Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Root | \(-1.97506\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.97506 | 1.39658 | 0.698289 | − | 0.715816i | \(-0.253945\pi\) | ||||
0.698289 | + | 0.715816i | \(0.253945\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.90086 | 0.950432 | ||||||||
\(5\) | 3.88400 | 1.73698 | 0.868489 | − | 0.495708i | \(-0.165091\pi\) | ||||
0.868489 | + | 0.495708i | \(0.165091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64382 | 0.999270 | 0.499635 | − | 0.866236i | \(-0.333467\pi\) | ||||
0.499635 | + | 0.866236i | \(0.333467\pi\) | |||||||
\(8\) | −0.195801 | −0.0692260 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.67114 | 2.42583 | ||||||||
\(11\) | −4.76488 | −1.43667 | −0.718333 | − | 0.695700i | \(-0.755094\pi\) | ||||
−0.718333 | + | 0.695700i | \(0.755094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.33092 | 0.923832 | 0.461916 | − | 0.886924i | \(-0.347162\pi\) | ||||
0.461916 | + | 0.886924i | \(0.347162\pi\) | |||||||
\(14\) | 5.22171 | 1.39556 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.18845 | −1.04711 | ||||||||
\(17\) | 7.28945 | 1.76795 | 0.883975 | − | 0.467533i | \(-0.154857\pi\) | ||||
0.883975 | + | 0.467533i | \(0.154857\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.43957 | 1.24792 | 0.623962 | − | 0.781455i | \(-0.285522\pi\) | ||||
0.623962 | + | 0.781455i | \(0.285522\pi\) | |||||||
\(20\) | 7.38296 | 1.65088 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.41093 | −2.00642 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.0855 | 2.01710 | ||||||||
\(26\) | 6.57877 | 1.29020 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.02554 | 0.949738 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.87216 | 1.23428 | 0.617138 | − | 0.786855i | \(-0.288292\pi\) | ||||
0.617138 | + | 0.786855i | \(0.288292\pi\) | |||||||
\(32\) | −7.88083 | −1.39315 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 14.3971 | 2.46908 | ||||||||
\(35\) | 10.2686 | 1.73571 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.05053 | −1.48790 | −0.743949 | − | 0.668236i | \(-0.767050\pi\) | ||||
−0.743949 | + | 0.668236i | \(0.767050\pi\) | |||||||
\(38\) | 10.7435 | 1.74282 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.760490 | −0.120244 | ||||||||
\(41\) | −5.39284 | −0.842220 | −0.421110 | − | 0.907010i | \(-0.638359\pi\) | ||||
−0.421110 | + | 0.907010i | \(0.638359\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4237 | −1.58960 | −0.794799 | − | 0.606873i | \(-0.792424\pi\) | ||||
−0.794799 | + | 0.606873i | \(0.792424\pi\) | |||||||
\(44\) | −9.05739 | −1.36545 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.97506 | −0.291207 | ||||||||
\(47\) | −8.49635 | −1.23932 | −0.619660 | − | 0.784870i | \(-0.712730\pi\) | ||||
−0.619660 | + | 0.784870i | \(0.712730\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.0102125 | −0.00145893 | ||||||||
\(50\) | 19.9194 | 2.81703 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.33163 | 0.878039 | ||||||||
\(53\) | 7.62772 | 1.04775 | 0.523874 | − | 0.851796i | \(-0.324486\pi\) | ||||
0.523874 | + | 0.851796i | \(0.324486\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.5068 | −2.49546 | ||||||||
\(56\) | −0.517662 | −0.0691755 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.97506 | −0.259338 | ||||||||
\(59\) | 10.2552 | 1.33511 | 0.667554 | − | 0.744562i | \(-0.267341\pi\) | ||||
0.667554 | + | 0.744562i | \(0.267341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.452237 | 0.0579030 | 0.0289515 | − | 0.999581i | \(-0.490783\pi\) | ||||
0.0289515 | + | 0.999581i | \(0.490783\pi\) | |||||||
\(62\) | 13.5729 | 1.72376 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.18823 | −0.898528 | ||||||||
\(65\) | 12.9373 | 1.60468 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0887 | 1.47687 | 0.738435 | − | 0.674325i | \(-0.235565\pi\) | ||||
0.738435 | + | 0.674325i | \(0.235565\pi\) | |||||||
\(68\) | 13.8562 | 1.68032 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 20.2811 | 2.42406 | ||||||||
\(71\) | −12.0747 | −1.43300 | −0.716501 | − | 0.697586i | \(-0.754258\pi\) | ||||
−0.716501 | + | 0.697586i | \(0.754258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.12294 | 0.716636 | 0.358318 | − | 0.933600i | \(-0.383350\pi\) | ||||
0.358318 | + | 0.933600i | \(0.383350\pi\) | |||||||
\(74\) | −17.8753 | −2.07797 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.3399 | 1.18607 | ||||||||
\(77\) | −12.5975 | −1.43562 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.83566 | −1.10660 | −0.553299 | − | 0.832983i | \(-0.686631\pi\) | ||||
−0.553299 | + | 0.832983i | \(0.686631\pi\) | |||||||
\(80\) | −16.2679 | −1.81881 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.6512 | −1.17623 | ||||||||
\(83\) | 10.0824 | 1.10668 | 0.553341 | − | 0.832955i | \(-0.313352\pi\) | ||||
0.553341 | + | 0.832955i | \(0.313352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.3122 | 3.07089 | ||||||||
\(86\) | −20.5874 | −2.22000 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.932967 | 0.0994546 | ||||||||
\(89\) | 0.490243 | 0.0519657 | 0.0259828 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259828 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.80636 | 0.923157 | ||||||||
\(92\) | −1.90086 | −0.198179 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −16.7808 | −1.73081 | ||||||||
\(95\) | 21.1273 | 2.16762 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.789164 | −0.0801274 | −0.0400637 | − | 0.999197i | \(-0.512756\pi\) | ||||
−0.0400637 | + | 0.999197i | \(0.512756\pi\) | |||||||
\(98\) | −0.0201703 | −0.00203751 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 19.1711 | 1.91711 | ||||||||
\(101\) | −5.14905 | −0.512350 | −0.256175 | − | 0.966630i | \(-0.582462\pi\) | ||||
−0.256175 | + | 0.966630i | \(0.582462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.12758 | −0.406702 | −0.203351 | − | 0.979106i | \(-0.565183\pi\) | ||||
−0.203351 | + | 0.979106i | \(0.565183\pi\) | |||||||
\(104\) | −0.652197 | −0.0639532 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.0652 | 1.46326 | ||||||||
\(107\) | −11.9691 | −1.15710 | −0.578549 | − | 0.815648i | \(-0.696381\pi\) | ||||
−0.578549 | + | 0.815648i | \(0.696381\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.1260 | 1.25724 | 0.628622 | − | 0.777711i | \(-0.283619\pi\) | ||||
0.628622 | + | 0.777711i | \(0.283619\pi\) | |||||||
\(110\) | −36.5521 | −3.48510 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.0735 | −1.04635 | ||||||||
\(113\) | 2.19956 | 0.206917 | 0.103459 | − | 0.994634i | \(-0.467009\pi\) | ||||
0.103459 | + | 0.994634i | \(0.467009\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.88400 | −0.362185 | ||||||||
\(116\) | −1.90086 | −0.176491 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.2545 | 1.86458 | ||||||||
\(119\) | 19.2720 | 1.76666 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.7041 | 1.06401 | ||||||||
\(122\) | 0.893196 | 0.0808661 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.0630 | 1.17309 | ||||||||
\(125\) | 19.7520 | 1.76667 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8159 | 1.04849 | 0.524245 | − | 0.851567i | \(-0.324347\pi\) | ||||
0.524245 | + | 0.851567i | \(0.324347\pi\) | |||||||
\(128\) | 1.56448 | 0.138282 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 25.5520 | 2.24106 | ||||||||
\(131\) | −13.0941 | −1.14403 | −0.572017 | − | 0.820242i | \(-0.693839\pi\) | ||||
−0.572017 | + | 0.820242i | \(0.693839\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.3813 | 1.24701 | ||||||||
\(134\) | 23.8759 | 2.06256 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.42728 | −0.122388 | ||||||||
\(137\) | −7.92555 | −0.677126 | −0.338563 | − | 0.940944i | \(-0.609941\pi\) | ||||
−0.338563 | + | 0.940944i | \(0.609941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.89433 | 0.330313 | 0.165157 | − | 0.986267i | \(-0.447187\pi\) | ||||
0.165157 | + | 0.986267i | \(0.447187\pi\) | |||||||
\(140\) | 19.5192 | 1.64968 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −23.8482 | −2.00130 | ||||||||
\(143\) | −15.8714 | −1.32724 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.88400 | −0.322549 | ||||||||
\(146\) | 12.0932 | 1.00084 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.2038 | −1.41415 | ||||||||
\(149\) | −5.40852 | −0.443083 | −0.221542 | − | 0.975151i | \(-0.571109\pi\) | ||||
−0.221542 | + | 0.975151i | \(0.571109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.81356 | 0.798616 | 0.399308 | − | 0.916817i | \(-0.369250\pi\) | ||||
0.399308 | + | 0.916817i | \(0.369250\pi\) | |||||||
\(152\) | −1.06507 | −0.0863887 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −24.8808 | −2.00495 | ||||||||
\(155\) | 26.6915 | 2.14391 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.1417 | 1.36806 | 0.684030 | − | 0.729454i | \(-0.260226\pi\) | ||||
0.684030 | + | 0.729454i | \(0.260226\pi\) | |||||||
\(158\) | −19.4260 | −1.54545 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −30.6092 | −2.41987 | ||||||||
\(161\) | −2.64382 | −0.208362 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.30053 | −0.728474 | −0.364237 | − | 0.931306i | \(-0.618670\pi\) | ||||
−0.364237 | + | 0.931306i | \(0.618670\pi\) | |||||||
\(164\) | −10.2510 | −0.800472 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.9133 | 1.54557 | ||||||||
\(167\) | 16.9187 | 1.30921 | 0.654603 | − | 0.755972i | \(-0.272836\pi\) | ||||
0.654603 | + | 0.755972i | \(0.272836\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.90496 | −0.146535 | ||||||||
\(170\) | 55.9184 | 4.28874 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −19.8140 | −1.51080 | ||||||||
\(173\) | −3.35028 | −0.254717 | −0.127359 | − | 0.991857i | \(-0.540650\pi\) | ||||
−0.127359 | + | 0.991857i | \(0.540650\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 26.6642 | 2.01562 | ||||||||
\(176\) | 19.9574 | 1.50435 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.968260 | 0.0725742 | ||||||||
\(179\) | −9.84156 | −0.735593 | −0.367796 | − | 0.929906i | \(-0.619888\pi\) | ||||
−0.367796 | + | 0.929906i | \(0.619888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.83355 | −0.284945 | −0.142473 | − | 0.989799i | \(-0.545505\pi\) | ||||
−0.142473 | + | 0.989799i | \(0.545505\pi\) | |||||||
\(182\) | 17.3931 | 1.28926 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.195801 | 0.0144346 | ||||||||
\(185\) | −35.1523 | −2.58445 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −34.7333 | −2.53995 | ||||||||
\(188\) | −16.1504 | −1.17789 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 41.7277 | 3.02725 | ||||||||
\(191\) | −25.4250 | −1.83969 | −0.919843 | − | 0.392287i | \(-0.871684\pi\) | ||||
−0.919843 | + | 0.392287i | \(0.871684\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.0004 | 1.72759 | 0.863795 | − | 0.503844i | \(-0.168081\pi\) | ||||
0.863795 | + | 0.503844i | \(0.168081\pi\) | |||||||
\(194\) | −1.55865 | −0.111904 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0194126 | −0.00138661 | ||||||||
\(197\) | −23.4966 | −1.67406 | −0.837032 | − | 0.547154i | \(-0.815711\pi\) | ||||
−0.837032 | + | 0.547154i | \(0.815711\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.12765 | −0.434378 | −0.217189 | − | 0.976130i | \(-0.569689\pi\) | ||||
−0.217189 | + | 0.976130i | \(0.569689\pi\) | |||||||
\(200\) | −1.97474 | −0.139635 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −10.1697 | −0.715536 | ||||||||
\(203\) | −2.64382 | −0.185560 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.9458 | −1.46292 | ||||||||
\(206\) | −8.15222 | −0.567992 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.9514 | −0.967354 | ||||||||
\(209\) | −25.9189 | −1.79285 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.19073 | −0.495030 | −0.247515 | − | 0.968884i | \(-0.579614\pi\) | ||||
−0.247515 | + | 0.968884i | \(0.579614\pi\) | |||||||
\(212\) | 14.4992 | 0.995812 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.6397 | −1.61598 | ||||||||
\(215\) | −40.4856 | −2.76110 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.1688 | 1.23338 | ||||||||
\(218\) | 25.9247 | 1.75584 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −35.1789 | −2.37176 | ||||||||
\(221\) | 24.2806 | 1.63329 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.86810 | −0.593852 | −0.296926 | − | 0.954900i | \(-0.595961\pi\) | ||||
−0.296926 | + | 0.954900i | \(0.595961\pi\) | |||||||
\(224\) | −20.8355 | −1.39213 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.34427 | 0.288976 | ||||||||
\(227\) | −10.6725 | −0.708359 | −0.354180 | − | 0.935177i | \(-0.615240\pi\) | ||||
−0.354180 | + | 0.935177i | \(0.615240\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.91406 | 0.324730 | 0.162365 | − | 0.986731i | \(-0.448088\pi\) | ||||
0.162365 | + | 0.986731i | \(0.448088\pi\) | |||||||
\(230\) | −7.67114 | −0.505820 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.195801 | 0.0128549 | ||||||||
\(233\) | 22.8105 | 1.49436 | 0.747182 | − | 0.664619i | \(-0.231406\pi\) | ||||
0.747182 | + | 0.664619i | \(0.231406\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.9998 | −2.15267 | ||||||||
\(236\) | 19.4936 | 1.26893 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 38.0633 | 2.46728 | ||||||||
\(239\) | 22.1209 | 1.43088 | 0.715441 | − | 0.698673i | \(-0.246226\pi\) | ||||
0.715441 | + | 0.698673i | \(0.246226\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.77198 | −0.371806 | −0.185903 | − | 0.982568i | \(-0.559521\pi\) | ||||
−0.185903 | + | 0.982568i | \(0.559521\pi\) | |||||||
\(242\) | 23.1163 | 1.48597 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.859641 | 0.0550329 | ||||||||
\(245\) | −0.0396654 | −0.00253413 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.1188 | 1.15287 | ||||||||
\(248\) | −1.34557 | −0.0854440 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 39.0114 | 2.46730 | ||||||||
\(251\) | 18.2189 | 1.14997 | 0.574984 | − | 0.818165i | \(-0.305008\pi\) | ||||
0.574984 | + | 0.818165i | \(0.305008\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.76488 | 0.299565 | ||||||||
\(254\) | 23.3371 | 1.46430 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.4664 | 1.09165 | ||||||||
\(257\) | −6.94804 | −0.433407 | −0.216703 | − | 0.976237i | \(-0.569530\pi\) | ||||
−0.216703 | + | 0.976237i | \(0.569530\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.9280 | −1.48681 | ||||||||
\(260\) | 24.5921 | 1.52513 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −25.8616 | −1.59773 | ||||||||
\(263\) | −7.20446 | −0.444246 | −0.222123 | − | 0.975019i | \(-0.571299\pi\) | ||||
−0.222123 | + | 0.975019i | \(0.571299\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 29.6261 | 1.81992 | ||||||||
\(266\) | 28.4038 | 1.74155 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 22.9790 | 1.40366 | ||||||||
\(269\) | 4.24647 | 0.258912 | 0.129456 | − | 0.991585i | \(-0.458677\pi\) | ||||
0.129456 | + | 0.991585i | \(0.458677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.9356 | 1.21100 | 0.605501 | − | 0.795845i | \(-0.292973\pi\) | ||||
0.605501 | + | 0.795845i | \(0.292973\pi\) | |||||||
\(272\) | −30.5315 | −1.85124 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.6534 | −0.945659 | ||||||||
\(275\) | −48.0561 | −2.89789 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.38195 | −0.143117 | −0.0715586 | − | 0.997436i | \(-0.522797\pi\) | ||||
−0.0715586 | + | 0.997436i | \(0.522797\pi\) | |||||||
\(278\) | 7.69154 | 0.461308 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.01060 | −0.120156 | ||||||||
\(281\) | −13.4801 | −0.804155 | −0.402078 | − | 0.915606i | \(-0.631712\pi\) | ||||
−0.402078 | + | 0.915606i | \(0.631712\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.65647 | 0.455130 | 0.227565 | − | 0.973763i | \(-0.426924\pi\) | ||||
0.227565 | + | 0.973763i | \(0.426924\pi\) | |||||||
\(284\) | −22.9523 | −1.36197 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −31.3471 | −1.85359 | ||||||||
\(287\) | −14.2577 | −0.841605 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 36.1361 | 2.12565 | ||||||||
\(290\) | −7.67114 | −0.450465 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.6389 | 0.681113 | ||||||||
\(293\) | −25.5856 | −1.49473 | −0.747364 | − | 0.664415i | \(-0.768681\pi\) | ||||
−0.747364 | + | 0.664415i | \(0.768681\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 39.8310 | 2.31905 | ||||||||
\(296\) | 1.77210 | 0.103001 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.6821 | −0.618800 | ||||||||
\(299\) | −3.33092 | −0.192632 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.5584 | −1.58844 | ||||||||
\(302\) | 19.3824 | 1.11533 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22.7833 | −1.30671 | ||||||||
\(305\) | 1.75649 | 0.100576 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.19667 | −0.524882 | −0.262441 | − | 0.964948i | \(-0.584527\pi\) | ||||
−0.262441 | + | 0.964948i | \(0.584527\pi\) | |||||||
\(308\) | −23.9461 | −1.36446 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 52.7173 | 2.99414 | ||||||||
\(311\) | 10.3312 | 0.585831 | 0.292916 | − | 0.956138i | \(-0.405374\pi\) | ||||
0.292916 | + | 0.956138i | \(0.405374\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.7542 | −1.00353 | −0.501763 | − | 0.865005i | \(-0.667315\pi\) | ||||
−0.501763 | + | 0.865005i | \(0.667315\pi\) | |||||||
\(314\) | 33.8560 | 1.91060 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.6962 | −1.05175 | ||||||||
\(317\) | −2.01941 | −0.113421 | −0.0567106 | − | 0.998391i | \(-0.518061\pi\) | ||||
−0.0567106 | + | 0.998391i | \(0.518061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.76488 | 0.266782 | ||||||||
\(320\) | −27.9191 | −1.56072 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.22171 | −0.290994 | ||||||||
\(323\) | 39.6515 | 2.20627 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.5939 | 1.86346 | ||||||||
\(326\) | −18.3691 | −1.01737 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.05592 | 0.0583035 | ||||||||
\(329\) | −22.4628 | −1.23842 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2584 | −1.05854 | −0.529268 | − | 0.848455i | \(-0.677533\pi\) | ||||
−0.529268 | + | 0.848455i | \(0.677533\pi\) | |||||||
\(332\) | 19.1652 | 1.05183 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 33.4154 | 1.82841 | ||||||||
\(335\) | 46.9525 | 2.56529 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.62764 | 0.0886634 | 0.0443317 | − | 0.999017i | \(-0.485884\pi\) | ||||
0.0443317 | + | 0.999017i | \(0.485884\pi\) | |||||||
\(338\) | −3.76241 | −0.204648 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 53.8177 | 2.91867 | ||||||||
\(341\) | −32.7450 | −1.77324 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5337 | −1.00073 | ||||||||
\(344\) | 2.04096 | 0.110041 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.61700 | −0.355732 | ||||||||
\(347\) | −24.2893 | −1.30392 | −0.651959 | − | 0.758254i | \(-0.726053\pi\) | ||||
−0.651959 | + | 0.758254i | \(0.726053\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.452922 | 0.0242443 | 0.0121222 | − | 0.999927i | \(-0.496141\pi\) | ||||
0.0121222 | + | 0.999927i | \(0.496141\pi\) | |||||||
\(350\) | 52.6634 | 2.81498 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 37.5512 | 2.00149 | ||||||||
\(353\) | 2.13217 | 0.113484 | 0.0567421 | − | 0.998389i | \(-0.481929\pi\) | ||||
0.0567421 | + | 0.998389i | \(0.481929\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −46.8981 | −2.48909 | ||||||||
\(356\) | 0.931886 | 0.0493898 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.4377 | −1.02731 | ||||||||
\(359\) | −4.24403 | −0.223991 | −0.111996 | − | 0.993709i | \(-0.535724\pi\) | ||||
−0.111996 | + | 0.993709i | \(0.535724\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.5889 | 0.557313 | ||||||||
\(362\) | −7.57148 | −0.397948 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.7397 | 0.877398 | ||||||||
\(365\) | 23.7815 | 1.24478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.1283 | −0.946288 | −0.473144 | − | 0.880985i | \(-0.656881\pi\) | ||||
−0.473144 | + | 0.880985i | \(0.656881\pi\) | |||||||
\(368\) | 4.18845 | 0.218338 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −69.4279 | −3.60938 | ||||||||
\(371\) | 20.1663 | 1.04698 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.46611 | 0.386581 | 0.193290 | − | 0.981142i | \(-0.438084\pi\) | ||||
0.193290 | + | 0.981142i | \(0.438084\pi\) | |||||||
\(374\) | −68.6005 | −3.54725 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.66359 | 0.0857932 | ||||||||
\(377\) | −3.33092 | −0.171551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.6908 | −1.57648 | −0.788239 | − | 0.615369i | \(-0.789007\pi\) | ||||
−0.788239 | + | 0.615369i | \(0.789007\pi\) | |||||||
\(380\) | 40.1601 | 2.06017 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −50.2158 | −2.56927 | ||||||||
\(383\) | 16.3891 | 0.837442 | 0.418721 | − | 0.908115i | \(-0.362479\pi\) | ||||
0.418721 | + | 0.908115i | \(0.362479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −48.9287 | −2.49364 | ||||||||
\(386\) | 47.4023 | 2.41271 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.50009 | −0.0761556 | ||||||||
\(389\) | −0.876026 | −0.0444163 | −0.0222081 | − | 0.999753i | \(-0.507070\pi\) | ||||
−0.0222081 | + | 0.999753i | \(0.507070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.28945 | −0.368643 | ||||||||
\(392\) | 0.00199961 | 0.000100996 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −46.4072 | −2.33796 | ||||||||
\(395\) | −38.2017 | −1.92214 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.14689 | 0.308503 | 0.154252 | − | 0.988032i | \(-0.450703\pi\) | ||||
0.154252 | + | 0.988032i | \(0.450703\pi\) | |||||||
\(398\) | −12.1025 | −0.606643 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −42.2425 | −2.11212 | ||||||||
\(401\) | −8.06278 | −0.402636 | −0.201318 | − | 0.979526i | \(-0.564523\pi\) | ||||
−0.201318 | + | 0.979526i | \(0.564523\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.8906 | 1.14026 | ||||||||
\(404\) | −9.78764 | −0.486953 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.22171 | −0.259149 | ||||||||
\(407\) | 43.1247 | 2.13761 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.21546 | 0.158994 | 0.0794970 | − | 0.996835i | \(-0.474669\pi\) | ||||
0.0794970 | + | 0.996835i | \(0.474669\pi\) | |||||||
\(410\) | −41.3692 | −2.04308 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.84596 | −0.386543 | ||||||||
\(413\) | 27.1128 | 1.33413 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 39.1599 | 1.92228 | ||||||||
\(416\) | −26.2504 | −1.28703 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −51.1914 | −2.50385 | ||||||||
\(419\) | −29.0993 | −1.42160 | −0.710798 | − | 0.703396i | \(-0.751666\pi\) | ||||
−0.710798 | + | 0.703396i | \(0.751666\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9597 | 0.680352 | 0.340176 | − | 0.940362i | \(-0.389513\pi\) | ||||
0.340176 | + | 0.940362i | \(0.389513\pi\) | |||||||
\(422\) | −14.2021 | −0.691348 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.49351 | −0.0725314 | ||||||||
\(425\) | 73.5176 | 3.56613 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.19563 | 0.0578608 | ||||||||
\(428\) | −22.7516 | −1.09974 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −79.9616 | −3.85609 | ||||||||
\(431\) | −13.7446 | −0.662055 | −0.331028 | − | 0.943621i | \(-0.607395\pi\) | ||||
−0.331028 | + | 0.943621i | \(0.607395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.8189 | −1.19272 | −0.596361 | − | 0.802716i | \(-0.703387\pi\) | ||||
−0.596361 | + | 0.802716i | \(0.703387\pi\) | |||||||
\(434\) | 35.8844 | 1.72251 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.9507 | 1.19492 | ||||||||
\(437\) | −5.43957 | −0.260210 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.9294 | −0.760268 | −0.380134 | − | 0.924932i | \(-0.624122\pi\) | ||||
−0.380134 | + | 0.924932i | \(0.624122\pi\) | |||||||
\(440\) | 3.62365 | 0.172751 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 47.9556 | 2.28102 | ||||||||
\(443\) | 37.1050 | 1.76291 | 0.881456 | − | 0.472265i | \(-0.156564\pi\) | ||||
0.881456 | + | 0.472265i | \(0.156564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.90411 | 0.0902633 | ||||||||
\(446\) | −17.5150 | −0.829361 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.0044 | −0.897873 | ||||||||
\(449\) | 13.0638 | 0.616518 | 0.308259 | − | 0.951303i | \(-0.400254\pi\) | ||||
0.308259 | + | 0.951303i | \(0.400254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.6962 | 1.20999 | ||||||||
\(452\) | 4.18107 | 0.196661 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.0788 | −0.989279 | ||||||||
\(455\) | 34.2039 | 1.60350 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.3373 | 0.951341 | 0.475670 | − | 0.879624i | \(-0.342205\pi\) | ||||
0.475670 | + | 0.879624i | \(0.342205\pi\) | |||||||
\(458\) | 9.70557 | 0.453512 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.38296 | −0.344232 | ||||||||
\(461\) | 25.0320 | 1.16585 | 0.582927 | − | 0.812524i | \(-0.301907\pi\) | ||||
0.582927 | + | 0.812524i | \(0.301907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0134 | −1.02305 | −0.511524 | − | 0.859269i | \(-0.670919\pi\) | ||||
−0.511524 | + | 0.859269i | \(0.670919\pi\) | |||||||
\(464\) | 4.18845 | 0.194444 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 45.0521 | 2.08700 | ||||||||
\(467\) | −11.1367 | −0.515345 | −0.257672 | − | 0.966232i | \(-0.582956\pi\) | ||||
−0.257672 | + | 0.966232i | \(0.582956\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.9603 | 1.47579 | ||||||||
\(470\) | −65.1767 | −3.00638 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00797 | −0.0924241 | ||||||||
\(473\) | 49.6676 | 2.28372 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 54.8607 | 2.51718 | ||||||||
\(476\) | 36.6334 | 1.67909 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 43.6901 | 1.99834 | ||||||||
\(479\) | −26.1947 | −1.19687 | −0.598433 | − | 0.801173i | \(-0.704210\pi\) | ||||
−0.598433 | + | 0.801173i | \(0.704210\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.1466 | −1.37457 | ||||||||
\(482\) | −11.4000 | −0.519256 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22.2479 | 1.01127 | ||||||||
\(485\) | −3.06511 | −0.139180 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.1512 | 1.86474 | 0.932369 | − | 0.361508i | \(-0.117738\pi\) | ||||
0.932369 | + | 0.361508i | \(0.117738\pi\) | |||||||
\(488\) | −0.0885483 | −0.00400839 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0783415 | −0.00353911 | ||||||||
\(491\) | −23.0875 | −1.04192 | −0.520962 | − | 0.853580i | \(-0.674427\pi\) | ||||
−0.520962 | + | 0.853580i | \(0.674427\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.28945 | −0.328300 | ||||||||
\(494\) | 35.7857 | 1.61008 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.7837 | −1.29242 | ||||||||
\(497\) | −31.9233 | −1.43196 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.628061 | −0.0281159 | −0.0140579 | − | 0.999901i | \(-0.504475\pi\) | ||||
−0.0140579 | + | 0.999901i | \(0.504475\pi\) | |||||||
\(500\) | 37.5459 | 1.67910 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 35.9835 | 1.60602 | ||||||||
\(503\) | −35.0299 | −1.56190 | −0.780952 | − | 0.624591i | \(-0.785266\pi\) | ||||
−0.780952 | + | 0.624591i | \(0.785266\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.9989 | −0.889940 | ||||||||
\(506\) | 9.41093 | 0.418367 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 22.4604 | 0.996519 | ||||||||
\(509\) | −2.65516 | −0.117688 | −0.0588439 | − | 0.998267i | \(-0.518741\pi\) | ||||
−0.0588439 | + | 0.998267i | \(0.518741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.1879 | 0.716113 | ||||||||
\(512\) | 31.3682 | 1.38629 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.7228 | −0.605287 | ||||||||
\(515\) | −16.0315 | −0.706433 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 40.4841 | 1.78049 | ||||||||
\(518\) | −47.2592 | −2.07645 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.53313 | −0.111085 | ||||||||
\(521\) | 8.23178 | 0.360641 | 0.180321 | − | 0.983608i | \(-0.442287\pi\) | ||||
0.180321 | + | 0.983608i | \(0.442287\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.52821 | 0.416640 | 0.208320 | − | 0.978061i | \(-0.433201\pi\) | ||||
0.208320 | + | 0.978061i | \(0.433201\pi\) | |||||||
\(524\) | −24.8900 | −1.08733 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.2293 | −0.620425 | ||||||||
\(527\) | 50.0942 | 2.18214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 58.5133 | 2.54165 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 27.3368 | 1.18520 | ||||||||
\(533\) | −17.9631 | −0.778069 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −46.4881 | −2.00985 | ||||||||
\(536\) | −2.36697 | −0.102238 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.38704 | 0.361591 | ||||||||
\(539\) | 0.0486613 | 0.00209599 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.6497 | 1.91964 | 0.959821 | − | 0.280612i | \(-0.0905375\pi\) | ||||
0.959821 | + | 0.280612i | \(0.0905375\pi\) | |||||||
\(542\) | 39.3740 | 1.69126 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −57.4469 | −2.46302 | ||||||||
\(545\) | 50.9814 | 2.18381 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.0805 | −1.49993 | −0.749967 | − | 0.661476i | \(-0.769931\pi\) | ||||
−0.749967 | + | 0.661476i | \(0.769931\pi\) | |||||||
\(548\) | −15.0654 | −0.643562 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −94.9137 | −4.04713 | ||||||||
\(551\) | −5.43957 | −0.231734 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.0037 | −1.10579 | ||||||||
\(554\) | −4.70449 | −0.199874 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.40260 | 0.313940 | ||||||||
\(557\) | 23.6013 | 1.00002 | 0.500009 | − | 0.866020i | \(-0.333330\pi\) | ||||
0.500009 | + | 0.866020i | \(0.333330\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −34.7205 | −1.46852 | ||||||||
\(560\) | −43.0095 | −1.81748 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −26.6240 | −1.12307 | ||||||||
\(563\) | −5.46440 | −0.230297 | −0.115149 | − | 0.993348i | \(-0.536734\pi\) | ||||
−0.115149 | + | 0.993348i | \(0.536734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.54310 | 0.359411 | ||||||||
\(566\) | 15.1220 | 0.635625 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.36423 | 0.0992010 | ||||||||
\(569\) | −18.3374 | −0.768744 | −0.384372 | − | 0.923178i | \(-0.625582\pi\) | ||||
−0.384372 | + | 0.923178i | \(0.625582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.5394 | −1.86391 | −0.931957 | − | 0.362569i | \(-0.881900\pi\) | ||||
−0.931957 | + | 0.362569i | \(0.881900\pi\) | |||||||
\(572\) | −30.1695 | −1.26145 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −28.1598 | −1.17537 | ||||||||
\(575\) | −10.0855 | −0.420593 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.61196 | −0.400151 | −0.200076 | − | 0.979780i | \(-0.564119\pi\) | ||||
−0.200076 | + | 0.979780i | \(0.564119\pi\) | |||||||
\(578\) | 71.3709 | 2.96864 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.38296 | −0.306561 | ||||||||
\(581\) | 26.6560 | 1.10588 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.3452 | −1.50526 | ||||||||
\(584\) | −1.19888 | −0.0496098 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −50.5332 | −2.08751 | ||||||||
\(587\) | 26.4163 | 1.09032 | 0.545158 | − | 0.838333i | \(-0.316470\pi\) | ||||
0.545158 | + | 0.838333i | \(0.316470\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.3816 | 1.54028 | ||||||||
\(590\) | 78.6687 | 3.23874 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 37.9077 | 1.55800 | ||||||||
\(593\) | 14.0020 | 0.574993 | 0.287496 | − | 0.957782i | \(-0.407177\pi\) | ||||
0.287496 | + | 0.957782i | \(0.407177\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 74.8525 | 3.06865 | ||||||||
\(596\) | −10.2809 | −0.421120 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.57877 | −0.269026 | ||||||||
\(599\) | −27.8770 | −1.13902 | −0.569512 | − | 0.821983i | \(-0.692868\pi\) | ||||
−0.569512 | + | 0.821983i | \(0.692868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.86933 | −0.320997 | −0.160498 | − | 0.987036i | \(-0.551310\pi\) | ||||
−0.160498 | + | 0.987036i | \(0.551310\pi\) | |||||||
\(602\) | −54.4294 | −2.21838 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.6542 | 0.759030 | ||||||||
\(605\) | 45.4587 | 1.84816 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.6180 | −1.72981 | −0.864906 | − | 0.501933i | \(-0.832622\pi\) | ||||
−0.864906 | + | 0.501933i | \(0.832622\pi\) | |||||||
\(608\) | −42.8683 | −1.73854 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.46917 | 0.140463 | ||||||||
\(611\) | −28.3007 | −1.14492 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.58163 | −0.144660 | −0.0723302 | − | 0.997381i | \(-0.523044\pi\) | ||||
−0.0723302 | + | 0.997381i | \(0.523044\pi\) | |||||||
\(614\) | −18.1640 | −0.733039 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.46660 | 0.0993820 | ||||||||
\(617\) | −25.1171 | −1.01118 | −0.505589 | − | 0.862775i | \(-0.668725\pi\) | ||||
−0.505589 | + | 0.862775i | \(0.668725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.91575 | −0.0770004 | −0.0385002 | − | 0.999259i | \(-0.512258\pi\) | ||||
−0.0385002 | + | 0.999259i | \(0.512258\pi\) | |||||||
\(620\) | 50.7369 | 2.03764 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.4048 | 0.818160 | ||||||||
\(623\) | 1.29612 | 0.0519278 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 26.2895 | 1.05158 | ||||||||
\(626\) | −35.0656 | −1.40150 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 32.5841 | 1.30025 | ||||||||
\(629\) | −65.9734 | −2.63053 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 41.3427 | 1.64583 | 0.822913 | − | 0.568168i | \(-0.192348\pi\) | ||||
0.822913 | + | 0.568168i | \(0.192348\pi\) | |||||||
\(632\) | 1.92583 | 0.0766054 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.98845 | −0.158402 | ||||||||
\(635\) | 45.8930 | 1.82121 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0340170 | −0.00134780 | ||||||||
\(638\) | 9.41093 | 0.372582 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.07645 | 0.240193 | ||||||||
\(641\) | 21.8011 | 0.861090 | 0.430545 | − | 0.902569i | \(-0.358321\pi\) | ||||
0.430545 | + | 0.902569i | \(0.358321\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.00022 | −0.0788810 | −0.0394405 | − | 0.999222i | \(-0.512558\pi\) | ||||
−0.0394405 | + | 0.999222i | \(0.512558\pi\) | |||||||
\(644\) | −5.02554 | −0.198034 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 78.3141 | 3.08123 | ||||||||
\(647\) | −47.7606 | −1.87766 | −0.938831 | − | 0.344379i | \(-0.888090\pi\) | ||||
−0.938831 | + | 0.344379i | \(0.888090\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.8646 | −1.91810 | ||||||||
\(650\) | 66.3501 | 2.60246 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.6790 | −0.692365 | ||||||||
\(653\) | 20.8681 | 0.816631 | 0.408316 | − | 0.912841i | \(-0.366116\pi\) | ||||
0.408316 | + | 0.912841i | \(0.366116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −50.8574 | −1.98716 | ||||||||
\(656\) | 22.5876 | 0.881898 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −44.3654 | −1.72954 | ||||||||
\(659\) | 38.0743 | 1.48316 | 0.741582 | − | 0.670863i | \(-0.234076\pi\) | ||||
0.741582 | + | 0.670863i | \(0.234076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0049 | 0.933684 | 0.466842 | − | 0.884341i | \(-0.345392\pi\) | ||||
0.466842 | + | 0.884341i | \(0.345392\pi\) | |||||||
\(662\) | −38.0364 | −1.47833 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.97413 | −0.0766112 | ||||||||
\(665\) | 55.8568 | 2.16603 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 32.1601 | 1.24431 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 92.7341 | 3.58263 | ||||||||
\(671\) | −2.15486 | −0.0831873 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.39075 | −0.169251 | −0.0846255 | − | 0.996413i | \(-0.526969\pi\) | ||||
−0.0846255 | + | 0.996413i | \(0.526969\pi\) | |||||||
\(674\) | 3.21469 | 0.123825 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.62107 | −0.139272 | ||||||||
\(677\) | 11.7070 | 0.449938 | 0.224969 | − | 0.974366i | \(-0.427772\pi\) | ||||
0.224969 | + | 0.974366i | \(0.427772\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.08641 | −0.0800690 | ||||||||
\(680\) | −5.54356 | −0.212586 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −64.6734 | −2.47647 | ||||||||
\(683\) | 29.3902 | 1.12458 | 0.562292 | − | 0.826939i | \(-0.309920\pi\) | ||||
0.562292 | + | 0.826939i | \(0.309920\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.7829 | −1.17615 | ||||||||
\(686\) | −36.6053 | −1.39760 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 43.6590 | 1.66449 | ||||||||
\(689\) | 25.4073 | 0.967942 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.9740 | −0.645723 | −0.322861 | − | 0.946446i | \(-0.604645\pi\) | ||||
−0.322861 | + | 0.946446i | \(0.604645\pi\) | |||||||
\(692\) | −6.36842 | −0.242091 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −47.9728 | −1.82102 | ||||||||
\(695\) | 15.1256 | 0.573747 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.3108 | −1.48900 | ||||||||
\(698\) | 0.894547 | 0.0338591 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 50.6850 | 1.91571 | ||||||||
\(701\) | 43.4787 | 1.64217 | 0.821084 | − | 0.570808i | \(-0.193370\pi\) | ||||
0.821084 | + | 0.570808i | \(0.193370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49.2310 | −1.85678 | ||||||||
\(704\) | 34.2510 | 1.29088 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.21117 | 0.158490 | ||||||||
\(707\) | −13.6132 | −0.511976 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.31290 | 0.349753 | 0.174877 | − | 0.984590i | \(-0.444047\pi\) | ||||
0.174877 | + | 0.984590i | \(0.444047\pi\) | |||||||
\(710\) | −92.6267 | −3.47622 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.0959900 | −0.00359738 | ||||||||
\(713\) | −6.87216 | −0.257364 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −61.6447 | −2.30538 | ||||||||
\(716\) | −18.7075 | −0.699131 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.38221 | −0.312821 | ||||||||
\(719\) | −33.4838 | −1.24873 | −0.624367 | − | 0.781131i | \(-0.714643\pi\) | ||||
−0.624367 | + | 0.781131i | \(0.714643\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.9126 | −0.406406 | ||||||||
\(722\) | 20.9138 | 0.778331 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.28705 | −0.270821 | ||||||||
\(725\) | −10.0855 | −0.374565 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.2045 | −0.489726 | −0.244863 | − | 0.969558i | \(-0.578743\pi\) | ||||
−0.244863 | + | 0.969558i | \(0.578743\pi\) | |||||||
\(728\) | −1.72429 | −0.0639065 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 46.9699 | 1.73843 | ||||||||
\(731\) | −75.9829 | −2.81033 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.77920 | 0.250395 | 0.125198 | − | 0.992132i | \(-0.460043\pi\) | ||||
0.125198 | + | 0.992132i | \(0.460043\pi\) | |||||||
\(734\) | −35.8044 | −1.32156 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.88083 | 0.290491 | ||||||||
\(737\) | −57.6012 | −2.12177 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.2217 | −1.18530 | −0.592648 | − | 0.805462i | \(-0.701917\pi\) | ||||
−0.592648 | + | 0.805462i | \(0.701917\pi\) | |||||||
\(740\) | −66.8197 | −2.45634 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 39.8297 | 1.46219 | ||||||||
\(743\) | 35.2349 | 1.29264 | 0.646321 | − | 0.763065i | \(-0.276307\pi\) | ||||
0.646321 | + | 0.763065i | \(0.276307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.0067 | −0.769626 | ||||||||
\(746\) | 14.7460 | 0.539890 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −66.0234 | −2.41405 | ||||||||
\(749\) | −31.6442 | −1.15625 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.3638 | −0.414670 | −0.207335 | − | 0.978270i | \(-0.566479\pi\) | ||||
−0.207335 | + | 0.978270i | \(0.566479\pi\) | |||||||
\(752\) | 35.5865 | 1.29771 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.57877 | −0.239585 | ||||||||
\(755\) | 38.1159 | 1.38718 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.9819 | −0.689910 | −0.344955 | − | 0.938619i | \(-0.612106\pi\) | ||||
−0.344955 | + | 0.938619i | \(0.612106\pi\) | |||||||
\(758\) | −60.6161 | −2.20168 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.13674 | −0.150055 | ||||||||
\(761\) | −3.79127 | −0.137434 | −0.0687168 | − | 0.997636i | \(-0.521890\pi\) | ||||
−0.0687168 | + | 0.997636i | \(0.521890\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.7028 | 1.25633 | ||||||||
\(764\) | −48.3294 | −1.74850 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.3694 | 1.16955 | ||||||||
\(767\) | 34.1591 | 1.23341 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.9385 | 1.72871 | 0.864354 | − | 0.502884i | \(-0.167728\pi\) | ||||
0.864354 | + | 0.502884i | \(0.167728\pi\) | |||||||
\(770\) | −96.6371 | −3.48256 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 45.6216 | 1.64196 | ||||||||
\(773\) | 48.7564 | 1.75365 | 0.876823 | − | 0.480812i | \(-0.159658\pi\) | ||||
0.876823 | + | 0.480812i | \(0.159658\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 69.3090 | 2.48965 | ||||||||
\(776\) | 0.154519 | 0.00554690 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.73020 | −0.0620308 | ||||||||
\(779\) | −29.3347 | −1.05103 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.5345 | 2.05875 | ||||||||
\(782\) | −14.3971 | −0.514839 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0427745 | 0.00152766 | ||||||||
\(785\) | 66.5786 | 2.37629 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.87475 | 0.280705 | 0.140352 | − | 0.990102i | \(-0.455176\pi\) | ||||
0.140352 | + | 0.990102i | \(0.455176\pi\) | |||||||
\(788\) | −44.6638 | −1.59108 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −75.4507 | −2.68442 | ||||||||
\(791\) | 5.81525 | 0.206766 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.50637 | 0.0534926 | ||||||||
\(794\) | 12.1405 | 0.430849 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.6478 | −0.412846 | ||||||||
\(797\) | 5.88439 | 0.208436 | 0.104218 | − | 0.994554i | \(-0.466766\pi\) | ||||
0.104218 | + | 0.994554i | \(0.466766\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −61.9337 | −2.19106 | ||||||||
\(800\) | −79.4819 | −2.81011 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15.9245 | −0.562313 | ||||||||
\(803\) | −29.1751 | −1.02957 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.2686 | −0.361921 | ||||||||
\(806\) | 45.2104 | 1.59247 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.00819 | 0.0354679 | ||||||||
\(809\) | 3.36443 | 0.118287 | 0.0591436 | − | 0.998249i | \(-0.481163\pi\) | ||||
0.0591436 | + | 0.998249i | \(0.481163\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.9912 | 1.40428 | 0.702141 | − | 0.712038i | \(-0.252228\pi\) | ||||
0.702141 | + | 0.712038i | \(0.252228\pi\) | |||||||
\(812\) | −5.02554 | −0.176362 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 85.1739 | 2.98534 | ||||||||
\(815\) | −36.1233 | −1.26534 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −56.7004 | −1.98370 | ||||||||
\(818\) | 6.35072 | 0.222048 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39.8151 | −1.39040 | ||||||||
\(821\) | −41.2944 | −1.44119 | −0.720593 | − | 0.693359i | \(-0.756130\pi\) | ||||
−0.720593 | + | 0.693359i | \(0.756130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.7752 | −0.445314 | −0.222657 | − | 0.974897i | \(-0.571473\pi\) | ||||
−0.222657 | + | 0.974897i | \(0.571473\pi\) | |||||||
\(824\) | 0.808183 | 0.0281544 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 53.5494 | 1.86322 | ||||||||
\(827\) | 0.0598083 | 0.00207974 | 0.00103987 | − | 0.999999i | \(-0.499669\pi\) | ||||
0.00103987 | + | 0.999999i | \(0.499669\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.8700 | 1.10689 | 0.553446 | − | 0.832885i | \(-0.313313\pi\) | ||||
0.553446 | + | 0.832885i | \(0.313313\pi\) | |||||||
\(830\) | 77.3432 | 2.68462 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −23.9434 | −0.830089 | ||||||||
\(833\) | −0.0744434 | −0.00257931 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 65.7122 | 2.27406 | ||||||||
\(836\) | −49.2683 | −1.70398 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −57.4730 | −1.98537 | ||||||||
\(839\) | 10.1762 | 0.351321 | 0.175661 | − | 0.984451i | \(-0.443794\pi\) | ||||
0.175661 | + | 0.984451i | \(0.443794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 27.5712 | 0.950165 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.6686 | −0.470492 | ||||||||
\(845\) | −7.39886 | −0.254529 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.9435 | 1.06323 | ||||||||
\(848\) | −31.9483 | −1.09711 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 145.202 | 4.98037 | ||||||||
\(851\) | 9.05053 | 0.310248 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.6152 | −0.842807 | −0.421404 | − | 0.906873i | \(-0.638462\pi\) | ||||
−0.421404 | + | 0.906873i | \(0.638462\pi\) | |||||||
\(854\) | 2.36145 | 0.0808071 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.34356 | 0.0801012 | ||||||||
\(857\) | −21.6841 | −0.740715 | −0.370357 | − | 0.928889i | \(-0.620765\pi\) | ||||
−0.370357 | + | 0.928889i | \(0.620765\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.9541 | −0.851422 | −0.425711 | − | 0.904859i | \(-0.639976\pi\) | ||||
−0.425711 | + | 0.904859i | \(0.639976\pi\) | |||||||
\(860\) | −76.9576 | −2.62423 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.1465 | −0.924612 | ||||||||
\(863\) | −24.6724 | −0.839859 | −0.419930 | − | 0.907557i | \(-0.637945\pi\) | ||||
−0.419930 | + | 0.907557i | \(0.637945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.0125 | −0.442438 | ||||||||
\(866\) | −49.0189 | −1.66573 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 34.5363 | 1.17224 | ||||||||
\(869\) | 46.8657 | 1.58981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.2665 | 1.36438 | ||||||||
\(872\) | −2.57008 | −0.0870339 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.7435 | −0.363404 | ||||||||
\(875\) | 52.2208 | 1.76538 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.5718 | −1.30248 | −0.651239 | − | 0.758873i | \(-0.725750\pi\) | ||||
−0.651239 | + | 0.758873i | \(0.725750\pi\) | |||||||
\(878\) | −31.4615 | −1.06177 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 77.5148 | 2.61302 | ||||||||
\(881\) | 4.63783 | 0.156253 | 0.0781263 | − | 0.996943i | \(-0.475106\pi\) | ||||
0.0781263 | + | 0.996943i | \(0.475106\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.57549 | 0.0866721 | 0.0433360 | − | 0.999061i | \(-0.486201\pi\) | ||||
0.0433360 | + | 0.999061i | \(0.486201\pi\) | |||||||
\(884\) | 46.1541 | 1.55233 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 73.2847 | 2.46205 | ||||||||
\(887\) | 7.91018 | 0.265598 | 0.132799 | − | 0.991143i | \(-0.457604\pi\) | ||||
0.132799 | + | 0.991143i | \(0.457604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.2391 | 1.04773 | ||||||||
\(890\) | 3.76073 | 0.126060 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.8571 | −0.564416 | ||||||||
\(893\) | −46.2165 | −1.54658 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.2247 | −1.27771 | ||||||||
\(896\) | 4.13621 | 0.138181 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.8017 | 0.861015 | ||||||||
\(899\) | −6.87216 | −0.229199 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.6018 | 1.85237 | ||||||||
\(902\) | 50.7516 | 1.68984 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.430676 | −0.0143241 | ||||||||
\(905\) | −14.8895 | −0.494944 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.5276 | −0.681606 | −0.340803 | − | 0.940135i | \(-0.610699\pi\) | ||||
−0.340803 | + | 0.940135i | \(0.610699\pi\) | |||||||
\(908\) | −20.2870 | −0.673247 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 67.5548 | 2.23942 | ||||||||
\(911\) | −49.7236 | −1.64742 | −0.823708 | − | 0.567014i | \(-0.808099\pi\) | ||||
−0.823708 | + | 0.567014i | \(0.808099\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.0412 | −1.58993 | ||||||||
\(914\) | 40.1675 | 1.32862 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.34096 | 0.308634 | ||||||||
\(917\) | −34.6184 | −1.14320 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.2858 | 1.49384 | 0.746921 | − | 0.664913i | \(-0.231531\pi\) | ||||
0.746921 | + | 0.664913i | \(0.231531\pi\) | |||||||
\(920\) | 0.760490 | 0.0250726 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 49.4396 | 1.62821 | ||||||||
\(923\) | −40.2199 | −1.32385 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −91.2789 | −3.00123 | ||||||||
\(926\) | −43.4777 | −1.42877 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.88083 | 0.258701 | ||||||||
\(929\) | −19.7525 | −0.648057 | −0.324028 | − | 0.946047i | \(-0.605037\pi\) | ||||
−0.324028 | + | 0.946047i | \(0.605037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0555516 | −0.00182063 | ||||||||
\(932\) | 43.3596 | 1.42029 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.9957 | −0.719720 | ||||||||
\(935\) | −134.904 | −4.41185 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.5188 | 0.670321 | 0.335160 | − | 0.942161i | \(-0.391210\pi\) | ||||
0.335160 | + | 0.942161i | \(0.391210\pi\) | |||||||
\(938\) | 63.1236 | 2.06106 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −62.7282 | −2.04597 | ||||||||
\(941\) | 48.6773 | 1.58683 | 0.793417 | − | 0.608678i | \(-0.208300\pi\) | ||||
0.793417 | + | 0.608678i | \(0.208300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.39284 | 0.175615 | ||||||||
\(944\) | −42.9532 | −1.39801 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 98.0966 | 3.18939 | ||||||||
\(947\) | 52.1168 | 1.69357 | 0.846785 | − | 0.531936i | \(-0.178535\pi\) | ||||
0.846785 | + | 0.531936i | \(0.178535\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.3950 | 0.662051 | ||||||||
\(950\) | 108.353 | 3.51544 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.77347 | −0.122299 | ||||||||
\(953\) | −49.9080 | −1.61668 | −0.808339 | − | 0.588717i | \(-0.799633\pi\) | ||||
−0.808339 | + | 0.588717i | \(0.799633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −98.7506 | −3.19550 | ||||||||
\(956\) | 42.0488 | 1.35996 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −51.7361 | −1.67152 | ||||||||
\(959\) | −20.9537 | −0.676632 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.2265 | 0.523437 | ||||||||
\(962\) | −59.5414 | −1.91969 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.9717 | −0.353376 | ||||||||
\(965\) | 93.2178 | 3.00079 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0712 | 0.356027 | 0.178014 | − | 0.984028i | \(-0.443033\pi\) | ||||
0.178014 | + | 0.984028i | \(0.443033\pi\) | |||||||
\(968\) | −2.29167 | −0.0736570 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.05378 | −0.194375 | ||||||||
\(971\) | 0.191618 | 0.00614932 | 0.00307466 | − | 0.999995i | \(-0.499021\pi\) | ||||
0.00307466 | + | 0.999995i | \(0.499021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.2959 | 0.330072 | ||||||||
\(974\) | 81.2761 | 2.60425 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.89417 | −0.0606309 | ||||||||
\(977\) | −9.08511 | −0.290659 | −0.145329 | − | 0.989383i | \(-0.546424\pi\) | ||||
−0.145329 | + | 0.989383i | \(0.546424\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.33595 | −0.0746573 | ||||||||
\(980\) | −0.0753984 | −0.00240851 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −45.5992 | −1.45513 | ||||||||
\(983\) | 1.42571 | 0.0454730 | 0.0227365 | − | 0.999741i | \(-0.492762\pi\) | ||||
0.0227365 | + | 0.999741i | \(0.492762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −91.2609 | −2.90781 | ||||||||
\(986\) | −14.3971 | −0.458497 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 34.4413 | 1.09573 | ||||||||
\(989\) | 10.4237 | 0.331454 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.4287 | 1.41132 | 0.705662 | − | 0.708549i | \(-0.250650\pi\) | ||||
0.705662 | + | 0.708549i | \(0.250650\pi\) | |||||||
\(992\) | −54.1583 | −1.71953 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −63.0505 | −1.99984 | ||||||||
\(995\) | −23.7998 | −0.754505 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.76382 | −0.182542 | −0.0912709 | − | 0.995826i | \(-0.529093\pi\) | ||||
−0.0912709 | + | 0.995826i | \(0.529093\pi\) | |||||||
\(998\) | −1.24046 | −0.0392660 | ||||||||
\(999\) | 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 | 6003.2.a.s.1.17 | 20 | ||
3.2 | odd | 2 | 2001.2.a.o.1.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.o.1.4 | ✓ | 20 | 3.2 | odd | 2 | ||
6003.2.a.s.1.17 | 20 | 1.1 | even | 1 | trivial |