Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.197331 | −0.139534 | −0.0697670 | − | 0.997563i | \(-0.522226\pi\) | ||||
−0.0697670 | + | 0.997563i | \(0.522226\pi\) | |||||||
\(3\) | 2.44280 | 1.41035 | 0.705176 | − | 0.709032i | \(-0.250868\pi\) | ||||
0.705176 | + | 0.709032i | \(0.250868\pi\) | |||||||
\(4\) | −1.96106 | −0.980530 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.482041 | −0.196792 | ||||||||
\(7\) | −1.78119 | −0.673228 | −0.336614 | − | 0.941643i | \(-0.609282\pi\) | ||||
−0.336614 | + | 0.941643i | \(0.609282\pi\) | |||||||
\(8\) | 0.781640 | 0.276351 | ||||||||
\(9\) | 2.96728 | 0.989095 | ||||||||
\(10\) | −0.197331 | −0.0624015 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.79048 | −1.38289 | ||||||||
\(13\) | 5.00904 | 1.38926 | 0.694629 | − | 0.719368i | \(-0.255568\pi\) | ||||
0.694629 | + | 0.719368i | \(0.255568\pi\) | |||||||
\(14\) | 0.351485 | 0.0939382 | ||||||||
\(15\) | 2.44280 | 0.630729 | ||||||||
\(16\) | 3.76788 | 0.941970 | ||||||||
\(17\) | −6.94282 | −1.68388 | −0.841940 | − | 0.539571i | \(-0.818587\pi\) | ||||
−0.841940 | + | 0.539571i | \(0.818587\pi\) | |||||||
\(18\) | −0.585537 | −0.138012 | ||||||||
\(19\) | −4.83335 | −1.10885 | −0.554423 | − | 0.832235i | \(-0.687061\pi\) | ||||
−0.554423 | + | 0.832235i | \(0.687061\pi\) | |||||||
\(20\) | −1.96106 | −0.438506 | ||||||||
\(21\) | −4.35110 | −0.949488 | ||||||||
\(22\) | 0.197331 | 0.0420711 | ||||||||
\(23\) | −0.570816 | −0.119023 | −0.0595117 | − | 0.998228i | \(-0.518954\pi\) | ||||
−0.0595117 | + | 0.998228i | \(0.518954\pi\) | |||||||
\(24\) | 1.90939 | 0.389753 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.988439 | −0.193849 | ||||||||
\(27\) | −0.0799170 | −0.0153800 | ||||||||
\(28\) | 3.49303 | 0.660120 | ||||||||
\(29\) | −3.97018 | −0.737244 | −0.368622 | − | 0.929579i | \(-0.620170\pi\) | ||||
−0.368622 | + | 0.929579i | \(0.620170\pi\) | |||||||
\(30\) | −0.482041 | −0.0880082 | ||||||||
\(31\) | −5.21743 | −0.937079 | −0.468539 | − | 0.883443i | \(-0.655220\pi\) | ||||
−0.468539 | + | 0.883443i | \(0.655220\pi\) | |||||||
\(32\) | −2.30680 | −0.407788 | ||||||||
\(33\) | −2.44280 | −0.425237 | ||||||||
\(34\) | 1.37003 | 0.234959 | ||||||||
\(35\) | −1.78119 | −0.301077 | ||||||||
\(36\) | −5.81902 | −0.969837 | ||||||||
\(37\) | 3.33047 | 0.547527 | 0.273763 | − | 0.961797i | \(-0.411731\pi\) | ||||
0.273763 | + | 0.961797i | \(0.411731\pi\) | |||||||
\(38\) | 0.953769 | 0.154722 | ||||||||
\(39\) | 12.2361 | 1.95934 | ||||||||
\(40\) | 0.781640 | 0.123588 | ||||||||
\(41\) | 1.30184 | 0.203313 | 0.101656 | − | 0.994820i | \(-0.467586\pi\) | ||||
0.101656 | + | 0.994820i | \(0.467586\pi\) | |||||||
\(42\) | 0.858607 | 0.132486 | ||||||||
\(43\) | 4.44442 | 0.677768 | 0.338884 | − | 0.940828i | \(-0.389951\pi\) | ||||
0.338884 | + | 0.940828i | \(0.389951\pi\) | |||||||
\(44\) | 1.96106 | 0.295641 | ||||||||
\(45\) | 2.96728 | 0.442337 | ||||||||
\(46\) | 0.112640 | 0.0166078 | ||||||||
\(47\) | −10.7328 | −1.56554 | −0.782769 | − | 0.622312i | \(-0.786193\pi\) | ||||
−0.782769 | + | 0.622312i | \(0.786193\pi\) | |||||||
\(48\) | 9.20419 | 1.32851 | ||||||||
\(49\) | −3.82735 | −0.546765 | ||||||||
\(50\) | −0.197331 | −0.0279068 | ||||||||
\(51\) | −16.9599 | −2.37487 | ||||||||
\(52\) | −9.82304 | −1.36221 | ||||||||
\(53\) | −10.1135 | −1.38920 | −0.694599 | − | 0.719397i | \(-0.744418\pi\) | ||||
−0.694599 | + | 0.719397i | \(0.744418\pi\) | |||||||
\(54\) | 0.0157701 | 0.00214604 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −1.39225 | −0.186047 | ||||||||
\(57\) | −11.8069 | −1.56386 | ||||||||
\(58\) | 0.783440 | 0.102871 | ||||||||
\(59\) | −0.898038 | −0.116915 | −0.0584573 | − | 0.998290i | \(-0.518618\pi\) | ||||
−0.0584573 | + | 0.998290i | \(0.518618\pi\) | |||||||
\(60\) | −4.79048 | −0.618449 | ||||||||
\(61\) | 13.2417 | 1.69543 | 0.847713 | − | 0.530455i | \(-0.177979\pi\) | ||||
0.847713 | + | 0.530455i | \(0.177979\pi\) | |||||||
\(62\) | 1.02956 | 0.130754 | ||||||||
\(63\) | −5.28531 | −0.665886 | ||||||||
\(64\) | −7.08056 | −0.885069 | ||||||||
\(65\) | 5.00904 | 0.621295 | ||||||||
\(66\) | 0.482041 | 0.0593351 | ||||||||
\(67\) | −4.29196 | −0.524347 | −0.262173 | − | 0.965021i | \(-0.584439\pi\) | ||||
−0.262173 | + | 0.965021i | \(0.584439\pi\) | |||||||
\(68\) | 13.6153 | 1.65110 | ||||||||
\(69\) | −1.39439 | −0.167865 | ||||||||
\(70\) | 0.351485 | 0.0420104 | ||||||||
\(71\) | −2.39877 | −0.284682 | −0.142341 | − | 0.989818i | \(-0.545463\pi\) | ||||
−0.142341 | + | 0.989818i | \(0.545463\pi\) | |||||||
\(72\) | 2.31935 | 0.273338 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −0.657206 | −0.0763986 | ||||||||
\(75\) | 2.44280 | 0.282071 | ||||||||
\(76\) | 9.47849 | 1.08726 | ||||||||
\(77\) | 1.78119 | 0.202986 | ||||||||
\(78\) | −2.41456 | −0.273395 | ||||||||
\(79\) | 8.48581 | 0.954728 | 0.477364 | − | 0.878706i | \(-0.341592\pi\) | ||||
0.477364 | + | 0.878706i | \(0.341592\pi\) | |||||||
\(80\) | 3.76788 | 0.421262 | ||||||||
\(81\) | −9.09708 | −1.01079 | ||||||||
\(82\) | −0.256893 | −0.0283691 | ||||||||
\(83\) | 7.45000 | 0.817744 | 0.408872 | − | 0.912592i | \(-0.365922\pi\) | ||||
0.408872 | + | 0.912592i | \(0.365922\pi\) | |||||||
\(84\) | 8.53278 | 0.931002 | ||||||||
\(85\) | −6.94282 | −0.753054 | ||||||||
\(86\) | −0.877022 | −0.0945718 | ||||||||
\(87\) | −9.69837 | −1.03977 | ||||||||
\(88\) | −0.781640 | −0.0833231 | ||||||||
\(89\) | −9.68874 | −1.02700 | −0.513502 | − | 0.858088i | \(-0.671652\pi\) | ||||
−0.513502 | + | 0.858088i | \(0.671652\pi\) | |||||||
\(90\) | −0.585537 | −0.0617210 | ||||||||
\(91\) | −8.92207 | −0.935287 | ||||||||
\(92\) | 1.11940 | 0.116706 | ||||||||
\(93\) | −12.7452 | −1.32161 | ||||||||
\(94\) | 2.11791 | 0.218446 | ||||||||
\(95\) | −4.83335 | −0.495891 | ||||||||
\(96\) | −5.63506 | −0.575125 | ||||||||
\(97\) | 14.8362 | 1.50639 | 0.753194 | − | 0.657799i | \(-0.228512\pi\) | ||||
0.753194 | + | 0.657799i | \(0.228512\pi\) | |||||||
\(98\) | 0.755255 | 0.0762923 | ||||||||
\(99\) | −2.96728 | −0.298223 | ||||||||
\(100\) | −1.96106 | −0.196106 | ||||||||
\(101\) | −18.1023 | −1.80125 | −0.900623 | − | 0.434602i | \(-0.856889\pi\) | ||||
−0.900623 | + | 0.434602i | \(0.856889\pi\) | |||||||
\(102\) | 3.34672 | 0.331375 | ||||||||
\(103\) | 11.0685 | 1.09061 | 0.545305 | − | 0.838238i | \(-0.316414\pi\) | ||||
0.545305 | + | 0.838238i | \(0.316414\pi\) | |||||||
\(104\) | 3.91527 | 0.383924 | ||||||||
\(105\) | −4.35110 | −0.424624 | ||||||||
\(106\) | 1.99571 | 0.193840 | ||||||||
\(107\) | 11.4458 | 1.10651 | 0.553253 | − | 0.833013i | \(-0.313386\pi\) | ||||
0.553253 | + | 0.833013i | \(0.313386\pi\) | |||||||
\(108\) | 0.156722 | 0.0150806 | ||||||||
\(109\) | −4.52758 | −0.433664 | −0.216832 | − | 0.976209i | \(-0.569572\pi\) | ||||
−0.216832 | + | 0.976209i | \(0.569572\pi\) | |||||||
\(110\) | 0.197331 | 0.0188148 | ||||||||
\(111\) | 8.13569 | 0.772206 | ||||||||
\(112\) | −6.71132 | −0.634160 | ||||||||
\(113\) | −15.4078 | −1.44944 | −0.724720 | − | 0.689043i | \(-0.758031\pi\) | ||||
−0.724720 | + | 0.689043i | \(0.758031\pi\) | |||||||
\(114\) | 2.32987 | 0.218212 | ||||||||
\(115\) | −0.570816 | −0.0532289 | ||||||||
\(116\) | 7.78577 | 0.722890 | ||||||||
\(117\) | 14.8633 | 1.37411 | ||||||||
\(118\) | 0.177211 | 0.0163136 | ||||||||
\(119\) | 12.3665 | 1.13363 | ||||||||
\(120\) | 1.90939 | 0.174303 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.61300 | −0.236570 | ||||||||
\(123\) | 3.18013 | 0.286743 | ||||||||
\(124\) | 10.2317 | 0.918834 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.04295 | 0.0929138 | ||||||||
\(127\) | −11.9381 | −1.05933 | −0.529666 | − | 0.848206i | \(-0.677683\pi\) | ||||
−0.529666 | + | 0.848206i | \(0.677683\pi\) | |||||||
\(128\) | 6.01081 | 0.531286 | ||||||||
\(129\) | 10.8568 | 0.955892 | ||||||||
\(130\) | −0.988439 | −0.0866919 | ||||||||
\(131\) | 6.02423 | 0.526340 | 0.263170 | − | 0.964750i | \(-0.415232\pi\) | ||||
0.263170 | + | 0.964750i | \(0.415232\pi\) | |||||||
\(132\) | 4.79048 | 0.416958 | ||||||||
\(133\) | 8.60913 | 0.746506 | ||||||||
\(134\) | 0.846937 | 0.0731642 | ||||||||
\(135\) | −0.0799170 | −0.00687816 | ||||||||
\(136\) | −5.42678 | −0.465343 | ||||||||
\(137\) | −17.4750 | −1.49299 | −0.746493 | − | 0.665393i | \(-0.768264\pi\) | ||||
−0.746493 | + | 0.665393i | \(0.768264\pi\) | |||||||
\(138\) | 0.275157 | 0.0234229 | ||||||||
\(139\) | 11.2114 | 0.950936 | 0.475468 | − | 0.879733i | \(-0.342279\pi\) | ||||
0.475468 | + | 0.879733i | \(0.342279\pi\) | |||||||
\(140\) | 3.49303 | 0.295215 | ||||||||
\(141\) | −26.2181 | −2.20796 | ||||||||
\(142\) | 0.473352 | 0.0397228 | ||||||||
\(143\) | −5.00904 | −0.418877 | ||||||||
\(144\) | 11.1804 | 0.931698 | ||||||||
\(145\) | −3.97018 | −0.329706 | ||||||||
\(146\) | −0.197331 | −0.0163312 | ||||||||
\(147\) | −9.34947 | −0.771131 | ||||||||
\(148\) | −6.53126 | −0.536866 | ||||||||
\(149\) | −12.6487 | −1.03622 | −0.518109 | − | 0.855314i | \(-0.673364\pi\) | ||||
−0.518109 | + | 0.855314i | \(0.673364\pi\) | |||||||
\(150\) | −0.482041 | −0.0393585 | ||||||||
\(151\) | −3.11872 | −0.253798 | −0.126899 | − | 0.991916i | \(-0.540502\pi\) | ||||
−0.126899 | + | 0.991916i | \(0.540502\pi\) | |||||||
\(152\) | −3.77794 | −0.306431 | ||||||||
\(153\) | −20.6013 | −1.66552 | ||||||||
\(154\) | −0.351485 | −0.0283234 | ||||||||
\(155\) | −5.21743 | −0.419074 | ||||||||
\(156\) | −23.9957 | −1.92120 | ||||||||
\(157\) | −18.7273 | −1.49460 | −0.747301 | − | 0.664485i | \(-0.768651\pi\) | ||||
−0.747301 | + | 0.664485i | \(0.768651\pi\) | |||||||
\(158\) | −1.67451 | −0.133217 | ||||||||
\(159\) | −24.7053 | −1.95926 | ||||||||
\(160\) | −2.30680 | −0.182368 | ||||||||
\(161\) | 1.01673 | 0.0801298 | ||||||||
\(162\) | 1.79513 | 0.141039 | ||||||||
\(163\) | −17.6943 | −1.38593 | −0.692963 | − | 0.720973i | \(-0.743695\pi\) | ||||
−0.692963 | + | 0.720973i | \(0.743695\pi\) | |||||||
\(164\) | −2.55298 | −0.199354 | ||||||||
\(165\) | −2.44280 | −0.190172 | ||||||||
\(166\) | −1.47012 | −0.114103 | ||||||||
\(167\) | −20.7265 | −1.60386 | −0.801932 | − | 0.597415i | \(-0.796194\pi\) | ||||
−0.801932 | + | 0.597415i | \(0.796194\pi\) | |||||||
\(168\) | −3.40100 | −0.262393 | ||||||||
\(169\) | 12.0905 | 0.930039 | ||||||||
\(170\) | 1.37003 | 0.105077 | ||||||||
\(171\) | −14.3419 | −1.09675 | ||||||||
\(172\) | −8.71578 | −0.664572 | ||||||||
\(173\) | 11.0769 | 0.842158 | 0.421079 | − | 0.907024i | \(-0.361651\pi\) | ||||
0.421079 | + | 0.907024i | \(0.361651\pi\) | |||||||
\(174\) | 1.91379 | 0.145084 | ||||||||
\(175\) | −1.78119 | −0.134646 | ||||||||
\(176\) | −3.76788 | −0.284015 | ||||||||
\(177\) | −2.19373 | −0.164891 | ||||||||
\(178\) | 1.91189 | 0.143302 | ||||||||
\(179\) | −3.70277 | −0.276758 | −0.138379 | − | 0.990379i | \(-0.544189\pi\) | ||||
−0.138379 | + | 0.990379i | \(0.544189\pi\) | |||||||
\(180\) | −5.81902 | −0.433724 | ||||||||
\(181\) | 4.23567 | 0.314835 | 0.157418 | − | 0.987532i | \(-0.449683\pi\) | ||||
0.157418 | + | 0.987532i | \(0.449683\pi\) | |||||||
\(182\) | 1.76060 | 0.130504 | ||||||||
\(183\) | 32.3469 | 2.39115 | ||||||||
\(184\) | −0.446173 | −0.0328923 | ||||||||
\(185\) | 3.33047 | 0.244861 | ||||||||
\(186\) | 2.51501 | 0.184410 | ||||||||
\(187\) | 6.94282 | 0.507709 | ||||||||
\(188\) | 21.0476 | 1.53506 | ||||||||
\(189\) | 0.142348 | 0.0103543 | ||||||||
\(190\) | 0.953769 | 0.0691937 | ||||||||
\(191\) | 0.744661 | 0.0538817 | 0.0269409 | − | 0.999637i | \(-0.491423\pi\) | ||||
0.0269409 | + | 0.999637i | \(0.491423\pi\) | |||||||
\(192\) | −17.2964 | −1.24826 | ||||||||
\(193\) | 2.39299 | 0.172251 | 0.0861255 | − | 0.996284i | \(-0.472551\pi\) | ||||
0.0861255 | + | 0.996284i | \(0.472551\pi\) | |||||||
\(194\) | −2.92764 | −0.210192 | ||||||||
\(195\) | 12.2361 | 0.876246 | ||||||||
\(196\) | 7.50567 | 0.536119 | ||||||||
\(197\) | −3.10788 | −0.221427 | −0.110714 | − | 0.993852i | \(-0.535314\pi\) | ||||
−0.110714 | + | 0.993852i | \(0.535314\pi\) | |||||||
\(198\) | 0.585537 | 0.0416123 | ||||||||
\(199\) | −8.87127 | −0.628868 | −0.314434 | − | 0.949279i | \(-0.601815\pi\) | ||||
−0.314434 | + | 0.949279i | \(0.601815\pi\) | |||||||
\(200\) | 0.781640 | 0.0552703 | ||||||||
\(201\) | −10.4844 | −0.739514 | ||||||||
\(202\) | 3.57214 | 0.251335 | ||||||||
\(203\) | 7.07166 | 0.496333 | ||||||||
\(204\) | 33.2595 | 2.32863 | ||||||||
\(205\) | 1.30184 | 0.0909243 | ||||||||
\(206\) | −2.18416 | −0.152177 | ||||||||
\(207\) | −1.69377 | −0.117725 | ||||||||
\(208\) | 18.8735 | 1.30864 | ||||||||
\(209\) | 4.83335 | 0.334330 | ||||||||
\(210\) | 0.858607 | 0.0592495 | ||||||||
\(211\) | −11.5535 | −0.795377 | −0.397688 | − | 0.917521i | \(-0.630187\pi\) | ||||
−0.397688 | + | 0.917521i | \(0.630187\pi\) | |||||||
\(212\) | 19.8332 | 1.36215 | ||||||||
\(213\) | −5.85973 | −0.401502 | ||||||||
\(214\) | −2.25861 | −0.154395 | ||||||||
\(215\) | 4.44442 | 0.303107 | ||||||||
\(216\) | −0.0624663 | −0.00425029 | ||||||||
\(217\) | 9.29325 | 0.630867 | ||||||||
\(218\) | 0.893432 | 0.0605109 | ||||||||
\(219\) | 2.44280 | 0.165069 | ||||||||
\(220\) | 1.96106 | 0.132215 | ||||||||
\(221\) | −34.7769 | −2.33935 | ||||||||
\(222\) | −1.60542 | −0.107749 | ||||||||
\(223\) | −24.6790 | −1.65263 | −0.826314 | − | 0.563209i | \(-0.809566\pi\) | ||||
−0.826314 | + | 0.563209i | \(0.809566\pi\) | |||||||
\(224\) | 4.10885 | 0.274534 | ||||||||
\(225\) | 2.96728 | 0.197819 | ||||||||
\(226\) | 3.04043 | 0.202246 | ||||||||
\(227\) | 24.6063 | 1.63318 | 0.816589 | − | 0.577219i | \(-0.195862\pi\) | ||||
0.816589 | + | 0.577219i | \(0.195862\pi\) | |||||||
\(228\) | 23.1541 | 1.53342 | ||||||||
\(229\) | −22.0208 | −1.45518 | −0.727588 | − | 0.686014i | \(-0.759359\pi\) | ||||
−0.727588 | + | 0.686014i | \(0.759359\pi\) | |||||||
\(230\) | 0.112640 | 0.00742724 | ||||||||
\(231\) | 4.35110 | 0.286282 | ||||||||
\(232\) | −3.10325 | −0.203739 | ||||||||
\(233\) | −11.7764 | −0.771497 | −0.385748 | − | 0.922604i | \(-0.626057\pi\) | ||||
−0.385748 | + | 0.922604i | \(0.626057\pi\) | |||||||
\(234\) | −2.93298 | −0.191735 | ||||||||
\(235\) | −10.7328 | −0.700130 | ||||||||
\(236\) | 1.76111 | 0.114638 | ||||||||
\(237\) | 20.7292 | 1.34650 | ||||||||
\(238\) | −2.44029 | −0.158181 | ||||||||
\(239\) | −9.10364 | −0.588866 | −0.294433 | − | 0.955672i | \(-0.595131\pi\) | ||||
−0.294433 | + | 0.955672i | \(0.595131\pi\) | |||||||
\(240\) | 9.20419 | 0.594128 | ||||||||
\(241\) | 28.1635 | 1.81417 | 0.907085 | − | 0.420948i | \(-0.138302\pi\) | ||||
0.907085 | + | 0.420948i | \(0.138302\pi\) | |||||||
\(242\) | −0.197331 | −0.0126849 | ||||||||
\(243\) | −21.9826 | −1.41019 | ||||||||
\(244\) | −25.9678 | −1.66242 | ||||||||
\(245\) | −3.82735 | −0.244521 | ||||||||
\(246\) | −0.627538 | −0.0400104 | ||||||||
\(247\) | −24.2105 | −1.54047 | ||||||||
\(248\) | −4.07815 | −0.258963 | ||||||||
\(249\) | 18.1989 | 1.15331 | ||||||||
\(250\) | −0.197331 | −0.0124803 | ||||||||
\(251\) | 31.2318 | 1.97134 | 0.985668 | − | 0.168699i | \(-0.0539567\pi\) | ||||
0.985668 | + | 0.168699i | \(0.0539567\pi\) | |||||||
\(252\) | 10.3648 | 0.652921 | ||||||||
\(253\) | 0.570816 | 0.0358869 | ||||||||
\(254\) | 2.35575 | 0.147813 | ||||||||
\(255\) | −16.9599 | −1.06207 | ||||||||
\(256\) | 12.9750 | 0.810937 | ||||||||
\(257\) | 19.5259 | 1.21799 | 0.608997 | − | 0.793173i | \(-0.291572\pi\) | ||||
0.608997 | + | 0.793173i | \(0.291572\pi\) | |||||||
\(258\) | −2.14239 | −0.133380 | ||||||||
\(259\) | −5.93222 | −0.368610 | ||||||||
\(260\) | −9.82304 | −0.609199 | ||||||||
\(261\) | −11.7807 | −0.729205 | ||||||||
\(262\) | −1.18877 | −0.0734423 | ||||||||
\(263\) | 20.8901 | 1.28814 | 0.644070 | − | 0.764966i | \(-0.277244\pi\) | ||||
0.644070 | + | 0.764966i | \(0.277244\pi\) | |||||||
\(264\) | −1.90939 | −0.117515 | ||||||||
\(265\) | −10.1135 | −0.621268 | ||||||||
\(266\) | −1.69885 | −0.104163 | ||||||||
\(267\) | −23.6677 | −1.44844 | ||||||||
\(268\) | 8.41680 | 0.514138 | ||||||||
\(269\) | 16.8032 | 1.02451 | 0.512256 | − | 0.858833i | \(-0.328810\pi\) | ||||
0.512256 | + | 0.858833i | \(0.328810\pi\) | |||||||
\(270\) | 0.0157701 | 0.000959738 0 | ||||||||
\(271\) | 29.2510 | 1.77687 | 0.888437 | − | 0.458999i | \(-0.151792\pi\) | ||||
0.888437 | + | 0.458999i | \(0.151792\pi\) | |||||||
\(272\) | −26.1597 | −1.58616 | ||||||||
\(273\) | −21.7949 | −1.31908 | ||||||||
\(274\) | 3.44835 | 0.208322 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 2.73448 | 0.164597 | ||||||||
\(277\) | −16.9208 | −1.01667 | −0.508336 | − | 0.861159i | \(-0.669739\pi\) | ||||
−0.508336 | + | 0.861159i | \(0.669739\pi\) | |||||||
\(278\) | −2.21235 | −0.132688 | ||||||||
\(279\) | −15.4816 | −0.926860 | ||||||||
\(280\) | −1.39225 | −0.0832029 | ||||||||
\(281\) | −18.2585 | −1.08921 | −0.544607 | − | 0.838692i | \(-0.683321\pi\) | ||||
−0.544607 | + | 0.838692i | \(0.683321\pi\) | |||||||
\(282\) | 5.17364 | 0.308086 | ||||||||
\(283\) | −16.7785 | −0.997380 | −0.498690 | − | 0.866780i | \(-0.666185\pi\) | ||||
−0.498690 | + | 0.866780i | \(0.666185\pi\) | |||||||
\(284\) | 4.70414 | 0.279139 | ||||||||
\(285\) | −11.8069 | −0.699381 | ||||||||
\(286\) | 0.988439 | 0.0584476 | ||||||||
\(287\) | −2.31882 | −0.136876 | ||||||||
\(288\) | −6.84493 | −0.403341 | ||||||||
\(289\) | 31.2027 | 1.83545 | ||||||||
\(290\) | 0.783440 | 0.0460052 | ||||||||
\(291\) | 36.2419 | 2.12454 | ||||||||
\(292\) | −1.96106 | −0.114762 | ||||||||
\(293\) | −24.9399 | −1.45700 | −0.728502 | − | 0.685044i | \(-0.759783\pi\) | ||||
−0.728502 | + | 0.685044i | \(0.759783\pi\) | |||||||
\(294\) | 1.84494 | 0.107599 | ||||||||
\(295\) | −0.898038 | −0.0522858 | ||||||||
\(296\) | 2.60323 | 0.151310 | ||||||||
\(297\) | 0.0799170 | 0.00463725 | ||||||||
\(298\) | 2.49597 | 0.144588 | ||||||||
\(299\) | −2.85924 | −0.165354 | ||||||||
\(300\) | −4.79048 | −0.276579 | ||||||||
\(301\) | −7.91637 | −0.456292 | ||||||||
\(302\) | 0.615419 | 0.0354134 | ||||||||
\(303\) | −44.2203 | −2.54039 | ||||||||
\(304\) | −18.2115 | −1.04450 | ||||||||
\(305\) | 13.2417 | 0.758218 | ||||||||
\(306\) | 4.06528 | 0.232396 | ||||||||
\(307\) | −5.36373 | −0.306124 | −0.153062 | − | 0.988217i | \(-0.548913\pi\) | ||||
−0.153062 | + | 0.988217i | \(0.548913\pi\) | |||||||
\(308\) | −3.49303 | −0.199034 | ||||||||
\(309\) | 27.0381 | 1.53815 | ||||||||
\(310\) | 1.02956 | 0.0584751 | ||||||||
\(311\) | −5.05281 | −0.286519 | −0.143259 | − | 0.989685i | \(-0.545758\pi\) | ||||
−0.143259 | + | 0.989685i | \(0.545758\pi\) | |||||||
\(312\) | 9.56423 | 0.541468 | ||||||||
\(313\) | −23.2503 | −1.31418 | −0.657092 | − | 0.753810i | \(-0.728214\pi\) | ||||
−0.657092 | + | 0.753810i | \(0.728214\pi\) | |||||||
\(314\) | 3.69548 | 0.208548 | ||||||||
\(315\) | −5.28531 | −0.297793 | ||||||||
\(316\) | −16.6412 | −0.936140 | ||||||||
\(317\) | 28.4200 | 1.59623 | 0.798113 | − | 0.602507i | \(-0.205832\pi\) | ||||
0.798113 | + | 0.602507i | \(0.205832\pi\) | |||||||
\(318\) | 4.87512 | 0.273383 | ||||||||
\(319\) | 3.97018 | 0.222288 | ||||||||
\(320\) | −7.08056 | −0.395815 | ||||||||
\(321\) | 27.9598 | 1.56057 | ||||||||
\(322\) | −0.200633 | −0.0111808 | ||||||||
\(323\) | 33.5571 | 1.86716 | ||||||||
\(324\) | 17.8399 | 0.991106 | ||||||||
\(325\) | 5.00904 | 0.277852 | ||||||||
\(326\) | 3.49164 | 0.193384 | ||||||||
\(327\) | −11.0600 | −0.611619 | ||||||||
\(328\) | 1.01757 | 0.0561858 | ||||||||
\(329\) | 19.1172 | 1.05396 | ||||||||
\(330\) | 0.482041 | 0.0265355 | ||||||||
\(331\) | 29.6745 | 1.63106 | 0.815528 | − | 0.578717i | \(-0.196447\pi\) | ||||
0.815528 | + | 0.578717i | \(0.196447\pi\) | |||||||
\(332\) | −14.6099 | −0.801822 | ||||||||
\(333\) | 9.88247 | 0.541556 | ||||||||
\(334\) | 4.08998 | 0.223794 | ||||||||
\(335\) | −4.29196 | −0.234495 | ||||||||
\(336\) | −16.3944 | −0.894389 | ||||||||
\(337\) | −14.0488 | −0.765285 | −0.382642 | − | 0.923897i | \(-0.624986\pi\) | ||||
−0.382642 | + | 0.923897i | \(0.624986\pi\) | |||||||
\(338\) | −2.38583 | −0.129772 | ||||||||
\(339\) | −37.6381 | −2.04422 | ||||||||
\(340\) | 13.6153 | 0.738392 | ||||||||
\(341\) | 5.21743 | 0.282540 | ||||||||
\(342\) | 2.83011 | 0.153035 | ||||||||
\(343\) | 19.2856 | 1.04132 | ||||||||
\(344\) | 3.47394 | 0.187302 | ||||||||
\(345\) | −1.39439 | −0.0750715 | ||||||||
\(346\) | −2.18581 | −0.117510 | ||||||||
\(347\) | 22.0207 | 1.18213 | 0.591067 | − | 0.806623i | \(-0.298707\pi\) | ||||
0.591067 | + | 0.806623i | \(0.298707\pi\) | |||||||
\(348\) | 19.0191 | 1.01953 | ||||||||
\(349\) | −24.3363 | −1.30269 | −0.651346 | − | 0.758781i | \(-0.725795\pi\) | ||||
−0.651346 | + | 0.758781i | \(0.725795\pi\) | |||||||
\(350\) | 0.351485 | 0.0187876 | ||||||||
\(351\) | −0.400308 | −0.0213668 | ||||||||
\(352\) | 2.30680 | 0.122953 | ||||||||
\(353\) | −11.4548 | −0.609675 | −0.304837 | − | 0.952404i | \(-0.598602\pi\) | ||||
−0.304837 | + | 0.952404i | \(0.598602\pi\) | |||||||
\(354\) | 0.432891 | 0.0230079 | ||||||||
\(355\) | −2.39877 | −0.127314 | ||||||||
\(356\) | 19.0002 | 1.00701 | ||||||||
\(357\) | 30.2089 | 1.59883 | ||||||||
\(358\) | 0.730671 | 0.0386171 | ||||||||
\(359\) | 17.4891 | 0.923041 | 0.461520 | − | 0.887130i | \(-0.347304\pi\) | ||||
0.461520 | + | 0.887130i | \(0.347304\pi\) | |||||||
\(360\) | 2.31935 | 0.122240 | ||||||||
\(361\) | 4.36126 | 0.229540 | ||||||||
\(362\) | −0.835830 | −0.0439302 | ||||||||
\(363\) | 2.44280 | 0.128214 | ||||||||
\(364\) | 17.4967 | 0.917077 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −6.38304 | −0.333647 | ||||||||
\(367\) | 19.0440 | 0.994091 | 0.497045 | − | 0.867725i | \(-0.334418\pi\) | ||||
0.497045 | + | 0.867725i | \(0.334418\pi\) | |||||||
\(368\) | −2.15077 | −0.112116 | ||||||||
\(369\) | 3.86292 | 0.201096 | ||||||||
\(370\) | −0.657206 | −0.0341665 | ||||||||
\(371\) | 18.0141 | 0.935246 | ||||||||
\(372\) | 24.9940 | 1.29588 | ||||||||
\(373\) | 7.73068 | 0.400279 | 0.200140 | − | 0.979767i | \(-0.435860\pi\) | ||||
0.200140 | + | 0.979767i | \(0.435860\pi\) | |||||||
\(374\) | −1.37003 | −0.0708427 | ||||||||
\(375\) | 2.44280 | 0.126146 | ||||||||
\(376\) | −8.38918 | −0.432639 | ||||||||
\(377\) | −19.8868 | −1.02422 | ||||||||
\(378\) | −0.0280896 | −0.00144477 | ||||||||
\(379\) | 7.51613 | 0.386078 | 0.193039 | − | 0.981191i | \(-0.438166\pi\) | ||||
0.193039 | + | 0.981191i | \(0.438166\pi\) | |||||||
\(380\) | 9.47849 | 0.486236 | ||||||||
\(381\) | −29.1623 | −1.49403 | ||||||||
\(382\) | −0.146945 | −0.00751834 | ||||||||
\(383\) | −2.81371 | −0.143774 | −0.0718870 | − | 0.997413i | \(-0.522902\pi\) | ||||
−0.0718870 | + | 0.997413i | \(0.522902\pi\) | |||||||
\(384\) | 14.6832 | 0.749300 | ||||||||
\(385\) | 1.78119 | 0.0907780 | ||||||||
\(386\) | −0.472211 | −0.0240349 | ||||||||
\(387\) | 13.1879 | 0.670377 | ||||||||
\(388\) | −29.0947 | −1.47706 | ||||||||
\(389\) | −18.0770 | −0.916542 | −0.458271 | − | 0.888813i | \(-0.651531\pi\) | ||||
−0.458271 | + | 0.888813i | \(0.651531\pi\) | |||||||
\(390\) | −2.41456 | −0.122266 | ||||||||
\(391\) | 3.96307 | 0.200421 | ||||||||
\(392\) | −2.99161 | −0.151099 | ||||||||
\(393\) | 14.7160 | 0.742325 | ||||||||
\(394\) | 0.613281 | 0.0308967 | ||||||||
\(395\) | 8.48581 | 0.426967 | ||||||||
\(396\) | 5.81902 | 0.292417 | ||||||||
\(397\) | 10.2941 | 0.516646 | 0.258323 | − | 0.966059i | \(-0.416830\pi\) | ||||
0.258323 | + | 0.966059i | \(0.416830\pi\) | |||||||
\(398\) | 1.75058 | 0.0877485 | ||||||||
\(399\) | 21.0304 | 1.05284 | ||||||||
\(400\) | 3.76788 | 0.188394 | ||||||||
\(401\) | −17.8361 | −0.890692 | −0.445346 | − | 0.895358i | \(-0.646919\pi\) | ||||
−0.445346 | + | 0.895358i | \(0.646919\pi\) | |||||||
\(402\) | 2.06890 | 0.103187 | ||||||||
\(403\) | −26.1343 | −1.30184 | ||||||||
\(404\) | 35.4997 | 1.76618 | ||||||||
\(405\) | −9.09708 | −0.452037 | ||||||||
\(406\) | −1.39546 | −0.0692554 | ||||||||
\(407\) | −3.33047 | −0.165086 | ||||||||
\(408\) | −13.2566 | −0.656298 | ||||||||
\(409\) | 13.4983 | 0.667450 | 0.333725 | − | 0.942670i | \(-0.391694\pi\) | ||||
0.333725 | + | 0.942670i | \(0.391694\pi\) | |||||||
\(410\) | −0.256893 | −0.0126870 | ||||||||
\(411\) | −42.6879 | −2.10564 | ||||||||
\(412\) | −21.7060 | −1.06938 | ||||||||
\(413\) | 1.59958 | 0.0787101 | ||||||||
\(414\) | 0.334234 | 0.0164267 | ||||||||
\(415\) | 7.45000 | 0.365706 | ||||||||
\(416\) | −11.5549 | −0.566523 | ||||||||
\(417\) | 27.3872 | 1.34116 | ||||||||
\(418\) | −0.953769 | −0.0466504 | ||||||||
\(419\) | 4.54853 | 0.222210 | 0.111105 | − | 0.993809i | \(-0.464561\pi\) | ||||
0.111105 | + | 0.993809i | \(0.464561\pi\) | |||||||
\(420\) | 8.53278 | 0.416357 | ||||||||
\(421\) | 3.75818 | 0.183163 | 0.0915813 | − | 0.995798i | \(-0.470808\pi\) | ||||
0.0915813 | + | 0.995798i | \(0.470808\pi\) | |||||||
\(422\) | 2.27987 | 0.110982 | ||||||||
\(423\) | −31.8472 | −1.54847 | ||||||||
\(424\) | −7.90513 | −0.383907 | ||||||||
\(425\) | −6.94282 | −0.336776 | ||||||||
\(426\) | 1.15631 | 0.0560232 | ||||||||
\(427\) | −23.5860 | −1.14141 | ||||||||
\(428\) | −22.4459 | −1.08496 | ||||||||
\(429\) | −12.2361 | −0.590765 | ||||||||
\(430\) | −0.877022 | −0.0422938 | ||||||||
\(431\) | 15.2119 | 0.732732 | 0.366366 | − | 0.930471i | \(-0.380602\pi\) | ||||
0.366366 | + | 0.930471i | \(0.380602\pi\) | |||||||
\(432\) | −0.301118 | −0.0144875 | ||||||||
\(433\) | −8.94042 | −0.429649 | −0.214825 | − | 0.976653i | \(-0.568918\pi\) | ||||
−0.214825 | + | 0.976653i | \(0.568918\pi\) | |||||||
\(434\) | −1.83385 | −0.0880275 | ||||||||
\(435\) | −9.69837 | −0.465001 | ||||||||
\(436\) | 8.87886 | 0.425220 | ||||||||
\(437\) | 2.75895 | 0.131979 | ||||||||
\(438\) | −0.482041 | −0.0230328 | ||||||||
\(439\) | 36.9901 | 1.76544 | 0.882720 | − | 0.469900i | \(-0.155710\pi\) | ||||
0.882720 | + | 0.469900i | \(0.155710\pi\) | |||||||
\(440\) | −0.781640 | −0.0372632 | ||||||||
\(441\) | −11.3568 | −0.540802 | ||||||||
\(442\) | 6.86255 | 0.326418 | ||||||||
\(443\) | −4.88064 | −0.231886 | −0.115943 | − | 0.993256i | \(-0.536989\pi\) | ||||
−0.115943 | + | 0.993256i | \(0.536989\pi\) | |||||||
\(444\) | −15.9546 | −0.757171 | ||||||||
\(445\) | −9.68874 | −0.459290 | ||||||||
\(446\) | 4.86993 | 0.230598 | ||||||||
\(447\) | −30.8982 | −1.46143 | ||||||||
\(448\) | 12.6118 | 0.595853 | ||||||||
\(449\) | 30.5866 | 1.44347 | 0.721736 | − | 0.692168i | \(-0.243344\pi\) | ||||
0.721736 | + | 0.692168i | \(0.243344\pi\) | |||||||
\(450\) | −0.585537 | −0.0276025 | ||||||||
\(451\) | −1.30184 | −0.0613011 | ||||||||
\(452\) | 30.2156 | 1.42122 | ||||||||
\(453\) | −7.61841 | −0.357944 | ||||||||
\(454\) | −4.85559 | −0.227884 | ||||||||
\(455\) | −8.92207 | −0.418273 | ||||||||
\(456\) | −9.22876 | −0.432176 | ||||||||
\(457\) | −20.5889 | −0.963110 | −0.481555 | − | 0.876416i | \(-0.659928\pi\) | ||||
−0.481555 | + | 0.876416i | \(0.659928\pi\) | |||||||
\(458\) | 4.34539 | 0.203047 | ||||||||
\(459\) | 0.554849 | 0.0258981 | ||||||||
\(460\) | 1.11940 | 0.0521925 | ||||||||
\(461\) | 0.456150 | 0.0212450 | 0.0106225 | − | 0.999944i | \(-0.496619\pi\) | ||||
0.0106225 | + | 0.999944i | \(0.496619\pi\) | |||||||
\(462\) | −0.858607 | −0.0399460 | ||||||||
\(463\) | 31.2147 | 1.45067 | 0.725336 | − | 0.688395i | \(-0.241684\pi\) | ||||
0.725336 | + | 0.688395i | \(0.241684\pi\) | |||||||
\(464\) | −14.9592 | −0.694462 | ||||||||
\(465\) | −12.7452 | −0.591043 | ||||||||
\(466\) | 2.32385 | 0.107650 | ||||||||
\(467\) | 39.9991 | 1.85094 | 0.925470 | − | 0.378821i | \(-0.123670\pi\) | ||||
0.925470 | + | 0.378821i | \(0.123670\pi\) | |||||||
\(468\) | −29.1477 | −1.34735 | ||||||||
\(469\) | 7.64481 | 0.353005 | ||||||||
\(470\) | 2.11791 | 0.0976920 | ||||||||
\(471\) | −45.7471 | −2.10792 | ||||||||
\(472\) | −0.701942 | −0.0323095 | ||||||||
\(473\) | −4.44442 | −0.204355 | ||||||||
\(474\) | −4.09050 | −0.187883 | ||||||||
\(475\) | −4.83335 | −0.221769 | ||||||||
\(476\) | −24.2514 | −1.11156 | ||||||||
\(477\) | −30.0097 | −1.37405 | ||||||||
\(478\) | 1.79643 | 0.0821668 | ||||||||
\(479\) | 3.89811 | 0.178109 | 0.0890547 | − | 0.996027i | \(-0.471615\pi\) | ||||
0.0890547 | + | 0.996027i | \(0.471615\pi\) | |||||||
\(480\) | −5.63506 | −0.257204 | ||||||||
\(481\) | 16.6825 | 0.760656 | ||||||||
\(482\) | −5.55753 | −0.253138 | ||||||||
\(483\) | 2.48368 | 0.113011 | ||||||||
\(484\) | −1.96106 | −0.0891391 | ||||||||
\(485\) | 14.8362 | 0.673677 | ||||||||
\(486\) | 4.33785 | 0.196769 | ||||||||
\(487\) | 12.6004 | 0.570980 | 0.285490 | − | 0.958382i | \(-0.407844\pi\) | ||||
0.285490 | + | 0.958382i | \(0.407844\pi\) | |||||||
\(488\) | 10.3502 | 0.468534 | ||||||||
\(489\) | −43.2238 | −1.95465 | ||||||||
\(490\) | 0.755255 | 0.0341189 | ||||||||
\(491\) | 1.61450 | 0.0728614 | 0.0364307 | − | 0.999336i | \(-0.488401\pi\) | ||||
0.0364307 | + | 0.999336i | \(0.488401\pi\) | |||||||
\(492\) | −6.23643 | −0.281160 | ||||||||
\(493\) | 27.5643 | 1.24143 | ||||||||
\(494\) | 4.77747 | 0.214949 | ||||||||
\(495\) | −2.96728 | −0.133370 | ||||||||
\(496\) | −19.6587 | −0.882700 | ||||||||
\(497\) | 4.27268 | 0.191656 | ||||||||
\(498\) | −3.59120 | −0.160926 | ||||||||
\(499\) | 8.65917 | 0.387638 | 0.193819 | − | 0.981037i | \(-0.437913\pi\) | ||||
0.193819 | + | 0.981037i | \(0.437913\pi\) | |||||||
\(500\) | −1.96106 | −0.0877013 | ||||||||
\(501\) | −50.6307 | −2.26201 | ||||||||
\(502\) | −6.16301 | −0.275068 | ||||||||
\(503\) | −24.8528 | −1.10813 | −0.554065 | − | 0.832473i | \(-0.686924\pi\) | ||||
−0.554065 | + | 0.832473i | \(0.686924\pi\) | |||||||
\(504\) | −4.13121 | −0.184019 | ||||||||
\(505\) | −18.1023 | −0.805541 | ||||||||
\(506\) | −0.112640 | −0.00500744 | ||||||||
\(507\) | 29.5347 | 1.31168 | ||||||||
\(508\) | 23.4113 | 1.03871 | ||||||||
\(509\) | 13.9830 | 0.619784 | 0.309892 | − | 0.950772i | \(-0.399707\pi\) | ||||
0.309892 | + | 0.950772i | \(0.399707\pi\) | |||||||
\(510\) | 3.34672 | 0.148195 | ||||||||
\(511\) | −1.78119 | −0.0787953 | ||||||||
\(512\) | −14.5820 | −0.644439 | ||||||||
\(513\) | 0.386267 | 0.0170541 | ||||||||
\(514\) | −3.85307 | −0.169952 | ||||||||
\(515\) | 11.0685 | 0.487736 | ||||||||
\(516\) | −21.2909 | −0.937281 | ||||||||
\(517\) | 10.7328 | 0.472027 | ||||||||
\(518\) | 1.17061 | 0.0514337 | ||||||||
\(519\) | 27.0586 | 1.18774 | ||||||||
\(520\) | 3.91527 | 0.171696 | ||||||||
\(521\) | −20.0362 | −0.877801 | −0.438900 | − | 0.898536i | \(-0.644632\pi\) | ||||
−0.438900 | + | 0.898536i | \(0.644632\pi\) | |||||||
\(522\) | 2.32469 | 0.101749 | ||||||||
\(523\) | −13.7534 | −0.601396 | −0.300698 | − | 0.953719i | \(-0.597220\pi\) | ||||
−0.300698 | + | 0.953719i | \(0.597220\pi\) | |||||||
\(524\) | −11.8139 | −0.516092 | ||||||||
\(525\) | −4.35110 | −0.189898 | ||||||||
\(526\) | −4.12227 | −0.179740 | ||||||||
\(527\) | 36.2237 | 1.57793 | ||||||||
\(528\) | −9.20419 | −0.400561 | ||||||||
\(529\) | −22.6742 | −0.985833 | ||||||||
\(530\) | 1.99571 | 0.0866881 | ||||||||
\(531\) | −2.66473 | −0.115640 | ||||||||
\(532\) | −16.8830 | −0.731972 | ||||||||
\(533\) | 6.52096 | 0.282454 | ||||||||
\(534\) | 4.67037 | 0.202107 | ||||||||
\(535\) | 11.4458 | 0.494845 | ||||||||
\(536\) | −3.35477 | −0.144904 | ||||||||
\(537\) | −9.04513 | −0.390326 | ||||||||
\(538\) | −3.31580 | −0.142954 | ||||||||
\(539\) | 3.82735 | 0.164856 | ||||||||
\(540\) | 0.156722 | 0.00674424 | ||||||||
\(541\) | 9.38822 | 0.403631 | 0.201815 | − | 0.979424i | \(-0.435316\pi\) | ||||
0.201815 | + | 0.979424i | \(0.435316\pi\) | |||||||
\(542\) | −5.77213 | −0.247934 | ||||||||
\(543\) | 10.3469 | 0.444029 | ||||||||
\(544\) | 16.0157 | 0.686667 | ||||||||
\(545\) | −4.52758 | −0.193940 | ||||||||
\(546\) | 4.30080 | 0.184057 | ||||||||
\(547\) | −11.0381 | −0.471954 | −0.235977 | − | 0.971759i | \(-0.575829\pi\) | ||||
−0.235977 | + | 0.971759i | \(0.575829\pi\) | |||||||
\(548\) | 34.2694 | 1.46392 | ||||||||
\(549\) | 39.2919 | 1.67694 | ||||||||
\(550\) | 0.197331 | 0.00841422 | ||||||||
\(551\) | 19.1893 | 0.817491 | ||||||||
\(552\) | −1.08991 | −0.0463897 | ||||||||
\(553\) | −15.1149 | −0.642749 | ||||||||
\(554\) | 3.33900 | 0.141861 | ||||||||
\(555\) | 8.13569 | 0.345341 | ||||||||
\(556\) | −21.9862 | −0.932422 | ||||||||
\(557\) | −0.509545 | −0.0215901 | −0.0107951 | − | 0.999942i | \(-0.503436\pi\) | ||||
−0.0107951 | + | 0.999942i | \(0.503436\pi\) | |||||||
\(558\) | 3.05500 | 0.129328 | ||||||||
\(559\) | 22.2623 | 0.941595 | ||||||||
\(560\) | −6.71132 | −0.283605 | ||||||||
\(561\) | 16.9599 | 0.716049 | ||||||||
\(562\) | 3.60298 | 0.151982 | ||||||||
\(563\) | 1.21450 | 0.0511851 | 0.0255926 | − | 0.999672i | \(-0.491853\pi\) | ||||
0.0255926 | + | 0.999672i | \(0.491853\pi\) | |||||||
\(564\) | 51.4152 | 2.16497 | ||||||||
\(565\) | −15.4078 | −0.648209 | ||||||||
\(566\) | 3.31092 | 0.139169 | ||||||||
\(567\) | 16.2036 | 0.680489 | ||||||||
\(568\) | −1.87498 | −0.0786722 | ||||||||
\(569\) | −10.3628 | −0.434432 | −0.217216 | − | 0.976124i | \(-0.569698\pi\) | ||||
−0.217216 | + | 0.976124i | \(0.569698\pi\) | |||||||
\(570\) | 2.32987 | 0.0975875 | ||||||||
\(571\) | 6.63977 | 0.277866 | 0.138933 | − | 0.990302i | \(-0.455633\pi\) | ||||
0.138933 | + | 0.990302i | \(0.455633\pi\) | |||||||
\(572\) | 9.82304 | 0.410722 | ||||||||
\(573\) | 1.81906 | 0.0759923 | ||||||||
\(574\) | 0.457576 | 0.0190988 | ||||||||
\(575\) | −0.570816 | −0.0238047 | ||||||||
\(576\) | −21.0100 | −0.875418 | ||||||||
\(577\) | 29.8080 | 1.24093 | 0.620463 | − | 0.784236i | \(-0.286945\pi\) | ||||
0.620463 | + | 0.784236i | \(0.286945\pi\) | |||||||
\(578\) | −6.15726 | −0.256108 | ||||||||
\(579\) | 5.84560 | 0.242935 | ||||||||
\(580\) | 7.78577 | 0.323286 | ||||||||
\(581\) | −13.2699 | −0.550528 | ||||||||
\(582\) | −7.15165 | −0.296445 | ||||||||
\(583\) | 10.1135 | 0.418859 | ||||||||
\(584\) | 0.781640 | 0.0323445 | ||||||||
\(585\) | 14.8633 | 0.614520 | ||||||||
\(586\) | 4.92141 | 0.203302 | ||||||||
\(587\) | −23.0396 | −0.950948 | −0.475474 | − | 0.879730i | \(-0.657723\pi\) | ||||
−0.475474 | + | 0.879730i | \(0.657723\pi\) | |||||||
\(588\) | 18.3349 | 0.756117 | ||||||||
\(589\) | 25.2177 | 1.03908 | ||||||||
\(590\) | 0.177211 | 0.00729565 | ||||||||
\(591\) | −7.59194 | −0.312291 | ||||||||
\(592\) | 12.5488 | 0.515754 | ||||||||
\(593\) | 42.5797 | 1.74854 | 0.874270 | − | 0.485441i | \(-0.161341\pi\) | ||||
0.874270 | + | 0.485441i | \(0.161341\pi\) | |||||||
\(594\) | −0.0157701 | −0.000647055 0 | ||||||||
\(595\) | 12.3665 | 0.506977 | ||||||||
\(596\) | 24.8048 | 1.01604 | ||||||||
\(597\) | −21.6708 | −0.886925 | ||||||||
\(598\) | 0.564217 | 0.0230726 | ||||||||
\(599\) | 26.9798 | 1.10236 | 0.551182 | − | 0.834385i | \(-0.314177\pi\) | ||||
0.551182 | + | 0.834385i | \(0.314177\pi\) | |||||||
\(600\) | 1.90939 | 0.0779506 | ||||||||
\(601\) | −5.95279 | −0.242819 | −0.121410 | − | 0.992602i | \(-0.538741\pi\) | ||||
−0.121410 | + | 0.992602i | \(0.538741\pi\) | |||||||
\(602\) | 1.56215 | 0.0636683 | ||||||||
\(603\) | −12.7355 | −0.518629 | ||||||||
\(604\) | 6.11599 | 0.248856 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 8.72604 | 0.354471 | ||||||||
\(607\) | 40.2772 | 1.63480 | 0.817401 | − | 0.576069i | \(-0.195414\pi\) | ||||
0.817401 | + | 0.576069i | \(0.195414\pi\) | |||||||
\(608\) | 11.1496 | 0.452175 | ||||||||
\(609\) | 17.2747 | 0.700005 | ||||||||
\(610\) | −2.61300 | −0.105797 | ||||||||
\(611\) | −53.7610 | −2.17494 | ||||||||
\(612\) | 40.4004 | 1.63309 | ||||||||
\(613\) | −38.8448 | −1.56893 | −0.784463 | − | 0.620176i | \(-0.787061\pi\) | ||||
−0.784463 | + | 0.620176i | \(0.787061\pi\) | |||||||
\(614\) | 1.05843 | 0.0427148 | ||||||||
\(615\) | 3.18013 | 0.128235 | ||||||||
\(616\) | 1.39225 | 0.0560954 | ||||||||
\(617\) | −31.6436 | −1.27392 | −0.636962 | − | 0.770895i | \(-0.719809\pi\) | ||||
−0.636962 | + | 0.770895i | \(0.719809\pi\) | |||||||
\(618\) | −5.33546 | −0.214624 | ||||||||
\(619\) | −8.31936 | −0.334383 | −0.167192 | − | 0.985924i | \(-0.553470\pi\) | ||||
−0.167192 | + | 0.985924i | \(0.553470\pi\) | |||||||
\(620\) | 10.2317 | 0.410915 | ||||||||
\(621\) | 0.0456179 | 0.00183058 | ||||||||
\(622\) | 0.997076 | 0.0399791 | ||||||||
\(623\) | 17.2575 | 0.691408 | ||||||||
\(624\) | 46.1042 | 1.84564 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.58800 | 0.183373 | ||||||||
\(627\) | 11.8069 | 0.471523 | ||||||||
\(628\) | 36.7254 | 1.46550 | ||||||||
\(629\) | −23.1229 | −0.921970 | ||||||||
\(630\) | 1.04295 | 0.0415523 | ||||||||
\(631\) | −5.92133 | −0.235724 | −0.117862 | − | 0.993030i | \(-0.537604\pi\) | ||||
−0.117862 | + | 0.993030i | \(0.537604\pi\) | |||||||
\(632\) | 6.63285 | 0.263840 | ||||||||
\(633\) | −28.2230 | −1.12176 | ||||||||
\(634\) | −5.60815 | −0.222728 | ||||||||
\(635\) | −11.9381 | −0.473748 | ||||||||
\(636\) | 48.4486 | 1.92111 | ||||||||
\(637\) | −19.1714 | −0.759597 | ||||||||
\(638\) | −0.783440 | −0.0310167 | ||||||||
\(639\) | −7.11784 | −0.281577 | ||||||||
\(640\) | 6.01081 | 0.237598 | ||||||||
\(641\) | −49.7037 | −1.96318 | −0.981588 | − | 0.191010i | \(-0.938824\pi\) | ||||
−0.981588 | + | 0.191010i | \(0.938824\pi\) | |||||||
\(642\) | −5.51734 | −0.217752 | ||||||||
\(643\) | 32.9861 | 1.30085 | 0.650423 | − | 0.759572i | \(-0.274592\pi\) | ||||
0.650423 | + | 0.759572i | \(0.274592\pi\) | |||||||
\(644\) | −1.99388 | −0.0785697 | ||||||||
\(645\) | 10.8568 | 0.427488 | ||||||||
\(646\) | −6.62185 | −0.260533 | ||||||||
\(647\) | −16.9040 | −0.664565 | −0.332282 | − | 0.943180i | \(-0.607819\pi\) | ||||
−0.332282 | + | 0.943180i | \(0.607819\pi\) | |||||||
\(648\) | −7.11064 | −0.279332 | ||||||||
\(649\) | 0.898038 | 0.0352511 | ||||||||
\(650\) | −0.988439 | −0.0387698 | ||||||||
\(651\) | 22.7016 | 0.889745 | ||||||||
\(652\) | 34.6996 | 1.35894 | ||||||||
\(653\) | 11.7221 | 0.458719 | 0.229360 | − | 0.973342i | \(-0.426337\pi\) | ||||
0.229360 | + | 0.973342i | \(0.426337\pi\) | |||||||
\(654\) | 2.18248 | 0.0853417 | ||||||||
\(655\) | 6.02423 | 0.235386 | ||||||||
\(656\) | 4.90517 | 0.191515 | ||||||||
\(657\) | 2.96728 | 0.115765 | ||||||||
\(658\) | −3.77241 | −0.147064 | ||||||||
\(659\) | −30.0878 | −1.17205 | −0.586026 | − | 0.810292i | \(-0.699309\pi\) | ||||
−0.586026 | + | 0.810292i | \(0.699309\pi\) | |||||||
\(660\) | 4.79048 | 0.186469 | ||||||||
\(661\) | 25.3985 | 0.987888 | 0.493944 | − | 0.869494i | \(-0.335555\pi\) | ||||
0.493944 | + | 0.869494i | \(0.335555\pi\) | |||||||
\(662\) | −5.85569 | −0.227588 | ||||||||
\(663\) | −84.9530 | −3.29930 | ||||||||
\(664\) | 5.82322 | 0.225985 | ||||||||
\(665\) | 8.60913 | 0.333848 | ||||||||
\(666\) | −1.95012 | −0.0755655 | ||||||||
\(667\) | 2.26624 | 0.0877493 | ||||||||
\(668\) | 40.6459 | 1.57264 | ||||||||
\(669\) | −60.2859 | −2.33079 | ||||||||
\(670\) | 0.846937 | 0.0327200 | ||||||||
\(671\) | −13.2417 | −0.511190 | ||||||||
\(672\) | 10.0371 | 0.387190 | ||||||||
\(673\) | −8.13256 | −0.313487 | −0.156744 | − | 0.987639i | \(-0.550100\pi\) | ||||
−0.156744 | + | 0.987639i | \(0.550100\pi\) | |||||||
\(674\) | 2.77226 | 0.106783 | ||||||||
\(675\) | −0.0799170 | −0.00307601 | ||||||||
\(676\) | −23.7102 | −0.911932 | ||||||||
\(677\) | 45.6107 | 1.75296 | 0.876480 | − | 0.481438i | \(-0.159886\pi\) | ||||
0.876480 | + | 0.481438i | \(0.159886\pi\) | |||||||
\(678\) | 7.42717 | 0.285239 | ||||||||
\(679\) | −26.4261 | −1.01414 | ||||||||
\(680\) | −5.42678 | −0.208108 | ||||||||
\(681\) | 60.1084 | 2.30336 | ||||||||
\(682\) | −1.02956 | −0.0394239 | ||||||||
\(683\) | 5.02751 | 0.192372 | 0.0961862 | − | 0.995363i | \(-0.469336\pi\) | ||||
0.0961862 | + | 0.995363i | \(0.469336\pi\) | |||||||
\(684\) | 28.1254 | 1.07540 | ||||||||
\(685\) | −17.4750 | −0.667684 | ||||||||
\(686\) | −3.80565 | −0.145300 | ||||||||
\(687\) | −53.7925 | −2.05231 | ||||||||
\(688\) | 16.7460 | 0.638437 | ||||||||
\(689\) | −50.6590 | −1.92996 | ||||||||
\(690\) | 0.275157 | 0.0104750 | ||||||||
\(691\) | −34.6652 | −1.31873 | −0.659363 | − | 0.751825i | \(-0.729174\pi\) | ||||
−0.659363 | + | 0.751825i | \(0.729174\pi\) | |||||||
\(692\) | −21.7224 | −0.825762 | ||||||||
\(693\) | 5.28531 | 0.200772 | ||||||||
\(694\) | −4.34537 | −0.164948 | ||||||||
\(695\) | 11.2114 | 0.425272 | ||||||||
\(696\) | −7.58064 | −0.287343 | ||||||||
\(697\) | −9.03842 | −0.342354 | ||||||||
\(698\) | 4.80231 | 0.181770 | ||||||||
\(699\) | −28.7674 | −1.08808 | ||||||||
\(700\) | 3.49303 | 0.132024 | ||||||||
\(701\) | 37.6721 | 1.42285 | 0.711427 | − | 0.702760i | \(-0.248049\pi\) | ||||
0.711427 | + | 0.702760i | \(0.248049\pi\) | |||||||
\(702\) | 0.0789931 | 0.00298140 | ||||||||
\(703\) | −16.0973 | −0.607123 | ||||||||
\(704\) | 7.08056 | 0.266858 | ||||||||
\(705\) | −26.2181 | −0.987430 | ||||||||
\(706\) | 2.26038 | 0.0850704 | ||||||||
\(707\) | 32.2437 | 1.21265 | ||||||||
\(708\) | 4.30204 | 0.161680 | ||||||||
\(709\) | −46.9947 | −1.76492 | −0.882462 | − | 0.470384i | \(-0.844115\pi\) | ||||
−0.882462 | + | 0.470384i | \(0.844115\pi\) | |||||||
\(710\) | 0.473352 | 0.0177646 | ||||||||
\(711\) | 25.1798 | 0.944317 | ||||||||
\(712\) | −7.57311 | −0.283814 | ||||||||
\(713\) | 2.97819 | 0.111534 | ||||||||
\(714\) | −5.96115 | −0.223091 | ||||||||
\(715\) | −5.00904 | −0.187328 | ||||||||
\(716\) | 7.26135 | 0.271369 | ||||||||
\(717\) | −22.2384 | −0.830508 | ||||||||
\(718\) | −3.45115 | −0.128796 | ||||||||
\(719\) | 3.78955 | 0.141326 | 0.0706631 | − | 0.997500i | \(-0.477488\pi\) | ||||
0.0706631 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(720\) | 11.1804 | 0.416668 | ||||||||
\(721\) | −19.7151 | −0.734229 | ||||||||
\(722\) | −0.860612 | −0.0320286 | ||||||||
\(723\) | 68.7978 | 2.55862 | ||||||||
\(724\) | −8.30641 | −0.308705 | ||||||||
\(725\) | −3.97018 | −0.147449 | ||||||||
\(726\) | −0.482041 | −0.0178902 | ||||||||
\(727\) | −28.4237 | −1.05418 | −0.527089 | − | 0.849810i | \(-0.676716\pi\) | ||||
−0.527089 | + | 0.849810i | \(0.676716\pi\) | |||||||
\(728\) | −6.97385 | −0.258468 | ||||||||
\(729\) | −26.4079 | −0.978072 | ||||||||
\(730\) | −0.197331 | −0.00730355 | ||||||||
\(731\) | −30.8568 | −1.14128 | ||||||||
\(732\) | −63.4342 | −2.34459 | ||||||||
\(733\) | −34.9522 | −1.29099 | −0.645494 | − | 0.763765i | \(-0.723348\pi\) | ||||
−0.645494 | + | 0.763765i | \(0.723348\pi\) | |||||||
\(734\) | −3.75798 | −0.138710 | ||||||||
\(735\) | −9.34947 | −0.344860 | ||||||||
\(736\) | 1.31676 | 0.0485363 | ||||||||
\(737\) | 4.29196 | 0.158096 | ||||||||
\(738\) | −0.762274 | −0.0280597 | ||||||||
\(739\) | 34.7267 | 1.27744 | 0.638720 | − | 0.769439i | \(-0.279464\pi\) | ||||
0.638720 | + | 0.769439i | \(0.279464\pi\) | |||||||
\(740\) | −6.53126 | −0.240094 | ||||||||
\(741\) | −59.1414 | −2.17261 | ||||||||
\(742\) | −3.55474 | −0.130499 | ||||||||
\(743\) | 14.3969 | 0.528170 | 0.264085 | − | 0.964499i | \(-0.414930\pi\) | ||||
0.264085 | + | 0.964499i | \(0.414930\pi\) | |||||||
\(744\) | −9.96212 | −0.365229 | ||||||||
\(745\) | −12.6487 | −0.463411 | ||||||||
\(746\) | −1.52550 | −0.0558526 | ||||||||
\(747\) | 22.1063 | 0.808826 | ||||||||
\(748\) | −13.6153 | −0.497824 | ||||||||
\(749\) | −20.3872 | −0.744931 | ||||||||
\(750\) | −0.482041 | −0.0176016 | ||||||||
\(751\) | −18.1726 | −0.663129 | −0.331565 | − | 0.943433i | \(-0.607576\pi\) | ||||
−0.331565 | + | 0.943433i | \(0.607576\pi\) | |||||||
\(752\) | −40.4398 | −1.47469 | ||||||||
\(753\) | 76.2932 | 2.78028 | ||||||||
\(754\) | 3.92428 | 0.142914 | ||||||||
\(755\) | −3.11872 | −0.113502 | ||||||||
\(756\) | −0.279152 | −0.0101527 | ||||||||
\(757\) | 46.0124 | 1.67235 | 0.836174 | − | 0.548464i | \(-0.184787\pi\) | ||||
0.836174 | + | 0.548464i | \(0.184787\pi\) | |||||||
\(758\) | −1.48317 | −0.0538710 | ||||||||
\(759\) | 1.39439 | 0.0506132 | ||||||||
\(760\) | −3.77794 | −0.137040 | ||||||||
\(761\) | −47.6641 | −1.72782 | −0.863911 | − | 0.503644i | \(-0.831992\pi\) | ||||
−0.863911 | + | 0.503644i | \(0.831992\pi\) | |||||||
\(762\) | 5.75463 | 0.208468 | ||||||||
\(763\) | 8.06450 | 0.291954 | ||||||||
\(764\) | −1.46032 | −0.0528327 | ||||||||
\(765\) | −20.6013 | −0.744842 | ||||||||
\(766\) | 0.555232 | 0.0200614 | ||||||||
\(767\) | −4.49831 | −0.162425 | ||||||||
\(768\) | 31.6953 | 1.14371 | ||||||||
\(769\) | −6.32788 | −0.228189 | −0.114095 | − | 0.993470i | \(-0.536397\pi\) | ||||
−0.114095 | + | 0.993470i | \(0.536397\pi\) | |||||||
\(770\) | −0.351485 | −0.0126666 | ||||||||
\(771\) | 47.6980 | 1.71780 | ||||||||
\(772\) | −4.69279 | −0.168897 | ||||||||
\(773\) | −45.8984 | −1.65085 | −0.825426 | − | 0.564510i | \(-0.809065\pi\) | ||||
−0.825426 | + | 0.564510i | \(0.809065\pi\) | |||||||
\(774\) | −2.60237 | −0.0935404 | ||||||||
\(775\) | −5.21743 | −0.187416 | ||||||||
\(776\) | 11.5966 | 0.416292 | ||||||||
\(777\) | −14.4912 | −0.519870 | ||||||||
\(778\) | 3.56716 | 0.127889 | ||||||||
\(779\) | −6.29223 | −0.225443 | ||||||||
\(780\) | −23.9957 | −0.859185 | ||||||||
\(781\) | 2.39877 | 0.0858348 | ||||||||
\(782\) | −0.782037 | −0.0279656 | ||||||||
\(783\) | 0.317285 | 0.0113388 | ||||||||
\(784\) | −14.4210 | −0.515036 | ||||||||
\(785\) | −18.7273 | −0.668407 | ||||||||
\(786\) | −2.90393 | −0.103580 | ||||||||
\(787\) | −21.2751 | −0.758376 | −0.379188 | − | 0.925320i | \(-0.623797\pi\) | ||||
−0.379188 | + | 0.925320i | \(0.623797\pi\) | |||||||
\(788\) | 6.09474 | 0.217116 | ||||||||
\(789\) | 51.0305 | 1.81673 | ||||||||
\(790\) | −1.67451 | −0.0595765 | ||||||||
\(791\) | 27.4442 | 0.975803 | ||||||||
\(792\) | −2.31935 | −0.0824145 | ||||||||
\(793\) | 66.3283 | 2.35539 | ||||||||
\(794\) | −2.03134 | −0.0720897 | ||||||||
\(795\) | −24.7053 | −0.876207 | ||||||||
\(796\) | 17.3971 | 0.616624 | ||||||||
\(797\) | 39.1362 | 1.38627 | 0.693137 | − | 0.720806i | \(-0.256228\pi\) | ||||
0.693137 | + | 0.720806i | \(0.256228\pi\) | |||||||
\(798\) | −4.14995 | −0.146907 | ||||||||
\(799\) | 74.5158 | 2.63618 | ||||||||
\(800\) | −2.30680 | −0.0815577 | ||||||||
\(801\) | −28.7492 | −1.01580 | ||||||||
\(802\) | 3.51962 | 0.124282 | ||||||||
\(803\) | −1.00000 | −0.0352892 | ||||||||
\(804\) | 20.5606 | 0.725115 | ||||||||
\(805\) | 1.01673 | 0.0358351 | ||||||||
\(806\) | 5.15712 | 0.181652 | ||||||||
\(807\) | 41.0470 | 1.44492 | ||||||||
\(808\) | −14.1495 | −0.497777 | ||||||||
\(809\) | 12.4942 | 0.439272 | 0.219636 | − | 0.975582i | \(-0.429513\pi\) | ||||
0.219636 | + | 0.975582i | \(0.429513\pi\) | |||||||
\(810\) | 1.79513 | 0.0630746 | ||||||||
\(811\) | −46.0695 | −1.61772 | −0.808860 | − | 0.588002i | \(-0.799915\pi\) | ||||
−0.808860 | + | 0.588002i | \(0.799915\pi\) | |||||||
\(812\) | −13.8680 | −0.486670 | ||||||||
\(813\) | 71.4545 | 2.50602 | ||||||||
\(814\) | 0.657206 | 0.0230351 | ||||||||
\(815\) | −17.6943 | −0.619805 | ||||||||
\(816\) | −63.9030 | −2.23705 | ||||||||
\(817\) | −21.4814 | −0.751541 | ||||||||
\(818\) | −2.66364 | −0.0931320 | ||||||||
\(819\) | −26.4743 | −0.925088 | ||||||||
\(820\) | −2.55298 | −0.0891540 | ||||||||
\(821\) | −6.72168 | −0.234588 | −0.117294 | − | 0.993097i | \(-0.537422\pi\) | ||||
−0.117294 | + | 0.993097i | \(0.537422\pi\) | |||||||
\(822\) | 8.42364 | 0.293808 | ||||||||
\(823\) | 30.0782 | 1.04846 | 0.524230 | − | 0.851577i | \(-0.324353\pi\) | ||||
0.524230 | + | 0.851577i | \(0.324353\pi\) | |||||||
\(824\) | 8.65157 | 0.301392 | ||||||||
\(825\) | −2.44280 | −0.0850475 | ||||||||
\(826\) | −0.315646 | −0.0109827 | ||||||||
\(827\) | 44.4793 | 1.54670 | 0.773348 | − | 0.633982i | \(-0.218581\pi\) | ||||
0.773348 | + | 0.633982i | \(0.218581\pi\) | |||||||
\(828\) | 3.32159 | 0.115433 | ||||||||
\(829\) | 22.6261 | 0.785836 | 0.392918 | − | 0.919574i | \(-0.371466\pi\) | ||||
0.392918 | + | 0.919574i | \(0.371466\pi\) | |||||||
\(830\) | −1.47012 | −0.0510285 | ||||||||
\(831\) | −41.3342 | −1.43387 | ||||||||
\(832\) | −35.4668 | −1.22959 | ||||||||
\(833\) | 26.5726 | 0.920686 | ||||||||
\(834\) | −5.40434 | −0.187137 | ||||||||
\(835\) | −20.7265 | −0.717270 | ||||||||
\(836\) | −9.47849 | −0.327820 | ||||||||
\(837\) | 0.416962 | 0.0144123 | ||||||||
\(838\) | −0.897565 | −0.0310059 | ||||||||
\(839\) | 2.13174 | 0.0735957 | 0.0367978 | − | 0.999323i | \(-0.488284\pi\) | ||||
0.0367978 | + | 0.999323i | \(0.488284\pi\) | |||||||
\(840\) | −3.40100 | −0.117345 | ||||||||
\(841\) | −13.2377 | −0.456471 | ||||||||
\(842\) | −0.741606 | −0.0255574 | ||||||||
\(843\) | −44.6020 | −1.53617 | ||||||||
\(844\) | 22.6571 | 0.779891 | ||||||||
\(845\) | 12.0905 | 0.415926 | ||||||||
\(846\) | 6.28445 | 0.216064 | ||||||||
\(847\) | −1.78119 | −0.0612025 | ||||||||
\(848\) | −38.1065 | −1.30858 | ||||||||
\(849\) | −40.9866 | −1.40666 | ||||||||
\(850\) | 1.37003 | 0.0469917 | ||||||||
\(851\) | −1.90109 | −0.0651685 | ||||||||
\(852\) | 11.4913 | 0.393685 | ||||||||
\(853\) | 19.9441 | 0.682871 | 0.341436 | − | 0.939905i | \(-0.389087\pi\) | ||||
0.341436 | + | 0.939905i | \(0.389087\pi\) | |||||||
\(854\) | 4.65425 | 0.159265 | ||||||||
\(855\) | −14.3419 | −0.490483 | ||||||||
\(856\) | 8.94649 | 0.305785 | ||||||||
\(857\) | 41.4055 | 1.41439 | 0.707193 | − | 0.707021i | \(-0.249961\pi\) | ||||
0.707193 | + | 0.707021i | \(0.249961\pi\) | |||||||
\(858\) | 2.41456 | 0.0824318 | ||||||||
\(859\) | −28.9941 | −0.989266 | −0.494633 | − | 0.869102i | \(-0.664697\pi\) | ||||
−0.494633 | + | 0.869102i | \(0.664697\pi\) | |||||||
\(860\) | −8.71578 | −0.297206 | ||||||||
\(861\) | −5.66443 | −0.193043 | ||||||||
\(862\) | −3.00178 | −0.102241 | ||||||||
\(863\) | −52.7790 | −1.79662 | −0.898310 | − | 0.439363i | \(-0.855204\pi\) | ||||
−0.898310 | + | 0.439363i | \(0.855204\pi\) | |||||||
\(864\) | 0.184352 | 0.00627180 | ||||||||
\(865\) | 11.0769 | 0.376625 | ||||||||
\(866\) | 1.76422 | 0.0599507 | ||||||||
\(867\) | 76.2221 | 2.58864 | ||||||||
\(868\) | −18.2246 | −0.618584 | ||||||||
\(869\) | −8.48581 | −0.287861 | ||||||||
\(870\) | 1.91379 | 0.0648835 | ||||||||
\(871\) | −21.4986 | −0.728453 | ||||||||
\(872\) | −3.53894 | −0.119844 | ||||||||
\(873\) | 44.0232 | 1.48996 | ||||||||
\(874\) | −0.544427 | −0.0184155 | ||||||||
\(875\) | −1.78119 | −0.0602153 | ||||||||
\(876\) | −4.79048 | −0.161855 | ||||||||
\(877\) | 37.4470 | 1.26450 | 0.632248 | − | 0.774766i | \(-0.282133\pi\) | ||||
0.632248 | + | 0.774766i | \(0.282133\pi\) | |||||||
\(878\) | −7.29929 | −0.246339 | ||||||||
\(879\) | −60.9232 | −2.05489 | ||||||||
\(880\) | −3.76788 | −0.127015 | ||||||||
\(881\) | 3.87080 | 0.130410 | 0.0652052 | − | 0.997872i | \(-0.479230\pi\) | ||||
0.0652052 | + | 0.997872i | \(0.479230\pi\) | |||||||
\(882\) | 2.24106 | 0.0754603 | ||||||||
\(883\) | −44.6541 | −1.50273 | −0.751365 | − | 0.659887i | \(-0.770604\pi\) | ||||
−0.751365 | + | 0.659887i | \(0.770604\pi\) | |||||||
\(884\) | 68.1995 | 2.29380 | ||||||||
\(885\) | −2.19373 | −0.0737414 | ||||||||
\(886\) | 0.963102 | 0.0323560 | ||||||||
\(887\) | −17.1112 | −0.574537 | −0.287269 | − | 0.957850i | \(-0.592747\pi\) | ||||
−0.287269 | + | 0.957850i | \(0.592747\pi\) | |||||||
\(888\) | 6.35918 | 0.213400 | ||||||||
\(889\) | 21.2640 | 0.713172 | ||||||||
\(890\) | 1.91189 | 0.0640866 | ||||||||
\(891\) | 9.09708 | 0.304763 | ||||||||
\(892\) | 48.3970 | 1.62045 | ||||||||
\(893\) | 51.8753 | 1.73594 | ||||||||
\(894\) | 6.09717 | 0.203920 | ||||||||
\(895\) | −3.70277 | −0.123770 | ||||||||
\(896\) | −10.7064 | −0.357676 | ||||||||
\(897\) | −6.98456 | −0.233208 | ||||||||
\(898\) | −6.03569 | −0.201414 | ||||||||
\(899\) | 20.7142 | 0.690856 | ||||||||
\(900\) | −5.81902 | −0.193967 | ||||||||
\(901\) | 70.2163 | 2.33924 | ||||||||
\(902\) | 0.256893 | 0.00855360 | ||||||||
\(903\) | −19.3381 | −0.643533 | ||||||||
\(904\) | −12.0433 | −0.400555 | ||||||||
\(905\) | 4.23567 | 0.140799 | ||||||||
\(906\) | 1.50335 | 0.0499454 | ||||||||
\(907\) | −4.72103 | −0.156759 | −0.0783797 | − | 0.996924i | \(-0.524975\pi\) | ||||
−0.0783797 | + | 0.996924i | \(0.524975\pi\) | |||||||
\(908\) | −48.2545 | −1.60138 | ||||||||
\(909\) | −53.7147 | −1.78160 | ||||||||
\(910\) | 1.76060 | 0.0583634 | ||||||||
\(911\) | −12.3185 | −0.408132 | −0.204066 | − | 0.978957i | \(-0.565416\pi\) | ||||
−0.204066 | + | 0.978957i | \(0.565416\pi\) | |||||||
\(912\) | −44.4870 | −1.47311 | ||||||||
\(913\) | −7.45000 | −0.246559 | ||||||||
\(914\) | 4.06284 | 0.134387 | ||||||||
\(915\) | 32.3469 | 1.06935 | ||||||||
\(916\) | 43.1841 | 1.42684 | ||||||||
\(917\) | −10.7303 | −0.354346 | ||||||||
\(918\) | −0.109489 | −0.00361367 | ||||||||
\(919\) | −23.9263 | −0.789255 | −0.394628 | − | 0.918841i | \(-0.629126\pi\) | ||||
−0.394628 | + | 0.918841i | \(0.629126\pi\) | |||||||
\(920\) | −0.446173 | −0.0147099 | ||||||||
\(921\) | −13.1025 | −0.431743 | ||||||||
\(922\) | −0.0900125 | −0.00296440 | ||||||||
\(923\) | −12.0156 | −0.395497 | ||||||||
\(924\) | −8.53278 | −0.280708 | ||||||||
\(925\) | 3.33047 | 0.109505 | ||||||||
\(926\) | −6.15964 | −0.202418 | ||||||||
\(927\) | 32.8433 | 1.07872 | ||||||||
\(928\) | 9.15841 | 0.300640 | ||||||||
\(929\) | 18.0170 | 0.591118 | 0.295559 | − | 0.955325i | \(-0.404494\pi\) | ||||
0.295559 | + | 0.955325i | \(0.404494\pi\) | |||||||
\(930\) | 2.51501 | 0.0824706 | ||||||||
\(931\) | 18.4989 | 0.606278 | ||||||||
\(932\) | 23.0942 | 0.756476 | ||||||||
\(933\) | −12.3430 | −0.404092 | ||||||||
\(934\) | −7.89307 | −0.258269 | ||||||||
\(935\) | 6.94282 | 0.227054 | ||||||||
\(936\) | 11.6177 | 0.379737 | ||||||||
\(937\) | 22.6177 | 0.738888 | 0.369444 | − | 0.929253i | \(-0.379548\pi\) | ||||
0.369444 | + | 0.929253i | \(0.379548\pi\) | |||||||
\(938\) | −1.50856 | −0.0492562 | ||||||||
\(939\) | −56.7959 | −1.85346 | ||||||||
\(940\) | 21.0476 | 0.686499 | ||||||||
\(941\) | −9.04843 | −0.294970 | −0.147485 | − | 0.989064i | \(-0.547118\pi\) | ||||
−0.147485 | + | 0.989064i | \(0.547118\pi\) | |||||||
\(942\) | 9.02733 | 0.294126 | ||||||||
\(943\) | −0.743110 | −0.0241990 | ||||||||
\(944\) | −3.38370 | −0.110130 | ||||||||
\(945\) | 0.142348 | 0.00463057 | ||||||||
\(946\) | 0.877022 | 0.0285145 | ||||||||
\(947\) | −56.8462 | −1.84725 | −0.923627 | − | 0.383292i | \(-0.874790\pi\) | ||||
−0.923627 | + | 0.383292i | \(0.874790\pi\) | |||||||
\(948\) | −40.6511 | −1.32029 | ||||||||
\(949\) | 5.00904 | 0.162600 | ||||||||
\(950\) | 0.953769 | 0.0309444 | ||||||||
\(951\) | 69.4245 | 2.25124 | ||||||||
\(952\) | 9.66615 | 0.313282 | ||||||||
\(953\) | −40.0370 | −1.29693 | −0.648463 | − | 0.761246i | \(-0.724588\pi\) | ||||
−0.648463 | + | 0.761246i | \(0.724588\pi\) | |||||||
\(954\) | 5.92184 | 0.191727 | ||||||||
\(955\) | 0.744661 | 0.0240966 | ||||||||
\(956\) | 17.8528 | 0.577401 | ||||||||
\(957\) | 9.69837 | 0.313504 | ||||||||
\(958\) | −0.769219 | −0.0248523 | ||||||||
\(959\) | 31.1263 | 1.00512 | ||||||||
\(960\) | −17.2964 | −0.558239 | ||||||||
\(961\) | −3.77840 | −0.121884 | ||||||||
\(962\) | −3.29197 | −0.106137 | ||||||||
\(963\) | 33.9629 | 1.09444 | ||||||||
\(964\) | −55.2303 | −1.77885 | ||||||||
\(965\) | 2.39299 | 0.0770330 | ||||||||
\(966\) | −0.490107 | −0.0157689 | ||||||||
\(967\) | 30.2212 | 0.971849 | 0.485924 | − | 0.874001i | \(-0.338483\pi\) | ||||
0.485924 | + | 0.874001i | \(0.338483\pi\) | |||||||
\(968\) | 0.781640 | 0.0251229 | ||||||||
\(969\) | 81.9733 | 2.63336 | ||||||||
\(970\) | −2.92764 | −0.0940009 | ||||||||
\(971\) | −42.6660 | −1.36922 | −0.684609 | − | 0.728911i | \(-0.740027\pi\) | ||||
−0.684609 | + | 0.728911i | \(0.740027\pi\) | |||||||
\(972\) | 43.1092 | 1.38273 | ||||||||
\(973\) | −19.9696 | −0.640197 | ||||||||
\(974\) | −2.48646 | −0.0796712 | ||||||||
\(975\) | 12.2361 | 0.391869 | ||||||||
\(976\) | 49.8931 | 1.59704 | ||||||||
\(977\) | 49.0785 | 1.57016 | 0.785081 | − | 0.619394i | \(-0.212622\pi\) | ||||
0.785081 | + | 0.619394i | \(0.212622\pi\) | |||||||
\(978\) | 8.52939 | 0.272740 | ||||||||
\(979\) | 9.68874 | 0.309653 | ||||||||
\(980\) | 7.50567 | 0.239760 | ||||||||
\(981\) | −13.4346 | −0.428935 | ||||||||
\(982\) | −0.318591 | −0.0101666 | ||||||||
\(983\) | 19.4484 | 0.620308 | 0.310154 | − | 0.950686i | \(-0.399619\pi\) | ||||
0.310154 | + | 0.950686i | \(0.399619\pi\) | |||||||
\(984\) | 2.48572 | 0.0792418 | ||||||||
\(985\) | −3.10788 | −0.0990254 | ||||||||
\(986\) | −5.43928 | −0.173222 | ||||||||
\(987\) | 46.6995 | 1.48646 | ||||||||
\(988\) | 47.4782 | 1.51048 | ||||||||
\(989\) | −2.53695 | −0.0806702 | ||||||||
\(990\) | 0.585537 | 0.0186096 | ||||||||
\(991\) | 7.47462 | 0.237439 | 0.118720 | − | 0.992928i | \(-0.462121\pi\) | ||||
0.118720 | + | 0.992928i | \(0.462121\pi\) | |||||||
\(992\) | 12.0356 | 0.382130 | ||||||||
\(993\) | 72.4889 | 2.30036 | ||||||||
\(994\) | −0.843131 | −0.0267425 | ||||||||
\(995\) | −8.87127 | −0.281238 | ||||||||
\(996\) | −35.6891 | −1.13085 | ||||||||
\(997\) | 17.2522 | 0.546383 | 0.273192 | − | 0.961960i | \(-0.411921\pi\) | ||||
0.273192 | + | 0.961960i | \(0.411921\pi\) | |||||||
\(998\) | −1.70872 | −0.0540887 | ||||||||
\(999\) | −0.266162 | −0.00842098 |
(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 | 4015.2.a.c.1.12 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.c.1.12 | ✓ | 23 | 1.1 | even | 1 | trivial |