Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4923,2,Mod(1,4923)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4923, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4923.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4923 = 3^{2} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4923.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: | \(39.3103529151\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 547) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(2.35947\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4923.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35947 | 1.66840 | 0.834199 | − | 0.551463i | \(-0.185930\pi\) | ||||
0.834199 | + | 0.551463i | \(0.185930\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.56710 | 1.78355 | ||||||||
\(5\) | 4.18174 | 1.87013 | 0.935065 | − | 0.354477i | \(-0.115341\pi\) | ||||
0.935065 | + | 0.354477i | \(0.115341\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.82979 | −1.06956 | −0.534779 | − | 0.844992i | \(-0.679605\pi\) | ||||
−0.534779 | + | 0.844992i | \(0.679605\pi\) | |||||||
\(8\) | 3.69754 | 1.30728 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 9.86669 | 3.12012 | ||||||||
\(11\) | −2.48715 | −0.749904 | −0.374952 | − | 0.927044i | \(-0.622341\pi\) | ||||
−0.374952 | + | 0.927044i | \(0.622341\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.60177 | 1.27630 | 0.638150 | − | 0.769912i | \(-0.279700\pi\) | ||||
0.638150 | + | 0.769912i | \(0.279700\pi\) | |||||||
\(14\) | −6.67680 | −1.78445 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.59003 | 0.397506 | ||||||||
\(17\) | 5.70168 | 1.38286 | 0.691430 | − | 0.722444i | \(-0.256981\pi\) | ||||
0.691430 | + | 0.722444i | \(0.256981\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.542873 | 0.124544 | 0.0622718 | − | 0.998059i | \(-0.480165\pi\) | ||||
0.0622718 | + | 0.998059i | \(0.480165\pi\) | |||||||
\(20\) | 14.9167 | 3.33547 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.86836 | −1.25114 | ||||||||
\(23\) | −6.30681 | −1.31506 | −0.657530 | − | 0.753428i | \(-0.728399\pi\) | ||||
−0.657530 | + | 0.753428i | \(0.728399\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.4869 | 2.49738 | ||||||||
\(26\) | 10.8577 | 2.12938 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.0941 | −1.90761 | ||||||||
\(29\) | 4.16997 | 0.774344 | 0.387172 | − | 0.922007i | \(-0.373452\pi\) | ||||
0.387172 | + | 0.922007i | \(0.373452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.03942 | 0.905106 | 0.452553 | − | 0.891737i | \(-0.350513\pi\) | ||||
0.452553 | + | 0.891737i | \(0.350513\pi\) | |||||||
\(32\) | −3.64346 | −0.644078 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.4529 | 2.30716 | ||||||||
\(35\) | −11.8334 | −2.00021 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.02373 | −0.661496 | −0.330748 | − | 0.943719i | \(-0.607301\pi\) | ||||
−0.330748 | + | 0.943719i | \(0.607301\pi\) | |||||||
\(38\) | 1.28089 | 0.207788 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 15.4621 | 2.44478 | ||||||||
\(41\) | 2.04830 | 0.319890 | 0.159945 | − | 0.987126i | \(-0.448868\pi\) | ||||
0.159945 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.11938 | 1.08570 | 0.542848 | − | 0.839831i | \(-0.317346\pi\) | ||||
0.542848 | + | 0.839831i | \(0.317346\pi\) | |||||||
\(44\) | −8.87193 | −1.33749 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14.8807 | −2.19404 | ||||||||
\(47\) | 4.23012 | 0.617027 | 0.308513 | − | 0.951220i | \(-0.400169\pi\) | ||||
0.308513 | + | 0.951220i | \(0.400169\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00770 | 0.143956 | ||||||||
\(50\) | 29.4625 | 4.16663 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.4150 | 2.27635 | ||||||||
\(53\) | 8.60588 | 1.18211 | 0.591054 | − | 0.806632i | \(-0.298712\pi\) | ||||
0.591054 | + | 0.806632i | \(0.298712\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.4006 | −1.40242 | ||||||||
\(56\) | −10.4632 | −1.39821 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.83893 | 1.29191 | ||||||||
\(59\) | −2.15472 | −0.280520 | −0.140260 | − | 0.990115i | \(-0.544794\pi\) | ||||
−0.140260 | + | 0.990115i | \(0.544794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.53383 | −1.09264 | −0.546322 | − | 0.837575i | \(-0.683973\pi\) | ||||
−0.546322 | + | 0.837575i | \(0.683973\pi\) | |||||||
\(62\) | 11.8904 | 1.51008 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.7767 | −1.47209 | ||||||||
\(65\) | 19.2434 | 2.38685 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.63078 | −0.443570 | −0.221785 | − | 0.975096i | \(-0.571188\pi\) | ||||
−0.221785 | + | 0.975096i | \(0.571188\pi\) | |||||||
\(68\) | 20.3385 | 2.46640 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −27.9206 | −3.33715 | ||||||||
\(71\) | −7.43976 | −0.882938 | −0.441469 | − | 0.897277i | \(-0.645542\pi\) | ||||
−0.441469 | + | 0.897277i | \(0.645542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8830 | 1.27376 | 0.636881 | − | 0.770962i | \(-0.280224\pi\) | ||||
0.636881 | + | 0.770962i | \(0.280224\pi\) | |||||||
\(74\) | −9.49386 | −1.10364 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.93648 | 0.222130 | ||||||||
\(77\) | 7.03811 | 0.802067 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.82054 | 0.542353 | 0.271177 | − | 0.962530i | \(-0.412587\pi\) | ||||
0.271177 | + | 0.962530i | \(0.412587\pi\) | |||||||
\(80\) | 6.64907 | 0.743388 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.83290 | 0.533704 | ||||||||
\(83\) | −11.0018 | −1.20760 | −0.603801 | − | 0.797135i | \(-0.706348\pi\) | ||||
−0.603801 | + | 0.797135i | \(0.706348\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 23.8429 | 2.58613 | ||||||||
\(86\) | 16.7980 | 1.81137 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.19633 | −0.980333 | ||||||||
\(89\) | −2.44024 | −0.258665 | −0.129332 | − | 0.991601i | \(-0.541283\pi\) | ||||
−0.129332 | + | 0.991601i | \(0.541283\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0220 | −1.36508 | ||||||||
\(92\) | −22.4970 | −2.34548 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.98085 | 1.02945 | ||||||||
\(95\) | 2.27015 | 0.232913 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.35684 | 0.543904 | 0.271952 | − | 0.962311i | \(-0.412331\pi\) | ||||
0.271952 | + | 0.962311i | \(0.412331\pi\) | |||||||
\(98\) | 2.37763 | 0.240177 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 44.5421 | 4.45421 | ||||||||
\(101\) | −16.3478 | −1.62666 | −0.813332 | − | 0.581800i | \(-0.802349\pi\) | ||||
−0.813332 | + | 0.581800i | \(0.802349\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.8061 | −1.16329 | −0.581645 | − | 0.813443i | \(-0.697591\pi\) | ||||
−0.581645 | + | 0.813443i | \(0.697591\pi\) | |||||||
\(104\) | 17.0152 | 1.66848 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20.3053 | 1.97223 | ||||||||
\(107\) | 12.0397 | 1.16392 | 0.581959 | − | 0.813218i | \(-0.302286\pi\) | ||||
0.581959 | + | 0.813218i | \(0.302286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.39459 | 0.133577 | 0.0667886 | − | 0.997767i | \(-0.478725\pi\) | ||||
0.0667886 | + | 0.997767i | \(0.478725\pi\) | |||||||
\(110\) | −24.5399 | −2.33979 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.49943 | −0.425156 | ||||||||
\(113\) | −4.16686 | −0.391985 | −0.195992 | − | 0.980605i | \(-0.562793\pi\) | ||||
−0.195992 | + | 0.980605i | \(0.562793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.3734 | −2.45933 | ||||||||
\(116\) | 14.8747 | 1.38108 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.08399 | −0.468019 | ||||||||
\(119\) | −16.1345 | −1.47905 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.81408 | −0.437644 | ||||||||
\(122\) | −20.1353 | −1.82297 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.9761 | 1.61430 | ||||||||
\(125\) | 31.3083 | 2.80030 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.57110 | 0.760562 | 0.380281 | − | 0.924871i | \(-0.375827\pi\) | ||||
0.380281 | + | 0.924871i | \(0.375827\pi\) | |||||||
\(128\) | −20.4998 | −1.81195 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 45.4042 | 3.98221 | ||||||||
\(131\) | 19.4849 | 1.70241 | 0.851204 | − | 0.524836i | \(-0.175873\pi\) | ||||
0.851204 | + | 0.524836i | \(0.175873\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.53621 | −0.133207 | ||||||||
\(134\) | −8.56672 | −0.740052 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.0822 | 1.80778 | ||||||||
\(137\) | −16.6524 | −1.42271 | −0.711357 | − | 0.702830i | \(-0.751919\pi\) | ||||
−0.711357 | + | 0.702830i | \(0.751919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.41300 | −0.628763 | −0.314381 | − | 0.949297i | \(-0.601797\pi\) | ||||
−0.314381 | + | 0.949297i | \(0.601797\pi\) | |||||||
\(140\) | −42.2111 | −3.56749 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17.5539 | −1.47309 | ||||||||
\(143\) | −11.4453 | −0.957103 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.4377 | 1.44812 | ||||||||
\(146\) | 25.6782 | 2.12514 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.3530 | −1.17981 | ||||||||
\(149\) | 20.4476 | 1.67513 | 0.837566 | − | 0.546335i | \(-0.183978\pi\) | ||||
0.837566 | + | 0.546335i | \(0.183978\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4794 | 1.25970 | 0.629849 | − | 0.776717i | \(-0.283117\pi\) | ||||
0.629849 | + | 0.776717i | \(0.283117\pi\) | |||||||
\(152\) | 2.00729 | 0.162813 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.6062 | 1.33817 | ||||||||
\(155\) | 21.0735 | 1.69267 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.5044 | −1.31719 | −0.658596 | − | 0.752497i | \(-0.728849\pi\) | ||||
−0.658596 | + | 0.752497i | \(0.728849\pi\) | |||||||
\(158\) | 11.3739 | 0.904861 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.2360 | −1.20451 | ||||||||
\(161\) | 17.8469 | 1.40653 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.84622 | 0.222933 | 0.111467 | − | 0.993768i | \(-0.464445\pi\) | ||||
0.111467 | + | 0.993768i | \(0.464445\pi\) | |||||||
\(164\) | 7.30649 | 0.570541 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.9584 | −2.01476 | ||||||||
\(167\) | −11.3203 | −0.875995 | −0.437997 | − | 0.898976i | \(-0.644312\pi\) | ||||
−0.437997 | + | 0.898976i | \(0.644312\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.17626 | 0.628943 | ||||||||
\(170\) | 56.2567 | 4.31469 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 25.3956 | 1.93640 | ||||||||
\(173\) | 14.3600 | 1.09177 | 0.545884 | − | 0.837861i | \(-0.316194\pi\) | ||||
0.545884 | + | 0.837861i | \(0.316194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −35.3353 | −2.67110 | ||||||||
\(176\) | −3.95463 | −0.298092 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.75768 | −0.431556 | ||||||||
\(179\) | −9.00995 | −0.673435 | −0.336718 | − | 0.941606i | \(-0.609317\pi\) | ||||
−0.336718 | + | 0.941606i | \(0.609317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.6614 | −1.83306 | −0.916532 | − | 0.399961i | \(-0.869024\pi\) | ||||
−0.916532 | + | 0.399961i | \(0.869024\pi\) | |||||||
\(182\) | −30.7251 | −2.27749 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −23.3197 | −1.71915 | ||||||||
\(185\) | −16.8262 | −1.23708 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.1809 | −1.03701 | ||||||||
\(188\) | 15.0893 | 1.10050 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.35636 | 0.388591 | ||||||||
\(191\) | −0.990564 | −0.0716747 | −0.0358374 | − | 0.999358i | \(-0.511410\pi\) | ||||
−0.0358374 | + | 0.999358i | \(0.511410\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.7042 | −1.63428 | −0.817141 | − | 0.576438i | \(-0.804442\pi\) | ||||
−0.817141 | + | 0.576438i | \(0.804442\pi\) | |||||||
\(194\) | 12.6393 | 0.907449 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.59455 | 0.256754 | ||||||||
\(197\) | −10.6866 | −0.761389 | −0.380694 | − | 0.924701i | \(-0.624315\pi\) | ||||
−0.380694 | + | 0.924701i | \(0.624315\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.22512 | −0.228623 | −0.114311 | − | 0.993445i | \(-0.536466\pi\) | ||||
−0.114311 | + | 0.993445i | \(0.536466\pi\) | |||||||
\(200\) | 46.1709 | 3.26477 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −38.5721 | −2.71392 | ||||||||
\(203\) | −11.8001 | −0.828207 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.56544 | 0.598236 | ||||||||
\(206\) | −27.8562 | −1.94083 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.31693 | 0.507337 | ||||||||
\(209\) | −1.35021 | −0.0933958 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.91177 | −0.406983 | −0.203491 | − | 0.979077i | \(-0.565229\pi\) | ||||
−0.203491 | + | 0.979077i | \(0.565229\pi\) | |||||||
\(212\) | 30.6981 | 2.10835 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28.4072 | 1.94188 | ||||||||
\(215\) | 29.7714 | 2.03039 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.2605 | −0.968065 | ||||||||
\(218\) | 3.29049 | 0.222860 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −37.1001 | −2.50129 | ||||||||
\(221\) | 26.2378 | 1.76494 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.2358 | −0.819367 | −0.409684 | − | 0.912228i | \(-0.634361\pi\) | ||||
−0.409684 | + | 0.912228i | \(0.634361\pi\) | |||||||
\(224\) | 10.3102 | 0.688880 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.83157 | −0.653987 | ||||||||
\(227\) | −0.447253 | −0.0296852 | −0.0148426 | − | 0.999890i | \(-0.504725\pi\) | ||||
−0.0148426 | + | 0.999890i | \(0.504725\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.3140 | −0.747652 | −0.373826 | − | 0.927499i | \(-0.621954\pi\) | ||||
−0.373826 | + | 0.927499i | \(0.621954\pi\) | |||||||
\(230\) | −62.2273 | −4.10315 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.4186 | 1.01228 | ||||||||
\(233\) | −19.0486 | −1.24792 | −0.623958 | − | 0.781458i | \(-0.714476\pi\) | ||||
−0.623958 | + | 0.781458i | \(0.714476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.6893 | 1.15392 | ||||||||
\(236\) | −7.68609 | −0.500322 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −38.0690 | −2.46764 | ||||||||
\(239\) | −4.17495 | −0.270055 | −0.135027 | − | 0.990842i | \(-0.543112\pi\) | ||||
−0.135027 | + | 0.990842i | \(0.543112\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.77764 | 0.307755 | 0.153878 | − | 0.988090i | \(-0.450824\pi\) | ||||
0.153878 | + | 0.988090i | \(0.450824\pi\) | |||||||
\(242\) | −11.3587 | −0.730164 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −30.4411 | −1.94879 | ||||||||
\(245\) | 4.21392 | 0.269217 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.49817 | 0.158955 | ||||||||
\(248\) | 18.6334 | 1.18322 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 73.8711 | 4.67202 | ||||||||
\(251\) | −4.20802 | −0.265608 | −0.132804 | − | 0.991142i | \(-0.542398\pi\) | ||||
−0.132804 | + | 0.991142i | \(0.542398\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.6860 | 0.986169 | ||||||||
\(254\) | 20.2233 | 1.26892 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.8154 | −1.55096 | ||||||||
\(257\) | −19.5268 | −1.21805 | −0.609023 | − | 0.793152i | \(-0.708438\pi\) | ||||
−0.609023 | + | 0.793152i | \(0.708438\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3863 | 0.707509 | ||||||||
\(260\) | 68.6431 | 4.25707 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 45.9742 | 2.84029 | ||||||||
\(263\) | −5.05834 | −0.311910 | −0.155955 | − | 0.987764i | \(-0.549846\pi\) | ||||
−0.155955 | + | 0.987764i | \(0.549846\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.9875 | 2.21070 | ||||||||
\(266\) | −3.62465 | −0.222242 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.9514 | −0.791131 | ||||||||
\(269\) | 16.9375 | 1.03270 | 0.516349 | − | 0.856378i | \(-0.327291\pi\) | ||||
0.516349 | + | 0.856378i | \(0.327291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.5325 | −0.700547 | −0.350274 | − | 0.936647i | \(-0.613911\pi\) | ||||
−0.350274 | + | 0.936647i | \(0.613911\pi\) | |||||||
\(272\) | 9.06581 | 0.549695 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −39.2910 | −2.37365 | ||||||||
\(275\) | −31.0569 | −1.87280 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9882 | −0.900556 | −0.450278 | − | 0.892889i | \(-0.648675\pi\) | ||||
−0.450278 | + | 0.892889i | \(0.648675\pi\) | |||||||
\(278\) | −17.4908 | −1.04903 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −43.7545 | −2.61483 | ||||||||
\(281\) | 25.9673 | 1.54908 | 0.774541 | − | 0.632524i | \(-0.217981\pi\) | ||||
0.774541 | + | 0.632524i | \(0.217981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.6595 | −1.64419 | −0.822094 | − | 0.569351i | \(-0.807194\pi\) | ||||
−0.822094 | + | 0.569351i | \(0.807194\pi\) | |||||||
\(284\) | −26.5384 | −1.57477 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −27.0048 | −1.59683 | ||||||||
\(287\) | −5.79625 | −0.342142 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5091 | 0.912300 | ||||||||
\(290\) | 41.1438 | 2.41605 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 38.8209 | 2.27182 | ||||||||
\(293\) | −0.415058 | −0.0242480 | −0.0121240 | − | 0.999927i | \(-0.503859\pi\) | ||||
−0.0121240 | + | 0.999927i | \(0.503859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.01045 | −0.524609 | ||||||||
\(296\) | −14.8779 | −0.864759 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 48.2455 | 2.79479 | ||||||||
\(299\) | −29.0225 | −1.67841 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.1463 | −1.16122 | ||||||||
\(302\) | 36.5233 | 2.10168 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.863182 | 0.0495069 | ||||||||
\(305\) | −35.6862 | −2.04339 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.03206 | −0.287195 | −0.143597 | − | 0.989636i | \(-0.545867\pi\) | ||||
−0.143597 | + | 0.989636i | \(0.545867\pi\) | |||||||
\(308\) | 25.1057 | 1.43053 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 49.7224 | 2.82404 | ||||||||
\(311\) | 7.79527 | 0.442029 | 0.221015 | − | 0.975270i | \(-0.429063\pi\) | ||||
0.221015 | + | 0.975270i | \(0.429063\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4305 | −0.759134 | −0.379567 | − | 0.925164i | \(-0.623927\pi\) | ||||
−0.379567 | + | 0.925164i | \(0.623927\pi\) | |||||||
\(314\) | −38.9416 | −2.19760 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.1954 | 0.967315 | ||||||||
\(317\) | 9.15464 | 0.514176 | 0.257088 | − | 0.966388i | \(-0.417237\pi\) | ||||
0.257088 | + | 0.966388i | \(0.417237\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.3713 | −0.580684 | ||||||||
\(320\) | −49.2470 | −2.75299 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 42.1093 | 2.34666 | ||||||||
\(323\) | 3.09529 | 0.172226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 57.4619 | 3.18741 | ||||||||
\(326\) | 6.71557 | 0.371941 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.57366 | 0.418185 | ||||||||
\(329\) | −11.9703 | −0.659947 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.02794 | 0.496221 | 0.248110 | − | 0.968732i | \(-0.420190\pi\) | ||||
0.248110 | + | 0.968732i | \(0.420190\pi\) | |||||||
\(332\) | −39.2445 | −2.15382 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −26.7100 | −1.46151 | ||||||||
\(335\) | −15.1830 | −0.829534 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.1258 | −1.58658 | −0.793292 | − | 0.608841i | \(-0.791635\pi\) | ||||
−0.793292 | + | 0.608841i | \(0.791635\pi\) | |||||||
\(338\) | 19.2917 | 1.04933 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 85.0501 | 4.61249 | ||||||||
\(341\) | −12.5338 | −0.678743 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9569 | 0.915589 | ||||||||
\(344\) | 26.3242 | 1.41931 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 33.8819 | 1.82150 | ||||||||
\(347\) | 2.77201 | 0.148810 | 0.0744048 | − | 0.997228i | \(-0.476294\pi\) | ||||
0.0744048 | + | 0.997228i | \(0.476294\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.73834 | 0.0930509 | 0.0465255 | − | 0.998917i | \(-0.485185\pi\) | ||||
0.0465255 | + | 0.998917i | \(0.485185\pi\) | |||||||
\(350\) | −83.3727 | −4.45646 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.06183 | 0.482997 | ||||||||
\(353\) | 25.4703 | 1.35565 | 0.677825 | − | 0.735224i | \(-0.262923\pi\) | ||||
0.677825 | + | 0.735224i | \(0.262923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.1111 | −1.65121 | ||||||||
\(356\) | −8.70459 | −0.461342 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.2587 | −1.12356 | ||||||||
\(359\) | 32.6283 | 1.72205 | 0.861027 | − | 0.508559i | \(-0.169822\pi\) | ||||
0.861027 | + | 0.508559i | \(0.169822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7053 | −0.984489 | ||||||||
\(362\) | −58.1878 | −3.05828 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −46.4509 | −2.43469 | ||||||||
\(365\) | 45.5099 | 2.38210 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.81294 | 0.355632 | 0.177816 | − | 0.984064i | \(-0.443097\pi\) | ||||
0.177816 | + | 0.984064i | \(0.443097\pi\) | |||||||
\(368\) | −10.0280 | −0.522745 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −39.7008 | −2.06395 | ||||||||
\(371\) | −24.3528 | −1.26433 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6694 | 0.552440 | 0.276220 | − | 0.961095i | \(-0.410918\pi\) | ||||
0.276220 | + | 0.961095i | \(0.410918\pi\) | |||||||
\(374\) | −33.4595 | −1.73015 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.6410 | 0.806625 | ||||||||
\(377\) | 19.1892 | 0.988296 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2741 | 1.14415 | 0.572073 | − | 0.820203i | \(-0.306139\pi\) | ||||
0.572073 | + | 0.820203i | \(0.306139\pi\) | |||||||
\(380\) | 8.09787 | 0.415412 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.33721 | −0.119582 | ||||||||
\(383\) | 2.85301 | 0.145782 | 0.0728911 | − | 0.997340i | \(-0.476777\pi\) | ||||
0.0728911 | + | 0.997340i | \(0.476777\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.4315 | 1.49997 | ||||||||
\(386\) | −53.5698 | −2.72663 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.1084 | 0.970082 | ||||||||
\(389\) | 12.7913 | 0.648545 | 0.324273 | − | 0.945964i | \(-0.394881\pi\) | ||||
0.324273 | + | 0.945964i | \(0.394881\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.9594 | −1.81854 | ||||||||
\(392\) | 3.72599 | 0.188191 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25.2147 | −1.27030 | ||||||||
\(395\) | 20.1582 | 1.01427 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.584024 | 0.0293113 | 0.0146557 | − | 0.999893i | \(-0.495335\pi\) | ||||
0.0146557 | + | 0.999893i | \(0.495335\pi\) | |||||||
\(398\) | −7.60958 | −0.381434 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.8545 | 0.992726 | ||||||||
\(401\) | −1.23150 | −0.0614983 | −0.0307492 | − | 0.999527i | \(-0.509789\pi\) | ||||
−0.0307492 | + | 0.999527i | \(0.509789\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.1902 | 1.15519 | ||||||||
\(404\) | −58.3142 | −2.90124 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27.8421 | −1.38178 | ||||||||
\(407\) | 10.0076 | 0.496059 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.18813 | −0.0587492 | −0.0293746 | − | 0.999568i | \(-0.509352\pi\) | ||||
−0.0293746 | + | 0.999568i | \(0.509352\pi\) | |||||||
\(410\) | 20.2099 | 0.998096 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −42.1136 | −2.07479 | ||||||||
\(413\) | 6.09739 | 0.300033 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −46.0065 | −2.25837 | ||||||||
\(416\) | −16.7663 | −0.822038 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.18577 | −0.155821 | ||||||||
\(419\) | 2.74974 | 0.134333 | 0.0671667 | − | 0.997742i | \(-0.478604\pi\) | ||||
0.0671667 | + | 0.997742i | \(0.478604\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4727 | 1.29020 | 0.645100 | − | 0.764098i | \(-0.276816\pi\) | ||||
0.645100 | + | 0.764098i | \(0.276816\pi\) | |||||||
\(422\) | −13.9486 | −0.679009 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 31.8206 | 1.54534 | ||||||||
\(425\) | 71.1964 | 3.45353 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.1489 | 1.16865 | ||||||||
\(428\) | 42.9467 | 2.07591 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 70.2447 | 3.38750 | ||||||||
\(431\) | 14.7022 | 0.708179 | 0.354090 | − | 0.935212i | \(-0.384791\pi\) | ||||
0.354090 | + | 0.935212i | \(0.384791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.4192 | 1.65408 | 0.827040 | − | 0.562143i | \(-0.190023\pi\) | ||||
0.827040 | + | 0.562143i | \(0.190023\pi\) | |||||||
\(434\) | −33.6472 | −1.61512 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.97464 | 0.238242 | ||||||||
\(437\) | −3.42380 | −0.163782 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.3151 | 0.826403 | 0.413202 | − | 0.910640i | \(-0.364411\pi\) | ||||
0.413202 | + | 0.910640i | \(0.364411\pi\) | |||||||
\(440\) | −38.4566 | −1.83335 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 61.9073 | 2.94463 | ||||||||
\(443\) | −19.9059 | −0.945757 | −0.472878 | − | 0.881128i | \(-0.656785\pi\) | ||||
−0.472878 | + | 0.881128i | \(0.656785\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.2044 | −0.483737 | ||||||||
\(446\) | −28.8699 | −1.36703 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 33.3255 | 1.57448 | ||||||||
\(449\) | 9.26847 | 0.437406 | 0.218703 | − | 0.975791i | \(-0.429817\pi\) | ||||
0.218703 | + | 0.975791i | \(0.429817\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.09443 | −0.239887 | ||||||||
\(452\) | −14.8636 | −0.699125 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.05528 | −0.0495268 | ||||||||
\(455\) | −54.4547 | −2.55287 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.70114 | −0.453800 | −0.226900 | − | 0.973918i | \(-0.572859\pi\) | ||||
−0.226900 | + | 0.973918i | \(0.572859\pi\) | |||||||
\(458\) | −26.6951 | −1.24738 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −94.0767 | −4.38635 | ||||||||
\(461\) | −25.5277 | −1.18895 | −0.594473 | − | 0.804116i | \(-0.702639\pi\) | ||||
−0.594473 | + | 0.804116i | \(0.702639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.9438 | −1.80987 | −0.904937 | − | 0.425546i | \(-0.860082\pi\) | ||||
−0.904937 | + | 0.425546i | \(0.860082\pi\) | |||||||
\(464\) | 6.63036 | 0.307807 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −44.9447 | −2.08202 | ||||||||
\(467\) | 14.9435 | 0.691501 | 0.345751 | − | 0.938326i | \(-0.387624\pi\) | ||||
0.345751 | + | 0.938326i | \(0.387624\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.2743 | 0.474425 | ||||||||
\(470\) | 41.7373 | 1.92520 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.96714 | −0.366717 | ||||||||
\(473\) | −17.7070 | −0.814168 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.77881 | 0.311033 | ||||||||
\(476\) | −57.5535 | −2.63796 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.85067 | −0.450559 | ||||||||
\(479\) | −3.22823 | −0.147502 | −0.0737508 | − | 0.997277i | \(-0.523497\pi\) | ||||
−0.0737508 | + | 0.997277i | \(0.523497\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.5162 | −0.844268 | ||||||||
\(482\) | 11.2727 | 0.513458 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.1723 | −0.780560 | ||||||||
\(485\) | 22.4009 | 1.01717 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.84073 | −0.355297 | −0.177649 | − | 0.984094i | \(-0.556849\pi\) | ||||
−0.177649 | + | 0.984094i | \(0.556849\pi\) | |||||||
\(488\) | −31.5541 | −1.42839 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.94261 | 0.449161 | ||||||||
\(491\) | −18.3532 | −0.828269 | −0.414134 | − | 0.910216i | \(-0.635916\pi\) | ||||
−0.414134 | + | 0.910216i | \(0.635916\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.7758 | 1.07081 | ||||||||
\(494\) | 5.89437 | 0.265200 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.01280 | 0.359785 | ||||||||
\(497\) | 21.0529 | 0.944354 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.3880 | 1.18129 | 0.590644 | − | 0.806932i | \(-0.298874\pi\) | ||||
0.590644 | + | 0.806932i | \(0.298874\pi\) | |||||||
\(500\) | 111.680 | 4.99448 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.92869 | −0.443139 | ||||||||
\(503\) | 5.59404 | 0.249426 | 0.124713 | − | 0.992193i | \(-0.460199\pi\) | ||||
0.124713 | + | 0.992193i | \(0.460199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −68.3620 | −3.04207 | ||||||||
\(506\) | 37.0106 | 1.64532 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 30.5740 | 1.35650 | ||||||||
\(509\) | −38.7081 | −1.71571 | −0.857853 | − | 0.513895i | \(-0.828202\pi\) | ||||
−0.857853 | + | 0.513895i | \(0.828202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.7966 | −1.36236 | ||||||||
\(512\) | −17.5515 | −0.775676 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −46.0729 | −2.03219 | ||||||||
\(515\) | −49.3700 | −2.17550 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.5210 | −0.462711 | ||||||||
\(518\) | 26.8656 | 1.18041 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 71.1531 | 3.12027 | ||||||||
\(521\) | −5.16331 | −0.226209 | −0.113104 | − | 0.993583i | \(-0.536079\pi\) | ||||
−0.113104 | + | 0.993583i | \(0.536079\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.8624 | 1.43697 | 0.718487 | − | 0.695541i | \(-0.244835\pi\) | ||||
0.718487 | + | 0.695541i | \(0.244835\pi\) | |||||||
\(524\) | 69.5048 | 3.03633 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.9350 | −0.520391 | ||||||||
\(527\) | 28.7331 | 1.25163 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.7758 | 0.729384 | ||||||||
\(530\) | 84.9115 | 3.68832 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.47984 | −0.237581 | ||||||||
\(533\) | 9.42579 | 0.408276 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 50.3467 | 2.17668 | ||||||||
\(536\) | −13.4249 | −0.579869 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 39.9636 | 1.72295 | ||||||||
\(539\) | −2.50629 | −0.107954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.08381 | 0.0895898 | 0.0447949 | − | 0.998996i | \(-0.485737\pi\) | ||||
0.0447949 | + | 0.998996i | \(0.485737\pi\) | |||||||
\(542\) | −27.2105 | −1.16879 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −20.7738 | −0.890670 | ||||||||
\(545\) | 5.83180 | 0.249807 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −59.4010 | −2.53749 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −73.2778 | −3.12457 | ||||||||
\(551\) | 2.26376 | 0.0964396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.6411 | −0.580079 | ||||||||
\(554\) | −35.3643 | −1.50249 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26.4430 | −1.12143 | ||||||||
\(557\) | 29.8940 | 1.26665 | 0.633324 | − | 0.773887i | \(-0.281690\pi\) | ||||
0.633324 | + | 0.773887i | \(0.281690\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.7617 | 1.38567 | ||||||||
\(560\) | −18.8154 | −0.795098 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 61.2692 | 2.58449 | ||||||||
\(563\) | −41.3819 | −1.74404 | −0.872020 | − | 0.489470i | \(-0.837190\pi\) | ||||
−0.872020 | + | 0.489470i | \(0.837190\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.4247 | −0.733062 | ||||||||
\(566\) | −65.2619 | −2.74316 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.5088 | −1.15424 | ||||||||
\(569\) | −34.2607 | −1.43628 | −0.718141 | − | 0.695898i | \(-0.755007\pi\) | ||||
−0.718141 | + | 0.695898i | \(0.755007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.9912 | −0.962151 | −0.481075 | − | 0.876679i | \(-0.659754\pi\) | ||||
−0.481075 | + | 0.876679i | \(0.659754\pi\) | |||||||
\(572\) | −40.8265 | −1.70704 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −13.6761 | −0.570828 | ||||||||
\(575\) | −78.7526 | −3.28421 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.6464 | 0.568109 | 0.284054 | − | 0.958808i | \(-0.408320\pi\) | ||||
0.284054 | + | 0.958808i | \(0.408320\pi\) | |||||||
\(578\) | 36.5933 | 1.52208 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 62.2022 | 2.58280 | ||||||||
\(581\) | 31.1327 | 1.29160 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.4041 | −0.886468 | ||||||||
\(584\) | 40.2404 | 1.66516 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.979318 | −0.0404553 | ||||||||
\(587\) | 7.33098 | 0.302582 | 0.151291 | − | 0.988489i | \(-0.451657\pi\) | ||||
0.151291 | + | 0.988489i | \(0.451657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.73576 | 0.112725 | ||||||||
\(590\) | −21.2599 | −0.875256 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.39782 | −0.262949 | ||||||||
\(593\) | −15.0502 | −0.618037 | −0.309018 | − | 0.951056i | \(-0.600000\pi\) | ||||
−0.309018 | + | 0.951056i | \(0.600000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −67.4703 | −2.76601 | ||||||||
\(596\) | 72.9387 | 2.98769 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −68.4777 | −2.80026 | ||||||||
\(599\) | −26.1936 | −1.07024 | −0.535122 | − | 0.844775i | \(-0.679734\pi\) | ||||
−0.535122 | + | 0.844775i | \(0.679734\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7023 | −0.477345 | −0.238673 | − | 0.971100i | \(-0.576712\pi\) | ||||
−0.238673 | + | 0.971100i | \(0.576712\pi\) | |||||||
\(602\) | −47.5347 | −1.93737 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 55.2168 | 2.24674 | ||||||||
\(605\) | −20.1312 | −0.818450 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.53127 | 0.224507 | 0.112254 | − | 0.993680i | \(-0.464193\pi\) | ||||
0.112254 | + | 0.993680i | \(0.464193\pi\) | |||||||
\(608\) | −1.97793 | −0.0802158 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −84.2006 | −3.40918 | ||||||||
\(611\) | 19.4660 | 0.787512 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.0113 | 0.929416 | 0.464708 | − | 0.885464i | \(-0.346159\pi\) | ||||
0.464708 | + | 0.885464i | \(0.346159\pi\) | |||||||
\(614\) | −11.8730 | −0.479155 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 26.0237 | 1.04852 | ||||||||
\(617\) | 18.8683 | 0.759610 | 0.379805 | − | 0.925067i | \(-0.375991\pi\) | ||||
0.379805 | + | 0.925067i | \(0.375991\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.14818 | −0.247116 | −0.123558 | − | 0.992337i | \(-0.539431\pi\) | ||||
−0.123558 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(620\) | 75.1714 | 3.01896 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.3927 | 0.737481 | ||||||||
\(623\) | 6.90536 | 0.276657 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 68.4886 | 2.73954 | ||||||||
\(626\) | −31.6888 | −1.26654 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −58.8728 | −2.34928 | ||||||||
\(629\) | −22.9420 | −0.914757 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0198 | −1.27469 | −0.637344 | − | 0.770580i | \(-0.719967\pi\) | ||||
−0.637344 | + | 0.770580i | \(0.719967\pi\) | |||||||
\(632\) | 17.8241 | 0.709006 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.6001 | 0.857850 | ||||||||
\(635\) | 35.8421 | 1.42235 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.63718 | 0.183732 | ||||||||
\(638\) | −24.4709 | −0.968812 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −85.7249 | −3.38857 | ||||||||
\(641\) | 10.9848 | 0.433874 | 0.216937 | − | 0.976186i | \(-0.430393\pi\) | ||||
0.216937 | + | 0.976186i | \(0.430393\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.7503 | 1.21267 | 0.606336 | − | 0.795209i | \(-0.292639\pi\) | ||||
0.606336 | + | 0.795209i | \(0.292639\pi\) | |||||||
\(644\) | 63.6618 | 2.50863 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.30324 | 0.287342 | ||||||||
\(647\) | 26.5562 | 1.04403 | 0.522016 | − | 0.852936i | \(-0.325180\pi\) | ||||
0.522016 | + | 0.852936i | \(0.325180\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.35910 | 0.210363 | ||||||||
\(650\) | 135.580 | 5.31787 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.1528 | 0.397613 | ||||||||
\(653\) | 7.83426 | 0.306578 | 0.153289 | − | 0.988181i | \(-0.451013\pi\) | ||||
0.153289 | + | 0.988181i | \(0.451013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 81.4809 | 3.18372 | ||||||||
\(656\) | 3.25684 | 0.127158 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −28.2437 | −1.10105 | ||||||||
\(659\) | 36.0459 | 1.40415 | 0.702074 | − | 0.712104i | \(-0.252258\pi\) | ||||
0.702074 | + | 0.712104i | \(0.252258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.74525 | −0.262360 | −0.131180 | − | 0.991359i | \(-0.541877\pi\) | ||||
−0.131180 | + | 0.991359i | \(0.541877\pi\) | |||||||
\(662\) | 21.3012 | 0.827893 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −40.6795 | −1.57867 | ||||||||
\(665\) | −6.42405 | −0.249114 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.2992 | −1.01831 | ||||||||
\(668\) | −40.3808 | −1.56238 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −35.8238 | −1.38399 | ||||||||
\(671\) | 21.2249 | 0.819379 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.6652 | 1.25915 | 0.629576 | − | 0.776939i | \(-0.283229\pi\) | ||||
0.629576 | + | 0.776939i | \(0.283229\pi\) | |||||||
\(674\) | −68.7216 | −2.64706 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 29.1656 | 1.12175 | ||||||||
\(677\) | 28.5071 | 1.09562 | 0.547809 | − | 0.836603i | \(-0.315462\pi\) | ||||
0.547809 | + | 0.836603i | \(0.315462\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.1587 | −0.581738 | ||||||||
\(680\) | 88.1600 | 3.38078 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −29.5731 | −1.13241 | ||||||||
\(683\) | 27.5926 | 1.05580 | 0.527900 | − | 0.849306i | \(-0.322980\pi\) | ||||
0.527900 | + | 0.849306i | \(0.322980\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −69.6362 | −2.66066 | ||||||||
\(686\) | 40.0094 | 1.52757 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.3200 | 0.431571 | ||||||||
\(689\) | 39.6023 | 1.50873 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.93442 | −0.187714 | −0.0938571 | − | 0.995586i | \(-0.529920\pi\) | ||||
−0.0938571 | + | 0.995586i | \(0.529920\pi\) | |||||||
\(692\) | 51.2235 | 1.94723 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.54049 | 0.248273 | ||||||||
\(695\) | −30.9992 | −1.17587 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.6787 | 0.442363 | ||||||||
\(698\) | 4.10155 | 0.155246 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −126.045 | −4.76405 | ||||||||
\(701\) | 16.8337 | 0.635799 | 0.317900 | − | 0.948124i | \(-0.397023\pi\) | ||||
0.317900 | + | 0.948124i | \(0.397023\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.18437 | −0.0823851 | ||||||||
\(704\) | 29.2904 | 1.10392 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 60.0965 | 2.26176 | ||||||||
\(707\) | 46.2607 | 1.73981 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.51372 | −0.0568489 | −0.0284244 | − | 0.999596i | \(-0.509049\pi\) | ||||
−0.0284244 | + | 0.999596i | \(0.509049\pi\) | |||||||
\(710\) | −73.4058 | −2.75487 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.02288 | −0.338147 | ||||||||
\(713\) | −31.7826 | −1.19027 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −47.8612 | −1.78991 | ||||||||
\(716\) | −32.1394 | −1.20111 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 76.9855 | 2.87307 | ||||||||
\(719\) | 48.0138 | 1.79061 | 0.895306 | − | 0.445453i | \(-0.146957\pi\) | ||||
0.895306 | + | 0.445453i | \(0.146957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.4087 | 1.24421 | ||||||||
\(722\) | −44.1346 | −1.64252 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −87.9697 | −3.26937 | ||||||||
\(725\) | 52.0701 | 1.93383 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.7641 | −1.95691 | −0.978456 | − | 0.206456i | \(-0.933807\pi\) | ||||
−0.978456 | + | 0.206456i | \(0.933807\pi\) | |||||||
\(728\) | −48.1494 | −1.78454 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 107.379 | 3.97429 | ||||||||
\(731\) | 40.5924 | 1.50136 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.8293 | −0.658541 | −0.329271 | − | 0.944236i | \(-0.606803\pi\) | ||||
−0.329271 | + | 0.944236i | \(0.606803\pi\) | |||||||
\(734\) | 16.0749 | 0.593336 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.9786 | 0.847002 | ||||||||
\(737\) | 9.03030 | 0.332635 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.1098 | −1.32832 | −0.664160 | − | 0.747591i | \(-0.731211\pi\) | ||||
−0.664160 | + | 0.747591i | \(0.731211\pi\) | |||||||
\(740\) | −60.0207 | −2.20640 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −57.4598 | −2.10941 | ||||||||
\(743\) | 0.881568 | 0.0323416 | 0.0161708 | − | 0.999869i | \(-0.494852\pi\) | ||||
0.0161708 | + | 0.999869i | \(0.494852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 85.5065 | 3.13272 | ||||||||
\(746\) | 25.1741 | 0.921689 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −50.5849 | −1.84957 | ||||||||
\(749\) | −34.0697 | −1.24488 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.6390 | −0.497694 | −0.248847 | − | 0.968543i | \(-0.580052\pi\) | ||||
−0.248847 | + | 0.968543i | \(0.580052\pi\) | |||||||
\(752\) | 6.72600 | 0.245272 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 45.2764 | 1.64887 | ||||||||
\(755\) | 64.7309 | 2.35580 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.9724 | −0.725910 | −0.362955 | − | 0.931807i | \(-0.618232\pi\) | ||||
−0.362955 | + | 0.931807i | \(0.618232\pi\) | |||||||
\(758\) | 52.5552 | 1.90889 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.39397 | 0.304481 | ||||||||
\(761\) | −44.3290 | −1.60693 | −0.803463 | − | 0.595355i | \(-0.797011\pi\) | ||||
−0.803463 | + | 0.595355i | \(0.797011\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.94639 | −0.142869 | ||||||||
\(764\) | −3.53345 | −0.127836 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.73161 | 0.243223 | ||||||||
\(767\) | −9.91550 | −0.358028 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.4396 | −1.27799 | −0.638993 | − | 0.769213i | \(-0.720649\pi\) | ||||
−0.638993 | + | 0.769213i | \(0.720649\pi\) | |||||||
\(770\) | 69.4428 | 2.50255 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −80.9882 | −2.91483 | ||||||||
\(773\) | 35.9274 | 1.29222 | 0.646110 | − | 0.763244i | \(-0.276395\pi\) | ||||
0.646110 | + | 0.763244i | \(0.276395\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 62.9268 | 2.26040 | ||||||||
\(776\) | 19.8071 | 0.711033 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.1807 | 1.08203 | ||||||||
\(779\) | 1.11197 | 0.0398403 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.5038 | 0.662119 | ||||||||
\(782\) | −84.8451 | −3.03405 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.60226 | 0.0572236 | ||||||||
\(785\) | −69.0169 | −2.46332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.68054 | 0.166843 | 0.0834216 | − | 0.996514i | \(-0.473415\pi\) | ||||
0.0834216 | + | 0.996514i | \(0.473415\pi\) | |||||||
\(788\) | −38.1202 | −1.35798 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 47.5628 | 1.69221 | ||||||||
\(791\) | 11.7913 | 0.419251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.2707 | −1.39454 | ||||||||
\(794\) | 1.37799 | 0.0489030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.5043 | −0.407761 | ||||||||
\(797\) | −51.2468 | −1.81526 | −0.907628 | − | 0.419776i | \(-0.862109\pi\) | ||||
−0.907628 | + | 0.419776i | \(0.862109\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.1188 | 0.853262 | ||||||||
\(800\) | −45.4956 | −1.60851 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.90570 | −0.102604 | ||||||||
\(803\) | −27.0677 | −0.955199 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 74.6311 | 2.63040 | ||||||||
\(806\) | 54.7167 | 1.92731 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −60.4465 | −2.12650 | ||||||||
\(809\) | 4.96718 | 0.174637 | 0.0873183 | − | 0.996180i | \(-0.472170\pi\) | ||||
0.0873183 | + | 0.996180i | \(0.472170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.27601 | 0.185266 | 0.0926328 | − | 0.995700i | \(-0.470472\pi\) | ||||
0.0926328 | + | 0.995700i | \(0.470472\pi\) | |||||||
\(812\) | −42.0923 | −1.47715 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23.6127 | 0.827624 | ||||||||
\(815\) | 11.9021 | 0.416914 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.86492 | 0.135216 | ||||||||
\(818\) | −2.80336 | −0.0980170 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.5538 | 1.06699 | ||||||||
\(821\) | −32.6165 | −1.13832 | −0.569162 | − | 0.822225i | \(-0.692732\pi\) | ||||
−0.569162 | + | 0.822225i | \(0.692732\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.0761 | −1.43182 | −0.715912 | − | 0.698191i | \(-0.753989\pi\) | ||||
−0.715912 | + | 0.698191i | \(0.753989\pi\) | |||||||
\(824\) | −43.6535 | −1.52074 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.3866 | 0.500574 | ||||||||
\(827\) | 17.2551 | 0.600019 | 0.300010 | − | 0.953936i | \(-0.403010\pi\) | ||||
0.300010 | + | 0.953936i | \(0.403010\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.35445 | −0.255430 | −0.127715 | − | 0.991811i | \(-0.540764\pi\) | ||||
−0.127715 | + | 0.991811i | \(0.540764\pi\) | |||||||
\(830\) | −108.551 | −3.76786 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −54.1936 | −1.87882 | ||||||||
\(833\) | 5.74555 | 0.199072 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −47.3387 | −1.63822 | ||||||||
\(836\) | −4.81633 | −0.166576 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.48793 | 0.224122 | ||||||||
\(839\) | 7.34393 | 0.253541 | 0.126770 | − | 0.991932i | \(-0.459539\pi\) | ||||
0.126770 | + | 0.991932i | \(0.459539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.6113 | −0.400391 | ||||||||
\(842\) | 62.4615 | 2.15257 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.0879 | −0.725875 | ||||||||
\(845\) | 34.1910 | 1.17621 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.6228 | 0.468086 | ||||||||
\(848\) | 13.6836 | 0.469896 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 167.986 | 5.76187 | ||||||||
\(851\) | 25.3769 | 0.869908 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.4141 | 0.664725 | 0.332362 | − | 0.943152i | \(-0.392154\pi\) | ||||
0.332362 | + | 0.943152i | \(0.392154\pi\) | |||||||
\(854\) | 56.9787 | 1.94977 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44.5171 | 1.52156 | ||||||||
\(857\) | −11.7234 | −0.400462 | −0.200231 | − | 0.979749i | \(-0.564169\pi\) | ||||
−0.200231 | + | 0.979749i | \(0.564169\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.3903 | 1.13926 | 0.569632 | − | 0.821900i | \(-0.307086\pi\) | ||||
0.569632 | + | 0.821900i | \(0.307086\pi\) | |||||||
\(860\) | 106.198 | 3.62131 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 34.6894 | 1.18152 | ||||||||
\(863\) | 34.6843 | 1.18067 | 0.590334 | − | 0.807159i | \(-0.298996\pi\) | ||||
0.590334 | + | 0.807159i | \(0.298996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 60.0496 | 2.04175 | ||||||||
\(866\) | 81.2110 | 2.75966 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −50.8686 | −1.72659 | ||||||||
\(869\) | −11.9894 | −0.406713 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.7080 | −0.566129 | ||||||||
\(872\) | 5.15654 | 0.174623 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.07835 | −0.273254 | ||||||||
\(875\) | −88.5959 | −2.99509 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7682 | 0.397384 | 0.198692 | − | 0.980062i | \(-0.436331\pi\) | ||||
0.198692 | + | 0.980062i | \(0.436331\pi\) | |||||||
\(878\) | 40.8544 | 1.37877 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16.5372 | −0.557470 | ||||||||
\(881\) | 38.4286 | 1.29469 | 0.647346 | − | 0.762197i | \(-0.275879\pi\) | ||||
0.647346 | + | 0.762197i | \(0.275879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.7693 | −1.47296 | −0.736478 | − | 0.676462i | \(-0.763512\pi\) | ||||
−0.736478 | + | 0.676462i | \(0.763512\pi\) | |||||||
\(884\) | 93.5929 | 3.14787 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −46.9673 | −1.57790 | ||||||||
\(887\) | 20.7665 | 0.697271 | 0.348635 | − | 0.937258i | \(-0.386645\pi\) | ||||
0.348635 | + | 0.937258i | \(0.386645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.2544 | −0.813466 | ||||||||
\(890\) | −24.0771 | −0.807066 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −43.6462 | −1.46138 | ||||||||
\(893\) | 2.29642 | 0.0768467 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.6772 | −1.25941 | ||||||||
\(896\) | 58.0102 | 1.93798 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.8687 | 0.729767 | ||||||||
\(899\) | 21.0142 | 0.700864 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.0679 | 1.63469 | ||||||||
\(902\) | −12.0202 | −0.400227 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.4071 | −0.512433 | ||||||||
\(905\) | −103.127 | −3.42807 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.9518 | 0.430056 | 0.215028 | − | 0.976608i | \(-0.431016\pi\) | ||||
0.215028 | + | 0.976608i | \(0.431016\pi\) | |||||||
\(908\) | −1.59540 | −0.0529451 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −128.484 | −4.25921 | ||||||||
\(911\) | −5.57453 | −0.184692 | −0.0923462 | − | 0.995727i | \(-0.529437\pi\) | ||||
−0.0923462 | + | 0.995727i | \(0.529437\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.3631 | 0.905585 | ||||||||
\(914\) | −22.8896 | −0.757119 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −40.3583 | −1.33348 | ||||||||
\(917\) | −55.1382 | −1.82082 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.5634 | −0.810273 | −0.405137 | − | 0.914256i | \(-0.632776\pi\) | ||||
−0.405137 | + | 0.914256i | \(0.632776\pi\) | |||||||
\(920\) | −97.5167 | −3.21503 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −60.2320 | −1.98363 | ||||||||
\(923\) | −34.2361 | −1.12689 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −50.2439 | −1.65201 | ||||||||
\(926\) | −91.8869 | −3.01959 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.1931 | −0.498738 | ||||||||
\(929\) | −28.8268 | −0.945775 | −0.472888 | − | 0.881123i | \(-0.656788\pi\) | ||||
−0.472888 | + | 0.881123i | \(0.656788\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.547050 | 0.0179289 | ||||||||
\(932\) | −67.9484 | −2.22572 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 35.2587 | 1.15370 | ||||||||
\(935\) | −59.3009 | −1.93935 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.5358 | −0.507534 | −0.253767 | − | 0.967265i | \(-0.581670\pi\) | ||||
−0.253767 | + | 0.967265i | \(0.581670\pi\) | |||||||
\(938\) | 24.2420 | 0.791529 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 63.0994 | 2.05808 | ||||||||
\(941\) | 53.4497 | 1.74241 | 0.871205 | − | 0.490919i | \(-0.163339\pi\) | ||||
0.871205 | + | 0.490919i | \(0.163339\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.9182 | −0.420675 | ||||||||
\(944\) | −3.42605 | −0.111508 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −41.7791 | −1.35836 | ||||||||
\(947\) | −26.4923 | −0.860885 | −0.430443 | − | 0.902618i | \(-0.641643\pi\) | ||||
−0.430443 | + | 0.902618i | \(0.641643\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.0811 | 1.62570 | ||||||||
\(950\) | 15.9944 | 0.518927 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −59.6580 | −1.93353 | ||||||||
\(953\) | 26.3995 | 0.855162 | 0.427581 | − | 0.903977i | \(-0.359366\pi\) | ||||
0.427581 | + | 0.903977i | \(0.359366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.14228 | −0.134041 | ||||||||
\(956\) | −14.8925 | −0.481657 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.61691 | −0.246091 | ||||||||
\(959\) | 47.1229 | 1.52168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.60426 | −0.180783 | ||||||||
\(962\) | −43.6886 | −1.40858 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 17.0424 | 0.548897 | ||||||||
\(965\) | −94.9429 | −3.05632 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.1774 | 0.745334 | 0.372667 | − | 0.927965i | \(-0.378443\pi\) | ||||
0.372667 | + | 0.927965i | \(0.378443\pi\) | |||||||
\(968\) | −17.8002 | −0.572121 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 52.8542 | 1.69705 | ||||||||
\(971\) | −9.57093 | −0.307146 | −0.153573 | − | 0.988137i | \(-0.549078\pi\) | ||||
−0.153573 | + | 0.988137i | \(0.549078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.9772 | 0.672499 | ||||||||
\(974\) | −18.5000 | −0.592777 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.5690 | −0.434333 | ||||||||
\(977\) | −15.5814 | −0.498493 | −0.249247 | − | 0.968440i | \(-0.580183\pi\) | ||||
−0.249247 | + | 0.968440i | \(0.580183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.06925 | 0.193974 | ||||||||
\(980\) | 15.0315 | 0.480163 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −43.3039 | −1.38188 | ||||||||
\(983\) | 45.6013 | 1.45445 | 0.727227 | − | 0.686397i | \(-0.240809\pi\) | ||||
0.727227 | + | 0.686397i | \(0.240809\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.6885 | −1.42390 | ||||||||
\(986\) | 56.0984 | 1.78654 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.91125 | 0.283505 | ||||||||
\(989\) | −44.9006 | −1.42776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.6593 | 0.846860 | 0.423430 | − | 0.905929i | \(-0.360826\pi\) | ||||
0.423430 | + | 0.905929i | \(0.360826\pi\) | |||||||
\(992\) | −18.3609 | −0.582959 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 49.6738 | 1.57556 | ||||||||
\(995\) | −13.4866 | −0.427554 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.8151 | −0.690891 | −0.345446 | − | 0.938439i | \(-0.612272\pi\) | ||||
−0.345446 | + | 0.938439i | \(0.612272\pi\) | |||||||
\(998\) | 62.2616 | 1.97086 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4923.2.a.l.1.16 | 18 | ||
3.2 | odd | 2 | 547.2.a.b.1.3 | ✓ | 18 | ||
12.11 | even | 2 | 8752.2.a.s.1.18 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.3 | ✓ | 18 | 3.2 | odd | 2 | ||
4923.2.a.l.1.16 | 18 | 1.1 | even | 1 | trivial | ||
8752.2.a.s.1.18 | 18 | 12.11 | even | 2 |