Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.75355\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.75355 | −1.23142 | −0.615712 | − | 0.787971i | \(-0.711131\pi\) | ||||
−0.615712 | + | 0.787971i | \(0.711131\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.824838 | 0.311760 | 0.155880 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155880 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.75355 | −0.870748 | ||||||||
\(11\) | −4.01662 | −1.21106 | −0.605528 | − | 0.795824i | \(-0.707038\pi\) | ||||
−0.605528 | + | 0.795824i | \(0.707038\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.824838 | 0.220447 | ||||||||
\(15\) | 2.75355 | 0.710963 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.88498 | −1.18478 | −0.592391 | − | 0.805650i | \(-0.701816\pi\) | ||||
−0.592391 | + | 0.805650i | \(0.701816\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 5.85873 | 1.34408 | 0.672042 | − | 0.740513i | \(-0.265417\pi\) | ||||
0.672042 | + | 0.740513i | \(0.265417\pi\) | |||||||
\(20\) | −2.75355 | −0.615712 | ||||||||
\(21\) | −0.824838 | −0.179994 | ||||||||
\(22\) | −4.01662 | −0.856346 | ||||||||
\(23\) | 6.04631 | 1.26074 | 0.630372 | − | 0.776294i | \(-0.282903\pi\) | ||||
0.630372 | + | 0.776294i | \(0.282903\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 2.58202 | 0.516404 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.824838 | 0.155880 | ||||||||
\(29\) | −6.86586 | −1.27496 | −0.637479 | − | 0.770468i | \(-0.720023\pi\) | ||||
−0.637479 | + | 0.770468i | \(0.720023\pi\) | |||||||
\(30\) | 2.75355 | 0.502727 | ||||||||
\(31\) | 0.898245 | 0.161330 | 0.0806648 | − | 0.996741i | \(-0.474296\pi\) | ||||
0.0806648 | + | 0.996741i | \(0.474296\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.01662 | 0.699204 | ||||||||
\(34\) | −4.88498 | −0.837768 | ||||||||
\(35\) | −2.27123 | −0.383908 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.98543 | 0.819599 | 0.409800 | − | 0.912176i | \(-0.365599\pi\) | ||||
0.409800 | + | 0.912176i | \(0.365599\pi\) | |||||||
\(38\) | 5.85873 | 0.950411 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.75355 | −0.435374 | ||||||||
\(41\) | −8.56990 | −1.33839 | −0.669197 | − | 0.743085i | \(-0.733362\pi\) | ||||
−0.669197 | + | 0.743085i | \(0.733362\pi\) | |||||||
\(42\) | −0.824838 | −0.127275 | ||||||||
\(43\) | 12.5165 | 1.90875 | 0.954373 | − | 0.298617i | \(-0.0965252\pi\) | ||||
0.954373 | + | 0.298617i | \(0.0965252\pi\) | |||||||
\(44\) | −4.01662 | −0.605528 | ||||||||
\(45\) | −2.75355 | −0.410474 | ||||||||
\(46\) | 6.04631 | 0.891480 | ||||||||
\(47\) | −11.9912 | −1.74910 | −0.874549 | − | 0.484938i | \(-0.838842\pi\) | ||||
−0.874549 | + | 0.484938i | \(0.838842\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.31964 | −0.902806 | ||||||||
\(50\) | 2.58202 | 0.365153 | ||||||||
\(51\) | 4.88498 | 0.684035 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −6.44142 | −0.884797 | −0.442399 | − | 0.896818i | \(-0.645872\pi\) | ||||
−0.442399 | + | 0.896818i | \(0.645872\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 11.0599 | 1.49132 | ||||||||
\(56\) | 0.824838 | 0.110224 | ||||||||
\(57\) | −5.85873 | −0.776008 | ||||||||
\(58\) | −6.86586 | −0.901532 | ||||||||
\(59\) | −2.07171 | −0.269713 | −0.134857 | − | 0.990865i | \(-0.543057\pi\) | ||||
−0.134857 | + | 0.990865i | \(0.543057\pi\) | |||||||
\(60\) | 2.75355 | 0.355481 | ||||||||
\(61\) | −12.3179 | −1.57714 | −0.788570 | − | 0.614945i | \(-0.789178\pi\) | ||||
−0.788570 | + | 0.614945i | \(0.789178\pi\) | |||||||
\(62\) | 0.898245 | 0.114077 | ||||||||
\(63\) | 0.824838 | 0.103920 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.75355 | 0.341535 | ||||||||
\(66\) | 4.01662 | 0.494412 | ||||||||
\(67\) | 9.95884 | 1.21667 | 0.608333 | − | 0.793682i | \(-0.291838\pi\) | ||||
0.608333 | + | 0.793682i | \(0.291838\pi\) | |||||||
\(68\) | −4.88498 | −0.592391 | ||||||||
\(69\) | −6.04631 | −0.727890 | ||||||||
\(70\) | −2.27123 | −0.271464 | ||||||||
\(71\) | 5.23569 | 0.621363 | 0.310681 | − | 0.950514i | \(-0.399443\pi\) | ||||
0.310681 | + | 0.950514i | \(0.399443\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −2.85779 | −0.334479 | −0.167240 | − | 0.985916i | \(-0.553485\pi\) | ||||
−0.167240 | + | 0.985916i | \(0.553485\pi\) | |||||||
\(74\) | 4.98543 | 0.579544 | ||||||||
\(75\) | −2.58202 | −0.298146 | ||||||||
\(76\) | 5.85873 | 0.672042 | ||||||||
\(77\) | −3.31306 | −0.377559 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 8.39757 | 0.944800 | 0.472400 | − | 0.881384i | \(-0.343388\pi\) | ||||
0.472400 | + | 0.881384i | \(0.343388\pi\) | |||||||
\(80\) | −2.75355 | −0.307856 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.56990 | −0.946388 | ||||||||
\(83\) | −5.21802 | −0.572752 | −0.286376 | − | 0.958117i | \(-0.592451\pi\) | ||||
−0.286376 | + | 0.958117i | \(0.592451\pi\) | |||||||
\(84\) | −0.824838 | −0.0899972 | ||||||||
\(85\) | 13.4510 | 1.45897 | ||||||||
\(86\) | 12.5165 | 1.34969 | ||||||||
\(87\) | 6.86586 | 0.736097 | ||||||||
\(88\) | −4.01662 | −0.428173 | ||||||||
\(89\) | 15.1576 | 1.60670 | 0.803349 | − | 0.595508i | \(-0.203049\pi\) | ||||
0.803349 | + | 0.595508i | \(0.203049\pi\) | |||||||
\(90\) | −2.75355 | −0.290249 | ||||||||
\(91\) | −0.824838 | −0.0864666 | ||||||||
\(92\) | 6.04631 | 0.630372 | ||||||||
\(93\) | −0.898245 | −0.0931437 | ||||||||
\(94\) | −11.9912 | −1.23680 | ||||||||
\(95\) | −16.1323 | −1.65514 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 6.12659 | 0.622061 | 0.311030 | − | 0.950400i | \(-0.399326\pi\) | ||||
0.311030 | + | 0.950400i | \(0.399326\pi\) | |||||||
\(98\) | −6.31964 | −0.638380 | ||||||||
\(99\) | −4.01662 | −0.403685 | ||||||||
\(100\) | 2.58202 | 0.258202 | ||||||||
\(101\) | −17.5626 | −1.74754 | −0.873771 | − | 0.486338i | \(-0.838332\pi\) | ||||
−0.873771 | + | 0.486338i | \(0.838332\pi\) | |||||||
\(102\) | 4.88498 | 0.483685 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.27123 | 0.221649 | ||||||||
\(106\) | −6.44142 | −0.625646 | ||||||||
\(107\) | 20.3015 | 1.96262 | 0.981310 | − | 0.192434i | \(-0.0616381\pi\) | ||||
0.981310 | + | 0.192434i | \(0.0616381\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −3.09481 | −0.296429 | −0.148215 | − | 0.988955i | \(-0.547353\pi\) | ||||
−0.148215 | + | 0.988955i | \(0.547353\pi\) | |||||||
\(110\) | 11.0599 | 1.05452 | ||||||||
\(111\) | −4.98543 | −0.473196 | ||||||||
\(112\) | 0.824838 | 0.0779399 | ||||||||
\(113\) | 14.6484 | 1.37801 | 0.689004 | − | 0.724758i | \(-0.258048\pi\) | ||||
0.689004 | + | 0.724758i | \(0.258048\pi\) | |||||||
\(114\) | −5.85873 | −0.548720 | ||||||||
\(115\) | −16.6488 | −1.55251 | ||||||||
\(116\) | −6.86586 | −0.637479 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −2.07171 | −0.190716 | ||||||||
\(119\) | −4.02932 | −0.369367 | ||||||||
\(120\) | 2.75355 | 0.251363 | ||||||||
\(121\) | 5.13324 | 0.466658 | ||||||||
\(122\) | −12.3179 | −1.11521 | ||||||||
\(123\) | 8.56990 | 0.772722 | ||||||||
\(124\) | 0.898245 | 0.0806648 | ||||||||
\(125\) | 6.65802 | 0.595512 | ||||||||
\(126\) | 0.824838 | 0.0734824 | ||||||||
\(127\) | 14.5076 | 1.28735 | 0.643673 | − | 0.765301i | \(-0.277410\pi\) | ||||
0.643673 | + | 0.765301i | \(0.277410\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −12.5165 | −1.10202 | ||||||||
\(130\) | 2.75355 | 0.241502 | ||||||||
\(131\) | 13.3775 | 1.16880 | 0.584399 | − | 0.811467i | \(-0.301330\pi\) | ||||
0.584399 | + | 0.811467i | \(0.301330\pi\) | |||||||
\(132\) | 4.01662 | 0.349602 | ||||||||
\(133\) | 4.83251 | 0.419031 | ||||||||
\(134\) | 9.95884 | 0.860313 | ||||||||
\(135\) | 2.75355 | 0.236988 | ||||||||
\(136\) | −4.88498 | −0.418884 | ||||||||
\(137\) | −3.65086 | −0.311914 | −0.155957 | − | 0.987764i | \(-0.549846\pi\) | ||||
−0.155957 | + | 0.987764i | \(0.549846\pi\) | |||||||
\(138\) | −6.04631 | −0.514696 | ||||||||
\(139\) | 14.9078 | 1.26446 | 0.632232 | − | 0.774779i | \(-0.282139\pi\) | ||||
0.632232 | + | 0.774779i | \(0.282139\pi\) | |||||||
\(140\) | −2.27123 | −0.191954 | ||||||||
\(141\) | 11.9912 | 1.00984 | ||||||||
\(142\) | 5.23569 | 0.439370 | ||||||||
\(143\) | 4.01662 | 0.335887 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 18.9055 | 1.57001 | ||||||||
\(146\) | −2.85779 | −0.236513 | ||||||||
\(147\) | 6.31964 | 0.521235 | ||||||||
\(148\) | 4.98543 | 0.409800 | ||||||||
\(149\) | 2.99240 | 0.245147 | 0.122573 | − | 0.992459i | \(-0.460885\pi\) | ||||
0.122573 | + | 0.992459i | \(0.460885\pi\) | |||||||
\(150\) | −2.58202 | −0.210821 | ||||||||
\(151\) | −19.8765 | −1.61753 | −0.808765 | − | 0.588132i | \(-0.799863\pi\) | ||||
−0.808765 | + | 0.588132i | \(0.799863\pi\) | |||||||
\(152\) | 5.85873 | 0.475206 | ||||||||
\(153\) | −4.88498 | −0.394928 | ||||||||
\(154\) | −3.31306 | −0.266974 | ||||||||
\(155\) | −2.47336 | −0.198665 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −5.48855 | −0.438034 | −0.219017 | − | 0.975721i | \(-0.570285\pi\) | ||||
−0.219017 | + | 0.975721i | \(0.570285\pi\) | |||||||
\(158\) | 8.39757 | 0.668075 | ||||||||
\(159\) | 6.44142 | 0.510838 | ||||||||
\(160\) | −2.75355 | −0.217687 | ||||||||
\(161\) | 4.98723 | 0.393049 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 7.06211 | 0.553147 | 0.276574 | − | 0.960993i | \(-0.410801\pi\) | ||||
0.276574 | + | 0.960993i | \(0.410801\pi\) | |||||||
\(164\) | −8.56990 | −0.669197 | ||||||||
\(165\) | −11.0599 | −0.861016 | ||||||||
\(166\) | −5.21802 | −0.404997 | ||||||||
\(167\) | 16.9953 | 1.31513 | 0.657567 | − | 0.753396i | \(-0.271586\pi\) | ||||
0.657567 | + | 0.753396i | \(0.271586\pi\) | |||||||
\(168\) | −0.824838 | −0.0636377 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 13.4510 | 1.03165 | ||||||||
\(171\) | 5.85873 | 0.448028 | ||||||||
\(172\) | 12.5165 | 0.954373 | ||||||||
\(173\) | 4.34169 | 0.330093 | 0.165046 | − | 0.986286i | \(-0.447223\pi\) | ||||
0.165046 | + | 0.986286i | \(0.447223\pi\) | |||||||
\(174\) | 6.86586 | 0.520499 | ||||||||
\(175\) | 2.12975 | 0.160994 | ||||||||
\(176\) | −4.01662 | −0.302764 | ||||||||
\(177\) | 2.07171 | 0.155719 | ||||||||
\(178\) | 15.1576 | 1.13611 | ||||||||
\(179\) | 17.0414 | 1.27373 | 0.636865 | − | 0.770975i | \(-0.280231\pi\) | ||||
0.636865 | + | 0.770975i | \(0.280231\pi\) | |||||||
\(180\) | −2.75355 | −0.205237 | ||||||||
\(181\) | 17.2522 | 1.28234 | 0.641172 | − | 0.767397i | \(-0.278448\pi\) | ||||
0.641172 | + | 0.767397i | \(0.278448\pi\) | |||||||
\(182\) | −0.824838 | −0.0611411 | ||||||||
\(183\) | 12.3179 | 0.910562 | ||||||||
\(184\) | 6.04631 | 0.445740 | ||||||||
\(185\) | −13.7276 | −1.00927 | ||||||||
\(186\) | −0.898245 | −0.0658626 | ||||||||
\(187\) | 19.6211 | 1.43484 | ||||||||
\(188\) | −11.9912 | −0.874549 | ||||||||
\(189\) | −0.824838 | −0.0599982 | ||||||||
\(190\) | −16.1323 | −1.17036 | ||||||||
\(191\) | −16.2534 | −1.17606 | −0.588029 | − | 0.808840i | \(-0.700096\pi\) | ||||
−0.588029 | + | 0.808840i | \(0.700096\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −14.9122 | −1.07341 | −0.536703 | − | 0.843771i | \(-0.680330\pi\) | ||||
−0.536703 | + | 0.843771i | \(0.680330\pi\) | |||||||
\(194\) | 6.12659 | 0.439863 | ||||||||
\(195\) | −2.75355 | −0.197186 | ||||||||
\(196\) | −6.31964 | −0.451403 | ||||||||
\(197\) | 17.5228 | 1.24845 | 0.624224 | − | 0.781245i | \(-0.285415\pi\) | ||||
0.624224 | + | 0.781245i | \(0.285415\pi\) | |||||||
\(198\) | −4.01662 | −0.285449 | ||||||||
\(199\) | −8.66641 | −0.614346 | −0.307173 | − | 0.951654i | \(-0.599383\pi\) | ||||
−0.307173 | + | 0.951654i | \(0.599383\pi\) | |||||||
\(200\) | 2.58202 | 0.182576 | ||||||||
\(201\) | −9.95884 | −0.702443 | ||||||||
\(202\) | −17.5626 | −1.23570 | ||||||||
\(203\) | −5.66322 | −0.397480 | ||||||||
\(204\) | 4.88498 | 0.342017 | ||||||||
\(205\) | 23.5976 | 1.64813 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 6.04631 | 0.420248 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −23.5323 | −1.62776 | ||||||||
\(210\) | 2.27123 | 0.156730 | ||||||||
\(211\) | −7.82353 | −0.538594 | −0.269297 | − | 0.963057i | \(-0.586791\pi\) | ||||
−0.269297 | + | 0.963057i | \(0.586791\pi\) | |||||||
\(212\) | −6.44142 | −0.442399 | ||||||||
\(213\) | −5.23569 | −0.358744 | ||||||||
\(214\) | 20.3015 | 1.38778 | ||||||||
\(215\) | −34.4647 | −2.35047 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.740907 | 0.0502961 | ||||||||
\(218\) | −3.09481 | −0.209607 | ||||||||
\(219\) | 2.85779 | 0.193112 | ||||||||
\(220\) | 11.0599 | 0.745662 | ||||||||
\(221\) | 4.88498 | 0.328600 | ||||||||
\(222\) | −4.98543 | −0.334600 | ||||||||
\(223\) | −0.973709 | −0.0652044 | −0.0326022 | − | 0.999468i | \(-0.510379\pi\) | ||||
−0.0326022 | + | 0.999468i | \(0.510379\pi\) | |||||||
\(224\) | 0.824838 | 0.0551118 | ||||||||
\(225\) | 2.58202 | 0.172135 | ||||||||
\(226\) | 14.6484 | 0.974398 | ||||||||
\(227\) | 25.0223 | 1.66079 | 0.830395 | − | 0.557175i | \(-0.188115\pi\) | ||||
0.830395 | + | 0.557175i | \(0.188115\pi\) | |||||||
\(228\) | −5.85873 | −0.388004 | ||||||||
\(229\) | 20.2628 | 1.33900 | 0.669500 | − | 0.742812i | \(-0.266508\pi\) | ||||
0.669500 | + | 0.742812i | \(0.266508\pi\) | |||||||
\(230\) | −16.6488 | −1.09779 | ||||||||
\(231\) | 3.31306 | 0.217984 | ||||||||
\(232\) | −6.86586 | −0.450766 | ||||||||
\(233\) | −10.4040 | −0.681589 | −0.340795 | − | 0.940138i | \(-0.610696\pi\) | ||||
−0.340795 | + | 0.940138i | \(0.610696\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 33.0183 | 2.15388 | ||||||||
\(236\) | −2.07171 | −0.134857 | ||||||||
\(237\) | −8.39757 | −0.545481 | ||||||||
\(238\) | −4.02932 | −0.261182 | ||||||||
\(239\) | 26.4940 | 1.71375 | 0.856876 | − | 0.515523i | \(-0.172402\pi\) | ||||
0.856876 | + | 0.515523i | \(0.172402\pi\) | |||||||
\(240\) | 2.75355 | 0.177741 | ||||||||
\(241\) | 1.31680 | 0.0848228 | 0.0424114 | − | 0.999100i | \(-0.486496\pi\) | ||||
0.0424114 | + | 0.999100i | \(0.486496\pi\) | |||||||
\(242\) | 5.13324 | 0.329977 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −12.3179 | −0.788570 | ||||||||
\(245\) | 17.4014 | 1.11174 | ||||||||
\(246\) | 8.56990 | 0.546397 | ||||||||
\(247\) | −5.85873 | −0.372782 | ||||||||
\(248\) | 0.898245 | 0.0570386 | ||||||||
\(249\) | 5.21802 | 0.330679 | ||||||||
\(250\) | 6.65802 | 0.421090 | ||||||||
\(251\) | −13.8996 | −0.877337 | −0.438669 | − | 0.898649i | \(-0.644550\pi\) | ||||
−0.438669 | + | 0.898649i | \(0.644550\pi\) | |||||||
\(252\) | 0.824838 | 0.0519599 | ||||||||
\(253\) | −24.2857 | −1.52683 | ||||||||
\(254\) | 14.5076 | 0.910291 | ||||||||
\(255\) | −13.4510 | −0.842336 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.3217 | 1.39239 | 0.696193 | − | 0.717854i | \(-0.254876\pi\) | ||||
0.696193 | + | 0.717854i | \(0.254876\pi\) | |||||||
\(258\) | −12.5165 | −0.779242 | ||||||||
\(259\) | 4.11217 | 0.255518 | ||||||||
\(260\) | 2.75355 | 0.170768 | ||||||||
\(261\) | −6.86586 | −0.424986 | ||||||||
\(262\) | 13.3775 | 0.826465 | ||||||||
\(263\) | −16.1592 | −0.996420 | −0.498210 | − | 0.867056i | \(-0.666009\pi\) | ||||
−0.498210 | + | 0.867056i | \(0.666009\pi\) | |||||||
\(264\) | 4.01662 | 0.247206 | ||||||||
\(265\) | 17.7368 | 1.08956 | ||||||||
\(266\) | 4.83251 | 0.296300 | ||||||||
\(267\) | −15.1576 | −0.927628 | ||||||||
\(268\) | 9.95884 | 0.608333 | ||||||||
\(269\) | 6.48600 | 0.395459 | 0.197729 | − | 0.980257i | \(-0.436643\pi\) | ||||
0.197729 | + | 0.980257i | \(0.436643\pi\) | |||||||
\(270\) | 2.75355 | 0.167576 | ||||||||
\(271\) | −25.7060 | −1.56153 | −0.780763 | − | 0.624827i | \(-0.785170\pi\) | ||||
−0.780763 | + | 0.624827i | \(0.785170\pi\) | |||||||
\(272\) | −4.88498 | −0.296196 | ||||||||
\(273\) | 0.824838 | 0.0499215 | ||||||||
\(274\) | −3.65086 | −0.220556 | ||||||||
\(275\) | −10.3710 | −0.625394 | ||||||||
\(276\) | −6.04631 | −0.363945 | ||||||||
\(277\) | −16.0917 | −0.966856 | −0.483428 | − | 0.875384i | \(-0.660608\pi\) | ||||
−0.483428 | + | 0.875384i | \(0.660608\pi\) | |||||||
\(278\) | 14.9078 | 0.894111 | ||||||||
\(279\) | 0.898245 | 0.0537765 | ||||||||
\(280\) | −2.27123 | −0.135732 | ||||||||
\(281\) | 0.0961083 | 0.00573334 | 0.00286667 | − | 0.999996i | \(-0.499088\pi\) | ||||
0.00286667 | + | 0.999996i | \(0.499088\pi\) | |||||||
\(282\) | 11.9912 | 0.714066 | ||||||||
\(283\) | 5.39853 | 0.320909 | 0.160455 | − | 0.987043i | \(-0.448704\pi\) | ||||
0.160455 | + | 0.987043i | \(0.448704\pi\) | |||||||
\(284\) | 5.23569 | 0.310681 | ||||||||
\(285\) | 16.1323 | 0.955594 | ||||||||
\(286\) | 4.01662 | 0.237508 | ||||||||
\(287\) | −7.06879 | −0.417257 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 6.86306 | 0.403710 | ||||||||
\(290\) | 18.9055 | 1.11017 | ||||||||
\(291\) | −6.12659 | −0.359147 | ||||||||
\(292\) | −2.85779 | −0.167240 | ||||||||
\(293\) | 22.2615 | 1.30053 | 0.650266 | − | 0.759706i | \(-0.274657\pi\) | ||||
0.650266 | + | 0.759706i | \(0.274657\pi\) | |||||||
\(294\) | 6.31964 | 0.368569 | ||||||||
\(295\) | 5.70455 | 0.332131 | ||||||||
\(296\) | 4.98543 | 0.289772 | ||||||||
\(297\) | 4.01662 | 0.233068 | ||||||||
\(298\) | 2.99240 | 0.173345 | ||||||||
\(299\) | −6.04631 | −0.349667 | ||||||||
\(300\) | −2.58202 | −0.149073 | ||||||||
\(301\) | 10.3241 | 0.595070 | ||||||||
\(302\) | −19.8765 | −1.14377 | ||||||||
\(303\) | 17.5626 | 1.00894 | ||||||||
\(304\) | 5.85873 | 0.336021 | ||||||||
\(305\) | 33.9178 | 1.94213 | ||||||||
\(306\) | −4.88498 | −0.279256 | ||||||||
\(307\) | −2.18512 | −0.124711 | −0.0623557 | − | 0.998054i | \(-0.519861\pi\) | ||||
−0.0623557 | + | 0.998054i | \(0.519861\pi\) | |||||||
\(308\) | −3.31306 | −0.188779 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −2.47336 | −0.140477 | ||||||||
\(311\) | −0.0801534 | −0.00454508 | −0.00227254 | − | 0.999997i | \(-0.500723\pi\) | ||||
−0.00227254 | + | 0.999997i | \(0.500723\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 9.05156 | 0.511624 | 0.255812 | − | 0.966726i | \(-0.417657\pi\) | ||||
0.255812 | + | 0.966726i | \(0.417657\pi\) | |||||||
\(314\) | −5.48855 | −0.309737 | ||||||||
\(315\) | −2.27123 | −0.127969 | ||||||||
\(316\) | 8.39757 | 0.472400 | ||||||||
\(317\) | 4.18981 | 0.235323 | 0.117662 | − | 0.993054i | \(-0.462460\pi\) | ||||
0.117662 | + | 0.993054i | \(0.462460\pi\) | |||||||
\(318\) | 6.44142 | 0.361217 | ||||||||
\(319\) | 27.5775 | 1.54405 | ||||||||
\(320\) | −2.75355 | −0.153928 | ||||||||
\(321\) | −20.3015 | −1.13312 | ||||||||
\(322\) | 4.98723 | 0.277927 | ||||||||
\(323\) | −28.6198 | −1.59245 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.58202 | −0.143225 | ||||||||
\(326\) | 7.06211 | 0.391134 | ||||||||
\(327\) | 3.09481 | 0.171144 | ||||||||
\(328\) | −8.56990 | −0.473194 | ||||||||
\(329\) | −9.89081 | −0.545298 | ||||||||
\(330\) | −11.0599 | −0.608830 | ||||||||
\(331\) | 18.0911 | 0.994377 | 0.497188 | − | 0.867643i | \(-0.334366\pi\) | ||||
0.497188 | + | 0.867643i | \(0.334366\pi\) | |||||||
\(332\) | −5.21802 | −0.286376 | ||||||||
\(333\) | 4.98543 | 0.273200 | ||||||||
\(334\) | 16.9953 | 0.929940 | ||||||||
\(335\) | −27.4221 | −1.49823 | ||||||||
\(336\) | −0.824838 | −0.0449986 | ||||||||
\(337\) | −2.00641 | −0.109296 | −0.0546480 | − | 0.998506i | \(-0.517404\pi\) | ||||
−0.0546480 | + | 0.998506i | \(0.517404\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | −14.6484 | −0.795593 | ||||||||
\(340\) | 13.4510 | 0.729484 | ||||||||
\(341\) | −3.60791 | −0.195379 | ||||||||
\(342\) | 5.85873 | 0.316804 | ||||||||
\(343\) | −10.9866 | −0.593218 | ||||||||
\(344\) | 12.5165 | 0.674844 | ||||||||
\(345\) | 16.6488 | 0.896341 | ||||||||
\(346\) | 4.34169 | 0.233411 | ||||||||
\(347\) | −3.06551 | −0.164565 | −0.0822826 | − | 0.996609i | \(-0.526221\pi\) | ||||
−0.0822826 | + | 0.996609i | \(0.526221\pi\) | |||||||
\(348\) | 6.86586 | 0.368049 | ||||||||
\(349\) | 11.4089 | 0.610703 | 0.305351 | − | 0.952240i | \(-0.401226\pi\) | ||||
0.305351 | + | 0.952240i | \(0.401226\pi\) | |||||||
\(350\) | 2.12975 | 0.113840 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −4.01662 | −0.214087 | ||||||||
\(353\) | −27.4910 | −1.46320 | −0.731599 | − | 0.681735i | \(-0.761226\pi\) | ||||
−0.731599 | + | 0.681735i | \(0.761226\pi\) | |||||||
\(354\) | 2.07171 | 0.110110 | ||||||||
\(355\) | −14.4167 | −0.765160 | ||||||||
\(356\) | 15.1576 | 0.803349 | ||||||||
\(357\) | 4.02932 | 0.213254 | ||||||||
\(358\) | 17.0414 | 0.900664 | ||||||||
\(359\) | −12.5262 | −0.661106 | −0.330553 | − | 0.943787i | \(-0.607235\pi\) | ||||
−0.330553 | + | 0.943787i | \(0.607235\pi\) | |||||||
\(360\) | −2.75355 | −0.145125 | ||||||||
\(361\) | 15.3247 | 0.806564 | ||||||||
\(362\) | 17.2522 | 0.906754 | ||||||||
\(363\) | −5.13324 | −0.269425 | ||||||||
\(364\) | −0.824838 | −0.0432333 | ||||||||
\(365\) | 7.86906 | 0.411886 | ||||||||
\(366\) | 12.3179 | 0.643865 | ||||||||
\(367\) | 21.5573 | 1.12528 | 0.562642 | − | 0.826701i | \(-0.309785\pi\) | ||||
0.562642 | + | 0.826701i | \(0.309785\pi\) | |||||||
\(368\) | 6.04631 | 0.315186 | ||||||||
\(369\) | −8.56990 | −0.446131 | ||||||||
\(370\) | −13.7276 | −0.713664 | ||||||||
\(371\) | −5.31313 | −0.275844 | ||||||||
\(372\) | −0.898245 | −0.0465719 | ||||||||
\(373\) | 34.6777 | 1.79554 | 0.897772 | − | 0.440460i | \(-0.145185\pi\) | ||||
0.897772 | + | 0.440460i | \(0.145185\pi\) | |||||||
\(374\) | 19.6211 | 1.01458 | ||||||||
\(375\) | −6.65802 | −0.343819 | ||||||||
\(376\) | −11.9912 | −0.618399 | ||||||||
\(377\) | 6.86586 | 0.353610 | ||||||||
\(378\) | −0.824838 | −0.0424251 | ||||||||
\(379\) | −10.8080 | −0.555172 | −0.277586 | − | 0.960701i | \(-0.589534\pi\) | ||||
−0.277586 | + | 0.960701i | \(0.589534\pi\) | |||||||
\(380\) | −16.1323 | −0.827569 | ||||||||
\(381\) | −14.5076 | −0.743249 | ||||||||
\(382\) | −16.2534 | −0.831598 | ||||||||
\(383\) | 2.54440 | 0.130013 | 0.0650063 | − | 0.997885i | \(-0.479293\pi\) | ||||
0.0650063 | + | 0.997885i | \(0.479293\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 9.12267 | 0.464934 | ||||||||
\(386\) | −14.9122 | −0.759013 | ||||||||
\(387\) | 12.5165 | 0.636249 | ||||||||
\(388\) | 6.12659 | 0.311030 | ||||||||
\(389\) | 18.6438 | 0.945277 | 0.472639 | − | 0.881256i | \(-0.343302\pi\) | ||||
0.472639 | + | 0.881256i | \(0.343302\pi\) | |||||||
\(390\) | −2.75355 | −0.139431 | ||||||||
\(391\) | −29.5361 | −1.49371 | ||||||||
\(392\) | −6.31964 | −0.319190 | ||||||||
\(393\) | −13.3775 | −0.674806 | ||||||||
\(394\) | 17.5228 | 0.882787 | ||||||||
\(395\) | −23.1231 | −1.16345 | ||||||||
\(396\) | −4.01662 | −0.201843 | ||||||||
\(397\) | −12.1568 | −0.610133 | −0.305067 | − | 0.952331i | \(-0.598679\pi\) | ||||
−0.305067 | + | 0.952331i | \(0.598679\pi\) | |||||||
\(398\) | −8.66641 | −0.434408 | ||||||||
\(399\) | −4.83251 | −0.241928 | ||||||||
\(400\) | 2.58202 | 0.129101 | ||||||||
\(401\) | 17.1721 | 0.857536 | 0.428768 | − | 0.903415i | \(-0.358948\pi\) | ||||
0.428768 | + | 0.903415i | \(0.358948\pi\) | |||||||
\(402\) | −9.95884 | −0.496702 | ||||||||
\(403\) | −0.898245 | −0.0447448 | ||||||||
\(404\) | −17.5626 | −0.873771 | ||||||||
\(405\) | −2.75355 | −0.136825 | ||||||||
\(406\) | −5.66322 | −0.281061 | ||||||||
\(407\) | −20.0246 | −0.992581 | ||||||||
\(408\) | 4.88498 | 0.241843 | ||||||||
\(409\) | −2.80065 | −0.138483 | −0.0692415 | − | 0.997600i | \(-0.522058\pi\) | ||||
−0.0692415 | + | 0.997600i | \(0.522058\pi\) | |||||||
\(410\) | 23.5976 | 1.16540 | ||||||||
\(411\) | 3.65086 | 0.180084 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | −1.70882 | −0.0840858 | ||||||||
\(414\) | 6.04631 | 0.297160 | ||||||||
\(415\) | 14.3681 | 0.705300 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −14.9078 | −0.730038 | ||||||||
\(418\) | −23.5323 | −1.15100 | ||||||||
\(419\) | 40.3556 | 1.97150 | 0.985751 | − | 0.168210i | \(-0.0537988\pi\) | ||||
0.985751 | + | 0.168210i | \(0.0537988\pi\) | |||||||
\(420\) | 2.27123 | 0.110825 | ||||||||
\(421\) | −15.1113 | −0.736481 | −0.368240 | − | 0.929731i | \(-0.620040\pi\) | ||||
−0.368240 | + | 0.929731i | \(0.620040\pi\) | |||||||
\(422\) | −7.82353 | −0.380843 | ||||||||
\(423\) | −11.9912 | −0.583032 | ||||||||
\(424\) | −6.44142 | −0.312823 | ||||||||
\(425\) | −12.6131 | −0.611826 | ||||||||
\(426\) | −5.23569 | −0.253670 | ||||||||
\(427\) | −10.1602 | −0.491689 | ||||||||
\(428\) | 20.3015 | 0.981310 | ||||||||
\(429\) | −4.01662 | −0.193924 | ||||||||
\(430\) | −34.4647 | −1.66204 | ||||||||
\(431\) | 23.8797 | 1.15024 | 0.575122 | − | 0.818068i | \(-0.304955\pi\) | ||||
0.575122 | + | 0.818068i | \(0.304955\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −22.2116 | −1.06742 | −0.533712 | − | 0.845667i | \(-0.679203\pi\) | ||||
−0.533712 | + | 0.845667i | \(0.679203\pi\) | |||||||
\(434\) | 0.740907 | 0.0355647 | ||||||||
\(435\) | −18.9055 | −0.906448 | ||||||||
\(436\) | −3.09481 | −0.148215 | ||||||||
\(437\) | 35.4237 | 1.69455 | ||||||||
\(438\) | 2.85779 | 0.136551 | ||||||||
\(439\) | 13.5722 | 0.647765 | 0.323882 | − | 0.946097i | \(-0.395012\pi\) | ||||
0.323882 | + | 0.946097i | \(0.395012\pi\) | |||||||
\(440\) | 11.0599 | 0.527262 | ||||||||
\(441\) | −6.31964 | −0.300935 | ||||||||
\(442\) | 4.88498 | 0.232355 | ||||||||
\(443\) | 3.04113 | 0.144488 | 0.0722441 | − | 0.997387i | \(-0.476984\pi\) | ||||
0.0722441 | + | 0.997387i | \(0.476984\pi\) | |||||||
\(444\) | −4.98543 | −0.236598 | ||||||||
\(445\) | −41.7370 | −1.97853 | ||||||||
\(446\) | −0.973709 | −0.0461064 | ||||||||
\(447\) | −2.99240 | −0.141536 | ||||||||
\(448\) | 0.824838 | 0.0389700 | ||||||||
\(449\) | −14.6556 | −0.691641 | −0.345821 | − | 0.938301i | \(-0.612399\pi\) | ||||
−0.345821 | + | 0.938301i | \(0.612399\pi\) | |||||||
\(450\) | 2.58202 | 0.121718 | ||||||||
\(451\) | 34.4220 | 1.62087 | ||||||||
\(452\) | 14.6484 | 0.689004 | ||||||||
\(453\) | 19.8765 | 0.933881 | ||||||||
\(454\) | 25.0223 | 1.17436 | ||||||||
\(455\) | 2.27123 | 0.106477 | ||||||||
\(456\) | −5.85873 | −0.274360 | ||||||||
\(457\) | 19.5597 | 0.914966 | 0.457483 | − | 0.889218i | \(-0.348751\pi\) | ||||
0.457483 | + | 0.889218i | \(0.348751\pi\) | |||||||
\(458\) | 20.2628 | 0.946817 | ||||||||
\(459\) | 4.88498 | 0.228012 | ||||||||
\(460\) | −16.6488 | −0.776254 | ||||||||
\(461\) | 6.48694 | 0.302127 | 0.151063 | − | 0.988524i | \(-0.451730\pi\) | ||||
0.151063 | + | 0.988524i | \(0.451730\pi\) | |||||||
\(462\) | 3.31306 | 0.154138 | ||||||||
\(463\) | 30.7177 | 1.42757 | 0.713787 | − | 0.700362i | \(-0.246978\pi\) | ||||
0.713787 | + | 0.700362i | \(0.246978\pi\) | |||||||
\(464\) | −6.86586 | −0.318740 | ||||||||
\(465\) | 2.47336 | 0.114699 | ||||||||
\(466\) | −10.4040 | −0.481956 | ||||||||
\(467\) | 22.1129 | 1.02327 | 0.511633 | − | 0.859204i | \(-0.329041\pi\) | ||||
0.511633 | + | 0.859204i | \(0.329041\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 8.21444 | 0.379307 | ||||||||
\(470\) | 33.0183 | 1.52302 | ||||||||
\(471\) | 5.48855 | 0.252899 | ||||||||
\(472\) | −2.07171 | −0.0953581 | ||||||||
\(473\) | −50.2740 | −2.31160 | ||||||||
\(474\) | −8.39757 | −0.385713 | ||||||||
\(475\) | 15.1273 | 0.694090 | ||||||||
\(476\) | −4.02932 | −0.184684 | ||||||||
\(477\) | −6.44142 | −0.294932 | ||||||||
\(478\) | 26.4940 | 1.21181 | ||||||||
\(479\) | 28.0901 | 1.28347 | 0.641734 | − | 0.766927i | \(-0.278215\pi\) | ||||
0.641734 | + | 0.766927i | \(0.278215\pi\) | |||||||
\(480\) | 2.75355 | 0.125682 | ||||||||
\(481\) | −4.98543 | −0.227316 | ||||||||
\(482\) | 1.31680 | 0.0599788 | ||||||||
\(483\) | −4.98723 | −0.226927 | ||||||||
\(484\) | 5.13324 | 0.233329 | ||||||||
\(485\) | −16.8698 | −0.766020 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −43.1659 | −1.95603 | −0.978016 | − | 0.208529i | \(-0.933133\pi\) | ||||
−0.978016 | + | 0.208529i | \(0.933133\pi\) | |||||||
\(488\) | −12.3179 | −0.557603 | ||||||||
\(489\) | −7.06211 | −0.319360 | ||||||||
\(490\) | 17.4014 | 0.786116 | ||||||||
\(491\) | 4.59882 | 0.207542 | 0.103771 | − | 0.994601i | \(-0.466909\pi\) | ||||
0.103771 | + | 0.994601i | \(0.466909\pi\) | |||||||
\(492\) | 8.56990 | 0.386361 | ||||||||
\(493\) | 33.5396 | 1.51055 | ||||||||
\(494\) | −5.85873 | −0.263597 | ||||||||
\(495\) | 11.0599 | 0.497108 | ||||||||
\(496\) | 0.898245 | 0.0403324 | ||||||||
\(497\) | 4.31860 | 0.193716 | ||||||||
\(498\) | 5.21802 | 0.233825 | ||||||||
\(499\) | 14.7370 | 0.659717 | 0.329858 | − | 0.944030i | \(-0.392999\pi\) | ||||
0.329858 | + | 0.944030i | \(0.392999\pi\) | |||||||
\(500\) | 6.65802 | 0.297756 | ||||||||
\(501\) | −16.9953 | −0.759293 | ||||||||
\(502\) | −13.8996 | −0.620371 | ||||||||
\(503\) | 34.2400 | 1.52669 | 0.763343 | − | 0.645994i | \(-0.223557\pi\) | ||||
0.763343 | + | 0.645994i | \(0.223557\pi\) | |||||||
\(504\) | 0.824838 | 0.0367412 | ||||||||
\(505\) | 48.3594 | 2.15196 | ||||||||
\(506\) | −24.2857 | −1.07963 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 14.5076 | 0.643673 | ||||||||
\(509\) | −13.8444 | −0.613640 | −0.306820 | − | 0.951767i | \(-0.599265\pi\) | ||||
−0.306820 | + | 0.951767i | \(0.599265\pi\) | |||||||
\(510\) | −13.4510 | −0.595622 | ||||||||
\(511\) | −2.35722 | −0.104277 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.85873 | −0.258669 | ||||||||
\(514\) | 22.3217 | 0.984566 | ||||||||
\(515\) | 2.75355 | 0.121336 | ||||||||
\(516\) | −12.5165 | −0.551008 | ||||||||
\(517\) | 48.1641 | 2.11826 | ||||||||
\(518\) | 4.11217 | 0.180679 | ||||||||
\(519\) | −4.34169 | −0.190579 | ||||||||
\(520\) | 2.75355 | 0.120751 | ||||||||
\(521\) | −37.9825 | −1.66404 | −0.832021 | − | 0.554744i | \(-0.812816\pi\) | ||||
−0.832021 | + | 0.554744i | \(0.812816\pi\) | |||||||
\(522\) | −6.86586 | −0.300511 | ||||||||
\(523\) | −44.5784 | −1.94928 | −0.974639 | − | 0.223784i | \(-0.928159\pi\) | ||||
−0.974639 | + | 0.223784i | \(0.928159\pi\) | |||||||
\(524\) | 13.3775 | 0.584399 | ||||||||
\(525\) | −2.12975 | −0.0929498 | ||||||||
\(526\) | −16.1592 | −0.704576 | ||||||||
\(527\) | −4.38791 | −0.191141 | ||||||||
\(528\) | 4.01662 | 0.174801 | ||||||||
\(529\) | 13.5579 | 0.589473 | ||||||||
\(530\) | 17.7368 | 0.770435 | ||||||||
\(531\) | −2.07171 | −0.0899045 | ||||||||
\(532\) | 4.83251 | 0.209516 | ||||||||
\(533\) | 8.56990 | 0.371204 | ||||||||
\(534\) | −15.1576 | −0.655932 | ||||||||
\(535\) | −55.9011 | −2.41682 | ||||||||
\(536\) | 9.95884 | 0.430156 | ||||||||
\(537\) | −17.0414 | −0.735389 | ||||||||
\(538\) | 6.48600 | 0.279631 | ||||||||
\(539\) | 25.3836 | 1.09335 | ||||||||
\(540\) | 2.75355 | 0.118494 | ||||||||
\(541\) | 31.0027 | 1.33291 | 0.666455 | − | 0.745545i | \(-0.267811\pi\) | ||||
0.666455 | + | 0.745545i | \(0.267811\pi\) | |||||||
\(542\) | −25.7060 | −1.10417 | ||||||||
\(543\) | −17.2522 | −0.740362 | ||||||||
\(544\) | −4.88498 | −0.209442 | ||||||||
\(545\) | 8.52171 | 0.365030 | ||||||||
\(546\) | 0.824838 | 0.0352998 | ||||||||
\(547\) | −40.7446 | −1.74211 | −0.871056 | − | 0.491184i | \(-0.836564\pi\) | ||||
−0.871056 | + | 0.491184i | \(0.836564\pi\) | |||||||
\(548\) | −3.65086 | −0.155957 | ||||||||
\(549\) | −12.3179 | −0.525713 | ||||||||
\(550\) | −10.3710 | −0.442220 | ||||||||
\(551\) | −40.2252 | −1.71365 | ||||||||
\(552\) | −6.04631 | −0.257348 | ||||||||
\(553\) | 6.92664 | 0.294551 | ||||||||
\(554\) | −16.0917 | −0.683670 | ||||||||
\(555\) | 13.7276 | 0.582705 | ||||||||
\(556\) | 14.9078 | 0.632232 | ||||||||
\(557\) | −13.2768 | −0.562555 | −0.281277 | − | 0.959627i | \(-0.590758\pi\) | ||||
−0.281277 | + | 0.959627i | \(0.590758\pi\) | |||||||
\(558\) | 0.898245 | 0.0380258 | ||||||||
\(559\) | −12.5165 | −0.529391 | ||||||||
\(560\) | −2.27123 | −0.0959770 | ||||||||
\(561\) | −19.6211 | −0.828404 | ||||||||
\(562\) | 0.0961083 | 0.00405408 | ||||||||
\(563\) | −16.6142 | −0.700207 | −0.350103 | − | 0.936711i | \(-0.613854\pi\) | ||||
−0.350103 | + | 0.936711i | \(0.613854\pi\) | |||||||
\(564\) | 11.9912 | 0.504921 | ||||||||
\(565\) | −40.3351 | −1.69691 | ||||||||
\(566\) | 5.39853 | 0.226917 | ||||||||
\(567\) | 0.824838 | 0.0346400 | ||||||||
\(568\) | 5.23569 | 0.219685 | ||||||||
\(569\) | −12.6190 | −0.529018 | −0.264509 | − | 0.964383i | \(-0.585210\pi\) | ||||
−0.264509 | + | 0.964383i | \(0.585210\pi\) | |||||||
\(570\) | 16.1323 | 0.675707 | ||||||||
\(571\) | 1.19760 | 0.0501178 | 0.0250589 | − | 0.999686i | \(-0.492023\pi\) | ||||
0.0250589 | + | 0.999686i | \(0.492023\pi\) | |||||||
\(572\) | 4.01662 | 0.167943 | ||||||||
\(573\) | 16.2534 | 0.678997 | ||||||||
\(574\) | −7.06879 | −0.295045 | ||||||||
\(575\) | 15.6117 | 0.651052 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −0.301179 | −0.0125382 | −0.00626912 | − | 0.999980i | \(-0.501996\pi\) | ||||
−0.00626912 | + | 0.999980i | \(0.501996\pi\) | |||||||
\(578\) | 6.86306 | 0.285466 | ||||||||
\(579\) | 14.9122 | 0.619731 | ||||||||
\(580\) | 18.9055 | 0.785007 | ||||||||
\(581\) | −4.30402 | −0.178561 | ||||||||
\(582\) | −6.12659 | −0.253955 | ||||||||
\(583\) | 25.8727 | 1.07154 | ||||||||
\(584\) | −2.85779 | −0.118256 | ||||||||
\(585\) | 2.75355 | 0.113845 | ||||||||
\(586\) | 22.2615 | 0.919616 | ||||||||
\(587\) | 21.8124 | 0.900294 | 0.450147 | − | 0.892954i | \(-0.351372\pi\) | ||||
0.450147 | + | 0.892954i | \(0.351372\pi\) | |||||||
\(588\) | 6.31964 | 0.260618 | ||||||||
\(589\) | 5.26258 | 0.216841 | ||||||||
\(590\) | 5.70455 | 0.234852 | ||||||||
\(591\) | −17.5228 | −0.720792 | ||||||||
\(592\) | 4.98543 | 0.204900 | ||||||||
\(593\) | −5.08535 | −0.208830 | −0.104415 | − | 0.994534i | \(-0.533297\pi\) | ||||
−0.104415 | + | 0.994534i | \(0.533297\pi\) | |||||||
\(594\) | 4.01662 | 0.164804 | ||||||||
\(595\) | 11.0949 | 0.454848 | ||||||||
\(596\) | 2.99240 | 0.122573 | ||||||||
\(597\) | 8.66641 | 0.354693 | ||||||||
\(598\) | −6.04631 | −0.247252 | ||||||||
\(599\) | 37.2656 | 1.52263 | 0.761315 | − | 0.648382i | \(-0.224554\pi\) | ||||
0.761315 | + | 0.648382i | \(0.224554\pi\) | |||||||
\(600\) | −2.58202 | −0.105410 | ||||||||
\(601\) | 39.5448 | 1.61306 | 0.806532 | − | 0.591190i | \(-0.201342\pi\) | ||||
0.806532 | + | 0.591190i | \(0.201342\pi\) | |||||||
\(602\) | 10.3241 | 0.420778 | ||||||||
\(603\) | 9.95884 | 0.405555 | ||||||||
\(604\) | −19.8765 | −0.808765 | ||||||||
\(605\) | −14.1346 | −0.574653 | ||||||||
\(606\) | 17.5626 | 0.713431 | ||||||||
\(607\) | 2.47845 | 0.100597 | 0.0502986 | − | 0.998734i | \(-0.483983\pi\) | ||||
0.0502986 | + | 0.998734i | \(0.483983\pi\) | |||||||
\(608\) | 5.85873 | 0.237603 | ||||||||
\(609\) | 5.66322 | 0.229485 | ||||||||
\(610\) | 33.9178 | 1.37329 | ||||||||
\(611\) | 11.9912 | 0.485112 | ||||||||
\(612\) | −4.88498 | −0.197464 | ||||||||
\(613\) | 17.3008 | 0.698774 | 0.349387 | − | 0.936978i | \(-0.386390\pi\) | ||||
0.349387 | + | 0.936978i | \(0.386390\pi\) | |||||||
\(614\) | −2.18512 | −0.0881842 | ||||||||
\(615\) | −23.5976 | −0.951548 | ||||||||
\(616\) | −3.31306 | −0.133487 | ||||||||
\(617\) | 26.0657 | 1.04937 | 0.524683 | − | 0.851298i | \(-0.324184\pi\) | ||||
0.524683 | + | 0.851298i | \(0.324184\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −20.0939 | −0.807641 | −0.403821 | − | 0.914838i | \(-0.632318\pi\) | ||||
−0.403821 | + | 0.914838i | \(0.632318\pi\) | |||||||
\(620\) | −2.47336 | −0.0993326 | ||||||||
\(621\) | −6.04631 | −0.242630 | ||||||||
\(622\) | −0.0801534 | −0.00321386 | ||||||||
\(623\) | 12.5025 | 0.500904 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −31.2433 | −1.24973 | ||||||||
\(626\) | 9.05156 | 0.361773 | ||||||||
\(627\) | 23.5323 | 0.939789 | ||||||||
\(628\) | −5.48855 | −0.219017 | ||||||||
\(629\) | −24.3537 | −0.971047 | ||||||||
\(630\) | −2.27123 | −0.0904880 | ||||||||
\(631\) | 45.0779 | 1.79452 | 0.897261 | − | 0.441501i | \(-0.145554\pi\) | ||||
0.897261 | + | 0.441501i | \(0.145554\pi\) | |||||||
\(632\) | 8.39757 | 0.334037 | ||||||||
\(633\) | 7.82353 | 0.310957 | ||||||||
\(634\) | 4.18981 | 0.166399 | ||||||||
\(635\) | −39.9475 | −1.58527 | ||||||||
\(636\) | 6.44142 | 0.255419 | ||||||||
\(637\) | 6.31964 | 0.250393 | ||||||||
\(638\) | 27.5775 | 1.09181 | ||||||||
\(639\) | 5.23569 | 0.207121 | ||||||||
\(640\) | −2.75355 | −0.108843 | ||||||||
\(641\) | 5.02160 | 0.198341 | 0.0991707 | − | 0.995070i | \(-0.468381\pi\) | ||||
0.0991707 | + | 0.995070i | \(0.468381\pi\) | |||||||
\(642\) | −20.3015 | −0.801236 | ||||||||
\(643\) | 25.4848 | 1.00502 | 0.502511 | − | 0.864571i | \(-0.332410\pi\) | ||||
0.502511 | + | 0.864571i | \(0.332410\pi\) | |||||||
\(644\) | 4.98723 | 0.196524 | ||||||||
\(645\) | 34.4647 | 1.35705 | ||||||||
\(646\) | −28.6198 | −1.12603 | ||||||||
\(647\) | 15.6812 | 0.616492 | 0.308246 | − | 0.951307i | \(-0.400258\pi\) | ||||
0.308246 | + | 0.951307i | \(0.400258\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 8.32127 | 0.326638 | ||||||||
\(650\) | −2.58202 | −0.101275 | ||||||||
\(651\) | −0.740907 | −0.0290384 | ||||||||
\(652\) | 7.06211 | 0.276574 | ||||||||
\(653\) | −19.0441 | −0.745255 | −0.372627 | − | 0.927981i | \(-0.621543\pi\) | ||||
−0.372627 | + | 0.927981i | \(0.621543\pi\) | |||||||
\(654\) | 3.09481 | 0.121017 | ||||||||
\(655\) | −36.8356 | −1.43928 | ||||||||
\(656\) | −8.56990 | −0.334599 | ||||||||
\(657\) | −2.85779 | −0.111493 | ||||||||
\(658\) | −9.89081 | −0.385584 | ||||||||
\(659\) | 28.4790 | 1.10938 | 0.554692 | − | 0.832056i | \(-0.312836\pi\) | ||||
0.554692 | + | 0.832056i | \(0.312836\pi\) | |||||||
\(660\) | −11.0599 | −0.430508 | ||||||||
\(661\) | −36.2555 | −1.41017 | −0.705087 | − | 0.709121i | \(-0.749092\pi\) | ||||
−0.705087 | + | 0.709121i | \(0.749092\pi\) | |||||||
\(662\) | 18.0911 | 0.703131 | ||||||||
\(663\) | −4.88498 | −0.189717 | ||||||||
\(664\) | −5.21802 | −0.202498 | ||||||||
\(665\) | −13.3065 | −0.516005 | ||||||||
\(666\) | 4.98543 | 0.193181 | ||||||||
\(667\) | −41.5131 | −1.60739 | ||||||||
\(668\) | 16.9953 | 0.657567 | ||||||||
\(669\) | 0.973709 | 0.0376458 | ||||||||
\(670\) | −27.4221 | −1.05941 | ||||||||
\(671\) | 49.4761 | 1.91001 | ||||||||
\(672\) | −0.824838 | −0.0318188 | ||||||||
\(673\) | 19.2441 | 0.741804 | 0.370902 | − | 0.928672i | \(-0.379049\pi\) | ||||
0.370902 | + | 0.928672i | \(0.379049\pi\) | |||||||
\(674\) | −2.00641 | −0.0772839 | ||||||||
\(675\) | −2.58202 | −0.0993819 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −19.9685 | −0.767453 | −0.383726 | − | 0.923447i | \(-0.625359\pi\) | ||||
−0.383726 | + | 0.923447i | \(0.625359\pi\) | |||||||
\(678\) | −14.6484 | −0.562569 | ||||||||
\(679\) | 5.05345 | 0.193933 | ||||||||
\(680\) | 13.4510 | 0.515823 | ||||||||
\(681\) | −25.0223 | −0.958858 | ||||||||
\(682\) | −3.60791 | −0.138154 | ||||||||
\(683\) | −34.1733 | −1.30761 | −0.653803 | − | 0.756665i | \(-0.726828\pi\) | ||||
−0.653803 | + | 0.756665i | \(0.726828\pi\) | |||||||
\(684\) | 5.85873 | 0.224014 | ||||||||
\(685\) | 10.0528 | 0.384098 | ||||||||
\(686\) | −10.9866 | −0.419469 | ||||||||
\(687\) | −20.2628 | −0.773072 | ||||||||
\(688\) | 12.5165 | 0.477187 | ||||||||
\(689\) | 6.44142 | 0.245399 | ||||||||
\(690\) | 16.6488 | 0.633809 | ||||||||
\(691\) | −1.84750 | −0.0702824 | −0.0351412 | − | 0.999382i | \(-0.511188\pi\) | ||||
−0.0351412 | + | 0.999382i | \(0.511188\pi\) | |||||||
\(692\) | 4.34169 | 0.165046 | ||||||||
\(693\) | −3.31306 | −0.125853 | ||||||||
\(694\) | −3.06551 | −0.116365 | ||||||||
\(695\) | −41.0493 | −1.55709 | ||||||||
\(696\) | 6.86586 | 0.260250 | ||||||||
\(697\) | 41.8638 | 1.58571 | ||||||||
\(698\) | 11.4089 | 0.431832 | ||||||||
\(699\) | 10.4040 | 0.393516 | ||||||||
\(700\) | 2.12975 | 0.0804969 | ||||||||
\(701\) | 10.1157 | 0.382065 | 0.191033 | − | 0.981584i | \(-0.438816\pi\) | ||||
0.191033 | + | 0.981584i | \(0.438816\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | 29.2083 | 1.10161 | ||||||||
\(704\) | −4.01662 | −0.151382 | ||||||||
\(705\) | −33.0183 | −1.24354 | ||||||||
\(706\) | −27.4910 | −1.03464 | ||||||||
\(707\) | −14.4863 | −0.544813 | ||||||||
\(708\) | 2.07171 | 0.0778596 | ||||||||
\(709\) | −10.8613 | −0.407906 | −0.203953 | − | 0.978981i | \(-0.565379\pi\) | ||||
−0.203953 | + | 0.978981i | \(0.565379\pi\) | |||||||
\(710\) | −14.4167 | −0.541050 | ||||||||
\(711\) | 8.39757 | 0.314933 | ||||||||
\(712\) | 15.1576 | 0.568054 | ||||||||
\(713\) | 5.43107 | 0.203395 | ||||||||
\(714\) | 4.02932 | 0.150794 | ||||||||
\(715\) | −11.0599 | −0.413619 | ||||||||
\(716\) | 17.0414 | 0.636865 | ||||||||
\(717\) | −26.4940 | −0.989435 | ||||||||
\(718\) | −12.5262 | −0.467473 | ||||||||
\(719\) | −3.69888 | −0.137945 | −0.0689725 | − | 0.997619i | \(-0.521972\pi\) | ||||
−0.0689725 | + | 0.997619i | \(0.521972\pi\) | |||||||
\(720\) | −2.75355 | −0.102619 | ||||||||
\(721\) | −0.824838 | −0.0307186 | ||||||||
\(722\) | 15.3247 | 0.570327 | ||||||||
\(723\) | −1.31680 | −0.0489725 | ||||||||
\(724\) | 17.2522 | 0.641172 | ||||||||
\(725\) | −17.7278 | −0.658393 | ||||||||
\(726\) | −5.13324 | −0.190512 | ||||||||
\(727\) | 47.4382 | 1.75938 | 0.879692 | − | 0.475543i | \(-0.157749\pi\) | ||||
0.879692 | + | 0.475543i | \(0.157749\pi\) | |||||||
\(728\) | −0.824838 | −0.0305705 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.86906 | 0.291247 | ||||||||
\(731\) | −61.1428 | −2.26145 | ||||||||
\(732\) | 12.3179 | 0.455281 | ||||||||
\(733\) | 42.9033 | 1.58467 | 0.792335 | − | 0.610086i | \(-0.208865\pi\) | ||||
0.792335 | + | 0.610086i | \(0.208865\pi\) | |||||||
\(734\) | 21.5573 | 0.795696 | ||||||||
\(735\) | −17.4014 | −0.641861 | ||||||||
\(736\) | 6.04631 | 0.222870 | ||||||||
\(737\) | −40.0009 | −1.47345 | ||||||||
\(738\) | −8.56990 | −0.315463 | ||||||||
\(739\) | −18.5493 | −0.682348 | −0.341174 | − | 0.940000i | \(-0.610825\pi\) | ||||
−0.341174 | + | 0.940000i | \(0.610825\pi\) | |||||||
\(740\) | −13.7276 | −0.504637 | ||||||||
\(741\) | 5.85873 | 0.215226 | ||||||||
\(742\) | −5.31313 | −0.195051 | ||||||||
\(743\) | 1.24993 | 0.0458556 | 0.0229278 | − | 0.999737i | \(-0.492701\pi\) | ||||
0.0229278 | + | 0.999737i | \(0.492701\pi\) | |||||||
\(744\) | −0.898245 | −0.0329313 | ||||||||
\(745\) | −8.23971 | −0.301879 | ||||||||
\(746\) | 34.6777 | 1.26964 | ||||||||
\(747\) | −5.21802 | −0.190917 | ||||||||
\(748\) | 19.6211 | 0.717419 | ||||||||
\(749\) | 16.7455 | 0.611866 | ||||||||
\(750\) | −6.65802 | −0.243117 | ||||||||
\(751\) | 6.97426 | 0.254494 | 0.127247 | − | 0.991871i | \(-0.459386\pi\) | ||||
0.127247 | + | 0.991871i | \(0.459386\pi\) | |||||||
\(752\) | −11.9912 | −0.437274 | ||||||||
\(753\) | 13.8996 | 0.506531 | ||||||||
\(754\) | 6.86586 | 0.250040 | ||||||||
\(755\) | 54.7310 | 1.99186 | ||||||||
\(756\) | −0.824838 | −0.0299991 | ||||||||
\(757\) | 2.68607 | 0.0976270 | 0.0488135 | − | 0.998808i | \(-0.484456\pi\) | ||||
0.0488135 | + | 0.998808i | \(0.484456\pi\) | |||||||
\(758\) | −10.8080 | −0.392566 | ||||||||
\(759\) | 24.2857 | 0.881516 | ||||||||
\(760\) | −16.1323 | −0.585179 | ||||||||
\(761\) | −31.4888 | −1.14147 | −0.570734 | − | 0.821135i | \(-0.693341\pi\) | ||||
−0.570734 | + | 0.821135i | \(0.693341\pi\) | |||||||
\(762\) | −14.5076 | −0.525557 | ||||||||
\(763\) | −2.55272 | −0.0924147 | ||||||||
\(764\) | −16.2534 | −0.588029 | ||||||||
\(765\) | 13.4510 | 0.486323 | ||||||||
\(766\) | 2.54440 | 0.0919327 | ||||||||
\(767\) | 2.07171 | 0.0748051 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −39.1019 | −1.41005 | −0.705025 | − | 0.709182i | \(-0.749064\pi\) | ||||
−0.705025 | + | 0.709182i | \(0.749064\pi\) | |||||||
\(770\) | 9.12267 | 0.328758 | ||||||||
\(771\) | −22.3217 | −0.803895 | ||||||||
\(772\) | −14.9122 | −0.536703 | ||||||||
\(773\) | 29.1520 | 1.04852 | 0.524262 | − | 0.851557i | \(-0.324341\pi\) | ||||
0.524262 | + | 0.851557i | \(0.324341\pi\) | |||||||
\(774\) | 12.5165 | 0.449896 | ||||||||
\(775\) | 2.31929 | 0.0833112 | ||||||||
\(776\) | 6.12659 | 0.219932 | ||||||||
\(777\) | −4.11217 | −0.147523 | ||||||||
\(778\) | 18.6438 | 0.668412 | ||||||||
\(779\) | −50.2088 | −1.79892 | ||||||||
\(780\) | −2.75355 | −0.0985928 | ||||||||
\(781\) | −21.0298 | −0.752505 | ||||||||
\(782\) | −29.5361 | −1.05621 | ||||||||
\(783\) | 6.86586 | 0.245366 | ||||||||
\(784\) | −6.31964 | −0.225701 | ||||||||
\(785\) | 15.1130 | 0.539405 | ||||||||
\(786\) | −13.3775 | −0.477160 | ||||||||
\(787\) | 37.0525 | 1.32078 | 0.660389 | − | 0.750924i | \(-0.270391\pi\) | ||||
0.660389 | + | 0.750924i | \(0.270391\pi\) | |||||||
\(788\) | 17.5228 | 0.624224 | ||||||||
\(789\) | 16.1592 | 0.575284 | ||||||||
\(790\) | −23.1231 | −0.822683 | ||||||||
\(791\) | 12.0826 | 0.429607 | ||||||||
\(792\) | −4.01662 | −0.142724 | ||||||||
\(793\) | 12.3179 | 0.437420 | ||||||||
\(794\) | −12.1568 | −0.431429 | ||||||||
\(795\) | −17.7368 | −0.629058 | ||||||||
\(796\) | −8.66641 | −0.307173 | ||||||||
\(797\) | −28.2779 | −1.00166 | −0.500828 | − | 0.865547i | \(-0.666971\pi\) | ||||
−0.500828 | + | 0.865547i | \(0.666971\pi\) | |||||||
\(798\) | −4.83251 | −0.171069 | ||||||||
\(799\) | 58.5768 | 2.07230 | ||||||||
\(800\) | 2.58202 | 0.0912881 | ||||||||
\(801\) | 15.1576 | 0.535566 | ||||||||
\(802\) | 17.1721 | 0.606370 | ||||||||
\(803\) | 11.4787 | 0.405073 | ||||||||
\(804\) | −9.95884 | −0.351221 | ||||||||
\(805\) | −13.7326 | −0.484009 | ||||||||
\(806\) | −0.898245 | −0.0316393 | ||||||||
\(807\) | −6.48600 | −0.228318 | ||||||||
\(808\) | −17.5626 | −0.617849 | ||||||||
\(809\) | 15.9799 | 0.561822 | 0.280911 | − | 0.959734i | \(-0.409363\pi\) | ||||
0.280911 | + | 0.959734i | \(0.409363\pi\) | |||||||
\(810\) | −2.75355 | −0.0967498 | ||||||||
\(811\) | −37.0996 | −1.30274 | −0.651372 | − | 0.758758i | \(-0.725806\pi\) | ||||
−0.651372 | + | 0.758758i | \(0.725806\pi\) | |||||||
\(812\) | −5.66322 | −0.198740 | ||||||||
\(813\) | 25.7060 | 0.901548 | ||||||||
\(814\) | −20.0246 | −0.701861 | ||||||||
\(815\) | −19.4459 | −0.681158 | ||||||||
\(816\) | 4.88498 | 0.171009 | ||||||||
\(817\) | 73.3307 | 2.56552 | ||||||||
\(818\) | −2.80065 | −0.0979223 | ||||||||
\(819\) | −0.824838 | −0.0288222 | ||||||||
\(820\) | 23.5976 | 0.824065 | ||||||||
\(821\) | −3.11002 | −0.108541 | −0.0542703 | − | 0.998526i | \(-0.517283\pi\) | ||||
−0.0542703 | + | 0.998526i | \(0.517283\pi\) | |||||||
\(822\) | 3.65086 | 0.127338 | ||||||||
\(823\) | −26.3115 | −0.917162 | −0.458581 | − | 0.888653i | \(-0.651642\pi\) | ||||
−0.458581 | + | 0.888653i | \(0.651642\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 10.3710 | 0.361071 | ||||||||
\(826\) | −1.70882 | −0.0594576 | ||||||||
\(827\) | −36.0829 | −1.25472 | −0.627362 | − | 0.778727i | \(-0.715865\pi\) | ||||
−0.627362 | + | 0.778727i | \(0.715865\pi\) | |||||||
\(828\) | 6.04631 | 0.210124 | ||||||||
\(829\) | −0.0737644 | −0.00256194 | −0.00128097 | − | 0.999999i | \(-0.500408\pi\) | ||||
−0.00128097 | + | 0.999999i | \(0.500408\pi\) | |||||||
\(830\) | 14.3681 | 0.498723 | ||||||||
\(831\) | 16.0917 | 0.558214 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 30.8713 | 1.06963 | ||||||||
\(834\) | −14.9078 | −0.516215 | ||||||||
\(835\) | −46.7973 | −1.61949 | ||||||||
\(836\) | −23.5323 | −0.813881 | ||||||||
\(837\) | −0.898245 | −0.0310479 | ||||||||
\(838\) | 40.3556 | 1.39406 | ||||||||
\(839\) | −15.1825 | −0.524160 | −0.262080 | − | 0.965046i | \(-0.584408\pi\) | ||||
−0.262080 | + | 0.965046i | \(0.584408\pi\) | |||||||
\(840\) | 2.27123 | 0.0783649 | ||||||||
\(841\) | 18.1400 | 0.625518 | ||||||||
\(842\) | −15.1113 | −0.520771 | ||||||||
\(843\) | −0.0961083 | −0.00331014 | ||||||||
\(844\) | −7.82353 | −0.269297 | ||||||||
\(845\) | −2.75355 | −0.0947249 | ||||||||
\(846\) | −11.9912 | −0.412266 | ||||||||
\(847\) | 4.23409 | 0.145485 | ||||||||
\(848\) | −6.44142 | −0.221199 | ||||||||
\(849\) | −5.39853 | −0.185277 | ||||||||
\(850\) | −12.6131 | −0.432626 | ||||||||
\(851\) | 30.1435 | 1.03330 | ||||||||
\(852\) | −5.23569 | −0.179372 | ||||||||
\(853\) | −44.9003 | −1.53736 | −0.768679 | − | 0.639634i | \(-0.779086\pi\) | ||||
−0.768679 | + | 0.639634i | \(0.779086\pi\) | |||||||
\(854\) | −10.1602 | −0.347676 | ||||||||
\(855\) | −16.1323 | −0.551712 | ||||||||
\(856\) | 20.3015 | 0.693891 | ||||||||
\(857\) | 27.5661 | 0.941641 | 0.470821 | − | 0.882229i | \(-0.343958\pi\) | ||||
0.470821 | + | 0.882229i | \(0.343958\pi\) | |||||||
\(858\) | −4.01662 | −0.137125 | ||||||||
\(859\) | −17.7050 | −0.604087 | −0.302044 | − | 0.953294i | \(-0.597669\pi\) | ||||
−0.302044 | + | 0.953294i | \(0.597669\pi\) | |||||||
\(860\) | −34.4647 | −1.17524 | ||||||||
\(861\) | 7.06879 | 0.240904 | ||||||||
\(862\) | 23.8797 | 0.813345 | ||||||||
\(863\) | −28.7685 | −0.979291 | −0.489645 | − | 0.871922i | \(-0.662874\pi\) | ||||
−0.489645 | + | 0.871922i | \(0.662874\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −11.9551 | −0.406484 | ||||||||
\(866\) | −22.2116 | −0.754782 | ||||||||
\(867\) | −6.86306 | −0.233082 | ||||||||
\(868\) | 0.740907 | 0.0251480 | ||||||||
\(869\) | −33.7298 | −1.14421 | ||||||||
\(870\) | −18.9055 | −0.640955 | ||||||||
\(871\) | −9.95884 | −0.337443 | ||||||||
\(872\) | −3.09481 | −0.104804 | ||||||||
\(873\) | 6.12659 | 0.207354 | ||||||||
\(874\) | 35.4237 | 1.19822 | ||||||||
\(875\) | 5.49179 | 0.185657 | ||||||||
\(876\) | 2.85779 | 0.0965558 | ||||||||
\(877\) | 0.0975824 | 0.00329512 | 0.00164756 | − | 0.999999i | \(-0.499476\pi\) | ||||
0.00164756 | + | 0.999999i | \(0.499476\pi\) | |||||||
\(878\) | 13.5722 | 0.458039 | ||||||||
\(879\) | −22.2615 | −0.750863 | ||||||||
\(880\) | 11.0599 | 0.372831 | ||||||||
\(881\) | 27.4355 | 0.924325 | 0.462163 | − | 0.886795i | \(-0.347074\pi\) | ||||
0.462163 | + | 0.886795i | \(0.347074\pi\) | |||||||
\(882\) | −6.31964 | −0.212793 | ||||||||
\(883\) | 6.74837 | 0.227101 | 0.113550 | − | 0.993532i | \(-0.463778\pi\) | ||||
0.113550 | + | 0.993532i | \(0.463778\pi\) | |||||||
\(884\) | 4.88498 | 0.164300 | ||||||||
\(885\) | −5.70455 | −0.191756 | ||||||||
\(886\) | 3.04113 | 0.102169 | ||||||||
\(887\) | −53.6082 | −1.79999 | −0.899993 | − | 0.435904i | \(-0.856429\pi\) | ||||
−0.899993 | + | 0.435904i | \(0.856429\pi\) | |||||||
\(888\) | −4.98543 | −0.167300 | ||||||||
\(889\) | 11.9665 | 0.401342 | ||||||||
\(890\) | −41.7370 | −1.39903 | ||||||||
\(891\) | −4.01662 | −0.134562 | ||||||||
\(892\) | −0.973709 | −0.0326022 | ||||||||
\(893\) | −70.2532 | −2.35094 | ||||||||
\(894\) | −2.99240 | −0.100081 | ||||||||
\(895\) | −46.9242 | −1.56850 | ||||||||
\(896\) | 0.824838 | 0.0275559 | ||||||||
\(897\) | 6.04631 | 0.201880 | ||||||||
\(898\) | −14.6556 | −0.489064 | ||||||||
\(899\) | −6.16723 | −0.205689 | ||||||||
\(900\) | 2.58202 | 0.0860673 | ||||||||
\(901\) | 31.4662 | 1.04829 | ||||||||
\(902\) | 34.4220 | 1.14613 | ||||||||
\(903\) | −10.3241 | −0.343564 | ||||||||
\(904\) | 14.6484 | 0.487199 | ||||||||
\(905\) | −47.5047 | −1.57911 | ||||||||
\(906\) | 19.8765 | 0.660354 | ||||||||
\(907\) | 14.6663 | 0.486987 | 0.243494 | − | 0.969903i | \(-0.421707\pi\) | ||||
0.243494 | + | 0.969903i | \(0.421707\pi\) | |||||||
\(908\) | 25.0223 | 0.830395 | ||||||||
\(909\) | −17.5626 | −0.582514 | ||||||||
\(910\) | 2.27123 | 0.0752906 | ||||||||
\(911\) | −15.7552 | −0.521992 | −0.260996 | − | 0.965340i | \(-0.584051\pi\) | ||||
−0.260996 | + | 0.965340i | \(0.584051\pi\) | |||||||
\(912\) | −5.85873 | −0.194002 | ||||||||
\(913\) | 20.9588 | 0.693635 | ||||||||
\(914\) | 19.5597 | 0.646979 | ||||||||
\(915\) | −33.9178 | −1.12129 | ||||||||
\(916\) | 20.2628 | 0.669500 | ||||||||
\(917\) | 11.0343 | 0.364384 | ||||||||
\(918\) | 4.88498 | 0.161228 | ||||||||
\(919\) | −12.0221 | −0.396574 | −0.198287 | − | 0.980144i | \(-0.563538\pi\) | ||||
−0.198287 | + | 0.980144i | \(0.563538\pi\) | |||||||
\(920\) | −16.6488 | −0.548895 | ||||||||
\(921\) | 2.18512 | 0.0720021 | ||||||||
\(922\) | 6.48694 | 0.213636 | ||||||||
\(923\) | −5.23569 | −0.172335 | ||||||||
\(924\) | 3.31306 | 0.108992 | ||||||||
\(925\) | 12.8725 | 0.423244 | ||||||||
\(926\) | 30.7177 | 1.00945 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −6.86586 | −0.225383 | ||||||||
\(929\) | 23.3913 | 0.767444 | 0.383722 | − | 0.923449i | \(-0.374642\pi\) | ||||
0.383722 | + | 0.923449i | \(0.374642\pi\) | |||||||
\(930\) | 2.47336 | 0.0811047 | ||||||||
\(931\) | −37.0251 | −1.21345 | ||||||||
\(932\) | −10.4040 | −0.340795 | ||||||||
\(933\) | 0.0801534 | 0.00262411 | ||||||||
\(934\) | 22.1129 | 0.723558 | ||||||||
\(935\) | −54.0277 | −1.76689 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | −56.1198 | −1.83336 | −0.916678 | − | 0.399627i | \(-0.869140\pi\) | ||||
−0.916678 | + | 0.399627i | \(0.869140\pi\) | |||||||
\(938\) | 8.21444 | 0.268211 | ||||||||
\(939\) | −9.05156 | −0.295387 | ||||||||
\(940\) | 33.0183 | 1.07694 | ||||||||
\(941\) | 3.75419 | 0.122383 | 0.0611915 | − | 0.998126i | \(-0.480510\pi\) | ||||
0.0611915 | + | 0.998126i | \(0.480510\pi\) | |||||||
\(942\) | 5.48855 | 0.178827 | ||||||||
\(943\) | −51.8163 | −1.68737 | ||||||||
\(944\) | −2.07171 | −0.0674284 | ||||||||
\(945\) | 2.27123 | 0.0738831 | ||||||||
\(946\) | −50.2740 | −1.63455 | ||||||||
\(947\) | 48.9388 | 1.59030 | 0.795149 | − | 0.606414i | \(-0.207392\pi\) | ||||
0.795149 | + | 0.606414i | \(0.207392\pi\) | |||||||
\(948\) | −8.39757 | −0.272740 | ||||||||
\(949\) | 2.85779 | 0.0927678 | ||||||||
\(950\) | 15.1273 | 0.490796 | ||||||||
\(951\) | −4.18981 | −0.135864 | ||||||||
\(952\) | −4.02932 | −0.130591 | ||||||||
\(953\) | −56.1519 | −1.81894 | −0.909469 | − | 0.415772i | \(-0.863512\pi\) | ||||
−0.909469 | + | 0.415772i | \(0.863512\pi\) | |||||||
\(954\) | −6.44142 | −0.208549 | ||||||||
\(955\) | 44.7546 | 1.44823 | ||||||||
\(956\) | 26.4940 | 0.856876 | ||||||||
\(957\) | −27.5775 | −0.891456 | ||||||||
\(958\) | 28.0901 | 0.907549 | ||||||||
\(959\) | −3.01137 | −0.0972421 | ||||||||
\(960\) | 2.75355 | 0.0888703 | ||||||||
\(961\) | −30.1932 | −0.973973 | ||||||||
\(962\) | −4.98543 | −0.160737 | ||||||||
\(963\) | 20.3015 | 0.654207 | ||||||||
\(964\) | 1.31680 | 0.0424114 | ||||||||
\(965\) | 41.0615 | 1.32182 | ||||||||
\(966\) | −4.98723 | −0.160461 | ||||||||
\(967\) | −26.4792 | −0.851514 | −0.425757 | − | 0.904837i | \(-0.639992\pi\) | ||||
−0.425757 | + | 0.904837i | \(0.639992\pi\) | |||||||
\(968\) | 5.13324 | 0.164988 | ||||||||
\(969\) | 28.6198 | 0.919400 | ||||||||
\(970\) | −16.8698 | −0.541658 | ||||||||
\(971\) | −32.1713 | −1.03243 | −0.516213 | − | 0.856460i | \(-0.672659\pi\) | ||||
−0.516213 | + | 0.856460i | \(0.672659\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 12.2965 | 0.394209 | ||||||||
\(974\) | −43.1659 | −1.38312 | ||||||||
\(975\) | 2.58202 | 0.0826908 | ||||||||
\(976\) | −12.3179 | −0.394285 | ||||||||
\(977\) | −27.8028 | −0.889490 | −0.444745 | − | 0.895657i | \(-0.646706\pi\) | ||||
−0.444745 | + | 0.895657i | \(0.646706\pi\) | |||||||
\(978\) | −7.06211 | −0.225821 | ||||||||
\(979\) | −60.8822 | −1.94580 | ||||||||
\(980\) | 17.4014 | 0.555868 | ||||||||
\(981\) | −3.09481 | −0.0988098 | ||||||||
\(982\) | 4.59882 | 0.146754 | ||||||||
\(983\) | −13.9383 | −0.444561 | −0.222281 | − | 0.974983i | \(-0.571350\pi\) | ||||
−0.222281 | + | 0.974983i | \(0.571350\pi\) | |||||||
\(984\) | 8.56990 | 0.273199 | ||||||||
\(985\) | −48.2499 | −1.53737 | ||||||||
\(986\) | 33.5396 | 1.06812 | ||||||||
\(987\) | 9.89081 | 0.314828 | ||||||||
\(988\) | −5.85873 | −0.186391 | ||||||||
\(989\) | 75.6786 | 2.40644 | ||||||||
\(990\) | 11.0599 | 0.351508 | ||||||||
\(991\) | −16.6732 | −0.529642 | −0.264821 | − | 0.964298i | \(-0.585313\pi\) | ||||
−0.264821 | + | 0.964298i | \(0.585313\pi\) | |||||||
\(992\) | 0.898245 | 0.0285193 | ||||||||
\(993\) | −18.0911 | −0.574104 | ||||||||
\(994\) | 4.31860 | 0.136978 | ||||||||
\(995\) | 23.8634 | 0.756520 | ||||||||
\(996\) | 5.21802 | 0.165339 | ||||||||
\(997\) | −30.0597 | −0.952000 | −0.476000 | − | 0.879445i | \(-0.657914\pi\) | ||||
−0.476000 | + | 0.879445i | \(0.657914\pi\) | |||||||
\(998\) | 14.7370 | 0.466490 | ||||||||
\(999\) | −4.98543 | −0.157732 |
(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 | 8034.2.a.bc.1.3 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bc.1.3 | ✓ | 15 | 1.1 | even | 1 | trivial |