Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5733,2,Mod(1,5733)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5733, 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("5733.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5733.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: | \(45.7782354788\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.746052.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 7x^{3} + 8x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.19566\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5733.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.195656 | 0.138350 | 0.0691749 | − | 0.997605i | \(-0.477963\pi\) | ||||
0.0691749 | + | 0.997605i | \(0.477963\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.96172 | −0.980859 | ||||||||
\(5\) | 3.93251 | 1.75867 | 0.879336 | − | 0.476202i | \(-0.157987\pi\) | ||||
0.879336 | + | 0.476202i | \(0.157987\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.775135 | −0.274052 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.769420 | 0.243312 | ||||||||
\(11\) | −4.50627 | −1.35869 | −0.679346 | − | 0.733818i | \(-0.737737\pi\) | ||||
−0.679346 | + | 0.733818i | \(0.737737\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.77178 | 0.942944 | ||||||||
\(17\) | −2.28141 | −0.553323 | −0.276661 | − | 0.960967i | \(-0.589228\pi\) | ||||
−0.276661 | + | 0.960967i | \(0.589228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.78768 | 0.410123 | 0.205061 | − | 0.978749i | \(-0.434261\pi\) | ||||
0.205061 | + | 0.978749i | \(0.434261\pi\) | |||||||
\(20\) | −7.71448 | −1.72501 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.881681 | −0.187975 | ||||||||
\(23\) | −1.74021 | −0.362859 | −0.181430 | − | 0.983404i | \(-0.558072\pi\) | ||||
−0.181430 | + | 0.983404i | \(0.558072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.4646 | 2.09293 | ||||||||
\(26\) | −0.195656 | −0.0383714 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.65110 | −0.306602 | −0.153301 | − | 0.988180i | \(-0.548990\pi\) | ||||
−0.153301 | + | 0.988180i | \(0.548990\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.60523 | −1.00673 | −0.503365 | − | 0.864074i | \(-0.667905\pi\) | ||||
−0.503365 | + | 0.864074i | \(0.667905\pi\) | |||||||
\(32\) | 2.28824 | 0.404508 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.446372 | −0.0765522 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.14407 | 1.17448 | 0.587239 | − | 0.809414i | \(-0.300215\pi\) | ||||
0.587239 | + | 0.809414i | \(0.300215\pi\) | |||||||
\(38\) | 0.349771 | 0.0567404 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.04823 | −0.481967 | ||||||||
\(41\) | −8.11574 | −1.26746 | −0.633732 | − | 0.773552i | \(-0.718478\pi\) | ||||
−0.633732 | + | 0.773552i | \(0.718478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.81353 | 1.03905 | 0.519527 | − | 0.854454i | \(-0.326108\pi\) | ||||
0.519527 | + | 0.854454i | \(0.326108\pi\) | |||||||
\(44\) | 8.84004 | 1.33269 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.340483 | −0.0502015 | ||||||||
\(47\) | 3.54543 | 0.517154 | 0.258577 | − | 0.965991i | \(-0.416746\pi\) | ||||
0.258577 | + | 0.965991i | \(0.416746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.04747 | 0.289556 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.96172 | 0.272041 | ||||||||
\(53\) | −3.28965 | −0.451869 | −0.225934 | − | 0.974143i | \(-0.572543\pi\) | ||||
−0.225934 | + | 0.974143i | \(0.572543\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17.7210 | −2.38949 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.323048 | −0.0424183 | ||||||||
\(59\) | 4.50627 | 0.586667 | 0.293333 | − | 0.956010i | \(-0.405235\pi\) | ||||
0.293333 | + | 0.956010i | \(0.405235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.54467 | −0.965996 | −0.482998 | − | 0.875621i | \(-0.660452\pi\) | ||||
−0.482998 | + | 0.875621i | \(0.660452\pi\) | |||||||
\(62\) | −1.09670 | −0.139281 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.09585 | −0.886981 | ||||||||
\(65\) | −3.93251 | −0.487768 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6653 | −1.54731 | −0.773653 | − | 0.633609i | \(-0.781573\pi\) | ||||
−0.773653 | + | 0.633609i | \(0.781573\pi\) | |||||||
\(68\) | 4.47548 | 0.542732 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.54869 | −1.13322 | −0.566610 | − | 0.823986i | \(-0.691746\pi\) | ||||
−0.566610 | + | 0.823986i | \(0.691746\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.08004 | −0.126409 | −0.0632044 | − | 0.998001i | \(-0.520132\pi\) | ||||
−0.0632044 | + | 0.998001i | \(0.520132\pi\) | |||||||
\(74\) | 1.39778 | 0.162489 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.50693 | −0.402273 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.791698 | 0.0890730 | 0.0445365 | − | 0.999008i | \(-0.485819\pi\) | ||||
0.0445365 | + | 0.999008i | \(0.485819\pi\) | |||||||
\(80\) | 14.8326 | 1.65833 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.58789 | −0.175354 | ||||||||
\(83\) | −7.14643 | −0.784422 | −0.392211 | − | 0.919875i | \(-0.628290\pi\) | ||||
−0.392211 | + | 0.919875i | \(0.628290\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.97166 | −0.973114 | ||||||||
\(86\) | 1.33311 | 0.143753 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.49297 | 0.372352 | ||||||||
\(89\) | −11.2656 | −1.19415 | −0.597077 | − | 0.802184i | \(-0.703671\pi\) | ||||
−0.597077 | + | 0.802184i | \(0.703671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.41381 | 0.355914 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.693685 | 0.0715482 | ||||||||
\(95\) | 7.03008 | 0.721271 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.81353 | 0.894879 | 0.447439 | − | 0.894314i | \(-0.352336\pi\) | ||||
0.447439 | + | 0.894314i | \(0.352336\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −20.5287 | −2.05287 | ||||||||
\(101\) | −14.3171 | −1.42461 | −0.712303 | − | 0.701872i | \(-0.752348\pi\) | ||||
−0.712303 | + | 0.701872i | \(0.752348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.49214 | 0.738223 | 0.369111 | − | 0.929385i | \(-0.379662\pi\) | ||||
0.369111 | + | 0.929385i | \(0.379662\pi\) | |||||||
\(104\) | 0.775135 | 0.0760082 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.643641 | −0.0625160 | ||||||||
\(107\) | −10.9784 | −1.06132 | −0.530660 | − | 0.847585i | \(-0.678056\pi\) | ||||
−0.530660 | + | 0.847585i | \(0.678056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.4463 | −1.19214 | −0.596068 | − | 0.802934i | \(-0.703271\pi\) | ||||
−0.596068 | + | 0.802934i | \(0.703271\pi\) | |||||||
\(110\) | −3.46722 | −0.330586 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.65110 | 0.155323 | 0.0776613 | − | 0.996980i | \(-0.475255\pi\) | ||||
0.0776613 | + | 0.996980i | \(0.475255\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.84340 | −0.638150 | ||||||||
\(116\) | 3.23900 | 0.300733 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.881681 | 0.0811653 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.30650 | 0.846046 | ||||||||
\(122\) | −1.47616 | −0.133645 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.9959 | 0.987460 | ||||||||
\(125\) | 21.4897 | 1.92210 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.49297 | −0.398687 | −0.199343 | − | 0.979930i | \(-0.563881\pi\) | ||||
−0.199343 | + | 0.979930i | \(0.563881\pi\) | |||||||
\(128\) | −5.96483 | −0.527222 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.769420 | −0.0674826 | ||||||||
\(131\) | −12.6567 | −1.10582 | −0.552911 | − | 0.833240i | \(-0.686483\pi\) | ||||
−0.552911 | + | 0.833240i | \(0.686483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.47804 | −0.214070 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.76840 | 0.151639 | ||||||||
\(137\) | 9.28641 | 0.793392 | 0.396696 | − | 0.917950i | \(-0.370157\pi\) | ||||
0.396696 | + | 0.917950i | \(0.370157\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.86826 | −0.156781 | ||||||||
\(143\) | 4.50627 | 0.376834 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.49297 | −0.539212 | ||||||||
\(146\) | −0.211316 | −0.0174887 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.0147 | −1.15200 | ||||||||
\(149\) | 15.1649 | 1.24235 | 0.621177 | − | 0.783670i | \(-0.286655\pi\) | ||||
0.621177 | + | 0.783670i | \(0.286655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.14159 | 0.418416 | 0.209208 | − | 0.977871i | \(-0.432911\pi\) | ||||
0.209208 | + | 0.977871i | \(0.432911\pi\) | |||||||
\(152\) | −1.38570 | −0.112395 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.0426 | −1.77051 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7311 | 0.856438 | 0.428219 | − | 0.903675i | \(-0.359141\pi\) | ||||
0.428219 | + | 0.903675i | \(0.359141\pi\) | |||||||
\(158\) | 0.154901 | 0.0123232 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.99853 | 0.711397 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.37239 | 0.185820 | 0.0929101 | − | 0.995675i | \(-0.470383\pi\) | ||||
0.0929101 | + | 0.995675i | \(0.470383\pi\) | |||||||
\(164\) | 15.9208 | 1.24320 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.39824 | −0.108525 | ||||||||
\(167\) | 12.0784 | 0.934653 | 0.467327 | − | 0.884085i | \(-0.345217\pi\) | ||||
0.467327 | + | 0.884085i | \(0.345217\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.75536 | −0.134630 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.3662 | −1.01917 | ||||||||
\(173\) | −19.4097 | −1.47569 | −0.737846 | − | 0.674969i | \(-0.764157\pi\) | ||||
−0.737846 | + | 0.674969i | \(0.764157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.9967 | −1.28117 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.20419 | −0.165211 | ||||||||
\(179\) | −14.6444 | −1.09457 | −0.547286 | − | 0.836945i | \(-0.684339\pi\) | ||||
−0.547286 | + | 0.836945i | \(0.684339\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.44627 | 0.702136 | 0.351068 | − | 0.936350i | \(-0.385819\pi\) | ||||
0.351068 | + | 0.936350i | \(0.385819\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.34890 | 0.0994422 | ||||||||
\(185\) | 28.0941 | 2.06552 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.2807 | 0.751796 | ||||||||
\(188\) | −6.95513 | −0.507255 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.37548 | 0.0997878 | ||||||||
\(191\) | −12.5537 | −0.908357 | −0.454179 | − | 0.890911i | \(-0.650067\pi\) | ||||
−0.454179 | + | 0.890911i | \(0.650067\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.36859 | −0.674366 | −0.337183 | − | 0.941439i | \(-0.609474\pi\) | ||||
−0.337183 | + | 0.941439i | \(0.609474\pi\) | |||||||
\(194\) | 1.72442 | 0.123806 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.62276 | 0.543099 | 0.271550 | − | 0.962424i | \(-0.412464\pi\) | ||||
0.271550 | + | 0.962424i | \(0.412464\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.5289 | −0.959036 | −0.479518 | − | 0.877532i | \(-0.659188\pi\) | ||||
−0.479518 | + | 0.877532i | \(0.659188\pi\) | |||||||
\(200\) | −8.11151 | −0.573570 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.80123 | −0.197094 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −31.9152 | −2.22906 | ||||||||
\(206\) | 1.46588 | 0.102133 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.77178 | −0.261526 | ||||||||
\(209\) | −8.05579 | −0.557231 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.7995 | −1.08768 | −0.543840 | − | 0.839189i | \(-0.683030\pi\) | ||||
−0.543840 | + | 0.839189i | \(0.683030\pi\) | |||||||
\(212\) | 6.45338 | 0.443220 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.14799 | −0.146833 | ||||||||
\(215\) | 26.7943 | 1.82736 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.43519 | −0.164932 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 34.7636 | 2.34376 | ||||||||
\(221\) | 2.28141 | 0.153464 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.4737 | −1.50495 | −0.752474 | − | 0.658622i | \(-0.771139\pi\) | ||||
−0.752474 | + | 0.658622i | \(0.771139\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.323048 | 0.0214889 | ||||||||
\(227\) | −9.20249 | −0.610791 | −0.305395 | − | 0.952226i | \(-0.598789\pi\) | ||||
−0.305395 | + | 0.952226i | \(0.598789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.2922 | −1.01054 | −0.505269 | − | 0.862962i | \(-0.668607\pi\) | ||||
−0.505269 | + | 0.862962i | \(0.668607\pi\) | |||||||
\(230\) | −1.33895 | −0.0882880 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.27983 | 0.0840247 | ||||||||
\(233\) | 8.05579 | 0.527752 | 0.263876 | − | 0.964557i | \(-0.414999\pi\) | ||||
0.263876 | + | 0.964557i | \(0.414999\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9424 | 0.909504 | ||||||||
\(236\) | −8.84004 | −0.575438 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.7258 | −1.40533 | −0.702663 | − | 0.711523i | \(-0.748006\pi\) | ||||
−0.702663 | + | 0.711523i | \(0.748006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.4980 | 1.32039 | 0.660195 | − | 0.751094i | \(-0.270473\pi\) | ||||
0.660195 | + | 0.751094i | \(0.270473\pi\) | |||||||
\(242\) | 1.82088 | 0.117050 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.8005 | 0.947507 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.78768 | −0.113748 | ||||||||
\(248\) | 4.34481 | 0.275896 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.20460 | 0.265922 | ||||||||
\(251\) | 2.60871 | 0.164660 | 0.0823301 | − | 0.996605i | \(-0.473764\pi\) | ||||
0.0823301 | + | 0.996605i | \(0.473764\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.84187 | 0.493014 | ||||||||
\(254\) | −0.879078 | −0.0551583 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.0246 | 0.814040 | ||||||||
\(257\) | −8.99676 | −0.561202 | −0.280601 | − | 0.959824i | \(-0.590534\pi\) | ||||
−0.280601 | + | 0.959824i | \(0.590534\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.71448 | 0.478432 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.47637 | −0.152990 | ||||||||
\(263\) | −1.43392 | −0.0884194 | −0.0442097 | − | 0.999022i | \(-0.514077\pi\) | ||||
−0.0442097 | + | 0.999022i | \(0.514077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.9366 | −0.794689 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.8457 | 1.51769 | ||||||||
\(269\) | −8.16832 | −0.498031 | −0.249016 | − | 0.968499i | \(-0.580107\pi\) | ||||
−0.249016 | + | 0.968499i | \(0.580107\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.212317 | 0.0128973 | 0.00644867 | − | 0.999979i | \(-0.497947\pi\) | ||||
0.00644867 | + | 0.999979i | \(0.497947\pi\) | |||||||
\(272\) | −8.60497 | −0.521753 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.81695 | 0.109766 | ||||||||
\(275\) | −47.1565 | −2.84364 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.9749 | 1.38043 | 0.690215 | − | 0.723604i | \(-0.257516\pi\) | ||||
0.690215 | + | 0.723604i | \(0.257516\pi\) | |||||||
\(278\) | 0.782625 | 0.0469387 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.345228 | 0.0205946 | 0.0102973 | − | 0.999947i | \(-0.496722\pi\) | ||||
0.0102973 | + | 0.999947i | \(0.496722\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.9715 | 1.72217 | 0.861087 | − | 0.508457i | \(-0.169784\pi\) | ||||
0.861087 | + | 0.508457i | \(0.169784\pi\) | |||||||
\(284\) | 18.7318 | 1.11153 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.881681 | 0.0521349 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.7952 | −0.693834 | ||||||||
\(290\) | −1.27039 | −0.0745999 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.11873 | 0.123989 | ||||||||
\(293\) | 31.5427 | 1.84274 | 0.921372 | − | 0.388682i | \(-0.127070\pi\) | ||||
0.921372 | + | 0.388682i | \(0.127070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.7210 | 1.03175 | ||||||||
\(296\) | −5.53762 | −0.321868 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.96710 | 0.171880 | ||||||||
\(299\) | 1.74021 | 0.100639 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.00598 | 0.0578879 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.74274 | 0.386723 | ||||||||
\(305\) | −29.6695 | −1.69887 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.1941 | 1.03839 | 0.519197 | − | 0.854655i | \(-0.326231\pi\) | ||||
0.519197 | + | 0.854655i | \(0.326231\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.31278 | −0.244949 | ||||||||
\(311\) | −0.376623 | −0.0213563 | −0.0106782 | − | 0.999943i | \(-0.503399\pi\) | ||||
−0.0106782 | + | 0.999943i | \(0.503399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.9883 | −0.621095 | −0.310548 | − | 0.950558i | \(-0.600512\pi\) | ||||
−0.310548 | + | 0.950558i | \(0.600512\pi\) | |||||||
\(314\) | 2.09961 | 0.118488 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.55309 | −0.0873680 | ||||||||
\(317\) | −26.1806 | −1.47045 | −0.735225 | − | 0.677823i | \(-0.762923\pi\) | ||||
−0.735225 | + | 0.677823i | \(0.762923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.44031 | 0.416578 | ||||||||
\(320\) | −27.9045 | −1.55991 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.07844 | −0.226930 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.4646 | −0.580473 | ||||||||
\(326\) | 0.464174 | 0.0257082 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.29079 | 0.347351 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.0932 | −1.87393 | −0.936967 | − | 0.349419i | \(-0.886379\pi\) | ||||
−0.936967 | + | 0.349419i | \(0.886379\pi\) | |||||||
\(332\) | 14.0193 | 0.769408 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.36321 | 0.129309 | ||||||||
\(335\) | −49.8062 | −2.72120 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.7532 | 0.803657 | 0.401829 | − | 0.915715i | \(-0.368375\pi\) | ||||
0.401829 | + | 0.915715i | \(0.368375\pi\) | |||||||
\(338\) | 0.195656 | 0.0106423 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 17.5999 | 0.954487 | ||||||||
\(341\) | 25.2587 | 1.36784 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.28141 | −0.284754 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.79763 | −0.204162 | ||||||||
\(347\) | −29.9466 | −1.60762 | −0.803809 | − | 0.594888i | \(-0.797196\pi\) | ||||
−0.803809 | + | 0.594888i | \(0.797196\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4793 | 0.721532 | 0.360766 | − | 0.932656i | \(-0.382515\pi\) | ||||
0.360766 | + | 0.932656i | \(0.382515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.3114 | −0.549602 | ||||||||
\(353\) | 0.163532 | 0.00870392 | 0.00435196 | − | 0.999991i | \(-0.498615\pi\) | ||||
0.00435196 | + | 0.999991i | \(0.498615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.5503 | −1.99296 | ||||||||
\(356\) | 22.1000 | 1.17130 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.86527 | −0.151434 | ||||||||
\(359\) | −8.92130 | −0.470848 | −0.235424 | − | 0.971893i | \(-0.575648\pi\) | ||||
−0.235424 | + | 0.971893i | \(0.575648\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8042 | −0.831799 | ||||||||
\(362\) | 1.84822 | 0.0971404 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.24726 | −0.222312 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.6552 | −1.91339 | −0.956693 | − | 0.291098i | \(-0.905979\pi\) | ||||
−0.956693 | + | 0.291098i | \(0.905979\pi\) | |||||||
\(368\) | −6.56369 | −0.342156 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.49679 | 0.285765 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.1274 | 1.40460 | 0.702302 | − | 0.711879i | \(-0.252156\pi\) | ||||
0.702302 | + | 0.711879i | \(0.252156\pi\) | |||||||
\(374\) | 2.01147 | 0.104011 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.74819 | −0.141727 | ||||||||
\(377\) | 1.65110 | 0.0850360 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.8943 | −0.816434 | −0.408217 | − | 0.912885i | \(-0.633849\pi\) | ||||
−0.408217 | + | 0.912885i | \(0.633849\pi\) | |||||||
\(380\) | −13.7910 | −0.707465 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.45622 | −0.125671 | ||||||||
\(383\) | 1.15079 | 0.0588025 | 0.0294013 | − | 0.999568i | \(-0.490640\pi\) | ||||
0.0294013 | + | 0.999568i | \(0.490640\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.83302 | −0.0932985 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.2897 | −0.877750 | ||||||||
\(389\) | 14.3130 | 0.725699 | 0.362850 | − | 0.931848i | \(-0.381804\pi\) | ||||
0.362850 | + | 0.931848i | \(0.381804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.97013 | 0.200778 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.49144 | 0.0751377 | ||||||||
\(395\) | 3.11336 | 0.156650 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.9176 | 1.30077 | 0.650383 | − | 0.759607i | \(-0.274609\pi\) | ||||
0.650383 | + | 0.759607i | \(0.274609\pi\) | |||||||
\(398\) | −2.64701 | −0.132682 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 39.4703 | 1.97351 | ||||||||
\(401\) | 4.29631 | 0.214548 | 0.107274 | − | 0.994230i | \(-0.465788\pi\) | ||||
0.107274 | + | 0.994230i | \(0.465788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.60523 | 0.279216 | ||||||||
\(404\) | 28.0861 | 1.39734 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −32.1931 | −1.59575 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.7071 | 1.22169 | 0.610844 | − | 0.791751i | \(-0.290830\pi\) | ||||
0.610844 | + | 0.791751i | \(0.290830\pi\) | |||||||
\(410\) | −6.24441 | −0.308389 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.6975 | −0.724093 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.1034 | −1.37954 | ||||||||
\(416\) | −2.28824 | −0.112190 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.57617 | −0.0770928 | ||||||||
\(419\) | −24.9293 | −1.21787 | −0.608937 | − | 0.793218i | \(-0.708404\pi\) | ||||
−0.608937 | + | 0.793218i | \(0.708404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0000 | −0.487370 | −0.243685 | − | 0.969854i | \(-0.578356\pi\) | ||||
−0.243685 | + | 0.969854i | \(0.578356\pi\) | |||||||
\(422\) | −3.09127 | −0.150480 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.54993 | 0.123835 | ||||||||
\(425\) | −23.8741 | −1.15806 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 21.5365 | 1.04101 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.24247 | 0.252814 | ||||||||
\(431\) | 5.68851 | 0.274006 | 0.137003 | − | 0.990571i | \(-0.456253\pi\) | ||||
0.137003 | + | 0.990571i | \(0.456253\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.2598 | −0.589169 | −0.294584 | − | 0.955625i | \(-0.595181\pi\) | ||||
−0.294584 | + | 0.955625i | \(0.595181\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.4161 | 1.16932 | ||||||||
\(437\) | −3.11095 | −0.148817 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.02317 | −0.239743 | −0.119871 | − | 0.992789i | \(-0.538248\pi\) | ||||
−0.119871 | + | 0.992789i | \(0.538248\pi\) | |||||||
\(440\) | 13.7361 | 0.654845 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.446372 | 0.0212317 | ||||||||
\(443\) | −0.578803 | −0.0274997 | −0.0137499 | − | 0.999905i | \(-0.504377\pi\) | ||||
−0.0137499 | + | 0.999905i | \(0.504377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −44.3022 | −2.10012 | ||||||||
\(446\) | −4.39711 | −0.208209 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.36359 | 0.347509 | 0.173755 | − | 0.984789i | \(-0.444410\pi\) | ||||
0.173755 | + | 0.984789i | \(0.444410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.5717 | 1.72210 | ||||||||
\(452\) | −3.23900 | −0.152350 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.80052 | −0.0845028 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.91824 | 0.370399 | 0.185200 | − | 0.982701i | \(-0.440707\pi\) | ||||
0.185200 | + | 0.982701i | \(0.440707\pi\) | |||||||
\(458\) | −2.99202 | −0.139808 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13.4248 | 0.625936 | ||||||||
\(461\) | −9.53600 | −0.444136 | −0.222068 | − | 0.975031i | \(-0.571281\pi\) | ||||
−0.222068 | + | 0.975031i | \(0.571281\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.16049 | 0.100406 | 0.0502032 | − | 0.998739i | \(-0.484013\pi\) | ||||
0.0502032 | + | 0.998739i | \(0.484013\pi\) | |||||||
\(464\) | −6.22758 | −0.289108 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.57617 | 0.0730145 | ||||||||
\(467\) | −8.11900 | −0.375702 | −0.187851 | − | 0.982198i | \(-0.560152\pi\) | ||||
−0.187851 | + | 0.982198i | \(0.560152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.72792 | 0.125830 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.49297 | −0.160777 | ||||||||
\(473\) | −30.7036 | −1.41176 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.7074 | 0.858357 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.25079 | −0.194427 | ||||||||
\(479\) | 14.5533 | 0.664955 | 0.332478 | − | 0.943111i | \(-0.392115\pi\) | ||||
0.332478 | + | 0.943111i | \(0.392115\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.14407 | −0.325742 | ||||||||
\(482\) | 4.01056 | 0.182676 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.2567 | −0.829852 | ||||||||
\(485\) | 34.6593 | 1.57380 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.2590 | −1.50711 | −0.753554 | − | 0.657386i | \(-0.771662\pi\) | ||||
−0.753554 | + | 0.657386i | \(0.771662\pi\) | |||||||
\(488\) | 5.84814 | 0.264733 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.5563 | 1.01795 | 0.508977 | − | 0.860780i | \(-0.330024\pi\) | ||||
0.508977 | + | 0.860780i | \(0.330024\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.76684 | 0.169650 | ||||||||
\(494\) | −0.349771 | −0.0157370 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.1417 | −0.949290 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.3854 | −0.509682 | −0.254841 | − | 0.966983i | \(-0.582023\pi\) | ||||
−0.254841 | + | 0.966983i | \(0.582023\pi\) | |||||||
\(500\) | −42.1568 | −1.88531 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.510410 | 0.0227807 | ||||||||
\(503\) | −8.81825 | −0.393186 | −0.196593 | − | 0.980485i | \(-0.562988\pi\) | ||||
−0.196593 | + | 0.980485i | \(0.562988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −56.3022 | −2.50541 | ||||||||
\(506\) | 1.53431 | 0.0682084 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.81394 | 0.391056 | ||||||||
\(509\) | 19.2838 | 0.854738 | 0.427369 | − | 0.904077i | \(-0.359441\pi\) | ||||
0.427369 | + | 0.904077i | \(0.359441\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 14.4780 | 0.639844 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.76027 | −0.0776423 | ||||||||
\(515\) | 29.4629 | 1.29829 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.9767 | −0.702653 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.04823 | 0.133674 | ||||||||
\(521\) | 25.1168 | 1.10039 | 0.550193 | − | 0.835037i | \(-0.314554\pi\) | ||||
0.550193 | + | 0.835037i | \(0.314554\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.9648 | 1.31027 | 0.655134 | − | 0.755513i | \(-0.272612\pi\) | ||||
0.655134 | + | 0.755513i | \(0.272612\pi\) | |||||||
\(524\) | 24.8289 | 1.08466 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.280556 | −0.0122328 | ||||||||
\(527\) | 12.7878 | 0.557046 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9717 | −0.868333 | ||||||||
\(530\) | −2.53113 | −0.109945 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.11574 | 0.351532 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.1726 | −1.86651 | ||||||||
\(536\) | 9.81728 | 0.424042 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.59818 | −0.0689026 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.09973 | 0.219255 | 0.109627 | − | 0.993973i | \(-0.465034\pi\) | ||||
0.109627 | + | 0.993973i | \(0.465034\pi\) | |||||||
\(542\) | 0.0415412 | 0.00178435 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.22042 | −0.223823 | ||||||||
\(545\) | −48.9451 | −2.09658 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.92025 | 0.124861 | 0.0624305 | − | 0.998049i | \(-0.480115\pi\) | ||||
0.0624305 | + | 0.998049i | \(0.480115\pi\) | |||||||
\(548\) | −18.2173 | −0.778206 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.22647 | −0.393418 | ||||||||
\(551\) | −2.95165 | −0.125744 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.49519 | 0.190982 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.84687 | −0.332782 | ||||||||
\(557\) | −25.9874 | −1.10112 | −0.550561 | − | 0.834795i | \(-0.685586\pi\) | ||||
−0.550561 | + | 0.834795i | \(0.685586\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.81353 | −0.288182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.0675460 | 0.00284925 | ||||||||
\(563\) | 3.65069 | 0.153858 | 0.0769291 | − | 0.997037i | \(-0.475488\pi\) | ||||
0.0769291 | + | 0.997037i | \(0.475488\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.49297 | 0.273161 | ||||||||
\(566\) | 5.66845 | 0.238263 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.40152 | 0.310561 | ||||||||
\(569\) | 25.3533 | 1.06286 | 0.531432 | − | 0.847101i | \(-0.321654\pi\) | ||||
0.531432 | + | 0.847101i | \(0.321654\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.7253 | 1.16027 | 0.580133 | − | 0.814522i | \(-0.303000\pi\) | ||||
0.580133 | + | 0.814522i | \(0.303000\pi\) | |||||||
\(572\) | −8.84004 | −0.369621 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.2107 | −0.759438 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.5754 | −1.64755 | −0.823773 | − | 0.566920i | \(-0.808135\pi\) | ||||
−0.823773 | + | 0.566920i | \(0.808135\pi\) | |||||||
\(578\) | −2.30780 | −0.0959918 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.7374 | 0.528891 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.8241 | 0.613951 | ||||||||
\(584\) | 0.837175 | 0.0346426 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.17153 | 0.254943 | ||||||||
\(587\) | −8.24177 | −0.340174 | −0.170087 | − | 0.985429i | \(-0.554405\pi\) | ||||
−0.170087 | + | 0.985429i | \(0.554405\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0204 | −0.412882 | ||||||||
\(590\) | 3.46722 | 0.142743 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 26.9458 | 1.10747 | ||||||||
\(593\) | −11.9230 | −0.489618 | −0.244809 | − | 0.969571i | \(-0.578725\pi\) | ||||
−0.244809 | + | 0.969571i | \(0.578725\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −29.7492 | −1.21857 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.340483 | 0.0139234 | ||||||||
\(599\) | 35.6158 | 1.45522 | 0.727611 | − | 0.685990i | \(-0.240631\pi\) | ||||
0.727611 | + | 0.685990i | \(0.240631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.9252 | −1.58779 | −0.793896 | − | 0.608054i | \(-0.791950\pi\) | ||||
−0.793896 | + | 0.608054i | \(0.791950\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0863 | −0.410408 | ||||||||
\(605\) | 36.5979 | 1.48792 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.6966 | 0.555926 | 0.277963 | − | 0.960592i | \(-0.410341\pi\) | ||||
0.277963 | + | 0.960592i | \(0.410341\pi\) | |||||||
\(608\) | 4.09065 | 0.165898 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.80502 | −0.235039 | ||||||||
\(611\) | −3.54543 | −0.143433 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.16112 | 0.127676 | 0.0638382 | − | 0.997960i | \(-0.479666\pi\) | ||||
0.0638382 | + | 0.997960i | \(0.479666\pi\) | |||||||
\(614\) | 3.55979 | 0.143662 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.9297 | −0.842597 | −0.421299 | − | 0.906922i | \(-0.638426\pi\) | ||||
−0.421299 | + | 0.906922i | \(0.638426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.9544 | −1.24416 | −0.622082 | − | 0.782952i | \(-0.713713\pi\) | ||||
−0.622082 | + | 0.782952i | \(0.713713\pi\) | |||||||
\(620\) | 43.2414 | 1.73662 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.0736887 | −0.00295465 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32.1854 | 1.28742 | ||||||||
\(626\) | −2.14993 | −0.0859285 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.0515 | −0.840045 | ||||||||
\(629\) | −16.2986 | −0.649866 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.1218 | −0.601988 | −0.300994 | − | 0.953626i | \(-0.597318\pi\) | ||||
−0.300994 | + | 0.953626i | \(0.597318\pi\) | |||||||
\(632\) | −0.613673 | −0.0244106 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.12240 | −0.203437 | ||||||||
\(635\) | −17.6687 | −0.701159 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.45574 | 0.0576335 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.4568 | −0.927210 | ||||||||
\(641\) | 47.2414 | 1.86592 | 0.932962 | − | 0.359976i | \(-0.117215\pi\) | ||||
0.932962 | + | 0.359976i | \(0.117215\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.9249 | −1.57448 | −0.787241 | − | 0.616645i | \(-0.788491\pi\) | ||||
−0.787241 | + | 0.616645i | \(0.788491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.797972 | −0.0313958 | ||||||||
\(647\) | −29.8278 | −1.17265 | −0.586327 | − | 0.810075i | \(-0.699426\pi\) | ||||
−0.586327 | + | 0.810075i | \(0.699426\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.3065 | −0.797100 | ||||||||
\(650\) | −2.04747 | −0.0803084 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.65397 | −0.182263 | ||||||||
\(653\) | −25.1549 | −0.984387 | −0.492194 | − | 0.870486i | \(-0.663805\pi\) | ||||
−0.492194 | + | 0.870486i | \(0.663805\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −49.7727 | −1.94478 | ||||||||
\(656\) | −30.6107 | −1.19515 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.3155 | −0.674517 | −0.337258 | − | 0.941412i | \(-0.609500\pi\) | ||||
−0.337258 | + | 0.941412i | \(0.609500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.20074 | 0.357867 | 0.178934 | − | 0.983861i | \(-0.442735\pi\) | ||||
0.178934 | + | 0.983861i | \(0.442735\pi\) | |||||||
\(662\) | −6.67055 | −0.259258 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.53945 | 0.214972 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.87327 | 0.111253 | ||||||||
\(668\) | −23.6944 | −0.916763 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.74490 | −0.376478 | ||||||||
\(671\) | 33.9984 | 1.31249 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.3609 | 0.669212 | 0.334606 | − | 0.942358i | \(-0.391397\pi\) | ||||
0.334606 | + | 0.942358i | \(0.391397\pi\) | |||||||
\(674\) | 2.88655 | 0.111186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.96172 | −0.0754507 | ||||||||
\(677\) | 49.9825 | 1.92098 | 0.960492 | − | 0.278307i | \(-0.0897733\pi\) | ||||
0.960492 | + | 0.278307i | \(0.0897733\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.95425 | 0.266683 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.94202 | 0.189240 | ||||||||
\(683\) | −33.6153 | −1.28626 | −0.643128 | − | 0.765759i | \(-0.722364\pi\) | ||||
−0.643128 | + | 0.765759i | \(0.722364\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.5189 | 1.39532 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25.6991 | 0.979770 | ||||||||
\(689\) | 3.28965 | 0.125326 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.1309 | 0.575607 | 0.287803 | − | 0.957689i | \(-0.407075\pi\) | ||||
0.287803 | + | 0.957689i | \(0.407075\pi\) | |||||||
\(692\) | 38.0764 | 1.44745 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.85924 | −0.222414 | ||||||||
\(695\) | 15.7300 | 0.596674 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.5153 | 0.701317 | ||||||||
\(698\) | 2.63731 | 0.0998238 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.02467 | −0.0764705 | −0.0382353 | − | 0.999269i | \(-0.512174\pi\) | ||||
−0.0382353 | + | 0.999269i | \(0.512174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.7713 | 0.481680 | ||||||||
\(704\) | 31.9758 | 1.20513 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.0319960 | 0.00120419 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.4553 | −1.14377 | −0.571886 | − | 0.820333i | \(-0.693788\pi\) | ||||
−0.571886 | + | 0.820333i | \(0.693788\pi\) | |||||||
\(710\) | −7.34695 | −0.275726 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.73238 | 0.327260 | ||||||||
\(713\) | 9.75429 | 0.365301 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.7210 | 0.662727 | ||||||||
\(716\) | 28.7282 | 1.07362 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.74551 | −0.0651418 | ||||||||
\(719\) | −24.4246 | −0.910883 | −0.455442 | − | 0.890266i | \(-0.650519\pi\) | ||||
−0.455442 | + | 0.890266i | \(0.650519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.09219 | −0.115079 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.5309 | −0.688697 | ||||||||
\(725\) | −17.2782 | −0.641695 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.09307 | 0.114716 | 0.0573578 | − | 0.998354i | \(-0.481732\pi\) | ||||
0.0573578 | + | 0.998354i | \(0.481732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.831003 | −0.0307568 | ||||||||
\(731\) | −15.5445 | −0.574933 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.41427 | 0.310788 | 0.155394 | − | 0.987853i | \(-0.450335\pi\) | ||||
0.155394 | + | 0.987853i | \(0.450335\pi\) | |||||||
\(734\) | −7.17182 | −0.264717 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.98203 | −0.146779 | ||||||||
\(737\) | 57.0731 | 2.10231 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.22758 | −0.265871 | −0.132936 | − | 0.991125i | \(-0.542440\pi\) | ||||
−0.132936 | + | 0.991125i | \(0.542440\pi\) | |||||||
\(740\) | −55.1128 | −2.02599 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 53.9092 | 1.97774 | 0.988869 | − | 0.148791i | \(-0.0475383\pi\) | ||||
0.988869 | + | 0.148791i | \(0.0475383\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 59.6360 | 2.18489 | ||||||||
\(746\) | 5.30765 | 0.194327 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.1678 | −0.737406 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.2442 | 1.06714 | 0.533568 | − | 0.845757i | \(-0.320851\pi\) | ||||
0.533568 | + | 0.845757i | \(0.320851\pi\) | |||||||
\(752\) | 13.3726 | 0.487647 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.323048 | 0.0117647 | ||||||||
\(755\) | 20.2193 | 0.735857 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0597 | −0.801773 | −0.400887 | − | 0.916128i | \(-0.631298\pi\) | ||||
−0.400887 | + | 0.916128i | \(0.631298\pi\) | |||||||
\(758\) | −3.10981 | −0.112954 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.44926 | −0.197666 | ||||||||
\(761\) | 17.8161 | 0.645833 | 0.322917 | − | 0.946427i | \(-0.395337\pi\) | ||||
0.322917 | + | 0.946427i | \(0.395337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.6269 | 0.890971 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.225159 | 0.00813532 | ||||||||
\(767\) | −4.50627 | −0.162712 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.3069 | 0.407738 | 0.203869 | − | 0.978998i | \(-0.434648\pi\) | ||||
0.203869 | + | 0.978998i | \(0.434648\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.3785 | 0.661458 | ||||||||
\(773\) | −1.92821 | −0.0693528 | −0.0346764 | − | 0.999399i | \(-0.511040\pi\) | ||||
−0.0346764 | + | 0.999399i | \(0.511040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −58.6567 | −2.10701 | ||||||||
\(776\) | −6.83168 | −0.245243 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.80043 | 0.100400 | ||||||||
\(779\) | −14.5084 | −0.519816 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.0290 | 1.53970 | ||||||||
\(782\) | 0.776782 | 0.0277777 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 42.2003 | 1.50619 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.53155 | −0.197178 | −0.0985892 | − | 0.995128i | \(-0.531433\pi\) | ||||
−0.0985892 | + | 0.995128i | \(0.531433\pi\) | |||||||
\(788\) | −14.9537 | −0.532704 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.609148 | 0.0216725 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.54467 | 0.267919 | ||||||||
\(794\) | 5.07093 | 0.179961 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.5398 | 0.940679 | ||||||||
\(797\) | −13.8038 | −0.488955 | −0.244477 | − | 0.969655i | \(-0.578616\pi\) | ||||
−0.244477 | + | 0.969655i | \(0.578616\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.08857 | −0.286153 | ||||||||
\(800\) | 23.9456 | 0.846605 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.840601 | 0.0296826 | ||||||||
\(803\) | 4.86695 | 0.171751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.09670 | 0.0386296 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.0977 | 0.390415 | ||||||||
\(809\) | −28.2996 | −0.994961 | −0.497480 | − | 0.867475i | \(-0.665741\pi\) | ||||
−0.497480 | + | 0.867475i | \(0.665741\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.2124 | 0.428837 | 0.214418 | − | 0.976742i | \(-0.431214\pi\) | ||||
0.214418 | + | 0.976742i | \(0.431214\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.29879 | −0.220772 | ||||||||
\(815\) | 9.32946 | 0.326797 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.1804 | 0.426140 | ||||||||
\(818\) | 4.83410 | 0.169020 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 62.6087 | 2.18639 | ||||||||
\(821\) | 41.4011 | 1.44491 | 0.722453 | − | 0.691420i | \(-0.243014\pi\) | ||||
0.722453 | + | 0.691420i | \(0.243014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.1752 | 1.64443 | 0.822213 | − | 0.569180i | \(-0.192739\pi\) | ||||
0.822213 | + | 0.569180i | \(0.192739\pi\) | |||||||
\(824\) | −5.80742 | −0.202311 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.1124 | −0.734150 | −0.367075 | − | 0.930191i | \(-0.619641\pi\) | ||||
−0.367075 | + | 0.930191i | \(0.619641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.636752 | 0.0221153 | 0.0110577 | − | 0.999939i | \(-0.496480\pi\) | ||||
0.0110577 | + | 0.999939i | \(0.496480\pi\) | |||||||
\(830\) | −5.49861 | −0.190859 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.09585 | 0.246004 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 47.4983 | 1.64375 | ||||||||
\(836\) | 15.8032 | 0.546565 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.87757 | −0.168493 | ||||||||
\(839\) | −26.9432 | −0.930183 | −0.465092 | − | 0.885263i | \(-0.653979\pi\) | ||||
−0.465092 | + | 0.885263i | \(0.653979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2739 | −0.905995 | ||||||||
\(842\) | −1.95656 | −0.0674276 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 30.9941 | 1.06686 | ||||||||
\(845\) | 3.93251 | 0.135282 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −12.4078 | −0.426087 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.67112 | −0.160218 | ||||||||
\(851\) | −12.4322 | −0.426170 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.74784 | −0.231042 | −0.115521 | − | 0.993305i | \(-0.536854\pi\) | ||||
−0.115521 | + | 0.993305i | \(0.536854\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.50973 | 0.290856 | ||||||||
\(857\) | −45.0268 | −1.53809 | −0.769043 | − | 0.639197i | \(-0.779267\pi\) | ||||
−0.769043 | + | 0.639197i | \(0.779267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.7270 | 1.25311 | 0.626554 | − | 0.779378i | \(-0.284465\pi\) | ||||
0.626554 | + | 0.779378i | \(0.284465\pi\) | |||||||
\(860\) | −52.5629 | −1.79238 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.11299 | 0.0379087 | ||||||||
\(863\) | 43.4275 | 1.47829 | 0.739144 | − | 0.673547i | \(-0.235230\pi\) | ||||
0.739144 | + | 0.673547i | \(0.235230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −76.3288 | −2.59526 | ||||||||
\(866\) | −2.39871 | −0.0815114 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.56761 | −0.121023 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6653 | 0.429146 | ||||||||
\(872\) | 9.64754 | 0.326707 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.608676 | −0.0205888 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.0081 | 1.35098 | 0.675488 | − | 0.737371i | \(-0.263933\pi\) | ||||
0.675488 | + | 0.737371i | \(0.263933\pi\) | |||||||
\(878\) | −0.982815 | −0.0331684 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −66.8395 | −2.25316 | ||||||||
\(881\) | 35.4308 | 1.19370 | 0.596848 | − | 0.802355i | \(-0.296420\pi\) | ||||
0.596848 | + | 0.802355i | \(0.296420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.6654 | 0.762751 | 0.381375 | − | 0.924420i | \(-0.375451\pi\) | ||||
0.381375 | + | 0.924420i | \(0.375451\pi\) | |||||||
\(884\) | −4.47548 | −0.150527 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.113246 | −0.00380459 | ||||||||
\(887\) | 44.6881 | 1.50048 | 0.750240 | − | 0.661166i | \(-0.229938\pi\) | ||||
0.750240 | + | 0.661166i | \(0.229938\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.66800 | −0.290552 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 44.0870 | 1.47614 | ||||||||
\(893\) | 6.33810 | 0.212096 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −57.5892 | −1.92499 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.44073 | 0.0480779 | ||||||||
\(899\) | 9.25480 | 0.308665 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.50505 | 0.250029 | ||||||||
\(902\) | 7.15549 | 0.238252 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.27983 | −0.0425664 | ||||||||
\(905\) | 37.1476 | 1.23483 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.4748 | 1.80881 | 0.904403 | − | 0.426680i | \(-0.140317\pi\) | ||||
0.904403 | + | 0.426680i | \(0.140317\pi\) | |||||||
\(908\) | 18.0527 | 0.599100 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.4793 | 0.910431 | 0.455215 | − | 0.890381i | \(-0.349562\pi\) | ||||
0.455215 | + | 0.890381i | \(0.349562\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.2038 | 1.06579 | ||||||||
\(914\) | 1.54925 | 0.0512447 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.9990 | 0.991196 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.2880 | −1.59287 | −0.796437 | − | 0.604722i | \(-0.793284\pi\) | ||||
−0.796437 | + | 0.604722i | \(0.793284\pi\) | |||||||
\(920\) | 5.30456 | 0.174886 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.86578 | −0.0614461 | ||||||||
\(923\) | 9.54869 | 0.314299 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 74.7601 | 2.45810 | ||||||||
\(926\) | 0.422713 | 0.0138912 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.77812 | −0.124023 | ||||||||
\(929\) | 43.3154 | 1.42113 | 0.710566 | − | 0.703631i | \(-0.248439\pi\) | ||||
0.710566 | + | 0.703631i | \(0.248439\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.8032 | −0.517651 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.58853 | −0.0519784 | ||||||||
\(935\) | 40.4288 | 1.32216 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.2211 | 1.21596 | 0.607980 | − | 0.793952i | \(-0.291980\pi\) | ||||
0.607980 | + | 0.793952i | \(0.291980\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −27.3511 | −0.892095 | ||||||||
\(941\) | 15.9751 | 0.520773 | 0.260386 | − | 0.965504i | \(-0.416150\pi\) | ||||
0.260386 | + | 0.965504i | \(0.416150\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1231 | 0.459911 | ||||||||
\(944\) | 16.9967 | 0.553194 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00736 | −0.195316 | ||||||||
\(947\) | −27.7572 | −0.901988 | −0.450994 | − | 0.892527i | \(-0.648930\pi\) | ||||
−0.450994 | + | 0.892527i | \(0.648930\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.08004 | 0.0350595 | ||||||||
\(950\) | 3.66023 | 0.118754 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.0303 | −0.389700 | −0.194850 | − | 0.980833i | \(-0.562422\pi\) | ||||
−0.194850 | + | 0.980833i | \(0.562422\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −49.3677 | −1.59750 | ||||||||
\(956\) | 42.6199 | 1.37843 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.84744 | 0.0919965 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.418620 | 0.0135039 | ||||||||
\(962\) | −1.39778 | −0.0450663 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −40.2113 | −1.29512 | ||||||||
\(965\) | −36.8421 | −1.18599 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.40788 | 0.173906 | 0.0869528 | − | 0.996212i | \(-0.472287\pi\) | ||||
0.0869528 | + | 0.996212i | \(0.472287\pi\) | |||||||
\(968\) | −7.21380 | −0.231860 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.78131 | 0.217735 | ||||||||
\(971\) | 42.2752 | 1.35668 | 0.678338 | − | 0.734750i | \(-0.262700\pi\) | ||||
0.678338 | + | 0.734750i | \(0.262700\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6.50733 | −0.208508 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.4568 | −0.910881 | ||||||||
\(977\) | 10.8302 | 0.346488 | 0.173244 | − | 0.984879i | \(-0.444575\pi\) | ||||
0.173244 | + | 0.984879i | \(0.444575\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.7660 | 1.62249 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.41329 | 0.140834 | ||||||||
\(983\) | 21.5610 | 0.687688 | 0.343844 | − | 0.939027i | \(-0.388271\pi\) | ||||
0.343844 | + | 0.939027i | \(0.388271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.9766 | 0.955134 | ||||||||
\(986\) | 0.737005 | 0.0234710 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.50693 | 0.111570 | ||||||||
\(989\) | −11.8570 | −0.377030 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.62624 | 0.274022 | 0.137011 | − | 0.990570i | \(-0.456251\pi\) | ||||
0.137011 | + | 0.990570i | \(0.456251\pi\) | |||||||
\(992\) | −12.8261 | −0.407230 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.2024 | −1.68663 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.6967 | −0.687142 | −0.343571 | − | 0.939127i | \(-0.611637\pi\) | ||||
−0.343571 | + | 0.939127i | \(0.611637\pi\) | |||||||
\(998\) | −2.22763 | −0.0705144 | ||||||||
\(999\) | 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 | 5733.2.a.bm.1.4 | 5 | ||
3.2 | odd | 2 | 637.2.a.k.1.2 | 5 | |||
7.3 | odd | 6 | 819.2.j.h.352.2 | 10 | |||
7.5 | odd | 6 | 819.2.j.h.235.2 | 10 | |||
7.6 | odd | 2 | 5733.2.a.bl.1.4 | 5 | |||
21.2 | odd | 6 | 637.2.e.m.508.4 | 10 | |||
21.5 | even | 6 | 91.2.e.c.53.4 | ✓ | 10 | ||
21.11 | odd | 6 | 637.2.e.m.79.4 | 10 | |||
21.17 | even | 6 | 91.2.e.c.79.4 | yes | 10 | ||
21.20 | even | 2 | 637.2.a.l.1.2 | 5 | |||
39.38 | odd | 2 | 8281.2.a.bx.1.4 | 5 | |||
84.47 | odd | 6 | 1456.2.r.p.417.3 | 10 | |||
84.59 | odd | 6 | 1456.2.r.p.625.3 | 10 | |||
273.38 | even | 6 | 1183.2.e.f.170.2 | 10 | |||
273.194 | even | 6 | 1183.2.e.f.508.2 | 10 | |||
273.272 | even | 2 | 8281.2.a.bw.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.e.c.53.4 | ✓ | 10 | 21.5 | even | 6 | ||
91.2.e.c.79.4 | yes | 10 | 21.17 | even | 6 | ||
637.2.a.k.1.2 | 5 | 3.2 | odd | 2 | |||
637.2.a.l.1.2 | 5 | 21.20 | even | 2 | |||
637.2.e.m.79.4 | 10 | 21.11 | odd | 6 | |||
637.2.e.m.508.4 | 10 | 21.2 | odd | 6 | |||
819.2.j.h.235.2 | 10 | 7.5 | odd | 6 | |||
819.2.j.h.352.2 | 10 | 7.3 | odd | 6 | |||
1183.2.e.f.170.2 | 10 | 273.38 | even | 6 | |||
1183.2.e.f.508.2 | 10 | 273.194 | even | 6 | |||
1456.2.r.p.417.3 | 10 | 84.47 | odd | 6 | |||
1456.2.r.p.625.3 | 10 | 84.59 | odd | 6 | |||
5733.2.a.bl.1.4 | 5 | 7.6 | odd | 2 | |||
5733.2.a.bm.1.4 | 5 | 1.1 | even | 1 | trivial | ||
8281.2.a.bw.1.4 | 5 | 273.272 | even | 2 | |||
8281.2.a.bx.1.4 | 5 | 39.38 | odd | 2 |