Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, 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("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.456850\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18890 | 1.54779 | 0.773893 | − | 0.633316i | \(-0.218307\pi\) | ||||
0.773893 | + | 0.633316i | \(0.218307\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | 2.79129 | 1.39564 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.18890 | 0.893615 | ||||||||
\(7\) | −1.73205 | −0.654654 | −0.327327 | − | 0.944911i | \(-0.606148\pi\) | ||||
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.64575 | −0.797724 | −0.398862 | − | 0.917011i | \(-0.630595\pi\) | ||||
−0.398862 | + | 0.917011i | \(0.630595\pi\) | |||||||
\(12\) | 2.79129 | 0.805775 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.79129 | −1.01326 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.79129 | −0.447822 | ||||||||
\(17\) | −4.58258 | −1.11144 | −0.555719 | − | 0.831370i | \(-0.687557\pi\) | ||||
−0.555719 | + | 0.831370i | \(0.687557\pi\) | |||||||
\(18\) | −4.37780 | −1.03186 | ||||||||
\(19\) | −1.73205 | −0.397360 | −0.198680 | − | 0.980064i | \(-0.563665\pi\) | ||||
−0.198680 | + | 0.980064i | \(0.563665\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73205 | −0.377964 | ||||||||
\(22\) | −5.79129 | −1.23471 | ||||||||
\(23\) | 4.58258 | 0.955533 | 0.477767 | − | 0.878487i | \(-0.341446\pi\) | ||||
0.477767 | + | 0.878487i | \(0.341446\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | −4.83465 | −0.913663 | ||||||||
\(29\) | −4.58258 | −0.850963 | −0.425481 | − | 0.904967i | \(-0.639895\pi\) | ||||
−0.425481 | + | 0.904967i | \(0.639895\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.66930 | 1.73666 | 0.868329 | − | 0.495988i | \(-0.165194\pi\) | ||||
0.868329 | + | 0.495988i | \(0.165194\pi\) | |||||||
\(32\) | −7.38505 | −1.30551 | ||||||||
\(33\) | −2.64575 | −0.460566 | ||||||||
\(34\) | −10.0308 | −1.72027 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.58258 | −0.930429 | ||||||||
\(37\) | −7.93725 | −1.30488 | −0.652438 | − | 0.757842i | \(-0.726254\pi\) | ||||
−0.652438 | + | 0.757842i | \(0.726254\pi\) | |||||||
\(38\) | −3.79129 | −0.615028 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.64575 | −0.413197 | −0.206598 | − | 0.978426i | \(-0.566239\pi\) | ||||
−0.206598 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(42\) | −3.79129 | −0.585008 | ||||||||
\(43\) | −1.41742 | −0.216155 | −0.108078 | − | 0.994142i | \(-0.534469\pi\) | ||||
−0.108078 | + | 0.994142i | \(0.534469\pi\) | |||||||
\(44\) | −7.38505 | −1.11334 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.0308 | 1.47896 | ||||||||
\(47\) | 8.75560 | 1.27714 | 0.638568 | − | 0.769565i | \(-0.279527\pi\) | ||||
0.638568 | + | 0.769565i | \(0.279527\pi\) | |||||||
\(48\) | −1.79129 | −0.258550 | ||||||||
\(49\) | −4.00000 | −0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.58258 | −0.641689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.58258 | −0.217383 | −0.108692 | − | 0.994076i | \(-0.534666\pi\) | ||||
−0.108692 | + | 0.994076i | \(0.534666\pi\) | |||||||
\(54\) | −10.9445 | −1.48936 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | −1.73205 | −0.229416 | ||||||||
\(58\) | −10.0308 | −1.31711 | ||||||||
\(59\) | 3.36875 | 0.438574 | 0.219287 | − | 0.975660i | \(-0.429627\pi\) | ||||
0.219287 | + | 0.975660i | \(0.429627\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5826 | −1.35496 | −0.677480 | − | 0.735541i | \(-0.736928\pi\) | ||||
−0.677480 | + | 0.735541i | \(0.736928\pi\) | |||||||
\(62\) | 21.1652 | 2.68798 | ||||||||
\(63\) | 3.46410 | 0.436436 | ||||||||
\(64\) | −12.5826 | −1.57282 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.79129 | −0.712858 | ||||||||
\(67\) | −14.8655 | −1.81610 | −0.908052 | − | 0.418857i | \(-0.862431\pi\) | ||||
−0.908052 | + | 0.418857i | \(0.862431\pi\) | |||||||
\(68\) | −12.7913 | −1.55117 | ||||||||
\(69\) | 4.58258 | 0.551677 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.55945 | 0.422429 | 0.211215 | − | 0.977440i | \(-0.432258\pi\) | ||||
0.211215 | + | 0.977440i | \(0.432258\pi\) | |||||||
\(72\) | −3.46410 | −0.408248 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | −17.3739 | −2.01967 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.83465 | −0.554573 | ||||||||
\(77\) | 4.58258 | 0.522233 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.79129 | −0.639541 | ||||||||
\(83\) | 11.3060 | 1.24100 | 0.620498 | − | 0.784208i | \(-0.286931\pi\) | ||||
0.620498 | + | 0.784208i | \(0.286931\pi\) | |||||||
\(84\) | −4.83465 | −0.527504 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.10260 | −0.334562 | ||||||||
\(87\) | −4.58258 | −0.491304 | ||||||||
\(88\) | −4.58258 | −0.488504 | ||||||||
\(89\) | 4.28245 | 0.453939 | 0.226969 | − | 0.973902i | \(-0.427118\pi\) | ||||
0.226969 | + | 0.973902i | \(0.427118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.7913 | 1.33358 | ||||||||
\(93\) | 9.66930 | 1.00266 | ||||||||
\(94\) | 19.1652 | 1.97673 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.38505 | −0.753734 | ||||||||
\(97\) | −4.47315 | −0.454180 | −0.227090 | − | 0.973874i | \(-0.572921\pi\) | ||||
−0.227090 | + | 0.973874i | \(0.572921\pi\) | |||||||
\(98\) | −8.75560 | −0.884450 | ||||||||
\(99\) | 5.29150 | 0.531816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | −0.895533 | −0.447767 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | −10.0308 | −0.993198 | ||||||||
\(103\) | 15.1652 | 1.49427 | 0.747133 | − | 0.664674i | \(-0.231430\pi\) | ||||
0.747133 | + | 0.664674i | \(0.231430\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.46410 | −0.336463 | ||||||||
\(107\) | −1.41742 | −0.137028 | −0.0685138 | − | 0.997650i | \(-0.521826\pi\) | ||||
−0.0685138 | + | 0.997650i | \(0.521826\pi\) | |||||||
\(108\) | −13.9564 | −1.34296 | ||||||||
\(109\) | 2.74110 | 0.262550 | 0.131275 | − | 0.991346i | \(-0.458093\pi\) | ||||
0.131275 | + | 0.991346i | \(0.458093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.93725 | −0.753371 | ||||||||
\(112\) | 3.10260 | 0.293168 | ||||||||
\(113\) | −16.5826 | −1.55996 | −0.779979 | − | 0.625806i | \(-0.784770\pi\) | ||||
−0.779979 | + | 0.625806i | \(0.784770\pi\) | |||||||
\(114\) | −3.79129 | −0.355087 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.7913 | −1.18764 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.37386 | 0.678819 | ||||||||
\(119\) | 7.93725 | 0.727607 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | −0.363636 | ||||||||
\(122\) | −23.1642 | −2.09719 | ||||||||
\(123\) | −2.64575 | −0.238559 | ||||||||
\(124\) | 26.9898 | 2.42376 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.58258 | 0.675510 | ||||||||
\(127\) | 9.74773 | 0.864971 | 0.432485 | − | 0.901641i | \(-0.357637\pi\) | ||||
0.432485 | + | 0.901641i | \(0.357637\pi\) | |||||||
\(128\) | −12.7719 | −1.12889 | ||||||||
\(129\) | −1.41742 | −0.124797 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.58258 | 0.138270 | 0.0691351 | − | 0.997607i | \(-0.477976\pi\) | ||||
0.0691351 | + | 0.997607i | \(0.477976\pi\) | |||||||
\(132\) | −7.38505 | −0.642786 | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | −32.5390 | −2.81094 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.93725 | −0.680614 | ||||||||
\(137\) | −0.0953502 | −0.00814632 | −0.00407316 | − | 0.999992i | \(-0.501297\pi\) | ||||
−0.00407316 | + | 0.999992i | \(0.501297\pi\) | |||||||
\(138\) | 10.0308 | 0.853879 | ||||||||
\(139\) | 5.74773 | 0.487516 | 0.243758 | − | 0.969836i | \(-0.421620\pi\) | ||||
0.243758 | + | 0.969836i | \(0.421620\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.75560 | 0.737355 | ||||||||
\(142\) | 7.79129 | 0.653830 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.58258 | 0.298548 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.00000 | −0.329914 | ||||||||
\(148\) | −22.1552 | −1.82114 | ||||||||
\(149\) | 9.76465 | 0.799952 | 0.399976 | − | 0.916526i | \(-0.369019\pi\) | ||||
0.399976 | + | 0.916526i | \(0.369019\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.20520 | 0.504972 | 0.252486 | − | 0.967601i | \(-0.418752\pi\) | ||||
0.252486 | + | 0.967601i | \(0.418752\pi\) | |||||||
\(152\) | −3.00000 | −0.243332 | ||||||||
\(153\) | 9.16515 | 0.740959 | ||||||||
\(154\) | 10.0308 | 0.808305 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.16515 | −0.731459 | −0.365729 | − | 0.930721i | \(-0.619180\pi\) | ||||
−0.365729 | + | 0.930721i | \(0.619180\pi\) | |||||||
\(158\) | −13.1334 | −1.04484 | ||||||||
\(159\) | −1.58258 | −0.125506 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.93725 | −0.625543 | ||||||||
\(162\) | 2.18890 | 0.171976 | ||||||||
\(163\) | 10.6784 | 0.836393 | 0.418197 | − | 0.908357i | \(-0.362662\pi\) | ||||
0.418197 | + | 0.908357i | \(0.362662\pi\) | |||||||
\(164\) | −7.38505 | −0.576676 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24.7477 | 1.92080 | ||||||||
\(167\) | −4.28245 | −0.331386 | −0.165693 | − | 0.986177i | \(-0.552986\pi\) | ||||
−0.165693 | + | 0.986177i | \(0.552986\pi\) | |||||||
\(168\) | −3.00000 | −0.231455 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.46410 | 0.264906 | ||||||||
\(172\) | −3.95644 | −0.301676 | ||||||||
\(173\) | 7.41742 | 0.563936 | 0.281968 | − | 0.959424i | \(-0.409013\pi\) | ||||
0.281968 | + | 0.959424i | \(0.409013\pi\) | |||||||
\(174\) | −10.0308 | −0.760433 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.73930 | 0.357238 | ||||||||
\(177\) | 3.36875 | 0.253211 | ||||||||
\(178\) | 9.37386 | 0.702601 | ||||||||
\(179\) | 0.165151 | 0.0123440 | 0.00617200 | − | 0.999981i | \(-0.498035\pi\) | ||||
0.00617200 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.7477 | 1.39351 | 0.696754 | − | 0.717310i | \(-0.254627\pi\) | ||||
0.696754 | + | 0.717310i | \(0.254627\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.5826 | −0.782287 | ||||||||
\(184\) | 7.93725 | 0.585142 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 21.1652 | 1.55190 | ||||||||
\(187\) | 12.1244 | 0.886621 | ||||||||
\(188\) | 24.4394 | 1.78243 | ||||||||
\(189\) | 8.66025 | 0.629941 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.41742 | −0.536706 | −0.268353 | − | 0.963321i | \(-0.586479\pi\) | ||||
−0.268353 | + | 0.963321i | \(0.586479\pi\) | |||||||
\(192\) | −12.5826 | −0.908069 | ||||||||
\(193\) | 1.00905 | 0.0726331 | 0.0363165 | − | 0.999340i | \(-0.488438\pi\) | ||||
0.0363165 | + | 0.999340i | \(0.488438\pi\) | |||||||
\(194\) | −9.79129 | −0.702973 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.1652 | −0.797511 | ||||||||
\(197\) | 19.9663 | 1.42254 | 0.711269 | − | 0.702920i | \(-0.248121\pi\) | ||||
0.711269 | + | 0.702920i | \(0.248121\pi\) | |||||||
\(198\) | 11.5826 | 0.823138 | ||||||||
\(199\) | −1.41742 | −0.100479 | −0.0502393 | − | 0.998737i | \(-0.515998\pi\) | ||||
−0.0502393 | + | 0.998737i | \(0.515998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.8655 | −1.04853 | ||||||||
\(202\) | −19.7001 | −1.38609 | ||||||||
\(203\) | 7.93725 | 0.557086 | ||||||||
\(204\) | −12.7913 | −0.895569 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 33.1950 | 2.31281 | ||||||||
\(207\) | −9.16515 | −0.637022 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.58258 | 0.316983 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1652 | 1.25054 | 0.625270 | − | 0.780408i | \(-0.284989\pi\) | ||||
0.625270 | + | 0.780408i | \(0.284989\pi\) | |||||||
\(212\) | −4.41742 | −0.303390 | ||||||||
\(213\) | 3.55945 | 0.243890 | ||||||||
\(214\) | −3.10260 | −0.212089 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.66025 | −0.589256 | ||||||||
\(217\) | −16.7477 | −1.13691 | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −17.3739 | −1.16606 | ||||||||
\(223\) | −8.66025 | −0.579934 | −0.289967 | − | 0.957037i | \(-0.593644\pi\) | ||||
−0.289967 | + | 0.957037i | \(0.593644\pi\) | |||||||
\(224\) | 12.7913 | 0.854654 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −36.2976 | −2.41448 | ||||||||
\(227\) | −6.10985 | −0.405525 | −0.202763 | − | 0.979228i | \(-0.564992\pi\) | ||||
−0.202763 | + | 0.979228i | \(0.564992\pi\) | |||||||
\(228\) | −4.83465 | −0.320183 | ||||||||
\(229\) | 5.48220 | 0.362274 | 0.181137 | − | 0.983458i | \(-0.442022\pi\) | ||||
0.181137 | + | 0.983458i | \(0.442022\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.58258 | 0.301511 | ||||||||
\(232\) | −7.93725 | −0.521106 | ||||||||
\(233\) | −21.1652 | −1.38658 | −0.693288 | − | 0.720661i | \(-0.743838\pi\) | ||||
−0.693288 | + | 0.720661i | \(0.743838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.40315 | 0.612093 | ||||||||
\(237\) | −6.00000 | −0.389742 | ||||||||
\(238\) | 17.3739 | 1.12618 | ||||||||
\(239\) | −20.9753 | −1.35678 | −0.678390 | − | 0.734702i | \(-0.737322\pi\) | ||||
−0.678390 | + | 0.734702i | \(0.737322\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.73205 | −0.111571 | −0.0557856 | − | 0.998443i | \(-0.517766\pi\) | ||||
−0.0557856 | + | 0.998443i | \(0.517766\pi\) | |||||||
\(242\) | −8.75560 | −0.562832 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | −29.5390 | −1.89104 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.79129 | −0.369239 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 16.7477 | 1.06348 | ||||||||
\(249\) | 11.3060 | 0.716489 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.1652 | −1.14657 | −0.573287 | − | 0.819355i | \(-0.694332\pi\) | ||||
−0.573287 | + | 0.819355i | \(0.694332\pi\) | |||||||
\(252\) | 9.66930 | 0.609109 | ||||||||
\(253\) | −12.1244 | −0.762252 | ||||||||
\(254\) | 21.3368 | 1.33879 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.79129 | −0.174455 | ||||||||
\(257\) | −0.165151 | −0.0103019 | −0.00515093 | − | 0.999987i | \(-0.501640\pi\) | ||||
−0.00515093 | + | 0.999987i | \(0.501640\pi\) | |||||||
\(258\) | −3.10260 | −0.193160 | ||||||||
\(259\) | 13.7477 | 0.854242 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.16515 | 0.567309 | ||||||||
\(262\) | 3.46410 | 0.214013 | ||||||||
\(263\) | 9.00000 | 0.554964 | 0.277482 | − | 0.960731i | \(-0.410500\pi\) | ||||
0.277482 | + | 0.960731i | \(0.410500\pi\) | |||||||
\(264\) | −4.58258 | −0.282038 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.56670 | 0.402630 | ||||||||
\(267\) | 4.28245 | 0.262082 | ||||||||
\(268\) | −41.4938 | −2.53464 | ||||||||
\(269\) | −15.0000 | −0.914566 | −0.457283 | − | 0.889321i | \(-0.651177\pi\) | ||||
−0.457283 | + | 0.889321i | \(0.651177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.66025 | −0.526073 | −0.263036 | − | 0.964786i | \(-0.584724\pi\) | ||||
−0.263036 | + | 0.964786i | \(0.584724\pi\) | |||||||
\(272\) | 8.20871 | 0.497726 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.208712 | −0.0126088 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.7913 | 0.769945 | ||||||||
\(277\) | 16.5826 | 0.996350 | 0.498175 | − | 0.867076i | \(-0.334004\pi\) | ||||
0.498175 | + | 0.867076i | \(0.334004\pi\) | |||||||
\(278\) | 12.5812 | 0.754571 | ||||||||
\(279\) | −19.3386 | −1.15777 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.5112 | −1.04463 | −0.522316 | − | 0.852752i | \(-0.674932\pi\) | ||||
−0.522316 | + | 0.852752i | \(0.674932\pi\) | |||||||
\(282\) | 19.1652 | 1.14127 | ||||||||
\(283\) | 0.252273 | 0.0149961 | 0.00749803 | − | 0.999972i | \(-0.497613\pi\) | ||||
0.00749803 | + | 0.999972i | \(0.497613\pi\) | |||||||
\(284\) | 9.93545 | 0.589561 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.58258 | 0.270501 | ||||||||
\(288\) | 14.7701 | 0.870337 | ||||||||
\(289\) | 4.00000 | 0.235294 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.47315 | −0.262221 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4304 | 1.36882 | 0.684408 | − | 0.729099i | \(-0.260061\pi\) | ||||
0.684408 | + | 0.729099i | \(0.260061\pi\) | |||||||
\(294\) | −8.75560 | −0.510637 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.7477 | −0.799070 | ||||||||
\(297\) | 13.2288 | 0.767610 | ||||||||
\(298\) | 21.3739 | 1.23815 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.45505 | 0.141507 | ||||||||
\(302\) | 13.5826 | 0.781589 | ||||||||
\(303\) | −9.00000 | −0.517036 | ||||||||
\(304\) | 3.10260 | 0.177946 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 20.0616 | 1.14685 | ||||||||
\(307\) | −24.2487 | −1.38395 | −0.691974 | − | 0.721923i | \(-0.743259\pi\) | ||||
−0.691974 | + | 0.721923i | \(0.743259\pi\) | |||||||
\(308\) | 12.7913 | 0.728851 | ||||||||
\(309\) | 15.1652 | 0.862715 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.58258 | 0.0897396 | 0.0448698 | − | 0.998993i | \(-0.485713\pi\) | ||||
0.0448698 | + | 0.998993i | \(0.485713\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.7477 | −1.73796 | −0.868982 | − | 0.494843i | \(-0.835225\pi\) | ||||
−0.868982 | + | 0.494843i | \(0.835225\pi\) | |||||||
\(314\) | −20.0616 | −1.13214 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.7477 | −0.942133 | ||||||||
\(317\) | 20.9753 | 1.17809 | 0.589045 | − | 0.808100i | \(-0.299504\pi\) | ||||
0.589045 | + | 0.808100i | \(0.299504\pi\) | |||||||
\(318\) | −3.46410 | −0.194257 | ||||||||
\(319\) | 12.1244 | 0.678834 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.41742 | −0.0791129 | ||||||||
\(322\) | −17.3739 | −0.968208 | ||||||||
\(323\) | 7.93725 | 0.441641 | ||||||||
\(324\) | 2.79129 | 0.155072 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.3739 | 1.29456 | ||||||||
\(327\) | 2.74110 | 0.151583 | ||||||||
\(328\) | −4.58258 | −0.253030 | ||||||||
\(329\) | −15.1652 | −0.836082 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.4014 | −0.626675 | −0.313338 | − | 0.949642i | \(-0.601447\pi\) | ||||
−0.313338 | + | 0.949642i | \(0.601447\pi\) | |||||||
\(332\) | 31.5583 | 1.73199 | ||||||||
\(333\) | 15.8745 | 0.869918 | ||||||||
\(334\) | −9.37386 | −0.512915 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.10260 | 0.169261 | ||||||||
\(337\) | −3.25227 | −0.177163 | −0.0885813 | − | 0.996069i | \(-0.528233\pi\) | ||||
−0.0885813 | + | 0.996069i | \(0.528233\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.5826 | −0.900642 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.5826 | −1.38537 | ||||||||
\(342\) | 7.58258 | 0.410019 | ||||||||
\(343\) | 19.0526 | 1.02874 | ||||||||
\(344\) | −2.45505 | −0.132367 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.2360 | 0.872853 | ||||||||
\(347\) | 15.3303 | 0.822974 | 0.411487 | − | 0.911416i | \(-0.365010\pi\) | ||||
0.411487 | + | 0.911416i | \(0.365010\pi\) | |||||||
\(348\) | −12.7913 | −0.685685 | ||||||||
\(349\) | 18.3296 | 0.981159 | 0.490579 | − | 0.871396i | \(-0.336785\pi\) | ||||
0.490579 | + | 0.871396i | \(0.336785\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 19.5390 | 1.04143 | ||||||||
\(353\) | 17.4159 | 0.926953 | 0.463476 | − | 0.886109i | \(-0.346602\pi\) | ||||
0.463476 | + | 0.886109i | \(0.346602\pi\) | |||||||
\(354\) | 7.37386 | 0.391916 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.9536 | 0.633537 | ||||||||
\(357\) | 7.93725 | 0.420084 | ||||||||
\(358\) | 0.361500 | 0.0191059 | ||||||||
\(359\) | −33.3857 | −1.76203 | −0.881015 | − | 0.473088i | \(-0.843139\pi\) | ||||
−0.881015 | + | 0.473088i | \(0.843139\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0000 | −0.842105 | ||||||||
\(362\) | 41.0369 | 2.15685 | ||||||||
\(363\) | −4.00000 | −0.209946 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −23.1642 | −1.21081 | ||||||||
\(367\) | 25.7477 | 1.34402 | 0.672010 | − | 0.740542i | \(-0.265431\pi\) | ||||
0.672010 | + | 0.740542i | \(0.265431\pi\) | |||||||
\(368\) | −8.20871 | −0.427909 | ||||||||
\(369\) | 5.29150 | 0.275465 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.74110 | 0.142311 | ||||||||
\(372\) | 26.9898 | 1.39936 | ||||||||
\(373\) | −13.0000 | −0.673114 | −0.336557 | − | 0.941663i | \(-0.609263\pi\) | ||||
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 26.5390 | 1.37230 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.1652 | 0.782083 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 18.9564 | 0.975014 | ||||||||
\(379\) | −21.0707 | −1.08233 | −0.541164 | − | 0.840917i | \(-0.682016\pi\) | ||||
−0.541164 | + | 0.840917i | \(0.682016\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.74773 | 0.499391 | ||||||||
\(382\) | −16.2360 | −0.830706 | ||||||||
\(383\) | −2.83645 | −0.144936 | −0.0724680 | − | 0.997371i | \(-0.523088\pi\) | ||||
−0.0724680 | + | 0.997371i | \(0.523088\pi\) | |||||||
\(384\) | −12.7719 | −0.651764 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.20871 | 0.112420 | ||||||||
\(387\) | 2.83485 | 0.144103 | ||||||||
\(388\) | −12.4859 | −0.633873 | ||||||||
\(389\) | −15.1652 | −0.768904 | −0.384452 | − | 0.923145i | \(-0.625610\pi\) | ||||
−0.384452 | + | 0.923145i | \(0.625610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.0000 | −1.06202 | ||||||||
\(392\) | −6.92820 | −0.349927 | ||||||||
\(393\) | 1.58258 | 0.0798304 | ||||||||
\(394\) | 43.7042 | 2.20178 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 14.7701 | 0.742226 | ||||||||
\(397\) | 27.2759 | 1.36894 | 0.684468 | − | 0.729043i | \(-0.260034\pi\) | ||||
0.684468 | + | 0.729043i | \(0.260034\pi\) | |||||||
\(398\) | −3.10260 | −0.155519 | ||||||||
\(399\) | 3.00000 | 0.150188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.5058 | −0.624508 | −0.312254 | − | 0.949999i | \(-0.601084\pi\) | ||||
−0.312254 | + | 0.949999i | \(0.601084\pi\) | |||||||
\(402\) | −32.5390 | −1.62290 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −25.1216 | −1.24985 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.3739 | 0.862250 | ||||||||
\(407\) | 21.0000 | 1.04093 | ||||||||
\(408\) | −7.93725 | −0.392953 | ||||||||
\(409\) | 8.66025 | 0.428222 | 0.214111 | − | 0.976809i | \(-0.431315\pi\) | ||||
0.214111 | + | 0.976809i | \(0.431315\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0953502 | −0.00470328 | ||||||||
\(412\) | 42.3303 | 2.08546 | ||||||||
\(413\) | −5.83485 | −0.287114 | ||||||||
\(414\) | −20.0616 | −0.985974 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.74773 | 0.281467 | ||||||||
\(418\) | 10.0308 | 0.490623 | ||||||||
\(419\) | −24.1652 | −1.18054 | −0.590272 | − | 0.807204i | \(-0.700980\pi\) | ||||
−0.590272 | + | 0.807204i | \(0.700980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.2668 | 1.28017 | 0.640083 | − | 0.768306i | \(-0.278900\pi\) | ||||
0.640083 | + | 0.768306i | \(0.278900\pi\) | |||||||
\(422\) | 39.7617 | 1.93557 | ||||||||
\(423\) | −17.5112 | −0.851424 | ||||||||
\(424\) | −2.74110 | −0.133120 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.79129 | 0.377489 | ||||||||
\(427\) | 18.3296 | 0.887030 | ||||||||
\(428\) | −3.95644 | −0.191242 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.6356 | 1.42749 | 0.713747 | − | 0.700403i | \(-0.246996\pi\) | ||||
0.713747 | + | 0.700403i | \(0.246996\pi\) | |||||||
\(432\) | 8.95644 | 0.430917 | ||||||||
\(433\) | 17.7477 | 0.852901 | 0.426451 | − | 0.904511i | \(-0.359764\pi\) | ||||
0.426451 | + | 0.904511i | \(0.359764\pi\) | |||||||
\(434\) | −36.6591 | −1.75969 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.65120 | 0.366426 | ||||||||
\(437\) | −7.93725 | −0.379690 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.4955 | −1.93274 | −0.966371 | − | 0.257151i | \(-0.917216\pi\) | ||||
−0.966371 | + | 0.257151i | \(0.917216\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.00000 | 0.380952 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −25.9129 | −1.23116 | −0.615579 | − | 0.788075i | \(-0.711078\pi\) | ||||
−0.615579 | + | 0.788075i | \(0.711078\pi\) | |||||||
\(444\) | −22.1552 | −1.05144 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.9564 | −0.897613 | ||||||||
\(447\) | 9.76465 | 0.461852 | ||||||||
\(448\) | 21.7937 | 1.02965 | ||||||||
\(449\) | −37.4775 | −1.76867 | −0.884336 | − | 0.466852i | \(-0.845388\pi\) | ||||
−0.884336 | + | 0.466852i | \(0.845388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.00000 | 0.329617 | ||||||||
\(452\) | −46.2867 | −2.17715 | ||||||||
\(453\) | 6.20520 | 0.291546 | ||||||||
\(454\) | −13.3739 | −0.627667 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −1.73205 | −0.0810219 | −0.0405110 | − | 0.999179i | \(-0.512899\pi\) | ||||
−0.0405110 | + | 0.999179i | \(0.512899\pi\) | |||||||
\(458\) | 12.0000 | 0.560723 | ||||||||
\(459\) | 22.9129 | 1.06948 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.19975 | 0.0558780 | 0.0279390 | − | 0.999610i | \(-0.491106\pi\) | ||||
0.0279390 | + | 0.999610i | \(0.491106\pi\) | |||||||
\(462\) | 10.0308 | 0.466675 | ||||||||
\(463\) | −8.22330 | −0.382169 | −0.191085 | − | 0.981574i | \(-0.561201\pi\) | ||||
−0.191085 | + | 0.981574i | \(0.561201\pi\) | |||||||
\(464\) | 8.20871 | 0.381080 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −46.3284 | −2.14612 | ||||||||
\(467\) | −12.3303 | −0.570578 | −0.285289 | − | 0.958441i | \(-0.592090\pi\) | ||||
−0.285289 | + | 0.958441i | \(0.592090\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.7477 | 1.18892 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.16515 | −0.422308 | ||||||||
\(472\) | 5.83485 | 0.268571 | ||||||||
\(473\) | 3.75015 | 0.172432 | ||||||||
\(474\) | −13.1334 | −0.603237 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.1552 | 1.01548 | ||||||||
\(477\) | 3.16515 | 0.144922 | ||||||||
\(478\) | −45.9129 | −2.10001 | ||||||||
\(479\) | −32.3767 | −1.47933 | −0.739664 | − | 0.672977i | \(-0.765015\pi\) | ||||
−0.739664 | + | 0.672977i | \(0.765015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3.79129 | −0.172688 | ||||||||
\(483\) | −7.93725 | −0.361158 | ||||||||
\(484\) | −11.1652 | −0.507507 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 35.0224 | 1.58865 | ||||||||
\(487\) | 21.0707 | 0.954803 | 0.477401 | − | 0.878685i | \(-0.341579\pi\) | ||||
0.477401 | + | 0.878685i | \(0.341579\pi\) | |||||||
\(488\) | −18.3296 | −0.829740 | ||||||||
\(489\) | 10.6784 | 0.482892 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.5826 | −1.28991 | −0.644957 | − | 0.764219i | \(-0.723125\pi\) | ||||
−0.644957 | + | 0.764219i | \(0.723125\pi\) | |||||||
\(492\) | −7.38505 | −0.332944 | ||||||||
\(493\) | 21.0000 | 0.945792 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.3205 | −0.777714 | ||||||||
\(497\) | −6.16515 | −0.276545 | ||||||||
\(498\) | 24.7477 | 1.10897 | ||||||||
\(499\) | 16.5975 | 0.743006 | 0.371503 | − | 0.928432i | \(-0.378842\pi\) | ||||
0.371503 | + | 0.928432i | \(0.378842\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.28245 | −0.191326 | ||||||||
\(502\) | −39.7617 | −1.77465 | ||||||||
\(503\) | −18.1652 | −0.809944 | −0.404972 | − | 0.914329i | \(-0.632719\pi\) | ||||
−0.404972 | + | 0.914329i | \(0.632719\pi\) | |||||||
\(504\) | 6.00000 | 0.267261 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −26.5390 | −1.17980 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 27.2087 | 1.20719 | ||||||||
\(509\) | 29.6356 | 1.31357 | 0.656787 | − | 0.754076i | \(-0.271915\pi\) | ||||
0.656787 | + | 0.754076i | \(0.271915\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.4340 | 0.858868 | ||||||||
\(513\) | 8.66025 | 0.382360 | ||||||||
\(514\) | −0.361500 | −0.0159451 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.95644 | −0.174173 | ||||||||
\(517\) | −23.1652 | −1.01880 | ||||||||
\(518\) | 30.0924 | 1.32218 | ||||||||
\(519\) | 7.41742 | 0.325589 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.4955 | −1.20460 | −0.602299 | − | 0.798271i | \(-0.705748\pi\) | ||||
−0.602299 | + | 0.798271i | \(0.705748\pi\) | |||||||
\(522\) | 20.0616 | 0.878073 | ||||||||
\(523\) | −18.1652 | −0.794307 | −0.397153 | − | 0.917752i | \(-0.630002\pi\) | ||||
−0.397153 | + | 0.917752i | \(0.630002\pi\) | |||||||
\(524\) | 4.41742 | 0.192976 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.7001 | 0.858966 | ||||||||
\(527\) | −44.3103 | −1.93019 | ||||||||
\(528\) | 4.73930 | 0.206252 | ||||||||
\(529\) | −2.00000 | −0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.73750 | −0.292383 | ||||||||
\(532\) | 8.37386 | 0.363053 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9.37386 | 0.405647 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −25.7477 | −1.11213 | ||||||||
\(537\) | 0.165151 | 0.00712681 | ||||||||
\(538\) | −32.8335 | −1.41555 | ||||||||
\(539\) | 10.5830 | 0.455842 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.3923 | −0.446800 | −0.223400 | − | 0.974727i | \(-0.571716\pi\) | ||||
−0.223400 | + | 0.974727i | \(0.571716\pi\) | |||||||
\(542\) | −18.9564 | −0.814249 | ||||||||
\(543\) | 18.7477 | 0.804542 | ||||||||
\(544\) | 33.8426 | 1.45099 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.25227 | 0.0535433 | 0.0267717 | − | 0.999642i | \(-0.491477\pi\) | ||||
0.0267717 | + | 0.999642i | \(0.491477\pi\) | |||||||
\(548\) | −0.266150 | −0.0113694 | ||||||||
\(549\) | 21.1652 | 0.903307 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.93725 | 0.338138 | ||||||||
\(552\) | 7.93725 | 0.337832 | ||||||||
\(553\) | 10.3923 | 0.441926 | ||||||||
\(554\) | 36.2976 | 1.54214 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.0436 | 0.680399 | ||||||||
\(557\) | 13.0381 | 0.552440 | 0.276220 | − | 0.961094i | \(-0.410918\pi\) | ||||
0.276220 | + | 0.961094i | \(0.410918\pi\) | |||||||
\(558\) | −42.3303 | −1.79198 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.1244 | 0.511891 | ||||||||
\(562\) | −38.3303 | −1.61687 | ||||||||
\(563\) | 9.00000 | 0.379305 | 0.189652 | − | 0.981851i | \(-0.439264\pi\) | ||||
0.189652 | + | 0.981851i | \(0.439264\pi\) | |||||||
\(564\) | 24.4394 | 1.02908 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.552200 | 0.0232107 | ||||||||
\(567\) | −1.73205 | −0.0727393 | ||||||||
\(568\) | 6.16515 | 0.258684 | ||||||||
\(569\) | 19.7477 | 0.827868 | 0.413934 | − | 0.910307i | \(-0.364154\pi\) | ||||
0.413934 | + | 0.910307i | \(0.364154\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.0780 | −1.21688 | −0.608439 | − | 0.793601i | \(-0.708204\pi\) | ||||
−0.608439 | + | 0.793601i | \(0.708204\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.41742 | −0.309867 | ||||||||
\(574\) | 10.0308 | 0.418678 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 25.1652 | 1.04855 | ||||||||
\(577\) | −6.92820 | −0.288425 | −0.144212 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144212 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(578\) | 8.75560 | 0.364185 | ||||||||
\(579\) | 1.00905 | 0.0419347 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.5826 | −0.812422 | ||||||||
\(582\) | −9.79129 | −0.405862 | ||||||||
\(583\) | 4.18710 | 0.173412 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 51.2867 | 2.11864 | ||||||||
\(587\) | 18.7110 | 0.772284 | 0.386142 | − | 0.922439i | \(-0.373807\pi\) | ||||
0.386142 | + | 0.922439i | \(0.373807\pi\) | |||||||
\(588\) | −11.1652 | −0.460443 | ||||||||
\(589\) | −16.7477 | −0.690078 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.9663 | 0.821302 | ||||||||
\(592\) | 14.2179 | 0.584352 | ||||||||
\(593\) | 21.1660 | 0.869184 | 0.434592 | − | 0.900627i | \(-0.356893\pi\) | ||||
0.434592 | + | 0.900627i | \(0.356893\pi\) | |||||||
\(594\) | 28.9564 | 1.18810 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 27.2560 | 1.11645 | ||||||||
\(597\) | −1.41742 | −0.0580113 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.4955 | −1.61374 | −0.806870 | − | 0.590729i | \(-0.798840\pi\) | ||||
−0.806870 | + | 0.590729i | \(0.798840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.9129 | −1.17938 | −0.589690 | − | 0.807629i | \(-0.700750\pi\) | ||||
−0.589690 | + | 0.807629i | \(0.700750\pi\) | |||||||
\(602\) | 5.37386 | 0.219022 | ||||||||
\(603\) | 29.7309 | 1.21074 | ||||||||
\(604\) | 17.3205 | 0.704761 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19.7001 | −0.800262 | ||||||||
\(607\) | −19.7477 | −0.801536 | −0.400768 | − | 0.916180i | \(-0.631257\pi\) | ||||
−0.400768 | + | 0.916180i | \(0.631257\pi\) | |||||||
\(608\) | 12.7913 | 0.518755 | ||||||||
\(609\) | 7.93725 | 0.321634 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 25.5826 | 1.03411 | ||||||||
\(613\) | −21.7937 | −0.880238 | −0.440119 | − | 0.897940i | \(-0.645064\pi\) | ||||
−0.440119 | + | 0.897940i | \(0.645064\pi\) | |||||||
\(614\) | −53.0780 | −2.14205 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.93725 | 0.319801 | ||||||||
\(617\) | 3.36875 | 0.135621 | 0.0678104 | − | 0.997698i | \(-0.478399\pi\) | ||||
0.0678104 | + | 0.997698i | \(0.478399\pi\) | |||||||
\(618\) | 33.1950 | 1.33530 | ||||||||
\(619\) | −2.01810 | −0.0811143 | −0.0405572 | − | 0.999177i | \(-0.512913\pi\) | ||||
−0.0405572 | + | 0.999177i | \(0.512913\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.9129 | −0.919462 | ||||||||
\(622\) | 3.46410 | 0.138898 | ||||||||
\(623\) | −7.41742 | −0.297173 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −67.3037 | −2.69000 | ||||||||
\(627\) | 4.58258 | 0.183010 | ||||||||
\(628\) | −25.5826 | −1.02086 | ||||||||
\(629\) | 36.3731 | 1.45029 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.7937 | −0.867592 | −0.433796 | − | 0.901011i | \(-0.642826\pi\) | ||||
−0.433796 | + | 0.901011i | \(0.642826\pi\) | |||||||
\(632\) | −10.3923 | −0.413384 | ||||||||
\(633\) | 18.1652 | 0.722000 | ||||||||
\(634\) | 45.9129 | 1.82343 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.41742 | −0.175162 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 26.5390 | 1.05069 | ||||||||
\(639\) | −7.11890 | −0.281619 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.165151 | 0.00652309 | 0.00326154 | − | 0.999995i | \(-0.498962\pi\) | ||||
0.00326154 | + | 0.999995i | \(0.498962\pi\) | |||||||
\(642\) | −3.10260 | −0.122450 | ||||||||
\(643\) | −5.91915 | −0.233429 | −0.116714 | − | 0.993166i | \(-0.537236\pi\) | ||||
−0.116714 | + | 0.993166i | \(0.537236\pi\) | |||||||
\(644\) | −22.1552 | −0.873036 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.3739 | 0.683566 | ||||||||
\(647\) | −27.0000 | −1.06148 | −0.530740 | − | 0.847535i | \(-0.678086\pi\) | ||||
−0.530740 | + | 0.847535i | \(0.678086\pi\) | |||||||
\(648\) | 1.73205 | 0.0680414 | ||||||||
\(649\) | −8.91288 | −0.349861 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.7477 | −0.656395 | ||||||||
\(652\) | 29.8064 | 1.16731 | ||||||||
\(653\) | 48.8258 | 1.91070 | 0.955350 | − | 0.295477i | \(-0.0954787\pi\) | ||||
0.955350 | + | 0.295477i | \(0.0954787\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.73930 | 0.185039 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −33.1950 | −1.29408 | ||||||||
\(659\) | −24.4955 | −0.954207 | −0.477104 | − | 0.878847i | \(-0.658313\pi\) | ||||
−0.477104 | + | 0.878847i | \(0.658313\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.45505 | −0.0954904 | −0.0477452 | − | 0.998860i | \(-0.515204\pi\) | ||||
−0.0477452 | + | 0.998860i | \(0.515204\pi\) | |||||||
\(662\) | −24.9564 | −0.969960 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.5826 | 0.759951 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 34.7477 | 1.34645 | ||||||||
\(667\) | −21.0000 | −0.813123 | ||||||||
\(668\) | −11.9536 | −0.462497 | ||||||||
\(669\) | −8.66025 | −0.334825 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.9989 | 1.08088 | ||||||||
\(672\) | 12.7913 | 0.493435 | ||||||||
\(673\) | 5.83485 | 0.224917 | 0.112458 | − | 0.993656i | \(-0.464127\pi\) | ||||
0.112458 | + | 0.993656i | \(0.464127\pi\) | |||||||
\(674\) | −7.11890 | −0.274210 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.1652 | −0.813443 | −0.406721 | − | 0.913552i | \(-0.633328\pi\) | ||||
−0.406721 | + | 0.913552i | \(0.633328\pi\) | |||||||
\(678\) | −36.2976 | −1.39400 | ||||||||
\(679\) | 7.74773 | 0.297330 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.10985 | −0.234130 | ||||||||
\(682\) | −55.9977 | −2.14426 | ||||||||
\(683\) | −11.9337 | −0.456629 | −0.228314 | − | 0.973587i | \(-0.573321\pi\) | ||||
−0.228314 | + | 0.973587i | \(0.573321\pi\) | |||||||
\(684\) | 9.66930 | 0.369715 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 41.7042 | 1.59227 | ||||||||
\(687\) | 5.48220 | 0.209159 | ||||||||
\(688\) | 2.53901 | 0.0967990 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.6501 | 1.35619 | 0.678096 | − | 0.734973i | \(-0.262805\pi\) | ||||
0.678096 | + | 0.734973i | \(0.262805\pi\) | |||||||
\(692\) | 20.7042 | 0.787054 | ||||||||
\(693\) | −9.16515 | −0.348155 | ||||||||
\(694\) | 33.5565 | 1.27379 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.93725 | −0.300861 | ||||||||
\(697\) | 12.1244 | 0.459243 | ||||||||
\(698\) | 40.1216 | 1.51862 | ||||||||
\(699\) | −21.1652 | −0.800540 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.83485 | 0.107071 | 0.0535354 | − | 0.998566i | \(-0.482951\pi\) | ||||
0.0535354 | + | 0.998566i | \(0.482951\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7477 | 0.518505 | ||||||||
\(704\) | 33.2904 | 1.25468 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 38.1216 | 1.43472 | ||||||||
\(707\) | 15.5885 | 0.586264 | ||||||||
\(708\) | 9.40315 | 0.353392 | ||||||||
\(709\) | −36.3731 | −1.36602 | −0.683010 | − | 0.730409i | \(-0.739329\pi\) | ||||
−0.683010 | + | 0.730409i | \(0.739329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 7.41742 | 0.277980 | ||||||||
\(713\) | 44.3103 | 1.65943 | ||||||||
\(714\) | 17.3739 | 0.650201 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.460985 | 0.0172278 | ||||||||
\(717\) | −20.9753 | −0.783337 | ||||||||
\(718\) | −73.0780 | −2.72725 | ||||||||
\(719\) | −30.4955 | −1.13729 | −0.568644 | − | 0.822584i | \(-0.692532\pi\) | ||||
−0.568644 | + | 0.822584i | \(0.692532\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.2668 | −0.978227 | ||||||||
\(722\) | −35.0224 | −1.30340 | ||||||||
\(723\) | −1.73205 | −0.0644157 | ||||||||
\(724\) | 52.3303 | 1.94484 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.75560 | −0.324951 | ||||||||
\(727\) | 42.7477 | 1.58543 | 0.792713 | − | 0.609595i | \(-0.208668\pi\) | ||||
0.792713 | + | 0.609595i | \(0.208668\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.49545 | 0.240243 | ||||||||
\(732\) | −29.5390 | −1.09179 | ||||||||
\(733\) | 8.94630 | 0.330439 | 0.165220 | − | 0.986257i | \(-0.447167\pi\) | ||||
0.165220 | + | 0.986257i | \(0.447167\pi\) | |||||||
\(734\) | 56.3592 | 2.08026 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.8426 | −1.24745 | ||||||||
\(737\) | 39.3303 | 1.44875 | ||||||||
\(738\) | 11.5826 | 0.426361 | ||||||||
\(739\) | −48.7835 | −1.79453 | −0.897265 | − | 0.441493i | \(-0.854449\pi\) | ||||
−0.897265 | + | 0.441493i | \(0.854449\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | 0.220267 | ||||||||
\(743\) | 42.7690 | 1.56904 | 0.784521 | − | 0.620103i | \(-0.212909\pi\) | ||||
0.784521 | + | 0.620103i | \(0.212909\pi\) | |||||||
\(744\) | 16.7477 | 0.614001 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −28.4557 | −1.04184 | ||||||||
\(747\) | −22.6120 | −0.827330 | ||||||||
\(748\) | 33.8426 | 1.23741 | ||||||||
\(749\) | 2.45505 | 0.0897056 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.7477 | 0.574643 | 0.287321 | − | 0.957834i | \(-0.407235\pi\) | ||||
0.287321 | + | 0.957834i | \(0.407235\pi\) | |||||||
\(752\) | −15.6838 | −0.571930 | ||||||||
\(753\) | −18.1652 | −0.661975 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 24.1733 | 0.879173 | ||||||||
\(757\) | −17.7477 | −0.645052 | −0.322526 | − | 0.946561i | \(-0.604532\pi\) | ||||
−0.322526 | + | 0.946561i | \(0.604532\pi\) | |||||||
\(758\) | −46.1216 | −1.67521 | ||||||||
\(759\) | −12.1244 | −0.440086 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.7509 | −1.47722 | −0.738609 | − | 0.674134i | \(-0.764517\pi\) | ||||
−0.738609 | + | 0.674134i | \(0.764517\pi\) | |||||||
\(762\) | 21.3368 | 0.772951 | ||||||||
\(763\) | −4.74773 | −0.171879 | ||||||||
\(764\) | −20.7042 | −0.749050 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.20871 | −0.224330 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.79129 | −0.100722 | ||||||||
\(769\) | 15.5885 | 0.562134 | 0.281067 | − | 0.959688i | \(-0.409312\pi\) | ||||
0.281067 | + | 0.959688i | \(0.409312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.165151 | −0.00594778 | ||||||||
\(772\) | 2.81655 | 0.101370 | ||||||||
\(773\) | −34.7364 | −1.24938 | −0.624690 | − | 0.780873i | \(-0.714775\pi\) | ||||
−0.624690 | + | 0.780873i | \(0.714775\pi\) | |||||||
\(774\) | 6.20520 | 0.223041 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.74773 | −0.278127 | ||||||||
\(777\) | 13.7477 | 0.493197 | ||||||||
\(778\) | −33.1950 | −1.19010 | ||||||||
\(779\) | 4.58258 | 0.164188 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.41742 | −0.336982 | ||||||||
\(782\) | −45.9669 | −1.64377 | ||||||||
\(783\) | 22.9129 | 0.818839 | ||||||||
\(784\) | 7.16515 | 0.255898 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.46410 | 0.123560 | ||||||||
\(787\) | 32.1860 | 1.14731 | 0.573653 | − | 0.819099i | \(-0.305526\pi\) | ||||
0.573653 | + | 0.819099i | \(0.305526\pi\) | |||||||
\(788\) | 55.7316 | 1.98536 | ||||||||
\(789\) | 9.00000 | 0.320408 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.7219 | 1.02123 | ||||||||
\(792\) | 9.16515 | 0.325669 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 59.7042 | 2.11882 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.95644 | −0.140232 | ||||||||
\(797\) | 20.0780 | 0.711200 | 0.355600 | − | 0.934638i | \(-0.384276\pi\) | ||||
0.355600 | + | 0.934638i | \(0.384276\pi\) | |||||||
\(798\) | 6.56670 | 0.232459 | ||||||||
\(799\) | −40.1232 | −1.41946 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.56490 | −0.302626 | ||||||||
\(802\) | −27.3739 | −0.966605 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −41.4938 | −1.46337 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.0000 | −0.528025 | ||||||||
\(808\) | −15.5885 | −0.548400 | ||||||||
\(809\) | 36.8258 | 1.29472 | 0.647362 | − | 0.762182i | \(-0.275872\pi\) | ||||
0.647362 | + | 0.762182i | \(0.275872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.7665 | 0.658981 | 0.329491 | − | 0.944159i | \(-0.393123\pi\) | ||||
0.329491 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(812\) | 22.1552 | 0.777494 | ||||||||
\(813\) | −8.66025 | −0.303728 | ||||||||
\(814\) | 45.9669 | 1.61114 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.20871 | 0.287362 | ||||||||
\(817\) | 2.45505 | 0.0858914 | ||||||||
\(818\) | 18.9564 | 0.662796 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.4304 | 0.817725 | 0.408863 | − | 0.912596i | \(-0.365926\pi\) | ||||
0.408863 | + | 0.912596i | \(0.365926\pi\) | |||||||
\(822\) | −0.208712 | −0.00727967 | ||||||||
\(823\) | 40.5826 | 1.41462 | 0.707310 | − | 0.706904i | \(-0.249909\pi\) | ||||
0.707310 | + | 0.706904i | \(0.249909\pi\) | |||||||
\(824\) | 26.2668 | 0.915048 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.7719 | −0.444391 | ||||||||
\(827\) | 31.5583 | 1.09739 | 0.548695 | − | 0.836023i | \(-0.315125\pi\) | ||||
0.548695 | + | 0.836023i | \(0.315125\pi\) | |||||||
\(828\) | −25.5826 | −0.889056 | ||||||||
\(829\) | −3.33030 | −0.115666 | −0.0578331 | − | 0.998326i | \(-0.518419\pi\) | ||||
−0.0578331 | + | 0.998326i | \(0.518419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.5826 | 0.575243 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.3303 | 0.635107 | ||||||||
\(834\) | 12.5812 | 0.435652 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 12.7913 | 0.442396 | ||||||||
\(837\) | −48.3465 | −1.67110 | ||||||||
\(838\) | −52.8951 | −1.82723 | ||||||||
\(839\) | −1.35065 | −0.0466296 | −0.0233148 | − | 0.999728i | \(-0.507422\pi\) | ||||
−0.0233148 | + | 0.999728i | \(0.507422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.00000 | −0.275862 | ||||||||
\(842\) | 57.4955 | 1.98142 | ||||||||
\(843\) | −17.5112 | −0.603118 | ||||||||
\(844\) | 50.7042 | 1.74531 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −38.3303 | −1.31782 | ||||||||
\(847\) | 6.92820 | 0.238056 | ||||||||
\(848\) | 2.83485 | 0.0973491 | ||||||||
\(849\) | 0.252273 | 0.00865798 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.3731 | −1.24685 | ||||||||
\(852\) | 9.93545 | 0.340383 | ||||||||
\(853\) | −53.2566 | −1.82347 | −0.911736 | − | 0.410777i | \(-0.865258\pi\) | ||||
−0.911736 | + | 0.410777i | \(0.865258\pi\) | |||||||
\(854\) | 40.1216 | 1.37293 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.45505 | −0.0839119 | ||||||||
\(857\) | −22.7477 | −0.777048 | −0.388524 | − | 0.921439i | \(-0.627015\pi\) | ||||
−0.388524 | + | 0.921439i | \(0.627015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.2432 | 1.30484 | 0.652420 | − | 0.757857i | \(-0.273754\pi\) | ||||
0.652420 | + | 0.757857i | \(0.273754\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.58258 | 0.156174 | ||||||||
\(862\) | 64.8693 | 2.20946 | ||||||||
\(863\) | −34.8317 | −1.18569 | −0.592843 | − | 0.805318i | \(-0.701994\pi\) | ||||
−0.592843 | + | 0.805318i | \(0.701994\pi\) | |||||||
\(864\) | 36.9253 | 1.25622 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 38.8480 | 1.32011 | ||||||||
\(867\) | 4.00000 | 0.135847 | ||||||||
\(868\) | −46.7477 | −1.58672 | ||||||||
\(869\) | 15.8745 | 0.538506 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.74773 | 0.160778 | ||||||||
\(873\) | 8.94630 | 0.302787 | ||||||||
\(874\) | −17.3739 | −0.587680 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.93725 | −0.268022 | −0.134011 | − | 0.990980i | \(-0.542786\pi\) | ||||
−0.134011 | + | 0.990980i | \(0.542786\pi\) | |||||||
\(878\) | −88.6405 | −2.99147 | ||||||||
\(879\) | 23.4304 | 0.790286 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.4955 | 0.623128 | 0.311564 | − | 0.950225i | \(-0.399147\pi\) | ||||
0.311564 | + | 0.950225i | \(0.399147\pi\) | |||||||
\(882\) | 17.5112 | 0.589633 | ||||||||
\(883\) | 46.2432 | 1.55621 | 0.778103 | − | 0.628136i | \(-0.216182\pi\) | ||||
0.778103 | + | 0.628136i | \(0.216182\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −56.7207 | −1.90557 | ||||||||
\(887\) | −0.495454 | −0.0166357 | −0.00831786 | − | 0.999965i | \(-0.502648\pi\) | ||||
−0.00831786 | + | 0.999965i | \(0.502648\pi\) | |||||||
\(888\) | −13.7477 | −0.461344 | ||||||||
\(889\) | −16.8836 | −0.566256 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.64575 | −0.0886360 | ||||||||
\(892\) | −24.1733 | −0.809381 | ||||||||
\(893\) | −15.1652 | −0.507482 | ||||||||
\(894\) | 21.3739 | 0.714849 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 22.1216 | 0.739030 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −82.0345 | −2.73753 | ||||||||
\(899\) | −44.3103 | −1.47783 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.25227 | 0.241608 | ||||||||
\(902\) | 15.3223 | 0.510177 | ||||||||
\(903\) | 2.45505 | 0.0816990 | ||||||||
\(904\) | −28.7219 | −0.955275 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13.5826 | 0.451251 | ||||||||
\(907\) | 33.7477 | 1.12057 | 0.560287 | − | 0.828298i | \(-0.310691\pi\) | ||||
0.560287 | + | 0.828298i | \(0.310691\pi\) | |||||||
\(908\) | −17.0544 | −0.565969 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.9129 | 1.25611 | 0.628055 | − | 0.778169i | \(-0.283851\pi\) | ||||
0.628055 | + | 0.778169i | \(0.283851\pi\) | |||||||
\(912\) | 3.10260 | 0.102737 | ||||||||
\(913\) | −29.9129 | −0.989972 | ||||||||
\(914\) | −3.79129 | −0.125405 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.3024 | 0.505606 | ||||||||
\(917\) | −2.74110 | −0.0905191 | ||||||||
\(918\) | 50.1540 | 1.65533 | ||||||||
\(919\) | 35.8348 | 1.18208 | 0.591041 | − | 0.806641i | \(-0.298717\pi\) | ||||
0.591041 | + | 0.806641i | \(0.298717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.2487 | −0.799022 | ||||||||
\(922\) | 2.62614 | 0.0864872 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.7913 | 0.420802 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.0000 | −0.591517 | ||||||||
\(927\) | −30.3303 | −0.996178 | ||||||||
\(928\) | 33.8426 | 1.11094 | ||||||||
\(929\) | −15.9699 | −0.523954 | −0.261977 | − | 0.965074i | \(-0.584374\pi\) | ||||
−0.261977 | + | 0.965074i | \(0.584374\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.92820 | 0.227063 | ||||||||
\(932\) | −59.0780 | −1.93517 | ||||||||
\(933\) | 1.58258 | 0.0518112 | ||||||||
\(934\) | −26.9898 | −0.883134 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.4955 | −0.767563 | −0.383782 | − | 0.923424i | \(-0.625378\pi\) | ||||
−0.383782 | + | 0.923424i | \(0.625378\pi\) | |||||||
\(938\) | 56.3592 | 1.84019 | ||||||||
\(939\) | −30.7477 | −1.00341 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.4575 | −0.862490 | −0.431245 | − | 0.902235i | \(-0.641926\pi\) | ||||
−0.431245 | + | 0.902235i | \(0.641926\pi\) | |||||||
\(942\) | −20.0616 | −0.653643 | ||||||||
\(943\) | −12.1244 | −0.394823 | ||||||||
\(944\) | −6.03440 | −0.196403 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.20871 | 0.266888 | ||||||||
\(947\) | −38.5819 | −1.25374 | −0.626871 | − | 0.779123i | \(-0.715665\pi\) | ||||
−0.626871 | + | 0.779123i | \(0.715665\pi\) | |||||||
\(948\) | −16.7477 | −0.543941 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.9753 | 0.680171 | ||||||||
\(952\) | 13.7477 | 0.445566 | ||||||||
\(953\) | −56.0780 | −1.81655 | −0.908273 | − | 0.418378i | \(-0.862599\pi\) | ||||
−0.908273 | + | 0.418378i | \(0.862599\pi\) | |||||||
\(954\) | 6.92820 | 0.224309 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −58.5481 | −1.89358 | ||||||||
\(957\) | 12.1244 | 0.391925 | ||||||||
\(958\) | −70.8693 | −2.28968 | ||||||||
\(959\) | 0.165151 | 0.00533302 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.4955 | 2.01598 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.83485 | 0.0913517 | ||||||||
\(964\) | −4.83465 | −0.155714 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.3739 | −0.558995 | ||||||||
\(967\) | −21.5076 | −0.691638 | −0.345819 | − | 0.938301i | \(-0.612399\pi\) | ||||
−0.345819 | + | 0.938301i | \(0.612399\pi\) | |||||||
\(968\) | −6.92820 | −0.222681 | ||||||||
\(969\) | 7.93725 | 0.254981 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.4955 | 1.17119 | 0.585597 | − | 0.810602i | \(-0.300860\pi\) | ||||
0.585597 | + | 0.810602i | \(0.300860\pi\) | |||||||
\(972\) | 44.6606 | 1.43249 | ||||||||
\(973\) | −9.95536 | −0.319154 | ||||||||
\(974\) | 46.1216 | 1.47783 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.9564 | 0.606781 | ||||||||
\(977\) | −38.7726 | −1.24044 | −0.620222 | − | 0.784426i | \(-0.712958\pi\) | ||||
−0.620222 | + | 0.784426i | \(0.712958\pi\) | |||||||
\(978\) | 23.3739 | 0.747414 | ||||||||
\(979\) | −11.3303 | −0.362118 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.48220 | −0.175033 | ||||||||
\(982\) | −62.5644 | −1.99651 | ||||||||
\(983\) | −3.12250 | −0.0995924 | −0.0497962 | − | 0.998759i | \(-0.515857\pi\) | ||||
−0.0497962 | + | 0.998759i | \(0.515857\pi\) | |||||||
\(984\) | −4.58258 | −0.146087 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 45.9669 | 1.46389 | ||||||||
\(987\) | −15.1652 | −0.482712 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.49545 | −0.206543 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0000 | −0.412959 | −0.206479 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206479 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(992\) | −71.4083 | −2.26722 | ||||||||
\(993\) | −11.4014 | −0.361811 | ||||||||
\(994\) | −13.4949 | −0.428032 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 31.5583 | 0.999963 | ||||||||
\(997\) | −18.1652 | −0.575296 | −0.287648 | − | 0.957736i | \(-0.592873\pi\) | ||||
−0.287648 | + | 0.957736i | \(0.592873\pi\) | |||||||
\(998\) | 36.3303 | 1.15002 | ||||||||
\(999\) | 39.6863 | 1.25562 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))