ||
0.867763 | − | 0.496979i | \(-0.165557\pi\) | |||||||
\(4\) | −3.78339 | −1.89169 | ||||||||
\(5\) | 3.36793i | 1.50618i | 0.657916 | + | 0.753091i | \(0.271438\pi\) | ||||
−0.657916 | + | 0.753091i | \(0.728562\pi\) | |||||||
\(6\) | 4.14018 | 1.69022 | ||||||||
\(7\) | −2.55877 | − | 0.672816i | −0.967125 | − | 0.254301i | ||||
\(8\) | − | 4.28881i | − | 1.51632i | ||||||
\(9\) | 0.0361478 | 0.0120493 | ||||||||
\(10\) | −8.09942 | −2.56126 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 6.51342i | 1.88026i | ||||||||
\(13\) | −2.55877 | −0.709676 | −0.354838 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354838 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(14\) | 1.61803 | − | 6.15351i | 0.432438 | − | 1.64459i | ||||
\(15\) | 5.79817 | 1.49708 | ||||||||
\(16\) | 2.74724 | 0.686810 | ||||||||
\(17\) | −3.95924 | −0.960256 | −0.480128 | − | 0.877199i | \(-0.659410\pi\) | ||||
−0.480128 | + | 0.877199i | \(0.659410\pi\) | |||||||
\(18\) | 0.0869308i | 0.0204898i | ||||||||
\(19\) | −0.330604 | −0.0758459 | −0.0379229 | − | 0.999281i | \(-0.512074\pi\) | ||||
−0.0379229 | + | 0.999281i | \(0.512074\pi\) | |||||||
\(20\) | − | 12.7422i | − | 2.84924i | ||||||
\(21\) | −1.15831 | + | 4.40514i | −0.252764 | + | 0.961281i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.85410 | 0.595121 | 0.297561 | − | 0.954703i | \(-0.403827\pi\) | ||||
0.297561 | + | 0.954703i | \(0.403827\pi\) | |||||||
\(24\) | −7.38354 | −1.50716 | ||||||||
\(25\) | −6.34293 | −1.26859 | ||||||||
\(26\) | − | 6.15351i | − | 1.20680i | ||||||
\(27\) | − | 5.22698i | − | 1.00593i | ||||||
\(28\) | 9.68083 | + | 2.54552i | 1.82950 | + | 0.481059i | ||||
\(29\) | − | 2.49180i | − | 0.462715i | −0.972869 | − | 0.231358i | \(-0.925683\pi\) | ||
0.972869 | − | 0.231358i | \(-0.0743167\pi\) | |||||||
\(30\) | 13.9438i | 2.54578i | ||||||||
\(31\) | − | 0.222436i | − | 0.0399507i | −0.999800 | − | 0.0199753i | \(-0.993641\pi\) | ||
0.999800 | − | 0.0199753i | \(-0.00635877\pi\) | |||||||
\(32\) | − | 1.97087i | − | 0.348404i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 9.52144i | − | 1.63291i | ||||||
\(35\) | 2.26600 | − | 8.61776i | 0.383023 | − | 1.45667i | ||||
\(36\) | −0.136761 | −0.0227935 | ||||||||
\(37\) | −8.38006 | −1.37767 | −0.688836 | − | 0.724917i | \(-0.741878\pi\) | ||||
−0.688836 | + | 0.724917i | \(0.741878\pi\) | |||||||
\(38\) | − | 0.795060i | − | 0.128976i | ||||||
\(39\) | 4.40514i | 0.705387i | ||||||||
\(40\) | 14.4444 | 2.28386 | ||||||||
\(41\) | −9.53117 | −1.48852 | −0.744259 | − | 0.667891i | \(-0.767197\pi\) | ||||
−0.744259 | + | 0.667891i | \(0.767197\pi\) | |||||||
\(42\) | −10.5938 | − | 2.78558i | −1.63466 | − | 0.429825i | ||||
\(43\) | 1.73205i | 0.264135i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) | ||||
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.121743i | 0.0181484i | ||||||||
\(46\) | 6.86374i | 1.01200i | ||||||||
\(47\) | − | 1.23993i | − | 0.180863i | −0.995903 | − | 0.0904313i | \(-0.971175\pi\) | ||
0.995903 | − | 0.0904313i | \(-0.0288246\pi\) | |||||||
\(48\) | − | 4.72960i | − | 0.682659i | ||||||
\(49\) | 6.09464 | + | 3.44317i | 0.870662 | + | 0.491881i | ||||
\(50\) | − | 15.2539i | − | 2.15723i | ||||||
\(51\) | 6.81616i | 0.954453i | ||||||||
\(52\) | 9.68083 | 1.34249 | ||||||||
\(53\) | 0.302113 | 0.0414985 | 0.0207492 | − | 0.999785i | \(-0.493395\pi\) | ||||
0.0207492 | + | 0.999785i | \(0.493395\pi\) | |||||||
\(54\) | 12.5702 | 1.71059 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.88558 | + | 10.9741i | −0.385602 | + | 1.46647i | ||||
\(57\) | 0.569163i | 0.0753875i | ||||||||
\(58\) | 5.99244 | 0.786846 | ||||||||
\(59\) | − | 9.03006i | − | 1.17561i | −0.809001 | − | 0.587807i | \(-0.799991\pi\) | ||
0.809001 | − | 0.587807i | \(-0.200009\pi\) | |||||||
\(60\) | −21.9367 | −2.83202 | ||||||||
\(61\) | −5.68376 | −0.727731 | −0.363866 | − | 0.931451i | \(-0.618543\pi\) | ||||
−0.363866 | + | 0.931451i | \(0.618543\pi\) | |||||||
\(62\) | 0.534929 | 0.0679361 | ||||||||
\(63\) | −0.0924941 | − | 0.0243209i | −0.0116532 | − | 0.00306414i | ||||
\(64\) | 10.2342 | 1.27927 | ||||||||
\(65\) | − | 8.61776i | − | 1.06890i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.57998 | −0.803872 | −0.401936 | − | 0.915668i | \(-0.631663\pi\) | ||||
−0.401936 | + | 0.915668i | \(0.631663\pi\) | |||||||
\(68\) | 14.9793 | 1.81651 | ||||||||
\(69\) | − | 4.91358i | − | 0.591525i | ||||||
\(70\) | 20.7246 | + | 5.44942i | 2.47706 | + | 0.651330i | ||||
\(71\) | 5.35614 | 0.635656 | 0.317828 | − | 0.948148i | \(-0.397046\pi\) | ||||
0.317828 | + | 0.948148i | \(0.397046\pi\) | |||||||
\(72\) | − | 0.155031i | − | 0.0182706i | ||||||
\(73\) | 6.99173 | 0.818320 | 0.409160 | − | 0.912463i | \(-0.365822\pi\) | ||||
0.409160 | + | 0.912463i | \(0.365822\pi\) | |||||||
\(74\) | − | 20.1529i | − | 2.34273i | ||||||
\(75\) | 10.9199i | 1.26092i | ||||||||
\(76\) | 1.25080 | 0.143477 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −10.5938 | −1.19951 | ||||||||
\(79\) | − | 2.95520i | − | 0.332486i | −0.986085 | − | 0.166243i | \(-0.946836\pi\) | ||
0.986085 | − | 0.166243i | \(-0.0531636\pi\) | |||||||
\(80\) | 9.25250i | 1.03446i | ||||||||
\(81\) | −8.89025 | −0.987806 | ||||||||
\(82\) | − | 22.9212i | − | 2.53122i | ||||||
\(83\) | −7.89509 | −0.866599 | −0.433299 | − | 0.901250i | \(-0.642651\pi\) | ||||
−0.433299 | + | 0.901250i | \(0.642651\pi\) | |||||||
\(84\) | 4.38233 | − | 16.6664i | 0.478152 | − | 1.81845i | ||||
\(85\) | − | 13.3344i | − | 1.44632i | ||||||
\(86\) | −4.16535 | −0.449161 | ||||||||
\(87\) | −4.28984 | −0.459919 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.66560i | − | 0.388553i | −0.980947 | − | 0.194277i | \(-0.937764\pi\) | ||
0.980947 | − | 0.194277i | \(-0.0622359\pi\) | |||||||
\(90\) | −0.292776 | −0.0308613 | ||||||||
\(91\) | 6.54732 | + | 1.72158i | 0.686345 | + | 0.180471i | ||||
\(92\) | −10.7982 | −1.12579 | ||||||||
\(93\) | −0.382942 | −0.0397093 | ||||||||
\(94\) | 2.98187 | 0.307557 | ||||||||
\(95\) | − | 1.11345i | − | 0.114238i | ||||||
\(96\) | −3.39302 | −0.346299 | ||||||||
\(97\) | 13.6379i | 1.38472i | 0.721552 | + | 0.692361i | \(0.243429\pi\) | ||||
−0.721552 | + | 0.692361i | \(0.756571\pi\) | |||||||
\(98\) | −8.28036 | + | 14.6568i | −0.836443 | + | 1.48056i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 23.9978 | 2.39978 | ||||||||
\(101\) | 10.5657 | 1.05133 | 0.525663 | − | 0.850693i | \(-0.323817\pi\) | ||||
0.525663 | + | 0.850693i | \(0.323817\pi\) | |||||||
\(102\) | −16.3920 | −1.62305 | ||||||||
\(103\) | 17.7099i | 1.74501i | 0.488604 | + | 0.872506i | \(0.337506\pi\) | ||||
−0.488604 | + | 0.872506i | \(0.662494\pi\) | |||||||
\(104\) | 10.9741i | 1.07610i | ||||||||
\(105\) | −14.8362 | − | 3.90110i | −1.44786 | − | 0.380709i | ||||
\(106\) | 0.726543i | 0.0705680i | ||||||||
\(107\) | 18.1465i | 1.75429i | 0.480227 | + | 0.877144i | \(0.340554\pi\) | ||||
−0.480227 | + | 0.877144i | \(0.659446\pi\) | |||||||
\(108\) | 19.7757i | 1.90292i | ||||||||
\(109\) | 1.48774i | 0.142500i | 0.997458 | + | 0.0712499i | \(0.0226988\pi\) | ||||
−0.997458 | + | 0.0712499i | \(0.977301\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.4270i | 1.36935i | ||||||||
\(112\) | −7.02956 | − | 1.84839i | −0.664231 | − | 0.174656i | ||||
\(113\) | −11.5489 | −1.08643 | −0.543214 | − | 0.839594i | \(-0.682793\pi\) | ||||
−0.543214 | + | 0.839594i | \(0.682793\pi\) | |||||||
\(114\) | −1.36876 | −0.128196 | ||||||||
\(115\) | 9.61241i | 0.896362i | ||||||||
\(116\) | 9.42743i | 0.875315i | ||||||||
\(117\) | −0.0924941 | −0.00855108 | ||||||||
\(118\) | 21.7161 | 1.99913 | ||||||||
\(119\) | 10.1308 | + | 2.66384i | 0.928687 | + | 0.244194i | ||||
\(120\) | − | 24.8672i | − | 2.27006i | ||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 13.6687i | − | 1.23751i | ||||||
\(123\) | 16.4087i | 1.47952i | ||||||||
\(124\) | 0.841561i | 0.0755745i | ||||||||
\(125\) | − | 4.52290i | − | 0.404540i | ||||||
\(126\) | 0.0584884 | − | 0.222436i | 0.00521056 | − | 0.0198162i | ||||
\(127\) | 10.9380i | 0.970594i | 0.874349 | + | 0.485297i | \(0.161289\pi\) | ||||
−0.874349 | + | 0.485297i | \(0.838711\pi\) | |||||||
\(128\) | 20.6700i | 1.82699i | ||||||||
\(129\) | 2.98187 | 0.262539 | ||||||||
\(130\) | 20.7246 | 1.81766 | ||||||||
\(131\) | −5.67097 | −0.495475 | −0.247737 | − | 0.968827i | \(-0.579687\pi\) | ||||
−0.247737 | + | 0.968827i | \(0.579687\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.845942 | + | 0.222436i | 0.0733524 | + | 0.0192877i | ||||
\(134\) | − | 15.8240i | − | 1.36698i | ||||||
\(135\) | 17.6041 | 1.51512 | ||||||||
\(136\) | 16.9804i | 1.45606i | ||||||||
\(137\) | −17.6931 | −1.51162 | −0.755811 | − | 0.654789i | \(-0.772757\pi\) | ||||
−0.755811 | + | 0.654789i | \(0.772757\pi\) | |||||||
\(138\) | 11.8165 | 1.00589 | ||||||||
\(139\) | −1.78169 | −0.151121 | −0.0755605 | − | 0.997141i | \(-0.524075\pi\) | ||||
−0.0755605 | + | 0.997141i | \(0.524075\pi\) | |||||||
\(140\) | −8.57314 | + | 32.6043i | −0.724562 | + | 2.75557i | ||||
\(141\) | −2.13465 | −0.179770 | ||||||||
\(142\) | 12.8808i | 1.08093i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.0993067 | 0.00827556 | ||||||||
\(145\) | 8.39219 | 0.696934 | ||||||||
\(146\) | 16.8142i | 1.39155i | ||||||||
\(147\) | 5.92770 | − | 10.4924i | 0.488909 | − | 0.865401i | ||||
\(148\) | 31.7050 | 2.60613 | ||||||||
\(149\) | 14.0316i | 1.14951i | 0.818326 | + | 0.574755i | \(0.194903\pi\) | ||||
−0.818326 | + | 0.574755i | \(0.805097\pi\) | |||||||
\(150\) | −26.2609 | −2.14419 | ||||||||
\(151\) | 2.04228i | 0.166198i | 0.996541 | + | 0.0830992i | \(0.0264818\pi\) | ||||
−0.996541 | + | 0.0830992i | \(0.973518\pi\) | |||||||
\(152\) | 1.41790i | 0.115007i | ||||||||
\(153\) | −0.143118 | −0.0115704 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.749148 | 0.0601730 | ||||||||
\(156\) | − | 16.6664i | − | 1.33438i | ||||||
\(157\) | − | 7.62188i | − | 0.608293i | −0.952625 | − | 0.304146i | \(-0.901629\pi\) | ||
0.952625 | − | 0.304146i | \(-0.0983712\pi\) | |||||||
\(158\) | 7.10686 | 0.565392 | ||||||||
\(159\) | − | 0.520114i | − | 0.0412477i | ||||||
\(160\) | 6.63775 | 0.524760 | ||||||||
\(161\) | −7.30300 | − | 1.92029i | −0.575557 | − | 0.151340i | ||||
\(162\) | − | 21.3799i | − | 1.67976i | ||||||
\(163\) | −18.7978 | −1.47236 | −0.736180 | − | 0.676786i | \(-0.763372\pi\) | ||||
−0.736180 | + | 0.676786i | \(0.763372\pi\) | |||||||
\(164\) | 36.0601 | 2.81582 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 18.9866i | − | 1.47365i | ||||||
\(167\) | −19.5804 | −1.51518 | −0.757589 | − | 0.652731i | \(-0.773623\pi\) | ||||
−0.757589 | + | 0.652731i | \(0.773623\pi\) | |||||||
\(168\) | 18.8928 | + | 4.96777i | 1.45761 | + | 0.383272i | ||||
\(169\) | −6.45268 | −0.496360 | ||||||||
\(170\) | 32.0675 | 2.45946 | ||||||||
\(171\) | −0.0119506 | −0.000913888 | ||||||||
\(172\) | − | 6.55302i | − | 0.499663i | ||||||
\(173\) | 8.87650 | 0.674868 | 0.337434 | − | 0.941349i | \(-0.390441\pi\) | ||||
0.337434 | + | 0.941349i | \(0.390441\pi\) | |||||||
\(174\) | − | 10.3165i | − | 0.782091i | ||||||
\(175\) | 16.2301 | + | 4.26763i | 1.22688 | + | 0.322602i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.5460 | −1.16851 | ||||||||
\(178\) | 8.81529 | 0.660734 | ||||||||
\(179\) | 8.92364 | 0.666984 | 0.333492 | − | 0.942753i | \(-0.391773\pi\) | ||||
0.333492 | + | 0.942753i | \(0.391773\pi\) | |||||||
\(180\) | − | 0.460602i | − | 0.0343312i | ||||||
\(181\) | 12.0749i | 0.897517i | 0.893653 | + | 0.448759i | \(0.148134\pi\) | ||||
−0.893653 | + | 0.448759i | \(0.851866\pi\) | |||||||
\(182\) | −4.14018 | + | 15.7454i | −0.306891 | + | 1.16713i | ||||
\(183\) | 9.78507i | 0.723334i | ||||||||
\(184\) | − | 12.2407i | − | 0.902396i | ||||||
\(185\) | − | 28.2234i | − | 2.07503i | ||||||
\(186\) | − | 0.920926i | − | 0.0675255i | ||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.69114i | 0.342137i | ||||||||
\(189\) | −3.51680 | + | 13.3747i | −0.255810 | + | 0.972864i | ||||
\(190\) | 2.67770 | 0.194261 | ||||||||
\(191\) | 13.0286 | 0.942716 | 0.471358 | − | 0.881942i | \(-0.343764\pi\) | ||||
0.471358 | + | 0.881942i | \(0.343764\pi\) | |||||||
\(192\) | − | 17.6190i | − | 1.27154i | ||||||
\(193\) | − | 13.1052i | − | 0.943336i | −0.881776 | − | 0.471668i | \(-0.843652\pi\) | ||
0.881776 | − | 0.471668i | \(-0.156348\pi\) | |||||||
\(194\) | −32.7974 | −2.35472 | ||||||||
\(195\) | −14.8362 | −1.06244 | ||||||||
\(196\) | −23.0584 | − | 13.0268i | −1.64703 | − | 0.930488i | ||||
\(197\) | 5.90687i | 0.420847i | 0.977610 | + | 0.210424i | \(0.0674843\pi\) | ||||
−0.977610 | + | 0.210424i | \(0.932516\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.10548i | 0.503694i | 0.967767 | + | 0.251847i | \(0.0810380\pi\) | ||||
−0.967767 | + | 0.251847i | \(0.918962\pi\) | |||||||
\(200\) | 27.2036i | 1.92359i | ||||||||
\(201\) | 11.3280i | 0.799014i | ||||||||
\(202\) | 25.4091i | 1.78778i | ||||||||
\(203\) | −1.67652 | + | 6.37594i | −0.117669 | + | 0.447504i | ||||
\(204\) | − | 25.7882i | − | 1.80553i | ||||||
\(205\) | − | 32.1003i | − | 2.24198i | ||||||
\(206\) | −42.5900 | −2.96739 | ||||||||
\(207\) | 0.103170 | 0.00717078 | ||||||||
\(208\) | −7.02956 | −0.487412 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 9.38164 | − | 35.6791i | 0.647394 | − | 2.46209i | ||||
\(211\) | 0.357401i | 0.0246045i | 0.999924 | + | 0.0123023i | \(0.00391603\pi\) | ||||
−0.999924 | + | 0.0123023i | \(0.996084\pi\) | |||||||
\(212\) | −1.14301 | −0.0785024 | ||||||||
\(213\) | − | 9.22104i | − | 0.631815i | ||||||
\(214\) | −43.6399 | −2.98316 | ||||||||
\(215\) | −5.83342 | −0.397836 | ||||||||
\(216\) | −22.4175 | −1.52532 | ||||||||
\(217\) | −0.149659 | + | 0.569163i | −0.0101595 | + | 0.0386373i | ||||
\(218\) | −3.57782 | −0.242320 | ||||||||
\(219\) | − | 12.0369i | − | 0.813375i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.1308 | 0.681470 | ||||||||
\(222\) | −34.6950 | −2.32857 | ||||||||
\(223\) | − | 7.99684i | − | 0.535508i | −0.963487 | − | 0.267754i | \(-0.913719\pi\) | ||
0.963487 | − | 0.267754i | \(-0.0862814\pi\) | |||||||
\(224\) | −1.32603 | + | 5.04301i | −0.0885994 | + | 0.336950i | ||||
\(225\) | −0.229283 | −0.0152856 | ||||||||
\(226\) | − | 27.7736i | − | 1.84747i | ||||||
\(227\) | 27.4257 | 1.82031 | 0.910155 | − | 0.414268i | \(-0.135962\pi\) | ||||
0.910155 | + | 0.414268i | \(0.135962\pi\) | |||||||
\(228\) | − | 2.15336i | − | 0.142610i | ||||||
\(229\) | − | 0.177967i | − | 0.0117604i | −0.999983 | − | 0.00588018i | \(-0.998128\pi\) | ||
0.999983 | − | 0.00588018i | \(-0.00187173\pi\) | |||||||
\(230\) | −23.1166 | −1.52426 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.6868 | −0.701625 | ||||||||
\(233\) | − | 8.71447i | − | 0.570904i | −0.958393 | − | 0.285452i | \(-0.907856\pi\) | ||
0.958393 | − | 0.285452i | \(-0.0921437\pi\) | |||||||
\(234\) | − | 0.222436i | − | 0.0145411i | ||||||
\(235\) | 4.17600 | 0.272412 | ||||||||
\(236\) | 34.1642i | 2.22390i | ||||||||
\(237\) | −5.08763 | −0.330477 | ||||||||
\(238\) | −6.40618 | + | 24.3632i | −0.415251 | + | 1.57923i | ||||
\(239\) | 4.65639i | 0.301197i | 0.988595 | + | 0.150599i | \(0.0481201\pi\) | ||||
−0.988595 | + | 0.150599i | \(0.951880\pi\) | |||||||
\(240\) | 15.9290 | 1.02821 | ||||||||
\(241\) | −6.84861 | −0.441158 | −0.220579 | − | 0.975369i | \(-0.570795\pi\) | ||||
−0.220579 | + | 0.975369i | \(0.570795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 0.375639i | − | 0.0240972i | ||||||
\(244\) | 21.5039 | 1.37664 | ||||||||
\(245\) | −11.5963 | + | 20.5263i | −0.740863 | + | 1.31138i | ||||
\(246\) | −39.4608 | −2.51593 | ||||||||
\(247\) | 0.845942 | 0.0538260 | ||||||||
\(248\) | −0.953985 | −0.0605781 | ||||||||
\(249\) | 13.5921i | 0.861362i | ||||||||
\(250\) | 10.8770 | 0.687920 | ||||||||
\(251\) | 9.40501i | 0.593639i | 0.954934 | + | 0.296820i | \(0.0959260\pi\) | ||||
−0.954934 | + | 0.296820i | \(0.904074\pi\) | |||||||
\(252\) | 0.349941 | + | 0.0920152i | 0.0220442 | + | 0.00579641i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −26.3045 | −1.65049 | ||||||||
\(255\) | −22.9563 | −1.43758 | ||||||||
\(256\) | −29.2404 | −1.82753 | ||||||||
\(257\) | − | 5.70864i | − | 0.356095i | −0.984022 | − | 0.178047i | \(-0.943022\pi\) | ||
0.984022 | − | 0.178047i | \(-0.0569781\pi\) | |||||||
\(258\) | 7.17100i | 0.446447i | ||||||||
\(259\) | 21.4427 | + | 5.63824i | 1.33238 | + | 0.350343i | ||||
\(260\) | 32.6043i | 2.02203i | ||||||||
\(261\) | − | 0.0900731i | − | 0.00557539i | ||||||
\(262\) | − | 13.6379i | − | 0.842554i | ||||||
\(263\) | − | 3.07375i | − | 0.189535i | −0.995499 | − | 0.0947677i | \(-0.969789\pi\) | ||
0.995499 | − | 0.0947677i | \(-0.0302108\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.01750i | 0.0625043i | ||||||||
\(266\) | −0.534929 | + | 2.03438i | −0.0327986 | + | 0.124736i | ||||
\(267\) | −6.31065 | −0.386205 | ||||||||
\(268\) | 24.8946 | 1.52068 | ||||||||
\(269\) | − | 11.9261i | − | 0.727145i | −0.931566 | − | 0.363572i | \(-0.881557\pi\) | ||
0.931566 | − | 0.363572i | \(-0.118443\pi\) | |||||||
\(270\) | 42.3355i | 2.57646i | ||||||||
\(271\) | 1.55416 | 0.0944087 | 0.0472044 | − | 0.998885i | \(-0.484969\pi\) | ||||
0.0472044 | + | 0.998885i | \(0.484969\pi\) | |||||||
\(272\) | −10.8770 | −0.659513 | ||||||||
\(273\) | 2.96385 | − | 11.2718i | 0.179380 | − | 0.682198i | ||||
\(274\) | − | 42.5495i | − | 2.57051i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 18.5900i | 1.11898i | ||||||||
\(277\) | − | 12.6309i | − | 0.758918i | −0.925209 | − | 0.379459i | \(-0.876110\pi\) | ||
0.925209 | − | 0.379459i | \(-0.123890\pi\) | |||||||
\(278\) | − | 4.28473i | − | 0.256981i | ||||||
\(279\) | − | 0.00804058i | − | 0.000481377i | ||||||
\(280\) | −36.9599 | − | 9.71842i | −2.20878 | − | 0.580787i | ||||
\(281\) | − | 18.1496i | − | 1.08272i | −0.840792 | − | 0.541358i | \(-0.817910\pi\) | ||
0.840792 | − | 0.541358i | \(-0.182090\pi\) | |||||||
\(282\) | − | 5.13354i | − | 0.305698i | ||||||
\(283\) | 19.2128 | 1.14208 | 0.571042 | − | 0.820921i | \(-0.306539\pi\) | ||||
0.571042 | + | 0.820921i | \(0.306539\pi\) | |||||||
\(284\) | −20.2643 | −1.20247 | ||||||||
\(285\) | −1.91690 | −0.113547 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.3881 | + | 6.41272i | 1.43958 | + | 0.378531i | ||||
\(288\) | − | 0.0712427i | − | 0.00419802i | ||||||
\(289\) | −1.32445 | −0.0779091 | ||||||||
\(290\) | 20.1821i | 1.18513i | ||||||||
\(291\) | 23.4788 | 1.37635 | ||||||||
\(292\) | −26.4524 | −1.54801 | ||||||||
\(293\) | −22.2004 | −1.29696 | −0.648481 | − | 0.761231i | \(-0.724595\pi\) | ||||
−0.648481 | + | 0.761231i | \(0.724595\pi\) | |||||||
\(294\) | 25.2329 | + | 14.2553i | 1.47161 | + | 0.831388i | ||||
\(295\) | 30.4126 | 1.77069 | ||||||||
\(296\) | 35.9404i | 2.08900i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −33.7440 | −1.95474 | ||||||||
\(299\) | −7.30300 | −0.422343 | ||||||||
\(300\) | − | 41.3142i | − | 2.38527i | ||||||
\(301\) | 1.16535 | − | 4.43192i | 0.0671698 | − | 0.255452i | ||||
\(302\) | −4.91141 | −0.282620 | ||||||||
\(303\) | − | 18.1897i | − | 1.04497i | ||||||
\(304\) | −0.908249 | −0.0520917 | ||||||||
\(305\) | − | 19.1425i | − | 1.09610i | ||||||
\(306\) | − | 0.344179i | − | 0.0196754i | ||||||
\(307\) | −8.33503 | −0.475705 | −0.237853 | − | 0.971301i | \(-0.576444\pi\) | ||||
−0.237853 | + | 0.971301i | \(0.576444\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 30.4891 | 1.73447 | ||||||||
\(310\) | 1.80160i | 0.102324i | ||||||||
\(311\) | 24.0042i | 1.36115i | 0.732677 | + | 0.680577i | \(0.238271\pi\) | ||||
−0.732677 | + | 0.680577i | \(0.761729\pi\) | |||||||
\(312\) | 18.8928 | 1.06959 | ||||||||
\(313\) | 33.1290i | 1.87256i | 0.351256 | + | 0.936280i | \(0.385755\pi\) | ||||
−0.351256 | + | 0.936280i | \(0.614245\pi\) | |||||||
\(314\) | 18.3296 | 1.03440 | ||||||||
\(315\) | 0.0819109 | − | 0.311513i | 0.00461516 | − | 0.0175518i | ||||
\(316\) | 11.1807i | 0.628961i | ||||||||
\(317\) | 14.3722 | 0.807221 | 0.403611 | − | 0.914931i | \(-0.367755\pi\) | ||||
0.403611 | + | 0.914931i | \(0.367755\pi\) | |||||||
\(318\) | 1.25080 | 0.0701416 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 34.4679i | 1.92681i | ||||||||
\(321\) | 31.2407 | 1.74369 | ||||||||
\(322\) | 4.61803 | − | 17.5627i | 0.257353 | − | 0.978733i | ||||
\(323\) | 1.30894 | 0.0728314 | ||||||||
\(324\) | 33.6352 | 1.86862 | ||||||||
\(325\) | 16.2301 | 0.900285 | ||||||||
\(326\) | − | 45.2063i | − | 2.50375i | ||||||
\(327\) | 2.56127 | 0.141639 | ||||||||
\(328\) | 40.8773i | 2.25707i | ||||||||
\(329\) | −0.834246 | + | 3.17270i | −0.0459935 | + | 0.174917i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.28233 | −0.345308 | −0.172654 | − | 0.984983i | \(-0.555234\pi\) | ||||
−0.172654 | + | 0.984983i | \(0.555234\pi\) | |||||||
\(332\) | 29.8702 | 1.63934 | ||||||||
\(333\) | −0.302921 | −0.0166000 | ||||||||
\(334\) | − | 47.0883i | − | 2.57656i | ||||||
\(335\) | − | 22.1609i | − | 1.21078i | ||||||
\(336\) | −3.18215 | + | 12.1020i | −0.173601 | + | 0.660217i | ||||
\(337\) | 23.4303i | 1.27633i | 0.769899 | + | 0.638166i | \(0.220307\pi\) | ||||
−0.769899 | + | 0.638166i | \(0.779693\pi\) | |||||||
\(338\) | − | 15.5178i | − | 0.844059i | ||||||
\(339\) | 19.8824i | 1.07986i | ||||||||
\(340\) | 50.4492i | 2.73599i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 0.0287397i | − | 0.00155406i | ||||||
\(343\) | −13.2782 | − | 12.9109i | −0.716954 | − | 0.697121i | ||||
\(344\) | 7.42843 | 0.400514 | ||||||||
\(345\) | 16.5486 | 0.890945 | ||||||||
\(346\) | 21.3468i | 1.14761i | ||||||||
\(347\) | − | 17.9331i | − | 0.962697i | −0.876529 | − | 0.481349i | \(-0.840147\pi\) | ||
0.876529 | − | 0.481349i | \(-0.159853\pi\) | |||||||
\(348\) | 16.2301 | 0.870026 | ||||||||
\(349\) | 21.7893 | 1.16635 | 0.583176 | − | 0.812346i | \(-0.301810\pi\) | ||||
0.583176 | + | 0.812346i | \(0.301810\pi\) | |||||||
\(350\) | −10.2631 | + | 39.0313i | −0.548585 | + | 2.08631i | ||||
\(351\) | 13.3747i | 0.713887i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.3753i | 0.871570i | 0.900051 | + | 0.435785i | \(0.143529\pi\) | ||||
−0.900051 | + | 0.435785i | \(0.856471\pi\) | |||||||
\(354\) | − | 37.3861i | − | 1.98705i | ||||||
\(355\) | 18.0391i | 0.957415i | ||||||||
\(356\) | 13.8684i | 0.735024i | ||||||||
\(357\) | 4.58602 | − | 17.4410i | 0.242718 | − | 0.923075i | ||||
\(358\) | 21.4602i | 1.13420i | ||||||||
\(359\) | − | 18.2087i | − | 0.961019i | −0.876990 | − | 0.480509i | \(-0.840452\pi\) | ||
0.876990 | − | 0.480509i | \(-0.159548\pi\) | |||||||
\(360\) | 0.522133 | 0.0275188 | ||||||||
\(361\) | −18.8907 | −0.994247 | ||||||||
\(362\) | −29.0384 | −1.52623 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.7710 | − | 6.51342i | −1.29835 | − | 0.341396i | ||||
\(365\) | 23.5476i | 1.23254i | ||||||||
\(366\) | −23.5318 | −1.23003 | ||||||||
\(367\) | 0.841561i | 0.0439292i | 0.999759 | + | 0.0219646i | \(0.00699210\pi\) | ||||
−0.999759 | + | 0.0219646i | \(0.993008\pi\) | |||||||
\(368\) | 7.84090 | 0.408735 | ||||||||
\(369\) | −0.344531 | −0.0179356 | ||||||||
\(370\) | 67.8736 | 3.52858 | ||||||||
\(371\) | −0.773039 | − | 0.203267i | −0.0401342 | − | 0.0105531i | ||||
\(372\) | 1.44882 | 0.0751178 | ||||||||
\(373\) | − | 25.9152i | − | 1.34184i | −0.741530 | − | 0.670920i | \(-0.765899\pi\) | ||
0.741530 | − | 0.670920i | \(-0.234101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.78655 | −0.402095 | ||||||||
\(376\) | −5.31783 | −0.274246 | ||||||||
\(377\) | 6.37594i | 0.328378i | ||||||||
\(378\) | −32.1643 | − | 8.45744i | −1.65435 | − | 0.435004i | ||||
\(379\) | 8.80317 | 0.452188 | 0.226094 | − | 0.974105i | \(-0.427404\pi\) | ||||
0.226094 | + | 0.974105i | \(0.427404\pi\) | |||||||
\(380\) | 4.21262i | 0.216103i | ||||||||
\(381\) | 18.8308 | 0.964729 | ||||||||
\(382\) | 31.3320i | 1.60309i | ||||||||
\(383\) | − | 13.0944i | − | 0.669092i | −0.942379 | − | 0.334546i | \(-0.891417\pi\) | ||
0.942379 | − | 0.334546i | \(-0.108583\pi\) | |||||||
\(384\) | 35.5852 | 1.81595 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.5164 | 1.60414 | ||||||||
\(387\) | 0.0626099i | 0.00318264i | ||||||||
\(388\) | − | 51.5975i | − | 2.61947i | ||||||
\(389\) | −10.0467 | −0.509386 | −0.254693 | − | 0.967022i | \(-0.581974\pi\) | ||||
−0.254693 | + | 0.967022i | \(0.581974\pi\) | |||||||
\(390\) | − | 35.6791i | − | 1.80668i | ||||||
\(391\) | −11.3001 | −0.571469 | ||||||||
\(392\) | 14.7671 | − | 26.1387i | 0.745850 | − | 1.32020i | ||||
\(393\) | 9.76305i | 0.492481i | ||||||||
\(394\) | −14.2052 | −0.715649 | ||||||||
\(395\) | 9.95290 | 0.500785 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 15.4703i | − | 0.776431i | −0.921569 | − | 0.388215i | \(-0.873092\pi\) | ||
0.921569 | − | 0.388215i | \(-0.126908\pi\) | |||||||
\(398\) | −17.0877 | −0.856531 | ||||||||
\(399\) | 0.382942 | − | 1.45636i | 0.0191711 | − | 0.0729092i | ||||
\(400\) | −17.4255 | −0.871277 | ||||||||
\(401\) | −32.2447 | −1.61023 | −0.805113 | − | 0.593122i | \(-0.797895\pi\) | ||||
−0.805113 | + | 0.593122i | \(0.797895\pi\) | |||||||
\(402\) | −27.2423 | −1.35872 | ||||||||
\(403\) | 0.569163i | 0.0283520i | ||||||||
\(404\) | −39.9741 | −1.98879 | ||||||||
\(405\) | − | 29.9417i | − | 1.48782i | ||||||
\(406\) | −15.3333 | − | 4.03181i | −0.760979 | − | 0.200096i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 29.2332 | 1.44726 | ||||||||
\(409\) | 5.03296 | 0.248864 | 0.124432 | − | 0.992228i | \(-0.460289\pi\) | ||||
0.124432 | + | 0.992228i | \(0.460289\pi\) | |||||||
\(410\) | 77.1969 | 3.81248 | ||||||||
\(411\) | 30.4601i | 1.50249i | ||||||||
\(412\) | − | 67.0035i | − | 3.30103i | ||||||
\(413\) | −6.07557 | + | 23.1059i | −0.298959 | + | 1.13697i | ||||
\(414\) | 0.248109i | 0.0121939i | ||||||||
\(415\) | − | 26.5901i | − | 1.30526i | ||||||
\(416\) | 5.04301i | 0.247254i | ||||||||
\(417\) | 3.06733i | 0.150208i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 16.8991i | − | 0.825577i | −0.910827 | − | 0.412789i | \(-0.864555\pi\) | ||
0.910827 | − | 0.412789i | \(-0.135445\pi\) | |||||||
\(420\) | 56.1311 | + | 14.7594i | 2.73892 | + | 0.720184i | ||||
\(421\) | 24.9500 | 1.21599 | 0.607994 | − | 0.793942i | \(-0.291974\pi\) | ||||
0.607994 | + | 0.793942i | \(0.291974\pi\) | |||||||
\(422\) | −0.859502 | −0.0418399 | ||||||||
\(423\) | − | 0.0448209i | − | 0.00217926i | ||||||
\(424\) | − | 1.29571i | − | 0.0629250i | ||||||
\(425\) | 25.1132 | 1.21817 | ||||||||
\(426\) | 22.1754 | 1.07440 | ||||||||
\(427\) | 14.5435 | + | 3.82413i | 0.703807 | + | 0.185063i | ||||
\(428\) | − | 68.6552i | − | 3.31857i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 14.0286i | − | 0.676519i | ||||||
\(431\) | 20.0053i | 0.963622i | 0.876275 | + | 0.481811i | \(0.160021\pi\) | ||||
−0.876275 | + | 0.481811i | \(0.839979\pi\) | |||||||
\(432\) | − | 14.3598i | − | 0.690885i | ||||||
\(433\) | − | 38.5306i | − | 1.85166i | −0.377936 | − | 0.925832i | \(-0.623366\pi\) | ||
0.377936 | − | 0.925832i | \(-0.376634\pi\) | |||||||
\(434\) | −1.36876 | − | 0.359909i | −0.0657027 | − | 0.0172762i | ||||
\(435\) | − | 14.4479i | − | 0.692722i | ||||||
\(436\) | − | 5.62870i | − | 0.269566i | ||||||
\(437\) | −0.943579 | −0.0451375 | ||||||||
\(438\) | 28.9470 | 1.38314 | ||||||||
\(439\) | 24.1486 | 1.15255 | 0.576275 | − | 0.817256i | \(-0.304506\pi\) | ||||
0.576275 | + | 0.817256i | \(0.304506\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.220308 | + | 0.124463i | 0.0104909 | + | 0.00592681i | ||||
\(442\) | 24.3632i | 1.15884i | ||||||||
\(443\) | 20.4613 | 0.972145 | 0.486073 | − | 0.873918i | \(-0.338429\pi\) | ||||
0.486073 | + | 0.873918i | \(0.338429\pi\) | |||||||
\(444\) | − | 54.5828i | − | 2.59039i | ||||||
\(445\) | 12.3455 | 0.585232 | ||||||||
\(446\) | 19.2313 | 0.910630 | ||||||||
\(447\) | 24.1565 | 1.14256 | ||||||||
\(448\) | −26.1869 | − | 6.88571i | −1.23721 | − | 0.325319i | ||||
\(449\) | 0.723387 | 0.0341387 | 0.0170694 | − | 0.999854i | \(-0.494566\pi\) | ||||
0.0170694 | + | 0.999854i | \(0.494566\pi\) | |||||||
\(450\) | − | 0.551396i | − | 0.0259931i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 43.6939 | 2.05519 | ||||||||
\(453\) | 3.51596 | 0.165194 | ||||||||
\(454\) | 65.9553i | 3.09543i | ||||||||
\(455\) | −5.79817 | + | 22.0509i | −0.271822 | + | 1.03376i | ||||
\(456\) | 2.44103 | 0.114312 | ||||||||
\(457\) | 19.8078i | 0.926570i | 0.886209 | + | 0.463285i | \(0.153329\pi\) | ||||
−0.886209 | + | 0.463285i | \(0.846671\pi\) | |||||||
\(458\) | 0.427986 | 0.0199985 | ||||||||
\(459\) | 20.6949i | 0.965953i | ||||||||
\(460\) | − | 36.3674i | − | 1.69564i | ||||||
\(461\) | 35.2596 | 1.64220 | 0.821102 | − | 0.570781i | \(-0.193360\pi\) | ||||
0.821102 | + | 0.570781i | \(0.193360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.0616 | 0.839393 | 0.419696 | − | 0.907665i | \(-0.362137\pi\) | ||||
0.419696 | + | 0.907665i | \(0.362137\pi\) | |||||||
\(464\) | − | 6.84556i | − | 0.317797i | ||||||
\(465\) | − | 1.28972i | − | 0.0598094i | ||||||
\(466\) | 20.9571 | 0.970821 | ||||||||
\(467\) | − | 32.1510i | − | 1.48777i | −0.668308 | − | 0.743884i | \(-0.732981\pi\) | ||
0.668308 | − | 0.743884i | \(-0.267019\pi\) | |||||||
\(468\) | 0.349941 | 0.0161760 | ||||||||
\(469\) | 16.8367 | + | 4.42712i | 0.777445 | + | 0.204425i | ||||
\(470\) | 10.0427i | 0.463236i | ||||||||
\(471\) | −13.1217 | −0.604617 | ||||||||
\(472\) | −38.7282 | −1.78261 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | − | 12.2351i | − | 0.561975i | ||||||
\(475\) | 2.09700 | 0.0962170 | ||||||||
\(476\) | −38.3287 | − | 10.0783i | −1.75679 | − | 0.461939i | ||||
\(477\) | 0.0109207 | 0.000500027 | ||||||||
\(478\) | −11.1980 | −0.512185 | ||||||||
\(479\) | 33.4874 | 1.53008 | 0.765039 | − | 0.643984i | \(-0.222720\pi\) | ||||
0.765039 | + | 0.643984i | \(0.222720\pi\) | |||||||
\(480\) | − | 11.4274i | − | 0.521589i | ||||||
\(481\) | 21.4427 | 0.977701 | ||||||||
\(482\) | − | 16.4700i | − | 0.750188i | ||||||
\(483\) | −3.30593 | + | 12.5727i | −0.150425 | + | 0.572079i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −45.9315 | −2.08564 | ||||||||
\(486\) | 0.903362 | 0.0409773 | ||||||||
\(487\) | −39.5403 | −1.79174 | −0.895871 | − | 0.444315i | \(-0.853447\pi\) | ||||
−0.895871 | + | 0.444315i | \(0.853447\pi\) | |||||||
\(488\) | 24.3766i | 1.10347i | ||||||||
\(489\) | 32.3621i | 1.46346i | ||||||||
\(490\) | −49.3630 | − | 27.8877i | −2.22999 | − | 1.25984i | ||||
\(491\) | − | 19.8538i | − | 0.895991i | −0.894036 | − | 0.447996i | \(-0.852138\pi\) | ||
0.894036 | − | 0.447996i | \(-0.147862\pi\) | |||||||
\(492\) | − | 62.0805i | − | 2.79880i | ||||||
\(493\) | 9.86561i | 0.444325i | ||||||||
\(494\) | 2.03438i | 0.0915310i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.611085i | − | 0.0274385i | ||||||
\(497\) | −13.7051 | − | 3.60370i | −0.614759 | − | 0.161648i | ||||
\(498\) | −32.6871 | −1.46474 | ||||||||
\(499\) | −42.3220 | −1.89459 | −0.947297 | − | 0.320355i | \(-0.896198\pi\) | ||||
−0.947297 | + | 0.320355i | \(0.896198\pi\) | |||||||
\(500\) | 17.1119i | 0.765266i | ||||||||
\(501\) | 33.7093i | 1.50602i | ||||||||
\(502\) | −22.6178 | −1.00948 | ||||||||
\(503\) | −22.7626 | −1.01493 | −0.507467 | − | 0.861671i | \(-0.669418\pi\) | ||||
−0.507467 | + | 0.861671i | \(0.669418\pi\) | |||||||
\(504\) | −0.104307 | + | 0.396689i | −0.00464622 | + | 0.0176699i | ||||
\(505\) | 35.5845i | 1.58349i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.1088i | 0.493361i | ||||||||
\(508\) | − | 41.3828i | − | 1.83607i | ||||||
\(509\) | − | 31.6346i | − | 1.40218i | −0.713074 | − | 0.701089i | \(-0.752698\pi\) | ||
0.713074 | − | 0.701089i | \(-0.247302\pi\) | |||||||
\(510\) | − | 55.2069i | − | 2.44460i | ||||||
\(511\) | −17.8902 | − | 4.70415i | −0.791418 | − | 0.208099i | ||||
\(512\) | − | 28.9792i | − | 1.28071i | ||||||
\(513\) | 1.72806i | 0.0762959i | ||||||||
\(514\) | 13.7285 | 0.605539 | ||||||||
\(515\) | −59.6458 | −2.62831 | ||||||||
\(516\) | −11.2816 | −0.496643 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.5592 | + | 51.5667i | −0.595758 | + | 2.26571i | ||||
\(519\) | − | 15.2816i | − | 0.670790i | ||||||
\(520\) | −36.9599 | −1.62080 | ||||||||
\(521\) | 27.6431i | 1.21107i | 0.795820 | + | 0.605533i | \(0.207040\pi\) | ||||
−0.795820 | + | 0.605533i | \(0.792960\pi\) | |||||||
\(522\) | 0.216614 | 0.00948093 | ||||||||
\(523\) | 39.7393 | 1.73768 | 0.868840 | − | 0.495093i | \(-0.164866\pi\) | ||||
0.868840 | + | 0.495093i | \(0.164866\pi\) | |||||||
\(524\) | 21.4555 | 0.937286 | ||||||||
\(525\) | 7.34708 | − | 27.9415i | 0.320653 | − | 1.21947i | ||||
\(526\) | 7.39195 | 0.322304 | ||||||||
\(527\) | 0.880677i | 0.0383629i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.8541 | −0.645831 | ||||||||
\(530\) | −2.44694 | −0.106288 | ||||||||
\(531\) | − | 0.326417i | − | 0.0141653i | ||||||
\(532\) | −3.20052 | − | 0.841561i | −0.138760 | − | 0.0364863i | ||||
\(533\) | 24.3881 | 1.05637 | ||||||||
\(534\) | − | 15.1763i | − | 0.656741i | ||||||
\(535\) | −61.1161 | −2.64228 | ||||||||
\(536\) | 28.2202i | 1.21893i | ||||||||
\(537\) | − | 15.3628i | − | 0.662953i | ||||||
\(538\) | 28.6806 | 1.23651 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −66.6031 | −2.86614 | ||||||||
\(541\) | − | 5.89488i | − | 0.253441i | −0.991938 | − | 0.126720i | \(-0.959555\pi\) | ||
0.991938 | − | 0.126720i | \(-0.0404451\pi\) | |||||||
\(542\) | 3.73756i | 0.160542i | ||||||||
\(543\) | 20.7879 | 0.892094 | ||||||||
\(544\) | 7.80314i | 0.334557i | ||||||||
\(545\) | −5.01060 | −0.214631 | ||||||||
\(546\) | 27.1071 | + | 7.12767i | 1.16008 | + | 0.305036i | ||||
\(547\) | − | 5.87034i | − | 0.250997i | −0.992094 | − | 0.125499i | \(-0.959947\pi\) | ||
0.992094 | − | 0.125499i | \(-0.0400531\pi\) | |||||||
\(548\) | 66.9398 | 2.85953 | ||||||||
\(549\) | −0.205456 | −0.00876864 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.823799i | 0.0350950i | ||||||||
\(552\) | −21.0734 | −0.896943 | ||||||||
\(553\) | −1.98831 | + | 7.56169i | −0.0845514 | + | 0.321556i | ||||
\(554\) | 30.3757 | 1.29054 | ||||||||
\(555\) | −48.5890 | −2.06249 | ||||||||
\(556\) | 6.74082 | 0.285875 | ||||||||
\(557\) | 13.5359i | 0.573536i | 0.958000 | + | 0.286768i | \(0.0925808\pi\) | ||||
−0.958000 | + | 0.286768i | \(0.907419\pi\) | |||||||
\(558\) | 0.0193365 | 0.000818581 | ||||||||
\(559\) | − | 4.43192i | − | 0.187450i | ||||||
\(560\) | 6.22523 | − | 23.6750i | 0.263064 | − | 1.00045i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 43.6475 | 1.84116 | ||||||||
\(563\) | −32.8714 | −1.38536 | −0.692682 | − | 0.721243i | \(-0.743571\pi\) | ||||
−0.692682 | + | 0.721243i | \(0.743571\pi\) | |||||||
\(564\) | 8.07619 | 0.340069 | ||||||||
\(565\) | − | 38.8958i | − | 1.63636i | ||||||
\(566\) | 46.2043i | 1.94211i | ||||||||
\(567\) | 22.7481 | + | 5.98151i | 0.955332 | + | 0.251200i | ||||
\(568\) | − | 22.9714i | − | 0.963860i | ||||||
\(569\) | 25.7198i | 1.07823i | 0.842232 | + | 0.539115i | \(0.181241\pi\) | ||||
−0.842232 | + | 0.539115i | \(0.818759\pi\) | |||||||
\(570\) | − | 4.60989i | − | 0.193087i | ||||||
\(571\) | − | 16.0855i | − | 0.673156i | −0.941656 | − | 0.336578i | \(-0.890730\pi\) | ||
0.941656 | − | 0.336578i | \(-0.109270\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 22.4298i | − | 0.937019i | ||||||
\(574\) | −15.4218 | + | 58.6501i | −0.643691 | + | 2.44801i | ||||
\(575\) | −18.1034 | −0.754963 | ||||||||
\(576\) | 0.369943 | 0.0154143 | ||||||||
\(577\) | 5.97961i | 0.248934i | 0.992224 | + | 0.124467i | \(0.0397221\pi\) | ||||
−0.992224 | + | 0.124467i | \(0.960278\pi\) | |||||||
\(578\) | − | 3.18514i | − | 0.132484i | ||||||
\(579\) | −22.5618 | −0.937635 | ||||||||
\(580\) | −31.7509 | −1.31838 | ||||||||
\(581\) | 20.2017 | + | 5.31195i | 0.838110 | + | 0.220377i | ||||
\(582\) | 56.4635i | 2.34049i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 29.9862i | − | 1.24084i | ||||||
\(585\) | − | 0.311513i | − | 0.0128795i | ||||||
\(586\) | − | 53.3890i | − | 2.20548i | ||||||
\(587\) | 29.8075i | 1.23029i | 0.788415 | + | 0.615144i | \(0.210902\pi\) | ||||
−0.788415 | + | 0.615144i | \(0.789098\pi\) | |||||||
\(588\) | −22.4268 | + | 39.6969i | −0.924865 | + | 1.63707i | ||||
\(589\) | 0.0735383i | 0.00303009i | ||||||||
\(590\) | 73.1382i | 3.01105i | ||||||||
\(591\) | 10.1692 | 0.418304 | ||||||||
\(592\) | −23.0220 | −0.946199 | ||||||||
\(593\) | −27.7811 | −1.14083 | −0.570416 | − | 0.821356i | \(-0.693218\pi\) | ||||
−0.570416 | + | 0.821356i | \(0.693218\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.97161 | + | 34.1197i | −0.367800 | + | 1.39877i | ||||
\(596\) | − | 53.0868i | − | 2.17452i | ||||||
\(597\) | 12.2327 | 0.500651 | ||||||||
\(598\) | − | 17.5627i | − | 0.718194i | ||||||
\(599\) | 24.1040 | 0.984862 | 0.492431 | − | 0.870352i | \(-0.336108\pi\) | ||||
0.492431 | + | 0.870352i | \(0.336108\pi\) | |||||||
\(600\) | 46.8333 | 1.91196 | ||||||||
\(601\) | −17.8194 | −0.726870 | −0.363435 | − | 0.931620i | \(-0.618396\pi\) | ||||
−0.363435 | + | 0.931620i | \(0.618396\pi\) | |||||||
\(602\) | 10.6582 | + | 2.80252i | 0.434395 | + | 0.114222i | ||||
\(603\) | −0.237852 | −0.00968608 | ||||||||
\(604\) | − | 7.72673i | − | 0.314396i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 43.7439 | 1.77697 | ||||||||
\(607\) | 17.1827 | 0.697426 | 0.348713 | − | 0.937230i | \(-0.386619\pi\) | ||||
0.348713 | + | 0.937230i | \(0.386619\pi\) | |||||||
\(608\) | 0.651578i | 0.0264250i | ||||||||
\(609\) | 10.9767 | + | 2.88627i | 0.444799 | + | 0.116958i | ||||
\(610\) | 46.0352 | 1.86391 | ||||||||
\(611\) | 3.17270i | 0.128354i | ||||||||
\(612\) | 0.541470 | 0.0218876 | ||||||||
\(613\) | 43.3094i | 1.74925i | 0.484801 | + | 0.874625i | \(0.338892\pi\) | ||||
−0.484801 | + | 0.874625i | \(0.661108\pi\) | |||||||
\(614\) | − | 20.0446i | − | 0.808936i | ||||||
\(615\) | −55.2633 | −2.22843 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.5171 | −1.75193 | −0.875967 | − | 0.482371i | \(-0.839776\pi\) | ||||
−0.875967 | + | 0.482371i | \(0.839776\pi\) | |||||||
\(618\) | 73.3223i | 2.94946i | ||||||||
\(619\) | 18.6923i | 0.751305i | 0.926761 | + | 0.375653i | \(0.122581\pi\) | ||||
−0.926761 | + | 0.375653i | \(0.877419\pi\) | |||||||
\(620\) | −2.83432 | −0.113829 | ||||||||
\(621\) | − | 14.9183i | − | 0.598653i | ||||||
\(622\) | −57.7269 | −2.31464 | ||||||||
\(623\) | −2.46628 | + | 9.37945i | −0.0988094 | + | 0.375780i | ||||
\(624\) | 12.1020i | 0.484467i | ||||||||
\(625\) | −16.4819 | −0.659275 | ||||||||
\(626\) | −79.6707 | −3.18428 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 28.8365i | 1.15070i | ||||||||
\(629\) | 33.1786 | 1.32292 | ||||||||
\(630\) | 0.749148 | + | 0.196985i | 0.0298468 | + | 0.00784806i | ||||
\(631\) | −14.6230 | −0.582130 | −0.291065 | − | 0.956703i | \(-0.594010\pi\) | ||||
−0.291065 | + | 0.956703i | \(0.594010\pi\) | |||||||
\(632\) | −12.6743 | −0.504156 | ||||||||
\(633\) | 0.615296 | 0.0244558 | ||||||||
\(634\) | 34.5632i | 1.37268i | ||||||||
\(635\) | −36.8385 | −1.46189 | ||||||||
\(636\) | 1.96779i | 0.0780280i | ||||||||
\(637\) | −15.5948 | − | 8.81029i | −0.617888 | − | 0.349076i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.193613 | 0.00765920 | ||||||||
\(640\) | −69.6152 | −2.75178 | ||||||||
\(641\) | 48.1511 | 1.90185 | 0.950927 | − | 0.309416i | \(-0.100134\pi\) | ||||
0.950927 | + | 0.309416i | \(0.100134\pi\) | |||||||
\(642\) | 75.1298i | 2.96514i | ||||||||
\(643\) | − | 23.4440i | − | 0.924542i | −0.886739 | − | 0.462271i | \(-0.847035\pi\) | ||
0.886739 | − | 0.462271i | \(-0.152965\pi\) | |||||||
\(644\) | 27.6301 | + | 7.26519i | 1.08878 | + | 0.286288i | ||||
\(645\) | 10.0427i | 0.395432i | ||||||||
\(646\) | 3.14783i | 0.123850i | ||||||||
\(647\) | − | 2.36141i | − | 0.0928366i | −0.998922 | − | 0.0464183i | \(-0.985219\pi\) | ||
0.998922 | − | 0.0464183i | \(-0.0147807\pi\) | |||||||
\(648\) | 38.1286i | 1.49783i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 39.0313i | 1.53093i | ||||||||
\(651\) | 0.979863 | + | 0.257650i | 0.0384038 | + | 0.0100981i | ||||
\(652\) | 71.1195 | 2.78525 | ||||||||
\(653\) | −33.1101 | −1.29570 | −0.647850 | − | 0.761768i | \(-0.724332\pi\) | ||||
−0.647850 | + | 0.761768i | \(0.724332\pi\) | |||||||
\(654\) | 6.15952i | 0.240856i | ||||||||
\(655\) | − | 19.0994i | − | 0.746275i | ||||||
\(656\) | −26.1844 | −1.02233 | ||||||||
\(657\) | 0.252736 | 0.00986017 | ||||||||
\(658\) | −7.62993 | − | 2.00625i | −0.297446 | − | 0.0782118i | ||||
\(659\) | 4.56667i | 0.177892i | 0.996036 | + | 0.0889462i | \(0.0283499\pi\) | ||||
−0.996036 | + | 0.0889462i | \(0.971650\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 13.7734i | − | 0.535722i | −0.963458 | − | 0.267861i | \(-0.913683\pi\) | ||
0.963458 | − | 0.267861i | \(-0.0863167\pi\) | |||||||
\(662\) | − | 15.1082i | − | 0.587196i | ||||||
\(663\) | − | 17.4410i | − | 0.677352i | ||||||
\(664\) | 33.8605i | 1.31404i | ||||||||
\(665\) | −0.749148 | + | 2.84907i | −0.0290507 | + | 0.110482i | ||||
\(666\) | − | 0.728485i | − | 0.0282282i | ||||||
\(667\) | − | 7.11185i | − | 0.275372i | ||||||
\(668\) | 74.0803 | 2.86625 | ||||||||
\(669\) | −13.7672 | −0.532272 | ||||||||
\(670\) | 53.2940 | 2.05893 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 8.68197 | + | 2.28288i | 0.334914 | + | 0.0880640i | ||||
\(673\) | − | 29.9766i | − | 1.15551i | −0.816209 | − | 0.577757i | \(-0.803928\pi\) | ||
0.816209 | − | 0.577757i | \(-0.196072\pi\) | |||||||
\(674\) | −56.3469 | −2.17040 | ||||||||
\(675\) | 33.1544i | 1.27611i | ||||||||
\(676\) | 24.4130 | 0.938961 | ||||||||
\(677\) | −13.7766 | −0.529479 | −0.264740 | − | 0.964320i | \(-0.585286\pi\) | ||||
−0.264740 | + | 0.964320i | \(0.585286\pi\) | |||||||
\(678\) | −47.8145 | −1.83631 | ||||||||
\(679\) | 9.17582 | − | 34.8963i | 0.352135 | − | 1.33920i | ||||
\(680\) | −57.1887 | −2.19309 | ||||||||
\(681\) | − | 47.2157i | − | 1.80931i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.5882 | 0.558201 | 0.279101 | − | 0.960262i | \(-0.409964\pi\) | ||||
0.279101 | + | 0.960262i | \(0.409964\pi\) | |||||||
\(684\) | 0.0452139 | 0.00172880 | ||||||||
\(685\) | − | 59.5890i | − | 2.27678i | ||||||
\(686\) | 31.0489 | − | 31.9322i | 1.18545 | − | 1.21918i | ||||
\(687\) | −0.306385 | −0.0116893 | ||||||||
\(688\) | 4.75836i | 0.181411i | ||||||||
\(689\) | −0.773039 | −0.0294505 | ||||||||
\(690\) | 39.7971i | 1.51505i | ||||||||
\(691\) | 19.9764i | 0.759938i | 0.924999 | + | 0.379969i | \(0.124065\pi\) | ||||
−0.924999 | + | 0.379969i | \(0.875935\pi\) | |||||||
\(692\) | −33.5832 | −1.27664 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 43.1266 | 1.63706 | ||||||||
\(695\) | − | 6.00060i | − | 0.227616i | ||||||
\(696\) | 18.3983i | 0.697386i | ||||||||
\(697\) | 37.7361 | 1.42936 | ||||||||
\(698\) | 52.4003i | 1.98338i | ||||||||
\(699\) | −15.0027 | −0.567454 | ||||||||
\(700\) | −61.4048 | − | 16.1461i | −2.32088 | − | 0.610265i | ||||
\(701\) | − | 41.4302i | − | 1.56480i | −0.622778 | − | 0.782399i | \(-0.713996\pi\) | ||
0.622778 | − | 0.782399i | \(-0.286004\pi\) | |||||||
\(702\) | −32.1643 | −1.21396 | ||||||||
\(703\) | 2.77048 | 0.104491 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 7.18934i | − | 0.270766i | ||||||
\(706\) | −39.3805 | −1.48210 | ||||||||
\(707\) | −27.0352 | − | 7.10877i | −1.01676 | − | 0.267353i | ||||
\(708\) | 58.8166 | 2.21046 | ||||||||
\(709\) | 15.1482 | 0.568903 | 0.284451 | − | 0.958690i | \(-0.408189\pi\) | ||||
0.284451 | + | 0.958690i | \(0.408189\pi\) | |||||||
\(710\) | −43.3816 | −1.62808 | ||||||||
\(711\) | − | 0.106824i | − | 0.00400622i | ||||||
\(712\) | −15.7211 | −0.589172 | ||||||||
\(713\) | − | 0.634855i | − | 0.0237755i | ||||||
\(714\) | 41.9433 | + | 11.0288i | 1.56969 | + | 0.412742i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −33.7616 | −1.26173 | ||||||||
\(717\) | 8.01638 | 0.299377 | ||||||||
\(718\) | 43.7895 | 1.63421 | ||||||||
\(719\) | − | 25.7442i | − | 0.960098i | −0.877242 | − | 0.480049i | \(-0.840619\pi\) | ||
0.877242 | − | 0.480049i | \(-0.159381\pi\) | |||||||
\(720\) | 0.334458i | 0.0124645i | ||||||||
\(721\) | 11.9155 | − | 45.3157i | 0.443758 | − | 1.68764i | ||||
\(722\) | − | 45.4296i | − | 1.69072i | ||||||
\(723\) | 11.7905i | 0.438492i | ||||||||
\(724\) | − | 45.6839i | − | 1.69783i | ||||||
\(725\) | 15.8053i | 0.586994i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.52144i | − | 0.353130i | −0.984289 | − | 0.176565i | \(-0.943501\pi\) | ||
0.984289 | − | 0.176565i | \(-0.0564987\pi\) | |||||||
\(728\) | 7.38354 | − | 28.0802i | 0.273652 | − | 1.04072i | ||||
\(729\) | −27.3174 | −1.01176 | ||||||||
\(730\) | −56.6289 | −2.09593 | ||||||||
\(731\) | − | 6.85760i | − | 0.253637i | ||||||
\(732\) | − | 37.0207i | − | 1.36833i | ||||||
\(733\) | −39.7320 | −1.46753 | −0.733767 | − | 0.679402i | \(-0.762239\pi\) | ||||
−0.733767 | + | 0.679402i | \(0.762239\pi\) | |||||||
\(734\) | −2.02384 | −0.0747014 | ||||||||
\(735\) | 35.3377 | + | 19.9641i | 1.30345 | + | 0.736386i | ||||
\(736\) | − | 5.62506i | − | 0.207343i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 0.828552i | − | 0.0304994i | ||||||
\(739\) | 28.5519i | 1.05030i | 0.851010 | + | 0.525149i | \(0.175990\pi\) | ||||
−0.851010 | + | 0.525149i | \(0.824010\pi\) | |||||||
\(740\) | 106.780i | 3.92531i | ||||||||
\(741\) | − | 1.45636i | − | 0.0535007i | ||||||
\(742\) | 0.488830 | − | 1.85906i | 0.0179455 | − | 0.0682481i | ||||
\(743\) | − | 0.145438i | − | 0.00533560i | −0.999996 | − | 0.00266780i | \(-0.999151\pi\) | ||
0.999996 | − | 0.00266780i | \(-0.000849188\pi\) | |||||||
\(744\) | 1.64237i | 0.0602121i | ||||||||
\(745\) | −47.2572 | −1.73137 | ||||||||
\(746\) | 62.3227 | 2.28180 | ||||||||
\(747\) | −0.285391 | −0.0104419 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.2093 | − | 46.4328i | 0.446117 | − | 1.69662i | ||||
\(750\) | − | 18.7256i | − | 0.683763i | ||||||
\(751\) | 9.10902 | 0.332393 | 0.166196 | − | 0.986093i | \(-0.446851\pi\) | ||||
0.166196 | + | 0.986093i | \(0.446851\pi\) | |||||||
\(752\) | − | 3.40639i | − | 0.124218i | ||||||
\(753\) | 16.1915 | 0.590052 | ||||||||
\(754\) | −15.3333 | −0.558406 | ||||||||
\(755\) | −6.87825 | −0.250325 | ||||||||
\(756\) | 13.3054 | − | 50.6015i | 0.483913 | − | 1.84036i | ||||
\(757\) | −19.4693 | −0.707624 | −0.353812 | − | 0.935316i | \(-0.615115\pi\) | ||||
−0.353812 | + | 0.935316i | \(0.615115\pi\) | |||||||
\(758\) | 21.1705i | 0.768946i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.77538 | −0.173221 | ||||||||
\(761\) | 13.0673 | 0.473689 | 0.236845 | − | 0.971548i | \(-0.423887\pi\) | ||||
0.236845 | + | 0.971548i | \(0.423887\pi\) | |||||||
\(762\) | 45.2855i | 1.64052i | ||||||||
\(763\) | 1.00098 | − | 3.80679i | 0.0362378 | − | 0.137815i | ||||
\(764\) | −49.2922 | −1.78333 | ||||||||
\(765\) | − | 0.482010i | − | 0.0174271i | ||||||
\(766\) | 31.4903 | 1.13779 | ||||||||
\(767\) | 23.1059i | 0.834305i | ||||||||
\(768\) | 50.3398i | 1.81648i | ||||||||
\(769\) | 28.5921 | 1.03106 | 0.515529 | − | 0.856872i | \(-0.327595\pi\) | ||||
0.515529 | + | 0.856872i | \(0.327595\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.82790 | −0.353943 | ||||||||
\(772\) | 49.5822i | 1.78450i | ||||||||
\(773\) | − | 7.74692i | − | 0.278637i | −0.990248 | − | 0.139319i | \(-0.955509\pi\) | ||
0.990248 | − | 0.139319i | \(-0.0444912\pi\) | |||||||
\(774\) | −0.150568 | −0.00541207 | ||||||||
\(775\) | 1.41090i | 0.0506809i | ||||||||
\(776\) | 58.4904 | 2.09968 | ||||||||
\(777\) | 9.70670 | − | 36.9153i | 0.348226 | − | 1.32433i | ||||
\(778\) | − | 24.1609i | − | 0.866210i | ||||||
\(779\) | 3.15105 | 0.112898 | ||||||||
\(780\) | 56.1311 | 2.00981 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 27.1751i | − | 0.971781i | ||||||
\(783\) | −13.0246 | −0.465461 | ||||||||
\(784\) | 16.7434 | + | 9.45920i | 0.597979 | + | 0.337829i | ||||
\(785\) | 25.6700 | 0.916200 | ||||||||
\(786\) | −23.4788 | −0.837462 | ||||||||
\(787\) | −22.1352 | −0.789033 | −0.394517 | − | 0.918889i | \(-0.629088\pi\) | ||||
−0.394517 | + | 0.918889i | \(0.629088\pi\) | |||||||
\(788\) | − | 22.3480i | − | 0.796113i | ||||||
\(789\) | −5.29171 | −0.188390 | ||||||||
\(790\) | 23.9354i | 0.851583i | ||||||||
\(791\) | 29.5510 | + | 7.77029i | 1.05071 | + | 0.276280i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.5435 | 0.516453 | ||||||||
\(794\) | 37.2039 | 1.32032 | ||||||||
\(795\) | 1.75170 | 0.0621266 | ||||||||
\(796\) | − | 26.8828i | − | 0.952835i | ||||||
\(797\) | 16.0101i | 0.567106i | 0.958956 | + | 0.283553i | \(0.0915133\pi\) | ||||
−0.958956 | + | 0.283553i | \(0.908487\pi\) | |||||||
\(798\) | 3.50235 | + | 0.920926i | 0.123982 | + | 0.0326004i | ||||
\(799\) | 4.90918i | 0.173674i | ||||||||
\(800\) | 12.5011i | 0.441980i | ||||||||
\(801\) | − | 0.132504i | − | 0.00468179i | ||||||
\(802\) | − | 77.5443i | − | 2.73819i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 42.8581i | − | 1.51149i | ||||||
\(805\) | 6.46738 | − | 24.5960i | 0.227945 | − | 0.866894i | ||||
\(806\) | −1.36876 | −0.0482126 | ||||||||
\(807\) | −20.5317 | −0.722751 | ||||||||
\(808\) | − | 45.3142i | − | 1.59415i | ||||||
\(809\) | − | 14.9223i | − | 0.524639i | −0.964981 | − | 0.262320i | \(-0.915513\pi\) | ||
0.964981 | − | 0.262320i | \(-0.0844875\pi\) | |||||||
\(810\) | 72.0058 | 2.53003 | ||||||||
\(811\) | 6.89031 | 0.241951 | 0.120976 | − | 0.992655i | \(-0.461398\pi\) | ||||
0.120976 | + | 0.992655i | \(0.461398\pi\) | |||||||
\(812\) | 6.34293 | − | 24.1227i | 0.222593 | − | 0.846539i | ||||
\(813\) | − | 2.67562i | − | 0.0938382i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 63.3097i | − | 2.21764i | ||||||
\(816\) | 18.7256i | 0.655527i | ||||||||
\(817\) | − | 0.572624i | − | 0.0200336i | ||||||
\(818\) | 12.1036i | 0.423192i | ||||||||
\(819\) | 0.236671 | + | 0.0622316i | 0.00826997 | + | 0.00217455i | ||||
\(820\) | 121.448i | 4.24114i | ||||||||
\(821\) | 16.2509i | 0.567162i | 0.958948 | + | 0.283581i | \(0.0915224\pi\) | ||||
−0.958948 | + | 0.283581i | \(0.908478\pi\) | |||||||
\(822\) | −73.2526 | −2.55498 | ||||||||
\(823\) | 8.89861 | 0.310186 | 0.155093 | − | 0.987900i | \(-0.450432\pi\) | ||||
0.155093 | + | 0.987900i | \(0.450432\pi\) | |||||||
\(824\) | 75.9545 | 2.64600 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −55.5666 | − | 14.6109i | −1.93341 | − | 0.508380i | ||||
\(827\) | 0.562239i | 0.0195510i | 0.999952 | + | 0.00977549i | \(0.00311168\pi\) | ||||
−0.999952 | + | 0.00977549i | \(0.996888\pi\) | |||||||
\(828\) | −0.390331 | −0.0135649 | ||||||||
\(829\) | 6.47699i | 0.224955i | 0.993654 | + | 0.112478i | \(0.0358786\pi\) | ||||
−0.993654 | + | 0.112478i | \(0.964121\pi\) | |||||||
\(830\) | 63.9456 | 2.21959 | ||||||||
\(831\) | −21.7452 | −0.754332 | ||||||||
\(832\) | −26.1869 | −0.907867 | ||||||||
\(833\) | −24.1301 | − | 13.6323i | −0.836058 | − | 0.472332i | ||||
\(834\) | −7.37652 | −0.255428 | ||||||||
\(835\) | − | 65.9454i | − | 2.28214i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.16267 | −0.0401877 | ||||||||
\(838\) | 40.6402 | 1.40389 | ||||||||
\(839\) | 12.4170i | 0.428683i | 0.976759 | + | 0.214341i | \(0.0687605\pi\) | ||||
−0.976759 | + | 0.214341i | \(0.931240\pi\) | |||||||
\(840\) | −16.7311 | + | 63.6296i | −0.577277 | + | 2.19543i | ||||
\(841\) | 22.7909 | 0.785895 | ||||||||
\(842\) | 60.0014i | 2.06779i | ||||||||
\(843\) | −31.2461 | −1.07617 | ||||||||
\(844\) | − | 1.35219i | − | 0.0465442i | ||||||
\(845\) | − | 21.7322i | − | 0.747609i | ||||||
\(846\) | 0.107788 | 0.00370584 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.829977 | 0.0285015 | ||||||||
\(849\) | − | 33.0765i | − | 1.13518i | ||||||
\(850\) | 60.3938i | 2.07149i | ||||||||
\(851\) | −23.9175 | −0.819883 | ||||||||
\(852\) | 34.8867i | 1.19520i | ||||||||
\(853\) | 48.5706 | 1.66303 | 0.831513 | − | 0.555505i | \(-0.187475\pi\) | ||||
0.831513 | + | 0.555505i | \(0.187475\pi\) | |||||||
\(854\) | −9.19652 | + | 34.9751i | −0.314698 | + | 1.19682i | ||||
\(855\) | − | 0.0402489i | − | 0.00137648i | ||||||
\(856\) | 77.8268 | 2.66007 | ||||||||
\(857\) | 10.2702 | 0.350825 | 0.175412 | − | 0.984495i | \(-0.443874\pi\) | ||||
0.175412 | + | 0.984495i | \(0.443874\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.0409i | 1.70737i | 0.520787 | + | 0.853687i | \(0.325639\pi\) | ||||
−0.520787 | + | 0.853687i | \(0.674361\pi\) | |||||||
\(860\) | 22.0701 | 0.752584 | ||||||||
\(861\) | 11.0400 | − | 41.9862i | 0.376244 | − | 1.43088i | ||||
\(862\) | −48.1101 | −1.63864 | ||||||||
\(863\) | −23.6080 | −0.803626 | −0.401813 | − | 0.915722i | \(-0.631620\pi\) | ||||
−0.401813 | + | 0.915722i | \(0.631620\pi\) | |||||||
\(864\) | −10.3017 | −0.350471 | ||||||||
\(865\) | 29.8954i | 1.01647i | ||||||||
\(866\) | 92.6610 | 3.14875 | ||||||||
\(867\) | 2.28016i | 0.0774383i | ||||||||
\(868\) | 0.566216 | − | 2.15336i | 0.0192186 | − | 0.0730900i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 34.7452 | 1.17797 | ||||||||
\(871\) | 16.8367 | 0.570489 | ||||||||
\(872\) | 6.38063 | 0.216075 | ||||||||
\(873\) | 0.492981i | 0.0166849i | ||||||||
\(874\) | − | 2.26918i | − | 0.0767562i | ||||||
\(875\) | −3.04308 | + | 11.5731i | −0.102875 | + | 0.391241i | ||||
\(876\) | 45.5401i | 1.53866i | ||||||||
\(877\) | 40.3865i | 1.36376i | 0.731466 | + | 0.681878i | \(0.238837\pi\) | ||||
−0.731466 | + | 0.681878i | \(0.761163\pi\) | |||||||
\(878\) | 58.0742i | 1.95991i | ||||||||
\(879\) | 38.2199i | 1.28912i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.4238i | − | 0.519640i | −0.965657 | − | 0.259820i | \(-0.916337\pi\) | ||
0.965657 | − | 0.259820i | \(-0.0836632\pi\) | |||||||
\(882\) | −0.299317 | + | 0.529811i | −0.0100785 | + | 0.0178397i | ||||
\(883\) | −21.2723 | −0.715871 | −0.357936 | − | 0.933746i | \(-0.616519\pi\) | ||||
−0.357936 | + | 0.933746i | \(0.616519\pi\) | |||||||
\(884\) | −38.3287 | −1.28913 | ||||||||
\(885\) | − | 52.3578i | − | 1.75999i | ||||||
\(886\) | 49.2067i | 1.65313i | ||||||||
\(887\) | 52.6456 | 1.76766 | 0.883832 | − | 0.467804i | \(-0.154955\pi\) | ||||
0.883832 | + | 0.467804i | \(0.154955\pi\) | |||||||
\(888\) | 61.8745 | 2.07637 | ||||||||
\(889\) | 7.35930 | − | 27.9880i | 0.246823 | − | 0.938686i | ||||
\(890\) | 29.6893i | 0.995186i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30.2551i | 1.01302i | ||||||||
\(893\) | 0.409927i | 0.0137177i | ||||||||
\(894\) | 58.0932i | 1.94293i | ||||||||
\(895\) | 30.0542i | 1.00460i | ||||||||
\(896\) | 13.9071 | − | 52.8900i | 0.464605 | − | 1.76693i | ||||
\(897\) | 12.5727i | 0.419791i | ||||||||
\(898\) | 1.73965i | 0.0580529i | ||||||||
\(899\) | −0.554266 | −0.0184858 | ||||||||
\(900\) | 0.867467 | 0.0289156 | ||||||||
\(901\) | −1.19614 | −0.0398491 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.62993 | − | 2.00625i | −0.253908 | − | 0.0667639i | ||||
\(904\) | 49.5310i | 1.64738i | ||||||||
\(905\) | −40.6672 | −1.35182 | ||||||||
\(906\) | 8.45541i | 0.280912i | ||||||||
\(907\) | −48.8193 | −1.62102 | −0.810510 | − | 0.585725i | \(-0.800810\pi\) | ||||
−0.810510 | + | 0.585725i | \(0.800810\pi\) | |||||||
\(908\) | −103.762 | −3.44347 | ||||||||
\(909\) | 0.381927 | 0.0126677 | ||||||||
\(910\) | −53.0295 | − | 13.9438i | −1.75791 | − | 0.462233i | ||||
\(911\) | 8.39025 | 0.277981 | 0.138991 | − | 0.990294i | \(-0.455614\pi\) | ||||
0.138991 | + | 0.990294i | \(0.455614\pi\) | |||||||
\(912\) | 1.56363i | 0.0517769i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −47.6351 | −1.57563 | ||||||||
\(915\) | −32.9554 | −1.08947 | ||||||||
\(916\) | 0.673316i | 0.0222470i | ||||||||
\(917\) | 14.5107 | + | 3.81552i | 0.479186 | + | 0.126000i | ||||
\(918\) | −49.7684 | −1.64260 | ||||||||
\(919\) | 11.9849i | 0.395345i | 0.980268 | + | 0.197673i | \(0.0633383\pi\) | ||||
−0.980268 | + | 0.197673i | \(0.936662\pi\) | |||||||
\(920\) | 41.2258 | 1.35917 | ||||||||
\(921\) | 14.3495i | 0.472831i | ||||||||
\(922\) | 84.7947i | 2.79257i | ||||||||
\(923\) | −13.7051 | −0.451110 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 53.1541 | 1.74770 | ||||||||
\(926\) | 43.4357i | 1.42739i | ||||||||
\(927\) | 0.640176i | 0.0210261i | ||||||||
\(928\) | −4.91101 | −0.161212 | ||||||||
\(929\) | − | 35.5102i | − | 1.16505i | −0.812813 | − | 0.582525i | \(-0.802065\pi\) | ||
0.812813 | − | 0.582525i | \(-0.197935\pi\) | |||||||
\(930\) | 3.10161 | 0.101706 | ||||||||
\(931\) | −2.01491 | − | 1.13833i | −0.0660361 | − | 0.0373071i | ||||
\(932\) | 32.9702i | 1.07998i | ||||||||
\(933\) | 41.3253 | 1.35293 | ||||||||
\(934\) | 77.3188 | 2.52995 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.396689i | 0.0129662i | ||||||||
\(937\) | 34.0379 | 1.11197 | 0.555985 | − | 0.831192i | \(-0.312341\pi\) | ||||
0.555985 | + | 0.831192i | \(0.312341\pi\) | |||||||
\(938\) | −10.6466 | + | 40.4899i | −0.347625 | + | 1.32204i | ||||
\(939\) | 57.0343 | 1.86124 | ||||||||
\(940\) | −15.7994 | −0.515320 | ||||||||
\(941\) | −54.7684 | −1.78540 | −0.892700 | − | 0.450651i | \(-0.851192\pi\) | ||||
−0.892700 | + | 0.450651i | \(0.851192\pi\) | |||||||
\(942\) | − | 31.5560i | − | 1.02815i | ||||||
\(943\) | −27.2029 | −0.885849 | ||||||||
\(944\) | − | 24.8077i | − | 0.807423i | ||||||
\(945\) | −45.0449 | − | 11.8443i | −1.46531 | − | 0.385296i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.4024 | −0.565501 | −0.282750 | − | 0.959194i | \(-0.591247\pi\) | ||||
−0.282750 | + | 0.959194i | \(0.591247\pi\) | |||||||
\(948\) | 19.2485 | 0.625161 | ||||||||
\(949\) | −17.8902 | −0.580742 | ||||||||
\(950\) | 5.04301i | 0.163617i | ||||||||
\(951\) | − | 24.7429i | − | 0.802343i | ||||||
\(952\) | 11.4247 | − | 43.4490i | 0.370276 | − | 1.40819i | ||||
\(953\) | − | 5.02084i | − | 0.162641i | −0.996688 | − | 0.0813205i | \(-0.974086\pi\) | ||
0.996688 | − | 0.0813205i | \(-0.0259137\pi\) | |||||||
\(954\) | 0.0262629i | 0.000850294i | ||||||||
\(955\) | 43.8793i | 1.41990i | ||||||||
\(956\) | − | 17.6169i | − | 0.569772i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 80.5327i | 2.60189i | ||||||||
\(959\) | 45.2726 | + | 11.9042i | 1.46193 | + | 0.384407i | ||||
\(960\) | 59.3394 | 1.91517 | ||||||||
\(961\) | 30.9505 | 0.998404 | ||||||||
\(962\) | 51.5667i | 1.66258i | ||||||||
\(963\) | 0.655957i | 0.0211379i | ||||||||
\(964\) | 25.9109 | 0.834535 | ||||||||
\(965\) | 44.1375 | 1.42084 | ||||||||
\(966\) | −30.2357 | − | 7.95033i | −0.972819 | − | 0.255798i | ||||
\(967\) | 47.8640i | 1.53920i | 0.638525 | + | 0.769601i | \(0.279545\pi\) | ||||
−0.638525 | + | 0.769601i | \(0.720455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 2.25345i | − | 0.0723913i | ||||||
\(970\) | − | 110.459i | − | 3.54663i | ||||||
\(971\) | − | 48.2135i | − | 1.54725i | −0.633647 | − | 0.773623i | \(-0.718443\pi\) | ||
0.633647 | − | 0.773623i | \(-0.281557\pi\) | |||||||
\(972\) | 1.42119i | 0.0455846i | ||||||||
\(973\) | 4.55894 | + | 1.19875i | 0.146153 | + | 0.0384302i | ||||
\(974\) | − | 95.0891i | − | 3.04685i | ||||||
\(975\) | − | 27.9415i | − | 0.894845i | ||||||
\(976\) | −15.6146 | −0.499813 | ||||||||
\(977\) | −47.3991 | −1.51643 | −0.758215 | − | 0.652004i | \(-0.773928\pi\) | ||||
−0.758215 | + | 0.652004i | \(0.773928\pi\) | |||||||
\(978\) | −77.8265 | −2.48862 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 43.8734 | − | 77.6589i | 1.40149 | − | 2.48072i | ||||
\(981\) | 0.0537786i | 0.00171702i | ||||||||
\(982\) | 47.7458 | 1.52363 | ||||||||
\(983\) | − | 24.2686i | − | 0.774048i | −0.922070 | − | 0.387024i | \(-0.873503\pi\) | ||
0.922070 | − | 0.387024i | \(-0.126497\pi\) | |||||||
\(984\) | 70.3738 | 2.24343 | ||||||||
\(985\) | −19.8939 | −0.633873 | ||||||||
\(986\) | −23.7255 | −0.755574 | ||||||||
\(987\) | 5.46208 | + | 1.43623i | 0.173860 | + | 0.0457156i | ||||
\(988\) | −3.20052 | −0.101822 | ||||||||
\(989\) | 4.94345i | 0.157193i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.5976 | 0.844902 | 0.422451 | − | 0.906386i | \(-0.361170\pi\) | ||||
0.422451 | + | 0.906386i | \(0.361170\pi\) | |||||||
\(992\) | −0.438393 | −0.0139190 | ||||||||
\(993\) | 10.8156i | 0.343221i | ||||||||
\(994\) | 8.66641 | − | 32.9590i | 0.274882 | − | 1.04540i | ||||
\(995\) | −23.9308 | −0.758656 | ||||||||
\(996\) | − | 51.4240i | − | 1.62943i | ||||||
\(997\) | −7.24781 | −0.229540 | −0.114770 | − | 0.993392i | \(-0.536613\pi\) | ||||
−0.114770 | + | 0.993392i | \(0.536613\pi\) | |||||||
\(998\) | − | 101.779i | − | 3.22175i | ||||||
\(999\) | 43.8024i | 1.38585i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))