Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), 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: | \(14.6924739719\) |
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: | \( x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} - 1594 x^{7} + 2464 x^{6} + 9568 x^{5} + 15457 x^{4} + 4336 x^{3} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.7 | ||
Root | \(1.95202 - 1.95202i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.h.369.10 |
$q$-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 \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 0.493532i | − | 0.284941i | −0.989799 | − | 0.142470i | \(-0.954495\pi\) | ||
0.989799 | − | 0.142470i | \(-0.0455045\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.09069 | + | 1.95202i | 0.487771 | + | 0.872972i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.54439i | 1.71762i | 0.512297 | + | 0.858809i | \(0.328795\pi\) | ||||
−0.512297 | + | 0.858809i | \(0.671205\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.75643 | 0.918809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.61297 | 1.39086 | 0.695431 | − | 0.718593i | \(-0.255213\pi\) | ||||
0.695431 | + | 0.718593i | \(0.255213\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.54274i | − | 1.53728i | −0.639682 | − | 0.768640i | \(-0.720934\pi\) | ||
0.639682 | − | 0.768640i | \(-0.279066\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.963386 | − | 0.538289i | 0.248745 | − | 0.138986i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.16998i | − | 1.73897i | −0.493955 | − | 0.869487i | \(-0.664449\pi\) | ||
0.493955 | − | 0.869487i | \(-0.335551\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.35966 | 0.311928 | 0.155964 | − | 0.987763i | \(-0.450152\pi\) | ||||
0.155964 | + | 0.987763i | \(0.450152\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.24280 | 0.489419 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.62080 | + | 4.25810i | −0.524159 | + | 0.851620i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.84098i | − | 0.546747i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.66351 | 0.680297 | 0.340148 | − | 0.940372i | \(-0.389523\pi\) | ||||
0.340148 | + | 0.940372i | \(0.389523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.46616 | 0.802146 | 0.401073 | − | 0.916046i | \(-0.368637\pi\) | ||||
0.401073 | + | 0.916046i | \(0.368637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.27665i | − | 0.396313i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.87075 | + | 4.95651i | −1.49943 | + | 0.837804i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.32432i | − | 0.546514i | −0.961941 | − | 0.273257i | \(-0.911899\pi\) | ||
0.961941 | − | 0.273257i | \(-0.0881010\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.73552 | −0.438033 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.95216 | 1.39809 | 0.699046 | − | 0.715076i | \(-0.253608\pi\) | ||||
0.699046 | + | 0.715076i | \(0.253608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.68458i | − | 1.32439i | −0.749333 | − | 0.662193i | \(-0.769626\pi\) | ||
0.749333 | − | 0.662193i | \(-0.230374\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.00640 | + | 5.38061i | 0.448168 | + | 0.802094i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.59028i | 1.39889i | 0.714688 | + | 0.699443i | \(0.246569\pi\) | ||||
−0.714688 | + | 0.699443i | \(0.753431\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.6515 | −1.95021 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.53861 | −0.495505 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4676i | 1.43784i | 0.695095 | + | 0.718918i | \(0.255362\pi\) | ||||
−0.695095 | + | 0.718918i | \(0.744638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.03131 | + | 9.00463i | 0.678422 | + | 1.21418i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.671035i | − | 0.0888808i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.08543 | −0.271499 | −0.135750 | − | 0.990743i | \(-0.543344\pi\) | ||||
−0.135750 | + | 0.990743i | \(0.543344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.686197 | −0.0878586 | −0.0439293 | − | 0.999035i | \(-0.513988\pi\) | ||||
−0.0439293 | + | 0.999035i | \(0.513988\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.5263i | 1.57816i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.8196 | − | 6.04540i | 1.34200 | − | 0.749840i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.84324i | 1.08037i | 0.841545 | + | 0.540187i | \(0.181646\pi\) | ||||
−0.841545 | + | 0.540187i | \(0.818354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.493532 | 0.0594142 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.9040 | −1.88746 | −0.943729 | − | 0.330721i | \(-0.892708\pi\) | ||||
−0.943729 | + | 0.330721i | \(0.892708\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.44647i | 0.520420i | 0.965552 | + | 0.260210i | \(0.0837918\pi\) | ||||
−0.965552 | + | 0.260210i | \(0.916208\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.10151 | + | 1.29345i | 0.242661 | + | 0.149354i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.9631i | 2.38897i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.65227 | −0.973457 | −0.486728 | − | 0.873553i | \(-0.661810\pi\) | ||||
−0.486728 | + | 0.873553i | \(0.661810\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.86717 | 0.763019 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.43591i | 0.486904i | 0.969913 | + | 0.243452i | \(0.0782798\pi\) | ||||
−0.969913 | + | 0.243452i | \(0.921720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.9960 | − | 7.82021i | 1.51808 | − | 0.848221i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 1.80806i | − | 0.193844i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.2284 | −1.40220 | −0.701102 | − | 0.713061i | \(-0.747308\pi\) | ||||
−0.701102 | + | 0.713061i | \(0.747308\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.1884 | 2.64046 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 2.20419i | − | 0.228564i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.48297 | + | 2.65409i | 0.152149 | + | 0.272304i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.21785i | 0.123654i | 0.998087 | + | 0.0618270i | \(0.0196927\pi\) | ||||
−0.998087 | + | 0.0618270i | \(0.980307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.7153 | 1.27794 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4999 | 1.04478 | 0.522390 | − | 0.852706i | \(-0.325040\pi\) | ||||
0.522390 | + | 0.852706i | \(0.325040\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.32614i | − | 0.820399i | −0.911996 | − | 0.410200i | \(-0.865459\pi\) | ||
0.911996 | − | 0.410200i | \(-0.134541\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.44620 | + | 4.37800i | 0.238724 | + | 0.427249i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 9.60096i | − | 0.928160i | −0.885793 | − | 0.464080i | \(-0.846385\pi\) | ||
0.885793 | − | 0.464080i | \(-0.153615\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.2997 | −0.986534 | −0.493267 | − | 0.869878i | \(-0.664197\pi\) | ||||
−0.493267 | + | 0.869878i | \(0.664197\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.64066 | −0.155724 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 16.2479i | − | 1.52848i | −0.644933 | − | 0.764239i | \(-0.723115\pi\) | ||
0.644933 | − | 0.764239i | \(-0.276885\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.95202 | + | 1.09069i | −0.182027 | + | 0.101707i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 15.2782i | − | 1.41247i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 32.5832 | 2.98689 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.2795 | 0.934498 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 4.41817i | − | 0.398373i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1704 | − | 0.471594i | −0.999110 | − | 0.0421806i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.58555i | − | 0.140695i | −0.997523 | − | 0.0703473i | \(-0.977589\pi\) | ||
0.997523 | − | 0.0703473i | \(-0.0224108\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.28612 | −0.377371 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.69595 | −0.410287 | −0.205143 | − | 0.978732i | \(-0.565766\pi\) | ||||
−0.205143 | + | 0.978732i | \(0.565766\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.17882i | 0.535772i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.54566 | − | 3.09862i | 0.477294 | − | 0.266687i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.3059i | 0.880494i | 0.897877 | + | 0.440247i | \(0.145109\pi\) | ||||
−0.897877 | + | 0.440247i | \(0.854891\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.673372 | 0.0571147 | 0.0285573 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285573 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.73311 | 0.398599 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 25.5685i | − | 2.13814i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.99575 | + | 7.15126i | 0.331829 | + | 0.593880i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.73743i | 0.555694i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.74118 | 0.388413 | 0.194206 | − | 0.980961i | \(-0.437787\pi\) | ||||
0.194206 | + | 0.980961i | \(0.437787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.16664 | −0.257698 | −0.128849 | − | 0.991664i | \(-0.541128\pi\) | ||||
−0.128849 | + | 0.991664i | \(0.541128\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 19.7635i | − | 1.59779i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.87119 | + | 8.71805i | 0.391263 | + | 0.700251i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.07863i | 0.644745i | 0.946613 | + | 0.322373i | \(0.104480\pi\) | ||||
−0.946613 | + | 0.322373i | \(0.895520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.16609 | 0.409698 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.54439 | −0.358148 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.25691i | 0.176775i | 0.996086 | + | 0.0883876i | \(0.0281714\pi\) | ||||
−0.996086 | + | 0.0883876i | \(0.971829\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.44407 | − | 2.48311i | 0.345970 | − | 0.193310i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.01566i | − | 0.155976i | −0.996954 | − | 0.0779881i | \(-0.975150\pi\) | ||
0.996954 | − | 0.0779881i | \(-0.0248496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.7220 | −1.36323 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.74780 | 0.286602 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.17720i | 0.621701i | 0.950459 | + | 0.310850i | \(0.100614\pi\) | ||||
−0.950459 | + | 0.310850i | \(0.899386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.3505 | − | 11.9099i | −1.46276 | − | 0.900305i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.02922i | 0.0773612i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.48152 | −0.110734 | −0.0553670 | − | 0.998466i | \(-0.517633\pi\) | ||||
−0.0553670 | + | 0.998466i | \(0.517633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.93951 | −0.590139 | −0.295069 | − | 0.955476i | \(-0.595343\pi\) | ||||
−0.295069 | + | 0.955476i | \(0.595343\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.338660i | 0.0250345i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.48915 | − | 3.62579i | 0.477091 | − | 0.266574i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 33.0749i | − | 2.41867i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.9105 | 0.939101 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.2987 | −1.32405 | −0.662023 | − | 0.749484i | \(-0.730302\pi\) | ||||
−0.662023 | + | 0.749484i | \(0.730302\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.65357i | 0.262990i | 0.991317 | + | 0.131495i | \(0.0419777\pi\) | ||||
−0.991317 | + | 0.131495i | \(0.958022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.98360 | − | 5.33979i | −0.213660 | − | 0.382391i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.14216i | 0.651352i | 0.945481 | + | 0.325676i | \(0.105592\pi\) | ||||
−0.945481 | + | 0.325676i | \(0.894408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.0416302 | −0.00295109 | −0.00147554 | − | 0.999999i | \(-0.500470\pi\) | ||||
−0.00147554 | + | 0.999999i | \(0.500470\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.36442 | 0.307842 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.6484i | 1.16849i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.76402 | + | 17.4748i | 0.681949 | + | 1.22050i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.75643i | 0.191585i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.27207 | 0.433848 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.08537 | 0.0747202 | 0.0373601 | − | 0.999302i | \(-0.488105\pi\) | ||||
0.0373601 | + | 0.999302i | \(0.488105\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.84912i | 0.537813i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.9525 | − | 9.47218i | 1.15615 | − | 0.645997i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.2960i | 1.37778i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.19447 | 0.148289 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −39.7413 | −2.67329 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.2417i | 0.819766i | 0.912138 | + | 0.409883i | \(0.134430\pi\) | ||||
−0.912138 | + | 0.409883i | \(0.865570\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.22403 | + | 11.7371i | −0.481602 | + | 0.782476i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 6.60662i | − | 0.438497i | −0.975669 | − | 0.219248i | \(-0.929639\pi\) | ||
0.975669 | − | 0.219248i | \(-0.0703605\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.5008 | 1.68514 | 0.842571 | − | 0.538585i | \(-0.181041\pi\) | ||||
0.842571 | + | 0.538585i | \(0.181041\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.3460 | 0.680714 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5.15810i | − | 0.337918i | −0.985623 | − | 0.168959i | \(-0.945959\pi\) | ||
0.985623 | − | 0.168959i | \(-0.0540406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.7205 | + | 10.4600i | −1.22119 | + | 0.682336i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.27017i | 0.277377i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8196 | 0.893917 | 0.446959 | − | 0.894555i | \(-0.352507\pi\) | ||||
0.446959 | + | 0.894555i | \(0.352507\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.9170 | −0.960890 | −0.480445 | − | 0.877025i | \(-0.659525\pi\) | ||||
−0.480445 | + | 0.877025i | \(0.659525\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 11.9121i | − | 0.764161i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.8895 | − | 26.6480i | −0.951255 | − | 1.70248i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7.53624i | − | 0.479520i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.18926 | 0.138739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.8472 | −0.810905 | −0.405453 | − | 0.914116i | \(-0.632886\pi\) | ||||
−0.405453 | + | 0.914116i | \(0.632886\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.61297i | 0.290015i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.85952 | − | 6.90745i | −0.241693 | − | 0.432561i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 12.2196i | − | 0.762235i | −0.924527 | − | 0.381118i | \(-0.875539\pi\) | ||
0.924527 | − | 0.381118i | \(-0.124461\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.1070 | 0.938702 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0982 | 0.625062 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 25.2134i | − | 1.55472i | −0.629054 | − | 0.777361i | \(-0.716558\pi\) | ||
0.629054 | − | 0.777361i | \(-0.283442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.4330 | + | 11.4169i | −1.25519 | + | 0.701335i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.52862i | 0.399545i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.85220 | 0.356815 | 0.178407 | − | 0.983957i | \(-0.442906\pi\) | ||||
0.178407 | + | 0.983957i | \(0.442906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8405 | 0.780008 | 0.390004 | − | 0.920813i | \(-0.372474\pi\) | ||||
0.390004 | + | 0.920813i | \(0.372474\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 12.4312i | − | 0.752373i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.0896 | + | 19.6425i | −0.729033 | + | 1.18449i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 31.6190i | 1.89980i | 0.312547 | + | 0.949902i | \(0.398818\pi\) | ||||
−0.312547 | + | 0.949902i | \(0.601182\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.3106 | 0.737019 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4411 | −1.33873 | −0.669363 | − | 0.742935i | \(-0.733433\pi\) | ||||
−0.669363 | + | 0.742935i | \(0.733433\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.10282i | − | 0.0655559i | −0.999463 | − | 0.0327779i | \(-0.989565\pi\) | ||
0.999463 | − | 0.0327779i | \(-0.0104354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.30988 | − | 0.731891i | 0.0775904 | − | 0.0433535i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40.6821i | 2.40139i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −34.4086 | −2.02403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.601048 | 0.0352340 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 24.5092i | − | 1.43185i | −0.698180 | − | 0.715923i | \(-0.746006\pi\) | ||
0.698180 | − | 0.715923i | \(-0.253994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.27455 | − | 4.07080i | −0.132429 | − | 0.237011i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 13.1053i | − | 0.760449i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.54274 | 0.320545 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 39.4661 | 2.27479 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5.18204i | − | 0.297700i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.748428 | − | 1.33947i | −0.0428548 | − | 0.0766980i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.3319i | 1.95943i | 0.200401 | + | 0.979714i | \(0.435775\pi\) | ||||
−0.200401 | + | 0.979714i | \(0.564225\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.10921 | −0.233765 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6914 | −0.776369 | −0.388185 | − | 0.921582i | \(-0.626898\pi\) | ||||
−0.388185 | + | 0.921582i | \(0.626898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.65568i | 0.263155i | 0.991306 | + | 0.131577i | \(0.0420041\pi\) | ||||
−0.991306 | + | 0.131577i | \(0.957996\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −24.4516 | + | 13.6623i | −1.37769 | + | 0.769781i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.44552i | − | 0.0811884i | −0.999176 | − | 0.0405942i | \(-0.987075\pi\) | ||
0.999176 | − | 0.0405942i | \(-0.0129251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.8997 | 0.946199 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.73838 | −0.264470 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 9.74873i | − | 0.542434i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.6015 | + | 14.5264i | 1.30918 | + | 0.805779i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.08324i | 0.281104i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −43.5820 | −2.40275 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.9258 | 0.985292 | 0.492646 | − | 0.870230i | \(-0.336030\pi\) | ||||
0.492646 | + | 0.870230i | \(0.336030\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 9.16323i | − | 0.502142i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.2622 | + | 9.64522i | −0.943135 | + | 0.526975i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 11.2720i | − | 0.614026i | −0.951705 | − | 0.307013i | \(-0.900670\pi\) | ||
0.951705 | − | 0.307013i | \(-0.0993295\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.01887 | −0.435525 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.6023 | 1.11567 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 30.2268i | − | 1.63209i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.538289 | + | 0.963386i | 0.0289805 | + | 0.0518669i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.8228i | 1.11783i | 0.829226 | + | 0.558914i | \(0.188782\pi\) | ||||
−0.829226 | + | 0.558914i | \(0.811218\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.58121 | 0.459342 | 0.229671 | − | 0.973268i | \(-0.426235\pi\) | ||||
0.229671 | + | 0.973268i | \(0.426235\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.7468 | −0.840502 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.31628i | 0.389406i | 0.980862 | + | 0.194703i | \(0.0623744\pi\) | ||||
−0.980862 | + | 0.194703i | \(0.937626\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.3463 | − | 31.0450i | −0.920647 | − | 1.64770i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 16.0808i | − | 0.851087i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.9028 | −1.78932 | −0.894660 | − | 0.446747i | \(-0.852582\pi\) | ||||
−0.894660 | + | 0.446747i | \(0.852582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.1513 | −0.902701 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 5.07325i | − | 0.266276i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.67962 | + | 4.84972i | −0.454312 | + | 0.253846i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.3121i | − | 0.590488i | −0.955422 | − | 0.295244i | \(-0.904599\pi\) | ||
0.955422 | − | 0.295244i | \(-0.0954009\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.6760 | 1.28458 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −47.5689 | −2.46965 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.1518i | − | 1.14697i | −0.819214 | − | 0.573487i | \(-0.805590\pi\) | ||
0.819214 | − | 0.573487i | \(-0.194410\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.232746 | + | 5.51294i | −0.0120190 | + | 0.284687i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 20.3059i | − | 1.04581i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.82898 | −0.453514 | −0.226757 | − | 0.973951i | \(-0.572812\pi\) | ||||
−0.226757 | + | 0.973951i | \(0.572812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.782518 | −0.0400896 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.2152i | − | 1.08405i | −0.840364 | − | 0.542023i | \(-0.817659\pi\) | ||
0.840364 | − | 0.542023i | \(-0.182341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −40.9205 | + | 22.8642i | −2.08550 | + | 1.16527i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 23.9384i | − | 1.21686i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.8793 | −1.41354 | −0.706768 | − | 0.707445i | \(-0.749848\pi\) | ||||
−0.706768 | + | 0.707445i | \(0.749848\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.16998 | 0.362601 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.31760i | 0.116907i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.43694 | − | 16.8894i | −0.474824 | − | 0.849800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.8676i | − | 1.14769i | −0.818964 | − | 0.573845i | \(-0.805451\pi\) | ||
0.818964 | − | 0.573845i | \(-0.194549\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.04944 | 0.152663 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.37194 | −0.118449 | −0.0592246 | − | 0.998245i | \(-0.518863\pi\) | ||||
−0.0592246 | + | 0.998245i | \(0.518863\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 24.7548i | − | 1.23312i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.48994 | + | 13.4049i | 0.372178 | + | 0.666094i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.3350i | − | 0.760126i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.3125 | 0.905494 | 0.452747 | − | 0.891639i | \(-0.350444\pi\) | ||||
0.452747 | + | 0.891639i | \(0.350444\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.08630 | 0.250888 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 9.47698i | − | 0.466332i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.65900 | + | 4.83819i | −0.425053 | + | 0.237498i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 0.332331i | − | 0.0162743i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0541 | 1.07741 | 0.538706 | − | 0.842494i | \(-0.318913\pi\) | ||||
0.538706 | + | 0.842494i | \(0.318913\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.9042 | 1.84734 | 0.923670 | − | 0.383190i | \(-0.125174\pi\) | ||||
0.923670 | + | 0.383190i | \(0.125174\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 26.4349i | 1.28531i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 30.5305 | + | 18.7910i | 1.48095 | + | 0.911500i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.11835i | − | 0.150907i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.6189 | −0.609244 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.8877 | −1.63231 | −0.816156 | − | 0.577831i | \(-0.803899\pi\) | ||||
−0.816156 | + | 0.577831i | \(0.803899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.57737i | − | 0.268031i | −0.990979 | − | 0.134016i | \(-0.957213\pi\) | ||
0.990979 | − | 0.134016i | \(-0.0427872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.52937 | − | 1.97203i | 0.169220 | − | 0.0945515i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.35966i | 0.0650414i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.2124 | −0.726046 | −0.363023 | − | 0.931780i | \(-0.618255\pi\) | ||||
−0.363023 | + | 0.931780i | \(0.618255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −37.6292 | −1.79187 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.7086i | − | 0.556291i | −0.960539 | − | 0.278145i | \(-0.910280\pi\) | ||
0.960539 | − | 0.278145i | \(-0.0897197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.4280 | − | 25.8221i | −0.683954 | − | 1.22408i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 2.33992i | − | 0.110675i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.1523 | 0.667889 | 0.333945 | − | 0.942593i | \(-0.391620\pi\) | ||||
0.333945 | + | 0.942593i | \(0.391620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.2960 | 1.94455 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.56284i | 0.0734285i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.4727 | + | 49.1683i | 1.28794 | + | 2.30504i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.4278i | − | 0.487793i | −0.969801 | − | 0.243896i | \(-0.921574\pi\) | ||
0.969801 | − | 0.243896i | \(-0.0784257\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.3697 | −0.950778 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.5905 | 1.84391 | 0.921957 | − | 0.387291i | \(-0.126589\pi\) | ||||
0.921957 | + | 0.387291i | \(0.126589\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.5954i | 0.492408i | 0.969218 | + | 0.246204i | \(0.0791834\pi\) | ||||
−0.969218 | + | 0.246204i | \(0.920817\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.30263 | − | 2.40409i | 0.199530 | − | 0.111487i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.0553i | 1.57589i | 0.615746 | + | 0.787945i | \(0.288855\pi\) | ||||
−0.615746 | + | 0.787945i | \(0.711145\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.1871 | −1.85567 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.98706 | 0.183714 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 40.0617i | − | 1.84204i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.56339 | + | 5.78957i | −0.163500 | + | 0.265644i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 28.8532i | 1.32110i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.8776 | 0.542702 | 0.271351 | − | 0.962480i | \(-0.412530\pi\) | ||||
0.271351 | + | 0.962480i | \(0.412530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.4258 | −0.840145 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.24280i | 0.102051i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.37727 | + | 1.32830i | −0.107946 | + | 0.0603148i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.7980i | 1.12371i | 0.827237 | + | 0.561853i | \(0.189911\pi\) | ||||
−0.827237 | + | 0.561853i | \(0.810089\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.11386 | 0.0503704 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.6220 | −1.15630 | −0.578152 | − | 0.815929i | \(-0.696226\pi\) | ||||
−0.578152 | + | 0.815929i | \(0.696226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 26.2673i | − | 1.18302i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.8684 | + | 24.8206i | 0.623340 | + | 1.11560i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 72.2739i | − | 3.24193i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.7020 | 1.28488 | 0.642438 | − | 0.766337i | \(-0.277923\pi\) | ||||
0.642438 | + | 0.766337i | \(0.277923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.994790 | −0.0444439 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.8193i | 0.660760i | 0.943848 | + | 0.330380i | \(0.107177\pi\) | ||||
−0.943848 | + | 0.330380i | \(0.892823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.4521 | + | 20.4961i | 0.509614 | + | 0.912064i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.74635i | 0.388439i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.5059 | 0.997555 | 0.498777 | − | 0.866730i | \(-0.333783\pi\) | ||||
0.498777 | + | 0.866730i | \(0.333783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.2065 | −0.893883 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.86277i | − | 0.170545i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.2528 | − | 9.08123i | 0.716185 | − | 0.400167i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.2397i | 1.94566i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.03570 | 0.177148 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.1227 | −0.925404 | −0.462702 | − | 0.886514i | \(-0.653120\pi\) | ||||
−0.462702 | + | 0.886514i | \(0.653120\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.617011i | − | 0.0269800i | −0.999909 | − | 0.0134900i | \(-0.995706\pi\) | ||
0.999909 | − | 0.0134900i | \(-0.00429413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.87792 | + | 9.55006i | −0.256533 | + | 0.416799i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 32.0223i | − | 1.39491i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.74832 | −0.249456 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 49.6195i | − | 2.14926i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.7413 | − | 10.4717i | 0.810257 | − | 0.452729i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.731177i | 0.0315526i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −62.9738 | −2.71247 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5801 | 0.583856 | 0.291928 | − | 0.956440i | \(-0.405703\pi\) | ||||
0.291928 | + | 0.956440i | \(0.405703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.91840i | 0.168154i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.2338 | − | 20.1053i | −0.481203 | − | 0.861216i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.4825i | − | 1.08955i | −0.838581 | − | 0.544777i | \(-0.816614\pi\) | ||
0.838581 | − | 0.544777i | \(-0.183386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.89145 | −0.0807252 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.98113 | 0.212203 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 39.3193i | − | 1.67203i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.78944 | − | 3.20260i | −0.0759577 | − | 0.135943i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.2051i | 0.601891i | 0.953641 | + | 0.300945i | \(0.0973022\pi\) | ||||
−0.953641 | + | 0.300945i | \(0.902698\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.1364 | −2.03595 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.3235 | −0.689179 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 6.10564i | − | 0.257322i | −0.991689 | − | 0.128661i | \(-0.958932\pi\) | ||
0.991689 | − | 0.128661i | \(-0.0410679\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.7164 | − | 17.7214i | 1.33432 | − | 0.745547i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.2071i | 1.31057i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.28182 | −0.389114 | −0.194557 | − | 0.980891i | \(-0.562327\pi\) | ||||
−0.194557 | + | 0.980891i | \(0.562327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.76185 | 0.282975 | 0.141487 | − | 0.989940i | \(-0.454812\pi\) | ||||
0.141487 | + | 0.989940i | \(0.454812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.03097i | 0.377274i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.25810 | − | 2.62080i | −0.177575 | − | 0.109295i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.2132i | 1.29942i | 0.760182 | + | 0.649711i | \(0.225110\pi\) | ||||
−0.760182 | + | 0.649711i | \(0.774890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.80315 | 0.0749365 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.1585 | −0.836315 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.2867i | 1.99983i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.8233 | − | 16.6637i | 1.23304 | − | 0.688960i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 24.7138i | − | 1.02005i | −0.860161 | − | 0.510023i | \(-0.829637\pi\) | ||
0.860161 | − | 0.510023i | \(-0.170363\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.07246 | 0.250211 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.51195 | 0.185597 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.3119i | 0.834109i | 0.908882 | + | 0.417054i | \(0.136938\pi\) | ||||
−0.908882 | + | 0.417054i | \(0.863062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.5381 | + | 63.6031i | 1.45692 | + | 2.60747i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.0205458i | 0.000840885i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.2979 | 0.706772 | 0.353386 | − | 0.935478i | \(-0.385030\pi\) | ||||
0.353386 | + | 0.935478i | \(0.385030\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.9939 | 1.34585 | 0.672924 | − | 0.739711i | \(-0.265038\pi\) | ||||
0.672924 | + | 0.739711i | \(0.265038\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.3757i | 0.992657i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.2117 | + | 20.0658i | 0.455821 | + | 0.815790i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 35.8434i | − | 1.45484i | −0.686193 | − | 0.727419i | \(-0.740719\pi\) | ||
0.686193 | − | 0.727419i | \(-0.259281\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.21651 | 0.332950 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.1564 | 2.15048 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.1971i | 1.21965i | 0.792536 | + | 0.609825i | \(0.208760\pi\) | ||||
−0.792536 | + | 0.609825i | \(0.791240\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.62438 | − | 4.81885i | 0.347769 | − | 0.194315i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 5.34282i | − | 0.215094i | −0.994200 | − | 0.107547i | \(-0.965700\pi\) | ||
0.994200 | − | 0.107547i | \(-0.0342996\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.48462 | 0.0998652 | 0.0499326 | − | 0.998753i | \(-0.484099\pi\) | ||||
0.0499326 | + | 0.998753i | \(0.484099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.84098 | 0.114005 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 60.1148i | − | 2.40845i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.2629 | − | 22.3192i | −0.450514 | − | 0.892769i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 3.09546i | − | 0.123621i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.8353 | −0.950375 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.724918 | −0.0288585 | −0.0144293 | − | 0.999896i | \(-0.504593\pi\) | ||||
−0.0144293 | + | 0.999896i | \(0.504593\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 0.535666i | − | 0.0212908i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.09503 | − | 1.72934i | 0.122822 | − | 0.0686268i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 75.6665i | 2.99802i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −43.8382 | −1.73421 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.8404 | 1.06013 | 0.530067 | − | 0.847956i | \(-0.322167\pi\) | ||||
0.530067 | + | 0.847956i | \(0.322167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.47661i | − | 0.0976679i | −0.998807 | − | 0.0488340i | \(-0.984449\pi\) | ||
0.998807 | − | 0.0488340i | \(-0.0155505\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.67482 | − | 8.36660i | −0.184071 | − | 0.329435i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 35.7731i | − | 1.40639i | −0.710999 | − | 0.703193i | \(-0.751757\pi\) | ||
0.710999 | − | 0.703193i | \(-0.248243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.62000 | −0.377618 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0167 | 0.392585 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 14.5123i | − | 0.567909i | −0.958838 | − | 0.283955i | \(-0.908354\pi\) | ||
0.958838 | − | 0.283955i | \(-0.0916465\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.12182 | − | 9.16661i | −0.200126 | − | 0.358169i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.2564i | 0.478167i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.05918 | 0.313941 | 0.156970 | − | 0.987603i | \(-0.449827\pi\) | ||||
0.156970 | + | 0.987603i | \(0.449827\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.0801 | −1.05329 | −0.526647 | − | 0.850084i | \(-0.676551\pi\) | ||||
−0.526647 | + | 0.850084i | \(0.676551\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.6136i | 0.761729i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0612 | + | 6.73917i | −0.467714 | + | 0.261334i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.66351i | 0.141852i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.04167 | 0.233585 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.16541 | −0.122199 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.1388i | 0.776292i | 0.921598 | + | 0.388146i | \(0.126884\pi\) | ||||
−0.921598 | + | 0.388146i | \(0.873116\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.0972 | + | 7.44562i | 0.465620 | + | 0.286582i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 26.8739i | − | 1.03285i | −0.856333 | − | 0.516424i | \(-0.827263\pi\) | ||
0.856333 | − | 0.516424i | \(-0.172737\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.53439 | −0.212390 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.26058 | −0.124946 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 40.0529i | − | 1.53258i | −0.642495 | − | 0.766290i | \(-0.722100\pi\) | ||
0.642495 | − | 0.766290i | \(-0.277900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.1174 | + | 11.2405i | −0.768646 | + | 0.429479i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 12.5855i | − | 0.480166i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 58.0192 | 2.21036 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1106 | −0.955254 | −0.477627 | − | 0.878563i | \(-0.658503\pi\) | ||||
−0.477627 | + | 0.878563i | \(0.658503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 57.7833i | 2.19501i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.734440 | + | 1.31444i | 0.0278589 | + | 0.0498595i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 64.1868i | − | 2.43125i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.54568 | −0.0962866 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.6355 | −1.27039 | −0.635197 | − | 0.772350i | \(-0.719081\pi\) | ||||
−0.635197 | + | 0.772350i | \(0.719081\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 4.51994i | − | 0.170473i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.16235 | + | 9.23914i | 0.194425 | + | 0.347966i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.7157i | 1.79453i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.25559 | −0.234934 | −0.117467 | − | 0.993077i | \(-0.537477\pi\) | ||||
−0.117467 | + | 0.993077i | \(0.537477\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.8494 | −0.894421 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.46616i | 0.167259i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 49.9103 | − | 27.8873i | 1.86654 | − | 1.04292i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.82042i | − | 0.254713i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.8585 | −1.71024 | −0.855118 | − | 0.518434i | \(-0.826515\pi\) | ||||
−0.855118 | + | 0.518434i | \(0.826515\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.8372 | 1.40913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.36202i | 0.273797i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.60131 | + | 15.5996i | −0.356584 | + | 0.579354i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 15.5296i | − | 0.575961i | −0.957636 | − | 0.287981i | \(-0.907016\pi\) | ||
0.957636 | − | 0.287981i | \(-0.0929839\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.7225 | 0.545278 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −62.2683 | −2.30307 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 43.1452i | − | 1.59360i | −0.604240 | − | 0.796802i | \(-0.706523\pi\) | ||
0.604240 | − | 0.796802i | \(-0.293477\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.1516 | + | 7.34844i | −0.485105 | + | 0.271051i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.7936i | 1.50265i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.5882 | −1.23556 | −0.617781 | − | 0.786350i | \(-0.711968\pi\) | ||||
−0.617781 | + | 0.786350i | \(0.711968\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.71937 | −0.136635 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.8916i | − | 0.509632i | −0.966990 | − | 0.254816i | \(-0.917985\pi\) | ||
0.966990 | − | 0.254816i | \(-0.0820149\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.17115 | + | 9.25490i | 0.189456 | + | 0.339073i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2273i | 0.447372i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.6305 | 1.59422 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.4863 | 1.40439 | 0.702193 | − | 0.711987i | \(-0.252204\pi\) | ||||
0.702193 | + | 0.711987i | \(0.252204\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.34048i | 0.231060i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.45382 | − | 6.18136i | −0.125697 | − | 0.224963i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.03386i | 0.146613i | 0.997309 | + | 0.0733066i | \(0.0233552\pi\) | ||||
−0.997309 | + | 0.0733066i | \(0.976645\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.27665 | 0.0826370 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.28005 | −0.0826518 | −0.0413259 | − | 0.999146i | \(-0.513158\pi\) | ||||
−0.0413259 | + | 0.999146i | \(0.513158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 46.8059i | − | 1.69449i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 38.5789 | − | 21.5558i | 1.39482 | − | 0.779353i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.5590i | 0.417370i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.0050 | 1.73111 | 0.865553 | − | 0.500818i | \(-0.166967\pi\) | ||||
0.865553 | + | 0.500818i | \(0.166967\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.03074 | −0.217192 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.67822i | 0.132297i | 0.997810 | + | 0.0661483i | \(0.0210710\pi\) | ||||
−0.997810 | + | 0.0661483i | \(0.978929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.7049 | + | 19.0174i | −0.420452 | + | 0.683124i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 7.45577i | − | 0.267474i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.1719 | 0.436104 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −73.3646 | −2.62519 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 10.4079i | − | 0.371950i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15.7697 | + | 8.81128i | −0.562844 | + | 0.314488i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.9078i | 0.495761i | 0.968791 | + | 0.247881i | \(0.0797341\pi\) | ||||
−0.968791 | + | 0.247881i | \(0.920266\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.4436 | −0.443004 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 73.8369 | 2.62534 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.80341i | 0.135063i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.63460 | + | 10.0843i | 0.199839 | + | 0.357655i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.8982i | 0.492301i | 0.969232 | + | 0.246150i | \(0.0791657\pi\) | ||||
−0.969232 | + | 0.246150i | \(0.920834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.7621 | 2.43263 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −36.4630 | −1.28836 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.5114i | 0.723833i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.95651 | − | 8.87075i | −0.174694 | − | 0.312653i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 2.88824i | − | 0.101671i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.4828 | −1.03656 | −0.518279 | − | 0.855211i | \(-0.673427\pi\) | ||||
−0.518279 | + | 0.855211i | \(0.673427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.73889 | 0.236634 | 0.118317 | − | 0.992976i | \(-0.462250\pi\) | ||||
0.118317 | + | 0.992976i | \(0.462250\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 6.33722i | − | 0.222256i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.40555 | + | 2.46159i | −0.154320 | + | 0.0862258i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 11.8081i | − | 0.413113i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 69.4299 | 2.42608 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0521 | −0.525322 | −0.262661 | − | 0.964888i | \(-0.584600\pi\) | ||||
−0.262661 | + | 0.964888i | \(0.584600\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.5906i | 0.822316i | 0.911564 | + | 0.411158i | \(0.134876\pi\) | ||||
−0.911564 | + | 0.411158i | \(0.865124\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.69419 | + | 5.96662i | 0.337508 | + | 0.207731i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 44.2147i | − | 1.53750i | −0.639552 | − | 0.768748i | \(-0.720880\pi\) | ||
0.639552 | − | 0.768748i | \(-0.279120\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.30736 | 0.114870 | 0.0574348 | − | 0.998349i | \(-0.481708\pi\) | ||||
0.0574348 | + | 0.998349i | \(0.481708\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.6050 | 0.541331 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 97.8807i | 3.39136i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.93461 | − | 2.19845i | 0.136163 | − | 0.0760806i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 12.6883i | − | 0.438571i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.5243 | −0.950245 | −0.475122 | − | 0.879920i | \(-0.657596\pi\) | ||||
−0.475122 | + | 0.879920i | \(0.657596\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.5787 | −0.537197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.0754i | 0.381458i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.3291 | − | 34.5937i | −0.664943 | − | 1.19006i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.7139i | 1.60511i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.544277 | −0.0186795 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.32432 | 0.113956 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.90006i | 0.270493i | 0.990812 | + | 0.135246i | \(0.0431826\pi\) | ||||
−0.990812 | + | 0.135246i | \(0.956817\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.08769 | + | 7.31580i | 0.139796 | + | 0.250195i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.41234i | 0.287360i | 0.989624 | + | 0.143680i | \(0.0458936\pi\) | ||||
−0.989624 | + | 0.143680i | \(0.954106\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.63662 | −0.226439 | −0.113219 | − | 0.993570i | \(-0.536116\pi\) | ||||
−0.113219 | + | 0.993570i | \(0.536116\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0779 | 0.684253 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 43.7797i | − | 1.49028i | −0.666908 | − | 0.745140i | \(-0.732383\pi\) | ||
0.666908 | − | 0.745140i | \(-0.267617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.9621 | + | 8.91878i | −0.542727 | + | 0.303248i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.9817i | 0.576729i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.9127 | −1.35394 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.0158 | 1.66084 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.35692i | 0.113614i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.14310 | − | 50.7626i | 0.0724502 | − | 1.71609i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 2.93519i | − | 0.0991142i | −0.998771 | − | 0.0495571i | \(-0.984219\pi\) | ||
0.998771 | − | 0.0495571i | \(-0.0157810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.0961 | −0.407991 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.2151 | −0.681064 | −0.340532 | − | 0.940233i | \(-0.610607\pi\) | ||||
−0.340532 | + | 0.940233i | \(0.610607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 32.2407i | − | 1.08499i | −0.840060 | − | 0.542494i | \(-0.817480\pi\) | ||
0.840060 | − | 0.542494i | \(-0.182520\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.00907 | + | 1.12256i | −0.0675341 | + | 0.0377345i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.2726i | 0.546381i | 0.961960 | + | 0.273190i | \(0.0880789\pi\) | ||||
−0.961960 | + | 0.273190i | \(0.911921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.20535 | 0.241660 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.6780 | 1.06125 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.0395i | 0.436351i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.61588 | − | 2.89197i | −0.0540129 | − | 0.0966677i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 2.73552i | − | 0.0913362i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.3618 | 0.545697 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 75.0525 | 2.50036 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 19.4778i | − | 0.648180i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.65953 | − | 15.4981i | −0.287852 | − | 0.515174i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.6897i | 0.985830i | 0.870077 | + | 0.492915i | \(0.164069\pi\) | ||||
−0.870077 | + | 0.492915i | \(0.835931\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 28.9422 | 0.959954 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.7787 | 0.390246 | 0.195123 | − | 0.980779i | \(-0.437489\pi\) | ||||
0.195123 | + | 0.980779i | \(0.437489\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.4627i | 0.677216i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.661073 | + | 0.369373i | −0.0218544 | + | 0.0122111i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 21.3402i | − | 0.704716i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.4606 | 1.59857 | 0.799284 | − | 0.600954i | \(-0.205213\pi\) | ||||
0.799284 | + | 0.600954i | \(0.205213\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.9439 | 0.558320 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 88.1517i | 2.90155i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1553 | + | 8.71236i | 0.465423 | + | 0.286460i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 22.9504i | − | 0.753790i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.51219 | −0.312085 | −0.156042 | − | 0.987750i | \(-0.549874\pi\) | ||||
−0.156042 | + | 0.987750i | \(0.549874\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.5614 | −0.608324 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.75715i | 0.221219i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 64.5630 | − | 36.0744i | 2.11143 | − | 1.17976i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7865i | 1.33244i | 0.745757 | + | 0.666219i | \(0.232088\pi\) | ||||
−0.745757 | + | 0.666219i | \(0.767912\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.29772 | 0.0749834 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.8016 | 0.352123 | 0.176062 | − | 0.984379i | \(-0.443664\pi\) | ||||
0.176062 | + | 0.984379i | \(0.443664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.95216i | 0.291522i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.0813 | + | 25.2016i | 0.458066 | + | 0.819809i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.00967i | 0.162792i | 0.996682 | + | 0.0813962i | \(0.0259379\pi\) | ||||
−0.996682 | + | 0.0813962i | \(0.974062\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.6456 | 0.800031 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.713409 | −0.0231339 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.6780i | 0.637434i | 0.947850 | + | 0.318717i | \(0.103252\pi\) | ||||
−0.947850 | + | 0.318717i | \(0.896748\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.9582 | − | 35.7194i | −0.645831 | − | 1.15585i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 8.34051i | − | 0.269610i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −46.8341 | −1.51235 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.0534 | −0.356562 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 26.4643i | − | 0.852801i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −7.13186 | + | 3.98491i | −0.229583 | + | 0.128279i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 26.7448i | − | 0.860055i | −0.902816 | − | 0.430028i | \(-0.858504\pi\) | ||
0.902816 | − | 0.430028i | \(-0.141496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.81131 | −0.154561 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.5685 | −0.916806 | −0.458403 | − | 0.888744i | \(-0.651578\pi\) | ||||
−0.458403 | + | 0.888744i | \(0.651578\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.06007i | 0.0981012i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.16923 | − | 11.6481i | 0.229599 | − | 0.373038i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.0365i | 0.545047i | 0.962149 | + | 0.272524i | \(0.0878583\pi\) | ||||
−0.962149 | + | 0.272524i | \(0.912142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −61.0220 | −1.95027 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.3904 | −0.906436 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.7247i | 1.07565i | 0.843056 | + | 0.537826i | \(0.180754\pi\) | ||||
−0.843056 | + | 0.537826i | \(0.819246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.8457 | + | 9.97126i | −0.568612 | + | 0.317711i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 21.5091i | 0.684641i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.68458 | 0.276154 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.34150 | 0.0426140 | 0.0213070 | − | 0.999773i | \(-0.493217\pi\) | ||||
0.0213070 | + | 0.999773i | \(0.493217\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 8.84696i | − | 0.280750i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.0454056 | − | 0.0812632i | −0.00143945 | − | 0.00257622i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.1926i | 1.65296i | 0.562969 | + | 0.826478i | \(0.309659\pi\) | ||||
−0.562969 | + | 0.826478i | \(0.690341\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.44431 | −0.298805 |
(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 | 1840.2.e.h.369.7 | 16 | ||
4.3 | odd | 2 | 920.2.e.c.369.10 | yes | 16 | ||
5.2 | odd | 4 | 9200.2.a.dd.1.4 | 8 | |||
5.3 | odd | 4 | 9200.2.a.de.1.5 | 8 | |||
5.4 | even | 2 | inner | 1840.2.e.h.369.10 | 16 | ||
20.3 | even | 4 | 4600.2.a.bj.1.4 | 8 | |||
20.7 | even | 4 | 4600.2.a.bk.1.5 | 8 | |||
20.19 | odd | 2 | 920.2.e.c.369.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.c.369.7 | ✓ | 16 | 20.19 | odd | 2 | ||
920.2.e.c.369.10 | yes | 16 | 4.3 | odd | 2 | ||
1840.2.e.h.369.7 | 16 | 1.1 | even | 1 | trivial | ||
1840.2.e.h.369.10 | 16 | 5.4 | even | 2 | inner | ||
4600.2.a.bj.1.4 | 8 | 20.3 | even | 4 | |||
4600.2.a.bk.1.5 | 8 | 20.7 | even | 4 | |||
9200.2.a.dd.1.4 | 8 | 5.2 | odd | 4 | |||
9200.2.a.de.1.5 | 8 | 5.3 | odd | 4 |