Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [961,2,Mod(1,961)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(961, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("961.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 961 = 31^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 961.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: | \(7.67362363425\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 6x^{2} + 4 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.28825\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 961.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.381966 | 0.270091 | 0.135045 | − | 0.990839i | \(-0.456882\pi\) | ||||
0.135045 | + | 0.990839i | \(0.456882\pi\) | |||||||
\(3\) | −2.28825 | −1.32112 | −0.660560 | − | 0.750774i | \(-0.729681\pi\) | ||||
−0.660560 | + | 0.750774i | \(0.729681\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | −2.23607 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(6\) | −0.874032 | −0.356822 | ||||||||
\(7\) | −1.00000 | −0.377964 | −0.188982 | − | 0.981981i | \(-0.560519\pi\) | ||||
−0.188982 | + | 0.981981i | \(0.560519\pi\) | |||||||
\(8\) | −1.47214 | −0.520479 | ||||||||
\(9\) | 2.23607 | 0.745356 | ||||||||
\(10\) | −0.854102 | −0.270091 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 4.24264 | 1.22474 | ||||||||
\(13\) | −6.86474 | −1.90394 | −0.951968 | − | 0.306198i | \(-0.900943\pi\) | ||||
−0.951968 | + | 0.306198i | \(0.900943\pi\) | |||||||
\(14\) | −0.381966 | −0.102085 | ||||||||
\(15\) | 5.11667 | 1.32112 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −0.540182 | −0.131013 | −0.0655066 | − | 0.997852i | \(-0.520866\pi\) | ||||
−0.0655066 | + | 0.997852i | \(0.520866\pi\) | |||||||
\(18\) | 0.854102 | 0.201314 | ||||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 4.14590 | 0.927051 | ||||||||
\(21\) | 2.28825 | 0.499336 | ||||||||
\(22\) | −1.62054 | −0.345501 | ||||||||
\(23\) | −6.86474 | −1.43140 | −0.715698 | − | 0.698410i | \(-0.753891\pi\) | ||||
−0.715698 | + | 0.698410i | \(0.753891\pi\) | |||||||
\(24\) | 3.36861 | 0.687614 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.62210 | −0.514235 | ||||||||
\(27\) | 1.74806 | 0.336415 | ||||||||
\(28\) | 1.85410 | 0.350392 | ||||||||
\(29\) | 3.70246 | 0.687529 | 0.343765 | − | 0.939056i | \(-0.388298\pi\) | ||||
0.343765 | + | 0.939056i | \(0.388298\pi\) | |||||||
\(30\) | 1.95440 | 0.356822 | ||||||||
\(31\) | 0 | 0 | ||||||||
\(32\) | 4.14590 | 0.732898 | ||||||||
\(33\) | 9.70820 | 1.68998 | ||||||||
\(34\) | −0.206331 | −0.0353855 | ||||||||
\(35\) | 2.23607 | 0.377964 | ||||||||
\(36\) | −4.14590 | −0.690983 | ||||||||
\(37\) | −4.24264 | −0.697486 | −0.348743 | − | 0.937218i | \(-0.613391\pi\) | ||||
−0.348743 | + | 0.937218i | \(0.613391\pi\) | |||||||
\(38\) | 0.381966 | 0.0619631 | ||||||||
\(39\) | 15.7082 | 2.51533 | ||||||||
\(40\) | 3.29180 | 0.520479 | ||||||||
\(41\) | 7.47214 | 1.16695 | 0.583476 | − | 0.812131i | \(-0.301692\pi\) | ||||
0.583476 | + | 0.812131i | \(0.301692\pi\) | |||||||
\(42\) | 0.874032 | 0.134866 | ||||||||
\(43\) | 0.206331 | 0.0314652 | 0.0157326 | − | 0.999876i | \(-0.494992\pi\) | ||||
0.0157326 | + | 0.999876i | \(0.494992\pi\) | |||||||
\(44\) | 7.86629 | 1.18589 | ||||||||
\(45\) | −5.00000 | −0.745356 | ||||||||
\(46\) | −2.62210 | −0.386607 | ||||||||
\(47\) | 3.70820 | 0.540897 | 0.270449 | − | 0.962734i | \(-0.412828\pi\) | ||||
0.270449 | + | 0.962734i | \(0.412828\pi\) | |||||||
\(48\) | −7.19859 | −1.03903 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.23607 | 0.173084 | ||||||||
\(52\) | 12.7279 | 1.76505 | ||||||||
\(53\) | −5.24419 | −0.720345 | −0.360173 | − | 0.932886i | \(-0.617282\pi\) | ||||
−0.360173 | + | 0.932886i | \(0.617282\pi\) | |||||||
\(54\) | 0.667701 | 0.0908626 | ||||||||
\(55\) | 9.48683 | 1.27920 | ||||||||
\(56\) | 1.47214 | 0.196722 | ||||||||
\(57\) | −2.28825 | −0.303086 | ||||||||
\(58\) | 1.41421 | 0.185695 | ||||||||
\(59\) | −5.94427 | −0.773878 | −0.386939 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386939 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(60\) | −9.48683 | −1.22474 | ||||||||
\(61\) | −4.44897 | −0.569632 | −0.284816 | − | 0.958582i | \(-0.591933\pi\) | ||||
−0.284816 | + | 0.958582i | \(0.591933\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.23607 | −0.281718 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 15.3500 | 1.90394 | ||||||||
\(66\) | 3.70820 | 0.456448 | ||||||||
\(67\) | 6.00000 | 0.733017 | 0.366508 | − | 0.930415i | \(-0.380553\pi\) | ||||
0.366508 | + | 0.930415i | \(0.380553\pi\) | |||||||
\(68\) | 1.00155 | 0.121456 | ||||||||
\(69\) | 15.7082 | 1.89105 | ||||||||
\(70\) | 0.854102 | 0.102085 | ||||||||
\(71\) | 7.47214 | 0.886779 | 0.443390 | − | 0.896329i | \(-0.353776\pi\) | ||||
0.443390 | + | 0.896329i | \(0.353776\pi\) | |||||||
\(72\) | −3.29180 | −0.387942 | ||||||||
\(73\) | −4.24264 | −0.496564 | −0.248282 | − | 0.968688i | \(-0.579866\pi\) | ||||
−0.248282 | + | 0.968688i | \(0.579866\pi\) | |||||||
\(74\) | −1.62054 | −0.188384 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.85410 | −0.212680 | ||||||||
\(77\) | 4.24264 | 0.483494 | ||||||||
\(78\) | 6.00000 | 0.679366 | ||||||||
\(79\) | 11.1074 | 1.24968 | 0.624839 | − | 0.780754i | \(-0.285165\pi\) | ||||
0.624839 | + | 0.780754i | \(0.285165\pi\) | |||||||
\(80\) | −7.03444 | −0.786475 | ||||||||
\(81\) | −10.7082 | −1.18980 | ||||||||
\(82\) | 2.85410 | 0.315183 | ||||||||
\(83\) | −3.16228 | −0.347105 | −0.173553 | − | 0.984825i | \(-0.555525\pi\) | ||||
−0.173553 | + | 0.984825i | \(0.555525\pi\) | |||||||
\(84\) | −4.24264 | −0.462910 | ||||||||
\(85\) | 1.20788 | 0.131013 | ||||||||
\(86\) | 0.0788114 | 0.00849845 | ||||||||
\(87\) | −8.47214 | −0.908308 | ||||||||
\(88\) | 6.24574 | 0.665799 | ||||||||
\(89\) | 5.86319 | 0.621496 | 0.310748 | − | 0.950492i | \(-0.399420\pi\) | ||||
0.310748 | + | 0.950492i | \(0.399420\pi\) | |||||||
\(90\) | −1.90983 | −0.201314 | ||||||||
\(91\) | 6.86474 | 0.719620 | ||||||||
\(92\) | 12.7279 | 1.32698 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.41641 | 0.146091 | ||||||||
\(95\) | −2.23607 | −0.229416 | ||||||||
\(96\) | −9.48683 | −0.968246 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | −2.29180 | −0.231506 | ||||||||
\(99\) | −9.48683 | −0.953463 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.23607 | −0.222497 | −0.111249 | − | 0.993793i | \(-0.535485\pi\) | ||||
−0.111249 | + | 0.993793i | \(0.535485\pi\) | |||||||
\(102\) | 0.472136 | 0.0467484 | ||||||||
\(103\) | −2.70820 | −0.266847 | −0.133424 | − | 0.991059i | \(-0.542597\pi\) | ||||
−0.133424 | + | 0.991059i | \(0.542597\pi\) | |||||||
\(104\) | 10.1058 | 0.990958 | ||||||||
\(105\) | −5.11667 | −0.499336 | ||||||||
\(106\) | −2.00310 | −0.194559 | ||||||||
\(107\) | −7.47214 | −0.722359 | −0.361179 | − | 0.932496i | \(-0.617626\pi\) | ||||
−0.361179 | + | 0.932496i | \(0.617626\pi\) | |||||||
\(108\) | −3.24109 | −0.311874 | ||||||||
\(109\) | −14.7082 | −1.40879 | −0.704395 | − | 0.709808i | \(-0.748782\pi\) | ||||
−0.704395 | + | 0.709808i | \(0.748782\pi\) | |||||||
\(110\) | 3.62365 | 0.345501 | ||||||||
\(111\) | 9.70820 | 0.921462 | ||||||||
\(112\) | −3.14590 | −0.297259 | ||||||||
\(113\) | −14.2361 | −1.33922 | −0.669608 | − | 0.742714i | \(-0.733538\pi\) | ||||
−0.669608 | + | 0.742714i | \(0.733538\pi\) | |||||||
\(114\) | −0.874032 | −0.0818606 | ||||||||
\(115\) | 15.3500 | 1.43140 | ||||||||
\(116\) | −6.86474 | −0.637375 | ||||||||
\(117\) | −15.3500 | −1.41911 | ||||||||
\(118\) | −2.27051 | −0.209017 | ||||||||
\(119\) | 0.540182 | 0.0495184 | ||||||||
\(120\) | −7.53244 | −0.687614 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −1.69936 | −0.153852 | ||||||||
\(123\) | −17.0981 | −1.54168 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | −0.854102 | −0.0760895 | ||||||||
\(127\) | −9.48683 | −0.841820 | −0.420910 | − | 0.907102i | \(-0.638289\pi\) | ||||
−0.420910 | + | 0.907102i | \(0.638289\pi\) | |||||||
\(128\) | −10.0902 | −0.891853 | ||||||||
\(129\) | −0.472136 | −0.0415693 | ||||||||
\(130\) | 5.86319 | 0.514235 | ||||||||
\(131\) | −19.4164 | −1.69642 | −0.848210 | − | 0.529661i | \(-0.822319\pi\) | ||||
−0.848210 | + | 0.529661i | \(0.822319\pi\) | |||||||
\(132\) | −18.0000 | −1.56670 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 2.29180 | 0.197981 | ||||||||
\(135\) | −3.90879 | −0.336415 | ||||||||
\(136\) | 0.795221 | 0.0681896 | ||||||||
\(137\) | −6.86474 | −0.586494 | −0.293247 | − | 0.956037i | \(-0.594736\pi\) | ||||
−0.293247 | + | 0.956037i | \(0.594736\pi\) | |||||||
\(138\) | 6.00000 | 0.510754 | ||||||||
\(139\) | −1.00155 | −0.0849505 | −0.0424752 | − | 0.999098i | \(-0.513524\pi\) | ||||
−0.0424752 | + | 0.999098i | \(0.513524\pi\) | |||||||
\(140\) | −4.14590 | −0.350392 | ||||||||
\(141\) | −8.48528 | −0.714590 | ||||||||
\(142\) | 2.85410 | 0.239511 | ||||||||
\(143\) | 29.1246 | 2.43552 | ||||||||
\(144\) | 7.03444 | 0.586203 | ||||||||
\(145\) | −8.27895 | −0.687529 | ||||||||
\(146\) | −1.62054 | −0.134117 | ||||||||
\(147\) | 13.7295 | 1.13239 | ||||||||
\(148\) | 7.86629 | 0.646605 | ||||||||
\(149\) | 13.4164 | 1.09911 | 0.549557 | − | 0.835456i | \(-0.314796\pi\) | ||||
0.549557 | + | 0.835456i | \(0.314796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.03476 | −0.246965 | −0.123483 | − | 0.992347i | \(-0.539406\pi\) | ||||
−0.123483 | + | 0.992347i | \(0.539406\pi\) | |||||||
\(152\) | −1.47214 | −0.119406 | ||||||||
\(153\) | −1.20788 | −0.0976515 | ||||||||
\(154\) | 1.62054 | 0.130587 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −29.1246 | −2.33184 | ||||||||
\(157\) | −4.70820 | −0.375756 | −0.187878 | − | 0.982192i | \(-0.560161\pi\) | ||||
−0.187878 | + | 0.982192i | \(0.560161\pi\) | |||||||
\(158\) | 4.24264 | 0.337526 | ||||||||
\(159\) | 12.0000 | 0.951662 | ||||||||
\(160\) | −9.27051 | −0.732898 | ||||||||
\(161\) | 6.86474 | 0.541017 | ||||||||
\(162\) | −4.09017 | −0.321354 | ||||||||
\(163\) | −12.4164 | −0.972528 | −0.486264 | − | 0.873812i | \(-0.661641\pi\) | ||||
−0.486264 | + | 0.873812i | \(0.661641\pi\) | |||||||
\(164\) | −13.8541 | −1.08182 | ||||||||
\(165\) | −21.7082 | −1.68998 | ||||||||
\(166\) | −1.20788 | −0.0937499 | ||||||||
\(167\) | 7.40492 | 0.573010 | 0.286505 | − | 0.958079i | \(-0.407507\pi\) | ||||
0.286505 | + | 0.958079i | \(0.407507\pi\) | |||||||
\(168\) | −3.36861 | −0.259894 | ||||||||
\(169\) | 34.1246 | 2.62497 | ||||||||
\(170\) | 0.461370 | 0.0353855 | ||||||||
\(171\) | 2.23607 | 0.170996 | ||||||||
\(172\) | −0.382559 | −0.0291698 | ||||||||
\(173\) | 18.0000 | 1.36851 | 0.684257 | − | 0.729241i | \(-0.260127\pi\) | ||||
0.684257 | + | 0.729241i | \(0.260127\pi\) | |||||||
\(174\) | −3.23607 | −0.245326 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.3469 | −1.00606 | ||||||||
\(177\) | 13.6020 | 1.02239 | ||||||||
\(178\) | 2.23954 | 0.167860 | ||||||||
\(179\) | −16.4304 | −1.22806 | −0.614032 | − | 0.789281i | \(-0.710454\pi\) | ||||
−0.614032 | + | 0.789281i | \(0.710454\pi\) | |||||||
\(180\) | 9.27051 | 0.690983 | ||||||||
\(181\) | −18.1784 | −1.35119 | −0.675597 | − | 0.737271i | \(-0.736114\pi\) | ||||
−0.675597 | + | 0.737271i | \(0.736114\pi\) | |||||||
\(182\) | 2.62210 | 0.194363 | ||||||||
\(183\) | 10.1803 | 0.752552 | ||||||||
\(184\) | 10.1058 | 0.745011 | ||||||||
\(185\) | 9.48683 | 0.697486 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.29180 | 0.167593 | ||||||||
\(188\) | −6.87539 | −0.501439 | ||||||||
\(189\) | −1.74806 | −0.127153 | ||||||||
\(190\) | −0.854102 | −0.0619631 | ||||||||
\(191\) | 14.2361 | 1.03009 | 0.515043 | − | 0.857164i | \(-0.327776\pi\) | ||||
0.515043 | + | 0.857164i | \(0.327776\pi\) | |||||||
\(192\) | 10.7735 | 0.777512 | ||||||||
\(193\) | −7.29180 | −0.524875 | −0.262437 | − | 0.964949i | \(-0.584526\pi\) | ||||
−0.262437 | + | 0.964949i | \(0.584526\pi\) | |||||||
\(194\) | −2.67376 | −0.191965 | ||||||||
\(195\) | −35.1246 | −2.51533 | ||||||||
\(196\) | 11.1246 | 0.794615 | ||||||||
\(197\) | 7.40492 | 0.527579 | 0.263789 | − | 0.964580i | \(-0.415028\pi\) | ||||
0.263789 | + | 0.964580i | \(0.415028\pi\) | |||||||
\(198\) | −3.62365 | −0.257521 | ||||||||
\(199\) | 14.7310 | 1.04425 | 0.522127 | − | 0.852868i | \(-0.325139\pi\) | ||||
0.522127 | + | 0.852868i | \(0.325139\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.7295 | −0.968402 | ||||||||
\(202\) | −0.854102 | −0.0600944 | ||||||||
\(203\) | −3.70246 | −0.259862 | ||||||||
\(204\) | −2.29180 | −0.160458 | ||||||||
\(205\) | −16.7082 | −1.16695 | ||||||||
\(206\) | −1.03444 | −0.0720730 | ||||||||
\(207\) | −15.3500 | −1.06690 | ||||||||
\(208\) | −21.5958 | −1.49740 | ||||||||
\(209\) | −4.24264 | −0.293470 | ||||||||
\(210\) | −1.95440 | −0.134866 | ||||||||
\(211\) | −5.00000 | −0.344214 | −0.172107 | − | 0.985078i | \(-0.555058\pi\) | ||||
−0.172107 | + | 0.985078i | \(0.555058\pi\) | |||||||
\(212\) | 9.72327 | 0.667797 | ||||||||
\(213\) | −17.0981 | −1.17154 | ||||||||
\(214\) | −2.85410 | −0.195102 | ||||||||
\(215\) | −0.461370 | −0.0314652 | ||||||||
\(216\) | −2.57339 | −0.175097 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −5.61803 | −0.380501 | ||||||||
\(219\) | 9.70820 | 0.656020 | ||||||||
\(220\) | −17.5896 | −1.18589 | ||||||||
\(221\) | 3.70820 | 0.249441 | ||||||||
\(222\) | 3.70820 | 0.248878 | ||||||||
\(223\) | 21.8021 | 1.45998 | 0.729988 | − | 0.683460i | \(-0.239526\pi\) | ||||
0.729988 | + | 0.683460i | \(0.239526\pi\) | |||||||
\(224\) | −4.14590 | −0.277009 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.43769 | −0.361710 | ||||||||
\(227\) | 15.7082 | 1.04259 | 0.521295 | − | 0.853377i | \(-0.325449\pi\) | ||||
0.521295 | + | 0.853377i | \(0.325449\pi\) | |||||||
\(228\) | 4.24264 | 0.280976 | ||||||||
\(229\) | −4.24264 | −0.280362 | −0.140181 | − | 0.990126i | \(-0.544768\pi\) | ||||
−0.140181 | + | 0.990126i | \(0.544768\pi\) | |||||||
\(230\) | 5.86319 | 0.386607 | ||||||||
\(231\) | −9.70820 | −0.638753 | ||||||||
\(232\) | −5.45052 | −0.357844 | ||||||||
\(233\) | −4.52786 | −0.296630 | −0.148315 | − | 0.988940i | \(-0.547385\pi\) | ||||
−0.148315 | + | 0.988940i | \(0.547385\pi\) | |||||||
\(234\) | −5.86319 | −0.383288 | ||||||||
\(235\) | −8.29180 | −0.540897 | ||||||||
\(236\) | 11.0213 | 0.717425 | ||||||||
\(237\) | −25.4164 | −1.65097 | ||||||||
\(238\) | 0.206331 | 0.0133745 | ||||||||
\(239\) | 16.3516 | 1.05770 | 0.528848 | − | 0.848717i | \(-0.322624\pi\) | ||||
0.528848 | + | 0.848717i | \(0.322624\pi\) | |||||||
\(240\) | 16.0965 | 1.03903 | ||||||||
\(241\) | −14.7310 | −0.948909 | −0.474454 | − | 0.880280i | \(-0.657355\pi\) | ||||
−0.474454 | + | 0.880280i | \(0.657355\pi\) | |||||||
\(242\) | 2.67376 | 0.171876 | ||||||||
\(243\) | 19.2588 | 1.23545 | ||||||||
\(244\) | 8.24885 | 0.528078 | ||||||||
\(245\) | 13.4164 | 0.857143 | ||||||||
\(246\) | −6.53089 | −0.416394 | ||||||||
\(247\) | −6.86474 | −0.436793 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.23607 | 0.458567 | ||||||||
\(250\) | 4.27051 | 0.270091 | ||||||||
\(251\) | 23.7565 | 1.49950 | 0.749748 | − | 0.661723i | \(-0.230175\pi\) | ||||
0.749748 | + | 0.661723i | \(0.230175\pi\) | |||||||
\(252\) | 4.14590 | 0.261167 | ||||||||
\(253\) | 29.1246 | 1.83105 | ||||||||
\(254\) | −3.62365 | −0.227368 | ||||||||
\(255\) | −2.76393 | −0.173084 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | 23.9443 | 1.49360 | 0.746801 | − | 0.665047i | \(-0.231589\pi\) | ||||
0.746801 | + | 0.665047i | \(0.231589\pi\) | |||||||
\(258\) | −0.180340 | −0.0112275 | ||||||||
\(259\) | 4.24264 | 0.263625 | ||||||||
\(260\) | −28.4605 | −1.76505 | ||||||||
\(261\) | 8.27895 | 0.512454 | ||||||||
\(262\) | −7.41641 | −0.458187 | ||||||||
\(263\) | −2.70091 | −0.166545 | −0.0832725 | − | 0.996527i | \(-0.526537\pi\) | ||||
−0.0832725 | + | 0.996527i | \(0.526537\pi\) | |||||||
\(264\) | −14.2918 | −0.879599 | ||||||||
\(265\) | 11.7264 | 0.720345 | ||||||||
\(266\) | −0.381966 | −0.0234198 | ||||||||
\(267\) | −13.4164 | −0.821071 | ||||||||
\(268\) | −11.1246 | −0.679544 | ||||||||
\(269\) | −14.8098 | −0.902972 | −0.451486 | − | 0.892278i | \(-0.649106\pi\) | ||||
−0.451486 | + | 0.892278i | \(0.649106\pi\) | |||||||
\(270\) | −1.49302 | −0.0908626 | ||||||||
\(271\) | 28.0779 | 1.70561 | 0.852807 | − | 0.522227i | \(-0.174899\pi\) | ||||
0.852807 | + | 0.522227i | \(0.174899\pi\) | |||||||
\(272\) | −1.69936 | −0.103039 | ||||||||
\(273\) | −15.7082 | −0.950704 | ||||||||
\(274\) | −2.62210 | −0.158407 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −29.1246 | −1.75310 | ||||||||
\(277\) | −19.5927 | −1.17721 | −0.588604 | − | 0.808421i | \(-0.700322\pi\) | ||||
−0.588604 | + | 0.808421i | \(0.700322\pi\) | |||||||
\(278\) | −0.382559 | −0.0229443 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.29180 | −0.196722 | ||||||||
\(281\) | −31.3607 | −1.87082 | −0.935411 | − | 0.353563i | \(-0.884970\pi\) | ||||
−0.935411 | + | 0.353563i | \(0.884970\pi\) | |||||||
\(282\) | −3.24109 | −0.193004 | ||||||||
\(283\) | 24.0000 | 1.42665 | 0.713326 | − | 0.700832i | \(-0.247188\pi\) | ||||
0.713326 | + | 0.700832i | \(0.247188\pi\) | |||||||
\(284\) | −13.8541 | −0.822090 | ||||||||
\(285\) | 5.11667 | 0.303086 | ||||||||
\(286\) | 11.1246 | 0.657812 | ||||||||
\(287\) | −7.47214 | −0.441066 | ||||||||
\(288\) | 9.27051 | 0.546270 | ||||||||
\(289\) | −16.7082 | −0.982836 | ||||||||
\(290\) | −3.16228 | −0.185695 | ||||||||
\(291\) | 16.0177 | 0.938975 | ||||||||
\(292\) | 7.86629 | 0.460340 | ||||||||
\(293\) | −15.7082 | −0.917683 | −0.458842 | − | 0.888518i | \(-0.651735\pi\) | ||||
−0.458842 | + | 0.888518i | \(0.651735\pi\) | |||||||
\(294\) | 5.24419 | 0.305848 | ||||||||
\(295\) | 13.2918 | 0.773878 | ||||||||
\(296\) | 6.24574 | 0.363026 | ||||||||
\(297\) | −7.41641 | −0.430344 | ||||||||
\(298\) | 5.12461 | 0.296861 | ||||||||
\(299\) | 47.1246 | 2.72529 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.206331 | −0.0118927 | ||||||||
\(302\) | −1.15917 | −0.0667030 | ||||||||
\(303\) | 5.11667 | 0.293945 | ||||||||
\(304\) | 3.14590 | 0.180430 | ||||||||
\(305\) | 9.94820 | 0.569632 | ||||||||
\(306\) | −0.461370 | −0.0263748 | ||||||||
\(307\) | −16.1246 | −0.920280 | −0.460140 | − | 0.887846i | \(-0.652201\pi\) | ||||
−0.460140 | + | 0.887846i | \(0.652201\pi\) | |||||||
\(308\) | −7.86629 | −0.448223 | ||||||||
\(309\) | 6.19704 | 0.352537 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5279 | 0.937209 | 0.468605 | − | 0.883408i | \(-0.344757\pi\) | ||||
0.468605 | + | 0.883408i | \(0.344757\pi\) | |||||||
\(312\) | −23.1246 | −1.30917 | ||||||||
\(313\) | 21.0069 | 1.18738 | 0.593689 | − | 0.804694i | \(-0.297671\pi\) | ||||
0.593689 | + | 0.804694i | \(0.297671\pi\) | |||||||
\(314\) | −1.79837 | −0.101488 | ||||||||
\(315\) | 5.00000 | 0.281718 | ||||||||
\(316\) | −20.5942 | −1.15851 | ||||||||
\(317\) | 21.7639 | 1.22238 | 0.611192 | − | 0.791482i | \(-0.290690\pi\) | ||||
0.611192 | + | 0.791482i | \(0.290690\pi\) | |||||||
\(318\) | 4.58359 | 0.257035 | ||||||||
\(319\) | −15.7082 | −0.879491 | ||||||||
\(320\) | 10.5279 | 0.588525 | ||||||||
\(321\) | 17.0981 | 0.954322 | ||||||||
\(322\) | 2.62210 | 0.146124 | ||||||||
\(323\) | −0.540182 | −0.0300565 | ||||||||
\(324\) | 19.8541 | 1.10301 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.74265 | −0.262671 | ||||||||
\(327\) | 33.6560 | 1.86118 | ||||||||
\(328\) | −11.0000 | −0.607373 | ||||||||
\(329\) | −3.70820 | −0.204440 | ||||||||
\(330\) | −8.29180 | −0.456448 | ||||||||
\(331\) | 25.6321 | 1.40887 | 0.704433 | − | 0.709770i | \(-0.251201\pi\) | ||||
0.704433 | + | 0.709770i | \(0.251201\pi\) | |||||||
\(332\) | 5.86319 | 0.321784 | ||||||||
\(333\) | −9.48683 | −0.519875 | ||||||||
\(334\) | 2.82843 | 0.154765 | ||||||||
\(335\) | −13.4164 | −0.733017 | ||||||||
\(336\) | 7.19859 | 0.392715 | ||||||||
\(337\) | 5.86319 | 0.319388 | 0.159694 | − | 0.987167i | \(-0.448949\pi\) | ||||
0.159694 | + | 0.987167i | \(0.448949\pi\) | |||||||
\(338\) | 13.0344 | 0.708980 | ||||||||
\(339\) | 32.5756 | 1.76926 | ||||||||
\(340\) | −2.23954 | −0.121456 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.854102 | 0.0461845 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −0.303747 | −0.0163770 | ||||||||
\(345\) | −35.1246 | −1.89105 | ||||||||
\(346\) | 6.87539 | 0.369623 | ||||||||
\(347\) | −25.8384 | −1.38708 | −0.693539 | − | 0.720419i | \(-0.743950\pi\) | ||||
−0.693539 | + | 0.720419i | \(0.743950\pi\) | |||||||
\(348\) | 15.7082 | 0.842048 | ||||||||
\(349\) | 6.00000 | 0.321173 | 0.160586 | − | 0.987022i | \(-0.448662\pi\) | ||||
0.160586 | + | 0.987022i | \(0.448662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.0000 | −0.640513 | ||||||||
\(352\) | −17.5896 | −0.937526 | ||||||||
\(353\) | −15.8902 | −0.845750 | −0.422875 | − | 0.906188i | \(-0.638979\pi\) | ||||
−0.422875 | + | 0.906188i | \(0.638979\pi\) | |||||||
\(354\) | 5.19548 | 0.276137 | ||||||||
\(355\) | −16.7082 | −0.886779 | ||||||||
\(356\) | −10.8709 | −0.576159 | ||||||||
\(357\) | −1.23607 | −0.0654197 | ||||||||
\(358\) | −6.27585 | −0.331689 | ||||||||
\(359\) | 9.76393 | 0.515321 | 0.257660 | − | 0.966236i | \(-0.417048\pi\) | ||||
0.257660 | + | 0.966236i | \(0.417048\pi\) | |||||||
\(360\) | 7.36068 | 0.387942 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | −6.94355 | −0.364945 | ||||||||
\(363\) | −16.0177 | −0.840712 | ||||||||
\(364\) | −12.7279 | −0.667124 | ||||||||
\(365\) | 9.48683 | 0.496564 | ||||||||
\(366\) | 3.88854 | 0.203257 | ||||||||
\(367\) | 12.3153 | 0.642851 | 0.321426 | − | 0.946935i | \(-0.395838\pi\) | ||||
0.321426 | + | 0.946935i | \(0.395838\pi\) | |||||||
\(368\) | −21.5958 | −1.12576 | ||||||||
\(369\) | 16.7082 | 0.869794 | ||||||||
\(370\) | 3.62365 | 0.188384 | ||||||||
\(371\) | 5.24419 | 0.272265 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.7082 | −1.17579 | −0.587893 | − | 0.808939i | \(-0.700042\pi\) | ||||
−0.587893 | + | 0.808939i | \(0.700042\pi\) | |||||||
\(374\) | 0.875388 | 0.0452652 | ||||||||
\(375\) | −25.5834 | −1.32112 | ||||||||
\(376\) | −5.45898 | −0.281525 | ||||||||
\(377\) | −25.4164 | −1.30901 | ||||||||
\(378\) | −0.667701 | −0.0343428 | ||||||||
\(379\) | −19.4164 | −0.997354 | −0.498677 | − | 0.866788i | \(-0.666181\pi\) | ||||
−0.498677 | + | 0.866788i | \(0.666181\pi\) | |||||||
\(380\) | 4.14590 | 0.212680 | ||||||||
\(381\) | 21.7082 | 1.11214 | ||||||||
\(382\) | 5.43769 | 0.278217 | ||||||||
\(383\) | 19.0525 | 0.973536 | 0.486768 | − | 0.873531i | \(-0.338176\pi\) | ||||
0.486768 | + | 0.873531i | \(0.338176\pi\) | |||||||
\(384\) | 23.0888 | 1.17824 | ||||||||
\(385\) | −9.48683 | −0.483494 | ||||||||
\(386\) | −2.78522 | −0.141764 | ||||||||
\(387\) | 0.461370 | 0.0234528 | ||||||||
\(388\) | 12.9787 | 0.658894 | ||||||||
\(389\) | −33.7835 | −1.71289 | −0.856446 | − | 0.516237i | \(-0.827332\pi\) | ||||
−0.856446 | + | 0.516237i | \(0.827332\pi\) | |||||||
\(390\) | −13.4164 | −0.679366 | ||||||||
\(391\) | 3.70820 | 0.187532 | ||||||||
\(392\) | 8.83282 | 0.446125 | ||||||||
\(393\) | 44.4295 | 2.24117 | ||||||||
\(394\) | 2.82843 | 0.142494 | ||||||||
\(395\) | −24.8369 | −1.24968 | ||||||||
\(396\) | 17.5896 | 0.883908 | ||||||||
\(397\) | 1.29180 | 0.0648334 | 0.0324167 | − | 0.999474i | \(-0.489680\pi\) | ||||
0.0324167 | + | 0.999474i | \(0.489680\pi\) | |||||||
\(398\) | 5.62675 | 0.282044 | ||||||||
\(399\) | 2.28825 | 0.114556 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.70246 | 0.184892 | 0.0924460 | − | 0.995718i | \(-0.470531\pi\) | ||||
0.0924460 | + | 0.995718i | \(0.470531\pi\) | |||||||
\(402\) | −5.24419 | −0.261557 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.14590 | 0.206266 | ||||||||
\(405\) | 23.9443 | 1.18980 | ||||||||
\(406\) | −1.41421 | −0.0701862 | ||||||||
\(407\) | 18.0000 | 0.892227 | ||||||||
\(408\) | −1.81966 | −0.0900866 | ||||||||
\(409\) | 17.3531 | 0.858057 | 0.429028 | − | 0.903291i | \(-0.358856\pi\) | ||||
0.429028 | + | 0.903291i | \(0.358856\pi\) | |||||||
\(410\) | −6.38197 | −0.315183 | ||||||||
\(411\) | 15.7082 | 0.774829 | ||||||||
\(412\) | 5.02129 | 0.247381 | ||||||||
\(413\) | 5.94427 | 0.292498 | ||||||||
\(414\) | −5.86319 | −0.288160 | ||||||||
\(415\) | 7.07107 | 0.347105 | ||||||||
\(416\) | −28.4605 | −1.39539 | ||||||||
\(417\) | 2.29180 | 0.112230 | ||||||||
\(418\) | −1.62054 | −0.0792634 | ||||||||
\(419\) | −18.5967 | −0.908511 | −0.454255 | − | 0.890872i | \(-0.650095\pi\) | ||||
−0.454255 | + | 0.890872i | \(0.650095\pi\) | |||||||
\(420\) | 9.48683 | 0.462910 | ||||||||
\(421\) | −0.416408 | −0.0202945 | −0.0101472 | − | 0.999949i | \(-0.503230\pi\) | ||||
−0.0101472 | + | 0.999949i | \(0.503230\pi\) | |||||||
\(422\) | −1.90983 | −0.0929691 | ||||||||
\(423\) | 8.29180 | 0.403161 | ||||||||
\(424\) | 7.72016 | 0.374924 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.53089 | −0.316422 | ||||||||
\(427\) | 4.44897 | 0.215301 | ||||||||
\(428\) | 13.8541 | 0.669663 | ||||||||
\(429\) | −66.6443 | −3.21762 | ||||||||
\(430\) | −0.176228 | −0.00849845 | ||||||||
\(431\) | −0.111456 | −0.00536866 | −0.00268433 | − | 0.999996i | \(-0.500854\pi\) | ||||
−0.00268433 | + | 0.999996i | \(0.500854\pi\) | |||||||
\(432\) | 5.49923 | 0.264582 | ||||||||
\(433\) | −21.5958 | −1.03783 | −0.518913 | − | 0.854827i | \(-0.673663\pi\) | ||||
−0.518913 | + | 0.854827i | \(0.673663\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 18.9443 | 0.908308 | ||||||||
\(436\) | 27.2705 | 1.30602 | ||||||||
\(437\) | −6.86474 | −0.328385 | ||||||||
\(438\) | 3.70820 | 0.177185 | ||||||||
\(439\) | −25.0000 | −1.19318 | −0.596592 | − | 0.802544i | \(-0.703479\pi\) | ||||
−0.596592 | + | 0.802544i | \(0.703479\pi\) | |||||||
\(440\) | −13.9659 | −0.665799 | ||||||||
\(441\) | −13.4164 | −0.638877 | ||||||||
\(442\) | 1.41641 | 0.0673717 | ||||||||
\(443\) | 23.9443 | 1.13763 | 0.568813 | − | 0.822467i | \(-0.307403\pi\) | ||||
0.568813 | + | 0.822467i | \(0.307403\pi\) | |||||||
\(444\) | −18.0000 | −0.854242 | ||||||||
\(445\) | −13.1105 | −0.621496 | ||||||||
\(446\) | 8.32766 | 0.394326 | ||||||||
\(447\) | −30.7000 | −1.45206 | ||||||||
\(448\) | 4.70820 | 0.222442 | ||||||||
\(449\) | 42.1900 | 1.99107 | 0.995534 | − | 0.0944042i | \(-0.0300946\pi\) | ||||
0.995534 | + | 0.0944042i | \(0.0300946\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.7016 | −1.49277 | ||||||||
\(452\) | 26.3951 | 1.24152 | ||||||||
\(453\) | 6.94427 | 0.326270 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | −15.3500 | −0.719620 | ||||||||
\(456\) | 3.36861 | 0.157750 | ||||||||
\(457\) | −11.3137 | −0.529233 | −0.264616 | − | 0.964354i | \(-0.585245\pi\) | ||||
−0.264616 | + | 0.964354i | \(0.585245\pi\) | |||||||
\(458\) | −1.62054 | −0.0757231 | ||||||||
\(459\) | −0.944272 | −0.0440748 | ||||||||
\(460\) | −28.4605 | −1.32698 | ||||||||
\(461\) | 39.1065 | 1.82137 | 0.910686 | − | 0.413100i | \(-0.135554\pi\) | ||||
0.910686 | + | 0.413100i | \(0.135554\pi\) | |||||||
\(462\) | −3.70820 | −0.172521 | ||||||||
\(463\) | −15.1437 | −0.703787 | −0.351893 | − | 0.936040i | \(-0.614462\pi\) | ||||
−0.351893 | + | 0.936040i | \(0.614462\pi\) | |||||||
\(464\) | 11.6476 | 0.540724 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.72949 | −0.0801171 | ||||||||
\(467\) | 15.6525 | 0.724310 | 0.362155 | − | 0.932118i | \(-0.382041\pi\) | ||||
0.362155 | + | 0.932118i | \(0.382041\pi\) | |||||||
\(468\) | 28.4605 | 1.31559 | ||||||||
\(469\) | −6.00000 | −0.277054 | ||||||||
\(470\) | −3.16718 | −0.146091 | ||||||||
\(471\) | 10.7735 | 0.496418 | ||||||||
\(472\) | 8.75078 | 0.402787 | ||||||||
\(473\) | −0.875388 | −0.0402504 | ||||||||
\(474\) | −9.70820 | −0.445913 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.00155 | −0.0459060 | ||||||||
\(477\) | −11.7264 | −0.536914 | ||||||||
\(478\) | 6.24574 | 0.285674 | ||||||||
\(479\) | 25.4721 | 1.16385 | 0.581926 | − | 0.813242i | \(-0.302299\pi\) | ||||
0.581926 | + | 0.813242i | \(0.302299\pi\) | |||||||
\(480\) | 21.2132 | 0.968246 | ||||||||
\(481\) | 29.1246 | 1.32797 | ||||||||
\(482\) | −5.62675 | −0.256291 | ||||||||
\(483\) | −15.7082 | −0.714748 | ||||||||
\(484\) | −12.9787 | −0.589942 | ||||||||
\(485\) | 15.6525 | 0.710742 | ||||||||
\(486\) | 7.35621 | 0.333684 | ||||||||
\(487\) | −18.5911 | −0.842443 | −0.421222 | − | 0.906958i | \(-0.638399\pi\) | ||||
−0.421222 | + | 0.906958i | \(0.638399\pi\) | |||||||
\(488\) | 6.54949 | 0.296482 | ||||||||
\(489\) | 28.4118 | 1.28483 | ||||||||
\(490\) | 5.12461 | 0.231506 | ||||||||
\(491\) | 9.56564 | 0.431691 | 0.215846 | − | 0.976427i | \(-0.430749\pi\) | ||||
0.215846 | + | 0.976427i | \(0.430749\pi\) | |||||||
\(492\) | 31.7016 | 1.42922 | ||||||||
\(493\) | −2.00000 | −0.0900755 | ||||||||
\(494\) | −2.62210 | −0.117974 | ||||||||
\(495\) | 21.2132 | 0.953463 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.47214 | −0.335171 | ||||||||
\(498\) | 2.76393 | 0.123855 | ||||||||
\(499\) | −18.3848 | −0.823016 | −0.411508 | − | 0.911406i | \(-0.634998\pi\) | ||||
−0.411508 | + | 0.911406i | \(0.634998\pi\) | |||||||
\(500\) | −20.7295 | −0.927051 | ||||||||
\(501\) | −16.9443 | −0.757014 | ||||||||
\(502\) | 9.07417 | 0.405000 | ||||||||
\(503\) | 2.88854 | 0.128794 | 0.0643969 | − | 0.997924i | \(-0.479488\pi\) | ||||
0.0643969 | + | 0.997924i | \(0.479488\pi\) | |||||||
\(504\) | 3.29180 | 0.146628 | ||||||||
\(505\) | 5.00000 | 0.222497 | ||||||||
\(506\) | 11.1246 | 0.494549 | ||||||||
\(507\) | −78.0855 | −3.46790 | ||||||||
\(508\) | 17.5896 | 0.780410 | ||||||||
\(509\) | 4.78282 | 0.211995 | 0.105997 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.105997 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(510\) | −1.05573 | −0.0467484 | ||||||||
\(511\) | 4.24264 | 0.187683 | ||||||||
\(512\) | 22.3050 | 0.985749 | ||||||||
\(513\) | 1.74806 | 0.0771789 | ||||||||
\(514\) | 9.14590 | 0.403408 | ||||||||
\(515\) | 6.05573 | 0.266847 | ||||||||
\(516\) | 0.875388 | 0.0385368 | ||||||||
\(517\) | −15.7326 | −0.691918 | ||||||||
\(518\) | 1.62054 | 0.0712026 | ||||||||
\(519\) | −41.1884 | −1.80797 | ||||||||
\(520\) | −22.5973 | −0.990958 | ||||||||
\(521\) | 13.4164 | 0.587784 | 0.293892 | − | 0.955839i | \(-0.405049\pi\) | ||||
0.293892 | + | 0.955839i | \(0.405049\pi\) | |||||||
\(522\) | 3.16228 | 0.138409 | ||||||||
\(523\) | −29.0795 | −1.27156 | −0.635779 | − | 0.771871i | \(-0.719321\pi\) | ||||
−0.635779 | + | 0.771871i | \(0.719321\pi\) | |||||||
\(524\) | 36.0000 | 1.57267 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.03165 | −0.0449823 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 30.5410 | 1.32913 | ||||||||
\(529\) | 24.1246 | 1.04890 | ||||||||
\(530\) | 4.47907 | 0.194559 | ||||||||
\(531\) | −13.2918 | −0.576815 | ||||||||
\(532\) | 1.85410 | 0.0803855 | ||||||||
\(533\) | −51.2942 | −2.22180 | ||||||||
\(534\) | −5.12461 | −0.221764 | ||||||||
\(535\) | 16.7082 | 0.722359 | ||||||||
\(536\) | −8.83282 | −0.381520 | ||||||||
\(537\) | 37.5967 | 1.62242 | ||||||||
\(538\) | −5.65685 | −0.243884 | ||||||||
\(539\) | 25.4558 | 1.09646 | ||||||||
\(540\) | 7.24730 | 0.311874 | ||||||||
\(541\) | −27.8328 | −1.19663 | −0.598313 | − | 0.801262i | \(-0.704162\pi\) | ||||
−0.598313 | + | 0.801262i | \(0.704162\pi\) | |||||||
\(542\) | 10.7248 | 0.460670 | ||||||||
\(543\) | 41.5967 | 1.78509 | ||||||||
\(544\) | −2.23954 | −0.0960194 | ||||||||
\(545\) | 32.8885 | 1.40879 | ||||||||
\(546\) | −6.00000 | −0.256776 | ||||||||
\(547\) | −24.4164 | −1.04397 | −0.521985 | − | 0.852955i | \(-0.674808\pi\) | ||||
−0.521985 | + | 0.852955i | \(0.674808\pi\) | |||||||
\(548\) | 12.7279 | 0.543710 | ||||||||
\(549\) | −9.94820 | −0.424579 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.70246 | 0.157730 | ||||||||
\(552\) | −23.1246 | −0.984249 | ||||||||
\(553\) | −11.1074 | −0.472334 | ||||||||
\(554\) | −7.48373 | −0.317953 | ||||||||
\(555\) | −21.7082 | −0.921462 | ||||||||
\(556\) | 1.85698 | 0.0787534 | ||||||||
\(557\) | 23.2951 | 0.987046 | 0.493523 | − | 0.869733i | \(-0.335709\pi\) | ||||
0.493523 | + | 0.869733i | \(0.335709\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.41641 | −0.0599077 | ||||||||
\(560\) | 7.03444 | 0.297259 | ||||||||
\(561\) | −5.24419 | −0.221410 | ||||||||
\(562\) | −11.9787 | −0.505292 | ||||||||
\(563\) | 14.2361 | 0.599979 | 0.299989 | − | 0.953943i | \(-0.403017\pi\) | ||||
0.299989 | + | 0.953943i | \(0.403017\pi\) | |||||||
\(564\) | 15.7326 | 0.662461 | ||||||||
\(565\) | 31.8328 | 1.33922 | ||||||||
\(566\) | 9.16718 | 0.385325 | ||||||||
\(567\) | 10.7082 | 0.449702 | ||||||||
\(568\) | −11.0000 | −0.461550 | ||||||||
\(569\) | 30.7000 | 1.28701 | 0.643506 | − | 0.765441i | \(-0.277479\pi\) | ||||
0.643506 | + | 0.765441i | \(0.277479\pi\) | |||||||
\(570\) | 1.95440 | 0.0818606 | ||||||||
\(571\) | −6.86474 | −0.287280 | −0.143640 | − | 0.989630i | \(-0.545881\pi\) | ||||
−0.143640 | + | 0.989630i | \(0.545881\pi\) | |||||||
\(572\) | −54.0000 | −2.25785 | ||||||||
\(573\) | −32.5756 | −1.36087 | ||||||||
\(574\) | −2.85410 | −0.119128 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −10.5279 | −0.438661 | ||||||||
\(577\) | −30.0000 | −1.24892 | −0.624458 | − | 0.781058i | \(-0.714680\pi\) | ||||
−0.624458 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(578\) | −6.38197 | −0.265455 | ||||||||
\(579\) | 16.6854 | 0.693422 | ||||||||
\(580\) | 15.3500 | 0.637375 | ||||||||
\(581\) | 3.16228 | 0.131193 | ||||||||
\(582\) | 6.11822 | 0.253609 | ||||||||
\(583\) | 22.2492 | 0.921469 | ||||||||
\(584\) | 6.24574 | 0.258451 | ||||||||
\(585\) | 34.3237 | 1.41911 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −41.1884 | −1.70003 | −0.850014 | − | 0.526760i | \(-0.823407\pi\) | ||||
−0.850014 | + | 0.526760i | \(0.823407\pi\) | |||||||
\(588\) | −25.4558 | −1.04978 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 5.07701 | 0.209017 | ||||||||
\(591\) | −16.9443 | −0.696994 | ||||||||
\(592\) | −13.3469 | −0.548555 | ||||||||
\(593\) | −17.1803 | −0.705512 | −0.352756 | − | 0.935715i | \(-0.614755\pi\) | ||||
−0.352756 | + | 0.935715i | \(0.614755\pi\) | |||||||
\(594\) | −2.83282 | −0.116232 | ||||||||
\(595\) | −1.20788 | −0.0495184 | ||||||||
\(596\) | −24.8754 | −1.01894 | ||||||||
\(597\) | −33.7082 | −1.37958 | ||||||||
\(598\) | 18.0000 | 0.736075 | ||||||||
\(599\) | 23.9443 | 0.978336 | 0.489168 | − | 0.872189i | \(-0.337300\pi\) | ||||
0.489168 | + | 0.872189i | \(0.337300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.69161 | −0.354538 | −0.177269 | − | 0.984162i | \(-0.556726\pi\) | ||||
−0.177269 | + | 0.984162i | \(0.556726\pi\) | |||||||
\(602\) | −0.0788114 | −0.00321211 | ||||||||
\(603\) | 13.4164 | 0.546358 | ||||||||
\(604\) | 5.62675 | 0.228949 | ||||||||
\(605\) | −15.6525 | −0.636364 | ||||||||
\(606\) | 1.95440 | 0.0793919 | ||||||||
\(607\) | −25.1246 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(608\) | 4.14590 | 0.168138 | ||||||||
\(609\) | 8.47214 | 0.343308 | ||||||||
\(610\) | 3.79988 | 0.153852 | ||||||||
\(611\) | −25.4558 | −1.02983 | ||||||||
\(612\) | 2.23954 | 0.0905279 | ||||||||
\(613\) | 37.3584 | 1.50889 | 0.754447 | − | 0.656361i | \(-0.227905\pi\) | ||||
0.754447 | + | 0.656361i | \(0.227905\pi\) | |||||||
\(614\) | −6.15905 | −0.248559 | ||||||||
\(615\) | 38.2325 | 1.54168 | ||||||||
\(616\) | −6.24574 | −0.251648 | ||||||||
\(617\) | −47.1246 | −1.89717 | −0.948583 | − | 0.316529i | \(-0.897482\pi\) | ||||
−0.948583 | + | 0.316529i | \(0.897482\pi\) | |||||||
\(618\) | 2.36706 | 0.0952170 | ||||||||
\(619\) | 21.5958 | 0.868007 | 0.434003 | − | 0.900911i | \(-0.357101\pi\) | ||||
0.434003 | + | 0.900911i | \(0.357101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.0000 | −0.481543 | ||||||||
\(622\) | 6.31308 | 0.253132 | ||||||||
\(623\) | −5.86319 | −0.234904 | ||||||||
\(624\) | 49.4164 | 1.97824 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 8.02391 | 0.320700 | ||||||||
\(627\) | 9.70820 | 0.387708 | ||||||||
\(628\) | 8.72949 | 0.348345 | ||||||||
\(629\) | 2.29180 | 0.0913799 | ||||||||
\(630\) | 1.90983 | 0.0760895 | ||||||||
\(631\) | 4.65530 | 0.185325 | 0.0926623 | − | 0.995698i | \(-0.470462\pi\) | ||||
0.0926623 | + | 0.995698i | \(0.470462\pi\) | |||||||
\(632\) | −16.3516 | −0.650431 | ||||||||
\(633\) | 11.4412 | 0.454748 | ||||||||
\(634\) | 8.31308 | 0.330155 | ||||||||
\(635\) | 21.2132 | 0.841820 | ||||||||
\(636\) | −22.2492 | −0.882239 | ||||||||
\(637\) | 41.1884 | 1.63194 | ||||||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | 16.7082 | 0.660966 | ||||||||
\(640\) | 22.5623 | 0.891853 | ||||||||
\(641\) | 8.48528 | 0.335148 | 0.167574 | − | 0.985859i | \(-0.446407\pi\) | ||||
0.167574 | + | 0.985859i | \(0.446407\pi\) | |||||||
\(642\) | 6.53089 | 0.257754 | ||||||||
\(643\) | 23.6290 | 0.931836 | 0.465918 | − | 0.884828i | \(-0.345724\pi\) | ||||
0.465918 | + | 0.884828i | \(0.345724\pi\) | |||||||
\(644\) | −12.7279 | −0.501550 | ||||||||
\(645\) | 1.05573 | 0.0415693 | ||||||||
\(646\) | −0.206331 | −0.00811798 | ||||||||
\(647\) | −19.1313 | −0.752129 | −0.376064 | − | 0.926594i | \(-0.622723\pi\) | ||||
−0.376064 | + | 0.926594i | \(0.622723\pi\) | |||||||
\(648\) | 15.7639 | 0.619266 | ||||||||
\(649\) | 25.2194 | 0.989948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.0213 | 0.901583 | ||||||||
\(653\) | −6.65248 | −0.260331 | −0.130166 | − | 0.991492i | \(-0.541551\pi\) | ||||
−0.130166 | + | 0.991492i | \(0.541551\pi\) | |||||||
\(654\) | 12.8554 | 0.502688 | ||||||||
\(655\) | 43.4164 | 1.69642 | ||||||||
\(656\) | 23.5066 | 0.917778 | ||||||||
\(657\) | −9.48683 | −0.370117 | ||||||||
\(658\) | −1.41641 | −0.0552173 | ||||||||
\(659\) | 47.1803 | 1.83789 | 0.918943 | − | 0.394391i | \(-0.129045\pi\) | ||||
0.918943 | + | 0.394391i | \(0.129045\pi\) | |||||||
\(660\) | 40.2492 | 1.56670 | ||||||||
\(661\) | −45.8328 | −1.78269 | −0.891345 | − | 0.453326i | \(-0.850237\pi\) | ||||
−0.891345 | + | 0.453326i | \(0.850237\pi\) | |||||||
\(662\) | 9.79058 | 0.380522 | ||||||||
\(663\) | −8.48528 | −0.329541 | ||||||||
\(664\) | 4.65530 | 0.180661 | ||||||||
\(665\) | 2.23607 | 0.0867110 | ||||||||
\(666\) | −3.62365 | −0.140413 | ||||||||
\(667\) | −25.4164 | −0.984127 | ||||||||
\(668\) | −13.7295 | −0.531209 | ||||||||
\(669\) | −49.8885 | −1.92880 | ||||||||
\(670\) | −5.12461 | −0.197981 | ||||||||
\(671\) | 18.8754 | 0.728676 | ||||||||
\(672\) | 9.48683 | 0.365963 | ||||||||
\(673\) | 7.45363 | 0.287316 | 0.143658 | − | 0.989627i | \(-0.454113\pi\) | ||||
0.143658 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(674\) | 2.23954 | 0.0862638 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −63.2705 | −2.43348 | ||||||||
\(677\) | 21.2132 | 0.815290 | 0.407645 | − | 0.913141i | \(-0.366350\pi\) | ||||
0.407645 | + | 0.913141i | \(0.366350\pi\) | |||||||
\(678\) | 12.4428 | 0.477862 | ||||||||
\(679\) | 7.00000 | 0.268635 | ||||||||
\(680\) | −1.77817 | −0.0681896 | ||||||||
\(681\) | −35.9442 | −1.37739 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.8197 | −0.720114 | −0.360057 | − | 0.932930i | \(-0.617243\pi\) | ||||
−0.360057 | + | 0.932930i | \(0.617243\pi\) | |||||||
\(684\) | −4.14590 | −0.158522 | ||||||||
\(685\) | 15.3500 | 0.586494 | ||||||||
\(686\) | 4.96556 | 0.189586 | ||||||||
\(687\) | 9.70820 | 0.370391 | ||||||||
\(688\) | 0.649096 | 0.0247466 | ||||||||
\(689\) | 36.0000 | 1.37149 | ||||||||
\(690\) | −13.4164 | −0.510754 | ||||||||
\(691\) | −21.5836 | −0.821079 | −0.410539 | − | 0.911843i | \(-0.634660\pi\) | ||||
−0.410539 | + | 0.911843i | \(0.634660\pi\) | |||||||
\(692\) | −33.3738 | −1.26868 | ||||||||
\(693\) | 9.48683 | 0.360375 | ||||||||
\(694\) | −9.86939 | −0.374637 | ||||||||
\(695\) | 2.23954 | 0.0849505 | ||||||||
\(696\) | 12.4721 | 0.472755 | ||||||||
\(697\) | −4.03631 | −0.152886 | ||||||||
\(698\) | 2.29180 | 0.0867458 | ||||||||
\(699\) | 10.3609 | 0.391884 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.6525 | 1.04442 | 0.522210 | − | 0.852817i | \(-0.325108\pi\) | ||||
0.522210 | + | 0.852817i | \(0.325108\pi\) | |||||||
\(702\) | −4.58359 | −0.172997 | ||||||||
\(703\) | −4.24264 | −0.160014 | ||||||||
\(704\) | 19.9752 | 0.752844 | ||||||||
\(705\) | 18.9737 | 0.714590 | ||||||||
\(706\) | −6.06952 | −0.228429 | ||||||||
\(707\) | 2.23607 | 0.0840960 | ||||||||
\(708\) | −25.2194 | −0.947803 | ||||||||
\(709\) | −15.7326 | −0.590849 | −0.295425 | − | 0.955366i | \(-0.595461\pi\) | ||||
−0.295425 | + | 0.955366i | \(0.595461\pi\) | |||||||
\(710\) | −6.38197 | −0.239511 | ||||||||
\(711\) | 24.8369 | 0.931455 | ||||||||
\(712\) | −8.63141 | −0.323476 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −0.472136 | −0.0176692 | ||||||||
\(715\) | −65.1246 | −2.43552 | ||||||||
\(716\) | 30.4636 | 1.13848 | ||||||||
\(717\) | −37.4164 | −1.39734 | ||||||||
\(718\) | 3.72949 | 0.139183 | ||||||||
\(719\) | 9.10427 | 0.339532 | 0.169766 | − | 0.985484i | \(-0.445699\pi\) | ||||
0.169766 | + | 0.985484i | \(0.445699\pi\) | |||||||
\(720\) | −15.7295 | −0.586203 | ||||||||
\(721\) | 2.70820 | 0.100859 | ||||||||
\(722\) | −6.87539 | −0.255875 | ||||||||
\(723\) | 33.7082 | 1.25362 | ||||||||
\(724\) | 33.7047 | 1.25262 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.11822 | −0.227069 | ||||||||
\(727\) | −3.58359 | −0.132908 | −0.0664540 | − | 0.997789i | \(-0.521169\pi\) | ||||
−0.0664540 | + | 0.997789i | \(0.521169\pi\) | |||||||
\(728\) | −10.1058 | −0.374547 | ||||||||
\(729\) | −11.9443 | −0.442380 | ||||||||
\(730\) | 3.62365 | 0.134117 | ||||||||
\(731\) | −0.111456 | −0.00412236 | ||||||||
\(732\) | −18.8754 | −0.697654 | ||||||||
\(733\) | 12.4164 | 0.458610 | 0.229305 | − | 0.973355i | \(-0.426355\pi\) | ||||
0.229305 | + | 0.973355i | \(0.426355\pi\) | |||||||
\(734\) | 4.70401 | 0.173628 | ||||||||
\(735\) | −30.7000 | −1.13239 | ||||||||
\(736\) | −28.4605 | −1.04907 | ||||||||
\(737\) | −25.4558 | −0.937678 | ||||||||
\(738\) | 6.38197 | 0.234923 | ||||||||
\(739\) | 25.6622 | 0.943998 | 0.471999 | − | 0.881599i | \(-0.343533\pi\) | ||||
0.471999 | + | 0.881599i | \(0.343533\pi\) | |||||||
\(740\) | −17.5896 | −0.646605 | ||||||||
\(741\) | 15.7082 | 0.577055 | ||||||||
\(742\) | 2.00310 | 0.0735362 | ||||||||
\(743\) | 1.69936 | 0.0623433 | 0.0311717 | − | 0.999514i | \(-0.490076\pi\) | ||||
0.0311717 | + | 0.999514i | \(0.490076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.0000 | −1.09911 | ||||||||
\(746\) | −8.67376 | −0.317569 | ||||||||
\(747\) | −7.07107 | −0.258717 | ||||||||
\(748\) | −4.24922 | −0.155367 | ||||||||
\(749\) | 7.47214 | 0.273026 | ||||||||
\(750\) | −9.77198 | −0.356822 | ||||||||
\(751\) | 29.5410 | 1.07797 | 0.538984 | − | 0.842316i | \(-0.318808\pi\) | ||||
0.538984 | + | 0.842316i | \(0.318808\pi\) | |||||||
\(752\) | 11.6656 | 0.425402 | ||||||||
\(753\) | −54.3607 | −1.98101 | ||||||||
\(754\) | −9.70820 | −0.353552 | ||||||||
\(755\) | 6.78593 | 0.246965 | ||||||||
\(756\) | 3.24109 | 0.117877 | ||||||||
\(757\) | 19.1800 | 0.697109 | 0.348554 | − | 0.937289i | \(-0.386673\pi\) | ||||
0.348554 | + | 0.937289i | \(0.386673\pi\) | |||||||
\(758\) | −7.41641 | −0.269376 | ||||||||
\(759\) | −66.6443 | −2.41903 | ||||||||
\(760\) | 3.29180 | 0.119406 | ||||||||
\(761\) | −2.23954 | −0.0811832 | −0.0405916 | − | 0.999176i | \(-0.512924\pi\) | ||||
−0.0405916 | + | 0.999176i | \(0.512924\pi\) | |||||||
\(762\) | 8.29180 | 0.300380 | ||||||||
\(763\) | 14.7082 | 0.532473 | ||||||||
\(764\) | −26.3951 | −0.954942 | ||||||||
\(765\) | 2.70091 | 0.0976515 | ||||||||
\(766\) | 7.27740 | 0.262943 | ||||||||
\(767\) | 40.8059 | 1.47341 | ||||||||
\(768\) | −12.7279 | −0.459279 | ||||||||
\(769\) | 13.8754 | 0.500359 | 0.250180 | − | 0.968199i | \(-0.419510\pi\) | ||||
0.250180 | + | 0.968199i | \(0.419510\pi\) | |||||||
\(770\) | −3.62365 | −0.130587 | ||||||||
\(771\) | −54.7904 | −1.97323 | ||||||||
\(772\) | 13.5197 | 0.486586 | ||||||||
\(773\) | 26.9976 | 0.971035 | 0.485518 | − | 0.874227i | \(-0.338631\pi\) | ||||
0.485518 | + | 0.874227i | \(0.338631\pi\) | |||||||
\(774\) | 0.176228 | 0.00633437 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.3050 | 0.369926 | ||||||||
\(777\) | −9.70820 | −0.348280 | ||||||||
\(778\) | −12.9041 | −0.462636 | ||||||||
\(779\) | 7.47214 | 0.267717 | ||||||||
\(780\) | 65.1246 | 2.33184 | ||||||||
\(781\) | −31.7016 | −1.13437 | ||||||||
\(782\) | 1.41641 | 0.0506506 | ||||||||
\(783\) | 6.47214 | 0.231295 | ||||||||
\(784\) | −18.8754 | −0.674121 | ||||||||
\(785\) | 10.5279 | 0.375756 | ||||||||
\(786\) | 16.9706 | 0.605320 | ||||||||
\(787\) | 9.10427 | 0.324532 | 0.162266 | − | 0.986747i | \(-0.448120\pi\) | ||||
0.162266 | + | 0.986747i | \(0.448120\pi\) | |||||||
\(788\) | −13.7295 | −0.489092 | ||||||||
\(789\) | 6.18034 | 0.220026 | ||||||||
\(790\) | −9.48683 | −0.337526 | ||||||||
\(791\) | 14.2361 | 0.506176 | ||||||||
\(792\) | 13.9659 | 0.496257 | ||||||||
\(793\) | 30.5410 | 1.08454 | ||||||||
\(794\) | 0.493422 | 0.0175109 | ||||||||
\(795\) | −26.8328 | −0.951662 | ||||||||
\(796\) | −27.3128 | −0.968077 | ||||||||
\(797\) | −5.24419 | −0.185759 | −0.0928794 | − | 0.995677i | \(-0.529607\pi\) | ||||
−0.0928794 | + | 0.995677i | \(0.529607\pi\) | |||||||
\(798\) | 0.874032 | 0.0309404 | ||||||||
\(799\) | −2.00310 | −0.0708647 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.1105 | 0.463236 | ||||||||
\(802\) | 1.41421 | 0.0499376 | ||||||||
\(803\) | 18.0000 | 0.635206 | ||||||||
\(804\) | 25.4558 | 0.897758 | ||||||||
\(805\) | −15.3500 | −0.541017 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.8885 | 1.19293 | ||||||||
\(808\) | 3.29180 | 0.115805 | ||||||||
\(809\) | 22.0571 | 0.775487 | 0.387744 | − | 0.921767i | \(-0.373255\pi\) | ||||
0.387744 | + | 0.921767i | \(0.373255\pi\) | |||||||
\(810\) | 9.14590 | 0.321354 | ||||||||
\(811\) | −43.4164 | −1.52456 | −0.762278 | − | 0.647250i | \(-0.775919\pi\) | ||||
−0.762278 | + | 0.647250i | \(0.775919\pi\) | |||||||
\(812\) | 6.86474 | 0.240905 | ||||||||
\(813\) | −64.2492 | −2.25332 | ||||||||
\(814\) | 6.87539 | 0.240982 | ||||||||
\(815\) | 27.7639 | 0.972528 | ||||||||
\(816\) | 3.88854 | 0.136126 | ||||||||
\(817\) | 0.206331 | 0.00721861 | ||||||||
\(818\) | 6.62830 | 0.231753 | ||||||||
\(819\) | 15.3500 | 0.536373 | ||||||||
\(820\) | 30.9787 | 1.08182 | ||||||||
\(821\) | −14.3485 | −0.500765 | −0.250382 | − | 0.968147i | \(-0.580556\pi\) | ||||
−0.250382 | + | 0.968147i | \(0.580556\pi\) | |||||||
\(822\) | 6.00000 | 0.209274 | ||||||||
\(823\) | −14.9374 | −0.520684 | −0.260342 | − | 0.965517i | \(-0.583835\pi\) | ||||
−0.260342 | + | 0.965517i | \(0.583835\pi\) | |||||||
\(824\) | 3.98684 | 0.138888 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.27051 | 0.0790011 | ||||||||
\(827\) | −48.0532 | −1.67097 | −0.835486 | − | 0.549512i | \(-0.814814\pi\) | ||||
−0.835486 | + | 0.549512i | \(0.814814\pi\) | |||||||
\(828\) | 28.4605 | 0.989071 | ||||||||
\(829\) | 5.83308 | 0.202591 | 0.101296 | − | 0.994856i | \(-0.467701\pi\) | ||||
0.101296 | + | 0.994856i | \(0.467701\pi\) | |||||||
\(830\) | 2.70091 | 0.0937499 | ||||||||
\(831\) | 44.8328 | 1.55523 | ||||||||
\(832\) | 32.3206 | 1.12051 | ||||||||
\(833\) | 3.24109 | 0.112297 | ||||||||
\(834\) | 0.875388 | 0.0303122 | ||||||||
\(835\) | −16.5579 | −0.573010 | ||||||||
\(836\) | 7.86629 | 0.272061 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.10333 | −0.245380 | ||||||||
\(839\) | 7.41641 | 0.256043 | 0.128021 | − | 0.991771i | \(-0.459137\pi\) | ||||
0.128021 | + | 0.991771i | \(0.459137\pi\) | |||||||
\(840\) | 7.53244 | 0.259894 | ||||||||
\(841\) | −15.2918 | −0.527303 | ||||||||
\(842\) | −0.159054 | −0.00548135 | ||||||||
\(843\) | 71.7609 | 2.47158 | ||||||||
\(844\) | 9.27051 | 0.319104 | ||||||||
\(845\) | −76.3050 | −2.62497 | ||||||||
\(846\) | 3.16718 | 0.108890 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | −16.4977 | −0.566533 | ||||||||
\(849\) | −54.9179 | −1.88478 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.1246 | 0.998379 | ||||||||
\(852\) | 31.7016 | 1.08608 | ||||||||
\(853\) | −45.7082 | −1.56502 | −0.782510 | − | 0.622639i | \(-0.786061\pi\) | ||||
−0.782510 | + | 0.622639i | \(0.786061\pi\) | |||||||
\(854\) | 1.69936 | 0.0581508 | ||||||||
\(855\) | −5.00000 | −0.170996 | ||||||||
\(856\) | 11.0000 | 0.375972 | ||||||||
\(857\) | −6.00000 | −0.204956 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | −25.4558 | −0.869048 | ||||||||
\(859\) | 3.65375 | 0.124664 | 0.0623322 | − | 0.998055i | \(-0.480146\pi\) | ||||
0.0623322 | + | 0.998055i | \(0.480146\pi\) | |||||||
\(860\) | 0.855427 | 0.0291698 | ||||||||
\(861\) | 17.0981 | 0.582701 | ||||||||
\(862\) | −0.0425725 | −0.00145002 | ||||||||
\(863\) | −35.3252 | −1.20249 | −0.601243 | − | 0.799067i | \(-0.705327\pi\) | ||||
−0.601243 | + | 0.799067i | \(0.705327\pi\) | |||||||
\(864\) | 7.24730 | 0.246558 | ||||||||
\(865\) | −40.2492 | −1.36851 | ||||||||
\(866\) | −8.24885 | −0.280307 | ||||||||
\(867\) | 38.2325 | 1.29844 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47.1246 | −1.59859 | ||||||||
\(870\) | 7.23607 | 0.245326 | ||||||||
\(871\) | −41.1884 | −1.39562 | ||||||||
\(872\) | 21.6525 | 0.733245 | ||||||||
\(873\) | −15.6525 | −0.529756 | ||||||||
\(874\) | −2.62210 | −0.0886937 | ||||||||
\(875\) | −11.1803 | −0.377964 | ||||||||
\(876\) | −18.0000 | −0.608164 | ||||||||
\(877\) | −15.2918 | −0.516367 | −0.258184 | − | 0.966096i | \(-0.583124\pi\) | ||||
−0.258184 | + | 0.966096i | \(0.583124\pi\) | |||||||
\(878\) | −9.54915 | −0.322268 | ||||||||
\(879\) | 35.9442 | 1.21237 | ||||||||
\(880\) | 29.8446 | 1.00606 | ||||||||
\(881\) | 49.6737 | 1.67355 | 0.836775 | − | 0.547547i | \(-0.184438\pi\) | ||||
0.836775 | + | 0.547547i | \(0.184438\pi\) | |||||||
\(882\) | −5.12461 | −0.172555 | ||||||||
\(883\) | 33.9411 | 1.14221 | 0.571105 | − | 0.820877i | \(-0.306515\pi\) | ||||
0.571105 | + | 0.820877i | \(0.306515\pi\) | |||||||
\(884\) | −6.87539 | −0.231244 | ||||||||
\(885\) | −30.4149 | −1.02239 | ||||||||
\(886\) | 9.14590 | 0.307262 | ||||||||
\(887\) | −19.3607 | −0.650068 | −0.325034 | − | 0.945702i | \(-0.605376\pi\) | ||||
−0.325034 | + | 0.945702i | \(0.605376\pi\) | |||||||
\(888\) | −14.2918 | −0.479601 | ||||||||
\(889\) | 9.48683 | 0.318178 | ||||||||
\(890\) | −5.00776 | −0.167860 | ||||||||
\(891\) | 45.4311 | 1.52200 | ||||||||
\(892\) | −40.4233 | −1.35347 | ||||||||
\(893\) | 3.70820 | 0.124090 | ||||||||
\(894\) | −11.7264 | −0.392188 | ||||||||
\(895\) | 36.7394 | 1.22806 | ||||||||
\(896\) | 10.0902 | 0.337089 | ||||||||
\(897\) | −107.833 | −3.60043 | ||||||||
\(898\) | 16.1151 | 0.537769 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.83282 | 0.0943748 | ||||||||
\(902\) | −12.1089 | −0.403183 | ||||||||
\(903\) | 0.472136 | 0.0157117 | ||||||||
\(904\) | 20.9574 | 0.697034 | ||||||||
\(905\) | 40.6482 | 1.35119 | ||||||||
\(906\) | 2.65248 | 0.0881226 | ||||||||
\(907\) | −55.5410 | −1.84421 | −0.922105 | − | 0.386941i | \(-0.873532\pi\) | ||||
−0.922105 | + | 0.386941i | \(0.873532\pi\) | |||||||
\(908\) | −29.1246 | −0.966534 | ||||||||
\(909\) | −5.00000 | −0.165840 | ||||||||
\(910\) | −5.86319 | −0.194363 | ||||||||
\(911\) | −14.1908 | −0.470164 | −0.235082 | − | 0.971976i | \(-0.575536\pi\) | ||||
−0.235082 | + | 0.971976i | \(0.575536\pi\) | |||||||
\(912\) | −7.19859 | −0.238369 | ||||||||
\(913\) | 13.4164 | 0.444018 | ||||||||
\(914\) | −4.32145 | −0.142941 | ||||||||
\(915\) | −22.7639 | −0.752552 | ||||||||
\(916\) | 7.86629 | 0.259909 | ||||||||
\(917\) | 19.4164 | 0.641186 | ||||||||
\(918\) | −0.360680 | −0.0119042 | ||||||||
\(919\) | 24.5410 | 0.809534 | 0.404767 | − | 0.914420i | \(-0.367353\pi\) | ||||
0.404767 | + | 0.914420i | \(0.367353\pi\) | |||||||
\(920\) | −22.5973 | −0.745011 | ||||||||
\(921\) | 36.8971 | 1.21580 | ||||||||
\(922\) | 14.9374 | 0.491936 | ||||||||
\(923\) | −51.2942 | −1.68837 | ||||||||
\(924\) | 18.0000 | 0.592157 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.78437 | −0.190086 | ||||||||
\(927\) | −6.05573 | −0.198896 | ||||||||
\(928\) | 15.3500 | 0.503889 | ||||||||
\(929\) | −23.2951 | −0.764288 | −0.382144 | − | 0.924103i | \(-0.624814\pi\) | ||||
−0.382144 | + | 0.924103i | \(0.624814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | −0.196642 | ||||||||
\(932\) | 8.39512 | 0.274991 | ||||||||
\(933\) | −37.8198 | −1.23817 | ||||||||
\(934\) | 5.97871 | 0.195629 | ||||||||
\(935\) | −5.12461 | −0.167593 | ||||||||
\(936\) | 22.5973 | 0.738616 | ||||||||
\(937\) | −56.2492 | −1.83758 | −0.918791 | − | 0.394744i | \(-0.870833\pi\) | ||||
−0.918791 | + | 0.394744i | \(0.870833\pi\) | |||||||
\(938\) | −2.29180 | −0.0748298 | ||||||||
\(939\) | −48.0689 | −1.56867 | ||||||||
\(940\) | 15.3738 | 0.501439 | ||||||||
\(941\) | −50.8329 | −1.65710 | −0.828552 | − | 0.559912i | \(-0.810835\pi\) | ||||
−0.828552 | + | 0.559912i | \(0.810835\pi\) | |||||||
\(942\) | 4.11512 | 0.134078 | ||||||||
\(943\) | −51.2942 | −1.67037 | ||||||||
\(944\) | −18.7001 | −0.608636 | ||||||||
\(945\) | 3.90879 | 0.127153 | ||||||||
\(946\) | −0.334369 | −0.0108713 | ||||||||
\(947\) | −2.23954 | −0.0727752 | −0.0363876 | − | 0.999338i | \(-0.511585\pi\) | ||||
−0.0363876 | + | 0.999338i | \(0.511585\pi\) | |||||||
\(948\) | 47.1246 | 1.53054 | ||||||||
\(949\) | 29.1246 | 0.945425 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −49.8012 | −1.61492 | ||||||||
\(952\) | −0.795221 | −0.0257732 | ||||||||
\(953\) | −53.4550 | −1.73158 | −0.865788 | − | 0.500411i | \(-0.833182\pi\) | ||||
−0.865788 | + | 0.500411i | \(0.833182\pi\) | |||||||
\(954\) | −4.47907 | −0.145015 | ||||||||
\(955\) | −31.8328 | −1.03009 | ||||||||
\(956\) | −30.3175 | −0.980537 | ||||||||
\(957\) | 35.9442 | 1.16191 | ||||||||
\(958\) | 9.72949 | 0.314346 | ||||||||
\(959\) | 6.86474 | 0.221674 | ||||||||
\(960\) | −24.0903 | −0.777512 | ||||||||
\(961\) | 0 | 0 | ||||||||
\(962\) | 11.1246 | 0.358672 | ||||||||
\(963\) | −16.7082 | −0.538414 | ||||||||
\(964\) | 27.3128 | 0.879687 | ||||||||
\(965\) | 16.3050 | 0.524875 | ||||||||
\(966\) | −6.00000 | −0.193047 | ||||||||
\(967\) | 12.9041 | 0.414969 | 0.207485 | − | 0.978238i | \(-0.433472\pi\) | ||||
0.207485 | + | 0.978238i | \(0.433472\pi\) | |||||||
\(968\) | −10.3050 | −0.331214 | ||||||||
\(969\) | 1.23607 | 0.0397082 | ||||||||
\(970\) | 5.97871 | 0.191965 | ||||||||
\(971\) | 18.1115 | 0.581224 | 0.290612 | − | 0.956841i | \(-0.406141\pi\) | ||||
0.290612 | + | 0.956841i | \(0.406141\pi\) | |||||||
\(972\) | −35.7078 | −1.14533 | ||||||||
\(973\) | 1.00155 | 0.0321083 | ||||||||
\(974\) | −7.10117 | −0.227536 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.9960 | −0.448001 | ||||||||
\(977\) | 42.4853 | 1.35922 | 0.679612 | − | 0.733571i | \(-0.262148\pi\) | ||||
0.679612 | + | 0.733571i | \(0.262148\pi\) | |||||||
\(978\) | 10.8523 | 0.347020 | ||||||||
\(979\) | −24.8754 | −0.795021 | ||||||||
\(980\) | −24.8754 | −0.794615 | ||||||||
\(981\) | −32.8885 | −1.05005 | ||||||||
\(982\) | 3.65375 | 0.116596 | ||||||||
\(983\) | 3.00465 | 0.0958336 | 0.0479168 | − | 0.998851i | \(-0.484742\pi\) | ||||
0.0479168 | + | 0.998851i | \(0.484742\pi\) | |||||||
\(984\) | 25.1707 | 0.802413 | ||||||||
\(985\) | −16.5579 | −0.527579 | ||||||||
\(986\) | −0.763932 | −0.0243286 | ||||||||
\(987\) | 8.48528 | 0.270089 | ||||||||
\(988\) | 12.7279 | 0.404929 | ||||||||
\(989\) | −1.41641 | −0.0450391 | ||||||||
\(990\) | 8.10272 | 0.257521 | ||||||||
\(991\) | 4.44897 | 0.141326 | 0.0706631 | − | 0.997500i | \(-0.477488\pi\) | ||||
0.0706631 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −58.6525 | −1.86128 | ||||||||
\(994\) | −2.85410 | −0.0905266 | ||||||||
\(995\) | −32.9396 | −1.04425 | ||||||||
\(996\) | −13.4164 | −0.425115 | ||||||||
\(997\) | 48.6656 | 1.54126 | 0.770628 | − | 0.637285i | \(-0.219943\pi\) | ||||
0.770628 | + | 0.637285i | \(0.219943\pi\) | |||||||
\(998\) | −7.02236 | −0.222289 | ||||||||
\(999\) | −7.41641 | −0.234645 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))