Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1425,2,Mod(1,1425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1425, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1425.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1425 = 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1425.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: | \(11.3786822880\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 285) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1425.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64575 | −1.87083 | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||||
−0.935414 | + | 0.353553i | \(0.884973\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 5.00000 | 2.50000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.64575 | −1.08012 | ||||||||
\(7\) | 3.64575 | 1.37796 | 0.688982 | − | 0.724778i | \(-0.258058\pi\) | ||||
0.688982 | + | 0.724778i | \(0.258058\pi\) | |||||||
\(8\) | −7.93725 | −2.80624 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.64575 | 1.70226 | 0.851129 | − | 0.524957i | \(-0.175918\pi\) | ||||
0.851129 | + | 0.524957i | \(0.175918\pi\) | |||||||
\(12\) | 5.00000 | 1.44338 | ||||||||
\(13\) | 5.64575 | 1.56585 | 0.782925 | − | 0.622116i | \(-0.213727\pi\) | ||||
0.782925 | + | 0.622116i | \(0.213727\pi\) | |||||||
\(14\) | −9.64575 | −2.57794 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.0000 | 2.75000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | −2.64575 | −0.623610 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.64575 | 0.795568 | ||||||||
\(22\) | −14.9373 | −3.18463 | ||||||||
\(23\) | 1.29150 | 0.269297 | 0.134648 | − | 0.990893i | \(-0.457009\pi\) | ||||
0.134648 | + | 0.990893i | \(0.457009\pi\) | |||||||
\(24\) | −7.93725 | −1.62019 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −14.9373 | −2.92944 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 18.2288 | 3.44491 | ||||||||
\(29\) | −6.93725 | −1.28822 | −0.644108 | − | 0.764935i | \(-0.722771\pi\) | ||||
−0.644108 | + | 0.764935i | \(0.722771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −13.2288 | −2.33854 | ||||||||
\(33\) | 5.64575 | 0.982799 | ||||||||
\(34\) | −10.5830 | −1.81497 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.00000 | 0.833333 | ||||||||
\(37\) | 1.64575 | 0.270560 | 0.135280 | − | 0.990807i | \(-0.456807\pi\) | ||||
0.135280 | + | 0.990807i | \(0.456807\pi\) | |||||||
\(38\) | 2.64575 | 0.429198 | ||||||||
\(39\) | 5.64575 | 0.904044 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.35425 | −0.680019 | −0.340010 | − | 0.940422i | \(-0.610430\pi\) | ||||
−0.340010 | + | 0.940422i | \(0.610430\pi\) | |||||||
\(42\) | −9.64575 | −1.48837 | ||||||||
\(43\) | −0.354249 | −0.0540224 | −0.0270112 | − | 0.999635i | \(-0.508599\pi\) | ||||
−0.0270112 | + | 0.999635i | \(0.508599\pi\) | |||||||
\(44\) | 28.2288 | 4.25565 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.41699 | −0.503808 | ||||||||
\(47\) | −9.29150 | −1.35530 | −0.677652 | − | 0.735382i | \(-0.737003\pi\) | ||||
−0.677652 | + | 0.735382i | \(0.737003\pi\) | |||||||
\(48\) | 11.0000 | 1.58771 | ||||||||
\(49\) | 6.29150 | 0.898786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 28.2288 | 3.91462 | ||||||||
\(53\) | −0.708497 | −0.0973196 | −0.0486598 | − | 0.998815i | \(-0.515495\pi\) | ||||
−0.0486598 | + | 0.998815i | \(0.515495\pi\) | |||||||
\(54\) | −2.64575 | −0.360041 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −28.9373 | −3.86690 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 18.3542 | 2.41003 | ||||||||
\(59\) | 0.708497 | 0.0922385 | 0.0461193 | − | 0.998936i | \(-0.485315\pi\) | ||||
0.0461193 | + | 0.998936i | \(0.485315\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.708497 | −0.0907138 | −0.0453569 | − | 0.998971i | \(-0.514443\pi\) | ||||
−0.0453569 | + | 0.998971i | \(0.514443\pi\) | |||||||
\(62\) | −15.8745 | −2.01606 | ||||||||
\(63\) | 3.64575 | 0.459321 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −14.9373 | −1.83865 | ||||||||
\(67\) | −14.5830 | −1.78160 | −0.890799 | − | 0.454398i | \(-0.849854\pi\) | ||||
−0.890799 | + | 0.454398i | \(0.849854\pi\) | |||||||
\(68\) | 20.0000 | 2.42536 | ||||||||
\(69\) | 1.29150 | 0.155479 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.29150 | −0.390629 | −0.195315 | − | 0.980741i | \(-0.562573\pi\) | ||||
−0.195315 | + | 0.980741i | \(0.562573\pi\) | |||||||
\(72\) | −7.93725 | −0.935414 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | −4.35425 | −0.506171 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.00000 | −0.573539 | ||||||||
\(77\) | 20.5830 | 2.34565 | ||||||||
\(78\) | −14.9373 | −1.69131 | ||||||||
\(79\) | −14.5830 | −1.64072 | −0.820358 | − | 0.571850i | \(-0.806226\pi\) | ||||
−0.820358 | + | 0.571850i | \(0.806226\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.5203 | 1.27220 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 18.2288 | 1.98892 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.937254 | 0.101067 | ||||||||
\(87\) | −6.93725 | −0.743752 | ||||||||
\(88\) | −44.8118 | −4.77695 | ||||||||
\(89\) | −1.06275 | −0.112651 | −0.0563254 | − | 0.998412i | \(-0.517938\pi\) | ||||
−0.0563254 | + | 0.998412i | \(0.517938\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.5830 | 2.15769 | ||||||||
\(92\) | 6.45751 | 0.673242 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 24.5830 | 2.53554 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −13.2288 | −1.35015 | ||||||||
\(97\) | −12.9373 | −1.31358 | −0.656790 | − | 0.754074i | \(-0.728086\pi\) | ||||
−0.656790 | + | 0.754074i | \(0.728086\pi\) | |||||||
\(98\) | −16.6458 | −1.68147 | ||||||||
\(99\) | 5.64575 | 0.567419 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.29150 | −0.128509 | −0.0642547 | − | 0.997934i | \(-0.520467\pi\) | ||||
−0.0642547 | + | 0.997934i | \(0.520467\pi\) | |||||||
\(102\) | −10.5830 | −1.04787 | ||||||||
\(103\) | −10.5830 | −1.04277 | −0.521387 | − | 0.853320i | \(-0.674585\pi\) | ||||
−0.521387 | + | 0.853320i | \(0.674585\pi\) | |||||||
\(104\) | −44.8118 | −4.39415 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.87451 | 0.182068 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 5.00000 | 0.481125 | ||||||||
\(109\) | −5.29150 | −0.506834 | −0.253417 | − | 0.967357i | \(-0.581554\pi\) | ||||
−0.253417 | + | 0.967357i | \(0.581554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.64575 | 0.156208 | ||||||||
\(112\) | 40.1033 | 3.78940 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 2.64575 | 0.247797 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −34.6863 | −3.22054 | ||||||||
\(117\) | 5.64575 | 0.521950 | ||||||||
\(118\) | −1.87451 | −0.172562 | ||||||||
\(119\) | 14.5830 | 1.33682 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8745 | 1.89768 | ||||||||
\(122\) | 1.87451 | 0.169710 | ||||||||
\(123\) | −4.35425 | −0.392609 | ||||||||
\(124\) | 30.0000 | 2.69408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.64575 | −0.859312 | ||||||||
\(127\) | −4.00000 | −0.354943 | −0.177471 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177471 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(128\) | −7.93725 | −0.701561 | ||||||||
\(129\) | −0.354249 | −0.0311899 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2288 | 1.06843 | 0.534216 | − | 0.845348i | \(-0.320607\pi\) | ||||
0.534216 | + | 0.845348i | \(0.320607\pi\) | |||||||
\(132\) | 28.2288 | 2.45700 | ||||||||
\(133\) | −3.64575 | −0.316127 | ||||||||
\(134\) | 38.5830 | 3.33306 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −31.7490 | −2.72246 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | −3.41699 | −0.290874 | ||||||||
\(139\) | −13.8745 | −1.17682 | −0.588410 | − | 0.808563i | \(-0.700246\pi\) | ||||
−0.588410 | + | 0.808563i | \(0.700246\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.29150 | −0.782486 | ||||||||
\(142\) | 8.70850 | 0.730801 | ||||||||
\(143\) | 31.8745 | 2.66548 | ||||||||
\(144\) | 11.0000 | 0.916667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 26.4575 | 2.18964 | ||||||||
\(147\) | 6.29150 | 0.518914 | ||||||||
\(148\) | 8.22876 | 0.676400 | ||||||||
\(149\) | 0.583005 | 0.0477617 | 0.0238808 | − | 0.999715i | \(-0.492398\pi\) | ||||
0.0238808 | + | 0.999715i | \(0.492398\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5830 | 1.02399 | 0.511995 | − | 0.858988i | \(-0.328907\pi\) | ||||
0.511995 | + | 0.858988i | \(0.328907\pi\) | |||||||
\(152\) | 7.93725 | 0.643796 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | −54.4575 | −4.38831 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 28.2288 | 2.26011 | ||||||||
\(157\) | 2.70850 | 0.216162 | 0.108081 | − | 0.994142i | \(-0.465529\pi\) | ||||
0.108081 | + | 0.994142i | \(0.465529\pi\) | |||||||
\(158\) | 38.5830 | 3.06950 | ||||||||
\(159\) | −0.708497 | −0.0561875 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.70850 | 0.371082 | ||||||||
\(162\) | −2.64575 | −0.207870 | ||||||||
\(163\) | 7.64575 | 0.598861 | 0.299431 | − | 0.954118i | \(-0.403203\pi\) | ||||
0.299431 | + | 0.954118i | \(0.403203\pi\) | |||||||
\(164\) | −21.7712 | −1.70005 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.8745 | 1.23210 | ||||||||
\(167\) | 10.7085 | 0.828648 | 0.414324 | − | 0.910129i | \(-0.364018\pi\) | ||||
0.414324 | + | 0.910129i | \(0.364018\pi\) | |||||||
\(168\) | −28.9373 | −2.23256 | ||||||||
\(169\) | 18.8745 | 1.45189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −1.77124 | −0.135056 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 18.3542 | 1.39143 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 62.1033 | 4.68121 | ||||||||
\(177\) | 0.708497 | 0.0532539 | ||||||||
\(178\) | 2.81176 | 0.210750 | ||||||||
\(179\) | 3.29150 | 0.246018 | 0.123009 | − | 0.992406i | \(-0.460746\pi\) | ||||
0.123009 | + | 0.992406i | \(0.460746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.70850 | 0.498639 | 0.249319 | − | 0.968421i | \(-0.419793\pi\) | ||||
0.249319 | + | 0.968421i | \(0.419793\pi\) | |||||||
\(182\) | −54.4575 | −4.03666 | ||||||||
\(183\) | −0.708497 | −0.0523736 | ||||||||
\(184\) | −10.2510 | −0.755713 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.8745 | −1.16398 | ||||||||
\(187\) | 22.5830 | 1.65143 | ||||||||
\(188\) | −46.4575 | −3.38826 | ||||||||
\(189\) | 3.64575 | 0.265189 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2288 | −1.46370 | −0.731851 | − | 0.681465i | \(-0.761343\pi\) | ||||
−0.731851 | + | 0.681465i | \(0.761343\pi\) | |||||||
\(192\) | 13.0000 | 0.938194 | ||||||||
\(193\) | 6.35425 | 0.457389 | 0.228694 | − | 0.973498i | \(-0.426554\pi\) | ||||
0.228694 | + | 0.973498i | \(0.426554\pi\) | |||||||
\(194\) | 34.2288 | 2.45748 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 31.4575 | 2.24697 | ||||||||
\(197\) | −17.1660 | −1.22303 | −0.611514 | − | 0.791234i | \(-0.709439\pi\) | ||||
−0.611514 | + | 0.791234i | \(0.709439\pi\) | |||||||
\(198\) | −14.9373 | −1.06154 | ||||||||
\(199\) | −3.29150 | −0.233328 | −0.116664 | − | 0.993171i | \(-0.537220\pi\) | ||||
−0.116664 | + | 0.993171i | \(0.537220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.5830 | −1.02861 | ||||||||
\(202\) | 3.41699 | 0.240419 | ||||||||
\(203\) | −25.2915 | −1.77512 | ||||||||
\(204\) | 20.0000 | 1.40028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 28.0000 | 1.95085 | ||||||||
\(207\) | 1.29150 | 0.0897656 | ||||||||
\(208\) | 62.1033 | 4.30609 | ||||||||
\(209\) | −5.64575 | −0.390525 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.5830 | −1.27931 | −0.639653 | − | 0.768663i | \(-0.720922\pi\) | ||||
−0.639653 | + | 0.768663i | \(0.720922\pi\) | |||||||
\(212\) | −3.54249 | −0.243299 | ||||||||
\(213\) | −3.29150 | −0.225530 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.93725 | −0.540062 | ||||||||
\(217\) | 21.8745 | 1.48494 | ||||||||
\(218\) | 14.0000 | 0.948200 | ||||||||
\(219\) | −10.0000 | −0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.5830 | 1.51910 | ||||||||
\(222\) | −4.35425 | −0.292238 | ||||||||
\(223\) | 18.5830 | 1.24441 | 0.622205 | − | 0.782854i | \(-0.286237\pi\) | ||||
0.622205 | + | 0.782854i | \(0.286237\pi\) | |||||||
\(224\) | −48.2288 | −3.22242 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.5830 | −0.703971 | ||||||||
\(227\) | 21.2915 | 1.41317 | 0.706583 | − | 0.707630i | \(-0.250236\pi\) | ||||
0.706583 | + | 0.707630i | \(0.250236\pi\) | |||||||
\(228\) | −5.00000 | −0.331133 | ||||||||
\(229\) | 19.2915 | 1.27482 | 0.637409 | − | 0.770525i | \(-0.280006\pi\) | ||||
0.637409 | + | 0.770525i | \(0.280006\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.5830 | 1.35426 | ||||||||
\(232\) | 55.0627 | 3.61505 | ||||||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | −14.9373 | −0.976479 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.54249 | 0.230596 | ||||||||
\(237\) | −14.5830 | −0.947268 | ||||||||
\(238\) | −38.5830 | −2.50096 | ||||||||
\(239\) | 10.3542 | 0.669761 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.58301 | −0.295217 | −0.147609 | − | 0.989046i | \(-0.547158\pi\) | ||||
−0.147609 | + | 0.989046i | \(0.547158\pi\) | |||||||
\(242\) | −55.2288 | −3.55024 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.54249 | −0.226784 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.5203 | 0.734505 | ||||||||
\(247\) | −5.64575 | −0.359231 | ||||||||
\(248\) | −47.6235 | −3.02410 | ||||||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.6458 | −1.36627 | −0.683134 | − | 0.730293i | \(-0.739383\pi\) | ||||
−0.683134 | + | 0.730293i | \(0.739383\pi\) | |||||||
\(252\) | 18.2288 | 1.14830 | ||||||||
\(253\) | 7.29150 | 0.458413 | ||||||||
\(254\) | 10.5830 | 0.664037 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.00000 | −0.312500 | ||||||||
\(257\) | 26.5830 | 1.65820 | 0.829101 | − | 0.559099i | \(-0.188853\pi\) | ||||
0.829101 | + | 0.559099i | \(0.188853\pi\) | |||||||
\(258\) | 0.937254 | 0.0583509 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.93725 | −0.429405 | ||||||||
\(262\) | −32.3542 | −1.99885 | ||||||||
\(263\) | 16.5830 | 1.02255 | 0.511276 | − | 0.859417i | \(-0.329173\pi\) | ||||
0.511276 | + | 0.859417i | \(0.329173\pi\) | |||||||
\(264\) | −44.8118 | −2.75797 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.64575 | 0.591419 | ||||||||
\(267\) | −1.06275 | −0.0650390 | ||||||||
\(268\) | −72.9150 | −4.45399 | ||||||||
\(269\) | −22.2288 | −1.35531 | −0.677656 | − | 0.735379i | \(-0.737004\pi\) | ||||
−0.677656 | + | 0.735379i | \(0.737004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2915 | −0.928893 | −0.464446 | − | 0.885601i | \(-0.653747\pi\) | ||||
−0.464446 | + | 0.885601i | \(0.653747\pi\) | |||||||
\(272\) | 44.0000 | 2.66789 | ||||||||
\(273\) | 20.5830 | 1.24574 | ||||||||
\(274\) | 15.8745 | 0.959014 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.45751 | 0.388697 | ||||||||
\(277\) | 20.5830 | 1.23671 | 0.618356 | − | 0.785898i | \(-0.287799\pi\) | ||||
0.618356 | + | 0.785898i | \(0.287799\pi\) | |||||||
\(278\) | 36.7085 | 2.20163 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.77124 | −0.344284 | −0.172142 | − | 0.985072i | \(-0.555069\pi\) | ||||
−0.172142 | + | 0.985072i | \(0.555069\pi\) | |||||||
\(282\) | 24.5830 | 1.46390 | ||||||||
\(283\) | −25.5203 | −1.51702 | −0.758511 | − | 0.651660i | \(-0.774073\pi\) | ||||
−0.758511 | + | 0.651660i | \(0.774073\pi\) | |||||||
\(284\) | −16.4575 | −0.976574 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −84.3320 | −4.98666 | ||||||||
\(287\) | −15.8745 | −0.937043 | ||||||||
\(288\) | −13.2288 | −0.779512 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.9373 | −0.758395 | ||||||||
\(292\) | −50.0000 | −2.92603 | ||||||||
\(293\) | −26.5830 | −1.55300 | −0.776498 | − | 0.630120i | \(-0.783006\pi\) | ||||
−0.776498 | + | 0.630120i | \(0.783006\pi\) | |||||||
\(294\) | −16.6458 | −0.970800 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −13.0627 | −0.759257 | ||||||||
\(297\) | 5.64575 | 0.327600 | ||||||||
\(298\) | −1.54249 | −0.0893539 | ||||||||
\(299\) | 7.29150 | 0.421678 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.29150 | −0.0744410 | ||||||||
\(302\) | −33.2915 | −1.91571 | ||||||||
\(303\) | −1.29150 | −0.0741949 | ||||||||
\(304\) | −11.0000 | −0.630893 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.5830 | −0.604990 | ||||||||
\(307\) | −28.4575 | −1.62416 | −0.812078 | − | 0.583549i | \(-0.801664\pi\) | ||||
−0.812078 | + | 0.583549i | \(0.801664\pi\) | |||||||
\(308\) | 102.915 | 5.86413 | ||||||||
\(309\) | −10.5830 | −0.602046 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.06275 | 0.400492 | 0.200246 | − | 0.979746i | \(-0.435826\pi\) | ||||
0.200246 | + | 0.979746i | \(0.435826\pi\) | |||||||
\(312\) | −44.8118 | −2.53697 | ||||||||
\(313\) | −6.70850 | −0.379187 | −0.189593 | − | 0.981863i | \(-0.560717\pi\) | ||||
−0.189593 | + | 0.981863i | \(0.560717\pi\) | |||||||
\(314\) | −7.16601 | −0.404401 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −72.9150 | −4.10179 | ||||||||
\(317\) | 32.4575 | 1.82300 | 0.911498 | − | 0.411305i | \(-0.134927\pi\) | ||||
0.911498 | + | 0.411305i | \(0.134927\pi\) | |||||||
\(318\) | 1.87451 | 0.105117 | ||||||||
\(319\) | −39.1660 | −2.19288 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.4575 | −0.694230 | ||||||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | 5.00000 | 0.277778 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.2288 | −1.12037 | ||||||||
\(327\) | −5.29150 | −0.292621 | ||||||||
\(328\) | 34.5608 | 1.90830 | ||||||||
\(329\) | −33.8745 | −1.86756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.5830 | 1.79092 | 0.895462 | − | 0.445138i | \(-0.146845\pi\) | ||||
0.895462 | + | 0.445138i | \(0.146845\pi\) | |||||||
\(332\) | −30.0000 | −1.64646 | ||||||||
\(333\) | 1.64575 | 0.0901866 | ||||||||
\(334\) | −28.3320 | −1.55026 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 40.1033 | 2.18781 | ||||||||
\(337\) | 0.937254 | 0.0510555 | 0.0255277 | − | 0.999674i | \(-0.491873\pi\) | ||||
0.0255277 | + | 0.999674i | \(0.491873\pi\) | |||||||
\(338\) | −49.9373 | −2.71623 | ||||||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.8745 | 1.83441 | ||||||||
\(342\) | 2.64575 | 0.143066 | ||||||||
\(343\) | −2.58301 | −0.139469 | ||||||||
\(344\) | 2.81176 | 0.151600 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.0000 | −1.39575 | −0.697877 | − | 0.716218i | \(-0.745872\pi\) | ||||
−0.697877 | + | 0.716218i | \(0.745872\pi\) | |||||||
\(348\) | −34.6863 | −1.85938 | ||||||||
\(349\) | −19.1660 | −1.02593 | −0.512967 | − | 0.858409i | \(-0.671454\pi\) | ||||
−0.512967 | + | 0.858409i | \(0.671454\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.64575 | 0.301348 | ||||||||
\(352\) | −74.6863 | −3.98079 | ||||||||
\(353\) | 20.5830 | 1.09552 | 0.547761 | − | 0.836635i | \(-0.315480\pi\) | ||||
0.547761 | + | 0.836635i | \(0.315480\pi\) | |||||||
\(354\) | −1.87451 | −0.0996290 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.31373 | −0.281627 | ||||||||
\(357\) | 14.5830 | 0.771814 | ||||||||
\(358\) | −8.70850 | −0.460258 | ||||||||
\(359\) | 22.1033 | 1.16657 | 0.583283 | − | 0.812269i | \(-0.301768\pi\) | ||||
0.583283 | + | 0.812269i | \(0.301768\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −17.7490 | −0.932868 | ||||||||
\(363\) | 20.8745 | 1.09563 | ||||||||
\(364\) | 102.915 | 5.39421 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.87451 | 0.0979821 | ||||||||
\(367\) | 3.64575 | 0.190307 | 0.0951533 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951533 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(368\) | 14.2065 | 0.740567 | ||||||||
\(369\) | −4.35425 | −0.226673 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.58301 | −0.134103 | ||||||||
\(372\) | 30.0000 | 1.55543 | ||||||||
\(373\) | −20.9373 | −1.08409 | −0.542045 | − | 0.840349i | \(-0.682350\pi\) | ||||
−0.542045 | + | 0.840349i | \(0.682350\pi\) | |||||||
\(374\) | −59.7490 | −3.08955 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 73.7490 | 3.80332 | ||||||||
\(377\) | −39.1660 | −2.01715 | ||||||||
\(378\) | −9.64575 | −0.496124 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 53.5203 | 2.73833 | ||||||||
\(383\) | −2.58301 | −0.131985 | −0.0659927 | − | 0.997820i | \(-0.521021\pi\) | ||||
−0.0659927 | + | 0.997820i | \(0.521021\pi\) | |||||||
\(384\) | −7.93725 | −0.405046 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.8118 | −0.855696 | ||||||||
\(387\) | −0.354249 | −0.0180075 | ||||||||
\(388\) | −64.6863 | −3.28395 | ||||||||
\(389\) | −6.00000 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.16601 | 0.261256 | ||||||||
\(392\) | −49.9373 | −2.52221 | ||||||||
\(393\) | 12.2288 | 0.616859 | ||||||||
\(394\) | 45.4170 | 2.28808 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 28.2288 | 1.41855 | ||||||||
\(397\) | 2.00000 | 0.100377 | 0.0501886 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501886 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(398\) | 8.70850 | 0.436518 | ||||||||
\(399\) | −3.64575 | −0.182516 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.9373 | 0.546180 | 0.273090 | − | 0.961988i | \(-0.411954\pi\) | ||||
0.273090 | + | 0.961988i | \(0.411954\pi\) | |||||||
\(402\) | 38.5830 | 1.92435 | ||||||||
\(403\) | 33.8745 | 1.68741 | ||||||||
\(404\) | −6.45751 | −0.321273 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 66.9150 | 3.32094 | ||||||||
\(407\) | 9.29150 | 0.460563 | ||||||||
\(408\) | −31.7490 | −1.57181 | ||||||||
\(409\) | −17.2915 | −0.855010 | −0.427505 | − | 0.904013i | \(-0.640607\pi\) | ||||
−0.427505 | + | 0.904013i | \(0.640607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | −52.9150 | −2.60694 | ||||||||
\(413\) | 2.58301 | 0.127101 | ||||||||
\(414\) | −3.41699 | −0.167936 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −74.6863 | −3.66180 | ||||||||
\(417\) | −13.8745 | −0.679438 | ||||||||
\(418\) | 14.9373 | 0.730605 | ||||||||
\(419\) | 23.0627 | 1.12669 | 0.563344 | − | 0.826222i | \(-0.309514\pi\) | ||||
0.563344 | + | 0.826222i | \(0.309514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.41699 | 0.361482 | 0.180741 | − | 0.983531i | \(-0.442150\pi\) | ||||
0.180741 | + | 0.983531i | \(0.442150\pi\) | |||||||
\(422\) | 49.1660 | 2.39336 | ||||||||
\(423\) | −9.29150 | −0.451768 | ||||||||
\(424\) | 5.62352 | 0.273102 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.70850 | 0.421928 | ||||||||
\(427\) | −2.58301 | −0.125000 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 31.8745 | 1.53892 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.29150 | −0.351219 | −0.175610 | − | 0.984460i | \(-0.556190\pi\) | ||||
−0.175610 | + | 0.984460i | \(0.556190\pi\) | |||||||
\(432\) | 11.0000 | 0.529238 | ||||||||
\(433\) | 22.3542 | 1.07428 | 0.537138 | − | 0.843494i | \(-0.319505\pi\) | ||||
0.537138 | + | 0.843494i | \(0.319505\pi\) | |||||||
\(434\) | −57.8745 | −2.77807 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.4575 | −1.26709 | ||||||||
\(437\) | −1.29150 | −0.0617809 | ||||||||
\(438\) | 26.4575 | 1.26419 | ||||||||
\(439\) | −22.5830 | −1.07783 | −0.538914 | − | 0.842361i | \(-0.681165\pi\) | ||||
−0.538914 | + | 0.842361i | \(0.681165\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.29150 | 0.299595 | ||||||||
\(442\) | −59.7490 | −2.84197 | ||||||||
\(443\) | −37.2915 | −1.77177 | −0.885886 | − | 0.463902i | \(-0.846449\pi\) | ||||
−0.885886 | + | 0.463902i | \(0.846449\pi\) | |||||||
\(444\) | 8.22876 | 0.390520 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −49.1660 | −2.32808 | ||||||||
\(447\) | 0.583005 | 0.0275752 | ||||||||
\(448\) | 47.3948 | 2.23919 | ||||||||
\(449\) | −9.77124 | −0.461133 | −0.230567 | − | 0.973057i | \(-0.574058\pi\) | ||||
−0.230567 | + | 0.973057i | \(0.574058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.5830 | −1.15757 | ||||||||
\(452\) | 20.0000 | 0.940721 | ||||||||
\(453\) | 12.5830 | 0.591201 | ||||||||
\(454\) | −56.3320 | −2.64379 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.93725 | 0.371696 | ||||||||
\(457\) | −31.8745 | −1.49103 | −0.745513 | − | 0.666491i | \(-0.767796\pi\) | ||||
−0.745513 | + | 0.666491i | \(0.767796\pi\) | |||||||
\(458\) | −51.0405 | −2.38497 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.7490 | 1.19925 | 0.599626 | − | 0.800281i | \(-0.295316\pi\) | ||||
0.599626 | + | 0.800281i | \(0.295316\pi\) | |||||||
\(462\) | −54.4575 | −2.53359 | ||||||||
\(463\) | −1.52026 | −0.0706524 | −0.0353262 | − | 0.999376i | \(-0.511247\pi\) | ||||
−0.0353262 | + | 0.999376i | \(0.511247\pi\) | |||||||
\(464\) | −76.3098 | −3.54259 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.6235 | −2.20612 | ||||||||
\(467\) | 11.8745 | 0.549487 | 0.274743 | − | 0.961518i | \(-0.411407\pi\) | ||||
0.274743 | + | 0.961518i | \(0.411407\pi\) | |||||||
\(468\) | 28.2288 | 1.30487 | ||||||||
\(469\) | −53.1660 | −2.45498 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.70850 | 0.124801 | ||||||||
\(472\) | −5.62352 | −0.258844 | ||||||||
\(473\) | −2.00000 | −0.0919601 | ||||||||
\(474\) | 38.5830 | 1.77218 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 72.9150 | 3.34205 | ||||||||
\(477\) | −0.708497 | −0.0324399 | ||||||||
\(478\) | −27.3948 | −1.25301 | ||||||||
\(479\) | 9.64575 | 0.440726 | 0.220363 | − | 0.975418i | \(-0.429276\pi\) | ||||
0.220363 | + | 0.975418i | \(0.429276\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.29150 | 0.423656 | ||||||||
\(482\) | 12.1255 | 0.552301 | ||||||||
\(483\) | 4.70850 | 0.214244 | ||||||||
\(484\) | 104.373 | 4.74421 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.64575 | −0.120014 | ||||||||
\(487\) | 13.8745 | 0.628714 | 0.314357 | − | 0.949305i | \(-0.398211\pi\) | ||||
0.314357 | + | 0.949305i | \(0.398211\pi\) | |||||||
\(488\) | 5.62352 | 0.254565 | ||||||||
\(489\) | 7.64575 | 0.345753 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.2288 | −1.45446 | −0.727232 | − | 0.686392i | \(-0.759193\pi\) | ||||
−0.727232 | + | 0.686392i | \(0.759193\pi\) | |||||||
\(492\) | −21.7712 | −0.981523 | ||||||||
\(493\) | −27.7490 | −1.24975 | ||||||||
\(494\) | 14.9373 | 0.672059 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 66.0000 | 2.96349 | ||||||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 15.8745 | 0.711354 | ||||||||
\(499\) | 43.0405 | 1.92676 | 0.963379 | − | 0.268143i | \(-0.0864100\pi\) | ||||
0.963379 | + | 0.268143i | \(0.0864100\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7085 | 0.478420 | ||||||||
\(502\) | 57.2693 | 2.55605 | ||||||||
\(503\) | 2.00000 | 0.0891756 | 0.0445878 | − | 0.999005i | \(-0.485803\pi\) | ||||
0.0445878 | + | 0.999005i | \(0.485803\pi\) | |||||||
\(504\) | −28.9373 | −1.28897 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −19.2915 | −0.857612 | ||||||||
\(507\) | 18.8745 | 0.838246 | ||||||||
\(508\) | −20.0000 | −0.887357 | ||||||||
\(509\) | 24.1033 | 1.06836 | 0.534179 | − | 0.845371i | \(-0.320621\pi\) | ||||
0.534179 | + | 0.845371i | \(0.320621\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.4575 | −1.61279 | ||||||||
\(512\) | 29.1033 | 1.28619 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | −70.3320 | −3.10221 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.77124 | −0.0779746 | ||||||||
\(517\) | −52.4575 | −2.30708 | ||||||||
\(518\) | −15.8745 | −0.697486 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.1033 | −1.58171 | −0.790856 | − | 0.612002i | \(-0.790365\pi\) | ||||
−0.790856 | + | 0.612002i | \(0.790365\pi\) | |||||||
\(522\) | 18.3542 | 0.803344 | ||||||||
\(523\) | 12.7085 | 0.555704 | 0.277852 | − | 0.960624i | \(-0.410378\pi\) | ||||
0.277852 | + | 0.960624i | \(0.410378\pi\) | |||||||
\(524\) | 61.1438 | 2.67108 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −43.8745 | −1.91302 | ||||||||
\(527\) | 24.0000 | 1.04546 | ||||||||
\(528\) | 62.1033 | 2.70270 | ||||||||
\(529\) | −21.3320 | −0.927479 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.708497 | 0.0307462 | ||||||||
\(532\) | −18.2288 | −0.790317 | ||||||||
\(533\) | −24.5830 | −1.06481 | ||||||||
\(534\) | 2.81176 | 0.121677 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 115.749 | 4.99960 | ||||||||
\(537\) | 3.29150 | 0.142039 | ||||||||
\(538\) | 58.8118 | 2.53556 | ||||||||
\(539\) | 35.5203 | 1.52997 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 40.4575 | 1.73780 | ||||||||
\(543\) | 6.70850 | 0.287889 | ||||||||
\(544\) | −52.9150 | −2.26871 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −54.4575 | −2.33057 | ||||||||
\(547\) | 29.8745 | 1.27734 | 0.638671 | − | 0.769480i | \(-0.279485\pi\) | ||||
0.638671 | + | 0.769480i | \(0.279485\pi\) | |||||||
\(548\) | −30.0000 | −1.28154 | ||||||||
\(549\) | −0.708497 | −0.0302379 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.93725 | 0.295537 | ||||||||
\(552\) | −10.2510 | −0.436311 | ||||||||
\(553\) | −53.1660 | −2.26085 | ||||||||
\(554\) | −54.4575 | −2.31368 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −69.3725 | −2.94205 | ||||||||
\(557\) | 32.5830 | 1.38059 | 0.690293 | − | 0.723530i | \(-0.257482\pi\) | ||||
0.690293 | + | 0.723530i | \(0.257482\pi\) | |||||||
\(558\) | −15.8745 | −0.672022 | ||||||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.5830 | 0.953455 | ||||||||
\(562\) | 15.2693 | 0.644095 | ||||||||
\(563\) | −39.8745 | −1.68051 | −0.840255 | − | 0.542191i | \(-0.817595\pi\) | ||||
−0.840255 | + | 0.542191i | \(0.817595\pi\) | |||||||
\(564\) | −46.4575 | −1.95621 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 67.5203 | 2.83809 | ||||||||
\(567\) | 3.64575 | 0.153107 | ||||||||
\(568\) | 26.1255 | 1.09620 | ||||||||
\(569\) | −22.9373 | −0.961580 | −0.480790 | − | 0.876836i | \(-0.659650\pi\) | ||||
−0.480790 | + | 0.876836i | \(0.659650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.2915 | 1.14211 | 0.571057 | − | 0.820910i | \(-0.306534\pi\) | ||||
0.571057 | + | 0.820910i | \(0.306534\pi\) | |||||||
\(572\) | 159.373 | 6.66370 | ||||||||
\(573\) | −20.2288 | −0.845068 | ||||||||
\(574\) | 42.0000 | 1.75305 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 13.0000 | 0.541667 | ||||||||
\(577\) | 2.70850 | 0.112756 | 0.0563781 | − | 0.998409i | \(-0.482045\pi\) | ||||
0.0563781 | + | 0.998409i | \(0.482045\pi\) | |||||||
\(578\) | 2.64575 | 0.110049 | ||||||||
\(579\) | 6.35425 | 0.264074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.8745 | −0.907508 | ||||||||
\(582\) | 34.2288 | 1.41883 | ||||||||
\(583\) | −4.00000 | −0.165663 | ||||||||
\(584\) | 79.3725 | 3.28446 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 70.3320 | 2.90539 | ||||||||
\(587\) | 22.7085 | 0.937280 | 0.468640 | − | 0.883389i | \(-0.344744\pi\) | ||||
0.468640 | + | 0.883389i | \(0.344744\pi\) | |||||||
\(588\) | 31.4575 | 1.29729 | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.1660 | −0.706115 | ||||||||
\(592\) | 18.1033 | 0.744040 | ||||||||
\(593\) | −24.5830 | −1.00950 | −0.504752 | − | 0.863265i | \(-0.668416\pi\) | ||||
−0.504752 | + | 0.863265i | \(0.668416\pi\) | |||||||
\(594\) | −14.9373 | −0.612883 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.91503 | 0.119404 | ||||||||
\(597\) | −3.29150 | −0.134712 | ||||||||
\(598\) | −19.2915 | −0.788888 | ||||||||
\(599\) | 30.5830 | 1.24959 | 0.624794 | − | 0.780790i | \(-0.285183\pi\) | ||||
0.624794 | + | 0.780790i | \(0.285183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.2915 | 1.35799 | 0.678994 | − | 0.734143i | \(-0.262416\pi\) | ||||
0.678994 | + | 0.734143i | \(0.262416\pi\) | |||||||
\(602\) | 3.41699 | 0.139266 | ||||||||
\(603\) | −14.5830 | −0.593866 | ||||||||
\(604\) | 62.9150 | 2.55998 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.41699 | 0.138806 | ||||||||
\(607\) | −31.0405 | −1.25990 | −0.629948 | − | 0.776637i | \(-0.716924\pi\) | ||||
−0.629948 | + | 0.776637i | \(0.716924\pi\) | |||||||
\(608\) | 13.2288 | 0.536497 | ||||||||
\(609\) | −25.2915 | −1.02486 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −52.4575 | −2.12220 | ||||||||
\(612\) | 20.0000 | 0.808452 | ||||||||
\(613\) | −22.4575 | −0.907050 | −0.453525 | − | 0.891243i | \(-0.649834\pi\) | ||||
−0.453525 | + | 0.891243i | \(0.649834\pi\) | |||||||
\(614\) | 75.2915 | 3.03852 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −163.373 | −6.58247 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 28.0000 | 1.12633 | ||||||||
\(619\) | 12.7085 | 0.510798 | 0.255399 | − | 0.966836i | \(-0.417793\pi\) | ||||
0.255399 | + | 0.966836i | \(0.417793\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.29150 | 0.0518262 | ||||||||
\(622\) | −18.6863 | −0.749251 | ||||||||
\(623\) | −3.87451 | −0.155229 | ||||||||
\(624\) | 62.1033 | 2.48612 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.7490 | 0.709393 | ||||||||
\(627\) | −5.64575 | −0.225470 | ||||||||
\(628\) | 13.5425 | 0.540404 | ||||||||
\(629\) | 6.58301 | 0.262482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.58301 | 0.262065 | 0.131033 | − | 0.991378i | \(-0.458171\pi\) | ||||
0.131033 | + | 0.991378i | \(0.458171\pi\) | |||||||
\(632\) | 115.749 | 4.60425 | ||||||||
\(633\) | −18.5830 | −0.738608 | ||||||||
\(634\) | −85.8745 | −3.41051 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.54249 | −0.140469 | ||||||||
\(637\) | 35.5203 | 1.40736 | ||||||||
\(638\) | 103.624 | 4.10249 | ||||||||
\(639\) | −3.29150 | −0.130210 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.06275 | −0.0419759 | −0.0209880 | − | 0.999780i | \(-0.506681\pi\) | ||||
−0.0209880 | + | 0.999780i | \(0.506681\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.35425 | 0.329459 | 0.164730 | − | 0.986339i | \(-0.447325\pi\) | ||||
0.164730 | + | 0.986339i | \(0.447325\pi\) | |||||||
\(644\) | 23.5425 | 0.927704 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.5830 | 0.416383 | ||||||||
\(647\) | 24.5830 | 0.966458 | 0.483229 | − | 0.875494i | \(-0.339464\pi\) | ||||
0.483229 | + | 0.875494i | \(0.339464\pi\) | |||||||
\(648\) | −7.93725 | −0.311805 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.8745 | 0.857330 | ||||||||
\(652\) | 38.2288 | 1.49715 | ||||||||
\(653\) | −30.5830 | −1.19681 | −0.598403 | − | 0.801195i | \(-0.704198\pi\) | ||||
−0.598403 | + | 0.801195i | \(0.704198\pi\) | |||||||
\(654\) | 14.0000 | 0.547443 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −47.8967 | −1.87005 | ||||||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | 89.6235 | 3.49389 | ||||||||
\(659\) | 46.5830 | 1.81462 | 0.907308 | − | 0.420466i | \(-0.138134\pi\) | ||||
0.907308 | + | 0.420466i | \(0.138134\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.29150 | −0.361398 | −0.180699 | − | 0.983538i | \(-0.557836\pi\) | ||||
−0.180699 | + | 0.983538i | \(0.557836\pi\) | |||||||
\(662\) | −86.2065 | −3.35051 | ||||||||
\(663\) | 22.5830 | 0.877051 | ||||||||
\(664\) | 47.6235 | 1.84815 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.35425 | −0.168724 | ||||||||
\(667\) | −8.95948 | −0.346913 | ||||||||
\(668\) | 53.5425 | 2.07162 | ||||||||
\(669\) | 18.5830 | 0.718460 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.00000 | −0.154418 | ||||||||
\(672\) | −48.2288 | −1.86046 | ||||||||
\(673\) | 28.9373 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311675\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311675\pi\) | |||||||
\(674\) | −2.47974 | −0.0955160 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 94.3725 | 3.62971 | ||||||||
\(677\) | 12.4575 | 0.478781 | 0.239391 | − | 0.970923i | \(-0.423052\pi\) | ||||
0.239391 | + | 0.970923i | \(0.423052\pi\) | |||||||
\(678\) | −10.5830 | −0.406438 | ||||||||
\(679\) | −47.1660 | −1.81007 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.2915 | 0.815892 | ||||||||
\(682\) | −89.6235 | −3.43186 | ||||||||
\(683\) | 43.7490 | 1.67401 | 0.837005 | − | 0.547196i | \(-0.184305\pi\) | ||||
0.837005 | + | 0.547196i | \(0.184305\pi\) | |||||||
\(684\) | −5.00000 | −0.191180 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.83399 | 0.260923 | ||||||||
\(687\) | 19.2915 | 0.736017 | ||||||||
\(688\) | −3.89674 | −0.148562 | ||||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.0405 | 1.18084 | 0.590418 | − | 0.807097i | \(-0.298963\pi\) | ||||
0.590418 | + | 0.807097i | \(0.298963\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 20.5830 | 0.781884 | ||||||||
\(694\) | 68.7895 | 2.61122 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 55.0627 | 2.08715 | ||||||||
\(697\) | −17.4170 | −0.659716 | ||||||||
\(698\) | 50.7085 | 1.91934 | ||||||||
\(699\) | 18.0000 | 0.680823 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.58301 | −0.173098 | −0.0865489 | − | 0.996248i | \(-0.527584\pi\) | ||||
−0.0865489 | + | 0.996248i | \(0.527584\pi\) | |||||||
\(702\) | −14.9373 | −0.563770 | ||||||||
\(703\) | −1.64575 | −0.0620707 | ||||||||
\(704\) | 73.3948 | 2.76617 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −54.4575 | −2.04954 | ||||||||
\(707\) | −4.70850 | −0.177081 | ||||||||
\(708\) | 3.54249 | 0.133135 | ||||||||
\(709\) | −15.2915 | −0.574284 | −0.287142 | − | 0.957888i | \(-0.592705\pi\) | ||||
−0.287142 | + | 0.957888i | \(0.592705\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.5830 | −0.546905 | ||||||||
\(712\) | 8.43529 | 0.316126 | ||||||||
\(713\) | 7.74902 | 0.290203 | ||||||||
\(714\) | −38.5830 | −1.44393 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.4575 | 0.615046 | ||||||||
\(717\) | 10.3542 | 0.386687 | ||||||||
\(718\) | −58.4797 | −2.18244 | ||||||||
\(719\) | −14.8118 | −0.552386 | −0.276193 | − | 0.961102i | \(-0.589073\pi\) | ||||
−0.276193 | + | 0.961102i | \(0.589073\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.5830 | −1.43691 | ||||||||
\(722\) | −2.64575 | −0.0984647 | ||||||||
\(723\) | −4.58301 | −0.170444 | ||||||||
\(724\) | 33.5425 | 1.24660 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −55.2288 | −2.04973 | ||||||||
\(727\) | 44.1033 | 1.63570 | 0.817850 | − | 0.575432i | \(-0.195166\pi\) | ||||
0.817850 | + | 0.575432i | \(0.195166\pi\) | |||||||
\(728\) | −163.373 | −6.05499 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.41699 | −0.0524094 | ||||||||
\(732\) | −3.54249 | −0.130934 | ||||||||
\(733\) | −28.5830 | −1.05574 | −0.527869 | − | 0.849326i | \(-0.677009\pi\) | ||||
−0.527869 | + | 0.849326i | \(0.677009\pi\) | |||||||
\(734\) | −9.64575 | −0.356031 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.0850 | −0.629760 | ||||||||
\(737\) | −82.3320 | −3.03274 | ||||||||
\(738\) | 11.5203 | 0.424067 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.64575 | −0.207402 | ||||||||
\(742\) | 6.83399 | 0.250884 | ||||||||
\(743\) | −10.5830 | −0.388253 | −0.194126 | − | 0.980977i | \(-0.562187\pi\) | ||||
−0.194126 | + | 0.980977i | \(0.562187\pi\) | |||||||
\(744\) | −47.6235 | −1.74596 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 55.3948 | 2.02815 | ||||||||
\(747\) | −6.00000 | −0.219529 | ||||||||
\(748\) | 112.915 | 4.12858 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.4170 | −0.854498 | −0.427249 | − | 0.904134i | \(-0.640517\pi\) | ||||
−0.427249 | + | 0.904134i | \(0.640517\pi\) | |||||||
\(752\) | −102.207 | −3.72709 | ||||||||
\(753\) | −21.6458 | −0.788815 | ||||||||
\(754\) | 103.624 | 3.77375 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 18.2288 | 0.662973 | ||||||||
\(757\) | −7.87451 | −0.286204 | −0.143102 | − | 0.989708i | \(-0.545708\pi\) | ||||
−0.143102 | + | 0.989708i | \(0.545708\pi\) | |||||||
\(758\) | −26.4575 | −0.960980 | ||||||||
\(759\) | 7.29150 | 0.264665 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.7490 | −1.36840 | −0.684200 | − | 0.729294i | \(-0.739849\pi\) | ||||
−0.684200 | + | 0.729294i | \(0.739849\pi\) | |||||||
\(762\) | 10.5830 | 0.383382 | ||||||||
\(763\) | −19.2915 | −0.698399 | ||||||||
\(764\) | −101.144 | −3.65925 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.83399 | 0.246922 | ||||||||
\(767\) | 4.00000 | 0.144432 | ||||||||
\(768\) | −5.00000 | −0.180422 | ||||||||
\(769\) | 45.7490 | 1.64975 | 0.824876 | − | 0.565314i | \(-0.191245\pi\) | ||||
0.824876 | + | 0.565314i | \(0.191245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.5830 | 0.957364 | ||||||||
\(772\) | 31.7712 | 1.14347 | ||||||||
\(773\) | 19.2915 | 0.693867 | 0.346934 | − | 0.937890i | \(-0.387223\pi\) | ||||
0.346934 | + | 0.937890i | \(0.387223\pi\) | |||||||
\(774\) | 0.937254 | 0.0336889 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 102.686 | 3.68622 | ||||||||
\(777\) | 6.00000 | 0.215249 | ||||||||
\(778\) | 15.8745 | 0.569129 | ||||||||
\(779\) | 4.35425 | 0.156007 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.5830 | −0.664952 | ||||||||
\(782\) | −13.6680 | −0.488766 | ||||||||
\(783\) | −6.93725 | −0.247917 | ||||||||
\(784\) | 69.2065 | 2.47166 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.3542 | −1.15404 | ||||||||
\(787\) | −6.12549 | −0.218350 | −0.109175 | − | 0.994023i | \(-0.534821\pi\) | ||||
−0.109175 | + | 0.994023i | \(0.534821\pi\) | |||||||
\(788\) | −85.8301 | −3.05757 | ||||||||
\(789\) | 16.5830 | 0.590371 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.5830 | 0.518512 | ||||||||
\(792\) | −44.8118 | −1.59232 | ||||||||
\(793\) | −4.00000 | −0.142044 | ||||||||
\(794\) | −5.29150 | −0.187788 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.4575 | −0.583321 | ||||||||
\(797\) | −40.0000 | −1.41687 | −0.708436 | − | 0.705775i | \(-0.750599\pi\) | ||||
−0.708436 | + | 0.705775i | \(0.750599\pi\) | |||||||
\(798\) | 9.64575 | 0.341456 | ||||||||
\(799\) | −37.1660 | −1.31484 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.06275 | −0.0375503 | ||||||||
\(802\) | −28.9373 | −1.02181 | ||||||||
\(803\) | −56.4575 | −1.99234 | ||||||||
\(804\) | −72.9150 | −2.57151 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −89.6235 | −3.15685 | ||||||||
\(807\) | −22.2288 | −0.782489 | ||||||||
\(808\) | 10.2510 | 0.360628 | ||||||||
\(809\) | −40.5830 | −1.42682 | −0.713411 | − | 0.700746i | \(-0.752851\pi\) | ||||
−0.713411 | + | 0.700746i | \(0.752851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −46.3320 | −1.62694 | −0.813469 | − | 0.581609i | \(-0.802423\pi\) | ||||
−0.813469 | + | 0.581609i | \(0.802423\pi\) | |||||||
\(812\) | −126.458 | −4.43779 | ||||||||
\(813\) | −15.2915 | −0.536296 | ||||||||
\(814\) | −24.5830 | −0.861634 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 44.0000 | 1.54031 | ||||||||
\(817\) | 0.354249 | 0.0123936 | ||||||||
\(818\) | 45.7490 | 1.59958 | ||||||||
\(819\) | 20.5830 | 0.719228 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.6235 | −1.66207 | −0.831036 | − | 0.556218i | \(-0.812252\pi\) | ||||
−0.831036 | + | 0.556218i | \(0.812252\pi\) | |||||||
\(822\) | 15.8745 | 0.553687 | ||||||||
\(823\) | 22.2288 | 0.774846 | 0.387423 | − | 0.921902i | \(-0.373365\pi\) | ||||
0.387423 | + | 0.921902i | \(0.373365\pi\) | |||||||
\(824\) | 84.0000 | 2.92628 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.83399 | −0.237785 | ||||||||
\(827\) | 22.4575 | 0.780924 | 0.390462 | − | 0.920619i | \(-0.372315\pi\) | ||||
0.390462 | + | 0.920619i | \(0.372315\pi\) | |||||||
\(828\) | 6.45751 | 0.224414 | ||||||||
\(829\) | 13.2915 | 0.461633 | 0.230816 | − | 0.972997i | \(-0.425860\pi\) | ||||
0.230816 | + | 0.972997i | \(0.425860\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.5830 | 0.714017 | ||||||||
\(832\) | 73.3948 | 2.54451 | ||||||||
\(833\) | 25.1660 | 0.871951 | ||||||||
\(834\) | 36.7085 | 1.27111 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −28.2288 | −0.976312 | ||||||||
\(837\) | 6.00000 | 0.207390 | ||||||||
\(838\) | −61.0183 | −2.10784 | ||||||||
\(839\) | 40.4575 | 1.39675 | 0.698374 | − | 0.715733i | \(-0.253907\pi\) | ||||
0.698374 | + | 0.715733i | \(0.253907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.1255 | 0.659500 | ||||||||
\(842\) | −19.6235 | −0.676271 | ||||||||
\(843\) | −5.77124 | −0.198772 | ||||||||
\(844\) | −92.9150 | −3.19827 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 24.5830 | 0.845181 | ||||||||
\(847\) | 76.1033 | 2.61494 | ||||||||
\(848\) | −7.79347 | −0.267629 | ||||||||
\(849\) | −25.5203 | −0.875853 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.12549 | 0.0728609 | ||||||||
\(852\) | −16.4575 | −0.563825 | ||||||||
\(853\) | −25.2915 | −0.865965 | −0.432982 | − | 0.901402i | \(-0.642539\pi\) | ||||
−0.432982 | + | 0.901402i | \(0.642539\pi\) | |||||||
\(854\) | 6.83399 | 0.233854 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.0405 | 1.47024 | 0.735118 | − | 0.677939i | \(-0.237127\pi\) | ||||
0.735118 | + | 0.677939i | \(0.237127\pi\) | |||||||
\(858\) | −84.3320 | −2.87905 | ||||||||
\(859\) | 50.3320 | 1.71731 | 0.858653 | − | 0.512557i | \(-0.171302\pi\) | ||||
0.858653 | + | 0.512557i | \(0.171302\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.8745 | −0.541002 | ||||||||
\(862\) | 19.2915 | 0.657071 | ||||||||
\(863\) | 20.0000 | 0.680808 | 0.340404 | − | 0.940279i | \(-0.389436\pi\) | ||||
0.340404 | + | 0.940279i | \(0.389436\pi\) | |||||||
\(864\) | −13.2288 | −0.450051 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −59.1438 | −2.00979 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 109.373 | 3.71235 | ||||||||
\(869\) | −82.3320 | −2.79292 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −82.3320 | −2.78971 | ||||||||
\(872\) | 42.0000 | 1.42230 | ||||||||
\(873\) | −12.9373 | −0.437860 | ||||||||
\(874\) | 3.41699 | 0.115582 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −50.0000 | −1.68934 | ||||||||
\(877\) | 40.9373 | 1.38235 | 0.691176 | − | 0.722686i | \(-0.257093\pi\) | ||||
0.691176 | + | 0.722686i | \(0.257093\pi\) | |||||||
\(878\) | 59.7490 | 2.01643 | ||||||||
\(879\) | −26.5830 | −0.896623 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.8745 | −1.07388 | −0.536940 | − | 0.843621i | \(-0.680420\pi\) | ||||
−0.536940 | + | 0.843621i | \(0.680420\pi\) | |||||||
\(882\) | −16.6458 | −0.560492 | ||||||||
\(883\) | 36.8118 | 1.23881 | 0.619407 | − | 0.785070i | \(-0.287373\pi\) | ||||
0.619407 | + | 0.785070i | \(0.287373\pi\) | |||||||
\(884\) | 112.915 | 3.79774 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 98.6640 | 3.31468 | ||||||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | −13.0627 | −0.438357 | ||||||||
\(889\) | −14.5830 | −0.489098 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.64575 | 0.189140 | ||||||||
\(892\) | 92.9150 | 3.11103 | ||||||||
\(893\) | 9.29150 | 0.310928 | ||||||||
\(894\) | −1.54249 | −0.0515885 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −28.9373 | −0.966726 | ||||||||
\(897\) | 7.29150 | 0.243456 | ||||||||
\(898\) | 25.8523 | 0.862702 | ||||||||
\(899\) | −41.6235 | −1.38822 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.83399 | −0.0944139 | ||||||||
\(902\) | 65.0405 | 2.16561 | ||||||||
\(903\) | −1.29150 | −0.0429785 | ||||||||
\(904\) | −31.7490 | −1.05596 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −33.2915 | −1.10604 | ||||||||
\(907\) | −27.0405 | −0.897866 | −0.448933 | − | 0.893566i | \(-0.648196\pi\) | ||||
−0.448933 | + | 0.893566i | \(0.648196\pi\) | |||||||
\(908\) | 106.458 | 3.53292 | ||||||||
\(909\) | −1.29150 | −0.0428364 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.41699 | 0.179473 | 0.0897365 | − | 0.995966i | \(-0.471398\pi\) | ||||
0.0897365 | + | 0.995966i | \(0.471398\pi\) | |||||||
\(912\) | −11.0000 | −0.364246 | ||||||||
\(913\) | −33.8745 | −1.12108 | ||||||||
\(914\) | 84.3320 | 2.78946 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 96.4575 | 3.18705 | ||||||||
\(917\) | 44.5830 | 1.47226 | ||||||||
\(918\) | −10.5830 | −0.349291 | ||||||||
\(919\) | 57.1660 | 1.88573 | 0.942866 | − | 0.333171i | \(-0.108119\pi\) | ||||
0.942866 | + | 0.333171i | \(0.108119\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.4575 | −0.937707 | ||||||||
\(922\) | −68.1255 | −2.24359 | ||||||||
\(923\) | −18.5830 | −0.611667 | ||||||||
\(924\) | 102.915 | 3.38566 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.02223 | 0.132179 | ||||||||
\(927\) | −10.5830 | −0.347591 | ||||||||
\(928\) | 91.7712 | 3.01254 | ||||||||
\(929\) | 19.8745 | 0.652061 | 0.326031 | − | 0.945359i | \(-0.394289\pi\) | ||||
0.326031 | + | 0.945359i | \(0.394289\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.29150 | −0.206196 | ||||||||
\(932\) | 90.0000 | 2.94805 | ||||||||
\(933\) | 7.06275 | 0.231224 | ||||||||
\(934\) | −31.4170 | −1.02800 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −44.8118 | −1.46472 | ||||||||
\(937\) | −51.8745 | −1.69467 | −0.847333 | − | 0.531062i | \(-0.821793\pi\) | ||||
−0.847333 | + | 0.531062i | \(0.821793\pi\) | |||||||
\(938\) | 140.664 | 4.59284 | ||||||||
\(939\) | −6.70850 | −0.218924 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.2288 | −1.24622 | −0.623111 | − | 0.782133i | \(-0.714131\pi\) | ||||
−0.623111 | + | 0.782133i | \(0.714131\pi\) | |||||||
\(942\) | −7.16601 | −0.233481 | ||||||||
\(943\) | −5.62352 | −0.183127 | ||||||||
\(944\) | 7.79347 | 0.253656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.29150 | 0.172042 | ||||||||
\(947\) | −32.5830 | −1.05881 | −0.529403 | − | 0.848371i | \(-0.677584\pi\) | ||||
−0.529403 | + | 0.848371i | \(0.677584\pi\) | |||||||
\(948\) | −72.9150 | −2.36817 | ||||||||
\(949\) | −56.4575 | −1.83269 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.4575 | 1.05251 | ||||||||
\(952\) | −115.749 | −3.75145 | ||||||||
\(953\) | −10.5830 | −0.342817 | −0.171409 | − | 0.985200i | \(-0.554832\pi\) | ||||
−0.171409 | + | 0.985200i | \(0.554832\pi\) | |||||||
\(954\) | 1.87451 | 0.0606894 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 51.7712 | 1.67440 | ||||||||
\(957\) | −39.1660 | −1.26606 | ||||||||
\(958\) | −25.5203 | −0.824522 | ||||||||
\(959\) | −21.8745 | −0.706365 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −24.5830 | −0.792588 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22.9150 | −0.738043 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.4575 | −0.400814 | ||||||||
\(967\) | 36.3542 | 1.16907 | 0.584537 | − | 0.811367i | \(-0.301276\pi\) | ||||
0.584537 | + | 0.811367i | \(0.301276\pi\) | |||||||
\(968\) | −165.686 | −5.32536 | ||||||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 5.00000 | 0.160375 | ||||||||
\(973\) | −50.5830 | −1.62162 | ||||||||
\(974\) | −36.7085 | −1.17622 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.79347 | −0.249463 | ||||||||
\(977\) | −23.0405 | −0.737131 | −0.368566 | − | 0.929602i | \(-0.620151\pi\) | ||||
−0.368566 | + | 0.929602i | \(0.620151\pi\) | |||||||
\(978\) | −20.2288 | −0.646844 | ||||||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.29150 | −0.168945 | ||||||||
\(982\) | 85.2693 | 2.72105 | ||||||||
\(983\) | 18.4575 | 0.588703 | 0.294352 | − | 0.955697i | \(-0.404896\pi\) | ||||
0.294352 | + | 0.955697i | \(0.404896\pi\) | |||||||
\(984\) | 34.5608 | 1.10176 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 73.4170 | 2.33807 | ||||||||
\(987\) | −33.8745 | −1.07824 | ||||||||
\(988\) | −28.2288 | −0.898076 | ||||||||
\(989\) | −0.457513 | −0.0145481 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7490 | 0.881477 | 0.440738 | − | 0.897636i | \(-0.354717\pi\) | ||||
0.440738 | + | 0.897636i | \(0.354717\pi\) | |||||||
\(992\) | −79.3725 | −2.52008 | ||||||||
\(993\) | 32.5830 | 1.03399 | ||||||||
\(994\) | 31.7490 | 1.00702 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −30.0000 | −0.950586 | ||||||||
\(997\) | −37.2915 | −1.18103 | −0.590517 | − | 0.807025i | \(-0.701076\pi\) | ||||
−0.590517 | + | 0.807025i | \(0.701076\pi\) | |||||||
\(998\) | −113.875 | −3.60463 | ||||||||
\(999\) | 1.64575 | 0.0520693 |
(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 | 1425.2.a.p.1.1 | 2 | ||
3.2 | odd | 2 | 4275.2.a.u.1.2 | 2 | |||
5.2 | odd | 4 | 1425.2.c.i.799.1 | 4 | |||
5.3 | odd | 4 | 1425.2.c.i.799.4 | 4 | |||
5.4 | even | 2 | 285.2.a.d.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 855.2.a.g.1.1 | 2 | |||
20.19 | odd | 2 | 4560.2.a.bo.1.2 | 2 | |||
95.94 | odd | 2 | 5415.2.a.s.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
285.2.a.d.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
855.2.a.g.1.1 | 2 | 15.14 | odd | 2 | |||
1425.2.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1425.2.c.i.799.1 | 4 | 5.2 | odd | 4 | |||
1425.2.c.i.799.4 | 4 | 5.3 | odd | 4 | |||
4275.2.a.u.1.2 | 2 | 3.2 | odd | 2 | |||
4560.2.a.bo.1.2 | 2 | 20.19 | odd | 2 | |||
5415.2.a.s.1.1 | 2 | 95.94 | odd | 2 |