Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4026,2,Mod(1,4026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4026, 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("4026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4026.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: | \(32.1477718538\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.46101901.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 5x^{4} + 12x^{3} + 6x^{2} - 5x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.90193\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4026.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.05628 | −1.81402 | −0.907012 | − | 0.421104i | \(-0.861643\pi\) | ||||
−0.907012 | + | 0.421104i | \(0.861643\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.59539 | −0.603000 | −0.301500 | − | 0.953466i | \(-0.597487\pi\) | ||||
−0.301500 | + | 0.953466i | \(0.597487\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.05628 | −1.28271 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.49732 | 0.969982 | 0.484991 | − | 0.874519i | \(-0.338823\pi\) | ||||
0.484991 | + | 0.874519i | \(0.338823\pi\) | |||||||
\(14\) | −1.59539 | −0.426385 | ||||||||
\(15\) | 4.05628 | 1.04733 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.31489 | 1.77412 | 0.887061 | − | 0.461653i | \(-0.152744\pi\) | ||||
0.887061 | + | 0.461653i | \(0.152744\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.76811 | −0.405632 | −0.202816 | − | 0.979217i | \(-0.565009\pi\) | ||||
−0.202816 | + | 0.979217i | \(0.565009\pi\) | |||||||
\(20\) | −4.05628 | −0.907012 | ||||||||
\(21\) | 1.59539 | 0.348142 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −6.99038 | −1.45760 | −0.728798 | − | 0.684729i | \(-0.759921\pi\) | ||||
−0.728798 | + | 0.684729i | \(0.759921\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 11.4534 | 2.29069 | ||||||||
\(26\) | 3.49732 | 0.685881 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.59539 | −0.301500 | ||||||||
\(29\) | 0.0241165 | 0.00447832 | 0.00223916 | − | 0.999997i | \(-0.499287\pi\) | ||||
0.00223916 | + | 0.999997i | \(0.499287\pi\) | |||||||
\(30\) | 4.05628 | 0.740573 | ||||||||
\(31\) | 8.75593 | 1.57261 | 0.786305 | − | 0.617838i | \(-0.211991\pi\) | ||||
0.786305 | + | 0.617838i | \(0.211991\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 7.31489 | 1.25449 | ||||||||
\(35\) | 6.47134 | 1.09386 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.81967 | −0.792349 | −0.396175 | − | 0.918175i | \(-0.629663\pi\) | ||||
−0.396175 | + | 0.918175i | \(0.629663\pi\) | |||||||
\(38\) | −1.76811 | −0.286825 | ||||||||
\(39\) | −3.49732 | −0.560020 | ||||||||
\(40\) | −4.05628 | −0.641355 | ||||||||
\(41\) | −7.72352 | −1.20621 | −0.603105 | − | 0.797662i | \(-0.706070\pi\) | ||||
−0.603105 | + | 0.797662i | \(0.706070\pi\) | |||||||
\(42\) | 1.59539 | 0.246174 | ||||||||
\(43\) | 9.27497 | 1.41442 | 0.707210 | − | 0.707004i | \(-0.249954\pi\) | ||||
0.707210 | + | 0.707004i | \(0.249954\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −4.05628 | −0.604675 | ||||||||
\(46\) | −6.99038 | −1.03068 | ||||||||
\(47\) | −2.91348 | −0.424975 | −0.212487 | − | 0.977164i | \(-0.568156\pi\) | ||||
−0.212487 | + | 0.977164i | \(0.568156\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.45474 | −0.636391 | ||||||||
\(50\) | 11.4534 | 1.61976 | ||||||||
\(51\) | −7.31489 | −1.02429 | ||||||||
\(52\) | 3.49732 | 0.484991 | ||||||||
\(53\) | −6.04474 | −0.830308 | −0.415154 | − | 0.909751i | \(-0.636272\pi\) | ||||
−0.415154 | + | 0.909751i | \(0.636272\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 4.05628 | 0.546949 | ||||||||
\(56\) | −1.59539 | −0.213193 | ||||||||
\(57\) | 1.76811 | 0.234192 | ||||||||
\(58\) | 0.0241165 | 0.00316665 | ||||||||
\(59\) | −1.28905 | −0.167820 | −0.0839102 | − | 0.996473i | \(-0.526741\pi\) | ||||
−0.0839102 | + | 0.996473i | \(0.526741\pi\) | |||||||
\(60\) | 4.05628 | 0.523664 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 8.75593 | 1.11200 | ||||||||
\(63\) | −1.59539 | −0.201000 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −14.1861 | −1.75957 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 7.70883 | 0.941784 | 0.470892 | − | 0.882191i | \(-0.343932\pi\) | ||||
0.470892 | + | 0.882191i | \(0.343932\pi\) | |||||||
\(68\) | 7.31489 | 0.887061 | ||||||||
\(69\) | 6.99038 | 0.841543 | ||||||||
\(70\) | 6.47134 | 0.773473 | ||||||||
\(71\) | 5.90050 | 0.700260 | 0.350130 | − | 0.936701i | \(-0.386137\pi\) | ||||
0.350130 | + | 0.936701i | \(0.386137\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −13.4718 | −1.57676 | −0.788378 | − | 0.615191i | \(-0.789079\pi\) | ||||
−0.788378 | + | 0.615191i | \(0.789079\pi\) | |||||||
\(74\) | −4.81967 | −0.560276 | ||||||||
\(75\) | −11.4534 | −1.32253 | ||||||||
\(76\) | −1.76811 | −0.202816 | ||||||||
\(77\) | 1.59539 | 0.181811 | ||||||||
\(78\) | −3.49732 | −0.395994 | ||||||||
\(79\) | −12.4045 | −1.39562 | −0.697810 | − | 0.716283i | \(-0.745842\pi\) | ||||
−0.697810 | + | 0.716283i | \(0.745842\pi\) | |||||||
\(80\) | −4.05628 | −0.453506 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.72352 | −0.852920 | ||||||||
\(83\) | 17.4819 | 1.91889 | 0.959445 | − | 0.281896i | \(-0.0909633\pi\) | ||||
0.959445 | + | 0.281896i | \(0.0909633\pi\) | |||||||
\(84\) | 1.59539 | 0.174071 | ||||||||
\(85\) | −29.6713 | −3.21830 | ||||||||
\(86\) | 9.27497 | 1.00015 | ||||||||
\(87\) | −0.0241165 | −0.00258556 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −15.3912 | −1.63147 | −0.815734 | − | 0.578427i | \(-0.803667\pi\) | ||||
−0.815734 | + | 0.578427i | \(0.803667\pi\) | |||||||
\(90\) | −4.05628 | −0.427570 | ||||||||
\(91\) | −5.57958 | −0.584899 | ||||||||
\(92\) | −6.99038 | −0.728798 | ||||||||
\(93\) | −8.75593 | −0.907947 | ||||||||
\(94\) | −2.91348 | −0.300503 | ||||||||
\(95\) | 7.17196 | 0.735827 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −7.51149 | −0.762676 | −0.381338 | − | 0.924436i | \(-0.624537\pi\) | ||||
−0.381338 | + | 0.924436i | \(0.624537\pi\) | |||||||
\(98\) | −4.45474 | −0.449997 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 11.4534 | 1.14534 | ||||||||
\(101\) | −8.79915 | −0.875548 | −0.437774 | − | 0.899085i | \(-0.644233\pi\) | ||||
−0.437774 | + | 0.899085i | \(0.644233\pi\) | |||||||
\(102\) | −7.31489 | −0.724282 | ||||||||
\(103\) | −9.36709 | −0.922967 | −0.461483 | − | 0.887149i | \(-0.652683\pi\) | ||||
−0.461483 | + | 0.887149i | \(0.652683\pi\) | |||||||
\(104\) | 3.49732 | 0.342941 | ||||||||
\(105\) | −6.47134 | −0.631538 | ||||||||
\(106\) | −6.04474 | −0.587117 | ||||||||
\(107\) | −15.5823 | −1.50640 | −0.753200 | − | 0.657792i | \(-0.771491\pi\) | ||||
−0.753200 | + | 0.657792i | \(0.771491\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 15.1906 | 1.45499 | 0.727497 | − | 0.686110i | \(-0.240683\pi\) | ||||
0.727497 | + | 0.686110i | \(0.240683\pi\) | |||||||
\(110\) | 4.05628 | 0.386751 | ||||||||
\(111\) | 4.81967 | 0.457463 | ||||||||
\(112\) | −1.59539 | −0.150750 | ||||||||
\(113\) | −10.1615 | −0.955915 | −0.477957 | − | 0.878383i | \(-0.658623\pi\) | ||||
−0.477957 | + | 0.878383i | \(0.658623\pi\) | |||||||
\(114\) | 1.76811 | 0.165599 | ||||||||
\(115\) | 28.3550 | 2.64411 | ||||||||
\(116\) | 0.0241165 | 0.00223916 | ||||||||
\(117\) | 3.49732 | 0.323327 | ||||||||
\(118\) | −1.28905 | −0.118667 | ||||||||
\(119\) | −11.6701 | −1.06979 | ||||||||
\(120\) | 4.05628 | 0.370286 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 7.72352 | 0.696406 | ||||||||
\(124\) | 8.75593 | 0.786305 | ||||||||
\(125\) | −26.1769 | −2.34134 | ||||||||
\(126\) | −1.59539 | −0.142128 | ||||||||
\(127\) | −2.08914 | −0.185381 | −0.0926904 | − | 0.995695i | \(-0.529547\pi\) | ||||
−0.0926904 | + | 0.995695i | \(0.529547\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −9.27497 | −0.816615 | ||||||||
\(130\) | −14.1861 | −1.24421 | ||||||||
\(131\) | 18.2582 | 1.59523 | 0.797614 | − | 0.603169i | \(-0.206095\pi\) | ||||
0.797614 | + | 0.603169i | \(0.206095\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 2.82082 | 0.244596 | ||||||||
\(134\) | 7.70883 | 0.665942 | ||||||||
\(135\) | 4.05628 | 0.349109 | ||||||||
\(136\) | 7.31489 | 0.627247 | ||||||||
\(137\) | −8.18386 | −0.699194 | −0.349597 | − | 0.936900i | \(-0.613682\pi\) | ||||
−0.349597 | + | 0.936900i | \(0.613682\pi\) | |||||||
\(138\) | 6.99038 | 0.595061 | ||||||||
\(139\) | −21.3918 | −1.81443 | −0.907215 | − | 0.420668i | \(-0.861796\pi\) | ||||
−0.907215 | + | 0.420668i | \(0.861796\pi\) | |||||||
\(140\) | 6.47134 | 0.546928 | ||||||||
\(141\) | 2.91348 | 0.245359 | ||||||||
\(142\) | 5.90050 | 0.495159 | ||||||||
\(143\) | −3.49732 | −0.292461 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.0978233 | −0.00812378 | ||||||||
\(146\) | −13.4718 | −1.11493 | ||||||||
\(147\) | 4.45474 | 0.367421 | ||||||||
\(148\) | −4.81967 | −0.396175 | ||||||||
\(149\) | 15.9486 | 1.30656 | 0.653282 | − | 0.757115i | \(-0.273392\pi\) | ||||
0.653282 | + | 0.757115i | \(0.273392\pi\) | |||||||
\(150\) | −11.4534 | −0.935169 | ||||||||
\(151\) | 7.33832 | 0.597184 | 0.298592 | − | 0.954381i | \(-0.403483\pi\) | ||||
0.298592 | + | 0.954381i | \(0.403483\pi\) | |||||||
\(152\) | −1.76811 | −0.143413 | ||||||||
\(153\) | 7.31489 | 0.591374 | ||||||||
\(154\) | 1.59539 | 0.128560 | ||||||||
\(155\) | −35.5165 | −2.85276 | ||||||||
\(156\) | −3.49732 | −0.280010 | ||||||||
\(157\) | −10.6194 | −0.847518 | −0.423759 | − | 0.905775i | \(-0.639290\pi\) | ||||
−0.423759 | + | 0.905775i | \(0.639290\pi\) | |||||||
\(158\) | −12.4045 | −0.986852 | ||||||||
\(159\) | 6.04474 | 0.479379 | ||||||||
\(160\) | −4.05628 | −0.320677 | ||||||||
\(161\) | 11.1524 | 0.878930 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −3.56996 | −0.279621 | −0.139811 | − | 0.990178i | \(-0.544649\pi\) | ||||
−0.139811 | + | 0.990178i | \(0.544649\pi\) | |||||||
\(164\) | −7.72352 | −0.603105 | ||||||||
\(165\) | −4.05628 | −0.315781 | ||||||||
\(166\) | 17.4819 | 1.35686 | ||||||||
\(167\) | −7.41687 | −0.573934 | −0.286967 | − | 0.957940i | \(-0.592647\pi\) | ||||
−0.286967 | + | 0.957940i | \(0.592647\pi\) | |||||||
\(168\) | 1.59539 | 0.123087 | ||||||||
\(169\) | −0.768748 | −0.0591345 | ||||||||
\(170\) | −29.6713 | −2.27568 | ||||||||
\(171\) | −1.76811 | −0.135211 | ||||||||
\(172\) | 9.27497 | 0.707210 | ||||||||
\(173\) | −14.3532 | −1.09126 | −0.545628 | − | 0.838028i | \(-0.683709\pi\) | ||||
−0.545628 | + | 0.838028i | \(0.683709\pi\) | |||||||
\(174\) | −0.0241165 | −0.00182827 | ||||||||
\(175\) | −18.2727 | −1.38128 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 1.28905 | 0.0968911 | ||||||||
\(178\) | −15.3912 | −1.15362 | ||||||||
\(179\) | 3.34343 | 0.249899 | 0.124950 | − | 0.992163i | \(-0.460123\pi\) | ||||
0.124950 | + | 0.992163i | \(0.460123\pi\) | |||||||
\(180\) | −4.05628 | −0.302337 | ||||||||
\(181\) | −18.1342 | −1.34791 | −0.673953 | − | 0.738774i | \(-0.735405\pi\) | ||||
−0.673953 | + | 0.738774i | \(0.735405\pi\) | |||||||
\(182\) | −5.57958 | −0.413586 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | −6.99038 | −0.515338 | ||||||||
\(185\) | 19.5500 | 1.43734 | ||||||||
\(186\) | −8.75593 | −0.642016 | ||||||||
\(187\) | −7.31489 | −0.534918 | ||||||||
\(188\) | −2.91348 | −0.212487 | ||||||||
\(189\) | 1.59539 | 0.116047 | ||||||||
\(190\) | 7.17196 | 0.520309 | ||||||||
\(191\) | −15.6458 | −1.13209 | −0.566045 | − | 0.824374i | \(-0.691527\pi\) | ||||
−0.566045 | + | 0.824374i | \(0.691527\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 18.9924 | 1.36710 | 0.683551 | − | 0.729903i | \(-0.260435\pi\) | ||||
0.683551 | + | 0.729903i | \(0.260435\pi\) | |||||||
\(194\) | −7.51149 | −0.539293 | ||||||||
\(195\) | 14.1861 | 1.01589 | ||||||||
\(196\) | −4.45474 | −0.318196 | ||||||||
\(197\) | −22.8297 | −1.62655 | −0.813276 | − | 0.581878i | \(-0.802318\pi\) | ||||
−0.813276 | + | 0.581878i | \(0.802318\pi\) | |||||||
\(198\) | −1.00000 | −0.0710669 | ||||||||
\(199\) | −19.4535 | −1.37902 | −0.689510 | − | 0.724276i | \(-0.742174\pi\) | ||||
−0.689510 | + | 0.724276i | \(0.742174\pi\) | |||||||
\(200\) | 11.4534 | 0.809880 | ||||||||
\(201\) | −7.70883 | −0.543739 | ||||||||
\(202\) | −8.79915 | −0.619106 | ||||||||
\(203\) | −0.0384751 | −0.00270043 | ||||||||
\(204\) | −7.31489 | −0.512145 | ||||||||
\(205\) | 31.3288 | 2.18810 | ||||||||
\(206\) | −9.36709 | −0.652636 | ||||||||
\(207\) | −6.99038 | −0.485865 | ||||||||
\(208\) | 3.49732 | 0.242496 | ||||||||
\(209\) | 1.76811 | 0.122303 | ||||||||
\(210\) | −6.47134 | −0.446565 | ||||||||
\(211\) | 11.3970 | 0.784603 | 0.392302 | − | 0.919837i | \(-0.371679\pi\) | ||||
0.392302 | + | 0.919837i | \(0.371679\pi\) | |||||||
\(212\) | −6.04474 | −0.415154 | ||||||||
\(213\) | −5.90050 | −0.404295 | ||||||||
\(214\) | −15.5823 | −1.06519 | ||||||||
\(215\) | −37.6219 | −2.56579 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −13.9691 | −0.948284 | ||||||||
\(218\) | 15.1906 | 1.02884 | ||||||||
\(219\) | 13.4718 | 0.910340 | ||||||||
\(220\) | 4.05628 | 0.273475 | ||||||||
\(221\) | 25.5825 | 1.72087 | ||||||||
\(222\) | 4.81967 | 0.323475 | ||||||||
\(223\) | 21.5423 | 1.44258 | 0.721288 | − | 0.692635i | \(-0.243550\pi\) | ||||
0.721288 | + | 0.692635i | \(0.243550\pi\) | |||||||
\(224\) | −1.59539 | −0.106596 | ||||||||
\(225\) | 11.4534 | 0.763562 | ||||||||
\(226\) | −10.1615 | −0.675934 | ||||||||
\(227\) | 19.6763 | 1.30596 | 0.652980 | − | 0.757375i | \(-0.273518\pi\) | ||||
0.652980 | + | 0.757375i | \(0.273518\pi\) | |||||||
\(228\) | 1.76811 | 0.117096 | ||||||||
\(229\) | −6.12424 | −0.404701 | −0.202351 | − | 0.979313i | \(-0.564858\pi\) | ||||
−0.202351 | + | 0.979313i | \(0.564858\pi\) | |||||||
\(230\) | 28.3550 | 1.86967 | ||||||||
\(231\) | −1.59539 | −0.104969 | ||||||||
\(232\) | 0.0241165 | 0.00158332 | ||||||||
\(233\) | −16.9596 | −1.11106 | −0.555530 | − | 0.831497i | \(-0.687485\pi\) | ||||
−0.555530 | + | 0.831497i | \(0.687485\pi\) | |||||||
\(234\) | 3.49732 | 0.228627 | ||||||||
\(235\) | 11.8179 | 0.770915 | ||||||||
\(236\) | −1.28905 | −0.0839102 | ||||||||
\(237\) | 12.4045 | 0.805761 | ||||||||
\(238\) | −11.6701 | −0.756459 | ||||||||
\(239\) | 9.48939 | 0.613818 | 0.306909 | − | 0.951739i | \(-0.400705\pi\) | ||||
0.306909 | + | 0.951739i | \(0.400705\pi\) | |||||||
\(240\) | 4.05628 | 0.261832 | ||||||||
\(241\) | −6.07417 | −0.391272 | −0.195636 | − | 0.980677i | \(-0.562677\pi\) | ||||
−0.195636 | + | 0.980677i | \(0.562677\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.00000 | 0.0640184 | ||||||||
\(245\) | 18.0697 | 1.15443 | ||||||||
\(246\) | 7.72352 | 0.492433 | ||||||||
\(247\) | −6.18365 | −0.393456 | ||||||||
\(248\) | 8.75593 | 0.556002 | ||||||||
\(249\) | −17.4819 | −1.10787 | ||||||||
\(250\) | −26.1769 | −1.65558 | ||||||||
\(251\) | −1.76315 | −0.111289 | −0.0556447 | − | 0.998451i | \(-0.517721\pi\) | ||||
−0.0556447 | + | 0.998451i | \(0.517721\pi\) | |||||||
\(252\) | −1.59539 | −0.100500 | ||||||||
\(253\) | 6.99038 | 0.439482 | ||||||||
\(254\) | −2.08914 | −0.131084 | ||||||||
\(255\) | 29.6713 | 1.85809 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.0061 | −1.49746 | −0.748731 | − | 0.662874i | \(-0.769337\pi\) | ||||
−0.748731 | + | 0.662874i | \(0.769337\pi\) | |||||||
\(258\) | −9.27497 | −0.577434 | ||||||||
\(259\) | 7.68924 | 0.477786 | ||||||||
\(260\) | −14.1861 | −0.879786 | ||||||||
\(261\) | 0.0241165 | 0.00149277 | ||||||||
\(262\) | 18.2582 | 1.12800 | ||||||||
\(263\) | −3.36152 | −0.207280 | −0.103640 | − | 0.994615i | \(-0.533049\pi\) | ||||
−0.103640 | + | 0.994615i | \(0.533049\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | 24.5192 | 1.50620 | ||||||||
\(266\) | 2.82082 | 0.172956 | ||||||||
\(267\) | 15.3912 | 0.941928 | ||||||||
\(268\) | 7.70883 | 0.470892 | ||||||||
\(269\) | 18.7805 | 1.14507 | 0.572535 | − | 0.819881i | \(-0.305960\pi\) | ||||
0.572535 | + | 0.819881i | \(0.305960\pi\) | |||||||
\(270\) | 4.05628 | 0.246858 | ||||||||
\(271\) | 2.15131 | 0.130683 | 0.0653413 | − | 0.997863i | \(-0.479186\pi\) | ||||
0.0653413 | + | 0.997863i | \(0.479186\pi\) | |||||||
\(272\) | 7.31489 | 0.443530 | ||||||||
\(273\) | 5.57958 | 0.337692 | ||||||||
\(274\) | −8.18386 | −0.494405 | ||||||||
\(275\) | −11.4534 | −0.690668 | ||||||||
\(276\) | 6.99038 | 0.420772 | ||||||||
\(277\) | 19.4266 | 1.16723 | 0.583614 | − | 0.812031i | \(-0.301638\pi\) | ||||
0.583614 | + | 0.812031i | \(0.301638\pi\) | |||||||
\(278\) | −21.3918 | −1.28300 | ||||||||
\(279\) | 8.75593 | 0.524204 | ||||||||
\(280\) | 6.47134 | 0.386737 | ||||||||
\(281\) | −6.42452 | −0.383255 | −0.191627 | − | 0.981468i | \(-0.561376\pi\) | ||||
−0.191627 | + | 0.981468i | \(0.561376\pi\) | |||||||
\(282\) | 2.91348 | 0.173495 | ||||||||
\(283\) | −11.1655 | −0.663719 | −0.331860 | − | 0.943329i | \(-0.607676\pi\) | ||||
−0.331860 | + | 0.943329i | \(0.607676\pi\) | |||||||
\(284\) | 5.90050 | 0.350130 | ||||||||
\(285\) | −7.17196 | −0.424830 | ||||||||
\(286\) | −3.49732 | −0.206801 | ||||||||
\(287\) | 12.3220 | 0.727345 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 36.5076 | 2.14751 | ||||||||
\(290\) | −0.0978233 | −0.00574438 | ||||||||
\(291\) | 7.51149 | 0.440331 | ||||||||
\(292\) | −13.4718 | −0.788378 | ||||||||
\(293\) | −13.7647 | −0.804140 | −0.402070 | − | 0.915609i | \(-0.631709\pi\) | ||||
−0.402070 | + | 0.915609i | \(0.631709\pi\) | |||||||
\(294\) | 4.45474 | 0.259806 | ||||||||
\(295\) | 5.22876 | 0.304430 | ||||||||
\(296\) | −4.81967 | −0.280138 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 15.9486 | 0.923880 | ||||||||
\(299\) | −24.4476 | −1.41384 | ||||||||
\(300\) | −11.4534 | −0.661264 | ||||||||
\(301\) | −14.7972 | −0.852894 | ||||||||
\(302\) | 7.33832 | 0.422273 | ||||||||
\(303\) | 8.79915 | 0.505498 | ||||||||
\(304\) | −1.76811 | −0.101408 | ||||||||
\(305\) | −4.05628 | −0.232262 | ||||||||
\(306\) | 7.31489 | 0.418164 | ||||||||
\(307\) | 20.1444 | 1.14970 | 0.574851 | − | 0.818258i | \(-0.305060\pi\) | ||||
0.574851 | + | 0.818258i | \(0.305060\pi\) | |||||||
\(308\) | 1.59539 | 0.0909056 | ||||||||
\(309\) | 9.36709 | 0.532875 | ||||||||
\(310\) | −35.5165 | −2.01720 | ||||||||
\(311\) | −7.95965 | −0.451350 | −0.225675 | − | 0.974203i | \(-0.572459\pi\) | ||||
−0.225675 | + | 0.974203i | \(0.572459\pi\) | |||||||
\(312\) | −3.49732 | −0.197997 | ||||||||
\(313\) | 19.6501 | 1.11069 | 0.555345 | − | 0.831620i | \(-0.312586\pi\) | ||||
0.555345 | + | 0.831620i | \(0.312586\pi\) | |||||||
\(314\) | −10.6194 | −0.599286 | ||||||||
\(315\) | 6.47134 | 0.364619 | ||||||||
\(316\) | −12.4045 | −0.697810 | ||||||||
\(317\) | −10.4525 | −0.587072 | −0.293536 | − | 0.955948i | \(-0.594832\pi\) | ||||
−0.293536 | + | 0.955948i | \(0.594832\pi\) | |||||||
\(318\) | 6.04474 | 0.338972 | ||||||||
\(319\) | −0.0241165 | −0.00135026 | ||||||||
\(320\) | −4.05628 | −0.226753 | ||||||||
\(321\) | 15.5823 | 0.869720 | ||||||||
\(322\) | 11.1524 | 0.621497 | ||||||||
\(323\) | −12.9335 | −0.719641 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 40.0563 | 2.22193 | ||||||||
\(326\) | −3.56996 | −0.197722 | ||||||||
\(327\) | −15.1906 | −0.840042 | ||||||||
\(328\) | −7.72352 | −0.426460 | ||||||||
\(329\) | 4.64813 | 0.256260 | ||||||||
\(330\) | −4.05628 | −0.223291 | ||||||||
\(331\) | 16.3350 | 0.897855 | 0.448927 | − | 0.893568i | \(-0.351806\pi\) | ||||
0.448927 | + | 0.893568i | \(0.351806\pi\) | |||||||
\(332\) | 17.4819 | 0.959445 | ||||||||
\(333\) | −4.81967 | −0.264116 | ||||||||
\(334\) | −7.41687 | −0.405833 | ||||||||
\(335\) | −31.2692 | −1.70842 | ||||||||
\(336\) | 1.59539 | 0.0870355 | ||||||||
\(337\) | 16.2029 | 0.882627 | 0.441314 | − | 0.897353i | \(-0.354513\pi\) | ||||
0.441314 | + | 0.897353i | \(0.354513\pi\) | |||||||
\(338\) | −0.768748 | −0.0418144 | ||||||||
\(339\) | 10.1615 | 0.551898 | ||||||||
\(340\) | −29.6713 | −1.60915 | ||||||||
\(341\) | −8.75593 | −0.474160 | ||||||||
\(342\) | −1.76811 | −0.0956085 | ||||||||
\(343\) | 18.2747 | 0.986744 | ||||||||
\(344\) | 9.27497 | 0.500073 | ||||||||
\(345\) | −28.3550 | −1.52658 | ||||||||
\(346\) | −14.3532 | −0.771634 | ||||||||
\(347\) | 34.3941 | 1.84637 | 0.923186 | − | 0.384353i | \(-0.125575\pi\) | ||||
0.923186 | + | 0.384353i | \(0.125575\pi\) | |||||||
\(348\) | −0.0241165 | −0.00129278 | ||||||||
\(349\) | 5.63869 | 0.301832 | 0.150916 | − | 0.988547i | \(-0.451778\pi\) | ||||
0.150916 | + | 0.988547i | \(0.451778\pi\) | |||||||
\(350\) | −18.2727 | −0.976715 | ||||||||
\(351\) | −3.49732 | −0.186673 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −1.44339 | −0.0768241 | −0.0384121 | − | 0.999262i | \(-0.512230\pi\) | ||||
−0.0384121 | + | 0.999262i | \(0.512230\pi\) | |||||||
\(354\) | 1.28905 | 0.0685124 | ||||||||
\(355\) | −23.9341 | −1.27029 | ||||||||
\(356\) | −15.3912 | −0.815734 | ||||||||
\(357\) | 11.6701 | 0.617646 | ||||||||
\(358\) | 3.34343 | 0.176706 | ||||||||
\(359\) | −17.9121 | −0.945366 | −0.472683 | − | 0.881233i | \(-0.656714\pi\) | ||||
−0.472683 | + | 0.881233i | \(0.656714\pi\) | |||||||
\(360\) | −4.05628 | −0.213785 | ||||||||
\(361\) | −15.8738 | −0.835462 | ||||||||
\(362\) | −18.1342 | −0.953114 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −5.57958 | −0.292450 | ||||||||
\(365\) | 54.6455 | 2.86027 | ||||||||
\(366\) | −1.00000 | −0.0522708 | ||||||||
\(367\) | −2.10345 | −0.109799 | −0.0548997 | − | 0.998492i | \(-0.517484\pi\) | ||||
−0.0548997 | + | 0.998492i | \(0.517484\pi\) | |||||||
\(368\) | −6.99038 | −0.364399 | ||||||||
\(369\) | −7.72352 | −0.402070 | ||||||||
\(370\) | 19.5500 | 1.01635 | ||||||||
\(371\) | 9.64370 | 0.500676 | ||||||||
\(372\) | −8.75593 | −0.453974 | ||||||||
\(373\) | 35.0349 | 1.81404 | 0.907018 | − | 0.421092i | \(-0.138353\pi\) | ||||
0.907018 | + | 0.421092i | \(0.138353\pi\) | |||||||
\(374\) | −7.31489 | −0.378244 | ||||||||
\(375\) | 26.1769 | 1.35177 | ||||||||
\(376\) | −2.91348 | −0.150251 | ||||||||
\(377\) | 0.0843431 | 0.00434389 | ||||||||
\(378\) | 1.59539 | 0.0820579 | ||||||||
\(379\) | −19.6090 | −1.00725 | −0.503624 | − | 0.863923i | \(-0.668000\pi\) | ||||
−0.503624 | + | 0.863923i | \(0.668000\pi\) | |||||||
\(380\) | 7.17196 | 0.367914 | ||||||||
\(381\) | 2.08914 | 0.107030 | ||||||||
\(382\) | −15.6458 | −0.800508 | ||||||||
\(383\) | −24.4725 | −1.25049 | −0.625244 | − | 0.780430i | \(-0.715000\pi\) | ||||
−0.625244 | + | 0.780430i | \(0.715000\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −6.47134 | −0.329810 | ||||||||
\(386\) | 18.9924 | 0.966687 | ||||||||
\(387\) | 9.27497 | 0.471473 | ||||||||
\(388\) | −7.51149 | −0.381338 | ||||||||
\(389\) | −35.5397 | −1.80193 | −0.900967 | − | 0.433887i | \(-0.857142\pi\) | ||||
−0.900967 | + | 0.433887i | \(0.857142\pi\) | |||||||
\(390\) | 14.1861 | 0.718342 | ||||||||
\(391\) | −51.1339 | −2.58595 | ||||||||
\(392\) | −4.45474 | −0.224998 | ||||||||
\(393\) | −18.2582 | −0.921005 | ||||||||
\(394\) | −22.8297 | −1.15015 | ||||||||
\(395\) | 50.3163 | 2.53169 | ||||||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | −28.1055 | −1.41058 | −0.705288 | − | 0.708920i | \(-0.749182\pi\) | ||||
−0.705288 | + | 0.708920i | \(0.749182\pi\) | |||||||
\(398\) | −19.4535 | −0.975115 | ||||||||
\(399\) | −2.82082 | −0.141218 | ||||||||
\(400\) | 11.4534 | 0.572672 | ||||||||
\(401\) | 1.97149 | 0.0984517 | 0.0492258 | − | 0.998788i | \(-0.484325\pi\) | ||||
0.0492258 | + | 0.998788i | \(0.484325\pi\) | |||||||
\(402\) | −7.70883 | −0.384482 | ||||||||
\(403\) | 30.6223 | 1.52540 | ||||||||
\(404\) | −8.79915 | −0.437774 | ||||||||
\(405\) | −4.05628 | −0.201558 | ||||||||
\(406\) | −0.0384751 | −0.00190949 | ||||||||
\(407\) | 4.81967 | 0.238902 | ||||||||
\(408\) | −7.31489 | −0.362141 | ||||||||
\(409\) | 17.5750 | 0.869027 | 0.434513 | − | 0.900665i | \(-0.356920\pi\) | ||||
0.434513 | + | 0.900665i | \(0.356920\pi\) | |||||||
\(410\) | 31.3288 | 1.54722 | ||||||||
\(411\) | 8.18386 | 0.403680 | ||||||||
\(412\) | −9.36709 | −0.461483 | ||||||||
\(413\) | 2.05654 | 0.101196 | ||||||||
\(414\) | −6.99038 | −0.343559 | ||||||||
\(415\) | −70.9116 | −3.48091 | ||||||||
\(416\) | 3.49732 | 0.171470 | ||||||||
\(417\) | 21.3918 | 1.04756 | ||||||||
\(418\) | 1.76811 | 0.0864811 | ||||||||
\(419\) | 20.9628 | 1.02410 | 0.512051 | − | 0.858955i | \(-0.328886\pi\) | ||||
0.512051 | + | 0.858955i | \(0.328886\pi\) | |||||||
\(420\) | −6.47134 | −0.315769 | ||||||||
\(421\) | 2.69583 | 0.131387 | 0.0656934 | − | 0.997840i | \(-0.479074\pi\) | ||||
0.0656934 | + | 0.997840i | \(0.479074\pi\) | |||||||
\(422\) | 11.3970 | 0.554798 | ||||||||
\(423\) | −2.91348 | −0.141658 | ||||||||
\(424\) | −6.04474 | −0.293558 | ||||||||
\(425\) | 83.7806 | 4.06396 | ||||||||
\(426\) | −5.90050 | −0.285880 | ||||||||
\(427\) | −1.59539 | −0.0772062 | ||||||||
\(428\) | −15.5823 | −0.753200 | ||||||||
\(429\) | 3.49732 | 0.168852 | ||||||||
\(430\) | −37.6219 | −1.81429 | ||||||||
\(431\) | −26.5387 | −1.27832 | −0.639162 | − | 0.769072i | \(-0.720719\pi\) | ||||
−0.639162 | + | 0.769072i | \(0.720719\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −1.34440 | −0.0646076 | −0.0323038 | − | 0.999478i | \(-0.510284\pi\) | ||||
−0.0323038 | + | 0.999478i | \(0.510284\pi\) | |||||||
\(434\) | −13.9691 | −0.670538 | ||||||||
\(435\) | 0.0978233 | 0.00469027 | ||||||||
\(436\) | 15.1906 | 0.727497 | ||||||||
\(437\) | 12.3598 | 0.591248 | ||||||||
\(438\) | 13.4718 | 0.643708 | ||||||||
\(439\) | −30.0973 | −1.43646 | −0.718232 | − | 0.695804i | \(-0.755048\pi\) | ||||
−0.718232 | + | 0.695804i | \(0.755048\pi\) | |||||||
\(440\) | 4.05628 | 0.193376 | ||||||||
\(441\) | −4.45474 | −0.212130 | ||||||||
\(442\) | 25.5825 | 1.21684 | ||||||||
\(443\) | 15.3679 | 0.730149 | 0.365074 | − | 0.930978i | \(-0.381044\pi\) | ||||
0.365074 | + | 0.930978i | \(0.381044\pi\) | |||||||
\(444\) | 4.81967 | 0.228732 | ||||||||
\(445\) | 62.4312 | 2.95952 | ||||||||
\(446\) | 21.5423 | 1.02006 | ||||||||
\(447\) | −15.9486 | −0.754345 | ||||||||
\(448\) | −1.59539 | −0.0753750 | ||||||||
\(449\) | 10.2979 | 0.485988 | 0.242994 | − | 0.970028i | \(-0.421870\pi\) | ||||
0.242994 | + | 0.970028i | \(0.421870\pi\) | |||||||
\(450\) | 11.4534 | 0.539920 | ||||||||
\(451\) | 7.72352 | 0.363686 | ||||||||
\(452\) | −10.1615 | −0.477957 | ||||||||
\(453\) | −7.33832 | −0.344784 | ||||||||
\(454\) | 19.6763 | 0.923454 | ||||||||
\(455\) | 22.6324 | 1.06102 | ||||||||
\(456\) | 1.76811 | 0.0827994 | ||||||||
\(457\) | −21.1684 | −0.990217 | −0.495109 | − | 0.868831i | \(-0.664872\pi\) | ||||
−0.495109 | + | 0.868831i | \(0.664872\pi\) | |||||||
\(458\) | −6.12424 | −0.286167 | ||||||||
\(459\) | −7.31489 | −0.341430 | ||||||||
\(460\) | 28.3550 | 1.32206 | ||||||||
\(461\) | −24.9393 | −1.16154 | −0.580770 | − | 0.814067i | \(-0.697249\pi\) | ||||
−0.580770 | + | 0.814067i | \(0.697249\pi\) | |||||||
\(462\) | −1.59539 | −0.0742241 | ||||||||
\(463\) | −15.8084 | −0.734677 | −0.367339 | − | 0.930087i | \(-0.619731\pi\) | ||||
−0.367339 | + | 0.930087i | \(0.619731\pi\) | |||||||
\(464\) | 0.0241165 | 0.00111958 | ||||||||
\(465\) | 35.5165 | 1.64704 | ||||||||
\(466\) | −16.9596 | −0.785638 | ||||||||
\(467\) | −25.4798 | −1.17907 | −0.589533 | − | 0.807744i | \(-0.700688\pi\) | ||||
−0.589533 | + | 0.807744i | \(0.700688\pi\) | |||||||
\(468\) | 3.49732 | 0.161664 | ||||||||
\(469\) | −12.2986 | −0.567896 | ||||||||
\(470\) | 11.8179 | 0.545119 | ||||||||
\(471\) | 10.6194 | 0.489315 | ||||||||
\(472\) | −1.28905 | −0.0593335 | ||||||||
\(473\) | −9.27497 | −0.426463 | ||||||||
\(474\) | 12.4045 | 0.569759 | ||||||||
\(475\) | −20.2509 | −0.929177 | ||||||||
\(476\) | −11.6701 | −0.534897 | ||||||||
\(477\) | −6.04474 | −0.276769 | ||||||||
\(478\) | 9.48939 | 0.434035 | ||||||||
\(479\) | −5.99410 | −0.273878 | −0.136939 | − | 0.990580i | \(-0.543726\pi\) | ||||
−0.136939 | + | 0.990580i | \(0.543726\pi\) | |||||||
\(480\) | 4.05628 | 0.185143 | ||||||||
\(481\) | −16.8559 | −0.768565 | ||||||||
\(482\) | −6.07417 | −0.276671 | ||||||||
\(483\) | −11.1524 | −0.507450 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 30.4687 | 1.38351 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −18.9550 | −0.858934 | −0.429467 | − | 0.903082i | \(-0.641299\pi\) | ||||
−0.429467 | + | 0.903082i | \(0.641299\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | 3.56996 | 0.161439 | ||||||||
\(490\) | 18.0697 | 0.816305 | ||||||||
\(491\) | 37.8774 | 1.70938 | 0.854692 | − | 0.519135i | \(-0.173746\pi\) | ||||
0.854692 | + | 0.519135i | \(0.173746\pi\) | |||||||
\(492\) | 7.72352 | 0.348203 | ||||||||
\(493\) | 0.176409 | 0.00794508 | ||||||||
\(494\) | −6.18365 | −0.278216 | ||||||||
\(495\) | 4.05628 | 0.182316 | ||||||||
\(496\) | 8.75593 | 0.393153 | ||||||||
\(497\) | −9.41358 | −0.422257 | ||||||||
\(498\) | −17.4819 | −0.783384 | ||||||||
\(499\) | 29.3414 | 1.31350 | 0.656751 | − | 0.754108i | \(-0.271930\pi\) | ||||
0.656751 | + | 0.754108i | \(0.271930\pi\) | |||||||
\(500\) | −26.1769 | −1.17067 | ||||||||
\(501\) | 7.41687 | 0.331361 | ||||||||
\(502\) | −1.76315 | −0.0786934 | ||||||||
\(503\) | 11.6830 | 0.520921 | 0.260460 | − | 0.965485i | \(-0.416126\pi\) | ||||
0.260460 | + | 0.965485i | \(0.416126\pi\) | |||||||
\(504\) | −1.59539 | −0.0710642 | ||||||||
\(505\) | 35.6918 | 1.58827 | ||||||||
\(506\) | 6.99038 | 0.310760 | ||||||||
\(507\) | 0.768748 | 0.0341413 | ||||||||
\(508\) | −2.08914 | −0.0926904 | ||||||||
\(509\) | −30.6045 | −1.35652 | −0.678261 | − | 0.734822i | \(-0.737266\pi\) | ||||
−0.678261 | + | 0.734822i | \(0.737266\pi\) | |||||||
\(510\) | 29.6713 | 1.31387 | ||||||||
\(511\) | 21.4927 | 0.950783 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.76811 | 0.0780640 | ||||||||
\(514\) | −24.0061 | −1.05887 | ||||||||
\(515\) | 37.9956 | 1.67428 | ||||||||
\(516\) | −9.27497 | −0.408308 | ||||||||
\(517\) | 2.91348 | 0.128135 | ||||||||
\(518\) | 7.68924 | 0.337846 | ||||||||
\(519\) | 14.3532 | 0.630037 | ||||||||
\(520\) | −14.1861 | −0.622103 | ||||||||
\(521\) | −2.24959 | −0.0985563 | −0.0492782 | − | 0.998785i | \(-0.515692\pi\) | ||||
−0.0492782 | + | 0.998785i | \(0.515692\pi\) | |||||||
\(522\) | 0.0241165 | 0.00105555 | ||||||||
\(523\) | −19.7086 | −0.861797 | −0.430899 | − | 0.902400i | \(-0.641803\pi\) | ||||
−0.430899 | + | 0.902400i | \(0.641803\pi\) | |||||||
\(524\) | 18.2582 | 0.797614 | ||||||||
\(525\) | 18.2727 | 0.797484 | ||||||||
\(526\) | −3.36152 | −0.146569 | ||||||||
\(527\) | 64.0486 | 2.79000 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | 25.8655 | 1.12458 | ||||||||
\(530\) | 24.5192 | 1.06504 | ||||||||
\(531\) | −1.28905 | −0.0559401 | ||||||||
\(532\) | 2.82082 | 0.122298 | ||||||||
\(533\) | −27.0116 | −1.17000 | ||||||||
\(534\) | 15.3912 | 0.666044 | ||||||||
\(535\) | 63.2063 | 2.73265 | ||||||||
\(536\) | 7.70883 | 0.332971 | ||||||||
\(537\) | −3.34343 | −0.144279 | ||||||||
\(538\) | 18.7805 | 0.809686 | ||||||||
\(539\) | 4.45474 | 0.191879 | ||||||||
\(540\) | 4.05628 | 0.174555 | ||||||||
\(541\) | −16.5311 | −0.710726 | −0.355363 | − | 0.934728i | \(-0.615643\pi\) | ||||
−0.355363 | + | 0.934728i | \(0.615643\pi\) | |||||||
\(542\) | 2.15131 | 0.0924065 | ||||||||
\(543\) | 18.1342 | 0.778214 | ||||||||
\(544\) | 7.31489 | 0.313623 | ||||||||
\(545\) | −61.6173 | −2.63940 | ||||||||
\(546\) | 5.57958 | 0.238784 | ||||||||
\(547\) | −6.57762 | −0.281239 | −0.140619 | − | 0.990064i | \(-0.544909\pi\) | ||||
−0.140619 | + | 0.990064i | \(0.544909\pi\) | |||||||
\(548\) | −8.18386 | −0.349597 | ||||||||
\(549\) | 1.00000 | 0.0426790 | ||||||||
\(550\) | −11.4534 | −0.488376 | ||||||||
\(551\) | −0.0426406 | −0.00181655 | ||||||||
\(552\) | 6.99038 | 0.297530 | ||||||||
\(553\) | 19.7900 | 0.841558 | ||||||||
\(554\) | 19.4266 | 0.825356 | ||||||||
\(555\) | −19.5500 | −0.829849 | ||||||||
\(556\) | −21.3918 | −0.907215 | ||||||||
\(557\) | 17.6540 | 0.748022 | 0.374011 | − | 0.927424i | \(-0.377982\pi\) | ||||
0.374011 | + | 0.927424i | \(0.377982\pi\) | |||||||
\(558\) | 8.75593 | 0.370668 | ||||||||
\(559\) | 32.4375 | 1.37196 | ||||||||
\(560\) | 6.47134 | 0.273464 | ||||||||
\(561\) | 7.31489 | 0.308835 | ||||||||
\(562\) | −6.42452 | −0.271002 | ||||||||
\(563\) | −23.5153 | −0.991051 | −0.495525 | − | 0.868594i | \(-0.665024\pi\) | ||||
−0.495525 | + | 0.868594i | \(0.665024\pi\) | |||||||
\(564\) | 2.91348 | 0.122680 | ||||||||
\(565\) | 41.2180 | 1.73405 | ||||||||
\(566\) | −11.1655 | −0.469320 | ||||||||
\(567\) | −1.59539 | −0.0670000 | ||||||||
\(568\) | 5.90050 | 0.247579 | ||||||||
\(569\) | −21.6465 | −0.907469 | −0.453735 | − | 0.891137i | \(-0.649909\pi\) | ||||
−0.453735 | + | 0.891137i | \(0.649909\pi\) | |||||||
\(570\) | −7.17196 | −0.300400 | ||||||||
\(571\) | 38.7224 | 1.62048 | 0.810241 | − | 0.586097i | \(-0.199336\pi\) | ||||
0.810241 | + | 0.586097i | \(0.199336\pi\) | |||||||
\(572\) | −3.49732 | −0.146230 | ||||||||
\(573\) | 15.6458 | 0.653612 | ||||||||
\(574\) | 12.3220 | 0.514310 | ||||||||
\(575\) | −80.0639 | −3.33889 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −29.4016 | −1.22400 | −0.612002 | − | 0.790856i | \(-0.709636\pi\) | ||||
−0.612002 | + | 0.790856i | \(0.709636\pi\) | |||||||
\(578\) | 36.5076 | 1.51852 | ||||||||
\(579\) | −18.9924 | −0.789296 | ||||||||
\(580\) | −0.0978233 | −0.00406189 | ||||||||
\(581\) | −27.8904 | −1.15709 | ||||||||
\(582\) | 7.51149 | 0.311361 | ||||||||
\(583\) | 6.04474 | 0.250347 | ||||||||
\(584\) | −13.4718 | −0.557467 | ||||||||
\(585\) | −14.1861 | −0.586524 | ||||||||
\(586\) | −13.7647 | −0.568613 | ||||||||
\(587\) | 19.3932 | 0.800445 | 0.400222 | − | 0.916418i | \(-0.368933\pi\) | ||||
0.400222 | + | 0.916418i | \(0.368933\pi\) | |||||||
\(588\) | 4.45474 | 0.183710 | ||||||||
\(589\) | −15.4814 | −0.637902 | ||||||||
\(590\) | 5.22876 | 0.215265 | ||||||||
\(591\) | 22.8297 | 0.939090 | ||||||||
\(592\) | −4.81967 | −0.198087 | ||||||||
\(593\) | 29.1440 | 1.19680 | 0.598401 | − | 0.801197i | \(-0.295803\pi\) | ||||
0.598401 | + | 0.801197i | \(0.295803\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 47.3372 | 1.94063 | ||||||||
\(596\) | 15.9486 | 0.653282 | ||||||||
\(597\) | 19.4535 | 0.796178 | ||||||||
\(598\) | −24.4476 | −0.999737 | ||||||||
\(599\) | −14.7904 | −0.604318 | −0.302159 | − | 0.953258i | \(-0.597707\pi\) | ||||
−0.302159 | + | 0.953258i | \(0.597707\pi\) | |||||||
\(600\) | −11.4534 | −0.467584 | ||||||||
\(601\) | −0.0209419 | −0.000854238 0 | −0.000427119 | − | 1.00000i | \(-0.500136\pi\) | ||||
−0.000427119 | 1.00000i | \(0.500136\pi\) | ||||||||
\(602\) | −14.7972 | −0.603087 | ||||||||
\(603\) | 7.70883 | 0.313928 | ||||||||
\(604\) | 7.33832 | 0.298592 | ||||||||
\(605\) | −4.05628 | −0.164911 | ||||||||
\(606\) | 8.79915 | 0.357441 | ||||||||
\(607\) | −2.15688 | −0.0875449 | −0.0437725 | − | 0.999042i | \(-0.513938\pi\) | ||||
−0.0437725 | + | 0.999042i | \(0.513938\pi\) | |||||||
\(608\) | −1.76811 | −0.0717064 | ||||||||
\(609\) | 0.0384751 | 0.00155909 | ||||||||
\(610\) | −4.05628 | −0.164234 | ||||||||
\(611\) | −10.1894 | −0.412218 | ||||||||
\(612\) | 7.31489 | 0.295687 | ||||||||
\(613\) | 10.0404 | 0.405528 | 0.202764 | − | 0.979228i | \(-0.435008\pi\) | ||||
0.202764 | + | 0.979228i | \(0.435008\pi\) | |||||||
\(614\) | 20.1444 | 0.812962 | ||||||||
\(615\) | −31.3288 | −1.26330 | ||||||||
\(616\) | 1.59539 | 0.0642800 | ||||||||
\(617\) | 12.0455 | 0.484932 | 0.242466 | − | 0.970160i | \(-0.422044\pi\) | ||||
0.242466 | + | 0.970160i | \(0.422044\pi\) | |||||||
\(618\) | 9.36709 | 0.376800 | ||||||||
\(619\) | −48.0060 | −1.92952 | −0.964762 | − | 0.263124i | \(-0.915247\pi\) | ||||
−0.964762 | + | 0.263124i | \(0.915247\pi\) | |||||||
\(620\) | −35.5165 | −1.42638 | ||||||||
\(621\) | 6.99038 | 0.280514 | ||||||||
\(622\) | −7.95965 | −0.319153 | ||||||||
\(623\) | 24.5550 | 0.983775 | ||||||||
\(624\) | −3.49732 | −0.140005 | ||||||||
\(625\) | 48.9140 | 1.95656 | ||||||||
\(626\) | 19.6501 | 0.785377 | ||||||||
\(627\) | −1.76811 | −0.0706115 | ||||||||
\(628\) | −10.6194 | −0.423759 | ||||||||
\(629\) | −35.2554 | −1.40572 | ||||||||
\(630\) | 6.47134 | 0.257824 | ||||||||
\(631\) | 8.69115 | 0.345989 | 0.172995 | − | 0.984923i | \(-0.444656\pi\) | ||||
0.172995 | + | 0.984923i | \(0.444656\pi\) | |||||||
\(632\) | −12.4045 | −0.493426 | ||||||||
\(633\) | −11.3970 | −0.452991 | ||||||||
\(634\) | −10.4525 | −0.415122 | ||||||||
\(635\) | 8.47413 | 0.336285 | ||||||||
\(636\) | 6.04474 | 0.239689 | ||||||||
\(637\) | −15.5797 | −0.617288 | ||||||||
\(638\) | −0.0241165 | −0.000954781 0 | ||||||||
\(639\) | 5.90050 | 0.233420 | ||||||||
\(640\) | −4.05628 | −0.160339 | ||||||||
\(641\) | −44.0722 | −1.74075 | −0.870373 | − | 0.492393i | \(-0.836122\pi\) | ||||
−0.870373 | + | 0.492393i | \(0.836122\pi\) | |||||||
\(642\) | 15.5823 | 0.614985 | ||||||||
\(643\) | 3.08542 | 0.121677 | 0.0608384 | − | 0.998148i | \(-0.480623\pi\) | ||||
0.0608384 | + | 0.998148i | \(0.480623\pi\) | |||||||
\(644\) | 11.1524 | 0.439465 | ||||||||
\(645\) | 37.6219 | 1.48136 | ||||||||
\(646\) | −12.9335 | −0.508863 | ||||||||
\(647\) | 0.220969 | 0.00868720 | 0.00434360 | − | 0.999991i | \(-0.498617\pi\) | ||||
0.00434360 | + | 0.999991i | \(0.498617\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 1.28905 | 0.0505997 | ||||||||
\(650\) | 40.0563 | 1.57114 | ||||||||
\(651\) | 13.9691 | 0.547492 | ||||||||
\(652\) | −3.56996 | −0.139811 | ||||||||
\(653\) | −6.11922 | −0.239464 | −0.119732 | − | 0.992806i | \(-0.538203\pi\) | ||||
−0.119732 | + | 0.992806i | \(0.538203\pi\) | |||||||
\(654\) | −15.1906 | −0.593999 | ||||||||
\(655\) | −74.0605 | −2.89378 | ||||||||
\(656\) | −7.72352 | −0.301553 | ||||||||
\(657\) | −13.4718 | −0.525585 | ||||||||
\(658\) | 4.64813 | 0.181203 | ||||||||
\(659\) | −3.97739 | −0.154937 | −0.0774685 | − | 0.996995i | \(-0.524684\pi\) | ||||
−0.0774685 | + | 0.996995i | \(0.524684\pi\) | |||||||
\(660\) | −4.05628 | −0.157891 | ||||||||
\(661\) | −43.0060 | −1.67274 | −0.836371 | − | 0.548165i | \(-0.815327\pi\) | ||||
−0.836371 | + | 0.548165i | \(0.815327\pi\) | |||||||
\(662\) | 16.3350 | 0.634879 | ||||||||
\(663\) | −25.5825 | −0.993542 | ||||||||
\(664\) | 17.4819 | 0.678430 | ||||||||
\(665\) | −11.4421 | −0.443704 | ||||||||
\(666\) | −4.81967 | −0.186759 | ||||||||
\(667\) | −0.168583 | −0.00652758 | ||||||||
\(668\) | −7.41687 | −0.286967 | ||||||||
\(669\) | −21.5423 | −0.832872 | ||||||||
\(670\) | −31.2692 | −1.20804 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 1.59539 | 0.0615434 | ||||||||
\(673\) | −0.890377 | −0.0343215 | −0.0171608 | − | 0.999853i | \(-0.505463\pi\) | ||||
−0.0171608 | + | 0.999853i | \(0.505463\pi\) | |||||||
\(674\) | 16.2029 | 0.624112 | ||||||||
\(675\) | −11.4534 | −0.440843 | ||||||||
\(676\) | −0.768748 | −0.0295672 | ||||||||
\(677\) | 30.9340 | 1.18889 | 0.594445 | − | 0.804136i | \(-0.297372\pi\) | ||||
0.594445 | + | 0.804136i | \(0.297372\pi\) | |||||||
\(678\) | 10.1615 | 0.390250 | ||||||||
\(679\) | 11.9837 | 0.459893 | ||||||||
\(680\) | −29.6713 | −1.13784 | ||||||||
\(681\) | −19.6763 | −0.753997 | ||||||||
\(682\) | −8.75593 | −0.335282 | ||||||||
\(683\) | 31.7892 | 1.21638 | 0.608189 | − | 0.793792i | \(-0.291896\pi\) | ||||
0.608189 | + | 0.793792i | \(0.291896\pi\) | |||||||
\(684\) | −1.76811 | −0.0676054 | ||||||||
\(685\) | 33.1960 | 1.26836 | ||||||||
\(686\) | 18.2747 | 0.697733 | ||||||||
\(687\) | 6.12424 | 0.233654 | ||||||||
\(688\) | 9.27497 | 0.353605 | ||||||||
\(689\) | −21.1404 | −0.805384 | ||||||||
\(690\) | −28.3550 | −1.07946 | ||||||||
\(691\) | −42.3625 | −1.61154 | −0.805772 | − | 0.592226i | \(-0.798249\pi\) | ||||
−0.805772 | + | 0.592226i | \(0.798249\pi\) | |||||||
\(692\) | −14.3532 | −0.545628 | ||||||||
\(693\) | 1.59539 | 0.0606038 | ||||||||
\(694\) | 34.3941 | 1.30558 | ||||||||
\(695\) | 86.7712 | 3.29142 | ||||||||
\(696\) | −0.0241165 | −0.000914133 0 | ||||||||
\(697\) | −56.4967 | −2.13996 | ||||||||
\(698\) | 5.63869 | 0.213427 | ||||||||
\(699\) | 16.9596 | 0.641471 | ||||||||
\(700\) | −18.2727 | −0.690642 | ||||||||
\(701\) | 42.1024 | 1.59019 | 0.795093 | − | 0.606488i | \(-0.207422\pi\) | ||||
0.795093 | + | 0.606488i | \(0.207422\pi\) | |||||||
\(702\) | −3.49732 | −0.131998 | ||||||||
\(703\) | 8.52172 | 0.321403 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | −11.8179 | −0.445088 | ||||||||
\(706\) | −1.44339 | −0.0543229 | ||||||||
\(707\) | 14.0380 | 0.527955 | ||||||||
\(708\) | 1.28905 | 0.0484456 | ||||||||
\(709\) | 30.6239 | 1.15010 | 0.575052 | − | 0.818117i | \(-0.304982\pi\) | ||||
0.575052 | + | 0.818117i | \(0.304982\pi\) | |||||||
\(710\) | −23.9341 | −0.898230 | ||||||||
\(711\) | −12.4045 | −0.465206 | ||||||||
\(712\) | −15.3912 | −0.576811 | ||||||||
\(713\) | −61.2073 | −2.29223 | ||||||||
\(714\) | 11.6701 | 0.436742 | ||||||||
\(715\) | 14.1861 | 0.530531 | ||||||||
\(716\) | 3.34343 | 0.124950 | ||||||||
\(717\) | −9.48939 | −0.354388 | ||||||||
\(718\) | −17.9121 | −0.668475 | ||||||||
\(719\) | 18.3754 | 0.685288 | 0.342644 | − | 0.939465i | \(-0.388678\pi\) | ||||
0.342644 | + | 0.939465i | \(0.388678\pi\) | |||||||
\(720\) | −4.05628 | −0.151169 | ||||||||
\(721\) | 14.9441 | 0.556549 | ||||||||
\(722\) | −15.8738 | −0.590761 | ||||||||
\(723\) | 6.07417 | 0.225901 | ||||||||
\(724\) | −18.1342 | −0.673953 | ||||||||
\(725\) | 0.276217 | 0.0102584 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 37.1060 | 1.37618 | 0.688092 | − | 0.725623i | \(-0.258449\pi\) | ||||
0.688092 | + | 0.725623i | \(0.258449\pi\) | |||||||
\(728\) | −5.57958 | −0.206793 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 54.6455 | 2.02252 | ||||||||
\(731\) | 67.8453 | 2.50935 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | −1.08534 | −0.0400878 | −0.0200439 | − | 0.999799i | \(-0.506381\pi\) | ||||
−0.0200439 | + | 0.999799i | \(0.506381\pi\) | |||||||
\(734\) | −2.10345 | −0.0776399 | ||||||||
\(735\) | −18.0697 | −0.666510 | ||||||||
\(736\) | −6.99038 | −0.257669 | ||||||||
\(737\) | −7.70883 | −0.283959 | ||||||||
\(738\) | −7.72352 | −0.284307 | ||||||||
\(739\) | 5.10783 | 0.187894 | 0.0939472 | − | 0.995577i | \(-0.470052\pi\) | ||||
0.0939472 | + | 0.995577i | \(0.470052\pi\) | |||||||
\(740\) | 19.5500 | 0.718671 | ||||||||
\(741\) | 6.18365 | 0.227162 | ||||||||
\(742\) | 9.64370 | 0.354031 | ||||||||
\(743\) | −42.9820 | −1.57686 | −0.788428 | − | 0.615127i | \(-0.789105\pi\) | ||||
−0.788428 | + | 0.615127i | \(0.789105\pi\) | |||||||
\(744\) | −8.75593 | −0.321008 | ||||||||
\(745\) | −64.6922 | −2.37014 | ||||||||
\(746\) | 35.0349 | 1.28272 | ||||||||
\(747\) | 17.4819 | 0.639630 | ||||||||
\(748\) | −7.31489 | −0.267459 | ||||||||
\(749\) | 24.8598 | 0.908358 | ||||||||
\(750\) | 26.1769 | 0.955847 | ||||||||
\(751\) | 2.12348 | 0.0774868 | 0.0387434 | − | 0.999249i | \(-0.487665\pi\) | ||||
0.0387434 | + | 0.999249i | \(0.487665\pi\) | |||||||
\(752\) | −2.91348 | −0.106244 | ||||||||
\(753\) | 1.76315 | 0.0642529 | ||||||||
\(754\) | 0.0843431 | 0.00307159 | ||||||||
\(755\) | −29.7663 | −1.08331 | ||||||||
\(756\) | 1.59539 | 0.0580237 | ||||||||
\(757\) | −5.59093 | −0.203206 | −0.101603 | − | 0.994825i | \(-0.532397\pi\) | ||||
−0.101603 | + | 0.994825i | \(0.532397\pi\) | |||||||
\(758\) | −19.6090 | −0.712231 | ||||||||
\(759\) | −6.99038 | −0.253735 | ||||||||
\(760\) | 7.17196 | 0.260154 | ||||||||
\(761\) | −13.0742 | −0.473939 | −0.236969 | − | 0.971517i | \(-0.576154\pi\) | ||||
−0.236969 | + | 0.971517i | \(0.576154\pi\) | |||||||
\(762\) | 2.08914 | 0.0756814 | ||||||||
\(763\) | −24.2349 | −0.877362 | ||||||||
\(764\) | −15.6458 | −0.566045 | ||||||||
\(765\) | −29.6713 | −1.07277 | ||||||||
\(766\) | −24.4725 | −0.884228 | ||||||||
\(767\) | −4.50823 | −0.162783 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −0.481859 | −0.0173763 | −0.00868814 | − | 0.999962i | \(-0.502766\pi\) | ||||
−0.00868814 | + | 0.999962i | \(0.502766\pi\) | |||||||
\(770\) | −6.47134 | −0.233211 | ||||||||
\(771\) | 24.0061 | 0.864560 | ||||||||
\(772\) | 18.9924 | 0.683551 | ||||||||
\(773\) | −37.0758 | −1.33352 | −0.666762 | − | 0.745271i | \(-0.732320\pi\) | ||||
−0.666762 | + | 0.745271i | \(0.732320\pi\) | |||||||
\(774\) | 9.27497 | 0.333382 | ||||||||
\(775\) | 100.285 | 3.60236 | ||||||||
\(776\) | −7.51149 | −0.269647 | ||||||||
\(777\) | −7.68924 | −0.275850 | ||||||||
\(778\) | −35.5397 | −1.27416 | ||||||||
\(779\) | 13.6560 | 0.489278 | ||||||||
\(780\) | 14.1861 | 0.507945 | ||||||||
\(781\) | −5.90050 | −0.211136 | ||||||||
\(782\) | −51.1339 | −1.82854 | ||||||||
\(783\) | −0.0241165 | −0.000861853 0 | ||||||||
\(784\) | −4.45474 | −0.159098 | ||||||||
\(785\) | 43.0752 | 1.53742 | ||||||||
\(786\) | −18.2582 | −0.651249 | ||||||||
\(787\) | −5.67271 | −0.202210 | −0.101105 | − | 0.994876i | \(-0.532238\pi\) | ||||
−0.101105 | + | 0.994876i | \(0.532238\pi\) | |||||||
\(788\) | −22.8297 | −0.813276 | ||||||||
\(789\) | 3.36152 | 0.119673 | ||||||||
\(790\) | 50.3163 | 1.79017 | ||||||||
\(791\) | 16.2115 | 0.576416 | ||||||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 3.49732 | 0.124193 | ||||||||
\(794\) | −28.1055 | −0.997428 | ||||||||
\(795\) | −24.5192 | −0.869605 | ||||||||
\(796\) | −19.4535 | −0.689510 | ||||||||
\(797\) | −47.0014 | −1.66488 | −0.832438 | − | 0.554119i | \(-0.813055\pi\) | ||||
−0.832438 | + | 0.554119i | \(0.813055\pi\) | |||||||
\(798\) | −2.82082 | −0.0998560 | ||||||||
\(799\) | −21.3118 | −0.753957 | ||||||||
\(800\) | 11.4534 | 0.404940 | ||||||||
\(801\) | −15.3912 | −0.543823 | ||||||||
\(802\) | 1.97149 | 0.0696158 | ||||||||
\(803\) | 13.4718 | 0.475410 | ||||||||
\(804\) | −7.70883 | −0.271870 | ||||||||
\(805\) | −45.2372 | −1.59440 | ||||||||
\(806\) | 30.6223 | 1.07862 | ||||||||
\(807\) | −18.7805 | −0.661106 | ||||||||
\(808\) | −8.79915 | −0.309553 | ||||||||
\(809\) | 3.27711 | 0.115217 | 0.0576086 | − | 0.998339i | \(-0.481652\pi\) | ||||
0.0576086 | + | 0.998339i | \(0.481652\pi\) | |||||||
\(810\) | −4.05628 | −0.142523 | ||||||||
\(811\) | −14.9746 | −0.525828 | −0.262914 | − | 0.964819i | \(-0.584684\pi\) | ||||
−0.262914 | + | 0.964819i | \(0.584684\pi\) | |||||||
\(812\) | −0.0384751 | −0.00135021 | ||||||||
\(813\) | −2.15131 | −0.0754496 | ||||||||
\(814\) | 4.81967 | 0.168929 | ||||||||
\(815\) | 14.4808 | 0.507240 | ||||||||
\(816\) | −7.31489 | −0.256072 | ||||||||
\(817\) | −16.3992 | −0.573734 | ||||||||
\(818\) | 17.5750 | 0.614495 | ||||||||
\(819\) | −5.57958 | −0.194966 | ||||||||
\(820\) | 31.3288 | 1.09405 | ||||||||
\(821\) | −31.3319 | −1.09349 | −0.546745 | − | 0.837299i | \(-0.684133\pi\) | ||||
−0.546745 | + | 0.837299i | \(0.684133\pi\) | |||||||
\(822\) | 8.18386 | 0.285445 | ||||||||
\(823\) | 28.8828 | 1.00679 | 0.503395 | − | 0.864056i | \(-0.332084\pi\) | ||||
0.503395 | + | 0.864056i | \(0.332084\pi\) | |||||||
\(824\) | −9.36709 | −0.326318 | ||||||||
\(825\) | 11.4534 | 0.398757 | ||||||||
\(826\) | 2.05654 | 0.0715561 | ||||||||
\(827\) | −19.2429 | −0.669142 | −0.334571 | − | 0.942371i | \(-0.608591\pi\) | ||||
−0.334571 | + | 0.942371i | \(0.608591\pi\) | |||||||
\(828\) | −6.99038 | −0.242933 | ||||||||
\(829\) | 4.23675 | 0.147149 | 0.0735743 | − | 0.997290i | \(-0.476559\pi\) | ||||
0.0735743 | + | 0.997290i | \(0.476559\pi\) | |||||||
\(830\) | −70.9116 | −2.46138 | ||||||||
\(831\) | −19.4266 | −0.673900 | ||||||||
\(832\) | 3.49732 | 0.121248 | ||||||||
\(833\) | −32.5859 | −1.12904 | ||||||||
\(834\) | 21.3918 | 0.740738 | ||||||||
\(835\) | 30.0849 | 1.04113 | ||||||||
\(836\) | 1.76811 | 0.0611514 | ||||||||
\(837\) | −8.75593 | −0.302649 | ||||||||
\(838\) | 20.9628 | 0.724150 | ||||||||
\(839\) | 11.4086 | 0.393870 | 0.196935 | − | 0.980417i | \(-0.436901\pi\) | ||||
0.196935 | + | 0.980417i | \(0.436901\pi\) | |||||||
\(840\) | −6.47134 | −0.223283 | ||||||||
\(841\) | −28.9994 | −0.999980 | ||||||||
\(842\) | 2.69583 | 0.0929045 | ||||||||
\(843\) | 6.42452 | 0.221272 | ||||||||
\(844\) | 11.3970 | 0.392302 | ||||||||
\(845\) | 3.11826 | 0.107271 | ||||||||
\(846\) | −2.91348 | −0.100168 | ||||||||
\(847\) | −1.59539 | −0.0548182 | ||||||||
\(848\) | −6.04474 | −0.207577 | ||||||||
\(849\) | 11.1655 | 0.383198 | ||||||||
\(850\) | 83.7806 | 2.87365 | ||||||||
\(851\) | 33.6914 | 1.15492 | ||||||||
\(852\) | −5.90050 | −0.202148 | ||||||||
\(853\) | 17.1149 | 0.586001 | 0.293001 | − | 0.956112i | \(-0.405346\pi\) | ||||
0.293001 | + | 0.956112i | \(0.405346\pi\) | |||||||
\(854\) | −1.59539 | −0.0545930 | ||||||||
\(855\) | 7.17196 | 0.245276 | ||||||||
\(856\) | −15.5823 | −0.532593 | ||||||||
\(857\) | −4.10315 | −0.140161 | −0.0700805 | − | 0.997541i | \(-0.522326\pi\) | ||||
−0.0700805 | + | 0.997541i | \(0.522326\pi\) | |||||||
\(858\) | 3.49732 | 0.119397 | ||||||||
\(859\) | 11.5004 | 0.392390 | 0.196195 | − | 0.980565i | \(-0.437142\pi\) | ||||
0.196195 | + | 0.980565i | \(0.437142\pi\) | |||||||
\(860\) | −37.6219 | −1.28290 | ||||||||
\(861\) | −12.3220 | −0.419933 | ||||||||
\(862\) | −26.5387 | −0.903912 | ||||||||
\(863\) | −21.6785 | −0.737944 | −0.368972 | − | 0.929440i | \(-0.620290\pi\) | ||||
−0.368972 | + | 0.929440i | \(0.620290\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 58.2207 | 1.97956 | ||||||||
\(866\) | −1.34440 | −0.0456845 | ||||||||
\(867\) | −36.5076 | −1.23986 | ||||||||
\(868\) | −13.9691 | −0.474142 | ||||||||
\(869\) | 12.4045 | 0.420795 | ||||||||
\(870\) | 0.0978233 | 0.00331652 | ||||||||
\(871\) | 26.9603 | 0.913514 | ||||||||
\(872\) | 15.1906 | 0.514418 | ||||||||
\(873\) | −7.51149 | −0.254225 | ||||||||
\(874\) | 12.3598 | 0.418076 | ||||||||
\(875\) | 41.7624 | 1.41183 | ||||||||
\(876\) | 13.4718 | 0.455170 | ||||||||
\(877\) | 2.32846 | 0.0786264 | 0.0393132 | − | 0.999227i | \(-0.487483\pi\) | ||||
0.0393132 | + | 0.999227i | \(0.487483\pi\) | |||||||
\(878\) | −30.0973 | −1.01573 | ||||||||
\(879\) | 13.7647 | 0.464270 | ||||||||
\(880\) | 4.05628 | 0.136737 | ||||||||
\(881\) | 28.4074 | 0.957068 | 0.478534 | − | 0.878069i | \(-0.341168\pi\) | ||||
0.478534 | + | 0.878069i | \(0.341168\pi\) | |||||||
\(882\) | −4.45474 | −0.149999 | ||||||||
\(883\) | −26.2079 | −0.881967 | −0.440983 | − | 0.897515i | \(-0.645370\pi\) | ||||
−0.440983 | + | 0.897515i | \(0.645370\pi\) | |||||||
\(884\) | 25.5825 | 0.860433 | ||||||||
\(885\) | −5.22876 | −0.175763 | ||||||||
\(886\) | 15.3679 | 0.516293 | ||||||||
\(887\) | 1.65184 | 0.0554632 | 0.0277316 | − | 0.999615i | \(-0.491172\pi\) | ||||
0.0277316 | + | 0.999615i | \(0.491172\pi\) | |||||||
\(888\) | 4.81967 | 0.161738 | ||||||||
\(889\) | 3.33298 | 0.111785 | ||||||||
\(890\) | 62.4312 | 2.09270 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 21.5423 | 0.721288 | ||||||||
\(893\) | 5.15136 | 0.172384 | ||||||||
\(894\) | −15.9486 | −0.533403 | ||||||||
\(895\) | −13.5619 | −0.453324 | ||||||||
\(896\) | −1.59539 | −0.0532982 | ||||||||
\(897\) | 24.4476 | 0.816282 | ||||||||
\(898\) | 10.2979 | 0.343646 | ||||||||
\(899\) | 0.211162 | 0.00704265 | ||||||||
\(900\) | 11.4534 | 0.381781 | ||||||||
\(901\) | −44.2166 | −1.47307 | ||||||||
\(902\) | 7.72352 | 0.257165 | ||||||||
\(903\) | 14.7972 | 0.492419 | ||||||||
\(904\) | −10.1615 | −0.337967 | ||||||||
\(905\) | 73.5576 | 2.44514 | ||||||||
\(906\) | −7.33832 | −0.243799 | ||||||||
\(907\) | −52.6512 | −1.74825 | −0.874127 | − | 0.485698i | \(-0.838566\pi\) | ||||
−0.874127 | + | 0.485698i | \(0.838566\pi\) | |||||||
\(908\) | 19.6763 | 0.652980 | ||||||||
\(909\) | −8.79915 | −0.291849 | ||||||||
\(910\) | 22.6324 | 0.750255 | ||||||||
\(911\) | −12.9737 | −0.429836 | −0.214918 | − | 0.976632i | \(-0.568948\pi\) | ||||
−0.214918 | + | 0.976632i | \(0.568948\pi\) | |||||||
\(912\) | 1.76811 | 0.0585480 | ||||||||
\(913\) | −17.4819 | −0.578567 | ||||||||
\(914\) | −21.1684 | −0.700189 | ||||||||
\(915\) | 4.05628 | 0.134097 | ||||||||
\(916\) | −6.12424 | −0.202351 | ||||||||
\(917\) | −29.1289 | −0.961922 | ||||||||
\(918\) | −7.31489 | −0.241427 | ||||||||
\(919\) | 8.12884 | 0.268146 | 0.134073 | − | 0.990971i | \(-0.457194\pi\) | ||||
0.134073 | + | 0.990971i | \(0.457194\pi\) | |||||||
\(920\) | 28.3550 | 0.934836 | ||||||||
\(921\) | −20.1444 | −0.663781 | ||||||||
\(922\) | −24.9393 | −0.821333 | ||||||||
\(923\) | 20.6359 | 0.679240 | ||||||||
\(924\) | −1.59539 | −0.0524844 | ||||||||
\(925\) | −55.2018 | −1.81502 | ||||||||
\(926\) | −15.8084 | −0.519495 | ||||||||
\(927\) | −9.36709 | −0.307656 | ||||||||
\(928\) | 0.0241165 | 0.000791662 0 | ||||||||
\(929\) | −22.8797 | −0.750657 | −0.375329 | − | 0.926892i | \(-0.622470\pi\) | ||||
−0.375329 | + | 0.926892i | \(0.622470\pi\) | |||||||
\(930\) | 35.5165 | 1.16463 | ||||||||
\(931\) | 7.87647 | 0.258141 | ||||||||
\(932\) | −16.9596 | −0.555530 | ||||||||
\(933\) | 7.95965 | 0.260587 | ||||||||
\(934\) | −25.4798 | −0.833726 | ||||||||
\(935\) | 29.6713 | 0.970354 | ||||||||
\(936\) | 3.49732 | 0.114314 | ||||||||
\(937\) | −49.7726 | −1.62600 | −0.813000 | − | 0.582264i | \(-0.802167\pi\) | ||||
−0.813000 | + | 0.582264i | \(0.802167\pi\) | |||||||
\(938\) | −12.2986 | −0.401563 | ||||||||
\(939\) | −19.6501 | −0.641258 | ||||||||
\(940\) | 11.8179 | 0.385457 | ||||||||
\(941\) | 24.2116 | 0.789276 | 0.394638 | − | 0.918837i | \(-0.370870\pi\) | ||||
0.394638 | + | 0.918837i | \(0.370870\pi\) | |||||||
\(942\) | 10.6194 | 0.345998 | ||||||||
\(943\) | 53.9903 | 1.75817 | ||||||||
\(944\) | −1.28905 | −0.0419551 | ||||||||
\(945\) | −6.47134 | −0.210513 | ||||||||
\(946\) | −9.27497 | −0.301555 | ||||||||
\(947\) | −2.48161 | −0.0806415 | −0.0403207 | − | 0.999187i | \(-0.512838\pi\) | ||||
−0.0403207 | + | 0.999187i | \(0.512838\pi\) | |||||||
\(948\) | 12.4045 | 0.402881 | ||||||||
\(949\) | −47.1152 | −1.52942 | ||||||||
\(950\) | −20.2509 | −0.657027 | ||||||||
\(951\) | 10.4525 | 0.338946 | ||||||||
\(952\) | −11.6701 | −0.378230 | ||||||||
\(953\) | 49.4472 | 1.60175 | 0.800876 | − | 0.598830i | \(-0.204367\pi\) | ||||
0.800876 | + | 0.598830i | \(0.204367\pi\) | |||||||
\(954\) | −6.04474 | −0.195706 | ||||||||
\(955\) | 63.4638 | 2.05364 | ||||||||
\(956\) | 9.48939 | 0.306909 | ||||||||
\(957\) | 0.0241165 | 0.000779575 0 | ||||||||
\(958\) | −5.99410 | −0.193661 | ||||||||
\(959\) | 13.0564 | 0.421614 | ||||||||
\(960\) | 4.05628 | 0.130916 | ||||||||
\(961\) | 45.6662 | 1.47310 | ||||||||
\(962\) | −16.8559 | −0.543457 | ||||||||
\(963\) | −15.5823 | −0.502133 | ||||||||
\(964\) | −6.07417 | −0.195636 | ||||||||
\(965\) | −77.0385 | −2.47996 | ||||||||
\(966\) | −11.1524 | −0.358822 | ||||||||
\(967\) | 37.9534 | 1.22050 | 0.610250 | − | 0.792209i | \(-0.291069\pi\) | ||||
0.610250 | + | 0.792209i | \(0.291069\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 12.9335 | 0.415485 | ||||||||
\(970\) | 30.4687 | 0.978291 | ||||||||
\(971\) | 40.1816 | 1.28949 | 0.644744 | − | 0.764398i | \(-0.276964\pi\) | ||||
0.644744 | + | 0.764398i | \(0.276964\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 34.1282 | 1.09410 | ||||||||
\(974\) | −18.9550 | −0.607358 | ||||||||
\(975\) | −40.0563 | −1.28283 | ||||||||
\(976\) | 1.00000 | 0.0320092 | ||||||||
\(977\) | −13.1013 | −0.419148 | −0.209574 | − | 0.977793i | \(-0.567208\pi\) | ||||
−0.209574 | + | 0.977793i | \(0.567208\pi\) | |||||||
\(978\) | 3.56996 | 0.114155 | ||||||||
\(979\) | 15.3912 | 0.491906 | ||||||||
\(980\) | 18.0697 | 0.577215 | ||||||||
\(981\) | 15.1906 | 0.484998 | ||||||||
\(982\) | 37.8774 | 1.20872 | ||||||||
\(983\) | 54.8375 | 1.74905 | 0.874523 | − | 0.484984i | \(-0.161175\pi\) | ||||
0.874523 | + | 0.484984i | \(0.161175\pi\) | |||||||
\(984\) | 7.72352 | 0.246217 | ||||||||
\(985\) | 92.6039 | 2.95061 | ||||||||
\(986\) | 0.176409 | 0.00561802 | ||||||||
\(987\) | −4.64813 | −0.147952 | ||||||||
\(988\) | −6.18365 | −0.196728 | ||||||||
\(989\) | −64.8356 | −2.06165 | ||||||||
\(990\) | 4.05628 | 0.128917 | ||||||||
\(991\) | −47.5971 | −1.51197 | −0.755987 | − | 0.654587i | \(-0.772842\pi\) | ||||
−0.755987 | + | 0.654587i | \(0.772842\pi\) | |||||||
\(992\) | 8.75593 | 0.278001 | ||||||||
\(993\) | −16.3350 | −0.518377 | ||||||||
\(994\) | −9.41358 | −0.298581 | ||||||||
\(995\) | 78.9088 | 2.50158 | ||||||||
\(996\) | −17.4819 | −0.553936 | ||||||||
\(997\) | 10.4773 | 0.331819 | 0.165910 | − | 0.986141i | \(-0.446944\pi\) | ||||
0.165910 | + | 0.986141i | \(0.446944\pi\) | |||||||
\(998\) | 29.3414 | 0.928786 | ||||||||
\(999\) | 4.81967 | 0.152488 |
(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 | 4026.2.a.x.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4026.2.a.x.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial |