Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,2,Mod(1,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, 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("414.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.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: | \(3.30580664368\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 7 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 414.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.64575 | −0.736002 | −0.368001 | − | 0.929825i | \(-0.619958\pi\) | ||||
−0.368001 | + | 0.929825i | \(0.619958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.64575 | −0.520432 | ||||||||
\(11\) | 1.64575 | 0.496213 | 0.248106 | − | 0.968733i | \(-0.420192\pi\) | ||||
0.248106 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.29150 | 1.46760 | 0.733799 | − | 0.679366i | \(-0.237745\pi\) | ||||
0.733799 | + | 0.679366i | \(0.237745\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.29150 | 0.798307 | 0.399153 | − | 0.916884i | \(-0.369304\pi\) | ||||
0.399153 | + | 0.916884i | \(0.369304\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.354249 | 0.0812702 | 0.0406351 | − | 0.999174i | \(-0.487062\pi\) | ||||
0.0406351 | + | 0.999174i | \(0.487062\pi\) | |||||||
\(20\) | −1.64575 | −0.368001 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.64575 | 0.350875 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.29150 | −0.458301 | ||||||||
\(26\) | 5.29150 | 1.03775 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | −9.29150 | −1.72539 | −0.862694 | − | 0.505726i | \(-0.831225\pi\) | ||||
−0.862694 | + | 0.505726i | \(0.831225\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.29150 | −0.231961 | −0.115980 | − | 0.993252i | \(-0.537001\pi\) | ||||
−0.115980 | + | 0.993252i | \(0.537001\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.29150 | 0.564488 | ||||||||
\(35\) | −3.29150 | −0.556365 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.93725 | 1.14048 | 0.570239 | − | 0.821479i | \(-0.306851\pi\) | ||||
0.570239 | + | 0.821479i | \(0.306851\pi\) | |||||||
\(38\) | 0.354249 | 0.0574667 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.64575 | −0.260216 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.354249 | 0.0540224 | 0.0270112 | − | 0.999635i | \(-0.491401\pi\) | ||||
0.0270112 | + | 0.999635i | \(0.491401\pi\) | |||||||
\(44\) | 1.64575 | 0.248106 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −2.29150 | −0.324067 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.29150 | 0.733799 | ||||||||
\(53\) | 1.64575 | 0.226061 | 0.113031 | − | 0.993592i | \(-0.463944\pi\) | ||||
0.113031 | + | 0.993592i | \(0.463944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.70850 | −0.365214 | ||||||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.29150 | −1.22003 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.354249 | 0.0453569 | 0.0226784 | − | 0.999743i | \(-0.492781\pi\) | ||||
0.0226784 | + | 0.999743i | \(0.492781\pi\) | |||||||
\(62\) | −1.29150 | −0.164021 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.70850 | −1.08016 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9373 | −1.82488 | −0.912438 | − | 0.409215i | \(-0.865803\pi\) | ||||
−0.912438 | + | 0.409215i | \(0.865803\pi\) | |||||||
\(68\) | 3.29150 | 0.399153 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.29150 | −0.393410 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.29150 | −0.853406 | −0.426703 | − | 0.904392i | \(-0.640325\pi\) | ||||
−0.426703 | + | 0.904392i | \(0.640325\pi\) | |||||||
\(74\) | 6.93725 | 0.806439 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.354249 | 0.0406351 | ||||||||
\(77\) | 3.29150 | 0.375102 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.58301 | 0.965664 | 0.482832 | − | 0.875713i | \(-0.339608\pi\) | ||||
0.482832 | + | 0.875713i | \(0.339608\pi\) | |||||||
\(80\) | −1.64575 | −0.184001 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.00000 | −0.662589 | ||||||||
\(83\) | 13.6458 | 1.49782 | 0.748908 | − | 0.662674i | \(-0.230579\pi\) | ||||
0.748908 | + | 0.662674i | \(0.230579\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.41699 | −0.587556 | ||||||||
\(86\) | 0.354249 | 0.0381996 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.64575 | 0.175438 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5830 | 1.10940 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | −0.583005 | −0.0598151 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.29150 | −0.131132 | −0.0655661 | − | 0.997848i | \(-0.520885\pi\) | ||||
−0.0655661 | + | 0.997848i | \(0.520885\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.29150 | −0.229150 | ||||||||
\(101\) | −9.29150 | −0.924539 | −0.462270 | − | 0.886739i | \(-0.652965\pi\) | ||||
−0.462270 | + | 0.886739i | \(0.652965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.70850 | −0.661008 | −0.330504 | − | 0.943805i | \(-0.607219\pi\) | ||||
−0.330504 | + | 0.943805i | \(0.607219\pi\) | |||||||
\(104\) | 5.29150 | 0.518875 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.64575 | 0.159849 | ||||||||
\(107\) | 13.6458 | 1.31918 | 0.659592 | − | 0.751624i | \(-0.270729\pi\) | ||||
0.659592 | + | 0.751624i | \(0.270729\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.2288 | −1.74600 | −0.872999 | − | 0.487722i | \(-0.837828\pi\) | ||||
−0.872999 | + | 0.487722i | \(0.837828\pi\) | |||||||
\(110\) | −2.70850 | −0.258245 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | −6.58301 | −0.619277 | −0.309639 | − | 0.950854i | \(-0.600208\pi\) | ||||
−0.309639 | + | 0.950854i | \(0.600208\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.64575 | 0.153467 | ||||||||
\(116\) | −9.29150 | −0.862694 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.58301 | 0.603463 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.29150 | −0.753773 | ||||||||
\(122\) | 0.354249 | 0.0320722 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.29150 | −0.115980 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5830 | −0.939090 | −0.469545 | − | 0.882909i | \(-0.655582\pi\) | ||||
−0.469545 | + | 0.882909i | \(0.655582\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.70850 | −0.763786 | ||||||||
\(131\) | 21.8745 | 1.91118 | 0.955592 | − | 0.294692i | \(-0.0952170\pi\) | ||||
0.955592 | + | 0.294692i | \(0.0952170\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.708497 | 0.0614345 | ||||||||
\(134\) | −14.9373 | −1.29038 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.29150 | 0.282244 | ||||||||
\(137\) | −21.8745 | −1.86887 | −0.934433 | − | 0.356140i | \(-0.884093\pi\) | ||||
−0.934433 | + | 0.356140i | \(0.884093\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −3.29150 | −0.278183 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 8.70850 | 0.728241 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2915 | 1.26989 | ||||||||
\(146\) | −7.29150 | −0.603449 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.93725 | 0.570239 | ||||||||
\(149\) | −10.3542 | −0.848253 | −0.424127 | − | 0.905603i | \(-0.639419\pi\) | ||||
−0.424127 | + | 0.905603i | \(0.639419\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2915 | 1.40716 | 0.703581 | − | 0.710615i | \(-0.251583\pi\) | ||||
0.703581 | + | 0.710615i | \(0.251583\pi\) | |||||||
\(152\) | 0.354249 | 0.0287334 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.29150 | 0.265237 | ||||||||
\(155\) | 2.12549 | 0.170724 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.64575 | 0.290963 | 0.145481 | − | 0.989361i | \(-0.453527\pi\) | ||||
0.145481 | + | 0.989361i | \(0.453527\pi\) | |||||||
\(158\) | 8.58301 | 0.682827 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.64575 | −0.130108 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.708497 | −0.0554938 | −0.0277469 | − | 0.999615i | \(-0.508833\pi\) | ||||
−0.0277469 | + | 0.999615i | \(0.508833\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.6458 | 1.05912 | ||||||||
\(167\) | 19.1660 | 1.48311 | 0.741555 | − | 0.670892i | \(-0.234089\pi\) | ||||
0.741555 | + | 0.670892i | \(0.234089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.0000 | 1.15385 | ||||||||
\(170\) | −5.41699 | −0.415465 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.354249 | 0.0270112 | ||||||||
\(173\) | 15.8745 | 1.20692 | 0.603458 | − | 0.797395i | \(-0.293789\pi\) | ||||
0.603458 | + | 0.797395i | \(0.293789\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.58301 | −0.346443 | ||||||||
\(176\) | 1.64575 | 0.124053 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.2915 | −1.14294 | −0.571470 | − | 0.820623i | \(-0.693627\pi\) | ||||
−0.571470 | + | 0.820623i | \(0.693627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6458 | 1.16294 | 0.581470 | − | 0.813568i | \(-0.302478\pi\) | ||||
0.581470 | + | 0.813568i | \(0.302478\pi\) | |||||||
\(182\) | 10.5830 | 0.784465 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −11.4170 | −0.839394 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.41699 | 0.396130 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.583005 | −0.0422956 | ||||||||
\(191\) | −3.29150 | −0.238165 | −0.119082 | − | 0.992884i | \(-0.537995\pi\) | ||||
−0.119082 | + | 0.992884i | \(0.537995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.0000 | −1.58359 | −0.791797 | − | 0.610784i | \(-0.790854\pi\) | ||||
−0.791797 | + | 0.610784i | \(0.790854\pi\) | |||||||
\(194\) | −1.29150 | −0.0927245 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | −2.29150 | −0.162034 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.29150 | −0.653748 | ||||||||
\(203\) | −18.5830 | −1.30427 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.87451 | 0.689666 | ||||||||
\(206\) | −6.70850 | −0.467403 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.29150 | 0.366900 | ||||||||
\(209\) | 0.583005 | 0.0403273 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2915 | 0.777339 | 0.388670 | − | 0.921377i | \(-0.372935\pi\) | ||||
0.388670 | + | 0.921377i | \(0.372935\pi\) | |||||||
\(212\) | 1.64575 | 0.113031 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 13.6458 | 0.932804 | ||||||||
\(215\) | −0.583005 | −0.0397606 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.58301 | −0.175346 | ||||||||
\(218\) | −18.2288 | −1.23461 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.70850 | −0.182607 | ||||||||
\(221\) | 17.4170 | 1.17159 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.8745 | −1.33090 | −0.665448 | − | 0.746444i | \(-0.731759\pi\) | ||||
−0.665448 | + | 0.746444i | \(0.731759\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.58301 | −0.437895 | ||||||||
\(227\) | 7.06275 | 0.468771 | 0.234385 | − | 0.972144i | \(-0.424692\pi\) | ||||
0.234385 | + | 0.972144i | \(0.424692\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.06275 | 0.598883 | 0.299442 | − | 0.954115i | \(-0.403200\pi\) | ||||
0.299442 | + | 0.954115i | \(0.403200\pi\) | |||||||
\(230\) | 1.64575 | 0.108518 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.29150 | −0.610017 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.87451 | 0.644142 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.58301 | 0.426713 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.29150 | 0.340856 | 0.170428 | − | 0.985370i | \(-0.445485\pi\) | ||||
0.170428 | + | 0.985370i | \(0.445485\pi\) | |||||||
\(242\) | −8.29150 | −0.532998 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.354249 | 0.0226784 | ||||||||
\(245\) | 4.93725 | 0.315430 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.87451 | 0.119272 | ||||||||
\(248\) | −1.29150 | −0.0820105 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | 25.6458 | 1.61875 | 0.809373 | − | 0.587295i | \(-0.199807\pi\) | ||||
0.809373 | + | 0.587295i | \(0.199807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.64575 | −0.103467 | ||||||||
\(254\) | −10.5830 | −0.664037 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.5830 | −1.53345 | −0.766723 | − | 0.641978i | \(-0.778114\pi\) | ||||
−0.766723 | + | 0.641978i | \(0.778114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.8745 | 0.862120 | ||||||||
\(260\) | −8.70850 | −0.540078 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.8745 | 1.35141 | ||||||||
\(263\) | 30.5830 | 1.88583 | 0.942914 | − | 0.333035i | \(-0.108073\pi\) | ||||
0.942914 | + | 0.333035i | \(0.108073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.70850 | −0.166382 | ||||||||
\(266\) | 0.708497 | 0.0434408 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.9373 | −0.912438 | ||||||||
\(269\) | 11.4170 | 0.696106 | 0.348053 | − | 0.937475i | \(-0.386843\pi\) | ||||
0.348053 | + | 0.937475i | \(0.386843\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | 3.29150 | 0.199577 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.8745 | −1.32149 | ||||||||
\(275\) | −3.77124 | −0.227415 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.29150 | 0.317936 | 0.158968 | − | 0.987284i | \(-0.449183\pi\) | ||||
0.158968 | + | 0.987284i | \(0.449183\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.29150 | −0.196705 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.5203 | −1.27925 | −0.639623 | − | 0.768689i | \(-0.720910\pi\) | ||||
−0.639623 | + | 0.768689i | \(0.720910\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.70850 | 0.514944 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.16601 | −0.362706 | ||||||||
\(290\) | 15.2915 | 0.897948 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.29150 | −0.426703 | ||||||||
\(293\) | 32.2288 | 1.88282 | 0.941412 | − | 0.337259i | \(-0.109500\pi\) | ||||
0.941412 | + | 0.337259i | \(0.109500\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.93725 | 0.403220 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.3542 | −0.599806 | ||||||||
\(299\) | −5.29150 | −0.306015 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.708497 | 0.0408371 | ||||||||
\(302\) | 17.2915 | 0.995014 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.354249 | 0.0203176 | ||||||||
\(305\) | −0.583005 | −0.0333828 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.8745 | 1.70503 | 0.852514 | − | 0.522704i | \(-0.175077\pi\) | ||||
0.852514 | + | 0.522704i | \(0.175077\pi\) | |||||||
\(308\) | 3.29150 | 0.187551 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.12549 | 0.120720 | ||||||||
\(311\) | −13.1660 | −0.746576 | −0.373288 | − | 0.927716i | \(-0.621770\pi\) | ||||
−0.373288 | + | 0.927716i | \(0.621770\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.29150 | 0.299093 | 0.149547 | − | 0.988755i | \(-0.452219\pi\) | ||||
0.149547 | + | 0.988755i | \(0.452219\pi\) | |||||||
\(314\) | 3.64575 | 0.205742 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.58301 | 0.482832 | ||||||||
\(317\) | −21.2915 | −1.19585 | −0.597925 | − | 0.801552i | \(-0.704008\pi\) | ||||
−0.597925 | + | 0.801552i | \(0.704008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.2915 | −0.856160 | ||||||||
\(320\) | −1.64575 | −0.0920003 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | 1.16601 | 0.0648786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1255 | −0.672601 | ||||||||
\(326\) | −0.708497 | −0.0392400 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.00000 | −0.331295 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.8745 | −1.42219 | −0.711096 | − | 0.703095i | \(-0.751801\pi\) | ||||
−0.711096 | + | 0.703095i | \(0.751801\pi\) | |||||||
\(332\) | 13.6458 | 0.748908 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.1660 | 1.04872 | ||||||||
\(335\) | 24.5830 | 1.34311 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.1660 | 0.826145 | 0.413073 | − | 0.910698i | \(-0.364456\pi\) | ||||
0.413073 | + | 0.910698i | \(0.364456\pi\) | |||||||
\(338\) | 15.0000 | 0.815892 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.41699 | −0.293778 | ||||||||
\(341\) | −2.12549 | −0.115102 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0.354249 | 0.0190998 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15.8745 | 0.853419 | ||||||||
\(347\) | −15.2915 | −0.820891 | −0.410445 | − | 0.911885i | \(-0.634627\pi\) | ||||
−0.410445 | + | 0.911885i | \(0.634627\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | −4.58301 | −0.244972 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.64575 | 0.0877188 | ||||||||
\(353\) | 6.58301 | 0.350378 | 0.175189 | − | 0.984535i | \(-0.443946\pi\) | ||||
0.175189 | + | 0.984535i | \(0.443946\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.87451 | −0.524084 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.2915 | −0.808181 | ||||||||
\(359\) | 21.8745 | 1.15449 | 0.577246 | − | 0.816570i | \(-0.304127\pi\) | ||||
0.577246 | + | 0.816570i | \(0.304127\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8745 | −0.993395 | ||||||||
\(362\) | 15.6458 | 0.822322 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.5830 | 0.554700 | ||||||||
\(365\) | 12.0000 | 0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1660 | −0.582861 | −0.291431 | − | 0.956592i | \(-0.594131\pi\) | ||||
−0.291431 | + | 0.956592i | \(0.594131\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.4170 | −0.593541 | ||||||||
\(371\) | 3.29150 | 0.170886 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.9373 | −1.39476 | −0.697379 | − | 0.716702i | \(-0.745651\pi\) | ||||
−0.697379 | + | 0.716702i | \(0.745651\pi\) | |||||||
\(374\) | 5.41699 | 0.280106 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | −49.1660 | −2.53218 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.5203 | −1.72182 | −0.860910 | − | 0.508757i | \(-0.830105\pi\) | ||||
−0.860910 | + | 0.508757i | \(0.830105\pi\) | |||||||
\(380\) | −0.583005 | −0.0299075 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.29150 | −0.168408 | ||||||||
\(383\) | −31.7490 | −1.62230 | −0.811149 | − | 0.584839i | \(-0.801158\pi\) | ||||
−0.811149 | + | 0.584839i | \(0.801158\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.41699 | −0.276076 | ||||||||
\(386\) | −22.0000 | −1.11977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.29150 | −0.0655661 | ||||||||
\(389\) | 7.06275 | 0.358095 | 0.179048 | − | 0.983840i | \(-0.442698\pi\) | ||||
0.179048 | + | 0.983840i | \(0.442698\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.29150 | −0.166458 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | −14.1255 | −0.710731 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 14.0000 | 0.701757 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.29150 | −0.114575 | ||||||||
\(401\) | −9.87451 | −0.493109 | −0.246555 | − | 0.969129i | \(-0.579299\pi\) | ||||
−0.246555 | + | 0.969129i | \(0.579299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.83399 | −0.340425 | ||||||||
\(404\) | −9.29150 | −0.462270 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.5830 | −0.922259 | ||||||||
\(407\) | 11.4170 | 0.565919 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1660 | 0.749911 | 0.374955 | − | 0.927043i | \(-0.377658\pi\) | ||||
0.374955 | + | 0.927043i | \(0.377658\pi\) | |||||||
\(410\) | 9.87451 | 0.487667 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.70850 | −0.330504 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.4575 | −1.10240 | ||||||||
\(416\) | 5.29150 | 0.259437 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.583005 | 0.0285157 | ||||||||
\(419\) | −16.9373 | −0.827439 | −0.413720 | − | 0.910404i | \(-0.635771\pi\) | ||||
−0.413720 | + | 0.910404i | \(0.635771\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.2288 | 1.08336 | 0.541682 | − | 0.840584i | \(-0.317788\pi\) | ||||
0.541682 | + | 0.840584i | \(0.317788\pi\) | |||||||
\(422\) | 11.2915 | 0.549662 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.64575 | 0.0799247 | ||||||||
\(425\) | −7.54249 | −0.365864 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.708497 | 0.0342866 | ||||||||
\(428\) | 13.6458 | 0.659592 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.583005 | −0.0281150 | ||||||||
\(431\) | 33.8745 | 1.63168 | 0.815839 | − | 0.578279i | \(-0.196276\pi\) | ||||
0.815839 | + | 0.578279i | \(0.196276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.7085 | −0.899073 | −0.449537 | − | 0.893262i | \(-0.648411\pi\) | ||||
−0.449537 | + | 0.893262i | \(0.648411\pi\) | |||||||
\(434\) | −2.58301 | −0.123988 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18.2288 | −0.872999 | ||||||||
\(437\) | −0.354249 | −0.0169460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.7490 | 1.32439 | 0.662194 | − | 0.749332i | \(-0.269625\pi\) | ||||
0.662194 | + | 0.749332i | \(0.269625\pi\) | |||||||
\(440\) | −2.70850 | −0.129123 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17.4170 | 0.828442 | ||||||||
\(443\) | −25.1660 | −1.19567 | −0.597837 | − | 0.801618i | \(-0.703973\pi\) | ||||
−0.597837 | + | 0.801618i | \(0.703973\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −19.8745 | −0.941085 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.00000 | 0.0944911 | ||||||||
\(449\) | −11.4170 | −0.538801 | −0.269401 | − | 0.963028i | \(-0.586826\pi\) | ||||
−0.269401 | + | 0.963028i | \(0.586826\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.87451 | −0.464972 | ||||||||
\(452\) | −6.58301 | −0.309639 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.06275 | 0.331471 | ||||||||
\(455\) | −17.4170 | −0.816521 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.125492 | −0.00587027 | −0.00293514 | − | 0.999996i | \(-0.500934\pi\) | ||||
−0.00293514 | + | 0.999996i | \(0.500934\pi\) | |||||||
\(458\) | 9.06275 | 0.423474 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.64575 | 0.0767336 | ||||||||
\(461\) | −25.7490 | −1.19925 | −0.599626 | − | 0.800281i | \(-0.704684\pi\) | ||||
−0.599626 | + | 0.800281i | \(0.704684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.1660 | 0.983668 | 0.491834 | − | 0.870689i | \(-0.336327\pi\) | ||||
0.491834 | + | 0.870689i | \(0.336327\pi\) | |||||||
\(464\) | −9.29150 | −0.431347 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.6458 | −0.631450 | −0.315725 | − | 0.948851i | \(-0.602248\pi\) | ||||
−0.315725 | + | 0.948851i | \(0.602248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.8745 | −1.37948 | ||||||||
\(470\) | 9.87451 | 0.455477 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.583005 | 0.0268066 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.811762 | −0.0372462 | ||||||||
\(476\) | 6.58301 | 0.301732 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −24.0000 | −1.09773 | ||||||||
\(479\) | −42.5830 | −1.94567 | −0.972834 | − | 0.231506i | \(-0.925635\pi\) | ||||
−0.972834 | + | 0.231506i | \(0.925635\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 36.7085 | 1.67376 | ||||||||
\(482\) | 5.29150 | 0.241021 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.29150 | −0.376886 | ||||||||
\(485\) | 2.12549 | 0.0965136 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.1660 | 0.959123 | 0.479562 | − | 0.877508i | \(-0.340796\pi\) | ||||
0.479562 | + | 0.877508i | \(0.340796\pi\) | |||||||
\(488\) | 0.354249 | 0.0160361 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.93725 | 0.223042 | ||||||||
\(491\) | 21.8745 | 0.987183 | 0.493591 | − | 0.869694i | \(-0.335684\pi\) | ||||
0.493591 | + | 0.869694i | \(0.335684\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.5830 | −1.37739 | ||||||||
\(494\) | 1.87451 | 0.0843381 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.29150 | −0.0579902 | ||||||||
\(497\) | 12.0000 | 0.538274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.0405 | 1.38956 | 0.694782 | − | 0.719220i | \(-0.255501\pi\) | ||||
0.694782 | + | 0.719220i | \(0.255501\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 25.6458 | 1.14463 | ||||||||
\(503\) | 2.12549 | 0.0947710 | 0.0473855 | − | 0.998877i | \(-0.484911\pi\) | ||||
0.0473855 | + | 0.998877i | \(0.484911\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.2915 | 0.680463 | ||||||||
\(506\) | −1.64575 | −0.0731626 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.5830 | −0.469545 | ||||||||
\(509\) | 27.8745 | 1.23552 | 0.617758 | − | 0.786368i | \(-0.288041\pi\) | ||||
0.617758 | + | 0.786368i | \(0.288041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.5830 | −0.645114 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −24.5830 | −1.08431 | ||||||||
\(515\) | 11.0405 | 0.486503 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.87451 | −0.434280 | ||||||||
\(518\) | 13.8745 | 0.609611 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.70850 | −0.381893 | ||||||||
\(521\) | 28.4575 | 1.24675 | 0.623373 | − | 0.781925i | \(-0.285762\pi\) | ||||
0.623373 | + | 0.781925i | \(0.285762\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.06275 | −0.221378 | −0.110689 | − | 0.993855i | \(-0.535306\pi\) | ||||
−0.110689 | + | 0.993855i | \(0.535306\pi\) | |||||||
\(524\) | 21.8745 | 0.955592 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 30.5830 | 1.33348 | ||||||||
\(527\) | −4.25098 | −0.185176 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.70850 | −0.117650 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.708497 | 0.0307173 | ||||||||
\(533\) | −31.7490 | −1.37520 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.4575 | −0.970923 | ||||||||
\(536\) | −14.9373 | −0.645191 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.4170 | 0.492222 | ||||||||
\(539\) | −4.93725 | −0.212663 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5830 | 0.884933 | 0.442466 | − | 0.896785i | \(-0.354104\pi\) | ||||
0.442466 | + | 0.896785i | \(0.354104\pi\) | |||||||
\(542\) | 20.0000 | 0.859074 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.29150 | 0.141122 | ||||||||
\(545\) | 30.0000 | 1.28506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.7085 | 0.714404 | 0.357202 | − | 0.934027i | \(-0.383731\pi\) | ||||
0.357202 | + | 0.934027i | \(0.383731\pi\) | |||||||
\(548\) | −21.8745 | −0.934433 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.77124 | −0.160806 | ||||||||
\(551\) | −3.29150 | −0.140223 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1660 | 0.729973 | ||||||||
\(554\) | 5.29150 | 0.224814 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | 42.1033 | 1.78397 | 0.891986 | − | 0.452062i | \(-0.149312\pi\) | ||||
0.891986 | + | 0.452062i | \(0.149312\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.87451 | 0.0792832 | ||||||||
\(560\) | −3.29150 | −0.139091 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −45.3948 | −1.91316 | −0.956581 | − | 0.291468i | \(-0.905856\pi\) | ||||
−0.956581 | + | 0.291468i | \(0.905856\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.8340 | 0.455789 | ||||||||
\(566\) | −21.5203 | −0.904564 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 8.70850 | 0.365079 | 0.182540 | − | 0.983199i | \(-0.441568\pi\) | ||||
0.182540 | + | 0.983199i | \(0.441568\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.9373 | 0.792499 | 0.396250 | − | 0.918143i | \(-0.370311\pi\) | ||||
0.396250 | + | 0.918143i | \(0.370311\pi\) | |||||||
\(572\) | 8.70850 | 0.364121 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | −0.500870 | ||||||||
\(575\) | 2.29150 | 0.0955623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.7085 | 1.19515 | 0.597575 | − | 0.801813i | \(-0.296131\pi\) | ||||
0.597575 | + | 0.801813i | \(0.296131\pi\) | |||||||
\(578\) | −6.16601 | −0.256472 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.2915 | 0.634945 | ||||||||
\(581\) | 27.2915 | 1.13224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.70850 | 0.112174 | ||||||||
\(584\) | −7.29150 | −0.301725 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.2288 | 1.33136 | ||||||||
\(587\) | 20.7085 | 0.854731 | 0.427366 | − | 0.904079i | \(-0.359442\pi\) | ||||
0.427366 | + | 0.904079i | \(0.359442\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.457513 | −0.0188515 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.93725 | 0.285119 | ||||||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.8340 | −0.444150 | ||||||||
\(596\) | −10.3542 | −0.424127 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.29150 | −0.216386 | ||||||||
\(599\) | −30.5830 | −1.24959 | −0.624794 | − | 0.780790i | \(-0.714817\pi\) | ||||
−0.624794 | + | 0.780790i | \(0.714817\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.4575 | −1.32397 | −0.661985 | − | 0.749517i | \(-0.730286\pi\) | ||||
−0.661985 | + | 0.749517i | \(0.730286\pi\) | |||||||
\(602\) | 0.708497 | 0.0288762 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.2915 | 0.703581 | ||||||||
\(605\) | 13.6458 | 0.554779 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.8745 | 1.45610 | 0.728051 | − | 0.685523i | \(-0.240427\pi\) | ||||
0.728051 | + | 0.685523i | \(0.240427\pi\) | |||||||
\(608\) | 0.354249 | 0.0143667 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.583005 | −0.0236052 | ||||||||
\(611\) | −31.7490 | −1.28443 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.93725 | −0.118635 | −0.0593173 | − | 0.998239i | \(-0.518892\pi\) | ||||
−0.0593173 | + | 0.998239i | \(0.518892\pi\) | |||||||
\(614\) | 29.8745 | 1.20564 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.29150 | 0.132618 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.3542 | 0.496559 | 0.248280 | − | 0.968688i | \(-0.420135\pi\) | ||||
0.248280 | + | 0.968688i | \(0.420135\pi\) | |||||||
\(620\) | 2.12549 | 0.0853618 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.1660 | −0.527909 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.29150 | −0.331660 | ||||||||
\(626\) | 5.29150 | 0.211491 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.64575 | 0.145481 | ||||||||
\(629\) | 22.8340 | 0.910451 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.8745 | 0.950429 | 0.475215 | − | 0.879870i | \(-0.342370\pi\) | ||||
0.475215 | + | 0.879870i | \(0.342370\pi\) | |||||||
\(632\) | 8.58301 | 0.341414 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.2915 | −0.845594 | ||||||||
\(635\) | 17.4170 | 0.691172 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.8745 | −0.628971 | ||||||||
\(638\) | −15.2915 | −0.605396 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.64575 | −0.0650540 | ||||||||
\(641\) | 28.4575 | 1.12400 | 0.562002 | − | 0.827136i | \(-0.310031\pi\) | ||||
0.562002 | + | 0.827136i | \(0.310031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3542 | 0.960438 | 0.480219 | − | 0.877149i | \(-0.340557\pi\) | ||||
0.480219 | + | 0.877149i | \(0.340557\pi\) | |||||||
\(644\) | −2.00000 | −0.0788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.16601 | 0.0458761 | ||||||||
\(647\) | −13.1660 | −0.517609 | −0.258805 | − | 0.965930i | \(-0.583329\pi\) | ||||
−0.258805 | + | 0.965930i | \(0.583329\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −12.1255 | −0.475601 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.708497 | −0.0277469 | ||||||||
\(653\) | 15.8745 | 0.621217 | 0.310609 | − | 0.950538i | \(-0.399467\pi\) | ||||
0.310609 | + | 0.950538i | \(0.399467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.0000 | −1.40664 | ||||||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | −7.06275 | −0.275126 | −0.137563 | − | 0.990493i | \(-0.543927\pi\) | ||||
−0.137563 | + | 0.990493i | \(0.543927\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.6458 | 1.07530 | 0.537648 | − | 0.843170i | \(-0.319313\pi\) | ||||
0.537648 | + | 0.843170i | \(0.319313\pi\) | |||||||
\(662\) | −25.8745 | −1.00564 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.6458 | 0.529558 | ||||||||
\(665\) | −1.16601 | −0.0452159 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.29150 | 0.359768 | ||||||||
\(668\) | 19.1660 | 0.741555 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.5830 | 0.949724 | ||||||||
\(671\) | 0.583005 | 0.0225067 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.7085 | −0.489877 | −0.244938 | − | 0.969539i | \(-0.578768\pi\) | ||||
−0.244938 | + | 0.969539i | \(0.578768\pi\) | |||||||
\(674\) | 15.1660 | 0.584173 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.0000 | 0.576923 | ||||||||
\(677\) | 7.06275 | 0.271443 | 0.135722 | − | 0.990747i | \(-0.456665\pi\) | ||||
0.135722 | + | 0.990747i | \(0.456665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.58301 | −0.0991266 | ||||||||
\(680\) | −5.41699 | −0.207732 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.12549 | −0.0813893 | ||||||||
\(683\) | 33.8745 | 1.29617 | 0.648086 | − | 0.761567i | \(-0.275570\pi\) | ||||
0.648086 | + | 0.761567i | \(0.275570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.0000 | 1.37549 | ||||||||
\(686\) | −20.0000 | −0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.354249 | 0.0135056 | ||||||||
\(689\) | 8.70850 | 0.331767 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.8745 | 0.679978 | 0.339989 | − | 0.940429i | \(-0.389577\pi\) | ||||
0.339989 | + | 0.940429i | \(0.389577\pi\) | |||||||
\(692\) | 15.8745 | 0.603458 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.2915 | −0.580458 | ||||||||
\(695\) | 6.58301 | 0.249708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.7490 | −0.748047 | ||||||||
\(698\) | 2.00000 | 0.0757011 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.58301 | −0.173221 | ||||||||
\(701\) | 19.0627 | 0.719990 | 0.359995 | − | 0.932954i | \(-0.382778\pi\) | ||||
0.359995 | + | 0.932954i | \(0.382778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45751 | 0.0926869 | ||||||||
\(704\) | 1.64575 | 0.0620266 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.58301 | 0.247755 | ||||||||
\(707\) | −18.5830 | −0.698886 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.9373 | −1.46232 | −0.731160 | − | 0.682206i | \(-0.761021\pi\) | ||||
−0.731160 | + | 0.682206i | \(0.761021\pi\) | |||||||
\(710\) | −9.87451 | −0.370584 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.29150 | 0.0483672 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3320 | −0.535987 | ||||||||
\(716\) | −15.2915 | −0.571470 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 21.8745 | 0.816349 | ||||||||
\(719\) | 19.7490 | 0.736514 | 0.368257 | − | 0.929724i | \(-0.379955\pi\) | ||||
0.368257 | + | 0.929724i | \(0.379955\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4170 | −0.499675 | ||||||||
\(722\) | −18.8745 | −0.702436 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.6458 | 0.581470 | ||||||||
\(725\) | 21.2915 | 0.790747 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.3320 | 1.49583 | 0.747916 | − | 0.663793i | \(-0.231055\pi\) | ||||
0.747916 | + | 0.663793i | \(0.231055\pi\) | |||||||
\(728\) | 10.5830 | 0.392232 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.0000 | 0.444140 | ||||||||
\(731\) | 1.16601 | 0.0431265 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.3948 | −1.15959 | −0.579796 | − | 0.814762i | \(-0.696868\pi\) | ||||
−0.579796 | + | 0.814762i | \(0.696868\pi\) | |||||||
\(734\) | −11.1660 | −0.412145 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −24.5830 | −0.905527 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5830 | −0.389302 | −0.194651 | − | 0.980873i | \(-0.562357\pi\) | ||||
−0.194651 | + | 0.980873i | \(0.562357\pi\) | |||||||
\(740\) | −11.4170 | −0.419697 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.29150 | 0.120835 | ||||||||
\(743\) | 19.7490 | 0.724521 | 0.362261 | − | 0.932077i | \(-0.382005\pi\) | ||||
0.362261 | + | 0.932077i | \(0.382005\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.0405 | 0.624316 | ||||||||
\(746\) | −26.9373 | −0.986243 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.41699 | 0.198065 | ||||||||
\(749\) | 27.2915 | 0.997210 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.4575 | 1.54930 | 0.774648 | − | 0.632392i | \(-0.217927\pi\) | ||||
0.774648 | + | 0.632392i | \(0.217927\pi\) | |||||||
\(752\) | −6.00000 | −0.218797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −49.1660 | −1.79052 | ||||||||
\(755\) | −28.4575 | −1.03567 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.77124 | 0.209759 | 0.104880 | − | 0.994485i | \(-0.466554\pi\) | ||||
0.104880 | + | 0.994485i | \(0.466554\pi\) | |||||||
\(758\) | −33.5203 | −1.21751 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.583005 | −0.0211478 | ||||||||
\(761\) | 12.0000 | 0.435000 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.4575 | −1.31985 | ||||||||
\(764\) | −3.29150 | −0.119082 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.7490 | −1.14714 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.0405 | 0.902984 | 0.451492 | − | 0.892275i | \(-0.350892\pi\) | ||||
0.451492 | + | 0.892275i | \(0.350892\pi\) | |||||||
\(770\) | −5.41699 | −0.195215 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −22.0000 | −0.791797 | ||||||||
\(773\) | 1.64575 | 0.0591936 | 0.0295968 | − | 0.999562i | \(-0.490578\pi\) | ||||
0.0295968 | + | 0.999562i | \(0.490578\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.95948 | 0.106308 | ||||||||
\(776\) | −1.29150 | −0.0463622 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.06275 | 0.253212 | ||||||||
\(779\) | −2.12549 | −0.0761537 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.87451 | 0.353338 | ||||||||
\(782\) | −3.29150 | −0.117704 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | −6.00000 | −0.214149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.3542 | −1.58106 | −0.790529 | − | 0.612424i | \(-0.790194\pi\) | ||||
−0.790529 | + | 0.612424i | \(0.790194\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.1255 | −0.502562 | ||||||||
\(791\) | −13.1660 | −0.468129 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.87451 | 0.0665657 | ||||||||
\(794\) | 2.00000 | 0.0709773 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.0000 | 0.496217 | ||||||||
\(797\) | 35.5203 | 1.25819 | 0.629096 | − | 0.777328i | \(-0.283425\pi\) | ||||
0.629096 | + | 0.777328i | \(0.283425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.7490 | −0.698670 | ||||||||
\(800\) | −2.29150 | −0.0810169 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.87451 | −0.348681 | ||||||||
\(803\) | −12.0000 | −0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.29150 | 0.116010 | ||||||||
\(806\) | −6.83399 | −0.240717 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.29150 | −0.326874 | ||||||||
\(809\) | 12.0000 | 0.421898 | 0.210949 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210949 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.8745 | 1.04904 | 0.524518 | − | 0.851399i | \(-0.324246\pi\) | ||||
0.524518 | + | 0.851399i | \(0.324246\pi\) | |||||||
\(812\) | −18.5830 | −0.652136 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.4170 | 0.400165 | ||||||||
\(815\) | 1.16601 | 0.0408436 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.125492 | 0.00439041 | ||||||||
\(818\) | 15.1660 | 0.530267 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.87451 | 0.344833 | ||||||||
\(821\) | 8.12549 | 0.283582 | 0.141791 | − | 0.989897i | \(-0.454714\pi\) | ||||
0.141791 | + | 0.989897i | \(0.454714\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.2915 | −0.463313 | −0.231656 | − | 0.972798i | \(-0.574414\pi\) | ||||
−0.231656 | + | 0.972798i | \(0.574414\pi\) | |||||||
\(824\) | −6.70850 | −0.233702 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.8118 | 0.515055 | 0.257528 | − | 0.966271i | \(-0.417092\pi\) | ||||
0.257528 | + | 0.966271i | \(0.417092\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.4170 | −0.535454 | −0.267727 | − | 0.963495i | \(-0.586273\pi\) | ||||
−0.267727 | + | 0.963495i | \(0.586273\pi\) | |||||||
\(830\) | −22.4575 | −0.779512 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.29150 | 0.183450 | ||||||||
\(833\) | −9.87451 | −0.342131 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.5425 | −1.09157 | ||||||||
\(836\) | 0.583005 | 0.0201637 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.9373 | −0.585088 | ||||||||
\(839\) | −43.7490 | −1.51038 | −0.755192 | − | 0.655504i | \(-0.772456\pi\) | ||||
−0.755192 | + | 0.655504i | \(0.772456\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57.3320 | 1.97697 | ||||||||
\(842\) | 22.2288 | 0.766054 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.2915 | 0.388670 | ||||||||
\(845\) | −24.6863 | −0.849233 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.5830 | −0.569799 | ||||||||
\(848\) | 1.64575 | 0.0565153 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.54249 | −0.258705 | ||||||||
\(851\) | −6.93725 | −0.237806 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.1660 | 0.930146 | 0.465073 | − | 0.885272i | \(-0.346028\pi\) | ||||
0.465073 | + | 0.885272i | \(0.346028\pi\) | |||||||
\(854\) | 0.708497 | 0.0242443 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.6458 | 0.466402 | ||||||||
\(857\) | −36.0000 | −1.22974 | −0.614868 | − | 0.788630i | \(-0.710791\pi\) | ||||
−0.614868 | + | 0.788630i | \(0.710791\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.4170 | 0.457782 | 0.228891 | − | 0.973452i | \(-0.426490\pi\) | ||||
0.228891 | + | 0.973452i | \(0.426490\pi\) | |||||||
\(860\) | −0.583005 | −0.0198803 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.8745 | 1.15377 | ||||||||
\(863\) | −10.8340 | −0.368793 | −0.184397 | − | 0.982852i | \(-0.559033\pi\) | ||||
−0.184397 | + | 0.982852i | \(0.559033\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −26.1255 | −0.888293 | ||||||||
\(866\) | −18.7085 | −0.635741 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.58301 | −0.0876729 | ||||||||
\(869\) | 14.1255 | 0.479175 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −79.0405 | −2.67819 | ||||||||
\(872\) | −18.2288 | −0.617304 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.354249 | −0.0119826 | ||||||||
\(875\) | 24.0000 | 0.811348 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.2915 | −0.448822 | −0.224411 | − | 0.974495i | \(-0.572046\pi\) | ||||
−0.224411 | + | 0.974495i | \(0.572046\pi\) | |||||||
\(878\) | 27.7490 | 0.936484 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.70850 | −0.0913034 | ||||||||
\(881\) | −31.7490 | −1.06965 | −0.534826 | − | 0.844962i | \(-0.679623\pi\) | ||||
−0.534826 | + | 0.844962i | \(0.679623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.29150 | −0.245379 | −0.122689 | − | 0.992445i | \(-0.539152\pi\) | ||||
−0.122689 | + | 0.992445i | \(0.539152\pi\) | |||||||
\(884\) | 17.4170 | 0.585797 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.1660 | −0.845469 | ||||||||
\(887\) | −25.7490 | −0.864567 | −0.432284 | − | 0.901738i | \(-0.642292\pi\) | ||||
−0.432284 | + | 0.901738i | \(0.642292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.1660 | −0.709885 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.8745 | −0.665448 | ||||||||
\(893\) | −2.12549 | −0.0711269 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.1660 | 0.841207 | ||||||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.4170 | −0.380990 | ||||||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.41699 | 0.180466 | ||||||||
\(902\) | −9.87451 | −0.328785 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.58301 | −0.218947 | ||||||||
\(905\) | −25.7490 | −0.855926 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.5203 | −1.51148 | −0.755738 | − | 0.654874i | \(-0.772722\pi\) | ||||
−0.755738 | + | 0.654874i | \(0.772722\pi\) | |||||||
\(908\) | 7.06275 | 0.234385 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −17.4170 | −0.577368 | ||||||||
\(911\) | −3.29150 | −0.109052 | −0.0545262 | − | 0.998512i | \(-0.517365\pi\) | ||||
−0.0545262 | + | 0.998512i | \(0.517365\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.4575 | 0.743235 | ||||||||
\(914\) | −0.125492 | −0.00415091 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.06275 | 0.299442 | ||||||||
\(917\) | 43.7490 | 1.44472 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.0000 | −1.12156 | −0.560778 | − | 0.827966i | \(-0.689498\pi\) | ||||
−0.560778 | + | 0.827966i | \(0.689498\pi\) | |||||||
\(920\) | 1.64575 | 0.0542588 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −25.7490 | −0.847999 | ||||||||
\(923\) | 31.7490 | 1.04503 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.8967 | −0.522681 | ||||||||
\(926\) | 21.1660 | 0.695558 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.29150 | −0.305009 | ||||||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.06275 | −0.0348301 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.6458 | −0.446503 | ||||||||
\(935\) | −8.91503 | −0.291553 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.5830 | −0.933766 | −0.466883 | − | 0.884319i | \(-0.654623\pi\) | ||||
−0.466883 | + | 0.884319i | \(0.654623\pi\) | |||||||
\(938\) | −29.8745 | −0.975437 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.87451 | 0.322071 | ||||||||
\(941\) | 26.8118 | 0.874038 | 0.437019 | − | 0.899452i | \(-0.356034\pi\) | ||||
0.437019 | + | 0.899452i | \(0.356034\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.00000 | 0.195387 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.583005 | 0.0189551 | ||||||||
\(947\) | −2.12549 | −0.0690692 | −0.0345346 | − | 0.999404i | \(-0.510995\pi\) | ||||
−0.0345346 | + | 0.999404i | \(0.510995\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −38.5830 | −1.25246 | ||||||||
\(950\) | −0.811762 | −0.0263370 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.58301 | 0.213356 | ||||||||
\(953\) | 23.0405 | 0.746356 | 0.373178 | − | 0.927760i | \(-0.378268\pi\) | ||||
0.373178 | + | 0.927760i | \(0.378268\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.41699 | 0.175290 | ||||||||
\(956\) | −24.0000 | −0.776215 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −42.5830 | −1.37579 | ||||||||
\(959\) | −43.7490 | −1.41273 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3320 | −0.946194 | ||||||||
\(962\) | 36.7085 | 1.18353 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.29150 | 0.170428 | ||||||||
\(965\) | 36.2065 | 1.16553 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.8745 | 0.767752 | 0.383876 | − | 0.923385i | \(-0.374589\pi\) | ||||
0.383876 | + | 0.923385i | \(0.374589\pi\) | |||||||
\(968\) | −8.29150 | −0.266499 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.12549 | 0.0682454 | ||||||||
\(971\) | 20.2288 | 0.649172 | 0.324586 | − | 0.945856i | \(-0.394775\pi\) | ||||
0.324586 | + | 0.945856i | \(0.394775\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 21.1660 | 0.678203 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.354249 | 0.0113392 | ||||||||
\(977\) | 21.8745 | 0.699828 | 0.349914 | − | 0.936782i | \(-0.386211\pi\) | ||||
0.349914 | + | 0.936782i | \(0.386211\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.93725 | 0.157715 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.8745 | 0.698044 | ||||||||
\(983\) | 21.8745 | 0.697688 | 0.348844 | − | 0.937181i | \(-0.386574\pi\) | ||||
0.348844 | + | 0.937181i | \(0.386574\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.87451 | −0.314628 | ||||||||
\(986\) | −30.5830 | −0.973961 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.87451 | 0.0596360 | ||||||||
\(989\) | −0.354249 | −0.0112645 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.4575 | −0.459258 | −0.229629 | − | 0.973278i | \(-0.573751\pi\) | ||||
−0.229629 | + | 0.973278i | \(0.573751\pi\) | |||||||
\(992\) | −1.29150 | −0.0410052 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 12.0000 | 0.380617 | ||||||||
\(995\) | −23.0405 | −0.730434 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.5830 | −1.28528 | −0.642638 | − | 0.766170i | \(-0.722160\pi\) | ||||
−0.642638 | + | 0.766170i | \(0.722160\pi\) | |||||||
\(998\) | 31.0405 | 0.982570 | ||||||||
\(999\) | 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 | 414.2.a.g.1.1 | yes | 2 | |
3.2 | odd | 2 | 414.2.a.e.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 3312.2.a.z.1.1 | 2 | |||
12.11 | even | 2 | 3312.2.a.v.1.2 | 2 | |||
23.22 | odd | 2 | 9522.2.a.bc.1.2 | 2 | |||
69.68 | even | 2 | 9522.2.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.2.a.e.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
414.2.a.g.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
3312.2.a.v.1.2 | 2 | 12.11 | even | 2 | |||
3312.2.a.z.1.1 | 2 | 4.3 | odd | 2 | |||
9522.2.a.bb.1.1 | 2 | 69.68 | even | 2 | |||
9522.2.a.bc.1.2 | 2 | 23.22 | odd | 2 |