Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5290,2,Mod(1,5290)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5290, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5290.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5290 = 2 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5290.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: | \(42.2408626693\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1509.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x + 4 \) |
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 | \(2.92542\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5290.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.92542 | −1.68899 | −0.844497 | − | 0.535561i | \(-0.820100\pi\) | ||||
−0.844497 | + | 0.535561i | \(0.820100\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.92542 | −1.19430 | ||||||||
\(7\) | −4.55810 | −1.72280 | −0.861400 | − | 0.507928i | \(-0.830412\pi\) | ||||
−0.861400 | + | 0.507928i | \(0.830412\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.55810 | 1.85270 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0.925423 | 0.279026 | 0.139513 | − | 0.990220i | \(-0.455446\pi\) | ||||
0.139513 | + | 0.990220i | \(0.455446\pi\) | |||||||
\(12\) | −2.92542 | −0.844497 | ||||||||
\(13\) | 2.55810 | 0.709489 | 0.354745 | − | 0.934963i | \(-0.384568\pi\) | ||||
0.354745 | + | 0.934963i | \(0.384568\pi\) | |||||||
\(14\) | −4.55810 | −1.21820 | ||||||||
\(15\) | 2.92542 | 0.755341 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.92542 | −1.67966 | −0.839831 | − | 0.542848i | \(-0.817346\pi\) | ||||
−0.839831 | + | 0.542848i | \(0.817346\pi\) | |||||||
\(18\) | 5.55810 | 1.31006 | ||||||||
\(19\) | 3.29275 | 0.755408 | 0.377704 | − | 0.925926i | \(-0.376714\pi\) | ||||
0.377704 | + | 0.925926i | \(0.376714\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 13.3344 | 2.90980 | ||||||||
\(22\) | 0.925423 | 0.197301 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −2.92542 | −0.597149 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.55810 | 0.501685 | ||||||||
\(27\) | −7.48352 | −1.44020 | ||||||||
\(28\) | −4.55810 | −0.861400 | ||||||||
\(29\) | −1.26535 | −0.234970 | −0.117485 | − | 0.993075i | \(-0.537483\pi\) | ||||
−0.117485 | + | 0.993075i | \(0.537483\pi\) | |||||||
\(30\) | 2.92542 | 0.534107 | ||||||||
\(31\) | 10.4089 | 1.86950 | 0.934751 | − | 0.355304i | \(-0.115623\pi\) | ||||
0.934751 | + | 0.355304i | \(0.115623\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.70725 | −0.471272 | ||||||||
\(34\) | −6.92542 | −1.18770 | ||||||||
\(35\) | 4.55810 | 0.770459 | ||||||||
\(36\) | 5.55810 | 0.926350 | ||||||||
\(37\) | −9.70169 | −1.59495 | −0.797474 | − | 0.603353i | \(-0.793831\pi\) | ||||
−0.797474 | + | 0.603353i | \(0.793831\pi\) | |||||||
\(38\) | 3.29275 | 0.534154 | ||||||||
\(39\) | −7.48352 | −1.19832 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −0.925423 | −0.144527 | −0.0722634 | − | 0.997386i | \(-0.523022\pi\) | ||||
−0.0722634 | + | 0.997386i | \(0.523022\pi\) | |||||||
\(42\) | 13.3344 | 2.05754 | ||||||||
\(43\) | 1.26535 | 0.192964 | 0.0964822 | − | 0.995335i | \(-0.469241\pi\) | ||||
0.0964822 | + | 0.995335i | \(0.469241\pi\) | |||||||
\(44\) | 0.925423 | 0.139513 | ||||||||
\(45\) | −5.55810 | −0.828553 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.9670 | 1.59971 | 0.799854 | − | 0.600195i | \(-0.204910\pi\) | ||||
0.799854 | + | 0.600195i | \(0.204910\pi\) | |||||||
\(48\) | −2.92542 | −0.422248 | ||||||||
\(49\) | 13.7763 | 1.96804 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 20.2598 | 2.83694 | ||||||||
\(52\) | 2.55810 | 0.354745 | ||||||||
\(53\) | 3.11620 | 0.428043 | 0.214021 | − | 0.976829i | \(-0.431344\pi\) | ||||
0.214021 | + | 0.976829i | \(0.431344\pi\) | |||||||
\(54\) | −7.48352 | −1.01838 | ||||||||
\(55\) | −0.925423 | −0.124784 | ||||||||
\(56\) | −4.55810 | −0.609102 | ||||||||
\(57\) | −9.63268 | −1.27588 | ||||||||
\(58\) | −1.26535 | −0.166149 | ||||||||
\(59\) | −7.26535 | −0.945868 | −0.472934 | − | 0.881098i | \(-0.656805\pi\) | ||||
−0.472934 | + | 0.881098i | \(0.656805\pi\) | |||||||
\(60\) | 2.92542 | 0.377670 | ||||||||
\(61\) | 11.8925 | 1.52267 | 0.761337 | − | 0.648356i | \(-0.224543\pi\) | ||||
0.761337 | + | 0.648356i | \(0.224543\pi\) | |||||||
\(62\) | 10.4089 | 1.32194 | ||||||||
\(63\) | −25.3344 | −3.19183 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.55810 | −0.317293 | ||||||||
\(66\) | −2.70725 | −0.333240 | ||||||||
\(67\) | 7.85085 | 0.959133 | 0.479567 | − | 0.877505i | \(-0.340794\pi\) | ||||
0.479567 | + | 0.877505i | \(0.340794\pi\) | |||||||
\(68\) | −6.92542 | −0.839831 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.55810 | 0.544797 | ||||||||
\(71\) | −6.92542 | −0.821896 | −0.410948 | − | 0.911659i | \(-0.634802\pi\) | ||||
−0.410948 | + | 0.911659i | \(0.634802\pi\) | |||||||
\(72\) | 5.55810 | 0.655028 | ||||||||
\(73\) | −9.26535 | −1.08443 | −0.542214 | − | 0.840241i | \(-0.682414\pi\) | ||||
−0.542214 | + | 0.840241i | \(0.682414\pi\) | |||||||
\(74\) | −9.70169 | −1.12780 | ||||||||
\(75\) | −2.92542 | −0.337799 | ||||||||
\(76\) | 3.29275 | 0.377704 | ||||||||
\(77\) | −4.21817 | −0.480705 | ||||||||
\(78\) | −7.48352 | −0.847342 | ||||||||
\(79\) | 10.9670 | 1.23389 | 0.616944 | − | 0.787007i | \(-0.288370\pi\) | ||||
0.616944 | + | 0.787007i | \(0.288370\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 5.21817 | 0.579797 | ||||||||
\(82\) | −0.925423 | −0.102196 | ||||||||
\(83\) | −0.585493 | −0.0642662 | −0.0321331 | − | 0.999484i | \(-0.510230\pi\) | ||||
−0.0321331 | + | 0.999484i | \(0.510230\pi\) | |||||||
\(84\) | 13.3344 | 1.45490 | ||||||||
\(85\) | 6.92542 | 0.751168 | ||||||||
\(86\) | 1.26535 | 0.136446 | ||||||||
\(87\) | 3.70169 | 0.396863 | ||||||||
\(88\) | 0.925423 | 0.0986504 | ||||||||
\(89\) | −9.11620 | −0.966315 | −0.483158 | − | 0.875533i | \(-0.660510\pi\) | ||||
−0.483158 | + | 0.875533i | \(0.660510\pi\) | |||||||
\(90\) | −5.55810 | −0.585875 | ||||||||
\(91\) | −11.6601 | −1.22231 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −30.4506 | −3.15758 | ||||||||
\(94\) | 10.9670 | 1.13116 | ||||||||
\(95\) | −3.29275 | −0.337829 | ||||||||
\(96\) | −2.92542 | −0.298575 | ||||||||
\(97\) | 3.22373 | 0.327320 | 0.163660 | − | 0.986517i | \(-0.447670\pi\) | ||||
0.163660 | + | 0.986517i | \(0.447670\pi\) | |||||||
\(98\) | 13.7763 | 1.39161 | ||||||||
\(99\) | 5.14359 | 0.516950 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.70169 | 0.965354 | 0.482677 | − | 0.875798i | \(-0.339664\pi\) | ||||
0.482677 | + | 0.875798i | \(0.339664\pi\) | |||||||
\(102\) | 20.2598 | 2.00602 | ||||||||
\(103\) | 19.7433 | 1.94537 | 0.972683 | − | 0.232136i | \(-0.0745716\pi\) | ||||
0.972683 | + | 0.232136i | \(0.0745716\pi\) | |||||||
\(104\) | 2.55810 | 0.250842 | ||||||||
\(105\) | −13.3344 | −1.30130 | ||||||||
\(106\) | 3.11620 | 0.302672 | ||||||||
\(107\) | −6.00000 | −0.580042 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(108\) | −7.48352 | −0.720102 | ||||||||
\(109\) | −15.2927 | −1.46478 | −0.732390 | − | 0.680886i | \(-0.761595\pi\) | ||||
−0.732390 | + | 0.680886i | \(0.761595\pi\) | |||||||
\(110\) | −0.925423 | −0.0882356 | ||||||||
\(111\) | 28.3816 | 2.69386 | ||||||||
\(112\) | −4.55810 | −0.430700 | ||||||||
\(113\) | −7.26535 | −0.683467 | −0.341733 | − | 0.939797i | \(-0.611014\pi\) | ||||
−0.341733 | + | 0.939797i | \(0.611014\pi\) | |||||||
\(114\) | −9.63268 | −0.902183 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.26535 | −0.117485 | ||||||||
\(117\) | 14.2182 | 1.31447 | ||||||||
\(118\) | −7.26535 | −0.668830 | ||||||||
\(119\) | 31.5668 | 2.89372 | ||||||||
\(120\) | 2.92542 | 0.267053 | ||||||||
\(121\) | −10.1436 | −0.922145 | ||||||||
\(122\) | 11.8925 | 1.07669 | ||||||||
\(123\) | 2.70725 | 0.244105 | ||||||||
\(124\) | 10.4089 | 0.934751 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −25.3344 | −2.25696 | ||||||||
\(127\) | −18.2872 | −1.62273 | −0.811363 | − | 0.584543i | \(-0.801274\pi\) | ||||
−0.811363 | + | 0.584543i | \(0.801274\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.70169 | −0.325916 | ||||||||
\(130\) | −2.55810 | −0.224360 | ||||||||
\(131\) | −15.7017 | −1.37186 | −0.685932 | − | 0.727666i | \(-0.740605\pi\) | ||||
−0.685932 | + | 0.727666i | \(0.740605\pi\) | |||||||
\(132\) | −2.70725 | −0.235636 | ||||||||
\(133\) | −15.0087 | −1.30142 | ||||||||
\(134\) | 7.85085 | 0.678210 | ||||||||
\(135\) | 7.48352 | 0.644079 | ||||||||
\(136\) | −6.92542 | −0.593850 | ||||||||
\(137\) | −2.02739 | −0.173212 | −0.0866060 | − | 0.996243i | \(-0.527602\pi\) | ||||
−0.0866060 | + | 0.996243i | \(0.527602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.14915 | 0.521564 | 0.260782 | − | 0.965398i | \(-0.416020\pi\) | ||||
0.260782 | + | 0.965398i | \(0.416020\pi\) | |||||||
\(140\) | 4.55810 | 0.385230 | ||||||||
\(141\) | −32.0832 | −2.70190 | ||||||||
\(142\) | −6.92542 | −0.581169 | ||||||||
\(143\) | 2.36732 | 0.197966 | ||||||||
\(144\) | 5.55810 | 0.463175 | ||||||||
\(145\) | 1.26535 | 0.105082 | ||||||||
\(146\) | −9.26535 | −0.766806 | ||||||||
\(147\) | −40.3014 | −3.32400 | ||||||||
\(148\) | −9.70169 | −0.797474 | ||||||||
\(149\) | −8.70725 | −0.713326 | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(150\) | −2.92542 | −0.238860 | ||||||||
\(151\) | 13.0746 | 1.06399 | 0.531997 | − | 0.846746i | \(-0.321442\pi\) | ||||
0.531997 | + | 0.846746i | \(0.321442\pi\) | |||||||
\(152\) | 3.29275 | 0.267077 | ||||||||
\(153\) | −38.4922 | −3.11191 | ||||||||
\(154\) | −4.21817 | −0.339910 | ||||||||
\(155\) | −10.4089 | −0.836067 | ||||||||
\(156\) | −7.48352 | −0.599161 | ||||||||
\(157\) | 4.14915 | 0.331139 | 0.165569 | − | 0.986198i | \(-0.447054\pi\) | ||||
0.165569 | + | 0.986198i | \(0.447054\pi\) | |||||||
\(158\) | 10.9670 | 0.872491 | ||||||||
\(159\) | −9.11620 | −0.722962 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 5.21817 | 0.409978 | ||||||||
\(163\) | −7.82345 | −0.612780 | −0.306390 | − | 0.951906i | \(-0.599121\pi\) | ||||
−0.306390 | + | 0.951906i | \(0.599121\pi\) | |||||||
\(164\) | −0.925423 | −0.0722634 | ||||||||
\(165\) | 2.70725 | 0.210759 | ||||||||
\(166\) | −0.585493 | −0.0454431 | ||||||||
\(167\) | −6.58549 | −0.509601 | −0.254800 | − | 0.966994i | \(-0.582010\pi\) | ||||
−0.254800 | + | 0.966994i | \(0.582010\pi\) | |||||||
\(168\) | 13.3344 | 1.02877 | ||||||||
\(169\) | −6.45613 | −0.496625 | ||||||||
\(170\) | 6.92542 | 0.531156 | ||||||||
\(171\) | 18.3014 | 1.39954 | ||||||||
\(172\) | 1.26535 | 0.0964822 | ||||||||
\(173\) | −0.925423 | −0.0703586 | −0.0351793 | − | 0.999381i | \(-0.511200\pi\) | ||||
−0.0351793 | + | 0.999381i | \(0.511200\pi\) | |||||||
\(174\) | 3.70169 | 0.280625 | ||||||||
\(175\) | −4.55810 | −0.344560 | ||||||||
\(176\) | 0.925423 | 0.0697564 | ||||||||
\(177\) | 21.2542 | 1.59757 | ||||||||
\(178\) | −9.11620 | −0.683288 | ||||||||
\(179\) | −2.88380 | −0.215545 | −0.107773 | − | 0.994176i | \(-0.534372\pi\) | ||||
−0.107773 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(180\) | −5.55810 | −0.414276 | ||||||||
\(181\) | −5.82345 | −0.432854 | −0.216427 | − | 0.976299i | \(-0.569440\pi\) | ||||
−0.216427 | + | 0.976299i | \(0.569440\pi\) | |||||||
\(182\) | −11.6601 | −0.864302 | ||||||||
\(183\) | −34.7905 | −2.57179 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.70169 | 0.713283 | ||||||||
\(186\) | −30.4506 | −2.23274 | ||||||||
\(187\) | −6.40895 | −0.468668 | ||||||||
\(188\) | 10.9670 | 0.799854 | ||||||||
\(189\) | 34.1106 | 2.48118 | ||||||||
\(190\) | −3.29275 | −0.238881 | ||||||||
\(191\) | −21.1162 | −1.52791 | −0.763957 | − | 0.645267i | \(-0.776746\pi\) | ||||
−0.763957 | + | 0.645267i | \(0.776746\pi\) | |||||||
\(192\) | −2.92542 | −0.211124 | ||||||||
\(193\) | 3.85085 | 0.277190 | 0.138595 | − | 0.990349i | \(-0.455741\pi\) | ||||
0.138595 | + | 0.990349i | \(0.455741\pi\) | |||||||
\(194\) | 3.22373 | 0.231450 | ||||||||
\(195\) | 7.48352 | 0.535906 | ||||||||
\(196\) | 13.7763 | 0.984019 | ||||||||
\(197\) | −14.7763 | −1.05277 | −0.526383 | − | 0.850248i | \(-0.676452\pi\) | ||||
−0.526383 | + | 0.850248i | \(0.676452\pi\) | |||||||
\(198\) | 5.14359 | 0.365539 | ||||||||
\(199\) | −15.7017 | −1.11306 | −0.556532 | − | 0.830826i | \(-0.687868\pi\) | ||||
−0.556532 | + | 0.830826i | \(0.687868\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −22.9670 | −1.61997 | ||||||||
\(202\) | 9.70169 | 0.682609 | ||||||||
\(203\) | 5.76760 | 0.404806 | ||||||||
\(204\) | 20.2598 | 1.41847 | ||||||||
\(205\) | 0.925423 | 0.0646343 | ||||||||
\(206\) | 19.7433 | 1.37558 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.55810 | 0.177372 | ||||||||
\(209\) | 3.04718 | 0.210778 | ||||||||
\(210\) | −13.3344 | −0.920159 | ||||||||
\(211\) | −8.81789 | −0.607049 | −0.303524 | − | 0.952824i | \(-0.598163\pi\) | ||||
−0.303524 | + | 0.952824i | \(0.598163\pi\) | |||||||
\(212\) | 3.11620 | 0.214021 | ||||||||
\(213\) | 20.2598 | 1.38818 | ||||||||
\(214\) | −6.00000 | −0.410152 | ||||||||
\(215\) | −1.26535 | −0.0862963 | ||||||||
\(216\) | −7.48352 | −0.509189 | ||||||||
\(217\) | −47.4450 | −3.22078 | ||||||||
\(218\) | −15.2927 | −1.03576 | ||||||||
\(219\) | 27.1051 | 1.83159 | ||||||||
\(220\) | −0.925423 | −0.0623920 | ||||||||
\(221\) | −17.7159 | −1.19170 | ||||||||
\(222\) | 28.3816 | 1.90484 | ||||||||
\(223\) | 12.3816 | 0.829130 | 0.414565 | − | 0.910020i | \(-0.363934\pi\) | ||||
0.414565 | + | 0.910020i | \(0.363934\pi\) | |||||||
\(224\) | −4.55810 | −0.304551 | ||||||||
\(225\) | 5.55810 | 0.370540 | ||||||||
\(226\) | −7.26535 | −0.483284 | ||||||||
\(227\) | −6.81789 | −0.452519 | −0.226260 | − | 0.974067i | \(-0.572650\pi\) | ||||
−0.226260 | + | 0.974067i | \(0.572650\pi\) | |||||||
\(228\) | −9.63268 | −0.637940 | ||||||||
\(229\) | −21.7017 | −1.43409 | −0.717044 | − | 0.697028i | \(-0.754505\pi\) | ||||
−0.717044 | + | 0.697028i | \(0.754505\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.3399 | 0.811908 | ||||||||
\(232\) | −1.26535 | −0.0830745 | ||||||||
\(233\) | 7.85085 | 0.514326 | 0.257163 | − | 0.966368i | \(-0.417212\pi\) | ||||
0.257163 | + | 0.966368i | \(0.417212\pi\) | |||||||
\(234\) | 14.2182 | 0.929471 | ||||||||
\(235\) | −10.9670 | −0.715411 | ||||||||
\(236\) | −7.26535 | −0.472934 | ||||||||
\(237\) | −32.0832 | −2.08403 | ||||||||
\(238\) | 31.5668 | 2.04617 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 2.92542 | 0.188835 | ||||||||
\(241\) | 15.7017 | 1.01143 | 0.505717 | − | 0.862699i | \(-0.331228\pi\) | ||||
0.505717 | + | 0.862699i | \(0.331228\pi\) | |||||||
\(242\) | −10.1436 | −0.652055 | ||||||||
\(243\) | 7.18521 | 0.460932 | ||||||||
\(244\) | 11.8925 | 0.761337 | ||||||||
\(245\) | −13.7763 | −0.880134 | ||||||||
\(246\) | 2.70725 | 0.172608 | ||||||||
\(247\) | 8.42317 | 0.535954 | ||||||||
\(248\) | 10.4089 | 0.660969 | ||||||||
\(249\) | 1.71282 | 0.108545 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −0.762041 | −0.0480996 | −0.0240498 | − | 0.999711i | \(-0.507656\pi\) | ||||
−0.0240498 | + | 0.999711i | \(0.507656\pi\) | |||||||
\(252\) | −25.3344 | −1.59592 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −18.2872 | −1.14744 | ||||||||
\(255\) | −20.2598 | −1.26872 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.67986 | 0.416678 | 0.208339 | − | 0.978057i | \(-0.433194\pi\) | ||||
0.208339 | + | 0.978057i | \(0.433194\pi\) | |||||||
\(258\) | −3.70169 | −0.230457 | ||||||||
\(259\) | 44.2213 | 2.74778 | ||||||||
\(260\) | −2.55810 | −0.158647 | ||||||||
\(261\) | −7.03296 | −0.435329 | ||||||||
\(262\) | −15.7017 | −0.970054 | ||||||||
\(263\) | −16.0416 | −0.989169 | −0.494584 | − | 0.869130i | \(-0.664680\pi\) | ||||
−0.494584 | + | 0.869130i | \(0.664680\pi\) | |||||||
\(264\) | −2.70725 | −0.166620 | ||||||||
\(265\) | −3.11620 | −0.191427 | ||||||||
\(266\) | −15.0087 | −0.920240 | ||||||||
\(267\) | 26.6687 | 1.63210 | ||||||||
\(268\) | 7.85085 | 0.479567 | ||||||||
\(269\) | −23.5525 | −1.43602 | −0.718012 | − | 0.696031i | \(-0.754948\pi\) | ||||
−0.718012 | + | 0.696031i | \(0.754948\pi\) | |||||||
\(270\) | 7.48352 | 0.455433 | ||||||||
\(271\) | −8.99444 | −0.546373 | −0.273187 | − | 0.961961i | \(-0.588078\pi\) | ||||
−0.273187 | + | 0.961961i | \(0.588078\pi\) | |||||||
\(272\) | −6.92542 | −0.419915 | ||||||||
\(273\) | 34.1106 | 2.06447 | ||||||||
\(274\) | −2.02739 | −0.122479 | ||||||||
\(275\) | 0.925423 | 0.0558051 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1710 | 0.671200 | 0.335600 | − | 0.942005i | \(-0.391061\pi\) | ||||
0.335600 | + | 0.942005i | \(0.391061\pi\) | |||||||
\(278\) | 6.14915 | 0.368802 | ||||||||
\(279\) | 57.8539 | 3.46363 | ||||||||
\(280\) | 4.55810 | 0.272399 | ||||||||
\(281\) | −26.6687 | −1.59092 | −0.795462 | − | 0.606004i | \(-0.792772\pi\) | ||||
−0.795462 | + | 0.606004i | \(0.792772\pi\) | |||||||
\(282\) | −32.0832 | −1.91053 | ||||||||
\(283\) | 1.26535 | 0.0752174 | 0.0376087 | − | 0.999293i | \(-0.488026\pi\) | ||||
0.0376087 | + | 0.999293i | \(0.488026\pi\) | |||||||
\(284\) | −6.92542 | −0.410948 | ||||||||
\(285\) | 9.63268 | 0.570591 | ||||||||
\(286\) | 2.36732 | 0.139983 | ||||||||
\(287\) | 4.21817 | 0.248991 | ||||||||
\(288\) | 5.55810 | 0.327514 | ||||||||
\(289\) | 30.9615 | 1.82126 | ||||||||
\(290\) | 1.26535 | 0.0743041 | ||||||||
\(291\) | −9.43078 | −0.552842 | ||||||||
\(292\) | −9.26535 | −0.542214 | ||||||||
\(293\) | 25.4034 | 1.48408 | 0.742041 | − | 0.670355i | \(-0.233858\pi\) | ||||
0.742041 | + | 0.670355i | \(0.233858\pi\) | |||||||
\(294\) | −40.3014 | −2.35043 | ||||||||
\(295\) | 7.26535 | 0.423005 | ||||||||
\(296\) | −9.70169 | −0.563899 | ||||||||
\(297\) | −6.92542 | −0.401854 | ||||||||
\(298\) | −8.70725 | −0.504398 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2.92542 | −0.168899 | ||||||||
\(301\) | −5.76760 | −0.332439 | ||||||||
\(302\) | 13.0746 | 0.752357 | ||||||||
\(303\) | −28.3816 | −1.63048 | ||||||||
\(304\) | 3.29275 | 0.188852 | ||||||||
\(305\) | −11.8925 | −0.680961 | ||||||||
\(306\) | −38.4922 | −2.20045 | ||||||||
\(307\) | −20.4780 | −1.16874 | −0.584369 | − | 0.811488i | \(-0.698658\pi\) | ||||
−0.584369 | + | 0.811488i | \(0.698658\pi\) | |||||||
\(308\) | −4.21817 | −0.240353 | ||||||||
\(309\) | −57.7575 | −3.28571 | ||||||||
\(310\) | −10.4089 | −0.591188 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | −7.48352 | −0.423671 | ||||||||
\(313\) | 2.02739 | 0.114595 | 0.0572975 | − | 0.998357i | \(-0.481752\pi\) | ||||
0.0572975 | + | 0.998357i | \(0.481752\pi\) | |||||||
\(314\) | 4.14915 | 0.234150 | ||||||||
\(315\) | 25.3344 | 1.42743 | ||||||||
\(316\) | 10.9670 | 0.616944 | ||||||||
\(317\) | 2.25979 | 0.126923 | 0.0634613 | − | 0.997984i | \(-0.479786\pi\) | ||||
0.0634613 | + | 0.997984i | \(0.479786\pi\) | |||||||
\(318\) | −9.11620 | −0.511211 | ||||||||
\(319\) | −1.17099 | −0.0655626 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 17.5525 | 0.979687 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.8037 | −1.26883 | ||||||||
\(324\) | 5.21817 | 0.289898 | ||||||||
\(325\) | 2.55810 | 0.141898 | ||||||||
\(326\) | −7.82345 | −0.433301 | ||||||||
\(327\) | 44.7378 | 2.47400 | ||||||||
\(328\) | −0.925423 | −0.0510979 | ||||||||
\(329\) | −49.9889 | −2.75598 | ||||||||
\(330\) | 2.70725 | 0.149029 | ||||||||
\(331\) | −5.11620 | −0.281212 | −0.140606 | − | 0.990066i | \(-0.544905\pi\) | ||||
−0.140606 | + | 0.990066i | \(0.544905\pi\) | |||||||
\(332\) | −0.585493 | −0.0321331 | ||||||||
\(333\) | −53.9230 | −2.95496 | ||||||||
\(334\) | −6.58549 | −0.360342 | ||||||||
\(335\) | −7.85085 | −0.428938 | ||||||||
\(336\) | 13.3344 | 0.727449 | ||||||||
\(337\) | −0.856408 | −0.0466515 | −0.0233257 | − | 0.999728i | \(-0.507425\pi\) | ||||
−0.0233257 | + | 0.999728i | \(0.507425\pi\) | |||||||
\(338\) | −6.45613 | −0.351167 | ||||||||
\(339\) | 21.2542 | 1.15437 | ||||||||
\(340\) | 6.92542 | 0.375584 | ||||||||
\(341\) | 9.63268 | 0.521639 | ||||||||
\(342\) | 18.3014 | 0.989627 | ||||||||
\(343\) | −30.8869 | −1.66774 | ||||||||
\(344\) | 1.26535 | 0.0682232 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.925423 | −0.0497510 | ||||||||
\(347\) | 27.0087 | 1.44990 | 0.724951 | − | 0.688801i | \(-0.241863\pi\) | ||||
0.724951 | + | 0.688801i | \(0.241863\pi\) | |||||||
\(348\) | 3.70169 | 0.198432 | ||||||||
\(349\) | −21.6469 | −1.15873 | −0.579366 | − | 0.815067i | \(-0.696700\pi\) | ||||
−0.579366 | + | 0.815067i | \(0.696700\pi\) | |||||||
\(350\) | −4.55810 | −0.243641 | ||||||||
\(351\) | −19.1436 | −1.02181 | ||||||||
\(352\) | 0.925423 | 0.0493252 | ||||||||
\(353\) | −21.3486 | −1.13627 | −0.568136 | − | 0.822935i | \(-0.692335\pi\) | ||||
−0.568136 | + | 0.822935i | \(0.692335\pi\) | |||||||
\(354\) | 21.2542 | 1.12965 | ||||||||
\(355\) | 6.92542 | 0.367563 | ||||||||
\(356\) | −9.11620 | −0.483158 | ||||||||
\(357\) | −92.3461 | −4.88748 | ||||||||
\(358\) | −2.88380 | −0.152414 | ||||||||
\(359\) | 14.6687 | 0.774186 | 0.387093 | − | 0.922041i | \(-0.373479\pi\) | ||||
0.387093 | + | 0.922041i | \(0.373479\pi\) | |||||||
\(360\) | −5.55810 | −0.292938 | ||||||||
\(361\) | −8.15782 | −0.429359 | ||||||||
\(362\) | −5.82345 | −0.306074 | ||||||||
\(363\) | 29.6743 | 1.55750 | ||||||||
\(364\) | −11.6601 | −0.611154 | ||||||||
\(365\) | 9.26535 | 0.484971 | ||||||||
\(366\) | −34.7905 | −1.81853 | ||||||||
\(367\) | 1.17099 | 0.0611250 | 0.0305625 | − | 0.999533i | \(-0.490270\pi\) | ||||
0.0305625 | + | 0.999533i | \(0.490270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.14359 | −0.267765 | ||||||||
\(370\) | 9.70169 | 0.504367 | ||||||||
\(371\) | −14.2039 | −0.737432 | ||||||||
\(372\) | −30.4506 | −1.57879 | ||||||||
\(373\) | 8.88380 | 0.459986 | 0.229993 | − | 0.973192i | \(-0.426130\pi\) | ||||
0.229993 | + | 0.973192i | \(0.426130\pi\) | |||||||
\(374\) | −6.40895 | −0.331399 | ||||||||
\(375\) | 2.92542 | 0.151068 | ||||||||
\(376\) | 10.9670 | 0.565582 | ||||||||
\(377\) | −3.23690 | −0.166709 | ||||||||
\(378\) | 34.1106 | 1.75446 | ||||||||
\(379\) | 23.0746 | 1.18526 | 0.592631 | − | 0.805474i | \(-0.298089\pi\) | ||||
0.592631 | + | 0.805474i | \(0.298089\pi\) | |||||||
\(380\) | −3.29275 | −0.168914 | ||||||||
\(381\) | 53.4977 | 2.74077 | ||||||||
\(382\) | −21.1162 | −1.08040 | ||||||||
\(383\) | 21.9341 | 1.12078 | 0.560390 | − | 0.828229i | \(-0.310651\pi\) | ||||
0.560390 | + | 0.828229i | \(0.310651\pi\) | |||||||
\(384\) | −2.92542 | −0.149287 | ||||||||
\(385\) | 4.21817 | 0.214978 | ||||||||
\(386\) | 3.85085 | 0.196003 | ||||||||
\(387\) | 7.03296 | 0.357505 | ||||||||
\(388\) | 3.22373 | 0.163660 | ||||||||
\(389\) | 1.74331 | 0.0883895 | 0.0441947 | − | 0.999023i | \(-0.485928\pi\) | ||||
0.0441947 | + | 0.999023i | \(0.485928\pi\) | |||||||
\(390\) | 7.48352 | 0.378943 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 13.7763 | 0.695807 | ||||||||
\(393\) | 45.9341 | 2.31707 | ||||||||
\(394\) | −14.7763 | −0.744418 | ||||||||
\(395\) | −10.9670 | −0.551812 | ||||||||
\(396\) | 5.14359 | 0.258475 | ||||||||
\(397\) | −13.0087 | −0.652886 | −0.326443 | − | 0.945217i | \(-0.605850\pi\) | ||||
−0.326443 | + | 0.945217i | \(0.605850\pi\) | |||||||
\(398\) | −15.7017 | −0.787055 | ||||||||
\(399\) | 43.9067 | 2.19808 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −37.9889 | −1.89707 | −0.948537 | − | 0.316666i | \(-0.897436\pi\) | ||||
−0.948537 | + | 0.316666i | \(0.897436\pi\) | |||||||
\(402\) | −22.9670 | −1.14549 | ||||||||
\(403\) | 26.6271 | 1.32639 | ||||||||
\(404\) | 9.70169 | 0.482677 | ||||||||
\(405\) | −5.21817 | −0.259293 | ||||||||
\(406\) | 5.76760 | 0.286241 | ||||||||
\(407\) | −8.97817 | −0.445031 | ||||||||
\(408\) | 20.2598 | 1.00301 | ||||||||
\(409\) | 10.2598 | 0.507314 | 0.253657 | − | 0.967294i | \(-0.418367\pi\) | ||||
0.253657 | + | 0.967294i | \(0.418367\pi\) | |||||||
\(410\) | 0.925423 | 0.0457034 | ||||||||
\(411\) | 5.93098 | 0.292554 | ||||||||
\(412\) | 19.7433 | 0.972683 | ||||||||
\(413\) | 33.1162 | 1.62954 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.585493 | 0.0287407 | ||||||||
\(416\) | 2.55810 | 0.125421 | ||||||||
\(417\) | −17.9889 | −0.880919 | ||||||||
\(418\) | 3.04718 | 0.149043 | ||||||||
\(419\) | −16.9670 | −0.828894 | −0.414447 | − | 0.910073i | \(-0.636025\pi\) | ||||
−0.414447 | + | 0.910073i | \(0.636025\pi\) | |||||||
\(420\) | −13.3344 | −0.650651 | ||||||||
\(421\) | −16.4637 | −0.802393 | −0.401197 | − | 0.915992i | \(-0.631406\pi\) | ||||
−0.401197 | + | 0.915992i | \(0.631406\pi\) | |||||||
\(422\) | −8.81789 | −0.429248 | ||||||||
\(423\) | 60.9559 | 2.96378 | ||||||||
\(424\) | 3.11620 | 0.151336 | ||||||||
\(425\) | −6.92542 | −0.335932 | ||||||||
\(426\) | 20.2598 | 0.981590 | ||||||||
\(427\) | −54.2070 | −2.62326 | ||||||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | −6.92542 | −0.334363 | ||||||||
\(430\) | −1.26535 | −0.0610207 | ||||||||
\(431\) | −8.29831 | −0.399715 | −0.199858 | − | 0.979825i | \(-0.564048\pi\) | ||||
−0.199858 | + | 0.979825i | \(0.564048\pi\) | |||||||
\(432\) | −7.48352 | −0.360051 | ||||||||
\(433\) | −20.2598 | −0.973623 | −0.486812 | − | 0.873507i | \(-0.661840\pi\) | ||||
−0.486812 | + | 0.873507i | \(0.661840\pi\) | |||||||
\(434\) | −47.4450 | −2.27743 | ||||||||
\(435\) | −3.70169 | −0.177483 | ||||||||
\(436\) | −15.2927 | −0.732390 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 27.1051 | 1.29513 | ||||||||
\(439\) | −25.7575 | −1.22934 | −0.614670 | − | 0.788784i | \(-0.710711\pi\) | ||||
−0.614670 | + | 0.788784i | \(0.710711\pi\) | |||||||
\(440\) | −0.925423 | −0.0441178 | ||||||||
\(441\) | 76.5699 | 3.64618 | ||||||||
\(442\) | −17.7159 | −0.842660 | ||||||||
\(443\) | −22.1106 | −1.05051 | −0.525254 | − | 0.850945i | \(-0.676030\pi\) | ||||
−0.525254 | + | 0.850945i | \(0.676030\pi\) | |||||||
\(444\) | 28.3816 | 1.34693 | ||||||||
\(445\) | 9.11620 | 0.432149 | ||||||||
\(446\) | 12.3816 | 0.586283 | ||||||||
\(447\) | 25.4724 | 1.20480 | ||||||||
\(448\) | −4.55810 | −0.215350 | ||||||||
\(449\) | 15.0777 | 0.711560 | 0.355780 | − | 0.934570i | \(-0.384215\pi\) | ||||
0.355780 | + | 0.934570i | \(0.384215\pi\) | |||||||
\(450\) | 5.55810 | 0.262011 | ||||||||
\(451\) | −0.856408 | −0.0403267 | ||||||||
\(452\) | −7.26535 | −0.341733 | ||||||||
\(453\) | −38.2487 | −1.79708 | ||||||||
\(454\) | −6.81789 | −0.319979 | ||||||||
\(455\) | 11.6601 | 0.546633 | ||||||||
\(456\) | −9.63268 | −0.451091 | ||||||||
\(457\) | −22.9670 | −1.07435 | −0.537177 | − | 0.843470i | \(-0.680509\pi\) | ||||
−0.537177 | + | 0.843470i | \(0.680509\pi\) | |||||||
\(458\) | −21.7017 | −1.01405 | ||||||||
\(459\) | 51.8266 | 2.41906 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.1162 | 1.26293 | 0.631464 | − | 0.775405i | \(-0.282455\pi\) | ||||
0.631464 | + | 0.775405i | \(0.282455\pi\) | |||||||
\(462\) | 12.3399 | 0.574105 | ||||||||
\(463\) | 23.3486 | 1.08510 | 0.542551 | − | 0.840023i | \(-0.317459\pi\) | ||||
0.542551 | + | 0.840023i | \(0.317459\pi\) | |||||||
\(464\) | −1.26535 | −0.0587425 | ||||||||
\(465\) | 30.4506 | 1.41211 | ||||||||
\(466\) | 7.85085 | 0.363683 | ||||||||
\(467\) | −0.585493 | −0.0270934 | −0.0135467 | − | 0.999908i | \(-0.504312\pi\) | ||||
−0.0135467 | + | 0.999908i | \(0.504312\pi\) | |||||||
\(468\) | 14.2182 | 0.657235 | ||||||||
\(469\) | −35.7849 | −1.65239 | ||||||||
\(470\) | −10.9670 | −0.505872 | ||||||||
\(471\) | −12.1380 | −0.559291 | ||||||||
\(472\) | −7.26535 | −0.334415 | ||||||||
\(473\) | 1.17099 | 0.0538420 | ||||||||
\(474\) | −32.0832 | −1.47363 | ||||||||
\(475\) | 3.29275 | 0.151082 | ||||||||
\(476\) | 31.5668 | 1.44686 | ||||||||
\(477\) | 17.3201 | 0.793035 | ||||||||
\(478\) | 12.0000 | 0.548867 | ||||||||
\(479\) | 36.8179 | 1.68225 | 0.841126 | − | 0.540839i | \(-0.181893\pi\) | ||||
0.841126 | + | 0.540839i | \(0.181893\pi\) | |||||||
\(480\) | 2.92542 | 0.133527 | ||||||||
\(481\) | −24.8179 | −1.13160 | ||||||||
\(482\) | 15.7017 | 0.715192 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.1436 | −0.461072 | ||||||||
\(485\) | −3.22373 | −0.146382 | ||||||||
\(486\) | 7.18521 | 0.325928 | ||||||||
\(487\) | −13.1162 | −0.594352 | −0.297176 | − | 0.954823i | \(-0.596045\pi\) | ||||
−0.297176 | + | 0.954823i | \(0.596045\pi\) | |||||||
\(488\) | 11.8925 | 0.538347 | ||||||||
\(489\) | 22.8869 | 1.03498 | ||||||||
\(490\) | −13.7763 | −0.622348 | ||||||||
\(491\) | −21.1162 | −0.952961 | −0.476480 | − | 0.879185i | \(-0.658088\pi\) | ||||
−0.476480 | + | 0.879185i | \(0.658088\pi\) | |||||||
\(492\) | 2.70725 | 0.122052 | ||||||||
\(493\) | 8.76310 | 0.394670 | ||||||||
\(494\) | 8.42317 | 0.378976 | ||||||||
\(495\) | −5.14359 | −0.231187 | ||||||||
\(496\) | 10.4089 | 0.467375 | ||||||||
\(497\) | 31.5668 | 1.41596 | ||||||||
\(498\) | 1.71282 | 0.0767531 | ||||||||
\(499\) | −4.43634 | −0.198598 | −0.0992989 | − | 0.995058i | \(-0.531660\pi\) | ||||
−0.0992989 | + | 0.995058i | \(0.531660\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 19.2654 | 0.860712 | ||||||||
\(502\) | −0.762041 | −0.0340116 | ||||||||
\(503\) | −30.1939 | −1.34628 | −0.673139 | − | 0.739516i | \(-0.735055\pi\) | ||||
−0.673139 | + | 0.739516i | \(0.735055\pi\) | |||||||
\(504\) | −25.3344 | −1.12848 | ||||||||
\(505\) | −9.70169 | −0.431720 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.8869 | 0.838797 | ||||||||
\(508\) | −18.2872 | −0.811363 | ||||||||
\(509\) | 21.0218 | 0.931776 | 0.465888 | − | 0.884844i | \(-0.345735\pi\) | ||||
0.465888 | + | 0.884844i | \(0.345735\pi\) | |||||||
\(510\) | −20.2598 | −0.897119 | ||||||||
\(511\) | 42.2324 | 1.86825 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −24.6413 | −1.08794 | ||||||||
\(514\) | 6.67986 | 0.294636 | ||||||||
\(515\) | −19.7433 | −0.869994 | ||||||||
\(516\) | −3.70169 | −0.162958 | ||||||||
\(517\) | 10.1492 | 0.446359 | ||||||||
\(518\) | 44.2213 | 1.94297 | ||||||||
\(519\) | 2.70725 | 0.118835 | ||||||||
\(520\) | −2.55810 | −0.112180 | ||||||||
\(521\) | 18.3704 | 0.804823 | 0.402412 | − | 0.915459i | \(-0.368172\pi\) | ||||
0.402412 | + | 0.915459i | \(0.368172\pi\) | |||||||
\(522\) | −7.03296 | −0.307824 | ||||||||
\(523\) | 3.11620 | 0.136262 | 0.0681309 | − | 0.997676i | \(-0.478296\pi\) | ||||
0.0681309 | + | 0.997676i | \(0.478296\pi\) | |||||||
\(524\) | −15.7017 | −0.685932 | ||||||||
\(525\) | 13.3344 | 0.581960 | ||||||||
\(526\) | −16.0416 | −0.699448 | ||||||||
\(527\) | −72.0863 | −3.14013 | ||||||||
\(528\) | −2.70725 | −0.117818 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −3.11620 | −0.135359 | ||||||||
\(531\) | −40.3816 | −1.75241 | ||||||||
\(532\) | −15.0087 | −0.650708 | ||||||||
\(533\) | −2.36732 | −0.102540 | ||||||||
\(534\) | 26.6687 | 1.15407 | ||||||||
\(535\) | 6.00000 | 0.259403 | ||||||||
\(536\) | 7.85085 | 0.339105 | ||||||||
\(537\) | 8.43634 | 0.364055 | ||||||||
\(538\) | −23.5525 | −1.01542 | ||||||||
\(539\) | 12.7489 | 0.549133 | ||||||||
\(540\) | 7.48352 | 0.322040 | ||||||||
\(541\) | 24.9670 | 1.07342 | 0.536709 | − | 0.843768i | \(-0.319667\pi\) | ||||
0.536709 | + | 0.843768i | \(0.319667\pi\) | |||||||
\(542\) | −8.99444 | −0.386344 | ||||||||
\(543\) | 17.0361 | 0.731087 | ||||||||
\(544\) | −6.92542 | −0.296925 | ||||||||
\(545\) | 15.2927 | 0.655069 | ||||||||
\(546\) | 34.1106 | 1.45980 | ||||||||
\(547\) | −4.47486 | −0.191331 | −0.0956655 | − | 0.995414i | \(-0.530498\pi\) | ||||
−0.0956655 | + | 0.995414i | \(0.530498\pi\) | |||||||
\(548\) | −2.02739 | −0.0866060 | ||||||||
\(549\) | 66.0995 | 2.82106 | ||||||||
\(550\) | 0.925423 | 0.0394602 | ||||||||
\(551\) | −4.16649 | −0.177498 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −49.9889 | −2.12574 | ||||||||
\(554\) | 11.1710 | 0.474610 | ||||||||
\(555\) | −28.3816 | −1.20473 | ||||||||
\(556\) | 6.14915 | 0.260782 | ||||||||
\(557\) | −34.8727 | −1.47760 | −0.738801 | − | 0.673923i | \(-0.764608\pi\) | ||||
−0.738801 | + | 0.673923i | \(0.764608\pi\) | |||||||
\(558\) | 57.8539 | 2.44915 | ||||||||
\(559\) | 3.23690 | 0.136906 | ||||||||
\(560\) | 4.55810 | 0.192615 | ||||||||
\(561\) | 18.7489 | 0.791578 | ||||||||
\(562\) | −26.6687 | −1.12495 | ||||||||
\(563\) | 41.1051 | 1.73237 | 0.866186 | − | 0.499721i | \(-0.166564\pi\) | ||||
0.866186 | + | 0.499721i | \(0.166564\pi\) | |||||||
\(564\) | −32.0832 | −1.35095 | ||||||||
\(565\) | 7.26535 | 0.305656 | ||||||||
\(566\) | 1.26535 | 0.0531867 | ||||||||
\(567\) | −23.7849 | −0.998873 | ||||||||
\(568\) | −6.92542 | −0.290584 | ||||||||
\(569\) | 12.6799 | 0.531567 | 0.265784 | − | 0.964033i | \(-0.414369\pi\) | ||||
0.265784 | + | 0.964033i | \(0.414369\pi\) | |||||||
\(570\) | 9.63268 | 0.403468 | ||||||||
\(571\) | 2.09641 | 0.0877320 | 0.0438660 | − | 0.999037i | \(-0.486033\pi\) | ||||
0.0438660 | + | 0.999037i | \(0.486033\pi\) | |||||||
\(572\) | 2.36732 | 0.0989828 | ||||||||
\(573\) | 61.7738 | 2.58064 | ||||||||
\(574\) | 4.21817 | 0.176063 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.55810 | 0.231587 | ||||||||
\(577\) | −10.8179 | −0.450355 | −0.225177 | − | 0.974318i | \(-0.572296\pi\) | ||||
−0.225177 | + | 0.974318i | \(0.572296\pi\) | |||||||
\(578\) | 30.9615 | 1.28783 | ||||||||
\(579\) | −11.2654 | −0.468172 | ||||||||
\(580\) | 1.26535 | 0.0525409 | ||||||||
\(581\) | 2.66874 | 0.110718 | ||||||||
\(582\) | −9.43078 | −0.390918 | ||||||||
\(583\) | 2.88380 | 0.119435 | ||||||||
\(584\) | −9.26535 | −0.383403 | ||||||||
\(585\) | −14.2182 | −0.587849 | ||||||||
\(586\) | 25.4034 | 1.04940 | ||||||||
\(587\) | 23.3070 | 0.961982 | 0.480991 | − | 0.876726i | \(-0.340277\pi\) | ||||
0.480991 | + | 0.876726i | \(0.340277\pi\) | |||||||
\(588\) | −40.3014 | −1.66200 | ||||||||
\(589\) | 34.2740 | 1.41224 | ||||||||
\(590\) | 7.26535 | 0.299110 | ||||||||
\(591\) | 43.2268 | 1.77811 | ||||||||
\(592\) | −9.70169 | −0.398737 | ||||||||
\(593\) | 20.5307 | 0.843095 | 0.421548 | − | 0.906806i | \(-0.361487\pi\) | ||||
0.421548 | + | 0.906806i | \(0.361487\pi\) | |||||||
\(594\) | −6.92542 | −0.284154 | ||||||||
\(595\) | −31.5668 | −1.29411 | ||||||||
\(596\) | −8.70725 | −0.356663 | ||||||||
\(597\) | 45.9341 | 1.87996 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.37289 | −0.0560946 | −0.0280473 | − | 0.999607i | \(-0.508929\pi\) | ||||
−0.0280473 | + | 0.999607i | \(0.508929\pi\) | |||||||
\(600\) | −2.92542 | −0.119430 | ||||||||
\(601\) | −23.6743 | −0.965695 | −0.482847 | − | 0.875705i | \(-0.660397\pi\) | ||||
−0.482847 | + | 0.875705i | \(0.660397\pi\) | |||||||
\(602\) | −5.76760 | −0.235070 | ||||||||
\(603\) | 43.6358 | 1.77699 | ||||||||
\(604\) | 13.0746 | 0.531997 | ||||||||
\(605\) | 10.1436 | 0.412396 | ||||||||
\(606\) | −28.3816 | −1.15292 | ||||||||
\(607\) | −21.4145 | −0.869188 | −0.434594 | − | 0.900626i | \(-0.643108\pi\) | ||||
−0.434594 | + | 0.900626i | \(0.643108\pi\) | |||||||
\(608\) | 3.29275 | 0.133539 | ||||||||
\(609\) | −16.8727 | −0.683715 | ||||||||
\(610\) | −11.8925 | −0.481512 | ||||||||
\(611\) | 28.0548 | 1.13498 | ||||||||
\(612\) | −38.4922 | −1.55595 | ||||||||
\(613\) | 1.26535 | 0.0511071 | 0.0255536 | − | 0.999673i | \(-0.491865\pi\) | ||||
0.0255536 | + | 0.999673i | \(0.491865\pi\) | |||||||
\(614\) | −20.4780 | −0.826423 | ||||||||
\(615\) | −2.70725 | −0.109167 | ||||||||
\(616\) | −4.21817 | −0.169955 | ||||||||
\(617\) | −9.45613 | −0.380689 | −0.190345 | − | 0.981717i | \(-0.560961\pi\) | ||||
−0.190345 | + | 0.981717i | \(0.560961\pi\) | |||||||
\(618\) | −57.7575 | −2.32335 | ||||||||
\(619\) | 17.0056 | 0.683511 | 0.341756 | − | 0.939789i | \(-0.388978\pi\) | ||||
0.341756 | + | 0.939789i | \(0.388978\pi\) | |||||||
\(620\) | −10.4089 | −0.418033 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 41.5525 | 1.66477 | ||||||||
\(624\) | −7.48352 | −0.299581 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.02739 | 0.0810310 | ||||||||
\(627\) | −8.91430 | −0.356003 | ||||||||
\(628\) | 4.14915 | 0.165569 | ||||||||
\(629\) | 67.1883 | 2.67897 | ||||||||
\(630\) | 25.3344 | 1.00935 | ||||||||
\(631\) | −4.38155 | −0.174427 | −0.0872134 | − | 0.996190i | \(-0.527796\pi\) | ||||
−0.0872134 | + | 0.996190i | \(0.527796\pi\) | |||||||
\(632\) | 10.9670 | 0.436246 | ||||||||
\(633\) | 25.7961 | 1.02530 | ||||||||
\(634\) | 2.25979 | 0.0897478 | ||||||||
\(635\) | 18.2872 | 0.725705 | ||||||||
\(636\) | −9.11620 | −0.361481 | ||||||||
\(637\) | 35.2411 | 1.39630 | ||||||||
\(638\) | −1.17099 | −0.0463598 | ||||||||
\(639\) | −38.4922 | −1.52273 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 34.6139 | 1.36717 | 0.683584 | − | 0.729871i | \(-0.260420\pi\) | ||||
0.683584 | + | 0.729871i | \(0.260420\pi\) | |||||||
\(642\) | 17.5525 | 0.692743 | ||||||||
\(643\) | 32.3156 | 1.27440 | 0.637202 | − | 0.770697i | \(-0.280092\pi\) | ||||
0.637202 | + | 0.770697i | \(0.280092\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.70169 | 0.145754 | ||||||||
\(646\) | −22.8037 | −0.897198 | ||||||||
\(647\) | −26.3156 | −1.03457 | −0.517287 | − | 0.855812i | \(-0.673058\pi\) | ||||
−0.517287 | + | 0.855812i | \(0.673058\pi\) | |||||||
\(648\) | 5.21817 | 0.204989 | ||||||||
\(649\) | −6.72352 | −0.263921 | ||||||||
\(650\) | 2.55810 | 0.100337 | ||||||||
\(651\) | 138.797 | 5.43987 | ||||||||
\(652\) | −7.82345 | −0.306390 | ||||||||
\(653\) | 20.0274 | 0.783732 | 0.391866 | − | 0.920022i | \(-0.371830\pi\) | ||||
0.391866 | + | 0.920022i | \(0.371830\pi\) | |||||||
\(654\) | 44.7378 | 1.74938 | ||||||||
\(655\) | 15.7017 | 0.613516 | ||||||||
\(656\) | −0.925423 | −0.0361317 | ||||||||
\(657\) | −51.4977 | −2.00912 | ||||||||
\(658\) | −49.9889 | −1.94877 | ||||||||
\(659\) | −22.0285 | −0.858107 | −0.429053 | − | 0.903279i | \(-0.641153\pi\) | ||||
−0.429053 | + | 0.903279i | \(0.641153\pi\) | |||||||
\(660\) | 2.70725 | 0.105380 | ||||||||
\(661\) | 3.12936 | 0.121718 | 0.0608591 | − | 0.998146i | \(-0.480616\pi\) | ||||
0.0608591 | + | 0.998146i | \(0.480616\pi\) | |||||||
\(662\) | −5.11620 | −0.198847 | ||||||||
\(663\) | 51.8266 | 2.01278 | ||||||||
\(664\) | −0.585493 | −0.0227215 | ||||||||
\(665\) | 15.0087 | 0.582011 | ||||||||
\(666\) | −53.9230 | −2.08947 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −6.58549 | −0.254800 | ||||||||
\(669\) | −36.2213 | −1.40040 | ||||||||
\(670\) | −7.85085 | −0.303305 | ||||||||
\(671\) | 11.0056 | 0.424865 | ||||||||
\(672\) | 13.3344 | 0.514384 | ||||||||
\(673\) | −41.4866 | −1.59919 | −0.799596 | − | 0.600538i | \(-0.794953\pi\) | ||||
−0.799596 | + | 0.600538i | \(0.794953\pi\) | |||||||
\(674\) | −0.856408 | −0.0329876 | ||||||||
\(675\) | −7.48352 | −0.288041 | ||||||||
\(676\) | −6.45613 | −0.248313 | ||||||||
\(677\) | 38.9011 | 1.49509 | 0.747546 | − | 0.664210i | \(-0.231232\pi\) | ||||
0.747546 | + | 0.664210i | \(0.231232\pi\) | |||||||
\(678\) | 21.2542 | 0.816264 | ||||||||
\(679\) | −14.6941 | −0.563907 | ||||||||
\(680\) | 6.92542 | 0.265578 | ||||||||
\(681\) | 19.9452 | 0.764302 | ||||||||
\(682\) | 9.63268 | 0.368854 | ||||||||
\(683\) | 27.8782 | 1.06673 | 0.533366 | − | 0.845885i | \(-0.320927\pi\) | ||||
0.533366 | + | 0.845885i | \(0.320927\pi\) | |||||||
\(684\) | 18.3014 | 0.699772 | ||||||||
\(685\) | 2.02739 | 0.0774627 | ||||||||
\(686\) | −30.8869 | −1.17927 | ||||||||
\(687\) | 63.4866 | 2.42217 | ||||||||
\(688\) | 1.26535 | 0.0482411 | ||||||||
\(689\) | 7.97155 | 0.303692 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7520 | −1.16986 | −0.584930 | − | 0.811084i | \(-0.698878\pi\) | ||||
−0.584930 | + | 0.811084i | \(0.698878\pi\) | |||||||
\(692\) | −0.925423 | −0.0351793 | ||||||||
\(693\) | −23.4450 | −0.890602 | ||||||||
\(694\) | 27.0087 | 1.02523 | ||||||||
\(695\) | −6.14915 | −0.233251 | ||||||||
\(696\) | 3.70169 | 0.140312 | ||||||||
\(697\) | 6.40895 | 0.242756 | ||||||||
\(698\) | −21.6469 | −0.819347 | ||||||||
\(699\) | −22.9670 | −0.868693 | ||||||||
\(700\) | −4.55810 | −0.172280 | ||||||||
\(701\) | −6.17655 | −0.233285 | −0.116643 | − | 0.993174i | \(-0.537213\pi\) | ||||
−0.116643 | + | 0.993174i | \(0.537213\pi\) | |||||||
\(702\) | −19.1436 | −0.722528 | ||||||||
\(703\) | −31.9452 | −1.20484 | ||||||||
\(704\) | 0.925423 | 0.0348782 | ||||||||
\(705\) | 32.0832 | 1.20832 | ||||||||
\(706\) | −21.3486 | −0.803465 | ||||||||
\(707\) | −44.2213 | −1.66311 | ||||||||
\(708\) | 21.2542 | 0.798783 | ||||||||
\(709\) | −40.9539 | −1.53806 | −0.769028 | − | 0.639216i | \(-0.779259\pi\) | ||||
−0.769028 | + | 0.639216i | \(0.779259\pi\) | |||||||
\(710\) | 6.92542 | 0.259906 | ||||||||
\(711\) | 60.9559 | 2.28603 | ||||||||
\(712\) | −9.11620 | −0.341644 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −92.3461 | −3.45597 | ||||||||
\(715\) | −2.36732 | −0.0885329 | ||||||||
\(716\) | −2.88380 | −0.107773 | ||||||||
\(717\) | −35.1051 | −1.31102 | ||||||||
\(718\) | 14.6687 | 0.547432 | ||||||||
\(719\) | 7.22684 | 0.269515 | 0.134758 | − | 0.990879i | \(-0.456974\pi\) | ||||
0.134758 | + | 0.990879i | \(0.456974\pi\) | |||||||
\(720\) | −5.55810 | −0.207138 | ||||||||
\(721\) | −89.9920 | −3.35148 | ||||||||
\(722\) | −8.15782 | −0.303603 | ||||||||
\(723\) | −45.9341 | −1.70831 | ||||||||
\(724\) | −5.82345 | −0.216427 | ||||||||
\(725\) | −1.26535 | −0.0469940 | ||||||||
\(726\) | 29.6743 | 1.10132 | ||||||||
\(727\) | −28.7215 | −1.06522 | −0.532610 | − | 0.846361i | \(-0.678789\pi\) | ||||
−0.532610 | + | 0.846361i | \(0.678789\pi\) | |||||||
\(728\) | −11.6601 | −0.432151 | ||||||||
\(729\) | −36.6743 | −1.35831 | ||||||||
\(730\) | 9.26535 | 0.342926 | ||||||||
\(731\) | −8.76310 | −0.324115 | ||||||||
\(732\) | −34.7905 | −1.28589 | ||||||||
\(733\) | 10.5196 | 0.388550 | 0.194275 | − | 0.980947i | \(-0.437765\pi\) | ||||
0.194275 | + | 0.980947i | \(0.437765\pi\) | |||||||
\(734\) | 1.17099 | 0.0432219 | ||||||||
\(735\) | 40.3014 | 1.48654 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.26535 | 0.267623 | ||||||||
\(738\) | −5.14359 | −0.189338 | ||||||||
\(739\) | 15.6184 | 0.574534 | 0.287267 | − | 0.957851i | \(-0.407253\pi\) | ||||
0.287267 | + | 0.957851i | \(0.407253\pi\) | |||||||
\(740\) | 9.70169 | 0.356641 | ||||||||
\(741\) | −24.6413 | −0.905222 | ||||||||
\(742\) | −14.2039 | −0.521443 | ||||||||
\(743\) | −3.38711 | −0.124261 | −0.0621306 | − | 0.998068i | \(-0.519790\pi\) | ||||
−0.0621306 | + | 0.998068i | \(0.519790\pi\) | |||||||
\(744\) | −30.4506 | −1.11637 | ||||||||
\(745\) | 8.70725 | 0.319009 | ||||||||
\(746\) | 8.88380 | 0.325259 | ||||||||
\(747\) | −3.25423 | −0.119066 | ||||||||
\(748\) | −6.40895 | −0.234334 | ||||||||
\(749\) | 27.3486 | 0.999296 | ||||||||
\(750\) | 2.92542 | 0.106821 | ||||||||
\(751\) | −5.41451 | −0.197578 | −0.0987891 | − | 0.995108i | \(-0.531497\pi\) | ||||
−0.0987891 | + | 0.995108i | \(0.531497\pi\) | |||||||
\(752\) | 10.9670 | 0.399927 | ||||||||
\(753\) | 2.22929 | 0.0812400 | ||||||||
\(754\) | −3.23690 | −0.117881 | ||||||||
\(755\) | −13.0746 | −0.475833 | ||||||||
\(756\) | 34.1106 | 1.24059 | ||||||||
\(757\) | −3.11620 | −0.113260 | −0.0566301 | − | 0.998395i | \(-0.518036\pi\) | ||||
−0.0566301 | + | 0.998395i | \(0.518036\pi\) | |||||||
\(758\) | 23.0746 | 0.838106 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.29275 | −0.119440 | ||||||||
\(761\) | 5.96148 | 0.216104 | 0.108052 | − | 0.994145i | \(-0.465539\pi\) | ||||
0.108052 | + | 0.994145i | \(0.465539\pi\) | |||||||
\(762\) | 53.4977 | 1.93802 | ||||||||
\(763\) | 69.7059 | 2.52352 | ||||||||
\(764\) | −21.1162 | −0.763957 | ||||||||
\(765\) | 38.4922 | 1.39169 | ||||||||
\(766\) | 21.9341 | 0.792511 | ||||||||
\(767\) | −18.5855 | −0.671083 | ||||||||
\(768\) | −2.92542 | −0.105562 | ||||||||
\(769\) | −15.7017 | −0.566217 | −0.283109 | − | 0.959088i | \(-0.591366\pi\) | ||||
−0.283109 | + | 0.959088i | \(0.591366\pi\) | |||||||
\(770\) | 4.21817 | 0.152012 | ||||||||
\(771\) | −19.5414 | −0.703767 | ||||||||
\(772\) | 3.85085 | 0.138595 | ||||||||
\(773\) | −29.7849 | −1.07129 | −0.535645 | − | 0.844443i | \(-0.679931\pi\) | ||||
−0.535645 | + | 0.844443i | \(0.679931\pi\) | |||||||
\(774\) | 7.03296 | 0.252794 | ||||||||
\(775\) | 10.4089 | 0.373900 | ||||||||
\(776\) | 3.22373 | 0.115725 | ||||||||
\(777\) | −129.366 | −4.64098 | ||||||||
\(778\) | 1.74331 | 0.0625008 | ||||||||
\(779\) | −3.04718 | −0.109177 | ||||||||
\(780\) | 7.48352 | 0.267953 | ||||||||
\(781\) | −6.40895 | −0.229330 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.46929 | 0.338405 | ||||||||
\(784\) | 13.7763 | 0.492010 | ||||||||
\(785\) | −4.14915 | −0.148090 | ||||||||
\(786\) | 45.9341 | 1.63841 | ||||||||
\(787\) | −20.3156 | −0.724174 | −0.362087 | − | 0.932144i | \(-0.617936\pi\) | ||||
−0.362087 | + | 0.932144i | \(0.617936\pi\) | |||||||
\(788\) | −14.7763 | −0.526383 | ||||||||
\(789\) | 46.9285 | 1.67070 | ||||||||
\(790\) | −10.9670 | −0.390190 | ||||||||
\(791\) | 33.1162 | 1.17748 | ||||||||
\(792\) | 5.14359 | 0.182770 | ||||||||
\(793\) | 30.4221 | 1.08032 | ||||||||
\(794\) | −13.0087 | −0.461660 | ||||||||
\(795\) | 9.11620 | 0.323318 | ||||||||
\(796\) | −15.7017 | −0.556532 | ||||||||
\(797\) | −36.5855 | −1.29592 | −0.647962 | − | 0.761672i | \(-0.724379\pi\) | ||||
−0.647962 | + | 0.761672i | \(0.724379\pi\) | |||||||
\(798\) | 43.9067 | 1.55428 | ||||||||
\(799\) | −75.9514 | −2.68697 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −50.6687 | −1.79029 | ||||||||
\(802\) | −37.9889 | −1.34143 | ||||||||
\(803\) | −8.57437 | −0.302583 | ||||||||
\(804\) | −22.9670 | −0.809985 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.6271 | 0.937900 | ||||||||
\(807\) | 68.9011 | 2.42543 | ||||||||
\(808\) | 9.70169 | 0.341304 | ||||||||
\(809\) | −33.0087 | −1.16052 | −0.580261 | − | 0.814430i | \(-0.697050\pi\) | ||||
−0.580261 | + | 0.814430i | \(0.697050\pi\) | |||||||
\(810\) | −5.21817 | −0.183348 | ||||||||
\(811\) | 25.6073 | 0.899195 | 0.449597 | − | 0.893231i | \(-0.351567\pi\) | ||||
0.449597 | + | 0.893231i | \(0.351567\pi\) | |||||||
\(812\) | 5.76760 | 0.202403 | ||||||||
\(813\) | 26.3125 | 0.922821 | ||||||||
\(814\) | −8.97817 | −0.314685 | ||||||||
\(815\) | 7.82345 | 0.274044 | ||||||||
\(816\) | 20.2598 | 0.709235 | ||||||||
\(817\) | 4.16649 | 0.145767 | ||||||||
\(818\) | 10.2598 | 0.358725 | ||||||||
\(819\) | −64.8078 | −2.26457 | ||||||||
\(820\) | 0.925423 | 0.0323172 | ||||||||
\(821\) | −5.78493 | −0.201896 | −0.100948 | − | 0.994892i | \(-0.532188\pi\) | ||||
−0.100948 | + | 0.994892i | \(0.532188\pi\) | |||||||
\(822\) | 5.93098 | 0.206867 | ||||||||
\(823\) | −28.9011 | −1.00743 | −0.503715 | − | 0.863870i | \(-0.668034\pi\) | ||||
−0.503715 | + | 0.863870i | \(0.668034\pi\) | |||||||
\(824\) | 19.7433 | 0.687791 | ||||||||
\(825\) | −2.70725 | −0.0942545 | ||||||||
\(826\) | 33.1162 | 1.15226 | ||||||||
\(827\) | −7.98888 | −0.277800 | −0.138900 | − | 0.990306i | \(-0.544357\pi\) | ||||
−0.138900 | + | 0.990306i | \(0.544357\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.76310 | −0.234892 | −0.117446 | − | 0.993079i | \(-0.537471\pi\) | ||||
−0.117446 | + | 0.993079i | \(0.537471\pi\) | |||||||
\(830\) | 0.585493 | 0.0203228 | ||||||||
\(831\) | −32.6799 | −1.13365 | ||||||||
\(832\) | 2.55810 | 0.0886861 | ||||||||
\(833\) | −95.4065 | −3.30564 | ||||||||
\(834\) | −17.9889 | −0.622904 | ||||||||
\(835\) | 6.58549 | 0.227900 | ||||||||
\(836\) | 3.04718 | 0.105389 | ||||||||
\(837\) | −77.8956 | −2.69246 | ||||||||
\(838\) | −16.9670 | −0.586117 | ||||||||
\(839\) | −15.2106 | −0.525127 | −0.262564 | − | 0.964915i | \(-0.584568\pi\) | ||||
−0.262564 | + | 0.964915i | \(0.584568\pi\) | |||||||
\(840\) | −13.3344 | −0.460079 | ||||||||
\(841\) | −27.3989 | −0.944789 | ||||||||
\(842\) | −16.4637 | −0.567378 | ||||||||
\(843\) | 78.0173 | 2.68706 | ||||||||
\(844\) | −8.81789 | −0.303524 | ||||||||
\(845\) | 6.45613 | 0.222098 | ||||||||
\(846\) | 60.9559 | 2.09571 | ||||||||
\(847\) | 46.2355 | 1.58867 | ||||||||
\(848\) | 3.11620 | 0.107011 | ||||||||
\(849\) | −3.70169 | −0.127042 | ||||||||
\(850\) | −6.92542 | −0.237540 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 20.2598 | 0.694089 | ||||||||
\(853\) | −5.08880 | −0.174237 | −0.0871187 | − | 0.996198i | \(-0.527766\pi\) | ||||
−0.0871187 | + | 0.996198i | \(0.527766\pi\) | |||||||
\(854\) | −54.2070 | −1.85493 | ||||||||
\(855\) | −18.3014 | −0.625895 | ||||||||
\(856\) | −6.00000 | −0.205076 | ||||||||
\(857\) | 9.56366 | 0.326688 | 0.163344 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163344 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(858\) | −6.92542 | −0.236430 | ||||||||
\(859\) | 45.9889 | 1.56912 | 0.784560 | − | 0.620053i | \(-0.212889\pi\) | ||||
0.784560 | + | 0.620053i | \(0.212889\pi\) | |||||||
\(860\) | −1.26535 | −0.0431482 | ||||||||
\(861\) | −12.3399 | −0.420544 | ||||||||
\(862\) | −8.29831 | −0.282642 | ||||||||
\(863\) | −55.4034 | −1.88595 | −0.942977 | − | 0.332859i | \(-0.891987\pi\) | ||||
−0.942977 | + | 0.332859i | \(0.891987\pi\) | |||||||
\(864\) | −7.48352 | −0.254595 | ||||||||
\(865\) | 0.925423 | 0.0314653 | ||||||||
\(866\) | −20.2598 | −0.688456 | ||||||||
\(867\) | −90.5754 | −3.07610 | ||||||||
\(868\) | −47.4450 | −1.61039 | ||||||||
\(869\) | 10.1492 | 0.344286 | ||||||||
\(870\) | −3.70169 | −0.125499 | ||||||||
\(871\) | 20.0832 | 0.680495 | ||||||||
\(872\) | −15.2927 | −0.517878 | ||||||||
\(873\) | 17.9178 | 0.606426 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.55810 | 0.154092 | ||||||||
\(876\) | 27.1051 | 0.915796 | ||||||||
\(877\) | 9.98683 | 0.337231 | 0.168616 | − | 0.985682i | \(-0.446070\pi\) | ||||
0.168616 | + | 0.985682i | \(0.446070\pi\) | |||||||
\(878\) | −25.7575 | −0.869275 | ||||||||
\(879\) | −74.3156 | −2.50660 | ||||||||
\(880\) | −0.925423 | −0.0311960 | ||||||||
\(881\) | −32.7631 | −1.10382 | −0.551908 | − | 0.833905i | \(-0.686100\pi\) | ||||
−0.551908 | + | 0.833905i | \(0.686100\pi\) | |||||||
\(882\) | 76.5699 | 2.57824 | ||||||||
\(883\) | 28.2882 | 0.951975 | 0.475988 | − | 0.879452i | \(-0.342091\pi\) | ||||
0.475988 | + | 0.879452i | \(0.342091\pi\) | |||||||
\(884\) | −17.7159 | −0.595851 | ||||||||
\(885\) | −21.2542 | −0.714453 | ||||||||
\(886\) | −22.1106 | −0.742821 | ||||||||
\(887\) | −48.1380 | −1.61632 | −0.808158 | − | 0.588965i | \(-0.799536\pi\) | ||||
−0.808158 | + | 0.588965i | \(0.799536\pi\) | |||||||
\(888\) | 28.3816 | 0.952422 | ||||||||
\(889\) | 83.3548 | 2.79563 | ||||||||
\(890\) | 9.11620 | 0.305576 | ||||||||
\(891\) | 4.82901 | 0.161778 | ||||||||
\(892\) | 12.3816 | 0.414565 | ||||||||
\(893\) | 36.1117 | 1.20843 | ||||||||
\(894\) | 25.4724 | 0.851924 | ||||||||
\(895\) | 2.88380 | 0.0963949 | ||||||||
\(896\) | −4.55810 | −0.152275 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.0777 | 0.503149 | ||||||||
\(899\) | −13.1710 | −0.439277 | ||||||||
\(900\) | 5.55810 | 0.185270 | ||||||||
\(901\) | −21.5810 | −0.718967 | ||||||||
\(902\) | −0.856408 | −0.0285153 | ||||||||
\(903\) | 16.8727 | 0.561488 | ||||||||
\(904\) | −7.26535 | −0.241642 | ||||||||
\(905\) | 5.82345 | 0.193578 | ||||||||
\(906\) | −38.2487 | −1.27073 | ||||||||
\(907\) | 0.938589 | 0.0311653 | 0.0155827 | − | 0.999879i | \(-0.495040\pi\) | ||||
0.0155827 | + | 0.999879i | \(0.495040\pi\) | |||||||
\(908\) | −6.81789 | −0.226260 | ||||||||
\(909\) | 53.9230 | 1.78851 | ||||||||
\(910\) | 11.6601 | 0.386528 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | −9.63268 | −0.318970 | ||||||||
\(913\) | −0.541829 | −0.0179319 | ||||||||
\(914\) | −22.9670 | −0.759682 | ||||||||
\(915\) | 34.7905 | 1.15014 | ||||||||
\(916\) | −21.7017 | −0.717044 | ||||||||
\(917\) | 71.5699 | 2.36345 | ||||||||
\(918\) | 51.8266 | 1.71053 | ||||||||
\(919\) | −18.7235 | −0.617632 | −0.308816 | − | 0.951122i | \(-0.599933\pi\) | ||||
−0.308816 | + | 0.951122i | \(0.599933\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 59.9067 | 1.97399 | ||||||||
\(922\) | 27.1162 | 0.893024 | ||||||||
\(923\) | −17.7159 | −0.583127 | ||||||||
\(924\) | 12.3399 | 0.405954 | ||||||||
\(925\) | −9.70169 | −0.318990 | ||||||||
\(926\) | 23.3486 | 0.767282 | ||||||||
\(927\) | 109.735 | 3.60418 | ||||||||
\(928\) | −1.26535 | −0.0415372 | ||||||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | 30.4506 | 0.998513 | ||||||||
\(931\) | 45.3618 | 1.48667 | ||||||||
\(932\) | 7.85085 | 0.257163 | ||||||||
\(933\) | −35.1051 | −1.14929 | ||||||||
\(934\) | −0.585493 | −0.0191579 | ||||||||
\(935\) | 6.40895 | 0.209595 | ||||||||
\(936\) | 14.2182 | 0.464735 | ||||||||
\(937\) | 55.9067 | 1.82639 | 0.913196 | − | 0.407521i | \(-0.133607\pi\) | ||||
0.913196 | + | 0.407521i | \(0.133607\pi\) | |||||||
\(938\) | −35.7849 | −1.16842 | ||||||||
\(939\) | −5.93098 | −0.193550 | ||||||||
\(940\) | −10.9670 | −0.357706 | ||||||||
\(941\) | −16.2740 | −0.530518 | −0.265259 | − | 0.964177i | \(-0.585457\pi\) | ||||
−0.265259 | + | 0.964177i | \(0.585457\pi\) | |||||||
\(942\) | −12.1380 | −0.395478 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −7.26535 | −0.236467 | ||||||||
\(945\) | −34.1106 | −1.10962 | ||||||||
\(946\) | 1.17099 | 0.0380721 | ||||||||
\(947\) | −1.53627 | −0.0499220 | −0.0249610 | − | 0.999688i | \(-0.507946\pi\) | ||||
−0.0249610 | + | 0.999688i | \(0.507946\pi\) | |||||||
\(948\) | −32.0832 | −1.04202 | ||||||||
\(949\) | −23.7017 | −0.769389 | ||||||||
\(950\) | 3.29275 | 0.106831 | ||||||||
\(951\) | −6.61084 | −0.214371 | ||||||||
\(952\) | 31.5668 | 1.02308 | ||||||||
\(953\) | 38.3288 | 1.24159 | 0.620796 | − | 0.783972i | \(-0.286810\pi\) | ||||
0.620796 | + | 0.783972i | \(0.286810\pi\) | |||||||
\(954\) | 17.3201 | 0.560760 | ||||||||
\(955\) | 21.1162 | 0.683304 | ||||||||
\(956\) | 12.0000 | 0.388108 | ||||||||
\(957\) | 3.42563 | 0.110735 | ||||||||
\(958\) | 36.8179 | 1.18953 | ||||||||
\(959\) | 9.24106 | 0.298409 | ||||||||
\(960\) | 2.92542 | 0.0944176 | ||||||||
\(961\) | 77.3461 | 2.49504 | ||||||||
\(962\) | −24.8179 | −0.800161 | ||||||||
\(963\) | −33.3486 | −1.07464 | ||||||||
\(964\) | 15.7017 | 0.505717 | ||||||||
\(965\) | −3.85085 | −0.123963 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.03296 | −0.290480 | −0.145240 | − | 0.989396i | \(-0.546395\pi\) | ||||
−0.145240 | + | 0.989396i | \(0.546395\pi\) | |||||||
\(968\) | −10.1436 | −0.326027 | ||||||||
\(969\) | 66.7104 | 2.14305 | ||||||||
\(970\) | −3.22373 | −0.103508 | ||||||||
\(971\) | −51.4561 | −1.65131 | −0.825653 | − | 0.564178i | \(-0.809193\pi\) | ||||
−0.825653 | + | 0.564178i | \(0.809193\pi\) | |||||||
\(972\) | 7.18521 | 0.230466 | ||||||||
\(973\) | −28.0285 | −0.898551 | ||||||||
\(974\) | −13.1162 | −0.420270 | ||||||||
\(975\) | −7.48352 | −0.239665 | ||||||||
\(976\) | 11.8925 | 0.380669 | ||||||||
\(977\) | 42.1939 | 1.34990 | 0.674951 | − | 0.737863i | \(-0.264165\pi\) | ||||
0.674951 | + | 0.737863i | \(0.264165\pi\) | |||||||
\(978\) | 22.8869 | 0.731843 | ||||||||
\(979\) | −8.43634 | −0.269627 | ||||||||
\(980\) | −13.7763 | −0.440067 | ||||||||
\(981\) | −84.9986 | −2.71380 | ||||||||
\(982\) | −21.1162 | −0.673845 | ||||||||
\(983\) | −19.9584 | −0.636573 | −0.318287 | − | 0.947994i | \(-0.603107\pi\) | ||||
−0.318287 | + | 0.947994i | \(0.603107\pi\) | |||||||
\(984\) | 2.70725 | 0.0863041 | ||||||||
\(985\) | 14.7763 | 0.470811 | ||||||||
\(986\) | 8.76310 | 0.279074 | ||||||||
\(987\) | 146.239 | 4.65483 | ||||||||
\(988\) | 8.42317 | 0.267977 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −5.14359 | −0.163474 | ||||||||
\(991\) | −40.7763 | −1.29530 | −0.647650 | − | 0.761938i | \(-0.724248\pi\) | ||||
−0.647650 | + | 0.761938i | \(0.724248\pi\) | |||||||
\(992\) | 10.4089 | 0.330484 | ||||||||
\(993\) | 14.9670 | 0.474965 | ||||||||
\(994\) | 31.5668 | 1.00124 | ||||||||
\(995\) | 15.7017 | 0.497777 | ||||||||
\(996\) | 1.71282 | 0.0542726 | ||||||||
\(997\) | 21.4034 | 0.677852 | 0.338926 | − | 0.940813i | \(-0.389936\pi\) | ||||
0.338926 | + | 0.940813i | \(0.389936\pi\) | |||||||
\(998\) | −4.43634 | −0.140430 | ||||||||
\(999\) | 72.6028 | 2.29705 |
(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 | 5290.2.a.p.1.1 | ✓ | 3 | |
23.22 | odd | 2 | 5290.2.a.q.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5290.2.a.p.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
5290.2.a.q.1.1 | yes | 3 | 23.22 | odd | 2 |